Integral length scales in meters for winds <= 15 m s-1 (this study and [33], z0≈1 m), and >=15 m s-1 ([6] and [7], z0<0.1 m)
\r\n\t
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While hurricane track and strength forecasting has clearly improved in the last decade, increasing coastal development puts increasing population numbers in harm’s way [1]. In addition, the modified coastal environment with its human infrastructure is affected by coastal flooding from the storm’s surge, inland flooding from torrential rains, and damaging hurricane winds. Recent hurricane research has sought to characterize land-falling hurricanes better [2-7], particularly in order to understand the dynamics and development of hurricane winds during landfall and the associated potential for wind damage to structures and the natural environment. The necessary safety prerequisites to instrumentation observing land-falling hurricanes, and the amount of data they collect demand a high organization, quick response to meteorological developments, careful data analysis, and patience. Thus, as this research is only approximately a decade old few reports have appeared in the peer-reviewed literature so far.
Meteorological measurements inside urban areas are also relatively rare as guidelines for proper setup of representative weather stations usually lead to conflicts in such areas. However, meteorological measurements, as well as weather and impact forecasts in and for conurbations are becoming more important as urban populations increase. An increased (meteorological) focus has been put on the urban environment [8-12], and guidelines have been developed for urban measurements and site qualifications [13-15]. Micrometeorological observations in urban areas are especially challenging but many more observational data sets have been acquired in the last decade since Roth’s seminal review in 2000 [9, 16]. One of these is being acquired in Houston, Texas, since summer 2007 as part of a project to study atmospheric turbulence, and anthropogenic and biogenic trace gas fluxes over a typical urban landscape [17, 18]. Approximately a year after project measurements had begun, Hurricane Ike approached the Gulf Coast with a forecast track right through the City of Houston. While the author’s installations on the communications’ tower used for the study were designed to withstand high winds, the tower itself was not rated for a category three hurricane, and there was thus a good chance it would topple if Ike maintained its strength upon landfall. On September 12/13, 2008, at landfall near Galveston, Texas, Ike was finally rated “only” a category two storm on the Saffir-Simpson scale. The tower survived. However, due to the impacts of Ike’s enormous size and wind field the storm caused widespread disaster and power loss to approximately 2.1 million customers in the Houston metro area [19], and is now considered the USA’s second most costly hurricane in history at nearly 30 billion USD of estimated, accumulated damages [20].
A major impact of Ike to people and infrastructure in the Houston metro area stemmed from debris, both from natural vegetation and damaged human infrastructure [21]. Particularly the amount of damage to the energy (electricity) infrastructure was staggering, leaving sections of the metro area population without power for more than three weeks after the storm’s passage [19]. What was highly visible in Houston long before the storm, and had been concluded by us as the major culprit [22], was the lack of proper tree trimming leading to tree-debris-caused power line failures. Within the first year after the storm, it had been concluded that this was indeed the leading cause for the amount of failures, and that in conclusion future activities would focus on appropriate tree trimming [23, 24].
As the instrumented communication’s tower north of downtown Houston rode out the storm, albeit partially damaged, and power to the site was never lost due to a local diesel generator, it was possible to record meteorological and air quality data both during the storm and its aftermath. This chapter will focus on the storm’s meteorological characteristics as measured over the urban area north of downtown Houston. They represent, so far, the only recorded hurricane passage over an urban environment [22]. Firstly, there will be a review of the installation’s salient features and important past observations, followed by a brief description the hurricane’s development. The following sections will focus on the development of Ike’s winds over Houston in comparison to past findings, and their impacts in the neighborhood of the site. Lastly, connections between the hurricane’s thermodynamics, its rainbands and winds, and air quality will be explored. A more detailed view of the latter shall be reported elsewhere.
The Greater Houston Transportation Co. owns and operates a 91 m tall communications tower at 1406 Hays Street, 77009 Houston, TX, approximately 3.5 km NNE of downtown Houston (29.789° N, 95.354° W, 14 m above sea level). In 2007 the tower was equipped with meteorological and micrometeorological instrumentation to measure standard meteorological parameters plus atmospheric turbulence and surface energy exchanges. In June 2008, the existing 4-level gradient measurements were expanded by a level at 49 m above ground level (agl), and an extra sonic anemometer at 40 m agl. Details of the instrumentation can be found in [17], downloadable from the project’s website. On the top level, a MetOne model 034B wind speed (ws) and direction (wd) sensor was used, and on the lower levels MetOne 014A ws only models with standard metal cups were used. Both sensors have a starting threshold of <0.5 m s-1 and distance constants of <= 4.5 m, equivalent to a 95% of maximum response time of approximately 3 seconds in a typical 9 m s-1 wind. Data were recorded in 10-s intervals and stored as 1-min averages and standard deviations except atmospheric pressure, which is only recorded every 15 minutes, but was smoothed for the analysis purposes of this study. Micrometeorological data from the installed sonic anemometer at 60 m agl was recorded at 10 Hz up to approximately midnight on 12 September 2008 when increasing rainfall began to completely cut the signal. The sonic anemometer then did not recover until two days after the storm. Rainfall was recorded with a tipping bucket (model TE525) on the E side of the tower, ten meters agl, and atmospheric pressure from within the data logger enclosure at two meters agl. Lastly, carbon monoxide was measured by a model 48CTL gas filter correlation instrument, corrected for background drift every two hours and calibrated once a week (precision ±20 ppb). The instrument samples air from inlets at 40 and 60 m agl on the tower.
Figure 1 shows a picture of the instrumented tower in summer 2008 (a), and a bird’s eye view of the surrounding area with labels (b). A more detailed description of the underlying urban surface is given in [25] and our TARC report [17]. Of particular interest with respect to wind measurements is the location of the sensors relative to the lattice tower structure itself. Figure 2 shows the setup on the top level (60 m agl) and an example of the lower level installations.
a) Picture of the top four meteorological installations on the flux tower during summer 2008. Note temporary installation of an additional sonic anemometer at the 40 m agl. (b) Annotated bird’s eye view of the tower location (red dot) north of downtown Houston. Red lines indicate major thoroughfares.
As the wind climatology for Houston indicated rare occasions of northerly winds, the sonic and the lower level cup anemometers were installed on the south side of the tower. The top level ws/wd sensor was installed as a “backup” sensor on the NW side of the tower. As shown in Figures 1&2, the triangular tower lattice structure has a side length of 60 cm (2 ft), thus is bound to affect wind flows towards the cup anemometers for average wind directions between approximately 320 and 10 degrees as the sensors are within three times the largest horizontal tower dimension. A similar argument holds for the sonic anemometer at similar wind directions, and for the ws/wd sensor for SE wind directions. Though the effects may be smaller in both the latter cases due to larger distances from the tower, there is an additional electronics box installed on the tower at that level, which can cause an extra wake.
Meteorological instrumentation installed at the Yellow Cab tower in Houston at 60 m agl (right), and the lower levels (49, 40, 20, 13 m agl; left). The tower has a side length of 2 ft with vertical bars of 1 ½ inches diameter. Installed horizontal beams (solid black lines) consist mostly of aluminum pipes (Campbell Scientific Inc., Logan, Utah, USA). Note that the aspirated radiation shields (MetOne model 075B) are installed with an off-center beam.
Measurements from the tower since late summer 2007 were used to determine the structure of atmospheric turbulence at this urban site, and the underlying surfaces’ roughness lengths (z0) and displacement heights (d). Figure 3 shows the observed behavior of normalized longitudinal and vertical winds – as relevant for this study – with the atmospheric stability parameter ζ=(z-d)/L for daytime unstable conditions, where is z is measurement height and L is the Obhukov length. We observed surprisingly low directional heterogeneity in the data, thus these results were pooled. A comparison to the review of Roth [16] listed in Fig. 3 showed few differences as compared to past findings over urban areas.
A combination of methods to determine z0 and d [26] was used to arrive at values of z0 = 1±0.1 m, and d = 8
Normalized longitudinal and vertical wind standard deviations as function of atmospheric stability for unstable conditions, compared between our site and other urban data as summarized by Roth [16]. The grey line shows the expected ci=⅓ slope. For all i=u,v,w, we observed neutral stability values close to the literature data, namely 2.4, 1.8, and 1.3.
Despite some obvious surface heterogeneity, the lack of significant directional differences in the measured turbulence can be explained by the z=60 m agl measurement height, which is approximately six times the displacement height and therefore well above the recommended height for such measurements [16], inside the inertial sublayer. This height was initially chosen to integrate our flux measurements over a larger, more representative urban surface area. Flux footprint estimates [25] indicate that under typical wind speeds (4-6 m s-1) and turbulence conditions (friction velocity, u*=0.4-0.6 m s-1) at this site, 90% of measured fluxes are expected to come from less than 1.5 km distances, with maximum impacts from locations <=500 m from the tower [25], and total footprint sizes of 2-4 km2. However, for wind speeds between 20-30 m s-1 and associated turbulence discussed below, maximum impact areas move significantly closer to the tower (<=350 m) and footprint size contracts, so that a larger effect of the surface and its heterogeneity close to the tower on the measurements is to be expected. This is also evident through a decrease of the displacement height with observed wind speeds (or friction velocities) [17], likely because of the lack of tall trees closer to the tower.
