Physical systems are often neither completely closed nor completely open, but instead are best described by dynamical systems with partial escape or absorption. In this paper we introduce classical measures that explain the main properties of resonance eigenfunctions of chaotic quantum systems with partial escape. We construct a family of conditionally invariant measures with varying decay rates by interpolating between the natural measures of the forward and backward dynamics. Numerical simulations in a representative system show that our classical measures correctly describe the main features of the quantum eigenfunctions: their multifractal phase-space distribution, their product structure along stable and unstable directions, and their dependence on the decay rate. The (Jensen-Shannon) distance between classical and quantum measures goes to zero in the semiclassical limit for long- and short-lived eigenfunctions, while it remains finite for intermediate cases.

It is an important issue, particularly in the context of sustainable society, to predict critical transitions across which a system state abruptly shifts toward a contrasting state. In this study, we propose an indicator of critical transitions in multivariate dynamical systems, based on the concept of the dynamical network marker (DNM). The DNM is originally defined based on the eigendecomposition of the Jacobian matrix of a nonlinear system and corresponds to large-magnitude components of the dominant eigenvector, which contributes primarily to transitions. Our DNM-based indicator is derived from the sample covariance matrix of state variables in a target system. Simulation results to predict transitions in complex network systems consisting of a harvesting model consistently show the superiority of our indicator as a precursor of transitions regardless of network structure characteristics, as compared to a conventional indicator.

The motion of core-shell colloids during laser heating is studied using angle-dependent pump-probe dynamic light scattering. The cores consist of a single spherical gold nanoparticle whose localized surface plasmon resonance has a strong spectral overlap with the wavelength of the pump laser. They are homogeneously encapsulated in thick hydrogel shells composed of either chemically cross-linked poly-$N$-isopropylacrylamide or poly[2-(2-methoxyethoxy)ethyl methacrylate], both of which exhibit a temperature-dependent volume phase transition. Thus, upon heating beyond the transition temperature, the hydrogel shells shrink. Intensity-time autocorrelation functions are recorded while illuminating the samples with the pump laser and hence heating the gold cores. With increasing laser intensity, the dynamics changes from normal Brownian motion to superdiffusion. Nevertheless, in the high-$q$ limit, the relaxation times can be extracted and used to estimate the temperature increase, which can reach almost 10 K. This causes a significant deswelling of the hydrogel shells, which is also measured.

In a recent article, we showed how the properties of the density-density correlation function and its integral, the local structure factor, in the fluid interfacial region, in systems with short-ranged forces, can be understood microscopically by considering the resonances of the local structure factor [A. O. Parry and C. Rascón, Nat. Phys. 15, 287 (2019)]. Here, we illustrate, using mean-field square-gradient theory and the more microscopic Sullivan density functional model, and how this approach generalizes when there is liquid-gas asymmetry, i.e., when the bulk correlation lengths of the coexisting liquid and gas phases are different. In particular, we are able to express the correlation function exactly as a simple average of contributions arising from two effective Ising-symmetric systems referred to as the symmetric gas and symmetric liquid. When combined with our earlier results, this generates analytical approximations for the correlation function and the local structure factor, which are near indistinguishable from the numerical solution to the Ornstein-Zernike equations over the whole range of wave vectors. Our results highlight how asymmetry affects the correlation function structure and describes the crossover from a long-ranged Goldstone mode to short-ranged properties determined by the local density as the wave vector increases.

In this study, we present a nonintrusive reduced order modeling (ROM) framework for large-scale quasistationary systems. The framework proposed herein exploits the time series prediction capability of long short-term memory (LSTM) recurrent neural network architecture such that (1) in the training phase, the LSTM model is trained on the modal coefficients extracted from the high-resolution data snapshots using proper orthogonal decomposition (POD) transform, and (2) in the testing phase, the trained model predicts the modal coefficients for the total time recursively based on the initial time history. Hence, no prior information about the underlying governing equations is required to generate the ROM. To illustrate the predictive performance of the proposed framework, the mean flow fields and time series response of the field values are reconstructed from the predicted modal coefficients by using an inverse POD transform. As a representative benchmark test case, we consider a two-dimensional quasigeostrophic ocean circulation model which, in general, displays an enormous range of fluctuating spatial and temporal scales. We first demonstrate that the conventional Galerkin projection-based reduced order modeling of such systems requires a high number of POD modes to obtain a stable flow physics. In addition, ROM-Galerkin projection (ROM-GP) does not seem to capture the intermittent bursts appearing in the dynamics of the first few most energetic modes. However, the proposed nonintrusive ROM framework based on LSTM (ROM-LSTM) yields a stable solution even for a small number of POD modes. We also observe that the ROM-LSTM model is able to capture quasiperiodic intermittent bursts accurately, and yields a stable and accurate mean flow dynamics using the time history of a few previous time states, denoted as the lookback time window in this paper. We show several features of ROM-LSTM framework such as significantly higher accuracy than ROM-GP, and faster performance using larger time step size. Throughout the paper, we demonstrate our findings in terms of time series evolution of the field values and mean flow patterns, which suggest that the proposed fully nonintrusive ROM framework is robust and capable of predicting chaotic nonlinear fluid flows in an extremely efficient way compared to the conventional projection-based ROM framework.

