Quantum detailed balance conditions and quantum fluctuation relations are two important concepts in the dynamics of open quantum systems: both concern how such systems behave when they thermalize because of interaction with an environment. We prove that for thermalizing quantum dynamics the quantum detailed balance conditions yield validity of a quantum fluctuation relation (where only forward-time dynamics is considered). This implies that to have such a quantum fluctuation relation (which in turn enables a precise formulation of the second law of thermodynamics for quantum systems) it suffices to fulfill the quantum detailed balance conditions. We, however, show that the converse is not necessarily true; indeed, there are cases of thermalizing dynamics which feature the quantum fluctuation relation without satisfying detailed balance. We illustrate our results with three examples.

We demonstrate experimentally and corroborate numerically that an electrical lattice with nearest-neighbor and second-neighbor coupling can simultaneously support long-lived coherent structures in the form of both standard intrinsic localized modes (ILMs) as well as resonant ILMs. In the latter case, the wings of the ILM exhibit oscillations due to resonance with a plane-wave mode of the same frequency. This kind of localized mode has also been termed a nanopteron. Here we show experimentally and using realistic simulations of the system that the nanopteron can be stabilized via both direct and subharmonic driving. In the case of excitations at the zone center (i.e., at wave number $k=0$), we observed stable ILMs as well as a periodic localization pattern in certain driving regimes. In the zone boundary case (of wave number $k=\pi /a$, where $a$ is the lattice spacing), the ILMs are always resonant with a plane-wave mode, but they can nevertheless be stabilized by direct (staggered) and subharmonic driving.

In this paper, we study the stochastic resonance (SR) effect in an optomechanical system driven by a strong coupling field and two weak signals in both semiclassical and quantum frameworks. In the semiclassical description, the SR phenomena are found at the cooperation of input signals and system noises. When two signals coact on our system, the interference effect between the optically induced SR and the mechanically induced SR can be generated. In particular, a unique beating effect, which makes the SR effect robust against the initial phase difference of two signals, appears in the SR synchronization process with unsynchronized signals. In addition, the quantum stochastic resonance effect is numerically observed in the full quantum framework induced by pure quantum fluctuations.

We consider the one-dimensional Schrödinger equation on a ring, with the cubic term, of either self-attractive or repulsive sign, confined to a narrow segment. This setting can be realized in optics and Bose-Einstein condensates. For the nonlinearity coefficient represented by the $\delta$ function, all stationary states are obtained in an exact analytical form. The states with positive chemical potentials are found in alternating bands for the cases of the self-repulsion and attraction, while solutions with negative chemical potentials exist only in the latter case. These results provide a possibility to obtain exact solutions for band-gap states in the nonlinear system. Approximating the $\delta$ function by a narrow Gaussian, stability of the stationary modes is addressed through numerical computation of eigenvalues for small perturbations, and verified by simulations of the perturbed evolution. For positive chemical potentials, the stability is investigated in three lowest bands. In the case of the self-attraction, each band contains a stable subband, the transition to instability occurring with the increase of the total norm. As a result, multipeak states may be stable in higher bands. In the case of the self-repulsion, a single-peak ground state is stable in the first band, while the two higher ones are populated by weakly unstable two- and four-peak excited states. In the case of the self-attraction and negative chemical potentials, single-peak modes feature instability which transforms them into persistently oscillating states.

The sampling of interaction partners depends on often implicit modeling assumptions, yet has marked effects on the dynamics in evolutionary games. One particularly important aspect is whether or not competitors also interact. Population structures naturally affect sampling such that in a microscopic interpretation of the replicator dynamics in well-mixed populations competing individuals do not interact but do interact in structured populations. In social dilemmas interactions with competitors invariably inhibit cooperation, while limited local interactions in structured populations support cooperation by reducing exploitation through cluster formation. These antagonistic effects of population structures on cooperation affect interpretations and the conclusions depend on the details of the comparison. For example, in the snowdrift game, spatial structure may inhibit cooperation when compared to the replicator dynamics. However, modifying the replicator dynamics to include interactions between competitors lowers the equilibrium frequency of cooperators, which changes the conclusions, and space is invariably beneficial, just as in the prisoner's dilemma. These conclusions are confirmed by comparisons with random-matching models, which mimic population structures but randomly reshuffle individuals to inhibit spatial correlations. Finally, the differences in the dynamics with and without interactions among competing individuals underlie the differences between death-birth and birth-death updating in the spatial Moran process: death-birth updating supports cooperation because competitors tend not to interact whereas they tend to do for birth-death updating and hence cooperators provide direct support to competitors to their own detriment.

