The present work is devoted to the study of the thermo-optical and nonlinear optical properties of smectic samples containing gold nanoparticles with different shapes. By using the time-resolved Z-scan technique, we determine the effects of nanoparticle addition on the critical behavior of the thermal diffusivity and thermo-optical coefficient at the vicinity of the smectic-$A$–nematic phase transition. Our results reveal that introduction of gold nanoparticles affects the temperature dependence of thermo-optical parameters, due to the local distortions in the orientational order and heat generation provided by guest particles during the laser exposure. Further, we show that a nonlinear optical response may take place at temperatures where the smectic order is well established. We provide a detailed discussion of the effects associated with the introduction gold nanoparticles on the mechanisms behind the thermal transport and optical nonlinearity in liquid-crystal samples.

Stationary two-dimensional localized structures have been observed in a wide variety of dissipative systems. The existence, stability properties, dynamical evolution, and bifurcation diagram of an azimuthal symmetry breaking, rodlike localized structure in the isotropic prototype model of pattern formation, the Swift-Hohenberg model, is studied. These rodlike structures persist under the presence of nongradient perturbations. Interaction properties of the rodlike structures are studied. This allows us to envisage the possibility of different crystal-like configurations.

The classical capacity of quantum channels is well understood for channels with uncorrelated noise. For the case of correlated noise, however, there are still open questions. We calculate the classical capacity of a forgetful channel constructed by Markov switching between two depolarizing channels. Techniques have previously been applied to approximate the output entropy of this channel and thus its capacity. In this paper, we use a Metropolis-Hastings Monte Carlo approach to numerically calculate the entropy. The algorithm is implemented in parallel and its performance is studied and optimized. The effects of memory on the capacity are explored and previous results are confirmed to higher precision.

Predicting the long-lasting quasistationary state for a given initial state is one of central issues in Hamiltonian systems having long-range interaction. A recently proposed method is based on the Vlasov description and uniformly redistributes the initial distribution along contours of the asymptotic effective Hamiltonian, which is defined by the obtained quasistationary state and is determined self-consistently. The method, to which we refer as the rearrangement formula, was suggested to give precise prediction under limited situations. Restricting initial states consisting of a spatially homogeneous part and small perturbation, we numerically reveal two conditions that the rearrangement formula prefers: One is a no Landau damping condition for the unperturbed homogeneous part, and the other comes from the Casimir invariants. Mechanisms of these conditions are discussed. Clarifying these conditions, we validate to use the rearrangement formula as the response theory for an external field, and we shed light on improving the theory as a nonequilibrium statistical mechanics.

Stochastic thermodynamics uses Markovian jump processes to model random transitions between observable mesoscopic states. Physical currents are obtained from antisymmetric jump observables defined on the edges of the graph representing the network of states. The asymptotic statistics of such currents are characterized by scaled cumulants. In the present work, we use the algebraic and topological structure of Markovian models to prove a gauge invariance of the scaled cumulant-generating function. Exploiting this invariance yields an efficient algorithm for practical calculations of asymptotic averages and correlation integrals. We discuss how our approach generalizes the Schnakenberg decomposition of the average entropy-production rate, and how it unifies previous work. The application of our results to concrete models is presented in an accompanying publication.

Unlike macroscopic engines, the molecular machinery of living cells is strongly affected by fluctuations. Stochastic thermodynamics uses Markovian jump processes to model the random transitions between the chemical and configurational states of these biological macromolecules. A recently developed theoretical framework [A. Wachtel, J. Vollmer, and B. Altaner, Phys. Rev. E 92, 042132 (2015)] provides a simple algorithm for the determination of macroscopic currents and correlation integrals of arbitrary fluctuating currents. Here we use it to discuss energy conversion and nonequilibrium response in different models for the molecular motor kinesin. Methodologically, our results demonstrate the effectiveness of the algorithm in dealing with parameter-dependent stochastic models. For the concrete biophysical problem our results reveal two interesting features in experimentally accessible parameter regions: the validity of a nonequilibrium Green-Kubo relation at mechanical stalling as well as a negative differential mobility for superstalling forces.

In this study, we present a detailed analysis of the squeeze-out dynamics of nanoconfined water confined between two hydrophilic surfaces measured by small-amplitude dynamic atomic force microscopy. Explicitly considering the instantaneous tip-surface separation during squeeze-out, we confirm the existence of an adsorbed molecular water layer on mica and at least two hydration layers. We also confirm the previous observation of a sharp transition in the viscoelastic response of the nanoconfined water as the compression rate is increased beyond a critical value (previously determined to be about 0.8 nm/s). We find that below the critical value, the tip passes smoothly through the molecular layers of the film, while above the critical speed, the tip encounters “pinning” at separations where the film is able to temporarily order. Preordering of the film is accompanied by increased force fluctuations, which lead to increased damping preceding a peak in the film stiffness once ordering is completed. We analyze the data using both Kelvin-Voigt and Maxwell viscoelastic models. This provides a complementary picture of the viscoelastic response of the confined water film.

