Active processes play a major role in the formation of membraneless cellular structures (biological condensates). Classical coarsening theory predicts that only a single droplet remains following Ostwald ripening. However, in both the cell nucleus and cytoplasm there coexist several membraneless organelles of the same basic composition, suggesting that there is some mechanism for suppressing Ostwald ripening. One potential candidate is the active regulation of liquid-liquid phase separation by enzymatic reactions that switch proteins between different conformational states (e.g., different levels of phosphorylation). Recent theoretical studies have used mean-field methods to analyze the suppression of Ostwald ripening in three-dimensional (3D) systems consisting of a solute that switches between two different conformational states, an $S$ state that does not phase separate and a $P$ state that does. However, mean-field theory breaks down in the case of 2D systems, since the concentration around a droplet varies as $lnR$ rather than $R^{-1}$, where $R$ is the distance from the center of the droplet. It also fails to capture finite-size effects. In this paper we show how to go beyond mean-field theory by using the theory of diffusion in domains with small holes or exclusions (strongly localized perturbations). In particular, we use asymptotic methods to study the suppression of Ostwald ripening in a 2D or 3D solution undergoing active liquid-liquid phase separation. We proceed by partitioning the region outside the droplets into a set of inner regions around each droplet together with an outer region where mean-field interactions occur. Asymptotically matching the inner and outer solutions, we derive leading-order conditions for the existence and stability of a multidroplet steady state. We also show how finite-size effects can be incorporated into the theory by including higher-order terms in the asymptotic expansion, which depend on the positions of the droplets and the boundary of the 2D or 3D domain. The theoretical framework developed in this paper provides a general method for analyzing active phase separation for dilute droplets in bounded domains such as those found in living cells.

We use a continuous mesoscopic model to address the yielding properties of plastic composites, formed by a host material and inclusions with different elastic and/or plastic properties. We investigate the flow properties of the composed material under a uniform externally applied deviatoric stress. We show that due to the heterogeneities induced by the inclusions, a scalar modeling in terms of a single deviatoric strain of the same symmetry as the externally applied deformation gives inaccurate results. A realistic modeling must include all possible shear deformations. Implementing this model in a two-dimensional system, we show that the effect of harder inclusions is very weak to relatively high concentrations. For softer inclusions instead, the effect is much stronger; even a small concentration of inclusions affecting the form of the flow curve and the critical stress. We also present the details of a full three-dimensional simulation scheme and obtain the corresponding results for harder and softer inclusions.

The interaction between the oscillatory boundary-layer flow induced by Faraday waves and a sedimentary granular layer was studied in a Hele-Shaw cell vertically vibrated. The experimental parameters were the vibration frequency $f$ and acceleration $a$ and the particle diameter $d_p$. At a critical value for the depth of the supernatant fluid layer $\mathrm{\Delta }{h}_c$, a transition between a flat motionless granular layer and a second regime in which the granular layer undulates and oscillates periodically was observed. For the smallest value of $d_p$ (for which the Stokes number was $\text{St}\ll 1$) the reduced acceleration $\mathrm{\Gamma }=a/g$ ($g$ is the acceleration of gravity) is independent of $\mathrm{\Delta }{h}_c$, while for the larger ones, $\mathrm{\Gamma }$ depends linearly on $\mathrm{\Delta }{h}_c$. Finally, it is shown that at the onset of grain motion, the wave velocity $V_w=h_{w}f/2$ ($h_w$ is the wave amplitude) depends linearly on $\mathrm{\Delta }{h}_c$ and is independent of $d_p$.

The time-dependent behavior of one-dimensional ion transport into a permselective medium is theoretically modeled in this work for currents exceeding the diffusion limit. Leveraging the findings of Yariv [E. Yariv, Phys. Rev. E 80, 051201 (2009)], we derive three separate expressions for the potential drop for short, intermediate, and long times. We show that the potential drop correlates to the time evolution of the space-charge layer adjacent to the permselective interface. Our approximate models show remarkable correspondence to numerical simulations.

