http://www.bibsonomy.org/burst/user/statphys23/equationBibSonomy BuRST Feed for /user/statphys23/equation2008-08-21T04:16:52+02:00http://www.bibsonomy.org/bibtex/2fbf9edf2d04659a3f50ace0a4a169e0b/statphys23statphys232007-06-20T10:16:09+02:00dynamics topic-7 granular statphys23 molecular theory gases kinetic coefficients boltzmann restitution equation <span style="color:#555555;">N.V. <a href="http://www.bibsonomy.org/author/Brilliantov">Brilliantov</a> and T. <a href="http://www.bibsonomy.org/author/Poeschel">Poeschel</a> and W.T. <a href="http://www.bibsonomy.org/author/Kranz">Kranz</a> and A. <a href="http://www.bibsonomy.org/author/Zippelius">Zippelius</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyTranslations and Rotations Are Correlated in Granular Gases2007dynamics topic-7 granular statphys23 molecular theory gases kinetic coefficients boltzmann restitution equation In a granular gas of rough particles the axis of rotation is shown to be correlated with the translational velocity of the particles. The average relative orientation of angular and linear velocities depends on the restitution coefficients -- the parameters which characterize the dissipative nature of the collision [1,2]. Using the Boltzmann equation and pseudo-Liouville operator technique [1,3] we derive a simple analytical theory for these correlations. We also perform numerical simulations for a wide range of coefficients of normal and tangential restitution. Two different numerical methods were used: Direct simulation Monte Carlo (DSMC) [4] and event-driven molecular dynamics (MD). Surprisingly, the limit of smooth spheres was found to be singular: even an arbitrarily small roughness of the particles gives rise to orientational correlations. The results of the analytical theory are in a good agreement with the numerical simulations [5]. 1) N.V. Brilliantov and T. Poeschel, Kinetic Theory of Granular Gases (Oxford University Press, Oxford, 2004).\\ 2) T. Poeschel, and N.V. Brilliantov (Eds.), Granular Gas Dynamics, Lecture Notes in Physics, vol. 624, Springer (2003).\\ 3) T. Aspelmeier, M. Huthmann, and A. Zippelius, in Granular Gases, S. Luding and T. Poeschel (Eds), Lecture Notes in Physics vol. 425, Springer, Berlin, (2000), p. 680.\\ 4) T. Poeschel and T. Schwager, Computational Granular Dynamics (Springer, New York, 2005).\\ 5) N.V. Brilliantov, T. Poeschel, W.T. Kranz, and A. Zippelius, Phys. Rev. Lett., 98, (2007) 128001.http://www.bibsonomy.org/bibtex/2b9a607a6083a46124947f9a2ef42f285/statphys23statphys232007-06-20T10:16:09+02:00point group critical hopf topic-3 bifurcation equation out statphys23 complex oscillators dynamic renormalization noisy ginzburg-landau equilibrium coupled <span style="color:#555555;">T. <a href="http://www.bibsonomy.org/author/Risler">Risler</a> and J. <a href="http://www.bibsonomy.org/author/Prost">Prost</a> and F. <a href="http://www.bibsonomy.org/author/Julicher">Julicher</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyUniversal Critical Behavior of Noisy Coupled Oscillators2007point group critical hopf topic-3 bifurcation equation out statphys23 complex oscillators dynamic renormalization noisy ginzburg-landau equilibrium coupled We show that the synchronization transition of a large number of noisy coupled oscillators is an example for a dynamic critical point far from thermodynamic equilibrium. The universal behaviors of such critical oscillators, arranged on a lattice in a $d$-dimensional space and coupled by nearest neighbors interactions, can be studied using field theoretical methods. The field theory associated with the critical point of a homogeneous oscillatory instability (or Hopf bifurcation of coupled oscillators) is the complex Ginzburg-Landau equation with additive noise. We perform a perturbative renormalization group (RG) study in a $4-\epsilon$ dimensional space. We develop an RG scheme that eliminates the phase and frequency of the oscillations using a scale-dependent oscillating reference frame. Within a Callan-Symanzik RG scheme to two-loop order in perturbation theory, we find that the RG fixed point is formally related to the one of the model A dynamics of the real Ginzburg-Landau theory with an $O(2)$ symmetry of the order parameter. Therefore, the dominant critical exponents for coupled oscillators are the same as for this equilibrium field theory. This formal connection with an equilibrium critical point imposes a relation between the correlation and response functions of coupled oscillators in the critical regime. Since the system operates far from thermodynamic equilibrium, a strong violation of the fluctuation-dissipation relation occurs and is characterized by a universal divergence of an effective temperature. The formal relation between critical oscillators and equilibrium critical points suggests that long-range phase order exists in critical oscillators above two dimensions.http://www.bibsonomy.org/bibtex/2268992c81f0c024a85085ce438d68cd0/statphys23statphys232007-06-20T10:16:09+02:00molecular filling capillary topic-6 lucas-washburn dynamics equation statphys23 <span style="color:#555555;">D.I. <a href="http://www.bibsonomy.org/author/Dimitrov">Dimitrov</a> and A. <a href="http://www.bibsonomy.org/author/Milchev">Milchev</a> and K. <a href="http://www.bibsonomy.org/author/Binder">Binder</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyCapillary Rise in Nanopores: Molecular Dynamics Evidence for the Lucas-Washburn Equation2007molecular filling capillary topic-6 lucas-washburn dynamics equation statphys23 When a capillary is inserted into a liquid, the liquid will rapidly flow into it. This phenomenon, well studied and understood on the macroscale, is investigated by Molecular Dynamics simulations for coarse-grained models of nanotubes. Both a simple Lennard-Jones fluid and a model for a polymer melt are considered. In both cases after a transient period (of a few nanoseconds) the meniscus rises according to a square-root-of-time law. For the polymer melt, however, we find that the capillary flow exhibits a