Posters

Pre-poster Session

There will be a pre-poster session, when each poster can be briefly presented by one of the authors (the name of the presenting author should be underlined in the abstract). The pre-poster session will run on a "3 by 3" basis: each contributor to the pre-poster session will have an opportunity to talk for up to 3 (three) minutes and present up to 3 (three) slides. No discussion is supposed to take place during the pre-poster session.

Posters size

The maximum size of a poster is the dimension of an A0 sheet (portrait).

Posters abstracts

Anne-Florence Bitbol
Université Paris Diderot, Paris 7, France

Fluctuations of the Casimir-like force between two inclusions in a biological membrane
Anne-Florence Bitbol and Jean-Baptiste Fournier

Although Casimir forces are inseparable from their fluctuations, little is known about these fluctuations in soft matter systems. We use the membrane stress tensor to study the fluctuations of the membrane-mediated Casimir-like force. This method enables us to recover the Casimir force between two inclusions and to calculate its variance. We show that the Casimir force is dominated by its fluctuations. Furthermore, when the distance d between the inclusions is decreased from infinity, the variance of the Casimir force decreases as -1/d2. This distance dependence shares a common physical origin with the Casimir force itself.

References:
[1] A.-F. Bitbol, P. G. Dommersnes, and J.-B. Fournier, Phys. Rev. E 81, 050903(R) (2010)

Przemysław Chełminiak
Adam Mickiewicz University, Poznań, Poland

Evolution of scale-free networks without preferential linking

Since the seminal work published by A.-L. Barabasi and R. Albert in 1999, it has become evident that many systems existing in Nature self-organize into scale-free networks. A large-scale property of these networks is a connectivity distribution of their nodes, that is the probability P(k) that a given node interacts directly with k others. Intriguingly, for a diverse range of many real webs this probability follows the power law distribution with the characteristic exponent, usually ranging between two and four. To explain this particular phenomenon, the random network model has been established, which incorporates two essential mechanisms of continuous growth and preferential attachment of incoming nodes. However, as we show in this poster presentation the self-organization of the scale-free networks is also possible without the preferential linking. To this end we use the model of random walks on fractal lattices.

Vincent Démery
University of Toulouse, France

Perturbative methods for diffusion in fluctuating fields
V. Démery and D. S. Dean

Diffusion in quenched random potentials has been extensively studied. Here we investigate diffusion in time dependent fields where the diffusion can be coupled to the fluctuating field. Such diffusion can be active, if the particle affects the field, which is the case for a protein coupled to membrane curvature; it can also be passive, if the particle does not affect the field, as is seen for a tracer diffusing in a turbulent flow or a random potential field.

In the limit of a weak coupling between the particle and the field, we study how the field modifies the diffusion constant in these two cases. We present three different methods:
- Kubo formula: this method uses equilibrium properties and only applies to active diffusion.
- Probability density function approach: it is very similar to the method already applied for diffusion in quenched potential, and is only valid for passive diffusion.
- Path-integral approach: the effective diffusion equation is treated via a path-integral approach, and can deal with both diffusion types.

The general accuracy of these approaches are validated via numerical simulations. In general, for active diffusion the coupling with the field always slows down the particle, whereas for passive diffusion, the effect of the field depends on its speed of evolution: the particle slows down in a slow field, and speeds up in a fast field.

Ulisse Ferrari
Università di Roma "La Sapienza", Italy

On the decay exponents of mode coupling theory
U. Ferrari, F. Caltagirone, L. Leuzzi, G. Parisi , T. Rizzo

An important prediction of Mode-Coupling-Theory (MCT) is the relationship between the decay exponents in the β regime:

Γ²(1−a)

Γ(1−2 a)

Γ²(1+b)

Γ(1+2 b)

=λ

In the original structural glass context this relationship follows from the MCT equations that are obtained making rather uncontrolled approximations. As a consequence it is usually assumed that the relationship between the exponents is correct while λ has to be treated like a tunable parameter. On the other hand it is known that in some mean-field spin-glass models the dynamics is precisely described by MCT. In that context λ can be computed exactly, but again its computation becomes difficult when we consider more complex models including finite-dimensional ones.
What was unknown up to now was the physical meaning of λ, i.e. its connection to physical observables. Recently, it has been shown that λ is related to the static replicated Gibbs free energy which, in its simplest form reads

G(Q) = τ/2

∑
αβ

(Q_αβ)² +w₁/3!

