20 research outputs found
Discrete breathers in and related models
We touch upon the wide topic of discrete breather formation with a special
emphasis on the the model. We start by introducing the model and
discussing some of the application areas/motivational aspects of exploring time
periodic, spatially localized structures, such as the discrete breathers. Our
main emphasis is on the existence, and especially on the stability features of
such solutions. We explore their spectral stability numerically, as well as in
special limits (such as the vicinity of the so-called anti-continuum limit of
vanishing coupling) analytically. We also provide and explore a simple, yet
powerful stability criterion involving the sign of the derivative of the energy
vs. frequency dependence of such solutions. We then turn our attention to
nonlinear stability, bringing forth the importance of a topological notion,
namely the Krein signature. Furthermore, we briefly touch upon linearly and
nonlinearly unstable dynamics of such states. Some special aspects/extensions
of such structures are only touched upon, including moving breathers and
dissipative variations of the model and some possibilities for future work are
highlighted
Traveling waves and pattern formation for spatially discrete bistable reaction-diffusion equations (survey)
Analysis and Stochastic
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Discrete Breathers in a Forced-Damped Array of Coupled Pendula: Modeling, Computation, and Experiment
In this work, we present a mechanical example of an experimental realization of a stability reversal between on-site and intersite centered localized modes. A corresponding realization of a vanishing of the Peierls-Nabarro barrier allows for an experimentally observed enhanced mobility of the localized modes near the reversal point. These features are supported by detailed numerical computations of the stability and mobility of the discrete breathers in this system of forced and damped coupled pendula. Furthermore, additional exotic features of the relevant model, such as dark breathers are briefly discussed
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Traveling and stationary intrinsic localized modes and their spatial control in electrical lattices
This work focuses on the production of both stationary and traveling intrinsic localized modes (ILMs), also known as discrete breathers, in two closely related electrical lattices; we demonstrate experimentally that the interplay between these two ILM types can be utilized for the purpose of spatial control. We describe a novel mechanism that is responsible for the motion of driven ILMs in this system, and quantify this effect by modeling in some detail the electrical components comprising the lattice
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Traveling and stationary intrinsic localized modes and their spatial control in electrical lattices
This work focuses on the production of both stationary and traveling intrinsic localized modes (ILMs), also known as discrete breathers, in two closely related electrical lattices; we demonstrate experimentally that the interplay between these two ILM types can be utilized for the purpose of spatial control. We describe a novel mechanism that is responsible for the motion of driven ILMs in this system, and quantify this effect by modeling in some detail the electrical components comprising the lattice
An Ising machine based on networks of subharmonic electrical resonators
Combinatorial optimization problems are difficult to solve with conventional algorithms. Here we explore networks of nonlinear electronic oscillators evolving dynamically towards the solution to such problems. We show that when driven into subharmonic response, such oscillator networks can minimize the Ising Hamiltonian on non-trivial antiferromagnetically-coupled 3-regular graphs. In this context, the spin-up and spin-down states of the Ising machine are represented by the oscillatorsâ response at the even or odd driving cycles. Our experimental setting of driven nonlinear oscillators coupled via a programmable switch matrix leads to a unique energy minimizer when one exists, and probes frustration where appropriate. Theoretical modeling of the electronic oscillators and their couplings allows us to accurately reproduce the qualitative features of the ex- perimental results and extends the results to larger graphs. This suggests the promise of this setup as a prototypical one for exploring the capabilities of such an unconventional computing platform.JSF-19-02-0005, DMS-1809074, PHY-2110030, NPIF EPSRC Doctoral grant EP/R512461/
Understanding Injection Locking and Synchronization with Van der Pol-Like Self-sustained Oscillators
Experimental and numerical exploration of intrinsic localized modes in an atomic lattice
This review focuses attention on the experimental studies of intrinsic localized modes (ILMs) produced in driven atomic lattices. Production methods involve the application of modulational instability under carefully controlled conditions. One experimental approach is to drive the atomic lattice far from equilibrium to produce ILMs, the second is to apply a driver of only modest strength but nearby in frequency to a plane wave mode so that a slow transformation from large amplitude standing waves to ILMs takes place. Since, in either case, the number of ILMs produced is small, the experimental observation tool appropriate for this task is four-wave mixing. This nonlinear detection technique makes use of the nonlinearity associated with an ILM to enhance its signal over that produced by the more numerous, but linear, spin waves. The final topic deals with numerical simulations of a nonlinear nanoscale atomic lattice where the new feature is running ILMs