We propose a new, simple, thermodynamically based model in order to study the effect of film thickness on the glass transition of a polymer. The model equation of state incorporates the effect of a free surface by accounting for missing interactions, and is parametrized using experimental data for bulk samples, leaving no freely adjustable parameters. To this end we focus on connecting model agreement in the bulk limit with two key physical properties: pressure-volume-temperature data and surface tension data. For the case of polystyrene we show that accounting for these effects, alone, yields results in surprisingly good agreement with experiment for the shift in glass transition in going from bulk to freestanding film. Insight from this simple model indicates that only a small increase in the specific volume of a thin film (compared to bulk) may drive the shift in the glass transition temperature. Herein we focus on a molecular weight independent regime. Looking ahead we consider the possible contributions of chain confinement to the thermodynamic properties of the film.

We present a detailed calculation that enables us to estimate the reversal time of a molecular motor assembly that displays bidirectional motion in the limit of weak noise. We derive a Fokker-Planck equation by taking a large volume expansion of a master equation, and we consider a simple choice of transition rates that enables us to reduce the number of variables to 2. We use the Wentzell-Freidlin theory to define an effective nonequilibrium potential and analytically estimate the reversal time. We also present the results of stochastic simulations that match very well our simulation results.

We sought to measure infinitesimal phase response curves (iPRCs) from rat hippocampal CA1 pyramidal neurons. It is difficult to measure iPRCs from noisy neurons because of the dilemma that either the linearity or the signal-to-noise ratio of responses to external perturbations must be sacrificed. To overcome this difficulty, we used an iPRC measurement model formulated as the Langevin phase equation (LPE) to extract iPRCs in the Bayesian scheme. We then simultaneously verified the effectiveness of the measurement model and the reliability of the estimated iPRCs by demonstrating that LPEs with the estimated iPRCs could predict the stochastic behaviors of the same neurons, whose iPRCs had been measured, when they were perturbed by periodic stimulus currents. Our results suggest that the LPE is an effective model for real oscillating neurons and that many theoretical frameworks based on it may be applicable to real nerve systems.

The search through the proteins conformational space is thought as an early independent stage of the folding process, governed mainly by the hydrophobic effect. Because of the nanoscopic size of proteins, we assume that the effects of local thermal fluctuations work like folding assistants, managed by the nonextensive parameter $q.$ Using a 27-mer heteropolymer on a cubic lattice, we obtained—by Monte Carlo simulations—kinetic and thermodynamic amounts (such as the characteristic folding time and the native stability) as a function of temperature $T$ and $q$ for a few distinct native targets. We found that for each native structure, at a specific system temperature $T,$ there exists an optimum $q^{*}$ that minimizes the folding characteristic time ${\tau }_{\min }$; for $T=1,$ it is found that $q^{*}$ lies in the interval $1.15\pm 0.05,$ even for native structures presenting significantly different topological complexities. The distribution of ${\tau }_{\min }$ obtained for specific $q>1$ (nonextensive approach) and temperature $T$ can be fully reproduced for $q=1$ (Boltzmann approach), but only at higher temperatures $T{}^{\prime }>T$. However, assuming that the complete set of proteins of each organism is optimized to work in a narrow range of temperature, we conclude that—for the present problem—the two approaches, namely, $(T,q>1)$ and $(T>T^{\prime },q=1),$ cannot be equivalent; it is not a simple matter of reparametrization. Finally, by associating the nonextensive parameter $q$ with the instantaneous degree of compactness of the globule, $q$ becomes a dynamic variable, self-adjusted along the simulation. The results obtained through the $q$-variable approach are utterly consistent with those obtained by using a target-tuned parameter $q^{*}.$ However, in the former approach, $q$ is automatically adjusted by the chain conformational evolution, eliminating the need to seek for a specific optimized value of $q$ for each case. Besides, using the $q$-variable approach, different target structures are promptly characterized by inherent distributions of $q$, which reflect the overall complexity of their corresponding native topologies and energy landscapes.

