We propose a model of ion-electron plasma (or nucleus-electron plasma) that accounts for the electronic structure around nuclei (i.e., ion structure) as well as for ion-ion correlations. The model equations are obtained through the minimization of an approximate free-energy functional, and it is shown that the model fulfills the virial theorem. The main hypotheses of this model are (1) nuclei are treated as classical indistinguishable particles, (2) electronic density is seen as a superposition of a uniform background and spherically symmetric distributions around each nucleus (system of ions in a plasma), (3) free energy is approached using a cluster expansion (nonoverlapping ions), and (4) resulting ion fluid is modeled through an approximate integral equation. In the present paper, the model is described only in its average-atom version.

In this work we develop an improved phase-field based lattice Boltzmann (LB) method where a hybrid Allen-Cahn equation (ACE) with a flexible weight instead of a global weight is used to suppress the numerical dispersion and eliminate the coarsening phenomenon. Then two LB models are adopted to solve the hybrid ACE and the Navier-Stokes equations, respectively. Through the Chapman-Enskog analysis, the present LB model can correctly recover the hybrid ACE, and the macroscopic order parameter used to label different phases can be calculated explicitly. Finally, the present LB method is validated by five tests, including the diagonal translation of a circular interface, two stationary bubbles with different radii, a bubble rising under the gravity, the Rayleigh-Taylor instability in two-dimensional and three-dimensional cases, and the three-dimensional Plateau-Rayleigh instability. The numerical results show that the present LB method has a superior performance in reducing the numerical dispersion and the coarsening phenomenon.

Systematic microcanonical inflection-point analysis of precise numerical results obtained in extensive generalized-ensemble Monte Carlo simulations reveals a bifurcation of the coil-globule transition line for polymers with a bending stiffness exceeding a threshold value. The region, enclosed by the toroidal and random-coil phases, is dominated by structures crossing over from hairpins to loops upon lowering the energy. Conventional canonical statistical analysis is not sufficiently sensitive to allow for the identification of these separate phases.

Anomalous diffusion is present at all scales, from atomic to large ones. Some exemplary systems are ultracold atoms, telomeres in the nucleus of cells, moisture transport in cement-based materials, arthropods' free movement, and birds' migration patterns. The characterization of the diffusion gives critical information about the dynamics of these systems and provides an interdisciplinary framework with which to study diffusive transport. Thus, the problem of identifying underlying diffusive regimes and inferring the anomalous diffusion exponent $\alpha$ with high confidence is critical to physics, chemistry, biology, and ecology. Classification and analysis of raw trajectories combining machine learning techniques with statistics extracted from them have widely been studied in the Anomalous Diffusion Challenge [Muñoz-Gil et al., Nat. Commun. 12, 6253 (2021)]. Here we present a new data-driven method for working with diffusive trajectories. This method utilizes Gramian angular fields (GAF) to encode one-dimensional trajectories as images (Gramian matrices), while preserving their spatiotemporal structure for input to computer-vision models. This allows us to leverage two well-established pretrained computer-vision models, ResNet and MobileNet, to characterize the underlying diffusive regime and infer the anomalous diffusion exponent $\alpha$. Short raw trajectories of lengths between 10 and 50 are commonly encountered in single-particle tracking experiments and are the most difficult ones to characterize. We show that GAF images can outperform the current state-of-the-art while increasing accessibility to machine learning methods in an applied setting.

Based on the mathematical arguments formulated within the multifractal detrended fluctuation analysis (MFDFA) approach it is shown that, in the uncorrelated time series from the Gaussian basin of attraction, the effects resembling multifractality asymptotically disappear for positive moments when the length of time series increases. A hint is given that this applies to the negative moments as well and extends to the Lévy stable regime of fluctuations. The related effects are also illustrated and confirmed by numerical simulations. This documents that the genuine multifractality in time series may only result from the long-range temporal correlations, and the fatter distribution tails of fluctuations may broaden the width of the singularity spectrum only when such correlations are present. The frequently asked question of what makes multifractality in time series—temporal correlations or broad distribution tails—is thus ill posed. In the absence of correlations only the bifractal or monofractal cases are possible. The former corresponds to the Lévy stable regime of fluctuations while the latter to the ones belonging to the Gaussian basin of attraction in the sense of the central limit theorem.

