We present a general geometrical approach to the problem of escape from a metastable state in the presence of noise. The accompanying analysis leads to a simple condition, based on the norm of the drift field, for determining whether caustic singularities alter the escape trajectories when detailed balance is absent. We apply our methods to systems lacking detailed balance, including a nanomagnet with a biaxial magnetic anisotropy and subject to a spin-transfer torque. The approach described within allows determination of the regions of experimental parameter space that admit caustics.

We study the problem of a particle hopping on the Bethe lattice in the presence of a Coulomb potential. We obtain an exact solution to the particle's Green's function along with the full energy spectrum. In addition, we present a mapping of a generalized radial potential problem defined on the Bethe lattice to an infinite number of one-dimensional problems that are easily accessible numerically. The latter method is particularly useful when the problem admits no analytical solution.

We have studied the connectivity percolation transition in suspensions of attractive square-well spherocylinders by means of Monte Carlo simulation and connectedness percolation theory. In the 1980s the percolation threshold of slender fibers has been predicted to scale as the fibers' inverse aspect ratio [Phys. Rev. B 30, 3933 (1984)]. The main finding of our study is that the attractive spherocylinder system reaches this inverse scaling regime at much lower aspect ratios than found in suspensions of hard spherocylinders. We explain this difference by showing that third virial corrections of the pair connectedness functions, which are responsible for the deviation from the scaling regime, are less important for attractive potentials than for hard particles.

In systems exhibiting fluctuation-dominated phase ordering, a single order parameter does not suffice to characterize the order, and it is necessary to monitor a larger set. For hard-core sliding particles on a fluctuating surface and the related coarse-grained depth (CD) models, this set comprises the long-wavelength Fourier components of the density profile, which capture the breakup and remerging of particle-rich regions. We study both static and dynamic scaling laws obeyed by the Fourier modes $Q_{mL}$ and find that the mean value obeys the static scaling law $\langle Q_{mL}\rangle \sim L^{-\varphi }f(m/L)$ with $\varphi \simeq 2/3$ and $\varphi \simeq 3/5$ for Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) surface evolution, respectively, and $\varphi \simeq 3/4$ for the CD model. The full probability distribution $P\left(Q_{mL}\right)$ exhibits scaling as well. Further, time-dependent correlation functions such as the steady-state autocorrelation and cross-correlations of order-parameter components are scaling functions of $t/L^z$, where $L$ is the system size and $z$ is the dynamic exponent, with $z=2$ for EW and $z=3/2$ for KPZ surface evolution. In addition we find that the CD model shows temporal intermittency, manifested in the dynamical structure functions of the density and the weak divergence of the flatness as the scaled time approaches 0.

Ising spin glasses with bimodal and Gaussian near-neighbor interaction distributions are studied through numerical simulations. The non-self-averaging (normalized intersample variance) parameter $U_{22}(T,L)$ for the spin glass susceptibility [and for higher moments $U_{nn}(T,L)]$ is reported for dimensions $2,3,4,5$, and 7. In each dimension $d$ the non-self-averaging parameters in the paramagnetic regime vary with the sample size $L$ and the correlation length $\xi (T,L)$ as $U_{nn}(\beta ,L)={[K_d\xi (T,L)/L]}^d$ and so follow a renormalization group law due to Aharony and Harris [Phys. Rev. Lett. 77, 3700 (1996)]. Empirically, it is found that the $K_d$ values are independent of $d$ to within the statistics. The maximum values ${\left[U_{nn}(T,L)\right]}_{max}$ are almost independent of $L$ in each dimension, and remarkably the estimated thermodynamic limit critical ${\left[U_{nn}(T,L)\right]}_{max}$ peak values are also practically dimension-independent to within the statistics and so are “hyperuniversal.” These results show that the form of the spin-spin correlation function distribution at criticality in the large $L$ limit is independent of dimension within the ISG family. Inspection of published non-self-averaging data for three-dimensional Heisenberg and $XY$ spin glasses the light of the Ising spin glass non-self-averaging results show behavior which appears to be compatible with that expected on a chiral-driven ordering interpretation but incompatible with a spin-driven ordering scenario.

