This study focuses on group intelligence and synchronization phenomena in complex systems by analyzing an enhanced self-directed swarmalator model. In this model, individuals not only move through space and interact with each other but also adjust their phase coupling strength according to their own tendencies, resulting in various self-organizing patterns. Through numerical simulations and theoretical derivations, multiple dynamical states exhibiting radial or layered symmetry have been uncovered, and the system undergoes notable transitions at specific parameter thresholds. During this process, individual diversity, along with “like-attracts-like” or “opposites-attract” strategies, plays a pivotal role in shaping the global spatial configuration and phase evolution, providing potential insights for control strategies and multiscale optimization in novel distributed systems.

The mammalian target of rapamycin (mTOR) signaling pathway, a crucial nutrient sensor in cells, plays pivotal roles in maintaining metabolic homeostasis, cancer development, and aging-related physiological and pathological processes. Despite its significance, the regulatory mechanisms of mTOR signaling, particularly its physical properties, remain poorly understood. Here, we constructed an insulin-induced mTOR signaling model and identified time- and dose-dependent biphasic behaviors. Our findings demonstrate that the indirect negative feedback of mTORC1 on mTORC2 is central to generating these behaviors. By integrating concepts from potential landscape theory, entropy production, and dominant kinetic paths, we quantified the transitions between various cellular states—normal, tumor, prosurvival, and aging—from a physical properties perspective. Potential landscape and entropy analyses suggest that the levels of mTORC1 and mTORC2 regulate cellular fate transitions between multiple attractors, including normal, tumor, prosurvival, and aging. Dominant kinetic path analysis further revealed that the transition from normal state to tumor state requires crossing the aging state barrier, which inhibits tumor formation. The optimal transition paths between different states are irreversible. Despite the minimal action along these paths, the system still drives the transition paths to bypass the saddle points between the lowest states. This phenomenon arises from the driving forces in nonequilibrium systems, which depend not only on gradient forces within potential wells but also on curl forces. Our study provides new insights into the nonequilibrium dynamics of mTOR signaling in cell fate decisions. It enhances our understanding of tumorigenesis and aging from a physical perspective, offers guidance for targeted and personalized treatments, and suggests potential clues to uncover the physiological and pathological significance of mTOR signaling.

A common approach to closing turbulent species flux in multicomponent Reynolds-averaged Navier-Stokes models is to use the standard gradient diffusion approximation. While such an approach has been shown to work well when applied to many canonical turbulent mixing configurations, a gradient diffusion approach is fundamentally limited in its ability to capture complex phenomena such as countergradient transport. For this reason, complicated mixing applications may benefit by treating the turbulent diffusivity with a model transport equation in a manner analogous to second-moment momentum closure in Reynolds-stress transport models. The present work explores the development and application of two different scalar flux transport (SFT) models. Self-similarity constraints are derived for these models, and they are evaluated against gradient-diffusion-based models in several one- and two-dimensional problems of turbulent mixing. It is found that the new SFT models out-perform gradient diffusion models in problems involving rapid acceleration reversal and in problems involving anisotropic transport of materials. In addition, it is found that even a hybrid-SFT approach, in which an SFT equation is utilized along with a gradient diffusion closure, provides some measure of improvement over models that transport the mass flux rather than the scalar flux.

The Lanczos algorithm, introduced by Cornelius Lanczos, has been known for a long time and is widely used in computational physics. While often employed to approximate extreme eigenvalues and eigenvectors of an operator, interest in the sequence of basis vectors produced by the algorithm has been recently increased in the context of Krylov complexity. Although it is generally accepted and partially proven that the procedure is numerically stable for approximating the eigenvalues, there are numerical problems when investigating the Krylov basis constructed via the Lanczos procedure. In this paper, we show that the loss of orthogonality and the attempt of reorthogonalization fall short of understanding and addressing the problem. Instead, the sequence of numerical Lanczos vectors in finite-precision arithmetic escapes the true vector space spanned by the exact Lanczos vectors. This poses a real threat to the interpretation in view of the operator growth hypothesis.

