Optimizing the properties of the mosaic nanoscale morphology of bulk heterojunction (BHJ) organic photovoltaics (OPV) is not only challenging technologically but also intriguing from the mechanistic point of view. Among the recent breakthroughs is the identification and utilization of a three-phase (donor-mixed-acceptor) BHJ, where the (intermediate) mixed phase can inhibit mesoscale morphological changes, such as phase separation. Using a mean-field approach, we reveal and distinguish between generic mechanisms that alter, through transverse instabilities, the evolution of stripes: the bending (zigzag mode) and the pinching (cross-roll mode) of the donor-acceptor domains. The results are summarized in a parameter plane spanned by the mixing energy and illumination, and show that donor-acceptor mixtures with higher mixing energy are more likely to develop pinching under charge-flux boundary conditions. The latter is notorious as it leads to the formation of disconnected domains and hence to loss of charge flux. We believe that these results provide a qualitative road map for BHJ optimization, using mixed-phase composition and, therefore, an essential step toward long-lasting OPV. More broadly, the results are also of relevance to study the coexistence of multiple-phase domains in material science, such as in ion-intercalated rechargeable batteries.

The second law of thermodynamics states that the entropy never decreases for isolated macroscopical systems, which defines the arrow of time. For small systems, although the entropy increases on average, due to strong fluctuation, it may encounter a temporary decrease. The probability of negative entropy production follows the fluctuation theorem. Recently, it has been demonstrated theoretically the infima law that there exists a lower bound for the average values of the minima of the negative entropy production, which is $-k_B$. In this paper, we have constructed a horizontal Brownian motor immersed in a granular gas, whose dynamics is governed by the underdamped stochastic process. By recording the angular motion of the motor and measuring the key parameters of the system, we experimentally demonstrate that, despite the nonideal elements in the experiments and that the complex underlying dynamics, the average value of the minima of the negative entropy production is still bounded by $-k_B$, which may invoke further theoretical investigations of the applicability of the infima law in nonideal realistic small systems.

The Bures-Hall distance metric between quantum states is a unique measure that satisfies various useful properties for quantum information processing. In this work, we study the statistical behavior of quantum entanglement over the Bures-Hall ensemble as measured by von Neumann entropy. The average von Neumann entropy over such an ensemble has been recently obtained, whereas the main result of this work is an explicit expression of the corresponding variance that specifies the fluctuation around its average. The starting point of the calculations is the connection between correlation functions of the Bures-Hall ensemble and those of the Cauchy-Laguerre ensemble. The derived variance formula, together with the known mean formula, leads to a simple but accurate Gaussian approximation of the distribution of von Neumann entropy of finite-size systems. This Gaussian approximation is also conjectured to be the limiting distribution for large dimensional systems.

We study the first passage probability and mean number of sites visited by a discrete persistent random walker on a lattice in one and two dimensions. This is performed by using the multistate formulation of the process. We obtain explicit expressions for the generating functions of these quantities. To evaluate these expressions, we study the system in the strongly persistent limit. In the one-dimensional case, we recover the behavior of the continuous one-dimensional persistent random walk (telegrapher process). In two dimensions we obtain an explicit expression for the probability distribution in the strongly persistent limit, however, the Laplace transforms required to evaluate the first-passage processes could only be evaluated in the asymptotic limit corresponding to long times in which regime we recover the behavior of normal two-dimensional diffusion.

The motion of a free quantum particle in a thermal environment is usually described by the quantum Langevin equation, where the effect of the bath is encoded through a dissipative and a noise term, related to each other via the fluctuation dissipation theorem. The quantum Langevin equation can be derived starting from a microscopic model of the thermal bath as an infinite collection of harmonic oscillators prepared in an initial equilibrium state. The spectral properties of the bath oscillators and their coupling to the particle determine the specific form of the dissipation and noise. Here we investigate in detail the well-known Rubin bath model, which consists of a one-dimensional harmonic chain with the boundary bath particle coupled to the Brownian particle. We show how in the limit of infinite bath bandwidth, we get the Drude model, and a second limit of infinite system-bath coupling gives the Ohmic model. A detailed analysis of relevant equilibrium correlation functions, such as the mean squared displacement, velocity autocorrelation functions, and response function are presented, with the aim of understanding the various temporal regimes. In particular, we discuss the quantum-to-classical crossover time scales where the mean square displacement changes from a $\sim lnt$ to a $\sim t$ dependence. We relate our study to recent work using linear response theory to understand quantum Brownian motion.

