We propose a general model of third-order nonlinear optical susceptibility of isotropic gyrotropic medium with frequency and spatial dispersion. Our model allows for the description of the propagation of ultrashort (several oscillations) elliptically polarized laser pulses in such a medium and does not require smallness of the characteristic nonlocality dimension, unlike the conventional phenomenological model. We implemented our model numerically by means of a modified finite-difference time-domain method with an auxiliary differential equation. We have validated the correctness of our model by the comparison of the results obtained in our numerical simulations with generally known effects observed experimentally and described earlier theoretically for the monochromatic radiation or within the slowly varying envelope approach. We investigated effects accompanying the propagation of ultrashort (several oscillations) light pulses in nonlinear isotropic gyrotropic medium with frequency and spatial dispersion of cubic nonlinearity.

We present a polar coordinate lattice Boltzmann kinetic model for compressible flows. A method to recover the continuum distribution function from the discrete distribution function is indicated. Within the model, a hybrid scheme being similar to, but different from, the operator splitting is proposed. The temporal evolution is calculated analytically, and the convection term is solved via a modified Warming-Beam (MWB) scheme. Within the MWB scheme a suitable switch function is introduced. The current model works not only for subsonic flows but also for supersonic flows. It is validated and verified via the following well-known benchmark tests: (i) the rotational flow, (ii) the stable shock tube problem, (iii) the Richtmyer-Meshkov (RM) instability, and (iv) the Kelvin-Helmholtz instability. As an original application, we studied the nonequilibrium characteristics of the system around three kinds of interfaces, the shock wave, the rarefaction wave, and the material interface, for two specific cases. In one of the two cases, the material interface is initially perturbed, and consequently the RM instability occurs. It is found that the macroscopic effects due to deviating from thermodynamic equilibrium around the material interface differ significantly from those around the mechanical interfaces. The initial perturbation at the material interface enhances the coupling of molecular motions in different degrees of freedom. The amplitude of deviation from thermodynamic equilibrium around the shock wave is much higher than those around the rarefaction wave and material interface. By comparing each component of the high-order moments and its value in equilibrium, we can draw qualitatively the main behavior of the actual distribution function. These results deepen our understanding of the mechanical and material interfaces from a more fundamental level, which is indicative for constructing macroscopic models and other kinds of kinetic models.

A method is presented to obtain the linear response coefficients of a system coupled to a bath. The method is based on a systematic truncation of the Liouville equation for the reduced distribution function. The first-order truncation results are expected to be accurate in the low-temperature and weak-coupling regime. Explicit expressions for the conductivity of the Fröhlich polaron are obtained, and the discrepancy between the Kadanoff and the Feynman-Hellwarth-Iddings-Platzman mobility is elucidated.

We study bipartite entanglement entropies in the ground and excited states of free-fermion models, where a staggered potential, ${\mu }_s$, induces a gap in the spectrum. Ground-state entanglement entropies satisfy the “area law”, and the “area-law” coefficient is found to diverge as a logarithm of the staggered potential, when the system has an extended Fermi surface at ${\mu }_s=0$. On the square lattice, we show that the coefficient of the logarithmic divergence depends on the Fermi surface geometry and its orientation with respect to the real-space interface between subsystems and is related to the Widom conjecture as enunciated by Gioev and Klich [Phys. Rev. Lett. 96, 100503 (2006)]. For point Fermi surfaces in two-dimension, the “area-law” coefficient stays finite as ${\mu }_s\to 0$. The von Neumann entanglement entropy associated with the excited states follows a “volume law” and allows us to calculate an entropy density function $s_V\left(e\right)$, which is substantially different from the thermodynamic entropy density function $s_T\left(e\right)$, when the lattice is bipartitioned into two equal subsystems but approaches the thermodynamic entropy density as the fraction of sites in the larger subsystem, that is integrated out, approaches unity.

