The anisotropic shape of calamitic liquid crystal (LC) particles results in distinct values of energy when the nematogens are placed side by side or end to end. This anisotropy in energy which is governed by a parameter ${\kappa }^{\prime }$ has deep consequences on equilibrium and nonequilibrium properties. Using the Gay-Berne (GB) model, which exhibits the nematic (Nm) as well as the low-temperature smectic (Sm) order, we undertake large-scale Monte Carlo and molecular dynamics simulations to probe the effect of ${\kappa }^{\prime }$ on the equilibrium phase diagram and the nonequilibrium domain growth following a quench in the temperature $T$ or coarsening. There are two transitions in the GB model: (i) isotropic to Nm at $T_c^1$ and (ii) Nm to Sm at $T_c^2<T_c^1$. ${\kappa }^{\prime }$ decreases $T_c^1$ significantly but has relatively little effect on $T_c^2$. Domain growth in the Nm phase exhibits the well-known Lifshitz-Allen-Cahn (LAC) law, $L\left(t\right)\sim t^{1/2}$ and the evolution is via annihilation of string defects. The system exhibits dynamical scaling that is also robust with respect to ${\kappa }^{\prime }$. We find that the Sm phase at the quench temperatures $T$ ($T>T_c^1\to T<T_c^2$) that we consider has SmB order with a hexatic arrangement of the LC molecules in the layers (SmB-H phase). Coarsening in this phase exhibits a striking two-timescale scenario: First, the LC molecules align and develop orientational order (or nematicity), followed by the emergence of the characteristic layering (or smecticity) along with the hexatic bond-orientational-order within the layers. Consequently, the growth follows the LAC law $L\left(t\right)\sim t^{1/2}$ at early times and then shows a sharp crossover to a slower growth regime at later times. Our observations strongly suggest that $L\left(t\right)\sim t^{1/4}$ in this regime. Interestingly, the correlation function shows dynamical scaling in both the regimes and the scaling function is universal. The dynamics is also robust with respect to changes in ${\kappa }^{\prime }$, but the smecticity is more pronounced at larger values. Further, the early-time dynamics is governed by string defects, while the late-time evolution is dictated by interfacial defects. We believe this scenario is generic to the Sm phase even with other kinds of local order within the Sm layers.

Recent experimental utilization of liquid substrate in the production of two-dimensional crystals, such as graphene, together with a general interest in amorphous materials, raises the following question: is it beneficial to use a liquid substrate to optimize amorphous material production? Inspired by epitaxial growth, we use a two-dimensional coarse-grained model of interacting particles to show that introducing a motion for the substrate atoms improves the self-assembly process of particles that move on top of the substrate. We find that a specific amount of substrate liquidity (for a given sample temperature) is needed to achieve optimal self-assembly. Our results illustrate the opportunities that the combination of different degrees of freedom provides to the self-assembly processes.

Motivated by the growing importance of strong system-bath coupling in several branches of quantum information and related technological applications, we analyze and compare two strategies currently used to obtain (approximately) steady states in strong-coupling regime. The first strategy is based on perturbative expansions while the second one uses reaction coordinate mapping. Focusing on the widely used spin-boson model, we show that the predictions of these two strategies coincide in many situations. This confirms and strengthens the relevance of both techniques. Beyond that, it is also crucial to know precisely their respective range of validity. In that perspective, thanks to their different limitations, we use one to benchmark the other. We introduce and successfully test some very simple validity criteria for both strategies, bringing some answers to the question of the validity range.

Reaction-diffusion models are common in many areas of statistical physics, where they describe the late-time dynamics of chemical reactions. Using a Bose gas representation, which maps the real-time dynamics of the reactants to the imaginary-time evolution of an interacting Bose gas, we consider corrections to the late-time scaling of $k$-particle annihilation processes $kA\to \varnothing$ above the upper critical dimension, where mean-field theory sets the leading order. We establish that the leading corrections are not given by a small renormalization of the reaction rate due to $k$-particle memory effects, but instead set by higher-order correlation functions that capture memory effects of subclusters of reactants. Drawing on methods developed for ultracold quantum gases and nuclear physics, we compute these corrections exactly for various annihilation processes with $k>2$.

