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Two discretizations, linear and nonlinear, of basic notions of the complex analysis are considered. The underlying lattice is an arbitrary quasicrystallic rhombic tiling of a plane. The linear theory is based on the discrete Cauchy-Riemann…
This paper presents the rigorous mathematical construction and foundational properties of the Divergence-Free Radiant Transform (DFRT), a spectral transform specifically designed for divergence-free vector fields, with applications in…
In this paper, by arising condition in variation, from equal time to non-equal time, I reconsider how geometrodynamics equations allow to be derived from variational principle in general relativity and then find the variation of extrinsic…
This paper presents a geometric variational discretization of compressible fluid dynamics. The numerical scheme is obtained by discretizing, in a structure preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups…
Polymer self-consistent field theory techniques are used to derive quantum density functional theory without the use of the theorems of density functional theory. Instead, a free energy is obtained from a partition function that is…
We expand the quantum mechanical wavefunction in a complete set of square integrable orthonormal basis such that the matrix representation of the Hamiltonian operator is tridiagonal and symmetric. Consequently, the matrix wave equation…
We establish existence and regularity results for boundary value problems arising from the first variation of the Willmore energy in the graphical setting. Our focus lies on two-dimensional surfaces with fixed clamped boundary conditions,…
Hartle's model provides the most widely used analytic framework to describe isolated compact bodies rotating slowly in equilibrium up to second order in perturbations in the context of General Relativity. Apart from some explicit…
Spaces with a Weyl-type connection and torsion of a special type induced by the structure of the differentiability conditions in the algebra of complex quaternions are considered. The consistency of these conditions implies the self-duality…
The average energy curvature as a function of the particle number is a molecule-specific quantity, which measures the deviation of a given functional from the exact conditions of density functional theory (DFT). Related to the lack of…
The Debye-H\"uckel approximation to the free-energy of a simple fluid is written as a functional of the pair correlation function. This functional can be seen as the Debye-H\"uckel equivalent to the functional derived in the hyper-netted…
We investigate discretization strategies for a recently introduced class of energy-based models. The model class encompasses classical port-Hamiltonian systems, generalized gradient flows, and certain systems with algebraic constraints. Our…
We consider a metric measure space with a local regular Dirichlet form. We establish necessary and sufficient conditions for upper heat kernel bounds with sub-diffusive space-time exponent to hold. This characterization is stable under…
Starting from a general classical model of many interacting particles we present a well defined step by step procedure to derive the continuum-mechanics equations of nonlinear elasticity theory with fluctuations which describe the…
Existing theoretical works differ on whether three-dimensional Dirac and Weyl semimetals are stable to a short-range-correlated random potential. Numerical evidence suggests the semimetal to be unstable, while some field-theoretic instanton…
This paper develops a comprehensive mathematical framework for energy-based modeling of physical systems, with particular emphasis on preserving fundamental structural properties throughout the modeling and discretization process. The…
The paper deals with the Weyl equation which is the massless Dirac equation. We study the Weyl equation in the stationary setting, i.e. when the spinor field oscillates harmonically in time. We suggest a new geometric interpretation of the…
The construction of meta generalized gradient approximations based on the density matrix expansion (DME) is considered as one of the most accurate technique to design semilocal exchange energy functionals in two-dimensional density…
We present a unified derivation of the dynamical correlation functions including density-density, density-current and current-current, of three-dimensional Weyl/Dirac semimetals by use of the Passarino-Veltman reduction scheme at zero…
We give a variational formulation of classical statistical mechanics where the one-body density and the local entropy distribution constitute the trial fields. Using Levy's constrained search method it is shown that the grand potential is a…