488 research outputs found
Complex singularities and PDEs
In this paper we give a review on the computational methods used to
characterize the complex singularities developed by some relevant PDEs. We
begin by reviewing the singularity tracking method based on the analysis of the
Fourier spectrum. We then introduce other methods generally used to detect the
hidden singularities. In particular we show some applications of the Pad\'e
approximation, of the Kida method, and of Borel-Polya method. We apply these
techniques to the study of the singularity formation of some nonlinear
dispersive and dissipative one dimensional PDE of the 2D Prandtl equation, of
the 2D KP equation, and to Navier-Stokes equation for high Reynolds number
incompressible flows in the case of interaction with rigid boundaries
Velocity fluctuations and hydrodynamic diffusion in sedimentation
We study non-equilibrium velocity fluctuations in a model for the
sedimentation of non-Brownian particles experiencing long-range hydrodynamic
interactions. The complex behavior of these fluctuations, the outcome of the
collective dynamics of the particles, exhibits many of the features observed in
sedimentation experiments. In addition, our model predicts a final relaxation
to an anisotropic (hydrodynamic) diffusive state that could be observed in
experiments performed over longer time ranges.Comment: 7 pages, 5 EPS figures, EPL styl
Level Set Approach to Reversible Epitaxial Growth
We generalize the level set approach to model epitaxial growth to include
thermal detachment of atoms from island edges. This means that islands do not
always grow and island dissociation can occur. We make no assumptions about a
critical nucleus. Excellent quantitative agreement is obtained with kinetic
Monte Carlo simulations for island densities and island size distributions in
the submonolayer regime.Comment: 7 pages, 9 figure
Origin of Nonuniversality in Micellar Solutions: Comment
Rhynchospora caucasica Palla (Cyperaceae) Doğu Karadeniz'de, Rize'den tespit edilmiş ve Türkiye florası için yeni bir tür kaydı olarak verilmiştir. Taksonun betimi ve coğrafik dağılımı belirtilmiş, yakın akrabaları olan R. rugosa (Vahl) Gale subsp. rugosa ve R. rugosa (Vahl) Gale subsp. brownii (Roemer & Schultes) T.Koyama taksonları ile karşılaştırılmıştırR. caucasica Palla (Cyperaceae) is reported as a new record for Turkish flora in Rize province, NE Anatolia, Turkey. The description and distribution of the species are given. Also, it is compared with related taxa R. rugosa (Vahl) Gale subsp. rugosa and R. rugosa subsp. brownii (Roemer & Schultes) T. Koyam
Optimal randomized multilevel algorithms for infinite-dimensional integration on function spaces with ANOVA-type decomposition
In this paper, we consider the infinite-dimensional integration problem on
weighted reproducing kernel Hilbert spaces with norms induced by an underlying
function space decomposition of ANOVA-type. The weights model the relative
importance of different groups of variables. We present new randomized
multilevel algorithms to tackle this integration problem and prove upper bounds
for their randomized error. Furthermore, we provide in this setting the first
non-trivial lower error bounds for general randomized algorithms, which, in
particular, may be adaptive or non-linear. These lower bounds show that our
multilevel algorithms are optimal. Our analysis refines and extends the
analysis provided in [F. J. Hickernell, T. M\"uller-Gronbach, B. Niu, K.
Ritter, J. Complexity 26 (2010), 229-254], and our error bounds improve
substantially on the error bounds presented there. As an illustrative example,
we discuss the unanchored Sobolev space and employ randomized quasi-Monte Carlo
multilevel algorithms based on scrambled polynomial lattice rules.Comment: 31 pages, 0 figure
Asymptotic analysis of the linearized Navier-Stokes equation on an exterior circular domain: Explicit solution and the zero viscosity limit
In this paper we study and derive explicit formulas for the linearized Navier-Stokes equations on an exterior circular domain in space dimension two. Through an explicit construction, the solution is decomposed into an inviscid solution, a boundary layer solution and a corrector. Bounds on these solutions are given, in the appropriate Sobolev spaces, in terms of the norms of the initial and boundary data. The correction term is shown to be of the same order of magnitude as the square root of the viscosity. Copyright © 2001 by Marcel Dekker, Inc
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