slip length, comparable in size with the nanotube radius R. We show that a consistent description of the imbibition process in nanotubes is only possible upon modification of the Lucas-Washburn law which takes explicitly into account the slip length. We also demonstrate that the velocity field of the rising fluid close to the interface is not a simple diffusive spreading.http://www.bibsonomy.org/bibtex/29db770b3e327cd9b24156428f3aceb2b/statphys23statphys232007-06-20T10:16:09+02:00state equation motors topic-1 thermodynamics szilard paradox one-molecule demon molecular statphys23 model maxwell <span style="color:#555555;">T. <a href="http://www.bibsonomy.org/author/Hondou">Hondou</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyEquation of state in a small system: Violation of an assumption of Maxwell's demon2007state equation motors topic-1 thermodynamics szilard paradox one-molecule demon molecular statphys23 model maxwell An equation of state for an ideal gas with a small number of particles is studied. The equation of state is a basis both for studies of Maxwell's demon paradox [since Szilard (1929), including Landauer's principle] and for the proper interpretation and modeling of one-molecule experiment in biophysics. It has been assumed, even for the studies in Maxwell's demon, conventional equation of state, $PV=nRT$ holds for systems of small number of particles (for review, see {\em Maxwell's Demon 2} by Leff and Rex, IOP Publishing, 2003). We study the validity of the equation of state in small systems toward the construction of one-molecule thermodynamics. We consider a one-dimensional piston in thermal equilibrium, where the dynamical variables are $N$ thermal particles and a movable piston on one side (Figure 1). In systems of small number of particles, coarse-grained variable, $P$ (pressure) in the equation of state is no longer well-defined. Thus we discuss the validity of the equation of state in the following form, $f X=N k_{\rm B} T$, in which $f$, $X$ are a mechanical force externally exerted on the movable piston and a distance between the bottom and the movable piston, respectively (Fig. 1). In order to discuss the validity of the equation of state, we first discuss the extreme case of one thermal molecule in the piston, where the total energy of the system is written as $E=\frac{p_{\rm t}^{2}}{2m} + \frac{p_{\rm p}^{2}}{2M} + f X$, where $m (p_{\rm t}) $ and $M (p_{\rm p})$ are the masses (momenta) of the thermal particle and the piston, respectively. To keep the system isothermal, a thermal wall is introduced. The particle is reflected with a positive random velocity according to Maxwell's velocity distribution at the bottom of the piston. One naively expects that the equation of state for one molecule should be obtained by replacing $N$ by $1$ in the reference equation $f X = N k_{\rm B} T$; namely $f X = k_{\rm B} T$. The extension of conventional thermodynamics into those of one molecule has been naively performed since Szilard (Z. Phys. {\bf 53} p.840, 1929) until now. We found through numerical simulation, however, that the equation of state for one molecule is in fact $f \langle X \rangle = 2 k_{\rm B} T $, where the angular brackets indicate an average value. This result is obviously different from that which is conventionally assumed. We obtained the same analytical result using the Master equation of the distribution function in a phase space, which consists of Liouville terms and collision terms. A stochastic boundary condition is applied for the system at one end, which corresponds to the thermal wall in the numerical simulation. From straightforward calculation, one obtains a stationary solution, $\rho (x, p_{\rm t}, X, p_{\rm p}) = \frac{f^2}{2 \pi (k_{\rm B} T)^3 \sqrt{mM}} \exp\{-(\frac{p_{\rm t}^{2}/2m + p_{\rm p}^2 /2M + f X }{k_{\rm B} T}) \} \theta (X-x) ,$ where $\theta$ is a Heaviside step function. From this equation, we again obtain the same equation of state as by the numerical simulation. The result is independent of the masses of both the thermal particle and the movable piston, which is in contrast to the result by Hatano-Sasa (Prog. Theor. Phys. {\bf 100} p.695, 1998). Although we introduced a thermal wall and, correspondingly, a stochastic boundary condition, one may obtain the same generalized result for any number of thermal particles, N, without applying such boundary conditions, but instead using conventional Gibbs' statistical mechanics. The result is found to be the same as the conventional equation of state in the thermodynamic limit ($N \rightarrow \infty$). Impact of our finding on the studies of Maxwell's demon (Szilard's and the followers', including Landauer's) and on one-molecule experiments in biophysics will be discussed in the conference.http://www.bibsonomy.org/bibtex/2b849bae458e0c31eacf3defa5eddf2b1/statphys23statphys232007-06-20T10:16:09+02:00equation statphys23 markov stochastic turbulence fokker-planck properties topic-5 processes <span style="color:#555555;">R. <a href="http://www.bibsonomy.org/author/Stresing">Stresing</a> and J. <a href="http://www.bibsonomy.org/author/Peinke">Peinke</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyStochastic analysis of turbulence2007equation statphys23 markov stochastic turbulence fokker-planck properties topic-5 processes We present a more complete analysis of measurement data of fully developed, locally isotropic turbulence by means of the estimation of Kramers-Moyal coefficients, which provide access to the joint probabiltiy density function of increments for n-scales [1]. In this contribution we report on new findings based on this technique and based on the investigation of many different flow data over a large range of Re numbers.\\ In particular, our contribution includes the following aspects: 1. A method to reconstruct from given data the underlying stochastic process in form of a Fokker-Planck equation, which includes intermittency effects, will be presented. 