A linear lattice velocity model is developed, and a corresponding lattice Boltzmann flux solver (LBFS) is constructed based on it. This solver calculates the fluxes of the linearized Euler equations (LEEs), which are discretized by the finite volume method (FVM), and can simulate acoustic propagation in fluids. First, the expressions for the distribution function and the lattice velocity of the linear discrete velocity model are constructed using the moment relations in linear form. Second, based on Chapman-Enskog analysis and moment relations, the mesoscopic flux expression can be constructed by comparing the linear lattice Boltzmann equation and LEEs. Finally, the developed scheme is used to calculate the LEE flux term. The developed linear lattice velocity model-based LBFS has the following advantages: (i) It extends the lattice Boltzmann model-based flux solver from solving the macroscopic equations of fluid dynamics to solving linear equations; (ii) it also inherits the advantages of the Boltzmann model-type flux solver. The variables at the interface are calculated from the local solution of the lattice Boltzmann equation, making it more physical. In addition, least-squares-based finite differences and Gaussian integration are used for the FVM to discretize the LEE, making it a high-precision algorithm. Thus, the developed algorithm can accurately capture acoustic propagation in fluids and acoustic scattering in complex geometries. Several numerical cases for propagating acoustics in fluids are simulated to validate the accuracy and robustness of the present algorithm, and an accuracy test shows it approaches fourth-order accuracy.

We study a quantum battery made out of $N$ nonmutually interacting qubits coupled to a dissipative single electromagnetic field mode in a resonator. We quantify the charging energy, ergotropy, transfer rate, and power of the system, showing that collective enhancements are still present despite losses, and can even increase with dissipation. Moreover, we observe that a performance deterioration due to dissipation can be reduced by scaling up the battery size. This is useful for experimental realizations when controlling the quality of the resonator and the number of qubits are limiting factors.

Fluctuation relations of Jarzynski and Crooks enable efficient calculations of a free-energy difference between equilibrium states. In the present paper, we provide some numerical evidence that these relations can also be used for a two-dimensional Ising-doped voter model, which is a nonequilibrium system with a violated detailed balance. Adopting the method of Híjar and Sutmann, we implement a protocol that switches between periodic and antiperiodic boundary conditions and induces formation of an interface in the model. Assuming that a suitably interpreted Ising Hamiltonian can be considered as a pseudoenergy of the model, we examine fluctuations of work performed during these processes and estimate the surface tension. Our results confirm that the surface tension remains positive in this model except a limiting case of the voter model, where it seems to vanish. Comparing the free-energy estimates at different speeds of the switching process, we also estimate an effective temperature in the model. Perhaps coincidentally, the effective temperature of the voter model appears to be close to the critical temperature of the Ising model.

We develop a Fourier-Chebyshev pseudospectral direct numerical simulation (DNS) to examine a potentially singular solution of the radially bounded, three-dimensional (3D), axisymmetric Euler equations [G. Luo and T.Y. Hou, Proc. Natl. Acad. Sci. USA 111, 12968 (2014)]. We demonstrate that (a) the time of singularity is preceded, in any spectrally truncated DNS, by the formation of oscillatory structures called tygers, first investigated in the one-dimensional (1D) Burgers and two-dimensional (2D) Euler equations; (b) the analyticity-strip method can be generalized to obtain an estimate for the (potential) singularity time.

We analytically show that the interfacial fluid's molecular dynamics of capillary bridges induces both elastic and dissipative forces to the shearing plane. Surprisingly, the nanometer-sized, liquid-solid contact line of the bridges exerts a giant “shear” force on the solid surface, which is ${10}^5$ higher than the usual viscous interaction and comparable to that of solid-solid direct-contact friction. These results are consistent with previously reported experimental data and may provide clues to longstanding questions on the apparent viscosity of the nanoconfined fluids.

Studies of nucleation generally focus on the properties of the critical cluster, but the presence of defects within the crystal lattice means that the population of nuclei necessarily evolve through a distribution of precritical clusters with varying degrees of structural disorder on their way to forming a growing stable crystal. To investigate the role precritical clusters play in nucleation, we develop a simple thermodynamic model for crystal nucleation in terms of cluster size and the degree of cluster order that allows us to alter the work of forming the precritical clusters without affecting the properties of the critical cluster. The steady state and transient nucleation behavior of the system are then studied numerically, for different microscopic ordering kinetics. We find that the model exhibits a generic order-disorder transition in the precritical clusters. Independent of the types of ordering kinetics, increasing the accessibility of disordered precritical clusters decreases both the steady state nucleation rate and the nucleation lag time. Furthermore, the interplay between the free-energy surface and the microscopic ordering kinetics leads to three distinct nucleation pathways.

