This Rapid Communication sets forth the mechanism by which mesoscale staircase structures condense to form macroscopic states of enhanced confinement. Density, vorticity, and turbulent potential enstrophy are the variables for this model. Formation of the staircase structures is due to inhomogeneous mixing of (generalized) potential vorticity (PV). Such mixing results in the local sharpening of density and vorticity gradients. When PV gradients steepen, the density staircase structure develops into a lattice of mesoscale “jumps” and “steps,” which are, respectively, regions of local gradient steepening and flattening. The jumps then merge and migrate in radius, leading to the emergence of a new macroscale profile structure, so indicating that profile self-organization is a global process, which may be described by a local, but nonlinear model. This work predicts and demonstrates how mesoscale condensation of staircases leads to global states of enhanced confinement.

We show through calculations on typical lattice models that thermal conductance $\sigma$ can well describe the near-equilibrium thermal transport property of one-dimensional materials of finite length, which presents a situation often met in the application of nanoscale devices. The $\sigma$ generally contains contributions from the material itself and those from the thermal reservoirs. The intrinsic $\sigma$ of the material, i.e., the one with the fewest external influences, can be efficiently calculated with the help of the “blackbody”-like nonreflective thermal reservoir, either through the nonequilibrium method or through the Green-Kubo-type formula. $\sigma$ thus calculated would be helpful to guide the design of thermal management and heat control in nanoscale devices.

We apply a recently developed theory for metastability in open quantum systems to a one-dimensional dissipative quantum Ising model. Earlier results suggest this model features either a nonequilibrium phase transition or a smooth but sharp crossover, where the stationary state changes from paramagnetic to ferromagnetic, accompanied by strongly intermittent emission dynamics characteristic of first-order coexistence between dynamical phases. We show that for a range of parameters close to this transition or crossover point the dynamics of the finite system displays pronounced metastability, i.e., the system relaxes first to long-lived metastable states before eventual relaxation to the true stationary state. From the spectral properties of the quantum master operator we characterize the low-dimensional manifold of metastable states, which are shown to be probability mixtures of two, paramagnetic and ferromagnetic, metastable phases. We also show that for long times the dynamics can be approximated by a classical stochastic dynamics between the metastable phases that is directly related to the intermittent dynamics observed in quantum trajectories and thus the dynamical phases.

We study the effect of multiplicative noise in dynamical flows arising from the coupling of stochastic processes with intrinsic noise. Situations wherein such systems arise naturally are in chemical or biological oscillators that are coupled to each other in a drive-response configuration. Above a coupling threshold we find that there is a strong correlation between the drive and the response: This is a stochastic analog of the phenomenon of generalised synchronization. Since the dynamical fluctuations are large when there is intrinsic noise, it is necessary to employ measures that are sensitive to correlations between the variables of drive and the response, the permutation entropy, or the mutual information in order to detect the transition to generalized synchrony in such systems.

With the advent of online networks, societies have become substantially more interconnected with individual members able to easily both maintain and modify their own social links. Here, we show that active network maintenance exposes agents to confirmation bias, the tendency to confirm one's beliefs, and we explore how this bias affects collective opinion formation. We introduce a model of binary opinion dynamics on a complex, fluctuating network with stochastic rewiring and we analyze these dynamics in the mean-field limit of large networks and fast link rewiring. We show that confirmation bias induces a segregation of individuals with different opinions and stabilizes the consensus state. We further show that bias can have an unusual, nonmonotonic effect on the time to consensus and this suggests a novel avenue for large-scale opinion manipulation.

Aging is associated with the accumulation of damage throughout a persons life. Individual health can be assessed by the Frailty Index (FI). The FI is calculated simply as the proportion $f$ of accumulated age-related deficits relative to the total, leading to a theoretical maximum of $f\le 1$. Observational studies have generally reported a much more stringent bound, with $f\le f_{\text{max}}<1$. The value of $f_{\text{max}}$ in observational studies appears to be nonuniversal, but $f_{\text{max}}\approx 0.7$ is often reported. A previously developed network model of individual aging was unable to recover $f_{\text{max}}<1$ while retaining the other observed phenomenology of increasing $f$ and mortality rates with age. We have developed a computationally accelerated network model that also allows us to tune the scale-free network exponent $\alpha$. The network exponent $\alpha$ significantly affects the growth of mortality rates with age. However, we are only able to recover $f_{\text{max}}$ by also introducing a deficit sensitivity parameter $1-q$, which is equivalent to a false-negative rate $q$. Our value of $q=0.3$ is comparable to finite sensitivities of age-related deficits with respect to mortality that are often reported in the literature. In light of nonzero $q$, we use mutual information $I$ to provide a nonparametric measure of the predictive value of the FI with respect to individual mortality. We find that $I$ is only modestly degraded by $q<1$, and this degradation is mitigated when increasing number of deficits are included in the FI. We also find that the information spectrum, i.e., the mutual information of individual deficits versus connectivity, has an approximately power-law dependence that depends on the network exponent $\alpha$. Mutual information $I$ is therefore a useful tool for characterizing the network topology of aging populations.