Ike was a somewhat uncharacteristic hurricane due to its very large eye and wind field, filling nearly the entire Gulf of Mexico on 12 September 2008. Though its wind speeds classified Ike as a category two hurricane at landfall (maximum winds between 96 and 110 mph = 43-49 m s-1), a more holistic view called the hurricane severity index [27] ranks it similar to such disastrous landfalling hurricanes as Andrew in 1992 and Ivan in 2004. Most of Hurricane Ike’s history and measures, including its track, precipitation, and measured or estimated winds are described online [28], and shall not be repeated here. A track map through Houston and a brief analysis of our meteorological data were also given earlier [22]. For comparison purposes to this study, Figure 4 shows two important meteorological variables: Fig. 4a shows a precipitation radar image (KHGX Houston, located at the green-blue dot south of the eye) from the period of maximum wind speeds, approximately one hour before the minimum locally measured pressure at the tower site; Fig. 4b shows gridded, calculated maximum sustained wind speeds for Harris County, assembled from the original GIS data [28], which have generally been shown on a much larger scale [27, 29]. Note that Ike preserved its very large eye for a comparatively long time after landfall, and that the City of Houston, roughly outlined by the Beltway, was well within Ike’s eyewall. As a result of this, several additional rain bands passing over, and the flat Texas coastal terrain, widespread flooding occurred in central and north Houston. Particularly, the White Oak Bayou watershed area, at the SE corner of which the tower site is located, was listed as “Major Flooding / House flooding area from rainfall”. The same area was calculated to have experienced category one (74-95 mph = 33-43 m s-1) hurricane wind speeds, with a maximum of 38 m s-1 estimated for the tower site and much of central Houston (Fig. 4b). However, it needs to be pointed out here that these are NOAA AOML Hurricane Research Division (HRD) surface wind data that are – in this case – valid only for “open terrain exposure over land”. They are a standardized product reflecting speeds at 10 m agl for a flat surface (d=0) without significant roughness elements (z0<=0.1 m). Actually measured speeds are discussed below.
a) Precipitation radar image from 13 September, 09:00 GMT (03:00 CST) overlaid on a Texas county map (grey lines) and including interstate highways (red lines), the circular one in the center depicting Houston’s Beltway, which extends for approximately 19 km in its E-W direction. (b) Maximum sustained wind speeds (NOAA Atlantic Oceanographic & Meteorological Laboratory Hurricane Research Division H*Wind product) during Ike in Harris County, Texas, overlaid on the county border (black line) and major thoroughfares (green lines). The central dot marks the tower location.
In Figure 5 are depicted measured wind speeds at 60 and 20 m agl from the Yellow Cab tower for 12th (DOY 256) and 13th (DOY 257) September 2008. Wind direction is included in the form of arrows along the bottom, and approximate timing of rain band passages along the top of the graph. For northerly winds, which occurred in the afternoon of DOY 256 and for approximately four hours around midnight at the height of the storm, the measured 20-m agl wind speeds are clearly impacted by the tower structure as explained above. As the eye passed and wind direction shifted to the NW, the sensor moved out of the tower’s wake, and recorded its highest 1-min values of 22-25 m s-1 around 4 am Central Standard Time (CST = CDT - 1 h). This timing will be addressed again below.
Measured wind speeds during Hurricane Ike’s passage over Houston on September 12-13, 2008. Arrows along the bottom depict wind direction, numbers on the top locate the timing of rain band passages with labels 4a and 4b identifying the eyewall.
Considering a displacement height of close to ten meters for our site, the 20-m agl measurements come closest to the standardized H*Wind product shown in Fig. 4b. The large difference between the two (25 vs. 38 m s-1) is associated with the higher urban roughness length. Higher roughness lengths increase surface friction and therefore reduce wind speed.
Fig. 5 includes 10-min average wind speeds for the top level sensor and therefore allows a direct comparison between sustained winds and 1-min gustiness (10-s mean winds were not recorded). Only the latter revealed hurricane-force winds (>33 m s-1) at the top level, 60 m agl, while sustained (10-min) tropical storm force winds (>17 m s-1) were recorded for nearly 12 hours. However, extrapolating sustained top level to the 20-m agl wind speeds using the log-wind-law
where Û is 10-min average wind speed, u* is friction velocity, and k=0.4 is von Karmann’s constant, reduces the time of 17+ m s-1 wind speeds to a mere 15 min. This analyses shows that the rough urban surface was very efficient in slowing down Ike’s winds. Other surface maximum wind speed observations in the Houston urban area, compiled by Berg [20], ranged from 16 (west Houston) to 65 (Houston Hobby airport, south Houston) knots (see Fig. 5 for speed conversions), confirming that hurricane force winds were rare in the urban canopy even in the eyewall.
Higher surface roughness in the urban area though increases atmospheric turbulence. The latter was analyzed in two ways, investigating drag or wind force, and turbulence intensities, IU. The former was calculated following [30], also cited in [31], from the 20-m agl sustained wind speed data in combination with air density. The latter was calculated from 15-min non-overlapping segments for both the sonic and cup anemometers, except during the last six hours before midnight when lower data density due to rain required half-hourly or hourly averages. In Figure 6 we plotted the resulting wind force per area and its standard deviation. Mean values characterize static, while fluctuations characterize dynamic wind load on surface roughness elements. Under “normal” conditions (DOY 256 morning), loads rarely exceed 1 kg m-1 s-2, but during the hurricane, loads increased by a factor of 5-10 in the eyewall.
Wind force, proportional to Û2, time series during Hurricane Ike’s passage over Houston. The grey swath is an estimate of its standard deviation.
In Figure 7 are plotted turbulence intensities time series as calculated from the sonic anemometer data and the top level wind sensor, alongside the storm’s pressure, wind direction, and rain band timing characteristics. Due to the higher data density of 10 Hz vs. 0.017 Hz, values are much larger for the sonic vs. the cup anemometer. Prior to the storm, IU is influenced by atmospheric stability, leading to higher values during daytime unstable conditions. Values further increased when wind direction was northerly due to a reduction in wind speed but not its standard deviation in the tower’s wake. Sonic-derived longitudinal (Iu) and lateral (Iv) turbulence intensities can be compared to the high frequency data obtained from anemometers installed near the coast line during the landfall of other hurricanes [3-6, 32].
Turbulence intensities as measured by the sonic and top level cup anemometers as compared to storm passage characteristics of pressure (top panel) and wind direction (bottom panel). Lateral turbulence intensity of the 034B sensor depicted in the bottom panel is assessed from the 1-min wind direction fluctuation (right axis) and plotted as 10×σwd/360 (left axis). Note the surprise lull under northwesterly wind directions towards the end of the eyewall passage.
As expected, values are, in general, larger than those obtained over the relatively smooth surfaces encountered in those previous studies. However, the expected dependence of IU on surface roughness length is clear also in previous data [6]. In addition, IU also depends on measurement height and wind speed. Turbulence intensity data obtained from a tall tower over urban Beijing [33] are roughly consistent with the above results, Iu = 0.3-0.4, and Iv=0.25-0.35 at similar measurement heights. However, while a mean Iv/Iu ratio of 0.87 was obtained, other studies such as [33]and [6] obtained 0.75, close to the expected value from MO theory, suggesting that the tower’s wake influences reduced Iu more strongly than Iv. Nevertheless, use of the predictive formulas listed in [33] to compare the results to resulted in a reasonable fit using the formula
which leads to a value of 0.34 compared to a mean measured value of 0.29±0.09 (1 sd), not including wake-affected values for the two days entering the calculation (DOYs 255&256).
Wind speed influences on IU can be observed from the top level cup anemometer data. As the storm approached, IU dropped slightly and became less variable, more or less consistent with the pressure development. A similar result was presented in [33] for winds measured over Beijing, while not as clear for the coastal hurricane land fall measurements [4, 6].
A closer inspection of observed wind speeds and associated turbulence intensities in Figures 5 and 7 shows that rain band passage affected both measures. Wind speeds increased just prior to or shortly after rain band passage. Spikes are visible both prior to and after the first outer rain band passed over Houston, as well as prior to nearly all outer rain band passages. A similar argument can be made for the eye wall passage itself: Label 4a characterizes passage of the NW side of the eye wall, while label 4b characterizes passage of the SW side of the eye wall. Both were associated with heavy rainfall, but the period in between experienced slightly lower rainfall rates. In all these cases, short-term increased wind speeds were likely associated with mesoscale circulations within the storm associated with descending air between rain bands accelerating towards an inner rain band. Convection inside the rain band causes heavy rainfall and was generally associated with lulls in wind speed. In contrast, as can be seen from Figure 7 it was often associated with short-term increases of turbulence intensity as a likely effect of stronger convective activity.
With increasing wind speed in storms, large scale wave structures are expected to form, often called rolls. These have been investigated for hurricanes before through Doppler radar, integral length scales (Lx, x=u,v,w), and wind speed spectral analyses [2, 5-7, 34]. Several of these authors found that both sub-kilometer and meso-gamma scale (several kilometers) features can be observed in hurricanes. Compared to observations at lower wind speeds, these features lead to higher values at lower frequencies in the (normalized) wind power spectrum, particularly between 0.01 and 0.001 reduced frequency values. Some of these analyses have been repeated here; however, the loss of sonic anemometer data during rain prevents a detailed spectral analysis, and the data acquisition frequency of the cup anemometers limits integral length scale and spectral analysis.
R software [35] was used to calculate normalized, partially smoothed spectra from 2-hour de-trended segments of both sonic and cup anemometer data. Integral length scales were calculated from the sonic data by (i) selecting non-overlapping 10-min segments and calculating the auto-correlation function (acf), (ii) fitting an exponential decay curve to the acf, and (iii) integrating the exponential function out to twice the first zero-crossing observed in the acf. The procedure was similar to that described in [6] and [4].
