We develop a data-driven characterization of the pilot-wave hydrodynamic system in which a bouncing droplet self-propels along the surface of a vibrating bath. We consider drop motion in a confined one-dimensional geometry and apply the dynamic mode decomposition (DMD) in order to characterize the evolution of the wave field as the bath's vibrational acceleration is increased progressively. Dynamic mode decomposition provides a regression framework for adaptively learning a best-fit linear dynamics model over snapshots of spatiotemporal data. Thus, DMD reduces the complex nonlinear interactions between pilot waves and droplet to a low-dimensional linear superposition of DMD modes characterizing the wave field. In particular, it provides a low-dimensional characterization of the bifurcation structure of the pilot-wave physics, wherein the excitation and recruitment of additional modes in the linear superposition models the bifurcation sequence. This DMD characterization yields a fresh perspective on the bouncing-droplet problem that forges valuable new links with the mathematical machinery of quantum mechanics. Specifically, the analysis shows that as the vibrational acceleration is increased, the pilot-wave field undergoes a series of Hopf bifurcations that ultimately lead to a chaotic wave field. The established relation between the mean pilot-wave field and the droplet statistics allows us to characterize the evolution of the emergent statistics with increased vibrational forcing from the evolution of the pilot-wave field. We thus develop a numerical framework with the same basic structure as quantum mechanics, specifically a wave theory that predicts particle statistics.

The nonlinear Landau-Zener-Stückelberg-Majorana (LZSM) tunneling dynamics and interferometry of an extended Bose-Hubbard flux ladder are studied. Based on the mean-field theory, the dispersion relation of the system is given, and it is found that loop structures periodically appear in the band structure and the nonlinear LZSM interference occurs naturally without Floquet engineering, which can be effectively modulated by atomic interactions. The nonlinear energy bands and the unique chirality feature of the flux ladder system can be identified through the dynamics of nonlinear Landau-Zener tunneling. Remarkably, the critical position of the noise in the interference pattern can be employed to identify the loop structure in the energy band, establishing an effective link between the nonlinear loop structure and LZSM interferometry. The position, intensity, symmetry, and width of interference patterns strongly depend on the magnetic field, atomic interactions, rung-to-leg coupling ratio, and energy bias, which provides an effective way to measure these parameters using the nonlinear LZSM interferometry. This paper further expands the dynamics of flux ladder systems to complex interaction regions and has potential applications in the precise measurement of related nonlinear systems.

Particle-embedded materials consist of a dispersed phase of particles in a sticking matrix. We used a bond-based peridynamics method to investigate their elastic properties, rupture, and probability of failure. We performed an extensive two-dimensional parametric study where particles are disk-shaped inclusions diluted into a pore-filling matrix. Both particle and matrix are considered to be brittle elastic with a perfectly bonded interface. The inclusion volume fraction $\phi$ and the inclusion matrix toughness ratio $\beta$ ($\beta \ge 1$) were varied from 0.254–0.754 (jamming point) and 1.5–100.0, respectively. A total of 5000 uniaxial tensile tests up to failure were performed. We showed that the Halpin-Tsai model fits well all Young elastic moduli even for nearly in-contact particles. The stress distribution strongly depends on $\phi$ and $\beta$. As the highest stresses (at the origin of crack nucleation) occur between neighboring particles, we analyzed the average stress in gaps. We found that, regardless of the particle volume fraction, the yield stress is a power law of a grain-scaled stress concentration factor. We also investigated the probability of failure of the samples. We found that whatever $\phi$ and $\beta$, this probability follows a classical Weibull law. Finally, we showed that Weibull modulus, normalized by its value for infinitely rigid particles, is inversely proportional to a function of the stress concentration factor.

Finite-size effects in the static structure factor $S\left(k\right)$ are analyzed for an amorphous substance. As the number of particles is reduced, $S\left(0\right)$ increases greatly, up to an order of magnitude. Meanwhile, there is a decrease in the height of the first peak $S_{\mathrm{peak}}$. These finite-size effects are modeled accurately by the Binder formula for $S\left(0\right)$ and our empirical formula for $S_{\mathrm{peak}}$. Procedures are suggested to correct for finite-size effects in $S\left(k\right)$ data and in the hyperuniformity index $H\equiv S\left(0\right)/S_{\mathrm{peak}}$. These principles generally apply to $S\left(k\right)$ obtained from particle positions in noncrystalline substances. The amorphous substance we simulate is a two-dimensional liquid, with a soft Yukawa interaction modeling a dusty plasma experiment.