∑
αβγ

Q_αβ Q_βγ Q_γα+ w₂/3!

∑
αβ

(Q_αβ)³ + ...

through the following simple formula

λ = w₂/w₁

The coefficients w₁ and w₂ can also be related to physical observables which are indeed measurable in real experiments or numerical simulations. We have tested through analytical computations the connection between the MCT exponents a and b and the cubic cumulants w₁ and w₂ in many different mean field models. We have compared our results from static computations with analytical results derived in a purely dynamical framework, when available, and with results from numerical simulations otherwise.
When dynamical exact results exist they coincide with ours, as in the case of spherical p-spin or the SK model and, when only simulations are available, there is still good agreement despite the dynamical exponents are quite difficult to determine from numerical data.
Our current work is focused on verifying this relation in non-fully-connected models and structural glasses, but computations in this case are more involved and still in progress.

Maria Isabel Garcia de Soria
Universidad de Sevilla, Spain

Breakdown of hydrodynamics in the inelastic Maxwell model of granular gases
M. I. Garcia de Soria, J.J. Brey, and P. Maynar

Both the right and left eigenfunctions and eigenvalues of the linearized homogeneous Boltzmann equation for inelastic Maxwell molecules corresponding to the hydrodynamic modes are calculated. Also, some non-hydrodynamic modes are identified. It is shown that below a critical value of the parameter characterizing the inelasticity, one of the kinetic modes decays slower than one of the hydrodynamic ones. As a consequence, a closed hydrodynamic description does not exist in that regime. Some implications of this behavior on the formally computed Navier-Stokes transport coefficients are discussed.

Krzysztof Gontarek
Adam Mickiewicz University, Poznań, Poland

Ising-like model of financial markets
Krzysztof Gontarek and Adam Lipowski

Ising models are widely used to model financial markets. This is because local and global factors, that are crucial for the functioning of financial markets can be easily taken into account in this model.
In our work we show that stylized facts characteristic for financial markets could be reproduced using Ising-like model. In the model we take into account the agents (i.e., spins) imitation tendency, individual decisions, influence of external news and market trends (herding propensity). We examine fat tails distributions and relate a phase transition of the Ising model with crashes of financial markets.
In our approach we compare the strength of the market trend, considered as a sum of individual agents' opinions with the importance of imitation among neighbours (opinions of selected agents). In addition we try to find attributes of agents that would make it possible to identify "fundamentalist" and "noise" traders as classified in the investment theory.

Tomasz Gubiec
University of Warsaw, Poland

What is the true origin of autocorrelations on a stock exchange?
Tomasz Gubiec and Ryszard Kutner

We observed, in the context of the stock exchange trading, the backward price jumps of stocks. These jumps are a reminiscence of such a bid-ask bounce phenomenon where consecutive jumps have the same or almost the same lengths, but opposite signs that is, there are backward correlated.

To model these backward price jumps we extended the Continuous-Time Random Walk formalism in order to include the negative feedback, e.g. defined by one step memory. In the frame of our exactly solvable approach we describe the stochastic evolution of a typical share price on a stock exchange within a high-frequency time scale.

Our approach was validated by well agreement of the theoretical velocity autocorrelation function with its empirical counterpart. The agreement is even better if we used our formalism containing the two step memory. Notably, the parameters of the model were obtained from separated data sets, so as the comparison of the theoretical velocity autocorrelation function with corresponding empirical curve has no free parameters.

References:
[1] T. Gubiec, R. Kutner: Backward jump continuous-time random walk: An application to market trading, Phys. Rev. E 82, 046119 (2010).