We introduce and study a metapopulation model of random walkers interacting at the nodes of a complex network. The model integrates random relocation moves over the links of the network with local interactions depending on the node occupation probabilities. The model is highly versatile, as the motion of the walkers depends on the topological properties of the nodes, such as their degree, while any general nonlinear function of the occupation probability of a node can be considered as local reaction term. In addition to this, the relative strength of reaction and relocation can be tuned at will, depending on the specific application being examined. We derive an analytical expression for the occupation probability of the walkers at equilibrium in the most general case. We show that it depends on different order derivatives of the local reaction functions, on the degree of a node, and on the average degree of its neighbors at various distances. For such a reason, reactive random walkers are very sensitive to the structure of a network and are a powerful way to detect network properties such as symmetries or degree-degree correlations. As possible applications, we first discuss how the occupation probability of reactive random walkers can be used to define novel measures of functional centrality for the nodes of a network. We then illustrate how network components with the same symmetries can be revealed by tracking the evolution of reactive walkers. Finally, we show that the dynamics of our model is influenced by the presence of degree-degree correlations, so that assortative and disassortative networks can be classified by quantitative indicators based on reactive walkers.

Experiments show that when engineered cardiac tissue is stretched, cells grow preferentially at the free edge of the tissue compared to the interior. In order to understand why cells grow near the edge, the mechanical bidomain model is used to simulate these experiments. This mathematical model of mechanotransduction treats the intra- and extracellular spaces individually, and predicts the force on integrin proteins in the cell membrane. The bidomain equations are solved numerically using the finite-difference method. The simulations predict that the difference between intra- and extracellular displacements, which the model assumes is the driving force behind cellular growth and remodeling, is largest near the free edge of a sheet of tissue, and is smallest at the center, consistent with experiments.

We use the bond fluctuation model to study the contraction process of two polymer loops with $N$ segments that are connected each to the bottom and top parts of a Feringa engine. The change in the size of the molecules as well as the folding of the two strands follows approximately scaling predictions that are derived by assuming that the strands are confined inside an effective tube. Conformation data can be overlapped when plotting it as a function of $W_{\text{n}}{N}^{-1/4}$, where $W_{\text{n}}$ is the winding number of the two strands that is proportional to the number of blobs inside the “knotted” region of the molecule and $N$ is the degree of polymerization of the strands. Our data support a weak localization of the knots along the contour of flexible cyclic athermal polymers with a localization exponent $t\approx 0.78$.

We investigate the effects of large predeformation on the propagation of planar solitary waves in flexible mechanical metamaterials comprising an array of hinged rotating squares. The predictive framework of our theoretical analysis shows that the predeformation can be exploited to control the characteristics of the supported elastic vector solitons via the tuning of the metamaterial dispersive and nonlinear properties. Together with numerical tests, our study provides a better understanding of the tunable dynamic response of flexible nonlinear mechanical metamaterials and explores more advanced configurations and effects that could open avenues for the design of systems with enhanced tunability.

Estimation of mutual information between random variables has become crucial in a range of fields, from physics to neuroscience to finance. Estimating information accurately over a wide range of conditions relies on the development of flexible methods to describe statistical dependencies among variables, without imposing potentially invalid assumptions on the data. Such methods are needed in cases that lack prior knowledge of their statistical properties and that have limited sample numbers. Here we propose a powerful and generally applicable information estimator based on nonparametric copulas. This estimator, called the nonparametric copula-based estimator (NPC), is tailored to take into account detailed stochastic relationships in the data independently of the data's marginal distributions. The NPC estimator can be used both for continuous and discrete numerical variables and thus provides a single framework for the mutual information estimation of both continuous and discrete data. By extensive validation on artificial samples drawn from various statistical distributions, we found that the NPC estimator compares well against commonly used alternatives. Unlike methods not based on copulas, it allows an estimation of information that is robust to changes of the details of the marginal distributions. Unlike parametric copula methods, it remains accurate regardless of the precise form of the interactions between the variables. In addition, the NPC estimator had accurate information estimates even at low sample numbers, in comparison to alternative estimators. The NPC estimator therefore provides a good balance between general applicability to arbitrarily shaped statistical dependencies in the data and shows accurate and robust performance when working with small sample sizes. We anticipate that the nonparametric copula information estimator will be a powerful tool in estimating mutual information in a broad range of data.

