A preconditioned numerical solver for stiff nonlinear reaction-diffusion equations with fractional Laplacians that avoids dense matrices

The numerical solution of fractional partial differential equations poses significant computational challenges in regard to efficiency as a result of the spatial nonlocality of the fractional differential operators. The dense coefficient matrices that arise from spatial discretisation of these operators mean that even one-dimensional problems can be difficult to solve using standard methods on grids comprising thousands of nodes or more. In this work we address this issue of efficiency for one-dimensional, nonlinear space-fractional reaction–diffusion equations with fractional Laplacian operators. We apply variable-order, variable-stepsize backward differentiation formulas in a Jacobian-free Newton–Krylov framework to advance the solution in time. A key advantage of this approach is the elimination of any requirement to form the dense matrix representation of the fractional Laplacian operator. We show how a banded approximation to this matrix, which can be formed and factorised efficiently, can be used as part of an effective preconditioner that accelerates convergence of the Krylov subspace iterative solver. Our approach also captures the full contribution from the nonlinear reaction term in the preconditioner, which is crucial for problems that exhibit stiff reactions. Numerical examples are presented to illustrate the overall effectiveness of the solver.

On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process

Over the last 30 years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical models of the interlinked processes that underlie the healing mechanism has yielded considerable insight into aspects of this critical phenomenon that remain difficult to investigate empirically. In particular, the mathematical modeling of angiogenesis, i.e., capillary sprout growth, has offered new paradigms for the understanding of this highly complex and crucial step in the healing pathway. With the recent advances in imaging and cell tracking, the time is now ripe for an appraisal of the utility and importance of mathematical modeling in wound healing angiogenesis research. The purpose of this review is to pedagogically elucidate the conceptual principles that have underpinned the development of mathematical descriptions of wound healing angiogenesis, specifically those that have utilized a continuum reaction-transport framework, and highlight the contribution that such models have made toward the advancement of research in this field. We aim to draw attention to the common assumptions made when developing models of this nature, thereby bringing into focus the advantages and limitations of this approach. A deeper integration of mathematical modeling techniques into the practice of wound healing angiogenesis research promises new perspectives for advancing our knowledge in this area. To this end we detail several open problems related to the understanding of wound healing angiogenesis, and outline how these issues could be addressed through closer cross-disciplinary collaboration.

A polymerase chain reaction-based method for isolating clones from a complimentary DNA library in sheep

The sheep (Ovis aries) is favored by many musculoskeletal tissue engineering groups as a large animal model because of its docile temperament and ease of husbandry. The size and weight of sheep are comparable to humans, which allows for the use of implants and fixation devices used in human clinical practice. The construction of a complimentary DNA (cDNA) library can capture the expression of genes in both a tissue- and time-specific manner. cDNA libraries have been a consistent source of gene discovery ever since the technology became commonplace more than three decades ago. Here, we describe the construction of a cDNA library using cells derived from sheep bones based on the pBluescript cDNA kit. Thirty clones were picked at random and sequenced. This led to the identification of a novel gene, C12orf29, which our initial experiments indicate is involved in skeletal biology. We also describe a polymerase chain reaction-based cDNA clone isolation method that allows the isolation of genes of interest from a cDNA library pool. The techniques outlined here can be applied in-house by smaller tissue engineering groups to generate tools for biomolecular research for large preclinical animal studies and highlights the power of standard cDNA library protocols to uncover novel genes.

Fourier spectral methods for fractional-in-space reaction-diffusion equations

Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains ofRn. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator.

Double diffusive Marangoni convection flow of electrically conducting fluid in a square cavity with chemical reaction

Double diffusive Marangoni convection flow of viscous incompressible electrically conducting fluid in a square cavity is studied in this paper by taking into consideration of the effect of applied magnetic field in arbitrary direction and the chemical reaction. The governing equations are solved numerically by using alternate direct implicit (ADI) method together with the successive over relaxation (SOR) technique. The flow pattern with the effect of governing parameters, namely the buoyancy ratio W, diffusocapillary ratio w, and the Hartmann number Ha, is investigated. It is revealed from the numerical simulations that the average Nusselt number decreases; whereas the average Sherwood number increases as the orientation of magnetic field is shifted from horizontal to vertical. Moreover, the effect of buoyancy due to species concentration on the flow is stronger than the one due to thermal buoyancy. The increase in diffusocapillary parameter, w caus

