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Sample records for partially differentiated carbonaceous

  1. Magnetic Evidence for a Partially Differentiated Carbonaceous Chondrite Parent Body and Possible Implications for Asteroid 21 Lutetia

    Science.gov (United States)

    Weiss, Benjamin; Carporzen, L.; Elkins-Tanton, L.; Shuster, D. L.; Ebel, D. S.; Gattacceca, J.; Binzel, R. P.

    2010-10-01

    The origin of remanent magnetization in the CV carbonaceous chondrite Allende has been a longstanding mystery. The possibility of a core dynamo like that known for achondrite parent bodies has been discounted because chondrite parent bodies are assumed to be undifferentiated. Here we report that Allende's magnetization was acquired over several million years (Ma) during metasomatism on the parent planetesimal in a > 20 microtesla field 8-9 Ma after solar system formation. This field was present too recently and directionally stable for too long to have been the generated by the protoplanetary disk or young Sun. The field intensity is in the range expected for planetesimal core dynamos (Weiss et al. 2010), suggesting that CV chondrites are derived from the outer, unmelted layer of a partially differentiated body with a convecting metallic core (Elkins-Tanton et al. 2010). This suggests that asteroids with differentiated interiors could be present today but masked under chondritic surfaces. In fact, CV chondrites are spectrally similar to many members of the Eos asteroid family whose spectral diversity has been interpreted as evidence for a partially differentiated parent asteroid (Mothe-Diniz et al. 2008). CV chondrite spectral and polarimetric data also resemble those of asteroid 21 Lutetia (e.g., Belskaya et al. 2010), recently encountered by the Rosetta spacecraft. Ground-based measurements of Lutetia indicate a high density of 2.4-5.1 g cm-3 (Drummond et al. 2010), while radar data seem to rule out a metallic surface composition (Shepard et al. 2008). If Rosetta spacecraft measurements confirm a high density and a CV-like surface composition for Lutetia, then we propose Lutetia may be an example of a partially differentiated carbonaceous chondrite parent body. Regardless, the very existence of primitive achondrites, which contain evidence of both relict chondrules and partial melting, are prima facie evidence for the formation of partially differentiated bodies.

  2. Hyperbolic partial differential equations

    CERN Document Server

    Witten, Matthew

    1986-01-01

    Hyperbolic Partial Differential Equations III is a refereed journal issue that explores the applications, theory, and/or applied methods related to hyperbolic partial differential equations, or problems arising out of hyperbolic partial differential equations, in any area of research. This journal issue is interested in all types of articles in terms of review, mini-monograph, standard study, or short communication. Some studies presented in this journal include discretization of ideal fluid dynamics in the Eulerian representation; a Riemann problem in gas dynamics with bifurcation; periodic M

  3. Beginning partial differential equations

    CERN Document Server

    O'Neil, Peter V

    2011-01-01

    A rigorous, yet accessible, introduction to partial differential equations-updated in a valuable new edition Beginning Partial Differential Equations, Second Edition provides a comprehensive introduction to partial differential equations (PDEs) with a special focus on the significance of characteristics, solutions by Fourier series, integrals and transforms, properties and physical interpretations of solutions, and a transition to the modern function space approach to PDEs. With its breadth of coverage, this new edition continues to present a broad introduction to the field, while also addres

  4. Beginning partial differential equations

    CERN Document Server

    O'Neil, Peter V

    2014-01-01

    A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or

  5. Partial differential equations

    CERN Document Server

    Evans, Lawrence C

    2010-01-01

    This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...

  6. Partial differential equations

    CERN Document Server

    Agranovich, M S

    2002-01-01

    Mark Vishik's Partial Differential Equations seminar held at Moscow State University was one of the world's leading seminars in PDEs for over 40 years. This book celebrates Vishik's eightieth birthday. It comprises new results and survey papers written by many renowned specialists who actively participated over the years in Vishik's seminars. Contributions include original developments and methods in PDEs and related fields, such as mathematical physics, tomography, and symplectic geometry. Papers discuss linear and nonlinear equations, particularly linear elliptic problems in angles and gener

  7. Partial differential equations

    CERN Document Server

    Levine, Harold

    1997-01-01

    The subject matter, partial differential equations (PDEs), has a long history (dating from the 18th century) and an active contemporary phase. An early phase (with a separate focus on taut string vibrations and heat flow through solid bodies) stimulated developments of great importance for mathematical analysis, such as a wider concept of functions and integration and the existence of trigonometric or Fourier series representations. The direct relevance of PDEs to all manner of mathematical, physical and technical problems continues. This book presents a reasonably broad introductory account of the subject, with due regard for analytical detail, applications and historical matters.

  8. Partial differential equations

    CERN Document Server

    Sloan, D; Süli, E

    2001-01-01

    /homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! Over the second half of the 20th century the subject area loosely referred to as numerical analysis of partial differential equations (PDEs) has undergone unprecedented development. At its practical end, the vigorous growth and steady diversification of the field were stimulated by the demand for accurate and reliable tools for computational modelling in physical sciences and engineering, and by the rapid development of computer hardware and architecture. At the more theoretical end, the analytical insight in

  9. Elliptic partial differential equations

    CERN Document Server

    Han, Qing

    2011-01-01

    Elliptic Partial Differential Equations by Qing Han and FangHua Lin is one of the best textbooks I know. It is the perfect introduction to PDE. In 150 pages or so it covers an amazing amount of wonderful and extraordinary useful material. I have used it as a textbook at both graduate and undergraduate levels which is possible since it only requires very little background material yet it covers an enormous amount of material. In my opinion it is a must read for all interested in analysis and geometry, and for all of my own PhD students it is indeed just that. I cannot say enough good things abo

  10. Applied partial differential equations

    CERN Document Server

    Logan, J David

    2004-01-01

    This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory. This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of t...

  11. On Degenerate Partial Differential Equations

    OpenAIRE

    Chen, Gui-Qiang G.

    2010-01-01

    Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial differential equations, are presented, which arise naturally in some longstanding, fundamental problems in fluid mechanics and differential geometry. The solution to these fundamental problems greatly requires a deep understanding of nonlinear degenerate parti...

  12. Partial Differential Equations

    CERN Document Server

    1988-01-01

    The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.

  13. Introduction to partial differential equations

    CERN Document Server

    Greenspan, Donald

    2000-01-01

    Designed for use in a one-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, second-order partial differential equations, wave equation, potential equation, heat equation, approximate solution of partial differential equations, and more. Exercises appear at the ends of most chapters. 1961 edition.

  14. Elements of partial differential equations

    CERN Document Server

    Sneddon, Ian Naismith

    1957-01-01

    Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory.Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing independent st

  15. Basic linear partial differential equations

    CERN Document Server

    Treves, Francois

    1975-01-01

    Focusing on the archetypes of linear partial differential equations, this text for upper-level undergraduates and graduate students features most of the basic classical results. The methods, however, are decidedly nontraditional: in practically every instance, they tend toward a high level of abstraction. This approach recalls classical material to contemporary analysts in a language they can understand, as well as exploiting the field's wealth of examples as an introduction to modern theories.The four-part treatment covers the basic examples of linear partial differential equations and their

  16. Introduction to partial differential equations

    CERN Document Server

    Borthwick, David

    2016-01-01

    This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise.Within each section the author creates a narrative that answers the five questions: (1) What is the scientific problem we are trying to understand? (2) How do we model that with PDE? (3) What techniques can we use to analyze the PDE? (4) How do those techniques apply to this equation? (5) What information or insight did we obtain by developing and analyzing the PDE? The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspiration for the development of methods.

  17. Dynamics of partial differential equations

    CERN Document Server

    Wayne, C Eugene

    2015-01-01

    This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently. Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how solutions that start from arbitrary initial conditions evolve towards stable vortices. Weinstein considers the dynamics of localized states in nonlinear Schrodinger and Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent bifurcations results of solitary waves, their linear and nonlinear stability properties, and results about radiation damping where waves lose energy through radiation.   The articles, written independently, are combined into one volume to showcase the tools of dynamical systems theory at work in explaining qualitative phenomena associated with two classes of partial differential equ...

  18. Partial differential equations an introduction

    CERN Document Server

    Colton, David

    2004-01-01

    Intended for a college senior or first-year graduate-level course in partial differential equations, this text offers students in mathematics, engineering, and the applied sciences a solid foundation for advanced studies in mathematics. Classical topics presented in a modern context include coverage of integral equations and basic scattering theory. This complete and accessible treatment includes a variety of examples of inverse problems arising from improperly posed applications. Exercises at the ends of chapters, many with answers, offer a clear progression in developing an understanding of

  19. Abstract methods in partial differential equations

    CERN Document Server

    Carroll, Robert W

    2012-01-01

    Detailed, self-contained treatment examines modern abstract methods in partial differential equations, especially abstract evolution equations. Suitable for graduate students with some previous exposure to classical partial differential equations. 1969 edition.

  20. PARALLEL SOLUTION METHODS OF PARTIAL DIFFERENTIAL EQUATIONS

    Directory of Open Access Journals (Sweden)

    Korhan KARABULUT

    1998-03-01

    Full Text Available Partial differential equations arise in almost all fields of science and engineering. Computer time spent in solving partial differential equations is much more than that of in any other problem class. For this reason, partial differential equations are suitable to be solved on parallel computers that offer great computation power. In this study, parallel solution to partial differential equations with Jacobi, Gauss-Siedel, SOR (Succesive OverRelaxation and SSOR (Symmetric SOR algorithms is studied.