We calculate Nielsen's circuit complexity of coherent spin state operators. An expression for the complexity is obtained by using the small angle approximation of the Euler angle parametrization of a general $\text{SO}\left(3\right)$ rotation. This is then extended to arbitrary times for systems whose time evolutions are generated by couplings to an external field, as well as nonlinearly interacting Hamiltonians. In particular, we show how the Nielsen complexity relates to squeezing parameters of the one-axis twisted Hamiltonians in a transverse field, thus indicating its relation with pairwise entanglement. We further point out the difficulty with this approach for the Lipkin-Meshkov-Glick model and resolve the problem by computing the complexity in the Tait-Bryan parametrization.

Understanding how feature learning affects generalization is among the foremost goals of modern deep learning theory. Here, we study how the ability to learn representations affects the generalization performance of a simple class of models: deep Bayesian linear neural networks trained on unstructured Gaussian data. By comparing deep random feature models to deep networks in which all layers are trained, we provide a detailed characterization of the interplay between width, depth, data density, and prior mismatch. We show that both models display samplewise double-descent behavior in the presence of label noise. Random feature models can also display modelwise double descent if there are narrow bottleneck layers, while deep networks do not show these divergences. Random feature models can have particular widths that are optimal for generalization at a given data density, while making neural networks as wide or as narrow as possible is always optimal. Moreover, we show that the leading-order correction to the kernel-limit learning curve cannot distinguish between random feature models and deep networks in which all layers are trained. Taken together, our findings begin to elucidate how architectural details affect generalization performance in this simple class of deep regression models.

We investigate theoretically and numerically quantum reflection of dark solitons propagating through an external reflectionless potential barrier or in the presence of a position-dependent dispersion. We confirm that quantum reflection occurs in both cases with a sharp transition between complete reflection and complete transmission at a critical initial soliton speed. The critical speed is calculated numerically and analytically in terms of the soliton and potential parameters. Analytical expressions for the critical speed were derived using the exact trapped mode, time-independent, and time-dependent variational calculations. It is then shown that resonant scattering occurs at a critical speed, where the energy of the incoming soliton is resonant with that of a trapped mode. Reasonable agreement between analytical and numerical values for the critical speed is obtained as long as a periodic multisoliton ejection regime is avoided.

We study a simple model of identical “swarmalators,” generalizations of phase oscillators that swarm through space. We confine the movements to a one-dimensional (1D) ring and consider distributed (nonidentical) couplings; the combination of these two effects captures an aspect of the more realistic two-dimensional swarmalator model. We discover several collective states which we describe analytically. These states imitate the behavior of vinegar eels, catalytic microswimmers, and other swarmalators which move on quasi-1D rings.

Theoretically and experimentally, we study electroviscous phenomena resulting from charge-flow coupling in a nanoscale capillary. Our theoretical approach relies on Poisson-Boltzmann mean-field theory and on coupled linear relations for charge and hydrodynamic flows, including electro-osmosis and charge advection. With respect to the unperturbed Poiseuille flow, we define an electroviscous coupling parameter $\xi$, which turns out to be maximum where the film height $h_0$ is comparable to the Debye screening length $\lambda$. We also present dynamic atomic force microscopy data for the viscoelastic response of a confined water film in sphere-plane geometry; our theory provides a quantitative description for the electroviscous drag coefficient and the electrostatic repulsion as a function of the film height, with the surface charge density as the only free parameter. Charge regulation sets in at even smaller distances.

In this paper, direct numerical simulations have been performed to explore the equivalence of different thermal boundary conditions in compressible turbulent channel flows at fixed $\mathrm{Re}=6000,\mathrm{Ma}=1.5$. Three canonical types of thermal boundary conditions will be investigated at almost equivalent setups, including the first boundary condition with fixed wall temperature $T_w$ (constant Dirichlet boundary condition), the second boundary condition with fixed wall heat-flux $q_w$ (constant Neumann boundary condition), and the third boundary condition (Robin boundary condition). The turbulent statistics of the temperature and velocity fields, including mean profiles, root-mean-square values, second-order statistics, and normalized probability density functions, temperature stripes near the wall and the budget of internal energy have been analyzed in detail to clarify the differences caused by the different thermal boundary conditions. The results show that the three thermal boundary conditions have almost negligible effect on the velocity field, whereas some discernible deviations can be observed for the temperature field in the near-wall region with $y^{+}\lesssim 30$. Furthermore, the statistics from the second and third thermal boundary conditions are very close, enabling the usage of the second boundary condition to mimic the more complex third boundary conditions.

Goncharov's [Phys. Rev. Lett. 88, 134502 (2002)] nonlinear model of a single-mode Rayleigh-Taylor instability (RTI) is investigated for a partially ionized plasma in a predominantly neutral background. Terminal bubble and spike velocities are derived from the nonlinear equations in the case where the RTI dynamics is dominated by collisions between neutrals and ions. Direct numerical simulations are used to justify the use of Goncharov's model in this regime and observe its limitations.

