Related papers: A closed-form energy-minimization basis for gravit…
The effects of quantum fluctuations in fields confined by background configurations may be simply and transparently computed using the Green's function approach pioneered by Schwinger. Not only can total energies and surface forces be…
This article investigates reconstructing the internal mass density of a numerical asteroid model using the gradient of a simulated gravity field as synthetic measurement data. Our goal is to advance the mathematical inversion methodology…
We consider the question of quantitative stability of minimisers for a well-known variational problem for which the infimum of the energy is not achieved in the classical sense, namely for the Dirichlet energy of degree $1$ maps from closed…
We give an a posteriori analysis of a semi-discrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics, which involves an energy density depending not only on the strain but also the strain…
We consider the backreaction problem of a quantized minimally coupled massless scalar field in cosmology. The adiabatically regularized stress-energy tensor in a general Friedmann-Robertson-Walker background is approximately evaluated by…
The gravitational equations were derived in general relativity (GR) using the assumption of their covariance relative to arbitrary transformations of coordinates. It has been repeatedly expressed an opinion over the past century that such…
A discrete-to-continuum analysis for free-boundary problems related to crystalline films deposited on substrates is performed by $\Gamma$-convergence. The discrete model here introduced is characterized by an energy with two contributions,…
The Dirac-Fock (DF) model replaces the Hartree-Fock (HF) approximation in quantum chemistry when relativistic effects cannot be neglected. Since the Dirac operator is not bounded from below, the notion of ground state is problematic in this…
We propose a method to decompose the total energy of a supercell containing defects into contributions of individual atoms, using the energy density formalism within density functional theory. The spatial energy density is unique up to a…
In this work the Vacuum Energy Density Problem or Dark Energy Problem is studied on the basis of the earlier results by the author within the scope of the Holographic Principle. It is demonstrated that the previously introduced deformed…
The present paper is an attempt to demonstrate how the energy minimization principle may be considered as a governing rule for the physical equilibrium that determines the flow fields in tubes and networks. We previously investigated this…
We consider a setting in which an evolving surface is implicitly characterized as the zero level of a level set function. Such an implicit surface does not encode any information about the path of a single point on the evolving surface. In…
Decarbonizing the energy sector is one of the main challenges to combat the climate crisis. Cities play an important role to reach climate neutrality as more than 70% of global CO2 emissions originate from urban areas. Decarbonization of…
This short note is concerned with the rotational invariance of the stored energy density in continuum physics as a scalar function of a few vectors. A simple derivation is presented for the determination of the general form of the energy…
For a general dark-energy equation of state, we estimate the maximum possible radius of massive structures that are not destabilized by the acceleration of the cosmological expansion. A comparison with known stable structures constrains the…
We show that the warped de Sitter compactifications are possible under certain conditions in D-dimensional gravitational theory coupled to a dilaton, a form field strength, and a cosmological constant. We find that the solutions of field…
The condensed matter examples, in which the effective gravity appears in the low-energy corner as one of the collective modes of quantum vacuum, provide a possible answer to the question, why the vacuum energy is so small. This answer comes…
We establish the global existence of weak solutions to a nonlinear kinetic Fokker--Planck equation with degenerate diffusion, under either inflow or partial absorption-reflection boundary conditions. The novelty of our approach lies in…
We present here a formulation of the electronic ground-state energy in terms of the second order reduced density matrix, using a duality argument. It is shown that the computation of the ground-state energy reduces to the search of the…
The {\em instability of vacuum energy} in de Sitter space as discussed recently by Polyakov is argued to be a generic feature when external gravitational fields are present. It is related to the existence of {\em forbidden} (by momentum…