Timo Ikonen
Aalto University School of Science and Technology, Finland

Accelerated computation of rare events with path integral hyperdynamics
T. Ikonen, J. Shin, L.Y. Chen, S.-C. Ying, T. Ala-Nissila

We employ the recently proposed Path Integral Hyperdynamics (PIHD) method to study a variety of systems. First, we investigate the numerical properties of the method using the diffusion of Brownian particles in a 1D periodic potential as a test bench. We observe that the computational efficiency obtains a maximum value at finite strength of the bias force due to the increased error in path sampling induced by the bias. We also derive a simple mathematical model that quantitatively explains the observed behavior. In addition, we study the case of a Brownian particle driven by an external ac-force with amplitude A and frequency f. Here we use the PIHD method for parallel resampling of multiple parameter values (A,f) from a single simulation run. Finally, we consider the Kramers escape problem for polymers, where we extend the PIHD method for many-particle systems with internal degrees of freedom. We show that the method also works for many-particle systems with entropic activation barriers and obtain results that could be used in efficient separation of biopolymers.

Maciej Jagielski
University of Warsaw, Poland

Comparison of households' income in Poland with European Union and United States ones
Maciej Jagielski, Ryszard Kutner, Marek Pączkowski

We compared the empirical data for annual income of Polish and European households as well as annual income of individuals in United States (e.g. for years 2006 and 2008) with predictions of the most popular theoretical models. Particularly good agreements with Pareto distribution and predictions of the Yakovenko model were obtained. For the low society class well agreement with prediction of the cumulative exponential distribution was gained. However, it turned out that the cumulative distribution of annual income of Polish households can be described quite well by the Generalised Lotka-Volterra model. We also presented our generalisation of the Yakovenko model which allows to describe empirical cumulative distribution of annual income in entire regime that is, income of low, middle and rich classes.

Marcin Kędzierski
Institute of Fundamental Technological Research, Polish Academy of Science, Warsaw, Poland

Precise multipole method for calculating many-body hydrodynamic interactions in a microchannel
M. Kędzierski and E. Wajnryb

We introduce a novel and precise method for computing many-body hydrodynamic interactions in a cylindrical microchannel. The method is generic in the sense that we can easily change the radius and the character of particles (hard spheres, droplets, permeable spheres, etc.). These features are not available in any of the existing methods. Comparison with the available results validates our method. In particular we obtain excellent agreement with the analytically known expression for the single particle friction coefficient. Additionally we observe negative hydrodynamic coupling for finite particles which are consistent with the recently reported effect for point particles. As an example we compute the velocities of polymeric chains of particles in parabolic flow and compare them to unbounded space. The method will be helpful in the understanding of physical and physicochemical processes in a wide range of bio-, geophysical, and microfluidic systems.

Tomasz Kozioł
Adam Mickiewicz University, Poznań, Poland

Temperature driven changes of the graphite systems
Tomasz Kozioł, Małgorzata Śliwińska-Bartkowiak, Ravi Radhakrishnan

We report the simulation study of the graphite system done using the Car-Parrinello molecular dynamics method [1]. Total energy of the system, its electronic free energy and distance between graphene sheets [2] temperature dependencies have been estimated. Results of simulations for constant box volume and for constant pressure have been also compared. The similar calculations will be performed for nano-graphite systems activated carbon fibers (ACF).

References:
[1] R. Car and M. Parrinello, Phys. Rev. Lett. 55, 2471 (1985)
[2] Kirby, R.K., Hahn, T.A. and Rothrock, B.D., American Institute of Physics Handbook, pp. 4-119 to 4-142 (1972)

Marzena Kozłowska
University of Warsaw, Poland

Empirical symptoms of critical slowing down on financial markets
M. Kozłowska, T. Gubiec, R. Kutner, Z. Struzik

