Analytical expressions for pitchfork and Hopf bifurcation thresholds are given for a nonlinear stochastic differential delay equation with feedback. Our results assume that the delay time $\tau$ is small compared to other characteristic time scales, not a significant limitation close to the bifurcation line. A pitchfork bifurcation line is found, the location of which depends on the conditional average $⟨x\left(t\right)|x\left(t-\tau \right)⟩$, where $x\left(t\right)$ is the dynamical variable. This conditional probability incorporates the combined effect of fluctuation correlations and delayed feedback. We also find a Hopf bifurcation line which is obtained by a multiple scale expansion around the oscillatory solution near threshold. We solve the Fokker-Planck equation associated with the slowly varying amplitudes and use it to determine the threshold location. In both cases, the predicted bifurcation lines are in excellent agreement with a direct numerical integration of the governing equations. Contrary to the known case involving no delayed feedback, we show that the stochastic bifurcation lines are shifted relative to the deterministic limit and hence that the interaction between fluctuation correlations and delay affect the stability of the solutions of the model equation studied.

We propose a scheme for quantum Brownian motion of a particle in a fermionic bath. Based on the spin coherent-state representation of the noise operators and a canonical thermal distribution of the associated $c$ numbers, we derive a quantum analog of generalized Langevin equation for quantum-mechanical mean position of the particle subjected to an external force field. The approach allows us to map the quantum problem on a classical setting. The quantum dispersion around the mean can be estimated order by order by a set of quantum correction equations up to a desired degree of accuracy for a given nonlinear potential. We derive a quantum diffusion equation for free particle and show that quantization, in general, enhances the mean-square displacement. Increase in temperature leads to suppression of mean-square displacement. The method is based on canonical quantization procedure and may be used for understanding diffusive transport and thermally activated processes in a fermionic bath.

Molecular dynamics simulations are carried out to investigate the diffusion behavior of penetrable-sphere model fluids characterized by a finite energy barrier $ϵ$. The self-diffusion coefficient is evaluated from the time-dependent velocity autocorrelation function and mean-square displacement. Detailed insights into the cluster formation for penetrable spheres are gained from the Enskog factor, the effective particle volume fraction, the mean free path, and the collision frequency for both the soft-type penetrable and the hard-type reflective collisions. The simulation data are compared to theoretical predictions from the Boltzmann kinetic equation and from a simple extension to finite $ϵ$ of the Enskog prediction for impenetrable hard spheres $\left(ϵ\to \infty \right)$. A reasonable agreement between theoretical and simulation results is found in the cases of ${ϵ}^{\ast }\equiv ϵ/k_{B}T=0.2$, 0.5, and 1.0. However, for dense systems (packing fraction $\varphi >0.6$) with a highly repulsive energy barrier $\left({ϵ}^{\ast }=3.0\right)$, a poorer agreement was observed due to metastable static effects of clustering formation and dynamic effects of correlated collision processes among these cluster-forming particles.

We introduce slow bottleneck sites into a recent extension of the totally asymmetric exclusion process where hopping rates are allowed to vary dynamically with the availability of resources. In the context of messenger RNA (mRNA) translation in biology, this refers to the availability of amino acid-transfer-RNA (aa-tRNA) complexes which act as the source of amino acids for protein production. We study a simple designer mRNA with a single defect codon in the center. As well as the familiar queuing behavior we also observe a regime within the queuing phase where the queue becomes less severe as the aa-tRNAs become depleted.

By means of numerical simulations and epidemic analysis, the transition point of the stochastic asynchronous susceptible-infected-recovered model on a square lattice is found to be $c_0=0.1765005\left(10\right)$, where $c$ is the probability a chosen infected site spontaneously recovers rather than tries to infect one neighbor. This point corresponds to an infection/recovery rate of ${\lambda }_c=\left(1-c_0\right)/c_0=4.66571\left(3\right)$ and a net transmissibility of $\left(1-c_0\right)/\left(1+3c_0\right)=0.538410\left(2\right)$, which falls between the rigorous bounds of the site and bond thresholds. The critical behavior of the model is consistent with the two-dimensional percolation universality class, but local growth probabilities differ from those of dynamic percolation cluster growth, as is demonstrated explicitly.

A neutral ecology model is simulated on an island chain, in which neighboring islands can exchange individuals but only the first island is able to receive immigrants from a metacommunity. It is found by several measures that $\alpha$-diversity decreases along the chain. Subtle changes in taxon abundance distributions can be detected when islands in the chain are compared to diversity-matched single islands. The island chain is found to have unexpectedly rich dynamics. Significant $\beta$-diversity correlations are found between islands in the chain, which are absent between diversity-matched single islands. The results potentially apply to human microbial biodiversity and biogeography and suggest that measurements of interindividual and intraindividual $\beta$-diversity may give insights into microbial community assembly mechanisms.