Here, pre-storm wind speed spectra from both the top level sonic and cup anemometers were compared to height-of-storm cup anemometer data. A short-coming of the previous works is the lack of comparison between observed hurricane wind spectra and “normal” wind speed spectra at the same locations. Figure 8 shows the calculated power spectra for the 2-h, neutral stability longitudinal wind segments.
A comparison of longitudinal wind speed spectra between the night before the hurricane (DOY 256, hours 01:00-03:00 CST) and three periods of the highest encountered wind speeds before, during, and after the eyewall maximum. Smoothing was limited to highlight differences. The thick, dark grey line represents a standard spectrum. Note that the grey spectra from the previous night were obtained at an average wind speed of 6 m s-1, the offset being due to a slightly higher value recorded by the cup anemometer. Wind speeds for the blue spectra were all above 22 m s-1 (Fig. 3). To match power density levels (y-axis) the blue spectra were additionally normalized to the wind speeds’ standard deviation ratios.
The grey spectra match surprisingly well between the top level sensors at lower frequencies. At the same time, they are well characterized by the standard, smoothed “perturbed terrain” model spectrum [4], which shows a maximum at 2-3×10-2 and falls off below 1×10-2. In comparison, the visible meso-gamma scale features at reduced frequencies between 1-5×10-3 were strongly enhanced in the high wind speed spectra. This is consistent with the previous findings [4, 7]. For the wind speeds encountered here, these are features with wavelengths between approximately one and five kilometers, and might be associated with boundary layer rolls.
Previous analyses of hurricane winds integral length scales, corresponding to the frequencies of maximum power in the power spectrum, ranged from less than hundred to several hundred meters for Lu, but were all observed over relatively flat terrain or with ocean fetches [2, 4, 6, 7]. Comparative length scale data to the one observed in Houston come from the Beijing tall tower measurements [33]. That study reported highly variable values with means of approximately 100 and 200 m for z=47 and 120 m agl. Similar to the data above, that data base contained only wind speeds up to 15 m s-1 at z=120 m, but the authors did not analyze for wind speed correlation. As integral length scales were found to increase with wind speed [7] it is possible that larger average length scales would have resulted had wind speeds been higher. Here, length scale data were calculated between noontime on DOY 256 and midnight under the limitations described above. The results are summarized in Table 1.
\n\t\t\t\tLength scale\n\t\t\t | \n\t\t\t\n\t\t\t\tthis study (mean ± sd)\n\t\t\t | \n\t\t\tLi et al.(means) | \n\t\t\tYu et al.(mean ± sd) | \n\t\t\tMasters et al.(mean ± sd) 1 | \n\t\t|
\n\t\t\t | \n\t\t\t\tall data\n\t\t\t | \n\t\t\t\n\t\t\t\twake-free data\n\t\t\t | \n\t\t\t\n\t\t | ||
\n\t\t\t\tLu\n\t\t\t\t\n\t\t\t | \n\t\t\t217±168 | \n\t\t\t282±185 | \n\t\t\t104, 195 | \n\t\t\t122 ± 29 | \n\t\t\t130 ± 45 | \n\t\t
\n\t\t\t\tLv\n\t\t\t\t\n\t\t\t | \n\t\t\t177±137 | \n\t\t\t214±153 | \n\t\t\t44, 93 | \n\t\t\t\n\t\t\t | 90 ± 43 | \n\t\t
Integral length scales in meters for winds <= 15 m s-1 (this study and [33], z0≈1 m), and >=15 m s-1 ([6] and [7], z0<0.1 m)
1these values are averages over several landfalling hurricanes; the actual spread of the values for each hurricane was at times much larger than indicated by the sd of the means listed here
The observed values are broadly comparable. Similar to all observations is the relatively large variability of the data, with several values exceeding 400-500 m length scales, and a generally log-normal distribution. A slight dependence on wind speeds and a good correlation between Lu and Lv was observed in this study’s data and the data in [6]. The wind speed correlation suggests that values over 400 m should occur regularly for wind speeds exceeding 15 m s-1, which is consistent with observations in [6]. The values over Beijing appear lower, but were likely influenced by a large amount of data at lower wind speeds, but this was not elaborated on [33].
Sustained wind speeds and turbulence intensity account for the wind loads plotted in Figure 6. Typically, static loads exceed dynamic loads. However, dynamic wind loads can contribute significantly due to the increased turbulence created by wake effects of buildings in urban areas. Individual periods during which IU was increased [17] locally were previously highlighted and discussed above. However, a single site measurement cannot assess all local effects. Where and when damages most likely occur has instead been assessed through standardized measurements and models in the past. For instance, the results from extensive works on wind-throw in forests in [30, 36, 37], [38], [39], and [31] may be applicable to urban areas because, as in Houston, urban tree distribution is often patchy. In addition, buildings represent additional roughness elements causing similar or stronger wakes than other trees and stands in parks. While wind loads in Houston (Fig. 6) were seemingly not high enough to uproot trees, another measure to gauge surface impacts is momentum transfer or, more generically, (surface) friction velocity, u*.
Friction velocity was measured directly with the sonic anemometer, but also calculated by linearizing the log-law (equation 1) for 10-min section mean winds using the four measurement levels from 20-60 m agl. If the preset roughness length and displacement height values are correct, the linearization retrieves friction velocity from the slope of the curve and a near zero intercept under neutral and near neutral stabilities, including some allowance for error (e.g. ±1 for the intercept). The results are plotted in Figure 9. We found a generally excellent match between the sonic anemometer and the wind gradient values.
Friction velocity (upper panel) and wind direction (lower panel) time series during Hurricane Ike’s passage over Houston. Small black circles depict all gradient-calculated values, open dark grey squares represent sonic-measured values, and the light grey line is a straightforward calculation of u* using the log-law and only top level cup anemometer winds alongside preset z0 and d. The vertical dashed line marks the period when winds advected from over the large building on the NW side of the tower.
Biases were observed for three reasons: First, when strong instability is present, such as visible midday on DOY 255. Second, during periods when wind speeds at the lower levels are affected by the tower’s wake, generally between approximately 320 and 10 degrees; u* is first under-, then overestimated and a negative, then positive y-intercept in the linearization is observed. This can be explained by a temporary acceleration the wind undergoes approaching the sensor from close to the tower structure for approximately 0-10 deg. N. This increases the linearization slope and creates a negative intercept. As wind direction turns further N towards NNW, winds are slowed through the tower structure, which creates a lower slope and a positive intercept. In either case, large residuals and poor determination coefficients of the linearization resulted. In neither case were winds at the top level affected. Third, the strongest bias though was observed for NW wind directions during the latter part of the eyewall passage, marked by the vertical dashed line. Calculated u* plummeted and large positive intercepts were found from the linearization. At the same time, lateral turbulence intensity, Iv, dropped strongly, see Fig. 7, while strong updrafts turned the saucer-shape radiation shields from their horizontal into a vertical position (pictures are available online). For these wind directions, the flow advects over the large industrial building in 100 m distance, which occupies a significant fraction of the footprint at these wind speeds and likely produces a significant wake and associated turbulence. If only the top level sensor were affected at this wind direction, the linearization determination coefficient would again have been low and residuals high. This was, however, not the case. Thus, surface characteristics for this wind direction are most likely not well described by the preset z0 and d values for the encountered wind speeds.
In summary, Figure 9 shows extremely high, not previously measured friction velocities over an urban area. The corresponding large, turbulent downward momentum fluxes are the main destructive force in this environment. The results were observable after the storm. Figures 10 and 11 show the typical impacts in this neighborhood that led to the large scale power failures suffered all over the metro area.
Tree damage and debris along Hardy Road, ca. 2 km from the tower site.
View from the tower at 12 m agl towards NNW. The circles mark tree damage, the arrow on the lower left marks the local generator’s exhaust pipe.
Two of the three tall trees immediately north of the tower, shown in Figure 11 growing alongside Hays Street between some of the larger buildings, and immediately downwind of the largest building in the area seen on the left, were also severely damaged, the one on the left losing nearly its complete crown.
It is also interesting that damage was largely confined to trees, or secondary damage from falling trees; significantly less (tile) roof damage was reported. This has previously been interpreted as being due to a mature tree canopy extending beyond roofs in many parts of Houston [40], with the trees taking the brunt of the storm’s winds. However, in heterogeneous building areas such as the immediate surroundings of the tower site, small scale damage proportional to the encountered tropical storm force winds was caused. As shown in Figure 12, the local Yellow Cab headquarters suffered from a torn-off metal roof and a collapsed metal awning. In addition, not shown here, the company’s antennas on top of the tower were bent and the tower’s guy wires were loose, leading to significant sway of the tower. Similar damage kept cell-phone tower crews busy for months after the storm.
Another significant impact of hurricanes at landfall is the often torrential inland rainfall, leading to flash-floods and potential inundation of low lying areas. In this case, Houston was much more prepared, having learned lessons from many past floods, particularly tropical storm Allison in 2001. The next section will discuss Hurricane Ike’s thermodynamic properties and the associated rainfall as compared to independent measurements.
