A wide range of observations in studies of surfaces exposed to ion beams can be explained and analyzed successfully by continuum models of the Kuramoto-Sivashinsky type. Despite certain progress in the theoretical understanding of the model parameters on the basis of atomistic models, much of the applications are based on phenomenological determination of several unknown quantities. In this work a numerical tool is discussed and investigated, which allows us to determine model coefficients and complex model structures from experimental findings. The method resembles known approaches in machine learning and data-driven reconstruction techniques. To keep the discussion on a fundamental level, numerical simulations are conducted by employing a scaled test model. The reconstruction technique is demonstrated for this model system and shows a high accuracy in recovering input parameters for situations without beam noise. As an application to an unknown system to be explored, the algorithm is then applied to a system with lognormal distributed ion bombardment. The impact of the beam fluctuations in the proposed model are discussed. Perspectives of the numerical algorithm for an analysis of experimental data are addressed.

We propose an approach to the numerical simulation of thin-film flows based on the lattice Boltzmann method. We outline the basic features of the method, show in which limits the expected thin-film equations are recovered, and perform validation tests. The numerical scheme is applied to the viscous Rayleigh-Taylor instability of a thin film and to the spreading of a sessile drop toward its equilibrium contact angle configuration. We show that the Cox-Voinov law is satisfied and that the effect of a tunable slip length on the substrate is correctly captured. We address, then, the problem of a droplet sliding on an inclined plane, finding that the Capillary number scales linearly with the Bond number, in agreement with experimental results. At last, we demonstrate the ability of the method to handle heterogenous and complex systems by showcasing the controlled dewetting of a thin film on a chemically structured substrate.

Recombination is one of the leading forces of evolutionary dynamics. Although the importance of both recombination and migration in evolution is well recognized, there is currently no exact theory of evolutionary dynamics for large genome models that incorporates recombination, mutation, selection (quasispecies model with recombination), and spatial dynamics. To address this problem, we analyze the simplest spatial evolutionary process, namely, evolution of haploid populations with mutation, selection, recombination, and unidirectional migration, in its exact analytical form. This model is based on the quasispecies theory with recombination, but with replicators migrating from one habitat to another. In standard evolutionary models involving one habitat, the evolutionary processes depend on the ratios of fitness for different sequences. In the case of migration, we consider the absolute fitness values because there is no competition for resources between the population of different habitats. In the standard model without epistasis, recombination does not affect the mean fitness of the population. When migration is introduced, the situation changes drastically such that recombination can affect the mean fitness as strongly as mutation, as has been observed by Li and Nei for a few loci model without mutations. We have solved our model in the limit of large genome size for the fitness landscapes having different peaks in the first and second habitats and obtained the total population sizes for both habitats as well as the proportion of the population around two peak sequences in the second habitat. We identify four phases in the model and present the exact solutions for three of them.

We consider a quantum engine driven by repeated weak interactions with a heat bath of identical three-level atoms. This model was first introduced by Scully et al. [Science 299, 862 (2003)], who showed that coherence between the energy-degenerate ground states serves as a thermodynamic resource that allows operation of a thermal cycle with a coherence-dependent thermalization temperature. We consider a similar engine out of the quasistatic limit and find that the ground-state coherence also determines the rate of thermalization, therefore increasing the output power and the engine efficiency only when the thermalization temperature is reduced; revealing a more nuanced perspective of coherence as a resource. This allows us to optimize the output power by adjusting the coherence and relative stroke durations.

A trade-off between the precision of an arbitrary current and the dissipation, known as the thermodynamic uncertainty relation, has been investigated for various Markovian systems. Here, we study the thermodynamic uncertainty relation for underdamped Langevin dynamics. By employing information inequalities, we prove that for such systems, the relative fluctuation of a current at a steady state is constrained by both the entropy production and the average dynamical activity. We find that unlike what is the case for overdamped dynamics, the dynamical activity plays an important role in the bound. We illustrate our results with two systems, a single-well potential system and a periodically driven Brownian particle model, and numerically verify the inequalities.

For mean-field classical spin systems exhibiting a second-order phase transition in the stationary state, we obtain within the corresponding phase-space evolution according to the Vlasov equation the values of the critical exponents describing power-law behavior of response to a small external field. The exponent values so obtained significantly differ from the ones obtained on the basis of an analysis of the static phase-space distribution, with no reference to dynamics. This work serves as an illustration that cautions against relying on a static approach, with no reference to the dynamical evolution, to extract critical exponent values for mean-field systems.