The question of whether the early-warning signals are present in financial markets continues to fascinate both the research community and the general public. Interestingly, such early-warning signals have recently been identified and explained to be a consequence of a catastrophic bifurcation (CB) phenomenon observed in multiple physical systems, e.g. in ecosystems, climate dynamics and in medicine (epileptic seizure and asthma attack). In the present work we provide an analogical, positive identification of such phenomenon in the context of a well-defined daily bubble on a financial market typical of stock exchange of small and middle to large capitalisations. This we obtained by considering and verifying a list of indicators (following from CB) of a WIG (Warszawski Indeks Giełdowy) bubble on the Warsaw Stock Exchange, induced by the recent worldwide financial crisis. Technically, we focus on the largest relatively narrow peak (of one quarter width) in the time-dependent variance of detrended index WIG. In comparison with other peaks, this peak looks like a spike. By using several indicators within the range of the spike, such as: (i) a sudden strong increase in the variance and bimodal structure of the accumulative variance, (ii) linear indicators, such as the lag-1 autocorrelation function and AR(1) coefficient, both approaching their maximal values, (iii) the corresponding behavior of recovery rate and time, (iv) reddened power spectra, and (v) nonlinear indicators such as strongly nonvanishing accumulative skewness, we verify that indeed considered local spike seems to be the result of some catastrophic bifurcation.

Michał Kurzyński
Adam Mickiewicz University, Poznań, Poland

Stochastic models of action of biological machines

Biological machines are proteins that operate under isothermal conditions hence are referred to as free energy transducers. They can be formally considered as enzymes that simultaneously catalyze two chemical reactions: the free energy-donating and the free energy-accepting one. Most if not all biologically active proteins display a slow stochastic dynamics of transitions between a variety of conformational substates composing their native state. In the steady-state conditions, this dynamics is characterized by mean first-passage times between some distinguished substates and in the case of biological machines determines their main characteristics: the flux-force dependences and the ratio of the output to the input fluxes (the degree of coupling). The analytical theory derived for the reactions proceeding through single pairs (the gates) of conformational transition substates provides the degree of coupling value lower than unity for any network of conformational transitions. Monte Carlo simulations of random walk on various networks suggest that only scale-free networks with extended gates can provide the degree of coupling value higher than unity, i.e., a realization of a "biological molecular gear" suggested in some experiments.

Maciej Lisicki
University of Warsaw, Poland

One-particle correlation function in evanescent wave dynamic light scattering
Maciej Lisicki, Bogdan Cichocki

In Evanescent Wave Dynamic Light Scattering (EWDLS) experiments in colloidal suspensions one measures the scattered electric field time correlation function, which is connected to diffusive properties of the system. This technique allows to probe areas close to an interface but also introduces exponentially decaying illumination profile. The resulting decay of the correlation function stems from an interplay between the nonuniform illumination and hydrodynamic interactions with a planar surface.

A theoretical prediction is crucial for interpretation of new experimental data. We consider a dilute system, where effectively we have a one-particle problem. Hydrodynamic interactions with a surface result in strong modification of particles mobility when approaching it. We describe the effect of this change on the dynamics and relate it to the electric field correlation function decay rate. Comparing this to a case with no hydrodynamic interactions, we identify the influence of the penetration depth and the scattering vector.

Even for a dilute suspension the interactions are complex and it is not possible to have an analytic solution. We have employed a Brownian Dynamics simulation with a very precise numerical implementation of mobility matrix elements, which allows us to predict the shape of the electric field correlation function for given values of experimental parameters. We compare the results with recent experimental developments.

Hender Lopez
Loughborough University, UK

Meniscus draw-up in a precursor film model
Mariano Galvagno, Hender Lopez and Uwe Thiele

When a flat plate is dragged out of a liquid bath, a liquid film may be deposited on it - a technique widely used in coating processes. To control the deposition one needs to understand the velocity-dependent shape of the meniscus. At high velocities U a macroscopic film is deposited -- corresponding to the classical Landau-Levich problem [1]. For small U only a microscopic precursor film is deposited. Recent studies employ a slip model for contact line motion to discuss meniscus shapes and steady films of finite length [2].

