Related papers: The transformation matrices (distortion, orientati…
We study jammed near-crystalline materials composed of frictionless spheres in three dimensions. We analyze the fluctuations in positions and forces produced by small polydispersity in particle sizes. We generalize a recently developed…
A survey is presented of the dynamic features of non-itinerant off-center defects in crystals, such as rotation-like reorientation of isolated species by either impurity or host ions. The occurrence of off-center displacements in…
The aim of this paper is to understand the tendency to organization of the turbulence in two-dimensional ideal fluids. We show that nonlinear processes as inverse cascade of the energy and vorticity concentration are essentially determined…
The polarization matrix ($2\times2$) obtained from two component eigen-spinors of spherical harmonics help us to evaluate the differential matrix $N$ of the anisotropic optical medium. The geometric phase is realized through {\it helicity}…
The homotopy theory of topological defects in ordered media fails to completely characterize systems with broken translational symmetry. We argue that the problem can be understood in terms of the lack of rotational Goldstone modes in such…
Markov matrices have an important role in the filed of stochastic processes. In this paper, we will show and prove a series of conclusions on Markov matrices and transformations rather than pay attention to stochastic processes although…
The static behavior of orientational glasses is discussed in terms of a replica theory based on the infinite range random bond--random field model. A general version of the model applicable to dipolar and quadrupolar glasses is presented…
We discuss complex rephasing invariants of charged lepton and neutrino mass matrices and associated theorems which determine in general (i) the number of physically meaningful phases in these matrices and (ii) which elements of these…
The transformation formulas between two inertial frames for the minimum phase velocity and the phase velocity in an arbitrary direction are given. The derived transformation formula for the reciprocal of the phase velocity along the…
We present explicit descriptions of the decompositions of vertices of a hypercube graph with respect to its distinguished symmetric cycle.
In the paper, a new method determining the wave vector star channel in the reciprocal lattice space of crystal in the light of the translational symmetry breaking is proposed, and, in order to consider the phase transitions according to the…
Three-dimensional lattices are fundamental to solid-state physics. The description of a lattice with an atomic basis constitutes the necessary information to predict solid phase properties and evolution. Here, we present a new algorithm for…
Information transfer between triangle meshes is of great importance in computer graphics and geometry processing. To facilitate this process, a smooth and accurate map is typically required between the two meshes. While such maps can…
The geometry of rotations in dimensions 3, 4, and 5 is discussed using the matrix exponential map. Explicit closed formulas for the exponential of an antisymmetric matrix, as well as the logarithm of a rotation, are given for these…
The paper reports the recent results on application and extension of the matrix formulation of lagrangian hydrodynamic equations. The matrix approach is based on the notion of continuous deformation of infinitesimal material elements and…
The exploration of solid-solid phase transition suffers from the uncertainty of how atoms in two crystal structures match. We devised a theoretical framework to describe and classify crystal-structure matches (CSM). Such description fully…
Inverse melting, in which a crystal reversibly transforms into a liquid or amorphous phase upon decreasing the temperature, is considered to be very rare in nature. The search for such an unusual equilibrium phenomenon is often hampered by…
The inherent inconsistency in identifying the phase field in the phase field crystal Theory with the material mass and, simultaneously, with material distortion is discussed. In its current implementation, elastic relaxation in the phase…
A unification of characteristic mode decomposition for all method-of-moment formulations of field integral equations describing free-space scattering is derived. The work is based on an algebraic link between impedance and transition…
Equilibrium shape and orientation of vortex lattice are studied for an s-wave tetrahedral superconductor in the vicinity of the upper critical field. The phase diagram, which includes transitions between rhombic and rectangular lattices, is…