2. It is shown that a new length scale, $l_{mar}$, for turbulence can be defined, which corresponds to a memory effect in the cascade dynamics, and which is closely related to the Taylor micro-scale, $\lambda$. For length scales larger than $l_{mar}$, the complexity of turbulence can be treated as a Markov process [2]. 3. For longitudinal and transversal velocity increments we present the reconstruction of the two dimensional stochastic process equations, which shows that the cascade evolves differently for the longitudinal and transversal increments. A different ``speed'' of the cascade can explain the reported difference for these two components. The rescaling symmetry is compatible with the Kolmogorov constants and the von Karman equation and gives new insight into the use of extended self similarity (ESS) for transverse increments [3]. 4. We present first results from the analysis of data from non-isotropic flow situations and show how the cascade process and Markov properties for both longitudinal and transversal velocity increments change in these cases.\\ Literature: 1) Ch. Renner, J. Peinke, and R. Friedrich: Markov properties of small scale turbulence, J. Fluid Mech. 433, 383 (2001)\\ 2) St. Lueck, Ch. Renner, J. Peinke, and R. Friedrich: The Markov coherence length -- a new meaning for the Taylor length in turbulence, Phys. Lett., in press\\ 3) M. Siefert and J. Peinke: On a multi-scale approach to analyze the joint statistics of longitudinal and transverse increments experimentally in small scale turbulence, J. of Turbulence 7, (No 50) 1-35 (2006)http://www.bibsonomy.org/bibtex/28c054bd51e368635c9756bc1d113b895/statphys23statphys232007-06-20T10:16:09+02:00theory equation methods statphys23 liquid topic-6 montecarlo integral structure <span style="color:#555555;">D.L. <a href="http://www.bibsonomy.org/author/Cheung">Cheung</a> and L. <a href="http://www.bibsonomy.org/author/Anton">Anton</a> and M.P. <a href="http://www.bibsonomy.org/author/Allen">Allen</a> and A.J. <a href="http://www.bibsonomy.org/author/Masters">Masters</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyStructure of molecular fluids: hunting the bridge function2007theory equation methods statphys23 liquid topic-6 montecarlo integral structure The bridge function, $b(1,2)$, is an elusive quantity. It is a crucial ingredient for predicting liquid properties yet it is virtually an unknown quantity for non-spherical molecules. To remedy this situation we present novel Monte Carlo (MC) and Integral Equation Theory (IET) methodologies for its calculation [1]. We also, through Duh-Haymet (DH) scaling plots [2], test the hypothesis that $b(1,2)$ is a function of the indirect correlation function $\gamma(1,2)$. Results for a number of systems will be presented. In particular a systematic study $b(1,2)$ for hard spheroids with a range of aspect ratios will be made [1,3]. DH plots, direct comparison of $b(1,2)$ and $\gamma(1,2)$ will be used to test the universality of the hard spheroid bridge function. For most of the elongations studied, the relationship between $b(1,2)$ and $\gamma(1,2)$ resembles the hard-sphere case, but for fluids of thin hard platelets the behaviour is anomalous. Extension of previous work into mixtures and the nematic phase will also be discussed.\\ 1) D. L. Cheung, L. Anton, M. P. Allen, and A. J. Masters, Phys. Rev. E, 73, 061204, 2006 \\ 2) D. M. Duh and A. D. J. Haymet, J. Chem. Phys., 97, 7712, 1992 \\ 3) D. L. Cheung, L. Anton, M. P. Allen, and A. J. Masters, 'Structure of molecular fluids: closure relationships for hard spheriods', in preparationhttp://www.bibsonomy.org/bibtex/2d6bfa0d91ea39e6cf98dd3e37b74540a/statphys23statphys232007-06-20T10:16:09+02:00financial distributions topic-11 time communities series master rank-size ecological functions statphys23 equation population urban ditribution <span style="color:#555555;">G. <a href="http://www.bibsonomy.org/author/Cocho">Cocho</a> and R. <a href="http://www.bibsonomy.org/author/Mansilla">Mansilla</a> and G. <a href="http://www.bibsonomy.org/author/Martinez-mekler">Martinez-mekler</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyGeneric statistical distribution in finances and human and ecological communities2007financial distributions topic-11 time communities series master rank-size ecological functions statphys23 equation population urban ditribution Central limit theorems show that a collection of stochastic processes follow a reduced class of probability distributions. Such is the case for statistically independent variables leading to Gausssian and Levy distributions. On the other hand, the case of strongly correlated variables such as fluctuations in phase transitions give a power law behavior. We have found a ubiquitous distribution for population-rank data given by: $f(r)=Ae^{-dr}(N+1-r)^{b}/r^{a}$, where $r$ is the rank, $N$ the maximum value of $r$, $A$ a normalization factor and $a,b,d$ are parameters. In most of the cases we have found that d is close to zero. Here we show that a master equation, which generalizes Hubbell's death and birth ecological community approach [1,2], has as limiting probability distribution the above expression. We show that this distribution fits remarkably well ecological community and urban population data. In both cases the master equation suggests underlying population migration behaviors. The distribution also shows excellent agreement with financial time series data. However for this case the validity of our equations remains unclear. 1) Hubbell, D.P., A unified theory of biogeography and relative species abundance and its applications to tropical rain forests and coral reefs, Coral Reefs, volume 16, S9-S21 (1997).