Insight into evolution of invasive patterns on fingering phenomenon during immiscible two-phase flow through pore structure

Understanding fingering, as a challenge to stable displacement during the immiscible flow, has become a crucial phenomenon for geological carbon sequestration, enhanced oil recovery, and groundwater protection. Typically governed by gravity, viscous and capillary forces, these factors lead invasive fluids to occupy pore space irregularly and incompletely. Previous studies have demonstrated capillary numbers,describing the viscous and capillary forces, to quantificationally induce evolution of invasion patterns.While the evolution mechanisms of invasive patterns have not been deeply elucidated under the constant capillary number and three variable parameters including velocity, viscosity, and interfacial tension.Our research employs two horizontal visualization systems and a two-phase laminar flow simulation to investigate the tendency of invasive pattern transition by various parameters at the pore scale. We showed that increasing invasive viscosity or reducing interfacial tension in a homogeneous pore space significantly enhanced sweep efficiency, under constant capillary number. Additionally, in the fingering crossover pattern, the region near the inlet was prone to capillary fingering with multi-directional invasion, while the viscous fingering with unidirectional invasion was more susceptible occurred in the region near the outlet. Furthermore, increasing invasive viscosity or decreasing invasive velocity and interfacial tension promoted the extension of viscous fingering from the outlet to the inlet, presenting that the subsequent invasive fluid flows toward the outlet. In the case of invasive trunk along a unidirectional path, the invasive flow increased exponentially closer to the outlet, resulting in a significant decrease in the width of the invasive interface. Our work holds promising applications for optimizing invasive patterns in heterogeneous porous media.

Convergence Phenomenon with Fourier Series of tg(x2)and Alike

The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generalized functions and the convergence is weak convergence in the sense of the convergence of continuous linear functionals defining them. The figures show that the approximations of the Fourier series possess oscillations around the function which they represent in a broad band embedding them. This is some analogue to the Gibbs phenomenon. A modification of Fourier series by expansion in powers cosn(x)for the symmetric part of functions and sin(x)cosn−1(x)for the antisymmetric part (analogous to Taylor series) is discussed and illustrated by examples. The Fourier series and their convergence behavior are illustrated also for some 2π-periodic delta-function-like sequences connected with the Poisson theorem showing non-vanishing oscillations around the singularities similar to the Gibbs phenomenon in the neighborhood of discontinuities of functions. .

Overflowing phenomenon during ultrasonic treatment in Al-Si alloys

At the late stage of solidification with ultrasonic treatment （UST） in Al-Si alloys, a part of semisolid overflows and climbs along the probe. The interesting phenomenon and its influence on the solidification microstructure were investigated in order to better study the mechanism of UST. It is considered that the overflowing phenomenon occurs due to the changes of vibration and flow in the remaining semisolid. Because the overflowed portion comes from the region with intense UST effect and vibrates with the probe during solidification, great modification of primary and euteetic Si （about 10 pm in length） and refinement of primary a（Al） （about 70 μm in size） are observed in this portion.

Weighted L^p-boundedness of Multilinear Oscillatory Singular Integrals with Calderón-Zygmund Kernel

In this paper, weighted L p-boundedness is obtained for a class of multilinear oscillatory singular integrals with Calderón-Zygmund kernel.

INFLUENCE OF VIRTUAL PHOTON FIELD ON COLLAPSE AND REVIVAL PHENOMENON IN TWO PHOTON J C MODEL WITHOUT RWA

The time evolution of system in two photon Jaynes Cummings (J C) model without rotating waves approximation (RWA) is obtained by using the theory of ordinary differential equations. Based on the evolution, the mean value of the atom inversion operator 〈 S 3(t)〉 is gi ven. The influence of the “counter rotating term” on the collapse and revival phenomenon is discussed from the comparison between the cases with RWA and without RWA. It shows that the influence of the virtual photon field makes the quantum fluctuations appear on the collapse and revival phenomenon.

关于《纯粹理性批判》中“Appearance”与“Phenomenon”的翻译

康德《纯粹理性批判》中“Appearance”与“Phenomenon”既存在本体论、认识论意义上的差异 ,又存在具体与抽象、变化规定与实体永恒。

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.

