We address the out-of-equilibrium dynamics of a many-body system when one of its Hamiltonian parameters is driven across a first-order quantum transition (FOQT). In particular, we consider systems subject to boundary conditions favoring one of the two phases separated by the FOQT. These issues are investigated within the paradigmatic one-dimensional quantum Ising model, at the FOQTs driven by the longitudinal magnetic field $h$, with boundary conditions that favor the same magnetized phase (EFBC) or opposite magnetized phases (OFBC). We study the dynamic behavior for an instantaneous quench and for a protocol in which $h$ is slowly varied across the FOQT. We develop a dynamic finite-size scaling theory for both EFBC and OFBC, which displays some remarkable differences with respect to the case of neutral boundary conditions. The corresponding relevant timescale shows a qualitative different size dependence in the two cases: it increases exponentially with the size in the case of EFBC, and as a power of the size in the case of OFBC.

The standard phase-ordering process is obtained by quenching a system, like the Ising model, to below the critical point. This is usually done with periodic boundary conditions to ensure ergodicity breaking in the low-temperature phase. With this arrangement the infinite system is known to remain permanently out of equilibrium, i.e., there exists a well-defined asymptotic state which is time invariant but different from the ordered ferromagnetic state. In this paper we establish the critical nature of this invariant state by demonstrating numerically that the quench dynamics with periodic and antiperiodic boundary conditions are indistinguishable from each other. However, while the asymptotic state does not coincide with the equilibrium state for the periodic case, it coincides instead with the equilibrium state of the antiperiodic case, which in fact is critical. The specific example of the Ising model is shown to be one instance of a more general phenomenon, since an analogous picture emerges in the spherical model, where boundary conditions are kept fixed to periodic, while the breaking or preserving of ergodicity is managed by imposing the spherical constraint either sharply or smoothly.

Anomalous behavior of a nonlinear climate-vegetation model governed by the multiplicative and additive noises is revealed on the basis of stochastic sensitivity analysis. A specific feature of this model is the bistability with the coexistence of “snowball” equilibrium and “warm” attractor in the form of equilibrium or cycle. It is found that multiplicative and additive noises shift probabilistic distribution in opposite directions. The multiplicative noise introduced into the death rate of vegetation changes the dispersion of random states and their localization in the phase diagram. This type of noise cools down the system and is responsible for its transition to the snowball state. On the contrary, the additive noise warms up the climate with increasing noise intensity. A cumulative effect of multiplicative and additive noises occurs under their simultaneous influence. This effect determining the evolutionary behavior of a climate-vegetation system depends on the ratio of intensities of these noises.

We study the stationary dynamics of an active interacting Brownian particle system. We measure the violations of the fluctuation dissipation theorem, and the corresponding effective temperature, in a locally resolved way. Quite naturally, in the homogeneous phases the diffusive properties and effective temperature are also homogeneous. Instead, in the inhomogeneous phases (close to equilibrium and within the MIPS sector) the particles can be separated in two groups with different diffusion properties and effective temperatures. Notably, at fixed activity strength the effective temperatures in the two phases remain distinct and approximately constant within the MIPS region, with values corresponding to the ones of the whole system at the boundaries of this sector of the phase diagram. We complement the study of the globally averaged properties with the theoretical and numerical characterization of the fluctuation distributions of the single-particle diffusion, linear response, and effective temperature in the homogeneous and inhomogeneous phases. We also distinguish the behavior of the (time-delayed) effective temperature from the (instantaneous) kinetic temperature, showing that the former is independent of the friction coefficient.

In a two-dimensional liquid crystal, each topological defect has a topological charge and a characteristic orientation and hence can be regarded as an oriented particle. Theories predict that the trajectories of annihilating defects depend on their relative orientation. Recently, these predictions have been tested in experiments on smectic-$C$ films. Those experiments find curved trajectories that are similar to the predictions, but the detailed relationship between the defect orientations and the far-field director is different. To understand this difference, we extend the previous theories by adding the effects of elastic anisotropy and find that it significantly changes the curved trajectories.

