We study ensembles of globally coupled or forced identical phase oscillators subject to independent white Cauchy noise. We demonstrate that if the oscillators are forced in several harmonics, stationary synchronous regimes can be exactly described with a finite number of complex order parameters. The corresponding distribution of phases is a product of wrapped Cauchy distributions. For sinusoidal forcing, the Ott-Antonsen low-dimensional reduction is recovered.

Gene regulatory networks (GRNs) orchestrate the spatiotemporal levels of gene expression, thereby regulating various cellular functions ranging from embryonic development to tissue homeostasis. Some patterns called “motifs” recurrently appear in the GRNs. Owing to the prevalence of these motifs they have been subjected to much investigation, both in the context of understanding cellular decision making and engineering synthetic circuits. Mounting experimental evidence suggests that (1) the copy number of genes associated with these motifs varies, and (2) proteins produced from these genes bind to decoy binding sites on the genome as well as promoters driving the expression of other genes. Together, these two processes engender competition for protein resources within a cell. To unravel how competition for protein resources affects the dynamical properties of regulatory motifs, we propose a simple kinetic model that explicitly incorporates copy number variation (CNV) of genes and decoy binding of proteins. Using quasi-steady-state approximations, we theoretically investigate the transient and steady-state properties of three of the commonly found motifs: Autoregulation, toggle switch, and repressilator. While protein resource competition alters the timescales to reach the steady state for all these motifs, the dynamical properties of the toggle switch and repressilator are affected in multiple ways. For toggle switch, the basins of attraction of the known attractors are dramatically altered if one set of proteins binds to decoys more frequently than the other, an effect which gets suppressed as the copy number of the toggle switch is enhanced. For repressilators, protein sharing leads to an emergence of oscillation in regions of parameter space that were previously nonoscillatory. Intriguingly, both the amplitude and frequency of oscillation are altered in a nonlinear manner through the interplay of CNV and decoy binding. Overall, competition for protein resources within a cell provides an additional layer of regulation of gene regulatory motifs.

The drop-and-dry is a common technique allowing for creation of periodic nanoparticle (NP) structures for sensing, photonics, catalysis, etc. However, the reproducibility and scalability of this approach for fabrication of NP-based structures faces serious challenges due to the complexity of the simple, at first glance, evaporation process. In this work we study the effect of the spatial confinement on the NP self-assembly under slow solvent evaporation, when the air-liquid-substrate contact line (CL) expands from the center towards the walls of a cylindrical cell, forming a toroid. Using in situ video monitoring of the stick-slip CL motion, we find regular hydrodynamic perturbations in the meniscus, and reveal fine details of the formation of quasiperiodic rings of close packed NP layers. We report that drying of the toroidal NP droplet has a number of important differences from drying of the classical hemispherical colloidal drops. In toroidal drops we observe linear-in-time average meniscus motion, in contrast to the hemispherical drops where the meniscus moves as a square root of time. While both droplet geometries produce NP ring patterns, the ring width for the toroidal drop decreases with increasing ring radius, while it decreases with decreasing the radius of the hemispherical drop. We suggest that free ligands are the main cause of the Marangoni instabilities driving the periodic vorticity in the meniscus. In addition, we show that the usually ignored contact line tension may yield a considerable contribution to the CL pinning causing the CL slip-stick motion and the ring formation.

Propagation of waves in materials that exhibit stealthy-hyperuniform long-range correlations is investigated. By using a modal decomposition of the field that takes multiple scattering into account at all orders, we study the impact of the concentration of particles on the transparency of such materials at low frequency. An upper frequency limit for transparency is defined that include both the particle size and the degree of stealthiness. We show that the independent scattering approximation is not relevant to calculate elastic mean free paths when wavelength becomes comparable to the size of particles. We find that transparency is very robust with regard to the degree of heterogeneity of the host random medium and the polydispersity of particles. Finally, it is shown that resonances can be used as the frequency filter.

Multiphase materials, such as composite materials, exhibit multiple competing failure mechanisms during the growth of a macroscopic defect. For the simulation of the overall fracture process in such materials, we develop a two-phase spring network model that accounts for the architecture between the different components as well as the respective disorders in their failure characteristics. In the specific case of a plain weave architecture, we show that any offset between the layers reduces the delocalization of the stresses at the crack tip and thereby substantially lowers the strength and fracture toughness of the overall laminate. The avalanche statistics of the broken springs do not show a distinguishable dependence on the offsets between layers. The power-law exponents are found to be much smaller than that of disordered spring network models in the absence of a crack. A discussion is developed on the possibility of the avalanche statistics being those near breakdown.

