Notes

"Five-Early" Design: The Magic Gun versus COVID-19.
Geometric frustration results from a discrepancy between the locally favored arrangement of the constituents of a system and the geometry of the embedding space. Geometric frustration can be either noncumulative, which implies an extensive energy growth, or cumulative, which implies superextensive energy scaling and highly cooperative ground-state configurations which may depend on the dimensions of the system. Cumulative geometric frustration was identified in a variety of continuous systems including liquid crystals, filament bundles, and molecular crystals. However, a spin-lattice model which clearly demonstrates cumulative geometric frustration was lacking. In this paper we describe a nonlinear variation of the XY-spin model on a triangular lattice that displays cumulative geometric frustration. The model is studied numerically and analyzed in three distinct parameter regimes, which are associated with different energy minimizing configurations. We show that, despite the difference in the ground-state structure in the different regimes, in all cases the superextensive power-law growth of the frustration energy for small domains grows with the same universal exponent that is predicted from the structure of the underlying compatibility condition.We applied an alternative method for measuring characteristic lengths reported recently by one of us [J. M. Kim, J. Stat. Mech. (2021) 03321310.1088/1742-5468/abe599] to the models in the Manna universality class, i.e., the stochastic Manna sandpile and conserved lattice gas models in various dimensions. The universality of the Manna model has been under long debate particularly in one dimension since the work of M. Basu et al. [Phys. Rev. Lett. 109, 015702 (2012)10.1103/PhysRevLett.109.015702], who claimed that the Manna model belongs to the directed percolation (DP) universality class and that the independent Manna universality class does not exist. We carried out Monte Carlo simulations for the stochastic Manna sandpile model in one, two, and three dimensions and the conserved lattice gas model in three dimensions, using both the natural initial states (NISs) and uniform initial states (UISs). In two and three dimensions, the results for R(t), defined by R(t)=L[〈ρ_a^2〉/〈ρ_a〉^2-1]^1/d, L and ρ_a being, respectively, the system size and activity density, yielded consistent results for the two initial states. R(t) is proportional to the correlation length following R(t)∼t^1/z at the critical point. In one dimension, the data of R(t) for the Manna model using NISs yielded anomalous behavior, suggesting that NISs require much longer prerun time steps to homogenize the distribution of particles and larger systems to eliminate the finite-size effect than those employed in the literature. On the other hand, data from UISs yielded a power-law behavior, and the estimated critical exponents differed from the values in the DP class.We derive universal bounds for the finite-time survival probability of the stochastic work extracted in steady-state heat engines and the stochastic heat dissipated to the environment. We also find estimates for the time-dependent thresholds that these quantities do not surpass with a prescribed probability. At long times, the tightest thresholds are proportional to the large deviation functions of stochastic entropy production. Our results entail an extension of martingale theory for entropy production, for which we derive universal inequalities involving its maximum and minimum statistics that are valid for generic Markovian dynamics in nonequilibrium stationary states. We test our main results with numerical simulations of a stochastic photoelectric device.The two-dimensional Loewner exploration process is generalized to the case where the random force is self-similar with positively correlated increments. We model this random force by a fractional Brownian motion with Hurst exponent H≥1/2≡H_BM, where H_BM stands for the one-dimensional Brownian motion. By manipulating the deterministic force, we design a scale-invariant equation describing self-similar traces which lack conformal invariance. The model is investigated in terms of the "input diffusivity parameter" κ, which coincides with the one of the ordinary Schramm-Loewner evolution (SLE) at H=H_BM. In our numerical investigation, we focus on the scaling properties of the traces generated for κ=2,3, κ=4, and κ=6,8 as the representatives, respectively, of the dilute phase, the transition point, and the dense phase of the ordinary SLE. The resulting traces are shown to be scale invariant. Using two equivalent schemes, we extract the fractal dimension, D_f(H), of the traces which decrease monotonically with increasing H, reaching D_f=1 at H=1 for all κ values. The left passage probability (LPP) test demonstrates that, for H values not far from the uncorrelated case (small ε_H≡H-H_BM/H_BM), the prediction of the ordinary SLE is applicable with an effective diffusivity parameter κ_eff. Not surprisingly, the κ_eff's do not fulfill the prediction of SLE for the relation between D_f(H) and the diffusivity parameter.The linear (Winkler) foundation is a simple model widely used for decades to account for the surface response of elastic bodies. It models the response as purely local, linear, and perpendicular to the surface. We extend this model to the case in which the foundation is made of a structured material such as a polymer network, which has characteristic scales of length and time. We use the two-fluid model of viscoelastic structured materials to treat a film of finite thickness, supported on a rigid solid and subjected to a concentrated normal force at its free surface. We obtain the foundation modulus (Winkler constant) as a function of the film's thickness, intrinsic correlation length, and viscoelastic