This paper presents a simple physics-based model for the interpretation of key metrics in laser direct drive. The only input parameters required are target scale, in-flight aspect ratio, and beam-to-target radius, and the importance of each has been quantified with a tailored set of cryogenic implosion experiments. These analyses lead to compact and accurate predictions of the fusion yield and areal density as a function of hydrodynamic stability, and they suggest new ways to take advantage of direct drive. To provide examples, we discuss how the inferred mix width behaves relative to theory and then show how it could be exploited to perform a direct drive implosion with a Lawson metric or ${\chi }_{\text{no}\alpha }$ of $0.24\pm 0.02$—using a novel parameter space at high velocities and beam radii on the OMEGA laser—that projects to ignition at a laser energy of $\le 2.0$ MJ.

We study driven $q$-state Potts models with thermodynamically consistent dynamics and global coupling. For a wide range of parameters, these models exhibit a dynamical phase transition from decoherent oscillations into a synchronized phase. Starting from a general microscopic dynamics for individual oscillators, we derive the normal form of the high-dimensional Hopf bifurcation that underlies the phase transition. The normal-form equations are exact in the thermodynamic limit and close to the bifurcation. Exploiting the symmetry of the model, we solve these equations and thus uncover the intricate stable synchronization patterns of driven Potts models, characterized by a rich phase diagram. Making use of thermodynamic consistency, we show that synchronization reduces dissipation in such a way that the most stable synchronized states dissipate the least entropy. Close to the phase transition, our findings condense into a linear dissipation-stability relation that connects entropy production with phase-space contraction, a stability measure. At finite system size, our findings suggest a minimum-dissipation principle for driven Potts models that holds arbitrarily far from equilibrium.

A lattice-based model for continuum percolation is applied to the case of randomly located, partially aligned sticks with unequal lengths in 2D which are allowed to cross each other. Results are obtained for the critical number of sticks per unit area at the percolation threshold in terms of the distributions over length and orientational angle and are compared with findings from computer simulations. Consistent with findings from computer simulations, our model shows that the percolation threshold is (i) elevated by increasing degrees of alignment for a fixed length distribution, and (ii) lowered by increasing degrees of length dispersity for a fixed orientational distribution. The impact of length dispersity is predicted to be governed entirely by the first and second moments of the stick length distribution, and the threshold is shown to be quite sensitive to particulars of the orientational distribution function.

We describe a method to estimate Rényi entanglement entropy of a spin system which is based on the replica trick and generative neural networks with explicit probability estimation. It can be extended to any spin system or lattice field theory. We demonstrate our method on a one-dimensional quantum Ising spin chain. As the generative model, we use a hierarchy of autoregressive networks, allowing us to simulate up to 32 spins. We calculate the second Rényi entropy and its derivative and cross-check our results with the numerical evaluation of entropy and results available in the literature.

We analyzed spin polarization dynamics in a two-dimensional system of spin $1/2$ charged particles with spin-orbit interaction in perpendicular magnetic field in the presence of external noise. It was shown that spin polarization reveals quantum oscillations, collapses, and revivals. The hierarchy of time scales corresponding to quantum oscillations, collapses, and revivals was identified and analyzed. It was demonstrated that variation of external magnetic field and noise intensity results in the significant changing of spin fluctuations spectra, which modifies from the triplet structure to the well resolved fine structure.

We show that when the Aubry transition occurs in incommensurately distorted structures, the amplitude of the distortions is not necessarily large as suggested by the standard Frenkel-Kontorova mechanical model. By modifying the shape of the potential in such a way that the mechanical force is locally stronger (i.e., increasing the nonlinearities), the transition may occur at a small amplitude of the potential with small distortions. A phason gap then opens, while the phonon spectrum resembles a standard undistorted spectrum at higher energies. This may explain the existence of pinned phases with very small distortions as experimentally observed in charge-density waves.

