We study the near-equilibrium critical dynamics of the $\text{O}\left(3\right)$ nonlinear sigma model describing isotropic antiferromagnets with a nonconserved order parameter reversibly coupled to the conserved total magnetization. To calculate response and correlation functions, we set up a description in terms of Langevin stochastic equations of motion, and their corresponding Janssen–De Dominicis response functional. We find that in equilibrium, the dynamics is well-separated from the statics, at least to one-loop order in a perturbative treatment with respect to the static and dynamical nonlinearities. Since the static nonlinear sigma model must be analyzed in a dimensional $d=2+\varepsilon$ expansion about its lower critical dimension $d_{\text{lc}}=2$, whereas the dynamical mode-coupling terms are governed by the upper critical dimension $d_c=4$, a simultaneous perturbative dimensional expansion is not feasible, and the reversible critical dynamics for this model cannot be accessed at the static critical renormalization group fixed point. However, in the coexistence limit addressing the long-wavelength properties of the low-temperature ordered phase, we can perform an $\epsilon =4-d$ expansion near $d_c$. This yields anomalous scaling features induced by the massless Goldstone modes, namely subdiffusive relaxation for the conserved magnetization density with asymptotic scaling exponent $z_{\mathrm{\Gamma }}=d-2$, which may be observable in neutron scattering experiments. Intriguingly, if initialized near the critical point, the renormalization group flow for the effective dynamical exponents recovers their universal critical values $z_c=d/2$ in an intermediate crossover region.

We show that the occurrence of chaotic diffusion in a typical class of time-delayed systems with linear instantaneous and nonlinear delayed term can be well described by an antipersistent random walk. We numerically investigate the dependence of all relevant quantities characterizing the random walk on the strength of the nonlinearity and on the delay. With the help of analytical considerations, we show that for a decreasing nonlinearity parameter the resulting dependence of the diffusion coefficient is well described by Markov processes of increasing order.

Employing Langevin dynamics simulations, we investigated the kinetics of the collapse transition for a polymer of length $N$ when a particular monomer at a position $1\le X\le N$ is pinned. The results are compared with the kinetics of a free polymer. The equilibrium $\theta$-point separating the coil from the globule phase is located by a crossover in $\langle R_g^2\rangle /N$ plots of different chain lengths. Our simulation supports a three-stage mechanism for free and pinned polymer collapse: the formation of pearls, the coarsening of pearls, and the formation of a compact globule. Pinning the central monomer has negligible effects on the kinetics as it does not break the symmetry. However, pinning a monomer elsewhere causes the process to be delayed by a constant factor ${\varphi }_X$ depending linearly upon $X$. The total collapse time scales with $N$ as ${\tau }_c\sim {\varphi }_X{N}^{1.60\pm 0.03}$, which implies ${\tau }_c$ is maximum when an end monomer is pinned ($X=1$ or $N$), while when pinning the central monomer ($X=N/2$) it is minimum and identical to that of a free polymer. The average cluster size $N_c\left(t\right)$ grows in time as $t^z$, where $z=1.00\pm 0.04$ for a free particle, whereas we identify two time regimes separated by a plateau for pinned polymers. At longer times, $z=1.00\pm 0.04$, while it deviates in early time regimes significantly, depending on the value of $X$.

Even though electrowetting-on-dielectric (EWOD) is a useful strategy in a wide array of biological and engineering processes with numerous droplet-manipulation applications, there is still a lack of complete theoretical interpretation on the dynamics of electrowetting. In this paper we present an effective theoretical model and use the Onsager variational principle to successfully derive general dynamic shape equations for electrowetting droplets in both the overdamped and underdamped regimes. It is found that the spreading and retraction dynamics of a droplet on EWOD substrates can be fairly well captured by our model, which agrees with previous experimental results very well in the overdamped regime. We also confirm that the transient dynamics of EW can be characterized by a timescale independent of liquid viscosity, droplet size, and applied voltage. Our model provides a complete fundamental explanation of EW-driven spreading dynamics, which is important for a wide range of applications, from self-cleaning to novel optical and digital microfluidic devices.

