International Journal of Modern Physics C
© World Scientific Publishing Company

DIFFUSION PHENOMENA AND OTHER WWW APPLICATIONS FOR AN INTRODUCTORY PHYSICS COURSE

Gianni Cattani^a,b, Maria Cecilia Coperchio^a,b, Franceso Luigi Navarria^a,b,c, Tiziano Rovelli^a,b

^aDepartment of Physics, University of Bologna
^bINFN Bologna
^cFaculty of Pharmacy, University of Bologna

The World Wide Web originated within the high-energy physics community from the need to exchange documentation in an efficient way. It can be used easily to produce and maintain didactic material for teaching physics. The material can be made accessible via the network in hypertext form, comprising text, pictures, animations, audio files. For didactic applications in physics the capability of an interactive link, beyond the use of simple electronic forms is necessary. This was not foreseen in the original WWW protocol, and it has been developed in an application presented here, to simulate a series of measurements in a diffusion process in solutions. The recent introduction of the Java language offers a natural way to create new powerful interactive Internet applications. We are currently developing and testing Java powered didactic applications.

Keywords: WWW; Java; Education; Diffusion; Simulations.

1. Introduction

Recent developments in educational strategies and in the computational field (hardware and software) favour the introduction and development of new didactic products for teaching physics. The use of hypermedia combines the possibility of creating attractive and varied paths with the ability of building courses which can be tailored to meet the needs of different kinds of students. Availability through the World Wide Web (WWW) [1] adds to these documents the advantage of being easily retrievable from everywhere.

The Web can be defined as a ``wide-area hypermedia information retrieval initiative aiming to give universal access to a large universe of documents'' [2]. It is mostly used via the Internet, and permits files resident on different computers situated in different places all over the world to be accessed, in a way virtually independent of the particular computer platform. These files, once decoded, can be texts, images, sounds and have a hypertextual structure: they can be hypermedia. With the introduction of attractive graphic browsers, such as NCSA Mosaic and Netscape, this new form of documentation has become very popular and an ever-increasing number of people has learnt to build more and more refined hypermedia. The use of the network permits quick interactions, rapid spread of information and feedback, and thus potentially a quick improvement in the quality of the products. An entire issue of the present journal has been recently devoted to physics education using the Web.

It was probably not an accident that the WWW was born at CERN within the literally world-wide scattered high-energy physics community. The large collaborations set up for building and exploiting the complex detectors at the LEP e⁺ e^- collider were amongst the first heavy users of this tool designed primarily to access and use remotely maintained information from different platforms [1]. The same tools were used shortly afterwards for controlling and monitoring the status of the detectors, from the documentation and help files to the synthetizing of online documents related to the status of the detector, such as high and low voltages, thresholds and so on, in addition to the usual monitoring histograms [3]. Since these initial steps, the possibilities of using the WWW for applied and research physics have become too numerous to mention here, and the number of users is still growing.

The Web was not initially designed for specific didactic applications and in particular for interactive applications, the only interactivity being provided by electronic forms returned by the client to the server and by scripts executed by the server [4]. In addition it should be mentioned that as the Web is a document shipping tool, there is a priori no way of maintaining a stable fixed connection between the client and the server. Partly to overcome these problems, and in perspective to develop an interactive Physics course including a virtual laboratory, about two years ago we proposed the ISHTAR project (Innovative Software for Higher education Telematics Application Research and development) [5] in collaboration with the Physics Departments of the Universities of Athens, Florence and Lisbon. As part of these initial ambitious goals, we produced a prototype on the diffusion of solutes in solutions, an application which provides some interactivity and makes it possible to simulate measurements. More recently, another solution to the same problem has become available with the introduction of the Java language: Web applications in Java can be highly interactive as they run directly on the client, eliminating the need of a per-action connection. Java has quickly improved the quality of Internet applications in terms of interactivity and speed. Java techniques are quite recent but they are spreading very quickly because of their effectiveness, a huge quantity of public-available documentation and, of course, because of the strong commercial interests which lay behind all this. We have started and are currently producing didactic material with embedded Java applets, and a first chapter on probability, statistics and errors in measurements should be available shortly from our server.

