Materials of the round table “Analytical methods and computer experiment in soft matter theory”
The paper contains materials of the discussion regarding the development, the problems of today and the prospects of analytical methods and computer simulations in soft matter theory which took place during the Workshop on modern problems of soft matter theory (August 27–31, 2000, Lviv, Ukraine)...
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Інститут фізики конденсованих систем НАН України
2001
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| Назва видання: | Condensed Matter Physics |
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| Цитувати: | Materials of the round table “Analytical methods and computer experiment in soft matter theory” / A. Trokhymchuk, D. Henderson, L. Lee // Condensed Matter Physics. — 2001. — Т. 4, № 2(26). — С. 375-382. — Бібліогр.: 2 назв. — англ. |
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irk-123456789-1204432017-06-13T03:04:29Z Materials of the round table “Analytical methods and computer experiment in soft matter theory” Trokhymchuk, A. Henderson, D. Lee, L. The paper contains materials of the discussion regarding the development, the problems of today and the prospects of analytical methods and computer simulations in soft matter theory which took place during the Workshop on modern problems of soft matter theory (August 27–31, 2000, Lviv, Ukraine). У статті подано матеріали дискусії щодо розвитку, сучасного стану та перспектив аналітичних методів і комп’ютерного моделювання в теоріі м’якої речовини, що відбулася підчас Наради із сучасних проблем теорії м’якої речовини (27–31 серпня 2000 р., м. Львів). 2001 Article Materials of the round table “Analytical methods and computer experiment in soft matter theory” / A. Trokhymchuk, D. Henderson, L. Lee // Condensed Matter Physics. — 2001. — Т. 4, № 2(26). — С. 375-382. — Бібліогр.: 2 назв. — англ. 1607-324X PACS: 07.05.T DOI:10.5488/CMP.4.2.375 http://dspace.nbuv.gov.ua/handle/123456789/120443 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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The paper contains materials of the discussion regarding the development,
the problems of today and the prospects of analytical methods and computer
simulations in soft matter theory which took place during the Workshop
on modern problems of soft matter theory (August 27–31, 2000, Lviv,
Ukraine). |
| format |
Article |
| author |
Trokhymchuk, A. Henderson, D. Lee, L. |
| spellingShingle |
Trokhymchuk, A. Henderson, D. Lee, L. Materials of the round table “Analytical methods and computer experiment in soft matter theory” Condensed Matter Physics |
| author_facet |
Trokhymchuk, A. Henderson, D. Lee, L. |
| author_sort |
Trokhymchuk, A. |
| title |
Materials of the round table “Analytical methods and computer experiment in soft matter theory” |
| title_short |
Materials of the round table “Analytical methods and computer experiment in soft matter theory” |
| title_full |
Materials of the round table “Analytical methods and computer experiment in soft matter theory” |
| title_fullStr |
Materials of the round table “Analytical methods and computer experiment in soft matter theory” |
| title_full_unstemmed |
Materials of the round table “Analytical methods and computer experiment in soft matter theory” |
| title_sort |
materials of the round table “analytical methods and computer experiment in soft matter theory” |
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Інститут фізики конденсованих систем НАН України |
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2001 |
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http://dspace.nbuv.gov.ua/handle/123456789/120443 |
| citation_txt |
Materials of the round table “Analytical
methods and computer experiment in
soft matter theory”
/ A. Trokhymchuk, D. Henderson, L. Lee // Condensed Matter Physics. — 2001. — Т. 4, № 2(26). — С. 375-382. — Бібліогр.: 2 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
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| first_indexed |
2025-07-08T17:53:32Z |
| last_indexed |
2025-07-08T17:53:32Z |
| _version_ |
1837102233573916672 |
| fulltext |
Condensed Matter Physics, 2001, Vol. 4, No. 2(26), pp. 375–382
Materials of the round table “Analytical
methods and computer experiment in
soft matter theory”
Collected and edited by
A.Trokhymchuk 1 , D.Henderson 2 , L.Lee 3
1 Institute for Condensed Matter Physics, National Academy of Science of
the Ukraine, Lviv, UA 79011, Ukraine
2 Department of Chemistry and Biochemistry, Brigham Young University,
Provo, UT 84602, USA
3 School of Chemical Engineering and Material Science, University of
Oklahoma, Norman, OK 73019, USA
The paper contains materials of the discussion regarding the development,
the problems of today and the prospects of analytical methods and com-
puter simulations in soft matter theory which took place during the Work-
shop on modern problems of soft matter theory (August 27–31, 2000, Lviv,
Ukraine).
