While it is known that Hamiltonian systems may undergo a phenomenon of condensation akin to Bose-Einstein condensation, not all the manifestations of this phenomenon have been uncovered yet. In this work, we present a novel form of condensation in conservative Hamiltonian systems that stands out due to its evolution through highly coherent states. The result is based on a deterministic approach to obtain exact explicit solutions representing the dynamical formation of condensates in finite time. We reveal a dual-cascade behavior during the process, featuring inverse and direct transfer of conserved quantities across the spectrum. The direct cascade yields the excitation of arbitrarily high modes in finite time, being associated with the formation of a small-scale coherent structure. We provide a fully analytic description of the processes involved.

We study the fluctuations of work caused by applying cyclic perturbations and obtain an exact sum rule satisfied by the moments of work for a broad class of quantum stationary ensembles. In the case of the canonical ensemble, the sum rule reproduces the Jarzynski equality. The sum rule can also be simplified into a linear relationship between the work average and the second moment of work, which we numerically confirm via an exact diagonalization of a spin model system.

We present two realizations of an Otto cycle with a quantum planar rotor as the working medium controlled by means of external fields. By comparing the quantum and the classical description of the working medium, we single out genuine quantum effects with regard to the performance and the engine and refrigerator modes of the Otto cycle. The first example is a rotating electric dipole subjected to a controlled electric field, equivalent to a quantum pendulum. Here we find a systematic disadvantage of the quantum rotor compared to its classical counterpart. In contrast, a genuine quantum advantage can be observed with a charged rotor generating a magnetic moment that is subjected to a controlled magnetic field. We prove that the classical rotor is inoperable as a working medium for any choice of parameters, whereas the quantum rotor supports an engine and a refrigerator mode, exploiting the quantum statistics during the cold strokes of the cycle.

The complexity of quantum states under dynamical evolution can be investigated by studying the spread with time of the state over a predefined basis. It is known that this complexity is minimized by choosing the Krylov basis, thus defining the spread complexity. We study the dynamics of spread complexity for quantum maps using the Arnoldi iterative procedure. The main illustrative quantum many-body model we use is the periodically kicked Ising spinchain with nonintegrable deformations, a chaotic system where we look at both local and nonlocal interactions. In the various cases, we find distinctive behavior of the Arnoldi coefficients and spread complexity for regular versus chaotic dynamics: suppressed fluctuations in the Arnoldi coefficients as well as larger saturation value in spread complexity in the chaotic case. We compare the behavior of the Krylov measures with that of standard spectral diagnostics of chaos. We also study the effect of changing the driving frequency on the complexity saturation.

How to maintain the sustainability of common resources is a persistent challenge, as overexploiters often undermine collective efforts by prioritizing personal gain. To mitigate the overexploitation of resources by violators, previous theoretical studies have revealed that the introduction of additional incentives, whether to reward rule-abiding cooperators or to punish those who overexploit, can be beneficial for the sustainability of common resources when the resource growth rate is not particularly low. However, these studies have typically considered rewarding and punishing in isolation, thus overlooking the role of their combination in common resource governance. Here, we introduce a hybrid incentive strategy based on reward and punishment within a feedback-evolving game, in which there is a complex interaction between human decision making and resource quantity. Our coevolutionary dynamics reveal that resources will be depleted entirely, even with cooperative strategies for prudent exploitation, when resource growth is slow. When the rate of resource growth is not particularly low, we find that the coupled system can generate a state where resource sustainability and cooperation can be maintained. Furthermore, when the rate of resource growth is moderate, we find that achieving this state cannot simply allocate all incentive budgets to reward. In addition, the increase in per capita incentives significantly promotes the stability of this state.

Extended-range percolation is a robust percolation process that has relevance for quantum communication problems. In extended-range percolation nodes can be trusted or untrusted. Untrusted facilitator nodes are untrusted nodes that can still allow communication between trusted nodes if they lie on a path of distance at most $R$ between two trusted nodes. In extended-range percolation the extended-range giant component (ERGC) includes trusted nodes connected by paths of trusted and untrusted facilitator nodes. Here, based on a message-passing algorithm, we develop a general theory of extended-range percolation, valid for arbitrary values of $R$ as long as the networks are locally treelike. This general framework allows us to investigate the properties of extended-range percolation on interdependent multiplex networks. While the extended-range nature makes multiplex networks more robust, interdependency makes them more fragile. From the interplay between these two effects a rich phase diagram emerges including discontinuous phase transitions and reentrant phases. The theoretical predictions are in excellent agreement with extensive Monte Carlo simulations. The proposed exactly solvable model constitutes a fundamental reference for the study of models defined through properties of extended-range paths.

