SUFFICIENT CONDITIONS ON DIFFUSIVITY FOR THE EXISTENCE AND NONEXISTENCE OF STABLE EQUILIBRIA WITH NONLINEAR FLUX ON THE BOUNDARY

A reaction-diffusion equation with variable diffusivity and non-linear flux boundary condition is considered. The goal is to give sufficient conditions on the diffusivity function for nonexistence and also for existence of nonconstant stable stationary solutions. Applications are given for the main result of nonexistence.

Coupling biomechanics to a cellular level model: An approach to patient-specific image driven multi-scale and multi-physics tumor simulation

Modeling of tumor growth has been performed according to various approaches addressing different biocomplexity levels and spatiotemporal scales. Mathematical treatments range from partial differential equation based diffusion models to rule-based cellular level simulators, aiming at both improving our quantitative understanding of the underlying biological processes and, in the mid- and long term, constructing reliable multi-scale predictive platforms to support patient-individualized treatment planning and optimization. The aim of this paper is to establish a multi-scale and multi-physics approach to tumor modeling taking into account both the cellular and the macroscopic mechanical level. Therefore, an already developed biomodel of clinical tumor growth and response to treatment is self-consistently coupled with a biomechanical model. Results are presented for the free growth case of the imageable component of an initially point-like glioblastoma multiforme tumor. The composite model leads to significant tumor shape corrections that are achieved through the utilization of environmental pressure information and the application of biomechanical principles. Using the ratio of smallest to largest moment of inertia of the tumor material to quantify the effect of our coupled approach, we have found a tumor shape correction of 20\% by coupling biomechanics to the cellular simulator as compared to a cellular simulation without preferred growth directions. We conclude that the integration of the two models provides additional morphological insight into realistic tumor growth behavior. Therefore, it might be used for the development of an advanced oncosimulator focusing on tumor types for which morphology plays an important role in surgical and/or radio-therapeutic treatment planning.

Invariant barriers to reactive front propagation in fluid flows

We present theory and experiments on the dynamics of reaction fronts in two-dimensional, vortex-dominated flows, for both time-independent and periodically driven cases. We find that the front propagation process is controlled by one-sided barriers that are either fixed in the laboratory frame (time-independent flows) or oscillate periodically (periodically driven flows). We call these barriers burning invariant manifolds (BIMs), since their role in front propagation is analogous to that of invariant manifolds in the transport and mixing of passive impurities under advection. Theoretically, the BIMs emerge from a dynamical systems approach when the advection-reaction-diffusion dynamics is recast as an ODE for front element dynamics. Experimentally, we measure the location of BIMs for several laboratory flows and confirm their role as barriers to front propagation.

Barriers to front propagation in ordered and disordered vortex flows

We present experiments on reactive front propagation in a two-dimensional (2D) vortex chain flow (both time-independent and time-periodic) and a 2D spatially disordered (time-independent) vortex-dominated flow. The flows are generated using magnetohydrodynamic forcing techniques, and the fronts are produced using the excitable, ferroin-catalyzed Belousov-Zhabotinsky chemical reaction. In both of these flows, front propagation is dominated by the presence of burning invariant manifolds (BIMs) that act as barriers, similar to invariant manifolds that dominate the transport of passive impurities. Convergence of the fronts onto these BIMs is shown experimentally for all of the flows studied. The BIMs are also shown to collapse onto the invariant manifolds for passive transport in the limit of large flow velocities. For the disordered flow, the measured BIMs are compared to those predicted using a measured velocity field and a three-dimensional set of ordinary differential equations that describe the dynamics of front propagation in advection-reaction-diffusion systems.

