We describe experimentally observed collective dynamics in colloidal suspensions of model hard-sphere particles using a modified mode coupling theory (MCT). This rescaled MCT is capable of describing quantitatively the wave-vector and time-dependent diffusion in these systems. Intermediate scattering functions of liquidlike structured dispersions are determined by means of static and dynamic light-scattering experiments. The structure and short-time dynamics of the systems can be described quantitatively employing a multicomponent Percus-Yevick ansatz for the partial structure factors and an effective, one-component description of hydrodynamic interactions based on the semianalytical $\delta \gamma$ expansion. Combined with a recently proposed empirical modification of MCT in which memory functions are calculated using effective structure factors at rescaled number densities, the scheme is able to model the collective dynamics over the entire accessible time and wave-vector range and predicts the volume-fraction-dependence of long-time self-diffusion coefficients and the zero-shear viscosity quantitatively. This highlights the potential of MCT as a practical tool for the quantitative analysis and prediction of experimental observations.

Geometric confinement and topological constraints present promising means of controlling active materials. By combining analytical arguments derived from the Born-Oppenheimer approximation with numerical simulations, we investigate the simultaneous impact of confinement together with curvature singularity by characterizing the dynamics of an active nematic on a cone. Here, the Born-Oppenheimer approximation means that textures can follow defect positions rapidly on the timescales of interest. Upon imposing strong anchoring boundary conditions at the base of a cone, we find a rich phase diagram of multidefect dynamics, including exotic periodic orbits of one or two $+1/2$ flank defects, depending on activity and nonquantized geometric charge at the cone apex. By characterizing the transitions between these ordered dynamical states, we present detailed understanding of (i) defect unbinding, (ii) defect absorption, and (iii) defect pair nucleation at the apex. Numerical simulations confirm theoretical predictions of not only the nature of the circular orbits but also defect unbinding from the apex.

It has been reported that slow dynamic nonlinear elastic relaxations, widely thought to proceed universally in proportion to the logarithm of time after cessation of mechanical conditioning, actually recover with a smaller slope at early times, with a time of transition that varies with the grain size of the material. This would constitute a heretofore unreported failure of the claimed universality, while suggesting application to nondestructive evaluation and structural health monitoring. Here, we present further observations at short times, in the single bead system, in cement paste, mortar, concrete, sandstone, and granite. Within the limits imposed by finite-duration ring-down such that the effective instant of conditioning cessation is imprecise, and the corresponding ambiguity as to the time at which relaxation begins, we find no reliable sign of such a transition, even in samples of large grain-size mortar and concrete similar to those described elsewhere as having clear and late cutoffs.

Differential equations of the form $\ddot{R}=-k{R}^{\gamma }$, with a positive constant $k$ and real parameter $\gamma$, are fundamental in describing phenomena such as the spherical gravitational collapse ($\gamma =-2$), the implosion of cavitation bubbles ($\gamma =-4$), and the orbital decay in binary black holes ($\gamma =-7$). While explicit elemental solutions exist for select integer values of $\gamma$, more comprehensive solutions encompassing larger subsets of $\gamma$ have been independently developed in hydrostatics (see Lane-Emden equation) and hydrodynamics (see Rayleigh-Plesset equation). I here present a universal explicit solution for all real $\gamma$, invoking the beta distribution. Although standard numerical ordinary differential equation solvers can readily evaluate more general second-order differential equations, this explicit solution reveals a hidden connection between collapse motions and probability theory that enables further analytical manipulations, it conceptually unifies distinct fields, and it offers insights into symmetry properties, thereby enhancing our understanding of these pervasive differential equations.

Anisotropic particles are often encountered in different fields of soft matter and complex fluids. In this work, we present an implementation of the coupled hydrodynamics of solid ellipsoidal particles and the surrounding fluid using the lattice Boltzmann method. A standard link-based mechanism is used to implement the solid-fluid boundary conditions. We develop an implicit method to update the position and orientation of the ellipsoid. This exploits the relations between the quaternion which describes the ellipsoid's orientation and the ellipsoid's angular velocity to obtain a stable and robust dynamic update. The proposed algorithm is validated by looking at four scenarios: (i) the steady translational velocity of a spheroid subject to an external force in different orientations, (ii) the drift of an inclined spheroid subject to an imposed force, (iii) three-dimensional rotational motions in a simple shear flow (Jeffrey's orbits), and (iv) developed fluid flows and self-propulsion exhibited by a spheroidal microswimmer. In all cases the comparison of numerical results shows good agreement with known analytical solutions, irrespective of the choice of the fluid properties, geometrical parameters, and lattice Boltzmann model, thus demonstrating the robustness of the proposed algorithm.

