EXISTENCE THEOREMS OF EXTREMAL SOLUTIONS FOR A CLASS OF NONLINEAR INTEGRO－DIFFERENTIAL EQUATIONS

ＥＸＩＳＴＥＮＣＥＴＨＥＯＲＥＭＳＯＦＥＸＴＲＥＭＡＬＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＮＯＮＬＩＮＥＡＲＩＮＴＥＧＲＯ－ＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＳｏｎｇＧｕａｎｇｘｉｎｇ（宋光兴）（ＲｅｃｅｉｖｅｄＭａｙ４，１９９５；Ｃｏｍ...     

ANALYTICAL SOLUTION OF RADIATED SOUND PRESSURE OF RING－STIFFENED CYLINDRICAL SHELLS IN FLUID MEDIUM

ＡＮＡＬＹＴＩＣＡＬＳＯＬＵＴＩＯＮＯＦＲＡＤＩＡＴＥＤＳＯＵＮＤＰＲＥＳＳＵＲＥＯＦＲＩＮＧ－ＳＴＩＦＦＥＮＥＤＣＹＬＩＮＤＲＩＣＡＬＳＨＥＬＬＳＩＮＦＬＵＩＤＭＥＤＩＵＭＸｉｅＧｕａｎｍｏ（谢官员模）ＬｕｏＤｏｎｇｐｉｎｇ（骆东平）（Ｒｅｃｅｉｖ...     

EXISTENCE OF POSITIVE SOLUTIONS FOR A CLASS OF SINGULAR TWO POINT BOUNDARY VALUE PROBLEMS OF SECOND ORDER NONLINEAR EQUATION

ＥＸＩＳＴＥＮＣＥＯＦＰＯＳＩＴＩＶＥＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＳＩＮＧＵＬＡＲＴＷＯＰＯＩＮＴＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＯＦＳＥＣＯＮＤＯＲＤＥＲＮＯＮＬＩＮＥＡＲＥＱＵＡＴＩＯＮ（杨作东）ＥＸＩＳＴＥＮＣＥＯＦＰＯＳ...     

A modified method of averaging for solving a class of nonlinear equations

ＡＭＯＤＩＦＩＥＤＭＥＴＨＯＤＯＦＡＶＥＲＡＧＩＮＧＦＯＲＳＯＬＶＩＮＧＡＣＬＡＳＳＯＦＮＯＮＬＩＮＥＡＲＥＱＵＡＴＩＯＮＳＺｈａｎｇＢａｏ－ｓｈａｎ（张宝善）（ＤｅｐａｒｉｍｅｎｔｏｆＭａｉｈ．,ＸｕｚｈｏｕＴｅａｃｈｅｒｓＣｏｌｌｅｇｅ,Ｘｕｚｈ...     

CHARACTERISTICS OF SUBDIFFERENTIALS OF FUNCTIONS

ＣＨＡＲＡＣＴＥＲＩＳＴＩＣＳＯＦＳＵＢＤＩＦＦＥＲＥＮＴＩＡＬＳＯＦＦＵＮＣＴＩＯＮＳ（郭兴明）ＣＨＡＲＡＣＴＥＲＩＳＴＩＣＳＯＦＳＵＢＤＩＦＦＥＲＥＮＴＩＡＬＳＯＦＦＵＮＣＴＩＯＮＳ￥ＧｕｏＸｉｎｇｍｉｎｇ（ＲｅｃｅｉｖｅｄＪｕｎｅ１６，１９９５...     

THE EXISTENCE OF PERIODIC SOLUTION OF THE FOURTH ORDINARY NONLINEAR DIFFERENTIAL EQUATION CAUSED BY FLOW－IN

ＴＨＥＥＸＩＳＴＥＮＣＥＯＦＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＯＦＴＨＥＦＯＵＲＴＨＯＲＤＩＮＡＲＹＮＯＮＬＩＮＥＡＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＣＡＵＳＥＤＢＹＦＬＯＷ－ＩＮＤＵＣＥＤＶＩＢＲＡＴＩＯＮＧｕＱｉｎｇ－ｆａｎｇ（顾清芳）Ｔａ...     