We study the explosive percolation with $k$-mer random sequential adsorption (RSA) process. We consider both the Achlioptas process (AP) and the inverse Achlioptas process (IAP), in which giant cluster formation is prohibited and accelerated, respectively. By employing finite-size scaling analysis, we confirm that the percolation transitions are continuous, and thus we calculate the percolation threshold and critical exponents. This allows us to determine the universality class of the $k$-mer explosive percolation transition. Interestingly, the numerical simulation suggests that the universality class of the explosive percolation transition with the AP alters when the $k$-mer size changes. In contrast, the universality class of the transition with the IAP is independent of $k$, but it differs from that of the RSA without the IAP.

We introduce methodologies for highly scalable quantum Monte Carlo simulations of electron-phonon models, and we report benchmark results for the Holstein model on the square lattice. The determinant quantum Monte Carlo (DQMC) method is a widely used tool for simulating simple electron-phonon models at finite temperatures, but it incurs a computational cost that scales cubically with system size. Alternatively, near-linear scaling with system size can be achieved with the hybrid Monte Carlo (HMC) method and an integral representation of the Fermion determinant. Here, we introduce a collection of methodologies that make such simulations even faster. To combat “stiffness” arising from the bosonic action, we review how Fourier acceleration can be combined with time-step splitting. To overcome phonon sampling barriers associated with strongly bound bipolaron formation, we design global Monte Carlo updates that approximately respect particle-hole symmetry. To accelerate the iterative linear solver, we introduce a preconditioner that becomes exact in the adiabatic limit of infinite atomic mass. Finally, we demonstrate how stochastic measurements can be accelerated using fast Fourier transforms. These methods are all complementary and, combined, may produce multiple orders of magnitude speedup, depending on model details.

The conformational and dynamical properties of isolated semiflexible active polar ring polymers are investigated analytically. A ring is modeled as a continuous Gaussian polymer exposed to tangential active forces. The analytical solution of the linear non-Hermitian equation of motion in terms of an eigenfunction expansion shows that ring conformations are independent of activity. In contrast, activity strongly affects the internal ring dynamics and yields characteristic time regimes, which are absent in passive rings. On intermediate timescales, flexible rings show an activity-enhanced diffusive regime, while semiflexible rings exhibit ballistic motion. Moreover, a second active time regime emerges on longer timescales, where rings display a snake-like motion, which is reminiscent to a tank-treading rotational dynamics in shear flow, dominated by the mode with the longest relaxation time.

We study statistics of data ranking, focusing on the recently discovered distribution-invariant discrete eigenvalue spectrum for an independent and identically distributed (IID) process. We employ a variant of a cumulative distribution function in rank and time that maps the sampling variability for an IID process onto a set of random walks. This mapping admits confidence bounds on whether the residual (data with signal removed) arises solely from IID sampling variability. Any deviations judged significant are regarded as signals, whether deterministic, chaotic, or random. Unlike our recent work on extracting unknown signals in arbitrary noise, here we focus on aspects that are easily combined with any other methods of signal extraction. The ubiquitous case of a single trace receives particular attention. The approach is illustrated on dark current and gamma-ray arrival datasets where we examine the residual for consistency with the expected sampling variability of IID noise.

Using phase-ordering kinetics and of renormalization group theories, we derive analytically the relaxation times of the long wavelength fluctuations of a phase-separated domain boundary in the vicinity of (and below) the critical temperature in the planar Ising universality class. For a conserved order parameter, the relaxation time grows like ${\mathrm{\Lambda }}^3$ at wavelength $\mathrm{\Lambda }$ and can be expressed in terms of parameters relevant at the microscopic scale: lattice spacing, bulk diffusion coefficient of the minority phase, and temperature. These results are supported by numerical simulations of 2D Ising models, enabling in addition calculating the nonuniversal numerical prefactor. We discuss the applications of these findings to the determination of the real timescale associated with elementary Monte Carlo moves from the measurement of long wavelength relaxation times on experimental systems or molecular dynamics simulations.

The dynamics of an interfacial flow that is initially Rayleigh-Taylor unstable but becomes statically stable for some intermediate period due to the reversal of the externally imposed acceleration field is studied. We discuss scenarios that consider both single and double-acceleration reversals. The accel-decel (AD) case consists of a single reversal imposed at an instant after the constant acceleration instability has entered a self-similar regime. The layer of mixed fluid ceases to grow upon acceleration reversal, and the dominant mechanics are due to internal wave oscillations. Variation of mass flux and the Reynolds stress anisotropy is observed due to the action of the internal waves. A second reversal of the AD case that is termed as accel-decel-accel, ADA is then explored; the response of the mixing layer is shown to depend strongly on the duration and the periodicity of the Reynolds stress anisotropy of the mixing layer during the deceleration period. We explore the effect of this variable deceleration period after the second acceleration reversal where the flow once again becomes Rayleigh-Taylor unstable based on metrics that include the integral mixing-layer width, bubble and spike amplitudes, mass flux, Reynolds stress anisotropy tensor, and the molecular mixing parameter.