We consider spin models on complex networks frequently used to model social and technological systems. We study the annealed ferromagnetic Ising model for random networks with either independent edges (Erdős-Rényi) or prescribed degree distributions (configuration model). Contrary to many physical models, the annealed setting is poorly understood and behaves quite differently than the quenched system. In annealed networks with a fluctuating number of edges, the Ising model changes the degree distribution, an aspect previously ignored. For random networks with Poissonian degrees, this gives rise to three distinct annealed critical temperatures depending on the precise model choice, only one of which reproduces the quenched one. In particular, two of these annealed critical temperatures are finite even when the quenched one is infinite because then the annealed graph creates a giant component for all sufficiently small temperatures. We see that the critical exponents in the configuration model with deterministic degrees are the same as the quenched ones, which are the mean-field exponents if the degree distribution has finite fourth moment and power-law-dependent critical exponents otherwise. Remarkably, the annealing for the configuration model with random independent and identically distributed degrees washes away the universality class with power-law critical exponents.

For a generic class of machines with broken time-reversal symmetry we show that in the linear response regime the relative fluctuation of the sum of output currents for time-forward and time-reversed processes is always lower bounded by the corresponding relative fluctuation of the sum of input currents. This bound is received when the same operating condition, for example, engine, refrigerator, or pump, is imposed on both the forward and the reversed processes. As a consequence, universal upper and lower bounds for the ratio between fluctuations of output and input current are obtained. Furthermore, we establish an important connection between our results and the recently obtained generalized thermodynamic uncertainty relations for time-reversal symmetry-broken systems. We illustrate these findings for two different types of machines: (1) a steady-state three-terminal quantum thermoelectric setup in presence of an external magnetic field and (2) a periodically driven classical Brownian heat engine.

An active environment is a reservoir containing active materials, such as bacteria and Janus particles. Given the self-propelled motion of these materials, powered by chemical energy, an active environment has unique, nonequilibrium environmental noise. Recently, studies on engines that harvest energy from active environments have attracted a great deal of attention because the theoretical and experimental findings indicate that these engines outperform conventional ones. Studies have explored the features of active environments essential for outperformance, such as the non-Gaussian or non-Markovian nature of the active noise. We systematically study the effects of the non-Gaussianity and non-Markovianity of active noise on engine performance. We show that non-Gaussianity is irrelevant to the performance of an engine driven by any linear force (including a harmonic trap) regardless of time dependency, whereas non-Markovianity is relevant. However, for a system driven by a general nonlinear force, both non-Gaussianity and non-Markovianity enhance engine performance. Also, the memory effect of an active reservoir should be considered when fabricating a cyclic engine.

We perform a detailed numerical study of the influence of distributions without a finite second moment on the Lyapunov exponent through the one-dimensional tight-binding Anderson model with diagonal disorder. Using the transfer matrix parametrization method and considering a specific distribution function, we calculate the Lyapunov exponent numerically and demonstrate its relation with the fractional lower order moments of the disorder probability density function. For the lower order of moments of disorder distribution with an infinite variance, we obtain the anomalous behavior near the band center.

Although hard rigid rods ($k$-mers) defined on the square lattice have been widely studied in the literature, their entropy per site, $s\left(k\right)$, in the full-packing limit is only known exactly for dimers ($k=2$) and numerically for trimers ($k=3$). Here, we investigate this entropy for rods with $k\le 7$, by defining and solving them on Husimi lattices built with diagonal and regular square-lattice clusters of effective lateral size $L$, where $L$ defines the level of approximation to the square lattice. Due to an $L$-parity effect, by increasing $L$ we obtain two systematic sequences of values for the entropies $s_L\left(k\right)$ for each type of cluster, whose extrapolations to $L\to \infty$ provide estimates of these entropies for the square lattice. For dimers, our estimates for $s\left(2\right)$ differ from the exact result by only $0.03\%$, while that for $s\left(3\right)$ differs from best available estimates by $3\%$. In this paper, we also obtain a new estimate for $s\left(4\right)$. For larger $k$, we find that the extrapolated results from the Husimi tree calculations do not lie between the lower and upper bounds established in the literature for $s\left(k\right)$. In fact, we observe that, to obtain reliable estimates for these entropies, we should deal with levels $L$ that increase with $k$. However, it is very challenging computationally to advance to solve the problem for large values of $L$ and for large rods. In addition, the exact calculations on the generalized Husimi trees provide strong evidence for the fully packed phase to be disordered for $k\ge 4$, in contrast to the results for the Bethe lattice wherein it is nematic.