Thermophoresis refers to the translation of particles under a temperature gradient. While the thermophoresis of spherical particles has been well studied, recent advances have shifted focus to anisotropic particles, which exhibit complex phenomena such as thermo-orientation and anomalous rotational diffusion with non-Gaussian angular displacement distributions. However, studies on how fluid rarefaction affects both translational and rotational thermal responses remain limited. In this work, nonequilibrium molecular dynamics simulations were employed to investigate the thermophoresis and thermo-orientation characteristics of mass-asymmetric rods with different surface roughnesses under various fluid rarefaction conditions. We propose that fluid rarefaction, in addition to temperature gradient, is a key parameter regulating thermal responses. Increasing fluid density enhances both thermophoretic force and thermo-orientation. Specifically, rough rods, due to their grooved structure that captures more fluid atoms, exhibit higher thermophoretic torque, stronger thermo-orientation, and lower rotational diffusion, while smooth rods, with a larger fluid–particle contact area, display greater thermophoretic force. By analyzing rotational diffusion dynamics, we reveal a strong link between thermo-orientation and rotational diffusion, offering insight into anisotropic thermophoresis. Our study further reveals that reducing the Knudsen number simultaneously increases both the Soret coefficient and thermo-orientation, a finding contrasting with previous studies based on temperature gradient and mass asymmetry variations.

Many physical systems, including some examples of active matter, granular assemblies, and biological systems, show fluctuation-dominated phase ordering (FDPO), where macroscopic fluctuations coexist with long-range order. Most of these systems are out of equilibrium. By contrast, a recent work has analytically demonstrated that an equilibrium one-dimensional truncated inverse distance square Ising (TIDSI) model shows FDPO. The analytical results rely on a cluster representation of the model that we term TIDSI-CL and are governed by the ratio, $c$, of the long-range interaction strength to the critical temperature. We show that the allowed range of $c$ is very narrow in the original TIDSI model while it is unbounded in TIDSI-CL. We perform Monte Carlo simulations for the TIDSI model and show consistency with the analytical results in the allowed range of $c$. The correlation length grows strongly on approaching the critical point, leading to a broad near-critical region. Within this region, $\alpha$, which is the cusp exponent of the power-law decay of the scaled correlation function at criticality, changes to ${\alpha }^{\text{eff}}$. We also investigate the coarsening dynamics of the model: The correlation function, domain size distribution, and aging behavior are consistent with the equilibrium properties upon replacing the system size, $L$, by the coarsening length, $\mathcal{L}\left(t\right)$. The mean largest cluster size shows logarithmic corrections due to finite $L$ and waiting time, $t_w$. The aging autocorrelation function exhibits two different scaling forms, characterized by exponents $\beta$ and $\gamma$, at short and long times compared to $t_w$, where $\beta =\alpha /2$.

Spatially discordant alternans (SDA) play a crucial role in cardiac arrhythmogenesis by creating steep repolarization gradients facilitating conduction block and reentry. While traditionally studied using electrical indicators, this work provides an alternative perspective by characterizing SDA through their magnetic field signatures. Using a one-dimensional idealized cardiac fiber model, we demonstrate that magnetic-field measurements effectively detect SDA and temperature-dependent changes in cardiac action potentials, offering a noninvasive alternative to conventional electrophysiological metrics. Our results reveal that the spatial organization of SDA is mirrored in the distribution of the magnetic field, with SDA nodes clearly identifiable via spatial mapping. Notably, magnetic restitution curves exhibit a distinct pattern from action potential duration (APD)-based indicators, closely following the dynamics of the action potential upstroke. These findings establish the cardiac magnetic field as a powerful diagnostic tool for detecting SDA, opening alternative avenues for biomagnetic monitoring of arrhythmic risk.