The three-dimensional classical Heisenberg model on a simple cubic lattice with Dzyaloshinskii-Moriya (DM) interactions between nearest-neighbors in all directions has been studied using Monte Carlo simulations. The Metropolis algorithm, combined with single histogram reweighting techniques and finite-size scaling analyses, has been used to obtain the thermodynamic behavior of the system in the thermodynamic limit. Simulations were performed with the same set of interaction parameters for both shifted boundary conditions (SBC) and fluctuating boundary conditions (FBC). Because of an incommensurability caused by the DM interaction, the SBC incorporated a fixed shift angle at the boundary which varies as a function of the DM interaction and lattice size. This SBC method decreases the simulation time significantly, but the distribution of states is somewhat different than that obtained with FBC. The ground state for nonzero DM interaction is a spiral configuration where the spins are restricted to lie in planes perpendicular to the DM vector. We found that this spiral configuration undergoes a conventional second-order phase transition into a disordered, paramagnetic state with the transition temperature being a function of the magnitude of the DM interaction. The limiting case with only DM interaction in the model has also been considered. The critical exponent $\nu$, the critical exponent ratios $\alpha /\nu$, $\beta /\nu$, $\gamma /\nu$, as well as the critical temperature $T_c$ and fourth-order cumulant of the order parameter $U_4^{*}$ at $T_c$ have been estimated for different magnitudes of DM interaction. The critical exponents and cumulants at the transition are different from those for the three-dimensional Heisenberg model, but the ratios $\alpha /\nu$, $\beta /\nu$, $\gamma /\nu$, $U_4^{*}/\nu$ are the same, implying that weak universality is valid for all values of DM interaction. Structure factor calculations for particular cases have been performed considering SBC and FBC in the simulations with different lattice sizes at the critical temperatures.

Random linear vector channels have been known to increase the transmission of information in several communications systems. For Gaussian priors, the statistics of a key metric, namely, the mutual information, which is related to the free energy of the system, have been analyzed in great detail for various types of channel randomness. However, for the realistic case of non-Gaussian priors, only the average mutual information has been obtained in the asymptotic limit of large channel matrices. In this paper, we employ methods from statistical physics, namely, the replica approach, to calculate the finite-size correction and the variance of the mutual information with non-Gaussian priors, both for the case of correlated Gaussian and uncorrelated non-Gaussian channel matrices in the same asymptotic limit. Furthermore, using the same methodology, we show that higher order cumulants of the mutual information should vanish in the large-system-size limit. In addition, we obtain closed-form expressions for the minimum mean-square error finite-size corrections and variance for both Gaussian and non-Gaussian channels. Finally, we provide numerical verification of the results using numerical methods on finite-sized systems.

Most of the previous studies on classical thermalization focus on the wave-vector space, encountering limitations when extended beyond quasi-integrable regions. In this study, we propose a scheme to study the thermalization of the classical Hamiltonian chain of interacting oscillators in real space by developing a thermalization indicator proposed by Parisi [Europhys. Lett. 40, 357 (1997)], which approaches zero in the thermal state. Upon reaching the steady state characterized by the generalized Gibbs ensemble for a harmonic chain, a quench protocol is implemented to change the Hamiltonian to a nonintegrable form instantaneously, thereby preparing nonequilibrium initial states. This approach enables investigations of thermalization in real space, particularly valuable for exploring regions beyond quasi-integrability. For the FPUT-$\beta$ lattice, we observe that the thermalization time as a function of the nonintegrable strength follows a $-2$ scaling law in the quasi-integrable region and $-1/4$ in the strongly integrable region. Moreover, numerical results reveal the thermalization time is proportional to the Lyapunov time, which bridges microscopic chaotic dynamics and the macroscopic thermalization process.

Active microscopic objects, such as an enzyme molecule, are modeled by the Langevin system with the odd elasticity, in which energy injection from the substrate to the enzyme is described by the antisymmetric part of the elastic matrix. By applying the Onsager-Machlup integral and large deviation theory to the Langevin system with odd elasticity, we can calculate the cumulant generating function of the irreversibility of the state transition. For an $N$-component system, we obtain a formal expression of the cumulant generating function and demonstrate that the oddness $\lambda$, which quantifies the antisymmetric part of the elastic matrix, leads to higher-order cumulants that do not appear in a passive elastic system. To demonstrate the effect of the oddness under the concrete parameter, we analyze the simplest two-component system and obtain the optimal transition path and cumulant generating function. The cumulants obtained from expansion of the cumulant generating function increase monotonically with the oddness. This implies that the oddness causes the uncertainty of stochastic state transitions.

