OSCILLATORY BEHAVIOUR OF A CLASS OF NONLINEAR DIFFERENTIAL EQUATIONS OF THIRD ORDER

This paper investigates the oscillatory and nonoscillatory behaviour of solu- tions of a class of third order nonlinear differential equations. Results extend and improve some known results in the literature.

OSCILLATORY AND ASYMPTOTIC BEHMIOUR OF A CLASS OF NONLINEAR DIFFERENTIALEQUATIONS OF THIRD ORDER

This paper deals with oscillatory /nonoscillatory behaviour of solutions of thirdorder nonlinear differential equations of the formwhere a,b,c E C([a,oo),R) such that a(t) does not change sign, b(t) 5 0, c(t) > 0,f∈C(R, R) such that (f(y)/y) ≥ β > 0 for y ≠ 0 and γ > 0 is a quotient of odd integers.It has been shown, under certain conditions on coefficient functions, that a solution of (1)and (2) which Las a zero is oscillatory and the nonoscillatory solutions of these equationstend to zero as t → ∞. The motivation for this work came from the observation that thewhere al b, c are constants such that b≤ 0, c > 0, has an oscillatory solution if and only ifand all nonoscillatory solutions of (3) tend to zero if and only if the equation has anoscillatory solution.

Oscillatory and anti-oscillatory motifs in genetic regulatory networks

Recently, self-sustained oscillatory genetic regulatory networks （GRNs） have attracted significant attention in the biological field. Given a GRN, it is important to anticipate whether the network could generate oscillation with proper parameters, and what the key ingredients for the oscillation are. In this paper the ranges of some function-related parameters which are favorable to sustained oscillations are considered. In particular, some oscillatory motifs appearing with high-frequency in most of the oscillatory GRNs are observed. Moreover, there are some anti-oscillatory motifs which have a strong oscillation repressing effect. Some conclusions analyzing these motif effects and constructing oscillatory GRNs are provided.

The Friction and Wear Properties of the Spherical Plain Bearings with Self-lubricating Composite Liner in Oscillatory Movement

A test method based on the condition simulation and a friction and wear test machine featuring in oscillatory movement were set up for self-lubricating spherical plain bearings (SPB). In the machine the condition parameters such as load, angle and frequency of oscillation and number of test cycles can be properly controlled. The data relating to the tribological properties of the bearing, in terms of friction coefficient, linear wear amount, temperature near friction surface and applied load, can be monitored and recorded simultaneously during test process by a computerized measuring system of the machine. Efforts were made to improve the measurement technology of the friction coefficient in oscillating motion. In result, a well-designed bearing torque mechanism was developed, which could reveal the relation between the friction coefficient and the displacement of oscillating angle in any defined cycle while the curve of friction coefficient vs number of testing cycles was continuously plotted. The tribological properties and service life of four kinds of the bearings, i.e, the sampleⅠ-Ⅳ with different self-lubricating composite liners, including three kinds of polytetrafluoroethylene (PTFE) fiber weave/epoxy resin composite liners and a PTFE plastic/copper grid composite liner, were evaluated by testing, and the wear mechanisms of the liner materials were analyzed.

Effect of High Frequency Oscillatory Ventilation on EVLW and Lung Capillary Permeability of Piglets with Acute Respiratory Distress Syndrome Caused by Pulmonary and Extrapulmonary Insults

