REMARK ON STABILITY OF ISHIKAWA ITERATIVE PROCEDURES

1　ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＰｒｅｌｉｍｉｎａｒｉｅｓＳｕｐｐｏｓｅＥｉｓａｒｅａｌＢａｎａｃｈｓｐａｃｅａｎｄＴｉｓａｓｅｌｆｍａｐｏｆＥ .Ｓｕｐｐｏｓｅｘ0 ∈Ｅａｎｄｘｎ+1=ｆ(Ｔ ,ｘｎ)ｄｅｆｉｎｅｓａｎｉｔｅｒａｔｉｏｎｐｒｏｃｅｄｕｒｅｗｈｉｃｈｙｉｅｌｄｓａｓｅｑｕｅｎｃｅｏｆｐｏｉｎｔｓ ｘｎ ∞ｎ=0 ｉｎＥ .Ｆｏｒａｎｅｘａｍｐｌｅ ,ｔｈｅｆｕｎｃｔｉｏｎｉｔｅｒａｔｉｏｎｘｎ+1=ｆ(Ｔ ,ｘｎ) =Ｔｘ0 .ＳｕｐｐｏｓｅＦ(Ｔ) =ｘ∈Ｅ :Ｔｘ=ｘ ≠ ａｎｄｔｈａｔ ｘｎ ｃｏｎｖｅｒｇｅｓｓ…     

NEW METHOD FOR LOW ORDER SPECTRAL MODEL AND ITS APPLICATION

In order to overcome the deficiency in classical method of low order spectral model, a new method for low order spectral model was advanced. Through calculating the multiple correlation coefficients between combinations of different functions and the recorded data under the least square criterion, the truncated functions which can mostly reflect the studied physical phenomenon were objectively distilled from these data. The new method overcomes the deficiency of artificially selecting the truncated functions in the classical low order spectral model. The new method being applied to study the inter-annual variation of summer atmospheric circulation over Northern Hemisphere, the truncated functions were obtained with the atmospheric circulation data of June 1994 and June 1998. The mechanisms for the two-summer atmospheric circulation variations over Northern Hemisphere were obtained with two-layer quasi-geostrophic baroclinic equation.     

STATISTIC MODELING OF THE CREEP BEHAVIOR OF METAL MATRIX COMPOSITES BASED ON FINITE ELEMENT ANALYSIS

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｃｒｅｅｐｂｅｈａｖｉｏｒｏｆｓｈｏｒｔｆｉｂｅｒｒｅｉｎｆｏｒｃｅＭｅｔａｌＭａｔｒｉｘＣｏｍｐｏｓｉｔｅｓ (ＭＭＣｓ)ｄｅｐｅｎｄｓｏｎｔｈｅｆｏｌｌｏｗｉｎｇｆａｃｔｏｒｓ,ｓｕｃｈａｓｔｈｅｃｒｅｅｐｐｒｏｐｅｒｔｙｏｆｔｈｅｍａｔｒｉｘ ,ｅｌａｓｔｉｃａｎｄｆｒａｃｔｕｒｅｓｐｒｏｐｅｒｔｉｅｓｏｆｔｈｅｆｉｂｅｒ,ｇｅｏｍｅｔｒｉｃｐａｒａｍｅｔｅｒｓｏｆｔｈｅｆｉｂｅｒｓ,ａｒｒａｎｇｅｍｅｎｔｏｆｔｈｅｆｉｂｅｒｓａｎｄｔｈｅｐｒｏｐｅｒｔｙｏｆｔｈｅｆ…     

