We introduce transfer learning for nonlinear dynamics, which enables efficient predictions of chaotic dynamics by utilizing a small amount of data. For the Lorenz chaos, by optimizing the transfer rate, we accomplish more accurate inference than the conventional method by an order of magnitude. Moreover, a surprisingly small amount of learning is enough to infer the energy dissipation rate of the Navier-Stokes turbulence because we can, thanks to the small-scale universality of turbulence, transfer a large amount of the knowledge learned from turbulence data at lower Reynolds number.

The rise of the World Airline Network over the past century has led to sharp changes in our notions of “distance” and “closeness”—in terms of both trade and travel, but also (less desirably) with respect to the spread of disease. When novel pathogens are discovered, countries, cities, and hospitals are caught trying to predict how much time they have to prepare. In this paper, by considering the early stages of epidemic spread as a simple branching process, we derive the full probability distribution of arrival times. We are able to rederive a number of past arrival time results (in suitable limits) and demonstrate the robustness of our approach, both to parameter values far outside the traditionally considered regime and to errors in the parameter values used. The branching process approach provides some theoretical justification to the “effective distance” introduced by Brockmann and Helbing [Science 342, 1337 (2013)]; however, we also observe that when compared to real-world data, the predictive power of all methods in this class is significantly lower than has been previously reported.

We study the $q$-state active Potts model (APM) on a two-dimensional lattice in which self-propelled particles have $q$ internal states corresponding to the $q$ directions of motion. A local alignment rule inspired by the ferromagnetic $q$-state Potts model and self-propulsion via biased diffusion according to the internal particle states elicits collective motion at high densities and low noise. We formulate a coarse-grained hydrodynamic theory with which we compute the phase diagrams of the APM for $q=4$ and $q=6$ and analyze the flocking dynamics in the coexistence region, where the high-density (polar liquid) phase forms a fluctuating stripe of coherently moving particles on the background of the low-density (gas) phase. A reorientation transition of the phase-separated profiles from transversal band motion to longitudinal lane formation is found, which is absent in the Vicsek model and the active Ising model. The origin of this reorientation transition is revealed by a stability analysis: for large velocities the transverse diffusivity approaches zero and stabilizes lanes. Computer simulations corroborate the analytical predictions of the flocking and reorientation transitions and validate the phase diagrams of the APM.

In the context of stochastic thermodynamics, a minimal model for nonequilibrium steady states has been recently proposed: the Brownian gyrator (BG). It describes the stochastic overdamped motion of a particle in a two-dimensional harmonic potential, as in the classic Ornstein-Uhlenbeck process, but considering the simultaneous presence of two independent thermal baths. When the two baths have different temperatures, the steady BG exhibits a rotating current, a clear signature of nonequilibrium dynamics. Here, we consider a time-dependent potential, and we apply a reverse-engineering approach to derive exactly the required protocol to switch from an initial steady state to a final steady state in a finite time $\tau$. The protocol can be built by first choosing an arbitrary quasistatic counterpart, with few constraints, and then adding a finite-time contribution which only depends upon the chosen quasistatic form and which is of order $1/\tau$. We also get a condition for transformations which, in finite time, conserve internal energy, useful for applications such as the design of microscopic thermal engines. Our study extends finite-time stochastic thermodynamics to transformations connecting nonequilibrium steady states.

We characterize the conditions under which a multitime quantum process with a finite temporal resolution can be approximately described by an equilibrium one. By providing a generalization of the notion of equilibration on average, where a system remains closed to a fixed equilibrium for most times, to one which can be operationally assessed at multiple times, we place an upper-bound on a new observable distinguishability measure comparing a multitime process with a finite temporal resolution against a fixed equilibrium one. While the same conditions on single-time equilibration, such as a large occupation of energy levels in the initial state remain necessary, we obtain genuine multitime contributions depending on the temporal resolution of the process and the amount of disturbance of the observer's operations on it.