As a last introductory remark, one should stress that there are practical limitations when borrowing existing material via links to other servers. Limitations are encountered because of the net's capabilities. For example, using an Astro-Physical Java calculator from Wisconsin and accessing the physics problems from Berkeley might be fashionable, but happens to be extremely lengthy at certain hours of the day, when perhaps you have scheduled your class or your demo. Not to mention that work and changes on the servers might clash because of time differences. In addition, for some non-English mother tongue countries there is in general a language problem: not only text, but help files and instructions have to be translated also, as soon as they go beyond the commands and the computer jargon in English which is permeating all other languages, basically because of computer usage itself.

The rest of the paper is organized as follows: Section 2 presents in some detail the package on diffusion phaenomena in solutions and the electronic physics problems generator; Section 3 describes the techniques used for constructing the package and creating the problem pages; Section 4 presents a brief description of the new package on statistics and measurements of physical quantities which comprises embedded Java applets; the summary and conclusions are presented in Section 5.

2. The package

The educational material is intended for teaching general physics to non-physics students, such as those oriented towards medical chemistry, biology, pharmacy, biotechnology, medical studies and so on. These students are not usually familiar with calculus, which has determined the content of the course and the simplified mathematics used in the main pages. At least in Italian universities so far, these students do not usually have easy access to university computers, as physics or mathematics students may do. Also, for the moment in Italy, the number of university students possessing a computer and in addition having regularly access to Internet is still quite small. The availability of powerful and relatively inexpensive PCs is changing this scenario rather rapidly and provides an additional motivation for developing didactic tools on the Web.

The aim of the project is to create eventually an interactive book [6] oriented towards the experimental aspect which would help to teach and learn physics with new tools. Ideally, in the end all items appearing in the programme of the physics course should be linked to Web pages. This should be complemented by an electronic physics problem section with solutions, so that the students can practice and cross-check their preparation.

The philosophy is not to replace the laboratory or the ``traditional lectures'' but rather to complement them, by making it possible to interact also in situations not easily reproducible in a laboratory, because of their danger or instability or long temporal evolution or other [7]. At the same time one renders available to the students a set of interactive lectures that they can consult everywhere at their own pace and where they can find complements and notes.

2.1 The content of ``The diffusion phaenomenon''

What we developed till now consists in a section devoted to diffusion phaenomena in solutions.
We present the experimental aspect of the subject, but some theoretical notions are also given in order to permit the student to understand the phenomena and to favour a situation in which students are invited to interact. After a brief introduction in which some experimental evidences of the diffusion phenomena are described, the student can choose whether to follow the discussion from the macroscopical or microscopical point of view. It is underlined that the two points of view and the corresponding analyses are complementary and not opposite.

Fig. 1 Reservoir of the Clack apparatus (schematic): the picture shown corresponds to the onset of stationary diffusion.

In the macroscopical analysis section the students can find the formulations of the two celebrated Fick's laws [9] and the explanation of the physical quantities involved. The discussion is limited to diffusion due to a concentration gradient in one dimension for simplicity, and additional terms, such as thermal diffusion or terms due to external forces acting differently on different molecular species, are just mentioned. Following the theoretical explanations, there is one page strictly devoted to the simulation of a particular measurement of the diffusion coefficient [8], namely one of the experiments by Clack [11]. This experiment may be executed in order to obtain the diffusion coefficient for different substances in water. The measurement is obtained indirectly, from two measurements of concentration of a solute diffusing in a vertical tube, assuming a constant temperature during the time in which the phenomenon takes place. In the original experiment [11] a solution of given concentration is placed at the bottom of the reservoir shown in Fig. 1, while at the top the concentration is always almost zero, as one puts initially pure solvent in the higher vessel. Knowing the geometry of the cell and measuring the quantity of solute traversing the cell per unit time, ie the small concentration difference in the top vessel after the onset of stationary diffusion, one obtains a measurement of the diffusion coefficient.

The simulation permits the user to interact in the Clack environment in a simplified way and to obtain the diffusion coefficient for different substances in water. The substances are salts, organic molecules, proteins, viruses, with a wide range of masses, ie radii and therefore of diffusion coefficients [12]. They are made available trough a clickable menu.

The simulation is divided into three steps. 1. Input of the starting conditions. The student can choose a substance among those available in the list, the starting concentration in the bottom of the reservoir, the temperature and the time interval between the two measurements (after the onset of a stationary diffusion). 2. Qualitative analysis. By pressing a button four pages are created. The first contains input and output values. The other three (linked to one another) contain three pictures which describe the main phases of the phenomenon: the starting condition, the establishment of the stationary diffusion, and the situation a time (as given in input) after the second frame. 3. Quantitative analysis. Here it is possible to simulate measurements. By clicking with the mouse on one of the frames (second or third picture), the value of the concentration at that point is stored on the server, and after collecting a certain number of data points the client may demand a graph reporting them [7].

In the microscopical analysis section, diffusion is considered as a consequence of the molecular motions at a given temperature. It is underlined out that this is just a different point of view concerning the same phenomena. After observing that the motion of the molecules of the solute in a solution is very similar to that of ideal gas molecules, the concept of osmotic pressure is introduced with the help of some animations (Fig. 2).

Fig. 2 Snapshot of an animation illustrating the osmotic pressure.

A typical model (the Stokes-Einstein's model) is presented in detail, underlining the importance of models in the understanding of the behaviour of nature. At the end of this section a discussion of transport phenomena through membranes and semipermeability is outlined.

2.2 The students

The package is primarily intended for CTF students at Bologna University (Chimica e Tecnologia Farmaceutiche; Pharmaceutical Chemistry and Technology) but it could be used by other kind of university students, comprising those belonging to other universities, by high-school students and possibly by a wider-public. So we have aimed at creating an hypermedia with a flexible and adaptable structure. In fact it is possible to explore it at different levels. Novice students can follow a main path where they can find basic notions. More advanced students can reach pages containing complements where it is possible to find rigorous mathematical demonstrations, hints, notes on the experimental details, an outline of the theory of measurements, references to other chapter of physics and so on.

2.3 The hypertext structure

During the development of the product it was always borne in mind that the hypothetical user might not be skilled in computing nor in using the WWW. It is very simple to navigate in the WWW, but anyway we carried out strategies to show clearly the package structure (Fig. 3) since the first pages in order to encourage the student to follow a path awarely.

Fig. 3 A web of documents

The structure document is self-evident and modular: the user is provided with all the informations she/he needs for a conscious navigation in the package. To interact with the environment is simple and intuitive, passing of parameters and calling of scripts are completely transparent. ``Forward'' and ``Back'' arrows suggest the main path which contains main information suitable for a novice user. Students who have already visited the course or who are more experienced in the subject are free to follow links to pages with complements (Pages flagged with ``Note'' and ``Appross'' in Fig. 3)

2.4 A random generator of simple physics problems

Among the things which the Web software can actually do there is the generation of simple physics problems. The problems are generated starting from a data-base which contains the texts and inserting random numbers in given fields, which correspond to the physical quantities needed to produce the problem page itself and a related page with the solutions. In this way a problem book is produced, which is infinitely varied, at least numerically and in the grouping of the problems.

The availability of interactive Web pages with physics problems and the corresponding formulae with numerical results is considered an important issue. These pages should help the students to test themselves and to verify whether they have understood the course by solving simple problems and checking the solutions.

A Fortran program has been written to generate the physics problems, with random numerical values in input, starting from a data base of about 300 texts which cover all the chapters of a general physics course. Several texts concern diffusion and the Fick's law, or closely related phenomena, such as viscosity and limiting velocity of particles moving in viscous fluids. First, three texts are chosen at random within the data-base. Then the values of the different physical quantities entering in the problems are chosen at random between given ad hoc limits, to provide reasonable numerical results. Another program is used to calculate and output the numerical results for each generated problem.