Life-threatening cardiac arrhythmias such as ventricular fibrillation are often based on chaotic spiral or scroll wave dynamics which can be self-terminating. In this work, we investigate the influence of conduction heterogeneities on the duration of such chaotic transients in generic models of excitable cardiac media. We observe that low and medium densities of heterogeneities extend the average transient lifetime, while at high densities very long transients, potentially persistent chaos, and periodic attractors occur.

We consider the problem of a graph subjected to adversarial perturbations, such as those arising from cyber attacks, where edges are covertly added or removed. The adversarial perturbations occur during the transmission of the graph between a sender and a receiver. To counteract potential perturbations, this study explores a repetition coding scheme with sender-assigned noise and majority voting on the receiver's end to rectify the graph's structure. The approach operates without prior knowledge of the attack's characteristics. We analytically derive a bound on the number of repetitions needed to satisfy probabilistic constraints on the quality of the reconstructed graph. The method can accurately and effectively decode Erdős-Rényi graphs that were subjected to nonrandom edge removal, namely, those connected to vertices with the highest eigenvector centrality, in addition to random addition and removal of edges by the attacker. The method is also effective against attacks on large scale-free graphs generated using the Barabási-Albert model but require a larger number of repetitions than needed to correct Erdős-Rényi graphs.

We introduce a comprehensive analytical benchmark, relying on Fokker-Planck formalism, to study microbial dynamics in the presence of both biotic and abiotic forces. In equilibrium, we observe a balance between the two kinds of forces, leading to no correlations between species abundances. This implies that real microbiomes, where correlations have been observed, operate out of equilibrium. Therefore, we analyze nonequilibrium dynamics, presenting an ansatz for an approximate solution that embodies the complex interplay of forces in the system. This solution is consistent with Taylor's law as a coarse-grained approximation of the relation between species abundance and variance, but implies subtler effects, predicting unobserved structure beyond Taylor's law. Motivated by this theoretical prediction, we refine the analysis of existing metagenomic data, unveiling a novel universal macroecological pattern. Finally, we speculate on the physical origin of Taylor's law: building upon an analogy with Brownian motion theory, we propose that Taylor's law emerges as a fluctuation-growth relation resulting from equipartition of environmental resources among microbial species.

The formation of tetra-PEG gels, a model network with a well-defined structure, was investigated using particle-tracking microrheology. The dynamic scaling and critical relaxation exponents in the sol-gel transition were determined by applying the time-cure superposition method. Some values of the exponents differed from those of the Rouse model theory. This was attributed to the failure of the theoretical assumption that the cluster structure formation follows the percolation model theory on a three-dimensional lattice.

This work further investigates an aspect of the phase behavior of hard circular arcs whose phase diagram has been recently calculated by Monte Carlo numerical simulations: the non-nematicity of the filamentary phase that hard minor circular arcs form. Both second-virial density-functional theory and further Monte Carlo numerical simulations find that the positional one-particle density function undulates in the direction transverse to the axes of the filaments while further Monte Carlo numerical simulations find that the mobility of the hard minor circular arcs across the filaments occurs via a mechanism reminiscent of the mechanism of diffusion in a smectic phase: the filamentary phase is not a {“modulated” [“splay(-bend)”]} nematic phase.

