Related papers: Delone sets and dynamical systems
We introduce a field theoretic formalism enabling the direct study of dislocation and interstitial dynamics. Explicit expressions for the energies of such defects are given. We provide links to earlier numerical, discrete elastic, time…
Basic concepts and definitions in differential geometry and topology which are important in the theory of solitons and instantons are reviewed. Many examples from soliton theory are discussed briefly, in order to highlight the application…
In the paper we present a proof of the local criterion for crystalline structures which generalizes the local criterion for regular systems. A Delone set is called a crystal if it is invariant with respect to a crystallgraphic group.…
In this paper we show that the dynamics associated with slow-roll models of inflation can be investigated through a method called deformation procedure. Using the latter, we explicitly derive an expression linking two slow-roll inflationary…
We derive a reduced-order model describing the inflation and deflation dynamics of a liquid-filled hyperelastic balloon, focusing on inviscid laminar flow and the extensional motion of the balloon. We initially study the flow and pressure…
Recent developments in theory and phenomenology relevant to deep inelastic lepton scattering are reviewed, concentrating on the following topics: Predicted behaviour of non-singlet and polarized structure functions at small $x$; Theoretical…
In this paper, we study a realistic model of quintessential inflation with radiation and matter. By the analysis of the dynamical system and numerical work about the evolution of the equation of state and cosmic density parameter, we show…
Models which allow an explicit application to structurally modulated substances are reviewed within the frame of a symmetry-based approach starting from discrete lattice theory. Focus is set on models formulated in terms of local variables…
The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this…
The basic concepts relevant for the theoretical description of deep inelastic scattering within the QCD improved parton model are introduced. Recent developments in low $x$ DIS and in deep inelastic diffraction are briefly summarised. This…
We consider two minimal models of active fluid droplets that exhibit complex dynamics including steady motion, deformation, rotation and oscillating motion. First we consider a droplet with a concentration of active contractile matter…
We review some recent developments which make use of the concept of `superstatistics', an effective description for nonequilibrium systems with a varying intensive parameter such as the inverse temperature. We describe how the asymptotic…
We consider localized soliton-like solutions in the presence of a stable scalar condensate background. By the analogy with classical mechanics, it can be shown that there may exist solutions of the nonlinear equations of motion that…
An analysis of discrete systems is important for understanding of various physical processes, such as excitations in crystal lattices and molecular chains, the light propagation in waveguide arrays, and the dynamics of Bose-condensate…
In quasicrystals, the phason degree of freedom and the inherent anharmonic potentials lead to complex dynamics which cannot be described by the usual phonon modes of motion. We have constructed simple one-dimensional model systems, the…
Results of a general study on the dynamics of cosmological scalar fields with arbitrary potentials are presented. Exact and approximate attractor solutions are found, with applications to quintessence, moduli stabilization and inflation.
The subject of moving curves (and surfaces) in three dimensional space (3-D) is a fascinating topic not only because it represents typical nonlinear dynamical systems in classical mechanics, but also finds important applications in a…
We introduce an extension of hamiltonian dynamics, defined on hyperkahler manifolds, which we call ``hyperhamiltonian dynamics''. We show that this has many of the attractive features of standard hamiltonian dynamics. We also discuss the…
These lectures deal mainly with solitons in three-dimensional Moyal-deformed sigma models. The topics are: static and moving (multi-)solitons of the (integrable) Ward sigma model, with space-space and time-space noncommutativity, their…
We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence…