The effect of a linear adsorption isotherm on the onset of fingering instability in a miscible displacement in the application of liquid chromatography, pollutant contamination in aquifers, etc., is investigated. Such fingering instability on the solute dynamics arise due to the miscible viscus fingering (VF) between the displacing fluid and sample solvent. We use a Fourier pseudo-spectral method to solve the initial value problem that appears in the linear stability analysis. The present linear stability analysis is of generic type and it captures the early-time-diffusion-dominated region which was never expressible through the quasi-steady-state analysis (QSSA). In addition, it measures the onset of instability more accurately than the QSSA methods. It is shown that the onset time depends nonmonotonically on the retention parameter of the solute adsorption. This qualitative influence of the retention parameter on the onset of instability resemblances with the results obtained from direct numerical simulations of the nonlinear equations. Moreover, the present linear stability method helps for an appropriate characterization of the linear and nonlinear regimes of miscible VF instability and also can be useful for the fluid flow problems with the unsteady base state.

Reconstructing heterogeneous materials from limited structural information has been a topic that attracts extensive research efforts and still poses many challenges. The Yeong-Torquato procedure is one of the most popular reconstruction techniques, in which the material reconstruction problem based on a set of spatial correlation functions is formulated as a constrained energy minimization (optimization) problem and solved using simulated annealing [Yeong and Torquato, Phys. Rev. E 57, 495 (1998)]. The standard two-point correlation function $S_2$ has been widely used in reconstructions, but can also lead to large structural degeneracy for certain nearly percolating systems. To improve reconstruction accuracy and reduce structural degeneracy, one can successively incorporate additional morphological information (e.g., nonconventional or higher-order correlation functions), which amounts to reshaping the energy landscape to create a deep (local) energy minimum. In this paper, we present a dynamic reconstruction procedure that allows one to use a series of auxiliary $S_2$ to achieve the same level of accuracy as those incorporating additional nonconventional correlation functions. In particular, instead of randomly sampling the microstructure space as in the simulated annealing scheme, our procedure utilizes a series of auxiliary microstructures that mimic a physical structural evolution process (e.g., grain growth). This amounts to constructing a series auxiliary energy landscapes that bias the convergence of the reconstruction to a favored (local) energy minimum. Moreover, our dynamic procedure can be naturally applied to reconstruct an actual microstructure evolution process. In contrast to commonly used evolution reconstruction approaches that separately generate individual static configurations, our procedure continuously evolves a single microstructure according to a time-dependent correlation function. The utility of our procedure is illustrated by successfully reconstructing nearly percolating hard-sphere packings and particle-reinforced composites as well as the coarsening process in a binary metallic alloy.

In the present study, we demonstrate how to perform, using quantum annealing, the singular value decomposition and the principal component analysis. Quantum annealing gives a way to find a ground state of a system, while the singular value decomposition requires the maximum eigenstate. The key idea is to transform the sign of the final Hamiltonian, and the maximum eigenstate is obtained by quantum annealing. Furthermore, the adiabatic time scale is obtained by the approximation focusing on the maximum eigenvalue.

Multiplex networks (MNs) have become a platform of recent research in network sciences because networks in many real-world systems interact and function together. One of the main scientific issues in MNs is how the interdependence changes the emerging patterns or phase transitions. Until now, studies of such an issue have concentrated on cluster-breakdown phenomena, aiming to understand the resilience of the system under random failures of edges. These studies have revealed that various phase transition (PT) types emerge in MNs. However, such studies are rather limited to percolation-related problems, i.e., the limit $q\to 1$ of the $q$-state Potts model. Thus, a systematic study of opinion formation in social networks with the effect of interdependence between different social communities, which may be seen as the study of the emerging pattern of the Ising model on MNs, is needed. Here we study a well-known spin model called the Ashkin-Teller (AT) model in scale-free networks. The AT model can be regarded as a model for interacting systems between two species of Ising spins placed on respective layers in double-layer networks. Our study shows that, depending on the interlayer coupling strength and a network topology, unconventional PT patterns can also emerge in interaction-based phenomena: continuous, discontinuous, successive, and mixed-order PTs and a continuous PT not satisfying the scaling relation. The origins of such rich PT patterns are elucidated in the framework of Landau-Ginzburg theory.

