For open quantum systems coupled to a thermal bath at inverse temperature $\beta$, it is well known that under the Born, Markov, and secular approximations, the system density matrix will approach the thermal Gibbs state with the bath inverse temperature $\beta$. We generalize this to systems where there exists a conserved quantity (e.g., the total particle number), where for a bath characterized by inverse temperature $\beta$ and chemical potential $\mu$, we find equilibration of both temperature and chemical potential. For couplings to multiple baths held at different temperatures and different chemical potentials, we identify a class of systems that equilibrates according to a single hypothetical average but in general nonthermal bath, which may be exploited to generate desired nonthermal states. Under special circumstances, the stationary state may again be described by a unique Boltzmann factor. These results are illustrated by several examples.

We investigate the sensitivity of the composite cellular automaton of  H. Fukś [Phys. Rev. E 55, R2081 (1997)] to noise and assess the density classification performance of the resulting probabilistic cellular automaton (PCA) numerically. We conclude that the composite PCA performs the density classification task reliably only up to very small levels of noise. In particular, it cannot outperform the noisy Gacs-Kurdyumov-Levin automaton, an imperfect classifier, for any level of noise. While the original composite CA is nonergodic, analyses of relaxation times indicate that its noisy version is an ergodic automaton, with the relaxation times decaying algebraically over an extended range of parameters with an exponent very close (possibly equal) to the mean-field value.

We propose a method by which the generalized transport properties and coefficients at all wavelengths and frequencies can be obtained by inversion of an exact kinetic equation. The necessary data are the density-density, energy-energy, and density-energy time correlation functions, which can be obtained by molecular-dynamics simulation. In addition, also the coupling between viscous stress tensor and energy flux vector can be obtained without approximation. This allows one to check the validity of the Markov assumption in a straightforward way. As a first test case, the theory is applied to liquid argon in two thermodynamic states. For this system, we calculate and discuss generalized thermodynamic (enthalpy, specific heats, and thermal expansion) and transport properties (longitudinal viscosity, thermal conductivity).

In the present paper, we extend the method described in paper I [D. Bertolini and A. Tani, preceding paper, Phys. Rev. E 83, 031201 (2011)] to molecular liquids, which allows us to solve the exact kinetic equation proposed by de Schepper et al. [Phys. Rev. A 38, 271 (1988)] without approximations. In particular, generalized thermodynamic properties (enthalpy, specific heat, and thermal expansion coefficient) and transport properties (longitudinal viscosity, thermal conductivity) have been calculated for three liquids of increasing complexity, namely dimethyl sulfoxide, hydrogen fluoride, and SPC/E water. All results have been obtained by the molecular formalism as well as the atomic one, corrected for intramolecular correlations that are due to the models adopted. As done for simple liquids, the coupling between the viscous stress tensor and the energy flux vector has been calculated exactly. We also show that the Markov assumption for the dynamics related to thermal conductivity can only be adopted with caution.

We study the Turing bifurcation in general two-species reaction-transport systems, where particle dispersal is governed by diffusion, including cross diffusion. By performing a linear stability analysis, we find conditions for the Turing instability and compare the results with the standard Turing conditions. We apply our results to two model systems, the Lengyel-Epstein model and the Brusselator, and find strong effects of cross diffusion on the Turing bifurcation.

Cities are living organisms. They are out of equilibrium, open systems that never stop developing and sometimes die. The local geography can be compared to a shell constraining its development. In brief, a city’s current layout is a step in a running morphogenesis process. Thus cities display a huge diversity of shapes and none of the traditional models, from random graphs, complex networks theory, or stochastic geometry, takes into account the geometrical, functional, and dynamical aspects of a city in the same framework. We present here a global mathematical model dedicated to cities that permits describing, manipulating, and explaining cities’ overall shape and layout of their street systems. This street-based framework conciliates the topological and geometrical sides of the problem. From the static analysis of several French towns (topology of first and second order, anisotropy, streets scaling) we make the hypothesis that the development of a city follows a logic of division or extension of space. We propose a dynamical model that mimics this logic and that, from simple general rules and a few parameters, succeeds in generating a large diversity of cities and in reproducing the general features the static analysis has pointed out.

We study the problem of synchronization-based parameters identification of dynamical systems from time series. Through theoretical analysis and numerical examples, we show that some recent research reports on this issue are not perfect or even incorrect. Long-time full rank and finite-time full rank conditions of Gram matrix are pointed out, which are sufficient for parameters identification of dynamical systems. The influence of additive noise on the proposed parameter identifier is also investigated. The mean filter is used to suppress the estimation fluctuation caused by the noise.

The work describes the experimental and theoretical investigation of water drop impact onto electrospun polymer nanofiber mats deposited on heated stainless-steel foils. The measurements encompass water spreading over and inside the mat, as well as the corresponding thermal field. The results show that the presence of polymer nanofiber mats prevents receding motion of drops after their complete spreading and promotes the moisture spreading inside the mat over a large area of the heater, which facilitates a tenfold enhancement of heat removal as the latent heat of drop evaporation.