We study the opinion dynamics of a generalized voter model in which $N$ voters are additionally influenced by two opposing news sources whose effect is to promote political polarization. As the influence of these news sources is increased, the mean time to reach consensus scales nonuniversally as $N^{\alpha }$. The parameter $\alpha$ quantifies the influence of the news sources and increases without bound as the news sources become increasingly influential. The time to reach a politically polarized state, in which roughly equal fractions of the populations are in each opinion state, is generally short, and the steady-state opinion distribution exhibits a transition from near consensus to a politically polarized state as a function of $\alpha$.

Strained amorphous solids often fail mechanically by creating a shear band. It had been understood that the shear-banding instability is usefully described as crossing a spinodal point (with disorder) in an appropriate thermodynamic description. It remained contested, however, whether the spinodal is critical (with divergent correlation length) or not. Here we offer evidence for critical spinodal by using particle pinning. For a finite concentration of pinned particles the correlation length is bounded by the average distance between pinned particles, but without pinning it is bounded by the system size.

We study a dynamical system consisting of two mutually coupled molecular lasers, each of which shows mixed-mode oscillations and chaos when uncoupled. The type of coupling, incoherent laser interaction via saturable absorbers is an example of inhibitory nonlinear coupling, which is also found in Hodgkin-Huxley models that describe action potentials in neurons. We have carried out extensive numerical bifurcation analysis and numerical simulations to show that for small-enough coupling, well below the chaotic synchronization threshold, the presence of distinctive resonances in a symmetric mirror configuration of the system generates a type of rare events characterized by very small amplitudes. When this symmetry is broken by introducing a relatively small difference between the lasers pump parameters near an in-phase Hopf bifurcation, we observe extreme rare events (rogue waves) in one of the lasers. In this case the outliers deviate from power-law distributions and are reminiscent of those known as dragon kings. We consider the conditions for both types of rare events to occur, their origin, as well as relevant statistical features.

Quantitative and qualitative nature of chemical noise propagation in biochemical reaction networks depend crucially on the topology of the networks. Multisite reversible phosphorylation-dephosphorylation of target proteins is one such recurrently found topology that regulates host of key functions in living cells. Here we analytically calculated the stochasticity in multistep reversible chemical reactions by determining variance of phosphorylated species at the steady state using linear noise approximation to investigate the effect of mass action and Michaelis-Menten kinetics on the noise of phosphorylated species. We probed the dependence of noise on the number of phosphorylation sites and the equilibrium constants of the reaction equilibria to investigate the chemical noise propagation in the multisite phosphorylation chain.

Coherent circulation rolls and their relevance for the turbulent heat transfer in a two-dimensional Rayleigh-Bénard convection model are analyzed. The flow is in a closed cell of aspect ratio four at a Rayleigh number $\mathrm{Ra}={10}^6$ and at a Prandtl number $\mathrm{Pr}=10$. Three different Lagrangian analysis techniques based on graph Laplacians (distance spectral trajectory clustering, time-averaged diffusion maps, and finite-element based dynamic Laplacian discretization) are used to monitor the turbulent fields along trajectories of massless Lagrangian particles in the evolving turbulent convection flow. The three methods are compared to each other and the obtained coherent sets are related to results from an analysis in the Eulerian frame of reference. We show that the results of these methods agree with each other and that Lagrangian and Eulerian coherent sets form basically a disjoint union of the flow domain. Additionally, a windowed time averaging of variable interval length is performed to study the degree of coherence as a function of this additional coarse graining which removes small-scale fluctuations that cause trajectories to disperse quickly. Finally, the coherent set framework is extended to study heat transport.

Thermodynamic consistency of pseudopotential lattice Boltzmann models is a major topic that needs comprehensive evaluations. When interface is flat, pseudopotential models can give density-pressure isotherms in excellent agreement with those from equation of state. When interface is curved, thermodynamic equilibriums are affected by interface curvature, and consistency of pseudopotential models has not been systematically evaluated. In this study, we show that the effect of Laplace pressure on phase equilibrium is quantitatively consistent with Kelvin equation at high reduced temperatures ($\ge 0.7$). At low temperatures, inconsistency that can be attributed to the effect of orientation of the interface was noted, and it can be improved by tuning of the pseudopotential. By relating interfacial tension of a simulated fluid to that of a real fluid, the lattice spacing of pseudopotential model is found to be on the order of several molecular diameters, the typical range of intermolecular interactions. Interfacial thickness at different temperatures in pseudopotential model compared well with experiments and molecular dynamics simulations, which confirms that the calculated length scale is reasonable. Evaluation of a free energy lattice Boltzmann model indicate that it is consistent with Kelvin equation at high temperatures. The free energy model, however, is not as accurate as the tested pseudopotential model, and discrepancies may come from the relative inaccuracies in the predictions of vapor densities and the thinner interfaces.

