Transition analysis of the non-OT G 2 stiff fluid spike solution

We use the technique developed in Moughal’s doctoral thesis to analyse the joint spike transition, revealing new groups of world-lines which undergo distinct transitions, and correcting misconceptions about spikes.

Multi-spike solutions of a hybrid reaction–transport model

Simulations of classical pattern-forming reaction–diffusion systems indicate that they often operate in the strongly nonlinear regime, with the final steady state consisting of a spatially repeating pattern of localized spikes. In activator–inhibitor systems such as the two-component Gierer–Meinhardt (GM) model, one can consider the singular limit D a ≪ D h , where D a and D h are the diffusivities of the activator and inhibitor, respectively. Asymptotic analysis can then be used to analyse the existence and linear stability of multi-spike solutions. In this paper, we analyse multi-spike solutions in a hybrid reaction–transport model, consisting of a slowly diffusing activator and an actively transported inhibitor that switches at a rate α between right-moving and left-moving velocity states. Such a model was recently introduced to account for the formation and homeostatic regulation of synaptic puncta during larval development in Caenorhabditis elegans . We exploit the fact that the hybrid model can be mapped onto the classical GM model in the fast switching limit α → ∞, which establishes the existence of multi-spike solutions. Linearization about the multi-spike solution yields a non-local eigenvalue problem that is used to investigate stability of the multi-spike solution by combining analytical results for α → ∞ with a graphical construction for finite α .

The potential of ingrowth 226-Ra as a new dating tool for late Holocene carbonate deposits

<p>One of the most commonly used methods for dating carbonate deposits, such as speleothems or calcareous sinter deposits, is the <sup>230</sup>Th/U-disequilibrium method. With this approach, ages up to 500 ka can be obtained. However, especially for late Holocene samples, substantial detrital contamination may represent a major problem for radiometric dating. The high <sup>232</sup>Th content, which is an indicator for the amount of detrital contamination, leads to elevated U/Th-ages and generally larger uncertainties, which limit the potential of the corresponding samples for paleoclimate reconstructions. Ingrowth <sup>226</sup>Ra shows the potential to be used as an alternative dating method. In combination with Ba, U and Th, it is possible to date samples with ages up to 8 ka.</p><p>In general, there are three sources of <sup>226</sup>Ra in carbonate samples. (i) excess <sup>226</sup>Ra incorporated during deposition of the material, (ii) detrital material present in the carbonate, and (iii) ingrowth <sup>226</sup>Ra produced by the radioactive decay of its parent <sup>230</sup>Th. Due to the geochemically similar behavior of Ra and Ba, it is possible to correct for the amount of excess <sup>226</sup>Ra. As for the <sup>230</sup>Th/U-disequilibrium method, <sup>232</sup>Th can be used to correct for detrital contamination.</p><p>To test our new method, we applied it to several calcareous sinter samples from different Roman aqueducts, which supplied drinking water to ancient cities such as Jerash or Cordoba . The separation of Ra, Ba, U and Th from the matrix of the samples is performed using a single aliquot of material and different ion exchange resins. Prior to the separation process, a calibrated mixed Ra-Ba-Th-U spike solution was added and equilibrated with the sample solution. The results are not only compared to model simulations for the new system, but also to ages obtained with the conventional <sup>230</sup>Th/U-method.</p>

Explicitly solvable eigenvalue problem and bifurcation delay in sub-diffusive Gierer–Meinhardt model

A spike solution is constructed on the infinite line for a sub-diffusive version of the Gierer–Meinhardt reaction – diffusion model. A non-local eigenvalue problem governs the spike's stability and is explicitly solvable for a certain choice of the kinetic parameters. Its solution generalises former results for the Gierer–Meinhardt model with regular diffusion, and the normal and anomalous systems' properties are juxtaposed. It is shown that a Hopf bifurcation occurs in the sub-diffusive system for larger values of the time parameter τo as compared to the normal counterpart, rendering the anomalous system more stable. Asymptotic solutions are obtained near important values of the diffusion anomaly index γ and collectively shown to be valid over most of the applicable range 0 < γ < 1. A bifurcation delay scenario is described for the sub-diffusive system, and the WKB exponent is computed analytically.

Radionuclide Incorporation in Secondary Crystalline Minerals from Chemical Weathering of Waste Glasses

ABSTRACTData from corrosion and radionuclide sequestration studies on two waste glasses indicated chemical weathering resulted in the formation of zeolite minerals such as herschelite and analcime. We also found that these minerals incorporated ∼8 – 22%, ∼1- 13% and ∼8 – 25% of spiked 125I, 99Tc, and 75Se respectively. Increasing concentrations of radionuclides in spike solution resulted in higher degree of sequestration as observed by significantly higher proportion of stable isotopes (∼70 – 95% I, ∼58 – 100% Re, and ∼100% Se) in secondary minerals. The radionuclide incorporation mechanisms for these minerals appear to be mainly isomorphic substitution of Se and Re in tetrahedral sites and iodide substitution for framework oxygen.

Uniqueness and critical spectrum of boundary spike solutions

We study the properties of single boundary spike solutions for the following singularly perturbed problem It is known that at a non-degenerate critical point of the mean curvature function H(P), there exists a single boundary spike solution. In this paper, we show that the single boundary spike solution is unique and moreover it has exactly (N − 1) small eigenvalues. We obtain the exact asymptotics of the small eigenvalues in terms of H(P).