Diffusion processes with boundaries are models of transport phenomena with wide applicability across many fields. These processes are described by their probability density functions (PDFs), which often obey Fokker-Planck equations (FPEs). While obtaining analytical solutions is often possible in the absence of boundaries, obtaining closed-form solutions to the FPE is more challenging once absorbing boundaries are present. As a result, analyses of these processes have largely relied on approximations or direct simulations. In this paper, we studied two-dimensional, time-homogeneous, spatially correlated diffusion with linear, axis-aligned, absorbing boundaries. Our main result is the explicit construction of a full family of closed-form solutions for their PDFs using the method of images. We found that such solutions can be built if and only if the correlation coefficient $\rho$ between the two diffusing processes takes one of a numerable set of values. Using a geometric argument, we derived the complete set of $\rho$'s where such solutions can be found. Solvable $\rho$'s are given by $\rho =-cos\left(\frac{\pi }{k}\right)$, where $k\in {\mathbb{Z}}^{+}\cup \{+\infty \}$. Solutions were validated in simulations. Qualitative behaviors of the process appear to vary smoothly over $\rho$, allowing extrapolation from our solutions to cases with unsolvable $\rho$'s.

The two-lane driven system is a type of important model to research some transport systems, and also a powerful tool to investigate properties of nonequilibrium state systems. This paper presents a driven bidirectional two-lane model. The dynamic characteristics of the model with periodic boundary are investigated by Monte Carlo simulation, simple mean field, and cluster mean field methods, respectively. By simulations, phase separations are observed in the system with some values of model parameters. When the phase separation does not occur, cluster mean field results are in good agreement with simulation results. According to the cluster mean field analysis and simulations, a conjecture about the condition that the phase separation happens is proposed. Based on the conjecture, the phase boundary distinguishing phase separation state and homogeneous state is determined, and a corresponding phase diagram is drawn. The conjecture is validated through observing directly the spatiotemporal diagram and investigating the coarsening process of the system by simulation, and a possible mechanism causing the phase separation is also discussed. These outcomes maybe contribute to understand deeply transport systems including the congestion and efficiency of the transport, and enrich explorations of nonequilibrium state systems.

This paper presents a multiple-scales analysis approach capable of capturing internally resonant wave interactions in weakly nonlinear lattices and metamaterials. Example systems considered include a diatomic chain and a locally resonant metamaterial-type lattice. At a number of regions in the band structure, both the frequency and wave number of one nonlinear plane wave may relate to another in a near-commensurate manner (such as in a 2:1 or 3:1 ratio) resulting in an internal resonance mechanism. As shown herein, nonlinear interactions in the lattice couple these waves and enable energy exchange. Near such internal resonances, previously derived higher-order dispersion corrections for single plane wave propagation may break down, leading to singularities in the predicted nonlinear dispersion relationships. Using the presented multiple-scales approach and the two example systems, this paper examines internal resonance occurring (i) within the same branch and (ii) between different branches of the band structure, resolving the aforementioned singularity issue while capturing energy exchange. The multiple-scales evolution equations, together with a local stability analysis, uncover multiple stable fixed points associated with periodic energy exchange between internally resonant propagating modes. Response results generated using direct numerical simulation verify the perturbation-based predictions for amplitude-dependent dispersion corrections and slow-scale energy exchange; importantly, these comparisons verify the exchange frequency predicted by the multiple-scales approach.

Transportation networks with intrinsic flow dynamics governed by the Kirchhoff's current law are ubiquitous in natural and engineering systems. There has been recent work on designing optimal transportation networks based on biological principles with the goal to minimize the total dissipation associated with the flow. Despite being biologically inspired, e.g., adaptive network design based on slime mold Physarum polycephalum, such methods generally lead to suboptimal networks due to the difficulty in finding a global or nearly global optimum of the nonconvex optimization function. Here we articulate a design paradigm that combines engineering control and biological principles to realize optimal transportation networks. In particular, we show how small control signals applied only to a fraction of edges in an adaptive network can lead to solutions that are far more optimal than those based solely on biological principles. We also demonstrate that control signals, if not properly designed, can lead to networks that are less optimal. Incorporating control principle into biology-based optimal network design has broad applications not only in biomedical science and engineering but also in other disciplines such as civil engineering for designing resilient infrastructure systems.

