Homogenization of the heat equation for a domain with a network of pipes with a well-mixed fluid

We consider the linear heat equation in a domain occupied by a solid material with a network of pipes in which a well-mixed fluid is circulating. The temperature of the fluid in the pipe is uniform and its time variation is determined by the thermal flux on the wall of the pipe, plus a given internal source; continuity of the temperature across the pipe is also assumed. We suppose that we deal with a periodic geometry, with cells of size with inclusions of size r_g; we study in detail in the case r, referring to a previous paper for the case r In the limit »0 we get a homogenized equation. The limit depends strongly on the ratio between the time variation of the temperature in the inclusions and the thermal flux through the interface. The homogenized equation has a new specific heat, which depends on the porosity and the constant of proportionality between the time variation of temperature and the flux on the boundary of the pipe. We also have a new thermal conductivity depending on the microstructure, and volume sources appear. The main tool is the energy method and we generalize the classical results for the more standard boundary conditions for parabolic equations. Finally, we consider the network of pipes forming a random ball structure. We prove convergence for this case. The homogenized equation is of the same form as in the periodic case but auxiliary problems are stochastic.     

Investigation of gain and hyperfine splitting in the niobium X-ray laser

Neon-like niobium X-ray lasers have been studied using both slab and thin-foil target geometries. Niobium foils of various lengths were irradiated from both sides with two beams of the frequency-doubled Nova laser system using a line focus. We looked for gain by measuring spectrally integrated line intensities at different plasma lengths. Gain was observed in four neon-like niobium lines corresponding to 3s–3p transitions. The line profile of theJ = 0–1 line ( = 145.9 ) shows splitting due to the hyperfine effect. Improved contrast in the hyperfine structure is observed as the plasma length is increased. Hyperfine splitting may be relevant to other 3s–3p transitions in neon-like niobium as well as other neon-like X-ray laser systems.     

Some Normal Cryptogroups as Semigroups of Isomorphisms

Given a Clifford semigroup G, we construct special G-operands L and R which we term conformai. Certain suboperands of L and R we call threads and fix some special G-isomorphisms, which we term coherent, of threads in R onto threads in L. On the set of all coherent G-isomorphisms of threads in L onto threads in R we define a sandwich-type multiplication. When we restrict our threads to be cyclic suboperands of L and R, this construction produces a normal cryptogroup which we represent as $ S=[Y;S_{\alpha},\chi_{{\alpha},{\beta}}] $ -Without any restriction on the threads this produces a semigroup isomorphic with a remarkable ideal of the translational hull of S. Conversely, given a strong semilattice of completely simple semigroups, satisfying certain conditions, we can represent it isomorphically as indicated above.     

First observation of lasing at 231 Å in neon-like nickel using the prepulse technique

We report lasing for the first time in nickel on the neon-like J=01, 3p3s transition at 231 Å as well as several weaker transitions including the J=2»1 lines at 298 Å and 304 Å. Amplification is seen only when the prepulse technique of using a low intensity prepulse before the main optical drive pulse is used to illuminate the nickel target. The prepulse technique is also shown to produce lasing in copper and dramatically improve the output of the germanium laser.     

A parallel projection method for overdetermined nonlinear systems of equations

We consider overdetermined nonlinear systems of equationsF(x)=0, whereF: ^{n m} ,mn. For this type of systems we define weighted least square distance (WLSD) solutions, which represent an alternative to classical least squares solutions and to other solutions based on residual normas. We introduce a generalization of the classical method of Cimmino for linear systems and we prove local convergence results. We introduce a practical strategy for improving the global convergence properties of the method. Finally, numerical experiments are presented.Work supported by FAPESP (Grant 90/3724/6), FINEP, CNPq and FAEP-UNICAMP.