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We present a new method to calculate formation of cosmological structure in the Newtonian limit. The method is based on Lagrangian perturbation theory plus two key theoretical extensions. One advance involves identifying and fixing a…
Photons propagating in Laguerre-Gaussian modes have characteristic orbital angular momentums, which are fundamental optical degrees of freedom. The orbital angular momentum of light has potential application in high capacity optical…
Intrinsic nonlinear elasticity deals with the deformations of elastic bodies as isometric immersions of Riemannian manifolds into the Euclidean spaces (see Ciarlet [9,10]). In this paper, we study the rigidity and continuity properties of…
This paper addresses some fundamental issues in nonconvex analysis. By using pure complementary energy principle proposed by the author, a class of fully nonlinear partial diforerential equations in nonlinear elasticity is able to converted…
This paper studies pattern formations in coupled elliptic PDE systems governed by transparent boundary conditions. Such systems unify diverse areas, including inverse boundary problems (via a single passive/active boundary measurement),…
Light is an excellent medium for both classical and quantum information transmission due to its speed, manipulability, and abundant degrees of freedom into which to encode information. Recently, space-division multiplexing has gained…
This work proposes a computational multiscale method for the mixed formulation of a second-order linear elliptic equation subject to a homogeneous Neumann boundary condition, based on a stable localized orthogonal decomposition (LOD) in…
We determine the orientations of the light distribution of individual elliptical galaxies by combining the profiles of photometric data from the literature with triaxial models. The orientation is given by a Bayesian probability…
We examine the Bose-Einstein-condensate (BEC) equivalent of transverse aspects of laser resonators. We model numerically repeated focussing of a 2-dimensional BEC, which could be achieved in practice by a series of far off-resonant light…
Lie-Poisson gauge formalism provides a semiclassical description of noncommutative $U(1)$ gauge theory with Lie algebra type noncommutativity. Using the Dirac approach to constrained Hamiltonian systems, we focus on a class of Lie-Poisson…
Complex Gaussian basis sets are optimized to accurately represent continuum radial wavefunctions over the whole space. First, attention is put on the technical ability of the optimization method to get more flexible series of Gaussian…
We explore a family of paraxial beams constructed by the linear superposition of Laguerre-Gaussian beams, representing an optical analogue to generalized $SU(2)$ Lie group coherent states. A single complex parameter controls a smooth…
$L^1$ based optimization is widely used in image denoising, machine learning and related applications. One of the main features of such approach is that it naturally provide a sparse structure in the numerical solutions. In this paper, we…
We present a general formalism that provides a systematic computation of the linear and non-linear perturbations for an arbitrary number of cosmological fluids in the early Universe going through various transitions, in particular the decay…
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…
We show how the elliptic Calogero-Moser integrable systems arise from a symplectic quotient construction, generalising the construction for A_{N-1} by Gorsky and Nekrasov to other algebras. This clarifies the role of (twisted) affine…
We consider uniformly strongly elliptic systems of the second order with bounded coefficients. First, sufficient conditions for the invariance of convex bodies obtained for linear systems without zero order term in bounded domains and…
Reparametrization invariant Lagrangian theories with higher derivatives are considered. We investigate the geometric structures behind these theories and construct the Hamiltonian formalism in a geometric way. The Legendre transformation…
This paper introduces arithmetic geometry for polynomial identity algebras using non-commutative (formal) deformation theory. Since formal deformation theory is inherently local the arithmetic and geometric results that follow give local…
We present elliptic-rogue wave solutions for integrable nonlinear soliton equations in theta functions. Unlike solutions generated on the plane wave background, these solutions depict rogue waves emerging on elliptic function backgrounds.…