A Graphics Generator for Physics Research

The great quantity of information which emerges from the necessity of an informational society can be mastered in a proper way, due to the perfection of the informatics systems used in all the fields. The pieces of information, due to the fact that they are numerous as concerns their content, become hard to work with, on the whole; thus, only a part of the content is represented as compound and flexible objects, by assuring both their direct usage and re-usage within other conditions and situations. An important factor in the trend of spreading and adapting the application on the web zone is represented by distributed systems and web services.


Introduction
The great quantity of information which emerges from the necessity of an informational society can be mastered in a proper way, due to the perfection of the informatics systems used in all the fields. The pieces of information, due to the fact that they are numerous as concerns their content, become hard to work with, on the whole; thus, only a part of the content is represented as compound and flexible objects, by assuring both their direct usage and re-usage within other conditions and situations. An important factor in the trend of spreading and adapting the application on the web zone is represented by distributed systems and web services.
Generally speaking, the administration of resources and fluxes in distributed systems of great dimensions are confronted with many difficulties. These are provoked by the complexity of the hardware and software platforms and, especially, by the dynamism which is characteristic of these systems' compounds.
These drawbacks can be met through two necessary conditions, based on the understanding of the performing characteristics of the resources of administration systems and of the delivery solutions for a better dynamic adaptation.
This chapter proposes to demonstrate the utility of distributed systems in the design of educational and research software in physics. Educational systems are generally rich in structured knowledge, but not so complex, which does not imply behavioural relations among users.
However, all of the existing architectures being their construction with the experts in the experience of the learning domain, but not from the user's perception, as well as from the study of the materials of the way one constructs the schemes of mental concepts' (Hansen, 2007). One has to underline that there is an intrinsic connection between the results obtained by the users and the method of teaching. Due to the restriction imposed by time and resources, the great part of the implementation is reduced to simple models of knowledge. Thus, the present educational systems do not propose to determine the real state of knowledge, and so the strategies used by the users are omitted as are the specific strategies for each and every domain.

Theoretical background
Because of problem which one follows wants to develop consists in realizing web services with numerical calculating methods, I provide a presentation of some points of view connected to the subject. The basic standards, originally proposed by IBM, Microsoft, HP and others, are: SOAP (Simple Object Access Protocol), which offers a standard modality of connecting to the web, UDDI (Universal Description, Discovery and Integration), which represents a standard modality of issuing one's own web services, and WSDL (Web Service Description Language), which provides further information for understanding and using the offered services (Landau 2008). WSIF (Web Services Invocation Framework) represents the invoking of the web services, defined by the standards WSDL and UDDI (Universal Resource Locator). This kind of invoking does not suppose the creation of SOAP XML messages. There are four kinds of transmitting an invoking: one-way -the final point receives an answer; request-answer -the final point receives a message and transmits a correlated message; solicitation-response -the final point transmits a message and receives a correlated message; notification -the final point transmits a message. The most used are one-way and request-answer. The location transparency is realized through link patterns, as a UDDI type. The web services revolute the way in which one application communicates with other applications, thus offering a universal pattern of data which can easily be adapted or transformed. Based on XML, the web services can communicate with platforms and different operating systems, irrespective of the programming language used for their writing. For easy communication among the business parameters: the Java language allows the applications' realization regardless of the platform used. The apparition of the Web services represents a means of communication on a large scale. This can be done by applying some standardized protocols, defined by standardized public organizations. The basic protocols of the Web service are not complete as regards the description and implementer terms, their security, reliability and complexity. It is known that by the fact of using Web technology, the information uses many sources. The portal is the mediator for the access to the information. The portal servers are, in their turn, elementary components in the interchange of information. The importance of these technologies is due to the fact that they emerged as a response to the present tendencies manifested in the software industry: distributed remaking, the development of applications based on the components, the development of the services for companies and the modifying of the Web paradigm, in the sense of the development of applications.