The existence and uniqueness of the decaying positive entire solutions for a class of semilinear elliptic equations

ＴＨＥＥＸＩＳＴＥＮＣＥＡＮＤＵＮＩＱＵＥＮＥＳＳＯＦＴＨＥＤＥＣＡＹＩＮＧＰＯＳＩＴＩＶＥＥＮＴＩＲＥＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＳＥＭＩＬＩＮＥＡＲＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＳＴｉａｎＧｅｎｂａｏ（田根宝）（ＳｈａｎｇｈａｉＩｎ...     

RUDIMENTAL EQUATIONS FOR THERMO－ELASTO－PLASTIC STRESS ANALYSIS DURING CONTINUOUS CASTING WITH PHASE CHANGE

ＲＵＤＩＭＥＮＴＡＬＥＱＵＡＴＩＯＮＳＦＯＲＴＨＥＲＭＯ－ＥＬＡＳＴＯ－ＰＬＡＳＴＩＣＳＴＲＥＳＳＡＮＡＬＹＳＩＳＤＵＲＩＮＧＣＯＮＴＩＮＵＯＵＳＣＡＳＴＩＮＧＷＩＴＨＰＨＡＳＥＣＨＡＮＧＥＺｈａｏＸｉｎｇ－ｈｕａ（赵兴华）;ＣｈｅｎｇＸｉａｏ－ｄｉ...     

MOTION EQUATIONS OF MULTILAYERED ELASTIC ELECTROCONDUCTIVE PLATES IN A MAGNETIC FIELD

ＭＯＴＩＯＮＥＱＵＡＴＩＯＮＳＯＦＭＵＬＴＩＬＡＹＥＲＥＤＥＬＡＳＴＩＣＥＬＥＣＴＲＯＣＯＮＤＵＣＴＩＶＥＰＬＡＴＥＳＩＮＡＭＡＧＮＥＴＩＣＦＩＥＬＤＧｏｕＸｉｎｇ－ｈｕａ（苟兴华）（ＳｉｃｈｕａｎＵｎｉｖｅｒｓｉｔｙ,Ｃｈｅｎｇｄｕ）ＺｈａｎｇＦａ...     

A STUDY OF THE ELASTO－PLASTIC AXIALLY TENSILE PROPERTIES OF METAL MATRIX COMPOSITES WITH FIBER－END DEBONDING

ＡＳＴＵＤＹＯＦＴＨＥＥＬＡＳＴＯ－ＰＬＡＳＴＩＣＡＸＩＡＬＬＹＴＥＮＳＩＬＥＰＲＯＰＥＲＴＩＥＳＯＦＭＥＴＡＬＭＡＴＲＩＸＣＯＭＰＯＳＩＴＥＳＷＩＴＨＦＩＢＥＲ－ＥＮＤＤＥＢＯＮＤＩＮＧＳｕＸｉａｏｆｅｎｇ（苏晓风）ＣｈｅｎＨａｏｒａｎ（陈浩然）（...     

Hybrid stress analysis by digitized photoelastic data and numerical methods

A method is presented that determines photoelastic isochromatic values at the nodal points of a grid mesh which in turn is generated by a computer program that accepts digitized input. Values of σ₁ - σ₂ are computed from the digitized fringe orders. The Laplace equation is solved to separate the principal stresses at each nodal point. The method is extended to digitize isoclinics. Subsequently, σ _x - σ _y and τ _xy are calculated to be used as starting values for the solution of the pertaining partial differential equations to enhance convergence. For further accelerating the rate of convergence, superfluous boundary conditions are added from the digitized data; significant improvement is demonstrated. Estimated values of σ _x - σ _y from the digitized data are further used in conjunction with the solution of the Laplace equation to determine the state of stress without solving the boundary value problems. Paper was presented at the 1988 SEM Spring Conference on Experimental Mechanics held in Portland, OR on June 5–10.     