Dynamics of an open $N$-state quantum system is often modeled with a Markovian master equation describing the evolution of the system density operator. By using generators of $\text{SU}\left(N\right)$ group as a basis, the density operator can be transformed into a real-valued “coherence-vector.” A generator of the dissipative evolution, so-called “Lindbladian,” can be expanded over the same basis and recast in the form of a real matrix. Together, these expansions result is a nonhomogeneous system of $N^2-1$ real-valued linear ordinary differential equations. Now one can, e.g., implement standard high-performance algorithms to integrate the system of equations forward in time while being sure in exact preservation of the trace (norm) and Hermiticity of the density operator. However, when performed in a straightforward way, the expansion turns to be an operation of the time complexity $O\left(N^{10}\right)$. The complexity can be reduced when the number of dissipative operators is independent of $N$, which is often the case for physically meaningful models. Here we present an algorithm to transform quantum master equation into a system of real-valued differential equations and propagate it forward in time. By using a specific scalable model, we evaluate computational efficiency of the algorithm and demonstrate that it is possible to handle the model system with $N={10}^3$ states on a single node of a computer cluster.

In this Rapid Communication, we demonstrate that specific frequencies in weakly nonlinear lattices avoid the generation of higher harmonics, and thus the lattices behave linearly. Using a multiple scales analysis, we present plane-wave solutions that persist at only a single frequency and wave number; i.e., whose spatiotemporal production of higher harmonics is remarkably small. We study monatomic and diatomic chains with quadratic and cubic stiffness nonlinearities as example systems. Direct numerical integration of the equations of motion confirms that finite amplitude plane waves assigned to these special frequencies produce negligible higher harmonics when injected into the lattices. Such findings provide new considerations for the operating frequency of nonlinear communications devices, sensors, and transducers for enhanced signal-to-noise ratios.

We consider heat transport in a one-dimensional harmonic chain attached at its ends to Langevin heat baths. The harmonic chain has mass impurities where the separation $d$ between any two successive impurities is randomly distributed according to a power-law distribution $P\left(d\right)\sim 1/d^{\alpha +1}$, being $\alpha >0$. In the regime where the first moment of the distribution is well defined ($1<\alpha <2$) the thermal conductivity $\kappa$ scales with the system size $N$ as $\kappa \sim N^{(\alpha -3)/\alpha }$ for fixed boundary conditions, whereas for free boundary conditions $\kappa \sim N^{(\alpha -1)/\alpha }$ if $N\gg 1$. When $\alpha =2$, the inverse localization length $\lambda$ scales with the frequency $\omega$ as $\lambda \sim {\omega }^{2}ln\omega$ in the low-frequency regime, due to the logarithmic correction, the size scaling law of the thermal conductivity acquires a nonclosed form. When $\alpha >2$, the thermal conductivity scales as in the uncorrelated disorder case. The situation $\alpha <1$ is only analyzed numerically, where $\lambda \left(\omega \right)\sim {\omega }^{2-\alpha }$, which leads to the following asymptotic thermal conductivity: $\kappa \sim N^{-(\alpha +1)/(2-\alpha )}$ for fixed boundary conditions and $\kappa \sim N^{(1-\alpha )/(2-\alpha )}$ for free boundary conditions.

We investigate motility-induced phase separation of active Brownian particles, which are modeled as purely repulsive spheres that move due to a constant swim force with freely diffusing orientation. We develop on the basis of power functional concepts an analytical theory for nonequilibrium phase coexistence and interfacial structure. Theoretical predictions are validated against Brownian dynamics computer simulations. We show that the internal one-body force field has four nonequilibrium contributions: (i) isotropic drag and (ii) interfacial drag forces against the forward motion, (iii) a superadiabatic spherical pressure gradient, and (iv) the quiet life gradient force. The intrinsic spherical pressure is balanced by the swim pressure, which arises from the polarization of the free interface. The quiet life force opposes the adiabatic force, which is due to the inhomogeneous density distribution. The balance of quiet life and adiabatic forces determines bulk coexistence via equality of two bulk state functions, which are independent of interfacial contributions. The internal force fields are kinematic functionals which depend on density and current but are independent of external and swim forces, consistent with power functional theory. The phase transition originates from nonequilibrium repulsion, with the agile gas being more repulsive than the quiet liquid.