We compare two methods of eigeninference from large sets of data. Our analysis points at the superiority of our eigeninference method based on one-point Green's functions and Padé approximants over a method based on fluctuations and two-point Green's functions. The first method is orders of magnitude faster than the second one; moreover, we found a source of potential instability of the second method and identified it as arising from the spurious zero and negative modes of the estimator for the variance operator of a certain multidimensional Gaussian distribution, inherent for that method. We also present eigeninference based on spectral moments of negative orders, for strictly positive spectra. Finally, we compare the cases of eigeninference of real-valued and complex-valued correlated Wishart distributions, reinforcing our conclusions on the advantage of the one-point Green's function method.

A self-consistent theory is proposed for the general problem of interacting undulating fluid membranes subject to the constraint that they do not interpenetrate. We implement the steric constraint via an exact functional integral representation and, through the use of a saddle-point approximation, transform it into a novel effective steric potential. The steric potential is found to consist of two contributions: one generated by zero-mode fluctuations of the membranes and the other by thermal bending fluctuations. For membranes of cross-sectional area $S$, we find that the bending fluctuation part scales with the intermembrane separation $d$ as $d^{-2}$ for $d\ll \sqrt{S}$ but crosses over to $d^{-4}$ scaling for $d\gg \sqrt{S}$, whereas the zero-mode part of the steric potential always scales as $d^{-2}$. For membranes interacting exclusively via the steric potential, we obtain closed-form expressions for the effective interaction potential and for the rms undulation amplitude $\sigma$, which becomes small at low temperatures $T$ and/or large bending stiffnesses $\kappa$. Moreover, $\sigma$ scales as $d$ for $d\ll \sqrt{S}$ but saturates at $\sqrt{k_{B}TS/\kappa }$ for $d\gg \sqrt{S}$. In addition, using variational Gaussian theory, we apply our self-consistent treatment to study intermembrane interactions subject to different types of potentials: (i) the Moreira-Netz potential for a pair of strongly charged membranes with an intervening solution of multivalent counterions, (ii) an attractive square well, (iii) the Morse potential, and (iv) a combination of hydration and van der Waals interactions.

Analysis of degree-degree dependencies in complex networks, and their impact on processes on networks requires null models, i.e., models that generate uncorrelated scale-free networks. Most models to date, however, show structural negative dependencies, caused by finite size effects. We analyze the behavior of these structural negative degree-degree dependencies, using rank based correlation measures, in the directed erased configuration model. We obtain expressions for the scaling as a function of the exponents of the distributions. Moreover, we show that this scaling undergoes a phase transition, where one region exhibits scaling related to the natural cutoff of the network while another region has scaling similar to the structural cutoff for uncorrelated networks. By establishing the speed of convergence of these structural dependencies we are able to assess statistical significance of degree-degree dependencies on finite complex networks when compared to networks generated by the directed erased configuration model.

We implement the spectral renormalization group on different deterministic nonspatial networks without translational invariance. We calculate the thermodynamic critical exponents for the Gaussian model on the Cayley tree and the diamond lattice and find that they are functions of the spectral dimension, $\tilde{d}$. The results are shown to be consistent with those from exact summation and finite-size scaling approaches. At $\tilde{d}=2$, the lower critical dimension for the Ising universality class, the Gaussian fixed point is stable with respect to a ${\psi }^4$ perturbation up to second order. However, on generalized diamond lattices, non-Gaussian fixed points arise for $2<\tilde{d}<4$.

