280 research outputs found
Polydispersed Granular Chains: From Long-lived Chaotic Anderson-like Localization to Energy Equipartition
We investigate the dynamics of highly polydispersed finite granular chains.
From the spatio-spectral properties of small vibrations, we identify which
particular single-particle displacements lead to energy localization. Then, we
address a fundamental question: Do granular nonlinearities lead to chaotic
dynamics and if so, does chaos destroy this energy localization? Our numerical
simulations show that for moderate nonlinearities, although the overall system
behaves chaotically, it can exhibit long lasting energy localization for
particular single particle excitations. On the other hand, for sufficiently
strong nonlinearities, connected with contact breaking, the granular chain
reaches energy equipartition and an equilibrium chaotic state, independent of
the initial position excitation
Non-Hermitian Acoustic Metamaterials: the role of Exceptional Points in sound absorption
Effective non-Hermitian Hamiltonians are obtained to describe coherent
perfect absorbing and lasing boundary conditions. PT -symmetry of the
Hamiltonians enables to design configurations which perfectly absorb at
multiple frequencies. Broadened and flat perfect absorption is predicted at the
exceptional point of PT -symmetry breaking while, for a particular case,
absorption is enhanced with the use of gain. The aforementioned phenomena are
illustrated for acoustic scattering through Helmholtz resonators revealing how
tailoring the non-Hermiticity of acoustic metamaterials leads to novel
mechanisms for enhanced absorption
Beating dark-dark solitons and Zitterbewegung in spin-orbit coupled Bose-Einstein condensates
We present families of beating dark-dark solitons in spin-orbit (SO) coupled
Bose-Einstein condensates. These families consist of solitons residing
simultaneously in the two bands of the energy spectrum. The soliton components
are characterized by two different spatial and temporal scales, which are
identified by a multiscale expansion method. The solitons are "beating" ones,
as they perform density oscillations with a characteristic frequency, relevant
to Zitterbewegung (ZB). We find that spin oscillations may occur, depending on
the parity of each soliton branch, which consequently lead to ZB oscillations
of the beating dark solitons. Analytical results are corroborated by numerical
simulations, illustrating the robustness of the solitons.Comment: 6 pages, 3 figure
Wave propagation in a strongly disordered 1D phononic lattice supporting rotational waves
We investigate the dynamical properties of a strongly disordered micropolar
lattice made up of cubic block units. This phononic lattice model supports both
transverse and rotational degrees of freedom hence its disordered variant
posses an interesting problem as it can be used to model physically important
systems like beam-like microstructures. Different kinds of single site
excitations (momentum or displacement) on the two degrees of freedom are found
to lead to different energy transport both superdiffusive and subdiffusive. We
show that the energy spreading is facilitated both by the low frequency
extended waves and a set of high frequency modes located at the edge of the
upper branch of the periodic case for any initial condition. However, the
second moment of the energy distribution strongly depends on the initial
condition and it is slower than the underlying one dimensional harmonic lattice
(with one degree of freedom). Finally, a limiting case of the micropolar
lattice is studied where Anderson localization is found to persist and no
energy spreading takes place
Conservation laws, exact travelling waves and modulation instability for an extended nonlinear Schr\"odinger equation
We study various properties of solutions of an extended nonlinear
Schr\"{o}dinger (ENLS) equation, which arises in the context of geometric
evolution problems -- including vortex filament dynamics -- and governs
propagation of short pulses in optical fibers and nonlinear metamaterials. For
the periodic initial-boundary value problem, we derive conservation laws
satisfied by local in time, weak (distributional) solutions, and
establish global existence of such weak solutions. The derivation is obtained
by a regularization scheme under a balance condition on the coefficients of the
linear and nonlinear terms -- namely, the Hirota limit of the considered ENLS
model. Next, we investigate conditions for the existence of traveling wave
solutions, focusing on the case of bright and dark solitons. The balance
condition on the coefficients is found to be essential for the existence of
exact analytical soliton solutions; furthermore, we obtain conditions which
define parameter regimes for the existence of traveling solitons for various
linear dispersion strengths. Finally, we study the modulational instability of
plane waves of the ENLS equation, and identify important differences between
the ENLS case and the corresponding NLS counterpart. The analytical results are
corroborated by numerical simulations, which reveal notable differences between
the bright and the dark soliton propagation dynamics, and are in excellent
agreement with the analytical predictions of the modulation instability
analysis.Comment: 27 pages, 5 figures. To be published in Journal of Physics A:
Mathematical and Theoretica
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