We study the formation of quasi-one- (quasi-1D) and quasi-two-dimensional (quasi-2D) symbiotic solitons bound by an interspecies dipolar interaction in a binary dipolar Bose-Einstein condensate. These binary solitons have a repulsive intraspecies contact interaction stronger than the intraspecies dipolar interaction, so that they can not be bound in isolation in the absence of an interspecies dipolar interaction. These symbiotic solitons are bound in the presence of an interspecies dipolar interaction and zero interspecies contact interaction. The quasi-1D solitons are free to move along the polarization $z$ direction of the dipolar atoms, whereas the quasi-2D solitons move in the $x\text{−}z$ plane. To illustrate these, we consider a ${}^{164}\mathrm{Er}\text{−}{}^{166}\mathrm{Er}$ mixture with scattering lengths $a\left({}^{164}\mathrm{Er}\right)=81a_0$ and $a\left({}^{166}\mathrm{Er}\right)=68a_0$ and with dipolar lengths $a_{\mathrm{dd}}\left({}^{164}\mathrm{Er}\right)\approx a_{\mathrm{dd}}\left({}^{166}\mathrm{Er}\right)\approx 65a_0$, where $a_0$ is the Bohr radius. In each of the two components $a>a_{\mathrm{dd}}$, which stops the binding of solitons in each component in isolation, whereas a binary quasi-1D or a quasi-2D ${}^{164}\mathrm{Er}\text{−}{}^{166}\mathrm{Er}$ soliton is bound in the presence of an interspecies dipolar interaction. The stationary states were obtained by imaginary-time propagation of the underlying mean-field model; dynamical stability of the solitons was established by real-time propagation over a long period of time.

We explore the dynamics of a swarmalator population comprising second-order harmonics in phase interaction. A key observation in our study is the emergence of the active asynchronous state in swarmalators with second-order harmonics, mirroring findings in the one-dimensional analog of the model, accompanied by the formation of clustered states. Particularly, we observe a transition from the static asynchronous state to the active phase wave state via the active asynchronous state. We have successfully delineated and quantified the stability boundary of the active asynchronous state through a completely data-driven method. This was achieved by utilizing the enhanced image processing capabilities of convolutional neural networks, specifically, the U-Net architecture. Complementing this data-driven analysis, our study also incorporates an analytical stability of the clustered states, providing a multifaceted perspective on the system's behavior. Our investigation not only sheds light on the nuanced behavior of swarmalators under second-order harmonics, but also demonstrates the efficacy of convolutional neural networks in analyzing complex dynamical systems.

Dense packing of particles has provided powerful models to elaborate the important structural features of matter in various systems such as liquid, glassy, and crystalline phases. The simplest sphere packing models can represent and capture salient properties of the building blocks for covalent, metallic, and ionic crystals; it, however, becomes insufficient to reflect the broken symmetry of the commonly anisotropic molecules in molecular crystals. Here, we develop spheroid models with a minimal degree of anisotropy, which serve as a simple geometrical representation for a rich spectrum of molecules—including both isotropic and anisotropic, convex and concave ones—in crystalline phases. Our models are determined via an inverse packing approach: Given a molecular crystal, an optimal spheroid model is constructed using a contact diagram, which depicts the packing relationship between neighboring molecules within the crystal. The spheroid models are capable of accurately capturing the broken symmetry and characterizing the equivalent volume of molecules in the crystalline phases. Moreover, our model retrieves such molecular information from low-quality x-ray diffraction data with poorly resolved structures, and by using soft spheroids, it can also describe the packing behavior in cocrystals.

Through a one-dimensional colloidal model for epitaxial growth, we characterize the nucleation and aggregation processes occurring in a gap between adjacent islands. The timescales associated with deposition, diffusion, aggregation, and nucleation inside the gap are studied in terms of the parameters defining the interaction between colloidal particles. Numerical results from molecular-dynamics (MD) simulations are compared with analytical models and good agreement is found between both data sets. The results for the timescales are used to calculate the associated rates to generate kinetic Monte Carlo (KMC) simulations, which allow exploring larger systems and longer timescales in comparison with MD simulations. The KMC simulations reproduce the global behavior of the densities of islands and monomers as well as the gap length distribution between adjacent islands.

We study the jamming transition in a model of elastic particles under shear at zero temperature, with a focus on the relaxation time ${\tau }_1$. This relaxation time is from two-step simulations where the first step is the ordinary shearing simulation and the second step is the relaxation of the energy after stopping the shearing. ${\tau }_1$ is determined from the final exponential decay of the energy. Such relaxations are done with many different starting configurations generated by a long shearing simulation in which the shear variable $\gamma$ slowly increases. We study the correlations of both ${\tau }_1$, determined from the decay, and the pressure, $p_1$, from the starting configurations as a function of the difference in $\gamma$. We find that the correlations of $p_1$ are longer lived than the ones of ${\tau }_1$ and find that the reason for this is that the individual ${\tau }_1$ is controlled both by $p_1$ of the starting configuration and a random contribution which depends on the relaxation path length—the average distance moved by the particles during the relaxation. We further conclude that it is ${\gamma }_{\tau }$, determined from the correlations of ${\tau }_1$, which is the relevant one when the aim is to generate data that may be used for determining the critical exponent that characterizes the jamming transition.

