Besides total energy, three-dimensional incompressible Hall magnetohydrodynamics (MHD) possesses two inviscid invariants, which are the magnetic helicity and the generalized helicity. Exact relations are derived for homogeneous (nonisotropic) stationary Hall MHD turbulence (and also for its inertialess electron MHD limit) with nonzero helicities and in the asymptotic limit of large Reynolds numbers. The universal laws are written only in terms of mixed second-order structure functions, i.e., the scalar product of two different increments. It provides, therefore, a direct measurement of the dissipation rates for the corresponding invariant flux. This study shows that the generalized helicity cascade is strongly linked to the left polarized fluctuations, while the magnetic helicity cascade is linked to the right polarized fluctuations.

We propose consistent scaling of solitary waves on inertia-dominated falling liquid films, which accurately accounts for the driving physical mechanisms and leads to a self-similar characterization of solitary waves. Direct numerical simulations of the entire two-phase system are conducted using a state-of-the-art finite volume framework for interfacial flows in an open domain that was previously validated against experimental film-flow data with excellent agreement. We present a detailed analysis of the wave shape and the dispersion of solitary waves on 34 different water films with Reynolds numbers $\mathrm{Re}=20–120$ and surface tension coefficients $\sigma =0.0512–0.072\mathrm{N}{\mathrm{m}}^{-1}$ on substrates with inclination angles $\beta ={19}^{\circ }–{90}^{\circ }$. Following a detailed analysis of these cases we formulate a consistent characterization of the shape and dispersion of solitary waves, based on a newly proposed scaling derived from the Nusselt flat film solution, that unveils a self-similarity as well as the driving mechanism of solitary waves on gravity-driven liquid films. Our results demonstrate that the shape of solitary waves, i.e., height and asymmetry of the wave, is predominantly influenced by the balance of inertia and surface tension. Furthermore, we find that the dispersion of solitary waves on the inertia-dominated falling liquid films considered in this study is governed by nonlinear effects and only driven by inertia, with surface tension and gravity having a negligible influence.

Based on equilibrium molecular simulations, it is usually difficult to efficiently visit the whole conformational space of complex systems, which are separated into some metastable regions by high free energy barriers. Nonequilibrium simulations could enhance transitions among these metastable regions and then be applied to sample equilibrium distributions in complex systems, since the associated nonequilibrium effects can be removed by employing the Jarzynski equality (JE). Here we present such a systematical method, named reweighted nonequilibrium ensemble dynamics (RNED), to efficiently sample equilibrium conformations. The RNED is a combination of the JE and our previous reweighted ensemble dynamics (RED) method. The original JE reproduces equilibrium from lots of nonequilibrium trajectories but requires that the initial distribution of these trajectories is equilibrium. The RED reweights many equilibrium trajectories from an arbitrary initial distribution to get the equilibrium distribution, whereas the RNED has both advantages of the two methods, reproducing equilibrium from lots of nonequilibrium simulation trajectories with an arbitrary initial conformational distribution. We illustrated the application of the RNED in a toy model and in a Lennard-Jones fluid to detect its liquid-solid phase coexistence. The results indicate that the RNED sufficiently extends the application of both the original JE and the RED in equilibrium sampling of complex systems.

Cell adhesion plays a crucial role in many biological processes of cells, e.g., immune responses, tissue morphogenesis, and stem cell differentiation. An essential problem in the molecular mechanism of cell adhesion is to characterize the binding affinity of membrane-anchored receptors and ligands under different physiological conditions. In this paper, a theoretical model is presented to study the binding affinity between a large number of anchored receptors and ligands under both tensile and compressive stresses, and corroborated by demonstrating excellent agreement with Monte Carlo simulations. It is shown that the binding affinity becomes lower as the magnitude of the applied stress increases, and drops to zero at a critical tensile or compressive stress. Interestingly, the critical compressive stress is found to be substantially smaller than the critical tensile stress for relatively long and flexible receptor-ligand complexes. This counterintuitive finding is explained by using the Euler instability theory of slender columns under compression. The tension-compression asymmetry in the binding affinity of anchored receptors and ligands depends subtly on the competition between the breaking and instability of their complexes. This study helps in understanding the role of mechanical forces in cell adhesion mediated by specific binding molecules.