Size-driven particle segregation can occur when an object such as a blade moves through an otherwise static bed of granular material. Here we use discrete element method (DEM) simulations to study segregation resulting from a subsurface blade moving through a bed of size-bidisperse spherical particles. Segregation increases with each pass of the blade until a surface layer of mostly large particles forms above a small-particle layer adjacent to the bottom wall. The rate of segregation decreases with each pass so that the degree of segregation asymptotically approaches its maximum value, and the number of passes to reach a steady segregation state increases as the bed depth is increased or the blade height decreased. In shallow beds, the characteristic number of passes for segregation, $\tau$, scales with the inverse of the granular inertial number, $I$. In deep beds with small blade heights, the effect of the blade is more localized to its immediate vicinity, resulting in many more passes of the blade to reach a steady segregation state, and a corresponding deviation from the shallow bed scaling of $\tau$ with $I^{-1}$.

Due to the high surface area to volume ratio of nanoparticles, nanocatalytic reactive flows are widely utilized in various applications, such as water purification, fuel cell, energy storage, and biodiesel production. The implementation of nanocatalysts in porous media flow, such as oil recovery and contaminant transport in soil, can trigger or modify the interfacial instabilities called viscous fingering. These instabilities grow at the interface of the fluids when a less viscous fluid displaces a high viscous one in porous media. Here the flow dynamics and the total amount of chemical product are investigated when two reactive miscible fluids meet in a porous medium while undergoing $\mathrm{A}+\mathrm{B}+\mathrm{n}$ $\to$ $\mathrm{C}+\mathrm{n}$ reaction. Nanocatalysts (n) are dispersed in the displacing fluid and deposited gradually with time. Four generic regimes are observed over time as a result of the particle deposition: (1) the initial diffusive regime, where the flow is stable with decreasing production rate, (2) the mixing-dominant fingering regime, where the flow is unstable and the production rate generally increases, (3) the transition regime, where the production rate generally decreases regardless of whether the system is stable or unstable, and (4) the final zero-production regime, where the product diffuses and fades away in the channel. Although the general trend shows a decreasing reaction rate with nanocatalysts deposition, there is a period in which the production rate increases due to the moderate deposition rates. Such an increase of production, however, is not observed in two groups: first, those systems in which the nanocatalysts do not change the viscosity of the base fluid and, second, a subgroup of the systems that are stable before and after the reaction in the absence of deposition.

We study the $O\left(2\right)$ model with ${\mathbb{Z}}_4$-symmetric perturbations within the framework of the nonperturbative renormalization group (RG) for spatial dimensionality $d=2$ and 3. In a unified framework we resolve the relatively complex crossover behavior emergent due to the presence of multiple RG fixed points. In $d=3$ the system is controlled by the $XY$, Ising, and low-$T$ fixed points in the presence of a dangerously irrelevant anisotropy coupling $\lambda$. In $d=2$ the anisotropy coupling is marginal and the physical picture is governed by the interplay between two distinct lines of RG fixed points, giving rise to nonuniversal critical behavior, and an isolated Ising fixed point. In addition to inducing crossover behavior in universal properties, the presence of the Ising fixed point yields a generic, abrupt change of critical temperature at a specific value of the anisotropy field.

In this paper, we study DNA breathing dynamics in the presence of an external periodic force by proposing and inspecting several probability distribution functions (PDFs) of relevant Brownian functionals which specify the bubble lifetime, reactivity, and average size. We model the bubble dynamics process by an overdamped Langevin equation of broken base pairs on the Poland-Scheraga free energy landscape. Introducing an effective time-independent description for timescales larger than $\tilde{T}=\frac{2\pi }{\omega }$ (where $\omega$ is the frequency of external periodic force) and using an elegant backward Fokker-Planck method we derive closed form expressions of several PDFs associated with such stochastic processes. For instance, with an initial bubble size of $x_0$, we derive the following analytical expressions: (i) the PDF $P\left(t_f\right|x_0)$ of the first passage time $t_f$ which specifies the lifetime of the DNA breathing process, (ii) the PDF $P\left(A\right|x_0)$ of the area $A$ until the first passage time, and it provides much valuable information about the average bubble size and reactivity of the process, and (iii) the PDF $P\left(M\right)$ associated with the maximum bubble size $M$ of the breathing process before complete denaturation. Our analysis is limited to two limits: (a) large bubble size and (b) small bubble size. We further confirm our analytical predictions by computing the same PDFs with direct numerical simulations of the corresponding Langevin equations. We obtain very good agreement of our theoretical predictions with the numerically simulated results. Finally, several nontrivial scaling behaviors in the asymptotic limits for the above-mentioned PDFs are predicted, which can be verified further from experimental observation. Our main conclusion is that the large bubble dynamics is unaffected by the rapidly oscillating force, but the small bubble dynamics is significantly affected by the same periodic force.