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Using a description of defects in solids in terms of three-dimensional gravity, we study the propagation of electrons in the background of disclinations and screw dislocations. We study the situations where there are bound states that are…
Dielectric relaxation in disordered dielectric mixtures are presented by emphasizing the interfacial polarization. The obtained results coincide with and cause confusion with those of the low frequency dispersion behavior. The considered…
In alloys exhibiting substitutional disorder, the variety of atomic environments manifests itself as a `disorder broadening' in their core level binding energy spectra. Disorder broadening can be measured experimentally, and in principle…
By choosing an electron gas resting instead of drifting in the laboratory coordinate system as the initial state, the first order perturbation calculation of the previous paper (Phys. Stat. Sol. (b) 198, 785(1996)) is revised and extended…
We study the stability of the ordered phase of flocking models with a scalar order parameter. Using both the active Ising model and a hydrodynamic description, we show that droplets of particles moving in the direction opposite to that of…
With the increased availability of high intensity time-of-flight neutron and synchrotron X-ray scattering sources that can access wide ranges of momentum transfer, the pair distribution function method has become a standard analysis…
We present a new perturbative formulation of non-equilibrium thermal field theory, based upon non-homogeneous free propagators and time-dependent vertices. Our approach to non-equilibrium dynamics yields time-dependent diagrammatic…
We study clustering through the partitions it induces on a finite labeled set $[n]=\{1,\dots,n\}$, and analyze how these partitions change under perturbations of a point configuration $X=(x_1,\dots,x_n)\in(\mathbb{R}^d)^n$. We equip the…
A Self Consistent Field Theory description of equilibrium, but non uniform, configurations adopted by semi flexible liquid crystal molecules is presented. Two cases are considered, isotropic-nematic phase boundaries, and topological defects…
The alternative approach to the displacement of gas/liquid equilibrium is developed on the basis of the Clapeyron equation. The phase transition in the system with well-established properties is taken as a reference process to search for…
Hierarchically nanostructured materials, where disorder is introduced in various length scales (at the atomic scale, the nanoscale, and the mesoscale) is one of the most promising directions to achieve extremely low thermal conductivities…
A circular twist disclination is a nontrivial example of a defect in an elastic continuum that causes large deformations. The minimal potential energy and the corresponding displacement field is calculated by solving the…
How do topological defects affect the degree of order in active matter? To answer this question we investigate an agent-based model of self-propelled particles, which accounts for polar alignment and short-ranged repulsive interactions. For…
We consider a singularly perturbed convection-diffusion problem that has in addition a shift term. We show a solution decomposition using asymptotic expansions and a stability result. Based upon this we provide a numerical analysis of high…
Disordered solids, straddling the solid-fluid boundary, lack a comprehensive continuum mechanical description. They exhibit a complex microstructure wherein multiple meta-stable states exist. Deforming disordered solids induces particles…
Disclination configurations of a nematic liquid crystal are studied within a self-consistent molecular field theory. The theory is based on a tensor order parameter, and can accommodate anisotropic elastic energies without the known…
When an amorphous solid is deformed homogeneously, the response exhibits heterogeneous plastic instabilities with localized cooperative rearrangement of cluster of particles. The heterogeneous behavior plays an important role in deciding…
The study shows that errors exist in the derivation of equilibrium equations in terms of displacement. It is discovered that when the equilibrium equations in terms of displacement are derived, the variation of the differential order of…
In this paper, we present a comprehensive investigation of stress propagation in a two-dimensional elastic circular disk. To accurately describe the displacements and stress fields within the disk, we employ a scalar and vector potential…
The interplay of interactions and disorder is studied using the Anderson-Hubbard model within the typical medium dynamical cluster approximation. Treating the interacting, non-local cluster self-energy ($\Sigma_c[{\cal \tilde{G}}](i,j\neq…