This article is the second of a three-part series that derives a self-consistent theoretical framework of the electromechanics of arbitrarily curved lipid membranes. Existing continuum theories commonly treat lipid membranes as strictly two-dimensional surfaces. While this approach is successful in many purely mechanical applications, strict surface theories fail to capture the electric potential drop across lipid membranes, the effects of surface charges, and electric fields within the membrane. Consequently, they do not accurately resolve Maxwell stresses in the interior of the membrane and its proximity. Furthermore, surface theories are generally unable to capture the effects of distinct velocities and tractions at the interfaces between lipid membranes and their surrounding bulk fluids. To address these shortcomings, we apply a recently proposed dimension reduction method to the three-dimensional, electromechanical balance laws. This approach allows us to derive an effective surface theory without taking the limit of vanishing thickness, thus incorporating effects arising from the finite thickness of lipid membranes. We refer to this effective surface theory as $(2+\delta )$-dimensional, where $\delta$ indicates the thickness. The resulting $(2+\delta )$-dimensional equations of motion satisfy velocity and traction continuity conditions at the membrane-bulk interfaces, capture the effects of Maxwell stresses, and can directly incorporate three-dimensional constitutive models.

This article is the final part of a three-part series that develops a self-consistent theoretical framework describing the electromechanics of arbitrarily curved lipid membranes at the continuum scale. Owing to their small thickness, lipid membranes are commonly modeled as two-dimensional surfaces. However, this approach breaks down when considering their electromechanical behavior as it requires accounting for their finite thickness. To address this, we developed a new dimension reduction procedure in part I [Y. A. D. Omar et al. Phys. Rev. E 109, 054401 (2024)] to derive effective surface theories that explicitly capture the finite thickness of lipid membranes. We applied this method to dimensionally reduce Gauss' law and the electromechanical balance laws and referred to the resulting theory as $(2+\delta )$-dimensional, where $\delta$ indicates the membrane thickness. However, the $(2+\delta )$-dimensional balance laws for thin bodies derived in part II [Y. A. D. Omar et al., Phys. Rev. E 112, 024406 (2025)] are general, and specific constitutive material models must be incorporated to specialize them to lipid membranes. In this work, we devise appropriate three-dimensional constitutive models that capture the material behavior of lipid membranes, which flow along their in-plane directions like viscous fluids but bend out-of-plane like elastic solids. The viscous material behavior is recovered by considering a three-dimensional Newtonian fluid model, leading to the same viscous stresses as strictly two-dimensional models of lipid membranes. The elastic resistance to bending is recovered by imposing a free energy penalty on local volume changes. While this material model does give rise to the characteristic bending resistance of lipid membranes, it differs in its higher-order curvature terms from the two-dimensional Canham-Helfrich-Evans theory. Furthermore, since lipid membranes only exhibit small midsurface stretch, they are often considered midsurface-area incompressible. In this work, this is captured by introducing reactive stresses that give rise to an effective surface tension. Finally, we use the viscous, elastic, and reactive stresses to derive the equations of motion and boundary conditions describing the electromechanics of lipid membranes. We conclude this article by providing the equations of motion and coupling and boundary conditions for a charged lipid membrane embedded in an electrolyte solution.

We investigate the positional behavior of a single bacterium confined within a vesicle by measuring the probability of locating the bacterium at a certain distance from the vesicle boundary. We observe that the distribution is biexponential in nature. Near the boundary, the distribution exhibits rapid exponential decay, transitioning to a slower exponential decay, and eventually becoming uniform further away from the boundary. The length scales associated with the decay are found to depend on the confinement radius. We interpret these observations using molecular simulations and analytical calculations based on the Fokker-Planck equation for an active Brownian particle model. Our findings reveal that the small length scale is strongly influenced by the translational diffusion coefficient, while the larger length scale is governed by rotational diffusivity and self-propulsion. These results are explained in terms of two dimensionless parameters that explicitly include the confinement radius. The scaling behavior predicted analytically for the observed length scales is confirmed through simulations.

