We study the evolution of step bunches on vicinal surfaces using a thermodynamically consistent step-flow model. By accounting for the dynamics of adatom diffusion on terraces and attachment-detachment at steps (referred to collectively as the dynamical effect), this model circumvents the quasistatic approximation that prevails in the literature. Furthermore, it generalizes the expression of the step chemical potential by incorporating the necessary coupling between the diffusion fields on adjacent terraces (referred to as the chemical effect). Having previously shown that these dynamical and chemical effects can explain the onset of step bunching without recourse to the inverse Ehrlich-Schwoebel (iES) barrier or other extraneous mechanisms, we are here interested in the evolution of step bunches beyond the linear-stability regime. In particular, the numerical resolution of the step-flow free boundary problem yields a robust power-law coarsening of the surface profile, with the bunch height growing in time as $H\sim t^{1/2}$ and the minimal interstep distance as a function of the number of steps in the bunch cell obeying ${\ell }_{\text{min}}\sim N^{-2/3}$. Although these exponents have previously been reported, the novelty of the present approach is that these scaling laws are obtained in the absence of an iES barrier or adatom electromigration. In order to validate our simulations, we take the continuum limit of the discrete step-flow system via Taylor expansions with respect to the terrace size, leading to a novel nonlinear evolution equation for the surface height. We investigate the existence of self-similar solutions of this equation and confirm the 1/2 coarsening exponent obtained numerically for $H$. We highlight the influence of the combined dynamical-chemical effect and show that it can be interpreted as an effective iES barrier in the setting of the standard Burton-Cabrera-Frank theory. Finally, we use a Padé approximant to derive an analytical expression for the velocity of steadily moving step bunches and compare it to numerical simulations.

We report intermittent large-intensity pulses that originate in Zeeman laser due to instabilities in quasiperiodic motion, one route follows torus-doubling to chaos and another goes via quasiperiodic intermittency in response to variation in system parameters. The quasiperiodic breakdown route to chaos via torus-doubling is well known; however, the laser model shows intermittent large-intensity pulses for parameter variation beyond the chaotic regime. During quasiperiodic intermittency, the temporal evolution of the laser shows intermittent chaotic bursting episodes intermediate to the quasiperiodic motion instead of periodic motion as usually seen during the Pomeau-Manneville intermittency. The intermittent bursting appears as occasional large-intensity events. In particular, this quasiperiodic intermittency has not been given much attention so far from the dynamical system perspective, in general. In both cases, the infrequent and recurrent large events show non-Gaussian probability distribution of event height extended beyond a significant threshold with a decaying probability confirming rare occurrence of large-intensity pulses.

In 1972, Robert May triggered a worldwide research program studying ecological communities using random matrix theory. Yet, it remains unclear if and when we can treat real communities as random ecosystems. Here, we draw on recent progress in random matrix theory and statistical physics to extend May's approach to generalized consumer-resource models. We show that in diverse ecosystems adding even modest amounts of noise to consumer preferences results in a transition to “typicality,” where macroscopic ecological properties of communities are indistinguishable from those of random ecosystems, even when resource preferences have prominent designed structures. We test these ideas using numerical simulations on a wide variety of ecological models. Our work offers an explanation for the success of random consumer resource models in reproducing experimentally observed ecological patterns in microbial communities and highlights the difficulty of scaling up bottom-up approaches in synthetic ecology to diverse communities.

Polymer chains undergoing adsorption are expected to show universal critical behavior which may be investigated using partition function zeros. The focus of this work is the adsorption transition for a continuum chain, allowing for investigation of a continuous range of the attractive interaction and comparison with recent high-precision lattice model studies. The partition function (Fisher) zeros for a tangent-hard-sphere $N$-mer chain (monomer diameter $\sigma$) tethered to a flat wall with an attractive square-well potential (range $\lambda \sigma$, depth $\epsilon$) have been computed for chains up to $N=1280$ with $0.01\le \lambda \le 2.0$. In the complex-Boltzmann-factor plane these zeros are concentrated in an annular region, centered on the origin and open about the real axis. With increasing $N$, the leading zeros, $w_1\left(N\right)$, approach the positive real axis as described by the asymptotic scaling law $w_1\left(N\right)-y_c\sim N^{-\varphi }$, where $y_c=e^{\epsilon /k_B{T}_c}$ is the critical point and $T_c$ is the critical temperature. In this work, we study the polymer adsorption transition by analyzing the trajectory of the leading zeros as they approach $y_c$ in the complex plane. We use finite-size scaling (including corrections to scaling) to determine the critical point and the scaling exponent $\varphi$ as well as the approach angle ${\theta }_c$, between the real axis and the leading-zero trajectory. Variation of the interaction range $\lambda$ moves the critical point, such that $T_c$ decreases with $\lambda$, while the results for $\varphi$ and ${\theta }_c$ are approximately independent of $\lambda$. Our values of $\varphi =0.479\left(9\right)$ and ${\theta }_c=56.8{\left(1.4\right)}^{\circ }$ are in agreement with the best lattice model results for polymer adsorption, further demonstrating the universality of these constants across both lattice and continuum models.

