Abstracts of Short Talks |
| D. Adams, Virginia Tech Coauthors: B. Schmittman and R. Zia Title:"Power Spectra of the Total Occupation in TASEPs" Abstract:We studied the power spectra of the total occupation of the TASEP (Totally Asymmetric Simple Exclusion Process). For the shock phase, the behavior is trivially diffusive. In the MaxCurrent phase, a simple power law is found. The spectra is more interesting in the High/Low Density phases, displaying damped oscillations. The data can be well understood in terms of biased diffusion with conserved noise. |
| A. Angel, Virginia Tech Coauthors: B. Schmittman and R. Zia Title:"Zero-range Process with Long-Range Interactions at a T-Junction" Abstract:A generalized zero-range process with a limited number of long-range interactions is studied as an example of a transport process in which particles at a T-junction make a choice of which branch to take based on traffic levels on each branch. A phase diagram can be constructed based on a self-consistent mean-field approximation, in good agreement with simulations. |
| N. Aral, Koc Universitym Istanbul Coauthor:A.N. Berker Title:"Correlations in Frustrated Systems with Chaotic Rescaling Behavior" Abstract:We have calculated spin-spin correlations in frustrated hierarchical Ising models that exhibit chaotic renormalization-group behavior. The correlations, as a function of distance, behave chaotically, but do not directly reflect the chaotic behavior of the interactions, e.g., exhibiting 3 bands instead of 4. The far correlations, but not the near correlations, are sensitive to small changes in temperature or frustration. The free energy and internal energy are smooth functions of temperature. The spectrum of Lyapunov exponents are calculated as a function of frustration. |
| B. Atkinson, Trent University Title:"Spectral Properties of Inhomogeneous d-Wave Superconductors with Coexisting Order" Abstract:The influence of static magnetic correlations on the temperature-dependent superfluid density is calculated for d-wave superconductors. In self-consistent calculations, itinerant holes form incommensurate spin density waves (SDW) which coexist with superconductivity. In the clean limit, the density of states is gapped, and the superfluid density is exponentially activated. In inhomogeneously-doped cases, the SDW are disordered and both the density of states and superfluid density obtain forms indistinguishable from those in dirty but pure d-wave superconductors. |
| P. Benetatos, University of Goettingen Coauthors:A. Zippelius Title:"Random Networks of Wormlike Chains" Abstract:We present a semimicroscopic replica field theory of the formation of a random network built from wormlike chains. We consider permanent cross-links which fix the orientation of the corresponding filaments to be locally parallel, and we treat them as quenched disorder. We show that, upon increasing the cross-links in the fluid, an isotropic amorphous solid phase emerges in which the orientations of the chains are frozen in random directions. A different transition to an orientationally ordered phase is also possible. |
| E. Ben-Naim, Los Alamos National Laboratory Coauthors:N.W. Hengartner Title:How to Choose a Champion? Abstract: League competition is investigate using a simple random process. In our model, a weak team can upset a strong team with a fixed probability. Teams play an equal number of head-to-head matches and the team with the largest number of wins is the champion. The total number of games needed for the best team to win the championship with certainty, $T$, rapidly grows as the cubic power of $N$, the number of teams, $T\sim N3$. This number can be substantially reduced using preliminary rounds where teams play a small number of games and subsequently, only the top few teams advance to the next round. When there are $k$ rounds, the total number of games needed for the best team to emerge as champion, $T_k$, grows as follows, $T_k\sim N^{\gamma_k}$ with $\gamma_k=[1-(2/3)^{k+1}]^{-1}$. For example, $\gamma_k=9/5,27/19,81/65$ for $k=1,2,3$. Using many rounds, the champion can be decided with the optimal number of games, $T\sim N$. We conclude that league format is an ineffective method of determining the best team, and that careful elimination from the bottom up is fair and efficient. |
| A. N. Berker, Koc University, Istanbul Coauthor:C. Guven Title:"Uniaxially Frustrated d=3 Spin Glasses" Abstract:We have studied a spin-glass model with ferromagnetic Kxy interactions within the xy plane, but random +Kz and -Kz interactions, with respective probabilities (1-p) and p, along the z direction, obtaining the global phase diagram for all (Kxy,Kz,p). For each cross-section of fixed Kz/Kxy, a ferromagnetic, spin-glass, antiferromagnetic phase diagram is obtained, with a Nishimori multicritical point. In contrast to the previous finding, in isotropic spin glasses, of reentrance at temperatures below the multicritical point, we find, for the uniaxially frustrated spin glass, the ferromagnetic-spinglass boundary extending to higher p as T is lowered. |
