Within the framework of Landau–de Gennes theory for nematic liquid crystals, we study the temperature-induced isotropic-nematic phase transition on a spherical shell under the assumption of degenerate tangential anchoring. Below a critical temperature, a thin layer of nematic coating a microscopic spherical particle exhibits nonuniform textures due to the geometrical frustration. We find the exact value of the critical threshold for the temperature and determine exactly the nematic textures at the transition by means of a weakly nonlinear analysis. The critical temperature is affected by the extrinsic curvature of the sphere, and the nematic alignment is consistent with the Poincaré-Hopf index theorem and experimental observations. The stability analysis of the bifurcate textures at the isotropic-nematic transition highlights that only the tetrahedral configuration is stable.

Vibrational heat transport in molecular junctions is a central issue in different contemporary research areas such as chemistry, materials science, mechanical engineering, thermoelectrics, and power generation. Our model system consists of a chain of molecules which are sandwiched between two solids that are maintained at different temperatures. We employ a quantum self-consistent reservoir model, which is built on a generalized quantum Langevin equation, to investigate quantum effects and far from equilibrium conditions on thermal conduction at nanoscale. The present self-consistent reservoir model can easily mimic the phonon-phonon scattering mechanisms. Different thermal environments are modeled as (i) Ohmic, (ii) sub-Ohmic, and (iii) super-Ohmic environments, and their effects are demonstrated for the thermal rectification properties of the system with spring graded or mass graded features. The behavior of heat current across molecular junctions as a function of chain length, temperature gradient, and phonon scattering rates are studied. Further, our analysis reveals the effects of vibrational mismatch between the solids phonon spectra on heat transfer characteristics in molecular junctions for different thermal environments.

This paper presents a conceptual design for quantum heat machines using a pair of coupled double quantum dots (DQDs), each DQD with an excess electron to interact, as an working substance. We define a compression ratio as the ratio between the Coulomb couplings which describes the interaction between the electrons during the isochoric processes of the quantum Otto cycle and then we analyze the arising of different regimes of operations of our thermal machine. We also show that we may change the operation mode of an Otto engine when considering the effects due to the quantum tunneling of a single electron between each individual DQD.

The agent-based yard-sale model of wealth inequality is generalized to incorporate exponential economic growth and its distribution. The distribution of economic growth is nonuniform and is determined by the wealth of each agent and a parameter $\lambda$. Our numerical results indicate that the model has a critical point at $\lambda =1$ between a phase for $\lambda <1$ with economic mobility and exponentially growing wealth of all agents and a nonstationary phase for $\lambda \ge 1$ with wealth condensation and no mobility. We define the energy of the system and show that the system can be considered to be in thermodynamic equilibrium for $\lambda <1$. Our estimates of various critical exponents are consistent with a mean-field theory [see W. Klein et al., following paper, Phys. Rev. E 104, 014151 (2021)]. The exponents do not obey the usual scaling laws unless a combination of parameters that we refer to as the Ginzburg parameter is held fixed as the phase transition is approached. The model illustrates that both poorer and richer agents benefit from economic growth if its distribution does not favor the richer agents too strongly. This work and the following theoretical paper contribute to our understanding of whether the methods of equilibrium statistical mechanics can be applied to economic systems.

We develop a mean-field theory of the growth, exchange, and distribution (GED) model introduced by Liu et al. [K. K. L. Liu et al., preceding paper, Phys. Rev. E 104, 014150 (2021)] that accurately describes the phase transition in the limit that the number of agents $N$ approaches infinity. The GED model is a generalization of the yard-sale model in which the additional wealth added by economic growth is nonuniformly distributed to the agents according to their wealth in a way determined by the parameter $\lambda$. The model is shown numerically to have a phase transition at $\lambda =1$ and be characterized by critical exponents and critical slowing down. Our mean-field treatment of the GED model correctly predicts the existence of the phase transition, a critical slowing down, and the values of the critical exponents and introduces an energy whose probability satisfies the Boltzmann distribution for $\lambda <1$, implying that the system is in thermodynamic equilibrium in the limit that $N\to \infty$. We show that the values of the critical exponents obtained by varying $\lambda$ for a fixed value of $N$ do not satisfy the usual scaling laws, but do satisfy scaling if a combination of parameters, which we refer to as the Ginzburg parameter, is much greater than one and is held constant. We discuss possible implications of our results for understanding economic systems and the subtle nature of the mean-field limit in systems with both additive and multiplicative noise.

