We propose and analyze an active hydrodynamic theory that characterizes the effects of the scaffold protein anillin. Anillin is found at major sites of cortical activity, such as adherens junctions and the cytokinetic furrow, where the canonical regulator of actomyosin remodeling is the small GTPase, RhoA. RhoA acts via intermediary “effectors” to increase both the rates of activation of myosin motors and the polymerization of actin filaments. Anillin has been shown to scaffold this action of RhoA—improving critical rates in the signaling pathway without altering the essential biochemistry—but its contribution to the wider spatiotemporal organization of the cortical cytoskeleton remains poorly understood. Here we combine analytics and numerics to show how anillin can nontrivially regulate the cytoskeleton at hydrodynamic scales. At short times, anillin can amplify or dampen existing contractile instabilities, as well as alter the parameter ranges over which they occur. At long times, it can change both the size and speed of steady-state traveling pulses. The primary mechanism that underpins these behaviors is established to be the advection of anillin by myosin II motors, with the specifics relying on the values of two coupling parameters. These codify anillin's effect on local signaling kinetics and can be traced back to its interaction with the acidic phospholipid phosphatidylinositol 4,5-bisphosphate (${\mathrm{PIP}}_2$), thereby establishing a putative connection between actomyosin remodeling and membrane composition.

Thin films or sheets subjected to external forces often undergo mechanical instability, leading to regular patterns of wrinkles, folds, and creases. As can be anticipated from the difficulty of flattening a curved globe, any natural curvature of the sheet will have a strong influence on these instabilities. Here, we develop a noninvasive synthetic schlieren imaging technique to image and reconstruct the surface of wrinkling curved sheets, confined to float on water. Our method circumvents the small-amplitude limit of related imaging techniques, and we demonstrate robust means to estimate the reconstruction accuracy. We then evaluate how the sign and magnitude of Gaussian curvature affect the wrinkling of thin curved sheets, and compare observations of the wrinkle wavelength, amplitude, and domain structure with recent theoretical predictions. While generally validating model predictions, we find that the assumption of a conserved surface area during wrinkling should be treated with some care. The control of wrinkling behavior demonstrated here can have applications in the design of liquid lenses, microfluidics, active textured surfaces, and flexible electronic components.

We propose a vertex representation of the tensor network (TN) for classical spin systems on hyperbolic lattices. The tensors form a network of regular $p$-sided polygons ($p>4$) with the coordination number 4. The response to multistate spin systems on the hyperbolic TN is analyzed for their entire parameter space. We show that entanglement entropy is sensitive to distinguish various hyperbolic geometries, whereas other thermodynamic quantities are not. We test the numerical accuracy of vertex TNs in the phase transitions of the first, second, and infinite order at the point of maximal entanglement entropy. The hyperbolic structure of TNs induces noncritical properties in the bulk, although boundary conditions significantly affect the total free energy in the thermodynamic limit. Thus a developed vertex-type TN can be used for the lowest-energy quantum states on the hyperbolic lattices.

For overdamped Langevin systems subjected to weak thermal noise and nonconservative forces, we establish a connection between Freidlin-Wentzell large deviations theory and stochastic thermodynamics. First, we derive a series expansion of the quasipotential around the detailed-balance solution, that is, the system's free energy, and identify the conditions for the linear response regime to hold, even far from equilibrium. Second, we prove that the escape rate from dissipative fixed points of the macroscopic dynamics is bounded by the entropy production of trajectories that relax into and escape from the attractors. These results provide the foundation to study the nonequilibrium thermodynamics of dissipative metastable states.

Predator-prey interactions are fundamental components of ecological systems, and spatial heterogeneity in the environment significantly influences their dynamics. This study investigates such types of spatially heterogeneous environments using local and nonlocal models. Initially, we scrutinize a local model incorporating the Allee effect and hunting cooperation among predators, laying the groundwork for understanding system dynamics. Subsequently, the nonlocal interaction captures spatial heterogeneity effects, enriching our comprehension of ecosystem dynamics. Significant ecological phenomena, such as the emergence of traveling waves, highlight the complex interactions between predator and prey populations. Extensive numerical simulations explore a range of solution categories including spatiotemporal chaos at low prey diffusion rate, shedding light on the spatial interaction of the prey-predator populations. We have discussed the patterns behind the traveling wave solutions for different parametric combinations and how Turing instability identifies such patterns. Nevertheless, we identify the traveling waves connecting two equilibrium points directly or indirectly through a stable limit cycle or saddle points.

