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Virtual Physics - issue No 12 - October 15, 1996
 

[Virtual Physics]

number 12, October 15, 1996

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a forum for virtual meetings of scientists and students involved in a research activity on
CONTEMPORARY PHYSICS

Editors:
Marcel Ausloos, ausloos@gw.unipc.ulg.ac.be, Institut de Physique, Université de Liège, Belgium,
Kenneth Holmlund, Kenneth.Holmlund@TP.UmU.SE, Umeå University, Sweden
Cameron L. Jones, cjones@swin.edu.au, Swinburne University of Technology, Australia
Zbigniew J.Koziol, (Editor-in-Chief) webex@ra.isisnet.com, WebExperts Inc., Canada
Michal Spalinski, Michal.Spalinski@fuw.edu.pl, Institute of Theoretical Physics, Warsaw University, Poland
Krzysztof P. Wroblewski, chris@nmr.biophys.upenn.edu, University of Pennsylvania, U.S.A.
Copyright (C) 1996 by Zbigniew Koziol.
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IN THIS ISSUE:

[0] Peer Review, by Alexander Berezin
[0] Nonlinear Response of HTSC Thin Film Microwave Resonators in an Applied DC Magnetic Field, by Durga P. Choudhury, Balam A. Willemsen, John S. Derov, and S. Sridhar
[0] The World of Virtual Reality, by Jedrzej Gajewski

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Peer Review

by Alexander Berezin berezin@mcmail.CIS.McMaster.CA

Received: September 30, 1996

Re : "Research and Funds", by Alex Braginski
Re : "Research and Funds", by Alexander Berezin
Re : "Research and Funds", by Ahmad Ibrahim
Re : "Myth of Competition and NSERC Policy of Selectivity", by Berezin and Hunter, Virtual Physics No 08, 1996

Letter by professor Alex Braginski is written from the standpoint which I would classify as a "strong pro-peer review" position.

Quoting Braginski:

"However, all "extras" and follow-up research should be proposed/applied for, and evaluated via a peer review, with funding administered by an agency. Not because it is a good or infallible system (it is not), but because all alternates are still worse. Most of NSERC or other bureaucrats are simply not able to evaluate basic work by themselves".

This paraphrase of a well known Winston Churchill's quote on a democracy is often used to back up the system of the (anonymous) peer review in science. Like other peer review defenders, Dr. Braginski is willing to admit that the peer review is not perfect, but because all alternatives are even worse we have to live with it for the sake of our own good.

For me, however, this argument far from obvious. Churchelleana does not apply always, and the alternative (peerless science) can indeed be a better option.

Being in science, like Dr. Braginski, for some 30 years I simply do not see a compelling reason to buy an argument that the "science is better with peer review than without". On a balance, my judgement is the opposite, namely that the overall effect of the peer review in science was and is of making a lot more harm than good.

While I do agree on a desirability of some editorial process for the research manuscripts, the prime purpose of it should be a clarity of presentation, avoidance of excessive length and detection of clear-cut rubbish and incompetence. (I would not even dispute strongly an issue of the peer review anonymity, PROVIDED it is used for the constructive improvements, but WITHOUT the power of the rejection).

Likewise, in allocating the research funding, the only thing peer review can do more-a-less reliably is to assess the overall competence of the researcher and his/her recent research activity. Only in cases when there is a clear deficiency on either of these points, denial of ANY operating funding is warranted. This is certainly not the practice of the Canadian NSERC which denies operating grants to one third of all professors of science and engineering at Canadian universities. To imply (as NSERC does) that 1/3 of all science-engineering workforce is incompetent and/or a dead wood is a sheer nonsense and a gross insult to the entire research community.

Another point which bothers me in Dr. Braginski's position is his inference that:

" The competence, quality and objectivity of peer and other reviews are really an ethical issue."

