navier stokes equations in a bounded cylindrical domain

... Fang, D, Zhang, T: Compressible Navier- Stokes equations with vacuum state in one dimension Commun Pure Appl Anal 3, 675–694 (2004) 14 Fang, D, Zhang, T: A note on compressible Navier- Stokes equations ... (2002) Xin, Z, Yao, Z: The existence, uniqueness and regularity for one-dimensional compressible Navier- Stokes equations (Preprint) Yang, T, Yao, Z, Zhu, C: Compressible Navier- Stokes equations ... et al [12], Fang and Zhang [13,14], Qin et al [15], authors studied the global existence and uniqueness under some assumptions on initial data When f ≠ 0, Qin and Zhao [16] proved the global...

Ngày tải lên: 20/06/2014, 22:20

... the Navier- Stokes equations with data in Lp ,” Archive for Rational Mechanics and Analysis, vol 45, no 3, pp 222–240, 1972 Y Giga, “Solutions for semilinear parabolic equations in Lp and regularity ... solutions of Navier- Stokes equations, ” Archiv der Mathematik, vol 46, no 5, pp 428–439, 1986 L Iskauriaza, G A Ser¨ gin, and V Shverak, “L3,∞ -solutions of Navier- Stokes equations and e backward uniqueness,” ... uniqueness,” Russian Mathematical Surveys, vol 58, no 2, pp 211–250, 2003 H Beir˜ o da Veiga, A new regularity class for the Navier- Stokes equations in Rn ,” Chinese Annals of a Mathematics Series...

Ngày tải lên: 22/06/2014, 02:20

... (Goddeau, 1996), and a plan-based model (Litman, 1987) However, a finite-state model has a weak point that dialogue flows should be predefined Although a plan-based model can manage complex dialogue ... of speakers’ intentions; a pair of a current intention and a next intention) that are extracted from a sequence of utterances in a current dialogue • Domain knowledge-level feature: In a goaloriented ... dialogue, dialogue participants accomplish a given task by using shared domain knowledge Since a frame-based model is more 231 3.1 Evaluation Data sets and experimental settings We collected a...

Ngày tải lên: 17/03/2014, 02:20

... the range of parameters (1.2) Since we show that the invariant measure for (1.1) is unique, its translational invariance follows immediately from the translational invariance of the equations ... Navier- Stokes equations To state the general ergodic result for the two-dimensional Navier- Stokes equations, we begin by looking at the algebraic structure of the Navier- Stokes nonlinearity in ... Annals of Mathematics, 164 (2006), 993–1032 Ergodicity of the 2D Navier- Stokes equations with degenerate stochastic forcing By Martin Hairer and Jonathan C Mattingly Abstract The stochastic...

Ngày tải lên: 29/03/2014, 07:20

... Da Prato G, Zabczyk J: Stochastic Equations in Infinite Dimensions Cambridge University Press, Cambridge; 1992 25 Pazy A: Semigroups of Linear Operators and Applications to Partial Equations In ... Chang et al Advances in Difference Equations 2011, 2011:9 http://www.advancesindifferenceequations.com/content/2011/1/9 Page of 12 Thus, using an estimate on Ito integral established in Ichikawa ... Almost automorphic and pseudo almost automorphic mild solutions to an abstract differential equation in Banach spaces Nonlinear Anal TMA 2010, 72:1886-1894 15 Zhao Z-H, Chang Y-K, Li W-S: Asymptotically...

Ngày tải lên: 21/06/2014, 03:20

... 43–52, Karl-Franzens-Univ Graz, Graz, Austria, 2004 21 L C˘ dariu and V Radu, A Hyers-Ulam-Rassias stability theorem for a quartic functional equation,” a Automation Computers and Applied Mathematics, ... T M Rassias, “On the stability of functional equations and a problem of Ulam,” Acta Applicandae Mathematicae, vol 62, no 1, pp 23–130, 2000 13 Z Daroczy and Z Pales, Eds., Functional Equations Results ... transformations,” Bulletin of the American Mathematical Society, vol 57, pp 223–237, 1951 Z Gajda, “On stability of additive mappings,” International Journal of Mathematics and Mathematical Sciences, vol...