Propagation features of circularly polarized (CP) electromagnetic waves in magnetized plasmas are determined by the plasma density and the magnetic field strength. This property can be applied to design a unique plasma photonic device for intense short-pulse lasers. We have demonstrated by numerical simulations that a thin plasma foil under an external magnetic field works as a polarizing plate to separate a linearly polarized laser into two CP waves traveling in the opposite direction. This plasma photonic device has an advantage for generating intense CP waves even with a relativistic amplitude. For various research purposes, intense CP lights are strongly required to create high energy density plasmas in the laboratory.

The problem of inferring pairwise and higher-order interactions in complex systems involving large numbers of interacting variables, from observational data, is fundamental to many fields. Known to the statistical physics community as the inverse problem, it has become accessible in recent years due to real and simulated big data being generated. Current approaches to the inverse problem rely on parametric assumptions, physical approximations, e.g., mean-field theory, and ignoring higher-order interactions which may lead to biased or incorrect estimates. We bypass these shortcomings using a cross-disciplinary approach and demonstrate that none of these assumptions and approximations are necessary: We introduce a universal, model-independent, and fundamentally unbiased estimator of all-order symmetric interactions, via the nonparametric framework of targeted learning, a subfield of mathematical statistics. Due to its universality, our definition is readily applicable to any system at equilibrium with binary and categorical variables, be it magnetic spins, nodes in a neural network, or protein networks in biology. Our approach is targeted, not requiring fitting unnecessary parameters. Instead, it expends all data on estimating interactions, hence substantially increasing accuracy. We demonstrate the generality of our technique both analytically and numerically on (i) the two-dimensional Ising model, (ii) an Ising-type model with four-point interactions, (iii) the restricted Boltzmann machine, and (iv) simulated individual-level human DNA variants and representative traits. The latter demonstrates the applicability of this approach to discover epistatic interactions causal of disease in population biomedicine.

The use of machine learning to develop neural network potentials (NNP) representing the interatomic potential energy surface allows us to achieve an optimal balance between accuracy and efficiency in computer simulation of materials. A key point in developing such potentials is the preparation of a training dataset of ab initio trajectories. Here we apply a deep potential molecular dynamics (DeePMD) approach to develop NNP for silica, which is the representative glassformer widely used as a model system for simulating network-forming liquids and glasses. We show that the use of a relatively small training dataset of high-temperature ab initio configurations is enough to fabricate NNP, which describes well both structural and dynamical properties of liquid silica. In particular, we calculate the pair correlation functions, angular distribution function, velocity autocorrelation functions, vibrational density of states, and mean-square displacement and reveal a close agreement with ab initio data. We show that NNP allows us to expand significantly the time-space scales achievable in simulations and thus calculating dynamical and transport properties with more accuracy than that for ab initio methods. We find that developed NNP allows us to describe the structure of the glassy silica with satisfactory accuracy even though no low-temperature configurations were included in the training procedure. The results obtained open up prospects for simulating structural and dynamical properties of liquids and glasses via NNP.

The small-world effect is a universal feature used to explain many different phenomena like percolation, diffusion, and consensus. Starting from any regular lattice of $N$ sites, the small-world effect can be attained by rewiring randomly an $O\left(N\right)$ number of links or by superimposing an equivalent number of new links onto the system. In a classical system this procedure is known to change radically its critical point and behavior, the new system being always effectively mean-field. Here, we prove that at the quantum level the above scenario does not apply: when an $O\left(N\right)$ number of new couplings are randomly superimposed onto a quantum Ising chain, its quantum critical point and behavior both remain unchanged. In other words, at zero temperature quantum fluctuations destroy any small-world effect. This exact result sheds new light on the significance of the quantum critical point as a thermodynamically stable feature of nature that has no analogy at the classical level and essentially prevents a naive application of network theory to quantum systems. The derivation is obtained by combining the quantum-classical mapping with a simple topological argument.

Using the main results of the Kuramoto theory of globally coupled phase oscillators combined with methods from probability and generalized function theory in a geometric analysis, we extend Kuramoto's results and obtain a mathematical description of the instantaneous frequency (phase-velocity) distribution. Our result is validated against numerical simulations, and we illustrate it in cases in which the natural frequencies have normal and Beta distributions. In both cases, we vary the coupling strength and compare systematically the distribution of time-averaged frequencies (a known result of Kuramoto theory) to that of instantaneous frequencies, focusing on their qualitative differences near the synchronized frequency and in their tails. For a class of natural frequency distributions with power-law tails, which includes the Cauchy-Lorentz distribution, we analyze the tails of the instantaneous frequency distribution by means of an asymptotic formula obtained from a power-series expansion.