Structural damage caused by Ike as viewed from the tower at approx. 18 m agl towards NE (top) and ESE (bottom)
Hurricanes have been called equivalents of heat engines [41]. A warm ocean in disequilibrium with the overlying (dry) air supplies large amounts of water vapor by evaporation at the ocean surface. When condensing in the atmosphere this energy is released as latent heat of vaporization during air flow towards a pressure minimum, and it is efficiently converted into kinetic energy, i.e. increasing wind speeds. Conservation of angular momentum forces these winds to spiral faster as they approach the low pressure center of the storm. Increased wind speeds also cause increased evaporation of surface ocean water, maximizing humidity towards the center of the storm, where often the most heavy precipitation occurs. The increase of entropy towards the storm’s eye can be depicted by calculating equivalent potential temperature (Θe), the temperature an air parcel would assume when brought adiabatically to surface reference pressure (potential T) and using latent heat of vaporization from condensing all its available water vapor to heat it. The distribution of Θe for a mature, symmetric hurricane over a uniformly warm ocean surface is presumably also close to symmetric, increasing towards the eyewall, and observational studies tend to confirm this structure, e.g. [42]. When hurricanes make landfall, their source of (latent heat) energy at the surface is cut off and drier air is eventually imported into the storm, leading to its inevitable dissipation over land. At a single measurement location, the 2-D thermodynamic structure of the hurricane can be observed via Θe when it moves past the sensor. Here, Ike’s track allowed for this observation from the time of its approach to the coastline to its passage into northeast Texas. In Figure 13, Θe is plotted alongside measured precipitation and wetness. The wetness sensor typically allows for the detection of light rain when there was not enough rainfall to be detected by the tipping rain bucket instrument.
Time series of Θe (thick blue line), precipitation (light blue line), and wetness (thin black line) during Hurricane Ike’s passage over Houston (wetness is plotted as the logarithm of the raw sensor signal, a resistance measurement). Similar to previous plots, radar-based evaluation of rain band passage timing is plotted along the top with bands 4a and 4b representing the eyewall.
It is clear from Fig. 13 that Θe near monotonously increased during the storm’s approach and into its eyewall. Rapid increases were observed in the outer rain bands, including bands 8 to 10 in the afternoon after landfall, when the storm’s center had migrated into northeast Texas and local precipitation had all but ceased. Increases in humidity as indicated by the wetness sensor were often clearly related to increases in Θe. Significant precipitation began to fall at the site shortly before 22:00 CST, and increased steadily into the eyewall. The highest rain rates were observed in the NW side of the eyewall, coincident with the highest wind speeds under still rising Θe levels (03:00 CST), and on the SW side of the eyewall just after the lowest pressure had been observed (04:00 CST). Then Θe rapidly dropped, and despite a short-term increase in an outer rain band with heavy precipitation (#5) fell to pre-storm levels before midday on DOY 257. The following afternoon rise, though associated with outer rain bands of the storm, was not associated with strong winds or significant precipitation any more.
This development, including its correlation with the winds as shown in Fig. 5, can be interpreted through the air circulation into the storm during and after landfall. For a straightforward elucidation, we carried out both a back trajectory analysis using HYSPLIT [43, 44] with 40 km resolution EDAS data, and an analysis of locally measured carbon monoxide concentrations as a tracer of continental air masses. In the first hours after landfall up to the approach of the eye closest to central Houston, the observed air masses were tropical marine in origin. As the storm approached the site it “imported” its Θe onto land. Beginning at approximately 04:00 CST, when the eye lay east of the tower site, the storm began to entrain drier continental air from north and northwest Texas into its western eyewall, which can explain the rapid decline in Θe. Figure 14 shows two back trajectory ensembles, one for just before the Θe decline, and one for six hours after decline had begun. This entrainment explains why Ike maintained much stronger wind speeds particularly on its eastern side throughout the morning [28] as this side continued to be fueled by Gulf of Mexico air masses. With the storm moving further north by midday and into the afternoon, wind direction had changed back to southerly flows with all air mass origins returning to the Gulf of Mexico (data not shown). This analysis is corroborated by the carbon monoxide data shown in Figure 15.
Typical continental boundary layer CO levels for September of 100-130 ppb were measured on DOY 256, with higher values during the morning and afternoon rush hour periods. As the storm approached and a tropical marine air mass was established, CO dropped to northern hemisphere marine background levels near 75 ppb, among the lowest levels measured in Houston. However, shortly after Θe levels began to drop and wind speeds plummeted, CO levels rose again to levels consistent with entraining continental air. Thus, the west side of the storm was rapidly deprived of its latent heat energy source. Nevertheless, short-term, small fluctuations in CO abundance, anti-correlated with Θe, could still be observed during the early afternoon of DOY 257. Later on, the reason for continued CO increases even after air mass origins had fully returned to tropical marine in the afternoon of DOY 257 can be found in a low nighttime boundary layer and large local CO emissions from electricity generators in the Houston metro area [45], including Yellow Cab’s own onsite diesel generator (see Fig. 12).
Back trajectory ensembles for 04:00 CST (left) and 10:00 CST (right) on DOY 257.
Time series of carbon monoxide (CO) levels as compared to Θe prior and during Ike’s passage over Houston. As in previous Figures, rain band passage timing is indicated along the top. The two vertical dashed lines mark the start times for the back trajectories plotted in Fig. 14.
In addition to Θe rainfall dynamics were analyzed. A time series analyses of the storm data showed principle periodicities of 20 and 50 minutes, corresponding to rain band recurrence. For the flooding potential, the total amount and intensity of rainfall is of particular interest. As Houston is flood-prone, several rain and flood gauges are maintained throughout the water sheds in the metro area. Thus, the locally measured rainfall was compared to the collection of data provided online [28] in Figure 16.
Rainfall development (blue line) during both Hurricane Ike’s and the subsequent day’s morning frontal passage over Houston. Vertical dark blue bars mark radar-derived precipitation totals, open squares mark totals observed at the nearest USGS gain gauge in the White-Oak-Bayou water shed. Pressure and rain band passage timing are plotted for orientation.
In general, a good agreement was found between the extrapolated radar data and the closest rain gauge to the tower. There appears to be a slight underestimation of the local measurements as compared to the references, which could be explained by the location of the rain gauge on the tower: As it is installed on the east side of the tower, rainfall approaching from the west and southwest during the second half of the eyewall passage may not have all reached the bucket. However, the highest rainfall rates were recorded during the NW eyewall passage consistent with the radar data [28], reaching 11 mm (10 min)-1. Nearly twice the intensity, 19 mm (10 min)-1, however, was observed during the post-storm frontal passage on DOY 258 fueled by storm-intensified humidity entrainment from the Gulf of Mexico [28], Fig. 16, which added almost as much rainfall to the total as caused by Ike during the previous day. Ultimately, a total of 327 mm (12.9 inches) of rain fell onsite within 36 hours, with up to 15 inches as estimated from the radar data for other areas of Houston [28], more than three times the long term average September rainfall for this area [46].
Hurricane Ike’s path after landfall during the early morning hours on 13 September 2008 crossed through Galveston Bay, went north along the eastern border of Harris County, then slightly northwest again towards north of Houston, until finally veering NNE towards northeast Texas. Most of Harris County, including the city of Houston and the economically important Ship Channel, went through the western, often less severe eyewall of the hurricane. Nevertheless, the Houston metro area suffered from widespread power outages caused by the hurricane’s impacts hours before the highest rain rates and wind speeds passed. Onsite measured rainfall compared well with independent data. While local flooding was caused by this three-times monthly average amount in 36 hours, the Houston drainage network including its improvements since tropical storm Allison in 2001 seemingly handled the amount of water adequately [47]. The same was not the case with respect to preparations for potential wind damage. This chapter described Ike’s wind field from approach to retreat as measured from a tower platform north of downtown Houston. Measured winds were likely representative of the larger metro area, showing tropical storm force winds at 20 m agl, strongly slowed by the rough urban surface as compared to standardized H*Wind products. However, although measured wind speeds were significantly lower than commonly cited, strong downward momentum fluxes in combination with high turbulence intensities, likely locally exaggerated by building wakes, caused “moderate” tree and building damage in the area equivalent to what would be expected from a category two hurricane. As this “moderate” damage dominantly occurred to a mature, poorly trimmed tree canopy in neighborhoods where power is distributed aboveground on poles, much higher than expected power line loss resulted.
Similar to previous measurements, the wind analysis results also indicate larger horizontal structures in the wind field not present at lower wind speeds. Significant interaction of these roll features with the underlying surface might contribute to the damage potential of the storm, but this cannot be evaluated with confidence from a single observing location. The extensive meteorological observations along the Gulf Coast during Hurricane Ike may, however, provide the opportunity for such an analysis once all data become analyzed in more detail.
Additional observations of equivalent potential temperature and air quality development during the approach and passage of Hurricane Ike revealed that Houston may have been spared even larger damage from high winds because of entrainment of drier continental air into the western eyewall. While higher wind speeds were maintained south and east of the eye, Houston in the west of the eye experienced overall lower winds and shorter durations of tropical storm force winds than observed on the east side of the eye [28].
I am indebted to the employees of Houston Yellow Cab at 1406 Hays Street, particularly William Hernandez, who were onsite during the storm to keep the power from their generator on and protect our equipment against water that had penetrated the flat roof structure shown in Fig. 12. The Greater Houston Transportation Co. has provided free access to its tower and base building for our study since 2007, thereby facilitating and supporting these unique urban measurements. We continue to be grateful for this private enterprise support of our academic goals. I also thank my graduate student Marty Hale for assembling Figure 4b. Our research was supported at the time by the Texas Air Research Center (TARC), Lamar University, Beaumont, TX, and a start-up grant to the author by Texas A&M University in College Station.
Ferrimagnetism is similar to ferromagnetism in many ways [1, 2, 3, 4]. They all have hysteresis curves as the applied magnetic field changes, resulting in the saturation magnetization (\n
The hysteresis (B-H) curves for (a) hard ferrimagnetism and (b) soft ferrimagnetism. The remnant polarization (\n\n\nB\nr\n\n\n) and the coercive field (\n\n\nH\nc\n\n\n) for the hard ferrites should be as large as possible. On the other hand, for the soft ferrites, the remnant polarization (\n\n\nB\nr\n\n\n) and the coercive field (\n\n\nH\nc\n\n\n) are very small or even close to zero.