If particles interact according to isotropic pair potentials that favor multiple length scales, in principle, a large variety of different complex structures can be achieved by self-assembly. Here, we study the specific example of colloid-polymer mixtures in which the effective interactions between colloids are dictated by a Aasakura-Osawa–type potential that possesses two length scales. Upon examining the phase behavior of two-dimensional colloid-polymer mixtures, we observe that nontrivial structures only occur in the vicinity of selected densities where triangular ordering is suppressed by the pair potential. Close to these densities, a large number of different phases self-assemble that correspond to tilings containing triangular, rhombic, square, hexagonal, and pentagonal tiles, and including some of the Archimedean tilings. We obtain the ground-state energies by minimizing the corresponding lattice sums with respect to particle positions in a unit cell as well as cell geometry and verify the occurrence of selected phases at finite temperatures by using Brownian dynamics simulations. We explain how the occurrence of nontrivial orderings can be predicted on a two-particle level by employing an enthalpylike pair potentials. Our work provides a manual on how to find the regions of nontrivial phases in parameter space for complex pair interactions in general.

Azobenzene-based molecular systems are used as photoreswitchable smart materials with applications in many areas, including designing surface orientational patterning of anisotropic molecules. It is important and challenging to probe the real-time photoresponsive behaviors of these systems, particularly the photodynamic processes from the mesoscopic to microscopic or macroscopic scales near surfaces. We report an unusual reversible interfacial wetting-dewetting switching of a dendrimer incorporating azobenzene moieties. The switching is accompanied by light-driven generation or extinction processes of the surface wetting nanostructures, which are composed of supramolecular polarly layered molecules. The resultant polar-nonpolar switching of the surface allows macroscopic wetting-dewetting and nonlinear optical responses. Our results provide unique insights into controlling transient structures of photoresponsive materials.

Increasing our understanding of single and multiphase flow properties requires an accurate description of the pore system. Recent imaging technology provides images at different resolutions by which the pore space can be characterized properly. An accurate prediction of flow properties cannot be achieved computationally if the simulation domain is small. For a large sample, however, one may upscale the fine-scale information through pore-network modeling to expedite the computations. Due to a small field of view of the available images, such modeling can be conducted with ease for simple and heterogeneous rock samples. For complex and multiscale systems, however, one single-resolution image may not be sufficient. Thus, one should integrate the valuable information that lies in both the fine- and coarse scale into the pore network. In this paper, multiscale pore networks are generated which can take the microporosity, either in the solid phase (i.e., grain filling) or pore space (pore filling), into account. The proposed method can use the available high-resolution images for different pores and/or grains and stochastically build several micronetworks, which avoids fewer simplifications as present in the current methods. Next, depending on the location of high-resolution images, the generated micronetworks are implanted in the designated spots. Furthermore, cementation is also quantified and simulated by eroding the pore space. Finally, all the above physics are integrated within several stochastic multiscale networks. The final models are then used to evaluate the flow properties by comparing the statistical characteristics and single or multiphase flow behavior (e.g., capillary pressure, absolute and relative permeability). The results indicate the importance of incorporating the micropores as they can effectively connect the large-scale and isolated macropores. Furthermore, the single- and multiscale pore networks manifested a significant difference between the capillary pressure and residual saturation. Finally, a representative elementary volume study based on the generated multiscale pore networks for different scenarios is performed and the results are compared.

Small log-periodic oscillations have been observed in many systems and have previously been studied via renormalization-group approaches in the context of critical phenomena [Gluzman and Sornette, Phys. Rev. E 65, 036142 (2002); Derrida and Giacomin, J. Stat. Phys. 154, 286 (2014)]. Here we report their appearance in a random walk model with damaged memory, and we develop an exact discrete-time solution, free from adjustable parameters. Our results shed light on log-periodicity and how it arises. We also discuss continuous-time approaches to the solution along with their limitations and advantages. We show that, as a direct consequence of memory damage, the first moment for the model acquires piecewise ballistic behavior. The piecewise segments are separated by regularly placed singular points. Log-periodicity in this model is seen to be due to memory damage. Remarkably, piecewise ballistic behavior is only observed if one uses the discrete-time solution, because the continuous-time solution does not correctly account for the model's discrete-time dynamics.