Polar-ordered fluids are of interest both fundamentally and from an application standpoint. The recently discovered ferroelectric nematic phase is an example of a polar-ordered fluid, and while there has been extensive research interest in these materials, some of the fundamental properties are yet to be fully understood. Here, we report the order parameters of one of the first known materials that exhibit a ferroelectric nematic phase, RM734, determined via Raman spectroscopy. Raman spectroscopy been used extensively to determined order parameters in liquid crystals systems but also to probe ferroelectric behavior in solid ferroelectric systems and is therefore a powerful technique to study the ferroelectric nematic phase. A reduction and subsequent recovery of order parameters $(\mathrm{\Delta }\langle P_2\rangle \approx 0.1,$ $\mathrm{\Delta }\langle P_4\rangle \approx 0.06)$ is observed near the onset of the N to ${\mathbf{N}}_{\mathbf{F}}$ transition, a feature that is confirmed via complementary birefringence measurements. This dip in order parameters has been attributed to splay fluctuations, which occur at the onset of the ${\mathbf{N}}_{\mathbf{F}}$ transition; here we suggest a different explanation. A broadening of the full-width half-maxima (FWHM), of the order of 1 ${\mathrm{cm}}^{-1}$, of the selected Raman peak is observed near the N to ${\mathbf{N}}_{\mathbf{F}}$ phase transition, which we relate to either a change in reorientational dynamics or the onset of polar order. The ${\mathbf{N}}_{\mathbf{F}}$ transition is analyzed using standard solid ferroelectric frameworks. An energetic barrier associated with the para- to ferroelectric transition is found to be of the order of $2.5\pm 0.6\mathrm{kJ}/\mathrm{mol}$, which is comparable to solid ferroelectric materials.

Amorphous solids can yield in either a ductile or brittle manner under strain: plastic deformation can set in gradually, or abruptly through a macroscopic stress drop. Developing a unified theory describing both ductile and brittle yielding constitutes a fundamental challenge of nonequilibrium statistical physics. Recently, it has been proposed that, in the absence of thermal effects, the nature of the yielding transition is controlled by physics akin to that of the quasistatically driven random field Ising model (RFIM), which has served as the paradigm for understanding the effect of quenched disorder in slowly driven systems with short-ranged interactions. However, this theoretical picture neglects both the dynamics of, and the elasticity-induced long-ranged interactions between, the mesoscopic material constituents. Here, we address these two aspects and provide a unified theory building on the Hébraud-Lequeux elastoplastic description. The first aspect is crucial to understanding the competition between the imposed deformation rate and the finite timescale of plastic rearrangements: We provide a dynamical description of the macroscopic stress drop, as well as predictions for the shifting of the brittle yield strain and the scaling of the peak susceptibility with inverse shear rate. The second is essential to capture properly the behavior in the limit of quasistatic driving, where avalanches of plasticity diverge with system size at any value of the strain. We fully characterise the avalanche behavior, which is radically different to that of the RFIM. In the quasistatic, infinite-size limit, we find that both models have mean-field Landau exponents, obscuring the effect of the interactions. We show, however, that the latter profoundly affect the behavior of finite systems approaching the spinodal-like brittle yield point, where we recover qualitatively the finite-size trends found in particle simulations. The interactions also modify the nature of the random critical point separating ductile and brittle yielding, where we predict critical behavior on top of the marginality present at any value of the strain. We finally discuss how all our predictions can be directly tested against particle simulations and eventually experiments, and make first steps in this direction.

Laser-plasma instabilities under ignition conditions for direct-drive inertial confinement fusion are studied using two-dimensional particle-in-cell simulations with a combination of in-plane (PP) and out-of-the-plane (SP) lasers. The results show that stimulated Raman side-scattering can induce significant pump depletion and form a gap in the Raman scattered-light spectra that have been observed in experiments.