Immiscible Newtonian displacement by a viscoplastic material in a capillary plane channel

The immiscible displacement in a capillary plane channel of a Newtonian liquid by a viscoplastic one that obeys a Papanastasiou’s constitutive equation is numerically analyzed. An elliptic mesh generation technique, coupled with the Galerkin finite element method is used to determine the velocity field and the configuration of the interface between the two materials. We investigate the displacement efficiency and the flow patterns of the problem as functions of the dimensionless parameters that govern the problem: the capillary number (Ca), the viscosity ratio of the two fluids (N _η ) and the yield number, (τ′₀). The numerical results showed that for a fixed viscosity ratio, the fraction of mass attached to the wall is a decreasing function of τ′₀. We constructed maps of streamlines in the Cartesian space defined by τ′₀ and Ca for fixed viscosity ratios in order to capture the rough location of bypass and recirculating flow regimes. Higher yield number values induce bypass flow regimes, especially for high Ca. The dimensionless forms of the momentum conservation equation and the force balance at the interface were essential for the understanding of the role played by the dimensionless numbers that govern the problem.     

Vortex ring generation due to the coalescence of a water drop at a free surface

 Results are presented of an experimental investigation of vortex ring formation by a fluid drop contacting a free surface with negligible velocity. The pool fluid is mixed with fluorescein dye, and a laser sheet is used to illuminate a plane of the flow. A series of representative images is recorded by a CCD camera and speculation is made regarding specific sources of vorticity flux through the free surface. Two scaling analyses previously presented by other investigators are demonstrated to be equivalent under the assumptions of this experiment, and they provide the motivation for a series of test runs in which the duration of the coalescence process, τ_*, is related to variations in drop diameter L and fluid surface tension σ. Experimental results are in agreement with the analyses, showing τ_*∼σ^-1/2 and τ_*∼L ^3/2. Received: 22 December 1995 / Accepted: 15 October 1996     

Stability of an Initially, Stably Stratified Fluid Subjected to a Step Change in Temperature

The onset of convective instability in an initially quiescent, stably stratified fluid layer between two horizontal plates is analyzed with linear theory. The bottom boundary is heated suddenly from below, subjected to a step change in surface temperature. The critical time t _c to mark the onset of Rayleigh-Bénard convection is predicted by propagation theory. This theory uses the length scaled by , where α denotes thermal diffusivity. Under the normal mode analysis the dimensionless disturbance equations are obtained as a function of τ(=αt/d ²) and ζ(=Z/), where d is the fluid layer depth and Z is the vertical distance. The resulting equations are transformed to self-similar ones by using scaling and finally fixing τ as τ_c under the frame of coordinates τ and ζ. For a given γ, Pr and τ_c, the minimum value of Ra is obtained from the marginal stability curve. Here γ denotes the temperature ratio to represent the degree of stabilizing effect, Pr is the Prandtl number and Ra is the Rayleigh number. With γ=0, the minimum Ra value approaches the well-known value of 1708 as τ_c increases. However, it is inversely proportional to τ_c ^3/2 as τ_c decreases. With increasing γ, the system becomes more stable. It is interesting that in the present system, propagation theory produces the stability criteria to bound the available experimental data over the whole domain of time. Received 5 November 2001 and accepted 29 March 2002 Published online: 2 October 2002 RID="*" ID="*" This work has been supported by both SK Chemicals Co. Ltd. and LG Chemical Ltd., Seoul under the Brain Korea 21 Project of the Ministry of Education. Communicated by H.J.S. Fernando     

A Non-Linear SGS Model Based On The Spatial Velocity Increment

A new subgrid scale (SGS) modelling concept for large-eddy simulation (LES) of incompressible flow is proposed based on the three-dimensional spatial velocity increment δ u _i . The new model is inspired by the structure function formulation developed by Métais and Lesieur [39] and applied in the context of the scale similarity type formulation. First, the similarity between the SGS stress tensor τ _ij and the velocity increment tensor Q _ij = δ u _i δ u _j is analyzed analytically and numerically using a priori tests of fully developed pipe flow at Re _τ = 180. Both forward and backward energy transfers between resolved and unresolved scales of the flow are well predicted with a SGS model based on Q _ij . Secondly, a posteriori tests are performed for two families of turbulent shear flows. LES of fully developed pipe flow up to Re _τ = 520 and LES of round turbulent jet at Re _D = 25000 carried out with a dynamic version of the model provide promising results that confirm the power of this approach for wall-bounded and free shear flows.     