  1. Partial differential equations of mathematical physics

    CERN Document Server

    Sobolev, S L

    1964-01-01

    Partial Differential Equations of Mathematical Physics emphasizes the study of second-order partial differential equations of mathematical physics, which is deemed as the foundation of investigations into waves, heat conduction, hydrodynamics, and other physical problems. The book discusses in detail a wide spectrum of topics related to partial differential equations, such as the theories of sets and of Lebesgue integration, integral equations, Green's function, and the proof of the Fourier method. Theoretical physicists, experimental physicists, mathematicians engaged in pure and applied math

  2. Introduction to partial differential equations with applications

    CERN Document Server

    Zachmanoglou, E C

    1988-01-01

    This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.

  3. Partial differential equations for scientists and engineers

    CERN Document Server

    Farlow, Stanley J

    1993-01-01

    Most physical phenomena, whether in the domain of fluid dynamics, electricity, magnetism, mechanics, optics, or heat flow, can be described in general by partial differential equations. Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations.This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing th

  4. Numerical Analysis of Partial Differential Equations

    CERN Document Server

    Lui, S H

    2011-01-01

    A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis

  5. Partial Differential Equations Modeling and Numerical Simulation

    CERN Document Server

    Glowinski, Roland

    2008-01-01

    This book is dedicated to Olivier Pironneau. For more than 250 years partial differential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at first and then those originating from human activity and technological development. Mechanics, physics and their engineering applications were the first to benefit from the impact of partial differential equations on modeling and design, but a little less than a century ago the Schrödinger equation was the key opening the door to the application of partial differential equations to quantum chemistry, for small atomic and molecular systems at first, but then for systems of fast growing complexity. Mathematical modeling methods based on partial differential equations form an important part of contemporary science and are widely used in engineering and scientific applications. In this book several experts in this field present their latest results and discuss trends in the numerical analy...

  6. Particle Systems and Partial Differential Equations I

    CERN Document Server

    Gonçalves, Patricia

    2014-01-01

    This book presents the proceedings of the international conference Particle Systems and Partial Differential Equations I, which took place at the Centre of Mathematics of the University of Minho, Braga, Portugal, from the 5th to the 7th of December, 2012.  The purpose of the conference was to bring together world leaders to discuss their topics of expertise and to present some of their latest research developments in those fields. Among the participants were researchers in probability, partial differential equations and kinetics theory. The aim of the meeting was to present to a varied public the subject of interacting particle systems, its motivation from the viewpoint of physics and its relation with partial differential equations or kinetics theory, and to stimulate discussions and possibly new collaborations among researchers with different backgrounds.  The book contains lecture notes written by François Golse on the derivation of hydrodynamic equations (compressible and incompressible Euler and Navie...

  7. Generalized solutions of nonlinear partial differential equations

    CERN Document Server

    Rosinger, EE

    1987-01-01

    During the last few years, several fairly systematic nonlinear theories of generalized solutions of rather arbitrary nonlinear partial differential equations have emerged. The aim of this volume is to offer the reader a sufficiently detailed introduction to two of these recent nonlinear theories which have so far contributed most to the study of generalized solutions of nonlinear partial differential equations, bringing the reader to the level of ongoing research.The essence of the two nonlinear theories presented in this volume is the observation that much of the mathematics concernin

  8. Canonical coordinates for partial differential equations

    Science.gov (United States)

    Hunt, L. R.; Villarreal, Ramiro

    1988-01-01

    Necessary and sufficient conditions are found under which operators of the form Sigma (m, j=1) x (2) sub j + X sub O can be made constant coefficient. In addition, necessary and sufficient conditions are derived which classify those linear partial differential operators that can be moved to the Kolmogorov type.

  9. Canonical coordinates for partial differential equations

    Science.gov (United States)

    Hunt, L. R.; Villarreal, Ramiro

    1987-01-01

    Necessary and sufficient conditions are found under which operators of the form Sigma(m, j=1) X(2)sub j + X sub 0 can be made constant coefficient. In addition, necessary and sufficient conditions are derived which classify those linear partial differential operators that can be moved to the Kolmogorov type.

  10. Partial differential operators of elliptic type

    CERN Document Server

    Shimakura, Norio

    1992-01-01

    This book, which originally appeared in Japanese, was written for use in an undergraduate course or first year graduate course in partial differential equations and is likely to be of interest to researchers as well. This book presents a comprehensive study of the theory of elliptic partial differential operators. Beginning with the definitions of ellipticity for higher order operators, Shimakura discusses the Laplacian in Euclidean spaces, elementary solutions, smoothness of solutions, Vishik-Sobolev problems, the Schauder theory, and degenerate elliptic operators. The appendix covers such preliminaries as ordinary differential equations, Sobolev spaces, and maximum principles. Because elliptic operators arise in many areas, readers will appreciate this book for the way it brings together a variety of techniques that have arisen in different branches of mathematics.

  11. Computational partial differential equations using Matlab

    CERN Document Server

    Li, Jichun

    2008-01-01

    Brief Overview of Partial Differential Equations The parabolic equations The wave equations The elliptic equations Differential equations in broader areasA quick review of numerical methods for PDEsFinite Difference Methods for Parabolic Equations Introduction Theoretical issues: stability, consistence, and convergence 1-D parabolic equations2-D and 3-D parabolic equationsNumerical examples with MATLAB codesFinite Difference Methods for Hyperbolic Equations IntroductionSome basic difference schemes Dissipation and dispersion errors Extensions to conservation lawsThe second-order hyperbolic PDE

  12. Stochastic partial differential equations an introduction

    CERN Document Server

    Liu, Wei

    2015-01-01

    This book provides an introduction to the theory of stochastic partial differential equations (SPDEs) of evolutionary type. SPDEs are one of the main research directions in probability theory with several wide ranging applications. Many types of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. The theory of SPDEs is based both on the theory of deterministic partial differential equations, as well as on modern stochastic analysis. Whilst this volume mainly follows the ‘variational approach’, it also contains a short account on the ‘semigroup (or mild solution) approach’. In particular, the volume contains a complete presentation of the main existence and uniqueness results in the case of locally monotone coefficients. Various types of generalized coercivity conditions are shown to guarantee non-explosion, but also a systematic approach to treat SPDEs with explosion in finite time is developed. It is, so far, the only book where the latter and t...

  13. Hamiltonian partial differential equations and applications

    CERN Document Server

    Nicholls, David; Sulem, Catherine

    2015-01-01

    This book is a unique selection of work by world-class experts exploring the latest developments in Hamiltonian partial differential equations and their applications. Topics covered within are representative of the field’s wide scope, including KAM and normal form theories, perturbation and variational methods, integrable systems, stability of nonlinear solutions as well as applications to cosmology, fluid mechanics and water waves. The volume contains both surveys and original research papers and gives a concise overview of the above topics, with results ranging from mathematical modeling to rigorous analysis and numerical simulation. It will be of particular interest to graduate students as well as researchers in mathematics and physics, who wish to learn more about the powerful and elegant analytical techniques for Hamiltonian partial differential equations.

  14. Observability of discretized partial differential equations

    Science.gov (United States)

    Cohn, Stephen E.; Dee, Dick P.

    1988-01-01

    It is shown that complete observability of the discrete model used to assimilate data from a linear partial differential equation (PDE) system is necessary and sufficient for asymptotic stability of the data assimilation process. The observability theory for discrete systems is reviewed and applied to obtain simple observability tests for discretized constant-coefficient PDEs. Examples are used to show how numerical dispersion can result in discrete dynamics with multiple eigenvalues, thereby detracting from observability.

  15. Ambit processes and stochastic partial differential equations

    DEFF Research Database (Denmark)

    Barndorff-Nielsen, Ole; Benth, Fred Espen; Veraart, Almut

    Ambit processes are general stochastic processes based on stochastic integrals with respect to Lévy bases. Due to their flexible structure, they have great potential for providing realistic models for various applications such as in turbulence and finance. This papers studies the connection betwe...... ambit processes and solutions to stochastic partial differential equations. We investigate this relationship from two angles: from the Walsh theory of martingale measures and from the viewpoint of the Lévy noise analysis....

  16. First-order partial differential equations

    CERN Document Server

    Rhee, Hyun-Ku; Amundson, Neal R

    2001-01-01

    This first volume of a highly regarded two-volume text is fully usable on its own. After going over some of the preliminaries, the authors discuss mathematical models that yield first-order partial differential equations; motivations, classifications, and some methods of solution; linear and semilinear equations; chromatographic equations with finite rate expressions; homogeneous and nonhomogeneous quasilinear equations; formation and propagation of shocks; conservation equations, weak solutions, and shock layers; nonlinear equations; and variational problems. Exercises appear at the end of mo

  17. Differential geometry techniques for sets of nonlinear partial differential equations

    Science.gov (United States)

    Estabrook, Frank B.

    1990-01-01

    An attempt is made to show that the Cartan theory of partial differential equations can be a useful technique for applied mathematics. Techniques for finding consistent subfamilies of solutions that are generically rich and well-posed and for introducing potentials or other usefully consistent auxiliary fields are introduced. An extended sample calculation involving the Korteweg-de Vries equation is given.

  18. Semi-bounded partial differential operators

    CERN Document Server

    Cialdea, Alberto

    2014-01-01

    This book examines the conditions for the semi-boundedness of partial differential operators, which are interpreted in different ways. For example, today we know a great deal about L2-semibounded differential and pseudodifferential operators, although their complete characterization in analytic terms still poses difficulties, even for fairly simple operators. In contrast, until recently almost nothing was known about analytic characterizations of semi-boundedness for differential operators in other Hilbert function spaces and in Banach function spaces. This book works to address that gap. As such, various types of semi-boundedness are considered and a number of relevant conditions which are either necessary and sufficient or best possible in a certain sense are presented. The majority of the results reported on are the authors’ own contributions.