The Web techniques used are similar to those used in ``The diffusion phaenome- non'' and are described in Section 3.4. The usage is transparent: a menu allows the user to select either groups of three problems covering all different chapters or groups related only to a specific subject to be chosen within a list. A script then runs the Fortran program to produce the problem page. Clicking on a ``solution'' button generates the corresponding solutions via another script. Appropriate links are provided to continue the generation or to return to the menu.

3. The techniques

The techniques implemented [13] are those used in the development of hypermedia on the WWW; ie the creation of HyperText Markup Language (HTML) files linked to compose a web of documents, implementation of forms and Common Gateway Interface (CGI) scripts to render the user able to interact in simulations. Several different tools are also used in building images and animations.

3.1 HTML

Hypertexts have been written in HTML2.0 and HTML3.0 extensions backward compatible have been included [14].

3.2 Images

The images included in the course are in GIF format. Formulas are written in LaTeX and then converted into GIFs by the LaTeX2HTML converter [15]. Graphs are generated through HBOOK [16] and HPLOT [17] routines and then converted into GIF from PostScript (ps) using ImageMagick.

A script modifies a GIF in a way dependent on starting conditions imposed by the user in a form. This is done using a graphic library and results in the quick creation of GIF files through a C code.

3.3 Animations

Animations are used to show the evolution of phaenomena or as a preliminary example before simulations. An example is shown in Fig. 2. Images are created with POV [18], a package which produces photo-like images in tga format. The tga are converted in GIFs using ImageMagick [19] and from the GIF an mpeg is generated using a script. Since the scripts which produce GIFs and mpeg can be run asincronously, it is virtually possible to built a tailored mpeg.

3.4 CGI-scripts and FORMS

The simulations are implemented through CGI-scripts: scripts which run on the server through the Common Gateway Interface. The scripts output can be sent to the client, so it is possible to obtain HTML pages built on line, images and other.

CGI-scripts are used to elaborate data sent from user in FORMS. Data are sent from the client and encapsulated in system variables on the server ready to be used within the script. It is also possible to build interactive images. In this type of pictures one can establish a correspondence between a zone of the figure and an URL. This means that the figure can be subdivided in clickable pads or scan lines, each corresponding to different URLs [13].

CGI-scripts are used as well to create the pages of random generated problems and the pages of solutions.

Fig. 4 The form used to input the starting conditions in the simulation of the Clack experiment.

3.5 Applications

The techniques described above were implemented in simulations. As discussed in Section 2.1, the simulation of the Clack environment mainly consists of two parts: the input of starting condition and the qualitative analysis, and the quantitative analysis. The student using a FORM (Fig. 4) can choose a substance among those available in a list, the starting concentration, the temperature and the time interval between two measurements. Pressing the ``submit'' button, data are sent to the server and a script is run. This uses gd [20] routines and produces four HTML files with inlined tailored images which describe the main phases of the phaenomenon (Fig 1).

After a qualitative analysis the user is guided to a page in which it is possible to perform measurements. By clicking on a chosen image is possible to read the value of physical quantities related to the selected points. This is achieved by calling a script everytime the image is pressed. The script receives the selected coordinates and produces the HTML output for the client. The values selected are stored, so it is possible to re-use data. The collected data can be sent to the server pressing a button. A FORTRAN script produce a graph in ps format. A shell converts the postscript file in GIF format and the GIF is then included in the HTML page (Fig. 5).

Fig. 5 Plot of the ``measurements'' of the concentration along the tube. The graph and the whole HTML page is the output of a CGI script.

3.6 Interactions and HTTP protocol

HTTP (Hyperetext Transfer Protocol) is the protocol introduced with the WWW. It is specifically devoted to transmission of hypertexts; one of his main characteristics is to be stateless [1]. This implies that when several users run a script which creates files the server can not distinguish them per-user. It has been necessary to bypass this problem in order to store created files and reuse them during the session. (E.g. the pictures created and displayed during the qualitative analysis are to be included in the HTML pages where it is possible to perform measurements).