We study the system with a precursor film model based on a Derjaguin pressure that describes partially wetting. As in [2] we find steady menisci at small U up to a saddle-node bifurcation at a limiting U_c. Depending on the inclination angle, in a small region below U_c, multiple steady solutions may exist. They correspond to menisci with a finite film-like 'foot'. The solution branches and the limits of the region of multiple steady solutions are traced employing numerical continuation [3]. We also performed time dependent calculation to study the stability of the different types of solution.

References:
[1] L. Landau, B. Levich, Acta Physicochim. URSS 17, 42 (1942)
[2] J. H. Snoeijer et al., J. Fluid Mech. 579, 63 (2007); J. Ziegler et al., J. Eur. Phys. J. Special Topics 166, 177 (2009)
[3] E. Doedel et. al, Int. J. Bifurcation Chaos, 1, 493 (1991); P. Beltrame, U. Thiele, SIAM J. Appl. Dyn. Syst. 9, 484 (2010)

Miguel Angel Gonzalez Maestre
Universidad de Extremadura, Spain

Is it possible to predict the close packing of hard spheres from virial series?
M.A.G. Maestre, A. Santos, M. Robles and M. Lopez del Haro

The question of whether the known virial coefficients are enough to determine the packing fraction η_∞ at which the fluid equation of state of a hard-sphere fluid diverges is addressed. It is found that the information derived from the direct Padé approximants to the compressibility factor constructed with the virial coefficients is inconclusive. An alternative approach is proposed which makes use of the same virial coefficients and of the equation of state in a form where the packing fraction is explicitly given as a function of the pressure. The results of this approach both for hard-disk and hard-sphere fluids, which can straightforwardly accommodate higher virial coefficients when available, lends support to the conjecture that η_∞ is equal to the maximum packing fraction corresponding to an ordered crystalline structure.

Jose Adrian Martinez Gonzalez
National Autonomous University of Mexico, Mexico

Nematic and smectic order in two-dimensional systems of v-shape particles

The nematic and smectic order in two dimensional systems of hard bent particles has been studied by means of the Onsager theory and Monte Carlo simulations. We found that the occurrence of both phases depends on the bent angle of the particle: in the hard needle limit we found the nematic phase, while increasing the bent angle the effects due to the excluded area lead to the smectic phase. The results obtained by both methodologies are in good agreement.

Peter Mason
IJLRDA, UPMC, Paris VI, France

Superfluid density as a model of a supersolid with cubic interaction
Peter Mason, Christophe Josserand and Sergio Rica

Recent observations have suggested the existence of a supersolid state in helium-4 systems. The defining experiment by Kim and Chan in 2005 placed helium-4 into a torsional oscillator, in which a torus is filled and rotated at constant speed. Measurement of the nonclassical rotational inertia fraction (NCRIF) supports the presence of a supersolid.

In this poster we will show recent work on impurities in a supersolid. Small impurity fields are placed within a condensate that mimic properties of the supersolid. This breaks the translation symmetry of the Hamiltonian and means the crystal scale spontaneously created. Numerical simulations of the Hamiltonian are shown together with calculations of the NCRIF.

Thiago Mattos
Max-Planck-Institute for Metals Research, Stuttgart, Germany

Phase transitions and crossovers in reaction-diffusion models with catalyst deactivation
Thiago Mattos and Fábio D. A. Aarão Reis

The activity of catalytic materials is reduced during operation by several mechanisms, one of them being poisoning of catalytic sites by chemisorbed impurities or products. Here we study the effects of poisoning in two reaction-diffusion models in one-dimensional lattices with randomly distributed catalytic sites. Unimolecular and bimolecular single-species reactions are considered, without reactant input during the operation. The models show transitions between a phase with continuous decay of reactant concentration and a phase with asymptotic non-zero reactant concentration and complete poisoning of the catalyst. The transition boundary depends on the initial reactant and catalyst concentrations and on the poisoning probability. The critical system behaves as in the two-species annihilation reaction, with reactant concentration decaying as t^−1/4 and the catalytic sites playing the role of the second species. In the unimolecular reaction, a significant crossover to the asymptotic scaling is observed even when one of those parameters is 10% far from criticality. Consequently, an effective power-law decay of concentration may persist up to long times and lead to an apparent change in the reaction kinetics. In the bimolecular single-species reaction, the critical scaling is followed by a two-dimensional rapid decay, thus two crossovers are found.