The complex Ginzburg-Landau (CGL) equation, an envelope model relevant in the description of several natural phenomena like binary-fluid convection and second-order phase transitions, and the Lugiato-Lefever (LL) equation, describing the dynamics of optical fields in pumped lossy cavities, can be viewed as nonintegrable generalizations of the nonlinear Schrödinger (NLS) equation, including diffusion, linear and nonlinear loss or gain terms, and external forcing. In this paper we treat the nonintegrable terms of both equations as small perturbations of the integrable focusing NLS equation, and we study the Cauchy problem of the CGL and LL equations corresponding to periodic initial perturbations of the unstable NLS background solution, in the simplest case of a single unstable mode. Using the approach developed in a recent paper by the authors with P. G. Grinevich [Phys. Rev. E 101, 032204 (2020)], based on the finite gap method and the theory of perturbations of soliton PDEs, we construct the proper analytic models describing quantitatively how the solution evolves, after a suitable transient, into a Fermi-Pasta-Ulam-Tsingou (FPUT) recurrence of anomalous waves (AWs) described by slowly varying lower dimensional patterns (attractors) in the $(x,t)$ plane, characterized by $\mathrm{\Delta }x=L/2$ or $\mathrm{\Delta }x=0$ in the case in which loss or gain, respectively, effects prevail, where $\mathrm{\Delta }x$ is the $x$-shift of the position of the AW during the recurrence and $L$ is the period. We also obtain, in the CGL case, the analytic condition for which loss and gain exactly balance, stabilizing the ideal FPUT recurrence of periodic NLS AWs; such a stabilization is not possible in the LL case due to the external forcing. These processes are described, to leading order, in terms of elementary functions of the initial data in the CGL case, and in terms of elementary and special functions of the initial data in the LL case.

We propose and demonstrate the localization of resonant modes in a Limaçon optical microcavity with layered phase space involving both major and minor partial barriers. By regulating the openness of the cavity through the refractive index control, the minor partial barriers, which do not directly confine the long-lived resonant modes, are submerged successively into the leaky region. During the invalidation process of the minor partial barriers, it is found that the quality factor and the conjugate momentum of the resonant modes exhibit changes with the emergence of turning points. Such phenomena are attributed to the joint confinement effect by the minor partial barriers together with the major one in the layered phase space. This paper helps to improve the understanding of complex dynamics, and sheds light on the fine design of photonic devices with high performance.

We report on the effects of additive noises in a nonchaotic logistic map. In this system, the Lyapunov exponent changes from negative to positive as the noise intensity is increased. When the Lyapunov exponent is negative, the synchronization of orbits with different initial conditions occurs. We find that the synchronization time cannot be determined solely by the Lyapunov exponent when the noise intensity is greater than a point at which the Lyapunov exponent is minimum. We show that this reduction of the synchronization time is attributed to initial nonstationary behaviors, where the critical point of the logistic map plays an important role.

We introduce families of one-dimensional Lindblad equations describing open many-particle quantum systems that are exactly solvable in the following sense: (i) The space of operators splits into exponentially many (in system size) subspaces that are left invariant under the dissipative evolution; (ii) the time evolution of the density matrix on each invariant subspace is described by an integrable Hamiltonian. The prototypical example is the quantum version of the asymmetric simple exclusion process (ASEP) which we analyze in some detail. We show that in each invariant subspace the dynamics is described in terms of an integrable spin-1/2 $XXZ$ Heisenberg chain with either open or twisted boundary conditions. We further demonstrate that Lindbladians featuring integrable operator-space fragmentation can be found in spin chains with arbitrary local physical dimensions.

Some convergence proofs for systems of oscillators with inhibitory pulse coupling assume that all initial phases reside in one half of their domain. A violation of this assumption can trigger deadlocks that prevent synchronization. We analyze the conditions for such deadlocks in star graphs, characterizing the domain of initial states leading to deadlocks and deriving its fraction of the state space. The results show that convergence is feasible from a wider range of initial phases. The same type of deadlock occurs in random graphs.

A coupled phase-oscillator model consists of phase oscillators, each of which has the natural frequency obeying a probability distribution and couples with other oscillators through a given periodic coupling function. This type of model is widely studied since it describes the synchronization transition, which emerges between the nonsynchronized state and partially synchronized states. The synchronization transition is characterized by several critical exponents, and we focus on the critical exponent defined by coupling strength dependence of the order parameter for revealing universality classes. In a typical interaction represented by the perfect graph, an infinite number of universality classes is yielded by dependency on the natural frequency distribution and the coupling function. Since the synchronization transition is also observed in a model on a small-world network, whose number of links is proportional to the number of oscillators, a natural question is whether the infinite number of universality classes remains in small-world networks irrespective of the order of links. Our numerical results suggest that the number of universality classes is reduced to one and the critical exponent is shared in the considered models having coupling functions up to second harmonics with unimodal and symmetric natural frequency distributions.

