SMM99 Short talks

99th Statistical Mechanics
Conference


RUTGERS UNIVERSITY,
HILL CENTER, ROOM 114
SUNDAY, MONDAY AND TUESDAY,
MAY 11-13, 2008

Schedule of Short Talks



Monday, Session A
8:50am - 10:05am


A1: R. Shirts, Brigham Young University
Title: Microcanonical Entropy: Re-evaluation of Boltzmann-Planck vs. Schluter Formulations
Abstract: Two different formulations have been used for evaluating microcanonical entropy, S = klnW. In the Boltzmann-Planck formula, W is the degeneracy of states at the system energy, whereas in the Schluter W is the number of quantum states up to the system energy [Z. Naturforschg. 3a, 350-360 (1948)]. The difference between the two entropies is of order 1/N. I will discuss advantages and disadvantages of both formulations. The Boltzmann-Planck formulation has the advantage of direct connection to information theory through the Shannon entropy. However, the Schluter entropy is directly proportional to N (extensive) and gives quantities in close agreement to corresponding canonical quantities even for small systems. The Schluter formulation makes the microcanonical ensemble inconsistent with the remainder of statistical mechanics in that W is not the partition function since it includes inaccessible states. However, the derivatives of the Schluter entropy are consistent with microcanonical thermodynamics of finite systems, whereas those of the Boltzmann-Planck entropy only do in the large N limit. I will argue that the Schluter formulation gives better results for molecular dynamics simulations of finite systems, especially if one seeks to compare the results with canonical calculations of macroscopic systems. I use identical harmonic oscillators and the ideal gas as examples to illustrate the differences between these two formulations.

A2: D-S. Lee, Northeastern University
Title: Critical phenomena of Boolean networks with heterogeneous connectivity
Coauthors: Heiko Rieger
Abstract: We present an analytic approach to understanding the phase transition of the Boolean networks with scale-free topology and derive its critical exponents. These results are discussed in connection with the dynamic stability of the gene transcriptional regulatory networks of yeast.

A3: E. Marino, Princeton University
Title: Stable mean-field solution of a short-range interacting SO(3) quantum spin-glass
Coauthors: E.C.Marino* and C.M.S. da Conceicao
Abstract: We present a mean-field solution for a quantum, short-range interacting, disordered, SO(3) Heisenberg spin model, in which the Gaussian distribution of couplings is centered in an AF coupling $\bar J>0$, and which, for weak disorder, can be treated as a perturbation of the pure AF Heisenberg system. The phase diagram contains, apart from a N\'eel phase at $T=0$, spin-glass and paramagnetic phases whose thermodynamic stability is demonstrated by an analysis of the Hessian matrix of the free-energy. The magnetic susceptibilities exhibit the typical cusp of a spin-glass transition.

A4: L. Piterbarg, USC
Title: Inertial particles driven by a telegraph noise
Coauthors: S. Musacchio, G. Falkovich, M. Vucelija
Abstract: We present a model for the Lagrangian dynamics of inertial particles in a compressible flow, where fluid velocity gradients are modelled by a telegraph noise. The model allows for an analytic investigation of the role of time correlation of the flow in the aggregation--disorder transition of inertial particle. The dependence on Stokes and Kubo numbers of Lyapunov exponent of particle trajectories reveals the presence of a region in parameter space $(St, Ku)$ where the leading Lyapunov exponent changes sign, thus signaling the transition. The asymptotics of short and long-correlated flows are discussed, as well as the fluid-tracer limit.

A5: D. Alberts, Williams College
Title: Abundance of RNA pseudoknots
Coauthors: Evan Miller and Teng Jian Khoo
Abstract: The pseudoknot fold is often seen in auto-catalytic RNA and in viruses. The relative probabilities of different pseudoknot folds predicted by a statistical-mechanical theory is consonant with a database of known folds. We extend that result to estimate the abundance of pseudoknot folds in RNA sequences, finding approximately 1 pseudoknot per 40,000 nucleotides. This theoretical probability density compares favorably to what we infer from structure databases and has implications for genome organization, RNA folding algorithms, and the RNA World.

