Stochastically forced dislocation density distribution in plastic deformation

The dynamical evolution of dislocations in plastically deformed metals is controlled by both deterministic factors arising out of applied loads and stochastic effects appearing due to fluctuations of internal stress. Such type of stochastic dislocation processes and the associated spatially inhomogeneous modes lead to randomness in the observed deformation structure. Previous studies have analyzed the role of randomness in such textural evolution but none of these models have considered the impact of a finite decay time (all previous models assumed instantaneous relaxation which is "unphysical") of the stochastic perturbations in the overall dynamics of the system. The present article bridges this knowledge gap by introducing a colored noise in the form of an Ornstein-Uhlenbeck noise in the analysis of a class of linear and nonlinear Wiener and Ornstein-Uhlenbeck processes that these structural dislocation dynamics could be mapped on to. Based on an analysis of the relevant Fokker-Planck model, our results show that linear Wiener processes remain unaffected by the second time scale in the problem but all nonlinear processes, both Wiener type and Ornstein-Uhlenbeck type, scale as a function of the noise decay time τ. The results are expected to ramify existing experimental observations and inspire new numerical and laboratory tests to gain further insight into the competition between deterministic and random effects in modeling plastically deformed samples

Thermoplastic deformation of silicon surfaces induced by ultrashort pulsed lasers in submelting conditions

A hybrid 2D theoretical model is presented to describe thermoplastic deformation effects on silicon surfaces induced by single and multiple ultrashort pulsed laser irradiation in submelting conditions. An approximation of the Boltzmann transport equation is adopted to describe the laser irradiation process. The evolution of the induced deformation field is described initially by adopting the differential equations of dynamic thermoelasticity while the onset of plastic yielding is described by the von Mise's stress. Details of the resulting picometre sized crater, produced by irradiation with a single pulse, are then discussed as a function of the imposed conditions and thresholds for the onset of plasticity are computed. Irradiation with multiple pulses leads to ripple formation of nanometre size that originates from the interference of the incident and a surface scattered wave. It is suggested that ultrafast laser induced surface modification in semiconductors is feasible in submelting conditions, and it may act as a precursor of the incubation effects observed at multiple pulse irradiation of materials surfaces.Comment: To appear in the Journal of Applied Physic

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

Transmissibility in Interactive Nanocomposite Diffusion: The Nonlinear Double-Diffusion Model

Model analogies and exchange of ideas between physics or chemistry with biology or epidemiology have often involved inter-sectoral mapping of techniques. Material mechanics has benefitted hugely from such interpolations from mathematical physics where dislocation patterning of platstically deformed metals and mass transport in nanocomposite materials with high diffusivity paths such as dislocation and grain boundaries, have been traditionally analyzed using the paradigmatic Walgraef-Aifantis (W-A) double-diffusivity (D-D) model. A long standing challenge in these studies has been the inherent nonlinear correlation between the diffusivity paths, making it extremely difficult to analyze their interdependence. Here, we present a novel method of approximating a closed form solution of the ensemble averaged density profiles and correlation statistics of coupled dynamical systems, drawing from a technique used in mathematical biology to calculate a quantity called the basic reproduction number R0, which is the average number of secondary infections generated from every infected. We show that the R0 formulation can be used to calculate the correlation between diffusivity paths, agreeing closely with the exact numerical solution of the D-D model. The method can be generically implemented to analyze other reaction-diffusion models

Molecular Genetics of T Cell Development

T cell development is guided by a complex set of transcription factors that act recursively, in different combinations, at each of the developmental choice points from T-lineage specification to peripheral T cell specialization. This review describes the modes of action of the major T-lineage-defining transcription factors and the signal pathways that activate them during intrathymic differentiation from pluripotent precursors. Roles of Notch and its effector RBPSuh (CSL), GATA-3, E2A/HEB and Id proteins, c-Myb, TCF-1, and members of the Runx, Ets, and Ikaros families are critical. Less known transcription factors that are newly recognized as being required for T cell development at particular checkpoints are also described. The transcriptional regulation of T cell development is contrasted with that of B cell development, in terms of their different degrees of overlap with the stem-cell program and the different roles of key transcription factors in gene regulatory networks leading to lineage commitment

The RhoA transcriptional program in pre-T cells

The GTPase RhoA is essential for the development of pre-T cells in the thymus. To investigate the mechanisms used by RhoA to control thymocyte development we have used Affymetrix gene profiling to identify RhoA regulated genes in T cell progenitors. The data show that RhoA plays a specific and essential role in pre-T cells because it is required for the expression of transcription factors of the Egr-1 and AP-1 families that have critical functions in thymocyte development. Loss of RhoA function in T cell progenitors causes a developmental block that pheno-copies the consequence of losing pre-TCR expression in Recombinase gene 2 (Rag2) null mice. Transcriptional profiling reveals both common and unique gene targets for RhoA and the pre-TCR indicating that RhoA participates in the pre-TCR induced transcriptional program but also mediates pre-TCR independent gene transcription

DETERMINATION OF VICKERS MICROHARDNESS IN β-Ga2O3 SINGLE CRYSTALS GROWN FROM THEIR OWN MELT

The results of microhardness measurements of β-Ga2O3 single crystals for (001) crystallographic face are reported. The crystals were grown by the free crystallization with the "Garnet-2M" equipment. Microhardness values ​​ were determined by the Vickers method at varying loads. A four-sided diamond pyramid was used as an indenter. The average value of gallium oxide microhardness was equal to 8.91 GPa. We have carried out comparison of the values ​​obtained with the microhardness for the other wide bandgap semiconductors - epitaxial GaN layers grown on 6H-SiC and GaP layers grown on GaP:S. The findings are usable for machining process development of β-Ga2O3 single crystal substrates. In particular, silicon carbide and electrocorundum may be recommended for β-Ga2O3 machine processing

High order amplitude equation for steps on creep curve

We consider a model proposed by one of the authors for a type of plastic instability found in creep experiments which reproduces a number of experimentally observed features. The model consists of three coupled non-linear differential equations describing the evolution of three types of dislocations. The transition to the instability has been shown to be via Hopf bifurcation leading to limit cycle solutions with respect to physically relevant drive parameters. Here we use reductive perturbative method to extract an amplitude equation of up to seventh order to obtain an approximate analytic expression for the order parameter. The analysis also enables us to obtain the bifurcation (phase) diagram of the instability. We find that while supercritical bifurcation dominates the major part of the instability region, subcritical bifurcation gradually takes over at one end of the region. These results are compared with the known experimental results. Approximate analytic expressions for the limit cycles for different types of bifurcations are shown to agree with their corresponding numerical solutions of the equations describing the model. The analysis also shows that high order nonlinearities are important in the problem. This approach further allows us to map the theoretical parameters to the experimentally observed macroscopic quantities.Comment: LaTex file and eps figures; Communicated to Phys. Rev.