Finite to infinite steady state solutions, bifurcations of an integro-differential equation

We consider a bistable integral equation which governs the stationary solutions of a convolution model of solid--solid phase transitions on a circle. We study the bifurcations of the set of the stationary solutions as the diffusion coefficient is varied to examine the transition from an infinite number of steady states to three for the continuum limit of the semi--discretised system. We show how the symmetry of the problem is responsible for the generation and stabilisation of equilibria and comment on the puzzling connection between continuity and stability that exists in this problem

Magnesium hydroxide as the neutralizing agent for radioactive hydrochloric acid solutions

The current technology at Los Alamos for removing actinides from acidic chloride waste streams is precipitation with approximately 10 M potassium hydroxide. Although successful, there are many inherent drawbacks to this precipitation technique which will be detailed in this paper. Magnesium hydroxide (K{sub sp} = 1.3 x 10{sup -11}) has limited solubility in water and as a result of the common ion effect, cannot generate a filtrate with a pH greater than 9. At a pH of 9, calcium (K{sub sp} = 5.5 x 10{sup -6}) will not coprecipitate as the hydroxide. This is an important factor since many acidic chloride feeds to hydroxide precipitation contain significant amounts of calcium. In addition, neutralization with Mg(OH){sub 2} produces a more filterable precipitate because neutralization occurs as the Mg(OH){sub 2} is dissolved by the acid rather than as a result of the much faster liquid/liquid reaction of KOH with the waste acid. This slower solid/liquid reaction allows time for crystal growth to occur and produces more easily filterable precipitates. On the other hand, neutralization of spent acid with strong KOH that yields numerous hydroxide ions in solution almost instantaneously forming a much larger volume of small crystallites that result in gelatinous, slow-filtering precipitates. Magnesium hydroxide also offers a safety advantage. Although mildly irritating, it is a weak base and safe and easy to handle. From a waste minimization perspective, Mg(OH){sub 2} offers many advantages. First, the magnesium hydroxide is added as a solid. This step eliminates the diluent water used in KOH neutralizations. Secondly, because the particle size of the precipitate is larger, more actinides are caught on the filter paper resulting in a smaller amount of actinide being transferred to the TA-50 Liquid Waste Treatment Facility. Third, the amount of solids that must be reprocessed is significantly smaller resulting in less waste generation from the downstream processes

Optimization of air-sparged plutonium oxalate/hydroxide precipitators

The high cost of waste management and experimental work makes numerical modeling an inexpensive and attractive tool for optimizing and understanding complex chemical processes. Multiphase {open_quotes}bubble{close_quotes} columns are used extensively at the Los Alamos Plutonium Facility for a variety of different applications. No moving parts and efficient mixing characteristics allow them to be used in glovebox operations. Initially, a bubble column for oxalate precipitations is being modeled to identify the effect of various design parameters such as, draft tube location, air sparge rate and vessel geometry. Two-dimensional planar and axisymmetric models have been completed and successfully compared to literature data. Also, a preliminary three-dimensional model has been completed. These results are discussed in this report along with future work

Kink Arrays and Solitary Structures in Optically Biased Phase Transition

An interphase boundary may be immobilized due to nonlinear diffractional interactions in a feedback optical device. This effect reminds of the Turing mechanism, with the optical field playing the role of a diffusive inhibitor. Two examples of pattern formation are considered in detail: arrays of kinks in 1d, and solitary spots in 2d. In both cases, a large number of equilibrium solutions is possible due to the oscillatory character of diffractional interaction.Comment: RevTeX 13 pages, 3 PS-figure

Lipodystrophy in HIV infected patients on long term Antiretroviral therapy in western Kenya

Changes in fat distribution has been observed in patients on highly active antiretroviral therapy. The frequently reported drugs that cause fat redistribution are stavudine and protease inhibitors. Stavudine also causes a high incidence of metabolic complications and peripheral neuropathy

Domain Walls in Non-Equilibrium Systems and the Emergence of Persistent Patterns

Domain walls in equilibrium phase transitions propagate in a preferred direction so as to minimize the free energy of the system. As a result, initial spatio-temporal patterns ultimately decay toward uniform states. The absence of a variational principle far from equilibrium allows the coexistence of domain walls propagating in any direction. As a consequence, *persistent* patterns may emerge. We study this mechanism of pattern formation using a non-variational extension of Landau's model for second order phase transitions. PACS numbers: 05.70.Fh, 42.65.Pc, 47.20.Ky, 82.20MjComment: 12 pages LaTeX, 5 postscript figures To appear in Phys. Rev.

The Speed of Fronts of the Reaction Diffusion Equation

We study the speed of propagation of fronts for the scalar reaction-diffusion equation $u_t = u_{xx} + f(u)$\, with $f(0) = f(1) = 0$. We give a new integral variational principle for the speed of the fronts joining the state $u=1$ to $u=0$. No assumptions are made on the reaction term $f(u)$ other than those needed to guarantee the existence of the front. Therefore our results apply to the classical case $f > 0$ in $(0,1)$, to the bistable case and to cases in which $f$ has more than one internal zero in $(0,1)$.Comment: 7 pages Revtex, 1 figure not include

Application of elastostatic Green function tensor technique to electrostriction in cubic, hexagonal and orthorhombic crystals

The elastostatic Green function tensor approach, which was recently used to treat electrostriction in numerical simulation of domain structure formation in cubic ferroelectrics, is reviewed and extended to the crystals of hexagonal and orthorhombic symmetry. The tensorial kernels appearing in the expressions for effective nonlocal interaction of electrostrictive origin are derived explicitly and their physical meaning is illustrated on simple examples. It is argued that the bilinear coupling between the polarization gradients and elastic strain should be systematically included in the Ginzburg-Landau free energy expansion of electrostrictive materials.Comment: 4 page

Avalanche of Bifurcations and Hysteresis in a Model of Cellular Differentiation

Cellular differentiation in a developping organism is studied via a discrete bistable reaction-diffusion model. A system of undifferentiated cells is allowed to receive an inductive signal emenating from its environment. Depending on the form of the nonlinear reaction kinetics, this signal can trigger a series of bifurcations in the system. Differentiation starts at the surface where the signal is received, and cells change type up to a given distance, or under other conditions, the differentiation process propagates through the whole domain. When the signal diminishes hysteresis is observed

Three-Fold Diffraction Symmetry in Epitaxial Graphene and the SiC Substrate

The crystallographic symmetries and spatial distribution of stacking domains in graphene films on SiC have been studied by low energy electron diffraction (LEED) and dark field imaging in a low energy electron microscope (LEEM). We find that the graphene diffraction spots from 2 and 3 atomic layers of graphene have 3-fold symmetry consistent with AB (Bernal) stacking of the layers. On the contrary, graphene diffraction spots from the buffer layer and monolayer graphene have apparent 6-fold symmetry, although the 3-fold nature of the satellite spots indicates a more complex periodicity in the graphene sheets.Comment: An addendum has been added for the arXiv version only, including one figure with five panels. Published paper can be found at http://link.aps.org/doi/10.1103/PhysRevB.80.24140