We show that disordered boundaries destroy bulk phase separation in scalar active systems in dimension $d<d_c=3$. This is in strong contrast with the equilibrium case where boundaries have no impact on the bulk of phase-separated systems. The underlying mechanism is revealed by considering a localized deformation of an otherwise flat wall, from which the case of a disordered boundary can be inferred. We find long-ranged correlations of the density field as well as a cascade of eddies which we show prevent bulk phase separation in low enough dimensions. The results are derived for dilute systems as well as in the presence of interactions, under the sole condition that the density field is the unique hydrodynamic mode. Our theoretical calculations are validated by numerical simulations of microscopic active systems.

We propose a simple percolation criterion for arbitrary percolation problems. The basic idea is to decompose the system of interest into a hierarchy of neighborhoods, such that the percolation problem can be expressed as a branching process. The criterion provides the exact percolation thresholds for a large number of exactly solved percolation problems, including random graphs, small-world networks, bond percolation on two-dimensional lattices with a triangular hypergraph, and site percolation on two-dimensional lattices with a generalized triangular hypergraph, as well as specific continuum percolation problems. The fact that the range of applicability of the criterion is so large bears the remarkable implication that all the listed problems are effectively treelike. With this in mind, we transfer the exact solutions known from duality to random lattices and site-bond percolation problems and introduce a method to generate simple planar lattices with a prescribed percolation threshold.

The free-energy landscape of the Sherrington-Kirkpatrick (SK) Ising spin glass is simple in the framework of the Thouless-Anderson-Palmer (TAP) equations as each solution (which are minima of the free energy) has associated with it a nearby index-one saddle point. The free-energy barrier to escape the minimum is just the difference between the saddle point free energy and that at its associated minimum. This difference is calculated for the states with free energies $f>f_c$. It is very small for these states, decreasing as $1/N^2$, where $N$ is the number of spins in the system. These states are not marginally stable. We argue that such small barriers are why numerical studies never find these states when $N$ is large. Instead, the states that are found are those that have marginal stability. For them the barriers are at least of $O\left(1\right)$. $f_c$ is the free energy per spin below which the states develop broken replica-symmetry-like overlaps with each other. In the regime $f<f_c$ we can only offer some possibilities based around scaling arguments. One of these suggest that the barriers might become as large as $N^{1/3}$. That might be consistent with recent numerical studies on the Viana-Bray model, which were at variance with the expectations of Cugliandolo and Kurchan for the SK model.

We study the distribution of occupation times for a one-dimensional random walk restricted to a finite interval by reflecting boundary conditions. At short times the classical bimodal distribution due to Lévy is reproduced with walkers staying mostly either to the left or right of the initial point. With increasing time, however, the boundaries suppress large excursions from the starting point, and the distribution becomes unimodal, converging to a $\delta$ distribution in the long-time limit. An approximate spectral analysis of the underlying Fokker-Planck equation yields results in excellent agreement with numerical simulations.

Complex contagion adoption dynamics are characterized by a node being more likely to adopt after multiple network neighbors have adopted. We show how to construct multitype branching processes to approximate complex contagion adoption dynamics on networks with clique-based clustering. This involves tracking the evolution of a cascade via different classes of clique motifs that account for the different numbers of active, inactive, and removed nodes. This discrete-time model assumes that active nodes become immediately and certainly removed in the next time step. This description allows for extensive Monte Carlo simulations (which are faster than network-based simulations), accurate analytical calculation of cascade sizes, determination of critical behavior, and other quantities of interest.

We examine the drag experienced by a pair of vertical rods moving in tandem through a granular bed immersed in a fluid as a function of their separation distance and speed. As in Newtonian fluids, the net drag experienced by the rods initially increases with distance from the value for a single rod before plateauing to twice the value. However, the drag acting on the two rods is remarkably different, with the leading rod experiencing roughly similar drag compared to a solitary rod, while the following rod experiences far less drag. The anomalous relationship of drag and the distance between the leading and following body is observed in both dry granular beds and while immersed in viscous Newtonian fluids across the quasistatic and the rate-dependent regimes. Through refractive index matching, we visualize the sediment flow past the two rods and show that a stagnant region develops in their reference frame between the rods for small separations. Thus, the following rod is increasingly shielded from the granular flow with decreasing separation distance, leading to a lower net drag. Care should be exercised in applying resistive force theory to multicomponent objects moving in granular sediments based on our result that drag is not additive at short separation distances.