We develop a mesoscale computational model to describe the interaction of a droplet with a solid. The model is based on the hybrid combination of the immersed boundary and the lattice Boltzmann computational schemes: the former is used to model the nonideal sharp interface of the droplet coupled with the inner and outer fluids, simulated with the lattice Boltzmann scheme. We further introduce an interaction force to model the wetting interactions of the droplet with the solid at mesoscale: this interaction force is designed with the key computational advantage of providing a regularization of the interface profile close to the contact line, avoiding abrupt curvature changes that could otherwise cause numerical instabilities. The proposed model substantially improves earlier immersed boundary–lattice Boltzmann models for wetting in that it allows a description of an ample variety of wetting interactions, ranging from hydrophobic to hydrophilic cases, without the need for any precalibration study on model parameters to be used. Model validations against analytical results for droplet shape at equilibrium and scaling laws for droplet spreading dynamics are addressed.

The random packing fraction of binary particles in $D$-dimensional Euclidean space ${\mathbb{R}}^D$ is studied using a geometric approach. First, the binary packing fraction of assemblies with small size difference are studied, using a recently developed model that has its foundations in the excluded volume model by Onsager for cylinders and spherocylinders ($D=3$). According to this model the packing increase by bidispersity is proportional to $\left(1-f\right){\left(u^D-1\right)}^2$, with $f$ as monosized packing fraction, $u$ as size ratio and $D$ as space dimension. The model predictions are compared with computational results for disks in two dimensions ($D=2$) and hyperspheres in the large-dimension limit $\left(D\to \infty \right)$, yielding very good agreement. Subsequently, the packing of hyperspheres with large size difference is modeled, employing the classic theory of Furnas. This theory, developed for three dimensions, starts from an infinite size ratio of larger and smaller particles ($u\to \infty$). Here, the pertaining equations are applied to hyperspheres, and successfully compared with computational results for hyperspheres in the large-dimension limit. Furthermore, an asymptotic approximation of the binary packing fraction for large size ratio is derived, which shows that the first order variation of the Furnas packing fraction ($u^{-1}=0$) is proportional to $(2-f)u^{-1}$. Finally, a normalized $D$-dimensional binary packing graph is presented, governing a simplified phase diagram that borders the binary random packing fraction of amorphous assemblies. To summarize, basic space-filling and geometric (“athermal”) theories on “simple” hard spheres appear to be a valuable tool for the study of hyperspheres’ random packing and amorphization.

We numerically investigate the multicritical behavior of the three-dimensional lattice system in which a SU(2) gauge field is coupled to two flavors of scalar fields transforming in the fundamental representation of the gauge group. In this system, a multicritical point is present, where the global symmetry $\mathrm{O}\left(2\right)\oplus \mathrm{O}\left(3\right)$ gets enlarged to O(5). Such a symmetry enlargement is hindered for generic systems by the instability of the O(5) multicritical point, but the SU(2) gauge symmetry prevents the appearance of the term triggering the instability. All the numerical results obtained in this lattice gauge model fully support the expectations coming from the $\mathrm{O}\left(2\right)\oplus \mathrm{O}\left(3\right)$ multicritical Landau-Ginzburg-Wilson ${\varphi }^4$ theory, and we discuss possible implications of these results for some models of deconfined quantum criticality.

Since perturbations are omnipresent in physics, understanding their impact on the dynamics of quantum many-body systems is a vitally important but notoriously difficult question. On the one hand, random-matrix and typicality arguments suggest a rather simple damping in the overwhelming majority of cases, e.g., exponential damping according to Fermi's golden rule. On the other hand, counterexamples are known to exist, and it remains unclear how frequent and under which conditions such counterexamples appear. In our work, we consider the spin-1/2 XXZ chain as a paradigmatic example of a quantum many-body system and study the dynamics of the magnetization current in the easy-axis regime. Using numerical simulations based on dynamical quantum typicality, we show that the standard autocorrelation function is damped in a nontrivial way and only a modified version of this function is damped in a simple manner. Employing projection-operator techniques in addition, we demonstrate that both the nontrivial and simple damping relation can be understood on perturbative grounds. Our results are in agreement with earlier findings for the particle current in the Hubbard chain.