With the aid of Brownian dynamics models, it is possible to estimate polymer tension by monitoring polymers’ transverse thermal fluctuations. To assess the precision of the approach, Brownian dynamics-based tension estimates were compared with the force applied to rhodamine-phalloidin labeled actin filaments bound to polymer beads and suspended between two optical traps. The transverse thermal fluctuations of each filament were monitored with a CCD camera, and the images were analyzed to obtain the filament’s transverse displacement variance as a function of position along the filament, the filament’s tension, and the camera’s exposure time. A linear Brownian dynamics model was used to estimate the filament’s tension. The estimated force was compared and agreed within 30% (when the tension $<0.1\text{pN}$) and 70% (when the tension $<1\text{pN}$) with the applied trap force. In addition, the paper presents concise asymptotic expressions for the mechanical compliance of a system consisting of a filament attached tangentially to bead handles (dumbbell system). The techniques described here can be used for noncontact estimates of polymers’ and fibers’ tension.

We consider an elastic chain at thermodynamic equilibrium with a heat bath, and derive an approximation to the probability density function, or pdf, governing the relative location and orientation of the two ends of the chain. Our motivation is to exploit continuum mechanics models for the computation of DNA looping probabilities, but here we focus on explaining the novel analytical aspects in the derivation of our approximation formula. Accordingly, and for simplicity, the current presentation is limited to the illustrative case of planar configurations. A path integral formalism is adopted, and, in the standard way, the first approximation to the looping pdf is obtained from a minimal energy configuration satisfying prescribed end conditions. Then we compute an additional factor in the pdf which encompasses the contributions of quadratic fluctuations about the minimum energy configuration along with a simultaneous evaluation of the partition function. The original aspects of our analysis are twofold. First, the quadratic Lagrangian describing the fluctuations has cross-terms that are linear in first derivatives. This, seemingly small, deviation from the structure of standard path integral examples complicates the necessary analysis significantly. Nevertheless, after a nonlinear change of variable of Riccati type, we show that the correction factor to the pdf can still be evaluated in terms of the solution to an initial value problem for the linear system of Jacobi ordinary differential equations associated with the second variation. The second novel aspect of our analysis is that we show that the Hamiltonian form of these linear Jacobi equations still provides the appropriate correction term in the inextensible, unshearable limit that is commonly adopted in polymer physics models of, e.g. DNA. Prior analyses of the inextensible case have had to introduce nonlinear and nonlocal integral constraints to express conditions on the relative displacement of the end points. Our approximation formula for the looping pdf is of quite general applicability as, in contrast to most prior approaches, no assumption is made of either uniformity of the elastic chain, nor of a straight intrinsic shape. If the chain is uniform the Jacobi system evaluated at certain minimum energy configurations has constant coefficients. In such cases our approximate pdf can be evaluated in an entirely explicit, closed form. We illustrate our analysis with a planar example of this type and compute an approximate probability of cyclization, i.e., of forming a closed loop, from a uniform elastic chain whose intrinsic shape is an open circular arc.

The art of making structural, polymeric, and metallic glasses is rapidly developing with many applications. A limitation is that under increasing external strain all amorphous solids (like their crystalline counterparts) have a finite yield stress which cannot be exceeded without effecting a plastic response which typically leads to mechanical failure. Understanding this is crucial for assessing the risk of failure of glassy materials under mechanical loads. Here we show that the statistics of the energy barriers $\Delta E$ that need to be surmounted changes from a probability distribution function that goes smoothly to zero as $\Delta E=0$ to a pdf which is finite at $\Delta E=0$. This fundamental change implies a dramatic transition in the mechanical stability properties with respect to external strain. We derive exact results for the scaling exponents that characterize the magnitudes of average energy and stress drops in plastic events as a function of system size.

We report an experimental study of a fingering pattern formation which occurs during the spreading of an immiscible thin ferrofluid drop subjected to a radial magnetic field. Our results indicate that this ferrohydrodynamic system works as a magnetic analog of conventional spin coating, where centrifugal driving is replaced with a magnetic body force induced by the radial applied field. In this context, a magnetically tunable pattern selection mechanism is proposed in which the shape and number of the arising fingered structures can be properly controlled.

Locked-to-sliding phase transition has been studied in the driven two-dimensional Frenkel-Kontorova model with the square symmetric substrate potential. It is found that as the driving force increases, the system transfers from the locked state to the sliding state where the motion of particles is in the direction different from that of driving force. With the further increase in driving force, at some critical value, the particles start to move in the direction of driving force. These two critical forces, the static friction or depinning force, and the kinetic friction force for which particles move in the direction of driving force have been analyzed for different system parameters. Different scenarios of phase transitions have been examined and dynamical phases are classified. In the case of zero misfit angle, the analytical expressions for static and kinetic friction force have been obtained.

