From phase transitions to dynamics of liquids: on the 50-th anniversary of Ihor Mryglod
The main idea of this Special issue of "Condensed Matter Physics" was to get together in one volume contributions from research fields that encompass I.Mryglod's interests over the last 25 years.
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Інститут фізики конденсованих систем НАН України
2010
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| Назва видання: | Condensed Matter Physics |
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| Цитувати: | From phase transitions to dynamics of liquids: on the 50-th anniversary of Ihor Mryglod / T. Bryk // Condensed Matter Physics. — 2010. — Т. 13, № 2. — С. 20101: 1-3. — Бібліогр.: 16 назв. — англ. |
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irk-123456789-320862012-04-10T01:19:57Z From phase transitions to dynamics of liquids: on the 50-th anniversary of Ihor Mryglod Bryk, T. Foreword The main idea of this Special issue of "Condensed Matter Physics" was to get together in one volume contributions from research fields that encompass I.Mryglod's interests over the last 25 years. 2010 Article From phase transitions to dynamics of liquids: on the 50-th anniversary of Ihor Mryglod / T. Bryk // Condensed Matter Physics. — 2010. — Т. 13, № 2. — С. 20101: 1-3. — Бібліогр.: 16 назв. — англ. 1607-324X http://dspace.nbuv.gov.ua/handle/123456789/32086 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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Foreword Foreword |
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Foreword Foreword Bryk, T. From phase transitions to dynamics of liquids: on the 50-th anniversary of Ihor Mryglod Condensed Matter Physics |
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The main idea of this Special issue of "Condensed Matter Physics" was to get together in one volume contributions from research fields that encompass I.Mryglod's interests over the last 25 years. |
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Article |
| author |
Bryk, T. |
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Bryk, T. |
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Bryk, T. |
| title |
From phase transitions to dynamics of liquids: on the 50-th anniversary of Ihor Mryglod |
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From phase transitions to dynamics of liquids: on the 50-th anniversary of Ihor Mryglod |
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From phase transitions to dynamics of liquids: on the 50-th anniversary of Ihor Mryglod |
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From phase transitions to dynamics of liquids: on the 50-th anniversary of Ihor Mryglod |
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From phase transitions to dynamics of liquids: on the 50-th anniversary of Ihor Mryglod |
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from phase transitions to dynamics of liquids: on the 50-th anniversary of ihor mryglod |
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Інститут фізики конденсованих систем НАН України |
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2010 |
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Foreword |
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http://dspace.nbuv.gov.ua/handle/123456789/32086 |
| citation_txt |
From phase transitions to dynamics of liquids: on the 50-th anniversary of Ihor Mryglod / T. Bryk // Condensed Matter Physics. — 2010. — Т. 13, № 2. — С. 20101: 1-3. — Бібліогр.: 16 назв. — англ. |
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Condensed Matter Physics |
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Condensed Matter Physics 2010, Vol. 13, No 2, 20101: 1–4
http://www.icmp.lviv.ua/journal
Foreword
From phase transitions to dynamics of liquids:
on the 50-th anniversary of Ihor Mryglod
Theoretical physics in Lviv has always been associated with the famous names of Marian
Smoluchowski, Stanislaw Ulam, Vasyl Milianchuk. In the 1960-1970-s a modern school of theoretical
physics in Lviv was founded mainly by efforts of Professor Ihor Yukhnovskii and his pupils. One
of the bright representatives of the modern school of theoretical physics in Lviv, Ihor Mryglod,
became a successor of I.Yukhnovskii and since 2006 has headed a leading academic institution in
Western Ukraine, the Institute for Condensed Matter Physics of National Academy of Sciences of
Ukraine.
Ihor Mryglod graduated in 1982 from Department of Physics of the Lviv State University and
was offered by Professor I. Yukhnovskii to join Lviv Division of statistical physics (LDSP) of the
Institute for Theoretical Physics of Ukrainian Academy of Sciences. At that time the LDSP was
known among the physicists first of all because of fundamental studies by I.Yukhnovskii on statis-
tical theory of interacting many-particle systems. Being closely related to a famous mathematician
and physicist Nikolai Bogolyubov, who was a founder of the Institute for Theoretical Physics in
Kiev and later headed the Joint Institute for Nuclear Research in Dubna, Russia, Ihor Yukhnovskii
during the 1970-1980-s accumulated in Lviv a group of young theoreticians, that organically became
a part of Bogolyubov’s school of theoretical physics. In the 1980-s the main focus of Yukhnovskii’s
research was on description of second order phase transitions within his original method of collec-
tive variables (CV) [1]. Within the framework of the CV method I.Yukhnovskii proposed a scheme
of description of second order phase transitions in phase space of CVs suggesting a division of
the reciprocal space into a set of shells and a successive integration out of the short-wavelength
fluctuations in corresponding shells, which led to a transformation of renormalization group (RG).
