Bulk and surface magnetoinductive breathers in binary metamaterials

We study theoretically the existence of bulk and surface discrete breathers in a one-dimensional magnetic metamaterial comprised of a periodic binary array of split-ring resonators. The two types of resonators differ in the size of their slits and this leads to different resonant frequencies. In the framework of the rotating-wave approximation (RWA) we construct several types of breather excitations for both the energy-conserved and the dissipative-driven systems by continuation of trivial breather solutions from the anticontinuous limit to finite couplings. Numerically-exact computations that integrate the full model equations confirm the quality of the RWA results. Moreover, it is demonstrated that discrete breathers can spontaneously appear in the dissipative-driven system as a results of a fundamental instability.Comment: 10 pages, 16 figure

Cooperative surmounting of bottlenecks

The physics of activated escape of objects out of a metastable state plays a key role in diverse scientific areas involving chemical kinetics, diffusion and dislocation motion in solids, nucleation, electrical transport, motion of flux lines superconductors, charge density waves, and transport processes of macromolecules, to name but a few. The underlying activated processes present the multidimensional extension of the Kramers problem of a single Brownian particle. In comparison to the latter case, however, the dynamics ensuing from the interactions of many coupled units can lead to intriguing novel phenomena that are not present when only a single degree of freedom is involved. In this review we report on a variety of such phenomena that are exhibited by systems consisting of chains of interacting units in the presence of potential barriers. In the first part we consider recent developments in the case of a deterministic dynamics driving cooperative escape processes of coupled nonlinear units out of metastable states. The ability of chains of coupled units to undergo spontaneous conformational transitions can lead to a self-organised escape. The mechanism at work is that the energies of the units become re-arranged, while keeping the total energy conserved, in forming localised energy modes that in turn trigger the cooperative escape. We present scenarios of significantly enhanced noise-free escape rates if compared to the noise-assisted case. The second part deals with the collective directed transport of systems of interacting particles overcoming energetic barriers in periodic potential landscapes. Escape processes in both time-homogeneous and time-dependent driven systems are considered for the emergence of directed motion. It is shown that ballistic channels immersed in the associated high-dimensional phase space are the source for the directed long-range transport

A Study of The Formation of Stationary Localized States Due to Nonlinear Impurities Using The Discrete Nonlinear Schr\"odinger Equation

The Discrete Nonlinear Schr$\ddot{o}$dinger Equation is used to study the formation of stationary localized states due to a single nonlinear impurity in a Caley tree and a dimeric nonlinear impurity in the one dimensional system. The rotational nonlinear impurity and the impurity of the form $-\chi \mid C \mid^{\sigma}$ where $\sigma$ is arbitrary and $\chi$ is the nonlinearity parameter are considered. Furthermore, $\mid C \mid$ represents the absolute value of the amplitude. Altogether four cases are studies. The usual Greens function approach and the ansatz approach are coherently blended to obtain phase diagrams showing regions of different number of states in the parameter space. Equations of critical lines separating various regions in phase diagrams are derived analytically. For the dimeric problem with the impurity $-\chi \mid C \mid^{\sigma}$, three values of $\mid \chi_{cr} \mid$, namely, $\mid \chi_{cr} \mid = 2$, at $\sigma = 0$ and $\mid \chi_{cr} \mid = 1$ and $\frac{8}{3}$ for $\sigma = 2$ are obtained. Last two values are lower than the existing values. Energy of the states as a function of parameters is also obtained. A model derivation for the impurities is presented. The implication of our results in relation to disordered systems comprising of nonlinear impurities and perfect sites is discussed.Comment: 10 figures available on reques

Demonstration of Calreticulin Expression in Hamster Pancreatic Adenocarcinoma with the Use of Fluorescent Gold Quantum Dots

