This work focuses on microscale transport behavior of binary mixtures in the context of ${\mathrm{CO}}_2$ and ${\mathrm{H}}_2$ storage in shale gas formations. To this end, a multiple relaxation time lattice Boltzmann (LB) model is implemented to simulate microscale transport behavior. In the LB model, a combined boundary scheme of bounce-back and specular reflection is used to model fluid-wall interactions and slippage effect, and a regularization algorithm is used to obtain accurate solutions for complex geometries. The binary LB model is validated using the Kramer problem and pseudobinary flows in slit and irregular nanopores. Subsequently, pressure-driven flows of ${\mathrm{CH}}_4\text{−}{\mathrm{CO}}_2$ and ${\mathrm{CH}}_4\text{−}{\mathrm{H}}_2$ binary mixtures are investigated in slit nanopores and irregular porous media under various pressure and composition conditions. The impact of simulation conditions on fluid velocity, mass flux, apparent permeability, Péclet number, and pressure drop is comprehensively examined. The dynamics of ${\mathrm{CO}}_2$ and ${\mathrm{H}}_2$ displacing ${\mathrm{CH}}_4$ in nanoconfined spaces are studied. The results point to different displacement mechanisms between ${\mathrm{CO}}_2$ and ${\mathrm{H}}_2$ due to their different molecular properties. In summary, this work provides deep insights relevant to subsurface storage of ${\mathrm{CO}}_2$ and ${\mathrm{H}}_2$ in shale gas reservoirs.

This paper presents a study of rare noise-induced transitions from stable laminar flow to transitional turbulence in plane Couette flow, which we will term buildup. We wish to study forced paths that go all the way from laminar to turbulent flow and to focus the investigation on whether these paths share the properties of noise-induced transitions in simpler systems. The forcing noise has a red spectrum without any component in the natural, large-scale, linear receptivity range of the flow. As we decreased the forcing energy injection rate, the transitions became rare. The rare paths from laminar to turbulent flow are computed using adaptive multilevel splitting, a rare event simulation method, and are validated against direct numerical simulations at moderately small energy injection rates. On the computed trajectories, the flow manages to nonlinearly redistribute energy from the small forced scales to the unforced large scales so that the reactive trajectories display forced streamwise velocity tubes at the natural scale of velocity streaks. As the trajectory proceeds, these tubes gradually grow in amplitude until they cross the separatrix between laminar and turbulent flow. Streamwise vortices manifest themselves only after velocity tubes have reached near-turbulent amplitude, displaying a two-stage process reminiscent of the “backward” path from turbulence to laminar flow. We checked that these were not time-reversed turbulence collapse paths. As the domain size is increased from a minimal flow unit (MFU) type flow at $L_x\times L_z=6\times 4$ (in half gap units) to a large domain $L_x\times L_z=36\times 24$, spatial localization and then extension of the generated coherent streaks and vortices in the spanwise direction is observed in the reactive paths. The paths systematically computed in MFU display many of the characteristics of instantons that often structure noise-induced transitions: such as concentration of trajectories, exponentially increasing waiting times before transition, and Gumbel distribution of trajectory durations. However, bisections started from successive states on the reactive trajectories indicate that for all sizes and energy injection rates investigated, the trajectory lacks two key ingredients of instantons. First, they do not visit the neighborhood of the nearest saddle point and do not display the natural relaxation path from that saddle to transitional wall turbulence. This discrepancy is observed for all system sizes. Second, the reactive paths do not concentrate more and more around the same trajectory as energy injection rate is decreased, but instead gradually move in phase space. They might reconnect with instantons at very small energy injection rate and exceedingly long waiting times. They would explain why classical instanton calculations have proved to be tremendously difficult in wall flows.