Key words: analytical theory, computer simulations
PACS: 07.05.T
1. In lieu of introduction
The last decade of the 20th century gave mixed prospects for the future devel-
opments of theoretical [i.e., analytical] approaches in the soft matter theory that
traditionally includes thermodynamic perturbation theory, integral equation theory
and density functional theory. Specifically, it may be not very promising to apply
theoretical approaches to sophisticated models in the soft matter theory that have
become very popular in different applications. Many basic and analytically solvable
models have been already solved within some physically reasonable approximations.
Rapid development of computer technology creates the necessary conditions for
the expansion of computer experiment methods that can be considered as a third
way to investigate condensed matter in between theory and experiment: Two ba-
sic methods of computer experiment have been developed: Monte Carlo (MC) and
Molecular Dynamics (MD). In both methods, a certain number of particles is dis-
tributed in a (usually cubic) box. The interactions are described by pair potentials
c© A.Trokhymchuk, D.Henderson, L.Lee 375
The round table “Analytical methods and computer experiment. . . ”
and it is generally assumed that the total potential can be developed as a sum of
these pair potentials.
In MC simulations, a large number of configurations are generated. Starting
from a given configuration, a trial move of a randomly chosen particle to a new
position is made. The energy change, ∆E, connected with this move is calculated,
and if the energy decreases, the move is accepted. If ∆E is positive, the Boltzmann
factor exp(−∆E/kBT ) is calculated and compared with a randomly chosen number
between 0 and 1. The move is accepted if the Boltzmann factor is larger than this
number and rejected if it is smaller. This way, millions of configurations, weighted by
the Boltzmann factor, are produced and thermodynamics and structural properties
of the studied system can be deduced by averaging procedures. In MD simulations,
the classical equations of motion are integrated numerically for the particles in the
box. The resulting knowledge of position and velocity is determined as a function
of time for each of the particles and means a complete classical description of the
system. Therefore, the thermodynamic, structural as well as dynamic properties of
the liquid concerned can be calculated using statistical mechanics. A comprehensive
description of both methods has been given by Allen and Tildesley [1] and Frenkel
and Smit [2].
With the disposal of such powerful tools, one can comment that he has no need
for analytical theory, saying that simulations can provide the numbers that are
needed. However, the purpose of theory was not to provide numbers but to pro-
vide understanding. For example, Copernicus, and more especially Kepler, inferred
from astronomical data, mostly due to Brahe, the details of the planetary orbits.
However, this provided no understanding. Surely, understanding and establishing
interconnections is the goal of science. It was Newton’s analytical work which estab-
lished that Kepler’s laws were a consequence of gravitational attraction with a simple
inverse square dependence together with the conservation of angular momentum. It
is unlikely that such far reaching concepts could have been achieved without ana-
lytical work. Perhaps even more importantly, the fact that the same laws governed
astronomical motions over much larger distances [the structure of nebulae is but
one example] would never have been discovered without the developments based on
Newton’s analytical theories. Would quantum mechanics have been discovered with-
out Planck and Bohr feeding their ideas into analytical formulae? Would simulations
have aided Maxwell or Einstein?
The future developments of the soft matter theory will determine the role of
analytical theories and computer experiment. However, scientists are trying to fore-
cast the future. The best way to do this is to have an understanding of the past
and a critical view what is going in the present. From our experience, we can say
that such kind of questions recently arise very often within scientists in their pri-
vate communications, discussions during group meetings and large scale conferences.
Nevertheless, no materials regarding those discussions are published so far. Partial
insight into this topic has been made during the two-hour round table conversation
organized within the Workshop on Modern Problems of Soft Matter Theory [August
27–31, 2000, Lviv, Ukraine]. We avoid to make some final conclusions following that
376
The round table “Analytical methods and computer experiment. . . ”
discussion. This is not because of they were not formulated, but because we are not
sure that one could do this in general. Thus, the goal of this publication is to present
for a larger number of scientists the view of the participants of the round table and,
perhaps, to initiate the future publications on this topic.