The chiral smectic phases of calamitic liquid crystals, $\mathrm{Sm}{C}^{*}$ and $\mathrm{Sm}{C}_A^{*}$, are characterized by the synclinic ferroelectric $F$ ordering and the anticlinic antiferroelectric $A$ ordering in adjacent layers. Various states with mixed $A$ and $F$ orderings are degenerate at the frustrated phase-transition point. The degeneracy lifting is commonly caused by the long-range interlayer interactions (LRILIs), producing a series of biaxial subphases specified by a relative ratio of both orderings, $q_T=\left[F\right]/(\left[A\right]+\left[F\right])$. Sandhya et al. [Phys. Rev. E 87, 012502 (2013)] established, however, the importance of thermal fluctuations in the degeneracy lifting in some binary mixtures of MC881 and MC452. They observed the most intriguing interplay of thermal fluctuations and LRILIs in the stabilization of an apparently single subphase. Since no other detailed experimental study of the subphase has so far been made, we carry out its dielectric investigations and clarify the following five points: (1) the subphase is surely a single phase from $\approx 80{}^{\circ }\mathrm{C}$ down to room temperature; (2) the imaginary part of complex permittivity ${\epsilon }^{″}$ shows the weak antiphase mode and hence it must be antiferroelectric $q_T=1/2$; (3) ${\epsilon }^{″}$ becomes much stronger above $\approx 80{}^{\circ }\mathrm{C}$, indicating the emergence of ferroelectric and/or ferrielectric states; (4) the dielectric amplitude gradually increases at least just above the 1/2 subphase, suggesting it be due to a continuous increase of $q_T$; and (5) at low temperatures the antiphase relaxation mode shows irregularities that indicate the important role played by the cooperative motion of the layer undulation as well as of the director tilting.

We imaged the pore-scale distribution of air and water within packed columns of glass spheres of different textures using x-ray microcomputed tomography after primary drainage and after secondary imbibition. Postimbibition residual air saturation increases with roughness size. Clusters larger than a critical size of about 15 to 40 pores are distributed according to a power law, with exponents ranging from $\tau =2.29\pm 0.04$ to $3.00\pm 0.13$ and displaying a weak negative correlation with roughness size. The largest cluster constitutes 7 to 20% of the total residual gas saturation, with no clear correlation with roughness size. These results imply that activities that enhance grain roughness by, e.g., creating acidic conditions in the subsurface, will promote capillary trapping of nonwetting phases under capillary-dominated conditions. Enhanced trapping, in turn, may be desirable in some engineering applications such as geological ${\mathrm{CO}}_2$ storage, but detrimental to others such as groundwater remediation and hydrocarbon recovery.

Low-temperature-differential (LTD) Stirling heat engines are able to operate with a small temperature difference between low-temperature heat reservoirs that exist in our daily lives, and thus they are considered to be an important sustainable energy technology. The author recently proposed a nonlinear dynamics model of an LTD kinematic Stirling heat engine to study the rotational mechanism of the engine [Y. Izumida, Europhys. Lett. 121, 50004 (2018)]. This paper presents our study of the nonequilibrium thermodynamics analysis of this engine model, where a load torque against which the engine does work is introduced. We demonstrate that the engine's rotational state is in a quasilinear response regime where the thermodynamic fluxes show a linear dependence on the thermodynamic forces. Significantly, it is found that the response coefficients of the quasilinear relations are symmetric, which is similar to Onsager symmetry in linear irreversible thermodynamics. Based on these relations, we formulate the maximum efficiency of the engine. We also elucidate that the symmetry of the quasilinear response coefficients emerges by reflecting the (anti-)reciprocity of the Onsager kinetic coefficients identified for the relaxation dynamics of the engine in the vicinity of an equilibrium state. We expect that the present study will pave the way for developing nonequilibrium thermodynamics of autonomous heat engines described as a nonlinear dynamical system.

In this paper, we unveil the geometrical template of phase space structures that governs transport in a Hamiltonian system described by a potential energy surface with an entrance/exit channel and two wells separated by an index-1 saddle. For the analysis of the nonlinear dynamics mechanisms, we apply the method of Lagrangian descriptors, a trajectory-based scalar diagnostic tool that is capable of providing a detailed phase space tomography of the interplay between the invariant manifolds of the system. Our analysis reveals that the stable and unstable manifolds of the two families of unstable periodic orbits (UPOs) that exist in the regions of the wells are responsible for controlling access to the potential wells of the trajectories that enter the system through the entrance/exit channel. We demonstrate that the heteroclinic and homoclinic connections that arise in the system between the manifolds of the families of UPOs characterize the branching ratio, a relevant quantity used to measure product distributions in chemical reaction dynamics.

