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This thesis describes a detailed investigation of the effects of matter inhomogeneities on the cosmological evolution of the fine structure constant using the Bekenstein-Sandvik-Barrow-Magueijo (BSBM) theory. We briefly review the…
The equilibrium configuration of an engineering structure, able to withstand a certain loading condition, is usually associated with a local minimum of the underlying potential energy. However, in the nonlinear context, there may be other…
We propose a canonical description of the dynamics of quantum systems on a class of Robertson-Walker space-times. We show that the worldline of an observer in such space-times determines a unique orbit in the local conformal group SO(4,1)…
This paper presents existence theories for several families of axisymmetric solitary waves on the surface of an otherwise cylindrical ferrofluid jet surrounding a stationary metal rod. The ferrofluid, which is governed by a general…
We develop a theory of massive spinning particles interacting with background fields in four spacetime dimensions in which holomorphy and chirality play a central role. Applying a perturbation theory of symplectic forms to the massive…
Turbulent magnetic fields are to some extent a universal feature in astrophysical phenomena. Charged particles that encounter these turbulence get on average accelerated according to the so-called second-order Fermi process. However, in…
The steady sliding state of periodic structures such as charge density waves and flux line lattices is numerically studied based on two and three dimensional driven random field XY models. We focus on the dynamical phase transition between…
The Hamilton-Jacobi analysis is applied to the dynamics of the scalar fluctuations about the Friedmann-Robertson-Walker (FRW). The gauge conditions are found from the consistency conditions. The physical degrees of freedom of the model are…
Self-consistent N-body simulations are efficient tools to study galactic dynamics. However, using them to study individual trajectories (or ensembles) in detail can be challenging. Such orbital studies are important to shed light on global…
Recently the phase space structures governing reaction dynamics in Hamiltonian systems have been identified and algorithms for their explicit construction have been developed. These phase space structures are induced by saddle type…
Exchange forces on the movable dot ("shuttle") in a magnetic shuttle device depend on the parity of the number of shuttling electrons. The performance of such a device can therefore be tuned by changing the strength $U$ of Coulomb…
This paper deals with the classical trajectories for two super-integrable systems: a system known in quantum chemistry as the Hartmann system and a system of potential use in quantum chemistry and nuclear physics. Both systems correspond to…
With the discovery over the last two decades of a large diversity of exoplanetary systems, it is now of prime importance to characterize star-planet interactions and how such systems evolve. We address this question by studying systems…
Among theoretical issues in General Relativity the problem of constructing its Hamiltonian formulation is still of interest. The most of attempts to quantize Gravity are based upon Dirac generalization of Hamiltonian dynamics for system…
The compelling original idea of a time crystal has referred to a structure that repeats in time as well as in space, an idea that has attracted significant interest recently. While obstructions to realize such structures became apparent…
We study the transition between Zeeman levels of an arbitrary spin placed into a regular time-dependent field and a random field with the Gaussian distribution. One component of the regular field changes its sign at some moment of time,…
Using the method of superbosonization we consider a model of a random magnetic field (RMF) acting on both orbital motion and spin of electrons in two dimensions. The method is based on exact integration over one particle degrees of freedom…
In this paper, two models of interest for Celestial Mechanics are presented and analysed, using both analytic and numerical techniques, from the point of view of the possible presence of regular and/or chaotic motion, as well as the…
We discuss the stability of three- and four-particle system interacting by pure Coulomb interactions, as a function of the masses and charges of the particles. We present a certain number of general properties which allow to answer a…
Astrophysical dynamos feature various spatial structures and dynamical regimes, ranging from hemispherical magnetic fields to the random reversals of the geodynamo. The recently observed Tayler-Spruit dynamo has been invoked to explain…