The assertions made in a recent paper [Phys. Rev. E 107, 014106 (2023)] regarding the validity of path thermodynamics are ill founded and contradict well-known results. Following up on a previous Comment, I show that, for both models of chemical reaction networks considered in the aforementioned paper, path thermodynamics yields values of the entropy production rates fully consistent with those expected from standard chemical thermodynamics in the large-system limit.

The Comment's author argues that a correct description of reactive systems should incorporate an explicit interaction with reservoirs, leading to a unified system-reservoir entity. However, this proposition has two major flaws. First, as we will emphasize, this entity inherently follows a thermodynamic equilibrium distribution. In the Comment, no indication is provided on how to maintain such a system-reservoir entity in a nonequilibrium state. Second, contrary to the author's claim, the inclusion of a system-reservoir interaction in the traditional stochastic modeling of reactive systems does not automatically alter the limited applicability of path thermodynamics to problematic reactive systems. We will provide a simple demonstration to illustrate that certain elementary reactions may not involve any changes in reservoir components, which seem to have been overlooked by the author.

Eigenlevel correlation diagrams has proven to be a very useful tool to understand eigenstate characteristics of classically chaotic systems. In particular, we showed in a previous publication [Phys. Rev. Lett. 80, 944 (1998)] how to unveil the scarring mechanism, a cornerstone in the theory of quantum chaos, using the Planck constant as the correlation parameter. By increasing the Planck constant, we induced a transition from order to chaos, in which scarred wave functions appeared as the interaction of pairs of eigenstates in broad avoided crossings, forming a well-defined frontier in the correlation diagram. In this paper, we demonstrate that this frontier can be obtained by means of the semiclassical quantization of the involved scarring periodic orbits. Additionally, in order to calculate the Maslov index of each scarring periodic orbit, which is necessary for the semiclassical quantization procedure, we introduce a straightforward method based on Lagrangian descriptors. We illustrate the theory using the vibrational eigenstates of the LiCN molecular system.

We investigate the transport properties of a complex porous structure with branched fractal architectures formed due to the gradual deposition of dimers in a model of multilayer adsorption. We thoroughly study the interplay between the orientational anisotropy parameter $p_0$ of deposited dimers and the formation of porous structures, as well as its impact on the conductivity of the system, through extensive numerical simulations. By systematically varying the value of $p_0$, several critical and off-critical scaling relations characterizing the behavior of the system are examined. The results demonstrate that the degree of orientational anisotropy of dimers plays a significant role in determining the structural and physical characteristics of the system. We find that the Einstein relation relating to the size scaling of the electrical conductance holds true only in the limiting case of $p_0\to 1$. Monitoring the fractal dimension of the interface of the multilayer formation for various $p_0$ values, we reveal that in a wide range of $p_0>0.2$ interface shows the characteristic of a self-avoiding random walk, compared to the limiting case of $p_0\to 0$ where it is characterized by the fractal dimension of the backbone of ordinary percolation cluster at criticality. Our results thus can provide useful information about the fundamental mechanisms underlying the formation and behavior of wide varieties of amorphous and disordered systems that are of paramount importance both in science and technology as well as in environmental studies.

Modeling water and other liquids in computational simulations requires a large set of parameters. Many works have been devoted to finding new, improved water models, with almost all of them designed for bulk systems. Here, we use carbon nanotubes as a play model to investigate the effects of introducing flexibility in water force fields during molecular dynamics simulations of nanoconfined water. We explore six different models to show that viscosity, diffusion, and dipole orientation are vastly influenced by the flexibility and the family of force fields used. Particularly, we found the level of confinement (decreasing the nanotube's diameter) to increase discrepancies in the description of the dipole alignment. In smaller (10,10) nanotubes, the flexible version of the transferable intermolecular potential with three points (TIP3P/Fs) features a high directionality, while its rigid counterpart shows a more distributed dipole orientation. Both viscosity and diffusion are also extremely dependent on the force-field family, with the flexible version of the simple point charge (SPC/Fw) featuring the lower confidence interval.

Longitudinal pulses that propagate in a medium near a van der Waals phase transition have a sigmoidal dependence on the strength of the stimulus arising from the phase structure. This response resembles the all-or-nothing property of action potentials, which raises the question if an acoustic system near a phase transition can be suitable for material-based neuromorphic computation. Herein, we investigate how information about the stimulus is stored within these pulses. We find that (1) the pulse propagates in parallel both digital and analog information about the stimulus amplitude; (2) the pulse encodes the type of stimulus, for instance, mechanical or thermal; and (3) a collision between two pulses stores information about both stimuli and may be used as a fading memory. Our results unravel a rich encoding of information in a phenomenon that is both common in a plethora of materials and mimics neuronal signaling. In addition, we show that these pulses carry more information than is typically considered by models of neural computation. Therefore, this phenomenon is an excellent candidate for in materio computation.