THE TRANSIENT ELLIPTIC FLOW OF POWER-LAW FLUID IN FRACTAL POROUS MEDIA

1　ＴｈｅＦｌｏｗＭｏｄｅｌｏｆＰｏｗｅｒ＿ＬａｗＦｌｕｉｄｉｎＲａｄｉｃａｌＦｒａｃｔａｌＲｅｓｅｒｖｏｉｒＴｈｅｔｒａｎｓｉｅｎｔｆｌｏｗｏｆｐｏｗｅｒ＿ｌａｗｆｌｕｉｄｉｎｒａｄｉｃａｌｆｒａｃｔａｌｒｅｓｅｒｖｏｉｒｉｓｓｔｕｄｉｅｄｉｎＲｅｆ.[1 ] ,ａｎｄａｎａｌｙｔｉｃａｌｓｏｌｕｔｉｏｎｏｆＬａｐｌａｃｅｓｐａｃｅｉｓｄｅｒｉｖｅｄ .ＩｎＲｅｆ.[2 ] ,ｔｈｅｔｒａｎｓｉｅｎｔｅｌｌｉｐｔｉｃａｌｆｌｏｗｉｓｒｅｓｅａｒｃｈｅｄｏｎｍｏｄｅｌｏｆｅｘｐａｎｄｉｎｇｒｅｃｔａｎｇｌｅ .Ｔ…     

Purely elastic interfacial instabilities in superposed flow of polymeric fluids

Purely elastic interfacial stability of superposed plane Poiseuille flow of polymeric liquids has been investigated utilizing both asymptotic and numerical techniques. It is shown that these instabilities are caused by an unfavorable jump in the first normal stress difference across the fluid interface. To determine the significance of these instabilities in finite experimental geometries, a comparison between the maximum growth rates of purely elastic instabilities with instabilities driven primarily by a viscosity or a combined viscosity and elasticity difference is made. Based on this comparison, it is shown that purely elastic interfacial instabilities can play a major role in superposed flow of polymeric liquids in finite experimental geometries.     

Beitrag zur Rohrströmung kompressibler Fluide mit Reibung und Wärmeübergang

Übersicht Die Strömung eines kompressiblen Fluids aus einem Druckkessel durch ein Rohr konstanten Kreisquerschnitts und mit konstanter Wandtemperatur, in dem Wandreibung wirksam ist, wird nach der Stromfadentheorie untersucht. Gegeben sind der Druck im Kessel und am Ende der Rohrleitung sowie die Temperatur der Rohrwand und im Kessel. Als Wärmeübergangshypothese wird die Reynolds-Analogie benutzt. Die Wandreibung wird durch die Rohrreibungszahl beschrieben. Die sich ergebende Differentialgleichung und das Eigenwertproblem für die Eintrittsmachzahl wird numerisch gelöst in Abhängigkeit von der dimensionslosen Rohrlänge für Austrittsmachzahlen 1. Eine analytische Näherungslösung für kleine Eintrittsmachzahlen und eine asymptotische Entwicklung für große Rohrlängen wird angegeben. Es zeigt sich, daß der Wärmeübergangsprozeß relativ schnell abgeschlossen ist und die End-Machzahl, der Druckverlustfaktor sowie das kritische Druckverhältnis vom Wärmeübergang fast unabhängig sind.

---

A note on the viscous pipe flow of a compressible fluid with heat transfer

Summary The flow of a compressible fluid from a pressure reservoir through a pipe with constant circular cross-section and constant pipe-wall temperature has been investigated by means of one-dimensional theory with wall-friction taken into account. The initial stagnation pressure and temperature, the pipe wall temperature and the pipe exit pressure are assumed to be given. The heat transfer is assumed to follow the Reynolds analogy, while wall friction is taken into account by the pipe friction coefficient. The resulting differential equation and the corresponding eigenvalue problem for the inlet Mach number have been solved numerically as function of the dimensionless pipe-length for exit Mach numbers 1. An analytic approximation for small pipe inlet Mach numbers and an asymptotic expansion for large pipe-lengths have been derived. It is found that the heat transfer is restricted to a relatively small distance past the inlet. The final Mach number, the pressure loss factor as well as the critical pressure ratio is approximately independent of any heat transfer.

