The Langevin equation (LE) for the one-dimensional relativistic Brownian motion is derived from a microscopic collision model. The model assumes that a heavy pointlike Brownian particle interacts with the lighter heat bath particles via elastic hard-core collisions. First, the commonly known, nonrelativistic LE is deduced from this model, by taking into account the nonrelativistic conservation laws for momentum and kinetic energy. Subsequently, this procedure is generalized to the relativistic case. There, it is found that the relativistic stochastic force is still $\delta$ correlated (white noise) but no longer corresponds to a Gaussian white noise process. Explicit results for the friction and momentum-space diffusion coefficients are presented and discussed.

An expression for the shear viscosity of a binary fluid mixture is derived using mode-coupling theory in order to study the mass dependence. The calculated results on shear viscosity for a binary isotopic Lennard-Jones fluid mixture show good agreement with results from molecular dynamics simulation carried out over a wide range of mass ratio at different composition. Also proposed is a new generalized Stokes-Einstein relation connecting the individual diffusivities to shear viscosity.

The effect of increasing structural disorder on the distribution of contact forces $P\left(f\right)$ inside three dimensional particle assemblies is systematically studied using computer simulations of model granular packings. Starting from a face-centered-cubic array, where all contact forces are identical, an increasing number of defects is introduced into the assembly, after which the system is then allowed to relax into a different mechanically stable state. Three distinct protocols for imposing disorder are compared. A quantitative measure of the disorder is obtained from distributions of the coordination number and three-particle contact angle. The distribution of normal contact forces show dramatic qualitative changes with increasing disorder. In the regime where the disorder is relatively weak, the pressure and the lowest normal mode frequency scale approximately linearly in the coordination number, with distance from the crystalline state. These results for $P\left(f\right)$ are discussed in the context of jamming phenomena in glassy and granular materials.

The high-temperature Redfield spin-lattice relaxation theory is used for calculating the relaxation times of the different dipolar quasi-invariants in an eight-spin system which represents methyl deuterated para-azoxyanisole $\left(\mathrm{PAA}{d}_6\right)$ in the nematic phase. According to previous experiments, this system can be considered as composed of weakly coupled pairs of strongly interacting spins, the ortho protons of the aromatic rings, thus, it possesses four quasi-invariants of the motion: Zeeman, dipolar intrapair and interpair, and singlet orders. We write the set of coupled differential equations which describe the relaxation of the generalized inverse spin temperatures of the four quasi-invariants. The relaxation constants are then calculated in terms of experimental two-spin spectral densities of the lattice motions. The relation between the multispin and the two-spin spectral densities is also deduced. Calculation shows that the Zeeman and singlet quasi-invariants are uncoupled from the dipolar ones, and that the relaxation time of the singlet order is much longer than those of the Zeeman and dipolar orders. The calculated cross relaxation rate between the dipolar orders through the lattice is small enough to be observable in the experiment. We also show that the nonsecular term associated with the collective motions dominates relaxation of the intrapair and interpair energies in $\mathrm{PAA}{d}_6$, while the local motions do not play a significant role, in qualitative agreement with the reported experimental behavior. The dipolar relaxation times predicted by the theory are significantly larger than the experimental ones, the difference being even more pronounced for the interpair quasi-invariant. We show that the discrepancy cannot be overcome neither by resorting to a realistic model for the spin system nor considering the various possible cross-relaxation pathways among the quasi-invariants. This feature points out the high- temperature approximation as a source of the discrepancy. We discuss the effect that slow and ultraslow molecular modes could have on the relaxation of the dipolar order.