I again beg to disagree. The administrative system (in this case - the grant allocation system) should not and must not operate on a basis of some nebulous ethical principles. To request "ethicity" (and who defines it ?) from the ANONYMOUS (sic - !) system is both a contradiction of terms and a practical impossibility. Who is going to guard the ethicity of the process ? Another "anonymous" panel ?

So, my overall conclusions remain the same:

(1) it is time to dismantle anonymous peer review for the manuscripts and replace it with a system of open added comments

(2) a radical "de-expertization" of funding panels is long overdue. We have too much "expertise" rather than too little. It is better to fund a few crackpots than to let the "experts" to eradicate the potentially important discoveries and developments.

(3) Proposals (futurology) is largely conterproductive and should be replaced by the overall robust ranking of the research record to determine the funding level. The available funding levels should be made much more equitable than now (perhaps, within the factor of 5).

(4) Too much money for a "prolific" researcher is misuse of funds. Yes, people should be given funds for their expenses, but PROVIDED they do the work themselves. This should include the graduate students support, but the professors should NOT be given funds to hire cheap research labor (mostly, postdocs) to do the work which they (professors) are supposed to do themselves. Building of "research empires" should be discouraged. Junior research positions should be made truly independent. Subcontracting "professor to postdoc" should be phased out as unfair and exploitive.

Alexander A. Berezin
Department of Engineering Physics
McMaster University, Hamilton,
Ontario, Canada
berezin@Mcmaster.ca

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Nonlinear Response of HTSC Thin Film Microwave Resonators in an Applied DC Magnetic Field

Durga P. Choudhury a,b, Balam A. Willemsen a,b, John S. Derov b and S. Sridhara

a Physics Department, Northeastern University, Boston, MA 02115, dpc@neu.edu, http://sagar.physics.neu.edu/, tel. 617-373-2948, fax 617-373-2943
b Rome Laboratory, Hanscom AFB., Bedford, MA 01730

A PostScript version is available at LANL server, http://xxx.lanl.gov/abs/supr-con/9609001

Abstract

The non-linear microwave surface impedance, Zs=Rs+iXs, of patterned YBCO thin films, was measured using a suspended line resonator in the presence of a perpendicular DC magnetic field, HDC, of magnitude comparable to that of the microwave field, Hrf. Signature of the virgin state was found to be absent even for relatively low microwave power levels. The microwave loss was initially found to decrease for small applied HDC before increasing again. Also, non-linearities inherent in the sample were found to be substantially suppressed at low powers at these applied fields. These two features together can lead to significant improvement in device performance.

Introduction

The microwave response of high-Tc superconductors (HTSC) is important both from the point of view of microwave applications of HTSC [1] and fundamental physics [2]. An understanding of the loss mechanisms, field and current profiles and nature of non-linearities can lead to improvement in fabricated devices that use them. While numerous experimental studies of non-linear microwave response of HTSC have been done [3], none of them to our knowledge have probed the non-linear response in the presence of DC magnetic fields, where the DC and microwave fields are of comparable magnitude. In this situation the effect of the microwave field cannot be considered as a small perturbative Lorentz force on the vortex lattice generated by the DC field, as is often done at high fields [4]. Such a situation can also act to test various models that have been proposed for the non-linear response.

Experimental Techniques

We used a patterned suspended resonant thin film of YBa2Cu3O7-x housed in a rectangular copper package to carry out this series of experiments. Similar methods have been used before\cite [5,6] with great success to investigate vortex dynamics and non-linearities in HTSC. The film, procured from Neocera Inc, was deposited on a 0.6 in x 0.22 in x 0.010 in LaAlO3 substrate by laser ablation, and was subsequently patterned in-house to a straight line of dimension 0.56 in x 0.004 in using methods described elsewhere [7]. In order to obtain the highest possible Q's, the package was mechanically polished and thoroughly cleaned before each set of experiments. The resonator was made symmetric by placing a blank substrate of the same material and dimensions on top of the film before it was loaded into the package.