We investigate simple one-dimensional driven diffusive systems with open boundaries. We are interested in the average on-site residence time defined as the time a particle spends on a given site before moving on to the next site. Using mean-field theory, we obtain an analytical expression for the on-site residence times. By comparing the analytic predictions with numerics, we demonstrate that the mean-field significantly underestimates the residence time due to the neglect of time correlations in the local density of particles. The temporal correlations are particularly long-lived near the average shock position, where the density changes abruptly from low to high. By using domain wall theory, we obtain highly accurate estimates of the residence time for different boundary conditions. We apply our analytical approach to residence times in a totally asymmetric exclusion process (TASEP), TASEP coupled to Langmuir kinetics $(\mathrm{TASEP}+\mathrm{LK})$, and TASEP coupled to mutually interactive LK $(\mathrm{TASEP}+\mathrm{MILK})$. The high accuracy of our predictions is verified by comparing these with detailed Monte Carlo simulations.

We uncover an optimization principle for the finite-time heat-work conversion process performed between two finite-sized heat reservoirs in the nonlinear response regime that is characterized by rather generic flux-force relations. We solve the problem of maximizing work output in a given time interval by means of the variational method. Moreover, in the limiting case that the cold reservoir is infinite, we find the corresponding optimized process can be determined by a single quantity, which plays the role similar to that of the Hamiltonian in classical mechanics. Some theoretical implications are discussed consequently, under the generalized tight-coupling condition which applies to both linear and nonlinear response cases. Our results can hopefully help design and control realistic thermodynamical processes.

We study the existence of chimera states in pulse-coupled networks of bursting Hindmarsh-Rose neurons with nonlocal, global, and local (nearest neighbor) couplings. Through a linear stability analysis, we discuss the behavior of the stability function in the incoherent (i.e., disorder), coherent, chimera, and multichimera states. Surprisingly, we find that chimera and multichimera states occur even using local nearest neighbor interaction in a network of identical bursting neurons alone. This is in contrast with the existence of chimera states in populations of nonlocally or globally coupled oscillators. A chemical synaptic coupling function is used which plays a key role in the emergence of chimera states in bursting neurons. The existence of chimera, multichimera, coherent, and disordered states is confirmed by means of the recently introduced statistical measures and mean phase velocity.

We study the infinite integrable nonlinear Schrödinger equation hierarchy beyond the Lakshmanan-Porsezian-Daniel equation which is a particular (fourth-order) case of the hierarchy. In particular, we present the generalized Lax pair and generalized soliton solutions, plane wave solutions, Akhmediev breathers, Kuznetsov-Ma breathers, periodic solutions, and rogue wave solutions for this infinite-order hierarchy. We find that “even- order” equations in the set affect phase and “stretching factors” in the solutions, while “odd-order” equations affect the velocities. Hence odd-order equation solutions can be real functions, while even-order equation solutions are always complex.

Empirical networks of weighted dyadic relations often contain “noisy” edges that alter the global characteristics of the network and obfuscate the most important structures therein. Graph pruning is the process of identifying the most significant edges according to a generative null model and extracting the subgraph consisting of those edges. Here, we focus on integer-weighted graphs commonly arising when weights count the occurrences of an “event” relating the nodes. We introduce a simple and intuitive null model related to the configuration model of network generation and derive two significance filters from it: the marginal likelihood filter (MLF) and the global likelihood filter (GLF). The former is a fast algorithm assigning a significance score to each edge based on the marginal distribution of edge weights, whereas the latter is an ensemble approach which takes into account the correlations among edges. We apply these filters to the network of air traffic volume between US airports and recover a geographically faithful representation of the graph. Furthermore, compared with thresholding based on edge weight, we show that our filters extract a larger and significantly sparser giant component.