Many real-life networks are incomplete. Dynamical observations can allow estimating missing edges. Such procedures, often summarized under the term ‘network inference’, typically evaluate the statistical correlations among pairs of nodes to determine connectivity. Here, we offer an alternative approach: completing an incomplete network by observing its collective behavior. We illustrate this approach for the case of patterns emerging in reaction-diffusion systems on graphs, where collective behaviors can be associated with eigenvectors of the network's Laplacian matrix. Our method combines a partial spectral decomposition of the network's Laplacian matrix with eigenvalue assignment by matching the patterns to the eigenvectors of the incomplete graph. We show that knowledge of a few collective patterns can allow the prediction of missing edges and that this result holds across a range of network architectures. We present a numerical case study using activator-inhibitor dynamics and we illustrate that the main requirement for the observed patterns is that they are not confined to subsets of nodes, but involve the whole network.

Interparticle forces are known to influence mechanical and physical properties of granular materials. A method for inferring forces in two-dimensional and three-dimensional experiments has recently been developed and applied to the problem of examining force statistics, energy dissipation, fracture mechanics, and force-property relations. However, a systematic analysis of uncertainties in the forces inferred through this method has not been undertaken. In this paper, our goal is therefore to perform such a systematic analysis. We first review and modify the force inference technique to eliminate its sensitivity to the choice of units and coordinate system origin. We then use discrete-element method simulations to perform a systematic study of how experimental uncertainties and data-processing errors lead to errors in inferred forces. For the considered experiments and simulations, we find that (1) errors in inferred force magnitudes and orientations increase as the ratio between particle stress uncertainties and a measure of stress imposed on the system increases, but remain small in the largest forces in a material; (2) the absence of a moderate number of particle stress tensors in the force inference procedure leads to negligible errors in inferred force magnitudes and orientations; and (3) particle stress tensors that cannot be directly measured during experiments can be “recovered” through the force inference procedure. Based on our results, we make recommendations for future experiment design to reduce uncertainties in inferred forces.

We examine the momentum and angular momentum (including spin) properties of linear waves, both longitudinal (Langmuir) and transverse (electromagnetic), in an isotropic nonrelativistic collisionless electron plasma. We focus on conserved quantities associated with the translational and rotational invariance of the wave fields with respect to the homogeneous medium; these are sometimes called pseudomomenta. There are two types of the momentum and angular momentum densities: (i) the kinetic ones associated with the energy flux density and the symmetrized (Belinfante) energy-momentum tensor and (ii) the canonical ones associated with the conserved Noether currents and canonical energy-momentum tensor. We find that the canonical momentum and spin densities of Langmuir waves are similar to those of sound waves in fluids or gases; they are naturally expressed via the electron velocity field. In turn, the momentum and spin densities of electromagnetic waves can be written either in the forms known for free-space electromagnetic fields, involving only the electric field, or in the dual-symmetric forms involving both electric and magnetic fields, as well as the effective permittivity of plasma. We derive these properties both within the phenomenological macroscopic approach and microscopic Lagrangian field theory for the coupled electromagnetic fields and electrons. Finally, we explore implications of the canonical momentum and spin densities in transport and electrodynamic phenomena: the Stokes drift, the wave-induced magnetization (inverse Faraday effect), etc.

In laser-produced high-energy-density plasmas, large-scale strong magnetic fields are spontaneously generated by the Biermann battery effects when temperature and density gradients are misaligned. Saturation of the magnetic field takes place when convection and dissipation balance field generation. While theoretical and numerical modeling provide useful insight into the saturation mechanisms, experimental demonstration remains elusive. In this letter, we report an experiment on the saturation dynamics and scaling of Biermann battery magnetic field in the regime where plasma convection dominates. With time-gated charged-particle radiography and time-resolved Thomson scattering, the field structure and evolution as well as corresponding plasma conditions are measured. In these conditions, the spatially resolved magnetic fields are reconstructed, leading to a picture of field saturation with a scaling of $B\sim 1/L_{\mathrm{T}}$ for a convectively dominated plasma, a regime where the temperature gradient scale ($L_{\mathrm{T}}$) exceeds the ion skin depth.

We compare ergodic properties of the kinetic energy for three stochastic models of subrecoil-laser-cooled gases. One model is based on a heterogeneous random walk (HRW), another is an HRW with long-range jumps (the exponential model), and the other is a mean-field-like approximation of the exponential model (the deterministic model). All the models show an accumulation of the momentum at zero in the long-time limit, and a formal steady state cannot be normalized, i.e., there exists an infinite invariant density. We obtain the exact form of the infinite invariant density and the scaling function for the exponential and deterministic models, and we devise a useful approximation for the momentum distribution in the HRW model. While the models are kinetically nonidentical, it is natural to wonder whether their ergodic properties share common traits, given that they are all described by an infinite invariant density. We show that the answer to this question depends on the type of observable under study. If the observable is integrable, the ergodic properties, such as the statistical behavior of the time averages, are universal as they are described by the Darling-Kac theorem. In contrast, for nonintegrable observables, the models in general exhibit nonidentical statistical laws. This implies that focusing on nonintegrable observables, we discover nonuniversal features of the cooling process, which hopefully can lead to a better understanding of the particular model most suitable for a statistical description of the process. This result is expected to hold true for many other systems, beyond laser cooling.

We consider large-scale point fields which naturally appear in the context of the Kardar-Parisi-Zhang (KPZ) phenomenon. Such point fields are geometrical objects formed by points of mass concentration, and by shocks separating the sources of these points. We introduce similarly defined point fields for processes of coalescing fractional Brownian motions (cfBMs). The case of the Hurst index 2/3 is of particular interest for us since, in this case, the power law of the density decay is the same as that in the KPZ phenomenon. In this paper, we present strong numerical evidence that statistical properties of points fields in these two different settings are very similar. We also discuss theoretical arguments in support of the conjecture that they are exactly the same in the large-time limit. This would indicate that two objects may, in fact, belong to the same universality class.

We consider the one-dimensional Schrödinger equation with a random potential and study the cumulant generating function of the logarithm of the wave function $\psi \left(x\right)$, known in the literature as the “generalized Lyapunov exponent”; this is tantamount to studying the statistics of the so-called “finite-size Lyapunov exponent.” The problem reduces to that of finding the leading eigenvalue of a certain nonrandom non-self-adjoint linear operator defined on a somewhat unusual space of functions. We focus on the case of Cauchy disorder, for which we derive a secular equation for the generalized Lyapunov exponent. Analytical expressions for the first four cumulants of $ln\left|\psi \right(x\left)\right|$ for arbitrary energy and disorder are deduced. In the universal (weak-disorder and high-energy) regime, we obtain simple asymptotic expressions for the generalized Lyapunov exponent and for all the cumulants. The large deviation function controlling the distribution of $ln\left|\psi \right(x\left)\right|$ is also obtained in several limits. As an application, we show that, for a disordered region of size $L$, the distribution ${\mathcal{W}}_L$ of the conductance $g$ exhibits the power-law behavior ${\mathcal{W}}_L\left(g\right)\sim g^{-1/2}$ as $g\to 0$.

Parrondo's paradox refers to the apparently paradoxical effect whereby a certain combination of biased random walks displays a counterintuitive reversal of the bias direction. We show that Parrondo's paradox can occur not only in the case of one-dimensional discrete-time quantum walks with a deterministic sequence of two quantum coins but also in the case of one-dimensional discrete-time quantum walks with a deterministic sequence of three quantum coins. Moreover, we show how Parrondo's paradox affects the time evolution of quantum entanglement for such quantum walks.

The distribution of the ratios of consecutive eigenvalue spacings of random matrices has emerged as an important tool to study spectral properties of many-body systems. This article numerically investigates the eigenvalue ratios distribution of various model networks, namely, small-world, Erdős-Rényi random, and (dis)assortative random having a diagonal disorder in the corresponding adjacency matrices. Without any diagonal disorder, the eigenvalues ratio distribution of these model networks depict Gaussian orthogonal ensemble (GOE) statistics. Upon adding diagonal disorder, there exists a gradual transition from the GOE to Poisson statistics depending upon the strength of the disorder. The critical disorder ($w_c$) required to procure the Poisson statistics increases with the randomness in the network architecture. We relate $w_c$ with the time taken by maximum entropy random walker to reach the steady state. These analyses will be helpful to understand the role of eigenvalues other than the principal one for various network dynamics such as transient behavior.