moduli, for three choices of boundary conditions. The results can be used to readily extend earlier applications of the Winkler model to more complex, microstructured substrates. They also provide a way to extract the intrinsic properties of such complex materials from mechanical surface measurements.Recent theoretical research has developed a general framework to understand director deformations and modulated phases in nematic liquid crystals. In this framework, there are four fundamental director deformation modes twist, bend, splay, and a fourth mode Δ related to saddle-splay. The first three of these modes are known to induce modulated phases. Here, we consider modulated phases induced by the fourth mode. We develop a theory for tetrahedral order in liquid crystals, and show that it couples to the Δ mode of director deformation. Because of geometric frustration, the Δ mode cannot fill space by itself, but rather must be accompanied by twist or splay. Hence, it may induce a spontaneous cholesteric phase, with either handedness, or a splay nematic phase.In many branches of earth sciences, the problem of rock study on the microlevel arises. However, a significant number of representative samples is not always feasible. Thus the problem of the generation of samples with similar properties becomes actual. In this paper we propose a deep learning architecture for three-dimensional porous medium reconstruction from two-dimensional slices. We fit a distribution on all possible three-dimensional structures of a specific type based on the given data set of samples. Then, given partial information (central slices), we recover the three-dimensional structure around such slices as the most probable one according to that constructed distribution. Technically, we implement this in the form of a deep neural network with encoder, generator, and discriminator modules. Numerical experiments show that this method provides a good reconstruction in terms of Minkowski functionals.Potassium ion channels are essential elements in cellular electrical excitability and help maintain a resting potential in nonexcitable cells. Their universality is based on a unique combination of strong selectivity for K^+ ions and near-diffusion-limited permeation efficiency. Understanding how the channel regulates the ion conduction would be instructive to the treatment of ion channelopathies. learn more In this work, by means of molecular dynamics simulations, we demonstrate the significantly enhanced permeation of KcsA channel in reaction to an external terahertz wave, due to the effective response of the K^+ ions in the selectivity filter regions of the channel. Compared to the case without external terahertz wave, a fourfold increase in the ion current through the channel is found.The classical D^2-Law states that the square of the droplet diameter decreases linearly with time during its evaporation process, i.e., D^2(t)=D_0^2-Kt, where D_0 is the droplet initial diameter and K is the evaporation constant. Though the law has been widely verified by experiments, considerable deviations are observed in many cases. In this work, a revised theoretical analysis of the single droplet evaporation in finite-size open systems is presented for both two-dimensional (2D) and 3D cases. Our analysis shows that the classical D^2-Law is only applicable for 3D large systems (L≫D_0, L is the system size), while significant deviations occur for small (L≤5D_0) and/or 2D systems. Theoretical solution for the temperature field is also derived. Moreover, we discuss in detail the proper numerical implementation of droplet evaporation in finite-size open systems by the mesoscopic lattice Boltzmann method (LBM). Taking into consideration shrinkage effects and an adaptive pressure boundary condition, droplet evaporation in finite-size 2D/3D systems with density ratio up to 328 within a wide parameter range (K=[0.003,0.18] in lattice units) is simulated, and remarkable agreement with the theoretical solution is achieved, in contrast to previous simulations. The present work provides insights into realistic droplet evaporation phenomena and their numerical modeling using diffuse-interface methods.Self-propelled particles can undergo complex dynamics due to a range of bulk and surface interactions. When a particle is embedded in a host solid near its bulk melting temperature, the latter may melt at the surface of the former in a process known as interfacial premelting. The thickness of the melt film depends on the temperature, impurities, material properties and geometry. A temperature gradient is accompanied by a thermomolecular pressure gradient that drives the interfacial liquid from high to low temperatures and hence the particle from low to high temperatures, in a process called thermal regelation. When the host material is ice and the embedded particle is a biological entity, one has a particularly different form of active matter, which addresses interplay between a wide range of problems, from extremophiles of both terrestrial and exobiological relevance to ecological dynamics in Earth's cryosphere. Of basic importance in all such settings is the combined influence of biological activity and thermal regelation in controlling the redistribution of bioparticles. Therefore, we recast this class of regelation phenomena in the stochastic framework of active Ornstein-Uhlenbeck dynamics and make predictions relevant to this and related problems of interest in biological and geophysical problems. We examine how thermal regelation compromises paleoclimate studies in the context of ice core dating and we find that the activity influences particle dynamics during thermal regelation by enhancing the effective diffusion coefficient. Therefore, accurate dating relies on a quantitative treatment of both effects.
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