The creation and evolution of millimeter-sized droplets of a Newtonian liquid generated on demand by the action of pressure pulses were studied experimentally and simulated numerically. The velocity response within a model, large-scale printhead was recorded by laser Doppler anemometry, and the waveform was used in Lagrangian finite-element simulations as an input. Droplet shapes and positions were observed by shadowgraphy and compared with their numerically obtained analogues.

We present a method for discovering dense packings of general convex hard particles and apply it to study the dense packing behavior of a one-parameter family of particles with tetrahedral symmetry representing a deformation of the ideal mathematical tetrahedron into a less ideal, physical, tetrahedron and all the way to the sphere. Thus, we also connect the two well-studied problems of sphere packing and tetrahedron packing on a single axis. Our numerical results uncover a rich optimal-packing behavior, compared to that of other continuous families of particles previously studied. We present four structures as candidates for the optimal packing at different values of asphericity, providing an atlas of crystal structures that might be observed in systems of nanoparticles with tetrahedral symmetry.

Recently, kinetic theory-based lattice Boltzmann (LB) models have been developed to model nonequilibrium gas flows. Depending on the order of quadratures, a hierarchy of LB models can be constructed which we have previously shown to capture rarefaction effects in the standing-shear wave problems. Here, we further examine the capability of high-order LB models in modeling nonequilibrium flows considering gas and surface interactions and their effect on the bulk flow. The Maxwellian gas and surface interaction model, which has been commonly used in other kinetic methods including the direct simulation Monte Carlo method, is used in the LB simulations. In general, the LB models with high-order Gauss-Hermite quadratures can capture flow characteristics in the Knudsen layer and higher order quadratures give more accurate prediction. However, for the Gauss-Hermite quadratures, the present simulation results show that the LB models with the quadratures obtained from the even-order Hermite polynomials perform significantly better than those from the odd-order polynomials. This may be attributed to the zero-velocity component in the odd-order discrete set, which does not participate in wall and gas collisions, and thus underestimates the wall effect.

Maximization of the entropy rate is an important issue to design diffusion processes aiming at a well-mixed state. We demonstrate that it is possible to construct maximal-entropy random walks with only local information on the graph structure. In particular, we show that an almost maximal-entropy random walk is obtained when the step probabilities are proportional to a power of the degree of the target node, with an exponent $\alpha$ that depends on the degree-degree correlations and is equal to 1 in uncorrelated graphs.

The lamellar ordering of bicontinuous microemulsions adjacent to a planar hydrophilic wall is investigated experimentally by grazing-incidence small-angle neutron scattering and theoretically by computer simulations. It is shown that precise depth information in neutron scattering can be obtained by tuning the scattering length density of the overall microemulsion. Neutron reflectometry completes the characterization. The nucleation of a lamellar phase at the wall is observed, and a perforated lamellar transition region is identified at the lamellar-microemulsion interface. The thickness of the lamellar region is about 400 Å, which corresponds to two bilayers.

We study diffusion of pointlike particles biased toward the $x$ axis by a quadratic potential $U(x,y)=\kappa (x)y^2$. This system mimics a channel with soft walls of some varying (effective) cross section $A(x)$, depending on the stiffness $\kappa (x)$. We show that diffusion in this geometry can also be mapped rigorously onto the longitudinal coordinate $x$ by a procedure known for channels with hard walls [P. Kalinay and J. K. Percus, Phys. Rev. E 74, 041203 (2006)]; i.e., we arrive at a one-dimensional evolution equation of the Fick-Jacobs type. On the other hand, the calculation presented serves as a prototype for mapping of the Smoluchowski equation with a wide class of potentials $U(x,y)$ varying in both the longitudinal as well as the transverse directions, which is necessary for understanding, e.g., stochastic resonance.

We have studied nucleation dynamics of the Ising model in scale-free networks whose degree distribution follows a power law with the exponent $\gamma$ by using the forward flux sampling method and focusing on how the network topology would influence the nucleation rate and pathway. For homogeneous nucleation, the new phase clusters grow from those nodes with smaller degree, while the cluster sizes follow a power-law distribution. Interestingly, we find that the nucleation rate $R_{\text{Hom}}$ decays exponentially with network size and, accordingly, the critical nucleus size increases linearly with network size, implying that homogeneous nucleation is not relevant in the thermodynamic limit. These observations are robust to the change of $\gamma$ and are also present in random networks. In addition, we have also studied the dynamics of heterogeneous nucleation, wherein $w$ impurities are initially added either to randomly selected nodes or to targeted ones with the largest degrees. We find that targeted impurities can enhance the nucleation rate $R_{\text{Het}}$ much more sharply than random ones. Moreover, $\ln (R_{\text{Het}}/R_{\text{Hom}})$ scales as $w^{(\gamma -2)/(\gamma -1)}$ and $w$ for targeted and random impurities, respectively. A simple mean-field analysis is also present to qualitatively illustrate the above simulation results.

