# Mechanical behaviour of heterogeneous nanochains in the $\Gamma$-limit of stochastic particle systems

@article{Lauerbach2019MechanicalBO, title={Mechanical behaviour of heterogeneous nanochains in the \$\Gamma\$-limit of stochastic particle systems}, author={Laura Lauerbach and Stefan Neukamm and Mathias Schaffner and Anja Schlomerkemper}, journal={arXiv: Analysis of PDEs}, year={2019} }

Nanochains of atoms, molecules and polymers have gained recent interest in the experimental sciences. This article contributes to an advanced mathematical modeling of the mechanical properties of nanochains that allow for heterogenities, which may be impurities or a deliberately chosen composition of different kind of atoms. We consider one-dimensional systems of particles which interact through a large class of convex-concave potentials, which includes the classical Lennard-Jones potentials… Expand

#### Figures from this paper

#### References

SHOWING 1-10 OF 26 REFERENCES

On Lennard-Jones systems with finite range interactions and their asymptotic analysis

- Physics, Computer Science
- Networks Heterog. Media
- 2018

This work provides an explicit expression for the continuum limit in the case of finite range interactions of Lennard-Jones type by means of $\Gamma$-convergence techniques and studies suitably rescaled energies in which bulk and surface contributions scale in the same way. Expand

Towards uniformly $\Gamma$-equivalent theories for nonconvex discrete systems

- Mathematics
- 2011

In this paper we consider a one-dimensional chain of atoms which
interact with their nearest and next-to-nearest neighbours
via a Lennard-Jones type potential. We prescribe the positions
in the… Expand

Integral Representation Results for Energies Defined on Stochastic Lattices and Application to Nonlinear Elasticity

- Mathematics
- 2011

This article is devoted to the study of the asymptotic behavior of a class of energies defined on stochastic lattices. Under polynomial growth assumptions, we prove that the energy functionals… Expand

Effective Cohesive Behavior of Layers of Interatomic Planes

- Mathematics
- 2006

A simple model of cleavage in brittle crystals consists of a layer of material containing N atomic planes separating in accordance with an interplanar potential under the action of an opening… Expand

TOWARDS UNIFORMLY Γ-EQUIVALENT THEORIES FOR NONCONVEX DISCRETE SYSTEMS

- 2010

In this paper we consider a one-dimensional chain of atoms which interact through nearest and next-to-nearest neighbour interactions of LennardJones type. We impose four Dirichlet boundary… Expand

Doping liquid crystals with nanoparticles. A computer simulation of the effects of nanoparticle shape.

- Materials Science, Medicine
- Physical chemistry chemical physics : PCCP
- 2016

It is found that the overall phase behaviour is not affected by the addition of small amounts of nanoparticles, with the lowest perturbation obtained with disc-like nanoparticles at the lowest concentration. Expand

Boundary layer energies for nonconvex discrete systems

- Mathematics
- 2011

In this work we consider a one-dimensional chain of atoms which interact through nearest and next-to-nearest neighbour interactions of Lennard–Jones type. We impose Dirichlet boundary conditions and… Expand

Stochastic Homogenization of Nonconvex Discrete Energies with Degenerate Growth

- Mathematics, Computer Science
- SIAM J. Math. Anal.
- 2017

The results in the present paper are to the authors' knowledge the first stochastic homogenization results for nonconvex energy functionals with degenerate growth under moment conditions. Expand

The minimal nanowire: Mechanical properties of carbyne

- Materials Science
- 2011

Advances in molecular assembly are converging to an ultimate in atomistic precision —nanostructures built by single atoms. Recent experimental studies confirm that single chains of carbon atoms… Expand

Surface energies in nonconvex discrete systems

- Mathematics
- 2007

We analyze the variational limit of one-dimensional next-to-nearest neighbours (NNN) discrete systems as the lattice size tends to zero when the energy densities are of multiwell or Lennard–Jones… Expand