We have studied the structure of complexes of the cationic surfactant dodecyltrimethylammonium bromide (DTAB) with DNA as a function of surfactant to DNA base molar ratio ($R$) and salt concentration. Small-angle x-ray scattering data show the formation of nematic gels at lower and higher salt concentrations, irrespective of the value of $R$. Two crystalline phases are observed over intermediate salt concentrations; a square ($S$) phase for $R>3$ and a hexagonal ($H_S$) phase for lower $R$. Electron density maps of these phases show intercalated structures, with DTAB micelles sandwiched between long DNA strands. The composition of these complexes, estimated using elemental analysis, indicates that the micelles are not very long, and they occupy only about half of the interstitial volume between the DNA strands. This phase behavior is strikingly different from that of complexes of DNA with longer chain surfactants cetyltrimethylammonium bromide (CTAB) and tetradecyltrimethylammonium bromide (TTAB), which show only a hexagonal ($H$) phase over similar ranges of $R$ and salt concentration, the $H_S$ structure observed in the present study being a $\sqrt{3}\times \sqrt{3}$ superlattice of the $H$ structure. Madelung energies of the $S$ and $H$ structures, calculated from the electrostatic interaction between their cylindrical constituents, suggest that the former is preferred in DTAB-DNA complexes due to the smaller micellar radius of DTAB. The propensity of DTAB to form short micelles seems also to favor the $H_S$ phase at lower $R$. These results illustrate the important role of micellar size in determining the structure of these two-dimensional macro-ion crystals.

A theorem that establishes a one-to-one relation between zero-temperature static spin-spin correlators and coupling constants for a general class of quantum spin Hamiltonians bilinear in the spin operators has been recently established by Quintanilla, using an argument in the spirit of the Hohenberg-Kohn theorem in density functional theory. Quintanilla's theorem gives a firm theoretical foundation to quantum spin Hamiltonian learning using spin structure factors as input data. Here we extend the validity of the theorem in two directions. First, following the same approach as Mermin, the proof is extended to the case of finite-temperature spin structure factors, thus ensuring that the application of this theorem to experimental data is sound. Second, we note that this theorem applies to all types of Hamiltonians expressed as sums of bilinear operators, so that it can also relate the density-density correlators to the Coulomb matrix elements for interacting electrons in the lowest Landau level.

Properties of the noise-driven escape kinetics are mainly determined by the stochastic component of the system dynamics. Nevertheless, the escape dynamics is also sensitive to deterministic forces. Here, we are exploring properties of the overdamped drifted escape from finite intervals under the action of symmetric $\alpha$-stable noises. We show that the properly rescaled mean first passage time follows the universal pattern as a function of the generalized Pécklet number, which can be used to efficiently discriminate between domains where drift or random force dominate. Stochastic driving of the $\alpha$-stable type is capable of diminishing the significance of the drift in the regime when the drift prevails.

Whole-brain models offer a promising method of predicting seizure spread, which is critical for successful surgical treatment of focal epilepsy. Existing methods are largely based on structural connectome, which ignores the effects of heterogeneity within the regional excitability of brains. In this study we used a whole-brain model to show that heterogeneity in nodal excitability had a significant impact on seizure propagation in the networks and compromised the prediction accuracy with structural connections. We then addressed this problem with an algorithm based on random walk with restart on graphs. We demonstrated that by establishing a relationship between the restarting probability and the excitability for each node, this algorithm could significantly improve the seizure spread prediction accuracy in heterogeneous networks and was more robust against the extent of heterogeneity. We also strategized surgical seizure control as a process to identify and remove the key nodes (connections) responsible for the early spread of seizures from the focal region. Compared to strategies based on structural connections, virtual surgery with a strategy based on a modified random walk with extended restart generated outcomes with a high success rate while maintaining low damage to the brain by removing fewer anatomical connections. These findings may have potential applications in developing personalized surgery strategies for epilepsy.