Over the past few decades, research has indicated that the buildup of waste proteins, like amyloid-$\beta$ ($\mathrm{A}\beta$), in the brain's interstitial spaces is linked to neurodegenerative diseases like Alzheimer's, but the details of how such proteins are removed from the brain are not well understood. We have developed a numerical model to investigate the aggregation and clearance mechanisms of $\mathrm{A}\beta$ in the interstitial spaces of the brain. The model describes the volume-averaged transport of $\mathrm{A}\beta$ in a segment of the brain interstitium modeled as a porous medium, oriented between the perivascular space (fluid-filled channel surrounding a blood vessel) of a penetrating arteriole and that of a venule. Our numerical approach solves $N$ coupled advection-diffusion-aggregation equations that model the production, aggregation, fragmentation, and clearance of $N$ species of $\mathrm{A}\beta$. We simulate $N=50$ species to investigate the oligomer-size dependence of clearance and aggregation. We introduce a timescale plot that helps predict $\mathrm{A}\beta$ buildup for different neurological conditions. We show that a sudden increase in monomer concentration, as occurs in conditions like traumatic brain injury, leads to significant plaque formation, which can qualitatively be predicted using the timescale plot. Our results also indicate that impaired protein clearance (as occurs with aging) and fragmentation are both mechanisms that sustain large intermediate oligomer concentrations. Our results provide novel insight into several known risk factors for Alzheimer's disease and cognitive decline, and we introduce a unique framing of $\mathrm{A}\beta$ dynamics as a competition between different timescales associated with production rates, aggregation rates, and clearance conditions.

Nanopores in solid-state membranes have been used to detect, identify, filter, and characterize nanoparticles and biological molecules. In this work, we simulate an ionic flow through a nanopore while an ellipsoidal nanoparticle translocates through a pore. We numerically solve the Poisson-Nernst-Planck equations to obtain the ionic current values for different aspect ratios, sizes, and orientations of a translocating particle. By extending the existing theoretical model for the ionic current in the nanopore to the particles of ellipsoidal shape, we propose semiempirical fitting formulas which describe our computed data within 5% accuracy. We also demonstrate how the derived formulas can be used to identify the dimensions of nanoparticles from the available experimental data which may have useful applications in bionanotechnology.

Estimating parameters from data is a fundamental problem in physics, customarily done by minimizing a loss function between a model and observed statistics. In scattering-based analysis, it is common to work in the reciprocal space. Researchers often employ their domain expertise to select a specific range of wave vectors for analysis, a choice that can vary depending on the specific case. We introduce another paradigm that defines a probabilistic generative model from the beginning of data processing and propagates the uncertainty for parameter estimation, termed the ab initio uncertainty quantification (AIUQ). As an illustrative example, we demonstrate this approach with differential dynamic microscopy (DDM) that extracts dynamical information through minimizing a loss function for the squared differences of the Fourier-transformed intensities, at a selected range of wave vectors. We first show that the conventional way of estimation in DDM is equivalent to fitting a temporal variogram in the reciprocal space using a latent factor model as the generative model. Then we derive the maximum marginal likelihood estimator, which optimally weighs the information at all wave vectors, therefore eliminating the need to select the range of wave vectors. Furthermore, we substantially reduce the computational cost of computing the likelihood function without approximation, by utilizing the generalized Schur algorithm for Toeplitz covariances. Simulated studies of a wide range of dynamical systems validate that the AIUQ method improves estimation accuracy and enables model selection with automated analysis. The utility of AIUQ is also demonstrated by three distinct sets of experiments: first in an isotropic Newtonian fluid, pushing limits of optically dense systems compared to multiple particle tracking; next in a system undergoing a sol-gel transition, automating the determination of gelling points and critical exponent; and lastly, in discerning anisotropic diffusive behavior of colloids in a liquid crystal. These studies demonstrate that the new approach does not require manually selecting the wave vector range and enables automated analysis.