Mathematical modeling of epidemics is fundamental to understand the mechanism of the disease outbreak and provides helpful indications for effectiveness of interventions for policy makers. The metapopulation network model has been used in the analysis of epidemic dynamics by taking individual migration between patches into account. However, so far, most of the previous studies unrealistically assume that transmission rates within patches are the same, neglecting the nonuniformity of intervention measures in hindering epidemics. Here, based on the assumption that interventions deployed in a patch depend on its population size or economic level, which have shown a positive correlation with the patch's degree in networks, we propose a metapopulation network model to explore a network structure-based intervention strategy, aiming at understanding the interplay between intervention strategy and other factors including mobility patterns, initial population, as well as the network structure. Our results demonstrate that interventions to patches with different intensity are able to suppress the epidemic spreading in terms of both the epidemic threshold and the final epidemic size. Specifically, the intervention strategy targeting the patches with high degree is able to efficiently suppress epidemics. In addition, a detrimental effect is also observed depending on the interplay between the intervention measures and the initial population distribution. Our study opens a path for understanding epidemic dynamics and provides helpful insights into the implementation of countermeasures for the control of epidemics in reality.

Swarmer cells of Caulobacter crescentus have been found to tether to glass at a point on the cell body. The rolling of the freely rotating flagellum near the glass surface causes the cell body to rotate. We describe the discovery of damped oscillations in the rotational speed of these cell bodies. We show that the damped oscillations are robust over multiple cells and that they depend more on the cell's accumulated rotation angle than on time. We also find that their phase is determined by the moment the flagellar motor changes the direction of its rotation. The oscillations occur only for one direction of cell rotation, when the flagellum is in pulling mode. We discuss possible explanations for these oscillations, including fluctuations in flagellar motor torque and periodic changes in flagellar orientation, and illustrate both of these cases using simplified computer models. Finally, we present the hypothesis that the oscillations are the result of fluctuations in the proton motive force, initiated by a sudden change in proton current that occurs when the motor switches rotation direction.

Branched networks constitute a ubiquitous structure in biology, arising in plants, lungs, and the circulatory system; however, the mechanisms behind their creation are not well understood. A commonly used model for network morphogenesis proposes that sprouts develop through interactions between leader (tip) cells and follower (stalk) cells. In this description, tip cells emerge from existing structures, travel up chemoattractant gradients, and form new networks by guiding the movement of stalk cells. Such dynamics have been mathematically represented by continuum “snail-trail” models in which the tip cell flux contributes to the stalk cell proliferation rate. Although snail-trail models constitute a classical depiction of leader-follower behavior, their accuracy has yet to be evaluated in a rigorous quantitative setting. Here, we extend the snail-trail modeling framework to two spatial dimensions by introducing a novel multiplicative factor to the stalk cell rate equation, which corrects for neglected network creation in directions other than that of the migrating front. Our derivation of this factor demonstrates that snail-trail models are valid descriptions of cell dynamics when chemotaxis dominates cell movement. We confirm that our snail-trail model accurately predicts the dynamics of tip and stalk cells in an existing agent-based model (ABM) for network formation [Pillay et al., Phys. Rev. E 95, 012410 (2017)]. We also derive conditions for which it is appropriate to use a reduced, one-dimensional snail-trail model to analyze ABM results. Our analysis identifies key metrics for cell migration that may be used to anticipate when simple snail-trail models will accurately describe experimentally observed cell dynamics in network formation.

Stochastic resonance is a noise phenomenon that benefits applications such as pattern formation, neural systems, microelectromechanical systems, and image processing. This study experimentally clarifies that the orientation of the liquid crystal molecules was switched between two stable positions when stochastic resonance was induced by colored noises in a liquid crystal light valve with optical feedback. Ornstein-Uhlenbeck and dichotomous noises were used for colored noise, and the noise was applied to the drive voltage of the liquid crystal light valve. The signal-to-noise ratio was measured with respect to changes in the noise type, noise intensity, and autocorrelation time of the noise. It was found that typical stochastic resonance was observed with a noise autocorrelation time of approximately 20 ms or more for both noise types, and dichotomous noise further enhanced the stochastic resonance compared to the Ornstein-Uhlenbeck noise. This suggests that it is possible to maximize stochastic resonance in a liquid crystal light valve by optimizing the conditions of colored noise.