Comprehensive measurements of the x-ray emissions in the peripheral direction of extended high-voltage discharges in 55-cm open air gaps are performed at voltages up to 1 MV. The data on the spatial, temporal, and spectral characteristics of x rays are obtained. We demonstrate that the emission of photons with energies within 5–17 keV predominates throughout the entire discharge gap. The generation of photons with energies of hundreds of keV (but not higher than 300 keV) is found to be characteristic of the cathode, near-cathode, anode, and near-anode regions of the discharge, whereas approximately in the midgap low-energy photons are primarily observed. By using nanosecond imaging, it is discovered that the x-ray generation can start almost synchronously throughout the entire discharge gap, tens of nanoseconds after the first interactions of the counterstreamers with the cathode. The very first x rays are detected during the discharge development stage, when a complex net of numerous plasma structures already formed in the gap, and the discharge prebreakdown current and voltage are of 500 A and 1 MV. In a single x-ray flash, high-energy photons are found to emerge with a 20–60 ns delay relative to the onset of the low-energy photon emission. The observed phenomena and possible x-ray generation mechanisms are analyzed.

In this research, $\sim 0.14$-micron-thick aluminum tamped by plastic is heated up to $\sim 110\mathrm{eV}$ by the x-ray pulse from the Z-pinch-driven dynamic Hohlraum on an 8-MA machine in China. After an $\sim 6-\mathrm{ns}$ heating stage, higher-energy xrays from an $\sim 2-\mathrm{ns}$- long backlight pulse pass through the hot aluminum. The transmission is estimated by comparing the radiation passing through the aluminum sample in one shot with the radiation through only the plastic in another shot, with the x-ray spectra obtained using an elliptically bent concave crystal spectrometer. The transmission reveals features corresponding to x-ray absorption in Li-like and a series of He-like aluminum ions that provide values for its temperature and density. One method involves using a tabulated opacity database, while the other involves analyzing the line shapes and line ratios of the absorption features. The challenges in these measurements are discussed both theoretically and experimentally.

A nonstochastic quantum engine is one that operates in a cycle of transformations in which no sources of stochasticity, such as thermal baths and projective measurements, are present and, therefore, no entropy is generated in the driven system. Defining work and heat as the energy corresponding to different types of transformations between pure states, we arrive at an expression similar to the first law of thermodynamics and prove a version of the Kelvin-Planck statement for the second law of thermodynamics. Essentially, the first law can be obtained thanks to the normalization condition of a quantum state and the second law can be obtained thanks to the orthogonalization condition between energy eigenstates. For nonstochastic engines that operate between two given energy gaps, we prove a version of Carnot's theorem. Regarding operationalization, we present a protocol that leads the system through a cycle in which heat exchange occurs by performing two quantum quenches separated by a precise time interval and involving an energy-level anticrossing. Furthermore, with this protocol it is possible to make the engine's efficiency as close to 1 as one wants; however, efficiency equal to 1 is a case prohibited by the version of the Kelvin-Planck statement that we proved. Finally, we illustrate these results in an exactly solvable single-qubit model.

We derive exact results for the critical Casimir force (CCF) within the Nagle-Kardar model with periodic boundary conditions (PBCs). The model represents a one-dimensional Ising chain with long-range equivalent-neighbor ferromagnetic interactions of strength $J_l/N>0$ superimposed on the nearest-neighbor interactions of strength $J_s$, which could be either ferromagnetic $(J_s>0)$ or antiferromagnetic $(J_s<0)$. In the infinite system limit, the model exhibits in the plane $(K_s=\beta J_s,K_l=\beta J_l)$ a critical line $2K_l=exp(-2K_s),K_s>-ln3/4$, which ends at a tricritical point $(K_l=\sqrt{3}/2,K_s=-ln3/4)$. The critical Casimir amplitudes are ${\mathrm{\Delta }}_{\mathrm{Cas}}^{\left(\mathrm{cr}\right)}=1/4$ at the critical line, and ${\mathrm{\Delta }}_{\mathrm{Cas}}^{\left(\mathrm{tr}\right)}=1/3$ at the tricritical point. Quite unexpectedly, with the imposed PBCs, the CCF exhibits very unusual behavior as a function of temperature and magnetic field. It is repulsive near the critical line and tricritical point, decaying rapidly with separation from those two singular regimes, and it becomes attractive when the maximum amplitude of the attraction exceeds the maximum amplitude of repulsion. This represents a violation of the widely accepted “boundary condition rule,” which holds that the CCF is attractive for equivalent BCs and repulsive for conflicting BCs independently of the actual bulk universality class of the phase transition under investigation.

