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Regis Monneau - One of the best experts on this subject based on the ideXlab platform.
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Atomic to Continuum Passage for Nanotubes: A Discrete Saint-Venant Principle and Error Estimates
Archive for Rational Mechanics and Analysis, 2014Co-Authors: Danny El Kass, Regis MonneauAbstract:We consider general infinite nanotubes of atoms in $${\mathbb{R}^3}$$ R 3 where each atom interacts with all the others through a two-body potential. At the equilibrium, the positions of the atoms satisfy a Euler–Lagrange equation. When there are no exterior forces and for a suitable geometry, a particular family of nanotubes is the set of perfect nanotubes at the equilibrium. When exterior forces are applied on the nanotube, we compare the nanotube to nanotubes of the previous family. In part I of the paper, this quantitative comparison is formulated in our first main result as a discrete Saint-Venant Principle. As a corollary, we also give a Liouville classification result. Our Saint-Venant Principle can be derived for a large class of potentials (including the Lennard-Jones potential), when the perfect nanotubes at the equilibrium are stable. The approach is designed to be applicable to nanotubes that can have general shapes like, for instance, carbon nanotubes or DNA, under the oversimplified assumption that all the atoms are identical. In part II of the paper, we derive from our Saint-Venant Principle a macroscopic mechanical model for general nanotubes. We prove that every solution is well approximated by the solution of a continuum model involving stretching and twisting, but no bending. We establish error estimates between the discrete and the continuous solution. More precisely we give two error estimates: one at the microscopic level and one at the macroscopic level.
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Atomic to continuum passage for nanotubes. Part I: a discrete Saint-Venant Principle
2012Co-Authors: Danny El Kass, Regis MonneauAbstract:We consider general nanotubes of atoms in $\R^3$ where each atom interacts with all others through a two-body potential. When there are no exterior forces, a particular family of nanotubes is the set of perfect nanotubes at the equilibrium. When exterior forces are applied on the nanotube, we compare the nanotube to nanotubes of the previous family. This quantitative comparison is formulated in our main result as a Saint-Venant Principle. This estimate can be derived for a large class of potentials (including Lennard-Jones potential), when the perfect nanotubes at the equilibrium are stable. The approach is designed to be applicable to general nanotubes that can be for instance carbon nanotubes or DNA. In a second paper (part II), we derive from our Saint-Venant Principle, a macroscopic mechanical model for general nanotubes.
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Atomic to continuum passage for nanotubes. Part II: error estimates
2012Co-Authors: Danny El Kass, Regis MonneauAbstract:We consider deformations in $\R^3$ of an infinite general nanotube of atoms where each atom interacts with all the other through a two-body potential. We compute the effect of an external force applied to the nanotube. At the equilibrium, the positions of the atoms satisfy an Euler-Lagrange equation. For large classes of potentials (including Lennard-Jones potential) and under suitable stability assumptions, we prove that every solution is well approximated by the solution of a continuum model involving stretching and twisting, but no bending. We establish an error estimate between the discrete and the continuous solution based on a Saint-Venant Principle that the reader can find in the companion paper (part I)
Dumitru Baleanu - One of the best experts on this subject based on the ideXlab platform.
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On a generalized relaxed Saint–Venant Principle
Boundary Value Problems, 2018Co-Authors: Marin Marin, Ravi P. Agarwal, Dumitru BaleanuAbstract:The goal of this paper is to obtain an extension of the relaxed Saint–Venant Principle in order to cover the thermoelasticity of dipolar porous bodies.
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on a generalized relaxed Saint Venant Principle
Boundary Value Problems, 2018Co-Authors: Marin Marin, Ravi P. Agarwal, Dumitru BaleanuAbstract:The goal of this paper is to obtain an extension of the relaxed Saint–Venant Principle in order to cover the thermoelasticity of dipolar porous bodies.
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On a generalized relaxed Saint–Venant Principle
SpringerOpen, 2018Co-Authors: Marin Marin, Ravi P. Agarwal, Dumitru BaleanuAbstract:Abstract The goal of this paper is to obtain an extension of the relaxed Saint–Venant Principle in order to cover the thermoelasticity of dipolar porous bodies. According to this Principle, for a finite time t>0 $t>0$, we identify a bounded domain Dt $\mathcal{D}_{t}$ so that outside of this domain the displacement field ui $u_{i}$, the dipolar displacement field φjk $\varphi_{jk}$, the temperature θ, and the change in volume fraction ϕ do not generate disturbances
Danny El Kass - One of the best experts on this subject based on the ideXlab platform.