  19. Solving Partial Differential Equations Using a New Differential Evolution Algorithm

    Directory of Open Access Journals (Sweden)

    Natee Panagant

    2014-01-01

    Full Text Available This paper proposes an alternative meshless approach to solve partial differential equations (PDEs. With a global approximate function being defined, a partial differential equation problem is converted into an optimisation problem with equality constraints from PDE boundary conditions. An evolutionary algorithm (EA is employed to search for the optimum solution. For this approach, the most difficult task is the low convergence rate of EA which consequently results in poor PDE solution approximation. However, its attractiveness remains due to the nature of a soft computing technique in EA. The algorithm can be used to tackle almost any kind of optimisation problem with simple evolutionary operation, which means it is mathematically simpler to use. A new efficient differential evolution (DE is presented and used to solve a number of the partial differential equations. The results obtained are illustrated and compared with exact solutions. It is shown that the proposed method has a potential to be a future meshless tool provided that the search performance of EA is greatly enhanced.

  20. Partial differential equations in several complex variables

    CERN Document Server

    Chen, So-Chin

    2001-01-01

    This book is intended both as an introductory text and as a reference book for those interested in studying several complex variables in the context of partial differential equations. In the last few decades, significant progress has been made in the fields of Cauchy-Riemann and tangential Cauchy-Riemann operators. This book gives an up-to-date account of the theories for these equations and their applications. The background material in several complex variables is developed in the first three chapters, leading to the Levi problem. The next three chapters are devoted to the solvability and regularity of the Cauchy-Riemann equations using Hilbert space techniques. The authors provide a systematic study of the Cauchy-Riemann equations and the \\bar\\partial-Neumann problem, including L^2 existence theorems on pseudoconvex domains, \\frac 12-subelliptic estimates for the \\bar\\partial-Neumann problems on strongly pseudoconvex domains, global regularity of \\bar\\partial on more general pseudoconvex domains, boundary ...

  1. Nonlinear partial differential equations of second order

    CERN Document Server

    Dong, Guangchang

    1991-01-01

    This book addresses a class of equations central to many areas of mathematics and its applications. Although there is no routine way of solving nonlinear partial differential equations, effective approaches that apply to a wide variety of problems are available. This book addresses a general approach that consists of the following: Choose an appropriate function space, define a family of mappings, prove this family has a fixed point, and study various properties of the solution. The author emphasizes the derivation of various estimates, including a priori estimates. By focusing on a particular approach that has proven useful in solving a broad range of equations, this book makes a useful contribution to the literature.

  2. A partial differential equation for pseudocontact shift.

    Science.gov (United States)

    Charnock, G T P; Kuprov, Ilya

    2014-10-07

    It is demonstrated that pseudocontact shift (PCS), viewed as a scalar or a tensor field in three dimensions, obeys an elliptic partial differential equation with a source term that depends on the Hessian of the unpaired electron probability density. The equation enables straightforward PCS prediction and analysis in systems with delocalized unpaired electrons, particularly for the nuclei located in their immediate vicinity. It is also shown that the probability density of the unpaired electron may be extracted, using a regularization procedure, from PCS data.

  3. Nonlinear elliptic partial differential equations an introduction

    CERN Document Server

    Le Dret, Hervé

    2018-01-01

    This textbook presents the essential parts of the modern theory of nonlinear partial differential equations, including the calculus of variations. After a short review of results in real and functional analysis, the author introduces the main mathematical techniques for solving both semilinear and quasilinear elliptic PDEs, and the associated boundary value problems. Key topics include infinite dimensional fixed point methods, the Galerkin method, the maximum principle, elliptic regularity, and the calculus of variations. Aimed at graduate students and researchers, this textbook contains numerous examples and exercises and provides several comments and suggestions for further study.

  4. Partial differential equation models in macroeconomics.

    Science.gov (United States)

    Achdou, Yves; Buera, Francisco J; Lasry, Jean-Michel; Lions, Pierre-Louis; Moll, Benjamin

    2014-11-13

    The purpose of this article is to get mathematicians interested in studying a number of partial differential equations (PDEs) that naturally arise in macroeconomics. These PDEs come from models designed to study some of the most important questions in economics. At the same time, they are highly interesting for mathematicians because their structure is often quite difficult. We present a number of examples of such PDEs, discuss what is known about their properties, and list some open questions for future research. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

  5. Boundary value problems and partial differential equations

    CERN Document Server

    Powers, David L

    2005-01-01

    Boundary Value Problems is the leading text on boundary value problems and Fourier series. The author, David Powers, (Clarkson) has written a thorough, theoretical overview of solving boundary value problems involving partial differential equations by the methods of separation of variables. Professors and students agree that the author is a master at creating linear problems that adroitly illustrate the techniques of separation of variables used to solve science and engineering.* CD with animations and graphics of solutions, additional exercises and chapter review questions* Nearly 900 exercises ranging in difficulty* Many fully worked examples

  6. Nonlinear partial differential equations and their applications

    CERN Document Server

    Lions, Jacques Louis

    2002-01-01

    This book contains the written versions of lectures delivered since 1997 in the well-known weekly seminar on Applied Mathematics at the Collège de France in Paris, directed by Jacques-Louis Lions. It is the 14th and last of the series, due to the recent and untimely death of Professor Lions. The texts in this volume deal mostly with various aspects of the theory of nonlinear partial differential equations. They present both theoretical and applied results in many fields of growing importance such as Calculus of variations and optimal control, optimization, system theory and control, op

  7. Partial differential equations and their applications

    International Nuclear Information System (INIS)

    Gauthier-Villars

    1998-01-01

    This book is dedicated to the French mathematician J.L.Lions. It represents a compilation of articles from about 80 authors. The topics treated are diverse but the more or less commune matter is the study of the characteristics of some partial differential equations. Stability, optimal approximation, numerical resolution, particular applications are among the subjects reviewed. An article deals with the MHD stability of fusion plasmas in tokamaks, another presents the scientific and technical challenges of nuclear energy in France. The latter that contains no equations can be considered as an enjoyable break in a sea of about 40 mathematical articles. (A.C.)

  8. ERC Workshop on Geometric Partial Differential Equations

    CERN Document Server

    Novaga, Matteo; Valdinoci, Enrico

    2013-01-01

    This book is the outcome of a conference held at the Centro De Giorgi of the Scuola Normale of Pisa in September 2012. The aim of the conference was to discuss recent results on nonlinear partial differential equations, and more specifically geometric evolutions and reaction-diffusion equations. Particular attention was paid to self-similar solutions, such as solitons and travelling waves, asymptotic behaviour, formation of singularities and qualitative properties of solutions. These problems arise in many models from Physics, Biology, Image Processing and Applied Mathematics in general, and have attracted a lot of attention in recent years.

  9. Numerical Methods for Partial Differential Equations

    CERN Document Server

    Guo, Ben-yu

    1987-01-01

    These Proceedings of the first Chinese Conference on Numerical Methods for Partial Differential Equations covers topics such as difference methods, finite element methods, spectral methods, splitting methods, parallel algorithm etc., their theoretical foundation and applications to engineering. Numerical methods both for boundary value problems of elliptic equations and for initial-boundary value problems of evolution equations, such as hyperbolic systems and parabolic equations, are involved. The 16 papers of this volume present recent or new unpublished results and provide a good overview of current research being done in this field in China.

  10. Inverse problems for partial differential equations

    CERN Document Server

    Isakov, Victor

    2017-01-01

    This third edition expands upon the earlier edition by adding nearly 40 pages of new material reflecting the analytical and numerical progress in inverse problems in last 10 years. As in the second edition, the emphasis is on new ideas and methods rather than technical improvements. These new ideas include use of the stationary phase method in the two-dimensional elliptic problems and of multi frequencies\\temporal data to improve stability and numerical resolution. There are also numerous corrections and improvements of the exposition throughout. This book is intended for mathematicians working with partial differential equations and their applications, physicists, geophysicists, and financial, electrical, and mechanical engineers involved with nondestructive evaluation, seismic exploration, remote sensing, and various kinds of tomography. Review of the second edition: "The first edition of this excellent book appeared in 1998 and became a standard reference for everyone interested in analysis and numerics of...

  11. Partial Differential Equations and Solitary Waves Theory

    CERN Document Server

    Wazwaz, Abdul-Majid

    2009-01-01

    "Partial Differential Equations and Solitary Waves Theory" is a self-contained book divided into two parts: Part I is a coherent survey bringing together newly developed methods for solving PDEs. While some traditional techniques are presented, this part does not require thorough understanding of abstract theories or compact concepts. Well-selected worked examples and exercises shall guide the reader through the text. Part II provides an extensive exposition of the solitary waves theory. This part handles nonlinear evolution equations by methods such as Hirota’s bilinear method or the tanh-coth method. A self-contained treatment is presented to discuss complete integrability of a wide class of nonlinear equations. This part presents in an accessible manner a systematic presentation of solitons, multi-soliton solutions, kinks, peakons, cuspons, and compactons. While the whole book can be used as a text for advanced undergraduate and graduate students in applied mathematics, physics and engineering, Part II w...

