Averaging Technique for the Oscillation of Second Order Damped Elliptic Equations

By using the averaging technique, we establish some oscillation theorems for the second order damped elliptic differential equation N↑∑↓i,j=1 Di[AIY（x）Djy]＋N↑∑↓i=1 bi（x）Diy＋c（x）f（y）=0 which extend and improve some known results in the literature.

Work conjugate principle-constrained volume averaging technique for multiphase porous media

Volume averaging is a standard method for the development of macroscopic balance equations for modelling the thermodynamic behaviors of multiphase porous media. However, work conjugate principle which is a common practice in continuum mechanics is not emphasized by the volume averaging technique resulting in the macroscopic balance equations are not capable of comprehensively describing the kinematic behaviors of multiphase porous media due to the loss of essential macroscopic variables. This study derives the macroscopic mass and momentum balance equations for the pore fluid of a fluid-solid porous medium by use of the volume averaging technique. We show(1) if the procedure of the volume averaging is implemented in its traditional manner, only the average flux of the pore fluid described by its mass average velocity is captured;(2) if the work conjugate principle is employed to define a work-conjugate velocity for the pore fluid at the macroscale, both the average flux(described by the mass average velocity) and the dispersive flux(described by the deviation of the mass average velocity from the work-conjugate one) are reproduced. This theoretical analysis demonstrates that the work conjugate principle is an essential thermodynamic constraint to improve the volume averaging technique, in the sense that the macroscopic balance equations are required to be capable of comprehensively describing the macroscopic kinematic behaviors of multiphase porous media.

A modified averaging scheme with application to the secondary Hopf bifurcation of a delayed van der Pol oscillator

In this paper, a modified averaging scheme is presented for a class of time-delayed vibration systems with slow variables. The new scheme is a combination of the averaging techniques proposed by Hale and by Lehman and Weibel, respectively. The averaged equation obtained from the modified scheme is simple enough but it retains the required information for the local nonlinear dynamics around an equilibrium. As an application of the present method, the delay value for which a secondary Hopf bifurcation occurs is successfully located for a delayed van der Pol oscillator.

Investigations of Tracking Phenomena in Silicone Rubber Using Moving Average Current Technique

In the present work, tracking phenomenon in Silicone rubber material has beenstudied under AC and DC voltage, with ammonium chloride as a contaminant. It is observed that thetracking is more severe under the DC voltages. The tracking time is less under negative DC comparedto the positive DC voltage. The tracking mechanism is explained in detail. The leakage currentduring the tracking studies was as measured and the moving average technique was adopted tounderstand the trend in current flow. The leakage current magnitude is high with thermally agedspecimens compared to the virgin specimen, irrespective of the type of applied voltage. It isrealized that the tracking time and the leakage current magnitude shows an inverse relationship.

Kinetic parameter estimation for cooling crystallization process based on cell average technique and automatic differentiation

In this paper,a cell average technique(CAT)based parameter estimation method is proposed for cooling crystallization involved with particle growth,aggregation and breakage,by establishing a more efficient and accurate solution in terms of the automatic differentiation(AD)algorithm.To overcome the deficiency of CAT that demands high computation cost for implementation,a set of ordinary differential equations(ODEs)entailed from CAT based discretized population balance equation(PBE)are solved by using the AD based high-order Taylor expansion.Moreover,an AD based trust-region reflective(TRR)algorithm and another interior-point(IP)algorithm are established for estimating the kinetic parameters associated with particle growth,aggregation and breakage.As a result,the estimation accuracy can be further improved while the computation cost can be significantly reduced,compared to the existing algorithms.Benchmark examples from the literature are used to illustrate the accuracy and efficiency of the AD-based CAT,TRR and IP algorithms in comparison with the existing algorithms.Moreover,seeded batch cooling crystallization experiments ofβform L-glutamic acid are performed to validate the proposed method.

Advanced Transformation Technique to Solve Multi-Objective Optimization Problems

Multi-objective optimization problem (MOOP) is an important class of optimization problem that ensures users to model a large variety of real world applications. In this paper an advanced transformation technique has been proposed to solve MOOP. An algorithm is suggested and the computer application of algorithm has been demonstrated by a flow chart. This method is comparatively easy to calculate. Applying on different types of examples, the result indicates that the proposed method gives better solution than other methods and it is less time consuming. Physical presentation and data analysis represent the worth of the method more compactly.

Role of Examples and Interpretation of Results in Developing Multi-Objective Optimization Techniques

The paper evaluates the suitability of examples used in developing averaging techniques of multi-objective optimization (MOO). Most of the examples used for proposing these techniques were not suitable. The results of these examples have also not been interpreted correctly. An appropriate example has also been solved with existing and improved averaging techniques of multi-objective optimization.

A Posteriori Error Estimate of Two Grid Mixed Finite Element Methods for Semilinear Elliptic Equations

In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the mixed method equations. Then, the averaging technique is used to construct the a posteriori error estimates of the two-grid mixed finite element method and theoretical analysis are given for the error estimators. Finally, we give some numerical examples to verify the reliability and efficiency of the a posteriori error estimator.