Some biological bonds exhibit a so-called catch regime, where the bond strengthens with increasing load. We build upon recent advances in slip-bond kinetics to develop an analytically tractable, microscopic catch-slip bond model. To facilitate the analysis of force-spectroscopy data, we calculate the bond's mean lifetime and the rupture-force distribution for static loading and linear force ramps. Our results are applicable for arbitrary forces and loading rates, covering the whole range of conditions found in experiments and all-atom simulations. A generalization to account for force transducers of finite stiffness is also provided.

The properties of a front between two different phases in the presence of a smoothly inhomogeneous external field that takes its critical value at the crossing point is analyzed. Two generic scenarios are studied. In the first, the system admits a bistable solution and the external field governs the rate in which one phase invades the other. The second mechanism corresponds to a continuous transition that, in the case of reactive systems, takes the form of a transcritical bifurcation at the crossing point. We solve for the front shape and for the response of competitive fronts to external noise, showing that static properties and also some of the dynamical features cannot discriminate between the two scenarios. A reliable indicator turns out to be the fluctuation statistics. These take a Gaussian form in the bifurcation case and a double-peaked shape in a bistable system. Our results are discussed in the context of biological processes, such as species and communities dynamics in the presence of a resource gradient.

Nonlinear dynamics induced in surface stabilized ferroelectric liquid crystals by strong alternating external electric fields is studied both theoretically and experimentally. As has already been shown, molecular reorientations induced by sufficiently strong fields of high-enough frequencies can reveal a long transient behavior that has a weakly chaotic character. The resulting complex dynamics of ferroelectric liquid crystals can be considered not only as a consequence of irregular motions of particular molecules but also as a repercussion of a surface-enforced partial decorrelation of nonlinear molecular motions within smectic layers. To achieve more insight into the nature of this phenomenon and to show that the underlying complex field-induced behavior of smectic liquid crystals is not exceptional, ranges of system parameters for which the chaotic behavior occurs are determined. It is proved that there exists a large enough set of initial phase trajectory points, for which weakly chaotic long-time transitory phenomena occur, and, thereby, it is demonstrated that such a chaotic behavior can be regarded as being typical for strongly field-driven thin liquid crystal systems. Additionally, the influence of low-amplitude random noise on the duration of the transient processes is numerically studied. The strongly nonlinear contribution to the electro-optic response, experimentally determined for liquid crystal samples at frequencies lower than the actual field frequency, is also analyzed for long-time signal sequences. Using a statistical approach to distinguish numerically response signals of samples from noise generated by measuring devices, it is shown that the distribution of sample signals distinctly differs from the device noise. This evidently corroborates the occurrence of the nonlinear low-frequency effect, found earlier for different surface stabilized liquid crystal samples.

We perform molecular dynamics simulations of the orientational ordering on nematic shells delimited by spherocylindrical nanoscopic colloidal particles. We show that under conditions of degenerate planar anchoring, the equilibrium director field structure in these shells exhibits pairs of $+1/2$ topological defects at the poles of spherical cups in the absence of an external electric field. In addition, a certain number of pairs of $\pm 1/2$ defects occurs on the spherical cups far from the poles, thus resulting in a total of eight valence spots. A strong field applied along the main spherocylindrical axis removes the $\pm 1/2$ defect pairs while it coalesces the polar ones into a single $+1$ topological defect. A strong transverse field destroys all defects on the spherical cups but generates four $+1/2$ defects in the cylindrical part. Therefore, an external field can be used to control the number of valence centers in spherocylindrical nematic shells, thus unveiling their capability of acting as multivalent building blocks for nanophotonic devices.

We propose a theoretical framework for predicting the protocol dependence of the jamming transition for frictionless spherical particles that interact via repulsive contact forces. We study isostatic jammed disk packings obtained via two protocols: isotropic compression and simple shear. We show that for frictionless systems, all jammed packings can be obtained via either protocol. However, the probability to obtain a particular jammed packing depends on the packing-generation protocol. We predict the average shear strain required to jam initially unjammed isotropically compressed packings from the density of jammed packings, shape of their basins of attraction, and path traversed in configuration space. We compare our predictions to simulations of shear strain-induced jamming and find quantitative agreement. We also show that the packing fraction range, over which shear strain-induced jamming occurs, tends to zero in the large system limit for frictionless packings with overdamped dynamics.

