Environmental heterogeneity can drive genetic heterogeneity in expanding populations; mutant strains may emerge that trade overall growth rate for an improved ability to survive in patches that are hostile to the wild type. This evolutionary dynamic is of practical importance when seeking to prevent the emergence of damaging traits. We show that a subcritical slow-spreading mutant can attain dominance even when the density of patches is below their percolation threshold and predict this transition using geometrical arguments. This work demonstrates a phenomenon of “assisted percolation”, where one subcritical process assists another to achieve supercriticality.

Cognition involves the global integration of distributed brain regions that are known to work cohesively as cognitive subsystems during brain functioning. Empirical evidence has suggested that spatiotemporal phase relationships between brain regions, measured as synchronization and metastability, may encode important task-relevant information. However, it remains largely unknown how phase relationships aggregate at the level of cognitive subsystems under different cognitive processing. Here, we probe this question by simulating task-relevant brain dynamics through regional stimulation of a whole-brain dynamical network model operating in the resting-state dynamical regime. The model is constructed with structurally embedded Stuart-Laudon oscillators and then fitted with human resting-state functional magnetic resonance imaging data. Based on this framework, we first demonstrate the plausibility of introducing the cognitive system partition into the modeling analysis framework by showing that the clustering of regions across functional networks is better circumscribed by the predefined partition. At the cognitive subsystem level, we focus on how task-relevant phase dynamics are organized in terms of synchronization and metastability. We found that patterns of cognitive synchronization are more task specific, whereas patterns of cognitive metastability are more consistent across different states, suggesting it may encode a more task-general property during cognitive processing, an inherent property conferred by brain organization. This consistent network architecture in cognitive metastability may be related to the distinct functional responses of realistic cognitive systems. We also provide empirical evidence to partially support our computational results. Our paper may provide insights for the mechanisms underlying task-relevant brain dynamics, and establish a model-based link between brain structure, dynamics, and cognition, a fundamental step for computationally aided brain interventions.

Modeling charge transport in DNA is essential to understand and control the electrical properties and develop DNA-based nanoelectronics. DNA is a fluctuating molecule that exists in a solvent environment, which makes the electron susceptible to decoherence. While knowledge of the Hamiltonian responsible for decoherence will provide a microscopic description, the interactions are complex and methods to calculate decoherence are unclear. One prominent phenomenological model to include decoherence is through fictitious probes that depend on spatially variant scattering rates. However, the built-in energy independence of the decoherence (E-indep) model overestimates the transmission in the bandgap and washes out distinct features inside the valence or conduction bands. In this study, we introduce a related model where the decoherence rate is energy-dependent (E-dep). This decoherence rate is maximum at energy levels and decays away from these energies. Our results show that the E-dep model allows for exponential transmission decay with the DNA length and maintains features within the bands’ transmission spectra. We further demonstrate that we can obtain DNA conductance values within the experimental range. Our model can help study and design nanoelectronics devices that utilize weakly coupled molecular structures such as DNA.

Molecular diffusion in bulk liquids proceeds according to Fick's law, which stipulates that the particle current is proportional to the conductive area. This constrains the efficiency of filtration systems in which both selectivity and permeability are valued. Previous studies have demonstrated that interactions between the diffusing species and solid boundaries can enhance or reduce particle transport relative to bulk conditions. However, only cases that preserve the monotonic relationship between particle current and conductive area are known. In this paper, we expose a system in which the diffusive current increases when the conductive area diminishes. These examples are based on the century-old theory of a charged particle interacting with an electrical double layer. This surprising discovery could improve the efficiency of filtration and may advance our understanding of biological pore structures.

Coupled first-order differential forms of a single-particle Schrödinger equation are presented. These equations are convenient to solve efficiently using the widely available ordinary differential equation solvers. This is particularly true because the solutions to the differential equation are two sets of complementary functions that share simple and consistent mathematical relationships at the boundary and across the domain for a given potential. The differential equations are derived from an integral equation obtained using the Green's function for the kinetic operator, making them universally applicable to various systems. These equations are applied to the Yukawa potential $-e^{-\alpha r}/r$ to calculate the critical screening parameter $\alpha =1.19061242106061770534277710636105$ using a standard quadruple precision calculation, which is the most accurate compared to similar calculations in the past that confirm the first 30 significant figures. Also reported is the interesting coincident point with the eigenvalue, $\alpha =-E=0.274376862689408994894705268554458$.