Soft magnetic materials include electrical steels and soft ferrites [3, 4]. Unlike the ferromagnetic metals which are conductors, soft ferrites have low electric conductivity, i.e., they are dielectric materials. The electrical steels have extensive applications in low-frequency systems, such as generators, motors, and transformers, while the soft ferrites are suitable for the high-frequency applications, such as circulators, isolators, phase shifters, and high-speed switches.
\nThis chapter will focus on the properties of the soft ferrites and their applications at high-frequency systems. The ferrites are crystals having small electric conductivity compared to ferromagnetic materials. Thus they are useful in high-frequency devices because of the absence of significant eddy current losses. Ferrites are ceramic-like materials with specific resistivities that may be as much as 1014 greater than that of metals and with dielectric constants around 10 to 16 or greater. Ferrites are made by sintering a mixture of metal oxides and have the general chemical composition MO·Fe2O3, where M is a divalent metal such as Mn, Mg, Fe, Zn, Ni, Cd, etc. Relative permeabilities of several thousands are common [5, 6]. The magnetic properties of ferrites arise mainly from the magnetic dipole moment associated with the electron spin [2].
\nThe magnetic dipole moment precesses around the applied DC magnetic field by treating the spinning electron as a gyroscopic top, which is a classical picture of the magnetization process. This picture also explains the anisotropic magnetic properties of ferrites, where the permeability of the ferrite is not a single scalar quantity, but instead is a generally a second-rank tensor or can be represented as a matrix. The left and right circularly polarized waves have different propagation constant along the direction of the external magnetic field, resulting in the nonreciprocity of a propagating wave. Since the permeability should be treated as a tensor (matrix), not a scalar permeability, it is generally much difficult to understand and to have intuition, even for the researchers.
\nThe properties of ferrites are very intriguing. Without a DC bias magnetic field \n
Figure 2 shows the Larmor precession with the circularly polarized fields [7]. Circular polarization may be referred to as right handed or left handed, depending on the direction in which the electric (magnetic) field vector rotates. For a right-hand circularly polarized (RHCP) wave, the fields rotate clockwise at a given position from the source looking in the direction of propagation. The magnetic dipole moment m processes around the \n
Larmor precession of a magnetic moment m around the applied DC bias field H0 (\n\n=\n\nH\n0\n\n\nz\n̂\n\n\n) with (a) a right-hand circularly polarized (RHCP) wave and (b) a left-hand circularly polarized (LHCP) wave. The frequency of the Larmor precession in both cases are the same, i.e., the Larmor frequency \n\n\nω\n0\n\n\n\n\n=\n\nμ\n0\n\nγ\n\nH\n0\n\n\n\n\n. \n\n\nH\nt\n+\n\n\n and \n\n\nH\nt\n−\n\n\n are the transverse components of the incident waves which rotate clockwise (RHCP) and counter-clockwise (LHCP) from the source viewpoint looking in the direction of propagation. The thumb points the direction of the wave propagation, and the fingers give the rotation of the transverse components [7].
A linearly polarized incident wave can be decomposed into RHCP and LHCP waves of equal amplitude. The orientation of the linearly polarized wave changes after the wave propagates a certain distance because of the distinct propagation constants. The phenomenon is the famous Faraday’s rotation [5, 6]. This unique property has various applications, such as phase shifters, isolators, and circulators. However, it is difficult to follow for students and even researchers in that the permeability is a tensor, not just a simple proportional constant.
\nHere we consider the simplest case for the pedagogic purpose—a circularly polarized plane wave is normally incident upon a semi-infinite medium. The wave characteristics such as the propagation constant k and the wave impedance Z are associated with the permeability μ, which is a tensor for the ferrite medium [5]. By finding the preferred eigenvalues, it will be shown that the properties of μ depend on the DC bias field \n
The permeability \n
Since the torque is equal to the time change rate of the angular momentum, we have
\nBy comparing Eqs. (1) and (2), we obtain
\nA large number of the magnetic dipole moment \n
M and H in Eq. (4) differ slightly from m and \n
Since the AC terms have an exp(−iωt) dependence, by substituting Eq. (5) and (6) into Eq. (4) the transverse component terms read
\n\n\n
where \n
The eigenvectors corresponding to these two eigenvalues are the right-hand circularly polarized wave (RHCP, denoted as +) and the left-hand circularly polarized wave (LHCP, denoted as -), respectively. The symbols, + and -, represent positive helicity and negative helicity, respectively. The LHCP wave has a relatively mild response over the entire frequency range. On the contrary, the RHCP wave has a much more dramatic response.
\nThe permeabilities of the RHCP and LHCP waves are
\nEq. (12) has a singularity when the wave frequency \n
For a resonant cavity with a quality factor (\n
the permeability for the RHCP wave now reads
\nTo conduct a complete simulation of a ferrite device, we need to know its complex permittivity, the saturation magnetization, and the resonance linewidth. We will discuss how to characterize the ferrite’s properties in the next section.
\nHere we will discuss the measurement of the most important properties of ferrites, including the dielectric properties (\n
Ferrites are ceramic-like materials with relative dielectric constants around 10 to 16 or greater. The resistivities of ferrites may be as high as 1014 greater than that of metals. Since ferrites are dielectric materials. The dielectric properties (\n
Figure 3 shows the ideal of the field enhancement method. Figure 3(a) shows the resonant frequency as functions of the dielectric constant (\n
(a) Resonant frequency versus dielectric constant based on full-wave simulations. The solid curve can be divided into three regions: low, transition, and ultrahigh. The dashed line is simulated with a much thinner sample of 1.00 mm in thickness, which exhibits the properties similar to those of perturbation. (b) Schematic diagram of the field enhancement method. It consists of a cylindrical resonant cavity and a metal rod. The sample is placed on the top of the metal rod. The metal rod focuses and enhances the electric field significantly. An SubMiniature version A (SMA) 3.5-mm adapter couples the wave from the top of the cavity [11].
Ferrites have a strong response to the applied magnetic field. The magnetic properties of ferrites arise mainly from the magnetic dipole moment associated with the electron spin. Relative permeabilities of several thousands are common. The saturation magnetization (\n
The hysteresis curve regarding the magnetization \n\nM\n\n and the internal bias \n\n\nH\n0\n\n\n. When the applied internal magnetic field \n\n\nH\n0\n\n\n is large enough, the magnetization will be saturated, denoted as (\n\n\nM\ns\n\n\nor\n\n4\nπ\n\nM\ns\n\n\n). When \n\n\nH\n0\n\n\n decreases to zero, the remnant polarization is denoted as \n\n\nM\nr\n\n\n. The polarization will change sign (from positive to negative) when \n\n\nH\n0\n\n\n is greater than \n\n−\n\nH\nc\n\n\n which is called the coercive field.
The idea is to place the sample at the maximum of the H-field. It exhibits resonant absorption when the internal bias field is changed to \n\n\nH\nr\n\n\n. By changing the magnetic field, we will obtain the absorption. \n\n\nH\n1\n\n\n and \n\n\nH\n2\n\n\n are associated with the 3-dB absorption. The difference between these two values is the resonance linewidth \n\nΔ\nH\n\n.
Note that the saturation magnetization is denoted as \n
The loss of ferrite material is related to the linewidth, \n
The idea is normally implemented using a TE10n (n even) cavity in the X-band region [9, 12]. The test sample is placed at the H-field maximum. The sample is spherical with a diameter of approximately 0.040 inches, which is much easier to estimate than the internal bias field \n
The three key parameters are obtained in three experimental setups under different sizes and geometries of the samples. If the samples’ properties are slightly different or the machining error is not negligible, the error will be large or even unacceptable. The ultimate goal is to integrate the measurements and to extract the parameters using one experimental setup. The three key parameters will be used in the design of the microwave ferrite devices in the next session.
\nThe ferrites are crystals having small electric conductivity compared to ferromagnetic materials. Thus they are useful in high-frequency situations because of the absence of significant eddy current losses. Three commonly used ferrite devices are discussed below. These are phase shifters, circulators, and isolators [13, 14, 15, 16].
\nThe phase shifters are important applications of ferrite materials, which are two-port components that provide variable phase shift by changing the bias magnetic field. Phase shifters find application in test and measurement systems, but the most significant use is in phase array antenna where the antenna beam can be steered in space by electronically controlled phase shifters. Because of the demand, many different types of phase shifters have been provided. One of the most useful designs is the latching nonreciprocal phase shifter using a ferrite toroid in the rectangular waveguide. We can analyze this geometry with a reasonable degree of approximation using the double ferrite slab geometry.
\nFigure 6 shows the full-wave simulation for a two-port phase shifter using high-frequency structure simulator (HFSS, ANSYS). A standard waveguide WR-90 is employed with a width of 22.86 mm and height of 10.16 mm. The field patterns are displayed in Figure 6(a) for an empty waveguide and a waveguide with two ferrite slabs. The phase difference \n
Simulation results. (a) The field pattern to the left is for the empty waveguide. The right figure shows field strength with ferrites. (b) The phase difference \n\nΔ\nϕ\n\n as a function of the internal bias field \n\n\nH\n0\n\n\n.