When a droplet impacts on a substrate, the air underneath the droplet is compressed to form an air layer of a dimple shape before the droplet wets the substrate. This air layer is important to the impact dynamics, and many studies have been performed to investigate the air layer during the impact process on unheated substrates. In this experimental study of the air layer, our results reveal that the air layer is profoundly affected by the substrate temperature, even if the substrate temperature is below the boiling point of the droplet fluid. We use high-speed imaging and color interferometry to measure the air layer with nanometer accuracy. The results show that the thickness of the air layer increases with increasing the substrate temperature. Compared with the impact of the droplet on the unheated substrate, the average thickness of the air layer on the heated substrate at 70 °C is about 12% thicker. This will affect the subsequent bubble entrapment, which is an important feature of the impact dynamics. A simplified model is proposed to consider the heat transfer in the air layer. Additionally, the effects of the Weber number, the fluid viscosity, and the size of the droplet on the air layer are also analyzed. This study sheds light on controlling the impact dynamics of droplets by adjusting the substrate temperature.

We derive the exact relation for the energy transfer in three-dimensional compressible two-fluid plasma turbulence. In the long-time limit, we obtain an exact law which expresses the scale-to-scale average energy flux rate in terms of two point increments of the fluid variables of each species, electric and magnetic field and current density, and puts a strong constraint on the turbulent dynamics. The incompressible single fluid and two-fluid limits and the compressible single fluid limit are recovered under appropriate assumption. In the single fluid limits, analyses are done with and without neglecting the electron mass thereby making the exact relation suitable for a broader range of application. In the compressible two-fluid regime, the total energy flux rate, unlike the single fluid case, is found to be unaltered by the presence of a background magnetic field. The exact relation provides a way to test whether a range of scales in a plasma is inertial or dissipative and is essential to understand the nonlinear nature of both space and dilute astrophysical plasmas.

Three-dimensionally extended dusty plasmas containing mixtures of two particle species of different size have been investigated under microgravity conditions. To distinguish the species even at small size disparities, one of the species is marked with a fluorescent dye, and a modified two-camera video microscopy setup is used for position determination and tracking. Phase separation is found even when the size disparity is below $5\%$. Particles are tracked to obtain the diffusion flux, and resulting diffusion coefficients are calculated to be about $-{10}^{-6}{\mathrm{mm}}^2/\mathrm{s}$, which is in the expected range for a phase separation process driven by plasma forces. Additionally, a measure for the strength of the phase separation is presented that allows us to quickly characterize measurements. There is a clear correlation between size disparity and phase separation strength.

Multibeam absolute instability thresholds for stimulated Raman scattering (SRS) and two-plasmon decay (TPD) are calculated in three dimensions for conditions relevant to direct-drive inertial confinement fusion experiments on the OMEGA laser and at the National Ignition Facility (NIF). Although multibeam effects are found to be significant for both instabilities, SRS is found to have less efficient multibeam coupling than TPD. The results are consistent with the observation of a TPD-dominated regime on the OMEGA laser and a SRS-dominated regime on the NIF despite the single-beam SRS threshold being lower than the single-beam TPD threshold on both facilities. The minimum instability threshold for NIF plasma parameters occurs for SRS near quarter-critical densities with a shared electromagnetic wave propagating along the beam axis.