Negative serial correlations in single spike trains are an effective method to reduce the variability of spike counts. One of the factors contributing to the development of negative correlations between successive interspike intervals is the presence of adaptation currents. In this work, based on a hidden Markov model and a proper statistical description of conditional responses, we obtain analytically these correlations in an adequate dynamical neuron model resembling adaptation. We derive the serial correlation coefficients for arbitrary lags, under a small adaptation scenario. In this case, the behavior of correlations is universal and depends on the first-order statistical description of an exponentially driven time-inhomogeneous stochastic process.

Numerous mathematical models exploring the emergence of complexity within developmental biology incorporate diffusion as the dominant mechanism of transport. However, self-organizing paradigms can exhibit the biologically undesirable property of extensive sensitivity, as illustrated by the behavior of the French-flag model in response to intrinsic noise and Turing’s model when subjected to fluctuations in initial conditions. Domain growth is known to be a stabilizing factor for the latter, though the interaction of intrinsic noise and domain growth is underexplored, even in the simplest of biophysical settings. Previously, we developed analytical Fourier methods and a description of domain growth that allowed us to characterize the effects of deterministic domain growth on stochastically diffusing systems. In this paper we extend our analysis to encompass stochastically growing domains. This form of growth can be used only to link the meso- and macroscopic domains as the “box-splitting” form of growth on the microscopic scale has an ill-defined thermodynamic limit. The extension is achieved by allowing the simulated particles to undergo random walks on a discretized domain, while stochastically controlling the length of each discretized compartment. Due to the dependence of diffusion on the domain discretization, we find that the description of diffusion cannot be uniquely derived. We apply these analytical methods to two justified descriptions, where it is shown that, under certain conditions, diffusion is able to support a consistent inhomogeneous state that is far removed from the deterministic equilibrium, without additional kinetics. Finally, a logistically growing domain is considered. Not only does this show that we can deal with nonmonotonic descriptions of stochastic growth, but it is also seen that diffusion on a stationary domain produces different effects to diffusion on a domain that is stationary “on average.”

The fluctuation-dissipation theorem together with the exact density response spectrum for ideal quantum gases has been utilized to yield a new expression for the static structure factor, which we use to derive exact analytical expressions for the temperature-dependent pair distribution function $g\left(r\right)$ of the ideal gases. The plots of bosonic and fermionic $g\left(r\right)$ display “Bose pile” and “Fermi hole” typically akin to bunching and antibunching as observed experimentally for ultracold atomic gases. The behavior of spin-scaled pair correlation for fermions is almost featureless, but bosons show a rich structure including long-range correlations near $T_c$. The coherent state at $T=0$ shows no correlation at all, just like single-mode lasers. The depicted decreasing trend in correlation with decrease in temperature for $T<T_c$ should be observable in accurate experiments.

The influence of directors has been one of the most engaging topics recently, but surprisingly little research has been done to quantitatively evaluate the influence and power of directors. We analyze the structure of the US corporate governance network for the 11-year period 1996–2006 based on director data from the Investor Responsibility Research Center director database, and we develop a centrality measure named the influence factor to estimate the influence of directors quantitatively. The US corporate governance network is a network of directors with nodes representing directors and links between two directors representing their service on common company boards. We assume that information flows in the network through information-sharing processes among linked directors. The influence factor assigned to a director is based on the level of information that a director obtains from the entire network. We find that, contrary to commonly accepted belief that directors of large companies, measured by market capitalization, are the most powerful, in some instances, the directors who are influential do not necessarily serve on boards of large companies. By applying our influence factor method to identify the influential people contained in the lists created by popular magazines such as Fortune, Networking World, and Treasury and Risk Management, we find that the influence factor method is consistently either the best or one of the two best methods in identifying powerful people compared to other general centrality measures that are used to denote the significance of a node in complex network theory.

