The transition from a nematic to an isotropic state in a self-closing spherical liquid crystal shell with tangential alignment is a stimulating phenomenon to investigate, as the topology dictates that the shell exhibits local isotropic points at all temperatures in the nematic phase range, in the form of topological defects. The defects may thus be expected to act as nucleation points for the phase transition upon heating beyond the bulk nematic stability range. Here we study this peculiar transition, theoretically and experimentally, for shells with two different configurations of four $+$1/2 defects, finding that the defects act as the primary nucleation points if they are co-localized in each other's vicinity. If the defects are instead spread out across the shell, they again act as nucleation points, albeit not necessarily the primary ones. Beyond adding to our understanding of how the orientational order-disorder transition can take place in the shell geometry, our results have practical relevance for, e.g., the use of curved liquid crystals in sensing applications or for liquid crystal elastomer actuators in shell shape, undergoing a shape change as a result of the nematic-isotropic transition.

A Laval nozzle can accelerate expanding gas above supersonic velocities, while cooling the gas in the process. This work investigates this process for microscopic Laval nozzles by means of nonequilibrium molecular dynamics simulations of stationary flow, using grand-canonical Monte Carlo particle reservoirs. We study the steady-state expansion of a simple fluid, a monoatomic gas interacting via a Lennard-Jones potential, through an idealized nozzle with atomically smooth walls. We obtain the thermodynamic state variables pressure, density, and temperature but also the Knudsen number, speed of sound, velocity, and the corresponding Mach number of the expanding gas for nozzles of different sizes. We find that the temperature is well defined in the sense that the each velocity components of the particles obey the Maxwell-Boltzmann distribution, but it is anisotropic, especially for small nozzles. The velocity autocorrelation function reveals a tendency towards condensation of the cooled supersonic gas, although the nozzles are too small for the formation of clusters. Overall we find that microscopic nozzles act qualitatively like macroscopic nozzles in that the particles are accelerated to supersonic speeds while their thermal motion relative to the stationary flow is cooled. We find that, like macroscopic Laval nozzles, microscopic nozzles also exhibit a sonic horizon, which is well defined on a microscopic scale. The sonic horizon is positioned only slightly further downstream compared to isentropic expansion through macroscopic nozzles, where it is situated in the most narrow part. We analyze the sonic horizon by studying space-time density correlations, i.e., how thermal fluctuations at two positions of the gas density are correlated in time and find that after the sonic horizon there are indeed no upstream correlations on a microscopic scale.

Mixing of two fluids can lead to the formation of a precipitate. If one of the fluids is injected into a confined space filled with the other, then a created precipitate disrupts the flow locally and forms complex spatiotemporal patterns. The relevance of controlling these patterns has been highlighted in the engineering and geological contexts. Here, we show that such injection patterns can be controlled consistently by injection rate and obstacles. Our experimental results revealed filament patterns for high-injection and low-reaction rates, and the injection rate can control the number of active filaments. Furthermore, appropriately spaced obstacles in the cells can straighten the motion of the advancing tip of the filament. A mathematical model based on a moving boundary adopting the effect of precipitation reproduced the phase diagram and the straight motion of filaments in structured cells. Our study clarifies the impact of the nonlinear permeability response on the precipitate density and that of the obstacles in the surrounding medium on the motion of the injected fluid with precipitation.

This study overviews and extends a recently developed stochastic finite-temperature Kohn-Sham density functional theory to study warm dense matter using Langevin dynamics, specifically under periodic boundary conditions. The method's algorithmic complexity exhibits nearly linear scaling with system size and is inversely proportional to the temperature. Additionally, a linear-scaling stochastic approach is introduced to assess the Kubo-Greenwood conductivity, demonstrating exceptional stability for dc conductivity. Utilizing the developed tools, we investigate the equation of state, radial distribution, and electronic conductivity of hydrogen at a temperature of 30 000 K. As for the radial distribution functions, we reveal a transition of hydrogen from gaslike to liquidlike behavior as its density exceeds $4{\text{g/cm}}^3$. As for the electronic conductivity as a function of the density, we identified a remarkable isosbestic point at frequencies around 7 eV, which may be an additional signature of a gas-liquid transition in hydrogen at 30 000 K.