Files interactively generated are rendered distinguishable per-user imposing them unique names linked to the user. The PID (Process IDentifier) of the first script which generates files is used as a unique label for all he files generated in one session. PID is passed to subsequent process in hidden field of FORMS.

4. Current developments

We are working at present on a new section devoted to statistics and the theory of measurement errors [21] [22]. In this part of the course we want to provide a minimal background for non physics students. There are two main paths, one is addressed to students who want to have a first look at the subject and the other to more experienced readers. There are chapters about measurements (techniques and instruments) and more theoretical parts on the methods to be used when analyzing data (statistical distributions and probability theory). Several scripts were developed in order to let the student get acquainted with the concepts: for instance a script produces a selected distribution after the student has put appropriate parameters in a FORM. This form is used to transfer the parameters to Fortran programs which produce a graphic output using the HBOOK [16] and HPLOT [17] packages. The student is free to ``play'' with the script even if there are some values suggested for the parameters in order to guide him to discover relations between the values of the parameters and the shapes of the distributions. In addition the approximation of one distribution (eg a poissonian or a binomial) by another one (usually a gaussian) with a suitable choice of the parameters can be followed interactively as shown in Fig. 6.

Fig. 6 Output from a script run to learn the relation between parameters and shape of a distribution. A Poisson distribution is shown with superimposed a gaussian having the same mean. The mean value can be chosen by the student in a form.

4.1 Java techniques

The Java language [23] [24] with the possibility of shipping code executable by the client renders didactic applications on the Web much more attractive. Java is a general-purpose concurrent class-based object oriented language, it is normally compiled to a bytecode instruction set and binary format defined in the Java Virtual Machine. This instruction set may be directly executed by an interpreter, or, for faster execution, higher performance and even highly optimised machine code can be generated at execution time.

What is exciting about Java is that it is a language designed for programming on the Internet. Java enables one to write completely new types of applications. In fact Java enriches the WWW of interactive content: small Java programs (applets) can be embedded in HTML3.2 [14] pages to provide interactive executable content on a Web page [23] [24].

4.2 Examples of Java usage

The Java language is used to develop applets. Existing applets have been inported, adapted and/or modified according to the needs of the hypertext. The applet [25] shown in Fig. 7 visualises how sample means tend to the mathematical expectation of the distribution as the sample size increases.

Fig. 7 An applet showing the random generation according to a given distribution.

The applet shown in Fig. 8 and 9 has been improved substantially starting from NoiseSphere [26]. It gives a visual feeling about the performances of different random number generators. In the main window (Fig. 9) the three projections of a sphere built with random points shot by a generator are displayed. The generator used can be selected among four possibilities, including the default Java random number generator, and its characteristics parameters are set in the Parameters window (Fig. 8).

Fig. 8 Window to set parameters value for a selected generator..

Fig. 9 The circles show the projections of a sphere filled by random points shot by a generator.

It is clear at a first glance that no random number generator within the four is really random because the points always tend to cluster along certain patterns, but they can behave better or worse, depending on the choice of the parameters.

5. Conclusions and outlook

We have presented applications for teaching physics based on the Web protocol. A prototype hypertext designed primarily for Pharmaceutical Chemistry and Technology students at the University of Bologna has been constructed. The hypertext comprises text files, animations and the possibility of simulating a series of measurements in a diffusion experiment.

A new package containing a brief introduction to statistics and the theory of measurement errors is on the way and is being tested at the moment [20] [21], as well as randomly generated simple physics problems with the corresponding numerical solutions. The package comprises simulations developed with CGI run by the server and Java applications automatically downloaded by the client and run by the client itself. As it is usual with such applications, e-mail boxes render an asynchronous dialogue with the tutor(s) possible and an e-mail archive will permit us to analyse the students' FAQs.

Accessing information on the Internet via the WWW rather than in more traditional forms should become substantially wide spread within a few years independently of physics and education. The continuous evolution of Internet techniques results in the creation of applications more and more interactive, refined and so effective from the didactical point of view. We anticipate that the use of the WWW, if well managed by developers and instructors, will permit an improvement in the quality of physics teaching, and we are at present evaluating the usefulness of the prototypes with the students.