We analyze the linear response properties of the uniformly heated granular gas. The intensity of the stochastic driving fixes the value of the granular temperature in the nonequilibrium steady state reached by the system. Here, we investigate two specific situations. First, we look into the “direct” relaxation of the system after a single (small) jump of the driving intensity. This study is carried out by two different methods. Not only do we linearize the evolution equations around the steady state, but we also derive generalized out-of-equilibrium fluctuation-dissipation relations for the relevant response functions. Second, we investigate the behavior of the system in a more complex experiment, specifically a Kovacs-like protocol with two jumps in the driving. The emergence of an anomalous Kovacs response is explained in terms of the properties of the direct relaxation function: it is the second mode changing sign at the critical value of the inelasticity that demarcates anomalous from normal behavior. The analytical results are compared with numerical simulations of the kinetic equation, and a good agreement is found.

The variation of the distribution of the liquid flow in porous media during evaporation is still a puzzle. We resolve it with the pore network modeling approach. The distribution of the evaporation-induced liquid flow in a pore network composed of about 2.5 million pores is determined. The probability density function of the magnitude of the normalized liquid flow rate is obtained. For the low normalized liquid flow rate, the probability density function is power-lawlike. The power-law exponent depends on both the liquid saturation and the location of the moving meniscus in the main liquid cluster. The evaporation-induced liquid flow in the pores in the pore network can be correlated. Whether the liquid flow distributions in various zones in the pore network are similar or not relies significantly on the location of the moving meniscus in the main liquid cluster. The functions depicting the relation between the power-law exponent and the local liquid saturation for the zones adjacent to and away from the open side of the pore network are different. These findings from the pore scale studies provide insights into developing the accurate continuum model for evaporation in porous media.

Theoretical results are given in the present paper, which can well explain the experimental observations performed under microgravity conditions in the PK-3 Plus Laboratory on board the International Space Station about the propagation of a solitary wave across an interface in a binary complex plasma. By using the traditional reductive perturbation method and the continuity conditions of both the electric potential and the momentum at the interface, we obtain the equivalent “initial conditions” for both the transmitted wave and the reflected waves from the incident wave. Then we obtain the numbers of the reflected and the transmitted solitary waves as well as all the wave amplitudes by using the inverse scattering method. The ripples of both reflection and transmission have also been given by using the Fourier series. The number of the reflected and the transmitted solitary waves produced by interface, as well as all the solitary wave amplitudes, depend on the system parameters such as the number density, electric charge, mass of the dust particles, and the effective temperature in both regions. The analytical results agree with observations in the experiments.

We devise a deterministic algorithm to efficiently sample high-quality solutions of certain spin-glass systems that encode hard optimization problems. We employ tensor networks to represent the Gibbs distribution of all possible configurations. Using approximate tensor-network contractions, we are able to efficiently map the low-energy spectrum of some quasi-two-dimensional Hamiltonians. We exploit the local nature of the problems to compute spin-glass droplets geometries, which provides a new form of compression of the low-energy spectrum. It naturally extends to sampling, which otherwise, for exact contraction, is #P-complete. In particular, for one of the hardest known problem-classes devised on chimera graphs known as deceptive cluster loops and for up to 2048 spins, we find on the order of ${10}^{10}$ degenerate ground states in a single run of our algorithm, computing better solutions than have been reported on some hard instances. Our gradient-free approach could provide new insight into the structure of disordered spin-glass complexes, with ramifications both for machine learning and noisy intermediate-scale quantum devices.

We study Nielsen complexity and Fubini-Study complexity for the transverse $\mathit{XY}$ spin chain and establish their nonanalyticity at the critical lines. We obtain the scaling behavior of both complexities near quantum phase transitions in the thermodynamic limit, as a function of the system parameters. The scaling of the Nielsen complexity with the system size is also established, close to criticality. We also obtain analytic expressions for the Fubini-Study complexity in some special cases for this model, while a numerical analysis in more generic situations is carried out. Our study clearly demonstrates the differences in the two notions of complexity in the transverse $\mathit{XY}$ model.

An important transition from a homogeneous steady state to an inhomogeneous steady state via the Turing bifurcation in coupled oscillators was reported recently [Phys. Rev. Lett. 111, 024103 (2013)]. However, the same in the quantum domain is yet to be observed. In this paper, we discover the quantum analog of the Turing bifurcation in coupled quantum oscillators. We show that a homogeneous steady state is transformed into an inhomogeneous steady state through this bifurcation in coupled quantum van der Pol oscillators. We demonstrate our results by a direct simulation of the quantum master equation in the Lindblad form. We further support our observations through an analytical treatment of the noisy classical model. Our study explores the paradigmatic Turing bifurcation at the quantum-classical interface and opens up the door toward its broader understanding.

