RADAR ECHO DELAY IN THE(Ω,Aμν)-FIELD THEORY

The present work aims to consider the.fourth test of general relativity theory by Shapiro.using radar echo delay in Yu’s(Ω,A_μν)-field theory.     

Methods of Small and Large δ in the Nonlinear Dynamics – A Comparative Analysis

New asymptotic approaches for dynamical systems containing a power nonlinear term x ⁿ are proposed and analyzed. Two natural limiting cases are studied: n 1 + , 1 and n . In the firstcase, the 'small method' (SM)is used and its applicability for dynamical problems with the nonlinearterm sin as well as the usefulness of the SMfor the problem with small denominators are outlined. For n , a new asymptotic approach is proposed(conditionally we call it the 'large method' –LM). Error estimations lead to the followingconclusion: the LM may be used, even for smalln, whereas the SM has a narrow application area. Both of the discussed approaches overlap all values ofthe parameter n.     

Ši’lnikov Chaos in the Generalized Lorenz Canonical Form of Dynamical Systems

This paper studies the generalized Lorenz canonical form of dynamical systems introduced by elikovský and Chen [International Journal of Bifurcation and Chaos 12(8), 2002, 1789]. It proves the existence of a heteroclinic orbit of the canonical form and the convergence of the corresponding series expansion. The ilnikov criterion along with some technical conditions guarantee that the canonical form has Smale horseshoes and horseshoe chaos. As a consequence, it also proves that both the classical Lorenz system and the Chen system have ilnikov chaos. When the system is changed into another ordinary differential equation through a nonsingular one-parameter linear transformation, the exact range of existence of ilnikov chaos with respect to the parameter can be specified. Numerical simulation verifies the theoretical results and analysis.     

Thin-Walled Beams: the Case of the Rectangular Cross-Section

In this paper we present an asymptotic analysis of the three-dimensional problem for a thin linearly elastic cantilever =×(0,l) with rectangular cross-section of sides and ², as goes to zero. Under suitable assumptions on the given loads, we show that the three-dimensional problem converges in a variational sense to the classical one-dimensional model for extension, flexure and torsion of thin-walled beams. Mathematics Subject Classifications (2000) 474K20, 74B10, 49J45.     

The modified Casson＇s equation and its application to pipe flows of shear-thickening fluid

A few additional data from our previous experiments were plotted to emphasize the shear-thickening behavior of deoxy sickle erythrocyte (SS) suspension. A constitutive equation (named as FX equation) was developed and applied to a cylindrical pipe flow of a shear-thickening fluid. A blunt velocity profile and its volume flow rate were calculated. The flow was non-viscous (potential) in the central part of the pipe (i.e. the central core or the central plug-flow), and became more and more viscous towards the wall of the pipe after a specific radial distance, which was determined by a critical shear rate of (named as Fungs shear rate). Furthermore, combining the FX equation with the original Cassons equation, the author obtained a modified Cassons equation by introducing .The English text was polished by Yunming Chen.     

“Thermal layer” effect in MHD: Interaction of a parallel shock with a layer of decreased density

Interaction of a parallel fast MHD shock with a layer of decreased density is discussed using ideal MHD approach. This is an extrapolation of gas dynamic thermal layer effect on ideal MHD. Computer simulations show that a magnetic field of a moderate intensity ( 1) may change the character of the flow for intermediate Mach numbers (M 5) and a new raking regime may occur which is not observed in the absence of a magnetic field. Self similar precursor analogous to that in gas dynamics may develop in the case of highM and low density in the layer but magnetic forces essentially decrease its growth rate. This problem appears in connection with cosmical shock propagation where planetary magnetic tails play the role of the thermal layer, and it may also be observed in the laboratory when the shock is strong enough to heat the walls ahead of it.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

The Devil’s Staircase Dimensions and Measure-Theoretical Entropy of Maps with Horizontal Gap

This work elucidates the measure-theoretical entropy and dimensions of a unimodal map with a horizontal gap. The measure-theoretical entropy and dimensions of the F_t (which is defined later) are shown to form a devils staircase structure with respect to the gap size t. Pesins formula for gap maps is also considered.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday.     

Symbolic Sequences Generated by a Special Class of Discrete Systems With Discontinuity and Input

In this paper, we study the symbolic sequences generated by aclass of discrete systems. This class contains the double-modulators, a typical example of discretetime electronic systems with discontinuity and input. First we develop ageneral theory and then we apply it to some examples in order to obtainsets of inadmissible sequences.     