Circulator, a nonreciprocal device, has been widely used in various microwave systems. Figure 7 schematically shows the function of a stripline circulator. The circulator is, in general, a three-port device. If the incident wave is injected from Port 1, then the wave will ideally go to Port 2, while Port 3 will be isolated as shown in Figure 7(a). On the other hand, if the wave is injected from Port 2, it will go to Port 3 and isolate from Port 1 as shown in Figure 7(b). There are three figures of merit for a circulator: transmission, reflection, and isolation. The transmission from Port 1 to Port 2 should be as high as possible, i.e., the insertion loss should be as small as possible. The reflection received at Port 1 due to the incident wave of Port 1 (S11) and the isolation from Port 1 to Port 3 (S13) should be as small as possible. The nonreciprocity of the circulator can be used to protect the oscillators from the damage of the reflected power in plasma or material processing systems. It can also be used to separate the transmitted and the received waves in radar or communication systems [13, 14, 15, 16, 17].
\nSchematic diagrams of the operation of a stripline circulator. (a) The incident wave is injected from Port 1 and the transmitted wave ideally goes to Port 2. (b) The incident wave from Port 2 will go to Port 3. The color spectrum is the electric field pattern inside the ferrite disks. It is a three-port, nonreciprocal device. A full-wave solver, high-frequency structure simulator (HFSS), is used [18].
In addition to the stripline circulator, there are other types such as the microstrip circulator and the waveguide circulator. The microstrip circulator is similar to the stripline circulator in many ways. Here we show a waveguide circulator which is capable of high-power operation. Figure 8(a) shows the structure of the nonreciprocal device and the simulated electric field strength. The simulation parameters are described in the caption. The circulator is, in general, a three-port device. If the incident wave is injected from Port 1, then the wave will ideally go to Port 2, while Port 3 will be isolated as shown in Figure 8(b). On the other hand, if the wave is injected from Port 2, it will go to Port 3 and be isolated from Port 1 as shown in Figure 8(b).
\n(a) Schematic diagrams of the operation of a waveguide circulator. A full-wave solver, HFSS, is used with the saturation magnetization (\n\n4\nπ\n\nM\ns\n\n\n) is 1600 G, the dielectric constant\n\n\nε\n′\n\n\n is 13.0, and the resonance linewidth \n\nΔ\nH\n\n is 10 Oe. The radius and thickness of the ferrite disks in rust red are R = 21.0 mm and t = 5 mm, respectively. The waveguide is a standard WR 340 with 86.36 × 43.18 mm2. The electric field pattern is displayed in color. (b) Simulation results of the waveguide circulator like the one in Part (a). The solid red curve is the transmission or insertion loss; the blue curve represents the reflection loss, and the black is the isolation.
The isolator is one of the useful microwave ferrite components. As shown in Figure 9, the isolator is generally a two-port device having unidirectional transmission characteristics (nonreciprocity). From Port 1 to Port 2 (S21), the forward transmission is high (i.e., low insertion loss in Figure 9(a)). However, from Port 2 to Port 1 (S12), the reverse transmission is low (i.e., high isolation in Figure 9(b)). Besides, the reflection (S11 and S22) should be as low as possible. The simulation parameters in Figure 9 are the same as Ex. 9.2 of Pozar’s textbook [5]. The simulation parameters and the sample’s geometry are described in the caption.
\nThe simulated field strength for a two-port isolator using the full-wave solver. (a) The high forward transmission (S21) and (b) the low reverse transmission (S12). The saturation magnetization (\n\n4\nπ\n\nM\ns\n\n\n) is 1700 G, the dielectric constant \n\n\nε\n′\n\n\n is 13.0, and the resonance linewidth \n\nΔ\nH\n\n is 200 Oe. The length and thickness of the ferrite are L = 24.0 mm and t = 0.5 mm.
An isolator is commonly used to prevent the high reflected power from damaging the precious and expansive microwave source. For example, the impedance of a plasma system changes a lot when the plasma is ignited. The radical change of the impedance will result in impedance mismatch and cause serious reflection which might kill the source instantly. An isolator can be used in place of a matching or tuning network. However, it should be realized that the reflected power will be absorbed by the ferrite of the isolator, as shown in Figure 9(b). When the ferrite absorbs the reflected energy, the temperature will rise and the performance will be compromised. Therefore, a simple isolator can be implemented by using a circulator with one port well terminated [19]. For example, if Port 3 in Figure 8(a) is matched with water load, the power injected from Port 2 will go to Port 3 and will be isolated from Port 1. The power handling capability can be improved.
\nCirculator and isolator can be implemented using the self-bias [20, 21, 22], just like the latch phase shifter (\n
Ferrimagnetism and ferromagnetism share many magnetic properties in common, such as hard and soft magnets, but the conductivity differentiates these two materials. Ferrites are ceramic materials and suitable for the high-frequency operation. The electromagnetic properties of ferrite materials are difficult to understand in that the magnetic susceptibility is a tensor and depends on the saturated magnetization \n
The complex permittivity \n
At high-power operation, the ferrite devices will be heated. The spin wave linewidth may be taken into account. Besides, the ferrites will become paramagnetism when the temperature exceeded the Curie temperature. These two factors are important for high-power operation, which are not considered in this chapter.
\nThis chapter was supported in part by the Ministry of Science and Technology of Taiwan and in part by China Steel Company/HIMAG Magnetic Corporation, Taiwan. The author is grateful to the Taiwan Branch of ANSYS Inc. for technical assistance and to Dr. Hsein-Wen Chao and Mr. Wei-Chien Kao for their assistance in the full-wave simulation. Dr. Hsin-Yu Yao and Mr. Shih-Chieh Su are appreciated for the discussion of the ferrites’ characterization.
\nIntechOpen aims to ensure that original material is published while at the same time giving significant freedom to our Authors. To that end we maintain a flexible Copyright Policy guaranteeing that there is no transfer of copyright to the publisher and Authors retain exclusive copyright to their Work.
',metaTitle:"Publication Agreement - Chapters",metaDescription:"IN TECH aims to guarantee that original material is published while at the same time giving significant freedom to our authors. For that matter, we uphold a flexible copyright policy meaning that there is no transfer of copyright to the publisher and authors retain exclusive copyright to their work.\n\nWhen submitting a manuscript the Corresponding Author is required to accept the terms and conditions set forth in our Publication Agreement as follows:",metaKeywords:null,canonicalURL:"/page/publication-agreement-chapters",contentRaw:'[{"type":"htmlEditorComponent","content":"The Corresponding Author (acting on behalf of all Authors) and INTECHOPEN LIMITED, incorporated and registered in England and Wales with company number 11086078 and a registered office at 5 Princes Gate Court, London, United Kingdom, SW7 2QJ conclude the following Agreement regarding the publication of a Book Chapter:
\\n\\n1. DEFINITIONS
\\n\\nCorresponding Author: The Author of the Chapter who serves as a Signatory to this Agreement. The Corresponding Author acts on behalf of any other Co-Author.
\\n\\nCo-Author: All other Authors of the Chapter besides the Corresponding Author.
\\n\\nIntechOpen: IntechOpen Ltd., the Publisher of the Book.
\\n\\nBook: The publication as a collection of chapters compiled by IntechOpen including the Chapter. Chapter: The original literary work created by Corresponding Author and any Co-Author that is the subject of this Agreement.
\\n\\n2. CORRESPONDING AUTHOR'S GRANT OF RIGHTS
\\n\\n2.1 Subject to the following Article, the Corresponding Author grants and shall ensure that each Co-Author grants, to IntechOpen, during the full term of copyright and any extensions or renewals of that term the following:
\\n\\nThe aforementioned licenses shall survive the expiry or termination of this Agreement for any reason.
\\n\\n2.2 The Corresponding Author (on their own behalf and on behalf of any Co-Author) reserves the following rights to the Chapter but agrees not to exercise them in such a way as to adversely affect IntechOpen's ability to utilize the full benefit of this Publication Agreement: (i) reprographic rights worldwide, other than those which subsist in the typographical arrangement of the Chapter as published by IntechOpen; and (ii) public lending rights arising under the Public Lending Right Act 1979, as amended from time to time, and any similar rights arising in any part of the world.
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\\n\\n2.3 All rights granted to IntechOpen in this Article are assignable, sublicensable or otherwise transferrable to third parties without the Corresponding Author's or any Co-Author’s specific approval.
\\n\\n2.4 The Corresponding Author (on their own behalf and on behalf of each Co-Author) will not assert any rights under the Copyright, Designs and Patents Act 1988 to object to derogatory treatment of the Chapter as a consequence of IntechOpen's changes to the Chapter arising from translation of it, corrections and edits for house style, removal of problematic material and other reasonable edits.
\\n\\n3. CORRESPONDING AUTHOR'S DUTIES
\\n\\n3.1 When distributing or re-publishing the Chapter, the Corresponding Author agrees to credit the Book in which the Chapter has been published as the source of first publication, as well as IntechOpen. The Corresponding Author warrants that each Co-Author will also credit the Book in which the Chapter has been published as the source of first publication, as well as IntechOpen, when they are distributing or re-publishing the Chapter.
\\n\\n3.2 When submitting the Chapter, the Corresponding Author agrees to:
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\\n\\nAll payments shall be due 30 days from the date of the issued invoice. The Corresponding Author or the payer on the Corresponding Author's and Co-Authors' behalf will bear all banking and similar charges incurred.
\\n\\n3.3 The Corresponding Author shall obtain in writing all consents necessary for the reproduction of any material in which a third-party right exists, including quotations, photographs and illustrations, in all editions of the Chapter worldwide for the full term of the above licenses, and shall provide to IntechOpen upon request the original copies of such consents for inspection (at IntechOpen's option) or photocopies of such consents.
\\n\\nThe Corresponding Author shall obtain written informed consent for publication from people who might recognize themselves or be identified by others (e.g. from case reports or photographs).