The chemotactic process of run-and-tumble bacteria results from modulating the tumbling rate in response to changes in chemoattractant gradients felt by the bacteria. The response has a characteristic memory time and is subject to important fluctuations. These ingredients are considered in a kinetic description of chemotaxis, allowing the computation of the stationary mobility and the relaxation times needed to reach the steady state. For large memory times, these relaxation times become large, implying that finite-time measurements give rise to nonmonotonic currents as a function of the imposed chemoattractant gradient, contrary to the stationary regime where the response is monotonic. The case of an inhomogeneous signal is analyzed. Contrary to the usual Keller–Segel model, the response is nonlocal, and the bacterial profile is smoothed with a characteristic length that grows with the memory time. Finally, the case of traveling signals is considered, where appreciable differences appear compared to memoryless chemotactic descriptions.

The mesogen CB7CB [1″,7″-bis(4-cyanobiphenyl-4′-yl)heptane], mixed with a small quantity of a long chain amphiphile, is examined for the structural features of twist-bend nematic $\left(N_{\mathrm{TB}}\right)$ drops acting as colloidal inclusions in the isotropic and nematic environments. In the isotropic phase, the drops nucleating in the radial (splay) geometry develop toward escaped radial, off-centered structures, involving both splay and bend distortions. With further growth, they transform into low-birefringence (near-homeotropic) objects, within which remarkably well-organized networks of parabolic focal conic defects evolve in time. In electrically reoriented near-homeotropic $N_{\mathrm{TB}}$ drops, the pseudolayers develop an undulatory boundary possibly attributable to saddle-splay elasticity. In the matrix of the planar nematic phase, $N_{\mathrm{TB}}$ droplets appearing as radial hedgehogs attain stability in the dipolar geometry, through their association with hyperbolic hedgehogs. With growth, on transformation of the hyperbolic defect into its topologically equivalent Saturn ring around the $N_{\mathrm{TB}}$ drop, the geometry turns quadrupolar. Significantly, dipoles are stable in smaller drops, while quadrupoles are stable in larger ones. The dipole-quadrupole transformation is reversible, but is hysteretic with respect to drop size. Importantly, this transformation is often mediated by nucleation of two loop disclinations, one appearing at a marginally lower temperature than the other. The existence of a metastable state with partial formation of a Saturn ring and persistence of the hyperbolic hedgehog raises a question relating to the conservation of topological charge. In twisted nematics, this state features in the formation of a giant unknot that binds all $N_{\mathrm{TB}}$ drops together.

Dirt cones are meter-scale structures encountered at the surface of glaciers, which consist of ice cones covered by a thin layer of ashes, sand, or gravel, and which form naturally from an initial patch of debris. In this article, we report field observations of cone formation in the French Alps, laboratory-scale experiments reproducing these structures in a controlled environment, and two-dimensional discrete-element-method–finite-element-method numerical simulations coupling the grain mechanics and thermal effects. We show that cone formation originates from the insulating properties of the granular layer, which reduces ice melting underneath as compared to bare ice melting. This differential ablation deforms the ice surface and induces a quasistatic flow of grains that leads to a conic shape, as the thermal length become small compared to the structure size. The cone grows until it reaches a steady state in which the insulation provided by the dirt layer exactly compensates for the heat flux coming from the increased external surface of the structure. These results allowed us to identify the key physical mechanisms at play and to develop a model able to quantitatively reproduce the various field observations and experimental findings.

Ori-kirigami structures offer a good avenue for designing mechanical metamaterials due to their unique advantage of being independent of material properties and scale limitations. Recently, the scientific community has been greatly interested in exploiting the complex energy landscape of ori-kirigami structures to construct multistable systems and play their valuable role in different applications. Here, we present three-dimensional ori-kirigami structures based on generalized waterbomb units, a cylindrical ori-kirigami structure based on waterbomb units, and a conical ori-kirigami structure based on trapezoidal waterbomb units. We investigate the inherent relationships between the unique kinematics and mechanical properties of these three-dimensional ori-kirigami structures and explore their potential usage as mechanical metamaterials that exhibit negative stiffness, snap-through, hysteresis effects, and multistability. What makes the structures even more attractive is their massive folding stroke, where the conical ori-kirigami structure can obtain a huge folding stroke of more than twice its initial height through penetration of its upper and lower boundaries. This study forms the foundation for designing and constructing three-dimensional ori-kirigami metamaterials based on generalized waterbomb units for various engineering applications.

On the basis of Landau–de Gennes theory and the finite-difference iterative method, the autonomic modulation of chiral inversion in a cylindrical cavity with degenerate planar anchoring is investigated. Under the applied helical twisting power (inversely related to the pitch $P$), a chiral inversion can be achieved due to the nonplanar geometry effect, and the inversion capacity rises with the increase of the helical twisting power. The combined effect of the saddle-splay $K_{24}$ contribution (corresponding to the $L_{24}$ term in Landau–de Gennes theory) and the helical twisting power are analyzed. It is found that the chiral inversion is more strongly modulated on the condition that the chirality of spontaneous twist is opposite to that of applied helical twisting power. Further, larger values of $K_{24}$ will induce larger modulation of the twist degree and smaller modulation of the inverted region. The autonomic modulation of chiral inversion shows great potential for chiral nematic liquid crystal materials to be used in smart devices, such as light-controlled switches and nanoparticle transporters.

