Quenched disorder affects significantly the behavior of phase transitions. The Imry-Ma-Aizenman-Wehr-Berker argument prohibits first-order or discontinuous transitions and their concomitant phase coexistence in low-dimensional equilibrium systems in the presence of random fields. Instead, discontinuous transitions become rounded or even continuous once disorder is introduced. Here we show that phase coexistence and first-order phase transitions are also precluded in nonequilibrium low-dimensional systems with quenched disorder: discontinuous transitions in two-dimensional systems with absorbing states become continuous in the presence of quenched disorder. We also study the universal features of this disorder-induced criticality and find them to be compatible with the universality class of the directed percolation with quenched disorder. Thus, we conclude that first-order transitions do not exist in low-dimensional disordered systems, not even in genuinely nonequilibrium systems with absorbing states.

The goal of the present work is to investigate the role of trivial disorder and nontrivial disorder in the three-state Hopfield model under a Gaussian random field. In order to control the nontrivial disorder, the Hebb interaction is used. This provides a way to control the system frustration by means of the parameter $a=\frac{p}{N}$, varying from trivial randomness to a highly frustrated regime, in the thermodynamic limit. We performed the thermodynamic analysis using the one-step replica-symmetry-breaking mean field theory to obtain the order parameters and phase diagrams for several strengths of $a$, the anisotropy constant, and the random field.

We numerically investigate head-on collisions of isothermal viscoelastic spheres. We find that the restitution coefficient oscillates against the impact speed if the solid viscosity inside the sphere is small enough. We confirm that the oscillation arises from the resonance between the duration of contact and the eigenfrequencies of the sphere. This oscillation disappears if there exists the strong solid viscosity in spheres. We also find that a sinusoidal behavior of the restitution coefficient against the initial phase in the eigenmodes for collisions between a thermally activated sphere and a flat wall. As a result, the restitution coefficient can exceed unity if the impact speed of the colliding sphere is nearly equal to or slower than the thermal speed. We have confirmed the existence of the fluctuation theorem for impact processes through our simulation.

Understanding the driving forces that lead to the stability of the secondary motifs found in proteins, namely $\alpha$-helix and $\beta$-sheet, is a major goal in structural biology. The thermodynamic stability of these repetitive units is a result of a delicate balance between many factors, which in addition to the peptide chain involves also the solvent. Despite the fact that the backbones of all amino acids are the same (except of that of proline), there are large differences in the propensity of the different amino acids to promote the helical structure. In this paper, we investigate by explicit-solvent molecular dynamics simulations the role of the side chains (modeled as coarse-grained single sites) in stabilizing $\alpha$ helices in an aqueous solution. Our model systems include four (six-mer–nine-mer) peptide lengths in which the magnitude of the effective attraction between the side chains is systematically increased. We find that these interactions between the side chains can induce (for the nine-mer almost completely) a transition from a coil to a helical state. This transition is found to be characterized by three states in which the intermediate state is a partially folded $\alpha$-helical conformation. In the absence of any interactions between the side chains the free energy change for helix formation has a small positive value indicating that favorable contributions from the side chains are necessary to stabilize the helical conformation. Thus, the helix-coil transition is controlled by the effective potentials between the side-chain residues and the magnitude of the required attraction per residue, which is on the order of the thermal energy, reduces with the length of the peptide. Surprisingly, the plots of the population of the helical state (or the change in the free energy for helix formation) as a function of the total effective interactions between the side chains in the helical state for all peptide lengths fall on the same curve.

The current study extends previous two-dimensional (2D) analysis of concentration polarization to account for three-dimensional effects in realistic heterogeneous ion-permselective systems, e.g., microchamber-nanoslot devices. An analytical solution of the electrodiffusive problem, decoupled from electroconvection along with the local electroneutrality approximation, was obtained using the separation of variables technique. It is able to account for the previously neglected effects of microchamber and nanoslot heights on concentration polarization in terms of concentration profiles, limiting current, and current-voltage curves. The resultant heterogeneity in the third dimension adds to that already existing in the 2D in plane problem to further increase geometric field-focusing effects. As a result the currents no longer scale linearly with the nanoslot area, but rather depend on its shape and relative size compared to that of the nonconducting region (i.e., level of heterogeneity). This is turn leads to pronounced current density intensification with increased system heterogeneity found to be in qualitative agreement with previously reported experiments in which both microchamber and nanoslot geometries were varied.

The dynamic properties of finite three-dimensional dust clusters in a dusty plasma under the influence of an ion focus are studied by normal modes. The mode analysis has been extended to account for the ion focus using the point-charge model for the horizontal interaction of the dust particles. From that, an analytical model for a few-particle system is derived accounting for three distinct dynamical regimes at different focus strengths, namely, absolutely unstable and fully stable configurations as well as an unstable oscillatory regime. The techniques of normal mode analysis (NMA) and instantaneous normal modes (INM) extended by the ion focus have been applied to dust systems in the experiment and compared to the model. From this, the ion focus strength has been derived. The specific sensitivity of NMA and INM allows one to identify equilibrium configurations in this nonequilibrium environment for these finite clusters.