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Atomic to Continuum Passage for Nanotubes: A Discrete Saint-Venant Principle and Error Estimates
Archive for Rational Mechanics and Analysis, 2014Co-Authors: Danny El Kass, Regis MonneauAbstract:We consider general infinite nanotubes of atoms in $${\mathbb{R}^3}$$ R 3 where each atom interacts with all the others through a two-body potential. At the equilibrium, the positions of the atoms satisfy a Euler–Lagrange equation. When there are no exterior forces and for a suitable geometry, a particular family of nanotubes is the set of perfect nanotubes at the equilibrium. When exterior forces are applied on the nanotube, we compare the nanotube to nanotubes of the previous family. In part I of the paper, this quantitative comparison is formulated in our first main result as a discrete Saint-Venant Principle. As a corollary, we also give a Liouville classification result. Our Saint-Venant Principle can be derived for a large class of potentials (including the Lennard-Jones potential), when the perfect nanotubes at the equilibrium are stable. The approach is designed to be applicable to nanotubes that can have general shapes like, for instance, carbon nanotubes or DNA, under the oversimplified assumption that all the atoms are identical. In part II of the paper, we derive from our Saint-Venant Principle a macroscopic mechanical model for general nanotubes. We prove that every solution is well approximated by the solution of a continuum model involving stretching and twisting, but no bending. We establish error estimates between the discrete and the continuous solution. More precisely we give two error estimates: one at the microscopic level and one at the macroscopic level.
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Atomic to continuum passage for nanotubes. Part I: a discrete Saint-Venant Principle
2012Co-Authors: Danny El Kass, Regis MonneauAbstract:We consider general nanotubes of atoms in $\R^3$ where each atom interacts with all others through a two-body potential. When there are no exterior forces, a particular family of nanotubes is the set of perfect nanotubes at the equilibrium. When exterior forces are applied on the nanotube, we compare the nanotube to nanotubes of the previous family. This quantitative comparison is formulated in our main result as a Saint-Venant Principle. This estimate can be derived for a large class of potentials (including Lennard-Jones potential), when the perfect nanotubes at the equilibrium are stable. The approach is designed to be applicable to general nanotubes that can be for instance carbon nanotubes or DNA. In a second paper (part II), we derive from our Saint-Venant Principle, a macroscopic mechanical model for general nanotubes.
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Atomic to continuum passage for nanotubes. Part II: error estimates
2012Co-Authors: Danny El Kass, Regis MonneauAbstract:We consider deformations in $\R^3$ of an infinite general nanotube of atoms where each atom interacts with all the other through a two-body potential. We compute the effect of an external force applied to the nanotube. At the equilibrium, the positions of the atoms satisfy an Euler-Lagrange equation. For large classes of potentials (including Lennard-Jones potential) and under suitable stability assumptions, we prove that every solution is well approximated by the solution of a continuum model involving stretching and twisting, but no bending. We establish an error estimate between the discrete and the continuous solution based on a Saint-Venant Principle that the reader can find in the companion paper (part I)
Ravi P. Agarwal - One of the best experts on this subject based on the ideXlab platform.
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On a generalized relaxed Saint–Venant Principle
Boundary Value Problems, 2018Co-Authors: Marin Marin, Ravi P. Agarwal, Dumitru BaleanuAbstract:The goal of this paper is to obtain an extension of the relaxed Saint–Venant Principle in order to cover the thermoelasticity of dipolar porous bodies.
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on a generalized relaxed Saint Venant Principle
Boundary Value Problems, 2018Co-Authors: Marin Marin, Ravi P. Agarwal, Dumitru BaleanuAbstract:The goal of this paper is to obtain an extension of the relaxed Saint–Venant Principle in order to cover the thermoelasticity of dipolar porous bodies.
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On a generalized relaxed Saint–Venant Principle
SpringerOpen, 2018Co-Authors: Marin Marin, Ravi P. Agarwal, Dumitru BaleanuAbstract:Abstract The goal of this paper is to obtain an extension of the relaxed Saint–Venant Principle in order to cover the thermoelasticity of dipolar porous bodies. According to this Principle, for a finite time t>0 $t>0$, we identify a bounded domain Dt $\mathcal{D}_{t}$ so that outside of this domain the displacement field ui $u_{i}$, the dipolar displacement field φjk $\varphi_{jk}$, the temperature θ, and the change in volume fraction ϕ do not generate disturbances
Marin Marin - One of the best experts on this subject based on the ideXlab platform.
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On a generalized relaxed Saint–Venant Principle
Boundary Value Problems, 2018Co-Authors: Marin Marin, Ravi P. Agarwal, Dumitru BaleanuAbstract:The goal of this paper is to obtain an extension of the relaxed Saint–Venant Principle in order to cover the thermoelasticity of dipolar porous bodies.
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on a generalized relaxed Saint Venant Principle
Boundary Value Problems, 2018Co-Authors: Marin Marin, Ravi P. Agarwal, Dumitru BaleanuAbstract:The goal of this paper is to obtain an extension of the relaxed Saint–Venant Principle in order to cover the thermoelasticity of dipolar porous bodies.
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On a generalized relaxed Saint–Venant Principle
SpringerOpen, 2018Co-Authors: Marin Marin, Ravi P. Agarwal, Dumitru BaleanuAbstract:Abstract The goal of this paper is to obtain an extension of the relaxed Saint–Venant Principle in order to cover the thermoelasticity of dipolar porous bodies. According to this Principle, for a finite time t>0 $t>0$, we identify a bounded domain Dt $\mathcal{D}_{t}$ so that outside of this domain the displacement field ui $u_{i}$, the dipolar displacement field φjk $\varphi_{jk}$, the temperature θ, and the change in volume fraction ϕ do not generate disturbances