The rock-paper-scissors (RPS) model successfully reproduces some of the main features of simple cyclic predator-prey systems with interspecific competition observed in nature. Still, lattice-based simulations of the spatial stochastic RPS model are known to give rise to significantly different results, depending on whether the three-state Lotka-Volterra or the four-state May-Leonard formulation is employed. This is true independently of the values of the model parameters and of the use of either a von Neumann or a Moore neighborhood. In this paper, we introduce a simple modification to the standard spatial stochastic RPS model in which the range of the search of the nearest neighbor may be extended up to a maximum Euclidean radius $R$. We show that, with this adjustment, the Lotka-Volterra and May-Leonard formulations can be designed to produce similar results, both in terms of dynamical properties and spatial features, by means of an appropriate parameter choice. In particular, we show that this modified spatial stochastic RPS model naturally leads to the emergence of spiral patterns in both its three- and four-state formulations.

In networks of nonlinear oscillators, symmetries place hard constraints on the system that can be exploited to predict universal dynamical features and steady states, providing a rare generic organizing principle for far-from-equilibrium systems. However, the robustness of this class of theories to symmetry-disrupting imperfections is untested in free-running (i.e., non-computer-controlled) systems. Here, we develop a model experimental reaction-diffusion network of chemical oscillators to test applications of the theory of dynamical systems with symmeries in the context of self-organizing systems relevant to biology and soft robotics. The network is a ring of four microreactors containing the oscillatory Belousov-Zhabotinsky reaction coupled to nearest neighbors via diffusion. Assuming homogeneity across the oscillators, theory predicts four categories of stable spatiotemporal phase-locked periodic states and four categories of invariant manifolds that guide and structure transitions between phase-locked states. In our experiments, we observed that three of the four phase-locked states were displaced from their idealized positions and, in the ensemble of measurements, appeared as clusters of different shapes and sizes, and that one of the predicted states was absent. We also observed the predicted symmetry-derived synchronous clustered transients that occur when the dynamical trajectories coincide with invariant manifolds. Quantitative agreement between experiment and numerical simulations is found by accounting for the small amount of experimentally determined heterogeneity in intrinsic frequency. We further elucidate how different patterns of heterogeneity impact each attractor differently through a bifurcation analysis. We show that examining bifurcations along invariant manifolds provides a general framework for developing intuition about how chemical-specific dynamics interact with topology in the presence of heterogeneity that can be applied to other oscillators in other topologies.

Link prediction is the problem of predicting the uncertain relationship between a pair of nodes from observed structural information of a network. Link prediction algorithms are useful in gaining insight into different network structures from partial observation of exemplars. Existing local and quasilocal link prediction algorithms with low computational complexity focus on regular complex networks with sufficiently many closed triangular motifs or on tree-like networks with the vast majority of open triangular motifs. However, the three-node motif cannot describe the local structural features of all networks, and we find the main structure of many networks is long line or closed circle that cannot be predicted well via traditional link prediction algorithms. Meanwhile, some global link prediction algorithms are effective but accompanied by high computational complexity. In this paper, we proposed a local method that is based on the natural characteristic of a long line—in contrast to the preferential attachment principle. Next, we test our algorithms for two kinds of symbolic long-circle-like networks: a metropolitan water distribution network and a sexual contact network. We find that our method is effective and performs much better than many traditional local and global algorithms. We adopt the community detection method to improve the accuracy of our algorithm, which shows that the long-circle-like networks also have clear community structure. We further suggest that the structural features are key for the link prediction problem. Finally, we propose a long-line network model to prove that our core idea is of universal significance.

We present a link-by-link rule-based method for constructing all members of the ensemble of spanning trees for any recursively generated, finitely articulated graph, such as the Dorogovtsev-Goltsev-Mendes (DGM) net. The recursions allow for many large-scale properties of the ensemble of spanning trees to be analytically solved exactly. We show how a judicious application of the prescribed growth rules selects for certain subsets of the spanning trees with particular desired properties (small world, extended diameter, degree distribution, etc.), and thus approximates and/or provides solutions to several optimization problems on undirected and unweighted networks. The analysis of spanning trees enhances the usefulness of recursive graphs as sophisticated models for everyday life complex networks.

We use the replica method to study the dynamical glass transition of the Gaussian core model, a system of ultrasoft repulsive spheres interacting via a Gaussian potential, focusing on low temperatures and low-to-moderate densities. At constant temperature, an amorphous glassy state is entered upon a first compression but this glass melts as the density is further increased. In addition to this reentrant transition, a second, smooth transition is discovered between a continuous and a discretized glass. The properties of the former are continuous functions of temperatures, whereas the latter exhibits a succession of stripes, characterized by discontinuous jumps of the glassiness parameters. The glass physics of ultrasoft particles is hence richer than that of impenetrable particles for reasons that can be attributed to the ability of the former to create and break out-of-equilibrium clusters of overlapping particles.

