We present or recall several equilibrium methods that allow one to compute isentropic processes, either during the compression or the release of the material. These methods are applied to compute the isentropic release of a shocked monoatomic liquid at high pressure and temperature. Moreover, equilibrium results of isentropic release are compared to the direct nonequilibrium simulation of the same process. We show that due to the viscosity of the liquid but also to nonequilibrium effects, the release of the system is not strictly isentropic.

Previous studies demonstrated empirically that human mobility exhibits Lévy flight behavior. However, our knowledge of the mechanisms governing this Lévy flight behavior remains limited. Here we analyze over $72000$ people’s moving trajectories, obtained from 50 taxicabs during a six-month period in a large street network, and illustrate that the human mobility pattern, or the Lévy flight behavior, is mainly attributed to the underlying street network. In other words, the goal-directed nature of human movement has little effect on the overall traffic distribution. We further simulate the mobility of a large number of random walkers and find that (1) the simulated random walkers can reproduce the same human mobility pattern, and (2) the simulated mobility rate of the random walkers correlates pretty well (an $R$ square up to 0.87) with the observed human mobility rate.

The second law of thermodynamics represents a universal principle applicable to all natural processes, physical systems, and engineering devices. Hatano and Sasa have recently put forward an extended form of the second law for transitions between nonequilibrium stationary states [Phys. Rev. Lett. 86, 3463 (2001)]. In this paper we further extend this form to an instantaneous interpretation, which is satisfied by quite general time-dependent stochastic processes including master-equation models and Langevin dynamics without the requirements of the stationarity for the initial and final states. The theory is applied to several thermodynamic processes, and its consistence with the classical thermodynamics is shown.

Systems with long-range interactions display a short-time relaxation toward quasistationary states (QSSs) whose lifetime increases with system size. The application of Lynden-Bell’s theory of “violent relaxation” to the Hamiltonian Mean Field model leads to the prediction of out-of-equilibrium first- and second-order phase transitions between homogeneous (zero magnetization) and inhomogeneous (nonzero magnetization) QSSs, as well as an interesting phenomenon of phase re-entrances. We compare these theoretical predictions with direct $N$-body numerical simulations. We confirm the existence of phase re-entrance in the typical parameter range predicted from Lynden-Bell’s theory, but also show that the picture is more complicated than initially thought. In particular, we exhibit the existence of secondary re-entrant phases: we find unmagnetized states in the theoretically magnetized region as well as persisting magnetized states in the theoretically unmagnetized region. We also report the existence of a region with negative specific heats for QSSs both in the numerical and analytical caloric curves.

We study stochastic dynamics of two-state particles coupled unidirectionally with delay. We give exact results for the stationary distribution function $p_{st}$ and the time correlation function (TCF) when the system consists of two $\left(N=2\right)$ and three $\left(N=3\right)$ particles. Based on these results, effects of delay are discussed and compared with the $N=1$ case, studied by Tsimring and Pikovsky [Phys. Rev. Lett. 87, 250602 (2001)]. Next, we consider the general $N$-particle system, for which we give exact expressions for $p_{st}$ and the TCF, which are inferred based on the $N=2$ and $N=3$ solutions and then confirmed via detailed arguments. It is pointed out that the stationary state is mapped to Ising spin model with ferro(antiferro)magnetic interaction when delay feedback is positive (negative).

Random-matrix theory is applied to transition-rate matrices in the Pauli master equation. We study the distribution and correlations of eigenvalues, which govern the dynamics of complex stochastic systems. Both the cases of identical and of independent rates of forward and backward transitions are considered. The first case leads to symmetric transition-rate matrices, whereas the second corresponds to general asymmetric matrices. The resulting matrix ensembles are different from the standard ensembles and show different eigenvalue distributions. For example, the fraction of real eigenvalues scales anomalously with matrix dimension in the asymmetric case.

Correlation functions and transport coefficients of self-diffusion and shear viscosity of a binary Lennard-Jones mixture with components differing only in their particle mass are studied up to high values of the mass ratio $\mu$, including the limiting case $\mu =\infty$, for different mole fractions $x$. Within a large range of $x$ and $\mu$ the product of the diffusion coefficient of the heavy species $D_2$ and the total shear viscosity of the mixture ${\eta }_m$ is found to remain constant, obeying a generalized Stokes-Einstein relation. At high liquid density, large mass ratios lead to a pronounced cage effect that is observable in the mean square displacement, the velocity autocorrelation function, and the van Hove correlation function.

The theory of the absorbance of a semi-infinite medium characterized by a second-rank dielectric tensor for the entire electromagnetic spectrum, as given by Scaife and Vij [J. Chem. Phys. 122, 174901 (2005)], is extended to include molecules of prolate spheriodal shape with longitudinal and transverse polarizabilities and to cover the case of elliptically polarized incident radiation. The theory is applied to the infrared transmission experiments of biaxial liquid crystals. It is found that the formula for the dependence on frequency and on angle of polarization of the absorbance $\mathbf{A}\left(\omega ,\theta \right)=-{\text{log}}_{10}\left[{10}^{\mathbf{A}\left(\omega ,0\right)}{\text{cos}}^2\theta +\phantom{(}{10}^{-\mathbf{A}\left(\omega ,\pi /2\right)}{\text{sin}}^2\theta )\right]$ is unaffected by the anisotropy of the molecules and by the elliptical polarization of the incident radiation. A small $\left(\pm 5\%\right)$ discrepancy between theory and experiment has been found for bands with high absorbances. It is found that this discrepancy does not depend on birefringence of the sample but may depend on the precise method of absorbance measurement and on effects at the surface of the cell containing the liquid crystal under test.