| T. Chou, UCLA Title:"Peeling and
Sliding in Nucleosome Repositioning" Abstract: Nucleosome particles comprising of dsDNA-wrapped histone complexes occlude parts of DNA from access by other enzymatic machinery. As part of the cell cycle, the nucleosome must be remodeled and the histones moved. Since the histone-dsDNA binding energy is typically large ($\sim 30k_{B}T$), rapid nucleosome remodeling is catalyzed by motors which can lead the motion of DNA replication forks. Whether histones are destabilized and detached, or pushed along the DNA, is unknown. We present a stochastic model for histone shifting or removal by a processing motor. We find that thermally induced shifting of histones competes with a peeling mechanism in which the histone particle is scrapped off DNA. The physical parameters that favor shifting versus peeling are explored. |
| E. Cortes, Universidad Autonoma Metropolitana, Mexico Coauthors: R. Rodriguez and J. Fujioka Title:"Noise Assisted Synchronization in an Ensemble of Bistable Systems" Abstract:We study a phenomenon of synchronization induced by noise in an activation process. Starting from an ensemble of time series of the transition time, in a periodically driven stochastic system, we show how the noise has a clear effect in the synchronization of the ensemble. This has as a consequence an enhancement of predictability of the system. We point out how this is related to the stochastic resonance. |
| W. De Roeck, K.U. Leuven/Harvard University Coauthors: C. Maes and J. Derezinski Title:"Quantum Fluctuations: From Hamiltonian Dynamics to Unravelings of Master Equations" Abstract:We present a rigorous scheme to calculate quantum fluctuations. One starts out with a hamiltonian dynamics for a small system coupled to reservoirs and one performs the weak coupling limit. As is well known since the work of E.B. Davies, the evolution of the small system in that limit is governed by a quantum master equation. One can however ask questions which are not answered by the solution of this master equation. Two such questions are : 1) Assume we are modelling a system in contact with reservoirs at different temperatures. What is the statistics of the heat currents? Is there a fluctuation relation for the entropy production? 2) Assume we are modelling an atom driven by a electromagnetic source. What is the statistics of emitted photons? On a heuristic level, one can (and in the case of question 2, physicists do) answer these questions by the technique of unravelings of master equations. Our aim is to derive this technique of unraveling from the original microscopic model by considering limits of reservoir fluctuations. |
| P. Ditlevsen, University of Copenhagen Title:"On Cascades and Statistical Equilibrium in a Shellmodel of Turbulence" Abstract: Fully developed turbulence is far from equilibrium in the sense that energy is not equipartitioned on the degrees of freedom of the system. In a shellmodel of 2D turbulence, exhibiting a forward cascade of enstrophy a parameter can be continuously changed, such that above a critical value the system is in equilibrium, while below it is in a cascade regime. This behavior can be understood in terms of eddy turnover timescales. |
| U. Edgal, North Carolina A&T State University Coauthor: D. Huber Title:"Multi-Scale Quantum Mixed Material Systems: Microstructure and Equilibrium Properties" Abstract:Partial Quantum Nearest Neighbor Probability Density Functions (PQNNPDF's) are formulated to determine microstructure for quantum mixed systems (involving Fermions and Bosons, variously mixed) in a manner analogous to that provided for classical multi-component systems. Developments on partial quantum m-tuplet distribution functions (a generalization of the partial quantum radial distribution function which are presently the more popular alternative for describing quantum material microstructure), along with their relationship to PQNNPDF's are briefly elucidated. Statistical thermodynamic properties of quantum mixed systems are also provided as an extension of the classical approach employed (throughout the thermodynamic phase space), for arbitrary material systems. A hallmark of this paper is that PQNNPDF's are related to the free energy of arbitrary equilibrium systems, with the degree of difficulty of the original equilibrium quantum statistical thermodynamic problem reduced dramatically. Results are expected to remain accurate and thus valid for arbitrary system scale (nano, micro, macro, etc.). Application to the simple case of dilute, weakly correlated quantum gas mixtures has been outlined where the second virial coefficient is derived. |
| N. Enaki, Inst. of Applied Phys. of Academy of Scie.