Services for numerical calculation
The purpose of the present study is the analysis of the surplus introduced by the Web service interface and its exposure in as simple as possible a variant of the facilities introduced by it. The study uses the book Numerical Library in Java for Scientists and Engineers, and so the present work does not re-implement the codes in that book, but only uses those already implemented. The passing from an interface with the user in a command line to an interface based on Web services represents a big advantage because it allows the combining and re-using of some procedures with a prior definition. Many discussions about the algorithms in the speciality literature on the Web omit important details, which can only be uncovered by encoding or be made suitable by reading the code. We also need the real code for object-oriented programming, found in the Numerical Library in Java for Scientists and Engineers (Lau, 2004). An orientation of these solutions is for scientific explanations which are based on numerical calculation, beginning with elementary structures, progressing to complicated ones, as the integration of ordinary differential equations (Lau, 2004). The digital technologies introduced to the market include Web technology; this completely fulfils all of the requests connected with the information cost, stocking and spreading (Petcu, 2008). From these first steps where the sites were using simple visiting cards, iterative processes have been created and developed. Once, with the movement towards an informational society, a novelty is represented by the distributed systems of large dimensions, by which facility is enabled access to a great variety of resources. The above mentioned book offers a general discussion for each subject, a certain amount of mathematical analysis (IBM, 2009), a certain discussion of the algorithm and, most importantly, the implementation of these ideas in a real mode as routines. There is a proper equilibrium among these ingredients for each subject. A starting point is concerned with the construction of the services and the inclusion of one or more methods in implementation is constituted by the analysis of the data structures from the elementary to the complex (Isbasoiu, 2009). The majority of the books on numerical analysis use a specific subject "standard", such as: linear equations, interpolation, extrapolation and ordinary differential equations. Other discussed points are: the functions' evaluation and especially mathematical functions, aleatory numbers, the Monte Carlo method, sorting, optimization, multidimensional methods, the Fourier transformation, the spectral methods and other methods concerning statistical descriptions and data modelling and relaxing methods. The book (Lau, 2004) says that there are seven groups of themes that should be focused on: vectors and matrices, algebraic evaluations, linear algebra, analytical evaluations, analytical problems, special functions, proximity and interpolation. Each group has the name Basic followed by the appropriate number for each theme. A schematic representation of these groupings is presented in Figure 1  Every group contains an impressive number of functions. Through an attentive analysis, we noticed the following: Basic 1 is the base for the construction of the other basics, and some functions of Basic 1 are applied even with the construction of the other functions of this basic; every basic interacts with the other basics; there are functions which do not interact or else do not represent the basis for the construction of other functions. In trying to conclude all of these representations in one, it appears in the following figure:

Fig. 2. All dependencies' representations
In the following table is presented the number of times a function is used by other functions: Table 1. The dependencies' representation A graphic representation of these dependencies, depending on the number of functions that appear, is realized as follows:

The functions for numeric calculation -Time comparison
The services were realized using the Eclipse platform. For each function, the response time is specified. We can notice that it varies a lot. We repeat the measurements for more complex input data, both for double type and integer type and vectors and matrices because these units of time depend on this input data.  Table 3. Time of response for every function without the Web Service A more elegant representation of time variation can be seen in the following graphic: In analysing with a focus on the two graphics ( Fig. 3 and Fig. 4), we can notice the following: a. generally, the response times are longer for complex parameters, the main cause stands for the value itself of those parameters b. the longest time belongs to those functions which resolve determinants, matrices and vectors c. there are extremely close response times for some functions d. we can see two groups of functions, corresponding to two types of functions e. it is clear that the only function which does not modify its time is Efrk, having the value of 13 ms -with the Web Service f. irrespective of the type of data introduced -or of their complexity -the response time is bigger, but still close g. by comparing the bits of response time with the Web Service there are significant differences, so with this case it is important to consider the complexity of the input data

Scenarios
The evaluation of a function and the discovery of its minimum (using the function Rnk1min) The resolution The determination of a vector for a function The settling of the minimum, the determination of the smallest integer number The determination of a matrix rank The gradient of a function calculated for the minimum Procedures used: initialization of the constants, initialization of the sub matrices, matrices' product, matrices' rank.
The resolution[L1] of a non-linear system (using the function Marquardt) Fig. 8. The graphical representation of the resolution of a non-linear system Procedures used: the product of two vectors, the product of a vector and a matrix.
The determination of the solutions of a non-linear system (using the function Gssnewton) Fig. 9. The graphical representation for the determination of the solutions of a non-linear system Procedures used: pivot method, the resolution of the systems through successive appeals, the interchanging of lines and columns for the inversion of a matrix, the product of two vectors, adding a multiple constant, systems with the same matrix coefficient, resolved through successive appeals.
The resolution of the systems with differential equations (using the function Multistep) Fig. 10. The graphical representation of the scenario for the resolution of systems with differential equations The resolution The back differentiation method The rapid method for systems of differential equations with more variables Data stocking The resolution