Recent studies in one dimension have revealed that the temporal advantage rendered by stochastic resetting to diffusing particles in attaining first passage may be annulled by a sufficiently strong attractive potential. We extend the results to higher dimensions. For a diffusing particle in an attractive potential $V\left(R\right)=k{R}^n$, in general $d$ dimensions, we study the critical strength $k=k_c$ above which resetting becomes disadvantageous. The point of continuous transition may be exactly found even in cases where the problem with resetting is not solvable, provided the first two moments of the problem without resetting are known. We find the dimensionless critical strength ${\kappa }_{c,n}\left(k_c\right)$ exactly when $d/n$ and $2/n$ take positive integral values. Also for the limiting case of a box potential (representing $n\to \infty$), and the special case of a logarithmic potential $kln\left(\frac{R}{a}\right)$, we find the corresponding transition points ${\kappa }_{c,\infty }$ and ${\kappa }_{c,l}$ exactly for any dimension $d$. The asymptotic forms of the critical strengths at large dimensions $d$ are interesting. We show that for the power law potential, for any $n\in (0,\infty )$, the dimensionless critical strength ${\kappa }_{c,n}\sim d^{\frac{1}{n}}$ at large $d$. For the box potential, asymptotically, ${\kappa }_{c,\infty }\sim (1-ln\left(\frac{d}{2}\right)/d)$, while for the logarithmic potential, ${\kappa }_{c,l}\sim d$.

We study the motility-induced aggregation of active Brownian particles (ABPs) on a porous, circular wall. We observe that the morphology of aggregated dense-phase on a static wall depends on the wall porosity, particle motility, and the radius of the circular wall. Our analysis reveals two morphologically distinct, dense aggregates; a connected dense cluster that spreads uniformly on the circular wall and a localized cluster that breaks the rotational symmetry of the system. These distinct morphological states are similar to the macroscopic structures observed in aggregates on planar, porous walls. We systematically analyze the parameter regimes where the different morphological states are observed. We further extend our analysis to motile circular rings. We show that the motile ring propels almost ballistically due to the force applied by the active particles when they form a localized cluster, whereas it moves diffusively when the active particles form a continuous cluster. This property demonstrates the possibility of extracting useful work from a system of ABPs, even without artificially breaking the rotational symmetry.

A twist-bend nematic $\left(N_{\mathrm{TB}}\right)$ liquid crystalline phase spontaneously forms modulated structures on a microscale level when confined in thin planar cells. Preliminary studies showed that these cells can be used as polarization gratings. Here we present a theoretical description of the formation of a two-dimensionally modulated structure. By considering the $N_{\mathrm{TB}}$ phase as a pseudolayer medium, a threshold condition for the onset of a modulated structure is calculated for weak and strong boundary conditions in the case of initially bookshelf or pretilt alignment of pseudolayers. Based on the modeled structure we determine spatial variation of the optic axis and calculate properties of the transmitted diffracted light. Results of the beam propagation method (BPM) and transfer matrix method are compared and it is shown that a more complex BPM gives better agreement with experimental results, meaning that even in thin cells the diffraction of light inside the grating should not be neglected.

For a radiating charged particle, the radiation reaction force plays an important role in determining its motion. Several formulas have been proposed to describe the radiation reaction force. Stationary solutions of the Lorentz-Abraham-Dirac (LAD), Mo-Papas, Landau-Lifshitz, and Ford-O'Connell equations are obtained and compared for a charged particle under a static magnetic and a rotating electric field. The behaviors of the obtained solutions look quite similar. The relative differences of the Lorentz factor, calculating the values using the LAD equation compared to the other equations, are evaluated; these values are shown to be less than ${10}^{-6}$ in the regime where classical radiation reactions are applicable.