The assembly, complete with a controlling heater and temperature sensor, was inserted into the sample chamber of a Cryo Industries Variable Temperature cryostat. Two independent carbon glass sensors and temperature controllers were used to stabilize the temperature of the cavity to the degree required for these experiments. A LakeShore DR91C was used for gross control of the vaporizer temperature, which was set slightly below the desired sample temperature. The desired sample temperature was obtained and finely controlled with a LakeShore DR93CA. Temperature stability of the order of 1 mK were typical for the experiments presented here, where the data took up to two hours to obtain for each run.

DC magnetic fields up to 1000 Oe was applied parallel to the c-axis of the sample using a custom-built Walker Scientific copper solenoid and a LakeShore 622 superconducting power supply. Unlike typical Helmholtz coil configurations, the solenoid has no polecaps, thus ensuring that there is no remanent field, save for possibly the geomagnetic fields. It is worth pointing out that our experiment does not use any superconducting ground planes unlike parallel plate or microstrip resonators, thus avoiding complications due to demagnetization effects from such plates.

Microwaves were inductively coupled to and from the resonator by means of loops at the ends of stainless steel coaxial lines. The microwave transmission amplitude S21 was then measured using an HP 8510C Automatic Network Analyzer. The coupling strength was adjusted by varying the distance between the loops and the resonator as well as their relative orientation. Coupling could thus be reduced to the point that the loaded and unloaded Q's are indistinguishable, simplifying the data extraction process. At the low input power levels that were used to carry out these experiments, the trace was very noisy. This coupled with the fact that we require extreme sensitivity to very small changes mean that we could not simply determine the Q from the maximum frequency and -3 dB bandwidth as is often done. In order to reduce the noise and obtain the required sensitivity:

  • The network analyzer was used in the "Step" mode, in which every frequency point is individually synthesized

  • The signal was heavily averaged to get rid of the random noise,

  • The trace was fitted using the method of least squares to Lorentzian shape, and

  • The frequency span was kept as narrow as possible, usually only about 20% larger than the -3 dB bandwidth.

The center frequency and the -3 dB bandwidth obtained from the fit agreed very well with those directly read off the trace, especially at low power levels where the trace is closest to Lorentzian shape, but provided significantly enhanced sensitivity to small changes.

[ Figure 1 ]

Figure 1. Block diagram of Experimental Setup

Results and Discussion

Ubiquitous intrinsic non-linearities have been observed in thin film specimens of High-Tc materials [6,8], and some aspects of these non-linearities appear to be explained by a current-induced critical state model [9]. The present experiments, which involve both microwave and DC fields of comparable magnitude so as to study the interplay of these two effects, were designed to further test these critical state and other ideas. Our experiments show that the presence of even relatively low microwave powers can induce vortices in the film, emulating the response of a DC field. The signature of this fact come from the observation that low DC field hysteresis does not show the virgin state response.

In a typical sample, the signature of the virgin state (i.e. absence of trapped flux tubes) in the low DC field hysteresis experiments manifests itself as a sharp rise in the -3 dB bandwidth as field is slowly increased from zero corresponding to initial penetration of flux. As the field is further increased to a value Hmax and then cycled between Hmax and -Hmax, where Hmax is a field of the order of a few hundred Gauss, this initial behavior is never reproduced; instead, it goes through a butterfly-shaped hysteresis loop [10].

The same experiment, performed on the films under discussion, yields two new observations :

  • The initial "virgin" response vanishes at higher microwave powers. This seems to indicate that microwave fields can create enough vortices in in the sample to wash away the virgin state response, mimicking the effect of an applied DC field.

  • A sharp dip in Rs is observed at a field scale HDC = 5 G in the virgin response, indicating that a small applied DC field serves to lower Rs.

[ Figure 2 ]

Figure 2. Low field hysteresis at -21 dBm and -11 dBm of input power, at 10K. Notice the absence of the "tail" corresponding to virgin response at higher powers. In order to highlight the similarities between the two plots, they have been superposed on each other by adding a constant of 10 kHz off the -21 dBm power plot.