On the Quasi‐Steadiness Hypothesis as Applied to Gas Exhaustion from a Receiver

A semiempirical method of determining the stabilization time for a quasisteady mode of gas exhaustion from a receiver after sudden opening of the nozzle and the time evolution of the real flow rate at the stage of the transitional process are considered. The numerical solution of the equations of exhaustion gas dynamics in a twodimensional formulation and the results of model experiments demonstrated that the method can be used to estimate the conditions of applicability of the quasisteadiness hypothesis and to determine the discharge coefficient of the nozzle with controlled accuracy.     

Some Results on Dynamics of Special Double-Loop ΣΔ-Modulators

The dynamic behaviour of a specific two-dimensional state space model with discontinuity is studied. This model arises from the study of double-loop -modulators with constant input. Using mathematical tools we explain certain simulation results, and some properties are derived. Simulations based on time-varying input are also provided.     

Design of a Beam with Controllable Force Elements

A method for solving the problem of design of an intellectual structure formulated for the pair optimal position of actuators, optimal control of actuators is developed. In the method proposed, physical and logical objects are treated as equivalent.     

Attractors for the Two-Dimensional Navier–Stokes-α Model: An α-Dependence Study

The two-dimensional Navier–Stokes- model is considered on the torus and on the sphere. Upper and lower bounds for the dimension of the global attractors are given. The dependence of the dimension of the global attractors on is studied. Special attention is given for the limiting cases when 0, that is, when the Navier–Stokes- model tends to the Navier–Stokes equations, and to the case when .     

Ishikawa Iterative Process in Uniformly Smooth Banach Spaces

ＬｅｔＥｂｅａｕｎｉｆｏｒｍｌｙｓｍｏｏｔｈＢａｎａｃｈｓｐａｃｅ ,ＫｂｅａｎｏｎｅｍｐｔｙｃｌｏｓｅｄｃｏｎｖｅｘｓｕｂｓｅｔｏｆＥ ,ａｎｄｓｕｐｐｏｓｅＴ :Ｋ→ＫｉｓａｃｏｎｔｉｎｕｏｕｓΦ＿ｓｔｒｏｎｇｌｙｐｓｅｕｄｏｃｏｎｔｒａｃｔｉｖｅｏｐｅｒａｔｏｒ.ＤｅｎｏｔｅｔｈｅｄｕａｌｓｐａｃｅｏｆＥｂｙＥ .ＷｅｄｅｎｏｔｅｂｙＪｔｈｅｄｕａｌｉｔｙｍａｐｆｒｏｍＥｔｏ 2 Ｅ ｄｅｆｉｎｅｄｂｙＪ(ｘ) =ｆ∈Ｅ :〈ｘ ,ｆ〉=‖ｘ‖2 =‖ｆ‖2 . ( 1 )Ｉｔｉｓｗｅｌｌ＿ｋｎｏｗｎｔｈａｔｉｆＥｉｓｕ…     

Asymptotic Modeling of Nonlinear Wave Processes in Shock‐Loaded Elastoplastic Materials

Nonlinear wave processes in shockloaded elastoplastic materials are modeled. A comparison of the results obtained with experimental data and numerical solutions of exact systems of dynamic equations shows that the model equations proposed qualitatively describe the stressdistribution evolution in both the elasticflow and plasticflow regions and can be used to solve one and twodimensional problems of pulsed deformation and fracture of elastoplastic media.     

On Ericksen’s Theorem for Unconstrained Hyperelastic Materials

After reviewing the proof of Ericksens theorem for the set of unconstrained, homogeneous, isotropic, hyperelastic materials, Ericksens result is sharpened to cover the subset of materials that possess a natural configuration and satisfy the empirical inequalities. Mathematics Subject Classifications (2000) 74B20.     

Permeability Effects of Turbulent Flow Through a Porous Insert in a Backward-Facing-Step Channel

In the present work, a k– model, based on the work of Lee and Howell (Proceedings of the ASME-JSME Thermal Engineering Hawaii, 1987), is rigorously derived based on time average of spatially averaged Navier–Stokes equations. The model is then employed to solve for a flow in a backward-facing step channel with a porous insert. The numerical solver is modified from the STREAM code (Lien and Leschziner, Comput. Meth. Appl. Mech. Eng. 114 (1994a) 123–148), and it has been validated against the experimental data of Seegmiller and Driver (AIAA Journal 23 (1985) 163–171). The code is then used to perform simulation for cases with a porous insert. The resistance of the porous insert can be altered by changing its permeability (), Forchheimers constant (F), or thickness (b). The goal is to examine the influence of each parameter on the resulting flow and turbulent kinetic energy (k) distributions. It is discovered that, by increasing the resistance of the insert, flow eventually enters a transitional regime towards relaminarization. This is due to the contribution of Darcys and Forchheimers terms in the governing equations, and modifying these two terms changes the levels of P_k and, hence, k and . Generally speaking, lowering or raising F results in a greater suppression of P_k than , causing the flow to relaminarize. Meanwhile, if the pore size is reasonably large to sustain turbulence within the porous media, increasing b reduces but does not eliminate the turbulent activity in the porous insert.     

