A method combining perturbation theory with a simplifying ansatz is used to describe the exciton-phonon dynamics in complex networks. This method, called ${\mathrm{PT}}^{*}$, is compared to exact calculations based on the numerical diagonalization of the exciton-phonon Hamiltonian for eight small-sized networks. It is shown that the accuracy of ${\mathrm{PT}}^{*}$ depends on the nature of the network, and three different situations were identified. For most graphs, ${\mathrm{PT}}^{*}$ yields a very accurate description of the dynamics. By contrast, for the Wheel graph and the Apollonian network, ${\mathrm{PT}}^{*}$ reproduces the dynamics only when the exciton occupies a specific initial state. Finally, for the complete graph, ${\mathrm{PT}}^{*}$ breaks down. These different behaviors originate in the interplay between the degenerate nature of the excitonic energy spectrum and the strength of the exciton-phonon interaction so that a criterion is established to determine whether or not ${\mathrm{PT}}^{*}$ is relevant. When it succeeds, our study shows the undeniable advantage of ${\mathrm{PT}}^{*}$ in that it allows us to perform very fast simulations when compared to exact calculations that are restricted to small-sized networks.

We experimentally study the effect of temperature and electric field on the quality $\left(Q\right)$ factor and free spectral range (FSR) of whispering-gallery-mode optical resonance of dye-doped nematic liquid crystal microdroplets. Both the $Q$ factor and the FSR are highly sensitive to the temperature and electric field and are tunable. The $Q$ factor decreases, whereas the FSR increases substantially, with increasing temperature and electric field. The variation of the $Q$ factor and FSR is understood based on the change in the effective refractive index and the dynamic size of the microdroplets.

We theoretically study the influence of the liquid crystal (LC) orientational state on the absorption, reflection, and transmission spectra of a graphene microribbon grating placed between a nematic LC and an isotropic dielectric substrate. We calculate the absorption, reflection, and transmission coefficients at normal incidence of a far-infrared transverse magnetic wave (THz) and show that control of the orientational state of the LC layer enables the manipulation of the magnitude of the absorption and reflection maxima. The influence the LC orientational state on the plasmonic resonance increases with increasing the isotropic substrate dielectric constant and the graphene microribbon width to grating spacing ratio.

In this paper, an enthalpy-based multiple-relaxation-time (MRT) lattice Boltzmann (LB) method is developed for solid-liquid phase-change heat transfer in metal foams under the local thermal nonequilibrium (LTNE) condition. The enthalpy-based MRT-LB method consists of three different MRT-LB models: one for flow field based on the generalized non-Darcy model, and the other two for phase-change material (PCM) and metal-foam temperature fields described by the LTNE model. The moving solid-liquid phase interface is implicitly tracked through the liquid fraction, which is simultaneously obtained when the energy equations of PCM and metal foam are solved. The present method has several distinctive features. First, as compared with previous studies, the present method avoids the iteration procedure; thus it retains the inherent merits of the standard LB method and is superior to the iteration method in terms of accuracy and computational efficiency. Second, a volumetric LB scheme instead of the bounce-back scheme is employed to realize the no-slip velocity condition in the interface and solid phase regions, which is consistent with the actual situation. Last but not least, the MRT collision model is employed, and with additional degrees of freedom, it has the ability to reduce the numerical diffusion across the phase interface induced by solid-liquid phase change. Numerical tests demonstrate that the present method can serve as an accurate and efficient numerical tool for studying metal-foam enhanced solid-liquid phase-change heat transfer in latent heat storage. Finally, comparisons and discussions are made to offer useful information for practical applications of the present method.

Although interdependent systems have usually been associated with increased fragility, we show that strengthening the interdependence between dynamical processes on different networks can make them more likely to survive over long times. By coupling the dynamics of networks that in isolation exhibit catastrophic collapse with extinction of nodal activity, we demonstrate system-wide persistence of activity for an optimal range of interdependence between the networks. This is related to the appearance of attractors of the global dynamics comprising disjoint sets (“islands”) of stable activity.