The second result was verified when we did a measurement of Rs against applied microwave power in a fixed HDC. The decrease in Rs reproduces itself, as is evident from fig.3. Another observation from the microwave power ramp experiments is that the non-linearities in the sample also get substantially suppressed at these low field for low microwave powers. As HDC is increased, Rs gradually rises and finally goes above it's zero field value. To further ensure that this observation is genuine and is not an artifact of some experimental inconsistency, we repeated the measurements on a film patterned out of a different albeit similar wafer. Although results obtained from this film were not quantitatively identical with those of the other, which would be expected because of the differences on growth, deposition and patterning of the two films, the two characteristic features described above was observed to a comparable extent in the second film. Also to rule out the effect of any stray remanent DC field, we carried out the microwave power ramp measurements with the DC field reversed and no such effects were found.

[ Figure 3 ]

Figure 3. Typical power dependence of resonance widths, taken at 10K

We have examined the present data in the framework of two proposed explanations for non-linear response in HTSC, viz. weak links and dynamics of a current-driven critical state. The weak link picture can be viewed in terms of a resistively shunted junction (RSJ) model, taking the effect of the DC field to be a DC current flowing on the surface in addition to the rf current. The equation of motion for the relative phase between the coupled grain then become [$\dot{\phi}+\sin \phi =i_{dc}+i_\omega \cos \omegat$]. The dynamic impedance can be calculated from [$Z_\omega =\dot{\phi}_\omega /i_\omega $]. While numerical calculations of this response yield very interesting effects as idc is varied, this approach does not seem to yield the results that are observed in this experiment.

The critical state model should also lead to ac + dc effects, so that the non-linearity should be modified by the DC magnetic field. However a calculation of this effect is not straight-forward, since it requires a prescription for the present case where the loss needs to be calculated when irf is varied over on rf cycle for finite HDC. The available prescription in the literature [11] does not consider this case, but instead considers a different method of varying irf and HDC. Hence, at the present, it is not possible to determine if the critical state model can explain these unusual results.

It is worth noting that the unusual decrease in Rs observed here can occur due to non-equilibrium effects and in fact have been seen in low Tc superconductors [12]. There it was shown that when the microwave frequency [$\omega >\tau ^{-1}$], where [$\tau $] is the quasiparticle relaxation time, a non-equilibrium quasiparticle distribution can occur which leads to a decrease of Rs in the presence of an idc. Another related phenomenon which occurs is an enhancement of the superconducting gap. While this condition is met in pure metals at low temperatures, it is not clear if this happens in the high Tc materials.

However it is interesting to note that in YBa2Cu3O7-x crystals, Rs(T) is non-monotonic and there are regions of temperature where [$%(\partial R_s/\partial T)<0$]. This unusual, apparently non-thermodynamic result, may imply that [$(\partial R_s/\partial i_{dc})<0$] need not be surprising.

Conclusion

We have described a novel effect in which both the microwave losses and non-linear response decrease in the presence of small magnetic fields. Although a clear explanation of this effect is lacking, and it could arise from non-equilibrium quasiparticle effects, the present observation implies that losses can be reduced by as much as 30% and could have interesting implications for device performance.

Work at Northeastern University was supported by the AFOSR through Rome Labs, Hanscom AFB.

References

[1] Zhi-Yuan Shen and Charles Wilker, Raising the power-handling capacity of hts circuits, Microwaves & RF, pp. 129--138, April 1994.

[2] T. C. L. Gerhard Sollner, Jay P. Sage, and Daniel E. Oates, Microwave intermodulation products and excess critical current in YBa2Cu3O7-x Josephson junctions, Appl. Phys. Lett., vol. 68, no. 7, pp. 1003--1005, February 1996.