We present an alternative type of parity-time ($\mathcal{PT}$)-symmetric generalized Scarf-II potentials, which makes possible for non-Hermitian Hamiltonians in the classical linear Schrödinger system to possess fully real spectra with unique features such as the multiple $\mathcal{PT}$-symmetric breaking behaviors and to support one-dimensional (1D) stable $\mathcal{PT}$-symmetric solitons of power-law waveform, namely power-law solitons, in focusing Kerr-type nonlinear media. Moreover, $\mathcal{PT}$-symmetric high-order solitons are also derived numerically in 1D and 2D settings. Around the exactly obtained nonlinear propagation constants, families of 1D and 2D localized nonlinear modes are also found numerically. The majority of fundamental nonlinear modes can still keep steady in general, whereas the 1D multipeak solitons and 2D vortex solitons are usually susceptible to suffering from instability. Likewise, similar results occur in the defocusing Kerr-nonlinear media. The obtained results will be useful for understanding the complex dynamics of nonlinear waves that form in $\mathcal{PT}$-symmetric nonlinear media in other physical contexts.

We use an artificial neural network to analyze asymmetric noisy random telegraph signals, and extract underlying transition rates. We demonstrate that a long short-term memory neural network can outperform other methods, particularly for noisy signals and measurements with limited bandwidths. Our technique gives reliable results as the signal-to-noise ratio approaches one, and over a wide range of underlying transition rates. We apply our method to random telegraph signals generated by quasiparticle poisoning in a superconducting double dot, allowing us to extend our measurement of quasiparticle dynamics to new temperature regimes.

Liquid crystal elastomers and glasses can have significant shape change determined by their director patterns. Cones deformed from circular director patterns have nontrivial Gaussian curvature localized at tips, curved interfaces, and intersections of interfaces. We employ a generalized metric compatibility condition to characterize two families of interfaces between circular director patterns, hyperbolic and elliptical interfaces, and find that the deformed interfaces are geometrically compatible. We focus on hyperbolic interfaces to design complex topographies and nonisometric origami, including $n$-fold intersections, symmetric and irregular tilings. The large design space of threefold and fourfold tiling is utilized to quantitatively inverse design an array of pixels to display target images. Taken together, our findings provide comprehensive design principles for the design of actuators, displays, and soft robotics in liquid crystal elastomers and glasses.

The classical Rayleigh-Bénard convection (RBC) system is known to exhibit either subcritical or supercritical transition to convection in the presence or absence of rotation and/or magnetic field. However, the simultaneous exhibition of subcritical and supercritical branches of convection in plane layer RBC depending on the initial conditions, to the best of our knowledge, has not been reported so far. Here, we report the phenomenon of simultaneous occurrence of subcritical and supercritical branches of convection in overstable RBC of electrically conducting low Prandtl number fluids (liquid metals) in the presence of an external uniform horizontal magnetic field and rotation about the vertical axis. Extensive three-dimensional (3D) direct numerical simulations (DNS) and low-dimensional modeling of the system, performed in the ranges $750\le \mathrm{Ta}\le 3000$ and $0<Q\le 1000$ of the Taylor number ($\mathrm{Ta}$, strength of the Coriolis force) and the Chandrasekhar number ($Q$, strength of the Lorenz force), respectively, establish the phenomenon convincingly. Detailed bifurcation analysis of a simple 3D model derived from the DNS data reveals that a supercritical Hopf bifurcation and a subcritical pitchfork bifurcation of the conduction state are responsible for this. The effect of Prandtl number on these transitions is also explored in detail.

We present three-dimensional measurements of particle-size-dependent acoustophoretic motion of microparticles with diameters from 4.8 $\mu \mathrm{m}$ down to 0.5 $\mu \mathrm{m}$ suspended in either homogeneous or inhomogeneous fluids inside a glass-silicon microchannel and exposed to a standing ultrasound wave. To study the crossover from radiation force dominated to streaming dominated motion as the particle size is decreased, we extend previous studies to long timescales, where the particles smaller than the crossover size move over distances comparable to the channel width. We observe a particle-size-dependent particle depletion at late times for the particles smaller than the crossover size. The mechanisms behind this depletion in homogeneous fluids are rationalized by numerical simulations which take the Brownian motion into account. Experimentally, the particle trajectories in inhomogeneous fluids show focusing in the bulk of the microchannel at early times, even for the particles below the critical size, which clearly demonstrates the potential to manipulate submicrometer particles.

