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Books on the topic 'Diffusion Operator'

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Published: 28 June 2021
Last updated: 17 February 2022

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1

Reddy, Satish C. Pseudospectra of the convection-diffusion operator. Ithaca, N.Y: Cornell Theory Center, Cornell University, 1993.

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2

Löbus, Jörg-Uwe. Generalized diffusion operators. Berlin: Akademie Verlag, 1993.

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3

Andreu-Vaillo, Fuensanta. Nonlocal diffusion problems. Providence, R.I: American Mathematical Society, 2010.

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4

Nonlocal diffusion problems. Providence, R.I: American Mathematical Society, 2010.

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5

Montseny, Gérard. Représentation diffusive. Paris: Hermès science, 2005.

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6

Diffusions and elliptic operators. New York: Springer, 1998.

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7

G, Pinsky Ross. Positive harmonic functions and diffusion. New York: Cambridge University Press, 1995.

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8

Long, Hongwei. Symmetric diffusion operators on infinite dimensional spaces. [s.l.]: typescript, 1997.

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9

Bakry, Dominique, Ivan Gentil, and Michel Ledoux. Analysis and Geometry of Markov Diffusion Operators. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-00227-9.

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10

Taira, Kazuaki. Diffusion processes and partial differential equations. Boston: Academic Press, 1988.

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11

Eberle, Andreas. Uniqueness and non-uniqueness of singular diffusion operators. Berlin: Springer, 1999.

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12

Colombo, Fabrizio, and Jonathan Gantner. Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-16409-6.

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13

Elworthy, K. David, Yves Le Jan, and Xue-Mei Li. On the Geometry of Diffusion Operators and Stochastic Flows. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/bfb0103064.

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14

Eberle, Andreas. Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/bfb0103045.

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15

service), SpringerLink (Online, ed. Elliptic Partial Differential Equations: Volume 1: Fredholm Theory of Elliptic Problems in Unbounded Domains. Basel: Springer Basel AG, 2011.

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16

author, Sarich Marco 1985, ed. Metastability and Markov state models in molecular dynamics: Modeling, analysis, algorithmic approaches. Providence, Rhode Island: American Mathematical Society, 2013.

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17

Epstein, Charles L., and Rafe Mazzeo. Degenerate Diffusion Operators Arising in Population Biology (AM-185). Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.001.0001.

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This book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics, mathematical finance, and economics. The results discussed in this book prove the uniqueness of the solution to the martingale problem and therefore the existence of the associated Markov process. The book uses an “integral kernel method” to develop mathematical foundations for the study of such degenerate elliptic operators and the stochastic processes they define. The precise nature of the degeneracies of the principal symbol for these operators leads to solutions of the parabolic and elliptic problems that display novel regularity properties. Dually, the adjoint operator allows for rather dramatic singularities, such as measures supported on high codimensional strata of the boundary. The book establishes the uniqueness, existence, and sharp regularity properties for solutions to the homogeneous and inhomogeneous heat equations, as well as a complete analysis of the resolvent operator acting on Hölder spaces. It shows that the semigroups defined by these operators have holomorphic extensions to the right half plane. The book also demonstrates precise asymptotic results for the long-time behavior of solutions to both the forward and backward Kolmogorov equations.
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18

Eberle, Andreas. Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators. Springer, 2000.

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19

Epstein, Charles L., and Rafe Mazzeo. The Semi-group on. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.003.0012.

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This chapter deals with the semi-group on the space Β‎⁰(P). It first describes the boundary behavior of elements of the adjoint operator at points in the interiors of hypersurface boundary components before discussing the null-space of the adjoint under the hypothesis that a generalized Kimura diffusion operator, L, meets bP cleanly. It then examines long time asymptotics, along with a lemma in which P is a compact manifold with corners and L is a generalized Kimura diffusion on P. It also considers the existence of irregular solutions to the homogeneous equations Lu = f, for functions that do not belong to the range of the generator of a C⁰-semi-group on Β‎⁰(P).
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20

Epstein, Charles L., and Rafe Mazzeo. Holder Estimates for the 1-dimensional Model Problems. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.003.0006.

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This chapter establishes Hölder space estimates for the 1-dimensional model problems. It gives a detailed treatment of the 1-dimensional case, in part because all of the higher dimensional estimates are reduced to estimates on heat kernels for the 1-dimensional model problems. It also presents the proof of parabolic Schauder estimates for the generalized Kimura diffusion operator using the explicit formula for the heat kernel, along with standard tools of analysis. Finally, it considers kernel estimates for degenerate model problems, explains how Hölder estimates are obtained for the 1-dimensional model problems, and describes the properties of the resolvent operator.
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21

Epstein, Charles L., and Rafe Mazzeo. The Model Solution Operators. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.003.0004.

