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11.
The barotropic compressible Navier–Stokes equations in an unbounded domain are studied. We prove the unique existence of the solution (u, p) of the system (1.1) in the Sobolev spaceHk + 3 × Hk + 2provided that the derivatives of the data of the problem are sufficiently small, wherek ≥ 0 is any integer. The proof follows from an analysis of the linearized problem, the solvability of the continuity equation, and the Schauder fixed point theory. Similar smoothness results are obtained for a linearized form of (1.1). 相似文献
12.
E. Jackiewicz M. Lukasiak M. Kopcewicz K. Szpila N. Bakun-Czubarow 《Hyperfine Interactions》1992,70(1-4):993-996
Terrestrial basalt rocks considered to be a good analogues of the Martian regolith were studied by using the Mössbauer spectroscopy and X-ray diffraction. The weathering of basalts was followed by the changes of the Fe2+/Fe3+ ratio. The basalt rock undergoes alteration from primary mineral composition (olivine+pyroxene+plagioclase) through smectite to kaolinite clay with oxides and hydroxides with the increase of the Fe2+/Fe3+ ratio. 相似文献
13.
Open circuit voltage (OCV) measurements in H2O/air concentration cells at T<580 K using Yb-doped SrCeO3 electrolyte indicate that under these conditions, protons are transported through the electrolyte as -ve ions, possibly as
hydroxyl (OH−) ions. The H+ ionic transport, which is generally reported, becomes the dominant mode for H2O/air concentration cells at temperatures greater than 750 K or when H2O/air electrodes are replaced by H2/Ar, and the anomalous OCV sign disappears. The combination of low temperature and the presence of hydrogen and oxygen as
provided by the H2O/air system appears to be necessary for the postulated hydroxyl ion electrode reactions to take place.
In addition to OCV measurements, results from impedance spectroscopy are used to provide evidence in support of the suggested
hydroxyl ion mode of protonic transport under the specified conditions. These findings are directly relevant in the development
of novel humidity sensors in the temperature range 450–580K and is reported in a separate paper in this conference.
Paper presented at the 3rd Euroconference on Solid State Ionics, Teulada, Sardinia, Italy, Sept. 15–22, 1996 相似文献
14.
C. Fallnich B. Ruffing Th. Herrmann A. Nebel R. Beigang R. Wallenstein 《Applied physics. B, Lasers and optics》1995,60(5):427-436
We report on a cw mode-locked non-critically phase matched KTP optical parametric oscillator synchronously pumped by a picosecond Ti:Sapphire laser. High average signal output power of up to 950 mW over a large tuning range has been achieved. For this OPO the influence of resonator-length detuning on the output power, pulse duration and spectral bandwidth has been investigated. The measured data are in good agreement with the results of a numerical simulation using a split-step Fourier method which considers the group-velocity mismatch, the group-velocity dispersion and the self-phase modulation. The numerical simulation also describes the measured strong pump depletion and its influence on the OPO output and efficiency. 相似文献
15.
16.
Brian R. Hunt 《Proceedings of the American Mathematical Society》1998,126(3):791-800
The Weierstrass nowhere differentiable function, and functions constructed from similar infinite series, have been studied often as examples of functions whose graph is a fractal. Though there is a simple formula for the Hausdorff dimension of the graph which is widely accepted, it has not been rigorously proved to hold. We prove that if arbitrary phases are included in each term of the summation for the Weierstrass function, the Hausdorff dimension of the graph of the function has the conjectured value for almost every sequence of phases. The argument extends to a much wider class of Weierstrass-like functions.
17.
We discuss an error estimation procedure for the global error of collocation schemes applied to solve singular boundary value problems with a singularity of the first kind. This a posteriori estimate of the global error was proposed by Stetter in 1978 and is based on the idea of Defect Correction, originally due to Zadunaisky. Here, we present a new, carefully designed modification of this error estimate which not only results in less computational work but also appears to perform satisfactorily for singular problems. We give a full analytical justification for the asymptotical correctness of the error estimate when it is applied to a general nonlinear regular problem. For the singular case, we are presently only able to provide computational evidence for the full convergence order, the related analysis is still work in progress. This global estimate is the basis for a grid selection routine in which the grid is modified with the aim to equidistribute the global error. This procedure yields meshes suitable for an efficient numerical solution. Most importantly, we observe that the grid is refined in a way reflecting only the behavior of the solution and remains unaffected by the unsmooth direction field close to the singular point. 相似文献
18.
A. K. Lopatin 《Ukrainian Mathematical Journal》1997,49(1):51-74
We consider the method of normal forms, the Bogolyubov averaging method, and the method of asymptotic decomposition proposed by Yu. A. Mitropol’skii and the author of this paper. Under certain assumptions about group-theoretic properties of a system of zero approximation, the results obtained by the method of asymptotic decomposition coincide with the results obtained by the method of normal forms or the Bogolyubov averaging method. We develop a new algorithm of asymptotic decomposition by a part of the variables and its partial case — the algorithm of averaging on a compact Lie group. For the first time, it became possible to consider asymptotic expansions of solutions of differential equations on noncommutative compact groups. 相似文献
19.
20.