The effect of high frequency oscillatory ventilation（HFOV） at early stage on hemodynamic parameters, extravascular lung water（EVLW）, lung capillary permeability, CC16 and s ICAM-1 in piglets with pulmonary or extrapulmonary acute respiratory distress syndrome（ARDS） was explored. Central vein pressure（CVP） and pulse indicator continuous cardiac output（Pi CCO） were monitored in 12 anesthetized and intubated healthy piglets. Pulmonary ARDS（ARDSp） and extrapulmonary ARDS（ARDSexp） models were respectively established by lung lavage of saline solution and intravenous injection of oleic acid. Then the piglets received HFOV for 4 h. EVLW index（EVLWI）, EVLW/intratroracic blood volume（ITBV） and pulmonary vascular permeability index（PVPI） were measured before and after modeling（T0 and T1）, and T2（1 h）, T3（2 h）, T4（3 h） and T5（4 h） after HFOV. CC16 and s ICAM-1 were also detected at T1 and T5. Results showed at T1, T3, T4 and T5, EVLWI was increased more significantly in ARDSp group than in ARDSexp group（P〈0.05）. The EVLWI in ARDSp group was increased at T1（P=0.008）, and sustained continuously within 2 h（P=0.679, P=0.216）, but decreased at T4（P=0.007） and T5（P=0.037）. The EVLWI in ARDSexp group was also increased at T1（P=0.003）, but significantly decreased at T3（P=0.002） and T4（P=0.019）. PVPI was increased after modeling in both two groups（P=0.004, P=0.012）, but there was no significant change within 4 h（T5） under HFOV in ARDSp group, while PVPI showed the increasing trends at first, then decreased in ARDSexp group after HFOV. The changes of EVLW/ITBV were similar to those of PVPI. No significant differences were found in ΔEVLWI（P=0.13）, ΔPVPI（P=0.28） and ΔEVLW/ITBV between the two groups（P=0.63）. The significant decreases in both CC16 and s ICAM-1 were found in both two groups 4 h after HFOV, but there was no significant difference between the two groups. It was concluded that EVLWI and lung capillary permeability were markedly increased in ARDSp and ARDSexp groups. EVLW could be decreased 4 h after the HFOV treatment. HFOV, EVLW/ITBV and PVPI were increased slightly at first, and then decreased in ARDSexp group, while in ARDSp group no significant difference was found after modeling. No significant differences were found in the decreases in EVLW and lung capillary permeability 4 h after HFOV.

Mobile bed thickness in skewed asymmetric oscillatory sheet flows

A new instantaneous mobile bed thickness model is presented for sediment transport in skewed asymmetric oscillatory sheet flows. The proposed model includes a basic bed load part and a suspended load part related to the Shields parameter, and takes into account the effects of mass conservation, phase-lag, and asymmetric boundary layer development, which are important in skewed asymmetric flows but usually absent in classical models. The proposed model is validated by erosion depth and sheet flow layer thickness data in both steady and unsteady flows, and applied to a new instantaneous sediment transport rate formula. With higher accuracy than classical empirical models in steady flows, the new formula can also be used for instantaneous sediment transport rate prediction in skewed asymmetric oscillatory sheet flows.

Utilization of Maxwell-Cattaneo law for MHD swirling flow through oscillatory disk subject to porous medium

The present study aims to investigate the salient features of incompressible, hydromagnetic, three-dimensional flow of viscous fluid subject to the oscillatory motion of a disk. The rotating disk is contained in a porous medium. Furthermore, a time-invariant version of the Maxwell-Cattaneo law is implemented in the energy equation. The flow problem is normalized by obtaining similarity variables. The resulting nonlinear system is solved numerically using the successive over-relaxation method. The main results are discussed through graphical representations and tables. It is perceived that the thermal relaxation time parameter decreases the temperature curves and increases the heat trans- fer rate. The oscillatory curves for the velocity field demonstrate a decreasing tendency with the increasing porosity parameter values. Two- and three-dimensional flow phenom- ena are also shown through graphical results.

Numerical solution of oscillatory flow of Maxwell fluid in a rectangular straight duct

A numerical analysis is presented for the oscillatory flow of Maxwell fluid in a rectangular straight duct subjected to a simple harmonic periodic pressure gradient.The numerical solutions are obtained by a finite difference scheme method.The stability of this finite difference scheme method is discussed.The distributions of the velocity and phase difference are given numerically and graphically.The effects of the Reynolds number,relaxation time,and aspect ratio of the cross section on the oscillatory flow are investigated.The results show that when the relaxation time of the Maxwell model and the Reynolds number increase,the resonance phenomena for the distributions of the velocity and phase difference enhance.