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This chapter introduces the model problems and the solution operator for the associated heat equations. These operators give a good approximation for the behavior of the heat kernel in neighborhoods of different types of boundary points. The chapter states and proves the elementary features of these operators and shows that the model heat operators have an analytic continuation to the right half plane. It first considers the model problem in 1-dimension and in higher dimensions before discussing the solution to the homogeneous Cauchy problem. It then describes the first steps toward perturbation theory and constructs the solution operator for generalized Kimura diffusions on a suitable scale of Hölder spaces. It also defines the resolvent families and explains why the estimates obtained here are not adequate for the perturbation theoretic arguments needed to construct the solution operator for generalized Kimura diffusions.
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22

Epstein, Charles L., and Rafe Mazzeo. Existence of Solutions. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.003.0010.

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This chapter proves existence of solutions to the inhomogeneous problem using the Schauder estimate and analyzes a generalized Kimura diffusion operator, L, defined on a manifold with corners, P. The discussion centers on the solution w = v + u, where v solves the homogeneous Cauchy problem with v(x, 0) = f(x) and u solves the inhomogeneous problem with u(x, 0) = 0. The chapter first provides definitions for the Wright–Fisher–Hölder spaces on a general compact manifold with corners before explaining the steps involved in the existence proof. It then verifies the induction hypothesis and treats the k = 0 case. It also shows how to perform the doubling construction for P and considers the existence of the resolvent operator and a contraction semi-group. Finally, it discusses the problem of higher regularity.
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23

Bass, Richard F. Diffusions and Elliptic Operators. Springer, 2013.

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24

Diffusions and Elliptic Operators. New York: Springer-Verlag, 1998. http://dx.doi.org/10.1007/b97611.

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25

Rafe, Mazzeo, ed. Degenerate diffusion operators arising in population biology. Princeton University Press, 2013.

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26

Epstein, Charles L., and Rafe Mazzeo. The Resolvent Operator. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.003.0011.

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This chapter describes the construction of a resolvent operator using the Laplace transform of a parametrix for the heat kernel and a perturbative argument. In the equation (μ‎-L) R(μ‎) f = f, R(μ‎) is a right inverse for (μ‎-L). In Hölder spaces, these are the natural elliptic estimates for generalized Kimura diffusions. The chapter first constructs the resolvent kernel using an induction over the maximal codimension of bP, and proves various estimates on it, along with corresponding estimates for the solution operator for the homogeneous Cauchy problem. It then considers holomorphic semi-groups and uses contour integration to construct the solution to the heat equation, concluding with a discussion of Kimura diffusions where all coefficients have the same leading homogeneity.
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27

Ledoux, Michel, Dominique Bakry, and Ivan Gentil. Analysis and Geometry of Markov Diffusion Operators. Springer, 2016.

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28

Analysis And Geometry Of Markov Diffusion Operators. Springer International Publishing AG, 2013.

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29

Epstein, Charles L., and Rafe Mazzeo. Maximum Principles and Uniqueness Theorems. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.003.0003.

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This chapter proves maximum principles for two parabolic and elliptic equations from which the uniqueness results follow easily. It also considers the main consequences of the maximum principle, both for the model operators on an open orthant and for the general Kimura diffusion operators on a compact manifold with corners, as well as their elliptic analogues. Of particular note in this regard is a generalization of the Hopf boundary point maximum principle. The chapter first presents maximum principles for the model operators before discussing Kimura diffusion operators on manifolds with corners. It then describes maximum principles for the heat equation as well as the corresponding maximum principle and uniqueness result for Kimura diffusion equations.
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30

Epstein, Charles L., and Rafe Mazzeo. Degenerate Diffusion Operators Arising in Population Biology (AM-185). Princeton University Press, 2013.

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31

Epstein, Charles L., and Rafe Mazzeo. Degenerate Diffusion Operators Arising in Population Biology (Am-185). Princeton University Press, 2013.

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32

Colombo, Fabrizio, and Jonathan Gantner. Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes. Birkhäuser, 2019.

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33

Elworthy, K. D., Y. Le Jan, and X.-M. Li. On the Geometry of Diffusion Operators and Stochastic Flows. Springer-Verlag Telos, 2000.

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34

Epstein, Charles L., and Rafe Mazzeo. Wright-Fisher Geometry. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.003.0002.

