Diffusion equation

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  • Diffusion is the transport of matter from one point to another by thermal motion of atoms or molecules. It is relatively fast in gases, slow in liquids, and very slow in solids. Diffusion plays a key rˆole in many processes as diverse as intermixing of gases and liquids, permeation of atoms or molecules through membranes, evaporation of liquids, drying of timber, doping silicon wafers to make semiconductor devices, and transport of thermal neutrons in nuclear power reactors.

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  • The “origin of this species” lies in the pages of the journal Biometrika and precedes the birth of either of the authors. There, in his remarkable landmark 1951 paper “Random dispersal in theoretical populations,” J.G. Skellam made a number of observations that have profoundly affected the study of spatial ecology.

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  • Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Convergence of a Mimetic Finite Difference Method for Static Diffusion Equation

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  • Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Properties of Positive Solution for Nonlocal Reaction-Diffusion Equation with Nonlocal Boundary

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  • Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Reverse Smoothing Effects, Fine Asymptotics, and Harnack Inequalities for Fast Diffusion Equations

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  • The increasing demand on ultra miniturized electronic devices for ever improving performances has led to the necessity of a deep and detailed understanding of the mathematical theory of charge transport in semiconductors.

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  • For example, a combined advective-diffusion equation, such as ∂u ∂2 u ∂u = −v +D 2 ∂t ∂x ∂x (19.3.21) might profitably use an explicit scheme for the advective term combined with a Crank-Nicholson or other implicit scheme for the diffusion term. The alternating-direction implicit (ADI) method, equation (19.3.16), is an example of operator splitting with a slightly different twist. Let us reinterpret (19.3.19)

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  • Tham khảo sách 'volume 4 mechanical engineers’ handbook third edition energy and power', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả

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  • This textbook has evolved from part of the first-year graduate curriculum in the Department of Materials Science and Engineering at the Massachusetts Institute of Technology (MIT) . This curriculum includes four required semester-long subjects- “Materials at Equilibrium,” “Mechanical Properties of Materials,” “Electrical, Optical, and Magnetic Properties of Materials,” and “Kinetic Processes in Materials.

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  • Tham khảo sách 'robotics designing the mechanisms for automated machinery', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả

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  • Starting from a derivation of the conservation equations for multicomponent multiphase flows in porous media and a discussion of convective vs. diffusive/dispersive transport, the reader is introduced to a mathematical framework, based on the method of characteristics, for solving convection-dominated transport problems.

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  • Tham khảo sách 'reliability in automotive and mechanical engineering determination of component and system reliab', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả

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  • Tham khảo sách 'the materials information company.publication information and alloy phase diagrams volume 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả

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  • This research monograph concerns the design and analysis of discrete-time approximations for stochastic differential equations (SDEs) driven by Wiener processes and Poisson processes or Poisson jump measures. In financial and actuarial modeling and other areas of application, such jump diffusions are often used to describe the dynamics of various state variables. In finance these may represent, for instance, asset prices, credit ratings, stock indices, interest rates, exchange rates or commodity prices.

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  • In this research monograph, we explain the development of a mechanistic, stochastic theory of nonfickian solute dispersion in porous media. We have included sufficient amount of background material related to stochastic calculus and the scale dependency of diffusivity in this book so that it could be read independently.

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  • In 1896, Karl Benz was granted a patent for his design of the first engine with horizontally opposed pistons. His design created an engine in which the corresponding pistons move in horizontal cylinders and reach top dead center simultaneously, thus automatically balancing each other with respect to their individual momentum. Engines of this design are often referred to as flat engines because of their shape and lower profile.

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  • The goal of this book is to expose the reader to modern computational tools for solving differential equation models that arise in chemical engineering, e.g., diffusion-reaction, mass-heat transfer, and fluid flow. The emphasis is placed on the understanding and proper use of software packages. In each chapter we outline numerical techniques that either illustrate a computational property of interest or are the underlying methods of a computer package. At the close of each chapter a survey of computer packages is accompanied by examples of their use....

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