We study the segregation phenomena for oppositely driven colloidal particles in two-dimensional ring geometries by means of Brownian dynamics simulations without hydrodynamic interactions. The particles interact via a repulsive Yukawa potential and are confined to a two-dimensional circular channel by hard walls, in which half of the particles are driven clockwise and the other half are driven counterclockwise. In addition to lane formation, which is commonly found in oppositely driven systems, we found band formation along the angular direction in channels with a very large radius. This indicates that a formation of lanes is prevented in the limit of channels with an infinitely large inner radius. The dependency of this segregation has been examined for the two control parameters, the interaction strength between the particles and the width of the circular channel.

Magnetohydrodynamic turbulence is central to laboratory and astrophysical plasmas, and is invoked for interpreting many observed scalings. Verifying predicted scaling law behavior requires extreme-resolution direct numerical simulations (DNS), with needed computing resources excluding systematic parameter surveys. We here present an analytic generator of realistically looking turbulent magnetic fields, that computes three-dimensional (3D) $O\left({1000}^3\right)$ solenoidal vector fields in minutes to hours on desktop computers. Our model is inspired by recent developments in 3D incompressible fluid turbulence theory, where a Gaussian white noise vector subjected to a nonlinear transformation results in an intermittent, multifractal random field. Our $B\times C$ model has only few parameters that have clear geometric interpretations. We directly compare a (costly) DNS with a swiftly $B\times C$-generated realization, in terms of its (1) characteristic sheetlike structures of current density, (2) volume-filling aspects across current intensity, (3) power-spectral behavior, (4) probability distribution functions of increments for magnetic field and current density, structure functions, and spectra of exponents, and (5) partial variance of increments. The model even allows to mimic time-evolving magnetic and current density distributions and can be used for synthetic observations on 3D turbulent data cubes.

Using machine learning techniques, we introduce a Markov state model (MSM) for a model glass former that reveals structural heterogeneities and their slow dynamics by coarse-graining the molecular dynamics into a low-dimensional feature space. The transition timescale between states is larger than the conventional structural relaxation time ${\tau }_{\alpha }$, but can be obtained from trajectories much shorter than ${\tau }_{\alpha }$. The learned map of states assigned to the particles corresponds to local excess Voronoi volume. These results resonate with classic free volume theories of the glass transition, singling out local packing fluctuations as one of the dominant slowly relaxing features.

The two-dimensional $q$-state clock model for $q\ge 5$ undergoes two Berezinskii-Kosterlitz-Thouless (BKT) phase transitions as temperature decreases. Here we report an extensive worm-type simulation of the square-lattice clock model for $q=5$–9 in a pair of flow representations, from high- and low-temperature expansions, respectively. By finite-size scaling analysis of susceptibilitylike quantities, we determine the critical points with a precision improving over the existing results. Due to the dual flow representations, each point in the critical region is observed to simultaneously exhibit a pair of anomalous dimensions, which are ${\eta }_1=1/4$ and ${\eta }_2=4/q^2$ at the two BKT transitions. Further, the approximate self-dual points ${\beta }_{\mathrm{sd}}\left(L\right)$, defined by the stringent condition that the susceptibilitylike quantities in both flow representations are identical, are found to be nearly independent of system size $L$ and behave as ${\beta }_{\mathrm{sd}}\simeq q/2\pi$ asymptotically at the large-$q$ limit. The exponent $\eta$ at ${\beta }_{\mathrm{sd}}$ is consistent with $1/q$ within statistical error as long as $q\ge 5$. Based on this, we further conjecture that $\eta \left({\beta }_{\mathrm{sd}}\right)=1/q$ holds exactly and is universal for systems in the $q$-state clock universality class. Our work provides a vivid demonstration of rich phenomena associated with the duality and self-duality of the clock model in two dimensions.