The effectiveness of physics-informed neural networks (PINNs) for learning the dynamics of constrained Hamiltonian systems is demonstrated using the Dirac theory of constraints for regular systems with holonomic constraints and systems with nonstandard Lagrangians. By utilizing Dirac brackets, we derive the Hamilton-Dirac equations and minimize their residuals, incorporating also energy conservation and the Dirac constraints, using appropriate regularization terms in the loss function. The resulting PINNs, referred to as Hamilton-Dirac neural networks (HDNNs), successfully learn constrained dynamics without deviating from the constraint manifold. Two examples with holonomic constraints are presented: the nonlinear pendulum in Cartesian coordinates and a two-dimensional, elliptically restricted harmonic oscillator. In both cases, HDNNs exhibit superior performance in preserving energy and constraints compared to traditional explicit solvers. To demonstrate applicability in systems with singular Lagrangians, we computed the guiding center motion in a strong magnetic field starting from the guiding center Lagrangian. The imposition of energy conservation during the neural network training proved essential for accurately determining the orbits of the guiding center. The HDNN architecture enables the learning of parametric dependencies in constrained dynamics by incorporating a problem-specific parameter as an input, in addition to the time variable. Additionally, an example of semisupervised, data-driven learning of guiding center dynamics with parameter inference is presented.

Based on the recently proposed framework of general relativistic stochastic mechanics [J. Stat. Phys. 190, 193 (2023); J. Stat. Phys. 190, 181 (2023)] and stochastic thermodynamics [SciPost Phys. Core 7, 082 (2024)] at the ensemble level, this work focuses on general relativistic stochastic thermodynamics at the trajectory level. The first law of stochastic thermodynamics is reformulated, and the fluctuation theorems are proved on this level, with an emphasis on maintaining fully general covariance and on the choice of observers.

The evolution operator method is used to solve the generalized Fokker-Planck equations and the generalized diffusion-wave equations in the ($1+1$)-dimensional space in which $x\in \mathbb{R}$ and $t\in {\mathbb{R}}_{+}$. These equations contain either the first- or the second-time derivatives smeared by memory functions, each of which forms an integral kernel [denoted by $f(\xi ,t), \xi \in {\mathbb{R}}_{+}$] of suitable evolution operators. If memory functions in the Laplace space are Stieltjes functions, then $f(\xi ,t)$ satisfies normalization, non-negativity, and infinite divisibility to be considered a probability density function. The evolution operators also contain exponential-like operators whose action on initial condition $p_0\left(x\right)>0$ leads to the parent process distribution functions. This makes the results fully analogous to those obtained within the standard subordination approach. The above conclusion is satisfied by the solution of the generalized Fokker-Planck equation. In the case of the generalized diffusion-wave equation, to get this property, we should employ a special class, namely, “diffusion-like” initial conditions. The key models of the operator method involve power-law memory functions. It leads to the characterization of $f(\xi ,t)$ by applying one-sided stable Lévy distributions. The paper also examines the properties of evolution operators in terms of evolution and self-reproduction.

The phenomenon of Anderson localization, occurring in a disordered medium, significantly influences the dynamics of quantum particles. A fascinating manifestation of this is the “quantum boomerang effect” (QBE), observed when a quantum particle, propelled with a finite initial velocity, reverses its average trajectory, eventually halting at its starting point. This effect has recently been demonstrated in an experiment replicating the quantum kicked-rotor model. This research delves into the classical analog of QBE. We uncover evidence of a similar effect in classical systems, characterized by the absence of typical diffusion processes. Our investigation encompasses both simplified probabilistic models and more complex phenomenological models that link classical with quantum mechanics. The results indicate that the boomerang effect is not confined to the quantum realm and may also be present in diverse systems exhibiting subdiffusive behavior.

Spectral statistics and correlations are the usual way to study the presence or absence of quantum chaos in quantum systems. We present our investigation on the study of the fluctuation average and variance of certain correlation functions as a diagnostic measure of quantum chaos and to possibly characterize quantum systems based on it. These quantities are related to eigenvector distribution and eigenvector correlation. Using the random matrix theory, certain analytical expressions of these quantities, for the Gaussian orthogonal ensemble case, were calculated before. So as a first step, we study these quantities for the Gaussian unitary ensemble case numerically and obtain certain analytical results for the same. We then carry out our investigations in physical systems, such as the mixed-field Ising model. For this model, we find that although the eigenvalue statistics follow the behavior of corresponding random matrices, the fluctuation average and variance of these correlation functions deviate from the expected random matrix theory behavior. We then turn our focus on the Rosenzweig-Porter model of the Gaussian orthogonal ensemble and Gaussian unitary ensemble types. By using the fluctuation average and variance of these correlations, we identify the three distinct phases of these models: the ergodic, the fractal, and the localized phases. We provide an alternative way to study and distinguish the three phases and firmly establish the use of these correlation fluctuations as an alternative way to characterize quantum chaos.

The binding rate constant for a target within a cluster of targets is smaller than for an isolated target due to competition between the targets; and the magnitude of this decrease in the binding rate constant depends upon the shape and the size of the cluster. We obtain a general formula for binding rate constants for clusters of arbitrary shapes and sizes using an approach based upon probabilities to visit a certain domain in space by a searching particle. We applied this result to various shapes of clusters including a spherical shell, a straight line, a random coil, and a random “cloud.” Our results could be applicable for targets localized on natural and artificial particles (e.g., receptors on the surfaces of living cells, and macro- and small molecules attached to magnetic beads) and to the target localized on polymers (e.g., DNA or RNA).