We derive the analytical dispersion relation of a high-energy laser beam's backward stimulated Brillouin scattering (BSBS) in a hot plasma, that accounts both for the random phase plate (RPP) induced spatial shaping and its associated phase randomness. Indeed, phase plates are mandatory in large laser facilities where a precise control of the focal spot size is required. While the focal spot size is well controlled, such techniques produce small scale intensity variations that can trigger laser-plasma instabilities such as BSBS. Quantifying the resulting instability variability is shown to be crucial for understanding accurately the backscattering temporal and spatial growth as well as the asymptotic reflectivity. Our model, validated by means of a large number of three-dimensional paraxial simulations and experimental data, offers three quantitative predictions. The first one addresses the temporal exponential growth of the reflectivity by deriving and solving the BSBS RPP dispersion relation. A large statistical variability of the temporal growth rate is shown to be directly related to the phase plate randomness. Then, we predict the portion of the beam's section that is absolutely unstable, thus helping to precisely assess the validity of the vastly used convective analysis. Finally, a simple analytical correction to the plane wave spatial gain is extracted from our theory giving a practical and effective asymptotic reflectivity prediction that includes the impact of phase plates smoothing techniques. Hence, our study sheds light on the long-time studied BSBS, deleterious to many high-energy experimental studies related to the physics of inertial confinement fusion.

In this study, the migration of microparticles towards the inertial equilibrium positions in a straight microchannel with a square cross section in the presence of an inhomogeneous oscillating electric field was examined. The dynamics of microparticles were simulated using the immersed boundary–lattice Boltzmann method of fluid-structure interaction simulation. Moreover, the lattice Boltzmann Poisson solver was applied to calculate the electric field required for calculation of the dielectrophoretic force using the equivalent dipole moment approximation. These numerical methods were implemented on a single GPU coupled with the AA pattern of storing distribution functions in memory to speed up the computationally demanding simulation of microparticles dynamics. In the absence of an electric field, spherical polystyrene microparticles migrate to four symmetric stable equilibrium positions corresponding to the sidewalls of the square cross-sectional microchannel. The equilibrium distance from the sidewall was increased by increasing the particle size. The equilibrium positions near electrodes disappeared and particles migrated to the other equilibrium positions far from the electrodes by the application of the high-frequency oscillatory electric field at voltages beyond a threshold value. Finally, a two-step dielectrophoresis-assisted inertial microfluidics methodology was introduced for particle separation based on the crossover frequencies and the observed threshold voltages of different particles. The proposed method exploited the synergistic effect of dielectrophoresis and inertial microfluidics methods to remove their limitations, allowing the separation of a broad range of polydisperse particle mixtures with a single device in a short time.

We consider two populations of the globally coupled Sakaguchi-Kuramoto model with the same intra- and interpopulations coupling strengths. The oscillators constituting the intrapopulation are identical whereas the interpopulations are nonidentical with a frequency mismatch. The asymmetry parameters ensure the permutation symmetry among the oscillators constituting the intrapopulation and a reflection symmetry among the oscillators constituting the interpopulation. We show that the chimera state manifests by spontaneously breaking the reflection symmetry and also exists in almost in the entire explored range of the asymmetry parameter without restricting to the near $\pi /2$ values of it. The saddle-node bifurcation mediates the abrupt transition from the symmetry breaking chimera state to the symmetry-preserving synchronized oscillatory state in the reverse trace, whereas the homoclinic bifurcation mediates the transition from the synchronized oscillatory state to synchronized steady state in the forward trace. We deduce the governing equations of motion for the macroscopic order parameters employing the finite-dimensional reduction by Watanabe and Strogatz. The analytical saddle-node and homoclinic bifurcation conditions agree well with the simulations results and the bifurcation curves.

