On positive solutions for some semilinear periodic parabolic eigenvalue problems

AbstractFor a bounded domain Ω in RN, N⩾2, satisfying a weak regularity condition, we study existence of positive and T-periodic weak solutions for the periodic parabolic problem Luλ=λg(x,t,uλ) in Ω×R, uλ=0 on ∂Ω×R. We characterize the set of positive eigenvalues with positive eigenfunctions associated, under the assumptions that g is a Caratheodory function such that ξ→g(x,t,ξ)/ξ is nonincreasing in (0,∞) a.e. (x,t)∈Ω×R satisfying some integrability conditions in (x,t) and ∫0Tesssupx∈Ωinfξ>0g(x,t,ξ)ξdt>0

Periodic parabolic problems with nonlinearities indefinite in sign

Let Ω ⊂ RN be a smooth bounded domain. We give sufficient conditions (which are also necessary in many cases) on two nonnegative functions a, b that are possibly discontinuous and unbounded for the existence of nonnegative solutions for semilinear Dirichlet periodic parabolic problems of the form Lu =λa (x, t) u p − b (x, t) u q in Ω × R, where 0 0. In some cases we also show the existence of solutions uλ in the interior of the positive cone and that uλ can be chosen such that λ → uλ is differentiable and increasing. A uniqueness theorem is also given in the case p ≤ q. All results remain valid for the corresponding elliptic problems

Ground test program for a full-size solar dynamic heat receiver

Test hardware, facilities, and procedures were developed to conduct ground testing of a full size, solar dynamic heat receiver in a partially simulated, low Earth orbit environment. The heat receiver was designed to supply 102 kW of thermal energy to a helium and xenon gas mixture continuously over a 94 minute orbit, including up to 36 minutes of eclipse. The purpose of the test program was to quantify the receiver thermodynamic performance, its operating temperatures, and thermal response to changes in environmental and power module interface boundary conditions. The heat receiver was tested in a vacuum chamber using liquid nitrogen cold shrouds and an aperture cold plate. Special test equipment were designed to provide the required ranges in interface boundary conditions that typify those expected or required for operation as part of the solar dynamic power module on the Space Station Freedom. The support hardware includes an infrared quartz lamp heater with 30 independently controllable zones and a closed Brayton cycle engine simulator to circulate and condition the helium xenon gas mixture. The test article, test support hardware, facilities, and instrumentation developed to conduct the ground test program are all described

Effects of energy dependence in the quasiparticle density of states on far-infrared absorption in the pseudogap state

We derive a relationship between the optical conductivity scattering rate 1/\tau(\omega) and the electron-boson spectral function \alpha^2F(\Omega) valid for the case when the electronic density of states, N(\epsilon), cannot be taken as constant in the vicinity of the Fermi level. This relationship turned out to be useful for analyzing the experimental data in the pseudogap state of cuprate superconductors.Comment: 8 pages, RevTeX4, 1 EPS figure; final version published in PR