Equilibrium and nonequilibrium molecular dynamics simulations were performed to better understand the hydrodynamic behavior of water flowing through silicon nanochannels. The water-silicon interaction potential was calibrated by means of size-independent molecular dynamics simulations of silicon wettability. The wettability of silicon was found to be dependent on the strength of the water-silicon interaction and the structure of the underlying surface. As a result, the anisotropy was found to be an important factor in the wettability of these types of crystalline solids. Using this premise as a fundamental starting point, the hydrodynamic slip in nanoconfined water was characterized using both equilibrium and nonequilibrium calculations of the slip length under low shear rate operating conditions. As was the case for the wettability analysis, the hydrodynamic slip was found to be dependent on the wetted solid surface atomic structure. Additionally, the interfacial water liquid structure was the most significant parameter to describe the hydrodynamic boundary condition. The calibration of the water-silicon interaction potential performed by matching the experimental contact angle of silicon led to the verification of the no-slip condition, experimentally reported for silicon nanochannels at low shear rates.

We study $F$ coupled $q$-state Potts models in a two-dimensional square lattice. The interaction between the different layers is attractive to favor a simultaneous alignment in all of them, and its strength is fixed. The nature of the phase transition for zero field is numerically determined for $F=2,3$. Using the Lee-Kosterlitz method, we find that it is continuous for $F=2$ and $q=2$, whereas it is abrupt for higher values of $q$ and/or $F$. When a continuous or a weakly first-order phase transition takes place, we also analyze the properties of the geometrical clusters. This allows us to determine the fractal dimension $D$ of the incipient infinite cluster and to examine the finite-size scaling of the cluster number density via data collapse. A mean-field approximation of the model, from which some general trends can be determined, is presented too. Finally, since this lattice model has been recently considered as a thermodynamic counterpart of the Axelrod model of social dynamics, we discuss our results in connection with this one.

Based on the fundamental Bogolyubov chain of equations, a model relating the structural and thermophysical properties of the nonequilibrium liquid systems under irradiation in stationary state is introduced. The obtained results suggest that the thermophysical properties of the liquid systems under irradiation are defined by the “effective temperature” that can be calculated from the perturbed momentum distribution functions of the systems. It is shown that the structural changes in the liquid systems under irradiation are caused by the changes in the coefficients of the Maxwell distribution function due to the momentum exchange between the active particles and the particles forming the liquid. To confirm the theoretical predictions, a qualitative comparison of the model with the existing experimental data on irradiation influence on the surface tension coefficients of liquids is performed.

In order to illuminate the properties of current fluctuations in more than one dimension, we use a lattice-based Markov process driven into a nonequilibrium steady state. Specifically, we perform a detailed study of the particle current fluctuations in a two-dimensional zero-range process with open boundary conditions and probe the influence of the underlying geometry by comparing results from a square and a triangular lattice. Moreover, we examine the structure of local currents corresponding to a given global current fluctuation and comment on the role of spatial inhomogeneities for the discrepancies observed in testing some recent fluctuation symmetries.

We present an approach for testing for the existence of continuous generators of discrete stochastic transition matrices. Typically, existing methods to ascertain the existence of continuous Markov processes are based on the assumption that only time-homogeneous generators exist. Here a systematic extension to time inhomogeneity is presented, based on new mathematical propositions incorporating necessary and sufficient conditions, which are then implemented computationally and applied to numerical data. A discussion concerning the bridging between rigorous mathematical results on the existence of generators to its computational implementation is presented. Our detection algorithm shows to be effective in more than $60\%$ of tested matrices, typically $80\%$ to $90\%$, and for those an estimate of the (nonhomogeneous) generator matrix follows. We also solve the embedding problem analytically for the particular case of three-dimensional circulant matrices. Finally, a discussion of possible applications of our framework to problems in different fields is briefly addressed.