The jamming transition of particles with finite-range interactions is characterized by a variety of critical phenomena, including power-law distributions of marginal contacts. We numerically study a recently proposed simple model of jamming, which is conjectured to lie in the same universality class as the jamming of spheres in all dimensions. We extract numerical estimates of the critical exponents, $\theta =0.451\pm 0.006$ and $\gamma =0.404\pm 0.004$, that match the exponents observed in sphere packing systems. We analyze finite-size scaling effects that manifest in a subcritical cutoff regime and size-independent but protocol-dependent scaling curves. Our results support the conjectured link with sphere jamming, provide more precise measurements of the critical exponents than previously reported, and shed light on the finite-size scaling behavior of continuous constraint satisfiability transitions.

We study theoretically the erosion threshold of a granular bed forced by a viscous fluid. We first introduce a model of interacting particles driven on a rough substrate. It predicts a continuous transition at some threshold forcing ${\theta }_c$, beyond which the particle current grows linearly $J\sim \theta -{\theta }_c$. The stationary state is reached after a transient time $t_{\mathrm{conv}}$ which diverges near the transition as $t_{\mathrm{conv}}\sim {|\theta -{\theta }_c|}^{-z}$ with $z\approx 2.5$. Both features are consistent with experiments. The model also makes quantitative testable predictions for the drainage pattern: The distribution $P\left(\sigma \right)$ of local current is found to be extremely broad with $P\left(\sigma \right)\sim J/\sigma$, and spatial correlations for the current are negligible in the direction transverse to forcing, but long-range parallel to it. We explain some of these features using a scaling argument and a mean-field approximation that builds an analogy with $q$ models. We discuss the relationship between our erosion model and models for the plastic depinning transition of vortex lattices in dirty superconductors, where our results may also apply.

By grinding crystals in a solution, the chirality of crystal structure (and the molecular chirality for the case of chiral molecules as well) can be converted, and the cause of the phenomenon is attributed to crystal growth with chiral clusters. We show that the recently found chirality conversion with a periodic change of temperature can also be explained by crystal growth with chiral clusters. With the use of a generalized Becker-Döring model, which includes enantio-selective incorporation of small chiral clusters to large solid clusters, the change of cluster distribution and the mass flow between clusters are studied. The chiral clusters act as a reservoir to pump out the minority species to the majority, and the exponential amplification of the enantiomeric excess found in the experiment is reproduced in the numerical calculation.

Velocity distribution functions link the micro- and macro-level theories of fluid flow through porous media. Here we study them for the fluid absolute velocity and its longitudinal and lateral components relative to the macroscopic flow direction in a model of a random porous medium. We claim that all distributions follow the power-exponential law controlled by an exponent $\gamma$ and a shift parameter $u_0$ and examine how these parameters depend on the porosity. We find that $\gamma$ has a universal value $1/2$ at the percolation threshold and grows with the porosity, but never exceeds 2.

Direct numerical simulations are performed of turbulent planar Couette flow which are seeded with two-way coupled particles at low volume concentration. Based on an understanding of the development of particle stress (horizontal momentum carried vertically on average by the particle phase) in monodisperse systems at various particle Stokes numbers, several bidisperse and continuously polydisperse systems are simulated which are chosen to understand how flows containing blends of particle Stokes numbers can be effectively modeled in the dilute regime. Under noninteracting conditions, the particle stresses from particles with different inertia and different feedback stresses are shown to be linearly additive, providing a convenient method for effectively representing dispersed phase stress in polydisperse systems. While this is true, it is demonstrated that a single effective particle size is in general not sufficient at representing the entire mixture.