Marek Niezgódka

Convergent numerical approximations of the thermomechanical phase transitions in shape memory alloys

SummaryDiscrete approximations are constructed to a nonlinear evolutionary system of partial differential equations arising from modelling the dynamics of solid-state phase transitions of thermomechenical nature in the case of one space dimension. The class of problems considered includes the so-called shape memory alloys, in particular. It is shown that the obtained discrete solutions converge to the solution of the original problem, and numerical simulations for the shape memory alloy Au23Cu30Zn47 demonstrate the quality of the discrete model.

Viscosity approach to modelling non-isothermal diffusive phase separation

A nonlinear parabolic system with a singular evolution term, arising from modelling dynamic phenomena of the non-isothermal diffusive phase separation, is studied. The system is subject to constraints entering into the main part of one of the equations. In the paper, questions related to the existence and uniqueness of solutions to the singular problem are studied with the use of viscosity approximations. To this purpose, a special regularization technique has been applied to the singular evolution term.

Mathematical Models of Dynamical Martensitic Transformations in Shape Memory Alloys

HE SHAPE MEMORY effect is a physical property characteristic of numerous solids, including various metallic alloys and non-metallic solid materials like polymers. This property consists in an ability of a solid, subject to plastic deformation, to recover its original shape after an appropriate thermal treatment (possibly complemented by a mechanical loading). The effect had already been discovered in the mid-thirties, but an explosive development of interest in it, as well

Infrastructural Approach to Modern Digital Library and Repository Management Systems

Traditional DLM Systems were usually implemented in the form of an either monolithic or distributed applications. The paper presents a modern approach, where a modular environment provides an infrastructure of components to build DMLS applications upon. A case study of an open Synat Software Platform is presented, together with its sample applications, and the key benefits of the approach are discussed.

Variational inequalities of Navier–Stokes type with time dependent constraints

Abstract We consider a class of parabolic variational inequalities with time dependent obstacle of the form | u ( x , t ) | ≤ p ( x , t ) , where u is the velocity field of a fluid governed by the Navier–Stokes variational inequality. The obstacle function p = p ( x , t ) , imposed on u, consists of three parts, which are respectively: the degenerate part p ( x , t ) = 0 , the finitely positive part 0 p ( x , t ) ∞ and the singular part p ( x , t ) = ∞ . In this paper, we shall propose a sequence of approximate obstacle problems with everywhere finitely positive obstacles, and prove an existence result for the original problem by discussing convergence of the approximate problems. The crucial step is to handle the nonlinear convection term. In this paper we propose a new approach to it.

Increasing the efficiency of the DaCS programming model for heterogeneous systems

Efficient programming of hybrid systems is usually done with the use of new programming models. It creates a unique opportunity to increase the performance of scientific applications and is also especially interesting in the context of future exascale applications development where extreme number of MPI processes tend to be a limitation. Future scientific codes will make use of hierarchical parallel programming models with message passing techniques used between nodes and optimized computational kernels used within multicore, multithreaded or accelerator nodes. In this article we consider the x86 and PowerXCell8i heterogeneous environment introduced in the High Performance Computing (HPC) sites like Roadrunner [6] or Nautilus [5]. Programming techniques for this environment are usually based on the IBM Data Communication and Synchronization library (DaCS). We describe our effort to increase the hybrid efficiency of the DaCS library and show how it affects the performance of scientific computations based on FFT kernels. The results are very promising especially for computational models that involve large three dimensional Fourier transformations.

Dynamics of Diffusive Phase Transitions Driven by Coupled Mechanisms

The paper gives an overview of basic set-ups for modelling dynamic phase separation phenomena in binary systems governed by various driving mechanisms coupled with diffusion. In particular, non-isothermal situations axe treated and two-scale systems with conserved macroscopic order parameters while including non-conserved mesoscopic components are considered.

Large-time solutions of the two-phase Stefan problem with delay

The paper is devoted to questions of an analysis of the large-time solutions to a class of two-phase Stefan problems with delay in the source terms of the governing equations. The case of one space dimension is considered. Results on the asymptotic behaviour of the solutions at t → ∞ are established.

Shape Memory Materials: Mathematical Modelling and Numerical Simulation

The shape memory effect is a physical property characteristic of numerous solids, including various metallic alloys and non-metailic solid materials like polymers. This property consists in an ability of a solid subject to plastic deformation to recover its original shape after an appropriate thermal treatment (possibly complemented by a mechanical loading). The effect has already been discovered in the mid-thirties, but an explosive development of the interest in it, as well as understanding of its enormous applicability range date from the late sixties and are related to the discovery of extraordinarily strong and, equally, preserved in time, shape memory property of Ti-Ni alloy (Nitinol), cf. [6,29]. The same type of effects has been discovered also in many other metallic alloys. There exists, in- between, an extensive literature devoted to the physics of shape memory effect (cf. [6,17,28]) and its applications (cf. [3,6,12]). It is not our objective to give any overview of these aspects. What we are going to expose is related to the most common characteristic features of the dynamical processes in materials exhibiting shape memory and then to construct phenomenological models capable of forecasting the developments in space and time both qualitatively and quantitatively. Since the behavior is strongly affected by the choice of a specific class of materials, we shall focus on metallic alloys, with Nitinol in mind, in particular. We shall discuss the applicability range of the models proposed and shall show some typical results of numerical experiments which visualize their forecasting value.