Unimolecular reaction chemistry of a charge-tagged beta-hydroxyperoxyl radical

β-Hydroxyperoxyl radicals are formed during atmospheric oxidation of unsaturated volatile organic compounds such as isoprene. They are intermediates in the combustion of alcohols. In these environments the unimolecular isomerization and decomposition of β-hydroxyperoxyl radicals may be of importance, either through chemical or thermal activation. We have used ion-trap mass spectrometry to generate the distonic charge-tagged β-hydroxyalkyl radical anion, ˙CH2C(OH)(CH3)CH2C(O)O−, and investigated its subsequent reaction with O2 in the gas phase under conditions that are devoid of complicating radical–radical reactions. Quantum chemical calculations and master equation/RRKM theory modeling are used to rationalize the results and discern a reaction mechanism. Reaction is found to proceed via initial hydrogen abstraction from the γ-methylene group and from the β-hydroxyl group, with both reaction channels eventually forming isobaric product ions due to loss of either ˙OH + HCHO or ˙OH + CO2. Isotope labeling studies confirm that a 1,5-hydrogen shift from the β-hydroxyl functionality results in a hydroperoxyalkoxyl radical intermediate that can undergo further unimolecular dissociations. Furthermore, this study confirms that the facile decomposition of β-hydroxyperoxyl radicals can yield ˙OH in the gas phase.

A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems

In order to simulate stiff biochemical reaction systems, an explicit exponential Euler scheme is derived for multidimensional, non-commutative stochastic differential equations with a semilinear drift term. The scheme is of strong order one half and A-stable in mean square. The combination with this and the projection method shows good performance in numerical experiments dealing with an alternative formulation of the chemical Langevin equation for a human ether a-go-go related gene ion channel mode

Revisiting the CO oxidation reaction on various Au/TiO2catalysts: Roles of the surface OH groups and the reaction mechanism

This work aims to understand the influence of TiO2 surface structure in Au/TiO2 catalysts on CO oxidation. Au nanoparticles (3 wt%) in the range of 4 to 8 nm were loaded onto four kinds of TiO2 surfaces, which had different surface structures and were synthesized by calcining hydrogen titanate nanotubes at various temperatures and in different atmospheres. The Au catalyst supported on anatase nanorods exhibited the highest activity in CO oxidation at 30 °C among all the five Au/TiO2 catalysts including the reference catalyst of Au/TiO2-P25. X-ray photoelectron spectroscopy (XPS) and infrared emission spectra (IES) results indicate that the anatase nanorods have the most active surface on which water molecules can be strongly adsorbed and OH groups can be formed readily. Theoretical calculation indicates that the surface OH can facilitate the O2 adsorption on the anatase surface. Such active surface features are conducive to the O2 activation and CO oxidation

Combining the diaza-Diels-Alder reaction and palladium-catalyzed aminations to prepare amino-substituted porphyrins

A strategy to tackle the synthesis of azoporphyrins with unsubstituted terminal meso positions was investigated. It comprised the combination of diaza-Diels–Alder (DADA) reaction of 1,3-dienes with dialkyl azodicarboxylates, decarboxylative hydrolysis of the bis(carbamates), palladium-catalyzed amination of bromoporphyrin precursors, and retro-DADA reactions to release the ultimate targets. The somewhat confused historical results on the DADA reactions of 1,3-cyclohexadiene were clarified, but the hydrolyses yielded extremely air-sensitive amines which decomposed completely in minutes via autooxidation and retro-DADA reaction. With anthracene or 2,3-dimethyl-1,3-butadiene as the diene, the synthesis of azoporphyrin was not achieved but three amino-substituted porphyrins were obtained in moderate yields under mild conditions. The X-ray crystal structures of several of the intermediates and the final aminoanthracene-porphyrin nickel(II) complex were determined.

A New Tetrahydrofurannulation Via Tandem Radical Cyclization Reaction-Reductive Deoxygenation Sequence

Treatment of bromoketals 2, derived from allyl alcohols 1, with tributyltin chloride, sodium cyanoborohydride and AIBN furnishes the tetrahydrofurannulated products 3 via a 5-exo-trig radical cyclisation reaction followed by reductive cleavage of ketal 4.