\\ 2) Volkov, I., Banavar J.R., Hubbell, S.P. and Maritan A, Neutral theory and relative species abundance in ecology, Nature, volume 424, 2035-1037 (2003).http://www.bibsonomy.org/bibtex/2779358d1c653072142ab6d5bf790300d/statphys23statphys232007-06-20T10:16:09+02:00structure surface equation adsorption density patterned statphys23 topic-7 polymer edwards <span style="color:#555555;">A.I. <a href="http://www.bibsonomy.org/author/Chervanyov">Chervanyov</a> and G. <a href="http://www.bibsonomy.org/author/Heinrich">Heinrich</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyTransfer operator formalism with applications to the adsorption of polymers onto chemically non-uniform surfaces.2007structure surface equation adsorption density patterned statphys23 topic-7 polymer edwards By developing and making use of the transfer operator formalism we theoretically investigate the adsorption of polymers onto chemically non-uniform surfaces. The developed approach makes it possible to solve the self-consistent field equations that describe the density structure of polymers adsorbed onto periodically and randomly patterned surfaces. We have calculated the polymer density excess near the patterned surface as a function of the typical size of the pattern-to-polymer gyration radius ratio, with the effect of the excluded volume taken into account. The obtained results are applied to the investigation of the polymer adsorption onto several host systems of practical importance, presented by the following two examples. The first example of the mentioned systems that has been in extensive experimental use is given by the periodic structure of aligned randomly oriented carbon nanotubes that provide a set of periodically distributed centers that adsorb polymers. The second example is the binary mixed brush, the recently developed self-adoptive material that changes its morphology in response to altering external conditions. By making use of the developed formalism, we quantitatively show that the relation between typical sizes of the surface patterns and polymers is the main factor that affects the polymer adsorption onto the above described surfaces. In the case of soft adsorbing surfaces given by the mixed brushes, we show that the competition between the depletion effect on the polymer structure in the interior of the brush and the binding interaction between the polymers and the brush surface leads to a rich adsorption-desorption behaviour of polymers. In this case, the reversible switching between different morphologies of the mixed brush proves can be effectively used to enhance or reduce the adsorption of polymers, depending on practical needs.http://www.bibsonomy.org/bibtex/2e676715358c4e65500abcd8deeb441f2/statphys23statphys232007-06-20T10:16:09+02:00topic-1 hecke model algebra qkz affine equation statphys23 loop <span style="color:#555555;">K. <a href="http://www.bibsonomy.org/author/Shigechi">Shigechi</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 July$A_k$ generalization of the $O(1)$ loop model on a cylinder2007topic-1 hecke model algebra qkz affine equation statphys23 loop We define and study the $A_{k}$ generalization of the $O(1)$ loop model on a cylinder. This model is a new hybrid generalization of the $O(1)$ loop model: defined by the affine Hecke algebra and with cylindric boundary conditions. First, we introduce a new class of the affine Hecke algebra which is characterized by the cylindric relations. We consider the spin representation of the affine Hecke algebra. The affine Hecke generator is obtained by twisting the standard Hecke generator by a diagonal matrix. Second, we consider the representation by the states of the $A_{k}$ generalized model. For this purpose, we introduce a novel graphical depiction, rhombus tiling with an integer on its face, to deal with the Yang-Baxter equation and $q$-symmetrizers. A state of the model is characterized by a path and constructed through the correspondence among an unrestricted path, a rhombus tiling and a word. The cylindric relations become clear by using the rhombus tiling. Finally, we solve the quantum Kniznik-Zamoldchikov (qKZ) equation at the Razumov-Stroganov point. This solution is identified with a special solution of the qKZ equation of the level $1+\frac{1}{k}-k$ constructed from a non-symmetric Macdonald polynomial. The sum rule for this model is written as the product of $k$ Schur functions.http://www.bibsonomy.org/bibtex/2df1dff1488ad4d7559c6ad7c659fe239/statphys23statphys232007-06-20T10:16:09+02:00transitions equations equation surface statphys23 layering many-phase topic-1 contour state model ising <span style="color:#555555;">A.G. <a href="http://www.bibsonomy.org/author/Basuev">Basuev</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyIsing Model in Half-space. Layering Transitions2007transitions equations equation surface statphys23 layering many-phase topic-1 contour state model ising The extension of Pirogov-Sinai theory is developed. Results applicable for bulk and surface phases of lattice models are proved, and state equation is constructed. The region of first-order phase transition is extended in external fields space to $\mathbb{C}^{\Phi },\Phi$ -- the phase set of a model. It is proved the next extension of Lee-Yang theorem: the partition functions with stable boundary condition have no zeros in external fields space $\mathbb{C}^{\Phi}.$ For Ising model in half-space with small values of temperature and mixing boundary condition it is proven for each external field $\mu $ the existence of the spin layer with the thickness $q(\mu)$ over the bottom boundary. In this layer the average of spin is approximately -1 and outside one is about +1. With the decreasing of the external field $\mu $ in points $\mu _{q}$ the thickness $q(\mu )$ changes stepwise with unit magnitude and $q(\mu )\rightarrow\infty$ when $\mu\rightarrow +0.$ In points $\mu_{q}$ there is the coexistence of two surface phases. The free surface energy is proven the piecewise analytical function in region Re $\mu>0$ and small values of temperature. It is considered also the model with the external arbitrary field $\mu _{0}$ in the zero-layer, the external field outside the zero-layer $\mu >0.