We present an accurate and efficient formulation for the calculation of phonons in real-space Kohn-Sham density functional theory. Specifically, employing a local exchange-correlation functional, norm-conserving pseudopotential in the Kleinman-Bylander representation, and local form for the electrostatics, we derive expressions for the dynamical matrix and associated Sternheimer equation that are particularly amenable to the real-space finite-difference method, within the framework of density functional perturbation theory. In particular, the formulation is applicable to insulating as well as metallic systems of any dimensionality, enabling the efficient and accurate treatment of semi-infinite and bulk systems alike, for both orthogonal and nonorthogonal cells. We also develop an implementation of the proposed formulation within the high-order finite-difference method. Through representative examples, we verify the accuracy of the computed phonon dispersion curves and density of states, demonstrating excellent agreement with established plane-wave results.

We present the (numerically) exact phase diagram of a magnetic polymer on the Sierpińsky gasket embedded in three dimensions using the renormalization group method. We report distinct phases of the magnetic polymer, including paramagnetic swollen, ferromagnetic swollen, paramagnetic collapsed, and ferromagnetic collapsed states. By evaluating critical exponents associated with phase transitions, we located the phase boundaries between different phases. If the model is extended to include a four-site interaction which disfavors configurations with a single spin of a given type, we find a rich variety of critical behaviors. Notably, we uncovered a phenomenon of reentrance, where the system transitions from a collapsed (paramagnetic) state to a swollen (paramagnetic) state followed by another collapse (paramagnetic) and ultimately reaching a ferromagnetic collapsed state. These findings shed new light on the complex behavior of (lattice) magnetic polymers.

The experimental control of synergistic chemomechanical dynamics of catalytically active microgels (microreactors) is a key prerequisite for the design of adaptive and biomimetic materials. Here, we report a minimalistic model of feedback-controlled microreactors based on the coupling between the hysteretic polymer volume phase transition and a volume-controlled permeability for the internal chemical conversion. We categorize regimes of mono- and bistability, excitability, damped oscillations, as well as sustained oscillatory states with tunable amplitude, as indicated by experiments and representable by the FitzHugh-Nagumo dynamics for neurons. We summarize the features of such a “colloidal neuron” in bifurcation diagrams with respect to microgel design parameters, such as permeability and relaxation times, as a guide for experimental synthesis.

When amorphous solids are subjected to simple or pure strain, they exhibit elastic increase in stress, punctuated by plastic events that become denser (in strain) upon increasing the system size. It is customary to assume in theoretical models that the stress released in each plastic event is redistributed according to the linear Eshelby kernel, causing avalanches of additional stress release. Here we demonstrate that, contrary to the uniform affine strain resulting from simple or pure strain, each plastic event is associated with a nonuniform strain that gives rise to a displacement field that contains quadrupolar and dipolar charges that typically screen the linear elastic phenomenology and introduce anomalous length scales and influence the form of the stress redistribution. An important question that opens up is how to take this into account in elastoplastic models of shear induced phenomena like shear banding.

Crack front waves (FWs) are dynamic objects that propagate along moving crack fronts in three-dimensional (3D) materials. We study FW dynamics in the framework of a 3D phase-field platform that features a rate-dependent fracture energy $\mathrm{\Gamma }\left(v\right)$ ($v$ is the crack propagation velocity) and intrinsic length scales, and quantitatively reproduces the high-speed oscillatory instability in the quasi-2D limit. We show that in-plane FWs feature a rather weak time dependence, with decay rate that increases with $d\mathrm{\Gamma }\left(v\right)/dv>0$, and largely retain their properties upon FW-FW interactions, similarly to a related experimentally observed solitonic behavior. Driving in-plane FWs into the nonlinear regime, we find that they propagate slower than predicted by a linear perturbation theory. Finally, by introducing small out-of-plane symmetry-breaking perturbations, coupled in- and out-of-plane FWs are excited, but the out-of-plane component decays under pure tensile loading. Yet, including a small antiplane loading component gives rise to persistent coupled in- and out-of-plane FWs.

