Modern statistical methods use complex, sophisticated models that can lead to intractable computations. Saddlepoint approximations can be the answer. Written from the user's point of view, this book ...explains in clear language how such approximate probability computations are made, taking readers from the very beginnings to current applications. The core material is presented in chapters 1-6 at an elementary mathematical level. Chapters 7-9 then give a highly readable account of higher-order asymptotic inference. Later chapters address areas where saddlepoint methods have had substantial impact: multivariate testing, stochastic systems and applied probability, bootstrap implementation in the transform domain, and Bayesian computation and inference. No previous background in the area is required. Data examples from real applications demonstrate the practical value of the methods. Ideal for graduate students and researchers in statistics, biostatistics, electrical engineering, econometrics, and applied mathematics, this is both an entry-level text and a valuable reference.
Due to the complexity of modeling the radiative transfer inside the accretion columns of neutron star binaries, their X-ray spectra are still commonly described with phenomenological models, e.g., a ...cut off power law. While the behavior of these models is well understood and they allow for a comparison of different sources and studying source behavior, the extent to which the underlying physics can be derived from the model parameters is very limited. During recent years, several physically motivated spectral models have been developed to overcome these limitations. Their application, however, is generally computationally much more expensive and they require a high number of parameters which are difficult to constrain. In particular, Becker & Wolff(2007) presented an analytical solution to the radiative transfer equation inside the accretion column assuming a velocity profile that is linear in the optical depth. An implementation of this model that is both fast and accurate enough to be fitted to observed spectra is available in XSPEC. The main difficulty of this implementation is that some solutions violate energy conservation and therefore have to be rejected by the user. We propose a novel fitting strategy that ensures energy conservation during theχ2-minimization which simplifies the application of the model considerably. We demonstrate this approach as well as a study of possible parameter degeneracies with a comprehensive Markov-Chain Monte Carlo analysis of the complete parameter space for a combined NuSTAR and Swift/XRT data-set of Cen X-3.The derived accretion-flow structure features a small column radius of∼63 m and a spectrum dominated by bulk-Comptonization of bremsstrahlung seed photons, in agreement with previous studies
Numerical Methods Lindfield, George; Penny, John
2012, 2012-09-01
eBook
Numerical Methods using MATLAB, 3e, is an extensive reference offering hundreds of useful and important numerical algorithms that can be implemented into MATLAB for a graphical interpretation to help ...researchers analyze a particular outcome. Many worked examples are given together with exercises and solutions to illustrate how numerical methods can be used to study problems that have applications in the biosciences, chaos, optimization, engineering and science across the board.
Numerical Methods using MATLAB, 3e, is an extensive reference offering hundreds of useful and important numerical algorithms that can be implemented into MATLAB, to help researchers analyze a particular outcome. Many worked examples are given, together with exercises and solutions, to illustrate how numerical methods can be used to study problems that have applications in the biosciences, chaos, optimization, engineering and science. Over 500 numerical algorithms, their fundamental principles, and applicationsGraphs are used extensively to clarify the complexity of problemsIncludes coded genetic algorithmsIncludes the Lagrange multiplier methodUser-friendly and written in a conversational style
In magnetic Cataclysmic Variables (mCVs), X-ray radiation originates from the shock heated multi-temperature plasma in the post-shock region near the white dwarf surface. These X-rays are modified by ...a complex distribution of absorbers in the pre-shock region. The presence of photo-ionized lines and warm absorber features in the soft X-ray spectra of these mCVs suggests that these absorbers are ionized. We developed the ionized complex absorber model zxipab, which is represented by a power-law distribution of ionized absorbers in the pre-shock ow. Using the ionized absorber model zxipab along with a cooling ow model and a reflection component, we model the broadband Chandra/HETG and NuSTAR spectra of two IPs: NY Lup and V1223 Sgr. We nd that this model describes well many of the H and He like emission lines from medium Z elements, which arises from the collisionally excited plasma. However the model fails to account for some of the He like triplets from medium Z elements, which points towards its photo-ionization origin. We do not find a compelling evidence for a blackbody component to model the soft excess seen in the residuals of the Chandra/HETG spectra, which could be due to the uncertainties in estimation of the interstellar absorption of these sources using Chandra/HETG data and/or excess fluxes seen in some photo-ionized emission lines which are not accounted by the cooling ow model. We describe the implications of this model with respect to the geometry of the pre-shock region in these two IPs
Provides a hands-on introduction to engineering analysis using one of the most powerful commercial general purposes finite element programs on the market. Students will find a practical and ...integrated approach that combines finite element theory with best practices for developing, verifying, validating and interpreting the results of finite element models, while engineering professionals will appreciate the deep insight presented on the program's structure and behavior. Additional topics covered include an introduction to commands, input files, batch processing, and other advanced features in ANSYS.
In this article, we address the problem of accuracy of finite volume schemes in the low Mach number limit. It has been known for years that collocated finite volume schemes are naturally correctly ...behaving in this limit on triangular meshes 21,22,16, but fail in general on other types of mesh. We are first interested in the general problem of the conservation of vorticity for the wave system. By enriching the approximation space for vectors, we prove that the Hodge-Helmholtz context developed for triangular meshes in 16 can be recovered in the quadrangular mesh case. This leads to a numerical scheme for the wave system that naturally preserves the vorticity under mild assumption on the numerical flux. The new approximation space is then used with the barotropic Euler system. Numerical tests show that the new numerical scheme is accurate for both steady and acoustic problems at low Mach number.
•New approximation space for vectors on quadrangular mesh.•Discrete preservation of the curl.•The curl preserved is defined in the adjoint sense.•A numerical scheme accurate for both steady and unsteady low Mach number flows without low Mach number fix.
This study uses Raina’s function to obtain a new coordinated pq-integral identity. Using this identity, we construct several new pq-Simpson’s type inequalities for generalized convex functions on ...coordinates. Setting psub.1=psub.2=1 in these inequalities yields well-known quantum Simpson’s type inequalities for coordinated generalized convex functions. Our results have important implications for the creation of post quantum mathematical frameworks.
This study deals with mixed convection of Formula omitted-Cu-water hybrid nanofluid in a wavy channel having a circular cylinder. A two-dimensional system of partial differential equations has been ...discretized by employing Galerkin finite element method. Numerical simulations are carried out for different ranges of the governing parameters such as Reynolds number ( Formula omitted), nanoparticle volume fraction ( Formula omitted) and wave amplitude ( Formula omitted). It is inferred that Reynolds number is a key factor in this study. As it rises, the fluid behavior switches from slower to faster mode. Average Nusselt number rises at lower wavy wall and with lift coefficient ( Formula omitted). The highest average Nusselt number is achieved at Formula omitted, which is promoting the heat transfer by roughly Formula omitted. Furthermore, an enhancement in the nanoparticle volume fraction leads to the decrease in the local Nusselt number on upper wavy wall. The flow philosophy is presented in the form of isotherm contours, streamline contours and some appropriate plots.
This paper introduces a novel eXtended virtual element method, an extension of the conforming virtual element method. The X-VEM is formulated by incorporating appropriate enrichment functions in the ...local spaces. The method is designed to handle highly generic enrichment functions, including singularities arising from fractured domains. By achieving consistency on the enrichment space, the method is proven to achieve arbitrary approximation orders even in the presence of singular solutions. The paper includes a complete convergence analysis under general assumptions on mesh regularity, and numerical experiments validating the method's accuracy on various mesh families, demonstrating optimal convergence rates in the L2-and H1-norms on fractured or L-shaped domains.
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