A6: M. Avlund, Harvard University
Title: Computer Models of Gene Segregation
Coauthors: Oskar Hallatschek and David Nelson
Abstract: A computer model is presented that allows studies of two or three different competing genotypes in a one dimensional stepping stone model. The model is inspired by experiments on gene segregation during range expansions of bacteria and yeast in two dimensions. We hope to adapt the model to study radial expansions, fitness advantages, mutations and gene surfing.

A7: K. Huang, Princeton University
Title: Getting into Shape: The Physics of Bacterial Morphology
Coauthors: Ranjan Mukhopadhyay, Bing Wen, Zemer Gitai, and Ned Wingreen
Abstract: Bacterial cells come in a wide variety of shapes and sizes, with the peptidoglycan cell wall as the primary stress-bearing structure that dictates cell shape. In recent years, cell shape has been shown to play a critical role in regulating many important biological functions including attachment, dispersal, motility, polar differentiation, predation, and cellular differentiation. Though many molecular details of the composition and assembly of the cell wall components are known, how the peptidoglycan network organizes to give the cell shape during normal growth, and how it reorganizes in response to damage or environmental forces have been relatively unexplored. We introduce a quantitative mechanical model of the bacterial cell wall that predicts the response of cell shape to peptidoglycan damage in the rod-shaped Gram-negative bacterium Escherichia coli. To test these predictions, we use time-lapse imaging experiments to show that damage often manifests as a bulge on the sidewall, coupled to large-scale bending of the cylindrical cell wall around the bulge. The direction of bending confirms the hypothesis of a longitudinal orientation of peptides and a circumferential orientation of glycan strands in the peptidogylcan layer. Our simulations based on our physical model also suggest a surprising robustness of cell shape to damage, allowing cells to grow and maintain their shape even under conditions that limit crosslinking. Finally, we show that many common bacterial cell shapes can be realized within the model via simple spatial patterning of peptidoglycan defects, suggesting that subtle patterning changes could underlie the great diversity of shapes observed in the bacterial kingdom.

A8: K. Korolev, Harvard University
Title: Defect-mediated emulsification in two dimensions
Coauthors: David R. Nelson
Abstract: We consider two dimensional dispersions of droplets of isotropic phase in a liquid with an XY-like order parameter, tilt, nematic, and hexatic symmetries being included. Strong anchoring boundary conditions are assumed. Textures for a single droplet and a pair of droplets are calculated and a universal droplet-droplet pair potential is obtained. The interaction of dispersed droplets via the ordered phase is attractive at large distances and repulsive at short distances, which results in a well defined preferred separation for two droplets and topological stabilization of the emulsion. This interaction also drives self-assembly into chains. Preferred separations and energy barriers to coalescence are calculated, and effects of thermal fluctuations and film thickness are discussed.

A9: S. Rahav, University of Maryland
Title: Fluctuation relations and coarse-graining
Coauthors: Christopher Jarzynski
Abstract: We consider the application of fluctuation relations to the dynamics of coarse-grained systems, as might arise in a hypothetical experiment in which a system is monitored with a low-resolution measuring apparatus. We analyze a stochastic, Markovian jump process with a specific structure that lends itself naturally to coarse-graining. A perturbative analysis yields a reduced stochastic jump process that approximates the coarse-grained dynamics of the original system. This leads to a non-trivial fluctuation relation that is approximately satisfied by the coarse-grained dynamics. We illustrate our results by computing the large deviations of a particular stochastic jump process. Our results highlight the possibility that observed deviations from fluctuation relations might be due to the presence of unobserved degrees of freedom.