We present an algorithm to efficiently sample first-passage times for fractional Brownian motion. To increase the resolution, an initial coarse lattice is successively refined close to the target, by adding exactly sampled midpoints, where the probability that they reach the target is non-negligible. Compared to a path of $N$ equally spaced points, the algorithm achieves the same numerical accuracy $N_{\mathrm{eff}}$, while sampling only a small fraction of all points. Though this induces a statistical error, the latter is bounded for each bridge, allowing us to bound the total error rate by a number of our choice, say $P_{\mathrm{error}}^{\mathrm{tot}}={10}^{-6}$. This leads to significant improvements in both memory and speed. For $H=0.33$ and $N_{\mathrm{eff}}=2^{32}$, we need $5000$ times less CPU time and $10000$ times less memory than the classical Davies-Harte algorithm. The gain grows for $H=0.25$ and $N_{\mathrm{eff}}=2^{42}$ to $3\times {10}^5$ for CPU and ${10}^6$ for memory. We estimate our algorithmic complexity as ${\mathcal{C}}^{\mathrm{ABSec}}\left(N_{\mathrm{eff}}\right)=O\left[{\left(ln{N}_{\mathrm{eff}}\right)}^3\right]$, to be compared to Davies-Harte, which has complexity ${\mathcal{C}}^{\mathrm{DH}}\left(N\right)=O\left(NlnN\right)$. Decreasing $P_{\mathrm{error}}^{\mathrm{tot}}$ results in a small increase in complexity, proportional to $ln(1/P_{\mathrm{error}}^{\mathrm{tot}})$. Our current implementation is limited to the values of $N_{\mathrm{eff}}$ given above, due to a loss of floating-point precision. Our algorithm can be adapted to other extreme events and arbitrary Gaussian processes. It enables one to numerically validate theoretical predictions that were hitherto inaccessible.

We compute the spectral form factor of two integrable quantum-critical many-body systems in one spatial dimension. The spectral form factor of the quantum Ising chain is periodic in time in the scaling limit described by a conformal field theory; we also compute corrections from lattice effects and deviation from criticality. Criticality in the random Ising chain is described by rare regions associated with a strong randomness fixed point, and these control the long-time limit of the spectral form factor.

We examine statistical properties of a laser beam propagating in a turbulent medium. We prove that the intensity fluctuations at large propagation distances possess a Gaussian probability density function and establish quantitative criteria for realizing the Gaussian statistics depending on the laser propagation distance, laser beam waist, laser frequency, and turbulence strength. We calculate explicitly the laser envelope pair correlation function and corrections to its higher-order correlation functions breaking Gaussianity. We discuss also statistical properties of the brightest spots in the speckle pattern.

We numerically study the spatiotemporal dynamics and predictability of a buoyancy-driven turbulent fire. A significant transition from order to disorder structures can be observed from the mean degree in the spatial horizontal visibility graph. The gravitational term (baroclinic torque term) in the vorticity equation has a significant impact on the formation of the order (disorder) structure in the near field (far field). The entropy flow transport from temperature to flow velocity fluctuations is predominant near the interface between hot combustion products and ambient air. The transfer entropy is an important measure for determining the predictability of flow velocity fluctuations in the near field obtained by reservoir computing.

A shock that is continuously driven by a moving exciter will propagate at a speed that depends on the exciter speed. We obtained this dependence experimentally, in a strongly coupled dusty plasma that was prepared as a single two-dimensional layer of charged microparticles. Attaining this result required an experimental advance, developing a method of driving a shock continuously, which we did using an exciter moving at a constant supersonic speed, analogous to a piston in a cylinder. The resulting compressional pulse was a shock that propagated steadily without weakening, ahead of the moving exciter. We compare our experimental results to an empirical form $M_{\mathrm{shock}}=1+s{M}_{\mathrm{exciter}}$, and to the prediction of a recent simulation.

In this research, the development of a pseudopotential multicomponent model with the capability of simulating high-viscosity-ratio flows is discussed and examined. The proposed method is developed based on the non-orthogonal central moments model in the lattice Boltzmann method, and the exact difference model (EDM) is used to apply the intercomponent interaction force. In contrast to the original Shan-Chen model, in which the applying force has the viscosity-dependent error term, the error term of this model does not depend on the viscosity. A GPU parallel cuda code has been developed and is employed to study the proposed method. Different cases are considered to evaluate the ability of the model, including the Laplace test, a static droplet, and a two-component concurrent channel flow. Also, wetting and nonwetting relative permeabilities for flows with dynamic viscosity ratios between 0.0002 and 5000 are predicted. Numerical results are compared with those of available analytical solutions. Very good agreement between these results are observed. The model has the capability of simulating multicomponent flows with very low kinematic viscosities of the order of ${10}^{-5}$ and dynamic viscosity ratios of up to an order of ${10}^4$, which is a much wider range compared with that of existing pseudopotential models. Furthermore, the results showed that the parallel processing on GPU significantly accelerated computations. The present parallel performance evaluation shows that the cuda parallel can achieve about 41 times improvement than the CPU serial implementation. The aforementioned enhancement increases the flexibility of the multicomponent lattice Boltzmann method and its applicability to a broader spectrum of engineering applications.