of Modova Republic Title:"Second Order Phase Transitions in Two-Quanta Interaction with Thermostat" Abstract: One of the most important problems of non-equilibrium statistical mechanics is to study the interaction of a small system with a large system (thermostat). In this communication, it is to study the interaction of such small system with thermostat, when the one quantum interaction is forbidden. In this situation all processes of absorption and generation of photons (or phonons) is beginning with two-quantum interaction of small system with the bath (large system). An interesting problem is the class of cooperative effects which appear in the two-photon interaction of system of radiators with zero temperature bath. Such an effect as a two photon cooperative fluorescence [1], two photon super radiance can be obtained using the method of two-quantum eliminations of boson electromagnetic field operators. For correct elimination of the EMF operators, the lemma of representation of EMF vacuum operator lying between the two sources operators in different time moments through the atomic operators is formulated. Using this method, the master equation, which describes these processes, is obtained. In this area the projection operator method for density matrix in the second order interaction with non zero temperature bath is studied. An example is superconductivity, where the Cooper-pair is created in the processes of the simultaneous two-phonon exchange between electrons [2]. It occurs when the one-phonon exchange integral between band electrons is smaller than the two-phonon exchange integral. This is possible in the many-band superconducting materials, in which the two-phonon exchange integral arises through virtual bands of material. Some estimates of two-phonon superconductivity have already been made. A more realistic model which takes into account the specifics of the many-band aspects of superconductor materials is proposed. In the two-phonon processes, a more complicated temperature dependence of the order parameter is expected. A rigorous study of this anomalous temperature dependence of the order parameter of superconductors is presented. One expects that the two-phonon exchange effects can amplify the superconductivity in a way similar to that the thermal field amplifies the two-photon super-radiance in a micro-cavity The Hamiltonian which describes two-quanta exchanges between the electrons at finite temperature effects was obtained. It is shown that at the first stage with increasing the temperature the two phonon correlations between the Cooper pairs increase. This effect can have many analogies with cooperative Lamb shift and two-photon super-radiance which are stimulated by thermal fields for small occupation numbers. 1. N.A.Enaki, V. Eremeev , Physics Letters A 357 (2006), pp.104-107 2. N.A.Enaki, V. Eremeev, New Journal of Physics 4 (2002), 1.1-1.12. |
| R. Fisch, Princeton University Title:"Subextensive Singularity in the 2D $\pm J$ Ising Spin Glass" Abstract: The statistics of low energy states of the 2D Ising spin glass with +1 and -1 bonds are studied for $L \times L$ square lattices with $L \le 48$, and $p$ = 0.5, where $p$ is the fraction of negative bonds, using periodic and/or antiperiodic boundary conditions. The behavior of the density of states near the ground state energy is analyzed as a function of $L$, in order to obtain the low temperature behavior of the model. For large finite $L$ there is a range of $T$ in which the heat capacity is proportional to $T^{5.33 \pm 0.12}$. The range of $T$ in which this behavior occurs scales slowly to $T = 0$ as $L$ increases. Our results indicate that this model obeys the ordinary hyperscaling relation $d \nu = 2 - \alpha$, even though $T_c = 0$. |
| B. Harris, University of Pennsylvania Title:"Ferroelectric Magnets" Abstract:I review the description of simultaneous magnetic and ferroelectric ordering by analyzing the symmetry of the respective order parameters. |
| C. Henley, Cornell University Coauthors:: S-A. Cheong Title:"Nontrivial Maps of Hardcore-Excluded Fermion Chains and Ladders to Non-interacting Fermions: The Intervening-Particle Expansion" Abstract:Consider a one-dimensional chain of F spinless fermions on N sites, which are excluded from occupying adjacent sites. By erasing one site after each fermion, we map this model to free fermions on (N-F) sites, but correlators such as the Green's function between sites i and j are nontrivial, since their separation in the mapped system depends on how many particles are in between. Such correlators must be written as a sum of minors of matrices (in which the entries are the noninteracting 2-point functions). By this means, numerically exact correlators can be evaluated at relatively large separations, permitting numerical evaluation of the oscillation wavevector and the power law envelope. When this is applied to three distinct limits of a ladder model, we found additional exponents not in the spectrum of free fermions (but, we believe, comprehensible via Luttinger liquid theory). |
