DSpace Collection:
http://hdl.handle.net/2440/1087
Mon, 24 Jun 2019 17:56:46 GMT2019-06-24T17:56:46ZApproximation of ruin probabilities via Erlangized scale mixtures
http://hdl.handle.net/2440/119613
Title: Approximation of ruin probabilities via Erlangized scale mixtures
Author: Peralta, O.; Rojas-Nandayapa, L.; Xie, W.; Yao, H.
Abstract: In this paper, we extend an existing scheme for numerically calculating the probability of ruin of a classical Cramér–Lundbergreserve process having absolutely continuous but otherwise general claim size distributions. We employ a dense class of distributions that we denominate Erlangized scale mixtures (ESM) that correspond to nonnegative and absolutely continuous distributions which can be written as a Mellin–Stieltjes convolution Π⋆G of a nonnegative distribution with an Erlang distribution G. A distinctive feature of such a class is that it contains heavy-tailed distributions. We suggest a simple methodology for constructing a sequence of distributions having the form Π⋆G with the purpose of approximating the integrated tail distribution of the claim sizes. Then we adapt a recent result which delivers an explicit expression for the probability of ruin in the case that the claim size distribution is modeled as an Erlangized scale mixture. We provide simplified expressions for the approximation of the probability of ruin and construct explicit bounds for the error of approximation. We complement our results with a classical example where the claim sizes are heavy-tailed.Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/2440/1196132018-01-01T00:00:00ZModeling u8niaxial nonuniform cell proliferation
http://hdl.handle.net/2440/119612
Title: Modeling u8niaxial nonuniform cell proliferation
Author: Lai De Oliveira, A.; Binder, B.
Abstract: Growth in biological systems occurs as a consequence of cell proliferation fueled by a nutrient supply. In general, the nutrient gradient of the system will be nonconstant, resulting in biased cell proliferation. We develop a uniaxial discrete cellular automaton with biased cell proliferation using a probability distribution which reflects the nutrient gradient of the system. An explicit probability mass function for the displacement of any tracked cell under the cellular automaton model is derived and verified against averaged simulation results; this displacement distribution has applications in predicting cell trajectories and evolution of expected site occupancies.Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/2440/1196122019-01-01T00:00:00ZA Rayleigh-Ritz method for Navier-Stokes flow through curved ducts
http://hdl.handle.net/2440/119535
Title: A Rayleigh-Ritz method for Navier-Stokes flow through curved ducts
Author: Harding, B.
Abstract: We present a Rayleigh–Ritz method for the approximation of fluid flow in a curved duct, including the secondary cross-flow, which is well known to develop for nonzero Dean numbers. Having a straightforward method to estimate the cross-flow for ducts with a variety of cross-sectional shapes is important for many applications. One particular example is in microfluidics where curved ducts with low aspect ratio are common, and there is an increasing interest in nonrectangular duct shapes for the purpose of size-based cell separation. We describe functionals which are minimized by the axial flow velocity and cross-flow stream function which solve an expansion of the Navier–Stokes model of the flow. A Rayleigh–Ritz method is then obtained by computing the coefficients of an appropriate polynomial basis, taking into account the duct shape, such that the corresponding functionals are stationary. Whilst the method itself is quite general, we describe an implementation for a particular family of duct shapes in which the top and bottom walls are described by a polynomial with respect to the lateral coordinate. Solutions for a rectangular duct and two nonstandard duct shapes are examined in detail. A comparison with solutions obtained using a finite-element method demonstrates the rate of convergence with respect to the size of the basis. An implementation for circular cross-sections is also described, and results are found to be consistent with previous studies.Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/2440/1195352019-01-01T00:00:00ZInvariant prolongation of the Killing tensor equation
http://hdl.handle.net/2440/119419
Title: Invariant prolongation of the Killing tensor equation
Author: Gover, A.; Leistner, T.
Abstract: The Killing tensor equation is a first-order differential equation on symmetric covariant tensors that generalises to higher rank the usual Killing vector equation on Riemannian manifolds. We view this more generally as an equation on any manifold equipped with an affine connection, and in this setting derive its prolongation to a linear connection. This connection has the property that parallel sections are in 1–1 correspondence with solutions of the Killing equation. Moreover, this connection is projectively invariant and is derived entirely using the projectively invariant tractor calculus which reveals also further invariant structures linked to the prolongation.Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/2440/1194192019-01-01T00:00:00Z