Evolution of the nonequilibrium thermodynamic entities corresponding to dynamics of the Hopf instabilities and traveling waves at a nonequilibrium steady state of a spatially extended glycolysis model is assessed here by implementing an analytically tractable scheme incorporating a complex Ginzburg-Landau equation (CGLE). In the presence of self and cross diffusion, a more general amplitude equation exploiting the multiscale Krylov-Bogoliubov averaging method serves as an essential tool to reveal the various dynamical instability criteria, especially Benjamin-Feir (BF) instability, to estimate the corresponding nonlinear dispersion relation of the traveling wave pattern. The critical control parameter, wave-number selection criteria, and magnitude of the complex amplitude for traveling waves are modified by self- and cross-diffusion coefficients within the oscillatory regime, and their variabilities are exhibited against the amplitude equation. Unlike the traveling waves, a low-amplitude broad region appears for the Hopf instability in the concentration dynamics as the system phase passes through minima during its variation with the control parameter. The total entropy production rate of the uniform Hopf oscillation and glycolysis wave not only qualitatively reflects the global dynamics of concentrations of intermediate species but almost quantitatively. Despite the crucial role of diffusion in generating and shaping the traveling waves, the diffusive part of the entropy production rate has a negligible contribution to the system's total entropy production rate. The Hopf instability shows a more complex and colossal change in the energy profile of the open nonlinear system than in the traveling waves. A detailed analysis of BF instability shows a contrary nature of the semigrand Gibbs free energy with discrete and continuous wave numbers for the traveling wave. We hope the Hopf and traveling wave pattern around the BF instability in terms of energetics and dissipation will open up new applications of such dynamical phenomena.

A Janus particle diffusing on a line is considered. Aside from its own driving force $f$ acting forward or backward according to its stochastic orientation, it moves in a position-dependent potential $U\left(x\right)$. We propose here the mapping scheme generating the effective generalized Fick-Jacobs equation, describing motion of the particle in the spatial coordinate $x$ only; the orientation is understood as the transverse coordinate. The self-propulsion, driving the system out of equilibrium, is reflected as an additional effective potential $-\gamma \left(x\right)$ in the reduced picture. It enables us to understand peculiarities of this system in a handy way. The additionally corrected potential redistributes the confined particles in quasiequilibrium causing their piling at the walls. In periodic asymmetric channels, it acquires a growing contribution, responsible for driving the ratchet effect.

We present molecular dynamics simulations of one- and two-dimensional bead-spring models sliding on incommensurate substrates after an initial kick, in the case where the coupling to the underlying substrate is weak, i.e., energy can dissipate only into the internal degrees of freedom of the sliding object, but not into the substrate below. We investigate how sliding friction is affected by structural defects and interaction anharmonicity. In their absence, we confirm earlier findings, namely, that at special resonance sliding velocities, friction is maximal. When sliding off-resonance, partially thermalized states are possible, whereby only a small number of vibrational modes becomes excited, but whose kinetic energies are already Maxwell-Boltzmann distributed. Anharmonicity and defects typically destroy partial thermalization and instead lead to full thermalization, implying much higher friction. For sliders with periodic boundaries, thermalization begins with vibrational modes whose spatial modulation is compatible with the incommensurate lattice. For a disk-shaped slider, modes corresponding to modulations compatible with the slider radius are initially the most dominant. By tuning the mechanical properties of the slider's edge, this effect can be controlled, resulting in significant changes in the sliding distance covered.

We report the occurrence of flow reversals induced by the attractor-merging crisis in Rayleigh-Bénard convection of electrically conducting low-Prandtl-number fluids in the presence of a uniform external horizontal magnetic field. The simultaneous collision of two coexisting chaotic attractors with an unstable fixed point and its associated stable manifold takes place in the higher-dimensional phase space of the system, leading to a single merged chaotic attractor. The effect of strength of the magnetic field on the flow reversal phenomena is also explored in detail.