We carry out a thermodynamic analysis to an organism. It is applicable to any type of organism because (1) it is based on a thermodynamic formalism applicable to all open thermodynamic systems and (2) uses a general model to describe the internal structure of the organism—the dynamic energy budget (DEB) model. Our results on the thermodynamics of DEB organisms are the following. (1) Thermodynamic constraints for the following types of organisms: (a) aerobic and exothermic, (b) anaerobic and exothermic, and (c) anaerobic and endothermic; showing that anaerobic organisms have a higher thermodynamic flexibility. (2) A way to compute the changes in the enthalpy and in the entropy of living biomass that accompany changes in growth rate solving the problem of evaluating the thermodynamic properties of biomass as a function of the amount of reserves. (3) Two expressions for Thornton’s coefficient that explain its experimental variability and theoretically underpin its use in metabolic studies. (4) A mechanism that organisms in non-steady-state use to rid themselves of internal entropy production: “dilution of entropy production by growth.” To demonstrate the practical applicability of DEB theory to quantify thermodynamic changes in organisms we use published data on Klebsiella aerogenes growing aerobically in a continuous culture. We obtain different values for molar entropies of the reserve and the structure of Klebsiella aerogenes proving that the reserve density concept of DEB theory is essential in discussions concerning (a) the relationship between organization and entropy and (b) the mechanism of storing entropy in new biomass. Additionally, our results suggest that the entropy of dead biomass is significantly different from the entropy of living biomass.

We use the Toda soliton formalism to propose a possible complex movement of $\alpha$ helices with a very important role in energy transduction during the power stroke of motor proteins. We find that this approach has advantages in comparison with the Davydov soliton model and its variants. We estimated the model’s parameters and calculated corresponding properties of the predicted solitary waves including propagation velocities and energies. The energies are found to be within the expected range.

A heuristic based on vertex invariants is developed to rapidly distinguish nonisomorphic graphs to a desired level of accuracy. The method is applied to sample subgraphs from an Escherichia coli protein interaction network, and as a probe for discovery of extended motifs. The network’s structure is described using statistical properties of its $N$-node subgraphs for $N⩽14$. The Zipf plots for subgraph occurrences are robust power laws that do not change when rewiring the network while fixing the degree sequence—although many specific subgraphs exchange rank. The exponent for the Zipf law depends on $N$. Studying larger subgraphs highlights some striking patterns for various $N$. Motifs, or connected pieces that are overabundant in the ensemble of subgraphs, have more edges, for a given number of nodes, than antimotifs and generally display a bipartite structure or tend toward a complete graph. In contrast, antimotifs, which are underabundant connected pieces, are mostly trees or contain at most a single, small loop.

The generation of vorticity in the two-dimensional creeping flow of an incompressible, electrically conducting viscous fluid past a localized magnetic field distribution is analyzed under the low magnetic Reynolds number approximation. It is shown that the Lorentz force produced by the interaction of the induced electric currents with the nonuniform magnetic field acts as an obstacle for the flow, creating different steady flow patterns that are reminiscent of those observed in the flow past bluff bodies. First, analytic solutions are obtained for a creeping flow past a magnetic point dipole, modeled as a Gaussian distribution. Using a perturbation scheme, the vorticity is expressed as an expansion in the small Reynolds number, and first- and second-order approximations are calculated. The induced magnetic field, pressure, and stream function are also determined. Further, full numerical finite difference solutions are obtained for a uniform creeping flow past a finite size magnetic field distribution produced by a square magnetized plate. Hartmann numbers in the range $1⩽\mathrm{Ha}⩽100$ are explored. Depending on the strength of the magnetic force, stagnation zones or steady vortical structures are obtained. The analysis contributes to the understanding of flows in nonuniform magnetic fields and flows produced by localized forces.

Propagation of femtosecond light pulses in a resonant absorption medium is studied. The propagation time of the light pulses was measured in a dye solution by the optical-Kerr-gate method. Nonadherence to the conventional group velocity $d\omega ∕dk$, which is defined in weak absorption region, was found. The observed wavelength dependences of the group delay and the spectral change in the anomalous dispersion region are qualitatively in good agreement with the theoretical prediction obtained from the new definitions of group velocity, which can be clearly defined even in strong absorption region.

