Pinned modes in lossy lattices with local gain and nonlinearity

We introduce a discrete linear lossy system with an embedded "hot spot" (HS), i.e., a site carrying linear gain and complex cubic nonlinearity. The system can be used to model an array of optical or plasmonic waveguides, where selective excitation of particular cores is possible. Localized modes pinned to the HS are constructed in an implicit analytical form, and their stability is investigated numerically. Stability regions for the modes are obtained in the parameter space of the linear gain and cubic gain/loss. An essential result is that the interaction of the unsaturated cubic gain and self-defocusing nonlinearity can produce stable modes, although they may be destabilized by finite amplitude perturbations. On the other hand, the interplay of the cubic loss and self-defocusing gives rise to a bistability.Comment: Phys. Rev. E (in press

Running-phase state in a Josephson washboard potential

We investigate the dynamics of the phase variable of an ideal underdamped Josephson junction in switching current experiments. These experiments have provided the first evidence for macroscopic quantum tunneling in large Josephson junctions and are currently used for state read-out of superconducting qubits. We calculate the shape of the resulting macroscopic wavepacket and find that the propagation of the wavepacket long enough after a switching event leads to an average voltage increasing linearly with time.Comment: 6 pages, 3 figure

Generation of a train of ultrashort pulses using periodic waves in tapered photonic crystal fibres

Funding This work was supported by the Ministry of Education , Nigeria for financial support through the TETFUND scholarship 55 scheme; CSIR [grant number 03(1264)/12/EMR-II].Peer reviewedPostprin

Pinned modes in two-dimensional lossy lattices with local gain and nonlinearity

We introduce a system with one or two amplified nonlinear sites ("hot spots", HSs) embedded into a two-dimensional linear lossy lattice. The system describes an array of evanescently coupled optical or plasmonic waveguides, with gain applied at selected HS cores. The subject of the analysis is discrete solitons pinned to the HSs. The shape of the localized modes is found in quasi-analytical and numerical forms, using a truncated lattice for the analytical consideration. Stability eigenvalues are computed numerically, and the results are supplemented by direct numerical simulations. In the case of self-focusing nonlinearity, the modes pinned to a single HS are stable or unstable when the nonlinearity includes the cubic loss or gain, respectively. If the nonlinearity is self-defocusing, the unsaturated cubic gain acting at the HS supports stable modes in a small parametric area, while weak cubic loss gives rise to a bistability of the discrete solitons. Symmetric and antisymmetric modes pinned to a symmetric set of two HSs are considered too.Comment: Philosophical Transactions of the Royal Society A, in press (a special issue on "Localized structures in dissipative media"

Thermal Softening and Degradation of Wood and Bark

A thermogravimetric analyzer was modified for the study of thermal softening of several Pacific Northwest woods and barks under constant load at a heating rate of 16 C/min.Several stages of thermal softening were found in barks and wood. Regardless of species, oven-dry samples start to soften at 180 C, with termination at about 500 C. The maximum rate of softening occurred at 380 C with an additional softening at 280 C for bark and 320 C for wood of hardwood species. An increase of moisture content decreased the softening temperature. When the moisture content of either material was higher than 10%, a new maximum rate of softening appeared at 160 C, while the 280 C, 320 C and 380 C maxima were retained. The absolute softening of wood and bark at 160 C increased with increasing moisture content to a limit at about 30%.In conjunction with results from infrared spectrum, X-ray diffraction and differential thermal analysis, the heating of oven-dry wood and bark was found to exhibit neither physical nor chemical changes at less than 200 C. The softening of wood and bark in the presence of water at temperature less than 200 C must occur only in the amorphous regions, with water serving as a plasticizer. Softening of wood and bark at more than 200 C is a combined response of physical and chemical degradations. These thermal responses of wood and bark, particularly bark, are expected to be important to the strength, dimensional stability, water resistance and fire-retardant properties of composite products

Symmetries of supergravity black holes

We investigate Killing tensors for various black hole solutions of supergravity theories. Rotating black holes of an ungauged theory, toroidally compactified heterotic supergravity, with NUT parameters and two U(1) gauge fields are constructed. If both charges are set equal, then the solutions simplify, and then there are concise expressions for rank-2 conformal Killing-Stackel tensors. These are induced by rank-2 Killing-Stackel tensors of a conformally related metric that possesses a separability structure. We directly verify the separation of the Hamilton-Jacobi equation on this conformally related metric, and of the null Hamilton-Jacobi and massless Klein-Gordon equations on the "physical" metric. Similar results are found for more general solutions; we mainly focus on those with certain charge combinations equal in gauged supergravity, but also consider some other solutions.Comment: 36 pages; v2: minor changes; v3: slightly shorte