By driving with a microwave pulse the lowest frequency antiferromagnetic resonance of the quasi-1D biaxial antiferromagnet ͑C 2 H 5 NH 3 ͒ 2 CuCl 4 into an unstable region, intrinsic localized spin waves have been generated and detected in the spin wave gap. These findings are consistent with the prediction that nonlinearity plus lattice discreteness can lead to localized excitations with dimensions comparable to the lattice constant.
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.
This work focuses on the production of both stationary and traveling intrinsic localized modes ͑ILMs͒, 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.
We investigate the role of the learning rate in a Kuramoto Model of coupled phase oscillators in which the coupling coefficients dynamically vary according to a Hebbian learning rule. According to the Hebbian theory, a synapse between two neurons is strengthened if they are simultaneously co-active. Two stable synchronized clusters in anti-phase emerge when the learning rate is larger than a critical value. In such a fast learning scenario, the network eventually constructs itself into an all-to-all coupled structure, regardless of initial conditions in connectivity. In contrast, when learning is slower than this critical value, only a single synchronized cluster can develop. Extending our analysis, we explore whether self-development of neuronal networks can be achieved through an interaction between spontaneous neural synchronization and Hebbian learning. We find that selfdevelopment of such neural systems is impossible if learning is too slow. Finally, we demonstrate that similar to the acquisition and consolidation of long-term memory, this network is capable of generating and remembering stable patterns.
The emergence of very stable traveling intrinsic localized modes (ILMs) locked to a uniform driver is demonstrated in a discrete electrical transmission line. The speed of these traveling ILMs is tunable by the driver amplitude and frequency. It is found to be quite sensitive to the ratio of intersite to on-site nonlinearity. The number of traveling ILMs can also be selected via the driving conditions and appears to be the result of a spatiotemporal pattern selection process.
We report the observation of spontaneous localization of energy in two spatial dimensions in the context of nonlinear electrical lattices. Both stationary and moving self-localized modes were generated experimentally and theoretically in a family of two-dimensional square as well as honeycomb lattices composed of 6 × 6 elements. Specifically, we find regions in driver voltage and frequency where stationary discrete breathers, also known as intrinsic localized modes (ILMs), exist and are stable due to the interplay of damping and spatially homogeneous driving. By introducing additional capacitors into the unit cell, these lattices can controllably induce mobile discrete breathers. When more than one such ILMs are experimentally generated in the lattice, the interplay of nonlinearity, discreteness, and wave interactions generates a complex dynamics wherein the ILMs attempt to maintain a minimum distance between one another. Numerical simulations show good agreement with experimental results and confirm that these phenomena qualitatively carry over to larger lattice sizes.
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