     

Radiation: Waves or particles? A quantized approach to time

A fundamental difficulty in theoretical physics is the dual and apparently incompatible interpretations of radiation as showing both continuous and extensive wave properties but also those of discrete atomic or smaller individual particles. Some of these contradictions are outlined. The explanation offered is of a quantized nature of time; units t_o=h/m_oc² for a particle at rest, and of similar interval unit s_o when in relative motion, with conventional relativistic corrections.

For many purposes this form of quantization replaces the need for a wave concept which then appears as a mathematical approach, chosen to avoid the physical concept of an intrinsicc time for any particle, just as we have for its intrinsic mass, spin and electrical charge. t_o and s_o are directly related to its frequency, energy and mass. The uncertainty principle and interference relations follow directly from this model, without any physical wave concept.     

FIXED POINTS OF INCREASING OPERATORS IN ORDERED SPACE WITH APPLICATIONS

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｖｅｓｔｉｇａｔｉｎｇｔｈｅｆｏｌｌｏｗｉｎｇｂｏｕｎｄａｒｙｐｒｏｂｌｅｍｉｎｏｒｄｉｎａｒｙｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎ :¨ｘ+ｆ(ｔ,ｘ(ｔ) ) =0 ,ａ<ｔ<ｂ,αｘ(ａ) -β ｘ(ａ) =0 ,γｘ(ｂ) +δ ｘ(ｂ) =0 ,( 1 )ｗｈｅｒｅα ,β,γ ,δ≥ 0 ,Δ=(ｂ-ａ)αγ+αδ+ βγ>0 .ｆ(ｔ,ｓ)ｍａｙｂｅｓｉｎｇｕｌａｒｉｎｔ =ａ ,ｂ.Ｉｔｈａｓｂｅｅｎｄｉｒｅｃｔｌｙｖｅｒｉｆｉｅｄｔｈａｔｘ(ｔ)ｉｓｔｈｅｓｏｌｕｔｉｏｎｏｆ( 1 )ｉｎＣ2 [ａ ,ｂ]ｉｆａｎｄｏｎｌｙｉｆｘ(…     

Dynamics of Self-Organized and Self-Assembled Structures,by Rashmi C. Desai and Raymond Kapral

The arrival of the first hard X-ray free electron laser facilities promises new advances in structural dynamics and nanoscale imaging that will have impact across the sciences. This introductory review is intended to cover the basic physics behind this potential and illustrate the current state-of-the-art by discussing a number of recent findings from the LCLS facility at the Stanford Linear Accelerator Centre (SLAC). We concentrate on the new science using these light sources rather than the new light source technology itself, although a brief introduction to the operation of LCLS is given. Emphasis is placed upon the new regime of high intensity X-ray matter interaction physics with ultrashort X-ray pulses. We discuss how the unique combination of X-ray parameters will open new opportunities for time resolved structural studies and how the high brightness enables a new class of coherent diffraction X-ray imaging. The potential importance of this new imaging method in the study of nanostructures and biological systems at the sub-cellular and molecular level will be outlined.     

Elongational viscosity by fiber spinning

Isothermal melt, fiber-spinning was recently analyzed by means of a nonlinear, integral, constitutive equation that incorporates shear history effects, spectrum of relaxation times, shear-thinning, and extension thinning or thickening when either the drawing force or the draw ratio is specified. The predictions agreed with experimental data on spinning of polystyrene, low-density polyethylene, and polypropylene melts. The predicted apparent elongational viscosity along the threadline (which, as shown in this work, must be identical to that measured experimentally by fiber spinning type of elongational rheometers) is compared with the true elongational viscosity predicted by the same constitutive equation under well-defined experimental conditions of constant extension rate, independent of any strain history. It is concluded that the apparent elongational viscosity, as measured by fiber-spinning, approaches the true elongational viscosity at low Weissenberg numbers (defined as the product of the liquid's relaxation time multiplied by the extension rate). At moderate Weissenberg numbers, the two viscosities may differ by an order of magnitude and their difference grows even larger at high Weissenberg numbers.