We experimentally clarify the interaction of acoustic pressure and heat release rate fluctuations during a transition to high-frequency combustion instability in a model rocket engine combustor. The dynamical state of acoustic pressure fluctuations undergoes a transition from high-dimensional chaotic oscillations to strongly correlated limit cycle oscillations. The coherent structure in the heat release rate field emerges with the initiation of weakly correlated limit cycle oscillations. The effect of the heat release rate on acoustic pressure fluctuations predominates during high-dimensional chaotic oscillations. In contrast, the effect of acoustic pressure on the heat release rate fluctuations markedly increases during the correlated limit cycle oscillations. These are reasonably shown by an ordinal pattern-based analysis involving the concepts of information theory, synchronization, and complex networks.

Landau free energy determines the landscape of order parameter fluctuations that occur in a physical system at thermal equilibrium and, in particular, characterizes the critical phenomena. We propose a semianalytical approach based on the fluctuating local field method, which allows us to estimate Landau free energy for small clusters with discrete (Ising model) and continuous (Heisenberg model) order parameter.

We study the counting of level crossings for inertial random processes exposed to stochastic resetting events. We develop the general approach of stochastic resetting for inertial processes with sudden changes in the state characterized by position and velocity. We obtain the level-crossing intensity in terms of that of underlying reset-free process for resetting events with Poissonian statistics. We apply this result to the random acceleration process and the inertial Brownian motion. In both cases, we show that there is an optimal resetting rate that maximizes the crossing intensity, and we obtain the asymptotic behavior of the crossing intensity for large and small resetting rates. Finally, we discuss the stationary distribution and the mean first-arrival time in the presence of resettings.

In-line holographic video microscopy records a wealth of information about the microscopic structure and dynamics of colloidal materials. Powerful analytical techniques are available to retrieve that information when the colloidal particles are well separated. Large assemblies of close-packed particles create holograms that are substantially more challenging to interpret. We demonstrate that Rayleigh-Sommerfeld back propagation is useful for analyzing holograms of colloidomer chains, close-packed linear assemblies of micrometer-scale emulsion droplets. Colloidomers are fully flexible chains and undergo three-dimensional configurational changes under the combined influence of random thermal forces and hydrodynamic forces. We demonstrate the ability of holographic reconstruction to track these changes as colloidomers sediment through water in a horizontal slit pore. Comparing holographically measured configurational trajectories with predictions of hydrodynamic models both validates the analytical technique for this valuable class of self-organizing materials and also provides insights into the influence of geometric confinement on colloidomer hydrodynamics.

One-dimensional systems, such as nanowires or electrons moving along strong magnetic field lines, have peculiar thermalization physics. The binary collision of pointlike particles, typically the dominant process for reaching thermal equilibrium in higher-dimensional systems, cannot thermalize a 1D system. We study how dilute classical 1D gases thermalize through three-body collisions. We consider a system of identical classical point particles with pairwise repulsive inverse power-law potential $V_{ij}\propto 1/{|x_i-x_j|}^n$ or the pairwise Lennard-Jones potential. Using Monte Carlo methods, we compute a collision kernel and use it in the Boltzmann equation to evolve a perturbed thermal state with temperature $T$ toward equilibrium. We explain the shape of the kernel and its dependence on the system parameters. Additionally, we implement molecular dynamics simulations of a many-body gas and show agreement with the Boltzmann evolution in the low-density limit. For the inverse power-law potential, the rate of thermalization is proportional to ${\rho }^2{T}^{\frac{1}{2}-\frac{1}{n}}$, where $\rho$ is the number density. The corresponding proportionality constant decreases with increasing $n$.

Describing statistical dependencies is foundational to empirical scientific research. For uncovering intricate and possibly nonlinear dependencies between a single target variable and several source variables within a system, a principled and versatile framework can be found in the theory of partial information decomposition (PID). Nevertheless, the majority of existing PID measures are restricted to categorical variables, while many systems of interest in science are continuous. In this paper, we present a novel analytic formulation for continuous redundancy—a generalization of mutual information—drawing inspiration from the concept of shared exclusions in probability space as in the discrete PID definition of $I_{\cap }^{\mathrm{sx}}$. Furthermore, we introduce a nearest-neighbor-based estimator for continuous PID and showcase its effectiveness by applying it to a simulated energy management system provided by the Honda Research Institute Europe GmbH. This work bridges the gap between the measure-theoretically postulated existence proofs for a continuous $I_{\cap }^{\mathrm{sx}}$ and its practical application to real-world scientific problems.