We investigate quantum phase transitions in the transverse field Ising chain with algebraically decaying long-range (LR) antiferromagnetic interactions using the variational Monte Carlo method with the restricted Boltzmann machine employed as a trial wave function ansatz. First, we measure the critical exponents and the central charge through the finite-size scaling analysis, verifying the contrasting observations in the previous tensor network studies. The correlation function exponent and the central charge deviate from the short-range (SR) Ising values at a small decay exponent ${\alpha }_{\mathrm{LR}}$, while the other critical exponents examined are very close to the SR Ising exponents regardless of ${\alpha }_{\mathrm{LR}}$ examined. However, in the further test of the critical Binder ratio, we find that the universal ratio of the SR limit does not hold for ${\alpha }_{\mathrm{LR}}<2$, implying a deviation in the criticality. On the other hand, we find evidence of the conformal invariance breakdown in the conformal field theory (CFT) test of the correlation function. The deviation from the CFT description becomes more pronounced as ${\alpha }_{\mathrm{LR}}$ decreases, although a precise breakdown threshold is yet to be determined.

We consider a Klein-Gordon chain that is periodically driven at one end and has dissipation at one or both boundaries. An interesting numerical observation in a recent study [Prem et al., Phys. Rev. B 107, 104304 (2023)] was that for driving frequency in the phonon band, there is a range of values of the driving amplitude $F_d\in (F_1,F_2)$ over which the energy current remains constant. In this range the system exhibits a traveling wave solution termed a “resonant nonlinear wave” (RNW). It was noted that the RNW mode occurs over a range $(F_1,F_2)$ and shrinks with increasing system size, $N$. Remarkably, we find that the RNW mode is in fact a stable solution even for $F_d>F_2$, and that in this regime there exist two attractors, both with finite basins of attraction. We improve the perturbative treatment for the RNW mode, presented in the earlier work, by including the contributions of third harmonics. We also consider the effect of thermal noise at the boundaries and find that the RNW mode is stable for small temperatures. Corresponding to the two attractors for large $F_d$ at zero temperature, the system can now be in two nonequilibrium steady states. Finally, we present results for a different driving protocol [Komorowski et al., Commun. Math. Phys. 400, 2181 (2023)] where $F_d$ is taken to scale with system size as $N^{-1/2}$ and dissipation is only at the nondriven end. We find that the steady state for this case can be characterized by Fourier's law. We point out interesting differences that occur because of our dynamics being nonlinear and Hamiltonian. Our results suggest the intriguing possibility of observing the high-current-carrying RNW phase in experiments by careful preparation of initial conditions.

Generic low-dimensional Hamiltonian systems feature a structured, mixed classical phase space. The traditional Percival classification of quantum spectra into regular states supported by quasi-integrable regions and irregular states supported by quasichaotic regions turns out to be insufficient to capture the richness of the Hilbert space. Berry's conjecture and the eigenstate thermalization hypothesis are not applicable and quantum effects such as tunneling, scarring, and localization do not obey the standard paradigms. We demonstrate these statements for a prototype Bose-Hubbard model. We highlight the hybridization of chaotic and regular regions from opposing perspectives of ergodicity and localization.

We study random graphs densifying by adding edges. In each step, two vertices are randomly chosen, and an edge between these vertices is created if the vertices belong to trees. An edge is added with probability $p$ if only one vertex belongs to a tree and an attempt fails otherwise. Simple random graphs generated by this procedure contain only trees and unicycles. In the thermodynamic limit, the fraction of vertices in unicycles exhibits a phase transition resembling a percolation transition in classical random graphs. In contrast to classical random graphs, where a giant component born at the transition point eventually engulfs all finite components and densifies forever, the evolution of simple random graphs freezes when trees disappear. We quantify simple random graphs in the supercritical phase and the properties of the frozen state.