| M. Hinczewski, F. Gursey Research Center, Istanbul Coauthor:A.N. Berker Title:"Inverted Berezinskii-Kosterlitz-Thouless Singularity and High-Temperature Algebraic Order in an Ising Model on a Scale-Free Hierarchical-Lattice Small-World Network" Abstract:We have obtained exact results for the Ising model on a random hierarchical lattice incorporating three key features characterizing many real-world networks: a scale-free degree distribution, a high clustering coefficient, and the small-world effect.[1] By varying the probability p of long-range bonds, the entire spectrum from an unclustered, non-small-world network to a highly-clustered, small-world system is studied, yielding qualitatively different spin ordering and correlation behaviors. For p<0.494, we find power-law critical behavior, with critical exponents continuously varying with p, and exponential decay of correlations away from Tc. For p>0.494, in fact where the network exhibits small-world character, we find an inverted Berezinskii-Kosterlitz-Thouless singularity, between a low-temperature phase with non-zero magnetization and finite correlation length and a high-temperature phase with zero magnetization and infinite correlation length, with power-law decay of correlations throughout the phase. [1] M. Hinczewski and A.N. Berker, Phys. Rev. E 73, 066126, 1-22 (2006). |
| S. Ji, Rutgers University Title:"Info-Statistical Mechanics' of Cell Metabolism" Abstract: With the technique of DNA microarrays invented at Stanford in the mid-1990's, it is now routine for cell biologists to measure the kinetics of the changes in the intracellular levels of several thousands of mRNA molecules simultaneously from living cells under various experimental and pathological conditions. In collaboration with N. Fefferman, A. Chaovalitwongse and W. Yoo, I have been analyzing the kinetics of the genome-wide transcription levels (TL) and transcription rates (TR) measured from budding yeast after shifting the nutrient from glucose to galactose [Mol Cell 15:303-313 (2004)]. The TL and TR data for each of the over 6,000 genes were measured in triplicates at 6 time points (0, 5, 120, 360, 450 and 850 minutes), generating a total of over 2x3x6x6000 = 216,000 numbers. These data can be displayed as matrices consisting of n rows and m columns, where n is the number of genes (~6,000 in this case) and m (=6) the number of experimental conditions or time points of measurements. These so-called 'expression matrices' ('expression' in this context being synonymous with transcription, the process of synthesyzing mRNA molecules from their DNA templates, catalyzed by a set of about 50 enzymes) carry two kinds of information 1)statistical mechanical information reflecting the Brownian motions of the molecular components of the cell including mRNA, DNA, and associated enzymes, and 2) genetic information responsible for non-random molecular motions of mRNA, DNA and associated proteins and enzymes. It may be suggested that statistical mechanical information is stored (primarily) in rows and genetic information in columns. Thus statistical mechanical laws can be applied only within (and not across) rows, while informatics laws are applicable within (and not across) columns. In conclusion, the expression matrices of living cells generated by DNA microarrays contain both random statistical information as well as non-random genetic information, reflecting the molecular characteristics of the metabolic machineries operating inside living cells. If this analysis is correct, it may be logical to view the study of cell metabolism as an example of what may be referred to as 'info-statistical mechanics', a new term coined here to represent the study of living systems wherein both statistical mechanics and informatics play essential and complementary roles. [S. Ji, BioSystems 54:107-130 (2000); Fundamenta Informaticae 49(1-3):147-165 (2002)]. |