It was recently conjectured by Vivo, Pato, and Oshanin [Phys. Rev. E 93, 052106 (2016)] that for a quantum system of Hilbert dimension $mn$ in a pure state, the variance of the von Neumann entropy of a subsystem of dimension $m\le n$ is given by$$-{\psi }_1(mn+1)+\frac{m+n}{mn+1}{\psi }_1\left(n\right)-\frac{(m+1)(m+2n+1)}{4n^2(mn+1)},$$where ${\psi }_1(·)$ is the trigamma function. We give a proof of this formula.

We study systems in which both long-ranged van der Waals and critical Casimir interactions are present. The latter arise as an effective force between bodies when immersed in a near-critical medium, say a nonpolar one-component fluid or a binary liquid mixture. They are due to the fact that the presence of the bodies modifies the order parameter profile of the medium between them as well as the spectrum of its allowed fluctuations. We study the interplay between these forces, as well as the total force (TF) between a spherical colloid particle and a thick planar slab and between two spherical colloid particles. We do that using general scaling arguments and mean-field-type calculations utilizing the Derjaguin and the surface integration approaches. They both are based on data of the forces between two parallel slabs separated at a distance $L$ from each other, confining the fluctuating fluid medium characterized by its temperature $T$ and chemical potential $\mu$. The surfaces of the colloid particles and the slab are coated by thin layers exerting strong preference to the liquid phase of the fluid, or one of the components of the mixture, modeled by strong adsorbing local surface potentials, ensuring the so-called $(+,+)$ boundary conditions. On the other hand, the core region of the slab and the particles influence the fluid by long-ranged competing dispersion potentials. We demonstrate that for a suitable set of colloids-fluid, slab-fluid, and fluid-fluid coupling parameters, the competition between the effects due to the coatings and the core regions of the objects involved result, when one changes $T, \mu$, or $L$, in sign change of the Casimir force (CF) and the TF acting between the colloid and the slab, as well as between the colloids. This can be used for governing the behavior of objects, say colloidal particles, at small distances, say in colloid suspensions for preventing flocculation. It can also provide a strategy for solving problems with handling, feeding, trapping, and fixing of microparts in nanotechnology. Data for specific substances in support of the experimental feasibility of the theoretically predicted behavior of the CF and TF have been also presented.

The detection of directional couplings between dynamics based on measured spike trains is a crucial problem in the understanding of many different systems. In particular, in neuroscience it is important to assess the connectivity between neurons. One of the approaches that can estimate directional coupling from the analysis of point processes is the nonlinear interdependence measure $L$. Although its efficacy has already been demonstrated, it still needs to be tested under more challenging and realistic conditions prior to an application to real data. Thus, in this paper we use the Hindmarsh-Rose model system to test the method in the presence of noise and for different spiking regimes. We also examine the influence of different parameters and spike train distances. Our results show that the measure $L$ is versatile and robust to various types of noise, and thus suitable for application to experimental data.

We present a semiclassical study of the spectrum of a few-body system consisting of two short-range interacting bosonic particles in one dimension, a particular case of a general class of integrable many-body systems where the energy spectrum is given by the solution of algebraic transcendental equations. By an exact mapping between $\delta$-potentials and boundary conditions on the few-body wave functions, we are able to extend previous semiclassical results for single-particle systems with mixed boundary conditions to the two-body problem. The semiclassical approach allows us to derive explicit analytical results for the smooth part of the two-body density of states that are in excellent agreement with numerical calculations. It further enables us to include the effect of bound states in the attractive case. Remarkably, for the particular case of two particles in one dimension, the discrete energy levels obtained through a requantization condition of the smooth density of states are essentially in perfect agreement with the exact ones.

Oscillations in far-from-equilibrium systems (e.g., chemical, biochemical, biological) are generated by the nonlinear interplay of positive and negative feedback effects operating at different time scales. Relaxation oscillations emerge when the time scales between the activators and the inhibitors are well separated. In addition to the large-amplitude oscillations (LAOs) or relaxation type, these systems exhibit small-amplitude oscillations (SAOs) as well as abrupt transitions between them (canard phenomenon). Localized cluster patterns in networks of relaxation oscillators consist of one cluster oscillating in the LAO regime or exhibiting mixed-mode oscillations (LAOs interspersed with SAOs), while the other oscillates in the SAO regime. Because the individual oscillators are monostable, localized patterns are a network phenomenon that involves the interplay of the connectivity and the intrinsic dynamic properties of the individual nodes. Motivated by experimental and theoretical results on the Belousov-Zhabotinsky reaction, we investigate the mechanisms underlying the generation of localized patterns in globally coupled networks of piecewise-linear relaxation oscillators where the global feedback term affects the rate of change of the activator (fast variable) and depends on the weighted sum of the inhibitor (slow variable) at any given time. We also investigate whether these patterns are affected by the presence of a diffusive type of coupling whose synchronizing effects compete with the symmetry-breaking global feedback effects.