Earth-moon Trajectory Optimization Using Solar Electric Propulsion

The optimization of the Earth-moon trajectory using solar electric propulsion is presented. A feasible method is proposed to optimize the transfer trajectory starting from a low Earth circular orbit （500 km altitude） to a low lunar circular orbit （200 km altitude）. Due to the use of low-thrust solar electric propulsion, the entire transfer trajectory consists of hundreds or even thousands of orbital revolutions around the Earth and the moon. The Earth-orbit ascending （from low Earth orbit to high Earth orbit） and lunar descending （from high lunar orbit to low lunar orbit） trajectories in the presence of J2 perturbations and shadowing effect are computed by an analytic orbital averaging technique. A direct/indirect method is used to optimize the control steering for the trans-lunar trajectory segment, a segment from a high Earth orbit to a high lunar orbit, with a fixed thrust-coast-thrust engine sequence. For the trans-lunar trajectory segment, the equations of motion are expressed in the inertial coordinates about the Earth and the moon using a set of nonsingular equinoctial elements inclusive of the gravitational forces of the sun, the Earth, and the moon. By way of the analytic orbital averaging technique and the direct/indirect method, the Earth-moon transfer problem is converted to a parameter optimization problem, and the entire transfer trajectory is formulated and optimized in the form of a single nonlinear optimization problem with a small number of variables and constraints. Finally, an example of an Earth-moon transfer trajectory using solar electric propulsion is demonstrated.

OSCILLATION CRITERIA FOR SECOND ORDER NONLINEAR DIFFERENTIAL EQUATION WITH DAMPING

By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed.Some sufficient oscillation criteria for previous equations were built up.Some oscillation criteria have been expanded and strengthened in some other known results.

Oscillation theorems for second-order nonlinear perturbed differential equations with damping

A class of second-order nonlinear damped perturbed differential equations is considered and its oscillation theorems are studied.These theorems are more general and deal with the cases which are not covered by the known criteria.Particularly,these criteria extend and unify some existing results.An example is given to verify the results.

DETECTION OF INCIPIENT LOCALIZED GEAR FAULTS IN GEARBOX BY COMPLEX CONTINUOUS WAVELET TRANSFORM

As far as the vibration signal processing is concerned, composition ofvibration signal resulting from incipient localized faults in gearbox is too weak to be detected bytraditional detecting technology available now. The method, which includes two steps: vibrationsignal from gearbox is first processed by synchronous average sampling technique and then it isanalyzed by complex continuous wavelet transform to diagnose gear fault, is introduced. Twodifferent kinds of faults in the gearbox, i.e. shaft eccentricity and initial crack in tooth fillet,are detected and distinguished from each other successfully.

OSCILLATION THEOREMS FOR A CLASS OF SECOND ORDER NEUTRAL DIFFERENTIAL EQUATIONS OF EMDEN-FOWLER TYPE

Some oscillation theorems are established by the averaging technique for a class of second order neutral differential equations of Emden-Fowler type. Our results essentially improve some known results in the previous literature.

OSCILLATION CRITERIA FOR CERTAIN EVEN ORDER NEUTRAL DIFFERENTIAL EQUATIONS

Using the generalized Riccati technique and the averaging technique, we establish several oscillation criteria for certain even order neutral differential equation. The results obtained in this paper extend and improve some known results in the previous literatures.

OSCILLATING CRITERIA FOR CERTAIN EVEN ORDER NEUTRAL DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENTS

By using the integral averaging technique, oscillating criteria for certain even order neutral differential equation with deviating arguments are established. These results extend some known oscillation criteria due to Xu and Xia.

OSCILLATION CRITERIA FOR CERTAIN NONLINEAR DIFFERENCE EQUATIONS

In this paper, we present new oscillation criteria for certain class of second-order difference equation obtained by using a technique similar to the integral averaging technique. Our theorem complement some known oscillation criteria.

A sub-sampling 4-bit 1.056-GS/s flash ADC with a novel track and hold amplifier for an IR-UWB receiver

A sub-sampling 4-bit 1.056-GS/s flash ADC with a novel track and hold amplifier（THA） in 0.13μm CMOS for an impulse radio ultra-wideband（IR-UWB） receiver is presented.The challenge is in implementing a sub-sampling ADC with ultra-high input signal that further exceeds the Nyquist frequency.This paper presents,to our knowledge for the second time,a sub-sampling ADC with input signals above 4 GHz operating at a sampling rate of 1.056 GHz.In this design,a novel THA is proposed to solve the degradation in amplitude and improve the linearity of signal with frequency increasing to giga Hz.A resistive averaging technique is carefully analyzed to relieve noise aliasing.A low-offset latch using a zero-static power dynamic offset cancellation technique is further optimized to realize the requirements of speed,power consumption and noise aliasing.The measurement results reveal that the spurious free dynamic range of the ADC is 30.1 dB even if the input signal is 4.2 GHz sampled at 1.056 GS/s.The core power of the ADC is 30 mW,excluding all of the buffers,and the active area is 0.6 mm^2.The ADC achieves a figure of merit of 3.75 pJ/conversion-step.

Oscillation Criteria for Second Order Mixed Nonlinear Elliptic Equations

By using the refinement of the standard integral averaging technique, we obtain some oscillation criteria for second order mixed nonlinear elliptic equations. The results established in this paper extend and improve some existing oscillation criteria for half-linear PDE in the literature.

OSCILLATION FOR A CLASS OF SECOND ORDER DELAY DIFFERENTIAL EQUATIONS WITH NONLINEAR NEUTRAL TERM

By the averaging technique,we establish some oscillation theorems for a class of second order delay differential equations with nonlinear neutral term,the results obtained extend some known results in the previous literatures.

OSCILLATION CRITERIA FOR CERTAIN NONLINEAR DELAY DIFFERENCE EQUATIONS

In this paper, we present new oscillation criteria for certain class of second order nonlinear delay difference equations by using an averaging technique.