The statistics of self-avoiding walks (SAWs) on deterministic fractal structures with infinite ramification, modeled by Sierpinski square lattices, is revisited in two and three dimensions using the reptation algorithm. The probability distribution function of the end-to-end distance of SAWs, consisting of up to 400 steps, is obtained and its scaling behavior at small distances is studied. The resulting scaling exponents are confronted with previous calculations for much shorter linear chains (20 to 30 steps) based on the exact enumeration (EE) technique. The present results coincide with the EE values in two dimensions, but differ slightly in three dimensions. A possible explanation for this discrepancy is discussed. Despite this, the violation of the so-called des Cloizeaux relation, a renormalization result that holds on regular lattices and on deterministic fractal structures with finite ramification, is confirmed numerically.

The best possible cooling agent is a system with negative specific heat. If in thermal contact with a second system, any acquisition of energy due to a random fluctuation lowers its temperature, and the energy transfer in this direction is further enhanced. It continues until all the energy is extracted from the second system and their temperatures are at par. We exhibit these microcanonical features with a simple mechanical model of interacting classical gas particles in a specially confined domain and subjected to gravitation. As predicted, most of the gas particles are cooled and collect in the lowest part of the container, where the energy is carried away by a few remaining particles.

Generalization of the one-dimensional totally asymmetric exclusion process (TASEP) with open boundary conditions in which particles are allowed to jump $l$ sites ahead with the probability $p_l\sim 1∕l^{\sigma +1}$ is studied by Monte Carlo simulations and the domain-wall approach. For $\sigma >1$ the standard TASEP phase diagram is recovered, but the density profiles display additional features when $1<\sigma <2$. At the first-order transition line, the domain wall is localized and phase separation is observed. In the maximum-current phase the profile has an algebraic decay with a $\sigma$-dependent exponent. Within the $\sigma \le 1$ regime, where the transitions are found to be absent, analytical results in the continuum mean-field approximation are derived in the limit $\sigma =-1$.

We study, in $d$ dimensions, the random walker with geometrically shrinking step sizes at each hop. We emphasize the integrated quantities such as expectation values, cumulants, and moments rather than a direct study of the probability distribution. We develop a $1∕d$ expansion technique and study various correlations of the first step to the position as time goes to infinity. We also show and substantiate with a study of the cumulants that to order $1∕d$ the system admits a continuum counterpart equation which can be obtained with a generalization of the ordinary technique to obtain the continuum limit. We also advocate that this continuum counterpart equation, which is nothing but the ordinary diffusion equation with a diffusion constant decaying exponentially in continuous time, captures all the qualitative aspects of the discrete system and is often a good starting point for quantitative approximations.

We report numerical results for velocity correlations in dense, gravity-driven granular flow down an inclined plane. For the grains on the surface layer, our results are consistent with experimental measurements reported by Pouliquen. We show that the correlation structure within planes parallel to the surface persists in the bulk. The two-point velocity correlation function exhibits exponential decay for small to intermediate values of the separation between spheres. The correlation lengths identified by exponential fits to the data show nontrivial dependence on the averaging time $\mathrm{\Delta }t$ used to determine grain velocities. We discuss the correlation length dependence on averaging time, incline angle, pile height, depth of the layer, system size, and grain stiffness and relate the results to other length scales associated with the rheology of the system. We find that correlation lengths are typically quite small, of the order of a particle diameter, and increase approximately logarithmically with a minimum pile height for which flow is possible, $h_{\mathrm{stop}}$, contrary to the theoretical expectation of a proportional relationship between the two length scales.

Dynamical four-point susceptibilities measure the extent of spatial correlations in the dynamics of glass forming systems. We show how these susceptibilities depend on the lengthscales that necessarily form part of their definition. The behavior of these susceptibilities is estimated by means of an analysis in terms of renewal processes within the context of dynamic facilitation. The analytic results are confirmed by numerical simulations of an atomistic model glass former, and of two kinetically constrained models. Hence we argue that the scenario predicted by the dynamic facilitation approach is generic.