Dynamics of active deformable particles in an external Poiseuille flow is investigated. To make the analysis general, we employ time-evolution equations derived from symmetry considerations that take into account an elliptical shape deformation. First, we clarify the relation of our model to that of rigid active particles. Then, we study the dynamical modes that active deformable particles exhibit by changing the strength of the external flow. We emphasize the difference between the active particles that tend to self-propel parallel to the elliptical shape deformation and those self-propelling perpendicularly. In particular, a swinging motion around the centerline far from the channel walls is discussed in detail.

Many physical systems are composed of polyhedral cells of varying sizes and shapes. These structures are simple in the sense that no more than three faces meet at an edge and no more than four edges meet at a vertex. This means that individual cells can usually be considered as simple, three-dimensional polyhedra. This paper is concerned with determining the distribution of combinatorial types of such polyhedral cells. We introduce the terms fundamental and vertex-truncated types and apply these concepts to the grain growth microstructure as a testing ground. For these microstructures, we demonstrate that most grains are of particular fundamental types, whereas the frequency of vertex-truncated types decreases exponentially with the number of truncations. This can be explained by the evolutionary process through which grain growth structures are formed and in which energetically unfavorable surfaces are quickly eliminated. Furthermore, we observe that these grain types are “round” in a combinatorial sense: there are no “short” separating cycles that partition the polyhedra into two parts of similar sizes. A particular microstructure derived from the Poisson–Voronoi initial condition is identified as containing an unusually large proportion of round grains. This microstructure has an average of 14.036 faces per grain and is conjectured to be more resistant to topological change than the steady-state grain growth microstructure.

In this work we propose a theoretical model that accounts for the main features of the loading-unloading process of a symmetric redox ${\mathrm{MnO}}_2$-based supercapacitor dominated by fast electrochemical reactions at the electrodes. The model is formulated on the basis of nonequilibrium thermodynamics from which we are able to deduce generalized expressions for the electrochemical affinity, the load-voltage and the current-voltage equations that constitute generalizations of the current-overpotential and Butler-Volmer equations, and that are used to describe experimental voltagram data with good agreement. These equations allowed us to derive the behavior of the energy dissipated per cycle showing that it has a nonmonotonic behavior and that in the operation regime it follows a power-law behavior as a function of the frequency. The existence of a maximum for the energy dissipated as a function of the frequency suggests the that the corresponding optimal operation frequency should be similar in value to ${\omega }_{\max }$.

The application of stochastic differential equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we introduce a nonparametric method for estimating the drift and diffusion terms of SDEs from a densely observed discrete time series. The use of Gaussian processes as priors permits working directly in a function-space view and thus the inference takes place directly in this space. To cope with the computational complexity that requires the use of Gaussian processes, a sparse Gaussian process approximation is provided. This approximation permits the efficient computation of predictions for the drift and diffusion terms by using a distribution over a small subset of pseudosamples. The proposed method has been validated using both simulated data and real data from economy and paleoclimatology. The application of the method to real data demonstrates its ability to capture the behavior of complex systems.

We present an algorithm for the optimization and thermal equilibration of spin glasses, or more generally, cost functions of the Ising form $H={\sum }_{\langle ij\rangle }{J}_{ij}{s}_i{s}_j+{\sum }_i{h}_i{s}_i$, defined on graphs with arbitrary connectivity. The algorithm consists of two repeated steps: (i) the optimized construction of a random tree of spin clusters on the input problem graph, and (ii) the thermal sampling of the generated tree. The randomly generated trees are constructed so as to optimize a balance between the size of the tree and the complexity required to draw Boltzmann samples from it. We benchmark the algorithm on several classes of problems and demonstrate its advantages over existing approaches.