  12. Partial differential equations mathematical techniques for engineers

    CERN Document Server

    Epstein, Marcelo

    2017-01-01

    This monograph presents a graduate-level treatment of partial differential equations (PDEs) for engineers. The book begins with a review of the geometrical interpretation of systems of ODEs, the appearance of PDEs in engineering is motivated by the general form of balance laws in continuum physics. Four chapters are devoted to a detailed treatment of the single first-order PDE, including shock waves and genuinely non-linear models, with applications to traffic design and gas dynamics. The rest of the book deals with second-order equations. In the treatment of hyperbolic equations, geometric arguments are used whenever possible and the analogy with discrete vibrating systems is emphasized. The diffusion and potential equations afford the opportunity of dealing with questions of uniqueness and continuous dependence on the data, the Fourier integral, generalized functions (distributions), Duhamel's principle, Green's functions and Dirichlet and Neumann problems. The target audience primarily comprises graduate s...

  13. Handbook of differential equations stationary partial differential equations

    CERN Document Server

    Chipot, Michel

    2006-01-01

    This handbook is volume III in a series devoted to stationary partial differential quations. Similarly as volumes I and II, it is a collection of self contained state-of-the-art surveys written by well known experts in the field. The topics covered by this handbook include singular and higher order equations, problems near critically, problems with anisotropic nonlinearities, dam problem, T-convergence and Schauder-type estimates. These surveys will be useful for both beginners and experts and speed up the progress of corresponding (rapidly developing and fascinating) areas of mathematics. Ke

  14. Compatible Spatial Discretizations for Partial Differential Equations

    Energy Technology Data Exchange (ETDEWEB)

    Arnold, Douglas, N, ed.

    2004-11-25

    From May 11--15, 2004, the Institute for Mathematics and its Applications held a hot topics workshop on Compatible Spatial Discretizations for Partial Differential Equations. The numerical solution of partial differential equations (PDE) is a fundamental task in science and engineering. The goal of the workshop was to bring together a spectrum of scientists at the forefront of the research in the numerical solution of PDEs to discuss compatible spatial discretizations. We define compatible spatial discretizations as those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. A wide variety of discretization methods applied across a wide range of scientific and engineering applications have been designed to or found to inherit or mimic intrinsic spatial structure and reproduce fundamental properties of the solution of the continuous PDE model at the finite dimensional level. A profusion of such methods and concepts relevant to understanding them have been developed and explored: mixed finite element methods, mimetic finite differences, support operator methods, control volume methods, discrete differential forms, Whitney forms, conservative differencing, discrete Hodge operators, discrete Helmholtz decomposition, finite integration techniques, staggered grid and dual grid methods, etc. This workshop seeks to foster communication among the diverse groups of researchers designing, applying, and studying such methods as well as researchers involved in practical solution of large scale problems that may benefit from advancements in such discretizations; to help elucidate the relations between the different methods and concepts; and to generally advance our understanding in the area of compatible spatial discretization methods for PDE. Particular points of emphasis included: + Identification of intrinsic properties of PDE models that are critical for the fidelity of numerical

  15. Teaching Modeling with Partial Differential Equations: Several Successful Approaches

    Science.gov (United States)

    Myers, Joseph; Trubatch, David; Winkel, Brian

    2008-01-01

    We discuss the introduction and teaching of partial differential equations (heat and wave equations) via modeling physical phenomena, using a new approach that encompasses constructing difference equations and implementing these in a spreadsheet, numerically solving the partial differential equations using the numerical differential equation…

  16. A Line-Tau Collocation Method for Partial Differential Equations ...

    African Journals Online (AJOL)

    This paper deals with the numerical solution of second order linear partial differential equations with the use of the method of lines coupled with the tau collocation method. The method of lines is used to convert the partial differential equation (PDE) to a sequence of ordinary differential equations (ODEs) which is then ...

  17. Parameter Estimation of Partial Differential Equation Models.

    Science.gov (United States)

    Xun, Xiaolei; Cao, Jiguo; Mallick, Bani; Carroll, Raymond J; Maity, Arnab

    2013-01-01

    Partial differential equation (PDE) models are commonly used to model complex dynamic systems in applied sciences such as biology and finance. The forms of these PDE models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system. Parameters in PDE models often have interesting scientific interpretations, but their values are often unknown, and need to be estimated from the measurements of the dynamic system in the present of measurement errors. Most PDEs used in practice have no analytic solutions, and can only be solved with numerical methods. Currently, methods for estimating PDE parameters require repeatedly solving PDEs numerically under thousands of candidate parameter values, and thus the computational load is high. In this article, we propose two methods to estimate parameters in PDE models: a parameter cascading method and a Bayesian approach. In both methods, the underlying dynamic process modeled with the PDE model is represented via basis function expansion. For the parameter cascading method, we develop two nested levels of optimization to estimate the PDE parameters. For the Bayesian method, we develop a joint model for data and the PDE, and develop a novel hierarchical model allowing us to employ Markov chain Monte Carlo (MCMC) techniques to make posterior inference. Simulation studies show that the Bayesian method and parameter cascading method are comparable, and both outperform other available methods in terms of estimation accuracy. The two methods are demonstrated by estimating parameters in a PDE model from LIDAR data.

  18. Partial Differential Equations in General Relativity

    International Nuclear Information System (INIS)

    Choquet-Bruhat, Yvonne

    2008-01-01

    General relativity is a physical theory basic in the modeling of the universe at the large and small scales. Its mathematical formulation, the Einstein partial differential equations, are geometrically simple, but intricate for the analyst, involving both hyperbolic and elliptic PDE, with local and global problems. Many problems remain open though remarkable progress has been made recently towards their solutions. Alan Rendall's book states, in a down-to-earth form, fundamental results used to solve different types of equations. In each case he gives applications to special models as well as to general properties of Einsteinian spacetimes. A chapter on ODE contains, in particular, a detailed discussion of Bianchi spacetimes. A chapter entitled 'Elliptic systems' treats the Einstein constraints. A chapter entitled 'Hyperbolic systems' is followed by a chapter on the Cauchy problem and a chapter 'Global results' which contains recently proved theorems. A chapter is dedicated to the Einstein-Vlasov system, of which the author is a specialist. On the whole, the book surveys, in a concise though precise way, many essential results of recent interest in mathematical general relativity, and it is very clearly written. Each chapter is followed by an up to date bibliography. In conclusion, this book will be a valuable asset to relativists who wish to learn clearly-stated mathematical results and to mathematicians who want to penetrate into the subtleties of general relativity, as a mathematical and physical theory. (book review)

  19. Partial Differential Equations in General Relativity

    Energy Technology Data Exchange (ETDEWEB)

    Choquet-Bruhat, Yvonne

    2008-09-07

    General relativity is a physical theory basic in the modeling of the universe at the large and small scales. Its mathematical formulation, the Einstein partial differential equations, are geometrically simple, but intricate for the analyst, involving both hyperbolic and elliptic PDE, with local and global problems. Many problems remain open though remarkable progress has been made recently towards their solutions. Alan Rendall's book states, in a down-to-earth form, fundamental results used to solve different types of equations. In each case he gives applications to special models as well as to general properties of Einsteinian spacetimes. A chapter on ODE contains, in particular, a detailed discussion of Bianchi spacetimes. A chapter entitled 'Elliptic systems' treats the Einstein constraints. A chapter entitled 'Hyperbolic systems' is followed by a chapter on the Cauchy problem and a chapter 'Global results' which contains recently proved theorems. A chapter is dedicated to the Einstein-Vlasov system, of which the author is a specialist. On the whole, the book surveys, in a concise though precise way, many essential results of recent interest in mathematical general relativity, and it is very clearly written. Each chapter is followed by an up to date bibliography. In conclusion, this book will be a valuable asset to relativists who wish to learn clearly-stated mathematical results and to mathematicians who want to penetrate into the subtleties of general relativity, as a mathematical and physical theory. (book review)

  20. Partial differential equations methods, applications and theories

    CERN Document Server

    Hattori, Harumi

    2013-01-01

    This volume is an introductory level textbook for partial differential equations (PDE's) and suitable for a one-semester undergraduate level or two-semester graduate level course in PDE's or applied mathematics. Chapters One to Five are organized according to the equations and the basic PDE's are introduced in an easy to understand manner. They include the first-order equations and the three fundamental second-order equations, i.e. the heat, wave and Laplace equations. Through these equations we learn the types of problems, how we pose the problems, and the methods of solutions such as the separation of variables and the method of characteristics. The modeling aspects are explained as well. The methods introduced in earlier chapters are developed further in Chapters Six to Twelve. They include the Fourier series, the Fourier and the Laplace transforms, and the Green's functions. The equations in higher dimensions are also discussed in detail. This volume is application-oriented and rich in examples. Going thr...

  1. Parameter Estimation of Partial Differential Equation Models

    KAUST Repository

    Xun, Xiaolei

    2013-09-01

    Partial differential equation (PDE) models are commonly used to model complex dynamic systems in applied sciences such as biology and finance. The forms of these PDE models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system. Parameters in PDE models often have interesting scientific interpretations, but their values are often unknown and need to be estimated from the measurements of the dynamic system in the presence of measurement errors. Most PDEs used in practice have no analytic solutions, and can only be solved with numerical methods. Currently, methods for estimating PDE parameters require repeatedly solving PDEs numerically under thousands of candidate parameter values, and thus the computational load is high. In this article, we propose two methods to estimate parameters in PDE models: a parameter cascading method and a Bayesian approach. In both methods, the underlying dynamic process modeled with the PDE model is represented via basis function expansion. For the parameter cascading method, we develop two nested levels of optimization to estimate the PDE parameters. For the Bayesian method, we develop a joint model for data and the PDE and develop a novel hierarchical model allowing us to employ Markov chain Monte Carlo (MCMC) techniques to make posterior inference. Simulation studies show that the Bayesian method and parameter cascading method are comparable, and both outperform other available methods in terms of estimation accuracy. The two methods are demonstrated by estimating parameters in a PDE model from long-range infrared light detection and ranging data. Supplementary materials for this article are available online. © 2013 American Statistical Association.

