Solutions of fourth-order parabolic equation modeling thin film growth

In this paper we study the well-posedness for a fourth-order parabolic equation modeling epitaxial thin film growth. Using Kato's Method [1], [2] and [3] we establish existence, uniqueness and regularity of the solution to the model, in suitable spaces, namelyC⁰([0,T];L^p(Ω)) where  with 1<α<2, n∈N and n≥2. We also show the global existence solution to the nonlinear parabolic equations for small initial data. Our main tools are L_p–L_q-estimates, regularization property of the linear part of e^−tΔ2 and successive approximations. Furthermore, we illustrate the qualitative behavior of the approximate solution through some numerical simulations. The approximate solutions exhibit some favorable absorption properties of the model, which highlight the stabilizing effect of our specific formulation of the source term associated with the upward hopping of atoms. Consequently, the solutions describe well some experimentally observed phenomena, which characterize the growth of thin film such as grain coarsening, island formation and thickness growth.

Using particle dispersal models to assist in the conservation and recovery of the overexploited native oyster (Ostrea edulis) in an enclosed sea lough

Oyster populations around the world have seen catastrophic decline which has been largely attributed to overexploitation, disease and pollution. While considerable effort and resources have been implemented into restoring these important environmental engineers, the success of oyster populations is often limited by poor understanding of site-specific dispersal patterns of propagules. Water-borne transport is a key factor controlling or regulating the dispersal of the larval stage of benthic marine invertebrates which have limited mobility. The distribution of the native oyster Ostrea edulis in Strangford Lough, Northern Ireland, together with their densities and population structure at subtidal and intertidal sites has been documented at irregular intervals between 1997 and 2013. This paper revisits this historical data and considers whether different prevailing environmental conditions can be used to explain the distribution, densities and population structure of O. edulis in Strangford Lough. The approach adopted involved comparing predictive 2D hydrodynamic models coupled with particle tracking to simulate the dispersal of oyster larvae with historical and recent field records of the distribution of both subtidal and intertidal, populations since 1995. Results from the models support the hypothesis that commercial stocks of O. edulis introduced into Strangford Lough in the 1990s resulted in the re-establishment of wild populations of oysters in the Northern Basin which in turn provided a potential source of propagules for subtidal populations. These results highlight that strategic site selection (while inadvertent in the case of the introduced population in 1995) for the re-introduction of important shellfish species can significantly accelerate their recovery and restoration.

Novel tools for conservation genomics: comparing two high-throughput approaches for SNP discovery in the transcriptome of the European hake

The growing accessibility to genomic resources using next-generation sequencing (NGS) technologies has revolutionized the application of molecular genetic tools to ecology and evolutionary studies in non-model organisms. Here we present the case study of the European hake (Merluccius merluccius), one of the most important demersal resources of European fisheries. Two sequencing platforms, the Roche 454 FLX (454) and the Illumina Genome Analyzer (GAII), were used for Single Nucleotide Polymorphisms (SNPs) discovery in the hake muscle transcriptome. De novo transcriptome assembly into unique contigs, annotation, and in silico SNP detection were carried out in parallel for 454 and GAII sequence data. High-throughput genotyping using the Illumina GoldenGate assay was performed for validating 1,536 putative SNPs. Validation results were analysed to compare the performances of 454 and GAII methods and to evaluate the role of several variables (e.g. sequencing depth, intron-exon structure, sequence quality and annotation). Despite well-known differences in sequence length and throughput, the two approaches showed similar assay conversion rates (approximately 43%) and percentages of polymorphic loci (67.5% and 63.3% for GAII and 454, respectively). Both NGS platforms therefore demonstrated to be suitable for large scale identification of SNPs in transcribed regions of non-model species, although the lack of a reference genome profoundly affects the genotyping success rate. The overall efficiency, however, can be improved using strict quality and filtering criteria for SNP selection (sequence quality, intron-exon structure, target region score).

On the numerical solution of the 2d wave equation with compact fdtd schemes

This paper discusses compact-stencil finite difference time domain (FDTD) schemes for approximating the 2D wave equation in the context of digital audio. Stability, accuracy, and efficiency are investigated and new ways of viewing and interpreting the results are discussed. It is shown that if a tight accuracy constraint is applied, implicit schemes outperform explicit schemes. The paper also discusses the relevance to digital waveguide mesh modelling, and highlights the optimally efficient explicit scheme.

Carbon Sink Conservation and Global Justice: Benefiting, Free Riding and Non-Compliance

It is often assumed that in order to avoid the most severe consequences of global anthropogenic climate change we have to preserve our existing carbon sinks, such as for instance tropical forests. Global carbon sink conservation raises a host of normative issues, though, since it is debatable who should pay the costs of carbon sink conservation, who has the duty to protect which sinks, and how far the duty to conserve one’s carbon sinks actually extends, especially if it conflicts with other duties one might have. According to some, forested states like Ecuador have a duty to preserve their tropical forests while the rich states of the global North have a duty of fairness to compensate states like Ecuador for the costs they incur. My aim in this paper is to critically analyse this standard line of argument and to criticise its validity both internally (i.e. with regard to its normative conclusion based on its premises) and externally (i.e. with regard to the argument’s underlying assumptions and its lack of contextualisation). As I will argue, the duty to conserve one’s forests is only a particular instantiation of a wider, more general duty to contribute towards global climate justice for which the context in which one operates (e.g. whether other agents are complying with their duties of global climate justice or not) matters significantly.

A Schamel equation for ion acoustic waves in superthermal plasmas

An investigation of the propagation of ion acoustic waves in nonthermal plasmas in the presence of trapped electrons has been undertaken. This has been motivated by space and laboratory plasma observations of plasmas containing energetic particles, resulting in long-tailed distributions, in combination with trapped particles, whereby some of the plasma particles are confined to a finite region of phase space. An unmagnetized collisionless electron-ion plasma is considered, featuring a non-Maxwellian-trapped electron distribution, which is modelled by a kappa distribution function combined with a Schamel distribution. The effect of particle trapping has been considered, resulting in an expression for the electron density. Reductive perturbation theory has been used to construct a KdV-like Schamel equation, and examine its behaviour. The relevant configurational parameters in our study include the superthermality index κ and the characteristic trapping parameter β. A pulse-shaped family of solutions is proposed, also depending on the weak soliton speed increment u₀. The main modification due to an increase in particle trapping is an increase in the amplitude of solitary waves, yet leaving their spatial width practically unaffected. With enhanced superthermality, there is a decrease in both amplitude and width of solitary waves, for any given values of the trapping parameter and of the incremental soliton speed. Only positive polarity excitations were observed in our parametric investigation.