We suggest a risk estimation method for financial records that is based on the statistics of return intervals between events above/below a certain threshold $Q$ and is particularly suited for multifractal records. The method is based on the knowledge of the probability $W_Q\left(t;\Delta t\right)$ that within the next $\Delta t$ units of time at least one event above $Q$ occurs, if the last event occurred $t$ time units ago. We propose an analytical estimate of $W_Q$ and show explicitly that the proposed method is superior to the conventional precursory pattern recognition technique widely used in signal analysis, which requires considerable fine tuning and is difficult to implement. We also show that the estimation of the Value at Risk, which is a standard tool in finances, can be improved considerably by the method.

The electrohydrodynamic (EHD) spraying technique has been utilized in applications such as inkjet printing and mass spectrometry technologies. In this paper, the role of electrical potential signals in jetting and on the oscillation of the meniscus is evaluated. The jetting and the meniscus oscillation behavior are experimentally investigated under ac voltage, ac voltage superimposed on dc voltage, and pulsed dc voltage. Based on this in-depth study of the meniscus behavior under various signals, the optimal signal is implemented to an EHD inkjet head for drop-on-demand operation. For applied ac voltage and ac voltage superimposed on dc voltage, the jetting phenomenon is a dynamic process due to sequential opposite sign signals. The jetting occurs at the end of the oscillation cycle, where the meniscus oscillates upward and arrives at its highest position.

The viscous-flow sintering of different agglomerate particle morphologies is studied by three-dimensional computer simulations based on the concept of fractional volume of fluid. For a fundamental understanding of particle sintering characteristics, the neck growth kinetics in agglomerate chains and in doublets consisting of differently sized primary particles is investigated. Results show that different sintering contacts in agglomerates even during the first stages are not completely independent from each other, even though differences are small. The neck growth kinetics of differently sized primary particles is determined by the smaller one up to a size difference by a factor of approximately 2, whereas for larger size differences, the kinetics becomes faster. In particular, the agglomerate sintering kinetics is investigated for particle chains of different lengths and for different particle morphologies each having ten primary particles and nine initial sintering contacts. For agglomerate chains, the kinetics approximately can be normalized by using the radius of the fully coalesced sphere. In general, different agglomerate morphologies show equal kinetics during the first sintering stages, whereas during advanced stages, compact morphologies show significantly faster sintering progress than more open morphologies. Hence, the overall kinetics cannot be described by simply using constant morphology correction factors such as fractal dimension or mean coordination number which are used in common sintering models. However, for the first stages of viscous-flow agglomerate sintering, which are the most important for many particle processes, a sintering equation is presented. Although we use agglomerates consisting of spherical primary particles, our methodology can be applied to other aggregate geometries as well.

We present a uniform asymptotic expansion of the wobbling kink to any order in the amplitude of the wobbling mode. The long-range behavior of the radiation is described by matching the asymptotic expansions in the far field and near the core of the kink. The complex amplitude of the wobbling mode is shown to obey a simple ordinary differential equation with nonlinear damping. We confirm the $t^{-1/2}$-decay law for the amplitude, which was previously obtained on the basis of energy considerations.

The amplitude of oscillations of the freely wobbling kink in the ${\varphi }^4$ theory decays due to the emission of second-harmonic radiation. We study the compensation of these radiation losses (as well as additional dissipative losses) by the resonant driving of the kink. We consider both direct and parametric driving at a range of resonance frequencies. In each case, we derive the amplitude equations which describe the evolution of the amplitude of the wobbling and the kink’s velocity. These equations predict multistability and hysteretic transitions in the wobbling amplitude for each driving frequency—the conclusion verified by numerical simulations of the full partial differential equation. We show that the strongest parametric resonance occurs when the driving frequency equals the natural wobbling frequency and not double that value. For direct driving, the strongest resonance is at half the natural frequency, but there is also a weaker resonance when the driving frequency equals the natural wobbling frequency itself. We show that this resonance is accompanied by the translational motion of the kink.

We obtain exact solutions and the survival probability for a Fokker-Planck equation subjected to the two-dimensional wedge domain. We consider a spatial dependence in the diffusion coefficient and the presence of external forces. The results show an anomalous spreading of the solution and, consequently, a nonusual behavior of the survival probability which can be connected to anomalous diffusion.

