Related papers: A closed-form energy-minimization basis for gravit…
With the idea of canceling the leading divergence in vacuum energy of $\varphi^4$ field theory a parameter is introduced that interpolates between free Hamiltonian with or without normal ordering. This leads to a condensate ground state…
We calculate the mass density of the Earth using a Gravito-Electro-Magnetic theory on an extended 5D Schwarzschild-de Sitter metric, in which we define the vacuum. Our results are in very good agreement with that of the Dziewonski-Anderson…
We present a continuum model to determine the dislocation structure and energy of low angle grain boundaries in three dimensions. The equilibrium dislocation structure is obtained by minimizing the grain boundary energy that is associated…
Exact free energy minimization is a convex optimization problem that is usually approximated with stochastic sampling methods. Deterministic approximations have been less successful because many desirable properties have been difficult to…
We consider the minimisation of power-law repulsive-attractive interaction energies which occur in many biological and physical situations. We show existence of global minimizers in the discrete setting and get bounds for their supports…
We consider the minimal energy problem on the unit sphere $\mathbb S^2$ in the Euclidean space $\mathbb R^3$ immersed in an external field $Q$, where the charges are assumed to interact via Newtonian potential $1/r$, $r$ being the Euclidean…
Although quintessence cosmologies seem to explain the amount of cosmological constant today, the required conditions are severe. For example, an extremely slowly varying and light scalar field that rolls toward the vanishing vacuum energy…
Algorithms for minimal enclosing ball problems are often geometric in nature. To highlight the metric ingredients underlying their efficiency, we focus here on a particularly simple geodesic-based method. A recent subgradient-based study…
The energy density of a conformally invariant scalar field around a cosmic string is estimated by the WKB method. This approach reproduces the precise value obtained by the other authors using the exact mode-sum method or the method of…
The theoretical vacuum energy density estimated on the basis of the Standard Model of particle physics and very general quantum assumptions is 59 to 123 orders of magnitude larger than the measured vacuum energy density for the observable…
Quantum field theory allows for the suppression of vacuum fluctuations, leading to sub-vacuum phenomena. One of these is the appearance of local negative energy density. Selected aspects of negative energy will be reviewed, including the…
The concordance model of cosmology favours a universe with a tiny positive cosmological constant. A tiniest positive constant curvature, profoundly alters the asymptotic structure, forcing a re-look at a theory of gravitational radiation.…
We study some exact and approximate solutions of Einstein's equations that can be used to describe the gravitational field of astrophysical compact objects in the limiting case of slow rotation and slight deformation. First, we show that…
The ground state of Bose--Einstein condensates can be described as the minimizer of the Gross--Pitaevskii energy functional subject to a mass conservation constraint. In this paper, we study the corresponding discrete optimization problem…
In this paper, we showed that for some given suitable density and pressure, there exist infinitely many compactly supported solutions with prescribed energy profile. The proof is mainly based on the convex integration scheme. We construct…
The internal stability of the electron has been debated for a century at both the classical and the quantum level. Recently, a local force density balance was established for the 1s electron in the H atom, based on the energy-momentum…
The following principle of minimum energy may be a powerful substitute to the dynamical perturbation method, when the latter is hard to apply. Fluid elements of self-gravitating barotropic flows, whose vortex lines extend to the boundary of…
The positive energy theorem precludes the possibility of Minkowski flat space decaying by any mechanism. In certain circumstances, however, large quantum fluctuations of the gravitational field could arise---not only at the Planck scale,…
The description of gravity in the form of an embedding theory is based on the hypothesis that our space-time is a four-dimensional surface in a flat ten-dimensional space. The choice of standard Einstein-Hilbert action leads in this case to…
This paper establishes a unified element-based framework for formation control by introducing the concept of the deformation gradient from continuum mechanics. Unlike traditional methods that rely on geometric constraints defined on graph…