We apply stochastic-trajectory analysis to derive exact expressions for the mean first-passage times of jump-and-drift transition paths across two or more consecutive thresholds. We perform the analysis of the crossing statistics in terms of dimensionless quantities and show that, for particles starting between two thresholds, such statistics are directly related to the probability of not crossing one threshold and to the splitting probability of crossing the second one. We additionally derive a relationship for the mean first-passage time of the transition paths crossing two consecutive thresholds for particles starting outside them. The results are relevant to several physical and engineering applications including the case of flow discharge in fluvial environments, which is shown.

The exact solution of the Lindblad equation with a quadratic Hamiltonian and linear coupling operators was derived within the chord representation, that is, for the Fourier transform of the Wigner function, also known as the characteristic function. It is here generalized for several degrees of freedom, so as to provide an explicit expression for the reduced density operator of any subsystem, as well as moments expressed as derivatives of this evolving chord function. The Wigner function is then the convolution of its straightforward classical evolution with a widening multidimensional Gaussian window, eventually ensuring its positivity. Futher on, positivity also holds for the Glauber-Sundarshan P function, which guarantees separability of the components. In the context of several degrees of freedom, a full dissipation matrix is defined, whose trace is equal to twice the previously derived dissipation coefficient. This governs the rate at which the phase space volume of the argument of the Wigner function contracts, while that of the chord function expands. Examples of Markovian evolution of a triatomic molecule and of an array of harmonic oscillators are discussed.

The Lorenz system was derived on the basis of a model of convective atmospheric motions and may serve as a paradigmatic model for considering a complex climate system. In this study we formulated the thermodynamic efficiency of convective atmospheric motions governed by the Lorenz system by treating it as a nonequilibrium thermodynamic system. Based on the fluid conservation equations under the Oberbeck-Boussinesq approximation, the work necessary to maintain atmospheric motion and heat fluxes at the boundaries were calculated. Using these calculations, the thermodynamic efficiency was formulated for stationary and chaotic dynamics. The numerical results show that for both stationary and chaotic dynamics, the efficiency tends to increase as the atmospheric motion is driven out of thermodynamic equilibrium when the Rayleigh number increases. However, it is shown that the efficiency is upper bounded by the maximum efficiency, which is expressed in terms of the parameters characterizing the fluid and the convective system. The analysis of the entropy generation rate was also performed for elucidating the difference between the thermodynamic efficiency of conventional heat engines and the present atmospheric heat engine. It is also found that there exists an abrupt drop in efficiency at the critical Hopf bifurcation point, where the dynamics change from stationary to chaotic. These properties are similar to those found previously in the Malkus-Lorenz waterwheel system.

We study the interface representation of the contact process at its directed-percolation critical point, where the scaling properties of the interface can be related to those of the original particle model. Interestingly, such a behavior happens to be intrinsically anomalous and more complex than that described by the standard Family-Vicsek dynamic scaling Ansatz of surface kinetic roughening. We expand on a previous numerical study by Dickman and Muñoz [Phys. Rev. E 62, 7632 (2000)] to fully characterize the kinetic roughening universality class for interface dimensions $d=1,2$, and 3. Beyond obtaining scaling exponent values, we characterize the interface fluctuations via their probability density function (PDF) and covariance, seen to display universal properties which are qualitatively similar to those recently assessed for the Kardar-Parisi-Zhang (KPZ) and other important universality classes of kinetic roughening. Quantitatively, while for $d=1$ the interface covariance seems to be well described by the KPZ, ${\mathrm{Airy}}_1$ covariance, no such agreement occurs in terms of the fluctuation PDF or the scaling exponents.

A microscopic formula for the viscosity of liquids and solids is derived rigorously from a first-principles (microscopically reversible) Hamiltonian for particle-bath atomistic motion. The derivation is done within the framework of nonaffine linear response theory. This formula may lead to a valid alternative to the Green-Kubo approach to describe the viscosity of condensed matter systems from molecular simulations without having to fit long-time tails. Furthermore, it provides a direct link between the viscosity, the vibrational density of states of the system, and the zero-frequency limit of the memory kernel. Finally, it provides a microscopic solution to Maxwell's interpolation problem of viscoelasticity by naturally recovering Newton's law of viscous flow and Hooke's law of elastic solids in two opposite limits.

