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It has been claimed that quasistatic granular materials, as well as nanoscale materials, exhibit departures from elasticity even at small loadings. It is demonstrated, using 2D and 3D models with interparticle harmonic interactions, that such departures are expected at small scales [below O(100) particle diameters], at which continuum elasticity is invalid, and vanish at large scales. The models exhibit force chains on small scales, and force and stress distributions which agree with experimental findings. Effects of anisotropy, disorder and boundary conditions are discussed as well.
We present a model for conductivity and energy diffusion in a linear chain described by a quadratic Hamiltonian with Gaussian noise. We show that when the correlation matrix is diagonal, the noise-averaged Liouville-von Neumann equation governing the
In this letter we continue the investigation of finite XXZ spin chains with periodic boundary conditions and odd number of sites, initiated in paper cite{S}. As it turned out, for a special value of the asymmetry parameter $Delta=-1/2$ the Hamiltonia
This review summarizes recent advances in our understanding of anomalous transport in spin chains, viewed through the lens of integrability. Numerical advances, based on tensor-network methods, have shown that transport in many canonical integrable s
The critical Casimir force (CCF) arises from confining fluctuations in a critical fluid and thus it is a fluctuating quantity itself. While the mean CCF is universal, its (static) variance has previously been found to depend on the microscopic detail
We investigate self-avoiding walk models of linear block copolymers adsorbed at a surface and desorbed by the action of a force. We rigorously establish the dependence of the free energy on the adsorption and force parameters, and the form of the pha