We consider a run-and-tumble particle whose speed and tumbling rate are space dependent on an infinite line. Unlike most of the previous work on such models, here we make the physical assumption that at large distances, these rates saturate to a constant. For our choice of rate functions, we show that a stationary state exists, and the exact steady-state distribution decays exponentially or faster and can be unimodal or bimodal. The effect of boundedness of rates is seen in the mean-squared displacement of the particle that displays qualitative features different from those observed in the previous studies where it approaches the stationary-state value monotonically in time; in contrast, here we find that if the initial position of the particle is sufficiently far from the origin, then the variance in its position either varies nonmonotonically or plateaus before reaching the stationary state. These results are captured quantitatively by the exact solution of the Green's function when the particle has uniform speed but the tumbling rates change as a step function in space; the insights provided by this limiting case are found to be consistent with the numerical results for the general model.

We study negative large deviations of the long-time empirical front velocity of the center of mass of the one-sided $N$-BBM ($N$-particle branching Brownian motion) system in one dimension. Employing the macroscopic fluctuation theory, we study the probability that $c$ is smaller than the limiting front velocity $c_0$, predicted by the deterministic theory, or even becomes negative. To this end, we determine the optimal path of the system, conditioned on the specified $c$. We show that for $c_0-c\ll c_0$ the properly defined rate function $s\left(c\right)$, coincides, up to a nonuniversal numerical factor, with the universal rate functions for front models belonging to the Fisher-Kolmogorov-Petrovsky-Piscounov universality class. For sufficiently large negative values of $c$, $s\left(c\right)$ approaches a simple bound, obtained under the assumption that the branching is completely suppressed during the whole time. Remarkably, for all $c\le c_{*}$, where $c_{*}<0$ is a critical value that we find numerically, the rate function $s\left(c\right)$ is equal to the simple bound. At the critical point $c=c_{*}$ the character of the optimal path changes, and the rate function exhibits a dynamical phase transition of second order.

There is a wide range of mathematical models that describe populations of large numbers of neurons. In this article, we focus on nonlinear noisy leaky integrate-and-fire (NNLIF) models that describe neuronal activity at the level of the membrane potential. We introduce a sequence of states, which we call pseudoequilibria, and give evidence of their defining role in the behavior of the NNLIF system when a significant synaptic delay is considered. The advantage is that these states are determined solely by the system's parameters and are derived from a sequence of firing rates that result from solving a recurrence equation. We propose a strategy to show convergence to an equilibrium for a weakly connected system with large transmission delay, based on following the sequence of pseudoequilibria. Unlike direct entropy dissipation methods, this technique allows us to see how a large delay favors convergence. We present a detailed numerical study to support our results. This study helps us understand, among other phenomena, the appearance of periodic solutions in strongly inhibitory networks.

The modified model with repulsive filling (${\mathrm{CSA}}_r$) for adsorption of monomers on a square lattice was studied. The deposition probability at empty sites $P$ was regulated using the power law $P=1-{(z/4)}^{\alpha }$, where $z$ is the number of NN sites filled by previously deposited particles and $\alpha (>0)$ is a parameter. The interval of $\alpha ={10}^{-3}-{10}^3$ was investigated in detail. The mean coordination number $\langle z\rangle$ at different values of $\alpha$ were analyzed. At relatively small $\alpha (<0.01)$ the steplike coverage $\phi \left(t\right)$ time dependencies were observed. The behavior was explained by accounting for the initial formation of the deposits with the checkerboard structures, followed by the filling of the channels between these structures and the formation of more compact clusters. Detailed analysis of the behavior of the total coverage ${\phi }_J\left(\alpha \right)$ and mean coordination number $\langle z_J\left(\alpha \right)\rangle$ in the jamming state was performed. The different percolation characteristics were also evaluated. At the percolation point the coverage function ${\phi }_p\left(\alpha \right)$ revealed rather unexpected behavior with maximum at $\alpha \approx 0.2$.