Systems of derivative equations
The inverse of a matrix The obtaining of a vector with unknown values The resolution The function applied The choice of the correct answer The inverse of a matrix Procedures used: the product of two vectors, the product of a vector and a matrix, matrices decomposition, particular cases: a smaller number of variables as against the number of binary numbers in the number of representation, the resolution of the linear systems whose matrix was distorted triangularly.
The resolution of the parabolic and hyperbolic equations (using the function Ark) Fig. 11. The graphic representation of the scenario for the resolution of parabolic and hyperbolic equations Procedures used: the initialization of a vector after certain constants, vectors with multiple setting forms, factors for multiplication, duplicate elements in a vector, the product of an element belonging to a vector and other elements belonging to another vector, adding a multiple constant from a vector to other elements from another vector being in a certain state, the resolution of the systems of linear equations The resolution of the systems with ordinary differential equations (using the function Efrk) Fig. 12. The graphical representation of the scenario for the resolution of the systems with ordinary differential equations Procedures used: adding a multiple constant from a vector to an element belonging to another vector which is in a certain state, matrices decomposition, permuting, resolution linear systems.
Resolution the autonomous systems of differential equations (using the function Efsirk) The resolution

Number of evaluations
The precision order of the method The absolute and relative tolerance The resolution The evaluation of the changing of the procedure of derivates The determination of the Boolean values The calculus reduction through constraints Automation 278 Fig. 13. The graphical representation of the scenario for the resolution of the autonomous systems of differential equations Procedures used: the product of an element of a vector and another element of another vector, the product of a vector and a matrix, the product of a vector represented by the index of a row and a matrix represented by the index of a column, matrices decomposition, permuting, the use of the partial pivot, factors for multiplication, decomposition of the linear system as the matrices type.
The resolution of the autonomous systems for differential equations (using the function Liniger1vs) Fig. 14. The graphical representation of the scenario for the resolution of the autonomous systems for differential equations Procedures used: the initialization of the matrices and constants, factor of multiplication, replacement the elements of a matrix with a succession of elements in a rectangular matrix, duplication of an element in a vector, the product of a vector and a matrix, adding a multiple constant, the product of two vectors, matrix decomposition, permutation of matrices, resolution the linear systems.
The resolution of the autonomous systems for differential equations (using the function Liniger2) The resolution The determination of the system functioning matrix The variables can be autonomic; they must not be used in derivation The reduction of the calculating time for the linear systems The reduction of the calculating time for the non-linear systems The resolution Use the Newtonian scheme Repetitions used in the Newtonian scheme for implicit equations The great number of integrations in Newton's procedure Fig. 15. The graphical representation of the scenario for the resolution of the autonomous systems for differential equations Procedures used: the product of an element of a vector and another element of another vector, the product of a vector and a matrix, the product of a matrix line and the column of another matrix, matrices decomposition, permuting, the resolution of the linear systems.
The determination of the number of differential equations (using the function Gms) The determination of the number of differential equations (using the function Impex) Fig. 17. The graphical representation of the scenario for the determination of the number of differential equations The resolution The elimination of some parameters The resolution of the implicit equations using Newton's procedure The resolution The determination of the asymptote Procedures used: the initializing of the matrices and constants, the initializing of a sub matrix, the replacement of an element in a vector, the replacement of a column in a matrix with complex constant elements, the product of an element of a vector and another element of other vector, the product of a vector and a matrix, the product of a line in a matrix and the column of another matrix, matrices decomposition, permuting, resolution the linear systems.
Estimations on the unknown variables (using the function Peide) Fig. 18. The graphical representation of the scenario for the estimations on the unknown variables Procedures used: initializing of the matrices and constants, initializing of a sub-matrix, factor of multiplication, replacement of an element in a vector, replacement of a column in a matrix with complex constant elements, the product of an element of a vector and another element of another vector, the product of a vector and a matrix, the product of a line in a matrix and the column of another matrix, matrix decomposition, permuting, resolution the linear systems, the maximum number of repetitions to be made.
Calculating the polynomial coefficients (using the function Minmaxpol) Fig. 19. The graphical representation of the scenario for the calculating polynomial coefficients Procedures used: adding a multiple constant from a vector into another vector, the duplicate settling of an element of a vector, calculating the Newtonian polynomial coefficients obtained through the interpolation of the corresponding coefficients, calculating the polynomial sum, determination of the polynomial degree.

