Related papers: Point interactions in acoustics: one dimensional m…
We consider a one dimensional evolution problem modeling the dynamics of an acoustic field coupled with a set of mechanical oscillators. We analyze solutions of the system of ordinary and partial differential equations with time-dependent…
We study the oscillation spectrum and acoustic properties of a liquid drop in the phase-separated fluid when the interfacial dynamics of phase conversion can be described in terms of the kinetic growth coefficient. For a readily mobile…
We investigate numerically and experimentally dynamical systems having three interacting frequencies: a discrete mapping (a circle map), an exactly solvable model (a system of coupled ordinary differential equations), and an experimental…
We study the entanglement dynamics of a system consisting of a large number of coupled harmonic oscillators in various configurations and for different types of nearest neighbour interactions. For a one-dimensional chain we provide compact…
Oscillator models are central to the study of system properties such as entrainment or synchronization. Due to their nonlinear nature, few system-theoretic tools exist to analyze those models. The paper develops a sensitivity analysis for…
The fundamental quantum dynamics of two interacting oscillator systems are studied in two different scenarios. In one case, both oscillators are assumed to be linear, whereas in the second case, one oscillator is linear and the other is a…
A system of a particle and a harmonic oscillator, which have pure point spectrum if uncoupled, is known to acquire absolutely continuous spectrum when the particle and the oscillator are coupled by a sufficiently strong point interaction.…
We study the dynamical behaviors of a system of five coupled nonlinear equations that describes the dynamics of acoustic-gravity waves in the atmosphere. A linear stability analysis together with the analysis of Lyapunov exponents spectra…
We show that, when music pieces are cast in the form of time series of pitch variations, the concepts and tools of dynamical systems theory can be applied to the analysis of {\it temporal dynamics} in music. (i) Phase space portraits are…
A focused acoustic standing wave creates a Hookean potential well for a small sphere and can levitate it stably against gravity. Exposing the trapped sphere to a second transverse traveling sound wave imposes an additional acoustical force…
In this tutorial, three examples of stochastic systems are considered: A strongly-damped oscillator, a weakly-damped oscillator and an undamped oscillator (integrator) driven by noise. The evolution of these systems is characterized by the…
We study the evolution of entanglement of a pair of coupled, non-resonant harmonic oscillators in contact with an environment. For both the cases of a common bath and of two separate baths for each of the oscillators, a full master equation…
Active phenomena which involve force generation and motion play a key role in a number of phenomena in living cells such as cell motility, muscle contraction and the active transport of material and organelles. Here we discuss mechanical…
An important design principle for biological oscillators divides the oscillators into two classes: fixed frequency, variable amplitude and fixed amplitude, variable frequency. Because of the interplay of nonlinearity and feedback, both…
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
The dynamics of hybrid systems -- i.e. ones in which classical and quantum degrees of freedom co-exist and interact -- feature both diffusion in the classical sector and decoherence in the quantum state. In this article, we will consider…
In this thesis, I go through the well-known solutions to the one and two-particle systems trapped in a quantum harmonic oscillator and then continue to the three, four and many-body quantum systems. This is done by developing new analytical…
A variety of models describing the interaction between flows and oscillating structures are discussed. The main aim is to analyze conditions under which structural instability (flutter) induced by a fluid flow can be suppressed or…
We study a system of one-dimensional (iso)spin-1/2 bosons in the regime of strong repulsive interactions. We argue that the low-energy spectrum of the system consists of acoustic density waves and the spin excitations described by an…
One dimensional systems are under intense investigation, both from theoretical and experimental points of view, since they have rather peculiar characteristics which are of both conceptual and technological interest. We analyze the…