共查询到20条相似文献,搜索用时 31 毫秒
1.
Anca-Veronica Ion 《Journal of Dynamics and Differential Equations》2012,24(2):325-340
When computing the third order terms of the series of powers of the function whose graph is the center manifold, at an equilibrium
point of a scalar delay differential equation with a single constant delay r > 0, some problems occur at the term w2,1z2[`(z)].{w_{2,1}z^2\overline{z}.} More precisely, in order to determine the values at 0, respectively −r of the function w
2,1(.), an algebraic system of equations must be solved. We show that the two equations are dependent, hence the system has an
infinity of solutions. Then we show how we can overcome this lack of uniqueness and provide a formula for w
2,1(0). 相似文献
2.
A test rig incorporating the injection from a single cylindrical hole with an inclination of 30° to a thermally uniform mainstream
flow was used for determining variations in flow structures due to injectant pulsation. The average blowing ratios ([`(M)] \overline{M} ) were 0.65, 1, and 1.25. The periodic variations in injectant flow were rendered by a loudspeaker-based pulsation system
to nondimensionalized excitation frequency (St St ) of 0, 0.2, 0.3, and 0.5. Pulsation resulting in a close-wall orientation of injectant fluid compared with steady blowing
bearing outward orientation was only observed in few cases. At [`(M)] \overline{M} = 0.65, jet fluid remains aligned and covers a significant part of the wall under steady blowing. At higher blowing ratios,
pulsation induces large spatial variations in the jet trajectory, collapsing of the jet body, and the shedding of wake structures
due to the periodic variation of injection flow rate. It was found that the pulsation improves wall coverage of the injectant
fluid under low frequency excitation as the separation of the jet from the wall becomes evident ([`(M)] \overline{M} = 1 and 1.25). 相似文献
3.
The streamwise evolution of an inclined circular cylinder wake was investigated by measuring all three velocity and vorticity
components using an eight-hotwire vorticity probe in a wind tunnel at a Reynolds number Red of 7,200 based on free stream velocity (U
∞) and cylinder diameter (d). The measurements were conducted at four different inclination angles (α), namely 0°, 15°, 30°, and 45° and at three downstream
locations, i.e., x/d = 10, 20, and 40 from the cylinder. At x/d = 10, the effects of α on the three coherent vorticity components are negligibly small for α ≤ 15°. When α increases further
to 45°, the maximum of coherent spanwise vorticity reduces by about 50%, while that of the streamwise vorticity increases
by about 70%. Similar results are found at x/d = 20, indicating the impaired spanwise vortices and the enhancement of the three-dimensionality of the wake with increasing
α. The streamwise decay rate of the coherent spanwise vorticity is smaller for a larger α. This is because the streamwise
spacing between the spanwise vortices is bigger for a larger α, resulting in a weak interaction between the vortices and hence
slower decaying rate in the streamwise direction. For all tested α, the coherent contribution to [`(v2)] \overline{{v^{2}}} is remarkable at x/d = 10 and 20 and significantly larger than that to [`(u2)] \overline{{u^{2}}} and [`(w2)]. \overline{{w^{2}}}. This contribution to all three Reynolds normal stresses becomes negligibly small at x/d = 40. The coherent contribution to [`(u2)] \overline{{u^{2}}} and [`(v2)] \overline{{v^{2}}} decays slower as moving downstream for a larger α, consistent with the slow decay of the coherent spanwise vorticity for
a larger α. 相似文献
4.
