UNSTEADY FLOWS OF A GENERALIZED SECOND GRADE FLUID WITH THE FRACTIONAL DERIVATIVE MODEL BETWEEN TWO PARALLEL PLATES

The fractional calculus approach in the constitutive relationship model of a generalized second grade fluid is introduced.Exact analytical solutions are obtained for a class of unsteady flows for the generalized second grade fluid with the fractional derivative model between two parallel plates by using the Laplace transform and Fourier transform for fractional calculus.The unsteady flows are generated by the impulsive motion or periodic oscillation of one of the plates.In addition,the solutions of the shear stresses at the plates are also determined.

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.

An inverse problem to estimate an unknown order of a Riemann-Liouville fractional derivative for a fractional Stokes' first problem for a heated generalized second grade fluid

In this paper,we propose a numerical method to estimate the unknown order of a Riemann-Liouville fractional derivative for a fractional Stokes＇ first problem for a heated generalized second grade fluid.The implicit numerical method is employed to solve the direct problem.For the inverse problem,we first obtain the fractional sensitivity equation by means of the digamma function,and then we propose an efficient numerical method,that is,the Levenberg-Marquardt algorithm based on a fractional derivative,to estimate the unknown order of a Riemann-Liouville fractional derivative.In order to demonstrate the effectiveness of the proposed numerical method,two cases in which the measurement values contain random measurement error or not are considered.The computational results demonstrate that the proposed numerical method could efficiently obtain the optimal estimation of the unknown order of a RiemannLiouville fractional derivative for a fractional Stokes＇ first problem for a heated generalized second grade fluid.

DECAY OF VORTEX VELOCITY AND DIFFUSION OF TEMPERATURE IN A GENERALIZED SECOND GRADE FLUID

The fractional calculus approach in the constitutive relationship model of viscoelastic fluid was introduced. The velocity and temperature fields of the vortex flow of a generalized second fluid with fractional derivative model were described by fractional partial differential equations. Exact analytical solutions of these differential equations were obtained by using the discrete Laplace transform of the sequential fractional derivatives and generalized Mittag-Leffler function. The influence of fractional coefficient on the decay of vortex velocity and diffusion of temperature was also analyzed.

Exact solutions for unsteady unidirectional flows of a generalized second-order fluid through a rectangular conduit

The exact solutions are obtained for unsteady unidirectional flows of a generalized second-order fluid through a rectangular conduit. The fractional calculus in the constitutive relationship of a non-Newtonian fluid is introduced. We construct the solutions by means of Fourier transform and the discrete Laplace transform of the sequential derivatives and the double finite Fourier transform. The solutions for Newtonian fluid between two infinite parallel plates appear as limiting cases of our solutions.

Quantum Gravitational Effects on Tunneling Rate of Reissner-Nordstroum Black Hole Emission and Generalized Second Law

The semi-classical black hole tunneling radiation (Parikh-Wilczek tunneling proposal) is calculated undera minimal length uncertainty analysis.It is shown that,the generalized second law of thermodynamics may bound thetunneling probability radiation of a Reissner-Nordstrom black hole radiation.

Exact solution for the rotational flow of a generalized second grade fluid in a circular cylinder

This paper deals with the rotational flow of a generalized second grade fluid, within a circular cylinder, due to a torsional shear stress. The fractional calculus approach in the constitutive relationship model of a second grade fluid is introduced. The velocity field and the resulting shear stress are determined by means of the Laplace and finite Hankel transforms to satisfy all imposed initial and boundary conditions. The solutions corresponding to second grade fluids as well as those for Newtonian fluids are obtained as limiting cases of our general solutions. The influence of the fractional coefficient on the velocity of the fluid is also analyzed by graphical illustrations.

Particular Solutions of Generalized Linear Second Differential Equations by Fractional Calculus

本文依据Ｋ．Ｎｉｓｈｉｍｕｔｏ教授于１９７９年所定义的分数微积分定义Ｌｅｍｍａｓ为基础，给出一种线性阶微分方程及偏微分方程（包括均匀及非均匀）的方法，使其更一般化，概括范围更宽、更广．

Study on generalized magneto-thermoelastic problems by FEM in time domain

This paper presents an investigation of temperature, displacement, stress, and induced magnetic field in a half space perfectly-conductive plate. Finite element equations regarding generalized magneto-thermoelasticity problems with two relaxation times （i.e., the G-L theory） are derived using the principle of virtual work. For avoiding numerical complication involved in inverse Laplace and Fourier transformation and low precision thereof, the equations are solved directly in time-domain. As a numerical example, the derived equation is used to investigate the generalized magneto-thermoelastic behavior of a semi-infinite plate under magnetic field and subjecting to a thermal shock loading. The results demonstrate that FEM can faithfully predict the deformation of the plate and the induced magnetic field, and most importantly can reveal the sophisticated second sound effect of heat conduction in two-dimensional generalized thermoelastic solids, which is usually difficult to model by routine transformation methods. A peak can be observed in the distribution of stress and induced front and the magnitude of magnetic field at the heat wave the peak decreases with time, which can not be obtained by transformation methods. The new method can also be used to study generalized piezo-thermoelastic problems.