We present a general analysis of exchange devices linking their efficiency to the geometry of the exchange surface and supply network. For certain parameter ranges, we show that the optimal exchanger consists of densely packed pipes which can span a thin sheet of large area (an “active layer”), which may be crumpled into a fractal surface and supplied with a fractal network of pipes. We derive the efficiencies of such exchangers, showing the potential for significant gains compared to regular exchangers (where the active layer is flat), using parameters relevant to biological systems.

The influence of initial conditions on miscible incompressible baroclinically driven Rayleigh-Taylor instability undergoing nonuniform acceleration is explored computationally using an implicit large eddy simulation (ILES) technique. We consider the particular case of evolution during multiple reversals of acceleration direction, where the flow is alternately statically stable or unstable. In the unstable phase, the flow is driven by the baroclinic release of potential energy, whereas in the stable phase, work is done against the density stratification with the energy exchange taking place by wavelike mechanisms. These dynamics are fundamentally different; here, we track the evolution of volume-averaged turbulent statistics that are most sensitive to changes in the distribution of spectral power and bandwidth of the initial conditions as the flow alternates between dynamical regimes due to acceleration reversal.

We report observations of strong nonlinear interactions between the spherical, translational, and shape oscillations of micrometer-size bubbles. This is achieved through high-speed recordings of single bubble dynamics driven by amplitude-modulated ultrasound. The features of mode coupling are highlighted through (i) the exponential growth of the parametrically excited mode ($n=3$) triggered by the spherical oscillations followed by a saturation due to energy transfer towards the translation and even modes, (ii) the excitation of modes well below their parametric pressure threshold, and (iii) clear modification of the breathing mode $R\left(t\right)$. These results are compared to recent theories accounting for nonlinear mode coupling, providing predictions in agreement with the observed bubble dynamics.

A boundary scheme is proposed to treat the linear heterogeneous surface reaction (i.e., general Robin boundary condition) for the lattice Boltzmann method (LBM) in this study. The basic idea of the present scheme is to compute the scalar variable gradient in the boundary condition with the moment of the nonequilibrium distribution functions. The unknown distribution functions on the boundary can then be obtained on the basis of the given boundary condition. For a straight wall, where the lattice nodes are located on the boundaries, both the scalar variable and its gradient can be expressed in terms of the distribution functions at the boundary node, and the scheme is purely local. The scheme is also extended to problems with a curved wall, in which a linear extrapolation is employed to realize the exact boundary position. A common feature of the two schemes lies in the easy treatment of the heterogenous reactions in comparison with existing methods. A number of simulations are performed to test the accuracy of the schemes. The results show that for flat walls the scheme can achieve second-order accuracy, while for curved walls the order of the accuracy is between 1.0 and 1.5.

Using the diagrammatic method, we derive a set of self-consistent equations that describe eigenvalue distributions of large correlated asymmetric random matrices. The matrix elements can have different variances and be correlated with each other. The analytical results are confirmed by numerical simulations. The results have implications for the dynamics of neural and other biological networks where plasticity induces correlations in the connection strengths within the network. We find that the presence of correlations can have a major impact on network stability.

We present a general method for transforming the continuous diffusion equation describing overdamped Brownian motion on a time-independent potential with multiple deep wells to a discrete master equation. The method is based on an expansion in localized basis states of local metastable potentials that match the full potential in the region of each potential well. Unlike previous basis methods for discretizing Brownian motion on a potential, this approach is valid for periodic potentials with varying multiple deep wells per period and can also be applied to nonperiodic systems. We apply the method to a range of potentials and find that potential wells that are deep compared to five times the thermal energy can be associated with a discrete localized state while shallower wells are better incorporated into the local metastable potentials of neighboring deep potential wells.

We carry out the thermodynamic analysis of a Markovian stochastic engine, driven by a spatially and temporally periodic modulation in a $d$-dimensional space. We derive the analytic expressions for the Onsager coefficients characterizing the linear response regime for the isothermal transfer of one type of work (a driver) to another (a load), mediated by a stochastic time-periodic machine. As an illustration, we obtain the explicit results for a Markovian kangaroo process coupling two orthogonal directions and find extremely good agreement with numerical simulations. In addition, we obtain and discuss expressions for the entropy production, power, and efficiency for the kangaroo process.

The power spectrum of a stationary process may be calculated in terms of the autocorrelation function using the Wiener-Khinchin theorem. We here generalize the Wiener-Khinchin theorem for nonstationary processes and introduce a time-dependent power spectrum $〈S_{t_m}\left(\omega \right)〉$ where $t_m$ is the measurement time. For processes with an aging autocorrelation function of the form $〈I\left(t\right)I(t+\tau )〉=t^{\mathrm{{\rm Y}}}{\varphi }_{\mathrm{EA}}(\tau /t)$, where ${\varphi }_{\mathrm{EA}}\left(x\right)$ is a nonanalytic function when $x$ is small, we find aging $1/f^{\beta }$ noise. Aging $1/f^{\beta }$ noise is characterized by five critical exponents. We derive the relations between the scaled autocorrelation function and these exponents. We show that our definition of the time-dependent spectrum retains its interpretation as a density of Fourier modes and discuss the relation to the apparent infrared divergence of $1/f^{\beta }$ noise. We illustrate our results for blinking-quantum-dot models, single-file diffusion, and Brownian motion in a logarithmic potential.