In this paper we categorize dynamical regimes demonstrated by starlike networks with chaotic nodes. This analysis is done in view of further studying of chaotic scale-free networks, since a starlike structure is the main motif of them. We analyze starlike networks of Hénon maps. They are found to demonstrate a huge diversity of regimes. Varying the coupling strength we reveal chaos, quasiperiodicity, and periodicity. The nodes can be both fully and phase synchronized. The hub node can be either synchronized with the subordinate nodes or oscillate separately from fully synchronized subordinates. There is a range of wild multistability where the zoo of regimes is the most various. One can hardly predict here even a qualitative nature of the expected solution, since each perturbation of the coupling strength or initial conditions results in a new character of dynamics.

We study models of a society composed of a mixture of conformist and reasonable contrarian agents that at any instant hold one of two opinions. Conformists tend to agree with the average opinion of their neighbors and reasonable contrarians tend to disagree, but revert to a conformist behavior in the presence of an overwhelming majority, in line with psychological experiments. The model is studied in the mean-field approximation and on small-world and scale-free networks. In the mean-field approximation, a large fraction of conformists triggers a polarization of the opinions, a pitchfork bifurcation, while a majority of reasonable contrarians leads to coherent oscillations, with an alternation of period-doubling and pitchfork bifurcations up to chaos. Similar scenarios are obtained by changing the fraction of long-range rewiring and the parameter of scale-free networks related to the average connectivity.

Interaction via pulses is common in many natural systems, especially neuronal. In this article we study one of the simplest possible systems with pulse interaction: a phase oscillator with delayed pulsatile feedback. When the oscillator reaches a specific state, it emits a pulse, which returns after propagating through a delay line. The impact of an incoming pulse is described by the oscillator's phase reset curve (PRC). In such a system we discover an unexpected phenomenon: for a sufficiently steep slope of the PRC, a periodic regular spiking solution bifurcates with several multipliers crossing the unit circle at the same parameter value. The number of such critical multipliers increases linearly with the delay and thus may be arbitrary large. This bifurcation is accompanied by the emergence of numerous “jittering” regimes with nonequal interspike intervals (ISIs). Each of these regimes corresponds to a periodic solution of the system with a period roughly proportional to the delay. The number of different “jittering” solutions emerging at the bifurcation point increases exponentially with the delay. We describe the combinatorial mechanism that underlies the emergence of such a variety of solutions. In particular, we show how a periodic solution exhibiting several distinct ISIs can imply the existence of multiple other solutions obtained by rearranging of these ISIs. We show that the theoretical results for phase oscillators accurately predict the behavior of an experimentally implemented electronic oscillator with pulsatile feedback.

Obtaining an accurate equation of state (EOS) of polystyrene (CH) is crucial to reliably design inertial confinement fusion (ICF) capsules using CH/CH-based ablators. With first-principles calculations, we have investigated the extended EOS of CH over a wide range of plasma conditions ($\rho =0.1\mathrm{to}100\mathrm{g}/{\mathrm{cm}}^3$ and $T=1000\mathrm{to}4000000\mathrm{K}$). When compared with the widely used SESAME-EOS table, the first-principles equation of state (FPEOS) of CH has shown significant differences in the low-temperature regime, in which strong coupling and electron degeneracy play an essential role in determining plasma properties. Hydrodynamic simulations of cryogenic target implosions on OMEGA using the FPEOS table of CH have predicted ∼30% decrease in neutron yield in comparison with the usual SESAME simulations. This is attributed to the ∼5% reduction in implosion velocity that is caused by the ∼10% lower mass ablation rate of CH predicted by FPEOS. Simulations using CH-FPEOS show better agreement with measurements of Hugoniot temperature and scattered light from ICF implosions.

The statistical property of acoustic emission (AE) events from a plunged granular bed is analyzed by means of actual-time and natural-time analyses. These temporal analysis methods allow us to investigate the details of AE events that follow a power-law distribution. In the actual-time analysis, the calm-time distribution, and the decay of the event-occurrence density after the largest event (i.e., the Omori-Utsu law) are measured. Although the former always shows a power-law form, the latter does not always obey a power law. Markovianity of the event-occurrence process is also verified using a scaling law by assuming that both of them exhibit power laws. We find that the effective shear strain rate is a key parameter to classify the emergence rate of power-law nature and Markovianity in granular AE events. For the natural-time analysis, the existence of self-organized critical states is revealed by calculating the variance of natural time ${\chi }_k$, where $k\mathrm{th}$ natural time of $N$ events is defined as ${\chi }_k=k/N$. In addition, the energy difference distribution can be fitted by a $q$-Gaussian form, which is also consistent with the criticality of the system.

The ability of a mutant individual to overtake the whole of a population is one of the fundamental problems in evolutionary dynamics. Fixation probability and Average Fixation Time (AFT) are two important parameters to quantify this ability. In this paper we introduce an analytical approach for exact calculation of AFT. Using this method we obtain AFT for two types of evolutionary graphs: cycle graph, as a highly homogeneous graph and star graph, as a highly heterogeneous graph. We use symmetries of these graphs to calculate AFT. Analytical results are confirmed with simulation. We also examine the effect of adding some random edges to each of these structures.