Under I.Yukhnovskii’s guidance Ihor Mryglod started his PhD work with a study of properties
of an approximate RG transformation for large values of a shell parameter s for n-component
isotropic model within the CV method. Solutions of the RG equations in the vicinity of a fixed
point were obtained in the form of asymptotic expansions on 1/s parameter and critical indices
were calculated. It was shown that in the region of intermediate values of s, the shell integration-out
c© T.Bryk 20101-1
http://www.icmp.lviv.ua/journal
can be performed in Gaussian approximation and the corresponding differential recurrent relations
were obtained.
Another problem focused on in I.Mryglod’s PhD work was a study of mechanisms of formation of
pre-transition clusters by approaching the second order phase transition using a method of Euler’s
equations. Some estimates of crossover temperature from high-temperature (effective mean-field
or single-particle) behavior to pre-transition regime were obtained, where a cluster of a new low-
temperature phase starts to play a leading role. In dynamics, this regime manifests as a formation
of central peak in the corresponding dynamic structure factor. A temperature dependence of the
crossover temperature on parameters of a generalized model of structural phase transition was
studied.
For the first time I.Mryglod performed calculations of universal (critical indices and universal
relations for critical amplitudes) and non-universal quantities (temperature of phase transition,
heat capacity, order parameter, susceptibility etc.), that characterize the phase transition in n-
component isotropic model using the method of approximate RG transformation. On this basis, the
common features and differences in critical behavior of systems of displacement and order-disorder
types were analyzed. The phase diagram was estimated for a generalized model of structural phase
transition.
Solutions of the three abovementioned problems formed the body of PhD thesis entitled “Appli-
cation of an approximate transformation of renormalization group to the study of critical behavior
of the n-component model of structural phase transition”, that was defended by Ihor Mryglod in
1988 at Kyiv University.
Big changes took place in the Soviet Union in 1989-1991-s, which also got reflected in academic
life of Ukraine. The national Academy of Sciences became more independent in forming its structure
and budget. In September 1990 in response to I.Yukhnovskii’s request, that was supported by
two famous physicists N.N.Bogoluybov and A.S.Davydov, the Academy set up an Institute for
Condensed Matter Physics (ICMP) in Lviv on the basis of LDSP of the Institute for Theoretical
Physics. The ICMP became the second academic institution of purely theoretical orientation in
Ukraine. Ihor Mryglod got appointed a scientific secretary of ICMP.
At that time the Iron Curtain was down, which made it possible to establish direct scientific
links between western and ukrainian researchers. In spring of 1992 I.Mryglod made a few-months
visit as an ÖAD fellow to Professor R.Folk at Johann Kepler University of Linz, Austria. That
visit to Linz initiated very fruitful and long-standing collaboration between ICMP and Professor
Folk’s group.
New directions of Ihor Mryglod’s research in the 1990-s became non-equilibrium statistical
mechanics and generalized hydrodynamics of liquids. Together with M.Tokarchuk he applied the
Zubarev’s method of non-equilibrium statistical operator to a consistent description of hydrody-
namic and kinetic processes in condensed matter. A real breakthrough in theoretical description of
collective dynamics in liquids turned out to be an approach of Generalized Collective Modes (GCM)
elaborated in 1994–1995 [3]. By contrast to a kinetic approach, developed earlier by I. de Schepper
and E.D.G. Cohen with coworkers [4], the GCM method was developed as an extension of hydrody-
namics by including some short-time orthogonal dynamic variables into treatment, which permitted
a systematic improvement of description of short-time behavior for time-dependent correlations in
addition to the standard long-time hydrodynamic correlations. The most important feature of the
GCM approach is in representation of all time correlation functions and the corresponding dy-
namic structure factors via a separable sum of contributions from generalized hydrodynamic and
non-hydrodynamic eigenmodes, that can exist in liquids [5].
