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.
This book covers adaptive mesh generation and moving mesh methods for solving time-dependent PDEs. It gives a general description of the components of moving mesh methods as well as examples of their ...application for a number of nontrivial physical problems.
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
This book aims to present meshfree methods in a friendly and straightforward manner, so that beginners can very easily understand, comprehend, program, implement, apply and extend these methods. It ...provides first the fundamentals of numerical analysis that are particularly important to meshfree methods. Typical meshfree methods, such as EFG, RPIM, MLPG, LRPIM, MWS and collocation methods are then introduced systematically detailing the formulation, numerical implementation and programming. Many well-tested computer source codes developed by the authors are attached with useful descriptions. The application of the codes can be readily performed using the examples with input and output files given in table form. These codes consist of most of the basic meshfree techniques, and can be easily extended to other variations of more complex procedures of meshfree methods. Readers can easily practice with the codes provided to effective learn and comprehend the basics of meshfree methods.
Micro-nano opto-electronic devices are demanded to be highly efficient and capable of multiple working wavelengths in several light-matter interaction applications, which is a challenge to surface ...plasmonics owing to the relatively higher intrinsic loss and larger dispersion. To cross the barriers, a plasmonic metasurface combining both high Q-factors (highest Q > 800) and multiple resonant wavelengths is proposed by arranging step-staged pyramid units in lattice modes. Different numerical relations for nonlinear frequency conversions have been constructed because of its strong tunability. Also, characteristics of high radiation efficiency (> 50%) and large localized optical density of state (> 10.sup.4) have been proved through the numerical simulation. Such tunable high-Q metasurface can be implemented to quantum nonlinear process and enable the strong light-matter interaction devices into reality.
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.
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