We study the late-time dynamics of a single active Brownian particle in two dimensions with speed $v_0$ and rotation diffusion constant $D_R$. We show that at late times $t\gg D_R^{-1}$, while the position probability distribution $P(x,y,t)$ in the $x\text{−}y$ plane approaches a Gaussian form near its peak describing the typical diffusive fluctuations, it has non-Gaussian tails describing atypical rare fluctuations when $\sqrt{x^2+y^2}\sim v_{0}t$. In this regime, the distribution admits a large deviation form, $P(x,y,t)\sim exp\left\{-t{D}_R\mathrm{\Phi }\left[\sqrt{x^2+y^2}/\left(v_{0}t\right)\right]\right\}$, where we compute the rate function $\mathrm{\Phi }\left(z\right)$ analytically and also numerically using an importance sampling method. We show that the rate function $\mathrm{\Phi }\left(z\right)$, encoding the rare fluctuations, still carries the trace of activity even at late times. Another way of detecting activity at late times is to subject the active particle to an external harmonic potential. In this case we show that the stationary distribution $P_{\text{stat}}(x,y)$ depends explicitly on the activity parameter $D_R^{-1}$ and undergoes a crossover, as $D_R$ increases, from a ring shape in the strongly active limit $\left(D_R\to 0\right)$ to a Gaussian shape in the strongly passive limit $(D_R\to \infty )$.

While cooperativity in ligand-induced receptor dimerization has been linked with receptor-receptor couplings via minimal representations of physical observables, effects arising from higher-order oligomer, e.g., trimer and tetramer, formations of unobserved receptors have received less attention. Here we propose a dimerization model of ligand-induced receptors in multivalent form representing physical observables under basis vectors of various aggregated receptor states. Our simulations of multivalent models not only reject Wofsy-Goldstein parameter conditions for cooperativity, but show that higher-order oligomer formations can shift cooperativity from positive to negative.

In biochemistry, heteropolymers encoding biological information are assembled out of equilibrium by sequentially incorporating available monomers found in the environment. Current models of polymerization treat monomer incorporation as a sequence of discrete chemical reactions between intermediate metastable states. In this paper, we use ideas from reaction rate theory and describe nonequilibrium assembly of a heteropolymer via a continuous reaction coordinate. Our approach allows for estimating the copy error and incorporation speed from the Gibbs free energy landscape of the process. We apply our theory to several examples from a simple reaction characterized by a free energy barrier to more complex cases incorporating error correction mechanisms, such as kinetic proofreading.

A vapor bubble collapsing near a solid boundary in a liquid produces a liquid jet that points toward the boundary. The direction of this jet has been studied for boundaries such as flat planes and parallel walls enclosing a channel. Extending these investigations to enclosed polygonal boundaries, we experimentally measure jet direction for collapsing bubbles inside a square and an equilateral triangular channel. Following the method of Tagawa and Peters [Phys. Rev. Fluids 3, 081601 (2018)] for predicting the jet direction in corners, we model the bubble as a sink in a potential flow and demonstrate by experiment that analytical solutions accurately predict jet direction within an equilateral triangle and square. We further use the method to develop predictions for several other polygons, specifically, a rectangle, an isosceles right triangle, and a ${30}^{\circ }\text{−}{60}^{\circ }\text{−}{90}^{\circ }$ right triangle.

The rapid growth of viscosity driven by temperature increase in turbulent plasmas under compression induces a sudden dissipation of kinetic energy, eventually leading to the relaminarization of the flow [Davidovits and Fisch, Phys. Rev. Lett. 116, 105004 (2016)]. The interdiffusion between species is also greatly enhanced, so that mixing layers appearing at interfaces between different materials are subjected to strong dynamical modifications. The result is a competition between the vanishing turbulent diffusion and the expanding plasma microscopic diffusion. In direct numerical simulations with conditions relevant to inertial confinement fusion, we evidence regimes where compressed spherical mixing layers are quickly diffused during the relaminarization process. Using one and two-point turbulent statistics, we also detail how mixing heterogeneities are smoothed out.

