Discrete soliton collisions in a waveguide array with saturable nonlinearity

We study the symmetric collisions of two mobile breathers/solitons in a model for coupled wave guides with a saturable nonlinearity. The saturability allows the existence of breathers with high power. Three main regimes are observed: breather fusion, breather reflection and breather creation. The last regime seems to be exclusive of systems with a saturable nonlinearity, and has been previously observed in continuous models. In some cases a ``symmetry breaking'' can be observed, which we show to be an numerical artifact.Comment: 5 pages, 7 figure

On Neuromechanical Approaches for the Study of Biological Grasp and Manipulation

Biological and robotic grasp and manipulation are undeniably similar at the level of mechanical task performance. However, their underlying fundamental biological vs. engineering mechanisms are, by definition, dramatically different and can even be antithetical. Even our approach to each is diametrically opposite: inductive science for the study of biological systems vs. engineering synthesis for the design and construction of robotic systems. The past 20 years have seen several conceptual advances in both fields and the quest to unify them. Chief among them is the reluctant recognition that their underlying fundamental mechanisms may actually share limited common ground, while exhibiting many fundamental differences. This recognition is particularly liberating because it allows us to resolve and move beyond multiple paradoxes and contradictions that arose from the initial reasonable assumption of a large common ground. Here, we begin by introducing the perspective of neuromechanics, which emphasizes that real-world behavior emerges from the intimate interactions among the physical structure of the system, the mechanical requirements of a task, the feasible neural control actions to produce it, and the ability of the neuromuscular system to adapt through interactions with the environment. This allows us to articulate a succinct overview of a few salient conceptual paradoxes and contradictions regarding under-determined vs. over-determined mechanics, under- vs. over-actuated control, prescribed vs. emergent function, learning vs. implementation vs. adaptation, prescriptive vs. descriptive synergies, and optimal vs. habitual performance. We conclude by presenting open questions and suggesting directions for future research. We hope this frank assessment of the state-of-the-art will encourage and guide these communities to continue to interact and make progress in these important areas

Field enhancement in subnanometer metallic gaps

Motivated by recent experiments [Ward et al., Nature Nanotech. 5, 732 (2010)], we present here a theoretical analysis of the optical response of sharp gold electrodes separated by a subnanometer gap. In particular, we have used classical finite difference time domain simulations to investigate the electric field distribution in these nanojunctions upon illumination. Our results show a strong confinement of the field within the gap region, resulting in a large enhancement compared to the incident field. Enhancement factors exceeding 1000 are found for interelectrode distances on the order of a few angstroms, which are fully compatible with the experimental findings. Such huge enhancements originate from the coupling of the incident light to the evanescent field of hybrid plasmons involving charge density oscillations in both electrodes.Comment: 4 pages, 3 figures, to appear in Physical Review

Thresholds for breather solutions on the Discrete Nonlinear Schr\"odinger Equation with saturable and power nonlinearity

We consider the question of existence of periodic solutions (called breather solutions or discrete solitons) for the Discrete Nonlinear Schr\"odinger Equation with saturable and power nonlinearity. Theoretical and numerical results are proved concerning the existence and nonexistence of periodic solutions by a variational approach and a fixed point argument. In the variational approach we are restricted to DNLS lattices with Dirichlet boundary conditions. It is proved that there exists parameters (frequency or nonlinearity parameters) for which the corresponding minimizers satisfy explicit upper and lower bounds on the power. The numerical studies performed indicate that these bounds behave as thresholds for the existence of periodic solutions. The fixed point method considers the case of infinite lattices. Through this method, the existence of a threshold is proved in the case of saturable nonlinearity and an explicit theoretical estimate which is independent on the dimension is given. The numerical studies, testing the efficiency of the bounds derived by both methods, demonstrate that these thresholds are quite sharp estimates of a threshold value on the power needed for the the existence of a breather solution. This it justified by the consideration of limiting cases with respect to the size of the nonlinearity parameters and nonlinearity exponents.Comment: 26 pages, 10 figure

Tuning the thermal conductance of molecular junctions with interference effects

We present an \emph{ab initio} study of the role of interference effects in the thermal conductance of single-molecule junctions. To be precise, using a first-principles transport method based on density functional theory, we analyze the coherent phonon transport in single-molecule junctions based on several benzene and oligo-phenylene-ethynylene derivatives. We show that the thermal conductance of these junctions can be tuned via the inclusion of substituents, which induces destructive interference effects and results in a decrease of the thermal conductance with respect to the unmodified molecules. In particular, we demonstrate that these interference effects manifest as antiresonances in the phonon transmission, whose energy positions can be controlled by varying the mass of the substituents. Our work provides clear strategies for the heat management in molecular junctions and more generally in nanostructured metal-organic hybrid systems, which are important to determine, how these systems can function as efficient energy-conversion devices such as thermoelectric generators and refrigerators

Discrete moving breather collisions in a Klein-Gordon chain of oscillators

We study collision processes of moving breathers with the same frequency, traveling with opposite directions within a Klein-Gordon chain of oscillators. Two types of collisions have been analyzed: symmetric and non-symmetric, head-on collisions. For low enough frequency the outcome is strongly dependent of the dynamical states of the two colliding breathers just before the collision. For symmetric collisions, several results can be observed: breather generation, with the formation of a trapped breather and two new moving breathers; breather reflection; generation of two new moving breathers; and breather fusion bringing about a trapped breather. For non-symmetric collisions the possible results are: breather generation, with the formation of three new moving breathers; breather fusion, originating a new moving breather; breather trapping with also breather reflection; generation of two new moving breathers; and two new moving breathers traveling as a ligand state. Breather annihilation has never been observed.Comment: 19 pages, 12 figure

Breathers and kinks in a simulated crystal experiment

We develop a simple 1D model for the scattering of an incoming particle hitting the surface of mica crystal, the transmission of energy through the crystal by a localized mode, and the ejection of atom(s) at the incident or distant face. This is the first attempt to model the experiment described in Russell and Eilbeck in 2007 (EPL, v. 78, 10004). Although very basic, the model shows many interesting features, for example a complicated energy dependent transition between breather modes and a kink mode, and multiple ejections at both incoming and distant surfaces. In addition, the effect of a heavier surface layer is modelled, which can lead to internal reflections of breathers or kinks at the crystal surface.Comment: 15 pages, 12 figures, based on a talk given at the conference "Localized Excitations in Nonlinear Complex Systems (LENCOS)", Sevilla (Spain) July 14-17, 200