2. The role of analytical methods and computer experiment in
the soft matter theory
Karl Heinzinger: Computer simulations, being neither experiment nor theory, can
take over the task of both. In the case of simple liquids, say liquid noble gases,
where the interactions between the particles are well known and where many-body
non-additive interactions do not play an important role, the results derived from
the simulations deserve a high degree of reliability. They can be used as a standard
either for or against analytical theories. In the case of complicated systems, say
interfaces, that cannot yet be treated analytically, and computer simulations can
play the role of the theory. They can predict properties of liquids which cannot [or
not directly] be measured and they can explain macroscopically measured properties
on a molecular level.
Myroslav Holovko: Analytical methods and computer experiments are complemen-
tary to one other. This is similar to the relationships that we have between theory
and real experiments. The information obtained from computer simulations should
be reproduced by an analytical theory. This gives a test for analytical methods but
is not limited only by this. In the process of such a comparison we learn more and
understand more about the properties and phenomena in model systems.
Marco Zoppi: In my opinion the two techniques are complementary. On the one
hand, computer experiments are a way to solve a well defined model up to a prese-
lected precision level. For example, you can decide to solve the problem of a pairwise-
additive Lennard-Jones liquid system, which however does not exist in nature, but
you can do it almost exactly using simulation. On the other hand, to solve the
same model system, analytically, is not possible, unless you resort to approxima-
tions, which in turn, may or may not be fully controlled. A comparison between the
two methods, and the results, can shed some light on the effects and applicability
range of the approximations. This, in turn, would improve the effectiveness of the
analytical method, giving a rather precise consciousness of its applicability limits.
Fumio Hirata: I wish to express my opinion on a general question which has often
been raised concerning to the importance of the integral equation methods in liquid
state theory. Why does one use the integral equation method to solve the problems
when the molecular simulation can replace it in many cases? We can answer the
question in two ways: one technical and the other more fundamental. Due to the
level of complication which characterizes the problems in chemistry, solutions to
statistical-mechanical equations are numerical in most of the cases. In that sense,
statistical-mechanical equations apparently are not any better than molecular simu-
lations. However, there are problems in which the molecular simulation fails to give
an answer to a question within a reasonable amount of computational resources cur-
377
The round table “Analytical methods and computer experiment. . . ”
rently available. A typical example of such questions is the protein folding based on
the first principles. For such cases, the difference between the statistical-mechanical
theory and the molecular simulations is not just technical but essential.
Dor Ben-Amotz: Obviously numerical methods are increasing in importance with
the evolving computer technology, as numerical methods may be used to model the
systems that are far too complex to treat analytically (at least at the same level
of detail). However, it is analytical theory that provides the language we use to
formulate the key issues and questions which are most interesting and important,
including those whose answers may require numerical or laboratory experiments.
Analytical theory also represents the sacred heart of all scientific endeavour, as it is
this branch of research which expresses our deep seated belief in the mystery of all
mysteries – that we live in a world which may yield itself to our understanding if we
think hard and have sufficient faith.
Lesser Blum: I believe that as scientists we have a common goal, which is to
understand nature. In our case, statistical mechanics tries to establish the connection
between molecular forces (which cannot be directly measured) and the behaviour of
macroscopic systems. The name of the game is to formulate simple enough theories
which from a given Hamiltonian model can predict the behaviour of systems of
variable complexity. The link between pure theory and pure experiment is provided
by simulation.
Marco Zoppi: Here I have a similar opinion that the problem is ill posed. Analyt-
ical theories and computer experiments can be dealing with exactly the same model
system, which, however, can be totally unrealistic. On the other hand, it is not al-
ways true that a computer experiment “probes” the reality. Most of the times it
gives answers, or numbers, which depend critically on he way we have modelled the
reality. Of course, IF we could have an infinitely precise potential model (including
all the many-body contributions) IF we could demonstrate that a limited simula-
tion sample is a good representative of a real physical system, IF the simulation
algorithm worked perfectly well, THEN the simulation results should mimic exactly
the reality. But, how sure are we about all those IFs? Of course, if we enclose the
concept of an error bar, most of the problems can be released, or decreased, but
HOW do we get rid of the unavoidable systematic errors that are always present in
the simulations? [and also in the experiments, of course.]