We propose an alternative homogenization method for one-dimensional continuum diffusion models with spatially variable (heterogeneous) diffusivity. Our method, which extends recent work on stochastic diffusion, assumes the constant-coefficient homogenized equation takes the form of an advection-diffusion equation with effective (diffusivity and velocity) coefficients. To calculate the effective coefficients, our approach involves solving two uncoupled boundary value problems over the heterogeneous medium and leads to coefficients depending on the spatially varying diffusivity (as usual) as well as the boundary conditions imposed on the heterogeneous model. Computational experiments comparing our advection-diffusion homogenized model to the standard homogenized model demonstrate that including an advection term in the homogenized equation leads to improved approximations of the solution of the original heterogeneous model.

We examine theoretically and experimentally the localized electrical modes existing in a bi-inductive electrical lattice containing a bulk or a surface capacitive impurity. By means of the formalism of lattice Green's functions, we are able to obtain closed-form expressions for the frequencies of the impurity (bound-state) eigenmodes and for their associated spatial profiles. This affords us a systematic understanding of how these mode properties change as a function of the system parameters. We test these analytical results against experimental measurements, in both the bulk and surface cases, and find very good agreement. Last, we turn to a series of quench experiments, where either a parameter of the lattice or the lattice geometry itself is rapidly switched between two values or configurations. In all cases, we are able to naturally explain the results of such quench experiments from the larger analytical picture that emerges as a result of the detailed characterization of the impurity-mode solution branches.

Signatures of criticality, such as power law scaling of observables, have been empirically found in a plethora of real-life settings, including biological systems. The presence of critical states is believed to have many functional advantages and is associated with optimal operational abilities. Typically, critical dynamics arises in the proximity of phase transition points between absorbing disordered states (subcriticality) and ordered active regimes (supercriticality) and requires a high degree of fine tuning to emerge, which is unlikely to occur in real biological systems. In the present study we propose a rather simple, and biologically relevant mechanism that profoundly expands the critical-like region. In particular, by means of numerical simulation we show that incorporating spatial heterogeneities into the square lattice of map-based excitable oscillators broadens the parameter space in which the distribution of excitation wave sizes follows closely a power law. Most importantly, this behavior is only observed if the spatial profile exhibits intermediate-sized patches with similar excitability levels, whereas for large and small spatial clusters only marginal widening of the critical state is detected. Furthermore, it turned out that the presence of spatial disorder in general amplifies the size of excitation waves, whereby the relatively highest contributions are observed in the proximity of the critical point. We argue that the reported mechanism is of particular importance for excitable systems with local interactions between individual elements.

We study experimentally a sediment of self-propelled Brownian particles with densities ranging from dilute to ergodic supercooled to nonergodic glass to nonergodic polycrystal. In a companion paper, we observe a nonmonotonic response to activity of relaxation of the nonergodic glass state: a dramatic slowdown when particles become weakly self-propelled, followed by a speedup at higher activities. Here we map ergodic supercooled states to standard passive glassy physics, provided a monotonic shift of the glass packing fraction and the replacement of the ambient temperature by the effective temperature. However, we show that this mapping fails beyond glass transition. This failure is responsible for the nonmonotonic response. Furthermore, we generalize our finding by examining the dynamical response of another class of nonergodic systems: polycrystals. We observe the same nonmonotonic response to activity. To explain this phenomenon, we measure the size of domains where particles move in the same direction. This size also shows a nonmonotonic response, with small lengths corresponding to slow relaxation. This suggests that the failure of the mapping of nonergodic active states to a passive situation is general and is linked to anisotropic relaxation mechanisms specific to active matter.

We present ground-state electronic properties of the liquid crystal 4-cyano-$4^{\prime }$-pentylbiphenyl (5CB) on the two-dimensional materials monolayer graphene, hexagonal boron nitride, and phosphorene. Our density functional theory results show that the physisorption is robust on all surfaces with the strongest binding of 5CB on phosphorene. All surfaces exhibit flexural distortion, especially monolayer graphene and hexagonal boron nitride. While we find type-I alignment for all three substrates, meaning the Fermi level of the system is in the HOMO-LUMO gap of 5CB, the band structures are qualitatively different. Unlike for graphene and phosphorene, the HOMO-LUMO of 5CB appear as localized states within the band gap of boron nitride. In addition, we find that the valence band for boron nitride is sensitive to the orientation of 5CB relative to the surface. The qualitatively different band structures demonstrate the importance of substrate selection for tailoring the electronic and optoelectronic properties of nematic liquid crystals on two-dimensional materials.

