Related papers: Discrete breathers in protein structures
Breathers are localized waves, that are periodic in time or space. The concept of breathers is useful for describing many physical systems including granular lattices, Bose-Einstein condensation, hydrodynamics, plasmas and optics. Breathers…
We study the effect of discreteness on various models for patterning in bacterial colonies. In a bacterial colony with branching pattern, there are discrete entities - bacteria - which are only two orders of magnitude smaller than the…
We study the stability of a stationary discrete breather (DB) on a nonlinear trimer in the framework of the discrete nonlinear Schr\"odinger equation (DNLS). In previous theoretical investigations of the dynamics of Bose-Einstein…
It is well known that any amount of energy injected in a harmonic oscillator which is resonant and weakly coupled with a second harmonic oscillator, tunnels back and forth between these two oscillators. When the two oscillators are…
In living cells, proteins involved in specialized biochemical functions are often spatially organized within biomolecular condensates. Increasing evidence suggests that some of these condensates, including DNA repair condensates, emerge…
We study metastable behavior in a discrete nonlinear Schr\"odinger equation from the viewpoint of Hamiltonian systems theory. When there are $n < \infty$ sites in this equation, we consider initial conditions in which almost all the energy…
In this communication, we examine a nonlinear model with an impurity emulating a bend. We justify the geometric interpretation of the model and connect it with earlier work on models including geometric effects. We focus on both the…
Physico-mechanical properties of polymers in solid state, in particular conditions of their structural transformations, are substantially defined by existence and mobility of elementary nonlinear excitations. The localized oscillatory…
We analyze typical models which intend to describe (parts of) the dynamics of H-Bonds in DNA. We show that these models generically allow for nonlinear localized excitatons (NLEs) (discrete breathers). We especially study the scattering of…
We consider an infinite chain of particles linearly coupled to their nearest neighbours and subject to an anharmonic local potential. The chain is assumed weakly inhomogeneous. We look for small amplitude discrete breathers. The problem is…
We explore the dynamics of strongly localized periodic solutions (discrete solitons, or discrete breathers) in a finite one-dimensional chain of asymmetric vibro-impact oscillators. The model involves a parabolic on-site potential with…
We investigate the existence and stability of discrete breathers in a chain of masses connected by linear springs and subjected to vibro-impact on-site potentials. The latter are comprised of harmonic springs and rigid constraints limiting…
We investigate the formation process of nonlinear vibrational modes representing broad H-bridge multi--site breathers in a DNA--shaped double strand. Within a network model of the double helix we take individual motions of the bases within…
Discrete breathers are ubiquitous structures in nonlinear anharmonic models ranging from the prototypical example of the Fermi-Pasta-Ulam model to Klein-Gordon nonlinear lattices, among many others. We propose a general criterion for the…
We study a locally resonant granular material in the form of a precompressed Hertzian chain with linear internal resonators. Using an asymptotic reduction, we derive an effective nonlinear Schr\"odinger (NLS) modulation equation. This, in…
Nonlinear lattice models can support "discrete breather" excitations that stay localized in space for all time. By contrast, the localized Wannier states of linear lattice models are dynamically unstable. Nevertheless, symmetric and…
A breathing mode in a Hamiltonian system is a function on the phase space whose evolution is exactly periodic for all solutions of the equations of motion. Such breathing modes are familiar from nonlinear dynamics in harmonic traps or…
We study the properties of discrete breathers, also known as intrinsic localized modes, in the one-dimensional Frenkel-Kontorova lattice of oscillators subject to damping and external force. The system is studied in the whole range of…
Discrete time quantum walks are unitary maps defined on the Hilbert space of coupled two-level systems. We study the dynamics of excitations in a nonlinear discrete time quantum walk, whose fine-tuned linear counterpart has a flat band…
Deriving emergent patterns from models of biological processes is a core concern of mathematical biology. In the context of partial differential equations (PDEs), these emergent patterns sometimes appear as local minimisers of a…