Vanadium Catalysis in Bromoperoxidation Reaction

Peroxidative bromination of phenol red to its tetrabromo derivative, bromophenol blue, required vanadate in addition to H2O2 when carried out in the pH range of 5-7. Excess H2O2, with ratio of H2O2:vanadate of 2:1 and above, prevented the reaction. Diperoxovanadate, known to be formed in such reaction mixtures, was ineffective by itself and needed uncomplexed vanadate (V-v) or vanadyl (V-iv) to support bromination. Bromide-assisted reduction of the excess vanadate to vanadyl appeared to be an essential secondary reaction. In the absence of phenol red oxygen was released, and concomitantly bromide was oxidized to a form competent to brominate phenol red added after termination of oxygen release. These findings indicated participation of reactions leading to an intermediate derived from vanadyl and diperoxovanadate, previously described from this laboratory (Arch. Biochem. Biophys. 316, 319-326, 1995). Continuous bromination of phenol red occurred when glucose oxidase-glucose system was used as a source of continuous flow of H2O2. A scheme of reactions involving peroxovanadates (mono-, di-, mu-, and bromo-) is proposed for the formation and utilization of an active brominating species and for the recycling of the product, mono-peroxovanadate, by H2O2, which explains the catalytic role of vanadium in the bromoperoxidation reaction.

In situ reaction furnace for real-time XRD studies

The new furnace at the Materials Characterization by X-ray Diffraction beamline at Elettra has been designed for powder diffraction measurements at high temperature (up to 1373 K at the present state). Around the measurement region the geometry of the radiative heating element assures a negligible temperature gradient along the capillary and can accommodate either powder samples in capillary or small flat samples. A double capillary holder allows flow-through of gas in the inner sample capillary while the outer one serves as the reaction chamber. The furnace is coupled to a translating curved imaging-plate detector, allowing the collection of diffraction patterns up to 2[theta] [asymptotically equal to] 130°.

Nanoporous Pt with High Surface Area by Reaction-Limited Aggregation of Nanoparticles

Nanoporous structures with high active surface areas are critical for a variety of applications. Here, we present a general templateless strategy to produce such porous structures by controlled aggregation of nanostructured subunits and apply the principles for synthesizing nanoporous Pt for electrocatalytic oxidation of methanol. The nature of the aggregate produced is controlled by tuning the electrostatic interaction between surfactant-free nanoparticles in the solution phase. When the repulsive force between the particles is very large, the particles are stabilized in the solution while instantaneous aggregation leading to fractal-like structures results when the repulsive force is very low. Controlling the repulsive interaction to an optimum, intermediate value results in the formation of compact structures with very large surface areas. In the case of Pt, nanoporous clusters with an extremely high specific surface area (39 m(2)/g) and high activity for methanol oxidation have been produced. Preliminary investigations indicate that the method is general and can be easily extended to produce nanoporous structures of many inorganic materials.

Enantiospecific approach to the tricyclic core structure of tricycloillicinone, ialibinones, and takaneones via ring-closing metathesis reaction

Enantiospecific synthesis of the tricyclic core structure present in the biologically active natural products tricycloillicinone, ialibinones, and takaneones, starting from the readily available campholenaldehyde employing a transannular RCM reaction as the key step, has been accomplished.

Metal-free graphitic carbon nitride as mechano-catalyst for hydrogen evolution reaction

Graphitic carbon nitride (g-C3N4), as a promising metal-free catalyst for photo-catalytic and electrochemical water splitting, has recently attracted tremendous research interest. However, the underlying catalytic mechanism for the hydrogen evolution reaction (HER) is not fully understood. By using density functional theory calculations, here we have established that the binding free energy of hydrogen atom (ΔGH∗0) on g-C3N4 is very sensitive to mechanical strain, leading to substantial tuning of the HER performance of g-C3N4 at different coverages. The experimentally-observed high HER activity in N-doped graphene supported g-C3N4 (Zheng et al., 2014) is actually attributed to electron-transfer induced strain. A more practical strategy to induce mechanical strain in g-C3N4 is also proposed by doping a bridge carbon atom in g-C3N4 with an isoelectronic silicon atom. The calculated ΔGH∗0 on the Si-doped g-C3N4 is ideal for HER. Our results indicate that g-C3N4 would be an excellent metal-free mechano-catalyst for HER and this finding is expected to guide future experiments to efficiently split water into hydrogen based on the g-C3N4 materials.