The concept of the existence of non-hydrodynamic modes, that cannot survive in liquids on
macroscopic spatial and time scales, appeared to be very fruitful for a description of collective
dynamics beyond hydrodynamic regime. The theory of non-hydrodynamic optic modes [6], heat
waves [7] and structural relaxation [8] in liquids was constructed within the GCM approach. Over
the last fifteen years the GCM approach has become one of the most powerful methods for the
analysis of dynamic processes in liquids on macro- and microscopic spatial and time scales. The
GCM approach permitted to establish the main microscopic mechanisms of formation of collective
20101-2
On the 50-th anniversary of Ihor Mryglod
dynamics and transport processes in dense fluids and their mixtures [9], opened new possibilities
for the analysis of time correlation functions and generalized transport coefficients [10] in complex
disordered systems. The development of GCM approach was summarized in Habilitation thesis,
defended by I.Mryglod in 2000 at Lviv University [11].
Success of the generalized hydrodynamic description of pure and many-component liquids has
opened new perspectives for the exploration of dynamical processes in more complex systems, such
as magnetic fluids. Analytical expressions for time-correlation functions of a Heisenberg model
ferrofluid in homogeneous magnetic field were obtained in hydrodynamic limit and it was shown
how the sound excitations contribute to the “spin density-spin density” time-correlation function,
as well as the Landau-Placzek ratio for the dynamic structure factor of Heisenberg ferrofluid was
obtained [12]. Pioneering studies were performed by computer simulations of ferromagnetic phase
transition in a Heisenberg fluid [13] as well as new algorithms for molecular dynamics simulations of
spin liquids were elaborated [14]. I.Mryglod together with Yu.Rudavskii and M.Tokarchuk received
S.Pekar Award of the National Academy of Sciences of Ukraine in 2003 for the development of the
theory for dynamic properties and phase transitions in magnetic liquids.
In 2002 a new department of quantum-statistical theory of catalytic processes was set up at
ICMP, and I.Mryglod became the head of this department. Theoretical issues of catalytic processes,
microscopic description of surface phenomena, ionic systems, prediction of phase diagrams became
new topics in the spectrum of I.Mryglod’s studies. Among the most interesting results obtained
during the recent years were the studies on gas-liquid criticality in ionic fluids[15] and crossover
behavior in fluids with long-range interactions [16].
The main idea of this Special issue of “Condensed Matter Physics” was to get together in
one volume contributions from research fields that encompass I.Mryglod’s interests over the last
25 years. The Editorial Board of “Condensed Matter Physics” expresses sincere gratitude to all
I.Mryglod’s colleagues from Ukraine and abroad who accepted the invitation to this Special issue
in honor of the 50-th anniversary of Ihor Mryglod.
References
1. Yukhnovskii I.R., Phase Transition of the Second Order. Collective Variables Method. World Scientific,
Singapore, 1987.
2. Mryglod I.M., Application of an approximate transformation of renormalization group to study
of critical behavior of the n-component model of structural phase transition. Ph.D. Thesis, Kiev
University, 1988.
3. Mryglod I.M., Omelyan I.P., Tokarchuk M.V., Mol. Phys., 1995, 84, 235.
4. de Schepper I.M., Cohen E.G.D., Bruin C., van Rijs J.C., Montfrooij W., de Graaf L.A., Phys.
Rev. A, 1988, 38, 271.
5. Mryglod I.M., Condens. Matter Phys., 1998, 1, 753.
6. Bryk T., Mryglod I., J. Phys.: Condens. Matter., 2000, 12, 6063.
7. Bryk T., Mryglod I., Phys. Rev. E, 2001, 63, 051202.
8. Bryk T., Mryglod I., Condens. Matter Phys., 2008, 11, 139.
9. Mryglod I.M., Condens. Matter Phys., 1997, No. 10, 115.
10. Mryglod I.M., Omelyan I.P., Mol. Phys., 1997, 92, 913.
11. Mryglod I.M., Statistical theory of collective excitations in liquids: An approach of generalized
collective modes. Dr.Sci. Thesis, Lviv University, 2000.
12. Mryglod I., Folk R., Dubyk S., Rudavskii Y., Physica A, 2000, 277, 389.
13. Mryglod I.M., Omelyan I.P., Folk R., Phys. Rev. Lett., 2001, 86, 3156.
14. Mryglod I.M., Omelyan I.P., Folk R., Phys. Rev. Lett., 2001, 86, 898.
15. Patsahan O., Mryglod I., J. Phys.: Condens. Matter, 2004, 16, L235.
16. Patsahan O.V., Caillol J.-M., Mryglod I.M., Eur. Phys. J. B, 2007, 58, 449.
Taras Bryk
Institute for Condensed Matter Physics of the
National Academy of Sciences of Ukraine
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