One notion of phase for stochastic oscillators is based on the mean return-time (MRT): a set of points represents a certain phase if the mean time to return from any point in this set to this set after one rotation is equal to the mean rotation period of the oscillator (irrespective of the starting point). For this so far only algorithmically defined phase, we derive here analytical expressions for the important class of isotropic stochastic oscillators. This allows us to evaluate cases from the literature explicitly and to study the behavior of the MRT phase in the limits of strong noise. We also use the same formalism to show that lines of constant return time variance (instead of constant mean return time) can be defined, and that they in general differ from the MRT isochrons.

A method for electrically controlled synchronous mode tuning in the transmittance and reflectance spectra of a photonic structure consisting of an asymmetric dielectric Fabry-Pérot microcavity and an ultrathin metallic film has been proposed. The excitation of a broadband Tamm plasmon polariton at a metal/Bragg mirror interface is accompanied by the two phenomena opposing one another. Due to the strong absorption induced by the metal, a sufficient rejection level in the reflection of the off-resonant radiation has been obtained in a wide spectral range, which almost coincides with the photonic band gap, while at the cavity mode frequencies the structure becomes transparent for the reflected radiation. This leads to the appearance of a series of narrow resonance peaks in the reflectance spectra that coincide in frequency with the transmittance peaks. Based on the structural transformations in the dual-frequency nematic liquid crystal used as a photonic structure defect, the tuning of the modes corresponding to the extraordinary waves to both the short- and long-wavelength spectral ranges has been implemented.

We report a unique phenomenon in which liquid metal droplets (LMDs) under a pure ac electric field pump fluid. Unlike the directional pumping that occurs upon reversing the electric field polarity under a dc signal, this phenomenon allows the direction of fluid motion to be switched by simply shifting the position of the LMD within the cylindrical chamber. The physical mechanism behind this phenomenon has been termed Marangoni flow, caused by nonlinear electrocapillary stress. Under the influence of a localized, asymmetric ac electric field, the polarizable surface of the position-offset LMD produces a net time-averaged interfacial tension gradient that scales with twice the field strength, and thus pumps fluid unidirectionally. However, the traditional linear RC circuit polarization model of the LMD/electrolyte interface fails to capture the correct pump-flow direction when the thickness of the LMD oxide skin is non-negligible compared to the Debye length. Therefore, we developed a physical description by treating the oxide layer as a distributed capacitance with variable thickness and connected with the electric double layer. The flow profile is visualized via microparticle imaging velocimetry, and excellent consistency is found with simulation results obtained from the proposed nonlinear model. Furthermore, we investigate the effects of relevant parameters on fluid pumping and discuss a special phenomenon that does not exist in dc control systems. To our knowledge, no previous work addresses LMDs in this manner and uses a zero-mean ac electric field to achieve stable, adjustable directional pumping of a low-conductivity solution.

This article proposes a statistical numerical method to address gas kinetics problems obeying the Boltzmann equation. This method is inspired by Monte Carlo algorithms used in linear transport physics, where virtual particles are followed backwards in time along their paths. The nonlinear character of gas kinetics translates, in the numerical simulations presented here, into branchings of the virtual particle paths. The obtained algorithms have displayed in the few tests presented here two noticeable qualities: (1) they involve no mesh and (2) they allow one to easily compute the gas density at rarefied places of the phase space, for example, at high kinetic energy.

