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A Birman-Schwinger Principle in Galactic Dynamics
This monograph develops an innovative approach that utilizes the Birman-Schwinger principle from quantum mechanics to investigate stability...
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Helically symmetric equilibria for some ideal and resistive MHD plasmas with incompressible flows
In this paper, the problem of finding exact solutions to the magnetohydrodynamic (MHD) equations in the presence of incompressible mass flows with...
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Regular and Singular Behaviours and New Morphologies in the Rayleigh Taylor Instability
The Rayleigh Taylor Instability is a fluid instability that develops when fluids of different densities are accelerated against their density...
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Introduction
The Birman-Schwinger principle is a widely used and well-established tool in mathematical quantum mechanics. It was introduced through the...
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Closing in on the Cosmos: Cosmology’s Rebirth and the Rise of the Dark Matter Problem
Influenced by the renaissance of general relativity that came to pass in the 1950s, the character of cosmology fundamentally changed in the 1960s as...
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Clean numerical simulation: a new strategy to obtain reliable solutions of chaotic dynamic systems
It is well-known that chaotic dynamic systems, e.g., three-body system and turbulent flow, have sensitive dependence on the initial conditions...
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Controller Tuning by Metaheuristics Optimization
Metaheuristics are suitable for optimizing a broad class of problems. Subsequently, metaheuristics have attracted the attention of researchers from...
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Topological Phase Transitions
This chapter aims to develop a systematic theory of topological phase transitions (TPTs) and explores a few typical examples, including (1) quantum...
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The Big-Bang Theory: Construction, Evolution and Status
Over the past century, rooted in the theory of general relativity, cosmology has developed a very successful physical model of the universe: the...
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Gravitational-Wave Research as an Emerging Field in the Max Planck Society: The Long Roots of GEO600 and of the Albert Einstein Institute
This chapter explores the interplay between the renaissance of general relativity and the advent of relativistic astrophysics following German...
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The Socio-Epistemic Networks of General Relativity, 1925–1970
We report the results of our analysis of the development of general relativity between 1925 and 1970 based on the conceptual and methodological...
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Preservation of Bifurcations of Hamiltonian Boundary Value Problems Under Discretisation
We show that symplectic integrators preserve bifurcations of Hamiltonian boundary value problems and that non-symplectic integrators do not. We...
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Mean Field Limits for Interacting Diffusions in a Two-Scale Potential
In this paper, we study the combined mean field and homogenization limits for a system of weakly interacting diffusions moving in a two-scale,...
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Simulation of collisionless ultrarelativistic electron–proton plasma dynamics in a self-consistent electromagnetic field
The evolution of a collisionless electron–proton plasma in the self-consistent approximation is investigated. The plasma is assumed to move initially...
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Inflation and the Origins of Structure
Guth (Phys. Rev. D 23:347–56, 1981) provided a persuasive rationale for inflationary cosmology based on its ability to solve fine-tuning problems of...
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Cosmology
In this chapter we will introduce the reader to the basic general relativistic cosmological models.
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Asymptotic solutions for linear and nonlinear MHD systems with a rapid jump near a surface. dynamics of the surface of the jump and evolution of the magnetic field
We review our recent results concerning the asymptotic solutions for both linear and nonlinearMHD equations.We describe the asymptotic structure of...
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Existence and Nonlinear Stability of Stationary States for the Magnetic Schrödinger–Poisson System
We study stationary states of the magnetic Schrödinger–Poisson system in the repulsive (plasma physics) Coulomb case. We prove the existence and...
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Post-Newtonian Gravitation
Einstein’s field equations relate space-time geometry to matter and energy distribution. These tensorial equations are so unwieldy that solutions are...
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Nonstationary contrasting structures in the vicinity of a critical point
Evolution equations of the internal transition layer (ITL) have been derived for the reaction-diffusion equation and for a pseudo-parabolic...