Related papers: Variational Principle for Planetary Interiors
This paper describes a path integral formulation of the free energy principle. The ensuing account expresses the paths or trajectories that a particle takes as it evolves over time. The main results are a method or principle of least action…
A method for designing variational principles for the dynamics of a possibly dissipative and non-conservatively forced chain of particles is demonstrated. Some qualitative features of the formulation are discussed.
The variational principle for a thin dust shell in General Relativity is constructed. The principle is compatible with the boundary-value problem of the corresponding Euler-Lagrange equations, and leads to ``natural boundary conditions'' on…
The virial theorem is considered for a system of randomly moving particles that are tightly bound to each other by the gravitational and electromagnetic fields, acceleration field and pressure field. The kinetic energy of the particles of…
Variational formulations of statics and dynamics of mechanical systems controlled by external forces are presented as examples of variational principles.
Astrophysical observations reveal a large diversity of radii and masses of exoplanets. It is important to characterize the interiors of exoplanets to understand planetary diversity and further determine how unique, or not, Earth is.…
Most our knowledge about rocky exoplanets is based on their measure of mass and radius. These two parameters are routinely measured and are used to categorise different populations of observed exoplanets. They are also tightly linked to the…
This chapter reviews the most recent advancements on the topic of terrestrial and giant planet interiors, including Solar System and extrasolar objects. Starting from an observed mass-radius diagram for known planets in the Universe, we…
The theory of causal fermion systems is a recent approach to fundamental physics. Giving quantum mechanics, general relativity and quantum field theory as limiting cases, it is a candidate for a unified physical theory. The dynamics is…
I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized…
Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables.…
The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic…
The great diversity of the thousands of planets known to date is proof of the multitude of ways in which formation and evolution processes can shape the life of planetary systems. Multiple formation and evolution paths, however, can result…
We introduce a new approach to a century old assumption which enhances not only planetary interior calculations but also high pressure material physics. We show that the polytropic index is the derivative of the bulk modulus with respect to…
Variation principle has been developed to calculate many-particle effects in crystals. Within the framework of quasi-particle concept the variation principle has been used to find one-electron states with taking into account of effects due…
A variational principle is suggested within Riemannnian geometry, in which an auxiliary metric and the Levi Civita connection are varied independently. The auxiliary metric plays the role of a Lagrange multiplier and introduces non-minimal…
The possibility of fundamental theories with very many ground states, each with different physical parameters, changes the way that we approach the major questions of particle physics. Most importantly, it raises the possibility that these…
Small bodies, the unaccreted leftovers of planetary formation, are often mistaken for the leftovers of planetary science in the sense that they are everything else after the planets and their satellites (or sometimes just their regular…
The virial theorem for non-relativistic complex fields in $D$ spatial dimensions and with arbitrary many-body potential is derived, using path-integral methods and scaling arguments recently developed to analyze quantum anomalies in…
The interiors of many planets consist mostly of fluid layers. When these layers are subject to superadiabatic temperature or compositional gradients, turbulent convection transports heat and momentum. In addition, planets are fast rotators.…