[3] Charles Wilker, Zhi-Yuan Shen, Philip Pang, Willam L. Holstein, and Dean W. Face, Nonlinear effects in high temperature superconductors: 3rd order intercetpt from harmonic generation, IEEE Trans. Appl. Supercond., vol. 5, no. 2, pp. 1665, June 1995.

[4] Mark W. Coffey and John R. Clem, Theory of rf magnetic permeability of isotropic type-{II} superconductors in a parallel field, Phys. Rev. B, vol. 45, no. 17, pp. 9872, May 1992.

[5] Balam A. Willemsen, John S. Derov, Jose H. Silva, and S. Sridhar, Vortex dynamics at microwave frequencies in patterned YBa2Cu3O7-x thin films, Appl. Phys. Lett., vol. 67, no. 4, pp. 551--553, July 1995.

[6] Balam A. Willemsen, John S. Derov, Jose H. Silva, and S. Sridhar, Nonlinear response of suspended high temperature superconducting thin film microwave resonators, IEEE Trans. Appl. Supercond., vol. 5, no. 2, pp. 1753--1755, June 1995.

[7] Balam A. Willemsen, Vortex Dynamics at high Frequencies in Layered Superconductors, PhD thesis, Northeastern University, Boston, MA 02115, October 1995.

[8] P. P. Nguyen, D. E. Oates, G. Dresselhaus, and M. S. Dresselhaus, Nonlinear surface impedance for YBa2Cu3O7-x thin films: Measurements and a coupled-grain model, Phys. Rev. B, vol. 48, no. 9, pp. 6400--6412, September 1993.

[9] S. Sridhar, Non-linear microwave impedance of superconductors and ac response of the critical state, Appl. Phys. Lett., vol. 65, no. 8, pp. 1054--1056, August 1994.

[10] J. S. Derov Balam A. Willemsen and S.Sridhar, Critical state flux penetration and linear microwave vortex response in YBa2Cu3O7-x films, Unpublished.

[11] Ernst Helmut Brandt and Mikhail Indenbom, Type-II-superconductor strip with current in a perpendicular magnetic field, Phys. Rev. B, vol. 48, pp. 12893--12906, 1993.

[12] Srinivas Sridhar, Microwave Dynamics of Quasiparticles and Critical Fields in Superconducting Films, PhD thesis, California Institute of Technology, 1983.

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The World of Virtual Reality

by Jedrzej Gajewski (gajewski@tuns.ca)
Technical University of Nova Scotia Halifax, NS.

History

The ease of use and availability allowed the Internet to explode in popularity and in 1995, the first Internet Virtual Reality languages began to appear. The language is platform-independent and describes 3-dimensional virtual reality scenes and model designs. Spatial Data Modeling Language (SDML) and Virtual Reality Modeling Language (VRML) became the two most accepted languages. SDML is suited towards CAD and GIS sources and works well for a variety of Landscape Planning, Design and Architectural databases. SDML is interpreted by CLRMosaic, a browser, available only for Silicon Graphics workstations. The VRML specifications were released by Silicon Graphics, Inc. and are based on the Open Inventor file format. Unlike SDML, VRML is supported by many viewers on different platforms including UNIX, Windows and now MacIntosh operating systems. This important factor allowed VRML to leap ahead of SDML in popularity, development and research.

IBM's current proposal is a faster, more compact binary version of VRML, where the ASCII text files will be replaced by binary ones. SGI is proposing an external interface that enables an external Java applet to communicate with a VRML world.

VRML Overview

In a way, the VRML language can be thought of as being similar to HTML. A text file that describes a model is downloaded from the server to the client. It is then processed by a VRML viewer, or a plug-in in your HTML browser. The models can be created using special 3D design packages and translated to VRML or can be designed by hand editing a file in a text editor.