Using density-functional theory we theoretically study the orientational properties of uniform phases of hard kites—two isosceles triangles joined by their common base. Two approximations are used: scaled particle theory and a new approach that better approximates third virial coefficients of two-dimensional hard particles. By varying some of their geometrical parameters, kites can be transformed into squares, rhombuses, triangles, and also very elongated particles, even reaching the hard-needle limit. Thus, a fluid of hard kites, depending on the particle shape, can stabilize isotropic, nematic, tetratic, and triatic phases. Different phase diagrams are calculated, including those of rhombuses, and kites with two of their equal interior angles fixed to ${90}^{\circ }, {60}^{\circ }$, and ${75}^{\circ }$. Kites with one of their unequal angles fixed to ${72}^{\circ }$, which have been recently studied via Monte Carlo simulations, are also considered. We find that rhombuses and kites with two equal right angles and not too large anisometry stabilize the tetratic phase but the latter stabilize it to a much higher degree. By contrast, kites with two equal interior angles fixed to ${60}^{\circ }$ stabilize the triatic phase to some extent, although it is very sensitive to changes in particle geometry. Kites with the two equal interior angles fixed to ${75}^{\circ }$ have a phase diagram with both tetratic and triatic phases, but we show the nonexistence of a particle shape for which both phases are stable at different densities. Finally, the success of the new theory in the description of orientational order in kites is shown by comparing with Monte Carlo simulations for the case where one of the unequal angles is fixed to ${72}^{\circ }$. These particles also present a phase diagram with stable tetratic and triatic phases.

Quantum entanglement of a system of two coupled quantum harmonic oscillators with a Hamiltonian $\widehat{H}=\frac{1}{2}\left(\frac{1}{m_1}{\widehat{p}}_1^2+\frac{1}{m_2}{\widehat{p}}_2^2+A{x}_1^2+B{x}_2^2+C{x}_1{x}_2\right)$ can be found in many applications of quantum and nonlinear physics, molecular chemistry, and biophysics. Despite this, the quantum entanglement of such a system is still a problem under study. This is primarily due to the fact that the system is multiparametric and the quantum entanglement of such a system is not defined in a simple analytical form. This paper solves this problem and shows that quantum entanglement depends on only one parameter that has a simple physical meaning: the reflection coefficient $R\in (0,1)$. The reflection coefficient $R$ has a simple analytical form and includes all the parameters of the system under consideration. It is shown that for certain values of the coefficient $R$, the quantum entanglement can be large. The developed theory can be used not only for calculating quantum entanglement, but also for many other applications in physics, chemistry, and biophysics, where coupled harmonic oscillators are considered.

We present an extensive experimental study of the distributions of the real and imaginary parts of the off-diagonal elements of the scattering matrix $\widehat{S}$ and the Wigner's reaction $\widehat{K}$ matrix for open microwave networks with broken time $\left(T\right)$ reversal invariance. Microwave Faraday circulators were applied in order to break $T$ invariance. The experimental distributions of the real and imaginary parts of the off-diagonal entries of the scattering matrix $\widehat{S}$ are compared with the theoretical predictions from the supersymmetry random matrix theory [A. Nock, S. Kumar, H.-J. Sommers, and T. Guhr, Ann. Phys. (NY) 342, 103 (2014)]. Furthermore, we show that the experimental results are in very good agreement with the recent predictions for the distributions of the real and imaginary parts of the off-diagonal elements of the Wigner's reaction $\widehat{K}$ matrix obtained within the framework of the Gaussian unitary ensemble of random matrix theory [S. B. Fedeli and Y. V. Fyodorov, J. Phys. A: Math. Theor. 53, 165701 (2020)]. Both theories include losses as tunable parameters and are therefore well adapted to the experimental verification.

The propagation of dispersive shock waves (DSWs) is investigated in the cylindrical Gardner (cG) equation, which is obtained by employing a similarity reduction to the two-space one-time ($2{\displaystyle +}1$) dimensional Gardner-Kadomtsev-Petviashvili (Gardner-KP) equation. We consider the steplike initial condition along a parabolic front. Then, the cG-Whitham modulation system, which is a description of DSW evolution in the cG equation, in terms of appropriate Riemann-type variables is derived. Our study is supported by numerical simulations. The comparison is given between the direct numerical solution of the cG equation and the DSW solution obtained from the numerical solution of the Whitham system. According to this comparison, a good agreement is found between the solutions.