| J. Joo, Sandia National Laboratories Coauthors:S. Plimpton, S. Martin, L. Swiler and J-L. Faulon Title:"Minimal Model of NF-¥êB Signaling Module" Abstract:Understanding the pleiotropism of NF-¥êB signal transduction is a challenge of clear medical importance and systems biology. Current mathematical modeling frameworks for NF-¥êB signal transduction, though limited to a small signaling module located in a downstream of IKK, heavily rely on the parameterizations and the numerical studies of ODE models and doubtless lack intuitive explanations about underlying mechanisms of the dynamic patterns of the NF-kB signaling. In this short talk we present a systematic way to derive a minimal model from an up-to-date and detailed NF-kB signaling network by means of sensitivity analysis. Using analysis of the minimal model, we predict a dose-response curve shape, existence of Hopf-bifurcation, and underlying mechanisms of all possible dynamic patterns of NF-¥êB signaling. Simulating the detailed NF-kB signaling network with large sets of the parameter values that are sampled from the biologically feasible parameter space, we present an ensemble of all possible dynamic patterns of NF-¥êB signaling and verify the prediction from the minimal model. |
| J. Katriel, Technion, Haifa, Israel Coauthors: S. Roy and M. Springborg Title:"Non-Universality of Commonly Used Correlation-Energy Density-Functionals" Abstract:The correlation energies of the helium isoelectronic sequence and of Hooke's atom isoelectronic sequence have been evaluated using an assortment of local, gradient and meta-gradient density functionals. The results are compared with the exact correlation energies, showing that while several of the more recent density functionals reproduce the exact correlation energies of the helium isoelectronic sequence rather closely, none are satisfactory for Hooke's atom isoelectronic sequence. |
| P. Kleban, University of Maine Coauthors:J. Simmons and R. Ziff Title:"Exact Factorization of Probabilities in Critical 2-D Percolation" Abstract:We consider the probability P of connecting various points in the upper half-plane at the 2-D percolation point. For two points, with x_0 on the edge and z in the half-plane, P(x_0,z) is given in terms of the potential at z of a 2-D dipole located at x_0. For three points, one finds the exact and universal factorization P(x_1,x_2,z) = C \sqrt{P(x_1,z)P(x_2,z)P(x_1,x_2)}, where we also have an exact expression for C. These results are calculated by use of conformal field theory. Computer simulations verify them very precisely. Furthermore, simulations show that the same factorization holds asymptotically, with the same value of C, when one or both of the points x_i are moved from the edge into the bulk. Peter Kleban, Jacob J. H. Simmons, and Robert M. Ziff, "Anchored critical percolation clusters and 2-d electrostatics", Phys. Rev. Letters 97, 115702 (2006) [arXiv: cond-mat/0605120]. |
| G. Lee-Dadswell, Cape Breton University Coauthors: B.G. Nickel and C.G. Gray Title:"Heat and Momentum Transport in 1-D: The Bulk Prandtl Number Abstract:In 1D systems with infinite thermal conductivities the heat current power spectrum is seen to go as omega^{-alpha} as omega -> 0, where alpha is a constant less than one. There is currently an intense debate over what the value of alpha is and whether it is system dependent. Various hydrodynamic arguments have been put forward which predict various values of alpha (alpha = 1/3 and alpha = 2/5 have been predicted). Many of these arguments assume that the momentum current power spectrum goes as omega^{-1/2} as omega -> 0. We have found strong evidence that for FPU chains with a nonzero thermal expansion coefficient the heat current power spectrum and the momentum current power spectrum diverge as omega -> 0 with the same power of omega, in contrast to much of the current theory. |
| P. Lugiewicz, Imperial College London Coauthors:B. Zegarlinski Title:"Long Time Behaviour of Hormander Diffusions in Infinite Dimensions" Abstract:We analyse the long time behaviour of semi-group dynamics generated by the Hormander type operators. The invariant measures are given by the Gibbs states describing (finite range) interactions in (compact) spin systems. The strong ergodic property holds true under assumption of strong mixing conditions. |
| Y. Nakamura, University of Tokyo Coauthors: N. Hatano Title:"A non-Hermitian Analysis of Strongly Correlated Quantum Systems" Abstract: We study a non-Hermitian generalization of strongly correlated quantum systems in which an imaginary vector potential is added to the momentum operator. In the tight-binding approximation, we make the hopping energy asymmetric in the Hermitian Hamiltonian. We conjecture that the non-Hermitian critical point where the energy gap vanishes is equal to the inverse correlation length of the Hermitian system. We confirm the conjecture for several exactly solved models[1,2]. We also argue the basis of our conjecture by noting the dispersion relation of the elementary excitation. [1] Y. Nakamura and N. Hatano, Physica B 378 (2006) 292. [2] Y. Nakamura and N. Hatano, J. Phys. Soc. Jpn. 75 (2006) 104001. |