VRML allows a user to explore a model by walking or flying around and inside a model, just as one would if they were exploring a real object. Predefined viewpoints can be created using the PerspectiveCamera and Orientation nodes. To enhance to the reality, VRML supports an array of different light sources and colors such as the Material node that includes diffuse, emissive, ambient, headlight and specular color values and positions. Applying texture maps to object surfaces makes it possible to create detail rich worlds. In addition, VRML supports flat and smooth shading techniques. However, shadowing is not implemented at this time as the rendering would be too expensive (performance wise).

It is always beneficial to optimize a model as to decrease it's download and render times as this may allow one to increase the detail of the virtual world. There are several ways to do so. The easiest way is to remove the white space and round off any numbers in the text file. Furthermore, one can re-use the same parts several times in different conditions by using the WWWInline or DEF and USE nodes. The ShapeHints node allows the backside of a solid object to be hidden or not drawn, as it will never be seen anyway and the removal of the object's internal polygons can greatly increase the efficiency of the entire model. The LOC node allows one to specify the amount of detail depending how far an object is away from the camera. Finally, the final models can be gzipped that reduce the file size by 90%.

Recently, version 2.0 of VRML was released that allows 3D animations. In other words, one can make their models, or parts of models move around in the virtual world in addition to the capability of navigating through the world yourself.

The most significant WWW site dealing with VRML is the VRML Repository and I will refer to that site several times throughout this text. It includes all the specifications of the language, almost all software related to VRML and anything else that may be of interest to a VRML programmer or surfer.

Viewing the Models

In order to learn and view VRML models, a VRML compatible browser is required. I recommend that you get a browser that supports both HTML and VRML viewing capabilities as many of the models are interlaced with HTML pages. You can get a listing of the available browsers to date for most operating systems at www.sdsc.edu/vrml/browsers.html.

Once a VRML browser is installed, a person needs to get accustomed to it. It is quite difficult at first to navigate through a 3-dimensional space using 2-dimensional navigation tools such as the keyboard and mouse. It is a good idea to read the navigational directions that come with the browser and to try to use the pre-defined viewpoints in the model if they are available.

It is important to remember that, as with HTML pages, different viewers render and project a model slightly differently. The same model may look different and in some cases terrible in one browser and spectacular in another. Although there is standard for the language itself, there is no standard for the rendering or interpretation algorithms. Also, some browsers may support VRML extensions that are not supported in another browser, making the model significantly different.

Learning and Understanding VRML

There are numerous books and tutorials available that teach VRML. I will not write a tutorial here but point you in the right direction. The best way to learn the basics of VRML is by example. I found Pioneer Joel's VRML Tutorial to be the best starting point as it is simple and quick. In just under one hour you can go off and create a simple VRML model. The next step would be to try other tutorials or read a VRML authoring book, which will explain every thing in more detail. At this point, it may be beneficial to quickly scan the VRML 1.0C specifications.

VRML 2.0 is very recent and most resources are still being developed. In fact, you will require a separate VRML 2.0 viewer (different from VRML 1.0) to view these worlds. Pioneer Joel's VRML 2.0 Tutorial provides an excellent introduction to VRML 2.0 and the VRML 2.0 specifications can supplement any other area of interest that one might have.

One may prefer to develop complex models using applications such as Geometry Modelers or Geometry Generators. However, it may be required to convert the models to VRML using Geometry translators. Keep in mind, when using translators, that quality may decrease and that data loss is possible.

VRML Application and Examples

The easiest way to get a feel of VRML's potential is to simply show examples of what has been done already. Although not all models here are related to physics, they show several different approaches used with VRML.

Below is a table that lists the URL and snapshot of the VRML world and key points of interest about the model. Version 1 of VRML has been used in each case. Click on the URL to enter the 3D world.