\\n\\n3.4 The Corresponding Author and any Co-Author shall respect confidentiality rights during and after the termination of this Agreement. The information contained in all correspondence and documents as part of the publishing activity between IntechOpen and the Corresponding Author and any Co-Author are confidential and are intended only for the recipient. The contents may not be disclosed publicly and are not intended for unauthorized use or distribution. Any use, disclosure, copying, or distribution is prohibited and may be unlawful.
\\n\\n4. CORRESPONDING AUTHOR'S WARRANTY
\\n\\n4.1 The Corresponding Author represents and warrants that the Chapter does not and will not breach any applicable law or the rights of any third party and, specifically, that the Chapter contains no matter that is defamatory or that infringes any literary or proprietary rights, intellectual property rights, or any rights of privacy. The Corresponding Author warrants and represents that: (i) the Chapter is the original work of themselves and any Co-Author and is not copied wholly or substantially from any other work or material or any other source; (ii) the Chapter has not been formally published in any other peer-reviewed journal or in a book or edited collection, and is not under consideration for any such publication; (iii) they themselves and any Co-Author are qualifying persons under section 154 of the Copyright, Designs and Patents Act 1988; (iv) they themselves and any Co-Author have not assigned and will not during the term of this Publication Agreement purport to assign any of the rights granted to IntechOpen under this Publication Agreement; and (v) the rights granted by this Publication Agreement are free from any security interest, option, mortgage, charge or lien.
\\n\\nThe Corresponding Author also warrants and represents that: (i) they have the full power to enter into this Publication Agreement on their own behalf and on behalf of each Co-Author; and (ii) they have the necessary rights and/or title in and to the Chapter to grant IntechOpen, on behalf of themselves and any Co-Author, the rights and licenses expressed to be granted in this Publication Agreement. If the Chapter was prepared jointly by the Corresponding Author and any Co-Author, the Corresponding Author warrants and represents that: (i) each Co-Author agrees to the submission, license and publication of the Chapter on the terms of this Publication Agreement; and (ii) they have the authority to enter into this Publication Agreement on behalf of and bind each Co-Author. The Corresponding Author shall: (i) ensure each Co-Author complies with all relevant provisions of this Publication Agreement, including those relating to confidentiality, performance and standards, as if a party to this Publication Agreement; and (ii) remain primarily liable for all acts and/or omissions of each such Co-Author.
\\n\\nThe Corresponding Author agrees to indemnify and hold IntechOpen harmless against all liabilities, costs, expenses, damages and losses and all reasonable legal costs and expenses suffered or incurred by IntechOpen arising out of or in connection with any breach of the aforementioned representations and warranties. This indemnity shall not cover IntechOpen to the extent that a claim under it results from IntechOpen's negligence or willful misconduct.
\\n\\n4.2 Nothing in this Publication Agreement shall have the effect of excluding or limiting any liability for death or personal injury caused by negligence or any other liability that cannot be excluded or limited by applicable law.
\\n\\n5. TERMINATION
\\n\\n5.1 IntechOpen has a right to terminate this Publication Agreement for quality, program, technical or other reasons with immediate effect, including without limitation (i) if the Corresponding Author or any Co-Author commits a material breach of this Publication Agreement; (ii) if the Corresponding Author or any Co-Author (being an individual) is the subject of a bankruptcy petition, application or order; or (iii) if the Corresponding Author or any Co-Author (being a company) commences negotiations with all or any class of its creditors with a view to rescheduling any of its debts, or makes a proposal for or enters into any compromise or arrangement with any of its creditors.
\\n\\nIn case of termination, IntechOpen will notify the Corresponding Author, in writing, of the decision.
\\n\\n6. INTECHOPEN’S DUTIES AND RIGHTS
\\n\\n6.1 Unless prevented from doing so by events outside its reasonable control, IntechOpen, in its discretion, agrees to publish the Chapter attributing it to the Corresponding Author and any Co-Author.
\\n\\n6.2 IntechOpen has the right to use the Corresponding Author’s and any Co-Author’s names and likeness in connection with scientific dissemination, retrieval, archiving, web hosting and promotion and marketing of the Chapter and has the right to contact the Corresponding Author and any Co-Author until the Chapter is publicly available on any platform owned and/or operated by IntechOpen.
\\n\\n6.3 IntechOpen is granted the authority to enforce the rights from this Publication Agreement, on behalf of the Corresponding Author and any Co-Author, against third parties (for example in cases of plagiarism or copyright infringements). In respect of any such infringement or suspected infringement of the copyright in the Chapter, IntechOpen shall have absolute discretion in addressing any such infringement which is likely to affect IntechOpen's rights under this Publication Agreement, including issuing and conducting proceedings against the suspected infringer.
\\n\\n7. MISCELLANEOUS
\\n\\n7.1 Further Assurance: The Corresponding Author shall and will ensure that any relevant third party (including any Co-Author) shall, execute and deliver whatever further documents or deeds and perform such acts as IntechOpen reasonably requires from time to time for the purpose of giving IntechOpen the full benefit of the provisions of this Publication Agreement.
\\n\\n7.2 Third Party Rights: A person who is not a party to this Publication Agreement may not enforce any of its provisions under the Contracts (Rights of Third Parties) Act 1999.
\\n\\n7.3 Entire Agreement: This Publication Agreement constitutes the entire agreement between the parties in relation to its subject matter. It replaces and extinguishes all prior agreements, draft agreements, arrangements, collateral warranties, collateral contracts, statements, assurances, representations and undertakings of any nature made by or on behalf of the parties, whether oral or written, in relation to that subject matter. Each party acknowledges that in entering into this Publication Agreement it has not relied upon any oral or written statements, collateral or other warranties, assurances, representations or undertakings which were made by or on behalf of the other party in relation to the subject matter of this Publication Agreement at any time before its signature (together "Pre-Contractual Statements"), other than those which are set out in this Publication Agreement. Each party hereby waives all rights and remedies which might otherwise be available to it in relation to such Pre-Contractual Statements. Nothing in this clause shall exclude or restrict the liability of either party arising out of its pre-contract fraudulent misrepresentation or fraudulent concealment.
\\n\\n7.4 Waiver: No failure or delay by a party to exercise any right or remedy provided under this Publication Agreement or by law shall constitute a waiver of that or any other right or remedy, nor shall it preclude or restrict the further exercise of that or any other right or remedy. No single or partial exercise of such right or remedy shall preclude or restrict the further exercise of that or any other right or remedy.
\\n\\n7.5 Variation: No variation of this Publication Agreement shall be effective unless it is in writing and signed by the parties (or their duly authorized representatives).
\\n\\n7.6 Severance: If any provision or part-provision of this Publication Agreement is or becomes invalid, illegal or unenforceable, it shall be deemed modified to the minimum extent necessary to make it valid, legal and enforceable. If such modification is not possible, the relevant provision or part-provision shall be deemed deleted.
\\n\\nAny modification to or deletion of a provision or part-provision under this clause shall not affect the validity and enforceability of the rest of this Publication Agreement.
\\n\\n7.7 No partnership: Nothing in this Publication Agreement is intended to, or shall be deemed to, establish or create any partnership or joint venture or the relationship of principal and agent or employer and employee between IntechOpen and the Corresponding Author or any Co-Author, nor authorize any party to make or enter into any commitments for or on behalf of any other party.
\\n\\n7.8 Governing law: This Publication Agreement and any dispute or claim (including non-contractual disputes or claims) arising out of or in connection with it or its subject matter or formation shall be governed by and construed in accordance with the law of England and Wales. The parties submit to the exclusive jurisdiction of the English courts to settle any dispute or claim arising out of or in connection with this Publication Agreement (including any non-contractual disputes or claims).
\\n\\nLast updated: 2020-11-27
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The Corresponding Author (acting on behalf of all Authors) and INTECHOPEN LIMITED, incorporated and registered in England and Wales with company number 11086078 and a registered office at 5 Princes Gate Court, London, United Kingdom, SW7 2QJ conclude the following Agreement regarding the publication of a Book Chapter:
\n\n1. DEFINITIONS
\n\nCorresponding Author: The Author of the Chapter who serves as a Signatory to this Agreement. The Corresponding Author acts on behalf of any other Co-Author.
\n\nCo-Author: All other Authors of the Chapter besides the Corresponding Author.
\n\nIntechOpen: IntechOpen Ltd., the Publisher of the Book.
\n\nBook: The publication as a collection of chapters compiled by IntechOpen including the Chapter. Chapter: The original literary work created by Corresponding Author and any Co-Author that is the subject of this Agreement.
\n\n2. CORRESPONDING AUTHOR'S GRANT OF RIGHTS
\n\n2.1 Subject to the following Article, the Corresponding Author grants and shall ensure that each Co-Author grants, to IntechOpen, during the full term of copyright and any extensions or renewals of that term the following:
\n\nThe aforementioned licenses shall survive the expiry or termination of this Agreement for any reason.
\n\n2.2 The Corresponding Author (on their own behalf and on behalf of any Co-Author) reserves the following rights to the Chapter but agrees not to exercise them in such a way as to adversely affect IntechOpen's ability to utilize the full benefit of this Publication Agreement: (i) reprographic rights worldwide, other than those which subsist in the typographical arrangement of the Chapter as published by IntechOpen; and (ii) public lending rights arising under the Public Lending Right Act 1979, as amended from time to time, and any similar rights arising in any part of the world.
\n\nThe Corresponding Author confirms that they (and any Co-Author) are and will remain a member of any applicable licensing and collecting society and any successor to that body responsible for administering royalties for the reprographic reproduction of copyright works.
\n\nSubject to the license granted above, copyright in the Chapter and all versions of it created during IntechOpen's editing process (including the published version) is retained by the Corresponding Author and any Co-Author.
