Scaling, Optimality, and Landscape Evolution

A nonlinear model is studied which describes the evolution of a landscape under the effects of erosion and regeneration by geologic uplift by mean of a simple differential equation. The equation, already in wide use among geomorphologists and in that context obtained phenomenologically, is here derived by reparametrization invariance arguments and exactly solved in dimension d=1. Results of numerical simulations in d=2 show that the model is able to reproduce the critical scaling characterizing landscapes associated with natural river basins. We show that configurations minimizing the rate of energy dissipation (optimal channel networks) are stationary solutions of the equation describing the landscape evolution. Numerical simulations show that a careful annealing of the equation in the presence of additive noise leads to configurations very close to the global minimum of the dissipated energy, characterized by mean field exponents. We further show that if one considers generalized river network configurations in which splitting of the flow (i.e., braiding) and loops are allowed, the minimization of the dissipated energy results in spanning loopless configurations, under the constraints imposed by the continuity equations. This is stated in the form of a general theorem applicable to generic networks, suggesting that other branching structures occurring in nature may possibly arise as optimal structures minimizing a cost function.     

Axial heat conduction effects in the entrance region of circular ducts

This paper describes the transport of thermal energy within a small distance after an abrupt wall temperature change in a circular duct. In general, the axial conduction becomes significant when the Peclet number is small. The results indicate that the inclusion of axial conduction in the fluid substantially increases the wall heat flux at near the thermal inlet location. The exact series solution leads to a modified Graetz type problem. This exact solution is augmented by an asymptotic solution describing the wall heat flux near the thermal entrance location.     

Long wave theory of absorption and reflection in molecular crystals

The theory of long waves originally developed by Born and Huang for ionic crystals and then adapted for molecular crystals with one molecule per unit cell by Hall is extended to include molecular crystals with two molecules per unit cell. A study is made of the non-analytic behaviour of the energy bands as the wave vector tends to zero and it is found that the energies of the optically excited levels will be different from the values usually assumed. The dispersion relation is obtained and used to discuss metallic reflectivity. The finite lifetime of the excited states can also be included in the theory and this has the effect of changing the position of maximum absorption as well as reducing the reflectivity. A comparison is made between the long wave theory, the simple form of Davydov theory and experiment.     

Frequency-dependent properties of the hydrogen atom: A generalized eigenvalue equation approach

The time-independent first-order perturbation equations which arise on considering the response of a system to a harmonic time-dependent perturbation are solved by using an expansion in terms of a complete discrete set of solutions of a generalized eigenvalue equation. Explicit formulae are obtained for several frequency-dependent properties of the hydrogen atom.     

Spin-coupled wavefunctions

A method recently introduced for constructing spin-coupled wave-functions is extended to deal with the singlet and triplet states of four-electron systems. The approach is applied to LiH (¹Σ, ³Σ), Be (¹ S) and BeH⁺ (¹Σ) using a simple one-configuration model, in which the orbitals are expressed in elliptical coordinates.     

Dynamics of digging in wet soil

Numerous animals live in, and locomote through, subsea soils. To move in a medium dominated by frictional interactions, many of these animals have adopted unique burrowing strategies. This paper presents a burrowing model inspired by the Atlantic razor clam (Ensis directus), which uses deformations of its body to cyclically loosen and re-pack the surrounding soil in order to locally manipulate burrowing drag. The model reveals how an anisotropic body - composed of a cylinder and sphere varying sinusoidally in size and relative displacement - achieves unidirectional motion through a medium with variable frictional properties. This net displacement is attained even though the body kinematics are reciprocal and inertia of both the model organism and the surrounding medium are negligible. Our results indicate that body aspect ratio has a strong effect on burrowing velocity and efficiency, with a well-defined maximum for given kinematics and soil material properties.     

Crystal and molecular structure of hydroxyjatrophone C

The structure of the title compound has been established by means of the x-ray diffraction method on a single crystal. The crystals are othorhombic, space groupP2₁2₁2₁ (No. 19) witha=10.222(4),b=10.622(2),c=16.434(3) Å,z=4. Full-matrix least squares refinement led toR=4.9%. The molecular stereochemistry, bond distances, bond angles, torsion angles, and hydrogen bond scheme have all been determined.Camille and Henry Dreyfus Teacher Scholar, 1978–1983; National Institutes of Health (National Cancer Institute) Career Development Award, 1980–1985.     

A Time of Flight Model for Cloud’s Radiative Transfer

A model for fast calculation of path radiance of finite clouds is presented. The calculations are simplified by using the reciprocity principle and the homogenousness property of the incident light. Comparisons with reasonably accurate calculations for spherical cloud and two-dimensional infinite layer were made.Presented at the 7th International Workshop on Multiple Scattering Lidar/Light Experiments (MUSCLE7), July 21–23 1994, Chiba, Japan.     

A short story of SIN!

A brief overview is given of the theory of surface-ion neutralization (SIN) by highlighting studies from the pioneering days to the present time. Emphasis is placed on the 1-electron time-dependent Newns-Anderson (TDNA) model, which has played such a key role in studying resonance charge transfer. Recently, a many-electron (ME) version of the TDNA approach has been formulated to treat two or more electron processes, such as Auger transitions. The equation-of-motion technique is used to obtain the TD coefficients from which the required SIN probabilities can be found. After outlining the ME method, two applications are described. The first deals with the Li⁺-Cs/W(110) system, while the second addresses the laser enhancement of SIN, in the case of Li⁺-KBr, and revises some earlier results.