The coarsening of stripe patterns when the system is evolved from random initial states is studied by varying the quench depth $\epsilon$, which is a measure of distance from the transition point of the stripe phase. The dynamics of the growth of stripe order, which is characterized by two length scales, depends on the quench depth. The growth exponents of the two length scales vary continuously with $\epsilon$. The decay exponents for free energy, stripe curvature, and densities of defects like grain boundaries and dislocations also show similar variation. This implies a breakdown of the standard picture of nonequilibrium dynamical scaling. In order to understand the variations with $\epsilon$ we propose an additional scaling with a length scale dependent on $\epsilon$. The main contribution to this length scale comes from the “pinning potential,” which is unique to systems where the order parameter is spatially periodic. The periodic order parameter gives rise to an $\epsilon$-dependent potential, which can pin defects like grain boundaries, dislocations, etc. This additional scaling provides a compact description of variations of growth exponents with quench depth in terms of just one exponent for each of the length scales. The relaxation of free energy, stripe curvature, and the defect densities have also been related to these length scales. The study is done at zero temperature using Swift-Hohenberg equation in two dimensions.

We investigate the formation of localized structures with varying widths in one- and two-dimensional systems. The mechanism of stabilization is attributed to strongly nonlocal coupling mediated by a Lorentzian type of kernel. We show that, in addition to stable dips found recently [see, e.g. Fernandez-Oto et al., Phys. Rev. Lett. 110, 174101 (2013)], there are stable localized peaks which appear as a result of strongly nonlocal coupling. We applied this mechanism to arid ecosystems by considering a prototype model of a Nagumo type. In one dimension, we study the front connecting the stable uniformly vegetated state to the bare one under the effect of strongly nonlocal coupling. We show that strongly nonlocal coupling stabilizes both—dip and peak—localized structures. We show analytically and numerically that the width of a localized structure, which we interpret as a fairy circle, increases strongly with the aridity parameter. This prediction is in agreement with published observations. In addition, we predict that the width of localized patch decreases with the degree of aridity. Numerical results are in close agreement with analytical predictions.

Indirect-drive implosions with a high-density carbon (HDC) capsule were conducted on the National Ignition Facility (NIF) to test HDC properties as an ablator material for inertial confinement fusion. A series of five experiments were completed with $76\text{−}\mu \mathrm{m}$-thick HDC capsules using a four-shock laser pulse optimized for HDC. The pulse delivered a total energy of $1.3$ MJ with a peak power of 360 TW. The experiment demonstrated good laser to target coupling $\left(\sim 90\%\right)$ and excellent nuclear performance. A deuterium and tritium gas-filled HDC capsule implosion produced a neutron yield of $1.6\times {10}^{15}\pm 3\times {10}^{13}$, a yield over simulated in one dimension of $70\%$.

We present a unified perspective on nonequilibrium heat engines by generalizing nonlinear irreversible thermodynamics. For tight-coupling heat engines, a generic constitutive relation for nonlinear response accurate up to the quadratic order is derived from the stalling condition and the symmetry argument. By applying this generic nonlinear constitutive relation to finite-time thermodynamics, we obtain the necessary and sufficient condition for the universality of efficiency at maximum power, which states that a tight-coupling heat engine takes the universal efficiency at maximum power up to the quadratic order if and only if either the engine symmetrically interacts with two heat reservoirs or the elementary thermal energy flowing through the engine matches the characteristic energy of the engine. Hence we solve the following paradox: On the one hand, the quadratic term in the universal efficiency at maximum power for tight-coupling heat engines turned out to be a consequence of symmetry [Esposito, Lindenberg, and Van den Broeck, Phys. Rev. Lett. 102, 130602 (2009); Sheng and Tu, Phys. Rev. E 89, 012129 (2014)]; On the other hand, typical heat engines such as the Curzon-Ahlborn endoreversible heat engine [Curzon and Ahlborn, Am. J. Phys. 43, 22 (1975)] and the Feynman ratchet [Tu, J. Phys. A 41, 312003 (2008)] recover the universal efficiency at maximum power regardless of any symmetry.