Vitrification of the antiferroelectric smectic-${\mathrm{C}}_A^{*}$ phase is reported for the orthoconic mixture W-1000 and its new derivative W-356. The crystallization is not observed even upon slow cooling and the cold crystallization on subsequent heating is also absent. Molecular dynamics in the smectic phases of both mixtures is investigated down to 173 K and the fragility parameters are determined from the temperature behavior of the $\alpha$-process. X-ray diffraction is applied to compare the structural parameters of W-356 and W-1000 as well as to study the structural changes during the glass transition of the Sm-${\mathrm{C}}_A^{*}$ phase. The evolution of the smectic layer order within the Sm-${\mathrm{C}}_A^{*}$ glass is reported, while the correlation length of the short-range order in the smectic layers is shown to be almost constant below the glass transition temperature. Electrooptic properties of W-356: spontaneous polarization, tilt angle and switching time are determined and compared with these of W-1000. The observed differences between the properties of W-356 and W-1000 might be explained by the dimer formation of components with the -$\mathrm{C}\equiv \mathrm{N}$ terminal group, present only in the W-356 mixture, and by the different structure of the aromatic molecular core in one of the W-356 components.

We develop a theory for the surface ripples produced by near-normal-incidence ion bombardment of a (001) GaAs surface with a small miscut along the [110] direction. We restrict our attention to the case in which the energy of the incident ions is below the sputter yield threshold and the sample temperature is just above the recrystallization temperature. Highly ordered, faceted ripples with their wave vector aligned with the [110] direction form when the ion beam is normally incident and there is no miscut. Two additional terms appear in the equation of motion when the beam is obliquely incident and/or there is a miscut: a linearly dispersive term and a nonlinearly dispersive term. The coefficients of these terms can become large as the threshold temperature for pattern formation is approached from above. In the absence of strong nonlinear dispersion, strong linear dispersion leads to ripples with a dramatically increased degree of order. These ripples are nearly sinusoidal even though they are on the surface of a single crystal. The exceptionally high degree of order is disrupted by nonlinear dispersion if the coefficient of that term is sufficiently large. However, by choosing the angle of ion incidence appropriately, the coefficient of the nonlinearly dispersive term can be made small. Ion bombardment will then produce highly ordered ripples. For a different range of parameter values, nucleation and growth of facets and spinodal decomposition can occur.

We study the behavior of cylindrical objects as they sink into a dry granular bed fluidized due to lateral oscillations. Somewhat unexpectedly, we have found that, within a large range of lateral shaking powers, cylinders with flat bottoms sink vertically, while those with a “foundation” consisting of a shallow ring attached to their bottom, tilt besides sinking. The latter scenario seems to dominate independently from the nature of the foundation when strong enough lateral vibrations are applied. We are able to explain the observed behavior by quasi-2D numerical simulations, which also demonstrate the influence of the intruder's aspect ratio. The vertical sink dynamics is explained with the help of a Newtonian equation of motion for the intruder. Our findings may shed light on the behavior of buildings and other manmade structures during earthquakes.

Rayleigh-Bénard convection with nonhomogeneous thermal boundaries (sinusoidal temperature patterns set in-phase at the top and bottom plates) is numerically studied in three- and two-dimensional domains. Two spatial convective scales occur: the one due to the self-organized clustering of plumes—which is known to appear in homogeneous conditions—and the scale induced by the boundary heterogeneities. The latter drives the convection patterning, both in 3D and 2D, when the wavelength of the perturbation is comparable with the self-organized one.

We study the photon emission by bremsstrahlung and nonlinear Compton scattering from interaction of ultra-intense laser pulses with cone target and flat foil using particle-in-cell simulations. The simulations are performed for laser pulses interacting with Al and Au targets. The strength of the two mechanisms of photon emission from bremsstrahlung and nonlinear Compton scattering are compared. When an ultra-intense ($I>{10}^{22}{\text{W/cm}}^2$) laser interacts with a cone and a foil target, photon emission by bremsstrahlung is found to be comparable to that from nonlinear Compton scattering. The obtained electron energy as well as the energy and number of photons emitted were found to be higher in case of cone shaped target compared with that of a foil target. The enhanced photon emission from cone shaped target is attributed to the guiding or collimation of hot electrons towards the cone tip from the self-generated magnetic field and electrostatic field along the cone surface which pushes the hot electrons towards the tip.