The present study describes the utilization of a gallium-arsenide gate-stack gate-all-around (GaAs-GS-GAA) fin field-effect transistor (FinFET) to accomplish the electrical identification of the breast cancer cell MDA-MB-231 by monitoring the device switching ratio. The proposed sensor uses four nanocavities carved beneath the gate electrodes for enhanced detection sensitivity. MDA-MB-231 (cancerous) and MCF-10A (healthy) breast cells have a distinct dielectric constant, and it changes when exposed to microwave frequencies spanning across 200 MHz and 13.6 GHz, which modifies the electrical characteristics, allowing for early diagnosis. First, a percentage shift in the primary DC characteristics is presented to demonstrate the advantage of GS-GAA FinFET over conventional FinFET. The sensor measures the switching-ratio-based sensitivity, which comes out to be 99.72% for MDA-MB-231 and 47.78% for MCF-10A. The sensor was tested for stability and reproducibility and found to be repeatable and sufficiently stable with settling times of 55.51, 60.80, and 71.58 ps for MDA-MB-231 cells, MCF-10A cells, and air, respectively. It can distinguish between viable and nonviable cells based on electrical response alterations. The possibility of early detection of cancerous breast cells using Bruggeman's model is also discussed. Further, the impact of biomolecule occupancy and frequency variations on the device sensitivity is carried out. This study also explains how to maximize the sensing performance by adjusting the fin height, fin width, work function, channel doping, temperature, and drain voltage. Lastly, this article compared the proposed breast cancer cell detectors to existing literature to evaluate their performance and found considerable improvement. The findings of this research have the potential to establish GaAs-GS-GAA FinFET as a promising contender for MDA-MB-231 breast cancer cell detection.

Biological membranes can exhibit various morphology due to the fluidity of the lipid molecules within the monolayers. The shape transformation of membranes has been well described by the classical Helfrich theory, which consists only a few phenomenological parameters, including the mean and the Gaussian curvature modulus. Though various methods have been proposed to measure the mean curvature modulus, determining the Gaussian curvature modulus remains difficult both in experiments and in simulations. In this paper we study the buckling process of a rectangular membrane and a circular membrane subject to compressive stresses and under different boundary conditions. We find that the buckling of a rectangular membrane takes place continuously, while the buckling of a circular membrane can be discontinuous depending on the boundary conditions. Furthermore, our results show that the stress-strain relationship of a buckled circular membrane can be used to determine the Gaussian curvature modulus effectively.

In this paper, we consider the Kelvin-Helmholtz instability in the magnetohydrodynamic flow. The motion of the interface is described by a current-vortex sheet. We examine the linear stability of the current-vortex sheet model and determine the growth rate of the interface. The interface is linearly stable for $M_A<2$ where $M_A$ represents the Alfvén Mach number. It is found that the interface is linearly unstable in the limit of the critical Alfvén Mach number $M_A=2$, due to resonance of eigenvalues. We perform numerical simulations for the current-vortex sheet for both regimes of $M_A<2$ and $M_A>2$. The numerical results show the stabilizing effects of the magnetic field on the evolution of the current-vortex sheet when the magnetic field is sufficiently large. For the regime $M_A<2$, the sheet oscillates both longitudinally and transversely and the transverse surface wave is pronounced for a large $M_A$. Remarkably, the interface is nonlinearly unstable for $M_A\approx 2$, for $M_A<2$, which may be due to the propagation of surface waves. For the regime $M_A>2$, the roll-up of the spiral is weakened and the spiral is more pinched and stretched for smaller $M_A$. A comparison of the unstable evolutions of large and small values of $M_A$ shows significant differences of the magnetic field and vortex sheet strength.