BACKGROUND: There is dire need for discovery of novel pancreatic cancer biomarkers and of agents with the potential for simultaneous diagnostic and therapeutic capacity. This study demonstrates calreticulin expression on hamster pancreatic adenocarcinoma via bio-conjugated gold quantum dots (AuQDs). MATERIALS AND METHODS: Hamster pancreatic adenocarcinoma cells were cultured, fixed and incubated with fluorescent AuQDs, bio-conjugated to anti-calreticulin antibodies. Anti-calreticulin and AuQDs were produced in-house. AuQDs were manufactured to emit in the near-infrared. Cells were further characterized under confocal fluorescence. RESULTS: AuQDs were confirmed to emit in the near-infrared. AuQD bio-conjugation to calreticulin was confirmed via dot-blotting. Upon laser excitation and post-incubation with bio-conjugated AuQDs, pancreatic cancer cell lines emitted fluorescence in near-infrared. CONCLUSION: Hamster pancreatic cancer cells express calreticulin, which may be labelled with AuQDs. This study demonstrates the application of nanoparticle-based theranostics in pancreatic cancer. Such biomarker-targeting nanosystems are anticipated to play a significant role in the management of pancreatic cancer

Extreme events in discrete nonlinear lattices

We perform statistical analysis on discrete nonlinear waves generated though modulational instability in the context of the Salerno model that interpolates between the intergable Ablowitz-Ladik (AL) equation and the nonintegrable discrete nonlinear Schrodinger (DNLS) equation. We focus on extreme events in the form of discrete rogue or freak waves that may arise as a result of rapid coalescence of discrete breathers or other nonlinear interaction processes. We find power law dependence in the wave amplitude distribution accompanied by an enhanced probability for freak events close to the integrable limit of the equation. A characteristic peak in the extreme event probability appears that is attributed to the onset of interaction of the discrete solitons of the AL equation and the accompanied transition from the local to the global stochasticity monitored through the positive Lyapunov exponent of a nonlinear map.Comment: 5 pages, 4 figures; reference added, figure 2 correcte

Thermal conductivity of one-dimensional lattices with self-consistent heat baths: a heuristic derivation

We derive the thermal conductivities of one-dimensional harmonic and anharmonic lattices with self-consistent heat baths (BRV lattice) from the Single-Mode Relaxation Time (SMRT) approximation. For harmonic lattice, we obtain the same result as previous works. However, our approach is heuristic and reveals phonon picture explicitly within the heat transport process. The results for harmonic and anharmonic lattices are compared with numerical calculations from Green-Kubo formula. The consistency between derivation and simulation strongly supports that effective (renormalized) phonons are energy carriers in anharmonic lattices although there exist some other excitations such as solitons and breathers.Comment: 4 pages, 3 figures. accepted for publication in JPS

Self-trapping transition for nonlinear impurities embedded in a Cayley tree

The self-trapping transition due to a single and a dimer nonlinear impurity embedded in a Cayley tree is studied. In particular, the effect of a perfectly nonlinear Cayley tree is considered. A sharp self-trapping transition is observed in each case. It is also observed that the transition is much sharper compared to the case of one-dimensional lattices. For each system, the critical values of $\chi$ for the self-trapping transitions are found to obey a power-law behavior as a function of the connectivity $K$ of the Cayley tree.Comment: 6 pages, 7 fig

Time evolution of models described by one-dimensional discrete nonlinear Schr\"odinger equation

The dynamics of models described by a one-dimensional discrete nonlinear Schr\"odinger equation is studied. The nonlinearity in these models appears due to the coupling of the electronic motion to optical oscillators which are treated in adiabatic approximation. First, various sizes of nonlinear cluster embedded in an infinite linear chain are considered. The initial excitation is applied either at the end-site or at the middle-site of the cluster. In both the cases we obtain two kinds of transition: (i) a cluster-trapping transition and (ii) a self-trapping transition. The dynamics of the quasiparticle with the end-site initial excitation are found to exhibit, (i) a sharp self-trapping transition, (ii) an amplitude-transition in the site-probabilities and (iii) propagating soliton-like waves in large clusters. Ballistic propagation is observed in random nonlinear systems. The effect of nonlinear impurities on the superdiffusive behavior of random-dimer model is also studied.Comment: 16 pages, REVTEX, 9 figures available upon request, To appear in Physical Review

Heat conduction in one dimensional nonintegrable systems

Two classes of 1D nonintegrable systems represented by the Fermi-Pasta-Ulam (FPU) model and the discrete $\phi^4$ model are studied to seek a generic mechanism of energy transport in microscopic level sustaining macroscopic behaviors. The results enable us to understand why the class represented by the $\phi^4$ model has a normal thermal conductivity and the class represented by the FPU model does not even though the temperature gradient can be established.Comment: 4 Revtex Pages, 4 Eps figures included, to appear in Phys. Rev. E, March 200