A10: Y. Shokef, University of Pennsylvania
Title: Stripes and their Zigzagging in Buckled Hard Spheres
Coauthors: Yilong Han, Ahmed Alsayed, Peter Yunker, Tom Lubensky, and Arjun Yodh
Abstract:We use a hard sphere model to describe recent experiments on buckled colloidal monolayers. Our detailed Monte Carlo simulations exhibit the experimentally observed behavior of short-ranged antiferromagnetic order and the formation of partially disordered zigzagged stripes. Using free volume calculations, we deduce the strength of the effective antiferromagnetic interaction between neighboring spheres. We explain how the geometrical frustration of the related triangular-lattice Ising model is partially removed by collective packing considerations. A tiling model explains how local deformations give rise to zigzagged stripes. However, these require a macroscopic deformation which is incompatible with the boundary conditions of the system, hence the stripes break into domains. We furthermore explore the slow dynamics of this system. We explain the experimentally measured stretched exponential correlation functions in terms of the absence of local zero energy modes and the fact that rearrangements in the zigzagged striped phase involve a sub-extensive number of particles. We allow spheres to slowly swell in the simulations and observe jamming as well as logarithmic relaxations.

A11: V. Vitelli, University of Pennsylvania
Title: Energy transport in jammed sphere packings
Coauthors: N. Xu, M. Wyart, A. J. Liu and S. R. Nagel
Abstract: Jammed solids are amorphous materials characterized by excess vibrational modes that shift toward zero frequency as the packing fraction is progressively decreased toward a critical value below which mechanical rigidity is lost. We evaluate the thermal diffusivity of a jammed solid using the Kubo Greenwood formula and demonstrate that these excess modes are delocalized but poorly conducting. Their onset corresponds to the crossover from phonons weakly scattered by disorder (that have a divergent diffusivity according to Rayleigh law) to more unusual vibrational modes with a small frequency-independent diffusivity. Our calculation suggests that, as the jamming transition is approached, both the density of states $and$ the thermal diffusivity are nearly constant down to the lowest frequencies we can probe.

A12: C. Dasgupta, Indian Institute of Science
Title: Growing length and time scales in glass forming liquids
Coauthors: Smarajit Karmakar and Srikanth Sastry
Abstract: Recent studies of spatial heterogeneity in the local dynamics of glass-forming liquids suggest the presence of a growing dynamical correlation length. Using finite-size scaling for the first time for a realistic glass former, we establish that the growth of dynamical heterogeneity with decreasing temperature is indeed governed by a growing dynamical length scale. However, the dependence of the simultaneously growing relaxation time on system size does not exhibit the same scaling behaviour as the dynamical heterogeneity. We show that the relaxation time is instead determined, for all studied system sizes and temperatures, by the configurational entropy, in accordance with the Adam-Gibbs relation, but in disagreement with the prevailing belief that the configurational entropy is not relevant at temperatures substantially higher than the critical temperature of mode coupling theory.

A13: P. Young, University of California Santa Cruz
Title: Size dependence of the minimum excitation gap in the Quantum Adiabatic Algorithm
Coauthors: S. Knysh and V. N. Smelyanskiy
Abstract: We study the minimum gap in the quantum version of the Exact Cover problem using Quantum Monte Carlo simulations, with a view to understanding the complexity of the quantum adiabatic algorithm for much large sizes than was possible before. For a range of sizes, N <128, where the classical Davis-Putnam algorithm shows exponential complexity, the quantum adiabatic algorithm shows polynomial complexity.