We numerically study interaction of a very intense ($I\sim {10}^{17}$ to $5\times {10}^{19}\mathrm{W}/{\mathrm{cm}}^2$) femtosecond obliquely incident $p$-polarized laser pulse with a steep-gradient ($L\sim \lambda$) plasma, i.e., within the conditions typical for modern experiments. It is shown that the hybrid stimulated Raman scattering–two-plasmon decay instability develops near the quarter-critical density surface and plays the dominant role for the plasma waves' excitation and energy absorption. The plasmons are excited as two wave packets confined near this surface with very wide $\approx {\omega }_0/c$ spatial spectra along its normal. Hence, phase-matching conditions for the 3/2 harmonic generation are fulfilled immediately and include the mechanism coming from the high harmonics of plasma waves. This mechanism has been proved experimentally by observing an additional 3/2 harmonic beam.

In this work, a variant of the Wang and Landau algorithm for calculation of the configurational energy density of states is proposed. The algorithm was developed for the purpose of using first-principles simulations, such as density functional theory, to calculate the partition function of disordered sublattices in crystal materials. The expensive calculations of first-principles methods make a parallel algorithm necessary for a practical computation of the configurational energy density of states within a supercell approximation of a solid-state material. The algorithm developed in this work is tested with the two-dimensional (2d) Ising model to bench mark the algorithm and to help provide insight for implementation to a materials science application. Tests with the 2d Ising model revealed that the algorithm has good performance compared to the original Wang and Landau algorithm and the $1/t$ algorithm, in particular the short iteration performance. A proof of convergence is presented within an adiabatic assumption, and the analysis is able to correctly predict the time dependence of the modification factor to the density of states. The algorithm was then applied to the lithium and lanthanum sublattice of the solid-state lithium ion conductor ${\mathrm{Li}}_{0.5}{\mathrm{La}}_{0.5}\mathrm{Ti}{\mathrm{O}}_3$. This was done to help understand the disordered nature of the lithium and lanthanum. The results find, overall, that the algorithm performs very well for the 2d Ising model and that the results for ${\mathrm{Li}}_{0.5}{\mathrm{La}}_{0.5}\mathrm{Ti}{\mathrm{O}}_3$ are consistent with experiment while providing additional insight into the lithium and lanthanum ordering in the material. The primary result is that the lithium and lanthanum become more mixed between layers along the $c$ axis for increasing temperature. In part, the simulation of the disordered ${\mathrm{Li}}_{0.5}{\mathrm{La}}_{0.5}\mathrm{Ti}{\mathrm{O}}_3$ system serves as a benchmark for what size systems are currently and in the near future practical to calculate with density functional theory methods.

The atomistic simulation of materials growing in the layer-by-layer mode by the pulsed-laser deposition is a significant challenge mainly due to the short timescales in which the fastest processes on the surface occur together with long periods between pulses. We present a kinetic Monte Carlo algorithm which overcomes the scaling problem by approximation of fast diffusion and by neglecting complex chemical processes. The atomic diffusion is modeled as a two-dimensional gas of material units on each layer. The model is based on a few elementary processes—the condensation of units on the surface, their dissolution back to the gas, and interlayer transport, which can be influenced by the Ehrlich-Schwoebel barrier. With these simplifications, the computational time of the algorithm scales only linearly with the size of the substrate while describing physically relevant growth kinetics. We demonstrate that the simplified model is suitable for simulations of layered growth of thin films in the range from quasicontinuous deposition to low-frequency cases. The model is successfully implemented to provide an alternative explanation of the time evolution of layer coverages by interlayer transport after pulses of deposition experimentally observed during perovskite growth [G. Eres et al., Phys. Rev. B 84, 195467 (2011)].

The anomalies of supercooled water may be explained by an underlying liquid-liquid phase transition (LLPT) between high- and low-density states. Recently, its observation at 185 K was inferred using solutions containing aqueous ionic liquids at a solute mole fraction of $x=0.156$ [Woutersen et al., Science 359, 1127 (2018)]. We employ x-ray diffraction, calorimetry, and dilatometry on these hydrazinium trifluoroacetate solutions at $x=0.00–0.40$ to show that the transition at 185 K is not related to a genuine LLPT of water. Continuous densification upon compression, continuous changes of halo position, and absence of thermal signatures for a high- to low-density transition rule out the possibility of an LLPT for $x\ge 0.13$. The data show that employing sophisticated solutions adds a layer of complexity that hampers extrapolation of the LLPT concept from one- to two-component systems. The possibility of an LLPT can only be probed for pure water or sufficiently dilute aqueous solutions.