  2. Asymptotic problems for stochastic partial differential equations

    Science.gov (United States)

    Salins, Michael

    Stochastic partial differential equations (SPDEs) can be used to model systems in a wide variety of fields including physics, chemistry, and engineering. The main SPDEs of interest in this dissertation are the semilinear stochastic wave equations which model the movement of a material with constant mass density that is exposed to both determinstic and random forcing. Cerrai and Freidlin have shown that on fixed time intervals, as the mass density of the material approaches zero, the solutions of the stochastic wave equation converge uniformly to the solutions of a stochastic heat equation, in probability. This is called the Smoluchowski-Kramers approximation. In Chapter 2, we investigate some of the multi-scale behaviors that these wave equations exhibit. In particular, we show that the Freidlin-Wentzell exit place and exit time asymptotics for the stochastic wave equation in the small noise regime can be approximated by the exit place and exit time asymptotics for the stochastic heat equation. We prove that the exit time and exit place asymptotics are characterized by quantities called quasipotentials and we prove that the quasipotentials converge. We then investigate the special case where the equation has a gradient structure and show that we can explicitly solve for the quasipotentials, and that the quasipotentials for the heat equation and wave equation are equal. In Chapter 3, we study the Smoluchowski-Kramers approximation in the case where the material is electrically charged and exposed to a magnetic field. Interestingly, if the system is frictionless, then the Smoluchowski-Kramers approximation does not hold. We prove that the Smoluchowski-Kramers approximation is valid for systems exposed to both a magnetic field and friction. Notably, we prove that the solutions to the second-order equations converge to the solutions of the first-order equation in an Lp sense. This strengthens previous results where convergence was proved in probability.

  3. Topics in numerical partial differential equations and scientific computing

    CERN Document Server

    2016-01-01

    Numerical partial differential equations (PDEs) are an important part of numerical simulation, the third component of the modern methodology for science and engineering, besides the traditional theory and experiment. This volume contains papers that originated with the collaborative research of the teams that participated in the IMA Workshop for Women in Applied Mathematics: Numerical Partial Differential Equations and Scientific Computing in August 2014.

  4. Lagrangian vector field and Lagrangian formulation of partial differential equations

    Directory of Open Access Journals (Sweden)

    M.Chen

    2005-01-01

    Full Text Available In this paper we consider the Lagrangian formulation of a system of second order quasilinear partial differential equations. Specifically we construct a Lagrangian vector field such that the flows of the vector field satisfy the original system of partial differential equations.

  5. A note on the Lie symmetries of complex partial differential

    Indian Academy of Sciences (India)

    Folklore suggests that the split Lie-like operators of a complex partial differential equation are symmetries of the split system of real partial differential equations. However, this is not the case generally. We illustrate this by using the complex heat equation, wave equation with dissipation, the nonlinear Burgers equation and ...

  6. Effective action for stochastic partial differential equations

    International Nuclear Information System (INIS)

    Hochberg, David; Molina-Paris, Carmen; Perez-Mercader, Juan; Visser, Matt

    1999-01-01

    Stochastic partial differential equations (SPDEs) are the basic tool for modeling systems where noise is important. SPDEs are used for models of turbulence, pattern formation, and the structural development of the universe itself. It is reasonably well known that certain SPDEs can be manipulated to be equivalent to (nonquantum) field theories that nevertheless exhibit deep and important relationships with quantum field theory. In this paper we systematically extend these ideas: We set up a functional integral formalism and demonstrate how to extract all the one-loop physics for an arbitrary SPDE subject to arbitrary Gaussian noise. It is extremely important to realize that Gaussian noise does not imply that the field variables undergo Gaussian fluctuations, and that these nonquantum field theories are fully interacting. The limitation to one loop is not as serious as might be supposed: Experience with quantum field theories (QFTs) has taught us that one-loop physics is often quite adequate to give a good description of the salient issues. The limitation to one loop does, however, offer marked technical advantages: Because at one loop almost any field theory can be rendered finite using zeta function technology, we can sidestep the complications inherent in the Martin-Siggia-Rose formalism (the SPDE analog of the Becchi-Rouet-Stora-Tyutin formalism used in QFT) and instead focus attention on a minimalist approach that uses only the physical fields (this ''direct approach'' is the SPDE analog of canonical quantization using physical fields). After setting up the general formalism for the characteristic functional (partition function), we show how to define the effective action to all loops, and then focus on the one-loop effective action and its specialization to constant fields: the effective potential. The physical interpretation of the effective action and effective potential for SPDEs is addressed and we show that key features carry over from QFT to the case of

  7. Effective action for stochastic partial differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Hochberg, David [Laboratorio de Astrofisica Espacial y Fisica Fundamental, Apartado 50727, 28080 Madrid, (Spain); Centro de Astrobiologia, INTA, Carratera Ajalvir, Km. 4, 28850 Torrejon, Madrid, (Spain); Molina-Paris, Carmen [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Perez-Mercader, Juan [Laboratorio de Astrofisica Espacial y Fisica Fundamental, Apartado 50727, 28080 Madrid, (Spain); Visser, Matt [Physics Department, Washington University, Saint Louis, Missouri 63130-4899 (United States)

    1999-12-01

    Stochastic partial differential equations (SPDEs) are the basic tool for modeling systems where noise is important. SPDEs are used for models of turbulence, pattern formation, and the structural development of the universe itself. It is reasonably well known that certain SPDEs can be manipulated to be equivalent to (nonquantum) field theories that nevertheless exhibit deep and important relationships with quantum field theory. In this paper we systematically extend these ideas: We set up a functional integral formalism and demonstrate how to extract all the one-loop physics for an arbitrary SPDE subject to arbitrary Gaussian noise. It is extremely important to realize that Gaussian noise does not imply that the field variables undergo Gaussian fluctuations, and that these nonquantum field theories are fully interacting. The limitation to one loop is not as serious as might be supposed: Experience with quantum field theories (QFTs) has taught us that one-loop physics is often quite adequate to give a good description of the salient issues. The limitation to one loop does, however, offer marked technical advantages: Because at one loop almost any field theory can be rendered finite using zeta function technology, we can sidestep the complications inherent in the Martin-Siggia-Rose formalism (the SPDE analog of the Becchi-Rouet-Stora-Tyutin formalism used in QFT) and instead focus attention on a minimalist approach that uses only the physical fields (this ''direct approach'' is the SPDE analog of canonical quantization using physical fields). After setting up the general formalism for the characteristic functional (partition function), we show how to define the effective action to all loops, and then focus on the one-loop effective action and its specialization to constant fields: the effective potential. The physical interpretation of the effective action and effective potential for SPDEs is addressed and we show that key features carry over from

  8. Reduced differential transform method for partial differential equations within local fractional derivative operators

    Directory of Open Access Journals (Sweden)

    Hossein Jafari

    2016-04-01

    Full Text Available The non-differentiable solution of the linear and non-linear partial differential equations on Cantor sets is implemented in this article. The reduced differential transform method is considered in the local fractional operator sense. The four illustrative examples are given to show the efficiency and accuracy features of the presented technique to solve local fractional partial differential equations.

  9. On the hierarchy of partially invariant submodels of differential equations

    OpenAIRE

    Golovin, Sergey V.

    2007-01-01

    It is noticed, that partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PIS of the higher rank. This introduce a hierarchic structure in the set of all PISs of a given system of differential equations. By using this structure one can significantly decrease an amount of calculations required in enumeration of all PISs for a given system of partially differential equations. An equivalence of the two-step and the direct ...

  10. Partial differential equations & boundary value problems with Maple

    CERN Document Server

    Articolo, George A

    2009-01-01

    Partial Differential Equations and Boundary Value Problems with Maple presents all of the material normally covered in a standard course on partial differential equations, while focusing on the natural union between this material and the powerful computational software, Maple. The Maple commands are so intuitive and easy to learn, students can learn what they need to know about the software in a matter of hours- an investment that provides substantial returns. Maple''s animation capabilities allow students and practitioners to see real-time displays of the solutions of partial differential equations.  Maple files can be found on the books website. Ancillary list: Maple files- http://www.elsevierdirect.com/companion.jsp?ISBN=9780123747327  Provides a quick overview of the software w/simple commands needed to get startedIncludes review material on linear algebra and Ordinary Differential equations, and their contribution in solving partial differential equationsIncorporates an early introduction to Sturm-L...

  11. On the hierarchy of partially invariant submodels of differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Golovin, Sergey V [Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk 630090 (Russian Federation)], E-mail: sergey@hydro.nsc.ru

    2008-07-04

    It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given.

  12. On the hierarchy of partially invariant submodels of differential equations

    Science.gov (United States)

    Golovin, Sergey V.

    2008-07-01

    It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given.

  13. On the hierarchy of partially invariant submodels of differential equations

    International Nuclear Information System (INIS)

    Golovin, Sergey V

    2008-01-01

    It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given

  14. Flow visualization via partial differential equations

    NARCIS (Netherlands)

    Preusser, T.; Rumpf, M.; Telea, A.C.; Möller, T.; Hamann, B.; Russell, R.D.

