Thermoelectric bonding study. the bonding of pbte and pbte-snte with non-magnetic electrodes

Low resistance, high strength, nonmagnetic electrode bonding to lead telluride and lead- telluride-tin telluride alloy

Lead telluride non-magnetic bonding research study Third quarterly report, Sep. 1 - Nov. 30, 1965

Diffusion bonding of tungsten electrodes to lead tellurium and lead tellurium-tin tellurium thermocouple

Optimal Lβ\mathfrak{L}^{\beta}-Control for the Global Cauchy Problem of the Relativistic Vlasov-Poisson System

Recently, M.K.-H. Kiessling and A.S. Tahvildar-Zadeh proved that a unique global classical solution to the relativistic Vlasov-Poisson system exists whenever the positive, integrable initial datum is spherically symmetric, compactly supported in momentum space, vanishes on characteristics with vanishing angular momentum, and for $\beta \ge 3/2$ has $\mathfrak{L}^{\beta}$-norm strictly below a positive, critical value $\mathcal{C}_{\beta}$. Everything else being equal, data leading to finite time blow-up can be found with $\mathfrak{L}^{\beta}$-norm surpassing $\mathcal{C}_{\beta}$ for any $\beta >1$, with $\mathcal{C}_{\beta}>0$ if and only if $\beta\geq 3/2$. In their paper, the critical value for $\beta = {3}/{2}$ is calculated explicitly while the value for all other $\beta$ is merely characterized as the infimum of a functional over an appropriate function space. In this work, the existence of minimizers is established, and the exact expression of $\mathcal{C}_{\beta}$ is calculated in terms of the famous Lane-Emden functions. Numerical computations of the $\mathcal{C}_{\beta}$ are presented along with some elementary asymptotics near the critical exponent ${3}/{2}$.Comment: 24 pages, 2 figures Refereed and accepted for publication in Transport Theory and Statistical Physic

Lead telluride bonding and segmentation study Semiannual phase report, Aug. 1, 1967 - Jan. 31, 1968

Constitutional studies of SnTe and Si-Ge metal systems, segmented Si-Ge-PdTe thermocouple efficiencies, and pore migration in PbSnTe thermoelement

Lead telluride bonding and segmentation study Interim report, 1 Nov. 1966 - 31 Jul. 1967

Lead telluride bonding and segmentation studies including couple design, test devices, and life testin

Integration of twisted Dirac brackets

The correspondence between Poisson structures and symplectic groupoids, analogous to the one of Lie algebras and Lie groups, plays an important role in Poisson geometry; it offers, in particular, a unifying framework for the study of hamiltonian and Poisson actions. In this paper, we extend this correspondence to the context of Dirac structures twisted by a closed 3-form. More generally, given a Lie groupoid $G$ over a manifold $M$, we show that multiplicative 2-forms on $G$ relatively closed with respect to a closed 3-form $\phi$ on $M$ correspond to maps from the Lie algebroid of $G$ into the cotangent bundle $T^*M$ of $M$, satisfying an algebraic condition and a differential condition with respect to the $\phi$-twisted Courant bracket. This correspondence describes, as a special case, the global objects associated to twisted Dirac structures. As applications, we relate our results to equivariant cohomology and foliation theory, and we give a new description of quasi-hamiltonian spaces and group-valued momentum maps.Comment: 42 pages. Minor changes, typos corrected. Revised version to appear in Duke Math.

Excitation Thresholds for Nonlinear Localized Modes on Lattices

Breathers are spatially localized and time periodic solutions of extended Hamiltonian dynamical systems. In this paper we study excitation thresholds for (nonlinearly dynamically stable) ground state breather or standing wave solutions for networks of coupled nonlinear oscillators and wave equations of nonlinear Schr\"odinger (NLS) type. Excitation thresholds are rigorously characterized by variational methods. The excitation threshold is related to the optimal (best) constant in a class of discr ete interpolation inequalities related to the Hamiltonian energy. We establish a precise connection among $d$, the dimensionality of the lattice, $2\sigma+1$, the degree of the nonlinearity and the existence of an excitation threshold for discrete nonlinear Schr\"odinger systems (DNLS). We prove that if $\sigma\ge 2/d$, then ground state standing waves exist if and only if the total power is larger than some strictly positive threshold, $\nu_{thresh}(\sigma, d)$. This proves a conjecture of Flach, Kaldko& MacKay in the context of DNLS. We also discuss upper and lower bounds for excitation thresholds for ground states of coupled systems of NLS equations, which arise in the modeling of pulse propagation in coupled arrays of optical fibers.Comment: To appear in Nonlinearit

Qualitative and quantitative analysis of stability and instability dynamics of positive lattice solitons

We present a unified approach for qualitative and quantitative analysis of stability and instability dynamics of positive bright solitons in multi-dimensional focusing nonlinear media with a potential (lattice), which can be periodic, periodic with defects, quasiperiodic, single waveguide, etc. We show that when the soliton is unstable, the type of instability dynamic that develops depends on which of two stability conditions is violated. Specifically, violation of the slope condition leads to an amplitude instability, whereas violation of the spectral condition leads to a drift instability. We also present a quantitative approach that allows to predict the stability and instability strength

Theory of Nonlinear Dispersive Waves and Selection of the Ground State

A theory of time dependent nonlinear dispersive equations of the Schroedinger / Gross-Pitaevskii and Hartree type is developed. The short, intermediate and large time behavior is found, by deriving nonlinear Master equations (NLME), governing the evolution of the mode powers, and by a novel multi-time scale analysis of these equations. The scattering theory is developed and coherent resonance phenomena and associated lifetimes are derived. Applications include BEC large time dynamics and nonlinear optical systems. The theory reveals a nonlinear transition phenomenon, ``selection of the ground state'', and NLME predicts the decay of excited state, with half its energy transferred to the ground state and half to radiation modes. Our results predict the recent experimental observations of Mandelik et. al. in nonlinear optical waveguides