Ngày tải lên: 22/06/2014, 06:20

... property, for instance, in the linear case dealt with in the following corollary Corollary 4.12 Assume that X is a Banach space, let K be a cone in X, and T : X → X is a linear bounded operator which ... the minimal linear manifold containing T(X) (3.63) 16 Journal of Inequalities and Applications Then, for all λ satisfying estimate (3.4) and all b ∈ X, any two solutions of (1.1) are K-comparable ... G Kre˘n and M A Rutman, “Linear operators leaving invariant a cone in a Banach space,” ı American Mathematical Society Translations, vol 1950, no 26, p 128, 1950 [9] M A Krasnosel’ski˘, Positive...

Ngày tải lên: 22/06/2014, 18:20

... boundary and vice versa Following again the reasoning from the previous paragraph and taking into account the grid point numbering as in figure 10.1, the governing equation can be discretized as: ¦ ... spring constant and the equilibrium position of the Lagrangian point Evidently, approximating the boundary as rigid in an accurate way requires large spring constants Lower values of can allow ... domain via a coordinate transformation, and then solve the (transformed!) equations and re-transform the solution to the physical domain The other method does not make use of a computational domain, ...

Ngày tải lên: 11/07/2014, 23:20

... exists a constant C such that h(x) = C (x) 42 Chapter Master Relation and Wave Propagators In this chapter, we will apply Laplace-Laplace-Fourier transform introduced in Chapter to establish ... solutions are mainly contributed to Matsumura, Nishida and Kawshima In [21] and [22], Matsumura and Nishida proved the existence and uniqueness of Cauchy problem of (1.1) in D space based on the assumption ... wave propagators: one called the interior wave propagator and the other the surface wave propagator Therefore, it is inevitable to investigate their structures At last, Green’s function of linearized...

Ngày tải lên: 10/09/2015, 09:06

... cross-correlation and Dr Lua Kim Boon for his assistance in the Labview programming I am also grateful to the Technical Staffs of the Fluid Mechanics Laboratory for their valuable technical assistance and ... 2500 and 6500 Later, Tsitverblit and Kit (1998) used linear stability analysis to further demonstrate that the axisymmetric oscillations in a cylindrical container are not the result of a local instability ... NavierStokes equations and continuity equation, together with boundary and initial conditions Since only two parameters are involved (i.e Re and the aspect ratio Λ = H/R), and the domain is confined,...

Ngày tải lên: 14/09/2015, 14:02

... viscosity and temperature obtained using a Haake Rheometer Since the data was sampled and acquired over about 20 minutes, Re is nominally constant For those cases with fixed Reynolds number and varying ... to allow efficient heat exchange between the fluid inside the cylinder and its surroundings, there is a gradual rise in the temperature of the fluid, resulting in an increase in Re at a rate ... crosssectional) viewing of the flow structure, was illuminated using a thin laser sheet (about 1.5mm) produced by directing a 5W Argon ion laser beam through a cylindrical lens (see Fig 2.1) In all cases,...

Ngày tải lên: 14/09/2015, 14:02

... is axisymmetric, and the equations governing the flow are the axisymmetric Navier- Stokes equations, together with the continuity equation and appropriate boundary and initial conditions A cylindrical ... rotating end 34 CHAPTER NUMERICAL SIMULATION METHOD Two kinds of rotating motions were considered: a constant rotation only and a constant rotation with a superimposed sinusoidal modulation In all ... is adopted, with the origin at the centre of the rotating end wall and the positive-z axis pointing towards the stationary endwall R H z Ω θ r Fig 3.1 Flow configuration in a confined cylinder...

Ngày tải lên: 14/09/2015, 14:02

... mm, and a matching rotating disk at the top and a stationary disk at the bottom of the cylinder The height H of the flow domain, and the aspect ratio Λ = H/R, can be varied by moving the rotating ... stationary disk In all cases, the flow images were illuminated using fluorescent lamps, and captured using a video or a still digital camera The second apparatus (see Fig 4.2) is a modification ... shrinking downstream bubble resulted in the formation of a helical instability of increasing wavelength as the aspect ratio was increased, until an S-shape structure was produced (see Figs 4.8(h) and...