Laser-direct-drive fusion target designs with solid deuterium-tritium (DT) fuel, a high-$Z$ gradient-density pusher shell (GDPS), and a Au-coated foam layer have been investigated through both 1D and 2D radiation-hydrodynamic simulations. Compared with conventional low-$Z$ ablators and DT-push-on-DT targets, these GDPS targets possess certain advantages of being instability-resistant implosions that can be high adiabat ($\alpha \ge 8$) and low hot-spot and pusher-shell convergence (${\mathrm{CR}}_{\mathrm{hs}}\approx 22$ and ${\mathrm{CR}}_{\mathrm{PS}}\approx 17$), and have a low implosion velocity ($v_{\mathrm{imp}}<3\times {10}^7\mathrm{cm}/\mathrm{s}$). Using symmetric drive with laser energies of 1.9 to $2.5\mathrm{MJ}$, 1D lilac simulations of these GDPS implosions can result in neutron yields corresponding to $\gtrsim 50-\mathrm{MJ}$ energy, even with reduced laser absorption due to the cross-beam energy transfer (CBET) effect. Two-dimensional draco simulations show that these GDPS targets can still ignite and deliver neutron yields from 4 to $\sim 10\mathrm{MJ}$ even if CBET is present, while traditional DT-push-on-DT targets normally fail due to the CBET-induced reduction of ablation pressure. If CBET is mitigated, these GDPS targets are expected to produce neutron yields of $>20\mathrm{MJ}$ at a driven laser energy of $\sim 2\mathrm{MJ}$. The key factors behind the robust ignition and moderate energy gain of such GDPS implosions are as follows: (1) The high initial density of the high-$Z$ pusher shell can be placed at a very high adiabat while the DT fuel is maintained at a relatively low-entropy state; therefore, such implosions can still provide enough compression $\rho R>1\mathrm{g}/\mathrm{c}{\mathrm{m}}^2$ for sufficient confinement; (2) the high-$Z$ layer significantly reduces heat-conduction loss from the hot spot since thermal conductivity scales as $\sim 1/Z$; and (3) possible radiation trapping may offer an additional advantage for reducing energy loss from such high-$Z$ targets.

We present experimental observations of ${\mathrm{K}}_{\beta }$ emission from highly charged Mg ions at solid density, driven by intense x rays from a free electron laser. The presence of ${\mathrm{K}}_{\beta }$ emission indicates the $n=3$ atomic shell is relocalized for high charge states, providing an upper constraint on the depression of the ionization potential. We explore the process of state relocalization in dense plasmas from first principles using finite-temperature density functional theory alongside a wave-function localization metric, and find excellent agreement with experimental results.

Four-dimensional (4D) rotations have applications in the fields of robotics, computer vision, and rigid-body mechanics. In the latter, they can be used to transform between equimomental systems of point masses. Here we provide an efficient algorithm to generate random 4D rotation matrices covering an arbitrary, predefined range of rotation angles. These matrices can be combined with Monte Carlo methods for the efficient sampling of the SO(4) group of 4D rotations. The matrices are unbiased and constructed such that repeated rotations result in uniform sampling over SO(4). The algorithm can be used to optimize the mass partitioning in coarse-grained simulation models of molecules involving coupled constraints for stable time integration.

In a recent paper [T. Wei et al., Phys. Rev. E 106, 034101 (2022)] a derivation of the resistance force acting on a small classical particle moving through a rarefied gas has been presented. Unfortunately, the obtained expression is inaccurate. The purpose of this Comment is to provide the accurate expression and to discuss several related aspects.

The relative speed distribution function [Eq. (2)] in the Comment is discussed. It shows that Eq. (2) in the Comment is not the distribution function that should be explored in our work and is therefore not applicable to our research.

We analyze the problem of supervised learning of ferromagnetic phase transitions from the statistical physics perspective. We consider two systems in two universality classes, the two-dimensional Ising model and two-dimensional Baxter-Wu model, and perform careful finite-size analysis of the results of the supervised learning of the phases of each model. We find that the variance of the neural network (NN) output function (VOF) as a function of temperature has a peak in the critical region. Qualitatively, the VOF is related to the classification rate of the NN. We find that the width of the VOF peak displays the finite-size scaling governed by the correlation length exponent $\nu$ of the universality class of the model. We check this conclusion using several NN architectures—a fully connected NN, a convolutional NN, and several members of the ResNet family—and discuss the accuracy of the extracted critical exponents $\nu$.

The master stability function (MSF) yields the stability of the globally synchronized state of a network of identical oscillators in terms of the eigenvalues of the adjacency matrix. In order to compute the MSF, one must have an accurate model of an uncoupled oscillator, but often such a model does not exist. We present a reservoir computing technique for estimating the MSF given only the time series of a single, uncoupled oscillator. We demonstrate the generality of our technique by considering a variety of coupling configurations of networks consisting of Lorenz oscillators or Hénon maps.