| M. Pleimling, Virginia Tech Coauthors:M. Henkel Title:"Aging in Disordered Magnets and Local Scale-Invariance" Abstract:The aging of the bond-disordered two-dimensional Ising model quenched to below its critical point is studied through the two-time autocorrelator and thermoremanent magnetization (TRM). The corresponding aging exponents are determined. The form of the scaling function of the TRM is well described by the theory of local scale-invariance. |
| A. Rashin, Rutgers University Coauthors:A. Rashin Title:"Statistical Mechanics of Hydrophobicity-Driven Folding in Lattice Proteins" Abstract:Two-dimensional lattice protein models were studied in two approximations of the conformational equilibrium to elucidate the role of surface hydrophobic groups in their stabilities. We demonstrate that stability of any compactly folded sequence is determined by its ability to "flip-flop" (refold) into alternative compact structures. The degree of stability required for folded sequences determines the average numbers of surface hydrophobic groups in stable lattice structures, which are in good agreement with ratios of core to surface hydrophobic groups in real proteins. However, the average destabilization of the native structure per surface hydrophobic group is small (0-0.25 kcal/ mol), often disagrees with the free energies derived from the ratios of core to surface hydrophobic groups in the same structures, and has a combinatorial entropic nature independent of the strength of structure-stabilizing interactions. This suggests that the free energies derived from the core-to-surface ratios of hydrophobic groups in real proteins have little to do with folding thermodynamics. On average, sequences with highly stable native structures are the least hydrophobic. The results suggest that in designing novel stable proteins, hydrophobic groups on the surface should be avoided to reduce the possibility of flip-flopping. The average stability of highly designable structures is never higher than that of some low designability structures, contrary to the accepted view. In the equilibrium approximation with alternative compact and partially unfolded structures, the requirement of high stability selects a unique 5 x 5 structure formed by only a few sequences, suggesting much stronger sequence selectivity than commonly thought. |
| Y. Shokef, University of Pennsylvania Coauthors: D. Levine Title:"Minimal Modeling of Driven Dissipative Systems" Abstract:By simple modeling of dissipative interactions we resolve fundamental questions related to systems far from thermal equilibrium, such as granular materials, foams and colloidal suspensions. We solve the non-Boltzmann energy distribution, demonstrate the violation of time-dependent fluctuation-dissipation relations, show that different measures of effective temperatures generally differ, and address further issues such as ergodicity breaking and detailed balance violation. |
| V. Sood, University of Calgary Coauthor:T. Antal and S. Redner Title:"Evolutionary Dynamics on Graphs Abstract: The evolution of two species with different fitness is investigated on degree-heterogeneous graphs. The population evolves either by one individual dying and being replaced by the offspring of a random neighbor (voter model (VM) dynamics) or by an individual giving birth to an offspring that takes over a random neighbor node (invasion process (IP) dynamics). The fixation probability for one species to take over a population of N individuals depends crucially on the dynamics and on the local environment. Starting with a single fitter mutant at a node of degree k, the fixation probability is proportional to k for VM dynamics and to 1/k for IP dynamics. |
| M. Stenlund, Rutgers University Title: "Asymptotic Expansion of Homoclinic Splitting Matrix Abstract: In the context of a pendulum coupled to several rotators, I will present an asymptotic formula for the matrix measuring the splitting of separatrices at a homoclinic point. |
| T. Taniguchi, Rockefeller University Coauthors:E.G.D. Cohen Title:"Onsager-Machlup Theory for Nonequilibrium Steady States and Fluctuation Theorems" Abstract:Onsager-Machlup theory for nonequilibrium steady states and its connection with fluctuation theorems are discussed for a dragged Brownian particle. Using a functional integral approach, the probability functional for a path is expressed in terms of a Lagrangian function from which entropy production rate and dissipation functions are introduced, and nonequilibrium thermodynamic relations like the energy conservation law and the second law of thermodynamics are derived. Using this Lagrangian function we establish two nonequilibrium detailed balance relations, which not only lead to a fluctuation theorem for work but also to one related to energy loss by friction. A simple argument for the extended fluctuation theorem for heat is also shown in the long time limit. |
