Related papers: A note about the perturbative dynamics of symmetri…
Perturbative Symmetry Approach is formulated in symbolic representation. Easily verifiable integrability conditions of a given equation are constructed in the frame of the approach. Generalisation for the case of non-local and non-evolution…
The linear stability parameter delta is commonly used as a figure of merit for the nonlinear dynamics of the tearing mode. It is shown, through state of the art numerical simulations, that factors other than delta can play a very important…
Characteristic modes of a spherical shell are found analytically as spherical harmonics normalized to radiate unitary power and to fulfill specific boundary conditions. The presented closed-form formulas lead to a proposal of precise…
A theoretical and experimental study of the spin-over mode induced by the elliptical instability of a flow contained in a slightly deformed rotating spherical shell is presented. This geometrical configuration mimics the liquid rotating…
Chromonic liquid crystals are lyotropic nematic phases whose applications span from food to drug industries. It has recently been suggested that the elastic energy density governing the equilibrium distortions of these materials may be…
We report on the buckling and subsequent collapse of orthotropic elastic spherical shells under volume and pressure control. Going far beyond what is known for isotropic shells, a rich morphological phase space with three distinct regimes…
A nonlinear cyclic system with delay and the overall negative feedback is considered. The characteristic equation of the linearized system is studied in detail. Sufficient conditions for the oscillation of all solutions and for the…
Despite the apparent ease with which a sheet of paper is crumpled and tossed away, crumpling dynamics are often considered a paradigm of complexity. This complexity arises from the infinite number of configurations a disordered crumpled…
Theoretical studies on the modulation of unidimensional regular waves over a flat bottom due to a current typically assign an asymmetry between the effects of opposing/following streams on the evolution of major sea variables, such as…
We investigate the gravitational fragmentation of expanding shells in the context of the linear thin--shell analysis. We make use of two very different numerical schemes; the FLASH Adaptive Mesh Refinement code and a version of the Benz…
Elasticity theory calculations predict the number N of depressions that appear at the surface of a spherical thin shell submitted to an external isotropic pressure. In a model that mainly considers curvature deformations, we show that N…
We describe some general results that constrain the dynamical fluctuations that can occur in non-equilibrium steady states, with a focus on molecular dynamics. That is, we consider Hamiltonian systems, coupled to external heat baths, and…
We complete a full classification of non-degenerate traveling waves of scalar balance laws from the point of view of spectral and nonlinear stability/instability under (piecewise) smooth perturbations. A striking feature of our analysis is…
This paper is concerned with decay and symmetry properties of solitary wave solutions to a nonlocal shallow water wave model. It is shown that all supercritical solitary wave solutions are symmetric and monotone on either side of the crest.…
Novel simple properties of the monopole component of the effective nucleon-nucleon interaction are presented, leading to the so-called monopole-based universal interaction. Shell structures are shown to change as functions of $N$ and $Z$…
This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause…
We consider evolution of initial disturbances in spatially extended systems with autonomous rhythmic activity, such as the heart. We consider the case when the activity is stable with respect to very smooth (changing little across the…
A nonlinear Schrodinger equation arising from light propagation down an inhomogeneous medium is considered. The inhomogeneity is reflected through a non-uniform coefficient of the non-linear term in the equation. In particular, a…
A model for a possible variable cosmic object is presented. The model consists of a massive shell surrounding a compact object. The gravitational and self-gravitational forces tend to collapse the shell, but the internal tangential stresses…
Time evolution equation for the Probability Distribution Function (PDF) is derived for system of weakly interacting waves. It is shown that a steady state for such system may correspond to strong intermittency.