This study investigates the role of spatial segregation, prompted by competition avoidance, as a key mechanism for emergent coexistence within microbial communities. Recognizing these communities as complex adaptive systems, we challenge the sufficiency of mean-field pairwise interaction models, and we consider the impact of spatial dynamics. We developed an individual-based spatial simulation depicting bacterial movement through a pattern of random walks influenced by competition avoidance, leading to the formation of spatially segregated clusters. This model was integrated with a Lotka-Volterra metapopulation framework focused on competitive interactions. Our findings reveal that spatial segregation combined with low diffusion rates and high compositional heterogeneity among patches can lead to emergent coexistence in microbial communities. This reveals a novel mechanism underpinning the formation of stable, coexisting microbe clusters, which is nonetheless incapable of promoting coexistence in the case of isolated pairs of species. This study underscores the importance of considering spatial factors in understanding the dynamics of microbial ecosystems.

Blue phases (BPs) consist of three-dimensional self-assembled structures formed by a double-twisted columnar arrangement of liquid crystal molecules. Although their unique optical and structural properties render BPs particularly useful for applications such as liquid crystal displays, BPs typically appear in a narrow temperature range between the isotropic and nematic phases. This thermodynamic instability impedes their practical applicability. However, the simulations we present here showed that, in a quasi-one-dimensional system confined to nanospace, a phase equivalent to the BP appears and persists between the nematic and smectic phases. Confinement to a nanotube (NT) with a relatively small radius enables the BP to be maintained over a wide temperature range, whereas for an NT with a relatively larger radius, the BP appears only in a very narrow temperature range between the aforementioned phases. We additionally showed that the pitch of the BP is dependent on and can be controlled by adjusting the radius of the NTs. This finding has significant implications for the potential application of these materials in fields such as photonics and chiral separation technologies.

We experimentally verify the “phase locking model,” which describes the formation of one-dimensional coherent structures by low-Stokes-number particles as proposed by Pushkin et al. [Phys. Rev. Lett. 106, 234501 (2011)] in thermocapillary liquid bridges: When the particles form the coherent structures in time-periodic flows, the synchronous coupling of the toroidal vortex and the azimuthally traveling wave is achieved for a range of azimuthal wave number $m$. We further propose coherent structures of rational wave numbers in the azimuthal direction and unveil those experimentally.

We propose alternative discretization schemes for improving the lattice Boltzmann pseudopotential model for incompressible multicomponent systems, with the purpose of modeling the flow of immiscible fluids with a large viscosity ratio. Compared to the original model of Shan-Chen [Phys. Rev. E 47, 1815 (1993)], the present discretization schemes consider: (i) an explicit force term, (ii) a second-order discretization of the stream term, (iii) a moments-based model for the kinetic nonequilibrium distributions, and (iv) a high-order discretization of the spatial derivative terms. To verify the accuracy of the proposed model, the effects of varying the viscosity ratio as well as both fluid's viscosities on spurious currents and capillary number are investigated for the problems dealing with a static bubble, two-component Poiseuille flow, and immiscible fluid-fluid displacement. The resulting algorithm maintains the simplicity of the pseudopotential model while allowing an easy implementation for multicomponent systems. The results of the model herein proposed show improved control of the interface region and interfacial tension, relatively smaller magnitudes of spurious current values with increasing viscosity ratio, and also a significantly wider stability range with respect to the previously best results in the literature.

The Hamiltonian of mean force is an effective Hamiltonian that allows a quantum system, nonweakly coupled to an environment, to be written in an effective Gibbs state. We present results on the structure of the Hamiltonian of mean force in extended quantum systems with local interactions. We show that its spatial structure exhibits a “skin effect”—its difference from the system Hamiltonian dies off exponentially with distance from the system-environment boundary. For spin systems, we identify the terms that can appear in the Hamiltonian of mean force at different orders in the inverse temperature.