This paper analyzes the influence of laterally enforced solutal gradients on the steady and bifurcated periodic dynamics in binary fluids contained in horizontally heated slots, taking into account the Soret and Dufour effects. Numerical Newton-Krylov continuation techniques to follow the primary and secondary branches of steady solutions and periodic orbits are applied. The stability of all these branches is also analyzed. A great variety of stable steady and periodic states is found, depending on the ratio of the thermal and solutal gradients. The proximity to parameters that balance the buoyancy forces delays the onset of center-symmetric oscillations to very large values of the thermal Rayleigh number, while large solutal gradients tend to restabilize the steady flows after the onset of center-symmetric oscillations, and to give rise to spatiotemporal symmetric waves of broken center symmetry at larger thermal Rayleigh number. The work done by the thermal buoyancy force is essential for the restabilization of the steady states and the change of the ulterior dynamics. It is also shown that the transition to temporal chaos depends strongly on the absence or intensity of the solutal gradients.

For a system of $N\gg 1$ spinless quantum particles, the projection operator is introduced, which, surprisingly, exactly transforms the inhomogeneous (with irrelevant initial correlations term) Nakajima-Zwanzig generalized master equation (GME) into completely closed (homogeneous) GME with initial correlations included into the kernel governing its evolution. The obtained equation is equivalent to the closed linear evolution equation for an $S$-particle ($S<N$) statistical operator, which holds for any initial condition and all timescales. Thus, the introduced projector implements the idea of the subdynamics in the subspace of $S$-particle complex. It also allows for precise treatment of the initial correlations on an equal footing with collisions. No “molecular chaos” -type approximation is used. The obtained homogeneous equation is further specialized in the linear approximation in the particles density $n$ for the kernel and considered in detail for the one-particle statistical operator. The influence of both the quantum correlations, caused by the particles' statistics, and initial correlations, related to the interparticle interaction, is considered in detail and at different timescales. Connection of the linear equation for a one-particle statistical operator to the nonlinear quantum Boltzmann equation is shown.

Many natural and human-made complex systems feature group interactions that adapt over time in response to their dynamic states. However, most of the existing adaptive network models fall short of capturing these group dynamics, as they focus solely on pairwise interactions. In this study, we employ adaptive higher-order networks to describe these systems by proposing a general framework by incorporating both adaptivity and group interactions. We demonstrate that global synchronization can exist in those complex structures and we provide the necessary conditions for the emergence of a stable synchronous state. We first study the setting in which both pairwise and higher-order interactions are allowed, but only the former adapt in time. We then extend this framework by including higher-order adaptive interactions. In both analyzed settings, we show that the necessary condition is strongly related to the master stability equation, allowing to separate the dynamical and structural properties. We illustrate our theoretical findings through the relevant examples involving adaptive higher-order networks of coupled generalized Kuramoto oscillators with phase lag, coupled with an all-to-all and a nonlocal ring-like structure. We also show that the interplay of group interactions and adaptive connectivity results in the formation of stability regions that can induce transitions between synchronization and desynchronization. Our findings also reveal that the introduction of higher-order adaptation significantly alters the synchronization stability compared to the case with constant higher-order interactions.

Singular-value statistics (SVS) has been recently presented as a random matrix theory tool able to properly characterize non-Hermitian random matrix ensembles [PRX Quantum 4, 040312 (2023)]. Here, we perform a numerical study of the SVS of the non-Hermitian adjacency matrices $\mathbf{A}$ of directed random graphs, where $\mathbf{A}$ are members of diluted real Ginibre ensembles. We consider two models of directed random graphs: Erdös-Rényi graphs and random geometric graphs. Specifically, we focus on the singular-value-spacing ratio $r$ and the minimum singular value ${\lambda }_{\min }$. We show that $\langle r\rangle$ (where $\langle ·\rangle$ represents ensemble average) can effectively characterize the crossover between mostly isolated vertices to almost complete graphs, while the probability density function of ${\lambda }_{\min }$ can clearly distinguish between different graph models.