We combine the coherent modified Redfield theory (CMRT) with the equation of motion-phase matching approach (PMA) to calculate two-dimensional photon-echo spectra for photoactive molecular complexes with an intermediate strength of the coupling to their environment. Both techniques are highly efficient, yet they involve approximations at different levels. By explicitly comparing with the numerically exact quasiadiabatic path integral approach, we show for the Fenna-Matthews-Olson complex that the CMRT describes the decay rates in the population dynamics well, but final stationary populations and the oscillation frequencies differ slightly. In addition, we use the combined CMRT+PMA to calculate two-dimensional photon-echo spectra for a simple dimer model. We find excellent agreement with the exact path integral calculations at short waiting times where the dynamics is still coherent. For long waiting times, differences occur due to different final stationary states, specifically for strong system-bath coupling. For weak to intermediate system-bath couplings, which is most important for natural photosynthetic complexes, the combined CMRT+PMA gives reasonable results with acceptable computational efforts.

We study the probability that two directed polymers in the same random potential do not intersect. We use the replica method to map the problem onto the attractive Lieb-Liniger model with generalized statistics between particles. Employing both the nested Bethe ansatz and known formula from MacDonald processes, we obtain analytical expressions for the first few moments of this probability and compare them to a numerical simulation of a discrete model at high temperature. From these observations, several large time properties of the noncrossing probabilities are conjectured. Extensions of our formalism to more general observables are discussed.

It is well known that the linear-noise approximation (LNA) agrees with the chemical master equation, up to second-order moments, for chemical systems composed of zero and first-order reactions. Here we show that this is also a property of the LNA for a subset of chemical systems with second-order reactions. This agreement is independent of the number of interacting molecules.

Dissipative electromagnetic response and scattering geometry are potential sources for the appearance of a negative Casimir entropy. We show that the dissipative contribution familiar from the plane-plane geometry appears also in the plane-sphere and the sphere-sphere geometries and adds to the negative Casimir entropy known to exist in these geometries even for perfectly reflecting objects. Taking the sphere-sphere geometry as an example, we carry out a scattering-channel analysis, which allows us to distinguish between the contributions of different polarizations. We demonstrate that dissipation and geometry share a common feature making possible negative values of the Casimir entropy. In both cases there exists a scattering channel whose contribution to the Casimir free energy vanishes in the high-temperature limit. While the mode-mixing channel is associated with the geometric origin, the transverse electric channel is associated with the dissipative origin of the negative Casimir entropy. By going beyond the Rayleigh limit, we find even for large distances that negative Casimir entropies can occur also for Drude-type metals provided the dissipation strength is sufficiently small.

The Carnot statement of the second law of thermodynamics poses an upper limit on the efficiency of all heat engines. Recently, it has been studied whether generic quantum features such as coherence and quantum entanglement could allow for quantum devices with efficiencies larger than the Carnot efficiency. The present study shows that this is not permitted by the laws of thermodynamics—independent of the model. We will show that rather the definition of heat has to be modified to account for the thermodynamic cost of maintaining non-Gibbsian equilibrium states. Our theoretical findings are illustrated for two experimentally relevant examples.

The ferromagnetic Ising model with antiferromagnetic dipole interactions is investigated by means of Monte Carlo simulations, focusing on the characterization of the phase transitions between the tetragonal liquid and stripe of width $h$ phases. The dynamic evolution of the physical observables is analyzed within the short-time regime for $0.5\le \delta \le 1.3$, where $\delta$ is the ratio between the short-range exchange and the long-range dipole interaction constants. The obtained results for the interval $0.5\le \delta \le 1.2$ indicate that the phase transition line between the $h=1$ stripe and tetragonal liquid phases is continuous. This finding contributes to clarifying the controversy about the order of this transition. This controversy arises from the difficulties introduced in the simulations due to the presence of long-range dipole interactions, such as an important increase in the simulation times that limits the system size used, strong finite size effects, as well as to the existence of multiple metastable states at low temperatures. The study of the short-time dynamics of the model allows us to avoid these hindrances. Moreover, due to the fact that the finite-size effects do not significantly affect the power-law behavior exhibited in the observables within the short-time regime, the results could be attributed to those corresponding to the thermodynamic limit. As a consequence of this, a careful characterization of the critical behavior for the whole transition line is performed by giving the complete set of critical exponents.

The concept of a nonequilibrium interfacial tension, defined via the work required to deform a system such that the interfacial area is changed while the volume is conserved, is investigated theoretically in the context of the relaxation of an initial perturbation of a colloidal fluid towards the equilibrium state. The corresponding general formalism is derived for systems with planar symmetry and applied to fluid models of colloidal suspensions and polymer solutions. It is shown that the nonequilibrium interfacial tension is not necessarily positive, that negative nonequilibrium interfacial tensions are consistent with strictly positive equilibrium interfacial tensions, and that the sign of the interfacial tension can influence the morphology of density perturbations during relaxation.