Phase transition usually consumes or releases energy to produce cooling or heating within different materials, providing a generalized framework for temperature regulation in practical applications. Because of the strong coupling between the enthalpy change in thermodynamics and heat-mass transfer kinetics, unveiling the mechanism of temperature regulation via the phase transition remains a great challenge. Here, we develop a new theoretical method by establishing a connection of enthalpy change from thermodynamics to phase transition dynamics to study evaporation-induced cooling as an example. Our new approach can spontaneously generate evaporative cooling at interfaces, and the predicted results are consistent with recent experiments. The evaporation-induced steady vapor is dictated by an anomalous cold-to-hot mass transfer through temperature-dependent chemical potentials, which enables temperature regulation inside liquids via a thermodynamic-kinetic interplay. Moreover, we show that a simple prohibition of heat exchange between liquids and reservoir can greatly enhance the cooling magnitude by a factor of $2\sim 4$, which is highly dependent on the thermodynamics and kinetic coefficients of liquids. Our new method paves the way for exploration of cooling or heating induced by different phase transitions, such as evaporation, sublimation, or condensation, in a unified framework, which can significantly promote the development of temperature regulation by phase transitions.

A model for anomalous transport of tracer particles diffusing in complex media in two dimensions is proposed. The model takes into account the characteristics of persistent motion that an active bath transfers to the tracer; thus, the model proposed here extends active Brownian motion, for which the stochastic dynamics of the orientation of the propelling force is described by scaled Brownian motion (sBm), identified by time-dependent diffusivity of the form $D_{\beta }\propto t^{\beta -1}, \beta >0$. If $\beta \ne 1$, sBm is highly nonstationary and suitable to describe such nonequilibrium dynamics induced by complex media. In this paper, we provide analytical calculations and computer simulations to show that genuine anomalous diffusion emerges in the long-time regime, with a time scaling of the mean-squared displacement $t^{2-\beta }$, while ballistic transport $t^2$, characteristic of persistent motion, is found in the short-time regime. We also analyze the time dependence of the kurtosis, and the intermediate scattering function of the position distribution, as well as the propulsion autocorrelation function, which defines the effective persistence time.

The highly and slightly condensed forms of chromatin, heterochromatin and euchromatin, respectively, segregate in the cell nucleus. Heterochromatin is more abundant in the nucleus periphery. Here we study the mechanism of heterochromatin segregation by modeling interphase chromosomes as diblock ring copolymers confined in a rigid spherical shell using molecular dynamics simulations. In our model, heterochromatin and euchromatin are distinguished by their bending stiffnesses only, while an interaction potential between the spherical shell and chromatin is used to model lamin-associated proteins. Our simulations indicate that in the absence of attractive interactions between the nuclear shell and the chromatin, most heterochromatin segregates towards the nuclear interior due to the depletion of less flexible heterochromatin segments from the nuclear periphery. This inverted chromatin distribution,which is opposite to the conventional case with heterochromatin dominating at the periphery, is in accord with experimental observations in rod cells. This “inversion” is also found to be independent of the heterochromatin concentration and chromosome number. The chromatin distribution at the periphery found in vivo can be recovered by further increasing the bending stiffness of heterochromatin segments or by turning on attractive interactions between the nuclear shell and heterochromatin. Our results indicate that the bending stiffness of chromatin could be a contributor to chromosome organization along with differential effects of $\mathrm{HP}1\alpha$-driven phase segregation and of loop extruders and interactions with the nuclear envelope and topological constraints.

The standard way to evaluate the solid surface energy using probe liquids relies on contact angle measurements. The measured contact angles rely on visible means and are different from their nanoscopic thermodynamic values. This compromises the surface-energy predictions so much that the surface energy-values can be hundreds of percentages higher than expected based on comparisons with different methods as reported in several studies. We consider the Owen-Wendt approach, which breaks the surface energy to polar and dispersive components, and present a technique for measuring surface energy of solids using probe liquids. Our method avoids the need to measure contact angles; instead, it uses solid-liquid work of adhesion measurements which are performed using a centrifugal adhesion balance. In agreement with the studies mentioned above, we found that indeed, the surface energies of the measured solids are significantly lower than those based on contact angle measurements. More importantly we found that our method results in a reasonable breakdown of the surface energy to polar and dispersive components with a higher polar component for more polar solids. This is in contrast with the surface energy based on contact angle measurements for which the breakdown did not make sense, i.e., the measurements reflected higher polar components of the surface energy for less polar solids.