Calcium waves driven by "sensitization" wave-fronts

OBJECTIVE: Cellular Ca(2+) waves are understood as reaction-diffusion systems sustained by Ca(2+)-induced Ca(2+) release (CICR) from Ca(2+) stores. Given the recently discovered sensitization of Ca(2+) release channels (ryanodine receptors; RyRs) of the sarcoplasmic reticulum (SR) by luminal SR Ca(2+), waves could also be driven by RyR sensitization, mediated by SR overloading via Ca(2+) pump (SERCA), acting in tandem with CICR. METHODS: Confocal imaging of the Ca(2+) indicator fluo-3 was combined with UV-flash photolysis of caged compounds and the whole-cell configuration of the patch clamp technique to carry out these experiments in isolated guinea pig ventricular cardiomyocytes. RESULTS: Upon sudden slowing of the SERCA in cardiomyocytes with a photoreleased inhibitor, waves indeed decelerated immediately. No secondary changes of Ca(2+) signaling or SR Ca(2+) content due to SERCA inhibition were observed in the short time-frame of these experiments. CONCLUSIONS: Our findings are consistent with Ca(2+) loading resulting in a zone of RyR 'sensitization' traveling within the SR, but inconsistent with CICR as the predominant mechanism driving the Ca(2+) waves. This alternative mode of RyR activation is essential to fully conceptualize cardiac arrhythmias triggered by spontaneous Ca(2+) release.

DYNAMICS AND CONTROL OF REACTIVE DISTILLATION PROCESS FOR MONOMER SYNTHESIS OF POLYCARBONATE PLANTS

Polycarbonate (PC) is an important engineering thermoplastic that is currently produced in large industrial scale using bisphenol A and monomers such as phosgene. Since phosgene is highly toxic, a non-phosgene approach using diphenyl carbonate (DPC) as an alternative monomer, as developed by Asahi Corporation of Japan, is a significantly more environmentally friendly alternative. Other advantages include the use of CO2 instead of CO as raw material and the elimination of major waste water production. However, for the production of DPC to be economically viable, reactive-distillation units are needed to obtain the necessary yields by shifting the reaction-equilibrium to the desired products and separating the products at the point where the equilibrium reaction occurs. In the field of chemical reaction engineering, there are many reactions that are suffering from the low equilibrium constant. The main goal of this research is to determine the optimal process needed to shift the reactions by using appropriate control strategies of the reactive distillation system. An extensive dynamic mathematical model has been developed to help us investigate different control and processing strategies of the reactive distillation units to increase the production of DPC. The high-fidelity dynamic models include extensive thermodynamic and reaction-kinetics models while incorporating the necessary mass and energy balance of the various stages of the reactive distillation units. The study presented in this document shows the possibility of producing DPC via one reactive distillation instead of the conventional two-column, with a production rate of 16.75 tons/h corresponding to start reactants materials of 74.69 tons/h of Phenol and 35.75 tons/h of Dimethyl Carbonate. This represents a threefold increase over the projected production rate given in the literature based on a two-column configuration. In addition, the purity of the DPC produced could reach levels as high as 99.5% with the effective use of controls. These studies are based on simulation done using high-fidelity dynamic models.

Geochemistry of abyssal peridotites from ODP Hole 209-1274A

Aqueous dihydrogen (H2,aq) is produced in copious amounts when seawater interacts with peridotite and H2O oxidizes ferrous iron in olivine to ferric iron in secondary magnetite and serpentine. Poorly understood in this process is the partitioning of iron and its oxidation state in serpentine, although both impose an important control on dihydrogen production. We present results of detailed petrographic, mineral chemical, magnetic and Mößbauer analyses of partially to fully serpentinized peridotites from the Ocean Drilling Program (ODP) Leg 209, Mid-Atlantic Ridge (MAR) 15°N area. These results are used to constrain the fate of iron during serpentinization and are compared with phase equilibria considerations and peridotite-seawater reaction path models. In samples from Hole 1274A, mesh-rims reveal a distinct in-to-out zoning from brucite at the interface with primary olivine, followed by a zone of serpentine + brucite ± magnetite and finally serpentine + magnetite in the outermost mesh-rim. The compositions of coexisting serpentine (Mg# 95) and brucite (Mg# 80) vary little throughout the core. About 30-50% of the iron in serpentine/brucite mesh-rims is trivalent, irrespective of subbasement depth and protolith (harzburgite versus dunite). Model calculations suggest that both partitioning and oxidation state of iron are very sensitive to temperature and water-to-rock ratio during serpentinization. At temperatures above 330 °C the dissolution of olivine and coeval formation of serpentine, magnetite and dihydrogen depends on the availability of an external silica source. At these temperatures the extent of olivine serpentinization is insufficient to produce much hydrogen, hence conditions are not reducing enough to form awaruite. At T < 330 °C, hydrogen generation is facilitated by the formation of brucite, as dissolution of olivine to form serpentine, magnetite and brucite requires no addition of silica. The model calculations suggest that the iron distribution observed in serpentine and brucite is consistent with formation temperatures ranging from <150 to 250 °C and bulk water-to-rock ratios between 0.1 and 5. These conditions coincide with peak hydrogen fugacities during serpentinization and are conducive to awaruite formation during main stage serpentinization. The development of the common brucite rims around olivine is either due to an arrested reaction olivine -> brucite -> serpentine + brucite, or reflects metastable olivine-brucite equilibria developing in the strong gradient in silica activity between orthopyroxene (talc-serpentine) and olivine (serpentine-brucite).