The production of polarized proton beams with multi-GeV energies in ultraintense laser interaction with targets is studied with three-dimensional particle-in-cell simulations. A near-critical density plasma target with prepolarized proton and tritium ions is considered for the proton acceleration. The prepolarized protons are initially accelerated by laser radiation pressure before injection and further acceleration in a bubblelike wakefield. The temporal dynamics of proton polarization is tracked via the Thomas-Bargmann-Michel-Telegdi equation and it is found that the proton polarization state can be altered by both the laser field and the magnetic component of the wakefield. The dependence of the proton acceleration and polarization on the ratio of the ion species is determined and it is found that the protons can be efficiently accelerated as long as their relative fraction is less than $20\%$, in which case the bubble size is large enough for the protons to obtain sufficient energy to overcome the bubble injection threshold.

In the present work, we reanalyze the energy loss experimental data from Cayzac et al. [Nat. Commun. 8, 15693 (2017)] using our successful ion charge state theoretical model. We predict lower nitrogen charge values, from $3.5+$ to $5.0+$, than the ones calculated by Cayzac et al., fitting better to their data. For energy loss estimations, we use the same stopping model, so our predictions agree better with the experimental data only due to our charge state model. Different projectile electron loss and capture processes are taken into account to estimate the projectile charge state. The projectile electron loss, or ionization, with plasma ions and free electrons are considered. On the other hand, the projectile electron capture, or recombination, with plasma free or bound electrons are also considered. The projectile ionization with plasma ions is shown as the main factor that modifies the mean charge of the projectile. Here, the new Kaganovich fitting formula for this projectile ionization is used because it seems to be more accurate than Gryzinsky's fitting in the low energy range. Our charge state model fits better with experimental data than any other model in the bibliography. Thus, it should be considered in any charge state and any energy loss estimation to obtain reliable results in future work.

A descriptor-based method combined with a partition approach is proposed to reconstruct three-dimensional (3D) microstructures based on a set of two-dimensional (2D) scanning electron microscopy (SEM) images. The features in the SEM images are identified and partitioned into small features using the watershed algorithm. The watershed algorithm first finds the local gray-level maxima, and partitions the features through the gray-level local minima. The 3D size distribution and radial distribution of the small spherical elements are inferred, respectively, based on the 2D size distribution and radial distribution using stereological analysis. The 3D microstructures are reconstructed by matching the inferred size distribution and radial distribution through a simulated annealing-based procedure. Combining with the proposed partition approach, the descriptor-based method can be applied to complex microstructures and the computational efficiency of the reconstruction can be largely improved. A case study is presented using a set of 2D SEM images with nanoscale pore structure from the low-density CSH (calcium silicate hydrate) phase of a hardened cement paste. Cross sections were randomly selected from the reconstructed 3D microstructure and compared with the original SEM images using the pore descriptors and the two-point correlation function with satisfactory agreement. Using the 3D reconstructed model, the properties of the sample material can be investigated on such a small scale as demonstrated in this paper on quantifying the absolute permeability.

We present results of a series of numerical simulations of an initially fully developed turbulent flow of a liquid metal in a long duct under the influence of a constant uniform transverse magnetic field and various wall conductances (ranging from perfectly insulated to perfectly conducting walls). The changes in the wall conductance caused the appearance of novel flow regimes characterized by the coexistence of locally turbulent or laminar flow regions and a nonmonotonic behavior of the corresponding wall-friction coefficients. In contrast to the situation where an increase in the imposed magnetic field will lead to continuous suppression of turbulence and final complete relaminarization of the flow in a specific range of wall-conducting parameters, we also observe an apparent partial and complete turbulence regeneration from the magnetohydrodynamic-suppressed laminar state.

The duration of the quasistationary states (QSSs) emerging in the $d$-dimensional classical inertial $\alpha \text{−}XY$ model, i.e., $N$ planar rotators whose interactions decay with the distance $r_{ij}$ as $1/r_{ij}^{\alpha }$ ($\alpha \ge 0$), is studied through first-principles molecular dynamics. These QSSs appear along the whole long-range interaction regime ($0\le \alpha /d\le 1$), for an average energy per rotator $U<U_c$ ($U_c=3/4$), and they do not exist for $U>U_c$. They are characterized by a kinetic temperature $T_{\text{QSS}}$, before a crossover to a second plateau occurring at the Boltzmann-Gibbs temperature $T_{\text{BG}}>T_{\text{QSS}}$. We investigate here the behavior of their duration $t_{\text{QSS}}$ when $U$ approaches $U_c$ from below, for large values of $N$. Contrary to the usual belief that the QSS merely disappears as $U\to U_c$, we show that its duration goes through a critical phenomenon, namely $t_{\text{QSS}}\propto {(U_c-U)}^{-\xi }$. Universality is found for the critical exponent $\xi \simeq 5/3$ throughout the whole long-range interaction regime.