Living cells employ excitable reaction-diffusion waves for internal cellular functions, in which curvature-inducing proteins are often involved. However, the role of their mechanochemical coupling is not well understood. Here, we report the membrane deformation induced by the excitable reaction-diffusion waves of curvature-inducing proteins and the alternation in the waves due to the deformation, using a coarse-grained simulation of tubular membranes with a modified FitzHugh-Nagumo model. Protein-propagating waves deform tubular membranes and large deformations induce budding and erase waves. The wave speed and shape are determined by a combination of membrane deformation and spatial distribution of the curvature-inducing protein. Waves are also undulated in the azimuthal direction depending on the condition. Rotationally symmetric waves locally deform the tubes into a symmetric shape but maintain a straight shape on average. Our simulation method can be applied to other chemical reaction models and used to investigate various biomembrane phenomena.

Acylphosphatase (AcP) is a small protein with 98 amino acid residues that catalyzes the hydrolysis of carboxyl-phosphate bonds. AcP is a typical two-state protein with slow folding rate due to its relatively large contact order in the native structure. The mechanical properties and unfolding behavior of AcP has been studied by atomic force microscope. Here using stable magnetic tweezers, we measured the force-dependent folding rates within a force range 1–3 pN, and unfolding rates 15–40 pN. The obtained unfolding rates show different force sensitivities at forces below and above ∼27 pN, which determines a free-energy landscape with two energy barriers. Our results indicate that the free-energy landscape of small globule proteins have general Bactrian camel shape, and large contact order of the native state produces a high barrier dominate at low forces.

We experimentally and theoretically investigate systems with a pair of source and inert particles that interact through a concentration field. The experimental system comprises a camphor disk as the source particle and a metal washer as the inert particle. Both are floated on an aqueous solution of glycerol at various concentrations, where the glycerol modifies the viscosity of the aqueous phase. The particles form a pair owing to the attractive lateral capillary force. As the camphor disk spreads surface-active molecules at the aqueous surface, the camphor disk and metal washer move together, driven by the surface tension gradient. The washer is situated in the front of the camphor disk, keeping the distance constant during their motion, which we call a pairing-induced motion. The pairing-induced motion exhibited a transition between circular and straight motions as the glycerol concentration in the aqueous phase changed. Numerical calculations using a model that considers forces caused by the surface tension gradient and lateral capillary interaction reproduced the observed transition in the pairing-induced motion. Moreover, this transition agrees with the result of the linear stability analysis on the reduced dynamical system obtained by the expansion with respect to the particle velocity. Our results reveal that the effect of the particle velocity cannot be overlooked to describe the interaction through the concentration field.

Mean-field models of glasses that present a random first order transition exhibit highly nontrivial fluctuations. Building on previous studies that focused on the critical scaling regime, we here obtain a fully quantitative framework for all equilibrium conditions. By means of the replica method we evaluate Gaussian fluctuations of the overlaps around the thermodynamic limit, decomposing them in thermal fluctuations inside each state and heterogeneous fluctuations between different states. We first test and compare our analytical results with numerical simulation results for the $p$-spin spherical model and the random orthogonal model, and then analyze the random Lorentz gas. In all cases, a strong quantitative agreement is obtained. Our analysis thus provides a robust scheme for identifying the key finite-size (or finite-dimensional) corrections to the mean-field treatment of these paradigmatic glass models.

We formulate a comprehensive hydrodynamic theory of two-dimensional liquid crystals with generic $p$-fold rotational symmetry, also known as $p$-atics, of which nematics $(p=2)$ and hexatics $(p=6)$ are the two best known examples. Previous hydrodynamic theories of $p$-atics are characterized by continuous $\mathrm{O}\left(2\right)$ rotational symmetry, which is higher than the discrete rotational symmetry of $p$-atic phases. By contrast, here we demonstrate that the discrete rotational symmetry allows the inclusion of additional terms in the hydrodynamic equations, which, in turn, lead to novel phenomena, such as the possibility of flow alignment at high shear rates, even for $p>2$. Furthermore, we show that any finite imposed shear will induce long-ranged orientational order in any $p$-atic liquid crystal, in contrast to the quasi-long-ranged order that occurs in the absence of shear. The induced order parameter scales like a nonuniversal power of the applied shear rate at small shear rates.

