Stochastically forced dislocation density distribution in plastic deformation

Graphene Oxide of Extra High Oxidation: A Wafer for Loading Guest Molecules

We present a new modification of graphene oxide with very high content (85 wt %) of oxygen-containing functional groups (hydroxy, epoxy, lactol, carboxyl, and carbonyl groups) that forms stable aqueous dispersion in up to 9 g·L^-1 concentration solutions. A novel faster method of the synthesis is described that produces up to 1 kg of the material and allows controlling the particle size in solution. The synthesized compound was characterized by various physicochemical methods and molecular dynamics modeling, revealing a unique structure in the form of a multilayered wafer of several sheets thick, where each sheet is highly corrugated. The ragged structure of the sheets forms pockets with hindered mobility of water that leads to the possibility of trapping guest molecules.

Mitigation of rare events in multistable systems driven by correlated noise

We consider rare transitions induced by colored noise excitation in multistable systems. We show that undesirable transitions can be mitigated by a simple time-delay feedback control if the control parameters are judiciously chosen. We devise a parsimonious method for selecting the optimal control parameters, without requiring any Monte Carlo simulations of the system. This method relies on a new nonlinear Fokker-Planck equation whose stationary response distribution is approximated by a rapidly convergent iterative algorithm. In addition, our framework allows us to accurately predict, and subsequently suppress, the modal drift and tail inflation in the controlled stationary distribution. We demonstrate the efficacy of our method on two examples, including an optical laser model perturbed by multiplicative colored noise.

Generating randomness: making the most out of disordering a false order into a real one

Randomness is far from a disturbing disorder in nature. Rather, it underlies many processes and functions. Randomness can be used to improve the efficacy of development and of systems under certain conditions. Moreover, valid unpredictable random-number generators are needed for secure communication, rendering predictable pseudorandom strings unsuitable. This paper reviews methods of generating randomness in various fields. The potential use of these methods is also discussed. It is suggested that by disordering a "false order," an effective disorder can be generated to improve the function of systems.

Double diffusivity model under stochastic forcing

The "double diffusivity" model was proposed in the late 1970s, and reworked in the early 1980s, as a continuum counterpart to existing discrete models of diffusion corresponding to high diffusivity paths, such as grain boundaries and dislocation lines. It was later rejuvenated in the 1990s to interpret experimental results on diffusion in polycrystalline and nanocrystalline specimens where grain boundaries and triple grain boundary junctions act as high diffusivity paths. Technically, the model pans out as a system of coupled Fick-type diffusion equations to represent "regular" and "high" diffusivity paths with "source terms" accounting for the mass exchange between the two paths. The model remit was extended by analogy to describe flow in porous media with double porosity, as well as to model heat conduction in media with two nonequilibrium local temperature baths, e.g., ion and electron baths. Uncoupling of the two partial differential equations leads to a higher-ordered diffusion equation, solutions of which could be obtained in terms of classical diffusion equation solutions. Similar equations could also be derived within an "internal length" gradient (ILG) mechanics formulation applied to diffusion problems, i.e., by introducing nonlocal effects, together with inertia and viscosity, in a mechanics based formulation of diffusion theory. While being remarkably successful in studies related to various aspects of transport in inhomogeneous media with deterministic microstructures and nanostructures, its implications in the presence of stochasticity have not yet been considered. This issue becomes particularly important in the case of diffusion in nanopolycrystals whose deterministic ILG-based theoretical calculations predict a relaxation time that is only about one-tenth of the actual experimentally verified time scale. This article provides the "missing link" in this estimation by adding a vital element in the ILG structure, that of stochasticity, that takes into account all boundary layer fluctuations. Our stochastic-ILG diffusion calculation confirms rapprochement between theory and experiment, thereby benchmarking a new generation of gradient-based continuum models that conform closer to real-life fluctuating environments.