We present extensive numerical simulations of a generalized XY model with nematic-like terms recently proposed by Poderoso et al. [Phys. Rev. Lett. 106, 067202 (2011)]. Using finite size scaling and focusing on the $q=3$ case, we locate the transitions between the paramagnetic (P), the nematic-like (N), and the ferromagnetic (F) phases. The results are compared with the recently derived lower bounds for the P-N and P-F transitions. While the P-N transition is found to be very close to the lower bound, the P-F transition occurs significantly above the bound. Finally, the transition between the nematic-like and the ferromagnetic phases is found to belong to the three-states Potts universality class.

Jarzynski equality and related fluctuation theorems can be formulated for various setups. Such an equality was recently derived for nonunitary quantum evolutions described by unital quantum operations, i.e., for completely positive, trace-preserving maps, which preserve the maximally mixed state. We analyze here a more general case of arbitrary quantum operations on finite systems and derive the corresponding form of the Jarzynski equality. It contains a correction term due to nonunitality of the quantum map. Bounds for the relative size of this correction term are established and they are applied for exemplary systems subjected to quantum channels acting on a finite-dimensional Hilbert space.

Randomness and frustration are important for the spin-glass transitions. Ising antiferromagnet on a stacked triangular lattice is a highly frustrated system. Phase diagram is obtained within a cluster approximation for the system with randomness in the interaction between Ising spins. To see the frustration effects, the phase diagram of the antiferromagnet is compared with the corresponding one of the ferromagnet. Spin-glass phase of the antiferromagnet appears much more easily by the randomness than that of the ferromagnet.

We perform a joint numerical and experimental study to systematically characterize the motion of 30 $\mu \mathrm{l}$ drops of pure water and of ethanol in water solutions, sliding over a periodic array of alternating hydrophobic and hydrophilic stripes with a large wettability contrast and a typical width of hundreds of microns. The fraction of the hydrophobic areas has been varied from about 20% to 80%. The effects of the heterogeneous patterning can be described by a renormalized value of the critical Bond number, i.e., the critical dimensionless force needed to depin the drop before it starts to move. Close to the critical Bond number we observe a jerky motion characterized by an evident stick-slip dynamics. As a result, dissipation is strongly localized in time, and the mean velocity of the drops can easily decrease by an order of magnitude compared to the sliding on the homogeneous surface. Lattice Boltzmann numerical simulations are crucial for disclosing to what extent the sliding dynamics can be deduced from the computed balance of capillary, viscous, and body forces by varying the Bond number, the surface composition, and the liquid viscosity. Beyond the critical Bond number, we characterize both experimentally and numerically the dissipation inside the droplet by studying the relation between the average velocity and the applied volume forces.

We present a combined numerical and analytical study of pattern formation in an active system where particles align, possess a density-dependent motility, and are subject to a logistic reaction. The model can describe suspensions of reproducing bacteria, as well as polymerizing actomyosin gels in vitro or in vivo. In the disordered phase, we find that motility suppression and growth compete to yield stable or blinking patterns, which, when dense enough, acquire internal orientational ordering to give asters or spirals. We predict these may be observed within chemotactic aggregates in bacterial fluids. In the ordered phase, the reaction term leads to previously unobserved never-settling patterns which can provide a simple framework to understand the formation of motile and spiral patterns in intracellular actin systems.

We present numerical simulations of a flow in a rapidly rotating cylinder subjected to a time-periodic forcing via axial oscillations of the sidewall. When the axial oscillation frequency is less than twice the rotation frequency, inertial waves in the form of shear layers are present. For very fast rotations, these waves approach the form of the characteristics predicted from the linearized inviscid problem first studied by Lord Kelvin. The driving mechanism for the inertial waves is the oscillating Stokes layer on the sidewall and the corner discontinuities where the sidewall meets the top and bottom end walls. A detailed numerical and theoretical analysis of the internal shear layers is presented. The system is physically realizable, and attractive because of the robustness of the Stokes layer that drives the inertial waves but beyond that does not interfere with them. We show that the system loses stability to complicated three-dimensional flow when the sidewall oscillation displacement amplitude is very large (of the order of the cylinder radius), but this is far removed from the displacement amplitudes of interest, and there is a large range of governing parameters which are physically realizable in experiments in which the inertial waves are robust. This is in contrast to many other physical realizations of inertial waves where the driving mechanisms tend to lead to instabilities and complicate the study of the waves. We have computed the response diagram of the system for a large range of forcing frequencies and compared the results with inviscid eigenmodes and ray tracing techniques.