$ In the latter case the phase diagram of layering transitions is also constructed (see figure 1, outside ABCD). The Antonov's rule is proved. Using the surface state equation the points $B_{0}$ and $B_{1}$ of coexistence phases $\{0,1,2\}$ and $\{0,2,3\}$ with the accuracy of $x^{7},x=\exp(-2\varepsilon)$ are constructed.http://www.bibsonomy.org/bibtex/23dda2bb12fa29801b783ef8fdd275397/statphys23statphys232007-06-20T10:16:09+02:00statphys23 expansion boltzmann h-theorem equation chapman-enskog hydrodynamics topic-1 <span style="color:#555555;">M. <a href="http://www.bibsonomy.org/author/Colangeli">Colangeli</a> and I.V. <a href="http://www.bibsonomy.org/author/Karlin">Karlin</a> and M. <a href="http://www.bibsonomy.org/author/Kroger">Kroger</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyFrom hyperbolic regularization to exact hydrodynamics for linear Grad System2007statphys23 expansion boltzmann h-theorem equation chapman-enskog hydrodynamics topic-1 The derivation of hydrodynamics from a microscopic description is the classical problem of physical kinetics. The Chapman-Enskog method derives the solution from the Boltzmann equation in the form of a series in powers of Knudsen number, where is the ratio between the particle mean free path and the length scale of variations of hydrodynamic fields. However, as first demonstrated by Bobylev for Maxwell’s molecules, even in the simplest case (one-dimensional linear deviation from global equilibrium), the Burnett and the super-Burnett hydrodynamics violate the basic physics behind the Boltzmann equation. Namely, the acoustic contributions at sufficiently short wave-lengths increase with time instead of decaying. Inspired by a recent hyperbolic regularization of Burnett’s hydrodynamic equations, we introduce a method to derive stable equations of linear hydrodynamics to any desired accuracy in Knudsen number, starting from a simple kinetic model – a thirteen Moments Grad System. We show that stability arises as interplay between two basic features of the resulting hydrodynamic equations, i.e. “hyperbolicity” and “dissipativity”.http://www.bibsonomy.org/bibtex/2d7e7daf3ad9126bff41de3d178a29f75/statphys23statphys232007-06-20T10:16:09+02:00function liquid density crystal equation nematic integral statphys23 topic-1 functional correlation pair theory <span style="color:#555555;">P. <a href="http://www.bibsonomy.org/author/Mishra">Mishra</a> and Y. <a href="http://www.bibsonomy.org/author/Singh">Singh</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyPair Correlation Functions in Nematics and the Density-Functional Theory of Freezing2007function liquid density crystal equation nematic integral statphys23 topic-1 functional correlation pair theory The freezing of a fluid of anisotropic molecules into a nematic phase is a typical example of a first-order phase transition in which the continuous symmetry of the isotropic phase is broken.In a nematic phase molecules are aligned along a particular but arbitrary direction so as to have a long range order in orientation while translational degrees of freedom remain disordered as in the isotropic fluid.It is shown that in the nematic phase there are two qualitatively different contributions to pair correlation functions;one that preserves rotational invariance and the other that breaks it and vanishes in the isotropic phase.The symmetry preserving part of the pair correlation passes smoothly without any abrupt change through the isotropic-nematic transition.We describe a method of solving the Ornstein-Zernike equation with a closure relation to get both the symmetry conserving and symmetry breaking parts of pair correlation functions.Using these correlation functions we construct a free energy functional to study the freezing transition and other properties of the ordered phase.The theory predicts accurately the isotropic-nematic transition in a system of anisotropic molecules and can be extended to study other ordred phases such as smectics and crystalline solids.http://www.bibsonomy.org/bibtex/23ac4612c53ad8caea069c822447f5a55/statphys23statphys232007-06-20T10:16:09+02:00lattice-boltzmann topic-3 aris-taylor statistics equation statphys23 random langevin dispersion beadpack analysis <span style="color:#555555;">R.S. <a href="http://www.bibsonomy.org/author/Maier">Maier</a> and D.M. <a href="http://www.bibsonomy.org/author/Kroll">Kroll</a> and H.T. <a href="http://www.bibsonomy.org/author/Davis">Davis</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulySimulations and Theory of Dispersion in Flow in Beadpacks2007lattice-boltzmann topic-3 aris-taylor statistics equation statphys23 random langevin dispersion beadpack analysis The flow of liquid through a cylindrical random beadpack is simulated using the Lattice-Boltzmann technique. Dispersion of tracer particles is simulated using the Langevin equation. In contradiction of conventional wisdom, we find that the longitudinal dispersivity is a strong function of the ratio R/d, where R is the radius of the cylinder and d is the diameter of the beads, even beyond R/d values of 50. With the Aris-Taylor analysis of the convective dispersion equation, we are able to show that this effect arises from the rapidly varying boundary layer near the wall of the cylinder. The reason the radius dependence of the dispersion has not received much attention is that in most beadpack experiments the dispersive flow is no fully developed. We give the criteria for fully developed flow in terms of R/d, flow rate and time.http://www.bibsonomy.org/bibtex/22c70e9bb3e86b52c2f4df059ed6edca8/statphys23statphys232007-06-20T10:16:09+02:00moment topic-7 equation hamburger granular gas statphys23 conditions boundary boltzmann problem equations <span style="color:#555555;">A.J. <a href="http://www.bibsonomy.org/author/Karwowski">Karwowski</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyBoltzmann Gas of Inelastic Spheres. Moment Equations2007moment topic-7 equation hamburger granular gas statphys23 conditions boundary boltzmann problem equations We describe a hierarchy of formal expansions that represent the Fourier transform F{f} of a solution f(v) of the Boltzmann equation for granular gas with constant coefficient of restitution. The approximations are based on a solution of the Hamburger moment problem where