A generalized theory of nonequilibrium thermodynamics for a Brownian motor operating between two different heat baths is presented. Via a simple paradigmatic model, we not only explore the thermodynamic feature of the engine in the regime of the nonequilibrium steady state but also study the short time behavior of the system for either the isothermal case with load or, in general, the nonisothermal case with or without load. Many elegant thermodynamic theories can be checked via the present model. Furthermore the dependence of the velocity, the efficiency, and the performance of the refrigerator on time $t$ is examined. Our study reveals a current reversal due to time $t$. In the early system relaxation period, the model works neither as a heat engine nor as a refrigerator and only after a certain period of time does the model start functioning as a heat engine or as a refrigerator. The performance of the engine also improves with time and at steady state the engine manifests a higher efficiency or performance as a refrigerator. Furthermore the effect of energy exchange via the kinetic energy on the performance of the heat engine is explored.

The theory of the elastic interaction of spherical colloidal particles immersed into a confined cholesteric liquid crystal is proposed. The case of weak anchoring on the particle surfaces is considered. We derive a general expression for the energy of the interaction between small spherical particles (with diameter much smaller than the cholesteric pitch) suspended in a cholesteric confined by two parallel planes. The resulting form of the interaction energy has a more complex spatial pattern and energy versus distance dependence than that in nematic colloids. The absence of translational symmetry related to helical periodicity and local nematic ordering in cholesteric liquid crystals manifest themselves in the complex nature of the interaction maps.

Biological molecular machines are proteins that operate under isothermal conditions and hence are referred to as free energy transducers. They can be formally considered as enzymes that simultaneously catalyze two chemical reactions: the free energy-donating (input) reaction and the free energy-accepting (output) one. Most if not all biologically active proteins display a slow stochastic dynamics of transitions between a variety of conformational substates composing their native state. This makes the description of the enzymatic reaction kinetics in terms of conventional rate constants insufficient. In the steady state, upon taking advantage of the assumption that each reaction proceeds through a single pair (the gate) of transition conformational substates of the enzyme-substrates complex, the degree of coupling between the output and the input reaction fluxes has been expressed in terms of the mean first-passage times on a conformational transition network between the distinguished substates. The theory is confronted with the results of random-walk simulations on the five-dimensional hypercube. The formal proof is given that, for single input and output gates, the output-input degree of coupling cannot exceed unity. As some experiments suggest such exceeding, looking for the conditions for increasing the degree of coupling value over unity challenges the theory. Performed simulations of random walks on several model networks involving more extended gates indicate that the case of the degree of coupling value higher than 1 is realized in a natural way on critical branching trees extended by long-range shortcuts. Such networks are scale-free and display the property of the small world. For short-range shortcuts, the networks are scale-free and fractal, representing a reasonable model for biomolecular machines displaying tight coupling, i.e., the degree of coupling equal exactly to unity. A hypothesis is stated that the protein conformational transition networks, as just as higher-level biological networks, the protein interaction network, and the metabolic network, have evolved in the process of self-organized criticality.

What if we played the Rubik's cube game by simple intuition? We would rotate the cube, probably in the hope of getting a more organized pattern in each next step. Yet frustration occurs easily, and we soon find ourselves trapped as the game progresses no further. Played in this completely strategy-less style, the entire problem of the Rubik's cube game can be compared to that of complex chemical reactions such as protein folding, only with less guidance in the searching process. In this work we look into this random-searching process by means of thermodynamics and compare the game's dynamics with that of a faithful stochastic model constructed from the statistical energy landscape theory (SELT). This comparison reveals the peculiar nature of SELT, which relies on the random energy approximation and often chops up energy correlations among nearby configurations. Our observation provides a general insight for the use of SELT in the studies of these frustrated systems.

We investigate the failure mechanisms of load-sharing complex systems. The system is composed of multiple nodes or components whose failures are determined based on the interaction of their respective strengths and loads (or capacity and demand, respectively) as well as the ability of a component to share its load with its neighbors when needed. We focus on two distinct mechanisms to model the interaction between components' strengths and loads. The failure mechanisms of these two models demonstrate temporal scaling phenomena, phase transitions, and multiple distinct failure modes excited by extremal dynamics. For critical ranges of parameters the models demonstrate power-law and exponential failure patterns. We identify the similarities and differences between the two mechanisms and the implications of our results for the failure mechanisms of complex systems in the real world.

We consider a two-dimensional collisionless ideal gas in the two vessels connected through a small hole. One of them is a well-behaved chaotic billiard, another one is known to be nonergodic. A significant part of the second vessel's phase space is occupied by an island of stability. In the works of Zaslavsky and coauthors, distribution of Poincaré recurrence times in similar systems was considered. We study the gas pressure in the vessels; it is uniform in the first vessel and not uniform in second one. An equation of the gas state in the first vessel is obtained. Despite the very different phase-space structure, behavior of the second vessel is found to be very close to the behavior of a good ergodic billiard but of different volume. The equation of state differs from the ordinary equation of ideal gas state by an amendment to the vessel's volume. Correlation of this amendment with a share of the phase space under remaining intact islands of stability is shown.