We study spectral parametric correlations in quantum chaotic systems and introduce the number covariance as a measure of such correlations. We derive analytic results for the classical random matrix ensembles using the binary correlation method and obtain compact expressions for the covariance. We illustrate the universality of this measure by presenting the spectral analysis of the quantum kicked rotors for the time-reversal invariant and time-reversal noninvariant cases. A local version of the parametric number variance introduced earlier is also investigated.

Recent extensive studies of the explosive percolation (EP) model revealed that the EP transition is second order with an extremely small value of the critical exponent $\beta$ associated with the order parameter. This result was obtained from static networks, in which the number of nodes in the system remains constant during the evolution of the network. However, explosive percolating behavior of the order parameter can be observed in social networks, which are often growing networks, where the number of nodes in the system increases as dynamics proceeds. However, extensive studies of the EP transition in such growing networks are still missing. Here we study the nature of the EP transition in growing networks by extending an existing growing network model to a general case in which $m$ node candidates are picked up in the Achiloptas process. When $m=2$, this model reduces to the existing model, which undergoes an infinite-order transition. We show that when $m\ge 3$, the transition becomes second order due to the suppression effect against the growth of large clusters. Using the rate-equation approach and performing numerical simulations, we also show that the exponent $\beta$ decreases algebraically with increasing $m$, whereas it does exponentially in a corresponding static random network model. Finally, we find that the hyperscaling relations hold but in different forms.

Dynamical processes on networks are currently being considered in different domains of cross-disciplinary interest. Reaction-diffusion systems hosted on directed graphs are in particular relevant for their widespread applications, from computer networks to traffic systems. Due to the peculiar spectrum of the discrete Laplacian operator, homogeneous fixed points can turn unstable, on a directed support, because of the topology of the network, a phenomenon which cannot be induced on undirected graphs. A linear analysis can be performed to single out the conditions that underly the instability. The complete characterization of the patterns, which are eventually attained beyond the linear regime of exponential growth, calls instead for a full nonlinear treatment. By performing a multiple time scale perturbative calculation, we here derive an effective equation for the nonlinear evolution of the amplitude of the most unstable mode, close to the threshold of criticality. This is a Stuart-Landau equation the complex coefficients of which appear to depend on the topological features of the embedding directed graph. The theory proves adequate versus simulations, as confirmed by operating with a paradigmatic reaction-diffusion model.

The crossover from back-and-forth jumps between structural minima to the no-return jumps of the viscous flow is modeled in terms of an ensemble of double-well potentials with a finite decay probability. The ensemble is characterized by the Kohlrausch-exponent $\beta$ of the time dependence $t^{\beta }$ of the response at short times. The model is applied to shear and dielectric data from the literature.

We present numerical studies of wetting on various topographic substrates, including random topographies. We find good agreement with recent predictions based on an analytical interface-displacement-type theory, except that we find critical end points within the physical parameter range. As predicted, Gaussian random surfaces are found to behave qualitatively different from non-Gaussian topographies. This shows that Gaussian random processes as models for rough surfaces must be used with great care, if at all, in the context of wetting phenomena.

In this study we analyze the phase and group velocity of three-dimensional linear traveling waves in two sheared flows: the plane channel and the wake flows. This was carried out by varying the wave number over a large interval of values at a given Reynolds number inside the ranges 20–100, 1000–8000, for the wake and channel flow, respectively. Evidence is given about the possible presence of both dispersive and nondispersive effects which are associated with the long and short ranges of wavelength. We solved the Orr-Sommerfeld and Squire eigenvalue problem and observed the least stable mode. It is evident that, at low wave numbers, the least stable eigenmodes in the left branch of the spectrum behave in a dispersive manner. By contrast, if the wave number is above a specific threshold, a sharp dispersive-to-nondispersive transition can be observed. Beyond this transition, the dominant mode belongs to the right branch of the spectrum. The transient behavior of the phase velocity of small three-dimensional traveling waves was also considered. Having chosen the initial conditions, we then show that the shape of the transient highly depends on the transition wavelength threshold value. We show that the phase velocity can oscillate with a frequency which is equal to the frequency width of the eigenvalue spectrum. Furthermore, evidence of intermediate self-similarity is given for the perturbation field.