Yield stress fluids (YSFs) display a dual nature highlighted by the existence of a critical stress ${\sigma }_{\text{y}}$ such that YSFs are solid for stresses $\sigma$ imposed below ${\sigma }_{\text{y}}$, whereas they flow like liquids for $\sigma >{\sigma }_{\text{y}}$. Under an applied shear rate $\dot{\gamma }$, the solid-to-liquid transition is associated with a complex spatiotemporal scenario that depends on the microscopic details of the system, on the boundary conditions, and on the system size. Still, the general phenomenology reported in the literature boils down to a simple sequence that can be divided into a short-time response characterized by the so-called “stress overshoot,” followed by stress relaxation towards a steady state. Such relaxation can be either (1) long-lasting, which usually involves the growth of a shear band that can be only transient or that may persist at steady state or (2) abrupt, in which case the solid-to-liquid transition resembles the failure of a brittle material, involving avalanches. In the present paper, we use a continuum model based on a spatially resolved fluidity approach to rationalize the complete scenario associated with the shear-induced yielding of YSFs. A key feature of our model is to provide a scaling for the coordinates of the stress overshoot, i.e., stress ${\sigma }_{\text{M}}$ and strain ${\gamma }_{\text{M}}$ as a function of $\dot{\gamma }$, which shows good agreement with experimental and numerical data extracted from the literature. Moreover, our approach shows that the power-law scaling ${\sigma }_{\text{M}}\left(\dot{\gamma }\right)$ is intimately linked to the growth dynamics of a fluidized boundary layer in the vicinity of the moving boundary. Yet such scaling is independent of the fate of that layer, and of the long-term behavior of the YSF, i.e., whether the steady-state flow profile is homogeneous or shear-banded. Finally, when including the presence of “long-range” correlations, we show that our model displays a ductile to brittle transition, i.e., the stress overshoot reduces into a sharp stress drop associated with avalanches, which impacts the scaling ${\sigma }_{\text{M}}\left(\dot{\gamma }\right)$. This generalized model nicely captures subtle avalanche-like features of the transient shear banding dynamics reported in experiments. Our work offers a unified picture of shear-induced yielding in YSFs, whose complex spatiotemporal dynamics are deeply connected to nonlocal effects.

We consider an active (self-propelling) particle in a viscoelastic fluid. The particle is charged and constrained to move in a two-dimensional harmonic trap. Its dynamics is coupled to a constant magnetic field applied perpendicular to its plane of motion via Lorentz force. Due to the finite activity, the generalized fluctuation-dissipation relation (GFDR) breaks down, driving the system away from equilibrium. While breaking GFDR, we have shown that the system can have finite classical orbital magnetism only when the dynamics of the system contains finite inertia. The orbital magnetic moment has been calculated exactly. Remarkably, we find that when the elastic dissipation timescale of the medium is larger (smaller) than the persistence timescale of the self-propelling particle, it is diamagnetic (paramagnetic). Therefore, for a given strength of the magnetic field, the system undergoes a transition from diamagnetic to paramagnetic state (and vice versa) simply by tuning the timescales of underlying physical processes, such as active fluctuations and viscoelastic dissipation. Interestingly, we also find that the magnetic moment, which vanishes at equilibrium, behaves nonmonotonically with respect to increasing persistence of self-propulsion, which drives the system out of equilibrium.

We studied random sequential adsorption (RSA) of parallel rectangles with random aspect ratio but fixed area using a newly developed algorithm that allows to generate strictly saturated packing of this kind. We determined saturated packing fraction for several different distributions of a random variable used for selecting side length ratio of deposited rectangles. It was also shown that the anisotropy of deposited rectangles changes during packing generation. Additionally, we examined the kinetics of packing growth, which near saturation obeys the power law with the exponent $1/d\approx 1/3$, typical for the RSA of unoriented anisotropic shapes on a two-dimensional surface. Kinetics in the low coverage limit is determined using the concept of the available surface function. The microstructural properties of obtained random packings are evaluated in terms of two-point density correlation function.