A LIPSCHITZ ESTIMATE FOR MULTILINEAR OSCILLATORY SINGULAR INTEGRALS WITH ROUGH KERNELS

In this paper, for the multilinear oscillatory singular integral operators TA1,A2,...Ar defined by TA1,A2,...,Arf（x） = p.v.∫R^n ^e^iP（x,y）Ω（x - y）/｜x - y｜^n＋M r∏s=1 Rms＋1（As;x,y）f（y）dy, n≥2 where P（x,y） is a nontrivial and real-valued polynomial defined on R^n×R^n,Ω（x） is homogeneous of degree zero on R^n, As（x） has derivatives of order ms in ∧βs （0〈βs〈 1）, Rms＋1 （As;x, y） denotes the （ms＋1）-st remainder of the Taylor series of As at x expended about y （s = 1, 2, ..., r）, M = ∑s^r =1 ms, the author proves that if 0 〈=β1=∑s^r=1 βs〈1,and Ω∈L^q（S^n-1） for some q 〉 1/（1 -β）, then for any p∈（1, ∞）, and some appropriate 0 〈β〈 1, TA1,A2,...,Ar, is bounded on L^P（R^n）.

Nonaffine Network Structural Model for Molten Low-Density Polyethylene and High-Density Polyethylene in Oscillatory Shear

We propose molten polymer's entanglement network deformation to be nonaffine and use transient network structural theory with the revised Liu's kinetics rate equation and the revised upper convected Maxwell constitutive equation to establish a nonaffine network structural constitutive model for studying the rheological behavior of molten Low Density Polyethylene (LDPE) and High Density Polyethylene (HDPE) in oscillatory shear. As a result, when the strain amplitude or frequency increases, the shear stress amplitude increases. At the same time, the accuracy of the nonaffine network model is higher than that of affine network model. It is clear that there is a small amount of nonaffine network deformation for LDPE melts which have long chain branches, and there is a larger amount of nonaffine network deformation in oscillatory shear for HDPE melts which has no long chain branches. So we had better consider the network deformation nonaffine when we establish the constitutive equations of polymer melts in oscillatory shear.

A CLASS OF OSCILLATORY SINGULAR INTEGRALS ON TRIEBEL-LIZORKIN SPACES

The boundedness on Triebel-Lizorkin spaces of oscillatory singular integral operator T in the form e^i｜x｜^aΩ（x）｜x｜^-n is studied,where a∈R,a≠0,1 and Ω∈L^1（S^n-1） is homogeneous of degree zero and satisfies certain cancellation condition. When kernel Ω（x＇ ）∈Llog＋L（S^n-1 ）, the Fp^a,q（R^n） boundedness of the above operator is obtained. Meanwhile ,when Ω（x） satisfies L^1- Dini condition,the above operator T is bounded on F1^0,1 （R^n）.

Controlling spiral wave with target wave in oscillatory systems

Spiral waves have been controlled by generating target waves with a localized inhomogeneity in the oscillatory medium. The competition between the spiral waves and target waves is discussed. The effect of the localized inhomogeneity size has also been studied.

NUMERICAL STUDY OF AN OSCILLATORY TURBULENT FLOW OVER A FLAT PLATE

Oscillatory turbulent flow over a flat plate was studied by using large eddy simulation (LES) and Reynolds-average Navier-Stokes (RANS) methods. A dynamic subgrid-scale model was employed in LES and Saffman's turbulence model was used in RANS. The flow behaviors were discussed for the accelerating and decelerating phases during the oscillating cycle. The friction force on the wall and its phase shift from laminar to turbulent regime were also investigated for different Reynolds numbers. (Edited author abstract) 11 Refs.