Pablo Maynar
Universidad de Sevilla, Spain

Fluctuating Navier-Stokes equations for inelastic hard spheres or disks
P. Maynar, J. J. Brey and M. I. Garcia de Soria

Starting from the kinetic equations for the fluctuations and correlations of a dilute gas of inelastic hard spheres or disks, a Boltzmann-Langevin equation for the one-particle distribution function of the homogeneous cooling state is constructed. This equation is the linear Boltzmann equation with a fluctuating white noise term. Balance equations for the fluctuating hydrodynamic fields are derived. New fluctuating forces appear as compared with the elastic limit. The fluctuations of the transverse velocity field can be described by means of a Langevin equation, but exhibiting two main differences with the Landau-Lifshitz theory: the noise is not white, and its second moment is not determined by the shear viscosity. This shows that the fluctuation-dissipation relations for molecular fluids do not straightforwardly carry over to inelastic gases. The equations for the other fields are also investigated obtaining similar results. The theoretical predictions are shown to be in good agreement with molecular dynamics simulation results.

Anna Myłyk
Institute of Fundamental Technological Research, Polish Academy of Science, Warsaw, Poland

Evolution and break-up of suspension drops settling under gravity in a viscous fluid close to a vertical wall
Anna Myłyk, Walter Meile, Günter Brenn and Maria L. Ekiel-Jeżewska

In this work, we analyze the dynamics of suspension drops sedimenting under gravity in a viscous fluid close to a vertical wall. The evolution of the drop shape and the destabilization rate are measured experimentally and evaluated numerically, using the point-particle model close the wall. The destabilization time and the distance traveled by the drop until break-up are smaller for a closer distance of the drop center from the wall. Destabilization times and lengths of individual drops with different random configurations of the particles differ significantly from each other, owing to the chaotic nature of the particle dynamics.

Marcin Napiórkowski
University of Warsaw, Poland

On the minimization of Hamiltonians over pure Gaussian states
Marcin Napiórkowski (co-authors of presented result are Jan Dereziński and Jan Philip Solovej)

A Hamiltonian defined as a polynomial in creation and annihilation operators is considered. After a minimization of its expectation value over pure Gaussian states, the Hamiltonian is Wick-ordered in creation and annihilation operators adapted to the minimizing state. I will show that this procedure eliminates from the Hamiltonian terms of degree 1 and 2 that do not preserve the particle number, and leaves only the terms that can be interpreted as quasiparticles excitations.

Piotr Nowakowski
University of Warsaw, Poland

Parallel solvation forces in 2D Ising strip
Piotr Nowakowski and Marek Napiórkowski

We consider the Ising model on a two dimensional square lattice of spins, forming a strip of infinite length and finite width. An inhomogeneous magnetic field is acting on boundary spins. Using method based on the exact diagonalization of the transfer matrix, we calculate the solvation force acting in the direction parallel to the boundaries. Several patterns of boundary fields are considered. We propose and check scaling laws for the parallel solvation force near the critical point.

Matteo Paoluzzi
Roma Tre University, Italy

Dynamic of the secondary processes in a mean-field exactly solvable model glass
Matteo Paoluzzi, Andrea Crisanti, Luca Leuzzi

The interrelation of dynamic processes active on separated time-scales in glasses and viscous liquids is investigated. Both a thermodynamic (static) and a dynamic approach are implemented on an exactly solvable spin model with quenched disordered interactions, developed to study the nature of polyamorphism and amorphous-to-amorphous transitions.

