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Adjoint based aerodynamic shape optimization of a semi-submerged inlet duct and upstream inlet surface
Aerodynamic performance of a semi-submerged inlet exposed to a significant amount of boundary layer ingestion is optimized using the open-source flow...
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Mathematics for Sustainable Humanity: Population, Climate, Energy, Economy, Policy, and Social Justice
Sustainable development means meeting our needs without compromising the ability of future generations to meet their own needs. Human activities have...
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Directed Percolation and Its Applications
As described briefly in Chap. 3, a variant of the classical percolation called directed percolation (DP), has been shown to have fascinating...
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In Situ Statistical Distribution-Based Data Summarization and Visual Analysis
As the era of exascale computing approaches, the need for effective, scalable, and flexible data reduction techniques is becoming more and more...
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A Semi-Markov Approach to Study a Group of Kinesin Motors
We propose a general mathematical and computational approach to study cellular transport driven by a group of kinesin motors. It is a framework for...
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Mathematical Modeling
Cosmology is a branch of astronomy that deals with the greatest spatial and temporal distances and the questions of the origin of the universe as a...
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Effect of inclined magnetic field on natural convection and entropy generation of non-Newtonian ferrofluid in a square cavity having a heated wavy cylinder
Magnetohydrodynamic (MHD) natural convection of non-Newtonian ferrofluid and entropy generation in a square enclosure containing a wavy cylinder was...
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Simulation of Dynamic Models
Most of the statistical methods presented in the previous chapters deal with inherently static data. With the exception of a few time-series...
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Markovian Embedding—A New Derivation of the Fokker-Planck Hierarchy
In this Chapter, we derive the FP hierarchy by using a Markovian embedding technique, which is inspired by the linear chain trick [3–5]. Markovian...
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Reducing Bias and Quantifying Uncertainty in Fluorescence Produced by PCR
We present a new approach for relating nucleic-acid content to fluorescence in a real-time Polymerase Chain Reaction (PCR) assay. By coupling a...
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Transmission probability of gas molecules through porous layers at Knudsen diffusion
Gas flow through layers of porous materials plays a crucial role in technical applications, geology, petrochemistry, and space sciences (e.g., fuel...
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On the decay of a porous thermoelasticity type III with constant delay
This paper focuses on the well-posedness and asymptotic stability of solutions of a delayed porous thermoelastic system of type III, where the delay...
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Large Deviations
Except for the law of the iterated logarithm, so far we have encountered two types of limit theorems for partial sums S n = X 1 + … + X n,...
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Random-field random surfaces
We study how the typical gradient and typical height of a random surface are modified by the addition of quenched disorder in the form of a random...
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Internal Gravity Waves from a Localized Source in Stratified Medium Flow with a Model Buoyancy Frequency Distribution
AbstractThe problem of calculating internal gravity wave fields generated by a localized source in a stratified flow of finite thickness with a model...
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Glauber Dynamics on the Erdős-Rényi Random Graph
We investigate the effect of disorder on the Curie-Weiss model with Glauber dynamics. In particular, we study metastability for spin-flip dynamics on...
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Transport Properties of Composite Materials
Composite materials constitute a large class of natural or man-made disordered media, which includes granular materials, composite solids,...
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GOE and \({\mathrm{Airy}}_{2\rightarrow 1}\) Marginal Distribution via Symplectic Schur Functions
We derive Sasamoto’s Fredholm determinant formula for the Tracy-Widom GOE distribution, as well as the one-point marginal distribution of the...
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Stochastic Toolkits
This chapter introduces the basic probability concepts and stochastic processes. It includes random variables, probability density function (PDF),...