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This chapter introduces the geometric preliminaries needed to analyze generalized Kimura diffusions, with particular emphasis on Wright–Fisher geometry. It begins with a discussion of the natural domains of definition for generalized Kimura diffusions: polyhedra in Euclidean space or, more generally, abstract manifolds with corners. Amongst the convex polyhedra, the chapter distinguishes the subclass of regular convex polyhedra P. P is a regular convex polyhedron if it is convex and if near any corner, P is the intersection of no more than N half-spaces with corresponding normal vectors that are linearly independent. These definitions establish that any regular convex polyhedron is a manifold with corners. The chapter concludes by defining the general class of elliptic Kimura operators on a manifold with corners P and shows that there is a local normal form for any operator L in this class.
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35

Gontrand, Christian. Micro-Nanoelectronics Components: Modeling of Diffusion and Operation Processes. Elsevier, 2018.

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36

Epstein, Charles L., and Rafe Mazzeo. Introduction. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.003.0001.

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This book proves the existence, uniqueness and regularity results for a class of degenerate elliptic operators known as generalized Kimura diffusions, which act on functions defined on manifolds with corners. It presents a generalization of the Hopf boundary point maximum principle that demonstrates, in the general case, how regularity implies uniqueness. The book is divided in three parts. Part I deals with Wright–Fisher geometry and the maximum principle; Part II is devoted to an analysis of model problems, and includes degenerate Hölder spaces; and Part III discusses generalized Kimura diffusions. This introductory chapter provides an overview of generalized Kimura diffusions and their applications in probability theory, model problems, perturbation theory, main results, and alternate approaches to the study of similar degenerate elliptic and parabolic equations.
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37

Organisation for Economic Co-operation and Development., ed. Innovative networks: Co-operation in national innovation systems. Paris: OECD, 2001.

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38

Rajeev, S. G. Finite Difference Methods. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.003.0014.

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This chapter offers a peek at the vast literature on numerical methods for partial differential equations. The focus is on finite difference methods (FDM): approximating differential operators by functions of difference operators. Padé approximants (Fornberg) give a unifying principle for deriving the various stencils used by numericists. Boundary value problems for the Poisson equation and initial value problems for the diffusion equation are solved using FDM. Numerical instability of explicit schemes are explained physically and implicit schemes introduced. A discrete version of theClebsch formulation of incompressible Euler equations is proposed. The chapter concludes with the radial basis function method and its application to a discrete version of the Lagrangian formulation of Navier–Stokes.
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39

Zamagni, Vera. A Worldwide Historical Perspective on Co-operatives and Their Evolution. Edited by Jonathan Michie, Joseph R. Blasi, and Carlo Borzaga. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199684977.013.7.

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The birth of co-operatives in Europe in the middle of the nineteenth century shaped this form of enterprise by differentiating it from the established capitalist one, both in terms of internal organization and in terms of sectors of activity. This chapter highlights first the process of diffusion of co-operatives in the nineteenth century by grouping them into models—consumer, worker, financial, and rural co-operatives—that formed the pillars of the movement. The second part of the chapter is devoted to the novelties that emerged after World War II, especially social co-operatives and service co-operatives, giving a general account of developments of co-operation in Western Europe, North America, and Japan. A final glance of the new opportunities offered for co-operation through the Web is offered.
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40

Nitzan, Abraham. Chemical Dynamics in Condensed Phases. Oxford University Press, 2006. http://dx.doi.org/10.1093/oso/9780198529798.001.0001.

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This text provides a uniform and consistent approach to diversified problems encountered in the study of dynamical processes in condensed phase molecular systems. Given the broad interdisciplinary aspect of this subject, the book focuses on three themes: coverage of needed background material, in-depth introduction of methodologies, and analysis of several key applications. The uniform approach and common language used in all discussions help to develop general understanding and insight on condensed phases chemical dynamics. The applications discussed are among the most fundamental processes that underlie physical, chemical and biological phenomena in complex systems. The first part of the book starts with a general review of basic mathematical and physical methods (Chapter 1) and a few introductory chapters on quantum dynamics (Chapter 2), interaction of radiation and matter (Chapter 3) and basic properties of solids (chapter 4) and liquids (Chapter 5). In the second part the text embarks on a broad coverage of the main methodological approaches. The central role of classical and quantum time correlation functions is emphasized in Chapter 6. The presentation of dynamical phenomena in complex systems as stochastic processes is discussed in Chapters 7 and 8. The basic theory of quantum relaxation phenomena is developed in Chapter 9, and carried on in Chapter 10 which introduces the density operator, its quantum evolution in Liouville space, and the concept of reduced equation of motions. The methodological part concludes with a discussion of linear response theory in Chapter 11, and of the spin-boson model in chapter 12. The third part of the book applies the methodologies introduced earlier to several fundamental processes that underlie much of the dynamical behaviour of condensed phase molecular systems. Vibrational relaxation and vibrational energy transfer (Chapter 13), Barrier crossing and diffusion controlled reactions (Chapter 14), solvation dynamics (Chapter 15), electron transfer in bulk solvents (Chapter 16) and at electrodes/electrolyte and metal/molecule/metal junctions (Chapter 17), and several processes pertaining to molecular spectroscopy in condensed phases (Chapter 18) are the main subjects discussed in this part.
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41

