On numerical approximation of an optimal control problem in linear elasticity

In this paper we apply the optimal control theory to a linear elasticity problem. An iterative method based on the optimality system characterizing the corresponding minimization of a cost functional is proposed. Convergence of the approximate solutions is proved provided that a parameter of penalization is not too small. Numerical solutions are presented to emphasize the role of this parameter. It is shown that the results are far from being good approximations of the expected ones, because the parameter can not be taken small enough in the iteration method. On the other hand, numerical results from a spectral analysis are shown without this limitation by the use of eigenfunction representations

Fatigue Deformation Mechanisms of Zirconia Ceramics

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65237/1/j.1151-2916.1992.tb05558.x.pd

Fatigue of Yttria-Stabilized Zirconia: I, Fatigue Damage, Fracture Origins, and Lifetime Prediction

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65792/1/j.1151-2916.1991.tb04088.x.pd

Vibration of elastic string with moving boundary

A mathematical model for the small vibration of an elastic string is considered. The model takes into account the change of tension due to the movement of the end points of the string. Under the assumptions that the velocity of the moving ends be less than the characteristic velocity of the equation, the global existence and the local umqueness of the solution are proved

Optimization of three-color laser field for the generation of single ultrashort attosecond pulse

This is the published version, also available here: http://dx.doi.org/10.1364/OE.19.023857.We present an efficient and realizable scheme for the generation of an ultrashort single attosecond (as) pulse. The feasibility of such a scheme is demonstrated by solving accurately the time-dependent Schrödinger equation using the time-dependent generalized pseudospectral (TDGPS) method. This scheme involves the use of the optimization of the three-color laser fields. The optimized laser pulse is synthesized by three one-color laser pulses with proper relative phases. It can provide a longer acceleration time for the tunneling and oscillating electrons, and allows the electrons to gain more kinetic energy. We show that the plateau of high-order harmonic generation is extended dramatically and a broadband supercontinuum spectra is produced. As a result, an isolated 23 as pulse with a bandwidth of 163 eV can be obtained directly by superposing the supercontinuum harmonics near the cutoff region. We will show that such a metrology can be realized experimentally

Ab initio study of the X 2Π and A 2Σ+ states of OH. I. Potential curves and properties

This is the published version, also available here: http://dx.doi.org/10.1063/1.1681891Accurate ab initio CI potential curves and molecular properties are presented for the X 2Π and A 2Σ+ states of OH. Results with known experimental values in parentheses are Re (X 2Π) = 1.841(1.834) bohr, Re (A 2Σ+) = 1.906(1.913) bohr, De (X 2Π) = 4.43(4.63) eV, De (A 2Σ+) = 2.29(2.53) eV, μ(OH,X 2Π,ν=0) = 1.634(1.668) D, and μ(OD,A 2Σ+,ν=0) = 1.861(1.72±0.10) D. Spectroscopic constants calculated from the theoretical potential curves are in satisfactory agreement with experimental results. Other molecular properties studied include quadrupole moments and the electric field gradient at the nuclei

Coherent control of the electron quantum paths for the generation of single ultrashort attosecond laser pulse

This is the published version, also available here: http://dx.doi.org/10.1103/PhysRevA.84.033414.We report a mechanism and a realizable approach for the coherent control of the generation of an isolated and ultrashort attosecond (as) laser pulse from atoms by optimizing the two-color laser fields with a proper time delay. Optimizing the laser pulse shape allows the control of the electron quantum paths and enables high-harmonic generation from the long- and short-trajectory electrons to be enhanced and split near the cutoff region. In addition, it delays the long-trajectory electron emission time and allows the production of extremely short attosecond pulses in a relatively narrow time duration. As a case study, we show that an isolated 30 as pulse with a bandwidth of 127 eV can be generated directly from the contribution of long-trajectory electrons alone