Consensus algorithms on networks have received increasing attention in recent years for various applications, ranging from distributed decision making to multivehicle coordination. In particular, second-order consensus models take into account the Newtonian dynamics of interacting physical agents. For this model class, we uncover a mechanism inhibiting the formation of collective consensus states via rather small time-periodic coupling modulations. We treat the model in its spectral decomposition and find analytically that, for certain intermediate coupling frequencies, parametric resonance is induced on a network level—at odds with the expected emergence of consensus for very short and long coupling time scales. Our formalism precisely predicts those resonance frequencies and links them to the Laplacian spectrum of the static backbone network. The excitation of the system is furthermore quantified within the theory of parametric resonance, which we extend to the domain of networks with time-periodic couplings.

When initially isotropic three-dimensional (3D) turbulence is compressed along two dimensions, the compression supplies energy directly to the flow components in the compressed directions, while the flow component in the noncompressed direction experiences the effects of compression only indirectly through the nonlinearity of the hydrodynamic equations. Here we study such 2D compressions using numerical simulations. For initially isotropic turbulence, we find that the nonlinearity can be insufficient to maintain isotropy, with the energy components parallel to the compression coming to dominate the turbulent energy, with a number of consequences. Among these are the possibilities for stronger and more easily sustained growth of turbulent energy than in 3D compressions and for an increasing turbulent Mach number even in a compression without thermal losses.

A method to calculate the bending rigidity $\kappa$, saddle-splay modulus $\overline{\kappa }$, and spontaneous curvature $C_0$ of a fluid membrane is proposed. Virtual work for the bending deformations into cylindrical and spherical shapes is calculated for a flat membrane. This method does not require a force decomposition, unlike the existing stress-profile method. The first derivative of the deformation gives $\kappa C_0$ and is a discrete form of the first moment of the stress profile. The second derivatives give $\kappa$ and $\overline{\kappa }$ and include the variance terms of the first derivatives, which are not accounted for in the stress-profile method. This method is examined for a solvent-free meshless membrane model and a dissipative-particle-dynamics two-bead amphiphilic molecular model. It is concluded that $\kappa$ and $\overline{\kappa }$ of a thin membrane can be accurately calculated, whereas for a thick membrane or one with an explicit solvent, a further extension to include the volume-fluctuation effects is required for an accurate estimation. The amplitude of the volume-fluctuation effects can be evaluated using the parameter dependence in the present method.

Population bursts in a large ensemble of coupled elements result from the interplay between the local excitable properties of the nodes and the global network topology. Here, collective excitability and self-sustained bursting oscillations are shown to spontaneously emerge in globally coupled populations of nonexcitable units subject to adaptive coupling. The ingredients to observe collective excitability are the coexistence of states with different degrees of synchronization joined to a global feedback acting, on a slow timescale, against the synchronization (desynchronization) of the oscillators. These regimes are illustrated for two paradigmatic classes of coupled rotators, namely, the Kuramoto model with and without inertia. For the bimodal Kuramoto model we analytically show that the macroscopic evolution originates from the existence of a critical manifold organizing the fast collective dynamics on a slow timescale. Our results provide evidence that adaptation can induce excitability by maintaining a network permanently out of equilibrium.

The noise-driven motion in a bistable potential acts as the archetypal model of various physical phenomena. Here, we contrast properties of the overdamped escape dynamics with the full (underdamped) dynamics. In the weak noise limit, for the overdamped particle driven by nonequilibrium, $\alpha$-stable noise the ratio of forward to backward transition rates depends only on the width of a potential barrier separating both minima. Using analytical and numerical methods, we show that in the regime of full dynamics, contrary to the overdamped case, the ratio of transition rates depends on both the widths and the heights of the potential barrier separating minima of the double-well potential. The derived analytical formula for the ratio of transition rates is corroborated by extensive numerical simulations. Results of numerical simulations follow especially well the analytical predictions in the weak noise limit when the most probable escape scenario is via a single, strong, noise kick, which is sufficient to induce a quasideterministic transition over the potential barrier. Such an escape trajectory can be analyzed in terms of the instantaneous velocity, which is fully characterized by its density function, which is of the same type as the probability density underlying the noise distribution.