(Table 7) Representative electron microprobe analyses for natroalunite and larger FeOx spheroids of experiment ADSU6

Acid-sulfate alteration of basalt by SO2-bearing volcanic vapors has been proposed as one possible origin for sulfate-rich deposits on Mars. To better define mineralogical signatures of acid-sulfate alteration, laboratory experiments were performed to investigate alteration pathways and geochemical processes during reaction of basalt with sulfuric acid. Pyroclastic cinders composed of phenocrysts including plagioclase, olivine, and augite embedded in glass were reacted with sulfuric acid at 145 °C for up to 137 days at a range of fluid : rock ratios. During the experiments, the phenocrysts reacted rapidly to form secondary products, while the glass was unreactive. Major products included amorphous silica, anhydrite, and Fe-rich natroalunite, along with minor iron oxides/oxyhydroxides (probably hematite) and trace levels of other sulfates. At the lowest fluid : rock ratio, hexahydrite and an unidentified Fe-silicate phase also occurred as major products. Reaction-path models indicated that formation of the products required both slow dissolution of glass and kinetic inhibitions to precipitation of a number of minerals including phyllosilicates and other aluminosilicates as well as Al- and Fe-oxides/oxyhydroxides. Similar models performed for Martian basalt compositions predict that the initial stages of acid-sulfate alteration of pyroclastic deposits on Mars should result in formation of amorphous silica, anhydrite, Fe-bearing natroalunite, and kieserite, along with relict basaltic glass. In addition, analysis of the experimental products indicates that Fe-bearing natroalunite produces a Mössbauer spectrum closely resembling that of jarosite, suggesting that it should be considered an alternative to the component in sulfate-rich bedrocks at Meridiani Planum that has previously been identified as jarosite.

Whole-rock geochemical analyses of serpentinized harzburgites from ODP Site 209-1270

Small-scale shear zones are present in drillcore samples of abyssal peridotites from the Mid-Atlantic ridge at 15°20'N (Ocean Drilling Program Leg 209). The shear zones act as pathways for both evolved melts and hydrothermal fluids. We examined serpentinites directly adjacent to such zones to evaluate chemical changes resulting from melt-rock and fluid-rock interaction and their influence on the mineralogy. Compared to fresh harzburgite and melt-unaffected serpentinites, serpentinites adjacent to melt-bearing veins show a marked enrichment in rare earth elements (REE), strontium and high field strength elements (HFSE) zirconium and niobium. From comparison with published chemical data of variably serpentinized and melt-unaffected harzburgites, one possible interpretation is that interaction with the adjacent melt veins caused the enrichment in HFSE, whereas the REE contents might also be enriched due to hydrothermal processes. Enrichment in alumina during serpentinization is corroborated by reaction path models for interaction of seawater with harzburgite-plagiogranite mixtures. These models explain both increased amounts of alumina in the serpentinizing fluid for increasing amounts of plagiogranitic material mixed with harzburgite, and the absence of brucite from the secondary mineralogy due to elevated silica activity. By destabilizing brucite, nearby melt veins might fundamentally influence the low-temperature alteration behaviour of serpentinites. Although observations and model results are in general agreement, due to absence of any unaltered protolith a quantification of element transport during serpentinization is not straightforward.

