Related papers: The inhomogeneous Fermi-Pasta-Ulam chain
We present a non-perturbative, mean-field theory for the Fermi-Pasta-Ulam-Tsingou model with quartic interaction, capturing the quasiperiodic features shown by the system at all energies in the thermodynamic limit. Starting from the true…
The spatiotemporal propagation of a momentum excitation on the finite Fermi-Pasta-Ulam lattices is investigated. The competition between the solitary wave and phonons gives rise to interesting propagation behaviors. For a moderate…
We study the statistics and short-times dynamics of the classical and the quantum Fermi-Pasta-Ulam chain in thermal equilibrium. We analyze the distributions of single-particle configurations by integrating out the rest of the system. At…
The system of N particles moving on a circle and interacting via a global repulsive cosine interaction is well known to display spatially inhomogeneous structures of extraordinary stability starting from certain low energy initial…
Pattern formation in the classical and fractional Schnakenberg equations is studied to understand the nonlocal effects of anomalous diffusion. Starting with linear stability analysis, we find that if the activator and inhibitor have the…
Fibonacci chains are special diatomic, harmonic chains with uniform nearest neighbour interaction and two kinds of atoms (mass-ratio $r$) arranged according to the self-similar binary Fibonacci sequence $ABAABABA...$, which is obtained by…
We study a new nonlinear partial differential equation of the fifth order for the description of perturbations in the Fermi-Pasta-Ulam mass chain. This fifth-order equation is an expansion of the Gardner equation for the description of the…
We consider a class of Hermitian Hamiltonians with position-dependent mass $H=((m^alpha)p(m^beta)p(m^alpha))/2+\V$ with $2(alpha)+\beta=-1$. We apply these Hamiltonians to different piecewise flat potentials and masses (step, barrier, well…
We study a reaction diffusion system of the activator-inhibitor type with inhomogeneous reaction terms showing spatiotemporal chaos. We analyze the topological properties of the unstable periodic orbits in the slow chaotic dynamics…
Analytically tracking patterns emerging from a small amplitude Turing instability to large amplitude remains a challenge as no general theory exists. In this paper, we consider a three component reaction-diffusion system with one of its…
A diffusive ratio-dependent Holling-Tanner system subject to Neumann boundary conditions is considered. The existence of multiple bifurcations, including Turing-Hopf bifurcation, Turing-Truing bifurcation, Hopf-double-Turing bifurcation and…
Topological properties of Harper and generalized Fibonacci chains are studied in crystalline cases, i.e., for rational values of the modulation frequency. The Harper and Fibonacci crystals at fixed frequency are connected by an…
We present a theorem that allows to simplify linear stability analysis of periodic and quasiperiodic nonlinear regimes in N-particle mechanical systems (both conservative and dissipative) with different kinds of discrete symmetry. This…
The symmetric harmonic three-mass system with finite rest lengths, despite its apparent simplicity, displays a wide array of interesting dynamics for different energy values. At low energy the system shows regular behavior that produces a…
Fermi acceleration in a Fermi-Ulam model, consisting of an ensemble of particles bouncing between two, infinitely heavy, stochastically oscillating hard walls, is investigated. It is shown that the widely used approximation, neglecting the…
On the linear level elliptic equilibria of Hamiltonian systems are mere superpositions of harmonic oscillators. Non-linear terms can produce instability, if the ratio of frequencies is rational and the Hamiltonian is indefinite. In this…
The Buneman instability occurring when an electron population is drifting with respect to the ions is analyzed in the quantum linear and nonlinear regimes. The one-dimensional low-frequency and collisional model of Shokri and Niknam [Phys.…
A finite (periodic) FPU chain is chosen as a convenient point for investigating the energy exchange phenomenon in nonlinear oscillatory systems. As we have recently shown, this phenomenon may occur as a consequence of the resonant…
Nonlinear normal mode solutions of the $\beta$-FPUT chain with fixed boundaries are presented in terms of the Jacobi sn function. Exact solutions for the two particle chain are found for arbitrary linear and nonlinear coupling strengths.…
We examine dynamic structure factors of spin-1/2 chains with nearest-neighbor interactions of XX and Dzyaloshinskii-Moriya type, and with periodic and random changes in the sign of these interactions. This special kind of inhomogeneity can…