In this paper, three-dimensional numerical simulations of ballooning in spiders using multiple silk threads are performed using the discrete elastic rods method. The ballooning of spiders is hypothesized to be caused by the presence of the negative electric charge of the spider silk threads and the positive electric potential field in the Earth's atmosphere. The numerical model presented here is first validated against experimental data from the open literature. After which, two cases are examined, in the first it is assumed that the electric charge is uniformly distributed along the threads while in the second, the electric charge is located at the thread tip. It is shown that the normalized terminal ballooning velocity, i.e., the velocity at which the spiders balloon after they reach steady-state, decrease linearly with the normalized lift force, especially for the tip located charge case. For the uniform electric charge case, this velocity shows a slightly weaker dependence on the normalized lift force. Moreover, it is shown in both cases that the normalized terminal ballooning velocity has no dependence on the normalized elastic bending stiffness of the threads and on the normalized viscous forces. Finally, the multithread bending process shows a three-dimensional conical sheet. Here we show that this behavior is caused by the Coulomb repelling forces owing to the threads electric charge which leads to dispersing the threads apart and thus avoid entanglement.

We construct one-dimensional nonlinear lattices having the special property such that the umklapp process vanishes and only the normal processes are included in the potential functions. These lattices have long-range quartic nonlinear and nearest-neighbor harmonic interactions with/without harmonic onsite potential. We study heat transport in two cases of the lattices with and without harmonic onsite potential by nonequilibrium molecular dynamics simulation. It is shown that the ballistic heat transport occurs in both cases, i.e., the scaling law $\kappa \propto N$ holds between the thermal conductivity $\kappa$ and the lattice size $N$. This result directly validates Peierls's hypothesis that only the umklapp processes can cause the thermal resistance while the normal ones do not.

Three-dimensional extended-magnetohydrodynamics simulations of the magnetized ablative Rayleigh-Taylor instability are presented. Previous two-dimensional (2D) simulations claiming perturbation suppression by magnetic tension are shown to be misleading, as they do not include the most unstable dimension. For perturbation modes along the applied field direction, the magnetic field simultaneously reduces ablative stabilization and adds magnetic tension stabilization; the stabilizing term is found to dominate for applied fields $>$ 5 T, with both effects increasing in importance at short wavelengths. For modes perpendicular to the applied field, magnetic tension does not directly stabilize the perturbation but can result in moderately slower growth due to the perturbation appearing to be 2D (albeit in a different orientation to 2D inertial confinement fusion simulations). In cases where thermal ablative stabilization is dominant the applied field increases the peak bubble-spike height. Resistive diffusion is shown to be important for short wavelengths and long timescales, reducing the effectiveness of tension stabilization.

In 1968, de Gennes and Meyer independently predicted that a cholesteric phase can form a stable oblique helicoidal (or heliconical) structure provided that $K_3<K_2$ where $K_3$ ($K_2$) is the bend (twist) constant. This structure usually develops under electric field when the material is of positive dielectric anisotropy and was observed for the first time in 2014 by Xiang et al. in a cholesteric phase made of a liquid crystal dimer material (CB7CB) in which $K_3$ is anomalously small. Following a recent theoretical prediction by Poy and Žumer, I show that confining a similar cholesteric phase between two glass plates treated for unidirectional anchoring can lead to a similar heliconical instability. In that case, the confinement induces a surface field that acts as an effective electric field $E$ with $E\equiv 1/d$ where $d$ is the sample thickness. The experiment was conducted in a mixture of CB7CB $+50$ wt% 8CB doped with a small amount of the chiral molecule R811. In addition, I show that this mixture presents an unexpected compensation point near the transition to the $N_{\mathrm{TB}}$ phase.

Chaotic dynamics in systems ranging from low-dimensional nonlinear differential equations to high-dimensional spatiotemporal systems including fluid turbulence is supported by nonchaotic, exactly recurring time-periodic solutions of the governing equations. These unstable periodic orbits capture key features of the turbulent dynamics and sufficiently large sets of orbits promise a framework to predict the statistics of the chaotic flow. Computing periodic orbits for high-dimensional spatiotemporally chaotic systems remains challenging as known methods either show poor convergence properties because they are based on time-marching of a chaotic system causing exponential error amplification, or they require constructing Jacobian matrices which is prohibitively expensive. We propose a new matrix-free method that is unaffected by exponential error amplification, is globally convergent, and can be applied to high-dimensional systems. The adjoint-based variational method constructs an initial value problem in the space of closed loops such that periodic orbits are attracting fixed points for the loop dynamics. We introduce the method for general autonomous systems. An implementation for the one-dimensional Kuramoto-Sivashinsky equation demonstrates the robust convergence of periodic orbits underlying spatiotemporal chaos. Convergence does not require accurate initial guesses and is independent of the period of the respective orbit.

