We present a challenging validation of phase field multicomponent lattice Boltzmann equation (MCLBE) simulation against the $\text{Re}=0$ Stokes flow regime Taylor-Einstein theory of dilute suspension viscosity. By applying a number of recent advances in the understanding and the elimination of the interfacial microcurrent artefact, extending to a three-dimensional class of stability-enhancing multiple relaxation time collision models (which require no explicit collision matrix, note) and developing new interfacial interpolation schemes, we are able to obtain data that show that MCLBE may be applied in new flow regimes. Our data represent one of the most stringent tests yet attempted on LBE—one which received wisdom would preclude on grounds of overwhelming artefact flow.

Periodic driving is used to operate machines that go from standard macroscopic engines to small nonequilibrium microsized systems. Two classes of such systems are small heat engines driven by periodic temperature variations, and molecular pumps driven by external stimuli. Well-known results that are valid for nonequilibrium steady states of systems driven by fixed thermodynamic forces, instead of an external periodic driving, have been generalized to periodically driven heat engines only recently. These results include a general expression for entropy production in terms of currents and affinities, and symmetry relations for the Onsager coefficients from linear-response theory. For nonequilibrium steady states, the Onsager reciprocity relations can be obtained from the more general fluctuation theorem for the currents. We prove a fluctuation theorem for the currents for periodically driven systems. We show that this fluctuation theorem implies a fluctuation dissipation relation, symmetry relations for Onsager coefficients, and further relations for nonlinear response coefficients. The setup in this paper is more general than previous studies, i.e., our results are valid for both heat engines and molecular pumps. The external protocol is assumed to be stochastic in our framework, which leads to a particularly convenient way to treat periodically driven systems.

The enhanced transport of particles by roughness in a tilted rough ratchet potential subject to a Lévy noise is investigated in this paper. Due to the roughness, the transport process exhibits quite different properties compared to the smooth case. We find that the roughness on the potential wall functions like a ladder to provide the convenience for particles to climb up but hinder them to slide down. The mean first passage time from one well to its right adjacent well and the mean velocity are, respectively, calculated versus the roughness, the external force, and the Lévy stability index. Our results show that the roughness is able to induce an enhancement on the mean velocity of particles and accelerate the barrier crossing process. The general conditions require a small external force and a small Lévy stability index. We find that with increasing external forces, the enhancement areas of roughness and Lévy stability index both shrink. However, for the Lévy stability index within the enhancement area, its increase will enlarge the enhancement area of roughness. On the contrary, under the same conditions we observe that for a Gaussian noise the roughness always reduces the corresponding mean velocity which is very different from the case of Lévy noise.

Local configurational symmetry in lattice structures may give rise to stationary, compact solutions, even in the absence of disorder and nonlinearity. These compact solutions are related to the existence of flat dispersion curves (bands). Nonlinearity can destabilize such compactons. One common flat-band-generating system is the one-dimensional cross-stitch model, in which compactons were shown to exist for the photonic lattice with Kerr nonlinearity. The compactons exist there already in the linear regime and are not generally destructed by that nonlinearity. Smooth nonlinearity of this kind does not permit performing complete stability analysis for this chain. We consider a discrete mechanical system with flat dispersion bands, in which the nonlinearity exists due to impact constraints. In this case, one can use the concept of the saltation matrix for the analytic construction of the monodromy matrix. Besides, we consider a smooth nonlinear lattice with linearly connected massless boxes, each containing two symmetric anharmonic oscillators. In this model, the flat bands and discrete compactons also readily emerge. This system also permits performing comprehensive stability analysis, at least in the anticontinuum limit, due to the reduced number of degrees of freedom. In both systems, there exist two types of localization. The first one is the complete localization, and the second one is the more common exponential localization. The latter type is associated with discrete breathers (DBs). Two principal mechanisms for the loss of stability are revealed. The first one is the possible internal instability of the symmetric and/or antisymmetric solution in the individual unit cell of the chain. One can interpret this instability pattern as internal resonance between the compacton and the DB. The other mechanism is global instability related to resonance of the stationary solution with the propagation frequencies. Different instability mechanisms lead to different bifurcations at the stability threshold.