Krzysztof Pomorski
University of Warsaw, Poland

Phenomenological description of new Josephson junction architectures

I describe the Josephson junction devices made by putting non-superconducting element on the top of superconductor strip. The non-superconducting material under numerical investigation is metal, ferromagnet and ferrielectric. Josephson effect is being induced in the given structure by means of Cooper pair diffusion from the superconductor into non-superconductor and by means of electric and magnetic fields occurring at the superconductor-nonsuperconductor interface. I use Time Dependent Ginzburg Landau (TDGL) formalism to describe the properties of the system, particularly in certain types of temperature gradients across the junction. The superconducting and non-superconducting order parameter distribution is being investigated for different geometries of the system. I also formulate the description of the system in terms of more fundamental formalisms as: Eilenberger, Usadel, Bogoliubov de Gennes and Keldysh. The use of Green function techniques gives fundamental transport equation by accounting the interplay of different physical phenomena occurring on microscopic level.

Grigory Sizov
Landau Institute for Theoretical Physics, Moscow, Russian Federation

Aggregation of particles in a random shear flow: why is inertia important
G. Falkovich, V. Lebedev, I. Kolokolov, G. Sizov, P. Vorobev

We consider dynamics of small inertial particles suspended in a two-dimensional incompressible random flow with strong shear component. Due to particles' inertia, their velocity field is not determined locally by fluid velocity and becomes compressible. Thus initially uniform spatial distribution of particles tends a multi-fractal set, with characteristic clusters and voids. While average distance between particles still grows exponentially, the rate of this growth decreases with inertia. In the isotropic random flow, investigated in [B.Mehlig, M.Wilkinson, K.Duncan, T.Weber, M.Ljunggren, Phys.Rev. E 72,051104(2005)], this effect leads to a phase transition between aggregating and non-aggregating phases, as maximum Lyapunov exponent reaches zero. In the white-noise limit one can describe dynamics of inter-particle separation by a Langevin equation. We reduce the corresponding Fokker-Planck equation to a quantum-mechanical problem of a harmonic oscillator with small perturbation. Performing expansion over small inertia, we calculate corrections to Lyapunov exponent of particle trajectories. Using instantonic approach at large N, we calculate growth rate of Nth moment of the distance between two particles.

Jacek Siódmiak
University of Technology and Life Sciences in Bydgoszcz, Poland

On the macroion-channelling filter controlling model (dis)ordered protein formations
Jacek Siódmiak, Adam Gadomski, Ivan Santamaría-Holek

We propose that the main mechanism controlling the selection rule of model (dis)ordered protein formations, such as non-Kossel crystal growth [1] and aggregation of lysozyme from aqueous solution, is a macroion-channeling filter having flicker-noise properties [2]. This filter is originated at the interfaces between growing solid-like object and its external liquid- type phase, and it can be considered as a series of voltage gated macroion sub-channels [1,2].

The effects of thermal deviations on a macroion-channelling filter have been disclosed as localized at the edge of (non)Markovianity of the system [3]. The Markovian (memory-less) part of the phase-space limit can be attributed to the thermal noise. The non-Markovian counterpart can in turn be first identified with the interactions of electrostatic and/or hydrophobic character. They can amplify their magnitude when coupled to local thermal Soret-like gradients, constituting virtually a constructive flickering filter, adequately supporting in the former case the electrostatics in macroions' transportation toward ultimate accretion spots. Otherwise, upon non-flickering limit, the thermal conditions may become fuzzy, thus, more some disorderly aggregate than a crystal is expected to form. The excess entropy at equilibrium, and overall entropy production close to equilibrium, the latter being identified with the growing rule of the aggregation, have been pointed out to unravel the nature of the studied diffusion limit [1-3].

The Fokker-Planck and Smoluchowski dynamics [2] of the channels considered in a phase- space of crystal sizes is studied by using both simulation and analytic argumentation lines, and represents a refreshing thought on how to utilize the presence of constructive-noise sources in protein formation, a field of utmost experimental and technological interest [1].