Schrödinger suggested that thermodynamical functions cannot be based on the gratuitous allegation that quantum-mechanical levels (typically the orthogonal eigenstates of the Hamiltonian operator) are the only allowed states for a quantum system [E. Schrödinger, Statistical Thermodynamics (Courier Dover, Mineola, 1967)]. Different authors have interpreted this statement by introducing density distributions on the space of quantum pure states with weights obtained as functions of the expectation value of the Hamiltonian of the system. In this work we focus on one of the best known of these distributions and prove that, when considered in composite quantum systems, it defines partition functions that do not factorize as products of partition functions of the noninteracting subsystems, even in the thermodynamical regime. This implies that it is not possible to define extensive thermodynamical magnitudes such as the free energy, the internal energy, or the thermodynamic entropy by using these models. Therefore, we conclude that this distribution inspired by Schrödinger's idea cannot be used to construct an appropriate quantum equilibrium thermodynamics.

Myosin-V is a highly processive dimeric protein that walks with 36-nm steps along actin tracks, powered by coordinated adenosine triphosphate (ATP) hydrolysis reactions in the two myosin heads. No previous theoretical models of the myosin-V walk reproduce all the observed trends of velocity and run length with adenosine diphosphate (ADP), ATP and external forcing. In particular, a result that has eluded all theoretical studies based upon rigorous physical chemistry is that run length decreases with both increasing [ADP] and [ATP]. We systematically analyze which mechanisms in existing models reproduce which experimental trends and use this information to guide the development of models that can reproduce them all. We formulate models as reaction networks between distinct mechanochemical states with energetically determined transition rates. For each network architecture, we compare predictions for velocity and run length to a subset of experimentally measured values, and fit unknown parameters using a bespoke Monte Carlo simulated annealing optimization routine. Finally we determine which experimental trends are replicated by the best-fit model for each architecture. Only two models capture them all: one involving [ADP]-dependent mechanical detachment, and another including [ADP]-dependent futile cycling and nucleotide pocket collapse. Comparing model-predicted and experimentally observed kinetic transition rates favors the latter.

We discuss the problem of the detection of hyperchaotic oscillations in coupled nonlinear systems when the available information about this complex dynamical regime is very limited. We demonstrate the ability of diagnosing the chaos-hyperchaos transition from return times into a Poincaré section and show that an appropriate selection of the secant plane allows a correct estimation of two positive Lyapunov exponents (LEs) from even a single sequence of return times. We propose a generalized approach for extracting dynamics from point processes that allows avoiding spurious identification of the dynamical regime caused by artifacts. The estimated LEs are nearly close to their expected values if the second positive LE is essentially different from the largest one. If both exponents become nearly close, an underestimation of the second LE may be obtained. Nevertheless, distinctions between chaotic and hyperchaotic regimes are clearly possible.

Simple practical expressions that allow estimation of thermodynamic properties of Yukawa fluids in a wide range of coupling, up to the fluid-solid phase transition, are presented. These expressions demonstrate excellent agreement with the available results from numerical simulations. The approach provides simple and accurate tools to estimate thermodynamic properties of Yukawa fluids and related systems in a broad range of parameters.

A hybrid spin-electron system defined on a one-dimensional double-tetrahedral chain, in which the localized Ising spin regularly alternates with two mobile electrons delocalized over a triangular plaquette, is exactly solved with the help of generalized decoration-iteration transformation. It is shown that a macroscopic degeneracy of ferromagnetic and ferrimagnetic ground states arising from chiral degrees of freedom of the mobile electrons cannot be lifted by a magnetic field in contrast to a macroscopic degeneracy of the frustrated ground state, which appears due to a kinetically driven frustration of the localized Ising spins. An anomalous behavior of all basic thermodynamic quantities can be observed on account of massive thermal excitations, which mimic a temperature-driven first-order phase transition from the nondegenerate frustrated state to the highly degenerate ferrimagnetic state at nonzero magnetic fields. A substantial difference in the respective degeneracies is responsible for an immense low-temperature peak of the specific heat and very abrupt (almost discontinuous) thermal variations of the entropy and sublattice magnetizations.