SPECTRUM DISTRIBUTION OF THE SEDOND ORDER GENERALIZED DISTRIBUTED PARAMETER SYSTEMS

Spectrum distribution of the second order generalized distributed parameter system was discussed via the functional analysis and operator theory in Hilbert space. The solutions of the problem and the constructive expression of the solutions are given by the generalized inverse one of bounded linear operator. This is theoretically important for studying the stabilization and asymptotic stability of the second order generalized distributed parameter system.

Response to Selection for Fast Growth in the Second Generation of Pacific Oyster (Crassostrea gigas)

Mass selection for fast growth was conducted in three Pacific oyster (Crassostrea gigas) stocks from China, Japan and Korea using previously established lines (CS1, JS1, and KS1). To determine whether continuous progress can be achieved by selection for growth, the progeny of three second-generation Pacific oyster lines was selected for shell height and evaluated via a 400-day farming experiment. When harvested at the end of the experiment, the selected crosses of CS2, JS2, and KS2 lines grew by 9.2%, 10.2% and 9.6% larger than the control crosses, respectively. During grow-out stage, the genetic gain of three selected lines was (10.2 ± 1.4)%, (10.4 ± 0.3)%, and (8.4 ± 1.6)%, respectively; and the corresponding realized heritability was 0.457 ± 0.143, 0.312 ± 0.071 and 0.332 ± 0.009, respectively. These results indicated that the selection for fast growth achieved steady progress in the second generation of oyster. Our work provides supportive evidence for the continuity of the Pacific oyster selective breeding program.

Growth performance and physiological parameters of the second generation selected and control groups of Pinctada martensii

In May of 2007,the second generation selected （SS） and control （SC） groups of pearl oyster Pinctada martensii were established by selecting 10% breeders with the largest and mean shell length,respectively,from the first generation selected group.Growth performance of the SS and SC groups were compared on the basis of measurement data at Days 8,18,60,95,195 and 365.On Day 365,100 individuals （60.0–75.0 mm at shell length） were sampled from each group and then subjected to the experiment where physiological parameters such as filtrate rate,oxygen consumption and ammonia excretion were measured at 15,20,25 and 30°C.The results show that the SS group had significantly larger mean shell length and shell height than the SC group at Days 8,18,60,95,195 and 365 （P 0.05）.The genetic gains at different ages varied from 6.0% to 17.0% for shell length and 5.7% to 14.6% for shell height,respectively.At 15,20,25 and 30 ° C,the SS groups had significantly larger filtrate rate than the SC group （P 0.05）.At 15 and 25 °C,the differences in oxygen consumption rate between the SS and SC groups were not significant （P 0.05）.At 20 and 30 °C,however,the oxygen consumption rate of the SS group was significantly larger than the SC group （P 0.05）.At 15,20,25 and 30 °C,there were no significant differences in ammonia excretion rate between the SS and SC groups （P 0.05）.The present results indicate that there existed considerable genetic variability in the base population and a further selection could be likely fruitful.Mass selection for faster growth might produce animals that had higher intake of metabolizable energy by virtue of faster filtrating behavior.

NEW METHOD FOR WEAK FAULT FEATURE EXTRACTION BASED ON SECOND GENERATION WAVELET TRANSFORM AND ITS APPLICATION

A new time-domain analysis method that uses second generation wavelettransform (SGWT) for weak fault feature extraction is proposed. To extract incipient fault feature,a biorthogonal wavelet with the characteristics of impact is constructed by using SGWT. Processingdetail signal of SGWT with a sliding window devised on the basis of rotating operation cycle, andextracting modulus maximum from each window, fault features in time-domain are highlighted. To makefurther analysis on the reason of the fault, wavelet package transform based on SGWT is used toprocess vibration data again. Calculating the energy of each frequency-band, the energy distributionfeatures of the signal are attained. Then taking account of the fault features and the energydistribution, the reason of the fault is worked out. An early impact-rub fault caused by axismisalignment and rotor imbalance is successfully detected by using this method in an oil refinery.