In this work, we study the Kuramoto model with biharmonic interaction and bimodal frequency distribution. Rich synchronous dynamics, such as standing wave states, stationary partial synchronous dynamics, and multiplicity of singular synchronous dynamics, are found. Notably, we find a symmetry-breaking synchronous dynamics when the peaks in frequency distribution are not well separated. We present the phase diagrams for two cases: the peaks in the frequency distribution are well separated and the peaks are not well separated. We find that reducing peak distance tends to make the transition between standing wave states and stationary partial synchronous states to be continuous when the multiplicity of singular synchronous state is present or to be discontinuous when the multiplicity is absent.

Power grid frequency control is a demanding task requiring expensive idle power plants to adapt the supply to the fluctuating demand. An alternative approach is controlling the demand side in such a way that certain appliances modify their operation to adapt to the power availability. This is especially important to achieve a high penetration of renewable energy sources. A number of methods to manage the demand side have been proposed. In this work we focus on dynamic demand control (DDC), where smart appliances can delay their switchings depending on the frequency of the system. We introduce a simple model to study the effects of DDC on the frequency of the power grid. The model includes the power plant equations, a stochastic model for the demand that reproduces, adjusting a single parameter, the statistical properties of frequency fluctuations measured experimentally, and a generic DDC protocol. We find that DDC can reduce small and medium-size fluctuations but it can also increase the probability of observing large frequency peaks due to the necessity of recovering pending task. We also conclude that a deployment of DDC around 30–40% already allows a significant reduction of the fluctuations while keeping the number of pending tasks low.

We propose a strategy for robust high-quality self-assembly of nontrivial periodic structures out of patchy particles and investigate it with Brownian dynamics simulations. Its first element is the use of specific patch-patch and shell-shell interactions between the particles, which can be implemented through differential functionalization of patched and shell regions with specific DNA strands. The other key element of our approach is the use of a layer-by-layer protocol that allows one to avoid the formation of undesired random aggregates. As an example, we design and self-assemble in silico a version of a double diamond lattice in which four particle types are arranged into bcc crystal made of four fcc sublattices. The lattice can be further converted to cubic diamond by selective removal of the particles of certain types. Our results demonstrate that by combining the directionality, selectivity of interactions, and the layer-by-layer protocol, a high-quality robust self-assembly can be achieved.

Light-induced modulations of the refractive index and pattern formation are desirable to generate complex photonic structures via exposure to light. Here we show that local modulations of the effective refractive index and reconfigurable defects can be locally induced in a hybridized thin birefringent film of a nematic liquid crystal (LC) on a photoresponsive (generating photoinduced electric fields) iron doped lithium niobate surface via exposure to a focused laser beam. Samples were studied with a tailored imaging approach, which provided the ability to investigate these optically excited, field-induced responses on a microscopic level. Upon exposure with a focused laser beam, the fluent LC was expanded on the substrate's surface and localized field-induced defects were optically created. Both umbilic (central) and line defects were observed. The formation of field-induced umbilic defects was modeled in numerical simulations. In addition, line defects were experimentally studied. It was seen that line defects interconnected the centers of two central defects (field-induced defects, which were present at the upper and lower surfaces of the LC layer). In addition, line disclinations separating reverse tilt domains (caused by the inhomogeneous distribution of the photogenerated fields) were seen. These line disclinations were pinned to the central defects. By exposure with two adjacent focused laser beams two umbilic defects were created side by side and interconnected with a line defect (the line defects pinned to each umbilic defect were joined in a single defect line). An alternative technique is presented to field-induce promising photonic motives (microlenses, resonators, line defects) in a liquid crystalline, hybridized birefringent film on a microscopic scale by using a low-power laser (opposed to the high power necessary to induce optical Kerr responses in a neat LC).

Model selection and parameter estimation are important for the effective integration of experimental data, scientific theory, and precise simulations. In this work, we develop a learning approach for the selection and identification of a dynamical system directly from noisy data. The learning is performed by extracting a small subset of important features from an overdetermined set of possible features using a nonconvex sparse regression model. The sparse regression model is constructed to fit the noisy data to the trajectory of the dynamical system while using the smallest number of active terms. Computational experiments detail the model's stability, robustness to noise, and recovery accuracy. Examples include nonlinear equations, population dynamics, chaotic systems, and fast-slow systems.