Chimera state has been well studied recently, but little attention has been paid to its transition to synchronization. We study this topic here by considering two groups of adaptively coupled Kuramoto oscillators. By searching the final states of different initial conditions, we find that the system can easily show a chimera state with robustness to initial conditions, in contrast to the sensitive dependence of chimera state on initial conditions in previous studies. Further, we show that, in the case of symmetric couplings, the behaviors of the two groups are always complementary to each other, i.e., robustness of chimera state, except a small basin of synchronization. Interestingly, we reveal that the basin of synchronization will be significantly increased when either the coupling of inner groups or that of intergroups are asymmetric. This transition from the attractor of chimera state to the attractor of synchronization is closely related to both the phase delay and the asymmetric degree of coupling strengths, resulting in a diversity of attractor's patterns. A theory based on the Ott-Antonsen ansatz is given to explain the numerical simulations. This finding may be meaningful for the control of competition between two attractors in biological systems, such as the cardiac rhythm and ventricular fibrillation, etc.

Hierarchical organization is an important, prevalent characteristic of complex systems; to understand their organization, the study of the underlying (generally complex) networks that describe the interactions between their constituents plays a central role. Numerous previous works have shown that many real-world networks in social, biologic, and technical systems present hierarchical organization, often in the form of a hierarchy of community structures. Many artificial benchmark graphs have been proposed to test different community detection methods, but no benchmark has been developed to thoroughly test the detection of hierarchical community structures. In this study, we fill this vacancy by extending the Lancichinetti-Fortunato-Radicchi (LFR) ensemble of benchmark graphs, adopting the rule of constructing hierarchical networks proposed by Ravasz and Barabási. We employ this benchmark to test three of the most popular community detection algorithms and quantify their accuracy using the traditional mutual information and the recently introduced hierarchical mutual information. The results indicate that the Ravasz-Barabási-Lancichinetti-Fortunato-Radicchi (RB-LFR) benchmark generates a complex hierarchical structure constituting a challenging benchmark for the considered community detection methods.

A detailed investigation of the thermal and dielectric properties of a series of binary mixtures exhibiting the nematic ($N$) and twist-bend nematic ($N_{\mathrm{TB}}$) liquid crystal phases is presented. The mixtures consist of an achiral, dimeric liquid crystal CB7CB, which forms the nematic and twist-bend nematic phases, and a calamitic liquid crystal 5CB, which shows the nematic phase. As the concentration of the calamitic liquid crystal is increased, the transition temperatures decrease linearly, and the width of the nematic phase increases. The enthalpies of phase transitions obtained from DSC measurements show that on increasing the concentration of 5CB in the binary mixtures, the enthalpy associated with the $N\text{−}{N}_{\mathrm{TB}}$ phase transitions reduces considerably compared to a clear first-order $N\text{−}{N}_{\mathrm{TB}}$ transition in pure CB7CB. The real and imaginary parts of the dielectric permittivity are measured as a function of frequency from 100 Hz to 2 MHz in the nematic and twist-bend nematic phases in planar and homeotropic devices. A significant decrease in the average dielectric permittivity as a function of temperature for mixtures forming the $N_{\mathrm{TB}}$ phase is observed. Measurements of the imaginary part of the dielectric permittivity show a relaxation peak in the measured frequency window for all of the mixtures exhibiting the $N_{\mathrm{TB}}$ phase. The activation energy associated with this relaxation process is calculated and is shown to remain constant irrespective of the composition of the mixtures.

This work focuses on quantitative representation of transport in systems with quenched disorder. Explicit mapping of the quenched trap model to continuous time random walk is presented. Linear temporal transformation, $t\to t/{\mathrm{\Lambda }}^{1/\alpha }$, for a transient process in the subdiffusive regime is sufficient for asymptotic mapping. An exact form of the constant ${\mathrm{\Lambda }}^{1/\alpha }$ is established. A disorder averaged position probability density function for a quenched trap model is obtained, and analytic expressions for the diffusion coefficient and drift are provided.

We consider motion of a particle in a one-dimensional tilted ratchet potential subject to two-sided tempered stable Lévy noise characterized by strength $\mathrm{\Omega }$, fractional index $\alpha$, skew $\theta$, and tempering $\lambda$. We derive analytic solutions to the corresponding Fokker-Planck Lévy equations for the probability density. Due to the periodicity of the potential, we carry out reduction to a compact domain and solve for the analog of steady-state solutions which we represent as wrapped probability density functions. By solving for the expected value of the current associated with the particle motion, we are able to determine thresholds for metastability of the system, namely when the particle stabilizes in a well of the potential and when the particle is in motion, for example as a consequence of the tilt of the potential. Because the noise may be asymmetric, we examine the relationship between skew of the noise and the tilt of the potential. With tempering, we find two remarkable regimes where the current may be reversed in a direction opposite to the tilt or where the particle may be stabilized in a well in circumstances where deterministically it should flow with the tilt.

