On some differential equations arising in a time domain inverse scattering problem for a dissipative wave equation

The problem of identification of one spatially varying material property, defined within a slab, from boundary measurements is examined. This inverse problem is described by a functional differential equation. Uniqueness and existence of the solution of this inverse problem and the associated direct problem is proven. Of major importance in any inverse problem are the properties of the operator mapping the boundary measurements to the material property. It is shown that this operator is continuous and differentiable

Mediators of mechanotransduction between bone cells

Mechanical forces are known to regulate the function of tissues in the body, including bone. Bone adapts to its mechanical environment by altering its shape and increasing its size in response to increases in mechanical load associated with exercise, and by decreasing its size in response to decreases in mechanical load associated with microgravity or prolonged bed rest. Changes in bone size and shape are produced by a cooperative action of two main types of the bone cells - osteoclasts that destroy bone and osteoblasts that build bone. These cell types come from different developmental origins, and vary greatly in their characteristics, such as size, shape, and expression of receptor subtypes, which potentially may affect their responses to mechanical stimuli. The objective of this study is to compare the responses of osteoclasts and osteoblasts to mechanical stimulation. This study has allowed us to conclude the following: 1. A mediator is released from a single source cell. 2. The response to the mediator changes with distance. 3. The value of the apparent diffusion coeficient increases with distance. 4. A plausible proposed mechanism is that ATP is released and degrades to ADP. 5. Future experiments are required to confim that ATP is the mediator as suggested

The null field approach to diffraction theory

The diffraction of both scalar and vector monochromatic waves by totally-reflecting bodies is considered from a computational viewpoint. Both direct and inverse scattering are covered. By invoking the optical extinction theorem (extended boundary condition) the conventional singular integral equation (for the density of reradiating sources existing in the surface of the scattering body) is transformed into infinite sets of non-singular integral equations - called the null field equations. There is a set corresponding to each separable coordinate system. Each set can be used to compute the scattering from bodies of arbitrary shape but each is most appropriate for particular types of body shape, as is confirmed by computational results. The general null field is extended to apply to multiple scattering bodies. This permits use of multipole expansions in a computationally convenient manner, for arbitrary numbers of separated, interacting bodies of arbitrary shape. The method is numerically investigated for pairs of elliptical and square cylinders. A generalisation of the Kirchoff, or physical optics, approach to diffraction theory is developed from the general null field method. Corresponding to each particular null field method is a physical optics approximation, which becomes exact when one of the coordinates being used is constant over the surface of the scattering body. Numerical results are presented showing the importance of choosing the physical optics approximation most appropriate for the scattering body concerned. Generalised physical optics is used to develop two inversion procedures to solve the inverse scattering problem for totally-reflecting bodies. One is similar to conventional methods based on planar physical optics and, like them, requires scattering data at all frequencies. The other enables shapes of certain bodies of revolution and cylindrical bodies to be reconstructed from scattered fields observed at two closely spaced frequencies. Computational results which confirm the potential usefulness of the latter method are presented

Improved shaping approach to the preliminary design of low-thrust trajectories

This paper presents a general framework for the development of shape-based approaches to low-thrust trajectory design. A novel shaping method, based on a three-dimensional description of the trajectory in spherical coordinates, is developed within this general framework. Both the exponential sinusoid and the inverse polynomial shaping are demonstrated to be particular two-dimensional cases of the spherical one. The pseudoequinoctial shaping is revisited within the new framework, and the nonosculating nature of the pseudoequinoctial elements is analyzed. A two step approach is introduced to solve the time of flight constraint, related to the design of low-thrust arcs with boundary constraints for both spherical and pseudoequinoctial shaping. The solution derived from the shaping approach is improved with a feedback linear-quadratic controller and compared against a direct collocation method based on finite elements in time. The new shaping approach and the combination of shaping and linear-quadratic controller are tested on three case studies: a mission to Mars, a mission to asteroid 1989ML, a mission to comet Tempel-1, and a mission to Neptune

Relationship between Canopy Closure and Pasture Production in Deciduous Tree Based Temperate Silvopastoral Systems

Experiments were carried out in New Zealand with 11 year-old alder (Alnus chordata) on lowland pasture, and with 30+ year-old poplar (Populus spp) on hill pasture. Alder tree shade decreased (P\u3c 0.001) tiller density and total herbage harvested, with the highest tiller density at the lowest shade level of 41% canopy closure (DifN 0.59). Net herbage accumulation (NHA) directly under a poplar canopy was 35% of the NHA of open pasture, but NHA in canopy gaps increased with gap size. These results suggested that keeping canopy closure percentage in the 40-50% range for a deciduous tree silvopastoral system, would maintain pasture production and tiller density at approximately two-thirds of that of unshaded pasture

The Hyperfine Molecular Hubbard Hamiltonian

An ultracold gas of heteronuclear alkali dimer molecules with hyperfine structure loaded into a one-dimensional optical lattice is investigated. The \emph{Hyperfine Molecular Hubbard Hamiltonian} (HMHH), an effective low-energy lattice Hamiltonian, is derived from first principles. The large permanent electric dipole moment of these molecules gives rise to long range dipole-dipole forces in a DC electric field and allows for transitions between rotational states in an AC microwave field. Additionally, a strong magnetic field can be used to control the hyperfine degrees of freedom independently of the rotational degrees of freedom. By tuning the angle between the DC electric and magnetic fields and the strength of the AC field it is possible to control the number of internal states involved in the dynamics as well as the degree of correlation between the spatial and internal degrees of freedom. The HMHH's unique features have direct experimental consequences such as quantum dephasing, tunable complexity, and the dependence of the phase diagram on the molecular state

Radar-aeolian roughness project

The objective is to establish an empirical relationship between measurements of radar, aeolian, and surface roughness on a variety of natural surfaces and to understand the underlying physical causes. This relationship will form the basis for developing a predictive equation to derive aeolian roughness from radar backscatter. Results are given from investigations carried out in 1989 on the principal elements of the project, with separate sections on field studies, radar data analysis, laboratory simulations, and development of theory for planetary applications

Elastic Wave Scattering from Multiple and Odd Shaped Flaws

Using the T-Matrix or Null Field method elastic wave scattering from the following geometries have been studied (a) Rotationally symmetric configurations consisting of two spheroidal cavities separated by a finite distance and with different eccentricities. Exact calculations are compared with single scattering approximations. The frequency spectra are interpreted for various scattering geometries and compared with experiments. The effect of change in distance between the scatterers is also discussed. (b) Scattering from rotationally symmetric cavities with odd shapes like Pinnochio , Rockwell Science Center sample #73 and Micky Mouse , Rockwell Science Center sample #70 was also studied and compared with numerical results using other techniques as well as experiments. Several ways of studying such problems is also discussed. (c) A numerical technique is proposed to study dynamic stress concentrations