Related papers: Variational Principle for Planetary Interiors
We show that stability of planetary systems is intimately connected with their internal order. An arbitrary initial distribution of planets is susceptible to catastrophic events in which planets either collide or are ejected from the…
A variational Perturbation theory based on the functional integral approach is formulated for many-particle systems. Using the variational action obtained through Jensen-Peierls' inequality, a perturbative expansion scheme for the…
Following Feynman's treatment of the non-relativistic polaron problem, similar techniques are used to study relativistic field theories: after integrating out the bosonic degrees of freedom the resulting effective action is formulated in…
The physical processes that determine the properties of our everyday world, and of the wider cosmos, are determined by some key numbers: the 'constants' of micro-physics and the parameters that describe the expanding universe in which we…
As a direct result of ongoing efforts to detect more exoplanetary systems, an ever-increasing number of multiple-planet systems are being announced. But how many of these systems are truly what they seem? In many cases, such systems are…
An extremely simple and unified base for physics comes out by starting all over from a single postulate on the common nature of matter and stationary forms of radiation quanta. Basic relativistic, gravitational (G) and quantum mechanical…
A relation between variational principles for equations of continuum mechanics in Eulerian and Lagrangian descriptions is considered. It is shown that for a system of differential equations in Eulerian variables corresponding Lagrangian…
The time dependent quantum variational principle is emerging as an important means of studying quantum dynamics, particularly in early universe scenarios. To date all investigations have worked within a Gaussian framework. Here we present…
Planet formation models have been developed during the last years in order to try to reproduce the observations of both the solar system, and the extrasolar planets. Some of these models have partially succeeded, focussing however on…
A discrete and exact algorithm for obtaining planetary systems is derived in a recent article (Eur. Phys. J. Plus 2022, 137:99). Here the algorithm is used to obtain planetary systems with forces different from the Newtonian inverse square…
A variation of fundamental constants of physics is proposed in a frame of static universe. It is shown when the velocity of light increases (decreases) the Planck's constant increases (decreases) and mass of bodies decreases (increases).…
The zonal winds on the surfaces of giant planets vary with latitude. Jupiter and Saturn, for example, have several bands of alternating eastward (prograde) and westward (retrograde) jets relative to the angular velocity of their global…
The gap between classical mechanics and quantum mechanics has an important interpretive implication: the Universe must have an irreducible fundamental level, which determines the properties of matter at higher levels of organization. We…
Covariational reasoning--considering how changes in one quantity affect another, related quantity--is a foundation of quantitative modeling in physics. Understanding quantitative models is a learning objective of introductory physics…
A principle is proposed according to which the dynamics of a quantum particle in a one-dimensional configuration space (OCS) is determined by a variational problem for two functionals: one is based on the mean value of the Hamilton…
The theory of the inflationary multiverse changes the way we think about our place in the world. According to its most popular version, our world may consist of infinitely many exponentially large parts, exhibiting different sets of…
Giant gaseous planets often reside on orbits in sufficient proximity to their host stars for the planetary quadrupole gravitational field to become non-negligible. In presence of an additional planetary companion, a precise characterization…
We discuss a recently proposed variational principle for deriving the variational equations associated to any Lagrangian system. The principle gives simultaneously the Lagrange and the variational equations of the system. We define a new…
The rich diversity of multi-planetary systems and their architectures is greatly contrasted by the uniformity exhibited within many of these systems. Previous studies have shown that compact Kepler systems tend to exhibit a peas-in-a-pod…
Variational integrators are a special kind of geometric discretisation methods applicable to any system of differential equations that obeys a Lagrangian formulation. In this thesis, variational integrators are developed for several…