Since the mid-1980s, mode-coupling theory (MCT) has been the de facto theoretic description of dense fluids and the transition from the fluid state to the glassy state. MCT, however, is limited by the approximations used in its construction and lacks an unambiguous mechanism to institute corrections. We use recent results from a new theoretical framework—developed from first principles via a self-consistent perturbation expansion in terms of an effective two-body potential—to numerically explore the kinetics of systems of classical particles, specifically hard spheres governed by Smoluchowski dynamics. We present here a full solution for such a system to the kinetic equation governing the density-density time correlation function and show that the function exhibits the characteristic two-step decay of supercooled fluids and an ergodic-nonergodic transition to a dynamically arrested state. Unlike many previous numerical studies—and in stark contrast to experiment—we have access to the full time and wave-number range of the correlation function with great precision and are able to track the solution unprecedentedly close to the transition, covering nearly 15 decades in scaled time. Using asymptotic approximation techniques analogous to those developed for MCT, we fit the solution to predicted forms and extract critical parameters. We find complete qualitative agreement with known glassy behavior (e.g. power-law divergence of the $\alpha$-relaxation time scale in the ergodic phase and square-root growth of the glass form factors in the nonergodic phase), as well as some limited quantitative agreement [e.g. the transition at packing fraction ${\eta }^{*}=0.60149761\left(10\right)]$, consistent with previous static solutions under this theory and with comparable colloidal suspension experiments. However, most importantly, we establish that this new theory is able to reproduce the salient features seen in other theories, experiments, and simulations but has the advantages of being derived from first principles and possessing a clear mechanism for making systematic corrections.

Using the scaling relation of the ground state quantum fidelity, we propose the most generic scaling relations of the irreversible work (the residual energy) of a closed quantum system at absolute zero temperature when one of the parameters of its Hamiltonian is suddenly changed. We consider two extreme limits: the heat susceptibility limit and the thermodynamic limit. It is argued that the irreversible entropy generated for a thermal quench at low enough temperatures when the system is initially in a Gibbs state is likely to show a similar scaling behavior. To illustrate this proposition, we consider zero-temperature and thermal quenches in one-dimensional (1D) and 2D Dirac Hamiltonians where the exact estimation of the irreversible work and the irreversible entropy is possible. Exploiting these exact results, we then establish the following. (i) The irreversible work at zero temperature shows an appropriate scaling in the thermodynamic limit. (ii) The scaling of the irreversible work in the 1D Dirac model at zero temperature shows logarithmic corrections to the scaling, which is a signature of a marginal situation. (iii) Remarkably, the logarithmic corrections do indeed appear in the scaling of the entropy generated if the temperature is low enough while they disappear for high temperatures. For the 2D model, no such logarithmic correction is found to appear.

Nonequilibrium and equilibrium fluid systems differ due to the existence of long-range correlations in nonequilibrium that are not present in equilibrium, except at critical points. Here we examine fluctuations of the temperature, of the pressure tensor, and of the heat current in a fluid maintained in a nonequilibrium stationary state (NESS) with a fixed temperature gradient, a system in which the nonequilibrium correlations are especially long-ranged. For this particular NESS, our results show that (i) the mean-squared fluctuations in nonequilibrium differ markedly in their system-size scaling compared to their equilibrium counterparts, and (ii) there are large, nonlocal correlations of the normal stress in this NESS. These terms provide important corrections to the fluctuating normal stress in linearized Landau-Lifshitz fluctuating hydrodynamics.

In this research, the dissipative particle dynamics method was used to investigate the problem of thinning and breakup in a liquid bridge. It was found that both the inertial-force-dominated thinning process and the thermal-fluctuation-dominated thinning process can be reproduced with the dissipative particle dynamics (DPD) method by varying the simulation parameters. A highly suspect viscous thinning regime was also found, but the conclusion is not irrefutable because of the complication of the shear viscosity of DPD fluid. We show in this article that the DPD method can serve as a good candidate to elucidate crossover problem in liquid bridge thinning from being hydrodynamics dominated to being thermal fluctuation dominated.

We present the linear stability analysis of horizontal Poiseuille flow in a fluid overlying a porous medium with anisotropic and inhomogeneous permeability. The generalized Darcy model is used to describe the flow in the porous medium with the Beavers-Joseph condition at the interface of the two layers and the eigenvalue problem is solved numerically. The effect of major system parameters on the stability characteristics is addressed in detail. It is shown that the anisotropic and inhomogeneous modulation of the permeability of the underlying porous layer provides an effective means for passive control of the flow stability.