Tests realized on the basis of the scenario
I realized a series of tests on the basis of these scenarios. I calculated the sum, the subtraction, the product, the division, the determinant, the inverse, the medium matrices and the covariant, for matrices beginning with 2X2 up to 9X9, both with the Web Service and without the Web Service.

A graphics generator for physics research
The proper architecture for the web service used for physics simulations is divided into a working area. At first, we realized a series of Web services which grounds the numerical calculation. These facts are oriented towards scientific applications, beginning with elementary structures, up to complex ones, such as the integration of ordinary differential equations. The passing from an interface of the type line command with the user, to an interface based on Web services, represents a great advantage because it allows the combination and use of certain procedures -routines -defined earlier on.
The methods for numerical calculation are practical, efficient and elegant, and the realization of a proper architecture of a Web service will significantly contribute to this process [2].
Beginning here, I would like to develop this idea, applying it to both physics and physics research. By selecting this, I chose the most representative phenomena in physics which allow for applications; next, I followed the interpretation of them from the point of view of numerical calculation. In order to set out every phenomenon, they are described physically and are mentioned in terms of the manner in which they are to be found within the created service. The platform is divided into two parts: the former is designated to numerical calculation; the latter is for the realization of graphics. Also, within this service, there is a static zone where I present the selected physical phenomena, as can be seen in the following image (retrieved on http://www.eliza-isbasoiu.muscel.ro 05/10/2009). In order to know the variables of the constants and equations at the basis of every simulation, the user receives pieces of information about the physical phenomena and the possible discussions after the simulation.

A motor with continuous current
One should notice that if we apply a tension to the motor terminals -given the same polarity as where it works as a generator -the rotor spins in the opposite direction as that of the generator (Maxwell, 1892). The parameters that vary are: external voltage, ranging from a minimum value and a maximum, R and r, and contrary[L2] electromotor tension. According to these values, the graph appears. Such findings may be established for efficiency (retrieved on http://www.eliza-isbasoiu.muscel.ro 05/10/2009).

Forces of inertia on the earth's surface
The Earth makes a revolutionary motion around the Sun, under the influence of the gravitational forces of different cosmic bodies in our solar system.
We consider a material mass point m, being at rest against the Earth in an A point. This can be seen by the following picture: Fig. 25. The graphical representation of the material point as against the Earth In the inertial system Si against the material points, thus act the gravitational forces of the Sun, Moon and Earth.
The determination of inertial forces on the earth's surface has been, for a long time, a very attractive notion in physics.
Mass: the point of mass is variable. The angle is also variable. (retrieved on http://www.eliza-isbasoiu.muscel.ro 05/10/2009). We consider a material point M, with the mass m, whereby the variability of its mass is given by the joining or detaching of some particles from M. These two situations are, in fact, two cases: the joining case and the detaching case.
The variables in this situation are greater. The time ranges between a maximum and a minimum. The matter the value it receives is v0. The angle, the reaction speed and the gravitational acceleration influence the graph (retrieved on http://www.elizaisbasoiu.muscel.ro 05/10/2009).

