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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...
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 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.
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.
In this paper the contact problem for a cylindrical shell and a stiff punch is studied. The existence and uniqueness of a solution is verified. The finite element method is discussed.
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...
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...
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.
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.
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.
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...
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....
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....
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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