Upscaling in Subsurface Transport Using Cluster Statistics of Percolation

Transport/flow problems in soils have been treated in random resistor network representations (RRNs). Two lines of argument can be used to justify such a representation. Solute transport at the pore-space level may probably be treated using a system of linear, first-order differential equations describing inter-pore probability fluxes. This equation is equivalent to a random impedance network representation. Alternatively, Darcys law with spatially variable hydraulic conductivity is equivalent to an RRN. Darcys law for the hydraulic conductivity is applicable at sufficiently low pressure head in saturated soils, but only for steady-state flow in unsaturated soils. The result given here will have two contributions, one of which is universal to any linear conductance problem, i.e., requires only the applicability of Darcys (or Ohms) law. The second contribution depends on the actual distribution of linear conductances appropriate. Although nonlinear effects in RRNs (including changes in resistance values resulting from current, analogous to changes in matric potential resulting from flow) have been treated within the framework of percolation theory, the theoretical development lags the corresponding development of the linear theory, which is, in principle, on a solid foundation. In practice, calculations of the nonlinear conductivity in relatively (compared with soils) well characterized solid-state systems such as amorphous or impure semiconductors, do not agree with each other or with experiment. In semiconductors, however, experiments do at least appear consistent with each other.In the limit of infinite system size the transport properties of a sufficiently inhomogeneous medium are best calculated through application of critical rate analysis with the system resistivity related to the critical (percolating) resistance value, R_c. Here well-known cluster statistics of percolation theory are used to derive the variability, W (R,x) in the smallest maximal resistance, R of a path spanning a volume x³ as well as to find the dependence of the mean value of the conductivity, (x). The functional form of the cluster statistics is a product of a power of cluster size, and a scaling function, either exponential or Gaussian, but which, in either case, cuts off cluster sizes at a finite value for any maximal resistance other than R_c. Either form leads to a maximum in W (R,x) at R=R_c. When the exponential form of the cluster statistics is used, and when individual resistors are exponential functions of random variables (as in stochastic treatments of the unsaturated zone by the McLaughlin group [see Graham and MacLaughlin (1991), or the series of papers by Yeh et al. (1985, 1995), etc.], or as is known for hopping conduction in condensed matter physics), then W (R,x) has a power law decay in R/R_c (or R_c/R, the power being an increasing function of x. If the statistics of the individual resistors are given by power law functions of random variables (as in Poiseiulles Law), then an exponential decay in R for W (R,x) is obtained with decay constant an increasing function of x. Use, instead, of the Gaussian cluster statistics alters the case of power law decay in R to an approximate power, with the value of the power a function of both R and x.     

Iterative Process for Certain Nonlinear Mappings with Lipschitz Condition

1　ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＰｒｅｌｉｍｉｎａｒｉｅｓＴｈｒｏｕｇｈｏｕｔｔｈｉｓｐａｐｅｒ,ｗｅａｓｓｕｍｅｔｈａｔＸｉｓａｒｅａｌＢａｎａｃｈｓｐａｃｅａｎｄＸ ｉｓｔｈｅｄｕａｌｓｐａｃｅｏｆＸ ,〈· ,·〉ｄｅｎｏｔｅｓｔｈｅｐａｉｒｉｎｇｏｆＸａｎｄＸ .ＴｈｅｍａｐｐｉｎｇＪ:Ｘ → 2 Ｘ ｄｅｆｉｎｅｄｂｙＪ(ｘ) =ｊ∈Ｘ :〈ｘ ,ｊ〉=‖ｘ‖·‖ｊ‖ ,‖ｊ‖ =‖ｘ‖ ,　　ｘ∈Ｘｉｓｃａｌｌｅｄｔｈｅｎｏｒｍａｌｉｚｅｄｄｕａｌｉｔｙｍａｐｐｉｎｇ .Ｄｅｆｉｎｉｔｉｏｎ 1 1　ＬｅｔＸｂｅａ…     

The ‘Missing’ Self-Similar Free Convection Boundary-Layer Flow Over a Vertical Permeable Surface in a Porous Medium

The free convection boundary-layer flow of a Darcy–Boussinesq fluid from a vertical permeable plate with an inverse-linear temperature distribution is considered. The outstanding characteristics of this self-similar flow which, according to the usual reduction procedure of pseudo-similarity to full similarity, should not exist at all, are analyzed in detail. Thus it is shown that this flow only exists if a lateral suction with a sufficiently large suction parameter _min = 1.079131 is applied. For the threshold value _min the solution is unique but above it multiple solutions are encountered for every given value of .