Using a hydrochemical simulation, temperature dependency of single-bubble sonoluminescence (SL) in a concentrated solution of sulfuric acid has theoretically been studied. With calculating the phase diagrams of an SL bubble in the solution of 85% acid, maximum acquirable SL emissions at different ambient temperatures were calculated. The results show that the SL emission in sulfuric acid increases with increment in the ambient temperature. This temperature dependency is in opposition to that observed in experiments for SL in water. The difference originates from different instability mechanisms determining the ultimate phase parameters of SL in water and sulfuric acid. In water, due to the smallness of viscosity, the ultimate phase parameters are determined by the shape instability. However, in sulfuric acid the phase parameters are restricted by positional instability due to the largeness of the liquid viscosity.

Using numerical simulations, we investigate the equilibrium dynamics of a single-component fluid with Yukawa interaction potential. We show that, for a wide range of densities and temperatures, the dynamics of the system are in striking agreement with a simple model of generalized hydrodynamics. Since the Yukawa potential can describe the ion-ion interactions in a plasma, our results have significant applicability for both analyzing and interpreting the results of x-ray scattering data from high-power lasers and fourth-generation light sources.

The heat flux in rotating Rayleigh-Bénard convection in a fluid of Prandtl number $\text{Pr}=0.1$ enclosed between free-slip top and bottom boundaries is investigated using direct numerical simulation in a wide range of Rayleigh numbers (${10}^4\le \text{Ra}\le {10}^8$) and Taylor numbers ($0\le \text{Ta}\le {10}^8$). The Nusselt number $\text{Nu}$ scales with the Rayleigh number $\text{Ra}$ as ${\text{Ra}}^{\beta }$ with $\beta =2/7$ for values of $\text{Nu}$ greater than a critical value ${\text{Nu}}_c$, which occurs for $\text{Ta}/\text{Ra}\sim 1$. The exponent $\beta$ is not universal for $\text{Nu}<{\text{Nu}}_c$ (for $\text{Ta}/\text{Ra}>1$) but a function of $\text{Ta}$ showing a minimum for some intermediate value of $\text{Ta}$. The critical Nusselt number ${\text{Nu}}_c$ and the corresponding critical Rossby number ${\text{Ro}}_c$ scale with $\text{Ta}$ as ${\text{Ta}}^{0.277\pm 0.001}$ and ${\text{Ta}}^{-0.015\pm 0.003}$, respectively.

Transfer-matrix methods, with the help of finite-size scaling and conformal invariance concepts, are used to investigate the critical behavior of two-dimensional square-lattice Ising spin-$1/2$ systems with first- and second-neighbor interactions, both antiferromagnetic, in a uniform external field. On the critical curve separating collinearly ordered and paramagnetic phases, our estimates of the conformal anomaly $c$ are very close to unity, indicating the presence of continuously varying exponents. This is confirmed by direct calculations, which also lend support to a weak-universality picture; however, small but consistent deviations from the Ising-like values $\eta =1/4$, $\gamma /\nu =7/4$, $\beta /\nu =1/8$ are found. For higher fields, on the line separating row-shifted $(2\times 2)$ and disordered phases, we find values of the exponent $\eta$ very close to zero.

Quasielastic neutron scattering (QENS) was used to investigate the diffusion dynamics of hydration water on the surface of rutile (TiO${}_2$) nanopowder. The dynamics measurements utilizing two inelastic instruments, a backscattering spectrometer and a disk chopper spectrometer, probed the fast, intermediate, and slow motions of the water molecules on the time scale of picoseconds to more than a nanosecond. We employed a model-independent analysis of the data collected at each value of the scattering momentum transfer to investigate the temperature dependence of several diffusion components. All of the probed components were present in the studied temperature range of 230–320 K, providing, at a first sight, no evidence of discontinuity in the hydration water dynamics. However, a qualitative change in the elastic scattering between 240 and 250 K suggested a surface freezing-melting transition, when the motions that were localized at lower temperatures became delocalized at higher temperatures. On the basis of our previous molecular dynamics simulations of this system, we argue that interpretation of QENS data from such a complex interfacial system requires at least qualitative input from simulations, particularly when comparing results from spectrometers with very different energy resolutions and dynamic ranges.