An effective temperature $\theta$, conjugated to a generalized entropy $s_q$, was introduced recently for a system of interacting particles. Since $\theta$ presents values much higher than those of typical room temperatures $T\ll \theta$, the thermal noise can be neglected ($T/\theta \simeq 0$) in these systems. Moreover, the consistency of this definition, as well as of a form analogous to the first law of thermodynamics, $du=\theta d{s}_q+\delta W$, were verified lately by means of a Carnot cycle, whose efficiency was shown to present the usual form, $\eta =1-({\theta }_2/{\theta }_1)$. Herein we explore further the heat contribution $\delta Q=\theta d{s}_q$ by proposing a way for a heat exchange between two such systems, as well as its associated thermal equilibrium. As a consequence, the zeroth principle is also established. Moreover, we consolidate the first-law proposal by following the usual procedure for obtaining different potentials, i.e., applying Legendre transformations for distinct pairs of independent variables. From these potentials we derive the equation of state, Maxwell relations, and define response functions. All results presented are shown to be consistent with those of standard thermodynamics for $T>0$.

Molecular dynamic simulations were carried out on rigid diatomic molecules, which exhibit both α (structural) and β (secondary) dynamics. The relaxation scenarios range from onset behavior, in which a distinct α process emerges on cooling, to merging behavior, associated with two relaxation peaks that converge at higher temperature. These properties, as well as the manifestation of the β peak as an excess wing, depend not only on thermodynamic conditions, but also on both the symmetry of the molecule and the correlation function (odd or even) used to analyze its dynamics. These observations help to reconcile divergent results obtained from different experiments. For example, the β process is more intense and the α-relaxation peak is narrower in dielectric relaxation spectra than in dynamic light scattering or NMR measurements. In the simulations herein, this follows from the weaker contribution of the secondary relaxation to even-order correlation functions, related to the magnitude of the relevant angular jumps.

We study the behavior of two macroions with dissociable charge groups, regulated by local variables such as $p\mathrm{H}$ and electrostatic potential, immersed in a monovalent salt solution, considering cases where the net charge can either change sign or remain of the same sign depending on these local parameters. The charge regulation in both cases is described by the proper free-energy function for each of the macroions, while the coupling between the charges is evaluated on the approximate Debye-Hückel level. The charge correlation functions and the ensuing charge fluctuation forces are calculated analytically and numerically. Strong attraction between like-charged macroions is found close to the point of zero charge, specifically due to asymmetric, anticorrelated charge fluctuations of the macroion charges. The general theory is then implemented for a system of two proteinlike macroions, generalizing the form and magnitude of the Kirkwood-Schumaker interaction.

A basic understanding of biological membranes is of paramount importance as these membranes comprise the very building blocks of life itself. Cells depend in their function on a range of properties of the membrane, which are important for the stability and function of the cell, information and nutrient transport, waste disposal, and finally the admission of drugs into the cell and also the deflection of bacteria and viruses. We have investigated the influence of ibuprofen on the structure and dynamics of L-$\alpha$-phosphatidylcholine (SoyPC) membranes by means of grazing incidence small-angle neutron scattering, neutron reflectometry, and grazing incidence neutron spin echo spectroscopy. From the results of these experiments, we were able to determine that ibuprofen induces a two-step structuring behavior in the SoyPC films, where the structure evolves from the purely lamellar phase for pure SoyPC over a superposition of two hexagonal phases to a purely hexagonal phase at high concentrations. A relaxation, which is visible when no ibuprofen is present in the membrane, vanishes upon addition of ibuprofen. This we attribute to a stiffening of the membrane. This behavior may be instrumental in explaining the toxic behavior of ibuprofen in long-term application.