The onset of Soret-driven convection in a horizontal layer of a colloidal suspension is investigated by considering a particulate medium model. We consider a dilute suspension of spherical solid particles being subjected to convection in a Rayleigh-Bénard geometry setup. The mathematical model takes into account the effects of thermophoresis, particle sedimentation, and Brownian diffusion. The equations governing the convective motion consist of the momentum equation which includes an extra body force term to account for the thermophoretic force effect, the conservation of particles equation whose mass-flux term couples the Soret and particle diffusion effects and whose advective term includes the sedimentation force, and the heat and mass balance equations. The horizontal boundaries are assumed rigid, perfectly thermally conducting, and impervious to mass flow. Furthermore, the model makes use of the effective viscosity of the suspension whose dependence on the particle concentration is through Einstein's formula. Moreover, we take into account the decrease of both the coefficient of Brownian diffusion and the mixture thermal diffusion with particle concentration due to the particles hindrance effect. The nondimensionalization leads to the emergence of an experimental parameter, $\beta$, which depicts the competition between the effects of thermophoresis, sedimentation, and particle diffusion. The parameter $\beta$ is a function of the particles radius, the shape of which is an inverted parabola having two zeros. A combination of asymptotic and numerical computations is used to determine the threshold for the onset of the mass dominated convection, which corresponds to $0<\beta \ll 1$. Our findings shed light on the role of particle sedimentation and particle size, as well as the influence of other processing variables on the fluid instability.

In this paper, we introduce a stable-phase approach for hierarchical annealing which addresses the very large computational costs associated with simulated annealing for the reconstruction of large-scale binary porous media images. Our presented method, which uses the two-point correlation function as the morphological descriptor, involves the reconstruction of three-phase and two-phase structures. We consider reconstructing the three-phase structures based on standard annealing and the two-phase structures based on standard and hierarchical annealings. From the result of the two-dimensional (2D) reconstruction, we find that the 2D generation does not fully capture the morphological information of the original image, even though the two-point correlation function of the reconstruction is in excellent agreement with that of the reference image. For the reconstructed three-dimensional (3D) microstructure, we calculate its permeability and compare it to that of the reference 3D microstructure. The result indicates that the reconstructed structure has a lower degree of connectedness than that of the actual sandstone. We also compare the computation time of our presented method to that of the standard annealing, which shows that our presented method of orders of magnitude improves the convergence rate. That is because only a small part of the pixels in the overall hierarchy need to be considered for sampling by the annealer.

Using molecular dynamics simulations of UO${}_2$—a type II superionic conductor—we identify a well-defined onset of dynamic disorder ($T_{\alpha }$), which is remarkably correlated to a nontrivial advance of dynamical heterogeneity (DH). Quantified by the correlations in the dynamic propensity and van Hove self-correlation function, the DH is shown to grow with increasing temperature from $T_{\alpha }$, peak at an intermediate temperature between $T_{\alpha }$ and $T_{\lambda }$—the superionic transition temperature—and then recede. Surprisingly, the DH attributes are not uniform across the temperatures—our investigation shows a low temperature (${\alpha }_T$) stage DH, which is characterized by weak correlations and a plateaulike period in the correlations of the propensity, and a high temperature (${\lambda }_T$) stage DH with strong correlations that are analogous to those in typical supercooled liquids. Our work, which has rigorously identified the onset of superionicity, gives a different direction for interpreting scattering experiments on the basis of statistical, correlated dynamics.

We provide an experimental proof of concept for a robust, continuously rotating microstructure—consisting of two metallodielectric (gold-polystyrene) Janus particles rigidly attached to each other—which is driven in uniform ac fields by asymmetric induced-charge electro-osmosis. The pairs (doublets) are stabilized on the substrate surface which is parallel to the plane of view and normal to the direction of the applied electric field. We find that the radius of orbit and angular velocity of the pair are predominantly dependent on the relative orientations of the interfaces between the metallic and dielectric hemispheres and that the electrohydrodynamic particle-particle interactions are small. Additionally, we verify that both the angular and linear velocities of the pair are proportional to the square of the applied field which is consistent with the theory for nonlinear electrokinetics. A simple kinematic rigid body model is used to predict the paths and doublet velocities (angular and linear) based on their relative orientations with good agreement.