Controlling dynamical fluctuations in open quantum systems is essential both for our comprehension of quantum nonequilibrium behavior and for its possible application in near-term quantum technologies. However, understanding these fluctuations is extremely challenging due, to a large extent, to a lack of efficient important sampling methods for quantum systems. Here, we devise a unified framework—based on population-dynamics methods—for the evaluation of the full probability distribution of generic time-integrated observables in Markovian quantum jump processes. These include quantities carrying information about genuine quantum features, such as quantum superposition or entanglement, not accessible with existing numerical techniques. The algorithm we propose provides dynamical free-energy and entropy functionals which, akin to their equilibrium counterpart, permit one to unveil intriguing phase-transition behavior in quantum trajectories. We discuss some applications and further disclose coexistence and hysteresis, between a highly entangled phase and a low entangled one, in large fluctuations of a strongly interacting few-body system.

The thermal rectifier is an analog of the electrical rectifier, in which heat flux in a forward direction is larger than that in the reverse direction. Owing to the controllability of the heat flux, the solid-state thermal rectifier is promising from both theoretical and applicational points of view. In this paper, we examine analytical expressions of thermal-rectification coefficients $R$ for thermal rectifiers with typical linear and nonlinear model functions as nonuniform thermal conductivities against temperature $T$. For the thermal rectifier with linear (quadratic) temperature-dependent thermal conductivity, a maximum value of $R$ is calculated to be 3 ($\simeq 14$). With use of a structural-phase-transition material, a maximum value of $R$ is found to ideally reach to ${\kappa }_2/{\kappa }_1$, where ${\kappa }_1$ (${\kappa }_2$) is the minimum (maximum) value of its $\kappa \left(T\right)$. Values of $R$ for the thermal rectifiers with an inverse $T$-dependent function and an exponential function of $\kappa$ are also analytically examined.

We perform a numerical study of a new microcanonical polymer model on a three-dimensional cubic lattice, consisting of ideal chains whose range and number of nearest-neighbor contacts are fixed to given values. Our simulations suggest an interesting exact relation concerning the internal energy per monomer of the interacting self-avoiding walk at the $\theta$ point.

We devise a simple method for detecting signals of unknown form buried in any noise, including heavy tailed. The method centers on signal-noise decomposition in rank and time: Only stationary white noise generates data with a jointly uniform rank-time probability distribution, $U(1,N)\times U(1,N)$, for $N$ data points in a time series. Signals of any kind distort this uniformity. Such distortions are captured by rank-time cumulative distributions permitting all-purpose efficient detection, even for single time series and noise of infinite variance.

Macromolecular diffusion in strongly confined geometries and crowded environments is still to a large extent an open subject in soft matter physics and biology. In this paper, we employ large-scale Langevin dynamics simulations to investigate how the diffusion of a tracer is influenced by the combined action of excluded-volume and weak attractive crowder-tracer interactions. We consider two species of tracers, standard hard-core particles described by the Weeks-Chandler-Andersen (WCA) repulsive potential and core-softened (CS) particles, which model, e.g., globular proteins, charged colloids, and nanoparticles covered by polymeric brushes. These systems are characterized by the presence of two length scales in the interaction and can show waterlike anomalies in their diffusion, stemming from the inherent competition between different length scales. Here we report a comprehensive study of both diffusion and structure of these two tracer species in an environment crowded by quenched configurations of polymers at increasing density. We analyze in detail how the tracer-polymer affinity and the system density affect transport as compared to the emergence of specific static spatial correlations. In particular, we find that, while hardly any differences emerge in the diffusion properties of WCA and CS particles, the propensity to develop structural order for large crowding is strongly frustrated for CS particles. Surprisingly, for large enough affinity for the crowding matrix, the diffusion coefficient of WCA tracers display a nonmonotonic trend as their density is increased when compared to the zero affinity scenario. This waterlike anomaly turns out to be even larger than what observed for CS particle and appears to be rooted in a similar competition between excluded-volume and affinity effects.