We study dynamics of a spiking network of synaptically connected bistable neuronal oscillators. We find that delays in axonal conduction result in the emergence of coexisting states with high and low activity levels (up and down states). In the network, where cellular bistability is present, propagation delays and noise play a crucial role in the emergence of transitions between the states.

A theoretical model is developed that describes nonlinear coupling between wall deformation and water and ion flows in a charged, deformable nanochannel whose viscoelasticity is governed by the Kelvin-Voigt model. Using continuum mean-field theories for mass and momentum conservation of the solid-liquid coupled system, a set of one-dimensional nonlinear partial differential equations is derived to capture the dynamics of wall deformations. For elastic but non-viscous walls undergoing small deformation, the problem simplifies to one of advection-diffusion type which is analytically solvable at first-order perturbation. Results unveil a rich coupling between the elasticity and charge distribution of the channel walls, which vanishes in the limit of weakly charged channels. This coupling significantly alters the quantitative response of the walls' relaxation dynamics and the channel's electrokinetic transport, thereby having important consequences for the description and understanding of electrokinetic flow through charged, viscoelastic media.

The coupling between a laser and a prestructured target with an arbitrary structure period is investigated with the help of two-dimensional (2D) particle-in-cell (PIC) simulations. It is shown that new electromagnetic (e.m.) waves will be generated after the coupling. Since the coupling is a resonant process, strong surface currents will be generated, which result in the generation of strong quasistatic magnetic fields. The frequencies which the newly excited e.m. waves contain are harmonics of the laser frequency and the frequencies can be controlled by the structure period. Also, the propagation directions of the newly excited e.m. waves are well controlled by the ratio between the structure period and the laser wavelength, which means e.m. waves excited by lasers with different frequencies have different propagation directions. As a result, the prestructured target can act as a new kind of optical gratings which can be used to split superintense laser pulses. The controlling of both the harmonic frequencies and the propagation directions can be explained by matching condition of the coupling, which is a formula resembling but physically different from the diffraction grating equation. The quasistatic magnetic fields are on the target front surface and as strong as hundreds of teslas, but the amplitude will be decreased by the newly excited e.m. waves when they are propagating along the target surface. Since the propagation directions are controlled by the structure period, with an optimal structure period, the prestructured target can also act as a source of strong quasistatic magnetic fields.

Multiparticle collision dynamics (MPCD) enables us to simulate fluid dynamics including both hydrodynamics and thermal fluctuations. Its main use concerns complex fluids, where the solvent interacts with concentrated solutes, whether they are colloidal particles, polymers, or electrolytes. A key difficulty concerns the way one couples the fluid to the solute particles, without losing the key advantages of the MPCD method in term of computational efficiency. In this paper, we investigate the dynamical properties of solutes that are coupled to the fluid within the collision step, i.e., when local momentum exchange between fluid particles occurs. We quantify how the volume where momentum exchange is performed (the size of the collision cells) constrains the hydrodynamic size of the solute. Moreover, we show that this volume should be taken smaller than the structural size of the solutes. Within these constraints, we find that the hydrodynamic properties of a 1-1 electrolyte solution are similar to the behavior predicted by the Fuoss-Onsager theory of electrolyte dynamics, and we quantify the limitations of the theory for 2-1 and 2-2 electrolytes. However, it is also clear that mapping the diffusion timescale to that of a real system cannot be done quantitatively with this methodology.

Heterogeneity in relaxation rates is a key feature of supercooled liquids. It implies the existence of a rate-exchange process to restore ergodicity, but the experimental characterization of that exchange has been incomplete and controversial. Here, a recently proposed, ensemble-based analysis is applied to single-molecule dichroism data to extract a detailed correlation function for rotational-rate exchange. A large, late phase is $8.7\pm 0.3$ times slower than the probe rotation and 22 times the alpha-relaxation time, and it has its own exchange-rate dispersion. A small, early phase tracks the initial rotational decay. We propose that the late phase is due to molecules in the core of spatial regions of correlated rates and that the early phase is due to molecules on the boundaries. The results imply that multiple processes and spatial fields are involved in the primary relaxation in supercooled liquids.