An alternating direction scheme on a nonuniform mesh for reaction-diffusion parabolic problems

In this paper we develop a numerical method for two-dimensionaltime-dependent reaction-diffusion problems. This method, whichcan immediately be generalized to higher dimensions, is shownto be uniformly convergent with respect to the diffusion problems.This method, which can immediately be generalized to higherdimensions, is shown to be uniformly convergent with respectto the diffusion parameter.     

The neuroblast and angioblast chemotaxic factor SDF-1 (CXCL12) expression is briefly up regulated by reactive astrocytes in brain following neonatal hypoxic-ischemic injury

Background  

Stromal cell-derived factor 1 (SDF-1 or CXCL12) is chemotaxic for CXCR4 expressing bone marrow-derived cells. It functions in brain embryonic development and in response to ischemic injury in helping guide neuroblast migration and vasculogenesis. In experimental adult stroke models SDF-1 is expressed perivascularly in the injured region up to 30 days after the injury, suggesting it could be a therapeutic target for tissue repair strategies. We hypothesized that SDF-1 would be expressed in similar temporal and spatial patterns following hypoxic-ischemic (HI) injury in neonatal brain.     

Symmetry Classification Using Noncommutative Invariant Differential Operators

Given a class F of differential equations, the symmetry classification problem is to determine for each member f ∈ F the structure of its Lie symmetry group G_f or, equivalently, of its Lie symmetry algebra. The components of the symmetry vector fields of the Lie algebra are solutions of an associated overdetermined "defining system" of differential equations. The usual computer classification method which applies a sequence of total derivative operators and eliminations to this associated system often fails on problems of interest due to the excessive size of expressions generated in intermediate computations. We provide an alternative classification method which exploits the knowledge of an equivalence group G preserving the class. A noncommutative differential elimination procedure due to Lemaire, Reid, and Zhang, where each step of the procedure is invariant under G, can be applied and an existence and uniqueness theorem for the output used to classify the structure of symmetry groups for each f ∈ F. The method is applied to a class of nonlinear diffusion convection equations v_x = u, v_t = B(u) u_x - K(u) which is invariant under a large but easily determined equivalence group G. In this example the complexity of the calculations is much reduced by the use of G-invariant differential operators.     

Search for superdeformation in180Os

Two-dimensional γ-ray energy correlations have been measured at high spins in¹⁸⁰0s with the TESSA2 spectrometer. The E_γ ? E_γcorrelation matrix displays ridges characteristic of rotational bands with different energy separations of 96± and 72± keV for the energy regions of 660 to 840 keV and 975 to 1170 keV, respectively. The separation of these ridges remains constant in both energy regions. The dynamical moments of inertia are θ⁽²⁾ =83±3 and 111±5 ?²/MeV, respectively. The latter value suggests superdeformation in¹⁸⁰0s with an axis ratio c/a=1.76 (β₂ ?0.64) at high spins.     

Loss of alignment gain in the πh 9/2[541 1/2−] ⊗ (νi 13/2)2 band in 167Tm and neighbouring odd-Z N = 98 nuclei

Theπh_9/2[541 1/2^?] band in ¹⁶⁷Tm has been studied through the ¹²⁴Sn(⁴⁸Ca, p4n)¹⁶⁷Tm reaction at E _beam = 210 MeV. The favoured signature of the πh_9/2[541 1/2^?] band is observed to spin 61/2h?. A remarkable small gain in aligned angular momentum at the AB-band crossing has been found. The crossing frequency and the gain in aligned angular momentum for ¹⁶⁷Tm are compared with data for the N = 98 isotones of Lu, Ta and Re, and contrasted with Cranked Shell Model predictions, based on frequency diabatic configurations. Large deviations are found for the gain in aligned angular momentum.     

Internal energy content of n-butylbenzene, bromobenzene, iodobenzene and aniline molecular ions generated by two-photon ionization at 266 nm. A photodissociation study

A technique to investigate photodissociation kinetics on a nanosecond time scale has been devised for molecular ions generated by multiphoton ionization (MPI) using mass-analyzed ion kinetic energy spectrometry. The branching ratio or rate constant has been determined for the photodissociation of the n-butylbenzene, bromobenzene, iodobenzene, and aniline molecular ions generated by MPI at 266 nm. The ion internal energies have been estimated by comparing the measured kinetic data with the previous energy dependence data. The analysis has shown that only those molecular ions generated by two-photon ionization contribute to the photodissociation signals. Around half of the available energy has been found to remain as molecular ion internal energy in the two-photon ionization process. Copyright 1999 John Wiley & Sons, Ltd.