Incompatible sets of gradients and metastability

We give a mathematical analysis of a concept of metastability induced by incompatibility. The physical setting is a single parent phase, just about to undergo transformation to a product phase of lower energy density. Under certain conditions of incompatibility of the energy wells of this energy density, we show that the parent phase is metastable in a strong sense, namely it is a local minimizer of the free energy in an $L^1$ neighbourhood of its deformation. The reason behind this result is that, due to the incompatibility of the energy wells, a small nucleus of the product phase is necessarily accompanied by a stressed transition layer whose energetic cost exceeds the energy lowering capacity of the nucleus. We define and characterize incompatible sets of matrices, in terms of which the transition layer estimate at the heart of the proof of metastability is expressed. Finally we discuss connections with experiment and place this concept of metastability in the wider context of recent theoretical and experimental research on metastability and hysteresis.Comment: Archive for Rational Mechanics and Analysis, to appea

Lattice deformations at martensite-martensite interfaces in Ni-Al

The atomic configurations at macrotwin interfaces between microtwinned martensite plates in $Ni_{65}Al_{35}$ material are investigated using high resolution transmission electron microscopy (HRTEM). The observed structures are interpreted in view of possible formation mechanisms of these interfaces. A distinction is made between cases in which the microtwins, originating from mutually perpendicular \{110\} austenite planes, enclose a final angle larger or smaller than $90^{\circ}$, measured over the boundary. Two different configurations, one with crossing microtwins and the other with ending microtwins producing a step configuration are described. The latter is related with the existence of microtwin sequences with changing variant widths. Although both features appear irrespective of the material’s preparation technique, rapid solidification seems to prefer the step configuration. Depending on the actual case, tapering, bending and tip splitting of the small microtwin variants is observed. Sever lattice deformations and reorientations occur in a region of 5 – 10 nm around the interface while sequences of single plane ledges gradually bending the microtwins are found up to 50 nm away form the interface. These structures and deformations are interpreted in view of the need to accommodate any remaining stresses

Singularity theory study of overdetermination in models for L-H transitions

Two dynamical models that have been proposed to describe transitions between low and high confinement states (L-H transitions) in confined plasmas are analysed using singularity theory and stability theory. It is shown that the stationary-state bifurcation sets have qualitative properties identical to standard normal forms for the pitchfork and transcritical bifurcations. The analysis yields the codimension of the highest-order singularities, from which we find that the unperturbed systems are overdetermined bifurcation problems and derive appropriate universal unfoldings. Questions of mutual equivalence and the character of the state transitions are addressed.Comment: Latex (Revtex) source + 13 small postscript figures. Revised versio

Anisotropic diffusion limited aggregation in three dimensions : universality and nonuniversality

We explore the macroscopic consequences of lattice anisotropy for diffusion limited aggregation (DLA) in three dimensions. Simple cubic and bcc lattice growths are shown to approach universal asymptotic states in a coherent fashion, and the approach is accelerated by the use of noise reduction. These states are strikingly anisotropic dendrites with a rich hierarchy of structure. For growth on an fcc lattice, our data suggest at least two stable fixed points of anisotropy, one matching the bcc case. Hexagonal growths, favoring six planar and two polar directions, appear to approach a line of asymptotic states with continuously tunable polar anisotropy. The more planar of these growths visually resembles real snowflake morphologies. Our simulations use a new and dimension-independent implementation of the DLA model. The algorithm maintains a hierarchy of sphere coverings of the growth, supporting efficient random walks onto the growth by spherical moves. Anisotropy was introduced by restricting growth to certain preferred directions

QCD Sum Rules Calculation of Heavy Λ\Lambda Semileptonic Decay

We set up sum rules for heavy lambda decays in a full QCD calculation which in the heavy quark mass limit incorporates the symmetries of heavy quark effective theory. For the semileptonic \La_c decay we obtain a reasonable agreement with experiment. For the \La_b semileptonic decay we find at the zero recoil point a violation of the heavy quark symmetry of about 20%.Comment: Revised version. Title changed. 11 pages (RevTex), 4 PS figure

Nitrogen metabolism in lentil (Lens culinaris) and dry bean (Phaseolus vulgaris) during drought

Non-Peer ReviewedPulse crops are an attractive addition to a crop rotation because of their ability to supply most of their own nitrogen, which in turn reduces input costs. In recent years, drought has devastated much of the prairie region. We examined the effects of drought stress on nitrogen fixation in lentils (Lens culinaris) and dry bans (Phaseolus vulgaris ) to better understand and improve the drought tolerance of future varieties. Ureides are the plant nitrogenous compounds that are transported after nitrogen fixation to various plant organs, where they are subsequently used to produce amino acids. By identifying and studying the components of nitrogen fixation, preliminary observations have been made as to how the fixation process is affected by drought stress. Plants were grown in a greenhouse until they reached the flowering stage, and were then subjected to a 13 - day drought cycle. Plants that underwent the stress treatment were compared to a well watered set of control plants. Measurements during the stress were plant dry weight, plant total nitrogen content, plant ureide content and amount fixation, as determined by the 15N isotope procedure. Initial screening involved four bean cultivars (CDC Rosalee, CDC Pintium, Earliray and Othello), and four lentil cultivars (CDC Grandora, CDC Milestone, CDC Richlea and FLIP 96-27L). Of the initial eight cultivars, the most and least drought tolerant were chosen for further screening. The most drought tolerant cultivars were CDC Pintium (bean) and CDC Milestone (lentil). The least tolerant varieties chosen for comparison were Othello (bean) and CDC Grandora (lentil). Drought stress reduced dry weight, plant nitrogen content and nitrogen fixation in general. Initial results indicate that ureides build up in the least tolerant bean cultivars, yet continue cycling in the more tolerant cultivars during drought. This indicates that drought stress impacts on the cycling of plant nitrogen compounds produced as a result of fixation. Further research will be undertaken to determine how tolerant plants avoid this interruption and what can be done to improve the plant’s cycling of its nitrogen. We anticipate plants with improved nitrogen metabolism will be more drought tolerant than existing cultivars