The entropy of strongly coupled Yukawa fluids is discussed from several perspectives. First, it is demonstrated that a vibrational paradigm of atomic dynamics in dense fluids can be used to obtain a simple and accurate estimate of the entropy without any adjustable parameters. Second, it is explained why a quasiuniversal value of the excess entropy of simple fluids at the freezing point should be expected, and it is demonstrated that a remaining very weak dependence of the freezing point entropy on the screening parameter in the Yukawa fluid can be described by a simple linear function. Third, a scaling of the excess entropy with the freezing temperature is examined, a modified form of the Rosenfeld-Tarazona scaling is put forward, and some consequences are briefly discussed. Fourth, the location of the Frenkel line on the phase diagram of Yukawa systems is discussed in terms of the excess entropy and compared with some predictions made in the literature. Fifth, the excess entropy scaling of the transport coefficients (self-diffusion, viscosity, and thermal conductivity) is reexamined using the contemporary datasets for the transport properties of Yukawa fluids. The results could be of particular interest in the context of complex (dusty) plasmas, colloidal suspensions, electrolytes, and other related systems with soft pairwise interactions.

We study living liquid crystals (LLCs), which are an amalgam of nematic liquid crystals (LCs) and active matter (AM). These LLCs are placed in contact with surfaces which impose planar/homeotropic boundary conditions on the director field of the LC and the polarization field of the AM. The interplay of LC-AM interactions and the surface-directed conditions yield controlled pattern dynamics in the LLC, which has important technological implications. We discuss two representative examples of this pattern dynamics.

A continuum mixture theory is formulated for large deformations, thermal effects, phase interactions, and degradation of soft biologic tissues suitable at high pressures and low to very high strain rates. Tissues consist of one or more solid and fluid phases and can demonstrate nonlinear anisotropic elastic, viscoelastic, thermoelastic, and poroelastic physics. Under extreme deformations or shock loading, tissues may fracture, tear, or rupture. Existing models do not account for all physics simultaneously, and most poromechanics and soft-tissue models assume incompressibility of some or all constituents, generally inappropriate for modeling shock waves or extreme compressions. Motivated by these prior limitations, a thermodynamically consistent formulation that combines a continuum theory of mixtures, compressible nonlinear anisotropic thermoelasticity, viscoelasticity, and phase-field mechanics of fracture is constructed to resolve the pertinent physics. A metric tensor of generalized Finsler space supplies geometric insight on effects of rearrangements of microstructure, for example degradation, growth, and remodeling. Shocks are modeled as singular surfaces. Hugoniot states and shock decay are analyzed: Solutions account for concurrent viscoelasticity, fracture, and interphase momentum and energy exchange not all contained in previous analyses. Suitability of the framework for representing blood, skeletal muscle, and liver is demonstrated by agreement with experimental data and observations across a range of loading rates and pressures. Insight into previously unresolved physics is obtained, for example importance of rate sensitivity of damage and quantification of effects of dissipation from viscoelasticity and phase interactions on shock decay.

Electroconvection, occurring near electrochemical interfaces, propels the movement of ions and water, leading to intricate phenomena rooted in the fine interplay between fluid, voltage, and ion. Here, neglecting ionic interactions, by incorporating the steric term into the Poisson-Nernst-Planck-Stokes coupling equation, direct numerical simulations of electroconvective vortex near nanoslot-bulk interfaces are conducted. For the steric effect, the steric number is introduced to discuss the factors and laws affecting the vortex. We illustrate the substantial enhancement of electroconvective vortex due to the steric effect of ions within the nanoslot. Upon increasing the steric number, the cation concentration in the nanoslot is enhanced, resulting in the expansion of the electric double layer (EDL). The EDLs on the walls inside the nanoslot come into contact with each other, causing the EDLs to overlap, consequently increasing the total charge within the EDLs inside the nanoslot. This EDL overlap enhances the charge density of the extended space charge layer, leading to the enhancement of the electroconvective vortex. Further, our scaling analysis, corroborated by direct numerical simulation and existing data, establishes the scaling of slip velocity, jointly regulated by the steric number and voltage difference. By modulating the membrane transport characteristics, the steric effect reduces flow structure size and flux fluctuations, which offers new perspectives for manipulating ion transport and flow instability.