| J. Thorarinson, Dartmouth College Coauthors:M. Gleiser Title:"Gauged Oscillations and the Path to Equipartition in the Abelian Higgs Model" Abstract: The Abelian Higgs model supports both topological and non-topological structures that localize energy in x and k space. We present some new non-pertubative solutions from vortex-anti-vortex decay at strong coupling which we call gauged oscillons. The punctuated release of energy from decay of these structures further extends the thermalization timescales of the system. |
| D. Vavylonis, Lehigh University Coauthors:I. Fujiwara and T.D. Pollard Title:"Actin Polymerization and Treadmilling at Steady State" Abstract:Actin proteins assemble into filaments which are treadmilling: at steady state actin filaments on average polymerize at the "barbed" end and depolymerize at the "pointed" end. The origin of this non-equilibrium behavior is the hydrolysis of ATP (bound to actin monomers) into ADP and inorganic phosphate. However so far no model consistent with both detailed balance and experimental measurements of rate constants has been able to explain this behavior quantitatively. Using TIRF microscopy, we measured actin elongation kinetics in the presence of inorganic phosphate. These measurements allowed us to propose a complete and consistent model of actin polymerization. |
| A. Toom, UFPE, Brazil Coauthors:A. Dias Ramos Title:"Non-Schrinking 1-D Non-Ergodicity Abstract:The states of our random process with continuous time are finite sequences of pluses and minuses, in the form of rings. Local interaction consists of three possible operations: a) if a plus and a minus are neighbors, they kill each other with a rate alpha; b) every component may change its state with a rate beta; c) every component may duplicate itself with a rate gamma. Computer simulation shows that for some values of these parameters, if we start with many zeros, zeros prevail forever with a large probability. |
| P. Verrocchio, University of Trento, Italy Coauthors: A. Cavagna and T. Grigera Title:"Mosaic Multi-state Scenario vs. One-state Description of Supercooled Liquids" Abstract: According to the mosaic scenario, relaxation in deeply supercooled liquids is ruled by two competing mechanisms: surface tension, opposing the creation of local excitations, and entropy, providing the drive to the configurational rearrangement of a given region. We test this scenario through numerical simulations well below the Mode Coupling temperature. Given an equilibrated configuration, we freeze all the particles outside a sphere and study the thermodynamics of this sphere. The frozen environment acts as a pinning field. By measuring the overlap between the unpinned and pinned equilibrium configurations of the sphere, we can see whether it has switched to a different state or not. We do not find any clear evidence of the mosaic scenario. Rather, our results seem compatible with the existence of one single state, the liquid. We do, however, find evidence of a growing static correlation length, which seems unrelated to the mosaic one. |
| D. Saakian, Yerevan Physics Institute Title:"Exact Solution of Finite Population Size Quasispecies Model" Abstract:We calculated exactly the distribution function for the single peak fitness landscape, when both the genome length and population size are large. The probability of the loosing the wild sequence also is calculated exactly, thus giving analytical solution of the Muller rachet after 40 years. |
| C. Song, City College of New York Coauthors:Hernan Makse Title:"Phase Diagram of Jammed Granular Matter With Friction" Abstract:Frictionless granular matter was found to undergo a jamming transition when the packing fraction $\phi$ is close to $0.64$ the coordination number $Z$ is $6$. In the presence of friction the situation is more complicated since both $\phi$ and $Z$ depend on friction coefficient. We develop a general theoretical approach to establish a relate between $\phi$ and $Z$. This result leads to a richer picture of the jamming transition and extends the idea of a critical point (J-point) to that of a critical plane. |
| R. Swendsen, Carnegie Mellon University Title:"Boltzmann's Definition of the Entropy" Abstract:A review of Boltzmann's papers shows that his definition of the entropy differs significantly from that commonly found in textbooks. The definition he wrote can be shown to be free of problems created by the usual textbook version. The difference is particularly important for applications to colloids. |