The effect of dynamical properties of the periodic Lorentz gas on the autocorrelation function and diffusion coefficient are investigated in various geometric transitions between billiards without horizon and infinite horizon. Numerical simulations are performed using a double square lattice which permits us to isolate different types of corridors and to describe the individual effects of each corridor. The results are compared with a stochastic model based on a escape-rate formalism which reveals the sensibility of the diffusion coefficient and clarifies the role of the open corridors mechanism on the dynamical transitions

We consider a class of either fermionic or bosonic noninteracting open quantum chains driven by dissipative interactions at the boundaries and study the interplay of coherent transport and dissipative processes, such as bulk dephasing and diffusion. Starting from the microscopic formulation, we show that the dynamics on large scales can be described in terms of fluctuating hydrodynamics. This is an important simplification as it allows us to apply the methods of macroscopic fluctuation theory to compute the large deviation (LD) statistics of time-integrated currents. In particular, this permits us to show that fermionic open chains display a third-order dynamical phase transition in LD functions. We show that this transition is manifested in a singular change in the structure of trajectories: while typical trajectories are diffusive, rare trajectories associated with atypical currents are ballistic and hyperuniform in their spatial structure. We confirm these results by numerically simulating ensembles of rare trajectories via the cloning method, and by exact numerical diagonalization of the microscopic quantum generator.

The number of clusters per site $n\left(p\right)$ in percolation at the critical point $p=p_c$ is not itself a universal quantity; it depends upon the lattice and percolation type (site or bond). However, many of its properties, including finite-size corrections, scaling behavior with $p$, and amplitude ratios, show various degrees of universal behavior. Some of these are universal in the sense that the behavior depends upon the shape of the system, but not lattice type. Here, we elucidate the various levels of universality for elements of $n\left(p\right)$ both theoretically and by carrying out extensive studies on several two- and three-dimensional systems, by high-order series analysis, Monte Carlo simulation, and exact enumeration. We find many results, including precise values for $n\left(p_c\right)$ for several systems, a clear demonstration of the singularity in $n^{\prime \prime }\left(p\right)$, and metric scale factors. We make use of the matching polynomial of Sykes and Essam to find exact relations between properties for lattices and matching lattices. We propose a criterion for an absolute metric factor $b$ based upon the singular behavior of the scaling function, rather than a relative definition of the metric that has previously been used.

Living beings on the Earth are subjected to and entrained (synchronized) to the natural 24-h light-dark cycle. Interestingly, they can also be entrained to an external artificial cycle of non-24-h periods. The range of these periods is called the entrainment range and it differs among species. In mammals, the entrainment range is regulated by a main clock located in the suprachiasmatic nucleus (SCN) which is composed of 10 000 neurons in the brain. Previous works have found that the entrainment range depends on the cellular coupling strength in the SCN. In particular, the entrainment range decreases with the increase of the cellular coupling strength, provided that all the neuronal oscillators are identical. However, the SCN neurons differ in the intrinsic periods that follow a normal distribution in a range from 22 to 28 h. In the present study, taking the dispersion of the intrinsic neuronal periods into account, we examined the relationship between the entrainment range and the coupling strength. Results from numerical simulations and theoretical analyses both show that the relationship is altered to be paraboliclike if the intrinsic neuronal periods are nonidentical, and the maximal entrainment range is obtained with a suitable coupling strength. Our results shed light on the role of the cellular coupling in the entrainment ability of the SCN network.

The modulation of neural quantities by presynaptic and postsynaptic activities via local feedback processes is investigated by incorporating nonlinear phenomena such as relative refractory period, synaptic enhancement, synaptic depression, and habituation. This is done by introducing susceptibilities, which quantify the response in either firing threshold or synaptic strength to unit change in either presynaptic or postsynaptic activity. Effects on the power spectra are then analyzed for a realistic corticothalamic model to determine the spectral signatures of various nonlinear processes and to what extent these are distinct. Depending on the feedback processes, there can be enhancements or reductions in low-frequency and/or alpha power, splitting of the alpha resonance, and/or appearance of new resonances at high frequencies. These features in the power spectra allow processes to be fully distinguished where they are unique, or partly distinguished if they are common to only a subset of feedbacks, and can potentially be used to constrain the types, strengths, and dynamics of feedbacks present.