We devise reduced-dimension metrics for effectively measuring the distance between two points (i.e., microstructures) in the microstructure space and quantifying the pathway associated with microstructural evolution, based on a recently introduced set of hierarchical $n$-point polytope functions $P_n$. The $P_n$ functions provide the probability of finding particular $n$-point configurations associated with regular $n$ polytopes in the material system, and are a special subset of the standard $n$-point correlation functions $S_n$ that effectively decompose the structural features in the system into regular polyhedral basis with different symmetries. The $n\mathrm{th}$ order metric ${\mathrm{\Omega }}_n$ is defined as the ${\mathbb{L}}_1$ norm associated with the $P_n$ functions of two distinct microstructures. By choosing a reference initial state (i.e., a microstructure associated with $t_0=0$), the ${\mathrm{\Omega }}_n\left(t\right)$ metrics quantify the evolution of distinct polyhedral symmetries and can in principle capture emerging polyhedral symmetries that are not apparent in the initial state. To demonstrate their utility, we apply the ${\mathrm{\Omega }}_n$ metrics to a two-dimensional binary system undergoing spinodal decomposition to extract the phase separation dynamics via the temporal scaling behavior of the corresponding ${\mathrm{\Omega }}_n\left(t\right)$, which reveals mechanisms governing the evolution. Moreover, we employ ${\mathrm{\Omega }}_n\left(t\right)$ to analyze pattern evolution during vapor deposition of phase-separating alloy films with different surface contact angles, which exhibit rich evolution dynamics including both unstable and oscillating patterns. The ${\mathrm{\Omega }}_n$ metrics have potential applications in establishing quantitative processing-structure-property relationships, as well as real-time processing control and optimization of complex heterogeneous material systems.

A growing body of empirical evidence suggests that the dynamics of wealth within a population tends to be nonergodic, even after rescaling the individual wealth with the population average. Despite these discoveries, the way in which nonergodicity manifests itself in models of economic interactions remains an open issue. Here we shed valuable insight on these properties by studying the nonergodicity of the population average wealth in a simple model for wealth dynamics in a growing and reallocating economy called reallocating geometric Brownian motion (RGBM). When the effective wealth reallocation in the economy is from the poor to the rich, the model allows for the existence of negative wealth within the population. In this work, we show that in the negative reallocation regime of RGBM, ergodicity breaks as the difference between the time-average and the ensemble growth rate of the average wealth in the population. In particular, the ensemble average wealth grows exponentially, whereas the time-average growth rate is nonexistent. Moreover, we find that the system is characterized with a critical self-averaging time period. Before this time period, the ensemble average is a fair approximation for the population average wealth. Afterwards, the nonergodicity forces the population average to oscillate between positive and negative values since the magnitude of this observable is determined by the most extreme wealth values in the population. This implies that the dynamics of the population average is an unstable phenomenon in a nonergodic economy. We use this result to argue that one should be cautious when interpreting economic well-being measures that are based on the population average wealth in nonergodic economies.

We investigate strongly nonlinear wave dynamics of continuum phononic material with discrete nonlinearity. The studied phononic material is a layered medium such that the elastic layers are connected through contact interfaces with rough surfaces. These contacts exhibit nonlinearity by virtue of nonlinear mechanical deformation of roughness under compressive loads and strong nonlinearity stemming from their inability to support tensile loads. We study the evolution of propagating Gaussian tone bursts using time-domain finite element simulations. The elastodynamic effects of nonlinearly coupled layers enable strongly nonlinear energy transfer in the frequency domain by activating acoustic resonances of the layers. Further, the interplay of strong nonlinearity and dispersion in our phononic material forms stegotons, which are solitarylike localized traveling waves. These stegotons satisfy properties of solitary waves, yet exhibit local variations in their spatial profiles and amplitudes due to the presence of layers. We also elucidate the role of rough contact nonlinearity on the interrelationship between the stegoton parameters as well as on the generation of secondary stegotons from the collision of counterpropagating stegotons. The phononic material exhibits strong acoustic attenuation at frequencies close to (and fractional multiples of) layer resonances, whereas it causes energy propagation as stegotons for other frequencies. This study sheds light on the wave phenomena achievable in continuum periodic media with local nonlinearity, and opens opportunities for advanced wave control through discrete and local contact nonlinearity.

We analyze the interaction with uniform external fields of nematic liquid crystals within a recent generalized free energy posited by Virga and falling in the class of quartic functionals in the spatial gradients of the nematic director. We review some known interesting solutions, i.e., uniform heliconical structures, which correspond to the so-called twist-bend nematic phase and we also study the transition between this phase and the standard uniform nematic one. The twist-bend phase is further reproduced by three-dimensional simulations. Moreover, we find liquid crystal configurations, which closely resemble some novel, experimentally detected, structures called Skyrmion tubes. Skyrmion tubes are characterized by a localized cylindrically symmetric pattern surrounded by either twist-bend or uniform nematic phase. We study the equilibrium differential equations and find numerical solutions and analytical approximations.