| P. Wang, City College of New York Coauthors:C. Song and H. Makse Title:"Coordination Number in Frictional Granular Packing" Abstract:A packing is static when the number of contact forces equal the number of force and torque balance equations. In a packing of perfectly smooth (frictionless,¦Ì -> 0) and rough (frictional, ¦Ì -> infinity) particles, this results in a minimal coordination number needed for mechanical stability in 3D as Zc = 6 and 4 respectively. Both simulation and analytic results was developed to predict Zc for various friction coefficient. |
| J. Wawrzycki, Inst. Nucl. Phys. PAS Krakow Title:"Points of Noncommutative Phase Space and Quantum Measurement" Abstract:In the lecture a geometric interpretation of the quantum measurement process will be given as the evaluation of the observable "function" (versus observable operator) at a "point" of a noncommutative phase space. On the one hand in the construction the noncommutative geometry of Connes will be exploited and on the other hand a generalization of Gelfand dual based on the Yoneda embedding theorem. To find a correct and usefull notion of "point" of noncommutative space still is a widely open question, we are showing intriguing interplay of the problem with quantum measurement proposing a solution which enables us to interpret geometrically the quantum measurement prosess. |
| O. White, MIT Coauthor: H. Sompolinsky Title: Trading Spaces For Time: A Model of a Mechanism for Short-Term Memory Abstract: The activity of cortical neurons rises while subjects from humans to rats perform tasks that require short-term memory. It is thought that this activity is causally related to the memory ability itself. But how? One mechanism proposes that dynamical attractors describe neuronal activity patterns; a stimulus, for example a spoken word or a picture, activates one from a menu of possible patterns of neuronal activity, each of which is a stable dynamical state. Do neurons in cortex actually operate in stable dynamical states? A recently proposed alternative posits that transient dynamics of cortical neuronal networks stores the temporal history of input stimuli. I will discuss this second potential mechanism for short-term memory, introducing a simple class of models and a framework for quantifying their associated memory. |
| R. Wortis, Trent University Title:"The Geometrically-Averaged Density of States as a Measure of Localization" Abstract:The effectiveness of the geometrically averaged density of states as an order parameter for the Anderson transition is examined by comparing it with the more standard inverse participation ratio in a disordered noninteracting system. We conclude that the suppression of the geometrically averaged density of states with increasing disorder strength is an unreliable measure of localization, while its scaling with system size does provide an upper bound on the localization transition. |
| Y. Wu, Virginia Tech Coauthors: Beat Schmittmann, Royce K. P. Zia Title:"Ideal Polymer Network on a Two-Dimensional Lattice" Abstract:We study the properties of idea polymer networks both near and away from the percolation threshold. The polymers are modeled by random walks on the bonds of a two-dimensional square lattice. We measure the percolation threshold and critical exponents of the networks for various polymer lengths. When the system is far from percolation, we use the effective medium theory to predict its diffusivity. |
| L. Xu, Imperial College London Coauthors: B. Zegarlinski and R. Olkiewicz Title:"Nonlinear Problem in Infinite Interacting Particle Systems" Abstract: We will first give an abract nonlinear generalization of Glauber Dynamics and its existence and uniqueness theorem, then derive a rule to construct such nonlinear models, which we can construct as many as we want according to such rule. Finally, we will consider a special model and get some relationships between the linear model and nonlinear model through tangent functional. |
| B. Yucesoy, Istanbul Technical University Coauthors:A.N. Berker Title:"Spin-Glass Hysteresis in d=3" Abstract: Using hard-spin mean-field theory, hysteresis loops are obtained for Ising spin-glass phases in d=3. The system is driven by a time-dependent magnetic field that is conjugate to the spin-glass order. The scaling behavior of the hysteresis loop areas is calculated. A similar calculation is done for the ferromagnetic phase with quenched antiferromagnetic bond impurities, driven by a time-dependent uniform field. |