The dynamics of Fermi-Pasta-Ulam (FPU) recurrence in a Manakov system is studied analytically. Exact Akhmediev breather (AB) solutions for this system are found that cannot be reduced to the ABs of a single-component nonlinear Schrödinger equation. Expansion-contraction cycle of the corresponding spectra with an infinite number of sidebands is calculated analytically using a residue theorem. A distinctive feature of these spectra is the asymmetry between positive and negative spectral modes. A practically important consequence of the spectral asymmetry is a nearly complete energy transfer from the central mode to one of the lowest-order (left or right) sidebands. Numerical simulations started with modulation instability of plane waves confirm the findings based on the exact solutions. It is also shown that the full growth-decay cycle of the AB leads to the nonlinear phase shift between the initial and final states in both components of the Manakov system. This finding shows that the final state of the FPU recurrence described by the vector ABs is not quite the same as the initial state. Our results are applicable and can be observed in a wide range of two-component physical systems such as two-component waves in optical fibers, two-directional waves in crossing seas, and two-component Bose-Einstein condensates.

Rhythmic activity has been observed in numerous animal species ranging from insects to humans, and in relation to a wide range of cognitive tasks. Various experimental and theoretical studies have investigated rhythmic activity. The theoretical efforts have mainly been focused on the neuronal dynamics, under the assumption that network connectivity satisfies certain fine-tuning conditions required to generate oscillations. However, it remains unclear how this fine-tuning is achieved. Here we investigated the hypothesis that spike-timing-dependent plasticity (STDP) can provide the underlying mechanism for tuning synaptic connectivity to generate rhythmic activity. We addressed this question in a modeling study. We examined STDP dynamics in the framework of a network of excitatory and inhibitory neuronal populations that has been suggested to underlie the generation of oscillations in the gamma range. Mean-field Fokker-Planck equations for the synaptic weight dynamics are derived in the limit of slow learning. We drew on this approximation to determine which types of STDP rules drive the system to exhibit rhythmic activity, and we demonstrate how the parameters that characterize the plasticity rule govern the rhythmic activity. Finally, we propose a mechanism that can ensure the robustness of self-developing processes in general, and for rhythmogenesis in particular.

Principal component analysis (PCA) has been applied to analyze random fields in various scientific disciplines. However, the explainability of PCA remains elusive unless strong domain-specific knowledge is available. This paper provides a theoretical framework that builds a duality between the PCA eigenmodes of a random field and eigenstates of a Schrödinger equation. Based on the duality we propose the Schrödinger PCA algorithm to replace the expensive PCA solver with a more sample-efficient Schrödinger equation solver. We verify the validity of the theory and the effectiveness of the algorithm with numerical experiments.

We consider a two-dimensional array of heterogeneous nonlocally coupled phase oscillators on a flat torus and study the bound states of two counter-rotating spiral chimeras, shortly two-core spiral chimeras, observed in this system. In contrast to other known spiral chimeras with motionless incoherent cores, the two-core spiral chimeras typically show a drift motion. Due to this drift, their incoherent cores become spatially modulated and develop specific fingerprint patterns of varying synchrony levels. In the continuum limit of infinitely many oscillators, the two-core spiral chimeras can be studied using the Ott-Antonsen equation. Numerical analysis of this equation allows us to reveal the stability region of different spiral chimeras, which we group into three main classes—symmetric, asymmetric, and meandering spiral chimeras.

In microgravity experiments, we quantified the net charge on systems of two identical, 434-$\mu \mathrm{m}$-diameter glass spheres before and after a collision. We find that charge conservation is significantly violated. Independent of the sign of the total charge, the systems regularly lose some of their net charges, that is, they slightly discharge. This implies that positive as well as negative charge carriers become entrained into the surrounding atmosphere during a collision.

For finite quenched random systems, on regular lattices, it is possible to define two types of variances (noises). It is demonstrated that their ratio is useful in calculating the correlation length of an infinite and rather general random system, as a function of temperature. The numerical method of obtaining those variables is not relevant. It can be real-space numerical renormalization, simulation, or any other method. It does not matter. The correlation length obtained by this technique may then be used to obtain directly the critical correlation exponent, $\nu$, rather than indirectly, using scaling relations, as is often done. The method is demonstrated by applying it to the random field Ising model.

The behavior of many magnetic and dielectric solids, and the more contemporary magnetic superlattices, is governed by dipolar interactions. They are anisotropic and long ranged, having varied consequences ranging from ground states with complicated magnetic order to the presence of glassy dynamics characterized by a plethora of relaxation times. These systems are well captured by the dipolar Ising model (DIM) with nearest-neighbor exchange interactions $\left(J\right)$ and long-range dipolar interactions $\left(D\right)$. Depending on the relative interaction strength $\mathrm{\Gamma }=J/D$, there are four phases of distinct magnetic order and symmetry. Using Monte Carlo simulations, we perform deep quenches to study domain growth or coarsening in the $d=3$ DIM. This important nonequilibrium phenomenon has not been addressed as dipolar interactions are notoriously difficult to handle theoretically. Our study reveals that, in spite of the anisotropy in interactions and diversity in ground state configurations, we observe universality in the ordering dynamics of all phases.