Machine learning (ML) may be oblivious to human bias but it is not immune to its perpetuation. Marginalization and iniquitous group representation are often traceable in the very data used for training and may be reflected or even enhanced by the learning models. In the present work, we aim to clarify the role played by data geometry in the emergence of ML bias. We introduce an exactly solvable high-dimensional model of data imbalance, where parametric control over the many bias-inducing factors allows for an extensive exploration of the bias inheritance mechanism. Through the tools of statistical physics, we analytically characterize the typical properties of learning models trained in this synthetic framework and obtain exact predictions for the observables that are commonly employed for fairness assessment. Simplifying the nature of the problem to its minimal components, we can retrace and unpack typical unfairness behavior observed on real-world datasets. Finally, we focus on the effectiveness of bias mitigation strategies, first by considering a loss-reweighing scheme that allows for an implicit minimization of different unfairness metrics and a quantification of the incompatibilities between existing fairness criteria. Then, we propose a mitigation strategy based on a matched inference setting that entails the introduction of coupled learning models. Our theoretical analysis of this approach shows that the coupled strategy can strike superior fairness-accuracy trade-offs.

Linear absorption of electromagnetic wave injected in a hot plasma is usually associated with non-normal incidence; here, it is shown that absorption can take place at normal incidence as well. By developing a kinetic model based on integral form of dielectric tensor in the presence of static electric field sustaining the density gradient, the mechanism of energy deposition by an injected electromagnetic wave in strongly inhomogeneous plasma is investigated, taking into account the kinetic effects of wave-particle interaction. Two key features of power absorption by plasma particles are explained successfully: (i) For steep-density-gradient plasma, absorption is nonzero and nonresonant in overdense regions for perpendicular as well as oblique injection, thereby heating the plasma due to abrupt change of wave electric field near critical density layer; and (ii) for shallow gradients, resonant absorption takes place at oblique angles due to Landau damping of an electrostatic wave excited near the resonance point. The developed model establishes the conditions for power absorption over a range of density scale lengths with evaluation of self-consistent stochastic heating in a hot plasma.

The accurate characterization of energy exchanges between nanoscale quantum systems and their environments is of paramount importance for quantum technologies, and central to quantum thermodynamics. Here, we show that, in order to accurately approximate steady-state heat currents via perturbative master equations, the coupling-induced reorganization correction to the system's energy must be carefully taken into account. Not doing so may yield sizable errors, especially at low or even moderate temperatures. In particular, we show how a “reorganized master equation” can produce very accurate estimates for the heat currents when the reorganization energy is weak and one works with environments with a broad spectrum. Notably, such master equation outperforms its “nonreorganized” counterpart in the calculation of heat currents, at modeling dynamics, and at correctly capturing equilibration. This is so even if both types of equation are derived to the same order of perturbation theory. Most importantly, working with reorganized master equations does not involve additional complications when compared with alternative approaches. Also, invoking the secular approximation to secure thermodynamic consistency does not compromise their precision.

Collisional Brownian engines have attracted significant attention due to their simplicity, experimental accessibility, and amenability to exact analytical solutions. While previous research has predominantly focused on optimizing mean values of power and efficiency, the joint statistical properties of these performance metrics remain largely unexplored. Using stochastic thermodynamics, we investigate the joint probability distributions of power and efficiency for collisional Brownian engines, revealing how thermodynamic fluctuations influence the probability of observing values exceeding their respective mean maxima. Our conditional probability analysis demonstrates that when power fluctuates above its maximum mean value, the probability of achieving high efficiency increases substantially, suggesting fluctuation regimes where the classical power-efficiency trade-off can be probabilistically overcome. Notably, our framework extends to a broader class of engines, as the essential features of the statistics of the system are fully determined by the Onsager coefficients. Our results contribute to a deeper understanding of the role of fluctuations in Brownian engines, highlighting how stochastic behavior can enable performance beyond traditional thermodynamic bounds.