To study the kinetics of phase separation in active matter systems, we consider models that impose a Vicsek-type self-propulsion rule on otherwise passive particles interacting via the Lennard-Jones potential. Two types of kinetics are of interest: one conserves the total momentum of all the constituents and the other does not. We carry out molecular dynamics simulations to obtain results on structural, growth, and aging properties. Results from our studies, with various finite boxes, show that there exist scalings with respect to the system sizes, in both the latter quantities, as in the standard passive cases. We have exploited this scaling picture to accurately estimate the corresponding exponents, in the thermodynamically large system size limit, for power-law time dependences. It is shown that certain analytical functions describe the behavior of these quantities quite accurately, including the finite-size limits. Our results demonstrate that even though the conservation of velocity has at best weak effects on the dynamics of evolution in the thermodynamic limit, the finite-size behavior is strongly influenced by the presence (or the absence) of it.

We revisit the studies of gravity-driven viscous falling films with and without imposed shear stress to provide new perspectives on phase speed and the critical Reynolds number for surface instability. We use the traditional long-wave expansion technique implemented for investigating the linear stability analysis [C. S. Yih, Phys. Fluids 6, 321 (1963)]. The principal purpose is to create a unified relationship between the leading-order phase speed and the critical Reynolds number that will hold for falling films on impermeable substrates with or without shear stress acting at the liquid film surface. The analytical result demonstrates that the critical Reynolds number for the onset of surface instability is $[5/\left(2c_0\right)]cot\theta$, where $c_0$ is the leading-order phase speed of the surface mode and $\theta$ is the angle of inclination with the horizontal. Clearly, the critical Reynolds number of the surface mode is explicitly dependent on the leading-order phase speed. Furthermore, we reveal that the basic parallel flow with or without imposed shear stress is linearly unstable to infinitesimal disturbances if the modified Reynolds number, ${\mathrm{Re}}_M=(\mathrm{Re}{c}_0/cot\theta )[\mathrm{Re}\mathrm{is}\mathrm{the}\mathrm{Reynolds}\mathrm{number},\mathrm{and}\theta \ne \pi /2]$, is greater than its critical value of $5/2$, which is independent of the shear stress applied at the film surface. In addition, it is demonstrated that ${\mathrm{Re}}_M$ controls the surface instability in the long-wave regime for both shear-imposed and non-shear-imposed film flows.

The temporal evolution of weak shocks in radiative media is theoretically investigated in this work. The structure of radiative shocks has traditionally been studied in a stationary framework. Their systematic classification is complex because layers of optically thick and thin regions alternate to form a radiatively driven precursor and a temperature-relaxation layer, between which the hydrodynamic shock is embedded. In this work we analyze the formation of weak shocks when two radiative plasmas with different pressures are put in contact. Applying a reductive perturbative method yields a Burgers-type equation that governs the temporal evolution of the perturbed variables including the radiation field. The conditions upon which optically thick and thin solutions exist have been derived and expressed as a function of the shock strength and Boltzmann number. Below a certain Boltzmann number threshold, weak shocks always become optically thick asymptotically in time, while thin solutions appear as transitory structures. The existence of an optically thin regime is related to the presence of an overdense layer in the compressed material. Scaling laws for the characteristic formation time and shock width are provided for each regime. The theoretical analysis is supported by FLASH simulations, and a comprehensive test case has been designed to benchmark radiative hydrodynamic codes.

We formulated two phase-field models to compute interfacial compositions, characterized by their high computational accuracy and efficiency. The inaugural model utilizes convergence calculations to fulfill the equal diffusion potential condition, while the subsequent model obviates the need for such calculations. Despite this, its computational outcomes strongly agree with those of the preceding model. Notably, in these models, the alteration in composition attributable to interfacial curvatures aligns with the Gibbs-Thomson effect within the equilibrium system. In this study, the solidification processes of Ni-Al-Cr and Ag-Cu-Sn alloys serve as case studies to underscore the computational precision and swiftness of the proposed models.