The geometry of walls forming a narrow pore may qualitatively affect the phase behavior of the confined fluid. Specifically, the nature of condensation in nanopores formed of sinusoidally shaped walls (with amplitude $A$ and period $P$) is governed by the wall mean separation $L$ as follows. For $L>L_t$, where $L_t$ increases with $A$, the pores exhibit standard capillary condensation similar to planar slits. In contrast, for $L<L_t$, the condensation occurs in two steps, such that the fluid first condenses locally via bridging transition connecting adjacent crests of the walls, before it condenses globally. For the marginal value of $L=L_t$, all the three phases (gaslike, bridge, and liquidlike) may coexist. We show that the locations of the phase transitions can be described using geometric arguments leading to modified Kelvin equations. However, for completely wet walls, to which we focus on, the phase boundaries are shifted significantly due to the presence of wetting layers. In order to take this into account, mesoscopic corrections to the macroscopic theory are proposed. The resulting predictions are shown to be in a very good agreement with a density-functional theory even for molecularly narrow pores. The limits of stability of the bridge phase, controlled by the pore geometry, is also discussed in some detail.

An important and incompletely answered question is whether machine learning methods can be used to discover the excitation of rogue waves (RWs) in nonlinear systems, especially their dynamic properties and phase transitions. In this work, a theory-guided neural network (TgNN) is constructed to explore the RWs of one-dimensional Bose-Einstein condensates. We find that such method is superior to the ordinary deep neural network due to theory guidance of underlying problems. The former can directly give any excited location, timing, and structure of RWs using only a small amount of dynamic evolution data as the training data, without the tedious step-by-step iterative calculation process. In addition, based on the TgNN approach, a phase transition boundary is also discovered, which clearly distinguishes the first-order RW phase from the non-RW phase. The results not only greatly reduce computational time for exploring RWs, but also provide a promising technique for discovering phase transitions in parameterized nonlinear systems.

We perform a quantitative analysis of Monte Carlo simulation results of phase separation in ternary blends upon evaporation of one component. Specifically, we calculate the average domain size and plot it as a function of simulation time to compute the exponent of the obtained power law. We compare and discuss results obtained by two different methods, for three different models: two-dimensional (2D) binary-state model (Ising model), 2D ternary-state model with and without evaporation. For the ternary-state models, we study additionally the dependence of the domain growth on concentration, temperature and initial composition. We reproduce the expected 1/3 exponent for the Ising model, while for the ternary-state model without evaporation and for the one with evaporation we obtain lower values of the exponent. It turns out that phase separation patterns that can form in this type of systems are complex. The obtained quantitative results give valuable insights towards devising computable theoretical estimations of size effects on morphologies as they occur in the context of organic solar cells.

We consider a class of nonlinear Langevin equations with additive, Gaussian white noise. Because of nonlinearity, the calculation of moments poses a serious problem for any direct solution of the Langevin equation. Based on multiple timescale analysis we introduce a scheme for directly solving the equations. We first derive the equations for the fast and slow dynamics, in the spirit of the Blekhman perturbation method in vibrational mechanics, the fast motion being described by the Brownian motion of a harmonic oscillator whose effect is subsumed in the slow motion resulting in a parametrically driven nonlinear oscillator. The multiple timescale perturbation theory is then used to obtain a secular divergence-free analytic solution for the slow nonlinear dynamics for calculation of the moments. Our analytical results for mean-square displacement are corroborated with direct numerical simulation of Langevin equations.

We propose a statistical test to identify nonstationary frequency-modulated stochastic processes from time-series data. Our method uses the instantaneous phase as a discriminatory statistics with reliable critical values derived from surrogate data. We simulated an oscillatory second-order autoregressive process to evaluate the size and power of the test. We found that the test we propose is able to correctly identify more than $99\%$ of nonstationary data when the frequency of the simulated data is doubled after the first half of the time series. Our method is easily interpretable, computationally cheap, and does not require choosing hyperparameters that are dependent on the data.