A14: V. Sacksteder, APCTP
Title: Sums Over Geometries and Improvements on the Mean Field Approximation
Abstract:The saddle points of a Lagrangian due to Efetov are analyzed. This Lagrangian was originally proposed as a tool for calculating systematic corrections to the Bethe approximation, a mean-field approximation which is important in statistical mechanics, glasses, coding theory, and combinatorial optimization. Detailed analysis shows that the trivial saddle point generates a sum over geometries reminiscent of dynamically triangulated quantum gravity, which suggests new possibilities to design sums over geometries for the specific purpose of obtaining improved mean field approximations to $D$-dimensional theories. In the case of the Efetov theory, the dominant geometries are locally tree-like, and the sum over geometries diverges in a way that is similar to quantum gravity's divergence when all topologies are included. Expertise from the field of dynamically triangulated quantum gravity about sums over geometries may be able to remedy these defects and fulfill the Efetov theory's original promise. The other saddle points of the Efetov Lagrangian are also analyzed; the Hessian at these points is nonnormal and pseudo-Hermitian, which is unusual for bosonic theories. The standard formula for Gaussian integrals is generalized to nonnormal kernels.

A15: P. Kleban, University of Maine
Title: Exact Factorization of Correlation Functions in Critical Systems
Coauthors: J. J. H.Simmons, Oxford and R. M. Ziff, Michigan
Abstract: We review recent results giving exact expressions for certain higher-order correlation functions in terms of lower-order correlation functions in critical systems, including percolation and q-state Potts models.

Tuesday, Session B
8:40am - 10:05am


B1: S. Ji, Rutgers University
Title: 'Stochastic Mechanics' of Molecular Machines
Abstract: We can divide machines into deterministic and stochastic machines. Deterministic machines (e.g., computers, cars, washing machines) are macroscopic in size, robust against thermal fluctuations (or Brownian motions), and obey deterministic rules. Stochastic machines are microscopic in size (e.g., enzymes, molecular motors, cells), depend in part on Brownian motions for their physiological functions, and exhibit stochastic behaviors that can be represented as time-dependent functions of some random variables (e.g., enzymatic activity). To view the remaining portion of this abstract, please see: http://www.rci.rutgers.edu/~sji

B2: D. David-Rus, Rutgers University
Title: Inheritance of Epigenetic Chromatin Silencing
Coauthors: Swagatam Mukhopadhyay, Joel L. Lebowitz, Anirvan M. Sengupta
Abstract: We formulate a model of inheritance of the epigenetic feature in the presence of cell cycle and study the conditions which govern the stability of epigenetic states.

B3: S. Boettcher, Emory University
Title: Ising Spin Glasses in d=2 to 7
Abstract: Simulations of bond-diluted Ising spin glasses from below the lower to above the upper critical dimension, at and above the bond-percolation threshold, provide a comprehensive view of low-temperature excitations, energy fluctuations, and corrections to scaling

B4: R. Fisch, Princeton University
Title: Scaling of bond distributions in the Ising spin glass


B5: M. Keskin, Erciyes University
Title: Kinetics of a mixed spin-1/2 and spin-3/2 Ising ferrimagnetic model
Coauthors: Bayram Deviren and Osman Canko
Abstract: We present a study, within a mean-field approach, of the kinetics of a mixed ferromagnetic model on square lattice in which two interpenetrating square sublattices have spins that can take two values, σ = ± 1/2, alternated with spins that can take the four values, S = ± 3/2, ± 12. We use the Glauber-type stochastic dynamics to describe the time evolution of the system with a crystal-field interaction in the presence of a time-dependent oscillating external magnetic field crystal-field. The nature (continuous and discontinuous) of transition is characterized by studying the thermal behaviors of average order parameters in a period. The dynamic phase transition points are obtained and the phase diagrams are presented in the reduced magnetic field amplitude (h) and reduced temperature (T) plane, and in the temperature and interaction parameter planes, namely in (h, T) and (d, T) planes, d is the reduced crystal-field interaction. The phase diagrams always exhibit a tricritical point in (h, T) plane, but do not exhibit in (d, T) plane for low values of h. Moreover, phase diagrams contain disordered (d), ferromagnetic (f), ferrimagnetic (i) phases, two coexistence or mixed phase regions, (f+d) and (i+d), that strongly depend on interaction parameters. The system also exhibits the reentrant behaviors in (d, T) plane for high values of h.