    2009-01-01

    The visualization of stationary and time-dependent flow is an important and chaltenging topic in scientific visualization. lts aim is 10 represent transport phenomena govemed by vector fjelds in an intuitively understandable way. In this paper. we review the use of methods based on partial

  15. From ordinary to partial differential equations

    CERN Document Server

    Esposito, Giampiero

    2017-01-01

    This book is addressed to mathematics and physics students who want to develop an interdisciplinary view of mathematics, from the age of Riemann, Poincaré and Darboux to basic tools of modern mathematics. It enables them to acquire the sensibility necessary for the formulation and solution of difficult problems, with an emphasis on concepts, rigour and creativity. It consists of eight self-contained parts: ordinary differential equations; linear elliptic equations; calculus of variations; linear and non-linear hyperbolic equations; parabolic equations; Fuchsian functions and non-linear equations; the functional equations of number theory; pseudo-differential operators and pseudo-differential equations. The author leads readers through the original papers and introduces new concepts, with a selection of topics and examples that are of high pedagogical value.

  16. Sparse dynamics for partial differential equations.

    Science.gov (United States)

    Schaeffer, Hayden; Caflisch, Russel; Hauck, Cory D; Osher, Stanley

    2013-04-23

    We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to the coefficients of the basis approximation. By reducing or compressing the information needed to represent the solution at every step, only the essential dynamics are represented. In many cases, there are natural bases derived from the differential equations, which promote sparsity. We find that our method successfully reduces the dynamics of convection equations, diffusion equations, weak shocks, and vorticity equations with high-frequency source terms.

  17. Partial differential equation models in the socio-economic sciences

    KAUST Repository

    Burger, Martin; Caffarelli, Luis; Markowich, Peter A.

    2014-01-01

    Mathematical models based on partial differential equations (PDEs) have become an integral part of quantitative analysis in most branches of science and engineering, recently expanding also towards biomedicine and socio-economic sciences

  18. A Priori Regularity of Parabolic Partial Differential Equations

    KAUST Repository

    Berkemeier, Francisco

    2018-01-01

    In this thesis, we consider parabolic partial differential equations such as the heat equation, the Fokker-Planck equation, and the porous media equation. Our aim is to develop methods that provide a priori estimates for solutions with singular

  19. Introduction to partial differential equations and Hilbert space methods

    CERN Document Server

    Gustafson, Karl E

    1997-01-01

    Easy-to-use text examines principal method of solving partial differential equations, 1st-order systems, computation methods, and much more. Over 600 exercises, with answers for many. Ideal for a 1-semester or full-year course.

  20. Exact solutions of some nonlinear partial differential equations using ...

    Indian Academy of Sciences (India)

    Nonlinear partial differential equations (NPDEs) are encountered in various ... such as physics, mechanics, chemistry, biology, mathematics and engineering. ... In §3, this method is applied to the generalized forms of Klein–Gordon equation,.

  1. International Conference on Multiscale Methods and Partial Differential Equations.

    Energy Technology Data Exchange (ETDEWEB)

    Thomas Hou

    2006-12-12

    The International Conference on Multiscale Methods and Partial Differential Equations (ICMMPDE for short) was held at IPAM, UCLA on August 26-27, 2005. The conference brought together researchers, students and practitioners with interest in the theoretical, computational and practical aspects of multiscale problems and related partial differential equations. The conference provided a forum to exchange and stimulate new ideas from different disciplines, and to formulate new challenging multiscale problems that will have impact in applications.

  2. Numerical Analysis for Stochastic Partial Differential Delay Equations with Jumps

    OpenAIRE

    Li, Yan; Hu, Junhao

    2013-01-01

    We investigate the convergence rate of Euler-Maruyama method for a class of stochastic partial differential delay equations driven by both Brownian motion and Poisson point processes. We discretize in space by a Galerkin method and in time by using a stochastic exponential integrator. We generalize some results of Bao et al. (2011) and Jacob et al. (2009) in finite dimensions to a class of stochastic partial differential delay equations with jumps in infinite dimensions.

  3. Auxiliary equation method for solving nonlinear partial differential equations

    International Nuclear Information System (INIS)

    Sirendaoreji,; Jiong, Sun

    2003-01-01

    By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation

  4. Partial differential equations with numerical methods

    CERN Document Server

    Larsson, Stig

    2003-01-01

    The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering. The main theme is the integration of the theory of linear PDEs and the numerical solution of such equations. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. As preparation, the two-point boundary value problem and the initial-value problem for ODEs are discussed in separate chapters. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. Some background on linear functional analysis and Sobolev spaces, and also on numerical linear algebra, is reviewed in two appendices.

  5. Elliptic partial differential equations of second order

    CERN Document Server

    Gilbarg, David

    2001-01-01

    From the reviews: "This is a book of interest to any having to work with differential equations, either as a reference or as a book to learn from. The authors have taken trouble to make the treatment self-contained. It (is) suitable required reading for a PhD student. Although the material has been developed from lectures at Stanford, it has developed into an almost systematic coverage that is much longer than could be covered in a year's lectures". Newsletter, New Zealand Mathematical Society, 1985 "Primarily addressed to graduate students this elegant book is accessible and useful to a broad spectrum of applied mathematicians". Revue Roumaine de Mathématiques Pures et Appliquées,1985.

  6. On the relation between elementary partial difference equations and partial differential equations

    NARCIS (Netherlands)

    van den Berg, I.P.

    1998-01-01

    The nonstandard stroboscopy method links discrete-time ordinary difference equations of first-order and continuous-time, ordinary differential equations of first order. We extend this method to the second order, and also to an elementary, yet general class of partial difference/differential

  7. Entropy and convexity for nonlinear partial differential equations.

    Science.gov (United States)

    Ball, John M; Chen, Gui-Qiang G

    2013-12-28

    Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological and social processes. The concept of entropy originated in thermodynamics and statistical physics during the nineteenth century to describe the heat exchanges that occur in the thermal processes in a thermodynamic system, while the original notion of convexity is for sets and functions in mathematics. Since then, entropy and convexity have become two of the most important concepts in mathematics. In particular, nonlinear methods via entropy and convexity have been playing an increasingly important role in the analysis of nonlinear partial differential equations in recent decades. This opening article of the Theme Issue is intended to provide an introduction to entropy, convexity and related nonlinear methods for the analysis of nonlinear partial differential equations. We also provide a brief discussion about the content and contributions of the papers that make up this Theme Issue.

  8. Convergence criteria for systems of nonlinear elliptic partial differential equations

    International Nuclear Information System (INIS)

    Sharma, R.K.

    1986-01-01

    This thesis deals with convergence criteria for a special system of nonlinear elliptic partial differential equations. A fixed-point algorithm is used, which iteratively solves one linearized elliptic partial differential equation at a time. Conditions are established that help foresee the convergence of the algorithm. Under reasonable hypotheses it is proved that the algorithm converges for such nonlinear elliptic systems. Extensive experimental results are reported and they show the algorithm converges in a wide variety of cases and the convergence is well correlated with the theoretical conditions introduced in this thesis

  9. Optimal moving grids for time-dependent partial differential equations

    Science.gov (United States)

    Wathen, A. J.

    1992-01-01

    Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of PDE solutions in the least-squares norm are reported.

  10. Advances in nonlinear partial differential equations and stochastics

    CERN Document Server

    Kawashima, S

    1998-01-01

    In the past two decades, there has been great progress in the theory of nonlinear partial differential equations. This book describes the progress, focusing on interesting topics in gas dynamics, fluid dynamics, elastodynamics etc. It contains ten articles, each of which discusses a very recent result obtained by the author. Some of these articles review related results.

  11. The Cousin problems in the viewpoint of partial differential equations

    International Nuclear Information System (INIS)

    Le Hung Son.

    1990-01-01

    In this paper we consider the Cousin problems for overdetermined systems of partial differential equations, which are generalizations of the Cauchy-Riemann system. The general methods for solving these problems are given. Applying the given methods we can solve the Cousin problems for many important systems in theoretical physics. (author). 19 refs

  12. Mild Solutions of Neutral Stochastic Partial Functional Differential Equations

    Directory of Open Access Journals (Sweden)

    T. E. Govindan

    2011-01-01

    Full Text Available This paper studies the existence and uniqueness of a mild solution for a neutral stochastic partial functional differential equation using a local Lipschitz condition. When the neutral term is zero and even in the deterministic special case, the result obtained here appears to be new. An example is included to illustrate the theory.

  13. Exact solutions of some nonlinear partial differential equations using ...

    Indian Academy of Sciences (India)

    The functional variable method is a powerful solution method for obtaining exact solutions of some nonlinear partial differential equations. In this paper, the functional variable method is used to establish exact solutions of the generalized forms of Klein–Gordon equation, the (2 + 1)-dimensional Camassa–Holm ...

  14. Constructing general partial differential equations using polynomial and neural networks.

    Science.gov (United States)

    Zjavka, Ladislav; Pedrycz, Witold

    2016-01-01

    Sum fraction terms can approximate multi-variable functions on the basis of discrete observations, replacing a partial differential equation definition with polynomial elementary data relation descriptions. Artificial neural networks commonly transform the weighted sum of inputs to describe overall similarity relationships of trained and new testing input patterns. Differential polynomial neural networks form a new class of neural networks, which construct and solve an unknown general partial differential equation of a function of interest with selected substitution relative terms using non-linear multi-variable composite polynomials. The layers of the network generate simple and composite relative substitution terms whose convergent series combinations can describe partial dependent derivative changes of the input variables. This regression is based on trained generalized partial derivative data relations, decomposed into a multi-layer polynomial network structure. The sigmoidal function, commonly used as a nonlinear activation of artificial neurons, may transform some polynomial items together with the parameters with the aim to improve the polynomial derivative term series ability to approximate complicated periodic functions, as simple low order polynomials are not able to fully make up for the complete cycles. The similarity analysis facilitates substitutions for differential equations or can form dimensional units from data samples to describe real-world problems. Copyright © 2015 Elsevier Ltd. All rights reserved.