We present a modified Wang-Landau sampling (MWLS) for continuous statistical models by partitioning the energy space into a set of windows with logarithmically shrinking width. To demonstrate its necessity and advantages, we apply this sampling to several continuous models, including the two-dimensional square XY spin model, triangular $J_1$-$J_2$ spin model, and Lennard-Jones cluster model. Given a finite number of bins for partitioning the energy space, the conventional Wang-Landau sampling may not generate sufficiently accurate density of states (DOS) around the energy boundaries. However, it is demonstrated that much more accurate DOS can be obtained by this MWLS, and thus a precise evaluation of the thermodynamic behaviors of the continuous models at extreme low temperature $(k_{B}T<0.1)$ becomes accessible. The present algorithm also allows efficient computation besides the highly reliable data sampling.

Many structural properties of conventional passive materials are known to arise from the symmetries of their microscopic constituents. By contrast, it is largely unclear how the interplay between particle shape and self-propulsion controls the meso- and macroscale behavior of active matter. Here we use large-scale simulations of homo- and heterogeneous self-propelled particle systems to identify generic effects of broken particle-shape symmetry on collective motion. We find that even small violations of fore-aft symmetry lead to fundamentally different collective behaviors, which may facilitate demixing of differently shaped species as well as the spontaneous formation of stable microrotors. These results suggest that variation of particle shape yields robust physical mechanisms to control self-assembly of active matter, with possibly profound implications for biology and materials design.

We analytically evaluate the large deviation function in a simple model of classical particle transfer between two reservoirs. We illustrate how the asymptotic long-time regime is reached starting from a special propagating initial condition. We show that the steady-state fluctuation theorem holds provided that the distribution of the particle number decays faster than an exponential, implying analyticity of the generating function and a discrete spectrum for its evolution operator.

We prove a general theorem which provides a strict lower bound on high-temperature Green-Kubo diffusion constants in locally interacting quantum lattice systems, under the assumption of existence of a quadratically extensive almost conserved quantity: an operator whose commutator with the lattice Hamiltonian is localized on the boundary sites only. We explicitly demonstrate and compute such a bound in two important models in one dimension: in the (isotropic) Heisenberg spin 1/2 chain and in the fermionic Hubbard chain.

The present work is devoted to the study of spectral characteristics of normal incident light transmitted by a multilayered structure composed of an alternated sequence of nematic and magnetic layers presenting a central magneto-optical defect. Using the Berreman 4 $\times$ 4 matrix formalism, we numerically obtain the transmission spectrum and the polarization rotation angle of the system as a function of the nematic optical axis direction. Our results reveal the emergence of a shift between the wavelengths of the resonant mode and polarization rotation angle, which strongly depends on the birefringence of the nematic layers. In particular, we show the existence of distinct regimes for the wavelength mismatch between the transmission of resonant modes and the maximum polarization rotation angle, which are governed by the ordinary and extraordinary refractive indices of nematic layers. The mechanism behind such shift is discussed under the light of propagation eigenmodes for a medium presenting circular and linear birefringence. The effects associated with the defect thickness are also analyzed.

Self-propelled pointlike particles move along circular trajectories when their translocation velocity is constant and the angular velocity related to their orientation vector is also constant. We investigate the collective behavior of ensembles of such circle swimmers by Brownian dynamics simulations. If the particles interact via a “velocity-trajectory coordination” rule within neighboring particles, a self-organized vortex pattern emerges. This vortex pattern is characterized by its particle-density correlation function $G_{\rho }$, the density correlation function $G_c$ of trajectory centers, and an order parameter $S$ representing the degree of the aggregation of the particles. Here we systematically vary the system parameters, such as the particle density and the interaction range, in order to reveal the transition of the system from a light-vortex-dominated to heavy-vortex-dominated state, where vortices contain mainly a single and many self-propelled particles, respectively. We also study a semidilute solution of curved, sinusoidal-beating flagella, as an example of circling self-propelled particles with explicit propulsion mechanism and excluded-volume interactions. Our simulation results are compared with previous experimental results for the vortices in sea-urchin sperm solutions near a wall. The properties of the vortices in simulations and experiments are found to agree quantitatively.

Standard models of population dynamics focus on the interaction, survival, and extinction of the competing species individually. Real ecological systems, however, are characterized by an abundance of species (or strategies, in the terminology of evolutionary-game theory) that form intricate, complex interaction networks. The description of the ensuing dynamics may be aided by studying associations of certain strategies rather than individual ones. Here we show how such a higher-level description can bear fruitful insight. Motivated from different strains of colicinogenic Escherichia coli bacteria, we investigate a four-strategy system which contains a three-strategy cycle and a neutral alliance of two strategies. We find that the stochastic, spatial model exhibits a mobility-dependent selection of either the three-strategy cycle or of the neutral pair. We analyze this intriguing phenomenon numerically and analytically.