We numerically investigate quantum quenches of a nonintegrable hard-core Bose-Hubbard model to test the accuracy of the microcanonical ensemble in small isolated quantum systems. We show that, in a certain range of system size, the accuracy increases with the dimension of the Hilbert space $D$ as $1/D$. We ascribe this rapid improvement to the absence of correlations between many-body energy eigenstates. Outside of that range, the accuracy is found to scale either as $1/\sqrt{D}$ or algebraically with the system size.

We consider the local load-sharing fiber bundle model in one to five dimensions. Depending on the breaking threshold distribution of the fibers, there is a transition where the fracture process becomes localized. In the localized phase, the model behaves as the invasion percolation model. The difference between the local load-sharing fiber bundle model and the equal load-sharing fiber bundle model vanishes with increasing dimensionality with the characteristics of a power law.

A class of autonomous quantum heat baths satisfying the eigenstate thermalization hypothesis (ETH) criteria is proposed. We show that such systems are expected to cause thermal relaxation of much smaller quantum systems coupled to one of the baths local observables. The process of thermalization is examined through residual fluctuations of local observables of the bath around their thermal values predicted by ETH. It is shown that such fluctuations perturb the small quantum system causing its decoherence to the thermal state. As an example, we investigate theoretically and numerically thermalization of a qubit coupled to a realistic ETH quantum heat bath.

We study the dynamics of a nonlinear oscillator near the critical point where period-two vibrations are first excited with the increasing amplitude of parametric driving. Above the threshold, quantum fluctuations induce transitions between the period-two states over the quasienergy barrier. We find the effective quantum activation energies for such transitions and their scaling with the difference of the driving amplitude from its critical value. We also find the scaling of the fluctuation correlation time with the quantum noise parameters in the critical region near the threshold. The results are extended to oscillators with nonlinear friction.

We perform numerical simulations of a two-dimensional bidisperse granular packing subjected to both a static confining pressure and a sinusoidal dynamic forcing applied by a wall on one edge of the packing. We measure the response experienced by a wall on the opposite edge of the packing and obtain the resonant frequency of the packing as the static or dynamic pressures are varied. Under increasing static pressure, the resonant frequency increases, indicating a velocity increase of elastic waves propagating through the packing. In contrast, when the dynamic amplitude is increased for fixed static pressure, the resonant frequency decreases, indicating a decrease in the wave velocity. This occurs both for compressional and for shear dynamic forcing and is in agreement with experimental results. We find that the average contact number $Z_c$ at the resonant frequency decreases with increasing dynamic amplitude, indicating that the elastic softening of the packing is associated with a reduced number of grain-grain contacts through which the elastic waves can travel. We image the excitations created in the packing and show that there are localized disturbances or soft spots that become more prevalent with increasing dynamic amplitude. Our results are in agreement with experiments on glass bead packings and earth materials such as sandstone and granite and may be relevant to the decrease in elastic wave velocities that has been observed to occur near fault zones after strong earthquakes, in surficial sediments during strong ground motion, and in structures during earthquake excitation.

Classic experiments on the distribution of ducks around separated food sources found consistency with the “ideal free” distribution in which the local population is proportional to the local supply rate. Motivated by this experiment and others, we examine the analogous problem in the microbial world: the distribution of chemotactic bacteria around multiple nearby food sources. In contrast to the optimization of uptake rate that may hold at the level of a single cell in a spatially varying nutrient field, nutrient consumption by a population of chemotactic cells will modify the nutrient field, and the uptake rate will generally vary throughout the population. Through a simple model we study the distribution of resource uptake in the presence of chemotaxis, consumption, and diffusion of both bacteria and nutrients. Borrowing from the field of theoretical economics, we explore how the Gini index can be used as a means to quantify the inequalities of uptake. The redistributive effect of chemotaxis can lead to a phenomenon we term “chemotactic levelling,” and the influence of these results on population fitness are briefly considered.