Structures, or spatial arrangements of matter and energy, including some fields (e.g., velocity or pressure) are ubiquitous in research applications and frequently require description for subsequent analysis, or stochastic reconstruction from limited data. The classical descriptors are two-point correlation functions (CFs), but the computation of three-point statistics is known to be advantageous in some cases as they can probe non-Gaussian signatures, not captured by their two-point counterparts. Moreover, $n$-point CFs with $n\ge 3$ are believed to possess larger information content and provide more information about studied structures. In this paper, we have developed algorithms and code to compute $S_3,C_3,F_{sss},F_{ssv}$, and $F_{svv}$ with a right-angle and arbitrary triangle pattern. The former was believed to be faster to compute, but with the help of precomputed regular positions we achieved the same speed for arbitrary pattern. In this work we also implement and demonstrate computations of directional three-point CFs—for this purpose right-triangular pattern seems to be superior due to explicit orientation and high coverage. Moreover, we assess the errors in CFs' evaluation due to image or pattern rotations and show that they have minor effect on accuracy of computations. The execution times of our algorithms for the same number of samples are orders of magnitude lower than in existing published counterparts. We show that the volume of data produced gets unwieldy very easily, especially if computations are performed in frequency domain. For these reasons until information content of different sets of correlation functions with different “$n$-pointness” is known, advantages of CFs with $n>3$ are not clear. Nonetheless, developed algorithms and code are universal enough to be easily extendable to any $n$ with increasing computational and random access memory (RAM) burden. All results are available as part of open-source package correlationfunctions.jl [V. Postnicov et al., Comput. Phys. Commun. 299, 109134 (2024).]. As described in this paper, three-point CFs computations can be immediately applied in a great number of research applications, for example: (1) flow and transport velocity fields analysis or any data with non-Gaussian signatures, (2) deep learning for structural and physical properties, and (3) structure taxonomy and categorization. In all these and numerous other potential cases the ability to compute directional three-point functions may be crucial. Notably, the organization of the code functions allows computation of cross correlation, i.e., one can compute three-point CFs for multiphase images (while binary structures were used in this paper for simplicity of explanations).

We prove a linear stability-dissipation relation (SDR) for $q$-state Potts models driven far from equilibrium by a nonconservative force. At a critical coupling strength, these models exhibit a synchronization transition from a decoherent into a synchronized state. In the vicinity of this transition, the SDR connects the entropy production rate per oscillator to the phase-space contraction rate, a measure of stability, in a simple way. For large but finite systems, we argue that the SDR implies a minimum-dissipation principle for driven Potts models as the dynamics selects stable nonequilibrium states with least dissipation. This principle holds arbitrarily far from equilibrium, for any stochastic dynamics, and for all $q$.

Hamiltonian neural networks (HNNs) are state-of-the-art models that regress the vector field of a dynamical system under the learning bias of Hamilton's equations. A recent observation is that embedding a bias regarding the additive separability of the Hamiltonian reduces the regression complexity and improves regression performance. We propose separable HNNs that embed additive separability within HNNs using observational, learning, and inductive biases. We show that the proposed models are more effective than the HNN at regressing the Hamiltonian and the vector field. Consequently, the proposed models predict the dynamics and conserve the total energy of the Hamiltonian system more accurately.

Large eddy simulations are a popular method for turbulent simulations because of their accuracy and efficiency. In this paper, a coupling algorithm is proposed that combines nonequilibrium moments (NM) and the volumetric strain-stretching (VSS) model within the framework of the lattice Boltzmann method (LBM). This algorithm establishes a relation between the NM and the eddy viscosity by using a special calculation form of the VSS model and Chapman-Enskog analysis. The coupling algorithm is validated in three typical flow cases: freely decaying homogeneous isotropic turbulence, homogeneous isotropic turbulence with body forces, and incompressible turbulent channel flow at $\mathrm{R}{\mathrm{e}}_{\tau }=180$. The results show that the coupling algorithm is accurate and efficient when compared with the results of direct numerical simulations. Using calculation format of the eddy viscosity, a uniform calculation format is used for each grid point of the flow field during the modeling process. The modeling process uses only the local distribution function to obtain the local eddy viscosity coefficients without any additional processing on the boundary, while optimizing the memory access process to fit the inherent parallelism of the LBM. The efficiency of the calculation is improved by about 20% compared to the central difference method within the lattice Boltzmann framework for calculating the eddy viscosity.

We introduce a machine-learning approach (denoted symmetry seeker neural network) capable of automatically discovering discrete symmetry groups in physical systems. This method identifies the finite set of parameter transformations that preserve the system's physical properties. Remarkably, the method accomplishes this without prior knowledge of the system's symmetry or the mathematical relationships between parameters and properties. Demonstrating its versatility, we showcase examples from mathematics, nanophotonics, and quantum chemistry.