\n\nSubject to the license granted above, the Corresponding Author and any Co-Author retains patent, trademark and other intellectual property rights to the Chapter.
\n\n2.3 All rights granted to IntechOpen in this Article are assignable, sublicensable or otherwise transferrable to third parties without the Corresponding Author's or any Co-Author’s specific approval.
\n\n2.4 The Corresponding Author (on their own behalf and on behalf of each Co-Author) will not assert any rights under the Copyright, Designs and Patents Act 1988 to object to derogatory treatment of the Chapter as a consequence of IntechOpen's changes to the Chapter arising from translation of it, corrections and edits for house style, removal of problematic material and other reasonable edits.
\n\n3. CORRESPONDING AUTHOR'S DUTIES
\n\n3.1 When distributing or re-publishing the Chapter, the Corresponding Author agrees to credit the Book in which the Chapter has been published as the source of first publication, as well as IntechOpen. The Corresponding Author warrants that each Co-Author will also credit the Book in which the Chapter has been published as the source of first publication, as well as IntechOpen, when they are distributing or re-publishing the Chapter.
\n\n3.2 When submitting the Chapter, the Corresponding Author agrees to:
\n\nThe Corresponding Author will be held responsible for the payment of the Open Access Publishing Fees.
\n\nAll payments shall be due 30 days from the date of the issued invoice. The Corresponding Author or the payer on the Corresponding Author's and Co-Authors' behalf will bear all banking and similar charges incurred.
\n\n3.3 The Corresponding Author shall obtain in writing all consents necessary for the reproduction of any material in which a third-party right exists, including quotations, photographs and illustrations, in all editions of the Chapter worldwide for the full term of the above licenses, and shall provide to IntechOpen upon request the original copies of such consents for inspection (at IntechOpen's option) or photocopies of such consents.
\n\nThe Corresponding Author shall obtain written informed consent for publication from people who might recognize themselves or be identified by others (e.g. from case reports or photographs).
\n\n3.4 The Corresponding Author and any Co-Author shall respect confidentiality rights during and after the termination of this Agreement. The information contained in all correspondence and documents as part of the publishing activity between IntechOpen and the Corresponding Author and any Co-Author are confidential and are intended only for the recipient. The contents may not be disclosed publicly and are not intended for unauthorized use or distribution. Any use, disclosure, copying, or distribution is prohibited and may be unlawful.
\n\n4. CORRESPONDING AUTHOR'S WARRANTY
\n\n4.1 The Corresponding Author represents and warrants that the Chapter does not and will not breach any applicable law or the rights of any third party and, specifically, that the Chapter contains no matter that is defamatory or that infringes any literary or proprietary rights, intellectual property rights, or any rights of privacy. The Corresponding Author warrants and represents that: (i) the Chapter is the original work of themselves and any Co-Author and is not copied wholly or substantially from any other work or material or any other source; (ii) the Chapter has not been formally published in any other peer-reviewed journal or in a book or edited collection, and is not under consideration for any such publication; (iii) they themselves and any Co-Author are qualifying persons under section 154 of the Copyright, Designs and Patents Act 1988; (iv) they themselves and any Co-Author have not assigned and will not during the term of this Publication Agreement purport to assign any of the rights granted to IntechOpen under this Publication Agreement; and (v) the rights granted by this Publication Agreement are free from any security interest, option, mortgage, charge or lien.
\n\nThe Corresponding Author also warrants and represents that: (i) they have the full power to enter into this Publication Agreement on their own behalf and on behalf of each Co-Author; and (ii) they have the necessary rights and/or title in and to the Chapter to grant IntechOpen, on behalf of themselves and any Co-Author, the rights and licenses expressed to be granted in this Publication Agreement. If the Chapter was prepared jointly by the Corresponding Author and any Co-Author, the Corresponding Author warrants and represents that: (i) each Co-Author agrees to the submission, license and publication of the Chapter on the terms of this Publication Agreement; and (ii) they have the authority to enter into this Publication Agreement on behalf of and bind each Co-Author. The Corresponding Author shall: (i) ensure each Co-Author complies with all relevant provisions of this Publication Agreement, including those relating to confidentiality, performance and standards, as if a party to this Publication Agreement; and (ii) remain primarily liable for all acts and/or omissions of each such Co-Author.
\n\nThe Corresponding Author agrees to indemnify and hold IntechOpen harmless against all liabilities, costs, expenses, damages and losses and all reasonable legal costs and expenses suffered or incurred by IntechOpen arising out of or in connection with any breach of the aforementioned representations and warranties. This indemnity shall not cover IntechOpen to the extent that a claim under it results from IntechOpen's negligence or willful misconduct.
\n\n4.2 Nothing in this Publication Agreement shall have the effect of excluding or limiting any liability for death or personal injury caused by negligence or any other liability that cannot be excluded or limited by applicable law.
\n\n5. TERMINATION
\n\n5.1 IntechOpen has a right to terminate this Publication Agreement for quality, program, technical or other reasons with immediate effect, including without limitation (i) if the Corresponding Author or any Co-Author commits a material breach of this Publication Agreement; (ii) if the Corresponding Author or any Co-Author (being an individual) is the subject of a bankruptcy petition, application or order; or (iii) if the Corresponding Author or any Co-Author (being a company) commences negotiations with all or any class of its creditors with a view to rescheduling any of its debts, or makes a proposal for or enters into any compromise or arrangement with any of its creditors.
\n\nIn case of termination, IntechOpen will notify the Corresponding Author, in writing, of the decision.
\n\n6. INTECHOPEN’S DUTIES AND RIGHTS
\n\n6.1 Unless prevented from doing so by events outside its reasonable control, IntechOpen, in its discretion, agrees to publish the Chapter attributing it to the Corresponding Author and any Co-Author.
\n\n6.2 IntechOpen has the right to use the Corresponding Author’s and any Co-Author’s names and likeness in connection with scientific dissemination, retrieval, archiving, web hosting and promotion and marketing of the Chapter and has the right to contact the Corresponding Author and any Co-Author until the Chapter is publicly available on any platform owned and/or operated by IntechOpen.
\n\n6.3 IntechOpen is granted the authority to enforce the rights from this Publication Agreement, on behalf of the Corresponding Author and any Co-Author, against third parties (for example in cases of plagiarism or copyright infringements). In respect of any such infringement or suspected infringement of the copyright in the Chapter, IntechOpen shall have absolute discretion in addressing any such infringement which is likely to affect IntechOpen's rights under this Publication Agreement, including issuing and conducting proceedings against the suspected infringer.
\n\n7. MISCELLANEOUS
\n\n7.1 Further Assurance: The Corresponding Author shall and will ensure that any relevant third party (including any Co-Author) shall, execute and deliver whatever further documents or deeds and perform such acts as IntechOpen reasonably requires from time to time for the purpose of giving IntechOpen the full benefit of the provisions of this Publication Agreement.
\n\n7.2 Third Party Rights: A person who is not a party to this Publication Agreement may not enforce any of its provisions under the Contracts (Rights of Third Parties) Act 1999.
\n\n7.3 Entire Agreement: This Publication Agreement constitutes the entire agreement between the parties in relation to its subject matter. It replaces and extinguishes all prior agreements, draft agreements, arrangements, collateral warranties, collateral contracts, statements, assurances, representations and undertakings of any nature made by or on behalf of the parties, whether oral or written, in relation to that subject matter. Each party acknowledges that in entering into this Publication Agreement it has not relied upon any oral or written statements, collateral or other warranties, assurances, representations or undertakings which were made by or on behalf of the other party in relation to the subject matter of this Publication Agreement at any time before its signature (together "Pre-Contractual Statements"), other than those which are set out in this Publication Agreement. Each party hereby waives all rights and remedies which might otherwise be available to it in relation to such Pre-Contractual Statements. Nothing in this clause shall exclude or restrict the liability of either party arising out of its pre-contract fraudulent misrepresentation or fraudulent concealment.
\n\n7.4 Waiver: No failure or delay by a party to exercise any right or remedy provided under this Publication Agreement or by law shall constitute a waiver of that or any other right or remedy, nor shall it preclude or restrict the further exercise of that or any other right or remedy. No single or partial exercise of such right or remedy shall preclude or restrict the further exercise of that or any other right or remedy.
\n\n7.5 Variation: No variation of this Publication Agreement shall be effective unless it is in writing and signed by the parties (or their duly authorized representatives).
\n\n7.6 Severance: If any provision or part-provision of this Publication Agreement is or becomes invalid, illegal or unenforceable, it shall be deemed modified to the minimum extent necessary to make it valid, legal and enforceable. If such modification is not possible, the relevant provision or part-provision shall be deemed deleted.
\n\nAny modification to or deletion of a provision or part-provision under this clause shall not affect the validity and enforceability of the rest of this Publication Agreement.
\n\n7.7 No partnership: Nothing in this Publication Agreement is intended to, or shall be deemed to, establish or create any partnership or joint venture or the relationship of principal and agent or employer and employee between IntechOpen and the Corresponding Author or any Co-Author, nor authorize any party to make or enter into any commitments for or on behalf of any other party.
\n\n7.8 Governing law: This Publication Agreement and any dispute or claim (including non-contractual disputes or claims) arising out of or in connection with it or its subject matter or formation shall be governed by and construed in accordance with the law of England and Wales. The parties submit to the exclusive jurisdiction of the English courts to settle any dispute or claim arising out of or in connection with this Publication Agreement (including any non-contractual disputes or claims).
\n\nLast updated: 2020-11-27
\n\n\n\n
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