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The initial value problem of fractional differential equations and its solving method are studied in this paper. Firstly, for easy understanding, a different version of the initialized operator theory is presented for Riemann-Liouville’s fractional-order derivative, addressing the initial history in a straightforward form. Then, the initial value problem of a single-term fractional differential equation is converted to an equivalent integral equation, a form that is easy for both theoretical and numerical analysis, and two illustrative examples are given for checking the correctness of the integral equation. Finally, the counter-example proposed in a recent paper, which claims that the initialized operator theory results in wrong solution of a fractional differential equation, is checked again carefully. It is found that solving the equivalent integral equation gives the exact solution, and the reason behind the result of the counter-example is that the calculation therein is based on the conventional Laplace transform for fractional-order derivative, not on the initialized operator theory. The counter-example can be served as a physical model of creep phenomena for some viscoelastic materials, and it is found that it fits experimental curves well.

We report recurrence spectra of He atoms in a magnetic field near the second and third ionization thresholds. The analysis of the recurrence spectra reveals the presence of new peaks. It is shown that these peaks are signatures of inelastic (interchannel) scattering events of active electrons by the atomic cores and they correspond to combinations of electron closed-orbits in different channels. Our calculations are based on a formulation combining the standard closed-orbit theory away from the core region with the close-coupling R-matrix theory in the core region. (c) 2006 Elsevier B.V. All rights reserved.

Fatigue and corrosion are two major concerns of aging aircraft research. Metal corrosion and fatigue act synergistically in various ways. They may be present separately or simultaneously. In this study Al 2024-T3 alloy was intermittently subjected to sequential corrosion and fatigue processes. Specimens were first subjected to various degrees of fatigue damage in air, then immersed in a corrosive solution for a fixed amount of time, and subsequently further fatigued in air to failure. The results are compared with those subjected to fatigue in air, and to corrosion then fatigue in air. We find that the total fatigue life (sum of fatigue cycles before and after corrosion) exceeds that of the virgin samples, provided that the initial fatigue cycle has consumed more than half of life solely fatigued in air. It is believed that the blunting of microcracks and the removal of other surface damage, such as intrusions/extrusions created at the initial stage of fatigue, are the major reasons for this increased fatigue life.

Formulas are presented that describe the general connections between the autocorrelation functions and the double-pulse excitation probabilities. The formulas are derived using the time-dependent perturbation theory and the rotating-wave approximation for the laser pulses. These formulas can be used to obtain the autocorrelation function from the double-pulse excitation probability or vice versa in many systems.

The dynamics of the wave packet generated by a short-pulse laser can be characterized by an autocorrelation function. The autocorrelation function is an experimentally measurable quantity. This paper shows that the autocorrelation function can be written as a sum of modified Gaussian functions that correspond to the closed orbits of the system. The autocorrelation function can be calculated by using existing algorithms in closed-orbit theory. As an application of the theory, the autocorrelation function is obtained for a system that consists of an H[sup [minus]] ion in a static electric field.

A Gaussian wave packet confined to move on a plane perpendicular to a magnetic field remains a Gaussian wave packet in its time evolution. The average position and momentum follow the Ehrenfest equations which are identical to the classical Hamilton equations. A set of nonlinear equations decoupled from the Ehrenfest equation is derived for the parameters describing the time evolution of the density distribution and phases of a wave packet. Explicit solutions are then obtained when the "internal" angular momentum of the wave packet vanishes. In this case it is shown that the motion of the wave packet is a superposition of a translational motion, a rotation and a vibration.

A real space amplitude method for the calculation of the quasi-bound resonance energies and widths for a single-channel one-dimensional potential is described and applied to the vibrational quasi-bound states of 3 He 4 He 2 2+ and 4 He 2 2+ , which have been detected recently, using the Coulomb explosion technique.

We have previously shown with X‐ray photoelectron spectroscopy that acetone remaining on the surface of a copper strip after degreasing, can react slowly with water vapor under ambient light to form acetic acid and cause severe corrosion. The reaction was completely inhibited in darkness. This suggested that copper reacted photochemically with acetone and water. This paper shows that acetone degreasing of the AA2024-T3, as per ASTM E1078-97 cleaning protocol, has a similar effect on constituent copper‐rich intermetallic particles. When an acetone‐degreased alloy was exposed to a mist of sodium chloride solution under ambient light, the formation of acetic acid together with a layer of chloride solution resulted in severe pitting. Pitting was inhibited under conditions of darkness. The slow reaction of surface‐absorbed acetone with water leading to the formation of acetic acid appeared to be prevented. There was also evidence for the redeposition of dissolved copper onto the alloy matrix under conditions that induced pitting. © 2000 The Electrochemical Society. All rights reserved.

The formation of CO(+) and CO in the expanding metal-rich ejecta of SN 1987A has been discussed by Lepp et al. (1988) and by Petuchowski et al. (1989), who concluded that it probably proceeded through the radiative association of C(+) and O to form CO(+) by the reactions (1) C(+) + O - CO(+) + hnu, followed by charge transfer of CO(+) with O, (2) CO(+) + O - CO + O(+), and by the radiative association of C and O to form CO, (3) C + O - CO + hnu. Petuchowski et al. estimated the rate coefficients of reactions (1) and (3) and concluded that the sequence of (1) and (2) constitutes the major source of CO. An alternative calculation of the rate coefficients is made here that indicates that reaction (3) is probably more important. 36 refs.

A detailed comparison is made of the theoretical photodetachment cross sections of H - in an electric field. It is found that, in contrast to the oscillatory structure of the cross section for photons polarized parallel to the applied field, the cross section for photons polarized perpendicular to the applied field is close to the smooth zero-field cross section. However, due to quantum tunneling, the threshold law is modified. A physical picture similar to that developed for atoms in a magnetic field explains the strong polarization dependence satisfactorily.

A scaling law is developed which expresses the eigenvalues of the Debye-Huckel potential in terms of a single parameter. A semi-classical quantization is shown to give an accurate approximation to the eigenvalues and it is used to obtain simple procedures for the calculation of the critical screening lengths and the numbers of discrete quantum states in any exponentially screened Coulomb potential.

A case of hemochromatosis in a young, adult woman is presented, the salient clinical findings being heart failure, skin pigmentation, amenorrhea, and enlargement of the liver. Only two similar cases in women have been described. The results of radioiron absorption studies show that 75 per cent of a total oral dose of 20 mg. of ferrous sulfate was retained in the body. The level of radioiron in the blood reached a maximum of 3.5 per cent of the administered dose after a period of thirty days, and in vivo counts showed a large deposition of radioiron in the liver. Counts over the heart seemed to indicate a real deposition in this organ. It is suggested that heart failure in hemochromatosis is related more to the rate at which iron is laid down in the cardiac muscle than to the absolute quantity deposited.