Quenching Time Estimates for Semilinear Parabolic Equations Controlled by Two Absorption Sources in Control System

This paper deals with the quenching solution of the initial boundary value problem for aclass of semilinear reaction-diffusion equation controlled by two absorption sources in control system and estimate upper bound and lower bound of the quenching time.We point that the number of absorption sources influences the time of quenching phenomenon.The solution can solve some boundary value problem in control system.

SUPERPLASTICITY OF A WATER-QUENCHED AND TEMPERED 40Cr STEEL

The superplastic deformation characteristics, of commercial 40Cr (i.e., 5140) steel that was water-quenched only 1 times and subsequent high-temperature tempered, were investigated. The results showed that the 40Cr steel has a fine grain of 10-15μm at room temperature, and exhibits a tensile elongation of 304%, a true flow stress of 89.3MPa and a strain rate sensitivity m-value of 0.227 at the initial strain rate of 1.0×10-3s-1and at the temperature of 750°C. The final fracture is caused by the development of neck. The experimental result of elongation is in good agreement with the theoretically predicated value according to the analytical expression (where ef, m, f, nv and ε is respectively elongation, average strain rate sensitivity, initial geometric defect, average strain hardening sensitivity at constant deformation velocity and average true strain). The fracture surface is intergraular, and superplastic deformation induces an equiaxed and grown grain. Decreasing strain rate increases tensile elongation and strain rate sensitivity m-value. The primary superplastic deformation mechanism is thought to be atom-diffusion-controlled grain boundary sliding.

Characterization of plasma current quench during disruption in EAST tokamak

A preliminary analysis of plasma current quenching is presented in this paper based on the disruption database.It demonstrates that 26.8%of discharges have been disrupted in the last 2012 campaign,in addition,the plasma disruptive rate grows with the increase of plasma current.The best-fit linear and instantaneous plasma current quench rate is extracted from the recent EAST disruptions,showing that an 80%-30%interval of the maximum plasma current is well fit for the EAST device.The lowest area-normalized current quench time is 3.33 ms/m;with the estimated plasma electron temperature being 7.3 eV;9.5 eV.In the disruption case the maximum eddy current goes up to 400 kA,and a fraction of currents are respectively driven on the upper and lower outer plate with nearly 100 MPa-200 MPa stress in the leg.

Quenching Phenomenon for a Parabolic MEMS Equation

This paper deals with the electrostatic MEMS-device parabolic equation u_t-?u =λf(x)/(1-u)~p in a bounded domain ? of R^N,with Dirichlet boundary condition,an initial condition u0(x) ∈ [0,1) and a nonnegative profile f,where λ > 0,p > 1.The study is motivated by a simplified micro-electromechanical system(MEMS for short) device model.In this paper,the author first gives an asymptotic behavior of the quenching time T*for the solution u to the parabolic problem with zero initial data.Secondly,the author investigates when the solution u will quench,with general λ,u0(x).Finally,a global existence in the MEMS modeling is shown.

Some Dichotomy Results for the Quenching Problem

It is shown that any solution to the semilinear problem{u（x,0=）u0（x）〈1,x∈[-1,1] u（±1,t）=0,t∈（0,T）, ut=uxx＋δ（1-u）^-p（x,t）∈（-1,1） ×（0,T）either touches 1 in finite time or converges smoothly to a steady state as t -~ ~e. Some extensions of this result to higher dimensions are also discussed.