The existence of beyond mean-field quasicycle oscillations in a simple spatial model of predator-prey interactions is derived from a path-integral formalism. The results agree substantially with those obtained from analysis of similar models using system size expansions of the master equation. In all of these analyses, the discrete nature of predator-prey populations and finite-size effects lead to persistent oscillations in time, but spatial patterns fail to form. The path-integral formalism goes beyond mean-field theory and provides a focus on individual realizations of the stochastic time evolution of population not captured in the standard master-equation approach.

The structure of unilamellar vesicles (ULVs), comprising long- and short-chain lipids, was investigated, and the formation of nanopores on the surface of the ULVs was confirmed under the condition of long- and short-chain lipids being separated. It was also revealed that the behavior of the structural phase transition from ULVs to bilayered micelles (bicelles) depends on the number of nanopores formed on the surface of the ULVs. Because both the rim structures of nanopores and bicelles are considered to be microdomains of short-chain lipids, this phase behavior was explained by considering the kinetic pathway of the growth of the rim domain. It was concluded that the phase segregation of lipids plays an essential role in the rim formation of nanopores as well as bicelles.

We propose a mathematical model of the $N$-person prisoner’s dilemma game played by a continuous population of agents with a time-dependent aspiration level. The model—a system of differential equations—takes into account the evolution of the aspiration level and of the mean frequency of the cooperators in the population. The dependence of the asymptotic level of cooperation on the individual payoffs and on the transition rates determining the agent’s reaction to the received payoffs is studied. In general the existence and the magnitude of the asymptotic level of cooperation depends on $N$, the payoffs and the transition rates, and decreases with increasing $N$.

Using a cellular automaton traffic model based on the stochastic optimal velocity model with appropriate assumptions for both incoming and outgoing vehicle boundaries, the so-called bottleneck issue on a lane-closing section was investigated in terms of game theory. In the system, two classified driver agents coexist: C agents (cooperative strategy) always driving in the first lane and D agents (defective strategy) trying to drive in a lower-density lane whether the first or the second lane. In high-density flow, D agents’ interruption into the first lane from the second just before the lane-closing section creates a heavier traffic jam, which reduces social efficiency. This particular event can be described with a prisoner’s dilemma game structure.

The electrical conductivity of carbon plasmas is measured in the range of densities from about 0.6 solid density down to about 0.05 solid density, and reported for values of internal energy ranging from $2\text{to}22\mathrm{kJ}∕\mathrm{gm}$. Plasmas are formed by rapid electrical discharge through thin graphite fibers immersed in a water bath. The pressure in the expanding plasma column is determined by use of a hydrodynamic model to describe the effect on the water surround. It is found that at constant internal energy per unit mass $U$, conductivity $\sigma$ varies with specific volume $v$ as $\sigma =v^{-\alpha }$, where $\alpha$ is about 1 for $U<6\mathrm{kJ}∕\mathrm{gm}$, and rises to about 1.5 for $U=22\mathrm{kJ}∕\mathrm{gm}$.

We study fluctuations in diffusion-limited reaction systems driven out of their stationary state. Using a numerically exact method, we investigate fluctuation ratios in various systems which differ by their level of violation of microscopic time reversibility. Studying a quantity that for an equilibrium system is related to the work done to the system, we observe that under certain conditions oscillations appear on top of an exponential behavior of transient fluctuation ratios. We argue that these oscillations encode properties of the probability currents in state space.

A phase-field model of nonisothermal solidification in dilute binary alloys is used to study the variation of growth velocity, dendrite tip radius, and radius selection parameter as a function of Lewis number at fixed undercooling. By the application of advanced numerical techniques, we have been able to extend the analysis to Lewis numbers of order 10 000, which are realistic for metals. A large variation in the radius selection parameter is found as the Lewis number is increased from 1 to 10 000.

Density fluctuation effects on the conformation of a polymer chain in a supercritical solvent were investigated by performing a multiscale simulation based on the density-functional theory. We found (a) a universal swelling of the polymer chain near the critical point, irrespective of whether the polymer chain is solvophilic or solvophobic, and (b) a characteristic collapse of the polymer chain having a strong solvophilicity at a temperature slightly higher than the critical point, where the isothermal compressibility becomes less than the ideal one.