  15. Function spaces and partial differential equations 2 volume set

    CERN Document Server

    Taheri, Ali

    2015-01-01

    This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour.

  16. Function spaces and partial differential equations volume 2 : contemporary analysis

    CERN Document Server

    Taheri, Ali

    2015-01-01

    This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour.

  17. Energy preserving integration of bi-Hamiltonian partial differential equations

    NARCIS (Netherlands)

    Karasozen, B.; Simsek, G.

    2013-01-01

    The energy preserving average vector field (AVF) integrator is applied to evolutionary partial differential equations (PDEs) in bi-Hamiltonian form with nonconstant Poisson structures. Numerical results for the Korteweg de Vries (KdV) equation and for the Ito type coupled KdV equation confirm the

  18. Stability test for a parabolic partial differential equation

    NARCIS (Netherlands)

    Vajta, Miklos

    2001-01-01

    The paper describes a stability test applied to coupled parabolic partial differential equations. The PDE's describe the temperature distribution of composite structures with linear inner heat sources. The distributed transfer functions are developed based on the transmission matrix of each layer.

  19. Multigrid methods for partial differential equations - a short introduction

    International Nuclear Information System (INIS)

    Linden, J.; Stueben, K.

    1993-01-01

    These notes summarize the multigrid methods and emphasis is laid on the algorithmic concepts of multigrid for solving linear and non-linear partial differential equations. In this paper there is brief description of the basic structure of multigrid methods. Detailed introduction is also contained with applications to VLSI process simulation. (A.B.)

  20. Book review: Partial Differential Equations and Fluid Mechanics

    NARCIS (Netherlands)

    Muntean, A.

    2011-01-01

    The baak is the result of the workshop Partial Differential Equations and Fluid Dynamics that look place at the Mathematics Institute of the University of Warwick. May 21st - 23rd, 2007. It contains ten review and research papers which provide an accessible summary of a wide range of active research

  1. Solution of partial differential equations by agent-based simulation

    International Nuclear Information System (INIS)

    Szilagyi, Miklos N

    2014-01-01

    The purpose of this short note is to demonstrate that partial differential equations can be quickly solved by agent-based simulation with high accuracy. There is no need for the solution of large systems of algebraic equations. This method is especially useful for quick determination of potential distributions and demonstration purposes in teaching electromagnetism. (letters and comments)

  2. Functional Determinants for Radially Separable Partial Differential Operators

    Directory of Open Access Journals (Sweden)

    G. V. Dunne

    2007-01-01

    Full Text Available Functional determinants of differential operators play a prominent role in many fields of theoretical and mathematical physics, ranging from condensed matter physics, to atomic, molecular and particle physics. They are, however, difficult to compute reliably in non-trivial cases. In one dimensional problems (i.e. functional determinants of ordinary differential operators, a classic result of Gel’fand and Yaglom greatly simplifies the computation of functional determinants. Here I report some recent progress in extending this approach to higher dimensions (i.e., functional determinants of partial differential operators, with applications in quantum field theory. 

  3. Calculation of similarity solutions of partial differential equations

    International Nuclear Information System (INIS)

    Dresner, L.

    1980-08-01

    When a partial differential equation in two independent variables is invariant to a group G of stretching transformations, it has similarity solutions that can be found by solving an ordinary differential equation. Under broad conditions, this ordinary differential equation is also invariant to another stretching group G', related to G. The invariance of the ordinary differential equation to G' can be used to simplify its solution, particularly if it is of second order. Then a method of Lie's can be used to reduce it to a first-order equation, the study of which is greatly facilitated by analysis of its direction field. The method developed here is applied to three examples: Blasius's equation for boundary layer flow over a flat plate and two nonlinear diffusion equations, cc/sub t/ = c/sub zz/ and c/sub t/ = (cc/sub z/)/sub z/

  4. Plane waves and spherical means applied to partial differential equations

    CERN Document Server

    John, Fritz

    2004-01-01

    Elementary and self-contained, this heterogeneous collection of results on partial differential equations employs certain elementary identities for plane and spherical integrals of an arbitrary function, showing how a variety of results on fairly general differential equations follow from those identities. The first chapter deals with the decomposition of arbitrary functions into functions of the type of plane waves. Succeeding chapters introduce the first application of the Radon transformation and examine the solution of the initial value problem for homogeneous hyperbolic equations with con

  5. Representations of Lie algebras and partial differential equations

    CERN Document Server

    Xu, Xiaoping

    2017-01-01

    This book provides explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic codes, combinatorics and algebraic varieties, summarizing the author’s works and his joint works with his former students.  Further, it presents various oscillator generalizations of the classical representation theorem on harmonic polynomials, and highlights new functors from the representation category of a simple Lie algebra to that of another simple Lie algebra. Partial differential equations play a key role in solving certain representation problems. The weight matrices of the minimal and adjoint representations over the simple Lie algebras of types E and F are proved to generate ternary orthogonal linear codes with large minimal distances. New multi-variable hypergeometric functions related to the root systems of simple Lie algebras are introduced in connection with quantum many-body systems in one dimension. In addition, the book identifies certai...

  6. CIME course on Control of Partial Differential Equations

    CERN Document Server

    Alabau-Boussouira, Fatiha; Glass, Olivier; Le Rousseau, Jérôme; Zuazua, Enrique

    2012-01-01

    The term “control theory” refers to the body of results - theoretical, numerical and algorithmic - which have been developed to influence the evolution of the state of a given system in order to meet a prescribed performance criterion. Systems of interest to control theory may be of very different natures. This monograph is concerned with models that can be described by partial differential equations of evolution. It contains five major contributions and is connected to the CIME Course on Control of Partial Differential Equations that took place in Cetraro (CS, Italy), July 19 - 23, 2010.  Specifically, it covers the stabilization of evolution equations, control of the Liouville equation, control in fluid mechanics, control and numerics for the wave equation, and Carleman estimates for elliptic and parabolic equations with application to control. We are confident this work will provide an authoritative reference work for all scientists who are interested in this field, representing at the same time a fri...

  7. Darboux transformations and linear parabolic partial differential equations

    International Nuclear Information System (INIS)

    Arrigo, Daniel J.; Hickling, Fred

    2002-01-01

    Solutions for a class of linear parabolic partial differential equation are provided. These solutions are obtained by first solving a system of (n+1) nonlinear partial differential equations. This system arises as the coefficients of a Darboux transformation and is equivalent to a matrix Burgers' equation. This matrix equation is solved using a generalized Hopf-Cole transformation. The solutions for the original equation are given in terms of solutions of the heat equation. These results are applied to the (1+1)-dimensional Schroedinger equation where all bound state solutions are obtained for a 2n-parameter family of potentials. As a special case, the solutions for integral members of the regular and modified Poeschl-Teller potentials are recovered. (author). Letter-to-the-editor

  8. Spectral methods for time dependent partial differential equations

    Science.gov (United States)

    Gottlieb, D.; Turkel, E.

    1983-01-01

    The theory of spectral methods for time dependent partial differential equations is reviewed. When the domain is periodic Fourier methods are presented while for nonperiodic problems both Chebyshev and Legendre methods are discussed. The theory is presented for both hyperbolic and parabolic systems using both Galerkin and collocation procedures. While most of the review considers problems with constant coefficients the extension to nonlinear problems is also discussed. Some results for problems with shocks are presented.

  9. Nonclassical Symmetries for Nonlinear Partial Differential Equations via Compatibility

    International Nuclear Information System (INIS)

    El-Sabbagh, Mostafa F.; Ahmad, Ali T.

    2011-01-01

    The determining equations for the nonclassical symmetry reductions of nonlinear partial differential equations with arbitrary order can be obtained by requiring the compatibility between the original equations and the invariant surface conditions. The (2+1)-dimensional shallow water wave equation, Boussinesq equation, and the dispersive wave equations in shallow water serve as examples illustrating how compatibility leads quickly and easily to the determining equations for their nonclassical symmetries. (general)

  10. Unconditionally stable difference methods for delay partial differential equations

    OpenAIRE

    Huang, Chengming; Vandewalle, Stefan

    2012-01-01

    This paper is concerned with the numerical solution of parabolic partial differential equations with time-delay. We focus in particular on the delay dependent stability analysis of difference methods that use a non-constrained mesh, i.e., the time step-size is not required to be a submultiple of the delay. We prove that the fully discrete system unconditionally preserves the delay dependent asymptotic stability of the linear test problem under consideration, when the following discretizati...

  11. Exp-function method for solving fractional partial differential equations.

    Science.gov (United States)

    Zheng, Bin

    2013-01-01

    We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for them are successfully established.

  12. Some overdetermined systems of complex partial differential equations

    International Nuclear Information System (INIS)

    Le Hung Son.

    1990-01-01

    In this paper we extend some properties of analytic functions on several complex variables to solutions of overdetermined systems of complex partial differential equations. It is proved that many global properties of analytic functions are true for solutions of the Vekua system in special cases. The relation between analytic functions and solutions of quasi-linear systems is discussed in the paper. (author). 8 refs

  13. System Entropy Measurement of Stochastic Partial Differential Systems

    Directory of Open Access Journals (Sweden)

    Bor-Sen Chen

    2016-03-01

    Full Text Available System entropy describes the dispersal of a system’s energy and is an indication of the disorder of a physical system. Several system entropy measurement methods have been developed for dynamic systems. However, most real physical systems are always modeled using stochastic partial differential dynamic equations in the spatio-temporal domain. No efficient method currently exists that can calculate the system entropy of stochastic partial differential systems (SPDSs in consideration of the effects of intrinsic random fluctuation and compartment diffusion. In this study, a novel indirect measurement method is proposed for calculating of system entropy of SPDSs using a Hamilton–Jacobi integral inequality (HJII-constrained optimization method. In other words, we solve a nonlinear HJII-constrained optimization problem for measuring the system entropy of nonlinear stochastic partial differential systems (NSPDSs. To simplify the system entropy measurement of NSPDSs, the global linearization technique and finite difference scheme were employed to approximate the nonlinear stochastic spatial state space system. This allows the nonlinear HJII-constrained optimization problem for the system entropy measurement to be transformed to an equivalent linear matrix inequalities (LMIs-constrained optimization problem, which can be easily solved using the MATLAB LMI-toolbox (MATLAB R2014a, version 8.3. Finally, several examples are presented to illustrate the system entropy measurement of SPDSs.