We study the probability distribution function of the long-time values of observables being time-evolved by Hamiltonians modeling clean and disordered one-dimensional chains of many spin-1/2 particles. In particular, we analyze the return probability and its version for a completely extended initial state, the so-called spectral form factor. We complement our analysis with the spin autocorrelation and connected spin-spin correlation functions, both of interest in experiments with quantum simulators. We show that the distribution function has a universal shape provided the central limit theorem holds. Explicitly, the shape is exponential for the return probability and spectral form factor, meanwhile it is Gaussian for the few-body observables. We also discuss implications over the so-called many-body localization. Remarkably, our approach requires only a single sample of the dynamics and small system sizes, which could be quite advantageous when dealing specially with disordered systems.

In systems far from equilibrium, the statistics of observables are connected to entropy production, leading to the thermodynamic uncertainty relation (TUR). However, the derivation of TURs often involves constraining the parity of observables, such as considering asymmetric currents, making it unsuitable for the general case. We propose a thermodynamic variational relation (TVR) between the statistics of general observables and entropy production, based on the variational representation of $f$ divergences. From this result, we derive a universal TUR and other relations for higher-order statistics of observables.

Motile organisms can form stable agglomerates such as cities or colonies. In the outbreak of a highly contagious disease, the control of large-scale epidemic spread depends on factors like the number and size of agglomerates, travel rate between them, and disease recovery rate. While the emergence of agglomerates permits early interventions, it also explains longer real epidemics. In this work, we study the spread of susceptible-infected-recovered (SIR) epidemics (or any sort of information exchange by contact) in one-dimensional spatially structured systems. By working in one dimension, we establish a necessary foundation for future investigation in higher dimensions and mimic micro-organisms in narrow channels. We employ a model of self-propelled particles which spontaneously form multiple clusters. For a lower rate of stochastic reorientation, particles have a higher tendency to agglomerate and therefore the clusters become larger and less numerous. We examine the time evolution averaged over many epidemics and how it is affected by the existence of clusters through the eventual recovery of infected particles before reaching new clusters. New terms appear in the SIR differential equations in the last epidemic stages. We show how the final number of ever-infected individuals depends nontrivially on single-individual parameters. In particular, the number of ever-infected individuals first increases with the reorientation rate since particles escape sooner from clusters and spread the disease. For higher reorientation rate, travel between clusters becomes too diffusive and the clusters too small, decreasing the number of ever-infected individuals.

We study the stationary states of variants of the noisy voter model, subject to fluctuating parameters or external environments. Specifically, we consider scenarios in which the herding-to-noise ratio switches randomly and on different timescales between two values. We show that this can lead to a phase in which polarized and heterogeneous states exist. Second, we analyze a population of noisy voters subject to groups of external influencers, and show how multipeak stationary distributions emerge. Our work is based on a combination of individual-based simulations, analytical approximations in terms of a piecewise-deterministic Markov processes (PDMP), and on corrections to this process capturing intrinsic stochasticity in the linear-noise approximation. We also propose a numerical scheme to obtain the stationary distribution of PDMPs with three environmental states and linear velocity fields.

Models for polarization drag—mechanical analog of the Faraday effect—are extended to include inertial corrections to the dielectrics properties of the rotating medium in its rest frame. Instead of the Coriolis-Faraday term originally proposed by Baranova and Zel'dovich [Proc. R. Soc. London A: Math. Phys. Sci. 368, 591 (1979)], inertia corrections due to the fictitious Coriolis and centrifugal forces are here derived by considering the effect of rotation on both the Lorentz and plasma dielectric models. These modified rest-frame properties are subsequently used to deduce laboratory properties. Although elegant and insightful, it is shown that the Coriolis-Faraday correction inferred from Larmor's theorem is limited in that it can only capture inertial corrections to polarization drag when the equivalent Faraday rotation is defined at the wave frequency of interest. This is notably not the case for low-frequency polarization drag in a rotating magnetized plasma, although it is verified here using the more general phenomenological models that the impact of fictitious forces is, in general, negligible in these conditions.