Craig Cowan Pierpaolo Esposito Nassif Ghoussoub Amir Moradifam 《Archive for Rational Mechanics and Analysis》2010,198(3):763-787
We study the regularity of the extremal solution of the semilinear biharmonic equation ${{\Delta^2} u=\frac{\lambda}{(1-u)^2}}We study the regularity of the extremal solution of the semilinear biharmonic equation
D2 u=\fracl(1-u)2{{\Delta^2} u=\frac{\lambda}{(1-u)^2}}, which models a simple micro-electromechanical system (MEMS) device on a ball
B ì \mathbbRN{B\subset{\mathbb{R}}^N}, under Dirichlet boundary conditions u=?n u=0{u=\partial_\nu u=0} on ?B{\partial B}. We complete here the results of Lin and Yang [14] regarding the identification of a “pull-in voltage” λ* > 0 such that a stable classical solution u
λ with 0 < u
λ < 1 exists for l ? (0,l*){\lambda\in (0,\lambda^*)}, while there is none of any kind when λ > λ*. Our main result asserts that the extremal solution ul*{u_{\lambda^*}} is regular (supB ul* < 1 ){({\rm sup}_B u_{\lambda^*} <1 )} provided
N \leqq 8{N \leqq 8} while ul*{u_{\lambda^*}} is singular (supB ul* = 1){({\rm sup}_B u_{\lambda^*} =1)} for
N \geqq 9{N \geqq 9}, in which case
1-C0|x|4/3 \leqq ul* (x) \leqq 1-|x|4/3{1-C_0|x|^{4/3} \leqq u_{\lambda^*} (x) \leqq 1-|x|^{4/3}} on the unit ball, where
C0:=(\fracl*[`(l)])\frac13{C_0:=\left(\frac{\lambda^*}{\overline{\lambda}}\right)^\frac{1}{3}} and
[`(l)]: = \frac89(N-\frac23)(N- \frac83){\bar{\lambda}:= \frac{8}{9}\left(N-\frac{2}{3}\right)\left(N- \frac{8}{3}\right)}. 相似文献
5.
The detailed mean flow and turbulence measurements of a turbulent air slot jet impinging on two different semi-circular convex surfaces were investigated in both free jet and impingement wall jet regions at a jet Reynolds number Rew=12,000, using a hot-wire X-probe anemometer. The parametric effects of dimensionless circumferential distance, S/W=2.79-7.74, slot jet-to-impingement surface distance Y/W=1-13, and surface curvature D/W=10.7 and 16 on the impingement wall jet flow development along a semi-circular convex surface were examined. The results show that the effect of surface curvature D/W increases with increasing S/W. Compared with transverse Reynolds normal stress, [`(v2 )] /Um2 \overline {v^2 } /U_{\rm m}^2 , the streamwise Reynolds normal stress, [`(u2 )] /Um2 \overline {u^2 } /U_{\rm m}^2 , is strongly affected by the examined dimensionless parameters of D/W, Y/W and S/W in the near-wall region. It is also evidenced that the Reynolds shear stress, -[`(uv)] /Um2 - \overline {uv} /U_{\rm m}^2 is much more sensitive to surface curvature, D/W. 相似文献
6.
Theodore Yaotsu Wu 《Acta Mechanica Sinica》2011,27(2):135-151
This article studies on Cauchy’s function f (z) and its integral, (2πi)J[ f (z)] ≡■C f (t)dt/(t z) taken along a closed simple contour C, in regard to their comprehensive properties over the entire z = x + iy plane consisted of the simply connected open domain D + bounded by C and the open domain D outside C. (1) With f (z) assumed to be C n (n < ∞-times continuously differentiable) z ∈ D + and in a neighborhood of C, f (z) and its derivatives f (n) (z) are proved uniformly continuous in the closed domain D + = [D + + C]. (2) Cauchy’s integral formulas and their derivatives z ∈ D + (or z ∈ D ) are proved to converge uniformly in D + (or in D = [D +C]), respectively, thereby rendering the integral formulas valid over the entire z-plane. (3) The same claims (as for f (z) and J[ f (z)]) are shown extended to hold for the complement function F(z), defined to be C n z ∈ D and about C. (4) The uniform convergence theorems for f (z) and F(z) shown for arbitrary contour C are adapted to find special domains in the upper or lower half z-planes and those inside and outside the unit circle |z| = 1 such that the four general- ized Hilbert-type integral transforms are proved. (5) Further, the singularity distribution of f (z) in D is elucidated by considering the direct problem exemplified with several typ- ical singularities prescribed in D . (6) A comparative study is made between generalized integral formulas and Plemelj’s formulas on their differing basic properties. (7) Physical sig- nificances of these formulas are illustrated with applicationsto nonlinear airfoil theory. (8) Finally, an unsolved inverse problem to determine all the singularities of Cauchy function f (z) in domain D , based on the continuous numerical value of f (z) z ∈ D + = [D + + C], is presented for resolution as a conjecture. 相似文献
7.