Transnational Policy Innovation: The Role of the OECD in the Diffusion of Regulatory Impact Analysis. Rowman & Littlefield Publishers, Incorporated, 2013.

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42

Taska, Lucy. Scientific Management. Edited by Adrian Wilkinson, Steven J. Armstrong, and Michael Lounsbury. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780198708612.013.2.

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This chapter reviews the continuing impact of Scientific Management, particularly in relation to the field of education. By outlining how Taylor and his followers used the language of science, efficiency and rationality to extend the application of Scientific Management to the reform of learning methods in the workplace and in educational institutions, it questions the assumption that managerialism in higher education emerged out of thin air in the 1990s. The chapter argues that the diffusion of Taylor’s philosophy, principles and methods to education resulted in the replacement of traditional co-operative modes of learning with a new orientation that privileged co-operation with managers and the managerialization of educational practices and institutions. It concludes by demonstrating how Taylor’s ghost continues to exert influence through standardized courses, metric measurements of student outcomes and academic research, and regulatory, accrediting and disciplinary mechanisms and organizations.
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43

Bahrami, Bahador. Making the most of individual differences in joint decisions. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198789710.003.0004.

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Evidence for and against the idea that “two heads are better than one” is abundant. This chapter considers the contextual conditions and social norms that predict madness or wisdom of crowds to identify the adaptive value of collective decision-making beyond increased accuracy. Similarity of competence among members of a collective impacts collective accuracy, but interacting individuals often seem to operate under the assumption that they are equally competent even when direct evidence suggest the opposite and dyadic performance suffers. Cross-cultural data from Iran, China, and Denmark support this assumption of similarity (i.e., equality bias) as a sensible heuristic that works most of the time and simplifies social interaction. Crowds often trade off accuracy for other collective benefits such as diffusion of responsibility and reduction of regret. Consequently, two heads are sometimes better than one, but no-one holds the collective accountable, not even for the most disastrous of outcomes.
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44

Clark, Jennifer. Policy Through Practice: Local Communities, Self-Organization, and Policy. Edited by Gordon L. Clark, Maryann P. Feldman, Meric S. Gertler, and Dariusz Wójcik. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198755609.013.54.

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Economic geography fixes the lens of analysis on both the scale of economic action and the processes that determine how economic resources are distributed and concentrated across places. This chapter focuses on institutional intermediaries and how they contribute to the evolving practices of self-organizing within local communities through third-sector strategies. The chapter presents three models of ‘third-sector intermediaries’ in cities and regions across the USA illustrating the ways in which third-sector policy strategies operate in local and regional economies both through city governments and in parallel to them. These strategies are the result of variations in the capacities of local communities to address regional economic challenges and increasingly contribute to that diverse landscape. The chapter concludes with a discussion of economic policy implications of these modes of policy design, delivery, and decision-making affecting regional economies and uneven development, local autonomy, institutional intermediaries, city governance, technology diffusion, and policy innovation.
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45

Chidester, David. Religion. University of California Press, 2018. http://dx.doi.org/10.1525/california/9780520297654.001.0001.

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Religion: Material Dynamics is a lively resource for thinking about religious materiality and the material study of religion. Deconstructing and reconstructing religion as material categories, social formations, and mobile circulations, the book explores the making, ordering, and circulating of religious things. Part 1 revitalizes basic categories—animism and sacred, space and time—by situating them in their material production and testing their analytical viability. Part 2 examines religious formations as configurations of power that operate in material cultures and cultural economies and are most clearly shown in the power relations of colonialism and imperialism. Part 3 explores the material dynamics of circulation through case studies of religious mobility, change, and diffusion as intimate as the body and as vast as the oceans. Each chapter offers insightful orientations and surprising possibilities for studying material religion. Exploring the material dynamics of religion from poetics to politics, the book provides an entry into the study of material religion that speaks to the interests of both students and specialists in religious studies, anthropology, history, and other fields that have made the material turn.
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