SnapshotURLComments
[] NCSA Relativity Group VRML Page
Spacetime Diagram for the Collision of 2 Black Holes
http://jean-luc.ncsa.uiuc.edu/Viz/VRML/POPs.wrl
simple lighting and smooth shading effects
[] Neural Signal Processing Group's Human Brain Project
The Brain - image from a Magnetic Resonance Scanner
http://hendrix.ei.dtu.dk/vrml/mriHeadD6.wrl.gz
amount of surface detail
[] The Naval Research Laboratory
http://overlord.nrl.navy.mil/vrml/nrl.wrl
use of lighting techniques, pre-defined viewpoints, object links
[] Image Library of Biological Macromolecules
DNA / Protein Complex
http://www.imb-jena.de/vrml/DNA/DNA_ drug_complexes/109d/109d_insight_1.wrl.gz
detail and precision
[] The Collider Detector at Fermilab
http://www.ocnus.com/models/CDF/detector.wrl
use of WWWInline node and lighting
[] Virtual Modeling Language in Chemistry
Nitrosamine Molecule
http://www.pc.chemie.th-darmstadt.de/vrml/ models/bns/nitro.wrl
lighting and shading
[] THe LaHave House Project
http://www.tuns.ca/~gajewski/vrml/ model4/model4b.wrl
background color, pre-defined viewpoints, the use of DEF and USE nodes, flat shading, transparency

Other examples can be found at: http://www.isisnet.com/MAX/vrml/struct.html, http://www.tuns.ca/~gajewski/vrml/, http://www.eit.com/www.lists/www-vrml.1995q3/0347.html, http://3dsite.com/cgi/VRML-index.html.

VRML can be applied to illustrate anything from simple to complex models or concepts. The applications of VRML are limitless, what can be created depends on ones needs and ingenuity.

More Information

As with any other product that is evolving on the WWW, up to the minute news and support can be obtained through the mailing lists, the newsgroups and other web pages.

____________________________________________________________
Virtual Physics: a forum for virtual meetings of scientists and students involved in a research activity on CONTEMPORARY PHYSICS

Editors:

Marcel Ausloos, ausloos@gw.unipc.ulg.ac.be, Institut de Physique B5,
Université de Liège, Sart Tilman, B-4000 Liège, Belgium, tel. (+32 41) 66 37 52
Kenneth Holmlund, Kenneth.Holmlund@TP.UmU.SE, Department of Theoretical Physics
Umeå University, S-907 42 Umeå, Sweden, tel. +46-(0)90-167717

Cameron L. Jones, cjones@swin.edu.au, Centre for Applied Colloid and BioColloid Science
Swinburne University of Technology, P.O. Box 218 Hawthorn, Victoria, 3122 Australia, tel. +613 9214 8935, fax +613 9819 0834
Zbigniew J. Koziol (Editor-in-Chief), WebEx@ra.isisnet.com, WebExperts Inc.,
2-6032 Compton Ave., Halifax, Nova Scotia, B3H 1E7 Canada, tel. (902) 423 2149
Michal Spalinski, Michal.Spalinski@fuw.edu.pl, Institute of Theoretical Physics,
Warsaw University, Hoza 69, 00-681 Warsaw, Poland, tel. (+48 2) 628 3031

Krzysztof P. Wroblewski, chris@nmr.biophys.upenn.edu, School of Medicine
University of Pennsylvania, Rm. C-501 Richards Bldg., Philadelphia, PA 19104-6089, U.S.A., tel. (215) 898-6396

Virtual Physics URL addresses:

CANADA - http://www.isisnet.com/MAX/vp.html
AUSTRALIA - http://www.swin.edu.au/chem/complex/vp.html
SWEDEN - http://www.tp.umu.se/vp.html

To subscribe a F R E E e-mail version or submit materials for publication, write to Zbigniew Koziol.
Copyright (C) 1996 by Zbigniew Koziol.
this copyright notice concerns the whole of the Virtual Physics edition but not specific articles published there which are property of their respective copyright owners
No responsibility is assumed by the publisher for any damage to persons or property as a matter of the product liability, negligence or otherwise, or from any use of methods, instructions or ideas contained in the material herein. The opinions expressed in this publication do not necessarily reflect the opinions of the Editors and certainly they have nothing to do with WebExperts Inc.
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