A High-Order Kernel Method for Diffusion and Reaction-Diffusion Equations on Surfaces

In this paper we present a high-order kernel method for numerically solving diffusion and reaction-diffusion partial differential equations (PDEs) on smooth, closed surfaces embedded in $\mathbb{R}^d$. For two-dimensional surfaces embedded in $\mathbb{R}^3$, these types of problems have received growing interest in biology, chemistry, and computer graphics to model such things as diffusion of chemicals on biological cells or membranes, pattern formations in biology, nonlinear chemical oscillators in excitable media, and texture mappings. Our kernel method is based on radial basis functions (RBFs) and uses a semi-discrete approach (or the method-of-lines) in which the surface derivative operators that appear in the PDEs are approximated using collocation. The method only requires nodes at "scattered" locations on the surface and the corresponding normal vectors to the surface. Additionally, it does not rely on any surface-based metrics and avoids any intrinsic coordinate systems, and thus does not suffer from any coordinate distortions or singularities. We provide error estimates for the kernel-based approximate surface derivative operators and numerically study the accuracy and stability of the method. Applications to different non-linear systems of PDEs that arise in biology and chemistry are also presented

A High-Order Radial Basis Function (RBF) Leray Projection Method for the Solution of the Incompressible Unsteady Stokes Equations

A new projection method based on radial basis functions (RBFs) is presented for discretizing the incompressible unsteady Stokes equations in irregular geometries. The novelty of the method comes from the application of a new technique for computing the Leray-Helmholtz projection of a vector field using generalized interpolation with divergence-free and curl-free RBFs. Unlike traditional projection methods, this new method enables matching both tangential and normal components of divergence-free vector fields on the domain boundary. This allows incompressibility of the velocity field to be enforced without any time-splitting or pressure boundary conditions. Spatial derivatives are approximated using collocation with global RBFs so that the method only requires samples of the field at (possibly scattered) nodes over the domain. Numerical results are presented demonstrating high-order convergence in both space (between 5th and 6th order) and time (up to 4th order) for some model problems in two dimensional irregular geometries.Comment: 34 pages, 8 figure

Lyophilisation of lentiviral pseudotypes for the development and distribution of virus neutralisation assay kits for rabies, Marburg and influenza viruses

Purpose: Some conventional serological assays can accurately quantify neutralising antibody responses raised against epitopes on virus glycoproteins, enabling mass vaccine evaluation and serosurveillance studies to take place. However, these assays often necessitate the handling of wild-type virus in expensive high biosafety laboratories, which restricts the scope of their application, particularly in resource-deprived areas. A solution to this issue is the use of lentiviral pseudotype viruses (PVs)—chimeric, replication-deficient virions that imitate the binding and entry mechanisms of their wild-type equivalents. Pseudotype virus neutralisation assays (PVNAs) bypass high biosafety requirements and yield comparable results to established assays. This study explores the potential for using lyophilisation of pseudotypes as a cost-effective, alternative means for production, distribution and storage of a PVNAbased diagnostic kit. Methods & Materials: Rabies, Marburg and H5 subtype Influenza virus pseudotypes were each suspended in cryoprotectant solutions of various molarities and subjected to freeze-drying before incubation at a variety of temperatures, humidities and time periods. Samples were then employed in antibody neutralisation assays using specific sera. Results: High levels of PV titre were retained post-lyophilisation, with acceptable levels of virus activity maintained even after medium-term storage in tropical conditions. Also, the performance of PVs in neutralisation assays was not affected by the lyophilisation process. Conclusion: These results confirm the viability of a freeze-dried PVNA-based diagnostic kit, which could considerably facilitate in-field serology for a number of clinically important viruses

A Radial Basis Function Method for Computing Helmholtz-Hodge Decompositions

A radial basis function (RBF) method based on matrix-valued kernels is presented and analyzed for computing two types of vector decompositions on bounded domains: one where the normal component of the divergence-free part of the field is specified on the boundary, and one where the tangential component of the curl-free part of the field specified. These two decompositions can then be combined to obtain a full Helmholtz-Hodge decomposition of the field, i.e. the sum of divergence-free, curl-free, and harmonic fields. All decompositions are computed from samples of the field at (possibly scattered) nodes over the domain, and all boundary conditions are imposed on the vector fields, not their potentials, distinguishing this technique from many current methods. Sobolev-type error estimates for the various decompositions are provided and demonstrated with numerical examples

Effective Temperature Of Uranus

NASA NGR 09-015-047, NGR 22-007-270, NGR 44-012-152Astronom

Study of Target Enhancement Algorithms to Counter the Hostile Nuclear Environment

A necessary requirement of strategic defense is the detection of incoming nuclear warheads in an environment that may include nuclear detonations of undetected or missed target warheads. A computer model is described which simulates incoming warheads as distant endoatmospheric targets. A model of the expected electromagnetic noise present in a nuclear environment is developed using estimates of the probability distributions. Predicted atmospheric effects are also included. Various image enhancement algorithms, both linear and nonlinear, are discussed concerning their anticipated ability to suppress the noise and atmospheric effects of the nuclear environment. These algorithms are then tested, using the combined target and noise models, and evaluated in terms of the stated figures of merit

Fast-track fisticuffs? An ethnographic exploration of time and white-collar boxing

Whilst white-collar boxing at first appears to be named according to the social class of its practitioners, this paper will argue that this initial appearance is misleading. Based on the analysis of 32 interviews and six months of ethnographic data collection at a boxing club in the English Midlands, it argues that white-collar boxers do not recognise the classed connotations of the term white-collar, to which sociologists tend to be accustomed. Within this lifeworld, white-collar has become a temporal signifier, referring to a version of the sport in which participation is for beginners and limited to eight weeks, culminating in a public boxing match in front of a large crowd. This eight-week participation model is outlined and identified as being drastically different from other forms of boxing, which are emblematic of modernity. White-collar boxing therefore provides entry into a wider discussion on the social construction of time. Acceleration and condensation of time are routinely discussed in this field, and it is suggested that a conceptual split between condensed and accelerated time allows for this white-collar boxing to be understood. Ultimately, white-collar boxing is theorised as the condensed reproduction of the idealised career of the professional boxer