Second Generation Wavelet Finite Element and Rotor Cracks Quantitative Identification Method

The presence of cracks in the rotor is one of the most dangerous and critical defects for rotating machinery. Defect of fatigue cracks may lead to long out-of-service periods, heavy damages of machines and severe economic consequences. With the method of finite element, vibration behavior of cracked rotors and crack detection was received considerable attention in the academic and engineering field. Various researchers studied the response of a cracked rotor and most of them are focused on the crack detection based on vibration behavior of cracked rotors. But it is often difficult to identify the crack parameters quantitatively. Second generation wavelets （SGW） finite element has good ability in modal analysis for singularity problems like a cracked rotor. Based on the fact that the feature of SGW could be designed depending on applications, a multiresolution finite element method is presented. The new model of SGW beam element is constructed. The first three natural frequencies of the rotor with different crack location and size were solved with SGW beam elements, and the database for crack diagnosis is obtained. The first three metrical natural frequencies are employed as inputs of the database and the intersection of the three frequencies contour lines predicted the normalized crack location and size. With the Bently RK4 rotor test rig, rotors with different crack location and size are tested and diagnosed. The experimental results denote the cracks quantitative identification method has higher identification precision. With SGW finite element method, a novel method is presented that has higher precision and faster computing speed to identify the crack location and size.

“Second-generation” stem cells for cardiac repair

Over the last years, stem cell therapy has emerged asan inspiring alternative to restore cardiac function after myocardial infarction. A large body of evidence has been obtained in this field but there is no conclusive data on the efficacy of these treatments. Preclinical studies and early reports in humans have been encouraging and have fostered a rapid clinical translation, but positive results have not been uniformly observed and when present, they have been modest. Several types of stem cells, manufacturing methods and delivery routes have been tested in different clinical settings but direct comparison between them is challenging and hinders further research. Despite enormous achievements, major barriers have been found and many fundamental issues remain to be resolved. A better knowledge of the molecular mechanisms implicated in cardiac development and myocardial regeneration is critically needed to overcome some of these hurdles. Genetic and pharmacological priming together with the discovery of new sources of cells have led to a "second generation" of cell products that holds an encouraging promise in cardiovascular regenerative medicine. In this report, we review recent advances in this field focusing on the new types of stem cells that are currently being tested in human beings and on the novel strategies employed to boost cell performance in order to improve cardiac function and outcomes after myocardial infarction.

Time-domain analysis of second-harmonic generation of primary Lamb wave propagation in an elastic plate

Within the second-order perturbation approximation, this paper investigates the physical process of generation of the time-domain second harmonic by a primary Lamb wave waveform in an elastic plate. The present work is performed based on the preconditions that the phase velocity matching is satisfied and that the transfer of energy from the primary Lamb wave to the double frequency Lamb wave is not zero. It investigates the influences of the difference between the group velocities of the primary Lamb wave and the double frequency Lamb wave, the propagation distance and the duration of the primary Lamb wave waveform on the envelope shape of the time-domain second harmonic. It finds that the maximum magnitude of the envelope of the second-harmonic waveform can grow within some propagation distance even if the condition of group velocity matching is not satisfied. Our analyses also indicate that the maximum magnitude of the envelope of the second-harmonic waveform is kept constant beyond a specific propagation distance. Furthermore, it concludes that the integration amplitude of the time-domain second-harmonic waveform always grows with propagation distance within the second-order perturbation. The present research yields new physical insight not previously available into the effect of generation of the time-domain second harmonic by propagation of a primary Lamb wave waveform.

The Lifting Scheme Based on the Second Generation Wavelets

The lifting scheme is a custom design construclion of Biorthogonal wavelets, a fast and efficient method to realize wavelet transform,which provides a wider range of application and efficiently reduces the computing time with its particular frame. This paper aims at introducing the second generation wavelets, begins with traditional Mallat algorithms, illustrates the lifting scheme and brings out the detail steps in the construction of Biorthogonal wavelets. Because of isolating the degrees of freedom remaining the biorthogonality relations, we can fully control over the lifting operators to design the wavelet for a particular application, such as increasing the number of the vanishing moments.

Generation of femtosecond laser pulses at 396 nm in K_3B_6O_(10)Cl crystal

K3B6O10Cl （KBOC）, a new nonlinear optical crystal, shows potential advantages for the generation of deep ultraviolet （UV） light compared with other borate crystals. In this paper we study for the first time the second harmonic generation （SHG） of a femtosecond Ti：sapphire amplifier with this crystal. Laser power is obtained to be as high as 220 mW at the central wavelength of 396 nm with a 1-mm-long crystal, and the maximum SHG conversion efficiency reaches 39.3%. The typical pulse duration is 83 fs, The results show that second harmonic （SH） conversion efficiency has the room to be further improved and that the new nonlinear crystal is very suited to generate the high efficiency deep ultraviolet laser radiation below 266 nm.

GENERALIZED HOMOGENEOUS FUNCTIONS AND THE TWO-BODY PROBLEM

A generalization of the homogeneous function concept is studied.An application is done with a solution of the two-body problem.