We solve the classical square-lattice dimer model with periodic boundaries and in the presence of a field $\mathit{t}$ that couples to the (vector) flux, by diagonalizing a modified version of Lieb's transfer matrix. After deriving the torus partition function in the thermodynamic limit, we show how the configuration space divides into topological sectors corresponding to distinct values of the flux. Additionally, we demonstrate in general that expectation values are $\mathit{t}$ independent at leading order, and obtain explicit expressions for dimer occupation numbers, dimer-dimer correlation functions, and the monomer distribution function. The last of these is expressed as a Toeplitz determinant, whose asymptotic behavior for large monomer separation is tractable using the Fisher-Hartwig conjecture. Our results reproduce those previously obtained using Pfaffian techniques.

We study the probability distribution of entanglement in the quantum symmetric simple exclusion process, a model of fermions hopping with random Brownian amplitudes between neighboring sites. We consider a protocol where the system is initialized in a pure product state of $M$ particles, and we focus on the late-time distribution of Rényi-$q$ entropies for a subsystem of size $\ell$. By means of a Coulomb gas approach from random matrix theory, we compute analytically the large-deviation function of the entropy in the thermodynamic limit. For $q>1$, we show that, depending on the value of the ratio $\ell /M$, the entropy distribution displays either two or three distinct regimes, ranging from low to high entanglement. These are connected by points where the probability density features singularities in its third derivative, which can be understood in terms of a transition in the corresponding charge density of the Coulomb gas. Our analytic results are supported by numerical Monte Carlo simulations.

Exponential random graphs are important to model the structure of real-world complex networks. Here we solve the two-star model with degree-degree correlations in the sparse regime. The model constraints the average correlation between the degrees of adjacent nodes (nearest neighbors) and between the degrees at the end-points of two-stars (next nearest neighbors). We compute exactly the network free energy and show that this model undergoes a first-order transition to a condensed phase. For non-negative degree correlations between next nearest neighbors, the degree distribution inside the condensed phase has a single peak at the largest degree, while for negative degree correlations between next nearest neighbors the condensed phase is characterized by a bimodal degree distribution. We calculate the degree assortativities and show they are nonmonotonic functions of the model parameters, with a discontinuous behavior at the first-order transition. The first-order critical line terminates at a second-order critical point, whose location in the phase diagram can be accurately determined. Our results can help to develop more detailed models of complex networks with correlated degrees.

In oscillatory media, waves can be generated by pacemaker regions which oscillate faster than their surroundings. In many chemical and biological systems, such waves can synchronize the whole medium and as such they are a means of transmitting information at a fixed speed over large distances. In this paper, we apply analytical tools to investigate the factors that determine the speed of these waves. More precisely, we apply singular perturbation and phase reduction methods to two types of negative-feedback oscillators, one built on underlying bistability and one including a time delay in the negative feedback. In both systems, we investigate the influence of time-scale separation on the resulting wave speed, as well as the effect of size and frequency of the pacemaker region. We compare our analytical estimates to numerical simulations which we described previously [J. Rombouts and L. Gelens, Phys. Rev. Research 2, 043038 (2020)].

We investigate the solution landscapes of the confined diblock copolymer and homopolymer in two-dimensional domain by using the extended Ohta–Kawasaki model. The projection saddle dynamics method is developed to compute the saddle points with mass conservation and construct the solution landscape by coupling with downward and upward search algorithms. A variety of stationary solutions are identified and classified in the solution landscape, including Flower class, Mosaic class, Core-shell class, and Tai-chi class. The relationships between different stable states are shown by either transition pathways connected by index-1 saddle points or dynamical pathways connected by a high-index saddle point. The solution landscapes also demonstrate the symmetry-breaking phenomena, in which more solutions with high symmetry are found when the domain size increases.