Marangoni flow driven by a temperature gradient was observed near the isotropic-nematic phase transition point. By applying the gradient to a liquid crystalline material in sandwich cells, it was possible to measure the flow field near the air interface using the photobleaching method. In the isotropic phase, the direction of the observed flow was opposite to that in the nematic phase. Moreover, when the measurement was performed in the coexistence state of these phases, the flow direction depended on the coating materials of the cell substrates. These singular flow properties are explained well by the singular changes in surface tension and the shape of the air interface near the transition point.

We consider a stochastic model where a gene switches between two states, an mRNA transcript is released in the active state, and subsequently it undergoes an arbitrary number of sequential unimolecular steps before being degraded. The reactions effectively describe various stages of the mRNA life cycle such as initiation, elongation, termination, splicing, export, and degradation. We construct a mean-field approach that leads to closed-form steady-state distributions for the number of transcript molecules at each stage of the mRNA life cycle. By comparison with stochastic simulations, we show that the approximation is highly accurate over all the parameter space, independent of the type of expression (constitutive or bursty) and of the shape of the distribution (unimodal, bimodal, and nearly bimodal). The theory predicts that in a population of identical cells, any bimodality is gradually washed away as the mRNA progresses through its life cycle.

We study the phonon modes of interacting particles on the surface of a truncated cone resting on a plane subject to gravity, inspired by recent colloidal experiments. We derive the ground-state configuration of the particles under gravitational pressure in the small-cone-angle limit and find an inhomogeneous triangular lattice with spatially varying density but robust local order. The inhomogeneity has striking effects on the normal modes such that an important feature of the cone geometry, namely its apex angle, can be extracted from the lattice excitations. The shape of the cone leads to energy crossings at long wavelengths and frequency-dependent quasilocalization at short wavelengths. We analytically derive the localization domain boundaries of the phonons in the limit of small cone angle and check our results with numerical results for eigenfunctions.

We study the statistics of avalanches, as a response to an applied force, undergone by a particle hopping on a one-dimensional lattice where the pinning forces at each site are independent and identically distributed (i.i.d.), each drawn from a continuous $f\left(x\right)$. The avalanches in this model correspond to the interrecord intervals in a modified record process of i.i.d. variables, defined by a single parameter $c>0$. This parameter characterizes the record formation via the recursive process $R_k>R_{k-1}-c$, where $R_k$ denotes the value of the $k\mathrm{th}$ record. We show that for $c>0$, if $f\left(x\right)$ decays slower than an exponential for large $x$, the record process is nonstationary as in the standard $c=0$ case. In contrast, if $f\left(x\right)$ has a faster than exponential tail, the record process becomes stationary and the avalanche size distribution $\pi \left(n\right)$ has a decay faster than $1/n^2$ for large $n$. The marginal case where $f\left(x\right)$ decays exponentially for large $x$ exhibits a phase transition from a nonstationary phase to a stationary phase as $c$ increases through a critical value $c_{\mathrm{crit}}$. Focusing on $f\left(x\right)=e^{-x}$ (with $x\ge 0$), we show that $c_{\mathrm{crit}}=1$ and for $c<1$, the record statistics is nonstationary. However, for $c>1$, the record statistics is stationary with avalanche size distribution $\pi \left(n\right)\sim n^{-1-\lambda \left(c\right)}$ for large $n$. Consequently, for $c>1$, the mean number of records up to $N$ steps grows algebraically $\sim N^{\lambda \left(c\right)}$ for large $N$. Remarkably, the exponent $\lambda \left(c\right)$ depends continuously on $c$ for $c>1$ and is given by the unique positive root of $c=-ln(1-\lambda )/\lambda$. We also unveil the presence of nontrivial correlations between avalanches in the stationary phase that resemble earthquake sequences.

Nanoindentation of viral capsids provides an efficient tool in order to probe their elastic properties. We investigate in the present work the various sources of stiffness heterogeneity as observed in atomic force microscopy experiments. By combining experimental results with both numerical and analytical modeling, we first show that for small viruses, a position-dependent stiffness is observed. This effect is strong and has not been properly taken into account previously. Moreover, we show that a geometrical model is able to reproduce this effect quantitatively. Our work suggests alternative ways of measuring stiffness heterogeneities on small viral capsids. This is illustrated on two different viral capsids: Adeno associated virus serotype 8 (AAV8) and hepatitis B virus (HBV with $T=4$). We discuss our results in light of continuous elasticity modeling.

Molecular motors move in a dynamic environment of the cytoskeleton which generates fluctuations exceeding the thermal agitation. Their efficient motility and force generation are generally achieved via complex gating and coupling mechanisms between chemical steps, conformational changes, and mechanical steps in the working cycle. However, the motors display various force-velocity relations seemingly related (also) to the asymmetry of their unbinding from the track depending on the direction of the applied force. Here we study theoretically how the motility of molecular motors changes when they operate under an oscillating external force. We explore the roles of the shape of the force-velocity relation and the asymmetry of the force-induced unbinding. We find that a motor speeds up under force oscillations if its unbinding has a strong load dependence and a moderate asymmetry with respect to the direction of load. Motors whose unbinding is slowed down under hindering forces withstand average loads higher than the usual stall force. The relation between the function, unbinding properties, and predicted responses to the oscillating force supports the idea that the asymmetry of the load induced unbinding could serve as an adaptation of motors to their different physiological functions.

A recent line of works studied wide deep neural networks (DNNs) by approximating them as Gaussian processes (GPs). A DNN trained with gradient flow was shown to map to a GP governed by the neural tangent kernel (NTK), whereas earlier works showed that a DNN with an i.i.d. prior over its weights maps to the so-called neural network Gaussian process (NNGP). Here we consider a DNN training protocol, involving noise, weight decay, and finite width, whose outcome corresponds to a certain non-Gaussian stochastic process. An analytical framework is then introduced to analyze this non-Gaussian process, whose deviation from a GP is controlled by the finite width. Our contribution is threefold: (i) In the infinite width limit, we establish a correspondence between DNNs trained with noisy gradients and the NNGP, not the NTK. (ii) We provide a general analytical form for the finite width correction (FWC) for DNNs with arbitrary activation functions and depth and use it to predict the outputs of empirical finite networks with high accuracy. Analyzing the FWC behavior as a function of $n$, the training set size, we find that it is negligible for both the very small $n$ regime, and, surprisingly, for the large $n$ regime [where the GP error scales as $O(1/n)$]. (iii) We flesh out algebraically how these FWCs can improve the performance of finite convolutional neural networks (CNNs) relative to their GP counterparts on image classification tasks.

Slow solitary positive-potential peaks sustained by trapped electron deficit in a plasma with asymmetric ion velocity distributions are in principle asymmetric, involving a potential change across the hole. It is shown theoretically how to construct such asymmetric electron holes, thus providing fully consistent solutions of the one-dimensional Vlasov-Poisson equation for a wide variety of prescribed background ion velocity distributions. Because of ion reflection forces experienced by the hole, there is generally only one discrete slow hole velocity that is in equilibrium. Moreover the equilibrium is unstable unless there is a local minimum in the ion velocity distribution, in which the hole velocity then resides. For stable equilibria with Maxwellian electrons, the potential drop across the hole is shown to be $\mathrm{\Delta }\varphi \simeq \frac{2}{9}{f}^{\prime \prime \prime }\frac{T_e}{e}{\left(\frac{e\psi }{m_i}\right)}^2$, where $\psi$ is the hole peak potential, $f^{\prime \prime \prime }$ is the third derivative of the background ion velocity distribution function at the hole velocity, and $T_e$ is the electron temperature. Potential asymmetry is small for holes of the amplitudes usually observed, $\psi \lesssim 0.5T_e/e$.

In recent years lines along which structure and dynamics are invariant to a good approximation, so-called isomorphs, have been identified in the thermodynamic phase diagrams of several model liquids and solids. This paper reports computer simulation data of the transverse and longitudinal collective dynamics at different length scales along an isomorph of the Lennard-Jones system. Our findings are compared to corresponding results along an isotherm and an isochore. Confirming the theoretical prediction, the reduced-unit dynamics of the transverse momentum density is invariant to a good approximation along the isomorph on all time and length scales. Likewise, the wave-vector dependent shear-stress autocorrelation function is found to be isomorph invariant (with minor deviations at very short times). A similar invariance is not seen along the isotherm or the isochore. Using a spatially nonlocal hydrodynamic model for the transverse momentum-density time-autocorrelation function, the macroscopic shear viscosity and its wave dependence are determined, demonstrating that the shear viscosity is isomorphic invariant on all length scales studied. This analysis implies the existence of a length scale that is isomorph invariant in reduced units, i.e., which characterizes each isomorph. The transverse sound-wave velocity, the Maxwell relaxation time, and the rigidity shear modulus are also isomorph invariant. In contrast to the isomorph invariance of all aspects of the transverse dynamics, the reduced-unit dynamics of the mass density is not invariant on length scales longer than the interparticle distance. By fitting to a generalized hydrodynamic model, we extract values for the wave-vector-dependent thermal diffusion coefficient, sound attenuation coefficient, and adiabatic sound velocity. The isomorph variation of these quantities in reduced units on long length scales can be eliminated by scaling with the density-scaling exponent, a fundamental quantity in the isomorph theory framework; this is an empirical observation that remains to be explained theoretically.