Journal ArticleDOI
a Mechanics for the Ricci Flow
TLDR
In this paper, the classical mechanics associated with a conformally flat Riemannian metric on a compact, n-dimensional manifold without boundary were constructed and the corresponding gradient Ricci flow equation was shown to equal the time-dependent Hamilton-Jacobi equation.Abstract:
We construct the classical mechanics associated with a conformally flat Riemannian metric on a compact, n-dimensional manifold without boundary. The corresponding gradient Ricci flow equation turns out to equal the time-dependent Hamilton–Jacobi equation of the mechanics so defined.read more
Citations
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Schroedinger vs. Navier-Stokes
TL;DR: This work supports the view that quantum mechanics has been argued to be a coarse-graining of some underlying deterministic theory by establishing a map between certain solutions of the Schroedinger equation, and the corresponding Solutions of the irrotational Navier–Stokes equation for viscous fluid flow.
Posted Content
Schroedinger vs. Navier-Stokes
TL;DR: In this paper, the quantum probability fluid (QPFL) model is proposed and it is shown that the viscosity of this fluid is proportional to Planck's constant, while the volume density of entropy is proportionally proportional to Boltzmann's constant.
Journal ArticleDOI
Two particle entanglement and its geometric duals
TL;DR: In this article, it was shown that for a system of two entangled particles, there is a dual description to the particle equations in terms of classical theory of conformally stretched spacetime.
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Metric Relativity and the Dynamical Bridge: Highlights of Riemannian Geometry in Physics
TL;DR: The notion of equivalent (dragged) metric as discussed by the authors was introduced to map the path of any accelerated body in Minkowski space-time onto a geodesic motion in such associated geometrical configurations.
Journal ArticleDOI
A new approach to nonlinear quartic oscillators
TL;DR: In this paper, the authors proved that damped quadratic nonlinear oscillators similar to Duffing and Helmholtz-Duffing damped equations which emerge in bubble dynamics with time-periodic straining flows and solitary-like wave's dynamics may be derived from a new functional approach based on nonstandard Lagrangians and fractional frictions.
References
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Book
Mathematical Methods of Classical Mechanics
TL;DR: In this paper, Newtonian mechanics: experimental facts investigation of the equations of motion, variational principles Lagrangian mechanics on manifolds oscillations rigid bodies, differential forms symplectic manifolds canonical formalism introduction to pertubation theory.
Book
Conformal Field Theory
TL;DR: This paper developed conformal field theory from first principles and provided a self-contained, pedagogical, and exhaustive treatment, including a great deal of background material on quantum field theory, statistical mechanics, Lie algebras and affine Lie algesas.
Book
Lectures on the Ricci Flow
TL;DR: In this article, the Ricci flow as a gradient flow has been studied in Riemannian manifolds and the maximum principle of Riemanian geometry has been discussed.
Journal ArticleDOI
The mathematical basis for deterministic quantum mechanics
TL;DR: In this paper, it is argued that this can be attributed to information loss, such as what one might suspect to happen during the formation and annihilation of virtual black holes, and a unique definition of energy in the quantum system in terms of the periodicity of the limit cycles of the deterministic model is proposed.