Low-frequency nonphononic modes and plastic rearrangements in glasses are spatially quasilocalized, i.e., they feature a disorder-induced short-range core and known long-range decaying elastic fields. Extracting the unknown short-range core properties, potentially accessible in computer glasses, is of prime importance. Here we consider a class of contour integrals, performed over the known long-range fields, which are especially designed for extracting the core properties. We first show that, in computer glasses of typical sizes used in current studies, the long-range fields of quasilocalized modes experience boundary effects related to the simulation box shape and the widely employed periodic boundary conditions. In particular, image interactions mediated by the box shape and the periodic boundary conditions induce the fields' rotation and orientation-dependent suppression of their long-range decay. We then develop a continuum theory that quantitatively predicts these finite-size boundary effects and support it by extensive computer simulations. The theory accounts for the finite-size boundary effects and at the same time allows the extraction of the short-range core properties, such as their typical strain ratios and orientation. The theory is extensively validated in both two and three dimensions. Overall, our results offer a useful tool for extracting the intrinsic core properties of nonphononic modes and plastic rearrangements in computer glasses.

Hook dynamics are important in the motility of singly flagellated bacteria during flick motility. Although the hook is relatively short, during reorientation events it may undergo large deformations, leading to nonlinear behavior. Here, we explore when these nonlinear and large deformations are important for the swimming dynamics in different ranges of hook flexibilities and flagellar motor torques. For this purpose, we investigate progressively more faithful models for the hook, starting with linear springs, then models that incorporate nonlinearities due to larger hook deformations. We also employ these models both with and without hydrodynamic interactions between the flagellum and cell body to test the importance of those hydrodynamic interactions. We show that for stiff hooks, bacteria swim with a flagellum rotating on-axis in orbits and hydrodynamic interactions between the cell body and flagellum change swimming speeds by about 40%. As the hook stiffness decreases, there is a critical hook stiffness that predicts the initiation of the dynamic instability causing flicks. We compare the transition value of stiffnesses predicted by our models to experiments and show that nonlinearity and large deflections do not significantly affect critical transition values, while hydrodynamic interactions can change transition values by up to 13%. Below the transition value, we observe precession of the flagellum, in which it deflects off-axis to undergo nearly circular stable trajectories. However, only slightly below the transition stiffness, nonlinearity in hook response destabilizes precession, leading to unstable deflections of the flagellum. We conclude that while the linear hook response can qualitatively predict transition stiffnesses, nonlinear models are necessary to capture the behavior of hooks for stiffnesses below transition. Furthermore, we show that for the lower range of hook stiffnesses observed in actual bacteria, models which capture the full deformations of hooks are necessary. Inclusion of the hydrodynamic interactions of the cell body, hook, and flagellum is required to quantitatively simulate nonlinear dynamics of soft hooks during flick motility.

A run-and-tumble particle in a one-dimensional box (infinite potential well) is studied. The steady state is analytically solved and analyzed, revealing the emergent length scale of the boundary layer where particles accumulate near the walls. The mesoscopic steady state entropy production rate of the system is derived from coupled Fokker-Planck equations with a linear reaction term, resulting in an exact analytic expression. The entropy production density is shown to peak at the walls. Additionally, the derivative of the entropy production rate peaks at a system size proportional to the length scale of the accumulation boundary layer, suggesting that the behavior of the entropy production rate and its derivatives as a function of the control parameter may signify a qualitative behavior change in the physics of active systems, such as phase transitions.

Two acoustic bubbles may attract or repel due to the secondary radiation force acting on them. We use here a dual-frequency levitation chamber in order to trap two oscillating microbubbles at close, fixed distance, and to perform measurements of the interaction force. We successfully compare our measurements to a commonly used theoretical model that assumes linear spherical oscillations, and disregards attenuation and multiple scattering between bubbles. The deviation from the model arises when nonspherical surface oscillations are triggered, leading to an additional hydrodynamic force induced by second-order liquid flow.