Superellipse sector particles (SeSPs) are segments of superelliptical curves that form a tunable set of hard-particle shapes for granular and colloidal systems. SeSPs allow for continuous parametrization of corner sharpness, aspect ratio, and particle curvature; rods, circles, rectangles, and staples are examples of shapes SeSPs can model. We investigate the space of allowable (nonoverlapping) configurations of two SeSPs, which depends on both the center-of-mass separation and relative orientation. Radial correlation plots of the allowed configurations reveal circular regions centered at each of the particle's two end points that indicate configurations of mutually entangled particle interactions. Simultaneous entanglement with both end points is geometrically impossible; the overlap of these two regions therefore represents an excluded area in which no particles can be placed regardless of orientation. The regions' distinct boundaries indicate a translational frustration with implications for the dynamics of particle rearrangements (e.g., under shear). Representing translational and rotational degrees of freedom as a hypervolume, we find a topological change that suggests geometric frustration arises from a phase transition in this space. The excluded area is a straightforward integration over excluded states; for arbitrary relative orientation this decreases sigmoidally with increasing opening aperture, with sharper SeSP corners resulting in a sharper decrease. Together, this work offers a path towards a unified theory for particle shape control of bulk material properties.

Rayleigh-Brillouin scattering (RBS) in gases has received considerable attention due to its applications in LIDAR (light detection and ranging) remote sensing and gas property measurements. In most cases, the RBS spectra in the kinetic regime are calculated based on kinetic model equations, which are difficult to be applied to complex gas mixtures. In this work, we employ two widely used molecular simulation methods, i.e., direct simulation Monte Carlo (DSMC) and molecular dynamics (MD), to calculate the spontaneous RBS spectra of binary gas mixtures. We validate these two methods by comparing the simulation results for mixtures of argon and helium with the experimental results. Then we extend the RBS calculations to gas mixtures involving polyatomic gases. The rotational relaxation numbers specific to each species pair in DSMC are determined by fitting the DSMC spectra to the MD spectra. Our results show that all the rotational relaxation numbers for air composed of ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$ increase with temperature in the range of 300–750 K. We further calculate the RBS spectra for binary mixtures composed of ${\mathrm{N}}_2$ and one noble monatomic gas, and the simulation results show that the rotational relaxation of ${\mathrm{N}}_2$ is greatly affected by the mass of the noble gas atoms. This work demonstrates that RBS is a promising and alternative way to study the rotational relaxation process in gas mixtures.

In a recent Letter [A. Lapolla and A. Godec, Phys. Rev. Lett. 125, 110602 (2020)], thermal relaxation was observed to occur faster from cold to hot (heating) than from hot to cold (cooling). Here we show that overdamped diffusion in anharmonic potentials generically exhibits both faster heating and faster cooling, depending on the initial temperatures and on the potential's degree of anharmonicity. We draw a relaxation-speed phase diagram that localizes the different behaviors in parameter space. In addition to faster-heating and faster-cooling regions, we identify a crossover region in the phase diagram, where heating is initially slower but asymptotically faster than cooling. The structure of the phase diagram is robust against the inclusion of a confining, harmonic term in the potential as well as moderate changes of the measure used to define initially equidistant temperatures.

The canonical problem of the icing of a water drop lying on a cold substrate is revisited to take into account the effects of atmospheric conditions on the icing front kinetics and on the tip formation. Here, we demonstrate both experimentally and theoretically that the air humidity induces liquid-vapor phase change at the icing droplet interface and that the associated heat transfer has a strong influence on both the icing front kinetics and the iced drop shape. The experimental results obtained in this study, as well as results from literature, compare well to a modified Stefan model accounting for the effects of humidity, showing a good agreement with the experimental data of both the front kinetics and tip angle.

We reinvestigate a simple model used in the literature concerning the thermodynamic analysis of protein cold denaturation. We derive an exact thermodynamic expression for cold denaturation and give a better approximation than exists in the literature for predicting cold denaturation temperatures in the two-state model. We discuss the “dark-side” implications of this work for previous temperature-dependent protein dynamics experiments and discuss microfluidic experimental technologies, which could explore the thermal stability range of proteins below the bulk freezing point of water.

We examine a modification of the Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) process in which the diffusing substance requires a parent density field for reproduction. A biological example would be the density of diffusing spores (propagules) and the density of a stationary fungus (parent). The parent produces propagules at a certain rate, and the propagules turn into the parent substance at another rate. We model this evolution by the FKPP process with delay, which reflects a finite time typically required for a new parent to mature before it begins to produce propagules. Although the FKPP process with other types of delays have been considered in the past as a pure mathematical construct, in our paper a delay in the FKPP model arises in a natural science setting. The speed of the resulting density fronts is shown to decrease with increasing delay time and has a nontrivial dependence on the rate of conversion of propagules into the parent substance. Remarkably, the fronts in this model are always slower than Fisher waves of the classical FKPP model. The largest speed is half the classical value, and it is achieved at zero delay and when the two rates are matched.