We report the results of an experimental study of the microstructure of dispersions of Carbopol ETD 2050, a model yield-stress fluid. Using two different light scattering instruments, measurements were made over three decades in scattering wave vector, from 0.02 to 25 $\mu$m${}^{-1}$. These measurements reveal microstructure characterized by two length scales: a longer length scale, $6\hspace{0.5em}\mu$m and larger, that depends on Carbopol concentration and the $p$H of the dispersion and a shorter length scale of approximately $400$ nm that is independent of both sample concentration and $p$H. We relate these results to shear rheology measurement of the yield stress of these materials.

We introduce and characterize free-energy functionals for modeling of solids with different crystallographic symmetries within the phase-field-crystal methodology. The excess free energy responsible for the emergence of periodic phases is inspired by classical density-functional theory, but uses only a minimal description for the modes of the direct correlation function to preserve computational efficiency. We provide a detailed prescription for controlling the crystal structure and introduce parameters for changing temperature and surface energies, so that phase transformations between body-centered-cubic (bcc), face-centered-cubic (fcc), hexagonal-close-packed (hcp), and simple-cubic (sc) lattices can be studied. To illustrate the versatility of our free-energy functional, we compute the phase diagram for fcc-bcc-liquid coexistence in the temperature-density plane. We also demonstrate that our model can be extended to include hcp symmetry by dynamically simulating hcp-liquid coexistence from a seeded crystal nucleus. We further quantify the dependence of the elastic constants on the model control parameters in two and three dimensions, showing how the degree of elastic anisotropy can be tuned from the shape of the direct correlation functions.

Photoisomerization-induced phase transition of neat liquid-crystalline azobenzene chromophore (LCAC) and its effect on phase diagrams of its mixtures with reactive mesogenic diacrylate monomer (RM257) have been investigated experimentally and theoretically. Upon irradiation with ultraviolet light, the nematic phase of LCAC transformed to isotropic, while the crystal phase showed corrugated textures on the surface (i.e., ripples). The phase-transition temperatures and corresponding morphologies of the blends have been investigated by means of differential scanning calorimetry and optical microscopy. A theoretical phase diagram of a binary nematic and crystalline system was constructed by self-consistently solving the combined free energies of Flory-Huggins, Maier-Saupe, and phase-field theory. The calculation revealed various coexistence regions such as nematic $+$ liquid ($N_1$ $+$ $L_2$), crystal $+$ liquid (Cr${}_1$ $+$ $L_2$), crystal $+$ nematic (Cr${}_1$ $+$ $N_2$), and crystal $+$ crystal (Cr${}_1$ $+$ Cr${}_2$) over a broad range of compositions including the single-phase nematic ($N_1$, $N_2$) of the corresponding constituents. The calculated liquidus lines were in good accord with the depressed mesophase-isotropic transition points. The present paper demonstrates the effect of trans-cis photoisomerization on the mesophase transitions of neat LCAC and the phase diagram of LCAC-RM257 as well as on the ripple formation (i.e., periodic undulation) on the azobenzene crystals.

We investigate theoretically the nonlinear evolution of a sand bedform sheared by a laminar viscous flow. On the basis of the hydrodynamic equations coupled with a sediment transport law, we derive a closed nonlinear and nonlocal equation for the spatiotemporal evolution of the bedform profile in the case of an unbounded flow. The numerical resolution of this equation shows that the bedform coarsens indefinitely in the course of time. During the coarsening process, the wavelength scales as the cube of the vertical extension $w$ as a result of the nonlinear interactions. Interestingly, in the case of a bounded flow, we argue that coarsening is interrupted when the flow perturbation induced by the bedform extends over the whole flow depth $h$, and we predict that the final wavelength ${\lambda }_f$ and vertical extension $w_f$ should scale respectively as $(\gamma /\nu )h^3$ and $h$ (where $\nu$ is the fluid viscosity and $\gamma$ the flow shear rate).

A biorthonormal transfer-matrix renormalization-group (BTMRG) method for non-Hermitian matrices is presented. This BTMRG produces a dual set of biorthonormal bases to construct the renormalized transfer matrix with only half the dimensions of the matrix of a conventional transfer-matrix renormalization group (TMRG). We show that under generic conditions, such biorthonormal bases always exist. Based on a special $\mathrm{E}·$S$·$E scheme (where S and E represent the system and environment blocks, respectively, and the two dots in between represent two additional physical sites), the BTMRG method can achieve zero truncation of any reduced state in describing both current left and right Perron states so as to reach a high degree of efficiency and accuracy. We believe that the BTMRG constitutes a more powerful and robust tool than conventional TMRG for non-Hermitian matrices and that it would allow us to better understand the collective behaviors and emerging phenomena of strongly correlated many-body systems. We also show that this scheme is particularly adapted to the calculation of the two-site correlation function of a one-dimensional quantum or two-dimensional classical lattice model.