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A survey of subpixel edge detection methods for images of heat-emitting metal specimens

Anna Fabijańska (2012)

International Journal of Applied Mathematics and Computer Science

In this paper the problem of accurate edge detection in images of heat-emitting specimens of metals is discussed. The images are provided by the computerized system for high temperature measurements of surface properties of metals and alloys. Subpixel edge detection is applied in the system considered in order to improve the accuracy of surface tension determination. A reconstructive method for subpixel edge detection is introduced. The method uses a Gaussian function in order to reconstruct the...

A thermodynamic approach to nonisothermal phase-field models

Irena Pawłow (2015)

Applicationes Mathematicae

The goal of this paper is to work out a thermodynamical setting for nonisothermal phase-field models with conserved and nonconserved order parameters in thermoelastic materials. Our approach consists in exploiting the second law of thermodynamics in the form of the entropy principle according to I. Müller and I. S. Liu, which leads to the evaluation of the entropy inequality with multipliers. As the main result we obtain a general scheme of phase-field models which involves an...

A unilateral boundary-value problem for the rod

Miroslav Bosák (1988)

Aplikace matematiky

A unilateral boundary-value condition at the left end of a simply supported rod is considered. Variational and (equivalent) classical formulations are introduced and all solutions to the classical problem are calculated in an explicit form. Formulas for the energies corresponding to the solutions are also given. The problem is solved and energies of the solutions are compared in the pertubed as well as the unperturbed cases.

Actions with the conservation property

Miroslav Šilhavý (1985)

Aplikace matematiky

The paper deals with the theory of actions on thermodynamical systems. It is proved that if an action has the conservation property at least at one state then it has the conservation property at every state and admits an everywhere defined continuous potential. An analogous result for semi-systems is also proved.

An analysis of the boundary layer in the 1D surface Cauchy–Born model

Kavinda Jayawardana, Christelle Mordacq, Christoph Ortner, Harold S. Park (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The surface Cauchy–Born (SCB) method is a computational multi-scale method for the simulation of surface-dominated crystalline materials. We present an error analysis of the SCB method, focused on the role of surface relaxation. In a linearized 1D model we show that the error committed by the SCB method is 𝒪(1) in the mesh size; however, we are able to identify an alternative “approximation parameter” – the stiffness of the interaction potential – with respect to which the relative error...

An analysis of the boundary layer in the 1D surface Cauchy–Born model∗

Kavinda Jayawardana, Christelle Mordacq, Christoph Ortner, Harold S. Park (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

The surface Cauchy–Born (SCB) method is a computational multi-scale method for the simulation of surface-dominated crystalline materials. We present an error analysis of the SCB method, focused on the role of surface relaxation. In a linearized 1D model we show that the error committed by the SCB method is 𝒪(1) in the mesh size; however, we are able to identify an alternative “approximation parameter” – the stiffness of the interaction potential – with respect to which the relative error...

An optimal scaling law for finite element approximations of a variational problem with non-trivial microstructure

Andrew Lorent (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this note we give sharp lower bounds for a non-convex functional when minimised over the space of functions that are piecewise affine on a triangular grid and satisfy an affine boundary condition in the second lamination convex hull of the wells of the functional.

Analysis of a discrete model for the contact problem between a membrane and an elastic obstacle

Aldo Maceri, Franco Maceri (1986)

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

In questo lavoro viene risolto il problema del contatto tra una membrana ed un suolo od ostacolo elastico con una approssimazione lineare a tratti della soluzione. Sono date alcune formulazioni equivalenti del problema discreto e se ne discutono le corrispondenti proprietà computazionali.

Analysis of a force-based quasicontinuum approximation

Matthew Dobson, Mitchell Luskin (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We analyze a force-based quasicontinuum approximation to a one-dimensional system of atoms that interact by a classical atomistic potential. This force-based quasicontinuum approximation can be derived as the modification of an energy-based quasicontinuum approximation by the addition of nonconservative forces to correct nonphysical “ghost” forces that occur in the atomistic to continuum interface during constant strain. The algorithmic simplicity and consistency with the purely atomistic model at...

Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics

Xavier Blanc, Claude Le Bris, Frédéric Legoll (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In order to describe a solid which deforms smoothly in some region, but non smoothly in some other region, many multiscale methods have recently been proposed. They aim at coupling an atomistic model (discrete mechanics) with a macroscopic model (continuum mechanics). We provide here a theoretical ground for such a coupling in a one-dimensional setting. We briefly study the general case of a convex energy, and next concentrate on a specific example of a nonconvex energy, the Lennard-Jones case....

Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics

Xavier Blanc, Claude Le Bris, Frédéric Legoll (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In order to describe a solid which deforms smoothly in some region, but non smoothly in some other region, many multiscale methods have recently been proposed. They aim at coupling an atomistic model (discrete mechanics) with a macroscopic model (continuum mechanics). We provide here a theoretical ground for such a coupling in a one-dimensional setting. We briefly study the general case of a convex energy, and next concentrate on a specific example of a nonconvex energy, the Lennard-Jones case....

Analysis of a quasicontinuum method in one dimension

Christoph Ortner, Endre Süli (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

The quasicontinuum method is a coarse-graining technique for reducing the complexity of atomistic simulations in a static and quasistatic setting. In this paper we aim to give a detailed a priori and a posteriori error analysis for a quasicontinuum method in one dimension. We consider atomistic models with Lennard–Jones type long-range interactions and a QC formulation which incorporates several important aspects of practical QC methods. First, we prove the existence, the local uniqueness...

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