Ngày tải lên: 14/09/2015, 14:02

... bifurcations, the same strategy as in the numerical work of Marques et al (2002) was adopted in this study, i.e., once a desired state was obtained at a particular point in (Λ, Re) parameter space, ... flow, a dye sheet that is released an arbitrarily small distance off-axis will have a non-axisymmetric appearance with a predominately m = azimuthal wavenumber (see Lopez and Perry1992) As Re is increased ... films placed 180º apart on the stationary endplate Showing (a) an LC1 state at Re = 2760 and Λ = 1.704, and (b) an LC2 state at Re = 2750 and Λ = 1.780, (each state is asymptotically stable) Now...

Ngày tải lên: 14/09/2015, 14:02

... spatial discretization, utilizing a Galerkin-Fourier expansion in the azimuthal coordinate θ and Chebyshev collocation in r and z The radial dependence of the variables is approximated by a Chebyshev ... parity To avoid including the origin in the collocation mesh, an odd number of GaussLobatto points in r is used and the equations are solved only in the interval [0, 1] Following Orszag and Patera ... boundary layer when ωf increases from 0.1 to 0.6 in steps of 0.1 We can clearly appreciate that the transition from an oscillating to a quiescent axial bubble is gradual and continuous with variation...

Ngày tải lên: 14/09/2015, 14:02

... was set at 2600 and below with the modulation amplitude A varying from 0.005 to 0.04, and the aspect ratio Λ was maintained at a constant value of 2.5 throughout Note that all flow visualization ... axis at mean rotation rates well below critical for the self-sustained vortex breakdown oscillations 150 CHAPTER HARMONICALLY FORCING ON A STEADY SWIRLING FLOW Previous linear stability analysis ... CHAPTER HARMONICALLY FORCING ON A STEADY SWIRLING FLOW would like to achieve comparable oscillations at lower Reynolds numbers, thereby subjecting the biological material to lower damaging...

Ngày tải lên: 14/09/2015, 14:02

... vortex breakdown in an enclosed cylindrical container”, Paper AIAA 2007-4360, 37th AIAA Fluid Dynamics Conference and Exhibit, 25-28 Jun 2007, Hyatt Regency, Miami, Florida, United States Y.D ... the rotating wave It will be a challenging task to examine if the numerically observed phenomena can be captured in laboratories 157 CHAPTER CONCLUSIONS AND RECOMMENDATIONS To explore the above-mentioned ... useful in applications where unsteady vortex breakdown is prevalent, such as the tail buffeting problem 156 CHAPTER CONCLUSIONS AND RECOMMENDATIONS 8.2 Recommendations A confined cylindrical container...

Ngày tải lên: 14/09/2015, 14:02

... Pacella, “Qualitative properties of positive solutions of semilinear elliptic equations in symmetric domains via the maximum principle,” Annales de l’Institut Henri Poincar´ Analyse Non Lin´aire, ... Differential Equations, vol 65 of CBMS Regional Conference Series in Mathematics, American Mathematical Society, Washington, DC, USA, 1986 23 A Ambrosetti and P H Rabinowitz, “Dual variational methods ... Ekeland, “On the variational principle,” Journal of Mathematical Analysis and Applications, vol 47, pp 324–353, 1974 22 P H Rabinowitz, Minimax Methods in Critical Point Theory with Applications...

Ngày tải lên: 21/06/2014, 11:20

... minimal surfaces with small interior boundaries are graphical away from the boundary Here small means contained in a small ball 527 PLANAR DOMAINS A “pair of pants” (in bold) Graphical annuli (dotted) ... surfaces with small interior boundaries are graphical away from the boundary Here small means contained in a small ball in R3 (and not that the interior boundary has small length) 534 TOBIAS ... surface with quadatric curvature decay into disjoint almost stable subdomains and a “remainder” with quadratic area growth For applications of the results of this part in [CM5], Σ will be a disk...

Ngày tải lên: 14/02/2014, 17:20

... the source domain, where the states of affairs themselves have mappees in the target domain, then the change event has a mappee that is a change event between the latter states of affairs Time-order ... source domain then its mappee takes a long time in the context of the target Also, qualitative duration comparisons map over Rate VNMA: Qualitative rate of progress of an event in the source domain ... to any mappee events Mental/Emotional States VNMA: If some agents in the source domain have mappees that are also agents, then their mental and emotional states map identically, provided that...

Ngày tải lên: 22/02/2014, 02:20