The majority-vote model with noise is one of the simplest nonequilibrium statistical model that has been extensively studied in the context of complex networks. However, the relationship between the critical noise where the order-disorder phase transition takes place and the topology of the underlying networks is still lacking. In this paper, we use the heterogeneous mean-field theory to derive the rate equation for governing the model's dynamics that can analytically determine the critical noise $f_c$ in the limit of infinite network size $N\to \infty$. The result shows that $f_c$ depends on the ratio of $\langle k\rangle$ to $\langle k^{3/2}\rangle$, where $\langle k\rangle$ and $\langle k^{3/2}\rangle$ are the average degree and the $3/2$ order moment of degree distribution, respectively. Furthermore, we consider the finite-size effect where the stochastic fluctuation should be involved. To the end, we derive the Langevin equation and obtain the potential of the corresponding Fokker-Planck equation. This allows us to calculate the effective critical noise $f_c\left(N\right)$ at which the susceptibility is maximal in finite-size networks. We find that the $f_c-f_c\left(N\right)$ decays with $N$ in a power-law way and vanishes for $N\to \infty$. All the theoretical results are confirmed by performing the extensive Monte Carlo simulations in random $k$-regular networks, Erdös-Rényi random networks, and scale-free networks.

We present breather solutions of the quintic integrable equation of the Schrödinger hierarchy. This equation has terms describing fifth-order dispersion and matching nonlinear terms. Using a Darboux transformation, we derive first-order and second-order breather solutions. These include first- and second-order rogue-wave solutions. To some extent, these solutions are analogous with the corresponding nonlinear Schrödinger equation (NLSE) solutions. However, the presence of a free parameter in the equation results in specific solutions that have no analogues in the NLSE case. We analyze new features of these solutions.

We evidence an interesting kind of hybrid synchronization in coupled chaotic systems where complete synchronization is restricted to only a subset of variables of two systems while other subset of variables may be in a phase synchronized state or desynchronized. Such hybrid synchronization is a generic emergent feature of coupled systems when a controller based coupling, designed by the Lyapunov function stability, is first engineered to induce complete synchronization in the identical case, and then a large parameter mismatch is introduced. We distinguish between two different hybrid synchronization regimes that emerge with parameter perturbation. The first, called hard hybrid synchronization, occurs when the coupled systems display global phase synchronization, while the second, called soft hybrid synchronization, corresponds to a situation where, instead, the global synchronization feature no longer exists. We verify the existence of both classes of hybrid synchronization in numerical examples of the Rössler system, a Lorenz-like system, and also in electronic experiment.

When placed onto a vibrating liquid bath, a droplet may adopt a permanent bouncing behavior, depending on both the forcing frequency and the forcing amplitude. The relationship between the droplet deformations and the bouncing mechanism is studied experimentally and theoretically through an asymmetric and dissipative bouncing spring model. Antiresonance phenomena are evidenced. Experiments and theoretical predictions show that both resonance at specific frequencies and antiresonance at Rayleigh frequencies play crucial roles in the bouncing mechanism. In particular, we show that they could be exploited for bouncing droplet size selection.

A consistent theoretical model that can be applied in a wide range of densities and temperatures is necessary for understanding the variation of a material's properties during compression and heating. Taking argon as an example, we show that the combination of self-consistent fluid variational theory and linear response theory is a promising route for studying warm dense matter. Following this route, the compositions, equations of state, and transport properties of argon plasma are calculated in a wide range of densities $(0.001-20\mathrm{g}/\mathrm{c}{\mathrm{m}}^3)$ and temperatures $(5-100\mathrm{kK})$. The obtained equations of state and electrical conductivities are found in good agreement with available experimental data. The plasma phase transition of argon is observed at temperatures below $30\mathrm{kK}$ and density about $2-6\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$. The minimum density for the metallization of argon is found to be about $5.8\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$, occurring at $30-40\mathrm{kK}$. The effects of many-particle correlations and dynamic screening on the electrical conductivity are also discussed through the effective potentials.