Ligaments and tendons have a significant role in the musculoskeletal system and are frequently subjected to injury. This study presents a model of collagen fibers, based on the study of a statistical distribution of fibers when they are subjected to quasistatic linear stretching. With respect to other methodologies, this model is able to describe the behavior of the bundle using less ad hoc hypotheses and is able to describe all the quasistatic stretch-load responses of the bundle, including the yield and failure regions described in the literature. It has two other important results: the first is that it is able to correlate the mechanical behavior of the bundle with its internal structure, and it suggests a methodology to deduce the fibers population distribution directly from the tensile-test data. The second is that it can follow fibers’ structure evolution during the stretching and it is possible to study the internal adaptation of fibers in physiological and pathological conditions.

The exact expression for the density matrix of the kink ground state of the ferromagnetic $XXZ$ chain is obtained. Utilizing this, we exactly calculate various correlation functions such as the longitudinal and transverse spin-spin correlation functions, and the ferromagnetic and antiferromagnetic string formation probabilities. The asymptotic behaviors of these correlation functions are also analyzed. As a consequence, we find that the spin-spin correlation functions decay exponentially for large distances, while the string formation probabilities exhibit Gaussian decay for large strings. We also evaluate the entanglement entropy, which shows interesting behaviors due to the lack of the translational invariance of the state.

We calculate the relaxational dynamical critical behavior of systems of $\mathrm{O}\left(n_{\parallel }\right)\oplus \mathrm{O}\left(n_{\perp }\right)$ symmetry including conservation of magnetization by renormalization group theory within the minimal subtraction scheme in two-loop order. Within the stability region of the Heisenberg fixed point and the biconical fixed point, strong dynamical scaling holds, with the asymptotic dynamical critical exponent $z=2\varphi ∕\nu -1$, where $\varphi$ is the crossover exponent and $\nu$ the exponent of the correlation length. The critical dynamics at $n_{\parallel }=1$ and $n_{\perp }=2$ is governed by a small dynamical transient exponent leading to nonuniversal nonasymptotic dynamical behavior. This may be seen, e.g., in the temperature dependence of the magnetic transport coefficients.

A simple fluid, described by pointlike particles interacting via the Lennard-Jones potential, is considered under confinement in a slit geometry between two walls at distance $L_z$ apart for densities inside the vapor-liquid coexistence curve. Equilibrium then requires the coexistence of a liquid “bridge” between the two walls, and vapor in the remaining pore volume. We study this equilibrium for several choices of the wall-fluid interaction (corresponding to the full range from complete wetting to complete drying, for a macroscopically thick film), and consider also the kinetics of state changes in such a system. In particular, we study how this equilibrium is established by diffusion processes, when a liquid is inserted into an initially empty capillary (partial or complete evaporation into vacuum), or when the volume available for the vapor phase increases. We compare the diffusion constants describing the rates of these processes in such inhomogeneous systems to the diffusion constants in the corresponding bulk liquid and vapor phases.

The process of tightening of the open trefoil knot tied on an elastic filament is analyzed. Evolution of the curvature profile is presented and discussed.

We consider unbounded precessing rotating flows in which vertical or horizontal shear is induced by the interaction between the solid-body rotation (with angular velocity ${\Omega }_0$) and the additional “precessing” Coriolis force (with angular velocity $-\epsilon {\Omega }_0$), normal to it. A “weak” shear flow, with rate $2\epsilon$ of the same order of the Poincaré “small” ratio $\epsilon$, is needed for balancing the gyroscopic torque, so that the whole flow satisfies Euler’s equations in the precessing frame (the so-called admissibility conditions). The base flow case with vertical shear (its cross-gradient direction is aligned with the main angular velocity) corresponds to Mahalov’s [Phys. Fluids A 5, 891 (1993)] precessing infinite cylinder base flow (ignoring boundary conditions), while the base flow case with horizontal shear (its cross-gradient direction is normal to both main and precessing angular velocities) corresponds to the unbounded precessing rotating shear flow considered by Kerswell [Geophys. Astrophys. Fluid Dyn. 72, 107 (1993)]. We show that both these base flows satisfy the admissibility conditions and can support disturbances in terms of advected Fourier modes. Because the admissibility conditions cannot select one case with respect to the other, a more physical derivation is sought: Both flows are deduced from Poincaré’s [Bull. Astron. 27, 321 (1910)] basic state of a precessing spheroidal container, in the limit of small $\epsilon$. A Rapid distortion theory (RDT) type of stability analysis is then performed for the previously mentioned disturbances, for both base flows. The stability analysis of the Kerswell base flow, using Floquet’s theory, is recovered, and its counterpart for the Mahalov base flow is presented. Typical growth rates are found to be the same for both flows at very small $\epsilon$, but significant differences are obtained regarding growth rates and widths of instability bands, if larger $\epsilon$ values, up to 0.2, are considered. Finally, both flow cases are briefly discussed in view of a subsequent nonlinear study using pseudospectral direct numerical simulations, which is a natural continuation of RDT.