Effect of initial conditions on decaying grid turbulence at low R λ

The transport equations for the second-order velocity structure functions 〈(δu)²〉 and 〈(δq)²〉 are used as a scale-by-scale budget to quantify the effect of initial conditions at low Reynolds numbers, typical of grid turbulence. The validity of these equations is first investigated via hot-wire measurements of velocity and transverse vorticity fluctuations. The transport equation for 〈(δq)²〉 is shown to be balanced at all scales, while anisotropy of the large scales leads to a significant imbalance in the equation for 〈(δu)²〉. The effect of using similarity to evaluate the transport equation is rigorously tested. This approach has the desirable benefit of requiring less extensive measurements to calculate the inhomogeneous term of the transport equation. The similarity form of the 〈(δq)²〉 equation produces nearly identical results as those obtained without the similarity assumption. In the case of the 〈(δu)²〉 equation, the similarity method forces a balance at large separation, although the imbalance due to large scale anisotropy remains. The initial conditions of the turbulence at constant R _M ≃ 10,400 (28≤ R _λ≤ 55) are changed by using three grids of different geometries. Initial conditions affect the shape and magnitude of the second- and third-order structure functions, as well as the anisotropy of the large scales. The effect of initial conditions on the scale-by-scale budget is restricted to the inhomogeneous term of the transport equations, while the dissipation term remains unaffected despite the low R _λ. Scales as small as λ are affected by the changes in initial conditions.     

Fatigue gage utilizing slip-initiation phenomenon in electroplated copper foil

Fundamental experiments are carried out to examine the parameter that dominates the slip-band initiation in electroplated copper foil under the condition where the mean stress as well as the stress amplitude varies. In the case of constant-amplitude stressing, the relation between the critical stress for the slip-band initiation σ _p and the number of cyclesN is well represented by σ _p ^α N=C. In other words, the slip bands appear when the total hysteresis energy applied to the copper foil attains a critical value. In the case of variable stresses, the range-pair mainly dominates the occurrence of the slip bands, and Miner's linear cumulative damage rule holds for the accumulation of the fatigue damage for the slip-band initiation. Accordingly, the parameter (Σσ _i ^α n _i/Σn _i)^1/α is equivalent to the critical stress σ _p under constant amplitude stressing, where σ _i andn _i are the stress amplitude and the number of cycles counted by the range-pair method, respectively, and α is the exponent of the σ _p -N relation. Based on these results, the applicability of the copper foil to the fatigue gage that accumulates and indicates a load experience is discussed.     

Euler–Poisson Systems as Action-Minimizing Paths in the Wasserstein Space

This paper uses a variational approach to establish existence of solutions (σ _t , v _t ) for the 1-d Euler–Poisson system by minimizing an action. We assume that the initial and terminal points σ ₀, σ _T are prescribed in , the set of Borel probability measures on the real line, of finite second-order moments. We show existence of a unique minimizer of the action when the time interval [0,T] satisfies T < π. These solutions conserve the Hamiltonian and they yield a path t → σ _t in . When σ _t  = δ _y(t) is a Dirac mass, the Euler–Poisson system reduces to . The kinetic version of the Euler–Poisson, that is the Vlasov–Poisson system was studied in Ambrosio and Gangbo (Comm Pure Appl Math, to appear) as a Hamiltonian system. WG gratefully acknowledges the support provided by NSF grants DMS-02-00267, DMS-03-54729 and DMS-06-00791. TN gratefully acknowledges the postdoctoral support provided by NSF grants DMS-03- 54729 and the School of Mathematics. AT gratefully acknowledges the support provided by the School of Mathematics.     

Vorticities in a LES Model for 3D Periodic Turbulent Flows

This paper is devoted to the study of a LES model to simulate turbulent 3D periodic flow. We focus our attention on the vorticity equation derived from this LES model for small values of the numerical grid size δ. We obtain entropy inequalities for the sequence of corresponding vorticities and corresponding pressures independent of δ, provided the initial velocity u₀ is in L_x² while the initial vorticity ω₀ = ∇ × u₀ is in L_x¹. When δ tends to zero, we show convergence, in a distributional sense, of the corresponding equations for the vorticities to the classical 3D equation for the vorticity.