We introduce an alternative route for obtaining reliable cyclic engines, based on two interacting Brownian particles under time-periodic drivings which can be used as a work-to-work converter or a heat engine. Exact expressions for the thermodynamic fluxes, such as power and heat, are obtained using the framework of stochastic thermodynamic. We then use these exact expression to optimize the driving protocols with respect to output forces, their phase difference. For the work-to-work engine, they are solely expressed in terms of Onsager coefficients and their derivatives, whereas nonlinear effects start to play a role since the particles are at different temperatures. Our results suggest that stronger coupling generally leads to better performance, but careful design is needed to optimize the external forces.

The stability analysis of synchronization patterns on generalized network structures is of immense importance nowadays. In this article, we scrutinize the stability of intralayer synchronous state in temporal multilayer hypernetworks, where each dynamic units in a layer communicate with others through various independent time-varying connection mechanisms. Here, dynamical units within and between layers may be interconnected through arbitrary generic coupling functions. We show that intralayer synchronous state exists as an invariant solution. Using fast-switching stability criteria, we derive the condition for stable coherent state in terms of associated time-averaged network structure, and in some instances we are able to separate the transverse subspace optimally. Using simultaneous block diagonalization of coupling matrices, we derive the synchronization stability condition without considering time-averaged network structure. Finally, we verify our analytically derived results through a series of numerical simulations on synthetic and real-world neuronal networked systems.

Self-propelled particles can undergo complex dynamics due to a range of bulk and surface interactions. When a particle is embedded in a host solid near its bulk melting temperature, the latter may melt at the surface of the former in a process known as interfacial premelting. The thickness of the melt film depends on the temperature, impurities, material properties and geometry. A temperature gradient is accompanied by a thermomolecular pressure gradient that drives the interfacial liquid from high to low temperatures and hence the particle from low to high temperatures, in a process called thermal regelation. When the host material is ice and the embedded particle is a biological entity, one has a particularly different form of active matter, which addresses interplay between a wide range of problems, from extremophiles of both terrestrial and exobiological relevance to ecological dynamics in Earth's cryosphere. Of basic importance in all such settings is the combined influence of biological activity and thermal regelation in controlling the redistribution of bioparticles. Therefore, we recast this class of regelation phenomena in the stochastic framework of active Ornstein-Uhlenbeck dynamics and make predictions relevant to this and related problems of interest in biological and geophysical problems. We examine how thermal regelation compromises paleoclimate studies in the context of ice core dating and we find that the activity influences particle dynamics during thermal regelation by enhancing the effective diffusion coefficient. Therefore, accurate dating relies on a quantitative treatment of both effects.

Because of helical phase wavefront distribution, vortex electromagnetic waves are considered to carry more information and additional degrees of freedom than traditional spherical waves. Therefore, a vortex wave carrying orbital angular momentum (OAM) can improve inversion and imaging accuracy. In this work, we revisit the reconstruction of three-dimensional objects in layered composite structures extended with OAM. In forward modeling, the concentric uniform circle array is used to generate electromagnetic vortex beams. To analyze the difference of vortex beams, the electric field radiation pattern and phase pattern distribution of OAM waves with different modes are calculated. Then, the scattered field of layered media illuminated by different OAM beams is determined by the dyadic Green's function and the stabilized biconjugate gradient technique with a fast Fourier transform algorithm. In the inversion, the variational Born iterative method is used to reconstruct targets in layered composite structures, and multiple OAM modes are used to improve the reconstruction results. The numerical results prove that the permittivity of the target can be better reconstructed by using the multiple OAM modes rather than the traditional spherical wave. With the increase of OAM mode number, the reconstructed target parameters are closer to the true value. We expect that our results will provide a better understanding of the OAM and pave the way for the improvement of inversion and optical imaging technology using vortex waves.