The oxygen and silicon dynamics in silica are compared via computer simulations. In agreement with experimental data and previous simulations a decoupling of oxygen and silicon dynamics is observed upon cooling. The origin of this decoupling is studied in the framework of the potential energy landscape. From analysis of the transition features between neighboring superstructures of minima, denoted metabasins, the differences between the oxygen and silicon dynamics can be quantified. The decoupling can be explicitly related to the presence of generalized rotational processes, giving rise to oxygen but not to silicon displacement. Closer analysis of these processes yields important insight into the nature of the potential energy landscape of silica. The physical picture of relaxation processes in silica, obtained in previous work for oxygen dynamics, is consistent with decoupling effects, elucidated here.

In this work, experimental data points from which the profile of the order parameter of nematic liquid crystals can be obtained, mainly magnetic susceptibility anisotropy and dielectric anisotropy, will be used to show that when rescaled they coalesce along a common line that extends from the nematic-isotropic phase transition region, until the nematic-crystalline phase transition region. A large set of experimental data of a diversity of nematic compounds that share the presence of a nematic-isotropic and a nematic-crystalline phase transition, without another phase within, has been collected from the liquid crystals literature. Taking for each of them the temperatures of these two phase transitions as fixed points, a common temperature scale has been constructed and, in this scale, the value of each physical quantity has been uniformly fixed at the nematic-crystalline phase transition temperature. This procedure has revealed the existence of a law of corresponding states that covers the entire nematic phase. As the values assumed by these physical quantities can be used to measure the macroscopic order parameter, the use of this temperature scale suggests that it presents a common behavior that covers the entire nematic phase.

We propose a solvable model for the migration-driven aggregate growth on completely connected scale-free networks. A reversible migration system is considered with the produce rate kernel $K(k;l\mid i;j)\sim k^u{i}^v(lj{)}^{\nu }$ or the generalized kernel $K(k;l\mid i;j)\sim (k^{\upsilon }{i}^{\omega }+k^{\omega }{i}^{\upsilon })(lj{)}^{\nu }$, at which an $i$-mer aggregate locating on the node with $j$ links gains one monomer from a $k$-mer aggregate locating on the node with $l$ links. It is found that the evolution behavior of the system depends crucially on the details of the rate kernel. In some cases, the aggregate size distribution approaches a scaling form and the typical size $S(t,l)$ of the aggregates locating on the nodes with $l$ links grows infinitely with time; while in other cases, a gelation transition may emerge in the system at a finite critical time. We also introduce a simplified model, in which the aggregates independently gain or lose one monomer at the rate $I_1(k;l)=I_2(k;l)\propto k^{\omega }{l}^{\nu }$, and find the similar results. Most intriguingly, these models exhibit that the evolution behavior of the total distribution of the aggregates with the same size is drastically different from that for the corresponding system in normal space. We test our analytical results with the population data of all counties in the U.S. during the past century and find good agreement between the theoretical predictions and the realistic data.

We investigate the effects of a time-delayed all-to-all coupling scheme in a large population of oscillators with natural frequencies following a bimodal distribution. The regions of parameter space corresponding to synchronized and incoherent solutions are obtained both numerically and analytically for particular frequency distributions. In particular, we find that bimodality introduces a new time scale that results in a quasiperiodic disposition of the regions of incoherence.

We discuss the interband light tunneling in a two-dimensional periodic photonic structure, as studied recently in experiments for optically induced photonic lattices [Trompeter et al., Phys. Rev. Lett. 96, 053903 (2006)]. We identify the Zener tunneling regime at the crossing of two Bloch bands, which occurs in the generic case of a Bragg reflection when the Bloch index crosses the edge of the irreducible Brillouin zone. Similarly, higher-order Zener tunneling involves four Bloch bands when the Bloch index passes through a high-symmetry point on the edge of the Brillouin zone. We derive simple analytical models that describe the tunneling effect, and calculate the corresponding tunneling probabilities.