Single-particle trajectories measured in microscopy experiments contain important information about dynamic processes occurring in a range of materials including living cells and tissues. However, extracting that information is not a trivial task due to the stochastic nature of the particles' movement and the sampling noise. In this paper, we adopt a deep-learning method known as a convolutional neural network (CNN) to classify modes of diffusion from given trajectories. We compare this fully automated approach working with raw data to classical machine learning techniques that require data preprocessing and extraction of human-engineered features from the trajectories to feed classifiers like random forest or gradient boosting. All methods are tested using simulated trajectories for which the underlying physical model is known. From the results it follows that CNN is usually slightly better than the feature-based methods, but at the cost of much longer processing times. Moreover, there are still some borderline cases in which the classical methods perform better than CNN.

The initial coalescence of a pendant drop at bulk liquid was jointly investigated by an ultrahigh-speed DC electrical device, a high-speed camera, and a fast micro-Particle Image Velocimetry (micro-PIV). Extended to highly viscous non-Newtonian liquids, the variation of the coalescing width vs time confirms the distinct regimes reported for drop-drop configuration: linear in the inertially limited viscous regime; square root in the inertial regime; possibly a transient viscous regime in between with a logarithmic correction. The measured flow fields during coalescence reveal the transformation of surface energy to kinetic energy, so that the highly located inertia could play a dominant role in relation to the viscous force.

The external electric field enables separation and transport of droplets effectively in microfluidic devices. Herein, a volume-of-fluid (VOF) + level-set (LS) + smoothed physical parameters (SPP) method associated with the dynamically adaptive grid technique is extended to simulate three-dimensional leaky dielectric droplets in the electric field. The effects of electric and hydrodynamic forces on droplet behaviors are investigated. It is demonstrated that the electric force could act toward the outside or inside of a droplet and produce different droplet deformations. For the dielectrophoretic migration of droplets in the nonuniform electric field, the electric force has a dominant effect. It is found that when the electric conductivity ratio is greater than 1, an unbalanced electric force toward a stronger electric field is generated, bringing about the migration toward a stronger electric field. In contrast, when the electric conductivity ratio is smaller than 1, the unbalanced electric force direction is reversed and the droplet migrates toward a weaker electric field. The hydrodynamic force produces little promotion or hindrance to droplet migration. A greater permittivity ratio usually produces greater electric force and migration velocity. The droplet migrates along one direction in a symmetric nonuniform electric field but tends to migrate along the normal direction of electric potential profiles in an asymmetric nonuniform electric field.

Fish may take advantage of environmental vortices to save the cost of locomotion. The complex hydrodynamics shed from multiple physical objects may significantly affect fish refuging (holding stationary). Taking a model of a self-propelled flapping plate, we numerically studied the locomotion of the plate in wakes of two tandem cylinders. In most simulations, the plate heaves at its initial position $G_0$ before the flow comes (releasing Style I). In the typical wake patterns, the plate may hold stationary, drift upstream, or drift downstream. The phase diagrams of these modes in the $G_0-A$ plane for the vortex shedding patterns were obtained, where $A$ is the flapping amplitude. It is observed that the plate is able to hold stationary at multiple equilibrium locations after it is released. Meanwhile, the minimum amplitude and the input power required for the plate seem inversely proportional to the shedding vortex strength. The effect of releasing style was also investigated. If the plate keeps stationary and does not flap until the vortex shedding is fully developed (releasing Style II), then the plate is able to hold stationary at some equilibrium locations but the flapping plate has a very minor effect on the shedding vortices. However, in Style I, the released plate is able to achieve more equilibrium locations through adjusting the phase of vortex shedding. The effort of the preflapping in Style I is not in vain, because although it consumes more energy, it becomes easier to hold stationary later. The relevant mechanism is explored.

We investigate the depinning dynamics of two-dimensional dusty plasmas driven over one-dimensional periodic substrates using Langevin dynamical simulations. We find that, for a specific range of substrate strengths, as the external driving force increases from zero, there are three different states, which are the pinned, the disordered plastic flow, and the moving ordered states, respectively. These three states are clearly observed using different diagnostics, including the collective drift velocity, static structural measures, the particle trajectories, the mean-squared displacements, and the kinetic temperature. We compare the observed depinning dynamics here with the depinning dynamics in other systems.