Femtosecond laser pulse propagation in a relativistic self-trapping (RST) regime in a near-critical density plasma makes it possible to maximize the total charge of the accelerating electrons and laser-to-electrons conversion rate, that can be used to provide a large amount of the terahertz range coherent transition radiation. The three-dimensional particle-in-cell simulations demonstrate how such transition radiation generates when electrons escape into vacuum either from the low-density target itself, or after passing through a thin foil located at the target end. The advantage of the RST regime for the generation of terahertz pulses is clearly demonstrated as compared to laser irradiation of such a standard target as a foil with preplasma on its front side. The simulation performed has shown that for the optimized laser-target matching a 2-J femtosecond laser pulse is able to produce quasiunipolar terahertz pulses with energy exceeding 100 mJ.

We propose an upwind hybrid discontinuous Galerkin (HDG) method for the first-order hyperbolic linear Boltzmann transport equation, featuring a flexible expansion suitable for multiscale scenarios. Within the HDG scheme, primal variables and numerical traces are introduced within and along faces of elements, respectively, interconnected through projection matrices. Given the variables in two stages, the HDG method offers significant flexibility in the selection of spatial orders. The global matrix system in this framework is exclusively constructed from numerical traces, thereby effectively reducing the degrees of freedom (DoFs). Additionally, the matrix system in each discrete direction features a blocked-lower-triangular stencil, enhancing the efficiency of solving hyperbolic equations through an upwind sweep sequence. Based on the proposed method, we perform an asymptotic analysis of the upwind-HDG method in the thick diffusion limit. The result reveals that the correct convergence of the upwind-HDG is closely associated with the properties of the response matrix $\mathcal{L}$. A series of numerical experiments, including comparisons with the even-parity HDG, confirms the accuracy and stability of the upwind-HDG method in managing thick diffusive regimes and multiscale heterogeneous problems.

The flocking of self-propelled particles in heterogeneous environments is relevant to both natural and artificial systems. The Vicsek model is a canonical choice to investigate such systems due to the minimal number of parameters required to define flocking. Prior research on the Vicsek model has investigated the effects of interaction rules, particle speed, and obstacle packing on the flocking behavior, but the effect of interaction radius remains an open question. Unlike obstacle-free domains, the locality of interactions not only affects how quickly the system can become polarized, but also how well the flocks can align or realign after colliding with obstacles. In this letter, we delve into this subtle relationship that exists in the scale of the perception of Vicsek particles in the presence of obstacles. We demonstrate that the presence of obstacles impacts group density, which provides the basis to identify distinct phases for collective behavior. This leads to the counter-intuitive result that obstacles, while generally confounding for macroscopic order, may enable global order even as noise in the system increases.

For self-propelled particles in a corrugated potential landscape, we describe a discontinuous change of the classical depinning transition and a host of unique behaviors sensitive to the persistence of the propulsion direction. Exact and semianalytic results for active Brownian particles corroborate a creep regime with a superexponentially suppressed drift velocity upon lowering the force towards the threshold value. This unusual nonlinear response emerges from the competition of two critical scaling laws with exponents of 1/2 for rapidly reorienting particles and $d/2$ for particles with a persistent orientation; the latter case depends on the dimensionality $d$ of rotational motion and also includes run-and-tumble particles. Additionally, different giant diffusion phenomena occur in the two regimes. Our findings extend to random dynamics with bounded noise near a saddle-node bifurcation and have potential applications in various nonequilibrium problems, including arrested active matter and cell migration.

We study the effect of parity deformation of the environmental field modes on the wireless charging performance of a qubit-based open quantum battery (QB) consisting of a qubit battery and a qubit charger, where there is no direct interaction between the qubits and the battery is charged by the mediation of the environment. The parity deformation introduces field nonlinearities, as well as qubit-environment intensity-dependent couplings. We analyze in detail charging characteristics—including the charging energy, efficiency, and ergotropy in both the weak and strong coupling regimes—and show that the memory effects of a mediator environment are critical in enhancing the charging performance. In the strong coupling regime, parity deformation of the environment fields can further trigger non-Markovian quantum memory of the charger-battery system, thereby enhancing the QB charging performance based on the non-Markovianity. Surprisingly, if the charging process is Markovian in the absence of the parity deformation, parity deformation is able to induce memory effects in the charger-battery dynamics and transforms the Markovian process to the non-Markovian one. This work highlights that proper engineering of the coupling to an environment can introduce an extra quantum memory source to the underlying charging process in favor of environment-mediated charging of the battery.