We investigate theoretically the dynamics of a confined active swimmer with velocity and orientation axis coupled to each other via a self-alignment torque. For an isotropic harmonic potential, this system is known to exhibit two distinct dynamical phases: a climbing one, where the particle is oriented radially and undergoes angular Brownian motion, and a circularly orbiting phase. Here we show that for nonradially symmetric confinement an assortment of complex phenomena emerge. For an elliptic harmonic potential the orbiting phase splits into several periodic orbits with a diversity of shapes: ovals, lemniscates, and generalized lemniscates with multiple lobes. These orbits can coexist in the parameter space and decay into one another induced by noise. For anharmonic confining potentials, we report transitions from periodic to chaotic dynamics, as one changes the intensity of the self-alignment torque and noise-induced complex orbits. These results demonstrate that the combination of the shape of the trapping potential and self-alignment torque can induce a rich variety of nontrivial dynamical states of a confined active particle.

This paper presents a numerical study of the Gay-Berne liquid crystal model with parameters corresponding to calamitic (rod-shaped) molecules. The focus is on the isotropic and nematic phases at temperatures above unity, where we find strong correlations between the virial and potential-energy thermal fluctuations, reflecting the hidden scale invariance symmetry. This implies the existence of isomorphs, which are curves in the thermodynamic phase diagram of approximately invariant physics. We study numerically one isomorph in the isotropic phase and one in the nematic phase. In both cases, good invariance of the dynamics is demonstrated via data for the mean-square displacement and the reduced-unit time-autocorrelation functions of the velocity, angular velocity, force, torque, and first- and second-order Legendre polynomial orientational order parameters. Deviations from isomorph invariance are observed at short times for the orientational time-autocorrelation functions, which reflects the fact that the moment of inertia is assumed to be constant and thus not isomorph-invariant in reduced units. Structural isomorph invariance is demonstrated from data for the radial distribution functions of the molecules and their orientations. For comparison, all quantities were also simulated along an isochore of similar temperature variation, in which case invariance is not observed. We conclude that the thermodynamic phase diagram of the calamitic Gay-Berne model is essentially one-dimensional in the studied regions as predicted by isomorph theory, a fact that potentially allows for simplifications of future theories and numerical studies.

Height distributions (HDs) are key quantities to uncover universality and geometry-dependence in evolving interfaces. To quantitatively characterize HDs, one uses adimensional ratios of their first central moments ($m_n$) or cumulants (${\kappa }_n$), especially the skewness $S$ and kurtosis $K$, whose accurate estimate demands an averaging over all $L^d$ points of the height profile at a given time, in translation-invariant interfaces, and over $N$ independent samples. One way of doing this is by calculating $m_n\left(t\right)$ [or ${\kappa }_n\left(t\right)$] for each sample and then carrying out an average of them for the $N$ interfaces, with $S$ and $K$ being calculated only at the end. Another approach consists in directly calculating the ratios for each interface and, then, averaging the $N$ values. It turns out, however, that $S$ and $K$ for the growth regime HDs display strong finite-size and -time effects when estimated from these “interface statistics,” as already observed in some previous works and clearly shown here, through extensive simulations of several discrete growth models belonging to the EW and KPZ classes on one- and two-dimensional substrates of sizes $L=\text{const}.$ and $L\sim t$. Importantly, I demonstrate that with “1-point statistics,” i.e., by calculating $m_n\left(t\right)$ [or ${\kappa }_n\left(t\right)$] once for all $N{L}^d$ heights together, these corrections become very weak, so that $S$ and $K$ attain values very close to the asymptotic ones already at short times and for small $L$'s. However, I find that this “1-point” (1-pt) approach fails in uncovering the universality of the HDs in the steady-state regime (SSR) of systems whose average height, $\overline{h}$, is a fluctuating variable. In fact, as demonstrated here, in this regime the 1-pt height evolves as $h\left(t\right)=\overline{h}\left(t\right)+s_{\lambda }{A}^{1/2}{L}^{\alpha }\zeta +\cdots$—where $P\left(\zeta \right)$ is the underlying SSR HD—and the fluctuations in $\overline{h}$ yield $S_{1\text{-pt}}\sim t^{-1/2}$ and $K_{1\text{-pt}}\sim t^{-1}$. Nonetheless, by analyzing $P(h-\overline{h})$, the cumulants of $P\left(\zeta \right)$ can be accurately determined. I also show that different, but universal, asymptotic values for $S$ and $K$ (related, so, to different HDs) can be found from the “interface statistics” in the SSR. This reveals the importance of employing the various complementary approaches to reliably determine the universality class of a given system through its different HDs.