We report experimental evidence of clogging due to the spontaneous development of hanging arches when a granular sample composed of spherical particles flows down a narrow vertical pipe. These arches, akin to the ones responsible for silo clogging, can only be possible due to the role of frictional forces; otherwise they will be unstable. We find that, contrary to the silo case, the probability of clogging in vertical narrow tubes does not decrease monotonically with the ratio of the pipe-to-particle diameters. This behavior is related to the clogging prevention caused by the spontaneous ordering of particles apparent in certain aspect ratios. More importantly, by means of numerical simulations, we discover that the interparticle normal force distributions broaden in systems with higher probability of clogging. This feature, which has been proposed before as a distinctive feature of jamming in sheared granular samples, suggests that clogging and jamming are connected in pipe flow.

We present a first-principles thermodynamic approach to provide an alternative to the Langevin equation by identifying the deterministic (no stochastic component) microforce ${\mathbf{F}}_{k,\text{BP}}$ acting on a nonequilibrium Brownian particle (BP) in its $k\mathrm{th}$ microstate ${\mathfrak{m}}_k$. (The prefix “micro” refers to microstate quantities and carry a suffix $k$.) The deterministic new equation is easier to solve using basic calculus. Being oblivious to the second law, ${\mathbf{F}}_{k,\text{BP}}$ does not always oppose motion but viscous dissipation emerges upon ensemble averaging. The equipartition theorem is always satisfied. We reproduce well-known results of the BP in equilibrium. We explain how the microforce is obtained directly from the mutual potential energy of interaction beween the BP and the medium after we average it over the medium so we only have to consider the particles in the BP. Our approach goes beyond the phenomenological and equilibrium approach of Langevin and unifies nonequilibrium viscous dissipation from mesoscopic to macroscopic scales and provides new insight into Brownian motion beyond Langevin's and Einstein's formulation.

An integrable model of a two-level medium with a permanent dipole moment (PDM) is proposed. The model describes the evolution of electromagnetic field pulses beyond the slow envelope approximation. The dipole-dipole interaction is taken into account in the approximation of the nearest neighbors in the form of a quadratic dispersion. It is found that such a generalization of the reduced Maxwell-Bloch equations is completely integrable. Breather solutions are derived. These solutions are used to study the combined influence of the quadratic dispersion and PDM. It is found that the model possess a number of unique features, which give possibilities for controlling the shape of field pulses. In particular, it is found that the shape and amplitude of the field pulse depends on both the signs of the dipole-dipole interaction and the sign and value of the permanent dipole moment.

Belief propagation is an algorithm that is known from statistical physics and computer science. It provides an efficient way of calculating marginals that involve large sums of products which are efficiently rearranged into nested products of sums to approximate the marginals. It allows a reliable estimation of the state and its variance of power grids that is needed for the control and forecast of power grid management. At prototypical examples of IEEE grids we show that belief propagation not only scales linearly with the grid size for the state estimation itself but also facilitates and accelerates the retrieval of missing data and allows an optimized positioning of measurement units. Based on belief propagation, we give a criterion for how to assess whether other algorithms, using only local information, are adequate for state estimation for a given grid. We also demonstrate how belief propagation can be utilized for coarse-graining power grids toward representations that reduce the computational effort when the coarse-grained version is integrated into a larger grid. It provides a criterion for partitioning power grids into areas in order to minimize the error of flow estimates between different areas.

Ligand binding to polymers modifies the physical and chemical properties of the polymers, leading to physical, chemical, and biological implications. McGhee and von Hippel obtained the equilibrium coverage as a function of the ligand affinity, through the computation of the possible binding sites for the ligand. Here, we complete this theory deriving the kinetic model for the ligand-binding dynamics and the associated equilibrium chemical potential, which turns out to be of the Tonks gas model type. At low coverage, the Tonks chemical potential becomes the Fermi chemical potential and even the ideal gas chemical potential. We also discuss kinetic models associated with these chemical potentials. These results clarify the kinetic models of ligand binding, their relations with the chemical potentials, and their range of validity. Our results highlight the inaccuracy of ideal and simplified kinetic approaches for medium and high coverages.