With synchronization being one of nature's most ubiquitous collective behaviors, the field of network synchronization has experienced tremendous growth, leading to significant theoretical developments. However, most previous studies consider uniform connection weights and undirected networks with positive coupling. In the present article, we incorporate the asymmetry in a two-layer multiplex network by assigning the ratio of the adjacent nodes' degrees as the weights to the intralayer edges. Despite the presence of degree-biased weighting mechanism and attractive-repulsive coupling strengths, we are able to find the necessary conditions for intralayer synchronization and interlayer antisynchronization and test whether these two macroscopic states can withstand demultiplexing in a network. During the occurrence of these two states, we analytically calculate the oscillator's amplitude. In addition to deriving the local stability conditions for interlayer antisynchronization via the master stability function approach, we also construct a suitable Lyapunov function to determine a sufficient condition for global stability. We provide numerical evidence to show the necessity of negative interlayer coupling strength for the occurrence of antisynchronization, and such repulsive interlayer coupling coefficients cannot destroy intralayer synchronization.

Bent-Core banana-shaped molecules exhibit tilted polar smectic phases with macroscopically chiral layer order even though the constituent molecules are achiral in nature. Here, we show that the excluded volume interactions between the bent-core molecules account for this spontaneous breaking of chiral symmetry in the layer. We have numerically computed excluded volume between two rigid bent-core molecules in a layer using two types of model structures of them and explored the different possible symmetries of the layer that are favored by the excluded volume effect. For both model structures of the molecule, the $C_2$ symmetric layer structure is favored for most values of tilt and bending angle. However, the $C_s$ and $C_1$ point symmetries of the layer are also possible for one of the model structures of the molecules. We have also developed a coupled $XY$-Ising model and performed Monte Carlo simulation to explain the statistical origin of spontaneous chiral symmetry breaking in this system. The coupled $XY$-Ising model accounts for the experimentally observed phase transitions as a function of temperature and electric field.

Most existing results in the analysis of quantum reservoir computing (QRC) systems with classical inputs have been obtained using the density matrix formalism. This paper shows that alternative representations can provide better insight when dealing with design and assessment questions. More explicitly, system isomorphisms are established that unify the density matrix approach to QRC with the representation in the space of observables using Bloch vectors associated with Gell-Mann bases. It is shown that these vector representations yield state-affine systems previously introduced in the classical reservoir computing literature and for which numerous theoretical results have been established. This connection is used to show that various statements in relation to the fading memory property (FMP) and the echo state property (ESP) are independent of the representation and also to shed some light on fundamental questions in QRC theory in finite dimensions. In particular, a necessary and sufficient condition for the ESP and FMP to hold is formulated using standard hypotheses, and contractive quantum channels that have exclusively trivial semi-infinite solutions are characterized in terms of the existence of input-independent fixed points.

Recent wildfire prevalence and destruction have led to new initiatives in the search for better land management techniques and prescriptions for controlled burns. With limited data on low-intensity prescribed burns, finding models that can represent fire behavior is of great importance to learning how to control fires with more accuracy while also maintaining the purpose for the burn, be it reducing fuels or managing the ecosystem. Here we use a data set of infrared temperatures collected in the New Jersey Pine Barrens from 2017 through 2020 to develop a model for very fine-scale fire behavior ($\approx 0.05 {\mathrm{m}}^2$). The model uses distributions from the data set to define five stages in fire behavior in a cellular automata framework. For each cell, the transition between each stage is probabilistically driven based on the radiant temperature values of the cell and its immediate neighbors in a coupled map lattice. With five distinct initial conditions, we performed 100 simulations and used the parameters derived from the data set to develop metrics for model verification. To validate the model, we also expanded it to include variables not in the data set that are important for fire behavior, e.g., fuel moisture levels and spotting ignitions. The model matches several metrics compared to the observational data set and exhibits behavioral characteristics expected from low-intensity wildfire behavior including a long and varied burn time for each cell after initial ignition, and lingering embers in the burn zone.

We consider the kinetics of the imperfect narrow escape problem, i.e., the time it takes for a particle diffusing in a confined medium of generic shape to reach and to be adsorbed by a small, imperfectly reactive patch embedded in the boundary of the domain, in two or three dimensions. Imperfect reactivity is modeled by an intrinsic surface reactivity $\kappa$ of the patch, giving rise to Robin boundary conditions. We present a formalism to calculate the exact asymptotics of the mean reaction time in the limit of large volume of the confining domain. We obtain exact explicit results in the two limits of large and small reactivities of the reactive patch, and a semianalytical expression in the general case. Our approach reveals an anomalous scaling of the mean reaction time as the inverse square root of the reactivity in the large-reactivity limit, valid for an initial position near the extremity of the reactive patch. We compare our exact results with those obtained within the “constant flux approximation”; we show that this approximation turns out to give exactly the next-to-leading-order term of the small-reactivity limit, and provides a good approximation of the reaction time far from the reactive patch for all reactivities, but not in the vicinity of the boundary of the reactive patch due to the above-mentioned anomalous scaling. These results thus provide a general framework to quantify the mean reaction times for the imperfect narrow escape problem.