In this paper we present an approach to anomalous diffusion based on subordination of stochastic processes. Application of such a methodology to analysis of the diffusion processes helps better understanding of physical mechanisms underlying the nonexponential relaxation phenomena. In the subordination framework we analyze a coupling between the very large jumps in physical and two different operational times, modeled by under- and overshooting subordinators, respectively. We show that the resulting diffusion processes display features by means of which all experimentally observed two-power-law dielectric relaxation patterns can be explained. We also derive the corresponding fractional equations governing the spatiotemporal evolution of the diffusion front of an excitation mode undergoing diffusion in the system under consideration. The commonly known type of subdiffusion, corresponding to the Mittag-Leffler (or Cole-Cole) relaxation, appears as a special case of the studied anomalous diffusion processes.

Critical exponents of the Kawasaki dynamics in the Ising chain are re-examined numerically through the spectrum gap of evolution operators constructed both in spin and domain-wall representations. At low-temperature regimes the latter provides a rapid finite-size convergence to these exponents, which tend to $z\simeq 3.11$ for instant quenches under ferromagnetic couplings, while approaching to $z\simeq 2$ in the antiferro case. The spin representation complements the evaluation of dynamic exponents at higher temperature scales, where the kinetics still remains slow.

The paper deals with theoretical study of non linear viscoelastic phenomena in ferrofluids placed in magnetic field. Our attention is focused on the study of nonstationary flow and Maxwell-like relaxation of the macroscopical viscous stress after alternation of the shear rate. We propose that these phenomena can be explained by finite rate of evolution of chainlike aggregates, consisting of the ferrofluid particles. Statistical model of the chains growth-disintegration is suggested. In this model the chain-single particle mechanism of the chains evolution is considered, the effects of the chain-chain interaction are ignored. The proposed model allows us to estimate the time-dependent function of distribution over number of particles in the chain. Having determined this function and using methods of hydromechanics of ferrofluids with chainlike aggregates, we have studied evolution of the ferrofluid viscosity after stepwise alternation of the fluid shear rate. The estimated time of relaxation is in a reasonable agreement with experimental results. Thus, our analysis shows that the observed macroscopical viscoelastic phenomena in ferrofluids can be provided by evolution of the chain ensemble.

We propose a minimal multiagent model for the collective dynamics of opinion formation in the society by modifying kinetic exchange dynamics studied in the context of income, money, or wealth distributions in a society. This model has an intriguing spontaneous symmetry-breaking transition to polarized opinion state starting from nonpolarized opinion state. In order to analyze the model, we introduce an iterative map version of the model, which has very similar statistical characteristics. An approximate theoretical analysis of the numerical results is also given, based on the iterative map version.

Expressions and bounds for Newman’s modularity are presented. These results reveal conditions for or properties of the maximum modularity of a network. The influence of the spectrum of the modularity matrix on the maximum modularity is discussed. The second part of the paper investigates how the maximum modularity, the number of clusters, and the hop count of the shortest paths vary when the assortativity of the graph is changed via degree-preserving rewiring. Via simulations, we show that the maximum modularity increases, the number of clusters decreases, and the average hop count and the effective graph resistance increase with increasing assortativity.

In this work, the anisotropic linear elastic properties of two-phase composite materials, made up of square inclusions embedded in a matrix, are investigated. The inclusions present a fractal hierarchical distribution and are supposed to have the same Poisson’s ratio as the matrix but a different Young’s modulus. The effective elastic moduli of the medium are computed at each fractal iteration by coupling a position-space renormalization-group technique with a finite element analysis. The study allows to obtain and generalize some fundamental properties of fractal composite materials.

In a previous report [C. Rojas, G. Urbina-Villalba, and M. García-Sucre, Phys. Rev. E 81, 016302 (2010)] it was shown that emulsion stability simulations are able to reproduce the lifetime of micrometer-size drops of hexadecane pressed by buoyancy against a planar water-hexadecane interface. It was confirmed that small drops $\left(r_i<10\mu \text{m}\right)$ stabilized with $\beta$-casein behave as nondeformable particles, moving with a combination of Stokes and Taylor tensors as they approach the interface. Here, a similar methodology is used to parametrize the potential of interaction of drops of soybean oil stabilized with bovine serum albumin. The potential obtained is then employed to study the lifetime of deformable drops in the range $10\le r_i\le 1000\mu \text{m}$. It is established that the average lifetime of these drops can be adequately replicated using the model of truncated spheres. However, the results depend sensibly on the expressions of the initial distance of deformation and the maximum film radius used in the calculations. The set of equations adequate for large drops is not satisfactory for medium-size drops $\left(10\le r_i\le 100\mu \text{m}\right)$, and vice versa. In the case of large particles, the increase in the interfacial area as a consequence of the deformation of the drops generates a very large repulsive barrier which opposes coalescence. Nevertheless, the buoyancy force prevails. As a consequence, it is the hydrodynamic tensor of the drops which determine the characteristic behavior of the lifetime as a function of the particle size. While the average values of the coalescence time of the drops can be justified by the mechanism of film thinning, the scattering of the experimental data of large drops cannot be rationalized using the methodology previously described. A possible explanation of this phenomenon required elaborate simulations which combine deformable drops, capillary waves, repulsive interaction forces, and a time-dependent surfactant adsorption.