Unique electro-optical properties of the oblique helicoidal cholesteric (${\mathrm{Ch}}_{\mathrm{OH}}$) stem from its heliconical director structure. An applied electric field preserves the single-harmonic modulation of the director while tuning the ${\mathrm{Ch}}_{\mathrm{OH}}$ period and the corresponding Bragg-peak wavelength within a broad spectral range. We use the response of ${\mathrm{Ch}}_{\mathrm{OH}}$ to the electric field to measure the elastic constants of twist $K_{22}$ and bend $K_{33}$ directly in the cholesteric phase. The temperature dependencies of $K_{22}$ and $K_{33}$ allow us to determine the range of the electric tunability of the ${\mathrm{Ch}}_{\mathrm{OH}}$ pitch and the heliconical angle. The data are important for understanding how molecular composition and chirality influence macroscopic elastic properties of the chiral liquid crystals and for the development of ${\mathrm{Ch}}_{\mathrm{OH}}$-based optical devices.

Different regimes are usually observed for fluid migration through an immersed granular layer. In this work, we report a puzzling behavior when injecting water at a constant flow rate through a nozzle at the bottom of an immersed granular layer in a Hele-Shaw cell. In a given range of parameters (granular layer height and fluid flow rate) the granular bed is not only fluidized, but the particle-laden jet also exhibits periodic oscillations. The frequency and amplitude of the oscillations are quantified. The Strouhal number displays a power-law behavior as a function of a nondimensional parameter, $J$, defined as the ratio between the jet velocity at the initial granular bed height and the inertial particle velocity. Fluid-particle coupling is responsible for the jet oscillations. This mechanism could be at the origin of the cyclic behavior of pockmarks and mud volcanoes in sedimentary basins.

Despite the development of an extensive toolbox of multiscale rarefied flow simulators, such simulations remain challenging due to the significant disparity of collisional and macroscopic spatiotemporal scales. Our study offers a novel and consistent numerical scheme for a coupled treatment of particles advection and collision governed by the BGK evolution, honoring positivity of the velocity distribution. Our method shares its framework, in spirit, with the unified gas kinetic class of multiscale schemes. Yet it provides attractive features for particle-based stochastic simulations, readily implementable to existing direct simulation Monte Carlo codes. Two main innovations are integrated in the presented BGK particle method. The first ingredient is a high-order time integration that can be interpreted probabilistically, independent of the time step size. The next one is identifying modified particle distributions that remain invariant under the advection-relaxation evolution. We demonstrate accuracy and performance of the devised scheme for prototypic gas flows over a wide range of rarefaction parameters. Due to the resulting robustness and flexibility of the devised exponential BGK integrator, the scheme paves the way towards more affordable simulations of large-scale and multiscale rarefied gas phenomena.

In classical statistics, the bias-variance trade-off describes how varying a model's complexity (e.g., number of fit parameters) affects its ability to make accurate predictions. According to this trade-off, optimal performance is achieved when a model is expressive enough to capture trends in the data, yet not so complex that it overfits idiosyncratic features of the training data. Recently, it has become clear that this classic understanding of the bias variance must be fundamentally revisited in light of the incredible predictive performance of overparameterized models—models that avoid overfitting even when the number of fit parameters is large enough to perfectly fit the training data. Here, we present results for one of the simplest examples of an overparameterized model: regression with random linear features (i.e., a two-layer neural network with a linear activation function). Using the zero-temperature cavity method, we derive analytic expressions for the training error, test error, bias, and variance. We show that the linear random features model exhibits three phase transitions: two different transitions to an interpolation regime where the training error is zero, along with an additional transition between regimes with large bias and minimal bias. Using random matrix theory, we show how each transition arises due to small nonzero eigenvalues in the Hessian matrix. Finally, we compare and contrast the phase diagram of the random linear features model to the random nonlinear features model and ordinary regression, highlighting the additional phase transitions that result from the use of linear basis functions.