We present accurate molecular dynamics calculations of the shear stress relaxation modulus of a simple atomic fluid over a wide range of densities. The high accuracy of the data enables us to study changes in the functional form of the shear relaxation modulus, and the properties that are derived from it, as the density is increased from the ideal gas limit to the upper limit of the fluid range. We show that the shear relaxation modulus of a dilute atomic fluid can be accurately described with a simple functional form consisting of a Gaussian plus a single exponential, whereas the dense fluid exhibits a more complicated relaxation function. The infinite-frequency shear modulus, the zero-shear viscosity, and the zero-shear first normal stress coefficient are calculated from the stress autocorrelation function. The ratio of the first normal stress coefficient to the viscosity is used to calculate the viscoelastic relaxation time. While the viscosity and the infinite-frequency shear modulus both increase monotonically with increasing density, the first normal stress coefficient and the viscoelastic relaxation time both decrease to a minimum at intermediate densities before increasing again. Our results for the viscosity and the first normal stress coefficient in the low-density limit both agree well with the predictions of kinetic theory.

The mechanical properties of a class of cellular material were measured. The composition of the material was progressively modified, while its pore structure was kept unchanged. Rigid foam, prepared from a thermoset resin, was gradually converted into reticulated vitreous carbon foam by pyrolysis at increasingly higher heat-treatment temperatures (HHT). The corresponding changes in the Young's modulus $Y$ and the compressive strength $\sigma$ of the materials were measured over a wide range of porosities. The materials exhibit a percolation behavior with a zero percolation threshold. At very low densities the Young's modulus and the compressive strength appear to follow the power laws predicted by percolation theory near the percolation threshold. But, whereas the exponent $\tau$ associated with the power-law behavior of $Y$ appears to vary significantly with the material's density and the HHT, the exponent associated with $\sigma$ does not change much. The possible cause of the apparent and surprising nonuniversality of $\tau$ is discussed in detail, in the light of the fact that only the materials’ composition varies, not the structure of their pore space that could have caused the nonuniversality.

We study one-dimensional exclusion processes in two coupled closed rings consisting of a common diffusive channel and two parallel active (driven) channels. Our model displays bulk-driven phase transition and phase coexistence in the form of a localized domain wall (DW) in one of the active channels in a limit where the diffusive and driven dynamics compete. By controlling a splitting parameter which tunes the in-coming currents into the active channels, the system can be brought to a delocalization transition, when delocalized DWs are formed in both the active channels. We characterize the DW fluctuations numerically.

We analytically compute the thermal conductivity of anharmonic crystals with self-consistent stochastic reservoirs. We develop an integral representation for the heat current, assume the approximation of discrete times, and in a perturbative analysis that is rigorously supported by a convergent cluster expansion compute the thermal conductivity for a chain with quartic anharmonic on-site potential. In the high anharmonicity regime, the result for the dependence of the conductivity on temperature is the same as for the system without inner reservoirs. The presented formalism is quite general and is also valid for inhomogeneous systems in any space dimension.

The cooling of the center of mass motion of optically trapped microspheres by feedback stabilization is advancing rapidly, and cooling below several millikelvin is possible. Such a controllable attenuation of the motion is an important step towards new experiments in different areas of physics. In this study we suggest going in the opposite direction, in controlling the motion of optically trapped spheres, namely, to increase the amplitude of their Brownian fluctuations. We show that the effective kinetic temperature of a Brownian particle may achieve 3000 K when an additional external random force is applied to the sphere. We demonstrate experimentally how the temperature increase affects the histogram of the position of the Brownian particle, its power spectral density, its response to an external perturbation, and the statistics of the Kramers transitions in a double-well potential. Effects related to the nonideal character of the white noise generated experimentally are also analyzed. This experimental technique allows tuning and controlling the kinetic temperature of the sphere with millisecond resolution over a wide range and along a single spatial direction, and has considerable potential for the study of thermodynamic processes at the microscopic scale.