one wishes to recover f(v) knowing finite sequences of its first moments. In particiular, we describe how to construct a hierarchy of weighted power series representations for F{f} that depend on the moments of f(v) alone. The constructed expansions can be Fourier inverted term by term, to recover the series representation of f. The first two representation correspond to the Maxwellian and Gaussian expansions. They have been exploited by Grad, Jenkins and Levermore in their study of the elastic and inelastic versions of the Boltzmann equation. The next representation has a weight that depends on the first 13 moments of the Boltzmann density f and it yields modified Grad's 13 moment equations for granular gas. The principal tools in deriving the moment equations are the exact Fourier transform of the inelastic, nonlinear Boltzmann equation and the finite version of the Hamburger moment expansion. We also show that it is possible to derive boundary conditions for the moments from the micriscopic boundary conditions for the Boltzmann equation itself.http://www.bibsonomy.org/bibtex/23cf9dc85ba01b9e44e1f75a312c2c60e/statphys23statphys232007-06-20T10:16:09+02:00granular boltzmann systems gas dissipative topic-7 statphys23 equation <span style="color:#555555;">P. <a href="http://www.bibsonomy.org/author/Viot">Viot</a> and J. <a href="http://www.bibsonomy.org/author/Piasecki">Piasecki</a> and J. <a href="http://www.bibsonomy.org/author/Talbot">Talbot</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyVariety of shape of the velocity distribution of a granular planar rotator in a thermalized bath2007granular boltzmann systems gas dissipative topic-7 statphys23 equation Granular gases are systems in which macroscopic particles lose a fraction of their kinetic energy at each collision. When an external energy supply is continuously brought to the particles, the system may reach a non-equilibrium steady state, whose properties differ significantly from those of thermal equilibrium (breakdown of the equipartition, non-gaussian statistics, modified hydrodynamics). All those characteristics are intimately related to the dissipative nature of collisions. The studies of granular gases have focused mainly on spherical particles. However, anisotropy for granular particles is ubiquitous in nature, and one expects that the anisotropy introduces additional effects. We analyze, both numerically and analytically by means of the Boltzmann equation, the kinetics of a granular planar rotator with a fixed center undergoing inelastic collisions with bath particles. The angular velocity distribution displays a large variety of behavior: when the mass of the rotator is much larger than the mass of the bath particles, a perturbative method allows to solve the Boltzmann equation and shows that the distribution is quasi-Gaussian in this Brownian limit. Conversely, in the limit of an infinitely light particle, an exact solution is obtained when the coefficient of restitution is equal to zero. Intermediate cases are obtained by a precise numerical method showing strong deviations to gaussian behavior.http://www.bibsonomy.org/bibtex/2c592943a260c6be009866087abd53417/statphys23statphys232007-06-20T10:16:09+02:00phase diagram critical transition point state equation potential liquid-liquid intermalocular topic-2 statphys23 <span style="color:#555555;">Y.U.D. <a href="http://www.bibsonomy.org/author/Fomin">Fomin</a> and V.N. <a href="http://www.bibsonomy.org/author/Ryzhov">Ryzhov</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyLiquid – liquid phase transitions: a generalized van der Waals theory2007phase diagram critical transition point state equation potential liquid-liquid intermalocular topic-2 statphys23 Despite the growing interest to the possible polimorphic phase transitions inliquids and glasses (see, for example, for the recent reviews [1]) the nature of different phases which can be found in dense (and possibly metastable) liquids is still puzzling. In recent years experimental evidences of such features of phase diagram as liquid-liquid transitions, polyamorphism, etc appeared for a wide range of systems including water, Si, I, Se, S, C, P, etc [1]. The complexity of the phase diagrams in these substances may be a result of complex interactions depending on the intermolecular orientations. At the same time exploring the possibility that simple fluids interacting through isotropic potentials may exibit the similar behavior represent a serious challenge for theorists.\newline The possibility of the existence of a liquid-liquid phase transition drastically depends on the shape of the interparticle potential. Recently, it was shown that the purely repulsive step potential [2] is sufficient to explane a liquid-liquid phase transition. The repulsive step potential is a potential which in addition to the hard sphere core has a repulsive soft core of a larger radius.\newline Note that the second phase transition, corresponding to the liquid-gas transformation, appears when tail is appended to the repulsive step potential [3]. In this talk in the framework of the thermodynamic perturbation theory for fluids we show how the phase diagram of a system of particles interacting through an isotropic potential with an attractive well and a repulsive component consisting of a hard core plus a finite shoulder, where a liquid-liquid phase transition exists in addition to the standard gas-liquid phase transition, changes by varying the parameters of the potential. We show that existence of the liquid-liquid transition is determined by the interplay of the parameters of the potential and the structure of a reference liquid. We also discuss the application of the generalized van der Waals theory to more realistic potentials. \newline It is necessary to emphasize that liquid-liquid transition is metastable with respect to freezing for all considered parameters. The work was supported by the Russian Foundation for Basic Research (Grant No 05-02-17280) and NWO-RFBR Grant No 047.016.001 \newline 1) Brazhkin, S.V. Buldyrev, V.N. Ryzhov, and H.E. Stanley [eds], New Kinds of Phase Transitions: Transformations in Disordered Substances [Proc. NATO Advanced Research Workshop, Volga River] (Kluwer, Dordrecht,2002).