The floating bodies
Knowledge of the conditions which determine the stability of floating bodies is very important in naval construction techniques. We assume a floating body which has a centre in the same place with the O point, as with the figure below, and that over the superior part of the body outside the liquid on which the F horizontal force acts, by tending to turn the body towards the left (Balibar, 2007). The factor which influences this phenomenon the most is represented by the surface marked by S. After we introduced the minimum and maximum of the value, we obtained the following graph (retrieved on http://www.eliza-isbasoiu.muscel.ro 05/10/2009). Fig. 29. The graphical representation of the limits between a body can or cannot float for a specific surface S The graphical interface which the user employs is a simple one but extremely efficient, because it is generalized for every area of study (retrieved on http://www.elizaisbasoiu.muscel.ro 05/10/2009). Fig. 30. The image of the graphical interface of the Web service -graphics generator When we press the button "generate graphs", the user is asked which essential parameter they want as a graphical representation. For example, for control electromotor tension, there are three variants: the exterior variation of U tension, the variable E contro electromotor tension, the R variable.
The following image presents this fact (retrieved on http://www.eliza-isbasoiu.muscel.ro 05/10/2009). The platform is divided into two working areas: the former is for numerical calculation; the latter is for the graph's realization.
We can represent the sound's intensity; we introduce two values, the minimum and the maximum, the representation being made after a desired pattern (retrieved on http://www.eliza-isbasoiu.muscel.ro 05/10/2009). All these solutions are oriented towards scientific applications, which are grounded on numerical calculations. They are followed by more complicated constructions.
There are many authors who deeply value such software architectures. Some of them consider it to be the separate profession of the software engineer [5]. Others consider it be independent, separate for the role of the software engineer and, thus, in need separate learning approaches.
The activity can be considered from: psychological points of view; systematic points of view; organizational points of view.
From the psychological point of view, the application is a creative process, which implies knowledge within close fields, such as: software engineering, computer science, logic, cognitive science and programming etc. From systematic point of view, the project is seen as an activity which implies the discovery of optimal solutions for a set of problems, taking into account the balance between obstacles and forces.
The organizational perspective offers the possibility that some software elements are re-used for other products.
The main ideas which result from the above examples are as follows: a. the necessity of knowing all of the equations and the particular cases which represent the bases of the physical phenomena; b. the possibility of their interpretation depending upon the input data; c. simulations for finding other particular cases; d. the practical understanding of the phenomena of physics; All of these comparisons between values and interpretations, based upon the graphs, depend upon users' objectives. It is very important that a possible user of the application can use the interface despite different levels of knowledge. The created Web service presents a few physics applications based upon numerical calculations. The selected phenomena can assure the construction of more complicated applications. This method displays ideal cases which are not present in nature, but also specific cases. If one interprets them correctly, one can find optimal solutions to a set of problems; besides this, there is the possibility of the further use of the results obtained. The main advantages of using the Web service are: the possibility of solving problems of great dimensions which exceed the computer's memory; the identification of common costs and their reduction; the reduction of the time response value; the fact that client can be involved in the problems' description.
The graphic must be defined within the text editor under the form equation (formula,min,max,step,precision).
a. the formula must be x variable, framed by double inverted commas this 'x'. The x variable must have a space before it and another space after it in an equation, whenever it appears. For example: "sin( x ) + cos( x + 4) + 2 * x " b. min, max represent the interval margins where the calculation is made; c. the step represents the incrementation value of the values for which the calculation was made; d. the precision represents the ranging interval of the graphical representation. It is recommended to use 0.01; one can also use other values in order to see the results.

Conclusion
We presented in this article concepts connected to the architecture of distributed systems, demonstrating the criteria for a proper choice in order to use adequate technology. The problem that we developed was represented by the realization of certain Web Services using methods of numeric calculation. The applications were created on the Eclipse platform; these were realized with the solutions offered by the book Numerical Library in Java for Scientists and Engineers. These solutions are oriented towards scientific applications based upon numeric calculation. They begin with elementary structures move on to more complex structures. By grouping and creating services for each and every structure, we realized that many of the functions used for their construction appeal to other functions; we created a table where those functions appear only once. We created a service for every function and followed the response time. We saw that, depending upon the function's complexity, this time differs. By way of comparison, we constructed a graphical representation with the time for both individual functions, with simple input data, and parameters with complex values. The next step would be to realize Web services for education in physics, as well as services for scientific research in physics, using these services.
So long as informatics and communications technology evolve, the implications that they will have on the educational system are difficult to be foresee. There will be always new opportunities and new difficulties, but there will also be results and benefits.
Computer simulations seem to offer the most efficient methods for using computers in physics. There, the processes used in research physics are encouraged: for determining the cause of an effect, in prognosis, and also for the interpretation of research data. As a rule, such simulations develop an inductive and deductive way of thinking, by assuring the capacity of problem solving, the formulation of new hypotheses and the realization of tests. We feel that users should be allowed to realize other experiments as a preliminary to the physics laboratory.
Beginning with these elements and using the Web services for numerical calculation subsequently realized, I selected a series of mathematical functions, namely those useful for the equations used for continuous electricity, the calculation of inertial forces on the earth's surface, the calculation of the dynamics of variable weight points for finding admissible resistance, and in the production and propagation of sounds.