Water exhibits rich ice phases depending upon its respective formation conditions, and in particular, the two-dimensional ice with nonhexagonal symmetry adsorbed on solids relates to the exceptional arrangement of water molecules. Despite extensive reporting of two-dimensional ice on various solid surfaces, the geometry and thermodynamics of ice formation from an aqueous salt solution are still unknown. In this Letter, we show the formation of single- and two-phase mixed two-dimensional rhombic ice from aqueous salt solutions with different concentrations under strong compressed confinement of graphene at ambient temperature by using classical molecular dynamics simulations and first-principles calculations. The two rhombic ice phases exhibit identical geometry and thermodynamic properties, but different projections of the oxygen atoms against solid surface symmetry, where they relate to the stable and metastable arrangements of water molecules confined between two graphene layers. A single-phase rhombic ice would grow from the confined saturated aqueous solutions since the previously stable rhombic molecular arrangement becomes an unstable high-energy state by introducing salt ions nearby. Our result reveals different rhombic ice phases growing from pure water and aqueous solutions, highlighting the deciding role of salt ions in the ice formation process due to their common presence in liquids.

In many physical or biological systems, diffusion can be described by Brownian motions with stochastic diffusion coefficients (DCs). In the present study, we investigate properties of the diffusion with a broad class of stochastic DCs with an approach that is different from subordination. We show that for a finite time, the propagator is non-Gaussian and heavy tailed. This means that when the mean square displacements are the same, for a finite time, some of the diffusing particles with stochastic DCs diffuse farther than the particles with deterministic DCs or exhibiting a fractional Brownian motion. We also show that when a stochastic DC is ergodic, the propagator converges to a Gaussian distribution in the long time limit. The speed of convergence is determined by the autocovariance function of the DC.

We investigate the percolation transition of aligned, overlapping, anisotropic shapes on lattices. Using the recently proposed lattice version of excluded volume theory, we show that shape-anisotropy leads to some intriguing consequences regarding the percolation behavior of anisotropic shapes. We consider a prototypical anisotropic shape—rectangle—on a square lattice and show that, for rectangles of width unity (sticks), the percolation threshold is a monotonically decreasing function of the stick length, whereas, for rectangles of width greater than two, it is a monotonically increasing function. Interestingly, for rectangles of width two, the percolation threshold is independent of its length. We show that this independence of threshold on the length of a side holds for $d$-dimensional hypercubiods as well as for specific integer values for the lengths of the remaining sides. The limiting case of the length of the rectangles going to infinity shows that the limiting threshold value is finite and depends upon the width of the rectangle. This “continuum” limit with the lattice spacing tending to zero only along a subset of the possible directions in $d$ dimensions results in a “semicontinuum” percolation system. We show that similar results hold for other anisotropic shapes and lattices in different dimensions. The critical properties of the aligned and overlapping rectangles are evaluated using Monte Carlo simulations. We find that the threshold values given by the lattice-excluded volume theory are in good agreement with the simulation results, especially for larger rectangles. We verify the isotropy of the percolation threshold and also compare our results with models where rectangles of mixed orientation are allowed. Our simulation results show that alignment increases the percolation threshold. The calculation of critical exponents places the model in the standard percolation universality class. Our results show that shape anisotropy of the aligned, overlapping percolating units has a marked influence on the percolation properties, especially when a subset of the dimensions of the percolation units is made to diverge.

