Related papers: The kinetic energy operator in the subspaces of wa…
This paper considers two frequently used matrix representations -- what we call the $\chi$- and $\mathcal{S}$-matrices -- of a quantum operation and their applications. The matrices defined with respect to an arbitrary operator basis, that…
When the Zeeman energy approaches the characteristic kinetic energy of electrons, Landau quantization becomes important. In the vicinity of magnetars, the Zeeman energy can even be relativistic. We start from the Dirac equation and derive a…
We present the applications of variation -- wavelet analysis to polynomial/rational approximations for orbital motion in transverse plane for a single particle in a circular magnetic lattice in case when we take into account multipolar…
We analyze the different ways to define the energy operator in geometric theories of quantum mechanics. In some formulations the operator contains the scalar curvature as a multiplicative term. We show that such term can be canceled or…
In this thesis I explore challenging discrete energy minimization problems that arise mainly in the context of computer vision tasks. This work motivates the use of such "hard-to-optimize" non-submodular functionals, and proposes methods…
We extend Korevaar-Schoen's theory of metric valued Sobolev maps to cover the case of the source space being an RCD space. In this situation it appears that no version of the `subpartition lemma' holds: to obtain both existence of the limit…
Ocean turbulence plays a key role in shaping large-scale circulation, heat uptake, and biogeochemical processes. The kinetic energy (KE) wavenumber spectrum is a fundamental diagnostic, quantifying how KE is distributed across spatial…
A phenomenological kinetic energy theory of buoyant multiphase plumes is constructed, being general enough to incorporate the dissolution of the dispersive phase. We consider an axisymmetric plume, and model the dissolution by means of the…
We construct a tridiagonal matrix representation of the wave operator that maps the wave equation into a three-term recursion relation for the expansion coefficients of the wavefunction. Finding a solution of the recursion relation is…
An explicit expression for the Jacobi metric for a general Lagrangian system is obtained as a series expansion in the square root of the kinetic energy of the system and the corresponding geodesics are described in terms of an appropriate…
The effective classical/quantum dynamics of a particle constrained on a closed line embedded in a higher dimensional configuration space is analyzed. By considering explicit examples it is shown how different reduction mechanisms produce…
Using the 1D Majda-McLaughlin-Tabak model as an example, we develop numerical experiments to study the validity of the Wave Kinetic Equation (WKE) at the kinetic limit (i.e., small nonlinearity and large domain). We show that the dynamics…
Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds…
We present the concept of approximate intermittent computing and demonstrate its application. Intermittent computations stem from the erratic energy patterns caused by energy harvesting: computations unpredictably terminate whenever energy…
We study the renormalization of dimension four composite operators and the energy-momentum tensor in noncommutative complex scalar field theory. The proper operator basis is defined and it is proved that the bare composite operators are…
The semiclassical description of the dynamics of wave packets in periodic potentials and subject to an applied force relies on the concepts of effective mass and anomalous transport. This picture is valid if the force changes slowly in time…
The representation of solutions of Maxwell's equations as superpositions of scalar wavelets with vector coefficients developed earlier is generalized to wavelets with polarization, which are matrix-valued. The construction proceeds in four…
We present methods for bounding infinite-time averages in dynamical systems governed by nonlinear PDEs. The methods rely on auxiliary functionals, which are similar to Lyapunov functionals but satisfy different inequalities. The…
Determining kinetic rate constants is a highly relevant problem in biochemistry, so various methods have been designed to extract them from experimental data. Such methods have two main components: the experimental apparatus and the…
We compute the relaxation of the total energy related to a variational model for nematic elastomers, involving a nonlinear elastic mechanical energy depending on the orientation of the molecules of the nematic elastomer, and a nematic…