Yura Kalyuzhnyi: In my opinion, our discussion has focused only on the role of
the theory from the short-term viewpoint. However it is important to stress the role
of the theory on a long-term scale. In this sense, the theory is very important, since
it gives us the definitions [or terminology] and the language, which is used not only in
experimental studies or in engineering but in the whole society. For example one can
hardly imagine any field of engineering without using the definition of the energy.
However, a couple of centuries ago this terminology did not exist and appeared as a
result of the studies that were mostly theoretical.
Fumio Hirata: There is an even more fundamental reason to develop the statistical
mechanical theories. Let us explain this point by taking just one example from the
solution chemistry. One of the most important findings in the solution chemistry
378
The round table “Analytical methods and computer experiment. . . ”
is the so-called “square root law” which appears in many of equilibrium and non-
equilibrium properties in electrolyte solutions in their concentration dependence: the
asymptotic concentration dependence in the limC → 0 is proportional to C 1/2, not
to C. As has been clarified by the statistical mechanics of solutions, the limiting be-
haviour is intimately related to the multi-body screening of the Coulomb interaction
among charged species. In the typical electrolyte solutions, the Coulomb interaction
between a pair of ions asymptotically behaves as e−κr/ǫr, that is, the Coulomb in-
teraction is screened by an exponential factor e−κr, where κ is th Debye screening
factor. The square root dependence of the screening constant upon concentrations
appearing in this equation is the physical origin of the limiting law. The exponential
screening behaviour is obtained mathematically from the integral equation theory
as a renormalization of the coulomb interactions. That is, the physically realized
phenomenon of screening has a clear “mathematical” interpretation based on the
statistical mechanical theory. Although the molecular simulation may reproduce the
exponential behaviour of screening in any precision, it will never answer the ques-
tion why it should be exponential, why it should produce the special concentration
dependence for many observable quantities.
Myroslav Holovko: However, the role of computer simulation continues to in-
crease. We can predict that this will continue in near future. Advanced simulation
methods lead to new insights and simulate new suggestions for improvements in an-
alytical studies. As examples of such new developments, we can consider the multi-
density integral equation approach in the theory of associating and polymeric fluids,
the replica Ornstein-Zernike integral equations for the liquids in porous media, the
application of the integral equation approach to the description of electronic density
of states of fluids and so on.
3. Prospects for Soft Matter Theory
Marco Zoppi: Personally I am more in favour of the applications of the existing
methods to modern objects. Probably because I am not a professional in simulation.
When you have some new experimental results, the first problem is to validate them
somehow. In this case a simulation can be very helpful. From this stage on, to
find the physical insight is not a trivial process and you may need some theoretical
approach. At any rate, developing new methods is always a knowledge increasing
process and sooner or later it will give its fruit.
Dor Ben-Amotz: In more practical terms, the importance of numerical experiments
in testing analytical theory is well appreciated. There is some danger, however, that
analytical theory and simulation can lead each other astray as they dance happily
together off the edge of anything resembling the real world. A good example is our
fondness for two-body additivity in modeling fluids and complex materials. Both
analytical theory and numerical simulations are quite happy to follow this path, as
they pat each other on the back congratulating each others success, in spite of the
fact that interactions between the molecules of water in this beer bottle bear no
resemblance to such two-body additive potentials.
379
The round table “Analytical methods and computer experiment. . . ”
Lesser Blum: In my perception, all three methods, i.e. theory, simulations, exper-
iment, are important. It is like the old story of which is the most important part of
the body: the head, the heart, or the stomach: We need all three. A case in point is
the biology study at the molecular level in general, and of biochannels in particular.
These are extremely important, complex and delicately precise structures which even
with the most powerful computers cannot be simulated in any even remotely close
to physiological conditions, for sufficiently long times. And theoretical approaches
are still too simplistic to account for the delicate mechanism of gating.