The clogging behavior of a symmetric binary mixture of colloidal particles that are driven in opposite directions through constrictions is explored by Brownian dynamics simulations and theory. A dynamical state with a spontaneously broken symmetry occurs where one species is flowing and the other is blocked for a long time, which can be tailored by the size of the constrictions. Moreover, we find self-organized oscillations in clogging and unclogging of the two species. Apart from statistical physics, our results are of relevance for fields like biology, chemistry, and crowd management, where ions, microparticles, pedestrians, or other particles are driven in opposite directions through constrictions.

Glass-forming liquids are often classified into strong glass formers with nearly Arrhenius behavior and fragile ones with super-Arrhenius behavior. We reveal a significant difference in the dynamics between these two types of glass formers through molecular dynamics simulations: In strong glass formers, the relaxation dynamics of density fluctuations is nondiffusive, whereas in fragile glass formers it exhibits diffusive behavior. We demonstrate that this distinction is a direct consequence of the fundamental difference in the underlying elementary relaxation process between these two dynamical classes of glass formers. For fragile glass formers, a density-exchange process proceeds the density relaxation, which takes place locally at the particle level in normal states but is increasingly cooperative and nonlocal as the temperature is lowered in supercooled states. On the other hand, in strong glass formers, such an exchange process is not necessary for density relaxation due to the presence of other local relaxation channels. Our finding provides a novel insight into Angell's classification scheme from a hydrodynamic perspective.

In a recent work on fluid infiltration in a Hele-Shaw cell with the pore-block geometry of Sierpinski carpets (SCs), the area filled by the invading fluid was shown to scale as $F\sim t^n$, with $n<1/2$, thus providing a macroscopic realization of anomalous diffusion [Filipovitch et al., Water Resour. Res. 52, 5167 (2016)]. The results agree with simulations of a diffusion equation with constant pressure at one of the borders of those fractals, but the exponent $n$ is very different from the anomalous exponent $\nu =1/D_W$ of single-particle diffusion in the same fractals ($D_W$ is the random-walk dimension). Here we use a scaling approach to show that those exponents are related as $n=\nu \left(D_F-D_B\right)$, where $D_F$ and $D_B$ are the fractal dimensions of the bulk and the border from which diffusing particles come, respectively. This relation is supported by accurate numerical estimates in two SCs and in two generalized Menger sponges (MSs), in which we performed simulations of single-particle random walks (RWs) with a rigid impermeable border and of a diffusive infiltration model in which that border is permanently filled with diffusing particles. This study includes one MS whose external border is also fractal. The exponent relation is also consistent with the recent simulational and experimental results on fluid infiltration in SCs, and explains the approximate quadratic dependence of $n$ on $D_F$ in these fractals. We also show that the mean-square displacement of single-particle RWs has log-periodic oscillations, whose periods are similar for fractals with the same scaling factor in the generator (even with different embedding dimensions), which is consistent with the discrete scale invariance scenario. The roughness of a diffusion front defined in the infiltration problem also shows this type of oscillation, which is enhanced in fractals with narrow channels between large lacunas.

Continuous-time Markov process models of contagions are widely studied, not least because of their utility in predicting the evolution of real-world contagions and in formulating control measures. It is often the case, however, that discrete-time approaches are employed to analyze such models or to simulate them numerically. In such cases, time is discretized into uniform steps and transition rates between states are replaced by transition probabilities. In this paper, we illustrate potential limitations to this approach. We show how discretizing time leads to a restriction on the values of the model parameters that can accurately be studied. We examine numerical simulation schemes employed in the literature, showing how synchronous-type updating schemes can bias discrete-time formalisms when compared against continuous-time formalisms. Event-based simulations, such as the Gillespie algorithm, are proposed as optimal simulation schemes both in terms of replicating the continuous-time process and computational speed. Finally, we show how discretizing time can affect the value of the epidemic threshold for large values of the infection rate and the recovery rate, even if the ratio between the former and the latter is small.

This work focuses on systems displaying domain patterns resulting from competing external and internal dynamics. To this end, we introduce a Lyapunov functional capable of describing the steady states of systems subject to external forces, by adding nonlocal terms to the Landau Ginzburg free energy of the system. Thereby, we extend the existing methodology treating long-range order interactions, to the case of external nonlocal forces. By studying the quadratic term of this Lyapunov functional, we compute the phase diagram in the temperature versus external field and we determine all possible modulated phases (domain patterns) as a function of the external forces and the temperature. Finally, we investigate patterning in chemical reactive mixtures and binary mixtures under irradiation, and we show that the last case opens the path toward micro-structural engineering of materials.