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We focus on the initial boundary value problem for a general scalar balance law in one space dimension. Under rather general assumptions on the flux and source functions, we prove the well-posedness of this problem and the stability of its…
The three-body problem is famously chaotic, with no closed-form analytical solutions. However, hierarchical systems of three or more bodies can be stable over indefinite timescales. A system is considered hierarchical if the bodies can be…
A simple quark-diquark model for the baryons is constructed as a partial solution to the well known missing resonances problem. A complete classification of the baryonic states in the quark-diquark framework is given and the spectrum is…
Three-body systems of scalar bosons are described in the framework of relativistic constraint dynamics. With help of a change of variables followed by a change of wave function, two redundant degrees of freedom get eliminated and the…
In this thesis a model framework for describing baryons as diquark-quark bound states is presented which is formulated in an explicitly covariant manner. The relativistic bound state problem for three quarks is considered. Diquarks are…
We extend our earlier work, regarding the perturbative stability of string configurations used for computing the interaction potential of heavy quarks within the gauge/gravity correspondence, to cover a more general class of gravity duals.…
We review the orbital stability of the planar circular restricted three-body problem, in the case of massless particles initially located between both massive bodies. We present new estimates of the resonance overlap criterion and the Hill…
In this dissertation, we review the study of quark and monopole bound-state potentials within the gauge/gravity correspondence. Their behaviors often differ from what is expected on general physical grounds and field-theory considerations.…
We consider baryon vertices within the gauge/gravity correspondence for a class of curved backgrounds. The holographic description based on the N=4 SYM theory for SU(N) allows classical solutions representing bound states of k-quarks with k…
String dynamics in a curved space-time is studied on the basis of an action functional including a small parameter of rescaled tension $\epsilon=\gamma/\alpha^{\prime}$, where $\gamma$ is a metric parametrizing constant. A rescaled slow…
A system of equations consisting of an infinite string coupled to a nonlinear oscillator is considered. The Cauchy problem for the system with the periodic initial data is studied. The main goal is to prove the convergence of the solutions…
Network systems and their control are highly important and appear in a variety of applications, including vehicle platooning and formation con- trol. Especially vehicle platoons are highly investigated and an interesting problem that arises…
We review the spectrum and electromagnetic properties of baryons described as relativistic three-quark bound states within QCD. The composite nature of baryons results in a rich excitation spectrum, whilst leading to highly non-trivial…
For vibrating systems, a delay in the application of a feedback control can destroy the stabilizing effect of the control. In this paper we consider a vibrating string that is fixed at one end and stabilized with a boundary feedback with…
It is argued that the internal dynamics of a baryon, as a bound state of QCD-strings and quarks, may be captured by a theory of matrix coordinates.
Relativistic constituent quark models generally describe three-quark systems with particular interactions. The corresponding invariant mass eigenvalue spectra and pertinent eigenstates should exhibit the multiplet structure anticipated for…
We present a relativistic quark model for baryons, based on the Bethe-Salpeter equation in instantaneous approximation. Confinement is implemented by an interaction kernel which essentially is a linearly rising potential with a…
We compute fermion quantum corrections to the energy of cosmic strings. A number of rather technical tools is needed to formulate this correction and we employ isospin and gauge invariance to verify consistency of these tools. These…
We solve the Cauchy problem for the relativistic closed string in Minkowski space $M^{3+1}$, including the cases where the initial data has a knot like topology. We give the general conditions for the world sheet of a closed knotted string…
We consider the initial boundary value problem for free-evolution formulations of general relativity coupled to a parametrized family of coordinate conditions that includes both the moving puncture and harmonic gauges. We concentrate…