Myroslav Holovko: Analytical approaches can be developed before the computer
simulations. As an example of such a situation, we have the theory of self-assembling
systems, where different semiphenomenological approaches are developed ranging
from microscopic-like models and Landau theories to membrane models. At present,
the applications of computer simulations for treating such simple self-assembly ef-
fects as the spontaneous appearance of micelles above the critical micelle concentra-
tion (CMC) of a surfactant in water are possible only for very simple systems. There
are a few problems with this treatment, such as a sufficiently small value of the CMC
and the large number of particles that are needed for the simulations, the problem
of long times of performing simulation for obtaining self-assembling aggregates, etc.
Peter Monson: In some sense the development of simulation has had a negative
consequence.With death of John Barker, studies such as his on intermolecular forces
have shut down and perhaps his pioneering work might be lost.
Douglas Henderson: I agree with Peter and share his admiration for John Barker.
In spirit of whimsey, I wonder if simulations should be restricted to those who had
first served an apprenticeship in analytical theory.
4. Instead of conclusions
Ariel Chialvo: The most typical scenario in the study of soft matter is the one
where we have to contend with two realms [worlds], i.e., the real and the mathemat-
ical worlds, as well as three interconnected targets, namely: laboratory experiments,
theoretical developments, and molecular-based simulations. In the quest for under-
standing of soft matter behaviour, neither one of these targets can stand alone, but
integrated with one another as indicated in figure 1.
The interconnection hinges around three essential ingredients associated with
this concerted effort are as follows:
(i) the realism of a [mathematical] model in describing the real world,
(ii) the accuracy of the theory in representing the model, and
(iii) the validity [adequacy] of the molecular-based simulation in representing the
model.
Thus, we must always address all three items to get the most from the interplay
between theory, simulation, and experiment. Otherwise, we may find ourselves con-
fronted with the dilemma about whether any disagreement in the comparison either
380
The round table “Analytical methods and computer experiment. . . ”
Nature
Models
Theory Simulation
Experiment
Methods
Figure 1. Schematic representation of the targeted systems and the tools of the
trade used in their study
(i) between theory and experiment results from an unrealistic [potential] model,
or (ii) between simulation and theory results from inaccuracies in the theory. To
solve this dilemma we should first establish the validity of the molecular-based sim-
ulation methodology independently from the associated theory or the experiment.
Consequently, we can inquire about the realism of a particular mathematical [in-
termolecular potentia] model by comparing the simulation results for that model
with the corresponding experimental data. At the same time, we can compare these
simulation results with those generated by the theoretical counterpart involving pre-
cisely the same potential model, and thus, we can assess the accuracy of the theory
in representing the mathematical model. In summary, and as my simulation mentor
used to say: ‘molecular simulation is a tool whose value strongly depends on the skills
of the practitioner who operates it’. Therefore, ‘we should never forget that the realm
we create is an artificial world, to mimic the real world which we hope to understand,
eventually’.
References
1. Allen M.P. and Tildesley D.J. Computer Simulations of Liquids. Oxford, Clarendon,
1987.
2. Frenkel D. and Smit B. Understanding Molecular Simulation. New–York, Academic,
1996.
381
The round table “Analytical methods and computer experiment. . . ”
Матеріали круглого столу “Аналітичні методи та
комп’ютерний експеримент в теоріі м’якої
речовини”
Зібрано і відредаговано
А.Трохимчуком 1 , Д.Гендерсоном 2 , Л.Лі 3
1 Інститут фізики конденсованих систем НАН України,
79011 Львів, вул. Свєнціцького, 1
2 Факультет хімії та біохімії, Університет Брайхем Янг,
Прово, UT 84602, США
3 Школа хімічної інженерії та матеріалознавства, Університет штату
Оклахоми, Норман, OK 73019, США
У статті подано матеріали дискусії щодо розвитку, сучасного стану та
перспектив аналітичних методів і комп’ютерного моделювання в те-
оріі м’якої речовини, що відбулася підчас Наради із сучасних проб-
лем теорії м’якої речовини (27–31 серпня 2000 р., м. Львів).
Ключові слова: аналітична теорія, комп’ютерне моделювання
PACS: 07.05.T
382
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