We apply the framework of optimal nonlinear control to steer the dynamics of a whole-brain network of FitzHugh-Nagumo oscillators. Its nodes correspond to the cortical areas of an atlas-based segmentation of the human cerebral cortex, and the internode coupling strengths are derived from diffusion tensor imaging data of the connectome of the human brain. Nodes are coupled using an additive scheme without delays and are driven by background inputs with fixed mean and additive Gaussian noise. Optimal control inputs to nodes are determined by minimizing a cost functional that penalizes the deviations from a desired network dynamic, the control energy, and spatially nonsparse control inputs. Using the strength of the background input and the overall coupling strength as order parameters, the network's state-space decomposes into regions of low- and high-activity fixed points separated by a high-amplitude limit cycle, all of which qualitatively correspond to the states of an isolated network node. Along the borders, however, additional limit cycles, asynchronous states, and multistability can be observed. Optimal control is applied to several state-switching and network synchronization tasks, and the results are compared to controllability measures from linear control theory for the same connectome. We find that intuitions from the latter about the roles of nodes in steering the network dynamics, which are solely based on connectome features, do not generally carry over to nonlinear systems, as had been previously implied. Instead, the role of nodes under optimal nonlinear control critically depends on the specified task and the system's location in state space. Our results shed new light on the controllability of brain network states and may serve as an inspiration for the design of new paradigms for noninvasive brain stimulation.

The spreading dynamics of an epidemic and the collective behavioral pattern of the population over which it spreads are deeply intertwined and the latter can critically shape the outcome of the former. Motivated by this, we design a parsimonious game-theoretic behavioral-epidemic model, in which an interplay of realistic factors shapes the coevolution of individual decision making and epidemics on a network. Although such a coevolution is deeply intertwined in the real world, existing models schematize population behavior as instantaneously reactive, thus being unable to capture human behavior in the long term. Our paradigm offers a unified framework to model and predict complex emergent phenomena, including successful collective responses, periodic oscillations, and resurgent epidemic outbreaks. The framework also allows us to provide analytical insights on the epidemic process and to assess the effectiveness of different policy interventions on ensuring a collective response that successfully eradicates the outbreak. Two case studies, inspired by real-world diseases, are presented to illustrate the potentialities of the proposed model.

We study entropy production in nanoscale devices, which are coupled to finite heat baths. This situation is of growing experimental relevance, but most theoretical approaches rely on a formulation of the second law valid only for infinite baths. We fix this problem by pointing out that Clausius' paper from 1865 already contains an adequate formulation of the second law for finite heat baths, which can be also rigorously derived from a microscopic quantum description. This Clausius inequality shows that nonequilibrium processes are less irreversible than previously thought. We use it to correctly extend Landauer's principle to finite baths and we demonstrate that any heat engine in contact with finite baths has a higher efficiency than previously thought. Importantly, our results are easy to study, requiring only the knowledge of the average bath energy.

We construct a density functional for the lattice gas or Ising model on square and cubic lattices based on lattice fundamental measure theory. To treat the nearest-neighbor attractions between the lattice gas particles, the model is mapped to a multicomponent model of hard particles with additional lattice polymers where effective attractions between particles arise from the depletion effect. The lattice polymers are further treated via the introduction of polymer clusters (labelled by the numbers of polymer they contain) such that the model becomes a multicomponent model of particles and polymer clusters with nonadditive hard interactions. The density functional for this nonadditive hard model is constructed with lattice fundamental measure theory. The resulting bulk phase diagram recovers the Bethe-Peierls approximation and planar interface tensions show a considerable improvement compared to the standard mean-field functional and are close to simulation results in three dimensions. We demonstrate the existence of planar interface solutions at chemical potentials away from coexistence when the equimolar interface position is constrained to arbitrary real values.

The spatial transition of the wake behind a thin pitching plate in the thrust regime is studied. The drag-to-thrust transition is seen to occur at a threshold pitching frequency which becomes smaller for higher pitching angle and aspect ratio. The reverse von Kármán wake shows deflected asymmetric vortex pairing in two dimensions, while a bifurcated wake with a swirling ring is the signature in three dimensions, both resulting in nearly the same scaling for the power coefficient. The wake transition in the thrust regime occurs through three spatial regions comprising the reverse von Kármán vortex street, transitional zone, and twin jet region. Near the trailing edge, reverse von Kármán shedding is marked by linear decay of the spanwise wake width and growth of secondary instability. A large volume of fluid resulting from inward horizontal acceleration renders a weak form drag in the subsequent transition zone which is followed by vertical bifurcation into twin jet formation in the far wake. The spanwise pressure gradient is seen to guide the wake compression, with a streamwise adverse pressure gradient aiding it in the near wake.

Emergent bath-mediated attraction and condensation arise when multiple particles are simultaneously driven through an equilibrated bath under geometric constraints. While such scenarios are observed in a variety of nonequilibrium phenomena with an abundance of experimental and numerical evidence, little quantitative understanding of how these interactions arise is currently available. Here we approach the problem by studying the behavior of two driven “tracer” particles, propagating through a bath in a 1D lattice with excluded-volume interactions. We apply the mean-field approximation to analytically explore the mechanism responsible for the tracers' emergent interactions and compute the resulting effective attractive potential. This mechanism is then numerically shown to extend to a realistic model of hard driven Brownian disks confined to a narrow 2D channel.