We introduce a multifractal optimal detrended fluctuation analysis to study the scaling properties of the one-dimensional Wolf-Villain (WV) model for surface growth. This model produces coarsened surface morphologies for long timescales (up to ${10}^9$ monolayers) and its universality class remains an open problem. Our results for the multifractal exponent $\tau \left(q\right)$ reveal an effective local roughness exponent consistent with a transient given by the molecular beam epitaxy (MBE) growth regime and Edwards-Wilkinson (EW) universality class for negative and positive $q$ values, respectively. Therefore, although the results corroborate that long-wavelength fluctuations belong to the EW class in the hydrodynamic limit, as conjectured in the recent literature, a bifractal signature of the WV model with an MBE regime at short wavelengths was observed.

The $k$-cardinality unbalanced assignment problem asks for assigning $k$ “agents” to $k$ “tasks” on a one-to-one basis, while minimizing the total cost associated with the assignment, with the total number of agents $N$ and the total number of tasks $M$ possibly different and larger than $k$. While many exact algorithms have been proposed to find such an optimal assignment, these methods are computationally prohibitive when the problem is large. We propose an approach to solving the $k$-cardinality assignment problem using techniques adapted from statistical physics. This paper provides a full description of this formalism, including all the proofs of its main claims. We derive a strongly concave free-energy function that captures the constraints of the $k$-assignment problem at a finite temperature. We prove that this free energy decreases monotonically as a function of $\beta$, the inverse of temperature, to the optimal assignment cost, providing a robust framework for temperature annealing. We also prove that for large enough $\beta$ values the exact solution to the $k$-assignment problem can be derived using simple round-off to the nearest integer of the elements of the computed assignment matrix. We show that this framework can be adapted to handle degenerate $k$-assignment problems. We describe a computer implementation of our framework that is optimized for the GPU parallel architecture, using the library CUDA. This implementation is found to be as efficient as state-of-the-art implementations of parallel Hungarian algorithms on generic assignment problems, and orders of magnitude faster than those algorithms for pathological assignment cases.

We study a discrete-space model of active matter with excluded volume. Particles are restricted to the sites of a triangular lattice and can assume one of three orientations. Varying the density and noise intensity, Monte Carlo simulations reveal a variety of spatial patterns. Ordered states occur in the form of condensed structures, which (away from the full occupancy limit) coexist with a low-density vapor. The condensed structures feature low particle mobility, particularly those that wrap the system via the periodic boundaries. As the noise intensity is increased, dense structures give way to a disordered phase. We characterize the parameter values associated with the condensed phases and perform a detailed study of the order-disorder transition at (i) full occupation and (ii) a density of 0.1. In the former case, the model possesses the same symmetry as the three-state Potts model and exhibits a continuous phase transition, as expected, with critical exponents consistent with those of the associated Potts model. In the low-density case, the transition is clearly discontinuous, with a strong dependence of the final state upon the initial configuration, hysteresis, and nonmonotonic dependence of the Binder cumulant upon noise intensity.

In nonequilibrium statistical mechanics, the asymmetric simple exclusion process (ASEP) serves as a paradigmatic example. We investigate the spectral characteristics of the ASEP, focusing on the spectral boundary of its generator matrix. We examine finite ASEP chains of length $L$, under periodic boundary conditions (PBCs) and open boundary conditions (OBCs). Notably, the spectral boundary exhibits $L$ spikes for PBCs and $L+1$ spikes for OBCs. Treating the ASEP generator as an interacting non-Hermitian fermionic model, we extend the model to have tunable interaction. In the noninteracting case, the analytically computed many-body spectrum shows a spectral boundary with prominent spikes. For PBCs, we use the coordinate Bethe ansatz to interpolate between the noninteracting case to the ASEP limit and show that these spikes stem from clustering of Bethe roots. The robustness of the spikes in the spectral boundary is demonstrated by linking the ASEP generator to random matrices with trace correlations or, equivalently, random graphs with distinct cycle structures, both displaying similar spiked spectral boundaries.