\newline 2) V.N.Ryzhov, S.M.Stishov Phys.Rev. E 74, 010201 (2003)\newline 3) Yu.D. Fomin, V.N. Ryzhov and E.E. Tareeva Phys. Rev. E 74, 041201 (2006)\newlinehttp://www.bibsonomy.org/bibtex/2a1e4b01918ccdee9528543afbdfb4c0b/statphys23statphys232007-06-20T10:16:09+02:00methods topic-3 statphys23 nonequilibrium boltzmann problems equation kinetic <span style="color:#555555;">V.V. <a href="http://www.bibsonomy.org/author/Aristov">Aristov</a> and A.A. <a href="http://www.bibsonomy.org/author/Frolova">Frolova</a> and S.A. <a href="http://www.bibsonomy.org/author/Zabelok">Zabelok</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyProblems of the Nonuniform Relaxation and Description of Complex Nonequilibrium Structures2007methods topic-3 statphys23 nonequilibrium boltzmann problems equation kinetic Some new possibilities of the spatially nonuniform relaxation problem (see [1, 2]) for the Boltzmann equation and for kinetic relaxation models are considered. This problem intends to describe the nonequilibrium structure in the open system as a result of the operation of relaxation processes and advection processes in gases (or fluids). Methods of direct solving the Boltzmann equation or kinetic models are used to study these new types of the problems. The developed hybrid method [3] which combines solution of the kinetic and continuum equations (in different zones of a flow) can be also applied. This approach now is being developed for multicomponent gases. For simple 1D cases for Maxwell molecules an analytical method of expansion on a small parameter (the inverse Mach number) can be used. This problem deal with the nonequilibrium phenomena on a scale of the characteristic length, which is the mean free path (this scale can be large for a low speed flow). There is no assumption of the local equilibrium as in the thermodynamics of irreversible processes. Study of 1D problem (for which the nonequilibrium boundary condition is accepted for the semi-infinite region) revealed interesting characteristics of the structures. The heat flux has the same sign as the temperature gradient. This denotes that, e.g. positive heat flux from the boundary with the nonequilibrium condition leads to increase of temperature in the flow. The behaviour of the nonequilibrium entropy, i.e. - H-function, is also investigated. Under some conditions the entropy can decrease downflow. Possible application of these nontraditional heat properties for constructing the thermal micro-scale devices is suggested, namely, the scheme of the micro-refrigerator (with a small efficiency) without mechanical parts is proposed. More complex structures can be obtained for gas mixtures: the 1D and 2D problems with nonequilibrium boundary conditions are studied. The influence of the nonequilibrium conditions on the spatial structures is determined. One can change the character of the spatial structures by changing the nonequilibrium distribution functions for gas components at the boundaries. The perspectives of development of this problem for multi-component mixtures with chemical reactions are discussed. It is supposed that the model of nonuniform relaxation could simulate properties of complex natural objects, because biological structures can be treated as open flux systems. Acknowledgements\\ This work was supported by the Program No 15 of the Presidium of the Russian Academy of Sciences. References\\ 1. Aristov, V.V., Phys. Letters A, 250 (1998) 354-359.\\ 2. Aristov, V.V., Direct methods for solving the Boltzmann equation and study of nonequilibrium flows, Kluwer Academic Publishers, Dordrecht, 2001.\\ 3. V.I.Kolobov, R.R.Arslanbekov, V.V.Aristov, A.A.Frolova, S.A.Zabelok. J. Comput. Physics. 223 (2007) 589-608.http://www.bibsonomy.org/bibtex/269c0aeef64b1004afbe7674f13f50ccb/statphys23statphys232007-06-20T10:16:09+02:00equation statphys23 boltzmann topic-1 relaxation time mobility approximation <span style="color:#555555;">L. <a href="http://www.bibsonomy.org/author/Giuggioli">Giuggioli</a> and P.E. <a href="http://www.bibsonomy.org/author/Parris">Parris</a> and V.M. <a href="http://www.bibsonomy.org/author/Kenkre">Kenkre</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyVariational Determination of a Relaxation Time to Equilibrium in the Boltzmann equation2007equation statphys23 boltzmann topic-1 relaxation time mobility approximation The Boltzmann equation, the work-horse of transport calculations in gas dynamics, solid state physics, and related branches of investigation, is essential to the analysis of transport coefficients such as viscosity, electrical mobility, thermal conductivity, Peltier coefficients and Lorenz numbers. The equation comes in two forms, one linear in the probability distribution (or density) $f_{k}(t)$, the other bilinear. The former is the so-called linearized Boltzmann equation, also known, in other contexts, as the gain-loss equation, and it is the subject of our study here: \begin{equation} \frac{df_{k}\left( t\right) }{dt}=\sum_{k^{\prime }}\left[ Q_{kk^{\prime }}f_{k^{\prime }}\left( t\right) -Q_{k^{\prime }k}f_{k}\left( t\right) % \right]. \label{Boltzmann} \end{equation} Here $k$ represents generally a quantum mechanical state and $Q_{k^{\prime }k}$ is the transition rate from state $k$ to state $k^{\prime }$ and is independent of the $f$'s. Although linear, Eq. (1) is not easily solved because of the summation in $k$-space which in the continuum limit would make (1) an integral equation. There is, however, an approximation, traditionally used in many, if not all, practical applications, that allows one to avoid solving Eq. (1) numerically: the so-called relaxation time approximation (RTA). In its most common form, the RTA consists of replacing the actual evolution in Eq. (1) by \begin{equation} \frac{df_{k}\left( t\right) }{dt}+\frac{f_{k}\left( t\right) -f_{k}^{th}}{% \tau _{k}}=0, \label{relax} \end{equation} where $\tau_{k}$ is called the relaxation time and $f_{k}^{th}$ is the thermal form to which the distribution tends at long times in the absence of driving forces. Although there are variants, the simplest and most common prescription for the relaxation time that one finds in the literature is \begin{equation} \frac{1}{\tau _{k}}=\sum_{k^{\prime }}Q_{k^{\prime }k}. \label{tau} \end{equation} Despite its common use, the RTA suffers from the main drawbacks that it is independent of initial conditions as well as for not conserving probability at all times. Using techniques from the calculus of variations we derive a variational principle for the Boltzmann equation and use it to obtain the approximation \begin{equation} f_{k}\left( t\right) =f_{k}^{th}+a_{k}e^{-t/\tau} \label{ansatzvar} \end{equation} with $$ 1/\tau=\sqrt{\frac{\sum_{k}\left(\sum_{k^{\prime}\neq k}Q_{k^{\prime }k}f_{k}(0)-\sum_{k^{\prime}\neq k}Q_{kk^{\prime}}f_{k^{\prime }}(0)\right)^{2}/f_{k}^{th}}{\sum_{k}\left(f_{k}(0)-f_{k}^{th}\right) ^{2}/f_{k}^{th}}}. \label{varrate} $$ It is obvious that Eq. (4) conserves probability at all times and allows us to extend the standard RTA using relaxation times that depend on the initial distribution. Tests of the approach on a calculation of the mobility of a particle moving in a 1D tight binding band indicate that our analysis provides a better approximation than the standard RTA. Reference: L. Giuggioli, P.E. Parris and V.M. Kenkre, J. Phys. Chem. B 110, 18921 (2006).http://www.bibsonomy.org/bibtex/2b97e0a5ce39389cd3a7203b2281580df/statphys23statphys232007-06-20T10:16:09+02:00statphys23 topic-6 cavitation water metastability limit state equation <span style="color:#555555;">E. <a href="http://www.bibsonomy.org/author/Herbert">Herbert</a> and J. <a href="http://www.bibsonomy.org/author/Dubail">Dubail</a> and S. <a href="http://www.bibsonomy.org/author/Balibar">Balibar</a> and F. <a href="http://www.bibsonomy.org/author/Caupin">Caupin</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyCavitation and equation of state in water at negative pressure2007statphys23 topic-6 cavitation water metastability limit state equation We use short acoustic bursts to quench liquid water at negative pressures [E.~Herbert \textit{et al.}, \textit{Phys. Rev. E}, 2006, \textbf{74}, 041603 (1-22)]. The acoustic wave is focused, allowing the study of a small volume of liquid, far from any surfaces. We find a well defined threshold for the nucleation of bubbles (cavitation). Two methods of calibration agree to give a cavitation pressure which increases monotonically from -26 MPa at 0\textsuperscript{o}C to -17 MPa at 80\textsuperscript{o}C. These values are among the most negative reported for water, but fall far from the theoretical expectation (around -120 MPa at 40\textsuperscript{o}C) which is thought to have been reached in one experiment with another method. We propose two alternative explanations. On one hand, cavitation in our experiment could be heterogeneous, occuring on impurities. We have performed a careful check of reproducibility and a detailed data analysis to investigate this possibility. On the other hand, the discrepant results can be brought into agreement if the equation of state of water at negative pressure is different from what is currently accepted. We describe our preliminary measurements to check this issue.http://www.bibsonomy.org/bibtex/2fd5c062707bd73e82959c2d190470639/statphys23statphys232007-06-20T10:16:09+02:00ginzburg-landau topic-5 complex oscillatory dynamics phase media statphys23 equation <span style="color:#555555;">N.T. <a href="http://www.bibsonomy.org/author/Tsukamoto">Tsukamoto</a> and H.F. <a href="http://www.bibsonomy.org/author/Fujisaka">Fujisaka</a> and K.O. <a href="http://www.bibsonomy.org/author/Ouchi">Ouchi</a> </span><em>Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, </em><em>Genova, Italy, </em><em>9-13 July2007. </em>Wed Jun 20 10:16:09 CEST 2007Genova, ItalyAbstract Book of the XXIII IUPAP International Conference on Statistical Physics9-13 JulyAnalysis of renormalized phase dynamics in oscillatory media2007ginzburg-landau topic-5 complex oscillatory dynamics phase media statphys23 equation The complex Ginzburg-Landau equation (CGLE), \begin{equation} \dot{\psi}=\psi+(1+ic_1)\nabla^2\psi-(1+ic_2)|\psi|^2\psi, \end{equation} is a universal equation which describes slow variation in systems near the supercritical Hopf bifurcation. Depending on the paramter values, Eq.~(1) exhibits several dynamics; homogeneous oscillation, plane wave, spiral and spatio-temporal chaos (defect-mediated and phase turbulences). It is known that the phase reduction method is a powerful tool to investigate some types of dynamical state like the phase turbulence. However, when the amplitude plays an important role (e.g., defect-mediated turbulence), the method is invalid and the dynamics cannot be described by only the phase variable. The aim of this study is to show that in spite of this fact, the behaviors observed in CGLE can be described by only the phase dynamics appropriately constructed. We construct a mapping model based on CGLE, \begin{equation} \psi_{n+1}(\mbox{\boldmath $x$})=\mathcal{L}F(\psi_n(\mbox{\boldmath $x$})), \end{equation} where $\mathcal{L}=e^{(1+ic_1)\nabla^2}$ is a linear operator, and $F(\psi)=|\psi|^{-(1+ic_2)}\psi$ for $\psi\ne 0$ and $F(\psi)=0$ for $\psi=0$. This mapping model has the same features in both the spatial coupling and the isochron structure as CGLE. In this presentation, we will show the results of analysis of the dynamics (2) by both numerical simulation and analytical treatment. It is found that Eq.~(2) reproduces the dynamics of CGLE. Furthermore, it is proved that the dynamics (2) can be described by only the renormalized phase $\theta_n=\arg\psi_n-c_2\ln |\psi_n|$ and the phase singular point ($\psi_n=0$). These results suggest that the CGLE dynamics can be described by the renormalized phase variable even if the amplitude component plays an important role in the dynamics.