Non-local dispersal and bistability

The scalar initial value problem [ u_t = ho Du + f(u), ] is a model for dispersal. Here $u$ represents the density at point $x$ of a compact spatial region $Omega in mathbb{R}^n$ and time $t$, and $u(cdot)$ is a function of $t$ with values in some function space $B$. $D$ is a bounded linear operator and $f(u)$ is a bistable nonlinearity for the associated ODE $u_t = f(u)$. Problems of this type arise in mathematical ecology and materials science where the simple diffusion model with $D=Delta$ is not sufficiently general. The study of the dynamics of the equation presents a difficult problem which crucially differs from the diffusion case in that the semiflow generated is not compactifying. We study the asymptotic behaviour of solutions and ask under what conditions each positive semi-orbit converges to an equilibrium (as in the case $D=Delta$). We develop a technique for proving that indeed convergence does hold for small $ho$ and show by constructing a counter-example that this result does not hold in general for all $ho$

Notes on lunar ilmenite

Opaques (mostly ilmenite) make up 0 to 5 percent of highland rocks, 1 to 11 percent of low-Ti mare basalts, and 10 to 34 percent of high-Ti mare basalts (Carter 1988). Apollos 11 and 17 sampled high-Ti basalts. Apollos 12 and 14 sampled low-Ti basalts. Apollo 15 sampled a complex mixture of mare and highland material. Apollo 16 sampled mainly highland material (Taylor 1975)

Long range intermolecular forces in triatomic systems: connecting the atom-diatom and atom-atom-atom representations

The long-range forces that act between three atoms are analysed in both atom-diatom and atom-atom-atom representations. Expressions for atom-diatom dispersion coefficients are obtained in terms of 3-body nonadditive coefficients. The anisotropy of atom-diatom C_6 dispersion coefficients arises primarily from nonadditive triple-dipole and quadruple-dipole forces, while pairwise-additive forces and nonadditive triple-dipole and dipole-dipole-quadrupole forces contribute significantly to atom-diatom C_8 coefficients. The resulting expressions are applied to dispersion coefficients for Li + Li_2 (triplet) and recommendations are made for the best way to obtain global triatomic potentials that dissociate correctly both to three separated atoms and to an atom and a diatomic molecule.Comment: To be published in a special issue of Molecular Physics in honour of Mark Chil

Clusters containing open-shell molecules. III. Quantum five-dimensional/two-surface bound-state calculations on ArnOH van der Waals clusters (X2Π, n=4 to 12)

This paper presents a theoretical study of the bound states of the open-shell OH radical in its ground electronic state(X2Π) interacting with n Ar atoms, for n from 4 to 12. After freezing the geometry of the Arn cage or subunit at the equilibrium structure (preceding paper), we carry out nonadiabatic five-dimensional quantum dynamics calculations on two coupled potential energy surfaces, using an extension of the method previously applied to closed-shell ArnHFclusters [J. Chem. Phys. 103, 1829 (1995)]. The method is based on a discrete variable representation (DVR) for the translational motion of OH relative to Arn, combined with a finite basis representation of the OH hindered rotation and electronic structure, including spin–orbit effects. The pattern of OH hindered rotor levels in clusters is similar to that in Ar–OH itself, though extended over three to four times the energy range for n=4 to 9. Ar12OH has a nearly spherical shell of Ar atoms around the OH, so the anisotropic splitting is very small. For n=10 and 11, the anisotropy may be viewed as arising from holes in an otherwise spherical shell, and the resulting patterns of hindered rotor levels are inverted versions of those for Ar2OH and Ar–OH

Non-local dispersal

We consider a model of spatial spread that has applications in both material science and biology. The classical models are based upon partial differential equations, in particular reaction-diffusion equations. Here the dispersal term is given in terms of an integral operator and we restrict ourselves to the scalar case

Ultracold collisions involving heteronuclear alkali metal dimers

We have carried out the first quantum dynamics calculations on ultracold atom-diatom collisions in isotopic mixtures. The systems studied are spin-polarized 7Li + 6Li7Li, 7Li + 6Li2, 6Li + 6Li7Li and 6Li + 7Li2. Reactive scattering can occur for the first two systems even when the molecules are in their ground rovibrational states, but is slower than vibrational relaxation in homonuclear systems. Implications for sympathetic cooling of heteronuclear molecules are discussed.Comment: 4 pages, 3 figure

Plasma and cavitation dynamics during pulsed laser microsurgery in vivo

We compare the plasma and cavitation dynamics underlying pulsed laser microsurgery in water and in fruit fly embryos (in vivo) - specifically for nanosecond pulses at 355 and 532 nm. We find two key differences. First, the plasma-formation thresholds are lower in vivo - especially at 355 nm - due to the presence of endogenous chromophores that serve as additional sources for plasma seed electrons. Second, the biological matrix constrains the growth of laser-induced cavitation bubbles. Both effects reduce the disrupted region in vivo when compared to extrapolations from measurements in water.Comment: 9 pages, 5 figure