Differential dynamic microscopy (DDM) is a form of video image analysis that combines the sensitivity of scattering and the direct visualization benefits of microscopy. DDM is broadly useful in determining dynamical properties including the intermediate scattering function for many spatiotemporally correlated systems. Despite its straightforward analysis, DDM has not been fully adopted as a routine characterization tool, largely due to computational cost and lack of algorithmic robustness. We present statistical analysis that quantifies the noise, reduces the computational order, and enhances the robustness of DDM analysis. We propagate the image noise through the Fourier analysis, which allows us to comprehensively study the bias in different estimators of model parameters, and we derive a different way to detect whether the bias is negligible. Furthermore, through use of Gaussian process regression (GPR), we find that predictive samples of the image structure function require only around 0.5%–5% of the Fourier transforms of the observed quantities. This vastly reduces computational cost, while preserving information of the quantities of interest, such as quantiles of the image scattering function, for subsequent analysis. The approach, which we call DDM with uncertainty quantification (DDM-UQ), is validated using both simulations and experiments with respect to accuracy and computational efficiency, as compared with conventional DDM and multiple particle tracking. Overall, we propose that DDM-UQ lays the foundation for important new applications of DDM, as well as to high-throughput characterization.

Dynamic wetting of droplets on soft solids has many industrial and biological applications which require an understanding of the underlying fluid transport mechanism. Here we study the case of a droplet on a viscoelastic substrate of variable thickness which is known to give rise to a spontaneous droplet transport. This phenomenon is known as droplet durotaxis and has been observed experimentally. Here we develop a model assuming a small linear gradient in substrate thickness to reveal the physical mechanism behind this transport phenomena. We show the variable thickness causes an asymmetric deformation along the drop contact line, which causes a variation in the contact angle. This generates a net driving force on the drop, causing it to move in the direction of higher thickness. The resulting drop velocity is determined by balancing the work done by the moving drop with the viscoelastic dissipation of the substrate (viscoelastic braking) and computed from a self-consistent model. We find our results to be in qualitative agreement to previously reported experimental findings.

Ion transport in electrolytes with nanoscale confinements is of great importance in many fields such as nanofluidics and electrochemical energy devices. The mobility and conductance for ions are often described by the classical Debye-Hückel-Onsager (DHO) theory but this theory fails for ions near dielectric interfaces. We propose a generalized DHO theory by using the Wentzel-Kramers-Brillouin techniques for the solution of the Onsager-Fuoss equation with variable coefficients. The theory allows to quantitatively measure physical quantities of ion transport in nanodevices and is demonstrated to well explain the abnormal increase or decrease of the ionic mobility tuned via the dielectric mismatch. By numerical calculations, our theory unravels the crucial role of the size of confinements and the ionic concentration on the ion transport, and demonstrates that the dielectric polarization can provide a giant enhancement on the conductance of electrolytes in nanodevices. This mechanism provides a practical guide for related nanoscale technologies with controllable transport properties.

We consider the problem of driving a finite-state classical system from some initial distribution $p$ to some final distribution $p^{\prime }$ with vanishing entropy production (EP), under the constraint that the driving protocols can only use some limited set of energy functions $\mathcal{E}$. Assuming no other constraints on the driving protocol, we derive a simple condition that guarantees that such a transformation can be carried out, which is stated in terms of the smallest probabilities in $\{p,p^{\prime }\}$ and a graph-theoretic property defined in terms of $\mathcal{E}$. Our results imply that a surprisingly small amount of control over the energy function is sufficient (in particular, any transformation $p\to p^{\prime }$ can be carried out as soon as one can control some one-dimensional parameter of the energy function, e.g., the energy of a single state). We also derive a lower bound on the EP under more general constraints on the transition rates, which is formulated in terms of a convex optimization problem.

We investigate a family of generalized Fokker-Planck equations that contains Richardson and porous media equations as members. Considering a confining drift term that is related to an effective potential, we show that each equation of this family has a stationary solution that depends on this potential. This stationary solution encompasses several well-known probability distributions. Moreover, we verify an $H$ theorem for the generalized Fokker-Planck equations using free-energy-like functionals. We show that the energy-like part of each functional is based on the effective potential and the entropy-like part is a generalized Tsallis entropic form, which has an unusual dependence on the position and can be related to a generalization of the Kullback-Leibler divergence. We also verify that the optimization of this entropic-like form subjected to convenient constraints recovers the stationary solution. The analysis presented here includes several studies about $H$ theorems for other generalized Fokker-Planck equations as particular cases.