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- S Flach, K Kladko, R S Mackay
- 1997

Discrete breathers are time-periodic, spatially localized solutions of equations of motion for classical degrees of freedom interacting on a lattice. They come in one-parameter families. We report on studies of energy properties of breather families in one-, two-and three-dimensional lattices. We show that breather energies have a positive lower bound if… (More)

- S Flach
- 1994

We consider time-periodic nonlinear localized excitations (NLEs) on one-dimensional translationally invariant Hamiltonian lattices with arbitrary finite interaction range and arbitrary finite number of degrees of freedom per unit cell. We analyse a mapping of the Fourier coefficients of the NLE solution. NLEs correspond to homoclinic points in the phase… (More)

- S Flach
- 1995

We present a numerical method for obtaining high-accuracy numerical solutions of spatially localized time-periodic excitations on a nonlinear Hamilto-nian lattice. We compare these results with analytical considerations of the spatial decay. We show that nonlinear contributions have to be considered, and obtain very good agreement between the latter and the… (More)

- S Flach, K Kladko, C R Willis
- 1994

We analyze the origin and features of localized excitations in a discrete two-dimensional Hamiltonian lattice. The lattice obeys discrete translational symmetry, and the localized excitations exist because of the presence of non-linearities. We connect the presence of these excitations with the existence of local integrability of the original N degree of… (More)

Vulnerabilities related to weak passwords are a pressing global economic and security issue. We report a novel, simple, and effective approach to address the weak-password problem. Building upon chaotic dynamics, criticality at phase transitions, CAPTCHA recognition, and computational round-off errors, we design an algorithm that strengthens the security of… (More)

- S Flach, G Mutschke
- 1994

The object of our study is the one-dimensional discrete Φ 4 model. We compare two equilibrium properties by use of molecular dynamics simulations: the Lyapunov spectrum and the time dependence of displacement-displacement and energy-energy correlation functions. Both properties imply the existence of a dynamical crossover of the system at the same… (More)

- S Flach
- 1995

We study tangent bifurcation of band edge plane waves in nonlinear Hamiltonian lattices. The lattice is translationally invariant. We argue for the breaking of permutational symmetry by the new bifurcated periodic orbits. The case of two coupled oscillators is considered as an example for the perturbation analysis, where the symmetry breaking can be traced… (More)

We give definitions for different types of moving spatially localized objects in discrete nonlinear lattices. We derive general analytical relations connecting frequency, velocity and localization length of moving discrete breathers and kinks in nonlinear one-dimensional lattices. Then we propose numerical algorithms to find these solutions.

We analyze the classical and quantum properties of the integrable dimer problem. The classical version exhibits exactly one bifurcation in phase space, which gives birth to permutational symmetry broken trajectories and a sepa-ratrix. The quantum analysis yields all tunneling rates (splittings) in leading order of perturbation. In the semiclassical regime… (More)

- S Flach, C R Willis
- 1994

We analyze the effect of internal degrees of freedom on the movability properties of localized excitations on nonlinear Hamiltonian lattices by means of properties of a local phase space which is at least of dimension six. We formulate generic properties of a movability separatrix in this local phase space. We prove that due to the presence of internal… (More)