We considered a stochastic version of the Bak-Sneppen model (SBSM) of ecological evolution where the number $M$ of sites mutated in a mutation event is restricted to only two. Here the mutation zone consists of only one site and this site is randomly selected from the neighboring sites at every mutation event in an annealed fashion. The critical behavior of the SBSM is found to be the same as the BS model in dimensions $d=1$ and 2. However on the scale-free graphs the critical fitness value is nonzero even in the thermodynamic limit but the critical behavior is mean-field like. Finally $⟨M⟩$ has been made even smaller than two by probabilistically updating the mutation zone, which also shows the original BS model behavior. We conjecture that a SBSM on any arbitrary graph with any small branching factor greater than unity will lead to a self-organized critical state.

Recently there has been a certain controversy about the scaling properties of reaction-subdiffusion fronts. Some works seem to suggest that these fronts should move with constant speed, as do classical reaction-diffusion fronts, while other authors have predicted propagation failure, i.e., that the front speed tends asymptotically to zero. In the present work we confirm by Monte Carlo experiments that the two situations can actually occur depending on the way the reaction process is implemented. Also, we present a general analytical model that includes these two different behaviors as particular cases. From our analysis, we reach two main conclusions. First, the differences found in the scaling properties show the lack of universality of reaction-subdiffusion fronts. Second, we prove that, contrary to the widespread belief, the tail of the waiting time distributions is not always decisive to determine the speed of these fronts, but sometimes it plays just a marginal role in the front dynamics.

An influence of diluted sites on surface growth has been investigated, using the restricted solid-on-solid model. It was found that, with respect to equilibrium growth, the surface width and the saturated width exhibited universal power-law behaviors, i.e., $W\sim t^{\beta }$ and $W_{\text{sat}}\sim L^{\zeta }$, regarding all cases with respect to the concentration of diluted sites $x=1-p$, with $p$ being the occupation probability on each lattice site. For $x<x_c$ ($=1-p_c$, $p_c$ being the percolation threshold), the growth appeared to be similar to that of a regular lattice, both in two and three dimensions. For $x=x_c$, the growth yielded nontrivial exponents which were different from those on a regular lattice. In nonequilibrium growth, a considerable amount of diluted sites $\left(x\le x_c\right)$ appeared to yield nonuniversal growth, unlike the case of a regular lattice. The cause of nonuniversal growth dynamics has been investigated, considering the growth on a backbone cluster and on lattices constructed with periodically and randomly diluted subcells.

The effect of substrate curvature on surfactant self-assembly has been studied using all-atom molecular-dynamics simulations. We studied aqueous sodium-dodecyl-sulfate (SDS) surfactants on graphite, on the outer surface of single walled carbon nanotubes (SWNTs) and within SWNTs. Our results reveal that although the chemical nature of the substrates is constant, the self-assembled structures change significantly as the curvature varies. For example, at large surface density, SDS surfactants yield micellar structures on graphite, layered self-assemblies outside SWNTs, and cylindrical lamellar structures inside SWNTs. Changes in substrate curvature as well as surfactant surface density affect significantly surfactant orientation and, more importantly, headgroup-headgroup distribution, headgroup-counterion packing, and counterion residence time next to the headgroups.

Selectivity of particles in a region of space can be achieved by applying external potentials to influence the particles in that region. We investigate static and dynamical properties of size selectivity in binary fluid mixtures of two particles sizes. We find that by applying an external potential that is attractive to both kinds of particles, due to crowding effects, this can lead to one species of particles being expelled from that region, while the other species is attracted into the region where the potential is applied. This selectivity of one species of particle over the other in a localized region of space depends on the density and composition of the fluid mixture. Applying an external potential that repels both kinds of particles leads to selectivity of the opposite species of particles to the selectivity with attractive potentials. We use equilibrium and dynamical density-functional theory to describe and understand the static and dynamical properties of this striking phenomenon. Selectivity by some ion channels is believed to be due to this effect.

In a system consisting of photoactive molecules that exhibit light-driven isomerization transformations, actinic light can diminish or enhance ordering to the extent that transitions from the equilibrium to a more disordered phase can be brought about isothermally. This feature enables light to be used as a thermodynamiclike parameter to investigate phase behavior and adds another dimension to the studies owing to the nonequilibrium character of the isothermal transitions. We have carried out experiments which exploit the combination of two recent findings, viz., an electric field can accelerate the return to the nematic liquid crystalline phase from a photodriven isotropic phase; and in a reentrant mesogen, the photoinduced phase can be more ordered. To photostimulate the nonequilibrium transitions a low power uv radiation $\left(0.1\text{mW}{\text{cm}}^{-2}\right)$ has been used. Unique temperature–electric-field phase diagrams of a liquid crystal exhibiting isotropic–nematic–smectic-$A$ –reentrant nematic sequence, mapped using light transmission as probe reveal that the electric field influences all the transitions, but the effect is maximum on the equilibrium reentrant nematic to the photoinduced smectic-$A$ transition. Temporal measurements have been performed under nonequilibrium conditions to study the dynamics of both the photochemical and the back relaxation processes across the different transitions. The electric field is indeed observed to accelerate the thermal back relaxation in each case, and especially the recovery of the reentrant phase is hastened by three orders of magnitude in time. We explore possible causes for the acceleration and present a finding which can be associated with one of the predictions of density-functional calculations for isomerization of azobenzenes.