Explicit numerical solutions of the time-dependent Schrödinger equation are more efficient than those obtained by commonly used implicit approaches. They are more practical, especially for a system with higher spatial dimensions. To that end, we introduce a generalization of an explicit three-level method to obtain solutions with spatial and temporal errors of the order of $O\left[{\left(\mathrm{\Delta }x\right)}^{2r}\right]$ and $O\left[{\left(\mathrm{\Delta }t\right)}^{2M+3}\right]$, where $\mathrm{\Delta }x$ and $\mathrm{\Delta }t$ are the spatial and temporal grid elements, and $r$ and $M$ are positive integers. Sample calculations illustrate the efficacy and stability of the algorithm.

In many branches of earth sciences, the problem of rock study on the microlevel arises. However, a significant number of representative samples is not always feasible. Thus the problem of the generation of samples with similar properties becomes actual. In this paper we propose a deep learning architecture for three-dimensional porous medium reconstruction from two-dimensional slices. We fit a distribution on all possible three-dimensional structures of a specific type based on the given data set of samples. Then, given partial information (central slices), we recover the three-dimensional structure around such slices as the most probable one according to that constructed distribution. Technically, we implement this in the form of a deep neural network with encoder, generator, and discriminator modules. Numerical experiments show that this method provides a good reconstruction in terms of Minkowski functionals.

Extended-range percolation on various regular lattices, including all 11 Archimedean lattices in two dimensions and the simple cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc) lattices in three dimensions, is investigated. In two dimensions, correlations between coordination number $z$ and site thresholds $p_c$ for Archimedean lattices up to 10th nearest neighbors (NN) are seen by plotting $z$ versus $1/p_c$ and $z$ versus $-1/ln(1-p_c)$ using the data of d'Iribarne et al. [J. Phys. A 32, 2611 (1999)] and others. The results show that all the plots overlap on a line with a slope consistent with the theoretically predicted asymptotic value of $z{p}_c\sim 4{\eta }_c=4.51235$, where ${\eta }_c$ is the continuum threshold for disks. In three dimensions, precise site and bond thresholds for bcc and fcc lattices with 2nd and 3rd NN, and bond thresholds for the sc lattice with up to the 13th NN, are obtained by Monte Carlo simulations, using an efficient single-cluster growth method. For site percolation, the values of thresholds for different types of lattices with compact neighborhoods also collapse together, and linear fitting is consistent with the predicted value of $z{p}_c\sim 8{\eta }_c=2.7351$, where ${\eta }_c$ is the continuum threshold for spheres. For bond percolation, Bethe-lattice behavior $p_c=1/(z-1)$ is expected to hold for large $z$, and the finite-$z$ correction is confirmed to satisfy $z{p}_c-1\sim a_1{z}^{-x}$, with $x=2/3$ for three dimensions as predicted by Frei and Perkins [Electron. J. Probab. 21, 56 (2016)] and by Xu et al. [Phys. Rev. E 103, 022127 (2021)]. Our analysis indicates that for compact neighborhoods, the asymptotic behavior of $z{p}_c$ has universal properties, depending only on the dimension of the system and whether site or bond percolation but not on the type of lattice.

We derive the most basic dynamical properties of random hyperbolic graphs (the distributions of contact and intercontact durations) in the hot regime (network temperature $T>1$). We show that for sufficiently large networks the contact distribution decays as a power law with exponent $2+T>3$ for durations $t>T$, while for $t<T$ it exhibits exponential-like decays. This result holds irrespective of the expected degree distribution, as long as it has a finite $T\text{th}$ moment. Otherwise, the contact distribution depends on the expected degree distribution and we show that if the latter is a power law with exponent $\gamma \in (2,T+1]$, then the former decays as a power law with exponent $\gamma +1>3$. However, the intercontact distribution exhibits power-law decays with exponent $2-T\in (0,1)$ for $T\in (1,2)$, while for $T>2$ it displays linear decays with a slope that depends on the observation interval. This result holds irrespective of the expected degree distribution as long as it has a finite $T\text{th}$ moment if $T\in (1,2)$, or a finite second moment if $T>2$. Otherwise, the intercontact distribution depends on the expected degree distribution and if the latter is a power law with exponent $\gamma \in (2,3)$, then the former decays as a power law with exponent $3-\gamma \in (0,1)$. Thus, hot random hyperbolic graphs can give rise to contact and intercontact distributions that both decay as power laws. These power laws, however, are unrealistic for the case of the intercontact distribution, as their exponent is always less than one. These results mean that hot random hyperbolic graphs are not adequate for modeling real temporal networks, in stark contrast to cold random hyperbolic graphs $(T<1)$. Since the configuration model emerges at $T\to \infty$, these results also suggest that this is not an adequate null temporal network model.