The linear theory of the incompressible Rayleigh-Taylor instability in elastic-plastic solid slabs is developed on the basis of the simplest constitutive model consisting in a linear elastic (Hookean) initial stage followed by a rigid-plastic phase. The slab is under the action of a constant acceleration, and it overlays a very thick ideal fluid. The boundaries of stability and plastic flow are obtained by assuming that the instability is dominated by the average growth of the perturbation amplitude and neglecting the effects of the higher oscillation frequencies during the stable elastic phase. The theory yields complete analytical expressions for such boundaries for arbitrary Atwood numbers and thickness of the solid slabs.

Double-shell ignition designs have been studied with the indirect-drive inertial confinement fusion (ICF) scheme in both simulations and experiments in which the inner-shell kinetic energy was limited to ∼10–15 kJ, even driven by megajoule-class lasers such as the National Ignition Facility. Since direct-drive ICF can couple more energy to the imploding shells, we have performed a detailed study on direct-drive double-shell ($D^{3}S$) implosions with state-of-the-art physics models implemented in radiation-hydrodynamic codes (lilac and draco), including nonlocal thermal transport, cross-beam energy transfer (CBET), and first-principles−based material properties. To mitigate classical unstable interfaces, we have proposed the use of a tungsten-beryllium–mixed inner shell with gradient-density layers that can be made by magnetron sputtering. In our $D^{3}S$ designs, a 70-μm-thick beryllium outer shell is driven symmetrically by a high-adiabat ($\alpha \ge 10$), 1.9-MJ laser pulse to a peak velocity of ∼240 km/s. Upon spherical impact, the outer shell transfers ∼30–40 kJ of kinetic energy to the inner shell filled with deuterium-tritium gas or liquid, giving neutron-yield energies of ∼6 MJ in one-dimensional simulations. Two-dimensional high-mode draco simulations indicated that such high-adiabat $D^{3}S$ implosions are not susceptible to laser imprint, but the long-wavelength perturbations from the laser port configuration along with CBET can be detrimental to the target performance. Nevertheless, neutron yields of ∼0.3–1.0-MJ energies can still be obtained from our high-mode draco simulations. The robust α-particle bootstrap is readily reached, which could provide a viable platform for burning-plasma physics studies. Once CBET mitigation and/or more laser energy becomes available, we anticipate that break-even or moderate energy gain might be feasible with the proposed $D^{3}S$ scheme.

A framework is presented for carrying out simulations of equilibrium systems in the microcanonical ensemble using annealing in an energy ceiling. The framework encompasses an equilibrium version of simulated annealing, population annealing, and hybrid algorithms that interpolate between these extremes. These equilibrium, microcanonical annealing algorithms are applied to the thermal first-order transition in the 20-state, two-dimensional Potts model. All of these algorithms are observed to perform well at the first-order transition though for the system sizes studied here, equilibrium simulated annealing is most efficient.

We study the synchronization and stability of power grids within the Kuramoto phase oscillator model with inertia with a bimodal natural frequency distribution representing the generators and the loads. The Kuramoto model describes the dynamics of the ac voltage phase and allows for a comprehensive understanding of fundamental network properties capturing the essential dynamical features of a power grid on coarse scales. We identify critical nodes through solitary frequency deviations and Lyapunov vectors corresponding to unstable Lyapunov exponents. To cure dangerous deviations from synchronization we propose time-delayed feedback control, which is an efficient control concept in nonlinear dynamic systems. Different control strategies are tested and compared with respect to the minimum number of controlled nodes required to achieve synchronization and Lyapunov stability. As a proof of principle, this fast-acting control method is demonstrated for different networks (the German and the Italian power transmission grid), operating points, configurations, and models. In particular, an extended version of the Kuramoto model with inertia is considered that includes the voltage dynamics, thus taking into account the interplay of amplitude and phase typical of the electrodynamical behavior of a machine.

