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Modeling the tip-sample interaction in atomic force microscopy with Timoshenko beam theory

Julio R. Claeyssen, Teresa Tsukazan, Leticia Tonetto, Daniela Tolfo (2013)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

A matrix framework is developed for single and multispan micro-cantilevers Timoshenko beam models of use in atomic force microscopy (AFM). They are considered subject to general forcing loads and boundary conditions for modeling tipsample interaction. Surface effects are considered in the frequency analysis of supported and cantilever microbeams. Extensive use is made of a distributed matrix fundamental response that allows to determine forced responses through convolution and to absorb non-homogeneous...

Modellazione e calcolo di strutture in materiale non resistente a trazione

Elio Sacco (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si affronta il problema del calcolo dello stato tensionale in strutture costituite da materiale non resistente a trazione ed elastico lineare a compressione. Si formula la legge costitutiva e se ne fornisce l'espressione esplicita nel caso di stati tensionali monoassiali, biassiali e triassiali. Si imposta quindi il problema dell'equilibrio elastico e si discute sulla condizione da imporre ai carichi affinché venga assicurata l'esistenza della soluzione. Si sviluppa la formulazione agli elementi...

Modelled behaviour of granular material during loading and unloading

Krejčí, Pavel, Siváková, Lenka, Chleboun, Jan (2019)

Programs and Algorithms of Numerical Mathematics

The main aim of this paper is to analyze numerically the model behaviour of a granular material during loading and unloading. The model was originally proposed by D. Kolymbas and afterward modified by E. Bauer. For our purposes the constitutive equation was transformed into a rate independent form by introducing a dimensionless time parameter. By this transformation we were able to derive explicit formulas for the strain-stress trajectories during loading-unloading cycles and compare the results...

Modelling and control in pseudoplate problem with discontinuous thickness

Ján Lovíšek (2009)

Applications of Mathematics

This paper concerns an obstacle control problem for an elastic (homogeneous) and isotropic) pseudoplate. The state problem is modelled by a coercive variational inequality, where control variable enters the coefficients of the linear operator. Here, the role of control variable is played by the thickness of the pseudoplate which need not belong to the set of continuous functions. Since in general problems of control in coefficients have no optimal solution, a class of the extended optimal control...

Modelling of singularities in elastoplastic materials with fatigue

Pavel Krejčí (1994)

Applications of Mathematics

The hypothesis that, on the macroscopic level, the accumulated fatigue of an elastoplastic material with kinematic hardening can be identified from the mathematical point of view with the dissipated energy, is used for the construction of a new constitutive elastoplastic fatigue model. Its analytical investigation characterizes conditions for the formation of singularities in a finite time. The corresponding constitutive law is then coupled with the dynamical equation of motion of a one-dimensional...

Molecular modelling of stresses and deformations in nanostructured materials

Gwidon Szefer (2004)

International Journal of Applied Mathematics and Computer Science

A molecular dynamics approach to the deformation and stress analysis in structured materials is presented. A new deformation measure for a lumped mass system of points is proposed. In full consistency with the continuum mechanical description, three kinds of stress tensors for the discrete system of atoms are defined. A computer simulation for a set of 10^5 atoms forming a sheet undergoing tension (Case 1) and contraction (Case 2) is given. Characteristic microstress distributions evoked by a crack...

Molecular Simulation in the Canonical Ensemble and Beyond

Zhidong Jia, Ben Leimkuhler (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we discuss advanced thermostatting techniques for sampling molecular systems in the canonical ensemble. We first survey work on dynamical thermostatting methods, including the Nosé-Poincaré method, and generalized bath methods which introduce a more complicated extended model to obtain better ergodicity. We describe a general controlled temperature model, projective thermostatting molecular dynamics (PTMD) and demonstrate that it flexibly accommodates existing alternative thermostatting...

Motion of spirals by crystalline curvature

Hitoshi Imai, Naoyuki Ishimura, TaKeo Ushijima (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Modern physics theories claim that the dynamics of interfaces between the two-phase is described by the evolution equations involving the curvature and various kinematic energies. We consider the motion of spiral-shaped polygonal curves by its crystalline curvature, which deserves a mathematical model of real crystals. Exploiting the comparison principle, we show the local existence and uniqueness of the solution.

Motion of spiral-shaped polygonal curves by nonlinear crystalline motion with a rotating tip motion

Tetsuya Ishiwata (2015)

Mathematica Bohemica

We consider a motion of spiral-shaped piecewise linear curves governed by a crystalline curvature flow with a driving force and a tip motion which is a simple model of a step motion of a crystal surface. We extend our previous result on global existence of a spiral-shaped solution to a linear crystalline motion for a power type nonlinear crystalline motion with a given rotating tip motion. We show that self-intersection of the solution curves never occurs and also show that facet extinction never...

Currently displaying 81 – 100 of 114