B6: H. Lee, Korea Institute for Advanced Study
Title: A Baker-Campbell-Hausdorff solution by differential equation
Coauthors: Hyunggyu Park
Abstract: We propose a procedure to the Baker-Campbell-Hausdorff (BCH) solution when the exponent is a linear combination of three operators of which commutation relations are equivalent to those of the spin operator along a direction and its ladder operators. The procedure converts the manipulation of BCH formula into that of a differential equation. We remark that the validity of the present method is restricted to the case when the branch of the complex plane can be determined.

B7: H. Jo, Korea Institute for Advanced Study
Title: Relevance of Abelian Symmetry and Stochasticity in Directed Sandpile Models
Coauthors: Meesoon Ha
Abstract: We consider three directed sandpile models without Abelian symmetry on (1+1)-dimensional space, where the topping rule is deterministic. Based on our numerical results, we revisit the debatable issue of the universality class in directed sandpile models, and discuss the scaling properties of avalanches and the formation of a spatial structure at the self-organized critical (metastable) state with the power-law decaying grain density along the transverse direction. We argue the scaling exponents characterizing the avalanche distributions as well as the scaling relations in terms of the exponents of the underlying particle dynamics.



B8: A. Toom, UFPE, Brazil
Title: Law of Large Numbers for Cellular Automata
Coauthors: Andrea Vanessa Rocha and Murilo de Medeiros Sampaio
Abstract: We prove the Law of Large Numbers or LLN for invariant measures of Cellular Automata or CA in two settings:
    a) CA is ergodic and the only condition is that the interaction between the components is weak; b) CA is not ergodic, admits sub-critical percolation interpretation and has (at least) two different invariant measures, one of which is degenerate, but the other is non-degenerate, and it is that one, for which LLN is proved.
The case b) is available at Toom's home page as Rocha's and Sampaio's master's theses; the case a) is in preparation.



B9: S. Huntsman, Equilibrium Networks; NPS
Title: Thermal traffic analysis
Abstract: We will briefly outline thermal traffic analysis and its application to monitoring computer network behavior.

B10: S. Gravel, Cornell University
Title: Think locally, act globally: how to search with iterated maps
Coauthors: Veit Elser
Abstract: The phase retrieval, boolean satisfaction, and packing problems all have in common that their solution can be expressed as the intersection of a number of simple constraints. We show how simple dynamical systems can be designed that take advantage of the geometrical nature of these constraints to achieve an efficient search for the solution. We discuss in particular applications to disordered constrained systems such as random kSAT and packing problems, and compare the results with the state of the art. We find intriguing similarities in performance behavior between this geometrical approach, local stochastic approaches such as walksat, and statistical approaches such as survey propagation.

B11: X. Xing, Syracuse University
Title: Topology of Smectic order on compact curved substrates
Abstract: We show that smectic order on arbitrary curved substrate can be described by differential form of rank one (1-form), whose geometric meaning is the differential of the local phase field of the density modulation. The exterior differential of 1-form is shown to be the local dislocation density. Elastic deformations are described by superposition of exact differential forms. More importantly, the global properties of the smectic order is intimately related to the substrate topology and can be naturally addressed by de Rham's cohomology theory. Low energy smectic states on compact surface with minimal number of defects can be classified by $b_1$ integer global topological charges, where $b_1$ is the first Betti number. States with distinct global charges are not mutually accessible via local fluctuations. We apply this formalism to study smectic ordering on torus as well as on sphere, and clarify the topological structures of all low energy smectic states.

B12: M-C. Huang, Chung-Yuan Christian University, Taiwan
Title: Fluctuations of gene regulatory networks induced by intrinsic Gaussian colored noise
Coauthors: Ming-Chang Huang*, Jinn-Wen Wu, and Yu-Pin Luo
Abstract: The intrinsic stochastic fluctuation associated with a gene regulatory is assumed to be Gaussian colored noise in nature. Based on stochastic differential equation with Ito calculus, we present the results of the intrinsic fluctuations for a two-dimensional gene regulatory network near a stable point. Then, the results are applied to analyze the fluctuations of auto-regulatory networks and general toggle switch.