Numerical modeling investigation on turbulent oscillatory flow over a plane rough bed composed by randomly arrayed particles

A three-dimensional numerical model is established to simulate the turbulent oscillatory boundary layer over a fixed and rough bed composed by randomly arrayed solid spheres based on the lattice Boltzmann method and the large eddy simulation model.The equivalent roughness height,the location of the theoretical bed and the time variation of the friction velocity are investigated using the log-fit method.The time series of turbulent intensity and Reynolds stress are also investigated.The equivalent roughness height of cases with Reynolds numbers of 1×10^4–6×10^4 is approximately 2.81 d（grain size）.The time variation of the friction velocity in an oscillatory cycle exhibits sinusoidal-like behavior.The friction factor depends on the relative roughness in the rough turbulent regime,and the pattern of solid particles arrayed as the rough bed in the numerical simulations has no obvious effect on the friction factor.

Oscillatory flow of second grade fluid in cylindrical tube

The unsteady oscillatory flow of an incompressible second grade fluid in a cylindrical tube with large wall suction is studied analytically. Flow in the tube is due to uniform suction at the permeable walls, and the oscillations in the velocity field are due to small amplitude time harmonic pressure waves. The physical quantities of interest are the velocity field, the amplitude of oscillation, and the penetration depth of the oscillatory wave. The analytical solution of the governing boundary value problem is obtained, and the effects of second grade fluid parameters are analyzed and discussed.

Mechanochemical model for myosinⅡdimer that can explain the spontaneous oscillatory contraction of muscle

The spontaneous oscillatory contraction（SPOC） of myofibrils is the essential property inherent to the contractile system of muscle. Muscle contraction results from cyclic interactions between actin filament and myosin II which is a dimeric motor protein with two heads. Taking the two heads of myosin II as an indivisible element and considering the effects of cooperative behavior between the two heads on rate constants in the mechanochemical cycle, the present work proposes the tenstate mechanochemical cycle model for myosin II dimer. The simulations of this model show that the proportion of myosin II in different states periodically changes with time, which results in the sustained oscillations of contractive tension, and serves as the primary factor for SPOC. The good fit of this model to experimental results suggests that the cooperative interaction between the two heads of myosin II dimer may be one of the underlying mechanisms for muscle contraction.

Some exact solutions of the oscillatory motion of a generalized second grade fluid in an annular region of two cylinders

The velocity field and the associated shear stress corresponding to the longitudinal oscillatory flow of a generalized second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and at t = 0＋ both cylinders suddenly begin to oscillate along their common axis with simple harmonic motions having angular frequencies Ω1 and Ω2. The solutions that have been obtained are presented under integral and series forms in terms of the generalized G and R functions and satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of ordinary second grade fluid and Newtonian fluid are also obtained as limiting cases of our general solutions. At the end, the effect of different parameters on the flow of ordinary second grade and generalized second grade fluid are investigated graphically by plotting velocity profiles.

WEIGHTED ESTIMATE FOR THE MULTILINEAR OSCILLATORY SINGULAR INTEGRAL OPERATORS

In this paper, the weighted Lp(Rn) boundedness for the multilinear oscillatory singular integral operators with polynomial phases is studied.

NON-CONVOLUTION TYPE OSCILLATORY SINGULAR INTEGRAL ON HARDY SPACE HK_p(R^n)

The authors considered non-convolution type oscillatory singular integral operators with real-analytic phases. A uniform boundedness from HKp to Hp of such operators is established. The result is false for general C phases.

A Numerical Study on the Structure and Dynamics of Turbulence in Oscillatory Bottom Layer Flow over A Flat or Rippled Bed

This paper is mainly concerned with the turbulence in oscillatory bottom boundary layers over flat or rippled seaheds. Owing to the strong shear and anisotmpy of oscillatory flow, an anisotropic turbulence mathematical model is set up using the finite difference method, and the computational results of the model are verified by comparisons with wellknown experiments. Turbulent energy, dissipation and Reynolds stress can all be computed with this mathematical model, and the development processes of a large coherent vortex structure over a rippled bed, such as main flow separation, coherent vortex formation and curling, coherent vortex ejection and breaking up, are successfully simulated.