Theodore Yaotsu Wu 《Acta Mechanica Sinica》2011,27(3):309-317
This is a series of studies on Wu’s conjecture and on its resolution to be presented herein. Both are devoted to expound all the comprehensive properties of Cauchy’s function f(z) (z = x + iy) and its integral J[f(z) ] ≡(2πi) -1 C f(t)(t z) -1dt taken along the unit circle as contour C,inside which(the open domain D+) f(z) is regular but has singularities distributed in open domain Doutside C. Resolution is given to the inverse problem that the singularities of f(z) can be determined in analytical form in terms of the values f(t) of f(z) numerically prescribed on C(|t| = 1) ,as so enunciated by Wu’s conjecture. The case of a single singularity is solved using complex algebra and analysis to acquire the solution structure for a standard reference. Multiple singularities are resolved by reducing them to a single one by elimination in principle,for which purpose a general asymptotic method is developed here for resolution to the conjecture by induction,and essential singularities are treated with employing the generalized Hilbert transforms. These new methods are applicable to relevant problems in mathematics,engineering and technology in analogy with resolving the inverse problem presented here. 相似文献
8.
G. Proust G. C. Kaschner I. J. Beyerlein B. Clausen D. W. Brown R. J. McCabe C. N. Tomé 《Experimental Mechanics》2010,50(1):125-133
Twinning is an important deformation mode in hexagonal metals to accommodate deformation along the c-axis. It differs from slip in that it accommodates shear by means of crystallographic reorientation of domains within the
grain. Such reorientation has been shown to be reversible (detwinning) in magnesium alloy aggregates. In this paper we perform
in-situ neutron diffraction reversal experiments on high-purity Zr at room temperature and liquid nitrogen temperature, and follow
the evolution of twin fraction. The experiments were motivated by previous studies done on clock-rolled Zr, subjected to deformation
history changes (direction and temperature), in the quasi-static regime, for temperatures ranging from 76 K to 450 K. We demonstrate
here for the first time that detwinning of { 10[`1] 2 }
á 10[`1][`1]
ñ\left\{ {10\overline 1 2} \right\}\left\langle {10\overline 1 \overline 1 } \right\rangle tensile twins is favored over the activation of a different twin variant in grains of high-purity polycrystalline Zr. A visco-plastic
self-consistent (VPSC) model developed previously, which includes combined slip and twin deformation, was used here to simulate
the reversal behavior of the material and to interpret the experimental results in terms of slip and twinning activities. 相似文献
9.
Giovany M. Figueiredo Marcelo F. Furtado 《Journal of Dynamics and Differential Equations》2012,24(1):13-28
We consider the quasilinear problem
-ep\textdiv(|?u|p-2?u) + V(z)up-1 = f(u) + up*-1, u ? W1,p(\mathbbRN), -\varepsilon^p\text{div}(|\nabla u|^{p-2}\nabla u) + V(z)u^{p-1} = f(u) + u^{p^*-1},\,u \in W^{1,p}\left(\mathbb{R}^N\right), 相似文献
10.
This paper deals with the rational function approximation of the irrational transfer function
G(s) = \fracX(s)E(s) = \frac1[(t0s)2m + 2z(t0s)m + 1]G(s) = \frac{X(s)}{E(s)} = \frac{1}{[(\tau _{0}s)^{2m} + 2\zeta (\tau _{0}s)^{m} + 1]} of the fundamental linear fractional order differential equation
(t0)2m\fracd2mx(t)dt2m + 2z(t0)m\fracdmx(t)dtm + x(t) = e(t)(\tau_{0})^{2m}\frac{d^{2m}x(t)}{dt^{2m}} + 2\zeta(\tau_{0})^{m}\frac{d^{m}x(t)}{dt^{m}} + x(t) = e(t), for 0<m<1 and 0<ζ<1. An approximation method by a rational function, in a given frequency band, is presented and the impulse and
the step responses of this fractional order system are derived. Illustrative examples are also presented to show the exactitude
and the usefulness of the approximation method. 相似文献
11.
We establish the existence and uniqueness results over the semi-infinite interval [0,∞) for a class of nonlinear third order
ordinary differential equations of the form
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