We study the critical behavior of a noisy kinetic opinion model subject to resilience to change depending on aging, defined as the number of interactions before a change of opinion state. In this model, the opinion of each agent can take three discrete values, the extreme ones $\pm 1$, and also the intermediate value 0, and it can evolve through kinetic exchange when interacting with another agent, or independently, by stochastic choice (noise). The probability of change by pairwise interactions depends on the age that the agent has remained in the same state, according to a given kernel. We particularly develop the cases where the probability decays either algebraically or exponentially with the age, and we also consider the anti-aging scenario where the probability increases with the age, meaning that it is more likely to change mind the longer the persistence in the current state. For the opinion dynamics in a complete graph, we obtain analytical predictions for the critical curves of the order parameters, in perfect agreement with agent-based simulations. We observe that sufficiently weak aging (slow change of the kernel with the age) favors partial consensus with respect to the aging-insensitive scenario, while for sufficiently strong aging, as well as for anti-aging, the opposite trend is observed.

Collective effects stemming from many interacting units have attracted remarkable recent interest, not only for their presence in several systems in nature but also for the possibility of being used for the construction of efficient engine setups. Notwithstanding, little is known about the influence of the engine design, and most studies are restricted to the simplest cases (e.g., simultaneous contact with two thermal baths), not necessarily constituting a realistic setup implementation. In order to investigate the design and its influence on the performance, we introduce the collisional also referred as sequential description for a minimal model for interacting heat engines, composed of two coupled nanomachines placed in contact with a distinct thermal reservoir and subjected to a nonequilibrium work source at each stage. Thermodynamic quantities are exactly obtained irrespective of the model details. Distinct kinds of work sources are investigated and the influence of the interaction, temperature, period, and time asymmetry has been undertaken. Results show that a careful design of interaction provides superior performance than the interactionless case, including optimal power outputs and efficiencies at maximum power greater than known bounds or even the system presenting efficiencies close to the ideal (Carnot) limit. As a complementary analysis, we also show that the case of the system simultaneously placed in contact with two thermal reservoirs constitutes a particular case of our framework.

We propose a minimal setup for a quantum heat pump consisting of two tunnel-coupled quantum dots, each hosting a single level and each being coupled to a different fermionic reservoir. The working principle relies on both non-Markovian system-bath coupling and driving-induced resonant coupling. We describe the system using a reaction-coordinate mapping in combination with Floquet-Born-Markov theory and characterize its performance.

We elucidate the universal spatiotemporal scaling properties of the time-dependent correlation functions in a class of two-component one-dimensional (1D) driven diffusive system that consists of two coupled asymmetric exclusion processes. By using a perturbative renormalization group framework, we show that the relevant scaling exponents have values same as those for the 1D Kardar-Parisi-Zhang (KPZ) equation. We connect these universal scaling exponents with the symmetries of the model equations. We thus establish that these models belong to the 1D KPZ universality class.

The recent discovery of the peritrichous, swarm-competent bacterium Enterobacter sp. SM3 has offered a new opportunity to investigate the connection between bacterial swimming and swarming. Here, we report the run-and-tumble behavior of SM3 as planktonic swimming cells and as swarming cells diluted in liquid medium, drawing comparison between the two states. Swimming cells of SM3 run for an average of 0.77 s with a speed of approximately $30\mu \mathrm{m}/\mathrm{s}$ before tumbling. Tumbles last for a duration of 0.12 s on average and cause changes in direction averaging ${69}^{\circ }$. Swimming cells exposed to the common chemoattractant serine in bulk solution suppress the frequency of tumbles in the steady state, lengthening the average run duration and decreasing the average tumble angle. When exposed to aspartate, cells do not demonstrate a notable change in run-and-tumble parameters in the steady state. For swarming cells of SM3, the frequency of tumbles is reduced, with the average run duration being 50% longer on average than that of swimming cells in the same liquid medium. Additionally, the average tumble angle of swarming cells is smaller by 35%. These findings reveal that the newly identified species, SM3, performs run-and-tumble motility similar to other species of peritrichous bacteria such as E. coli, both in the swimming and swarming states. We present a simple mechanical model, which provides a physical understanding of the run-and-tumble behavior of peritrichous bacteria.