Integration of III-V materials on Silicon Substrates for Multi-junction Solar Cell Applications

The work presented here aims to reduce the cost of multijunction solar cell technology by developing ways to manufacture them on cheap substrates such as silicon. In particular, our main objective is the growth of III-V semiconductors on silicon substrates for photovoltaic applications. The goal is to create a GaAsP/Si virtual substrates onto which other III-V cells could be integrated with an interesting efficiency potential. This technology involves several challenges due to the difficulty of growing III-V materials on silicon. In this paper, our first work done aimed at developing such structure is presented. It was focused on the development of phosphorus diffusion models on silicon and on the preparation of an optimal silicon surface to grow on it III-V materials.

Twist grain boundaries in three-dimensional lamellar Turing structures

Steady spatial self-organization of three-dimensional chemical reaction-diffusion systems is discussed with the emphasis put on the possible defects that may alter the Turing patterns. It is shown that one of the stable defects of a three-dimensional lamellar Turing structure is a twist grain boundary embedding a Scherk minimal surface.

Microtubule self-organization is gravity-dependent

Although weightlessness is known to affect living cells, the manner by which this occurs is unknown. Some reaction-diffusion processes have been theoretically predicted as being gravity-dependent. Microtubules, a major constituent of the cellular cytoskeleton, self-organize in vitro by way of reaction-diffusion processes. To investigate how self-organization depends on gravity, microtubules were assembled under low gravity conditions produced during space flight. Contrary to the samples formed on an in-flight 1 × g centrifuge, the samples prepared in microgravity showed almost no self-organization and were locally disordered.

Molecular phase space transport in water:non-stationary random walk model

Molecular transport in phase space is crucial for chemical reactions because it defines how pre-reactive molecular configurations are found during the time evolution of the system. Using Molecular Dynamics (MD) simulated atomistic trajectories we test the assumption of the normal diffusion in the phase space for bulk water at ambient conditions by checking the equivalence of the transport to the random walk model. Contrary to common expectations we have found that some statistical features of the transport in the phase space differ from those of the normal diffusion models. This implies a non-random character of the path search process by the reacting complexes in water solutions. Our further numerical experiments show that a significant long period of non-stationarity in the transition probabilities of the segments of molecular trajectories can account for the observed non-uniform filling of the phase space. Surprisingly, the characteristic periods in the model non-stationarity constitute hundreds of nanoseconds, that is much longer time scales compared to typical lifetime of known liquid water molecular structures (several picoseconds).

Numerical Analysis of Chemical Reactions by Monte Carlo Simulation

Добри Данков, Владимир Русинов, Мария Велинова, Жасмина Петрова - Изследвана е химическа реакция чрез два начина за моделиране на вероятността за химическа реакция използвайки Direct Simulation Monte Carlo метод. Изследван е порядъка на разликите при температурите и концентрациите чрез тези начини. Когато активността на химическата реакция намалява, намаляват и разликите между концентрациите и температурите получени по двата начина. Ключови думи: Механика на флуидите, Кинетична теория, Разреден газ, DSMC

Noise-induced standing waves in oscillatory systems with time-delayed feedback

In oscillatory reaction-diffusion systems, time-delay feedback can lead to the instability of uniform oscillations with respect to formation of standing waves. Here, we investigate how the presence of additive, Gaussian white noise can induce the appearance of standing waves. Combining analytical solutions of the model with spatio-temporal simulations, we find that noise can promote standing waves in regimes where the deterministic uniform oscillatory modes are stabilized. As the deterministic phase boundary is approached, the spatio-temporal correlations become stronger, such that even small noise can induce standing waves in this parameter regime. With larger noise strengths, standing waves could be induced at finite distances from the (deterministic) phase boundary. The overall dynamics is defined through the interplay of noisy forcing with the inherent reaction-diffusion dynamics.