Application of granular mechanics to the analysis of solid propellants

In this paper a theoretical method is developed for analyzing the mechanical behavior of granular solid propellant materials. The granular nature of the material is specifically taken into account and, the analysis allows for a media composed of non-uniformly sized particles with random stacking configuration. The voids between the particles are assumed to be filled with an elastic, homogeneous binder material. Three types of internal forces are assumed to be acting; the normal and tangential contact forces between the granular particles and, the elastic stresses in the binder. The paper consists of three main parts. First a model is developed to represent a general granular medium. Subsequently, in the second part this model is used to analyze the response of a granular medium to hydrostatic pressure loading. Finally the stress-strain relations are derived for a general loading condition. Because of the presence of the non-conservative frictional forces between the granular particles, the deformation of such a medium depends on the loading history. Consequently the stress-strain relations are in a differential, or incremental form

The determination of exhaust cloud dimensions from films of space shuttle launches

Principles of photogrammetry are used to calculate the dimension of ground clouds produced from the Space Shuttle launch system. For each of three launches (Missions 41C, 41D, and 51A), a 16 mm camera recorded the ground cloud from three different locations. Measurements were made from outlines of the cloud and other features of interest which were traced onto paper at one-minute intervals using a 16 mm stop-action projector. Cloud characteristics such as top, max width at top, average width, and base are presented as a function of time. A temperature inversion was present each launch day and the cloud responded by first rising into the inversion and then descending to about the inversion height. Max tops were achieved in about three to five minutes and ranged from 2200 m for Mission 41C to 3500 m for Mission 41D. Cloud bases rose steadily to between 700 and 1000 m after 10 minutes. Average widths ranged from 500 to 1700 m depending on mission and camera. Photographs of digitizations of selected film frames are included in the report to show the irregular cloud shapes. Error sources for this analysis are also discussed

Pairs of Bloch electrons and magnetic translation groups

A product of irreducible representations of magnetic translation group is considered. It leads to irreducible representations which were previously rejected as nonphysical. A very simple example indicates a possible application of these representations. In particular, they are important in descriptions of pairs of electrons in a magnetic field and a periodic potential. The periodicity of some properties with respect to the charge of a particle is briefly discussed.Comment: 4 pages, RevTex. Latex2.09, amsfont

Ecosystem Succession and Nutrient Retention: Vitousek and Reiners' Hypothesis

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/116356/1/bes22014953234.pd

Mathematical Modeling of the Neuronal Processes in Sugar Addiction

It has already been demonstrated that the body responds to enhanced intake of sugar and is conducive to a natural form of addiction. There are substantial neurochemical changes in the brain (especially dopamine and acetylcholine systems) similar to other addictive drugs. A mathematical model comprised by a system of delayed leaky integrate-and-re equations is established to simulate the effects of sugar on a reward-circuitry. Simulations with Neuron suggest agreement with the neurobiological hypotheses of hyperactivity of neural systems due to binge sugar intake

Berry phases in superconducting transitions

I generalize the concept of Berry's geometrical phase for quasicyclic Hamiltonians to the case in which the ground state evolves adiabatically to an excited state after one cycle, but returns to the ground state after an integer number of cycles. This allows to extend the charge Berry phase gamma_c related to the macroscopic polarization, to many-body systems with fractional number of particles per site. Under certain conditions, gamma_c and the spin Berry phase gamma_s jump in pi at the boundary of superconducting phases. In the extended Hubbard chain with on-site attraction U and nearest-neighbor interaction V at quarter filling, the transitions detected agree very well with exact results in two limits solved by the Bethe ansatz, and with previous numerical studies. In chains with spin SU(2) symmetry, gamma_s jumps when a spin gap opens.Comment: 5 pages, 3 figures, accepted in Europhys. Let

Exact Random Walk Distributions using Noncommutative Geometry

Using the results obtained by the non commutative geometry techniques applied to the Harper equation, we derive the areas distribution of random walks of length $N$ on a two-dimensional square lattice for large $N$, taking into account finite size contributions.Comment: Latex, 3 pages, 1 figure, to be published in J. Phys. A : Math. Ge

Entropy on the von Neumann lattice and its evaluation

Based on the recently introduced averaging procedure in phase space, a new type of entropy is defined on the von Neumann lattice. This quantity can be interpreted as a measure of uncertainty associated with simultaneous measurement of the position and momentum observables in the discrete subset of the phase space. Evaluating for a class of the coherent states, it is shown that this entropy takes a stationary value for the ground state, modulo a unit cell of the lattice in such a class. This value for the ground state depends on the ratio of the position lattice spacing and the momentum lattice spacing. It is found that its minimum is realized for the perfect square lattice, i.e., absence of squeezing. Numerical evaluation of this minimum gives 1.386....Comment: 14 pages, no figures; J. Phys. A, in pres

Dispersal limitation structures fungal community assembly in a long‐term glacial chronosequence

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/107360/1/emi12281.pd

Ectomycorrhizal fungi and the enzymatic liberation of nitrogen from soil organic matter: why evolutionary history matters

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/139921/1/nph14598.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/139921/2/nph14598_am.pd