Related papers: Disorder Perturbation Expansion for Athermal Cryst…
Using analytic and numerical methods, we study a $2d$ Hamiltonian model of interacting particles carrying ferro-magnetically coupled continuous spins which are also locally coupled to their own velocities. This model has been characterised…
For many nonlinear physical systems, approximate solutions are pursued by conventional perturbation theory in powers of the non-linear terms. Unfortunately, this often produces divergent asymptotic series, collectively dismissed by Abel as…
We derive exact results for displacement fields that develop as a response to external pinning forces in two dimensional athermal networks. For a triangular lattice arrangement of particles interacting through soft potentials, we develop a…
We study the disorder-to-order transition in a collection of polar self-propelled particles interacting through a distance dependent alignment interaction. Strength of the interaction, $a^{d}$ ($0<a<1$) decays with metric distance $d$…
We apply the linear $\delta$-expansion (LDE), originally developed as a nonperturbative, analytical approximation scheme in quantum field theory, to problems involving noninteracting electrons in disordered solids. The initial idea that the…
Small displacement methods have been successfully used to calculate the lattice dynamical properties of crystals. It involves displacing atoms by a small amount in order to calculate the induced forces on all atoms in a supercell for the…
The effect of increasing structural disorder on the distribution of contact forces P(f), inside three dimensional particle assemblies is systematically studied using computer simulations of model granular packings. Starting from a…
We generalize, and then use, a recently introduced formalism to study thermal fluctuations of atomic displacements in several two and three dimensional crystals. We study both close packed as well as open crystals with multi atom bases.…
Perturbation theory is a kind of estimation method based on theorem of Taylor expansion, and is useful to investigate electromagnetic solutions of small changes. By considering a sharp boundary as a limit of smoothed systems, previous study…
We apply the thermal (imaginary time) perturbative expansion to the relevant effective field theory to compute characteristics of the phase transition to the ordered state which can occur at low temperatures in the gas of (nonrelativistic)…
Structure-property relationships in ordered materials have long been a core principle in materials design. However, the intentional introduction of disorder into materials provides structural flexibility and thus access to material…
Finite temperature disordered solid solutions and magnetic materials are difficult to study directly using first principles calculations, due to the large unit cells and many independent samples that are required. In this work, we develop a…
The phase-field crystal model in its amplitude equation approximation is shown to provide an accurate description of the deformation field in defected crystalline structures, as well as of dislocation motion. We analyze in detail the…
The properties of crystals consisting of several components can be widely tuned. Often solid solutions are produced, where substitutional or interstitional disorder determines the crystal thermodynamic and mechanical properties. The…
The isostaticity theory for stress transmission in macroscopic planar particulate assemblies is extended here to non-rigid particles. It is shown that, provided that the mean coordination number in $d$ dimensions is $d+1$, macroscopic…
It has become increasingly clear that a full understanding of the physics of electrons in disordered systems requires an approach in which both disorder and interactions are taken into account. Work on small numbers of electrons has…
How topological defects affect the dynamics of particles hopping between lattice sites of a distorted, two-dimensional crystal is addressed. Perturbation theory and numerical simulations show that weak, short-ranged topological disorder…
An exactly solvable phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals is developed. The theory accounts for: an arbitrary number and arrangement of dislocation lines over a slip plane;…
Perturbation theory is an indispensable tool in quantum mechanics and electrodynamics that handles weak effects on particle motion or fields. However, its extension to plasmons involving complex motion of {\it both} particles and fields…
Crystals are a state of matter characterised by periodic order. Yet crystalline materials can harbour disorder in many guises, such as non-repeating variations in composition, atom displacements, bonding arrangements, molecular…