The formations of correct three-dimensional structures of proteins are essential to their functions. Cotranslational folding is vital for proteins to form correct structures in vivo. Although some experiments have shown that cotranslational folding can improve the efficiency of folding, its microscopic mechanism is not yet clear. Previously, we built a model of the ribosomal exit tunnel and investigated the cotranslational folding of a three-helix protein by using all-atom molecular dynamics simulations. Here we study the cotranslational folding of three β-sheet-enriched proteins using the same method. The results show that cotranslational folding can enhance the helical population in most cases and reduce non-native long-range contacts before emerging from the ribosomal exit tunnel. After exiting the tunnel, all proteins fall into local minimal states and the structural ensembles of cotranslational folding show more helical conformations than those of free folding. In particular, for one of the three proteins, the GTT WW domain, we find that one local minimum state of the cotranslational folding is the known folding intermediate, which is not found in free folding. This result suggests that the cotranslational folding may increase the folding efficiency by accelerating the sampling more than by avoiding the misfolded state, which is presently a mainstream viewpoint.

The classical $D^2$-Law states that the square of the droplet diameter decreases linearly with time during its evaporation process, i.e., $D^2\left(t\right)=D_0^2-Kt$, where $D_0$ is the droplet initial diameter and $K$ is the evaporation constant. Though the law has been widely verified by experiments, considerable deviations are observed in many cases. In this work, a revised theoretical analysis of the single droplet evaporation in finite-size open systems is presented for both two-dimensional (2D) and 3D cases. Our analysis shows that the classical $D^2$-Law is only applicable for 3D large systems ($L\gg D_0$, L is the system size), while significant deviations occur for small ($L\le 5D_0$) and/or 2D systems. Theoretical solution for the temperature field is also derived. Moreover, we discuss in detail the proper numerical implementation of droplet evaporation in finite-size open systems by the mesoscopic lattice Boltzmann method (LBM). Taking into consideration shrinkage effects and an adaptive pressure boundary condition, droplet evaporation in finite-size 2D/3D systems with density ratio up to 328 within a wide parameter range $(K=[0.003,0.18]$ in lattice units) is simulated, and remarkable agreement with the theoretical solution is achieved, in contrast to previous simulations. The present work provides insights into realistic droplet evaporation phenomena and their numerical modeling using diffuse-interface methods.

We present an exact Monte Carlo method to simulate the nonequilibrium dynamics of electron-phonon models in the adiabatic limit of zero phonon frequency. The classical nature of the phonons allows us to sample the equilibrium phonon distribution and efficiently evolve the electronic subsystem in a time-dependent electromagnetic field for each phonon configuration. We demonstrate that our approach is particularly useful for charge-density-wave systems experiencing pulsed electric fields, as they appear in pump-probe experiments. For the half-filled Holstein model in one and two dimensions, we calculate the out-of-equilibrium response of the current and the energy after a pulse is applied as well as the photoemission spectrum before and after the pump. Finite-size effects are under control for chains of 162 sites (in one dimension) or $16\times 16$ square lattices (in two dimensions).

We study the universality of work statistics of a system quenched through a quantum critical surface. By using the adiabatic perturbation theory, we obtain the general scaling behavior for all cumulants of work. These results extend the studies of Kibble-Zurek mechanism scaling of work statistics from an isolated quantum critical point to a critical surface. As an example, we study the scaling behavior of work statistics in the two-dimensional (2D) Kitaev honeycomb model featured with a critical line. By utilizing the trace formula for quadratic fermionic Hamiltonian, we obtain the exact characteristic function of work of the 2D Kitaev model at zero temperature. The results confirm our prediction.