References:
[1] A. Gadomski, J. Siódmiak, Kinetics of protein crystal growth in mass convection regime, Crystal Research & Technol. 37 (2002) 281-291.
[2] J. Siódmiak, I. Santamaría-Holek, A. Gadomski, On morphological selection rule of noisy character applied to model (dis)orderly protein formations, J. Chem. Phys. 132 (2010) 195103:1-11.
[3] I. Santamaría-Holek, A. Gadomski, J. M. Rubí, Controlling protein crystal growth rate by means of temperature, J. Phys.: Condensed Matter (in print).

Joakim Stenhammar
Lund University, Sweden

Nondielectric long-range solvation effects in molecular simulations of polar liquids
Joakim Stenhammar, Per Linse and Gunnar Karlström

The question of how to treat electrostatic interactions in computer simulations is one of long-standing interest. The problem becomes especially important for the calculation of dielectric properties, such as the dielectric constant ε, of homogeneous and isotropic dipolar systems, due to the sensitivity of these properties on the long-range part of the electrostatic interaction. In a recent paper [1], we derived fluctuation formulas describing the fluctuations of the electric multipole moments Q_lm in a homogenous sphere of dielectric medium, as well as the size of the electrostatic coupling between the sphere and its surroundings. Within the present project, we use these formulas to assess how well the expected dielectric behaviour is reproduced using i) the Ewald summation technique and ii) the reaction field (RF) method with a cubic cell for simulations of strongly polar liquids.

We find that the inherent periodicity of the Ewald method induces structural effects as the length scale of the simulation cell is approached, in that certain components of the multipole moments are suppressed by the repulsive interaction with its neighbouring cells, whereas other components are favoured by a corresponding attractive interaction. Our results agree well with numerical calculations of the effective multipole-multipole interaction energy in a primitive cubic lattice, indicating that it is indeed the periodicity of the Ewald system that gives rise to these effects. Furthermore, for the systems simulated using the RF approach, we get results that are strikingly similar to those of the Ewald simulations, indicating that there is indeed an implicit periodicity inherent in this method as well, presumably due to the use of toroidal boundary conditions.

The fact that the observed long-range interactions of the simulated systems are strongly nondielectric in their character leads us to the question of whether the Ewald and RF approaches are suitable for studying dielectric properties, as well as other properties depending strongly on the long-range behaviour of the electrostatic interactions.

References:
[1] J. Stenhammar, P. Linse, P. Malmqvist and G. Karlström, Electric multipole moment fluctuations in polar liquids, J. Chem. Phys., 130 124521 (2009)
[2] J. Stenhammar, P. Linse and G. Karlström, Nondielectric long-range solvation of polar liquids in cubic symmetry, J. Chem. Phys., 131, 164507 (2009)

Martin Trulsson
Theoretical Chemistry, Chemical Centre, Lund, Sweden

Stockmayer fluids and SPC/E water in hyperspherical geometry

The static dielectric constant for Stockmayer fluids and SPC/E water has been investigated via Monte Carlo simulations in the hyperspherical, S₃, geometry [1, 2] Simulations for Stockmayer fluids were performed in the Canonical (NVT) ensemble, while the simulations of SPC/E water were performed in the Isobaric (NPT) ensemble. Different system sizes were tested, ranging from 300 to 10000 particles. in order to illustrate how the static dielectric constant converges with system size.

Four different methods to evaluate the static dielectric constant were tested:
1) Sampling the total Kirkwood factor, g_k, on the hypersphere
2) Relating the fluctuations of the total Kirkwood factor to the static dielectric constant
3) Sampling the distance-dependent Kirkwood factor, G_k(r)
4) Using the two-center potential correlation formula [3]

Our results shows that the hyperspherical geometry is well suited for simulations of polar fluids One of the advantages of the S₃ geometry is that it avoids any periodic (and/or underlaying cubic) structure. A structure that might invoke convergent problem [4].

References:
[1] J. M. Caillol; Asymptotic behavior of the pair-correlation function of a polar liquid. J. Chem. Phys. 1992, 96, 7039
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