One of the primary regulatory processes in cells is transcription, during which RNA polymerase II (Pol-II) transcribes DNA into RNA. The binding of Pol-II to its site is regulated through interactions with transcription factors (TFs) that bind to DNA at enhancer cis-regulatory elements. Measuring the enhancer activity of large libraries of distinct DNA sequences is now possible using massively parallel reporter assays (MPRAs), and computational methods have been developed to identify the dominant statistical patterns of TF binding within these large datasets. Such methods are global in their approach and may overlook important regulatory sites that function only within the local context. Here we introduce a method for inferring functional regulatory sites (their number, location, and width) within an enhancer sequence based on measurements of its transcriptional activity from an MPRA method such as STARR-seq. The model is based on a mean-field thermodynamic description of Pol-II binding that includes interactions with bound TFs. Our method applied to simulated STARR-seq data for a variety of enhancer architectures shows how data quality impacts the inference and also how it can find local regulatory sites that may be missed in a global approach. We also apply the method to recently measured STARR-seq data on androgen receptor (AR) bound sequences, a TF that plays an important role in the regulation of prostate cancer. The method identifies key regulatory sites within these sequences, which are found to overlap with binding sites of known coregulators of AR.

The interaction of an ultra-intense laser with matter is an efficient source of high-energy particles, with efforts directed toward narrowing the divergence and simultaneously increasing the brightness. In this paper we report on emission of highly collimated, ultrabright, attosecond $\gamma$-photons and generation of dense electron-positron pairs via a tunable particle generation scheme, which utilizes the interaction of two high-power lasers with a thin wire target. Irradiating the target with a radially polarized laser pulse first produces a series of high charge, short duration, electron bunches with low transverse momentum. These electron bunches subsequently collide with a counter-propagating high-intensity laser. Depending on the intensity of the counter-propagating laser, the scheme generates highly collimated ultra-bright GeV-level $\gamma$-beams and/or electron-positron plasma of solid density level.

We address how the interplay between the finite availability and carrying capacity of particles at different parts of a spatially extended system can control the steady-state currents and density profiles in the one-dimensional current-carrying lanes connecting the different parts of the system. To study this, we set up a minimal model consisting of two particle reservoirs of the same finite carrying capacity connected by two equally sized antiparallel totally asymmetric simple exclusion processes (TASEPs). We focus on the steady-state currents and particle density profiles in the two TASEP lanes. The ensuing phases and the phase diagrams, which can be remarkably complex, are parametrized by the model parameters defining particle exchange between the TASEP lanes and the reservoirs and the filling fraction of the particles that determine the total resources available. These parameters may be tuned to make the densities of the two TASEP lanes globally uniform or piece-wise continuous in the form of a combination of a single localized domain wall and a spatially constant density or a pair of delocalized domain walls. Our model reveals that the two reservoirs can be preferentially populated or depopulated in the steady states.

The behavior of lattice models in which time reversibility is enforced at the level of trajectories (microscopic reversibility) is studied analytically. Conditions for ergodicity breaking are explored, and a few examples of systems characterized by an additional conserved quantity besides energy are presented. All the systems are characterized by ergodicity restoration when put in contact with a thermal bath, except for specific choices of the interactions between the atoms in the system and the bath. The study shows that the additional conserved quantities return to play a role in nonequilibrium conditions. The similarities with the behavior of some mesoscale systems, in which the transition rates satisfy detailed balance but not microscopic reversibility, are discussed.

We show that BPS-impurity theories may support BPS kink-kink solutions, i.e., an energetically degenerated family of solutions describing two kinks at any mutual distance. This requires a singular impurity. As an example we consider the sine-Gordon and ${\varphi }^6$ models coupled with such a BPS impurity. Interestingly, obtained solutions are identical to double sine-Gordon kinks and Christ-Lee kinks, respectively. We also study the spectral flow on the moduli space. All the modes have an odd number of nodes to cancel the singularity of the impurity.

The first protocells must have been driven by a reaction system in which autocatalysis is maintained inside the cell while food molecules outside the cell are unreactive. We show that if there is a second-order autocatalytic mechanism, then an active state can be stable inside the cell with a high catalyst concentration while the environment remains stable in an unreactive state with no catalyst. Addition of a small amount of catalyst to the environment does not cause the initiation of the autocatalytic cycle outside the cell. In contrast, for a first-order mechanism, addition of a small amount of catalyst initiates the reaction outside the cell unless there is continual removal of the catalyst from the environment. Hence, a second-order reaction mechanism maintains the difference between the inside and outside of a protocell much better than a first-order mechanism. The formose reaction, although a prebiotically plausible autocatalytic system, is first order and therefore is unlikely as a means of support for the first protocells. We give other theoretical examples of first- and second-order reaction networks but note there are few known real-world chemical systems that fit these schemes. However, we show that nonenzymatic RNA templating constitutes a second-order autocatalytic system with the necessary properties to support a protocell. Templating is maintained inside the cell but is not initiated outside the cell. If the reaction is driven by an external supply of activated nucleotides, then templating is itself a metabolic cycle. It is not necessary to have an additional separate metabolic cycle before templating reactions can occur. In this view, templating reactions, which are usually considered as the origin of replication and heredity, are also the origin of metabolism.