Collision between relativistic electron sheets and counterpropagating laser pulses is recognized as a promising way to produce intense attosecond x rays through coherent Thomson backscattering (TBS). In a double-layer scheme, the electrons in an ultrathin solid foil are first pushed out by an intense laser driver and then interact with the laser reflected off a second foil to form a high-density relativistic electron sheet with vanishing transverse momentum. However, the repulsion between these concentrated electrons can increase the thickness of the layer, reducing both its density and subsequently the coherent TBS. Here, we present a systematic study on the evolution of the flying electron layer and find that its resulting thickness is determined by the interplay between the intrinsic space-charge expansion and the velocity compression induced by the drive laser. How the laser driver, the target areal density, the reflector, and the collision laser intensity affect the properties of the produced x rays is explored. Multidimensional particle-in-cell simulations indicate that employing this scheme in the nonlinear regime has the potential to stably produce soft x rays with several gigawatt peak power in hundreds of terawatt ultrafast laser facilities. The pulse duration can be tuned to tens of attoseconds. This compact and intense attosecond x-ray source may have broad applications in attosecond science.

Annealing algorithms such as simulated annealing and population annealing are widely used both for sampling the Gibbs distribution and solving optimization problems (i.e., finding ground states). For both statistical mechanics and optimization, additional parameters beyond temperature are often needed such as chemical potentials, external fields, or Lagrange multipliers enforcing constraints. In this paper we derive a formalism for optimal annealing schedules in multidimensional parameter spaces using methods from nonequilibrium statistical mechanics. The results are closely related to work on optimal control of thermodynamic systems [Sivak and Crooks, Phys. Rev. Lett. 108, 190602 (2012)]. Within the formalism, we compare the efficiency of population annealing and multiple weighted runs of simulated annealing (“annealed importance sampling”) and discuss the effects of nonergodicity on both algorithms. Theoretical results are supported by numerical simulations of spin glasses.

Non-Gaussian displacement distributions are universal predictors of dynamic heterogeneity in slowly varying environments. Here, we explore heterogeneous dynamics in supercooled liquid using molecular dynamics simulations and show the efficiency of the relative-entropy based measure, negentropy, in quantifying dynamic heterogeneity over the widely used non-Gaussian parameter. Our analysis shows that the heterogeneity quantified by the negentropy is significantly different from the one obtained using the conventional moment-based definition that considers deviation from Gaussianity up to lower-order moments. We extract the timescales of dynamic heterogeneity using the two methods and show that the differential changes diverge as the system experiences strong intermittency near the glass transition. Further, we interpret the entropic timescales and discuss the general implications of our work.

Unidirectional social interactions are ubiquitous in real social networks whereas undirected interactions are intensively studied. We establish a voter model in a dynamical directed network. We analytically obtain the degree distribution of the evolving network at any given time. Furthermore, we find that the average degree is captured by an emergent game. However, we find that the fate of opinions is captured by another emergent game. Beyond expectation, the two emergent games are typically different due to the unidirectionality of the evolving networks. The Nash equilibrium analysis of the two games facilitates us to give the criterion under which the minority opinion with few disciples initially takes over the population eventually for in-group bias. Our work fosters the understanding of opinion dynamics ranging from methodology to research content.

Microresonator frequency comb generation from Kerr solitons has become a cutting edge technology, but challenges remain in creating, maintaining, and controlling the solitons. Pump modulation and dual pumping are promising techniques for meeting these challenges. Here we derive the equation of motion of solitons interacting with a modulated pump in the framework of synchronization theory. It implies that the soliton repetition rate locks to the modulation frequency whenever the latter is within a locking range of frequencies around an integer multiple of the free spectral range of the microresonator. We calculate explicitly, numerically, and in perturbation theory the width of the locking range as a function of the amplitude and frequency of the pump and the modulation phase. We show that a highly red-detuned, strong pump that is amplitude-modulated provides the best conditions for entrainment, and that the width of the locking range is proportional to the square of the modulation frequency, limiting the effectiveness of RF modulation as an entrainment method.

A self-learning physical reservoir computer is demonstrated using an adaptive oscillator. Whereas physical reservoir computing repurposes the dynamics of a physical system for computation through machine learning, adaptive oscillators can innately learn and store information in plastic dynamic states. The adaptive state(s) can be used directly as physical node(s), but these plastic states can also be used to self-learn the optimal reservoir parameters for more complex tasks requiring virtual nodes from the base oscillator. Both this self-learning property for reconfigurable computing and the morphable logic gate property of the adaptive oscillator make this an ideal candidate for a multipurpose neuromorphic processor.