Statistical models for families of evolutionary related proteins have recently gained interest: In particular, pairwise Potts models as those inferred by the direct-coupling analysis have been able to extract information about the three-dimensional structure of folded proteins and about the effect of amino acid substitutions in proteins. These models are typically requested to reproduce the one- and two-point statistics of the amino acid usage in a protein family, i.e., to capture the so-called residue conservation and covariation statistics of proteins of common evolutionary origin. Pairwise Potts models are the maximum-entropy models achieving this. Although being successful, these models depend on huge numbers of ad hoc introduced parameters, which have to be estimated from finite amounts of data and whose biophysical interpretation remains unclear. Here, we propose an approach to parameter reduction, which is based on selecting collective sequence motifs. It naturally leads to the formulation of statistical sequence models in terms of Hopfield-Potts models. These models can be accurately inferred using a mapping to restricted Boltzmann machines and persistent contrastive divergence. We show that, when applied to protein data, even 20–40 patterns are sufficient to obtain statistically close-to-generative models. The Hopfield patterns form interpretable sequence motifs and may be used to clusterize amino acid sequences into functional subfamilies. However, the distributed collective nature of these motifs intrinsically limits the ability of Hopfield-Potts models in predicting contact maps, showing the necessity of developing models going beyond the Hopfield-Potts models discussed here.

We examine statistical properties of integrable turbulence in the defocusing and focusing regimes of one-dimensional small-dispersion nonlinear Schrödinger equation (1D-NLSE). Specifically, we study the 1D-NLSE evolution of partially coherent waves having Gaussian statistics at time $t=0$. Using short time asymptotic expansions and taking advantage of the scale separation in the semiclassical regime we obtain a simple explicit formula describing an early stage of the evolution of the fourth moment of the random wave field amplitude, a quantitative measure of the “tailedness” of the probability density function. Our results show excellent agreement with numerical simulations of the full 1D-NLSE random field dynamics and provide insight into the emergence of the well-known phenomenon of heavy (respectively, low) tails of the statistical distribution occurring in the focusing (respectively, defocusing) regime of 1D-NLSE.

Plants transport water against the risk of cavitation inside xylem vessels, called “embolism.” As one of their hydraulic strategies, pit membranes composed of cellulose fibers have been known as safety valves that prevent the spreading of embolism towards adjacent xylem vessels. However, detailed observation of embolism spreading through a pit membrane is still lacking. Here, we hypothesized that the pit membranes normally remain to be wetted in xylem vessels and noticed in particular the hydraulic role of water film on air spreading that has been overlooked previously. For the hydrodynamic study of the embolism spreading through a wetted pit membrane, we investigated the penetration and spreading dynamics of air plugs through the wetted cellulose membrane in a channel flow. Air spreading exhibits two types of dynamics: continuous and discrete spreading. We elucidated the correlation of dynamic characteristics of air flow and pressure variations according to membrane thickness. Our study speculates that the thickness of pit membranes affects the behaviors of water film captured by cellulose fibers, and it is a crucial criterion for the reversible gating of further spreading of embolism throughout xylem networks.

We examine the ordering behavior of hard platelike particles in a very narrow, slitlike pore using the Parsons-Lee density functional theory and the restricted orientation approximation. We observe that the plates are orientationally ordered and align perpendicularly (face-on) to the walls at low densities, a first-order layering transition occurs between uniaxial nematic structures having $n$ and $n+1$ layers at intermediate densities, and even a phase transition between a monolayer with parallel (edge-on) orientational order and $n$ layers with a perpendicular one can be detected at high densities. In addition to this, the edge-on monolayer is usually biaxial nematic, and a uniaxial-biaxial nematic phase transition can be also seen at very high densities.

The Chapman-Enskog solution to the Enskog kinetic equation of polydisperse granular mixtures is revisited to determine the first-order contributions ${\varpi }_i$ to the partial temperatures. As expected, these quantities (which were neglected in previous attempts) are given in terms of the solution to a set of coupled integrodifferential equations analogous to those for elastic collisions. The solubility condition for this set of equations is confirmed and the coefficients ${\varpi }_i$ are calculated by using the leading terms in a Sonine polynomial expansion. These coefficients are given as explicit functions of the sizes, masses, composition, density, and coefficients of restitution of the mixture. Within the context of small gradients, the results apply for arbitrary degrees of inelasticity and are not restricted to specific values of the parameters of the mixture. In the case of elastic collisions, previous expressions of ${\varpi }_i$ for ordinary binary mixtures are recovered. Finally, the impact of the first-order coefficients ${\varpi }_i$ on the bulk viscosity ${\eta }_{\text{b}}$ and on the first-order contribution ${\zeta }^{\left(1\right)}$ to the cooling rate is assessed. It is shown that the effect of ${\varpi }_i$ on ${\eta }_{\text{b}}$ and ${\zeta }^{\left(1\right)}$ is not negligible, specially for disparate mass ratios and strong inelasticity.