We explore the possibility of describing experimental susceptibility spectra of the glass former propylene carbonate with a two-component schematic model of mode-coupling theory (MCT) from above the melting point down to temperatures far below the critical temperature of MCT. By introducing a phenomenological time-dependent hopping rate, the spectra are reproduced in the full frequency and temperature range available. Literature data of dielectric susceptibilities and depolarized Brillouin light-scattering spectra are combined with our measurements of photon correlation spectroscopy to cover up to 18 decades in frequency of spectra for two different dynamical variables. A consistent description of all data sets is obtained by adjusting only a few physically motivated parameters. In particular the excess wing or slow $\beta$-relaxation commonly observed in the susceptibility spectra can consistently be modeled as originating from a coupling of the individual experimental probe correlator to the collective density fluctuations.

We exploit a simple model to numerically and analytically investigate the effect of enforcing a time constraint for achieving a system-wide goal during an evolutionary dynamics. This situation is relevant to finding antibody specificities in the adaptive immune response as well as to artificial situations in which an evolutionary dynamics is used to generate a desired capability in a limited number of generations. When the likelihood of finding the target phenotype is low, we find that the optimal mutation rate can exceed the error threshold, in contrast to conventional evolutionary dynamics. We also show how a logarithmic correction to the usual inverse scaling of population size with mutation rate arises. Implications for natural and artificial evolutionary situations are discussed.

Modeling the structure and mechanics of microtubules, which play significant roles in various physiological functions of cells, has long been a fascinating issue. In this paper, a coarse-grained mechanochemical model is presented to study the mechanical–chemical coupling and dynamic attributes of microtubules. The interactions among tubulins are taken into account from the molecular basis. This model is used to characterize the conformations of sheet-ended microtubules, to analyze the distributions of interaction energy, and further to simulate the radial indentation process of a microtubule. This method also works for investigating the dynamic properties of microtubules, e.g., their assembly, growth, deformation, and structural evolution for different conditions. This study is helpful for understanding the structure–mechanics–function relationship of microtubules and lays a foundation for further investigation of their dynamic behavior.

The energy landscape paving (ELP) method is a class of heuristic global optimization algorithms based on Monte Carlo sampling. By incorporating the generation of an initial conformation based on a greedy strategy, the conformation update mechanism based on pull moves, and some heuristic off-trap strategies into an improved ELP method, we propose an alternative version of the ELP method, called the ELP–pull move method. We test the ELP-pull move method on both two-dimensional (2D) and 3D hydrophobic-hydrophilic protein-folding models. For ten 2D benchmark sequences of length ranging from 20 to 100, the proposed algorithm finds the lowest energies so far. Within the achieved results, the algorithm converges more rapidly and efficiently than previous methods. For all ten 3D sequences with a length of 64, the ELP–pull move method finds lower energies within comparable computational times. The numerical results demonstrate that our algorithm is a powerful method to study the lattice protein-folding model.

A theory is provided to analyze the dynamics of delay-coupled pools of spiking neurons based on stability analysis of stationary firing. Transitions between stable and unstable regimes can be predicted by bifurcation analysis of the underlying integral dynamics. Close to the bifurcation point the network exhibits slowly changing activities and allows for slow collective phenomena like continuous attractors.

A generalized model for interacting self-avoiding trails on a square lattice is presented and studied using numerical transfer matrix methods. The model differentiates between on-site double visits corresponding to collisions, and crossings. Rigidity is also included in the model. The model includes the Nienhuis $O(n=0)$ model and the interacting self-avoiding trail model as special cases. It is shown that the generic type of collapse found is the same as in the pure interacting self-avoiding trail model.

A hyperbolic plane can be modeled by a structure called the enhanced binary tree. We study the ferromagnetic Ising model on top of the enhanced binary tree using the renormalization-group analysis in combination with transfer-matrix calculations. We find a reasonable agreement with Monte Carlo calculations on the transition point, and the resulting critical exponents suggest the mean-field surface critical behavior.