Variational iteration solving method for El Nio phenomenon atmospheric physics of nonlinear model

A class of E1 Niйo atmospheric physics oscillation model is considered. The E1 Niйo atmospheric physics oscillation is an abnormal phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The conceptual oscillator model should consider the variations of both the eastern and western Pacific anomaly patterns. An E1 Niйo atmospheric physics model is proposed using a method for the variational iteration theory. Using the variational iteration method, the approximate expansions of the solution of corresponding problem are constructed. That is, firstly, introducing a set of functional and accounting their variationals, the Lagrange multiplicators are counted, and then the variational iteration is defined, finally, the approximate solution is obtained. From approximate expansions of the solution, the zonal sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the sea-air oscillation for E1 Niйo atmospheric physics model can be analyzed. E1 Niйo is a very complicated natural phenomenon. Hence basic models need to be reduced for the sea-air oscillator and are solved. The variational iteration is a simple and valid approximate method.

Genetic pattern of belt-wide petroliferous phenomenon in the eastern Pearl River Mouth Basin and its practical application

The Pearl River Mouth Basin （PRMB） covers an area of approximately 20× 104 km2.However,oil-gas fields detected in this area thus far are highly concentrated and controlled predominantly by second-order structural belts,the seven largest of which aggregate proved oil reserves of 7.7× 108 m3,accounting for 86％ of the total discovered reserve in the basin.These second-order structures have one common phenomenon：oil is contained in all traps present in them.In other words,they are all belt-wide petroliferous reservoirs.Research has identified eight types of second-order structural belts under two categories in the eastern PRMB.Their petroliferous properties are subject to three typical constraints：petroliferous properties of subsags hosting these structural belts,locations of these belts in the petroleum system,and availability of traps prior to the hydrocarbon expulsion and migration.The formation and distribution of oil reservoirs in these belts are characterized by subsag-belt integration and ＂three-in-one＂.The former indicates that sags and the second-order structural belts within the supply range of the sags constitute the basic units of hydrocarbon accumulations and are therefore inseparable.The latter indicates that a belt-wide petroliferous second-order structural belt always contains three important elements：hydrocarbon richness,effective pathway and pre-existing traps.

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.

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.

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）.

Effects of complement inhibition on the ABC phenomenon in rats

Researchers reported that intravenously injected PEGylated colloidal drug carriers lose their long-circulating characteristic and accumulated extensively in liver when they are administrated twice in the same animal with certain intervals. This phenomenon was referred to as the 'accelerated blood clearance(ABC) phenomenon'. Some former studies had found that complement-mediated phagocytosis, activated by antigen–antibody complex, was responsible for inducing the phenomenon. According to the theory, we have used cobra venom factor to deplete complement in vivo and to investigate the effect of complement inhibition on the ABC phenomenon. Rats were administered by injection of cobra venom factor solution to build up the model of complement exhaustion/inhibition, and the effect of the inhibition of complement on ABC phenomenon was carried out. It seemed that inhibition of complement didn’t affect the pharmacokinetic of the first infection. By contrast, in rats of which complement had been depleted, the second dose of PEGylated nanoemulsions showed enhanced circulation time compared with normal rats in a complement inhibition-independent manner, but the ABC phenomenon was not completely eliminated. It indicated that complement inhibition could certainly weaken the accelerated clearance;meanwhile, there were other factors causing the ABC effect.These findings provide novel insights into the attenuating of ABC phenomenon and lay foundation for further study of immune mechanism.

The effect of monosialylganglioside mix modifying the PEGylated liposomal epirubicin on the accelerated blood clearance phenomenon

PEGylated liposomes are potential candidates to improve the pharmacokinetic characteristics of encapsulated drugs, to extend their circulation half-life and facilitate their passive accumulation at tumour sites. However, PEG-modified liposomes can induce accelerated blood clearance(ABC) upon repeated administration, and the extent of ABC phenomenon on the cytotoxic drugs-containing PEGylated liposomes is related to the dose of the cytotoxic drugs.In this study, EPI served as a model cytotoxic drug, a hydrophilic surfactant molecule,monosialylganglioside(GM1) was chosen and modified on the liposomes together with PEG.It was shown that upon mixed modification, when GM1 contents reached 10% or 15% mol,the ABC phenomenon of the PEGylated liposomal EPI significantly reduced. We also found that GM1 played an important role in abrogating the ABC phenomenon in both the induction phase and the effectuation phase. The results suggested that GM1 incorporation unfortunately did not avoid occurrence of ABC phenomenon completely, but GM1 modification on PEGylated liposomes may provide a significant improvement in clinical practice of PEGylated liposomes. Further study must be necessary.

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）.

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.

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.