The study of the dynamics of one-dimensional chains with both harmonic and nonlinear interactions, as in the Fermi-Pasta-Ulam and related problems, has played a central role in efforts to identify the broad consequences of nonlinearity in these systems. Nevertheless, little is known about the dynamical behavior of purely nonlinear chains where there is a complete absence of the harmonic term, and hence sound propagation is not admissible, i.e., under conditions of “acoustic vacuum.” Here we study the dynamics of highly localized excitations, or breathers, which are known to be initiated by the quasistatic stretching of the bonds between adjacent particles. We show via detailed particle-dynamics-based studies that many low-energy pulses also form in the vicinity of the perturbation, and the breathers that form are “fragile” in the sense that they can be easily delocalized by scattering events in the system. We show that the localized excitations eventually disperse, allowing the system to attain an equilibrium-like state that is realizable in acoustic vacuum. We conclude with a discussion of how the dynamics is affected by the presence of acoustic oscillations.

The asymmetric simple exclusion process with additional Langmuir kinetics, i.e., attachment and detachment in the bulk, is a paradigmatic model for intracellular transport. Here we study this model in the presence of randomly distributed inhomogeneities (“defects”). Using Monte Carlo simulations, we find a multitude of coexisting high- and low-density domains. The results are generic for one-dimensional driven diffusive systems with short-range interactions and can be understood in terms of a local extremal principle for the current profile. This principle is used to determine current profiles and phase diagrams as well as statistical properties of ensembles of defect samples.

We study steady states of the motion of a large number of particles in a closed box that are excited by a vibrating boundary and experience a linear drag force from the interstitial fluid. The dissipation in such systems arises from two main sources: Inelasticity in particle collisions and the effects of interstitial fluid on the particles. In many applications, order of magnitude estimates suggest that the dissipation due to interstitial fluid effects may greatly exceed that due to inelasticity and one is naturally led to neglect inelastic effects. In this study, we show that, if one adopts a linear drag force and inelastic effects are neglected, a steady state only exists when the vibration speed of the boundary is below a critical value. For vibration speeds above this critical value, no steady state exists since the kinetic energy of the particles grows without bound. We show that, for vibration speeds above the critical value, inelastic effects must be included to obtain a steady state even if order of magnitude estimates suggest they are negligible. Numerical simulations confirm these theoretical predictions. We also show that inclusion of apparently small nonlinear drag terms can also play a similar role in preventing the kinetic energy of the particles growing without bound.

We investigate the statistics of isoheight lines of $\left(2+1\right)$-dimensional Kardar-Parisi-Zhang model at different level sets around the mean height in the saturation regime. We find that the exponent describing the distribution of the height-cluster size behaves differently for level cuts above and below the mean height, while the fractal dimensions of the height-clusters and their perimeters remain unchanged. The statistics of the winding angle confirms the previous observation that these contour lines are in the same universality class as self-avoiding random walks.

In a dynamical system the singular vector (SV) indicates which perturbation will exhibit maximal growth after a time interval $\tau$. We show that in systems with spatiotemporal chaos the SV exponentially localizes in space. Under a suitable transformation, the SV can be described in terms of the Kardar-Parisi-Zhang equation with periodic noise. A scaling argument allows us to deduce a universal power law ${\tau }^{-\gamma }$ for the localization of the SV. Moreover the same exponent $\gamma$ characterizes the finite-$\tau$ deviation of the Lyapunov exponent in excellent agreement with simulations. Our results may help improve existing forecasting techniques.

Three-dimensional finite systems of charged dust particles confined to concentric spherical shells in a dusty plasma, so-called “Yukawa balls,” have been studied experimentally with respect to their dynamic properties. For that purpose, the three-dimensional thermal Brownian motion of the dust particles around their equilibrium positions was reconstructed with high accuracy. From that the dynamic properties in the form of mode patterns and frequencies are obtained from singular value decomposition and normal mode analysis. The dynamics of the Yukawa balls was found to be dominated by large-scale low-frequency shearlike modes.