B13: A. Hanke, University of Texas at Brownsville
Title: Denaturation transition of stretched DNA
Coauthors: M. G. Ochoa and R. Metzler
Abstract: We generalize the Poland-Scheraga model to consider DNA denaturation in the presence of an external stretching force. We demonstrate the existence of a force-induced DNA denaturation transition and obtain the temperature-force phase diagram. The transition is determined by the loop exponent $c$ for which we find the new value $c=4\nu-1/2$ such that the transition is second order with $c=1.85<2$ in $d=3$. We show that a finite stretching force $F$ destabilizes DNA, corresponding to a lower melting temperature $T(F)$, in agreement with single-molecule DNA stretching experiments.

B14: B. Bagchi, Indian Institute of Science
Title: Protein diffusion along a DNA
Coauthors: Biman Bagchi, Paul Blainey and X Sunney Xie
Abstract: We study a model of target search by diffusion of protein along a DNA chain. It is argued that a protein move by rotating around the DNA in a helical path. The predicted dependence of the apparent translational diffusion then scales as 1/R3 where R is the radius of the protein. This compares favorably with recent single molecule experiments.



B15: M. Schechter, University of Bristish Columbia
Title: Are magnetic and electric dipolar glasses alike?
Coauthors: Philip Stamp
Abstract: Magnetic and electric dipolar glasses seemingly share the same effective Ising hamiltonian. However, a sharp phase transition is seen in the former, but not in the latter. We argue that this results in effective random fields which are inevitable in electric glasses, and are not allowed by the time-reversal symmetry in magnetic glasses. Furthermore, we argue that the Ising model in disordered systems with no time-reversal symmetry must come with an additional random field.

B16: G. Gradenigo, University of Trento, Italy
Title: A measure of surface tension among low temperature Inherent Structures
Coauthors: G.Gradenigo*, C.Cammarota, A.Cavagna, T.Grigera and P.Verrocchio
Abstract: We test a novel formulation of the mosaic scenario of the glass transition. Such formulation is based on fluctuating surface tensions among the metastable states. In order to detect the existence of a distribution of surface tensions, we build high stressed configurations made of patches of different Inherent Structures and quench them. At low enough temperatures we find that a surface tension is indeed left in the system and study the distribution of such tensions at different linear size R of the patches.

B17: F. Bouchet, INLN - CNRS, France
Title: Out of equilibrium phase transitions of two dimensional turbulent flows
Coauthors: Eric Simonnet
Abstract: One of the most important problem in turbulence is the prediction of large-scale structures of very high Reynolds' flows. The class of two dimensionnal and geostrophic flows is relevant for applications for geophysical applications (ocean and atmosphere).
We consider the two-dimensional Navier-Stokes equation with weak stochastic forcing and dissipation in the inertial limit. This is an example of dynamical system, where an out of equilibrium stationary state is reached, without detailed balance. The existence of an invariant measure has been mathematically proved recently, together with mixing and ergodic properties. This problem has however never been considered from a physical point of view. We thus address the following issues: when is the measure concentrated on an inertial equilibrium, how are the large scales selected by the forcing, what is the level of the fluctuations ?
The most striking result is the existence of out of equilibrium phase transitions. One observe transitions from one type of flow (unidirectional) to an other one (dipole), at random time. This is similar to the classical bystability in a two wheel potential with noise. But in our case, no such potential exists and the turbulent nature of the flow (infinite number of degrees of freedom) renders the phenomena much richer.
Analogies with the Earth magnetic field reversal, and with similar phenomena in experiment of two dimensionnal and geophysical flows can be discussed.