We investigate the modes of oscillation of heterogeneous ring networks of quadratic integrate-and-fire (QIF) neurons with nonlocal, space-dependent coupling. Perturbations of the equilibrium state with a particular wave number produce transient standing waves with a specific temporal frequency, analogously to those in a tense string. In the neuronal network, the equilibrium corresponds to a spatially homogeneous, asynchronous state. Perturbations of this state excite the network's oscillatory modes, which reflect the interplay of episodes of synchronous spiking with the excitatory-inhibitory spatial interactions. In the thermodynamic limit, an exact low-dimensional neural field model describing the macroscopic dynamics of the network is derived. This allows us to obtain formulas for the Turing eigenvalues of the spatially homogeneous state and hence to obtain its stability boundary. We find that the frequency of each Turing mode depends on the corresponding Fourier coefficient of the synaptic pattern of connectivity. The decay rate instead is identical for all oscillation modes as a consequence of the heterogeneity-induced desynchronization of the neurons. Finally, we numerically compute the spectrum of spatially inhomogeneous solutions branching from the Turing bifurcation, showing that similar oscillatory modes operate in neural bump states and are maintained away from onset.

Here we report an experimental observation of the self-organization effect of polystyrene particles formed by acoustically induced interaction forces. Two types of stable configurations are observed experimentally: one is mechanically equilibrium and featured by nonzero interparticle separations, and the other corresponds to a closely packed assembly, which is created by strong attractions among the aggregated particles. For the former case involving two or three particles, the most probable interparticle separations (counted for numerous independent initial arrangements) agree well with the theoretical predictions. For the latter case, the number of the final stable configurations grows with the particle number, and the occurrence probability of each configuration is interpreted by a simple geometric model.

We examine the effects of confinement on the dynamics of premelted films driven by thermomolecular pressure gradients. Our approach is to modify a well-studied setting in which the thermomolecular pressure gradient is driven by a temperature gradient parallel to an interfacially premelted elastic wall. The modification treats the increase in viscosity associated with the thinning of films, studied in a wide variety of materials, using a power law and we examine the consequent evolution of the confining elastic wall. We treat (1) a range of interactions that are known to underlie interfacial premelting and (2) a constant temperature gradient wherein the thermomolecular pressure gradient is a constant. The difference between the cases with and without the proximity effect arises in the volume flux of premelted liquid. The proximity effect increases the viscosity as the film thickness decreases thereby requiring the thermomolecular pressure driven flux to be accommodated at higher temperatures where the premelted film thickness is the largest. Implications for experiment and observations of frost heave are discussed.

Standard two-dimensional orientation-field-based phase-field models rely on a continuous scalar field to represent crystallographic orientation. The corresponding order parameter space is the unit circle, which is not simply connected. This topological property has important consequences for the resulting multigrain structures: (i) trijunctions may be singular; (ii) for each pair of grains there exist two different grain boundary solutions that cannot continuously transform to one another; (iii) if both solutions appear along a grain boundary, a topologically stable, singular point defect must exist between them. While (i) can be interpreted in the classical picture of grain boundaries, (ii) and therefore (iii) cannot. In addition, singularities cause difficulties, such as lattice pinning in numerical simulations. To overcome these problems, we propose two formulations of the model. The first is based on a three-component unit vector field, while in the second we utilize a two-component vector field with an additional potential. In both cases, the additional degree of freedom introduced makes the order parameter space simply connected, which removes the topological stability of these defects.

Cloaking is a challenging topic in the field of wave motion, and is of significant theoretical value. In this article, a type of carpet cloak has been theoretically designed for water waves by using the effective medium and transformation theory. This carpet cloak device, created by a three-dimensional printer, is composed of a periodic structure which realizes the equivalent anisotropic water depth. We demonstrate its excellent cloaking performance numerically and experimentally in a wide range of frequencies and angles of incidence, with low wave attenuation characteristics and simple device realization of this carpet cloak illustrating that water wave transformation is a powerful method with which to manipulate water waves.