Effect of Pulsatility on the Transport of Thrombin in an Idealized Cerebral Aneurysm Geometry

Computational models of cerebral aneurysm thrombosis are designed for use in research and clinical applications. A steady flow assumption is applied in many of these models. To explore the accuracy of this assumption a pulsatile-flow thrombin-transport computational fluid dynamics (CFD) model, which uses a symmetrical idealized aneurysm geometry, was developed. First, a steady-flow computational model was developed and validated using data from an in vitro experiment, based on particle image velocimetry (PIV). The experimental data revealed an asymmetric flow pattern in the aneurysm. The validated computational model was subsequently altered to incorporate pulsatility, by applying a data-derived flow function at the inlet boundary. For both the steady and pulsatile computational models, a scalar function simulating thrombin generation was applied at the aneurysm wall. To determine the influence of pulsatility on thrombin transport, the outputs of the steady model were compared to the outputs of the pulsatile model. The comparison revealed that in the pulsatile case, an average of 10.2% less thrombin accumulates within the aneurysm than the steady case for any given time, due to periodic losses of a significant amount of thrombin-concentrated blood from the aneurysm into the parent vessel’s bloodstream. These findings demonstrate that pulsatility may change clotting outcomes in cerebral aneurysms.

A new type of CGO solutions and its applications in corner scattering

We consider corner scattering for the operator ∇ · γ(x)∇ + k2ρ(x) in R2, with γ a positive definite symmetric matrix and ρ a positive scalar function. A corner is referred to one that is on the boundary of the (compact) support of γ(x) − I or ρ(x) − 1, where I stands for the identity matrix. We assume that γ is a scalar function in a small neighborhood of the corner. We show that any admissible incident field will be scattered by such corners, which are allowed to be concave. Moreover, we provide a brief discussion on the existence of non-scattering waves when γ − I has a jump across the corner. In order to prove the results, we construct a new type of complex geometric optics (CGO) solutions.

A New Relativistic Model for Polyatomic Gases Interacting with an Electromagnetic Field

Maxwell’s equations in materials are studied jointly with Euler equations using new knowledge recently appeared in the literature for polyatomic gases. For this purpose, a supplementary conservation law is imposed; one of the results is a restriction on the law linking the magnetic field in empty space and the electric field in materials to the densities of the 4-Lorentz force να and its dual μα: These are the derivatives of a scalar function with respect to να and μα, respectively. Obviously, two of Maxwell’s equations are not evolutive (Gauss’s magnetic and electric laws); to simplify this mathematical problem, a new symmetric hyperbolic set of equations is here presented which uses unconstrained variables and the solutions of the new set of equations, with initial conditions satisfying the constraints, restore the previous constrained set. This is also useful because it allows to maintain an overt covariance that would be lost if the constraints were considered from the beginning. This is also useful because in this way the whole set of equations becomes a symmetric hyperbolic system as usually in Extended Thermodynamics.

Sets of Fractional Operators and Numerical Estimation of the Order of Convergence of a Family of Fractional Fixed-Point Methods

Considering the large number of fractional operators that exist, and since it does not seem that their number will stop increasing soon at the time of writing this paper, it is presented for the first time, as far as the authors know, a simple and compact method to work the fractional calculus through the classification of fractional operators using sets. This new method of working with fractional operators, which may be called fractional calculus of sets, allows generalizing objects of conventional calculus, such as tensor operators, the Taylor series of a vector-valued function, and the fixed-point method, in several variables, which allows generating the method known as the fractional fixed-point method. Furthermore, it is also shown that each fractional fixed-point method that generates a convergent sequence has the ability to generate an uncountable family of fractional fixed-point methods that generate convergent sequences. So, it is presented a method to estimate numerically in a region Ω the mean order of convergence of any fractional fixed-point method, and it is shown how to construct a hybrid fractional iterative method to determine the critical points of a scalar function. Finally, considering that the proposed method to classify fractional operators through sets allows generalizing the existing results of the fractional calculus, some examples are shown of how to define families of fractional operators that satisfy some property to ensure the validity of the results to be generalized.

Stability for the Calderón’s problem for a class of anisotropic conductivities via an ad-hoc misfit functional

We address the stability issue in Calderón’s problem for a special class of anisotropic conductivities of the form σ=γA in a Lipschitz domain Ω⊆R<n>, n≧3, when A is a known Lipschitz continuous matrix-valued function and γ is the unknown piecewise affine scalar function on a given partition of Ω. We define an ad-hoc misfit functional encoding our data and establish estimates for this class of anisotropic conductivities in terms of both the misfit functional and the more commonly used local Dirichlet-to-Neumann map.

New Iterative Method with Application

In this paper, we consider iterative methods to find a simple root of a nonlinear equation f(x) = 0, where f : D∈R→R for an open interval D is a scalar function.

Description of Nonlinear Vortical Flows of Incompressible Fluid in Terms of a Quasi-Potential

As it was shown earlier, a wide class of nonlinear 3-dimensional (3D) fluid flows of incompressible viscous fluid can be described by only one scalar function dubbed the quasi-potential. This class of fluid flows is characterized by a three-component velocity field having a two-component vorticity field. Both these fields may, in general, depend on all three spatial variables and time. In this paper, the governing equations for the quasi-potential are derived and simple illustrative examples of 3D flows in the Cartesian coordinates are presented. The generalisation of the developed approach to the fluid flows in the cylindrical and spherical coordinate frames represents a nontrivial problem that has not been solved yet. In this paper, this gap is filled and the concept of a quasi-potential to the cylindrical and spherical coordinate frames is further developed. A few illustrative examples are presented which can be of interest for practical applications.

Functionally Graded Plate Fracture Analysis Using the Field Boundary Element Method

This paper describes the Field Boundary Element Method (FBEM) applied to the fracture analysis of a 2D rectangular plate made of Functionally Graded Material (FGM) to calculate Mode I Stress Intensity Factor (SIF). The case study of this Field Boundary Element Method is the transversely isotropic plane plate. Its material presents an exponential variation of the elasticity tensor depending on a scalar function of position, i.e., the elastic tensor results from multiplying a scalar function by a constant taken as a reference. Several examples using a parametric representation of the structural response show the suitability of the method that constitutes a Stress Intensity Factor evaluation of Functionally Graded Materials plane plates even in the case of more complex geometries.

Some Recent Developments in theory of Metric Spaces

The topology on a set X is formed by a non-negative real valued scalar function called metric, which may be understood as measuring some quantity. Because some of the set’s attributes are similar, there’s a distance between any two elements, or points. Quite evocative of the common concept of distance that we come across in our daily lives. Because its topology is entirely defined by a scalar distance function, this sort of topological space has a distinct advantage over all others. We may reasonably assume that we are familiar with the qualities of such a function and are capable of dealing with it successfully. Instead, a generic topology is frequently dictated by a set of perhaps abstract rules. Frecklet initially proposed the concept of a metric space in 1906, but it was Hausdorff who coined the phrase metric space a few years later.

Functionally Graded Plate Fracture by Field Boundary Element

The paper describes the Field Boundary Element Method applied to the fracture analysis of a 2D rectangular plate made of Functionally Graded Material to calculate Mode I Stress Intensity Factor. The object of the Field Boundary Element Method is the transversely isotropic plane plate. Its material presents an exponential variation of the elasticity tensor depending on a scalar function of position, i.e., the elastic tensor results from multiplying a scalar function by a constant taken as a reference. Several examples using a parametric representation of the structural response show the suitability of the method that constitutes a sight of Stress Intensity Factor evaluation of Functionally Graded Materials plane plates even in the case of more complex geometries.