Hydrodynamic turbulence exhibits nonequilibrium behavior with $k^{-5/3}$ energy spectrum, and equilibrium behavior with $k^{d-1}$ energy spectrum and zero viscosity, where $d$ is the space dimension. Using recursive renormalization group in Craya-Herring basis, we show that the nonequilibrium solution is valid only for $d<6$, whereas equilibrium solution with zero viscosity is the only solution for $d>6$. Thus, $d=6$ is the critical dimension for hydrodynamic turbulence. In addition, we show that the energy flux changes sign from positive to negative near $d=2.15$. We also compute the energy flux and Kolmogorov's constants for various $d$'s, and observe that our results are in good agreement with past numerical results.

The self-organization of clusters of particles is a fundamental phenomenon across various physical systems, including hydrodynamic and colloidal systems. One example is that of dense spherical particles submerged in a viscous fluid and subjected to horizontal oscillations. The interaction of the particles with the oscillating flow leads to the formation of one-particle-thick chains or multiple-particle-wide bands, both oriented perpendicular to the oscillation direction. In this study, we model the hydrodynamic interactions between such particles and parallel chains using simplified potentials. We first focus on the hydrodynamic interactions between chains, which we characterize using data from fully resolved numerical simulations. Based on these interactions, we propose a simplified model potential, called the Siren potential, which combines the representative hydrodynamic interactions: short-range attraction, mid-range repulsion, and long-range attraction. Through one-dimensional Monte Carlo simulations, we successfully replicate the characteristic patterns observed in hydrodynamic experiments and draw the phase diagram for the model potential. We further extend our analysis to two-dimensional systems, introducing a dipole-capillary model potential that accounts for both chain formation and Siren-like chain interactions. This potential is based on a system with colloidal particles at an interface, where chain formation is driven by an external electric field that induces a dipole moment parallel to the interface in each particle. The capillary force contributes the long-range attraction. Starting with parallel chains, the patterns in the two-dimensional Monte Carlo simulations of this colloidal system are similar to those observed in the hydrodynamic experiments. However, we identify that nonlinear interactions are important for some distinct steps in the chain formation. Still, the model potentials help clarify the dynamic behavior of the particles and chains due to the complex interactions encountered in both hydrodynamic and colloidal systems, drawing parallels between them.

Turbulent transport is regarded as one of the key issues in magnetic confinement nuclear fusion, both for tokamaks and stellarators. In this work, we show that a significant decrease in a microstability-based proxy, as opposed to a geometric one, for the turbulent heat flux, namely the quasilinear heat flux, can be obtained in an efficient manner by coupling stellarator optimization with linear gyrokinetic simulations. This is accomplished by computing the quasilinear heat flux at each step of the optimization process, as well as the deviation from quasisymmetry, and minimizing their sum, leading to a balance between neoclassical and the turbulent transport proxy.

We investigate a $2d$-conservative lattice gas exhibiting a dynamical active-absorbing phase transition with critical density ${\rho }_c$. We derive the hydrodynamic equation for this model, showing that all critical exponents governing the large scale behavior near criticality can be obtained from two independent ones. We show that as the supercritical density approaches criticality, distinct length scales naturally appear. Remarkably, this behavior is different from the subcritical one. Numerical simulations support the critical relations and the scale separation.

We provide an explicit solution of the problem of level-set percolation for multivariate Gaussians defined in terms of weighted graph Laplacians on complex networks. The solution requires an analysis of the heterogeneous microstructure of the percolation problem, i.e., a self-consistent determination of locally varying percolation probabilities. This is achieved using a cavity or message passing approach. It can be evaluated, both for single large instances of locally treelike graphs, and in the thermodynamic limit of random graphs of finite mean degree in the configuration model class.

The Eshelby problem refers to the response of a two-dimensional elastic sheet to cutting away a circle, deforming it into an ellipse, and pushing it back. The resulting response is dominated by the so-called Eshelby kernel, which was derived for purely elastic (infinite) material, but has been employed extensively to model the redistribution of stress after plastic events in amorphous solids with finite boundaries. Here, we discuss and solve the Eshelby problem directly for amorphous solids, taking into account possible screening effects and realistic boundary conditions. We find major modifications compared to the classical Eshelby solution. These modifications are needed for modeling correctly the spatial responses to plastic events in amorphous solids.