667,329 research outputs found
When is a Stokes line not a Stokes line?
No full textDuring the course of a Stokes phenomenon, an asymptotic expansion can change its form as a further series, prefactored by an exponentially small term and a Stokes multiplier, appears in the representation. The initially exponentially small contribution may nevertheless grow to dominate the behaviour for other values of the asymptotic or associated parameters.We introduce the concept of a higher order Stokes phenomenon, at which a Stokes multiplier itself can change value. We show that the higher order Stokes phenomenon can be used to explain the apparent sudden birth of Stokes lines at regular points, why some Stokes lines are irrelevant to a given problem and why it is indispensible to the proper derivation of expansions that involve three or more possible asymptotic contributions. We provide an example of how the higher order Stokes phenomenon can have important effects on the large time behaviour of linear partial differential equations.Subsequently we apply these techniques to Burgers equation, a non-linear partial differential equation developed to model turbulent fluid flow. We find that the higher order Stokes phenomenon plays a major, yet very subtle role in the smoothed shock wave formation of this equation
NAVIER–STOKES EQUATIONS ON THE β-PLANE
No full textMathematical analysis has been undertaken for the vorticity formulation of the two dimensional Navier–Stokes equation on the β-plane with periodic boundary conditions. This equation describes the flow of fluid near the equator of the Earth. The long time behaviour of the solution of this equation is investigated and we show that, given a sufficiently regular forcing, the solution of the equation is nearly zonal. We use this result to show that, for sufficiently large β, the global attractor of this system reduces to a point. Another result can be obtained if we assume that the forcing is time-independent and sufficiently smooth. If the forcing lies in some Gevrey space, the slow manifold of the Navier–Stokes equation on the β-plane can be approximated with O(εn/2) accuracy for arbitrary n = 0, 1, · · · , as well as with exponential accuracy
A sequential regularization method for time-dependent incompressible Navier--Stokes equations
No full textThe objective of the paper is to present a method, called the sequential regularization method (SRM), for the nonstationary incompressible Navier--Stokes equations from the viewpoint of regularization of differential-algebraic equations (DAEs), and to provide a way to apply a DAE method to partial differential-algebraic equations (PDAEs). The SRM is a functional iterative procedure. It is proved that its convergence rate is , where is the number of the SRM iterations and is the regularization parameter. The discretization and implementation issues of the method are considered. In particular, a simple explicit-difference scheme is analyzed and its stability is proved under the usual step-size condition of explicit schemes. It appears that the SRM formulation is new in the Navier--Stokes context. Unlike other regularizations or pseudocompressibility methods in the Navier--Stokes context, the regularization parameter in the SRM need not be very small and the regularized problem in the sequence may be essentially nonstiff in time direction for any . Hence the stability condition is independent of even for explicit time discretization. Numerical experiments are given to verify our theoretical results
Mennine-Stokes Collection; no.07719
No full textSepia stereoscope image of the Naid Queen Silver Mine in Georgetown, N. M. Thirteen unidentified individuals pose for the photograph. A small adobe home can be seen at the foot of a scrub covered hill. Image mounted a yellowed matte board. Verso: Written in black ink; "Scenery of New Mexico The Naid Queen Silver Mine Georgetown 1878 owners Meredith and Ailman." Written in blue ink; "This picture should be inserted on page 88 of my manuscript H B. A."Master file: image/tiff; 79,676 KB; Computer Hardware: Intel Pentium (R) 4 3.20 GHz/ 1.99 GB RAM manufactured by Dell; Operating system: Windows XP 2002; Creation software: Adobe Photoshop CS2 version 9.0.2; Scanner: flatbed reflective scanner Microtek 1000XL; Scanner software: Microtek SilverFast Ai 6.4.2r2b; Scanned by Jackie Becker on 2009-10-15
Proper general decomposition (PGD) for the resolution of Navier–Stokes equations
No full textIn this work, the PGD method will be considered for solving some problems of fluid mechanics by looking for the solution as a sum of tensor product functions. In the first stage, the equations of Stokes and Burgers will be solved. Then, we will solve the Navier–Stokes problem in the case of the lid-driven cavity for different Reynolds numbers (Re = 100, 1000 and 10,000). Finally, the PGD method will be compared to the standard resolution technique, both in terms of CPU time and accuracy.Région Poitou-Charente
Meeting Hazel Stokes
No full textHazel Stokes is a celebrity-obsessed usherette. She also wants to be famous. Since the late 1980s Hazel has had herself photographed with the actors, singers, comedians and entertainers who have performed at the theatre where she works. This book presents a selection of pictures from Hazel Stokes' collection
Three-dimensional investigation of the stokes eigenmodes in hollow circular cylinder
No full texthttp://dx.doi.org/10.1155/2013/857821This paper studies the influence of boundary conditions on a fluid medium of finite depth.We determine the frequencies and the modal shapes of the fluid.The fluid is assumed to be incompressible and viscous. A potential technique is used to obtain in three-dimensional cylindrical coordinates a general solution for a problem.The method consists in solving analytically partial differential equations obtained from the linearized Navier-Stokes equation. A finite element analysis is also used to check the validity of the present method. The results from the proposed method are in good agreement with numerical solutions. The effect of the fluid thickness on the Stokes eigenmodes is also investigated. It is found that frequencies are strongly influenced
Mennine-Stokes Collection; no.07721
No full textSepia image of a Mexican cart with furniture parked outside the bay window of a wood constructed home. A ceramic bowl is placed underneath the tongue of cart. Seen at left is what appears to be an unidentified man standing on the porch of the home. Image mounted on a dark brown matte board. Verso: Written in black ink; "This picture taken in our parlor in front of the night blooming c____ plant the last act before leaving our lovely home forever."Master file: image/tiff; 101,685 KB; Computer Hardware: Intel Pentium (R) 4 3.20 GHz/ 1.99 GB RAM manufactured by Dell; Operating system: Windows XP 2002; Creation software: Adobe Photoshop CS2 version 9.0.2; Scanner: flatbed reflective scanner Microtek 1000XL; Scanner software: Microtek SilverFast Ai 6.4.2r2b; Scanned by Jackie Becker on 2009-10-15
Large-time behavior of the weak solution to 3D Navier-Stokes equations
No full textThe weak solution to the Navier–Stokes equations in a bounded domain D ⊂ R[superscript 3] with a smooth boundary is proved to be unique provided that it satisfies an additional requirement. This solution exists for all t ≥ 0. In a bounded domain D the solution decays exponentially
fast as t → ∞if the force term decays at a suitable rat
Appropriate Similarity Measures for Author Cocitation Analysis
No full textWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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