A parallel array of wrinkles can be generated in a simple parallel plate capacitor arrangement with a soft dielectric elastomer plate constrained all around its periphery and coated with flexible electrodes. The direction of the wrinkles is predetermined and the phenomenon is reversible in a range of applied potentials. A model of the wrinkled plate as a prestretched neo-Hookean membrane with superposed small out-of-plane bending displacements yields good estimates of the potential range for wrinkling as well as the number of parallel wrinkles. The mechanics is controlled by the thickness and aspect ratios, prestretch, and a nondimensional electric potential.

Characterization of the non-Arrhenius behavior of glass-forming liquids is a broad avenue for research toward the understanding of the formation mechanisms of noncrystalline materials. In this context, this paper explores the main properties of the viscosity of glass-forming systems, considering super-Arrhenius diffusive processes. We establish the viscous activation energy as a function of the temperature, measure the degree of fragility of the system, and characterize the fragile-to-strong transition through the standard Angell's plot. Our results show that the non-Arrhenius behavior observed in fragile liquids can be understood through the non-Markovian dynamics that characterize the diffusive processes of these systems. Moreover, the fragile-to-strong transition corresponds to a change in the spatiotemporal range of correlations during the glass transition process.

An explicit expression for the temperature of an open two-level quantum system is obtained as a function of local properties under the hypothesis of weak interaction with the environment. This temperature is defined for both equilibrium and out-of-equilibrium states and coincides with the environment temperature if the system reaches thermal equilibrium with a heat reservoir. Additionally, we show that within this theoretical framework the total entropy production can be partitioned into two contributions: one due to heat transfer and another, associated to internal irreversibilities, related to the loss of internal coherence by the qubit. The positiveness of the heat capacity is established, as well as its consistency with the well-known results at thermal equilibrium. We apply these concepts to two different systems and show that they behave in analogous ways as their classical counterparts.

Diffusion in a quenched heterogeneous environment in the presence of bias is considered analytically. The first-passage-time statistics can be applied to obtain the drift and the diffusion coefficient in periodic quenched environments. We show several transition points at which sample-to-sample fluctuations of the drifts or the diffusion coefficients remain large even when the system size becomes large, i.e., non-self-averaging. Moreover, we find that the disorder average of the diffusion coefficient diverges or becomes 0 when the corresponding annealed model generates superdiffusion or subdiffusion, respectively. This result implies that anomalous diffusion in an annealed model is traced by anomaly of the diffusion coefficients in the corresponding quenched model.

We theoretically propose a simple setup based on a three-terminal triple quantum dot in the Coulomb blockade regime as a heat-flow allocator to spatially separate heat flow along two different channels at arbitrary proportion. We show that a constant output heat-flow ratio can be obtained in a wide range of system parameters, and any ratio of the output heat flow, whether it is an integer ratio or a fractional ratio, can be obtained by directly adjusting the ratio of the energy-dependent tunneling rate.

Using the integral transformation, the field-theoretical Hamiltonian of the statistical field theory of fluids is obtained along with the microscopic expressions for the coefficients of the Hamiltonian. Applying this approach to the liquid-vapor interface, we derive an explicit analytical expression for the surface tension in terms of temperature, density, and parameters of the intermolecular potential. We also demonstrate that a clear physical interpretation may be given to the formal statistical field arising in the integral transformation—it may be associated with the one-body local microscopic potential. The results of the theory, lacking any ad hoc or fitting parameters are in good agreement with available simulation data.