Modulus softening and permanent set in filled polymeric materials due to cyclic loading and unloading, commonly known as the Mullins effect, can have a significant impact on their use as support cushions. A quantitative analysis of such behavior is essential to ensure the effectiveness of such materials in long-term deployment. In this work we combine existing ideas of filler-induced modulus enhancement, strain amplification, and irreversible deformation within a simple non-Gaussian constitutive model to quantitatively interpret recent measurements on a relevant PDMS-based elastomeric cushion. We find that the experimental stress-strain data is consistent with the picture that during stretching (loading) two effects take place simultaneously: (1) the physical constraints (entanglements) initially present in the polymer network get disentangled, thus leading to a gradual decrease in the effective cross-link density, and (2) the effective filler volume fraction gradually decreases with increasing strain due to the irreversible pulling out of an initially occluded volume of the soft polymer domain.

It is commonly thought that if a rate constant is perturbed such that the intracellular concentration of a certain species increases, then the fluctuations in the concentration will correspondingly decrease in strength. We here test whether this conventional wisdom generally holds true. We study the dependence of the noise strength (the coefficient of variation) in protein concentrations as a function of the mean protein concentration for a system in which protein is transported in and out of an intracellular compartment and it is catalyzed into a product by a multisubunit enzyme inside the compartment. The mean protein concentration is varied through perturbation of one of the rate constants. For low protein concentrations, the noise strength scales as ${\left[P\right]}^{-1/2}$, where $\left[P\right]$ is the mean concentration; this is the conventional fluctuation scaling law. However, we show that over a wide range of physiological concentrations, there are manifest anomalous fluctuation scaling laws proportional to ${\left[P\right]}^0$ and ${\left[P\right]}^{(N-1)/2}$, where $N$ is the number of binding sites of the multisubunit enzyme. These laws are particularly conspicuous when the rate of protein import into the compartment is much larger than its export rate out of the compartment and when the enzyme exhibits positive cooperativity. The results imply that over a certain range of physiological concentrations, noise strength remains the same or increases with the mean protein concentration. This contradicts the popularly held notion that noise strength decreases with increasing concentration and suggests that noise can be important even when the number of molecules is large.

We develop a methodology for analyzing the percolation phenomena of two mutually coupled (interdependent) networks based on the cavity method of statistical mechanics. In particular, we take into account the influence of degree-degree correlations inside and between the networks on the network robustness against targeted (random degree-dependent) attacks and random failures. We show that the developed methodology is reduced to the well-known generating function formalism in the absence of degree-degree correlations. The validity of the developed methodology is confirmed by a comparison with the results of numerical experiments. Our analytical results indicate that the robustness of the interdependent networks depends on both the intranetwork and internetwork degree-degree correlations in a nontrivial way for both cases of random failures and targeted attacks.

We investigate common-noise-induced phase synchronization between uncoupled identical Hele-Shaw cells exhibiting oscillatory convection. Using the phase description method for oscillatory convection, we demonstrate that the uncoupled systems of oscillatory Hele-Shaw convection can exhibit in-phase synchronization when driven by weak common noise. We derive the Lyapunov exponent determining the relaxation time for the synchronization, and develop a method for obtaining the optimal spatial pattern of the common noise to achieve synchronization. The theoretical results are confirmed by direct numerical simulations.

We consider two-dimensional Yukawa systems in a perpendicular magnetic field. Computer simulations of both one-component and binary systems are used to explore the equilibrium particle dynamics in the fluid state. The mobility is found to scale with the inverse of the magnetic field strength (Bohm diffusion), for strong fields (${\omega }_c/{\omega }_p\gtrsim 1$). For bidisperse mixtures, the magnetic field dependence of the long-time mobility depends on the particle species, providing an external control of their mobility ratio. At large magnetic fields, the highly charged particles are almost immobilized by the magnetic field and form a porous matrix of obstacles for the mobile low-charge particles.