Related papers: Evolution with size in a locally periodic system: …
We present a perturbative approach to disordered systems in one spatial dimension that accesses the full range of phase disorder and clarifies the connection between localization and phase information. We consider a long chain of…
In this paper we study in detail the localized wave functions defined in Phys. Rev. Lett. {\bf 76}, 1613 (1994), in connection with the scarring effect of unstable periodic orbits in highly chaotic Hamiltonian system. These functions appear…
Wave localization is a fundamental phenomenon that appears universally in both natural materials and artificial structures and plays a crucial role in understanding the various physical properties of a system. Usually, a localized state has…
We establish logarithmic local energy decay for wave equations with a varying wavespeed in dimensions two and higher, where the wavespeed is assumed to be a short range perturbation of unity with mild radial regularity. The key ingredient…
The global response to weak time periodic forces of an array of noisy, coupled nonlinear systems might show a nonmonotonic dependence on the number of units in the array. This effect has been termed system size stochastic resonance. In this…
Growth and folding in one-layered model tissue sheets are studied in a stochastic, lattice-free single cell model which considers the discrete cellular structure of the tissue, and a coarse grained analytical approach. The polarity of the…
We model the formation and evolution of wrinkles in a floating elastic sheet under uniaxial compression. This is a canonical setup in the study of wrinkling, and whilst its static equilibrium configuration is well characterised, its…
We consider an abstract linear wave equation with a time-dependent dissipation that decays at infinity with the so-called scale invariant rate, which represents the critical case. We do not assume that the coefficient of the dissipation…
We analyze the evolution of a particle wave function when it propagates through free space in the longitudinal z-direction from a thin entrance slit to a detector behind a thin exit slit parallel to the horizontal y-axis. We consider an…
Quantum-chaotic systems exhibit several universal properties, ranging from level repulsion in the energy spectrum to wavefunction delocalization. On the other hand, if wavefunctions are localized, the levels exhibit no level repulsion and…
Chaotic evolution of structures in Coupled map lattice driven by identical noise on each site is studied (a structure is a group of neighbouring lattice-sites for whom values of dynamical variable follow certain predefined pattern). Number…
We prove local and global energy decay for the wave equation in a wave guide with damping at infinity. More precisely, the absorption index is assumed to converge slowly to a positive constant, and we obtain the diffusive phenomenon typical…
We consider a two-dimensional model of three species in rock-paper-scissors competition and study the self-organisation of the population into fascinating spiraling patterns. Within our individual-based metapopulation formulation, the…
Mathematical modelling of the evolution of the size-spectrum dynamics in aquatic ecosystems was discovered to be a powerful tool to have a deeper insight into impacts of human- and environmental driven changes on the marine ecosystem. In…
We study a nonuniversal contribution to the dephasing rate of conduction electrons due to local vibrational modes. The inelastic scattering rate is strongly influenced by multiphonon excitations, exhibiting oscillatory behaviour. For higher…
We study the large deviation function for the empirical measure of diffusing particles at one fixed position. We find that the large deviation function exhibits anomalous system size dependence in systems that satisfy the following…
We study the finite-size corrections of the dimer model on $\infty \times N$ square lattice with two different boundary conditions: free and periodic. We find that the finite-size corrections depend in a crucial way on the parity of $N$,…
This paper studies periodic traveling gravity waves at the free surface of water in a flow of constant vorticity over a flat bed. Using conformal mappings the free-boundary problem is transformed into a quasilinear pseudodifferential…
In this article we study the pointwise decay properties of solutions to the wave equation on a class of stationary asymptotically flat backgrounds in three space dimensions. Under the assumption that uniform energy bounds and a weak form of…
The propagation of nonlinear waves in one dimensional space, unsteady and compressible flow in Darcy-type porous media is analyzed. It is assumed that the weak discontinuity propagate long the characteristic path using the characteristics…