Biological and synthetic amphiphilic systems exhibit a wide range of morphologies. A density functional model for amphiphilic polymer phase mixtures is utilized to quantify localized equilibria and their stability, and ultimately predict and explain morphological preference. This is done by utilizing matched asymptotic expansions, which produces explicit connections between model parameters and macroscopic properties of equilibrium structures. Bilayers, cylindrical, and spherical micelle and vesicle configurations are found, and formulas which connect their geometry to ambient chemical potential are derived. Dynamics are studied in the context of a free boundary problem which describes the evolution of the hydrophobic-solvent domain interface. Linearization of this problem is used to explicitly determine growth rates and parameter regions of stability. All equilibria are found to have two branches of solutions terminating at a fold in the bifurcation diagram which signals the crossover from competitive stability to instability leading to ripening behavior. Ideally flat bilayers are determined to always possess a long wavelength buckling instability, suggesting that curved structures should be generically preferred. Spherical micelles exhibit morphological instabilities which are suppressed by large enough surface tension. Cylindrical micelles may have short-wavelength pearling and long-wavelength Rayleigh-Plateau-type instabilities. In addition, ideally infinite cylinders have an undulatory instability, suggesting that only finite length structures should be observed. A morphological phase diagram can be assembled which takes into account both existence and stability of different geometries. Consistent with experimental evidence, a bifurcation sequence from spheres to cylinders to vesicles is found as either surface tension or polymer composition increases. Coexistence of different stable morphologies is also observed.

The simplest extensions of single-particle dynamics in a momentum-conserving active fluid—an active suspension of two colloidal particles or a single particle confined by a wall—exhibit strong departures from Boltzmann behavior, resulting in either a breakdown of an effective temperature description or a steady state with nonzero-entropy production rate. This is a consequence of hydrodynamic interactions that introduce multiplicative noise in the stochastic description of particle positions. This results in fluctuation-induced interactions that depend on distance as a power law. We find that the dynamics of activated colloids in a passive fluid, with stochastic forcing localized on the particle, is different from that of passive colloids in an active fluctuating fluid.

A deflection effect of an intense laser beam with spin angular momentum is revealed theoretically by an analytical modeling using radiation pressure and momentum balance of laser plasma interaction in the relativistic regime as a deviation from the law of reflection. The reflected beam deflects out of the plane of incidence with a deflection angle up to several milliradians, when a nonlinear polarized laser, with the intensity $I_0\sim {10}^{19}\mathrm{W}/{\mathrm{cm}}^2$ and duration around tens of femtoseconds, is obliquely incident and reflected by an overdense plasma target. This effect originates from the asymmetric radiation pressure caused by spin angular momentum of the laser photons. The dependence of the deflection angle of a Gaussian-type laser on the parameters of laser pulse and plasma foil is theoretically derived, which is also confirmed by three-dimensional particle-in-cell simulations of circularly polarized laser beams with the different intensity and pulse duration.

Models for quantum absorption refrigerators serve as test beds for exploring concepts and developing methods in quantum thermodynamics. Here we depart from the minimal, ideal design and consider a generic multilevel model for a quantum absorption refrigerator, which potentially suffers from lossy processes. Based on a full-counting statistics approach, we derive a formal cooling condition for the refrigerator, which can be feasibly evaluated analytically and numerically. We exemplify our approach on a three-level model for a quantum absorption refrigerator that suffers from different forms of nonideality (heat leakage, competition between different cooling pathways) and examine the cooling current with different designs. This study assists in identifying the cooling window of imperfect thermal machines.

Network properties govern the rate and extent of various spreading processes, from simple contagions to complex cascades. Recently, the analysis of spreading processes has been extended from static networks to temporal networks, where nodes and links appear and disappear. We focus on the effects of accessibility, whether there is a temporally consistent path from one node to another, and reachability, the density of the corresponding accessibility graph representation of the temporal network. The level of reachability thus inherently limits the possible extent of any spreading process on the temporal network. We study reachability in terms of the overall levels of temporal concurrency between edges and the structural cohesion of the network agglomerating over all edges. We use simulation results and develop heterogeneous mean-field model predictions for random networks to better quantify how the properties of the underlying temporal network regulate reachability.