We study the phase-ordering dynamics of a ferromagnetic system with a scalar order-parameter on fractal graphs. We propose a scaling approach, inspired by renormalization-group ideas, where a crossover between distinct dynamical behaviors is induced by the presence of a length $\lambda$ associated with the topological properties of the graph. The transition between the early and the asymptotic stages is observed when the typical size $L\left(t\right)$ of the growing ordered domains reaches the crossover length $\lambda$. We consider two classes of inhomogeneous substrates with different activated processes, where the effects of the free-energy barriers can be analytically controlled during the evolution. On finitely ramified graphs, the free-energy barriers encountered by domains walls grow logarithmically with $L\left(t\right)$, whereas they increase as a power law on all other structures. This produces different asymptotic growth laws (power laws vs logarithmic) and a different dependence of the crossover length $\lambda$ on the model parameters. Our theoretical picture agrees very well with extensive numerical simulations.

We show that the system entropy change for the transitions between nonequilibrium steady states arbitrarily far from equilibrium for any constituting process is given by the relative entropy of the distributions of these steady states. This expression is then shown to relate to the dissipation relations of both S. Vaikuntanathan and C. Jarzynski [Europhys. Lett. 87, 60005 (2009)] and R. Kawai et al. [Phys. Rev. Lett. 98, 080602 (2007)] in the case of energy-conserving driving.

We investigate the Casimir or fluctuation-induced interaction between two cross-linkers bound to the same semiflexible filament. The calculation is complicated by the appearance of second-order derivatives in the bending Hamiltonian for such filaments, which requires a careful evaluation of the the path integral formulation of the partition function in order to arrive at the physically correct continuum limit and properly address ultraviolet divergences. Doing so based on the previous work of Kleinert [Kleinert, J. Math. Phys. 27, 3003 (1986)], we find that cross-linkers interact along a filament with an attractive logarithmic potential proportional to thermal energy. The proportionality constant depends on whether and how the cross-linkers constraint the relative angle between the two filaments to which they are bound. We comment on the implications of this Casimir interaction for equilibrium distribution of labile cross-linkers in semiflexible biopolymer, e.g., F-actin, networks, and bundles.

We examine the phenomenon of hydrodynamic-induced cooperativity for pairs of flagellated micro-organism swimmers, of which spermatozoa cells are an example. We consider semiflexible swimmers, where inextensible filaments are driven by an internal intrinsic force and torque-free mechanism (intrinsic swimmers). The velocity gain for swimming cooperatively, which depends on both the geometry and the driving, develops as a result of the near-field coupling of bending and hydrodynamic stresses. We identify the regimes where hydrodynamic cooperativity is advantageous and quantify the change in efficiency. When the filaments' axes are parallel, hydrodynamic interaction induces a directional instability that causes semiflexible swimmers that profit from swimming together to move apart from each other. Biologically, this implies that flagella need to select different synchronized collective states and to compensate for directional instabilities (e.g., by binding) in order to profit from swimming together. By analyzing the cooperative motion of pairs of externally actuated filaments, we assess the impact that stress distribution along the filaments has on their collective displacements.

Mixing zone dynamics of a reaction product $C$ during diffusion of two species ($A$ and $B$) are examined, using a two-dimensional particle tracking model (PT) for the reaction $A+B\to C$, allowing for both Fickian and non-Fickian transitions. The form of PT we use is equivalent to a continuous time random walk, which is a widely used model for anomalous transport and diffusion. It is shown that the basic patterns of the $C$ dynamics—the temporal evolution of the spatial profile and the temporal $C$ production—are similar for both modes of diffusion. However, the distinctive time scale for the non-Fickian case is very much larger even when the median transition steps are matched with the Fickian case. For immobile $C$, the spatial profile pattern is a broadening (Gaussian) reaction front evolving to a concentration-fluctuation dominated (Lorentzian) shape. The temporal $C$ production is fit well by a stretched exponential for both diffusion types. In analyzing experiments, the appearance of a Gaussian $C$ profile does not prove that the diffusion process is Fickian.

We study an ensemble of identical noisy phase oscillators with a blinking mean-field coupling, where one-cluster and two-cluster synchronous states alternate. In the thermodynamic limit the population is described by a nonlinear Fokker-Planck equation. We show that the dynamics of the order parameters demonstrates hyperbolic chaos. The chaoticity manifests itself in phases of the complex mean field, which obey a strongly chaotic Bernoulli map. Hyperbolicity is confirmed by numerical tests based on the calculations of relevant invariant Lyapunov vectors and Lyapunov exponents. We show how the chaotic dynamics of the phases is slightly smeared by finite-size fluctuations.

We construct the Darboux transformation of the coupled Sasa-Satsuma system and represent the $N$-soliton solutions in terms of the five-component Wronskian. We give the parametric criterion for the appearance of single- and double-hump soliton profiles, and analyze the structure and stability of double-hump solitons. We also reveal the polarization-changing collisions occurring in the femtosecond vector solitons with the third-order dispersion, self-steepening, and stimulated Raman scattering effects. Such nontrivial collisions may have applications in the ultrafast all-optical switching, computation, and signal control.

We investigate the mixed-type vector solitons of the $N$-coupled mixed derivative nonlinear Schrödinger ($N$-CMDNLS) equations from optical fibers. Mixed-type ($m$-bright-$n$-antidark or $m$-bright-$n$-dark) vector-soliton solutions are derived via the Hirota method. Such vector solitons are found to be independent of the sign of cubic nonlinearity in the $N$-CMDNLS equations, which is different from the case of the coupled nonlinear Schrödinger equations. The parameter conditions for the shape-preserving and shape-changing collisions of the mixed-type vector solitons are also given by an asymptotic analysis. As an example, the mixed-type vector-soliton collisions in the 3-CMDNLS equations are graphically illustrated. Those results may be useful to the ultrashort-pulse propagation in nonlinear fibers.

Using intermittent maps with infinite invariant measures, we investigate the universality of time-averaged observables under aging conditions. According to Aaronson's Darling-Kac theorem, in non-aged dynamical systems with infinite invariant measures, the distribution of the normalized time averages of integrable functions converges to the Mittag-Leffler distribution. This well known theorem holds when the start of observations coincides with the start of the dynamical processes. Introducing a concept of the aging limit where the aging time $t_a$ and the total measurement time $t$ goes to infinity while the aging ratio $t_a/t$ is kept constant, we obtain a novel distributional limit theorem of time-averaged observables integrable with respect to the infinite invariant density. Applying the theorem to the Lyapunov exponent in intermittent maps, we find that regular motions and a weakly chaotic behavior coexist in the aging limit. This mixed type of dynamics is controlled by the aging ratio and hence is very different from the usual scenario of regular and chaotic motions in Hamiltonian systems. The probability of finding regular motions in non-aged processes is zero, while in the aging regime it is finite and it increases when system ages.

Regimes of chemical reaction wave propagating in reactive gaseous mixtures, whose chemistry is governed by chain-branching kinetics, are studied depending on the characteristics of a transient thermal energy deposition localized in a finite volume of reactive gas. Different regimes of the reaction wave propagation are initiated depending on the amount of deposited thermal energy, power of the source, and the size of the hot spot. The main parameters which define regimes of the combustion waves facilitated by the transient deposition of thermal energy are acoustic time scale, duration of the energy deposition, ignition time scale, and size of the hot spot. The interplay between these parameters specifies the role of gasdynamical processes, the formation and steepness of the temperature gradient, and speed of the spontaneous wave. The obtained results show how ignition of one or another combustion regime depends on the value of energy, rate of the energy deposition, and size of the hot spot, which is important for the practical use and for risk assessment.

We perform numerical simulations of decaying rotating stratified turbulence and show, in the Boussinesq framework, that helicity (velocity-vorticity correlation), as observed in supercell storms and hurricanes, is spontaneously created due to an interplay between buoyancy and rotation common to large-scale atmospheric and oceanic flows. Helicity emerges from the joint action of eddies and of inertia-gravity waves (with inertia and gravity with respective associated frequencies $f$ and $N$), and it occurs when the waves are sufficiently strong. For $N/f<3$ the amount of helicity produced is correctly predicted by a quasilinear balance equation. Outside this regime, and up to the highest Reynolds number obtained in this study, namely $\text{Re}\approx 10000$, helicity production is found to be persistent for $N/f$ as large as $\approx 17$, and for ${\text{ReFr}}^2$ and ${\text{ReRo}}^2$, respectively, as large as $\approx 100$ and $\approx 24000$.

The liquid state and the freezing transition of finite two-dimensional dust systems are studied using the instantaneous normal mode (INM) analysis. This technique measures the instantaneous unstable modes of a cluster configuration and relates them to the liquid properties of the system. Here, the INM analysis has been applied to experiments on laser-heated dust clusters. From the experiments, diffusion constants and melting temperatures for clusters of different size have been derived. The INM diffusion constants have been compared to those derived from other standard approaches. The scatter of the diffusion constant retrieved by the INM is smaller than that retrieved by other methods, allowing a more reliable determination of melting temperatures. Moreover, the behavior of double-well and escape modes, which reflect certain topological properties of unstable modes, correlates very well with the behavior of the diffusion constant. Further, the dynamic nature of the unstable modes has been determined as mostly shearlike. Finally, the INM results on the experiments are checked against those from Langevin simulations.

We present analytic expressions for the amplitude of perturbations at the interface of two viscous fluids or two metals subjected to a shock. We derive a scaling law by collapsing this eight-parameter problem into two (three) nondimensional variables in the linear (nonlinear) regime. We propose a correspondence principle between viscosity and strength, and a method for measuring viscosity at high pressure and temperature as an alternative to the “Sakharov method.”

We show analytically that the $[0,1]$, $[1,1]$, and $[2,1]$ Padé approximants of the mean cluster number $S\left(p\right)$ for site and bond percolation on general $d$-dimensional lattices are upper bounds on this quantity in any Euclidean dimension $d$, where $p$ is the occupation probability. These results lead to certain lower bounds on the percolation threshold $p_c$ that become progressively tighter as $d$ increases and asymptotically exact as $d$ becomes large. These lower-bound estimates depend on the structure of the $d$-dimensional lattice and whether site or bond percolation is being considered. We obtain explicit bounds on $p_c$ for both site and bond percolation on five different lattices: $d$-dimensional generalizations of the simple-cubic, body-centered-cubic, and face-centered-cubic Bravais lattices as well as the $d$-dimensional generalizations of the diamond and kagomé (or pyrochlore) non-Bravais lattices. These analytical estimates are used to assess available simulation results across dimensions (up through $d=13$ in some cases). It is noteworthy that the tightest lower bound provides reasonable estimates of $p_c$ in relatively low dimensions and becomes increasingly accurate as $d$ grows. We also derive high-dimensional asymptotic expansions for $p_c$ for the 10 percolation problems and compare them to the Bethe-lattice approximation. Finally, we remark on the radius of convergence of the series expansion of $S$ in powers of $p$ as the dimension grows.

Macroscopic models beyond Fourier's law for fast-transient heating and heat transport in nanosystems have been proposed. Consequently, some basic quantities such as entropy and temperature need to be modified. From the viewpoint of the thermomass theory, we show that in nonequilibrium systems where heat conduction occurs, the static pressure of thermomass is lower than the total pressure, corresponding to a nonequilibrium temperature lower than the local-equilibrium temperature. The definition of entropy is also modified since the phonon kinetic energy conserves the ability to do work. The nonequilibrium temperature based on the thermomass theory is close to that in the extended irreversible thermodynamics. The microscopic foundation is explored through a phonon Boltzmann derivation. The higher-order contributions to the distribution function are found to be responsible for such modification of temperature. Therefore, the thermomass model gives not only non-Fourier conduction law, but also a physical picture about modified state variables in nonequilibrium states.