We propose a method to sample stationary properties of solutions of stochastic differential equations, which is accurate and efficient if there are rarely visited regions or rare transitions between distinct regions of the state space. The method is based on a complete, nonoverlapping partition of the state space into patches on which the stochastic process is ergodic. On each of these patches we run simulations of the process strictly truncated to the corresponding patch, which allows effective simulations also in rarely visited regions. The correct weight for each patch is obtained by counting the attempted transitions between all different patches. The results are patchworked to cover the whole state space. We extend the concept of truncated Markov chains which is originally formulated for processes which obey detailed balance to processes not fulfilling detailed balance. The method is illustrated by three examples, describing the one-dimensional diffusion of an overdamped particle in a double-well potential, a system of many globally coupled overdamped particles in double-well potentials subject to additive Gaussian white noise, and the overdamped motion of a particle on the circle in a periodic potential subject to a deterministic drift and additive noise. In an appendix we explain how other well-known Markov chain Monte Carlo algorithms can be related to truncated Markov chains.

We propose a mechanism that enables heat flow from a colder region to a hotter region without necessitating either particle transport or external work on the conductor, thereby bypassing the compressor part of a classical heat pump cycle. Our mechanism relies on thermostatting the kinetic and configurational temperatures of the same particle differently. We keep the two ends of a conductor, which in the present study is a single dimensional ${\varphi }^4$ chain, at the same kinetic temperature $T_0$, but at different configurational temperatures—one end hotter and the other end colder than $T_0$. While external energy is needed within the thermostatted regions to achieve this differential thermostatting, no external work is performed on the system itself. We show that the mechanism satisfies the statistical form of the second law of thermodynamics (the fluctuation theorem). The proposed mechanism reveals two interesting findings: (i) contrary to traditional thermodynamics where only the kinetic temperature is thought to govern heat conduction, configurational temperature can also play an important role, and (ii) the relative temperature difference between the kinetic and configurational variables governs the direction of heat flow. The challenge, however, is in developing experimental techniques to thermostat the kinetic and configurational variables of the same particle at different values.

The classical dimer model on the square lattice is a paradigmatic example of a system subject to strong local constraints. We study its behavior under local stochastic dynamics, by means of Monte Carlo simulations and theoretical arguments. We observe clear signatures of correlated dynamics in both global and local observables and over a broad range of time scales, indicating a breakdown of the simple continuum description that approximates well the statics. We show that this collective dynamics can be understood in terms of one-dimensional “strings” of high mobility, which govern both local and long-wavelength dynamical properties. We introduce a coarse-grained description of the strings, based on the Edwards-Wilkinson model, which leads to exact results in the limit of low string density and provides a detailed qualitative understanding of the dynamics in all flux sectors. We discuss the implications of our results for the dynamics of constrained systems more generally.

For heat conduction in one-dimensional (1D) nonlinear Hamiltonian lattices, it has been known that conserved quantities play an important role in determining the actual heat conduction behavior. In closed or microcanonical Hamiltonian systems, the total energy and stretch are always conserved. Depending on the existence of external on-site potential, the total momentum can be conserved or not. All the momentum-conserving lattices have anomalous heat conduction except the 1D coupled rotator lattice. It was recently claimed that “whenever stretch (momentum) is not conserved in a 1D model, the momentum (stretch) and energy fields exhibit normal diffusion.” The stretch in a coupled rotator lattice was also argued to be nonconserved due to the requirement of a finite partition function, which enables the coupled rotator lattice to fulfill this claim. In this work, we will systematically investigate stretch diffusion and heat conduction in terms of energy diffusion for typical 1D nonlinear lattices. Contrary to what was claimed, no clear connection between conserved quantities and heat conduction can be established. The actual situation might be more complicated than what was proposed.