  14. Reconsidering harmonic and anharmonic coherent states: Partial differential equations approach

    Energy Technology Data Exchange (ETDEWEB)

    Toutounji, Mohamad, E-mail: Mtoutounji@uaeu.ac.ae

    2015-02-15

    This article presents a new approach to dealing with time dependent quantities such as autocorrelation function of harmonic and anharmonic systems using coherent states and partial differential equations. The approach that is normally used to evaluate dynamical quantities involves formidable operator algebra. That operator algebra becomes insurmountable when employing Morse oscillator coherent states. This problem becomes even more complicated in case of Morse oscillator as it tends to exhibit divergent dynamics. This approach employs linear partial differential equations, some of which may be solved exactly and analytically, thereby avoiding the cumbersome noncommutative algebra required to manipulate coherent states of Morse oscillator. Additionally, the arising integrals while using the herein presented method feature stability and high numerical efficiency. The correctness, applicability, and utility of the above approach are tested by reproducing the partition and optical autocorrelation function of the harmonic oscillator. A closed-form expression for the equilibrium canonical partition function of the Morse oscillator is derived using its coherent states and partial differential equations. Also, a nonequilibrium autocorrelation function expression for weak electron–phonon coupling in condensed systems is derived for displaced Morse oscillator in electronic state. Finally, the utility of the method is demonstrated through further simplifying the Morse oscillator partition function or autocorrelation function expressions reported by other researchers in unevaluated form of second-order derivative exponential. Comparison with exact dynamics shows identical results.

  15. Hidden physics models: Machine learning of nonlinear partial differential equations

    Science.gov (United States)

    Raissi, Maziar; Karniadakis, George Em

    2018-03-01

    While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from small data. In particular, we introduce hidden physics models, which are essentially data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and nonlinear partial differential equations, to extract patterns from high-dimensional data generated from experiments. The proposed methodology may be applied to the problem of learning, system identification, or data-driven discovery of partial differential equations. Our framework relies on Gaussian processes, a powerful tool for probabilistic inference over functions, that enables us to strike a balance between model complexity and data fitting. The effectiveness of the proposed approach is demonstrated through a variety of canonical problems, spanning a number of scientific domains, including the Navier-Stokes, Schrödinger, Kuramoto-Sivashinsky, and time dependent linear fractional equations. The methodology provides a promising new direction for harnessing the long-standing developments of classical methods in applied mathematics and mathematical physics to design learning machines with the ability to operate in complex domains without requiring large quantities of data.

  16. Differential equation analysis in biomedical science and engineering partial differential equation applications with R

    CERN Document Server

    Schiesser, William E

    2014-01-01

    Features a solid foundation of mathematical and computational tools to formulate and solve real-world PDE problems across various fields With a step-by-step approach to solving partial differential equations (PDEs), Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R successfully applies computational techniques for solving real-world PDE problems that are found in a variety of fields, including chemistry, physics, biology, and physiology. The book provides readers with the necessary knowledge to reproduce and extend the com

  17. A Numerical Method for Partial Differential Algebraic Equations Based on Differential Transform Method

    Directory of Open Access Journals (Sweden)

    Murat Osmanoglu

    2013-01-01

    Full Text Available We have considered linear partial differential algebraic equations (LPDAEs of the form , which has at least one singular matrix of . We have first introduced a uniform differential time index and a differential space index. The initial conditions and boundary conditions of the given system cannot be prescribed for all components of the solution vector here. To overcome this, we introduced these indexes. Furthermore, differential transform method has been given to solve LPDAEs. We have applied this method to a test problem, and numerical solution of the problem has been compared with analytical solution.

  18. A Novel Partial Differential Algebraic Equation (PDAE) Solver

    DEFF Research Database (Denmark)

    Lim, Young-il; Chang, Sin-Chung; Jørgensen, Sten Bay

    2004-01-01

    For solving partial differential algebraic equations (PDAEs), the space-time conservation element/solution element (CE/SE) method is addressed in this study. The method of lines (MOL) using an implicit time integrator is compared with the CE/SE method in terms of computational efficiency, solution...... or nonlinear adsorption isotherm are solved by the two methods. The CE/SE method enforces both local and global flux conservation in space and time, and uses a simple stencil structure (two points at the previous time level and one point at the present time level). Thus, accurate and computationally...

  19. Optimal Control Problems for Partial Differential Equations on Reticulated Domains

    CERN Document Server

    Kogut, Peter I

    2011-01-01

    In the development of optimal control, the complexity of the systems to which it is applied has increased significantly, becoming an issue in scientific computing. In order to carry out model-reduction on these systems, the authors of this work have developed a method based on asymptotic analysis. Moving from abstract explanations to examples and applications with a focus on structural network problems, they aim at combining techniques of homogenization and approximation. Optimal Control Problems for Partial Differential Equations on Reticulated Domains is an excellent reference tool for gradu

  20. Estimating varying coefficients for partial differential equation models.

    Science.gov (United States)

    Zhang, Xinyu; Cao, Jiguo; Carroll, Raymond J

    2017-09-01

    Partial differential equations (PDEs) are used to model complex dynamical systems in multiple dimensions, and their parameters often have important scientific interpretations. In some applications, PDE parameters are not constant but can change depending on the values of covariates, a feature that we call varying coefficients. We propose a parameter cascading method to estimate varying coefficients in PDE models from noisy data. Our estimates of the varying coefficients are shown to be consistent and asymptotically normally distributed. The performance of our method is evaluated by a simulation study and by an empirical study estimating three varying coefficients in a PDE model arising from LIDAR data. © 2017, The International Biometric Society.

  1. Partial differential equation models in the socio-economic sciences.

    Science.gov (United States)

    Burger, Martin; Caffarelli, Luis; Markowich, Peter A

    2014-11-13

    Mathematical models based on partial differential equations (PDEs) have become an integral part of quantitative analysis in most branches of science and engineering, recently expanding also towards biomedicine and socio-economic sciences. The application of PDEs in the latter is a promising field, but widely quite open and leading to a variety of novel mathematical challenges. In this introductory article of the Theme Issue, we will provide an overview of the field and its recent boosting topics. Moreover, we will put the contributions to the Theme Issue in an appropriate perspective. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

  2. Convergence of method of lines approximations to partial differential equations

    International Nuclear Information System (INIS)

    Verwer, J.G.; Sanz-Serna, J.M.

    1984-01-01

    Many existing numerical schemes for evolutionary problems in partial differential equations (PDEs) can be viewed as method of lines (MOL) schemes. This paper treats the convergence of one-step MOL schemes. The main purpose is to set up a general framework for a convergence analysis applicable to nonlinear problems. The stability materials for this framework are taken from the field of nonlinear stiff ODEs. In this connection, important concepts are the logarithmic matrix norm and C-stability. A nonlinear parabolic equation and the cubic Schroedinger equation are used for illustrating the ideas. (Auth.)

  3. Controllability of partial differential equations governed by multiplicative controls

    CERN Document Server

    Khapalov, Alexander Y

    2010-01-01

    The goal of this monograph is to address the issue of the global controllability of partial differential equations in the context of multiplicative (or bilinear) controls, which enter the model equations as coefficients. The mathematical models we examine include the linear and nonlinear parabolic and hyperbolic PDE's, the Schrödinger equation, and coupled hybrid nonlinear distributed parameter systems modeling the swimming phenomenon. The book offers a new, high-quality and intrinsically nonlinear methodology to approach the aforementioned highly nonlinear controllability problems.

  4. Constrained Optimization and Optimal Control for Partial Differential Equations

    CERN Document Server

    Leugering, Günter; Griewank, Andreas

    2012-01-01

    This special volume focuses on optimization and control of processes governed by partial differential equations. The contributors are mostly participants of the DFG-priority program 1253: Optimization with PDE-constraints which is active since 2006. The book is organized in sections which cover almost the entire spectrum of modern research in this emerging field. Indeed, even though the field of optimal control and optimization for PDE-constrained problems has undergone a dramatic increase of interest during the last four decades, a full theory for nonlinear problems is still lacking. The cont

  5. Malliavin Calculus With Applications to Stochastic Partial Differential Equations

    CERN Document Server

    Sanz-Solé, Marta

    2005-01-01

    Developed in the 1970s to study the existence and smoothness of density for the probability laws of random vectors, Malliavin calculus--a stochastic calculus of variation on the Wiener space--has proven fruitful in many problems in probability theory, particularly in probabilistic numerical methods in financial mathematics.This book presents applications of Malliavin calculus to the analysis of probability laws of solutions to stochastic partial differential equations driven by Gaussian noises that are white in time and coloured in space. The first five chapters introduce the calculus itself

  6. Partial differential equations and boundary-value problems with applications

    CERN Document Server

    Pinsky, Mark A

    2011-01-01

    Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems-rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate th

  7. Superdiffusions and positive solutions of nonlinear partial differential equations

    CERN Document Server

    Dynkin, E B

    2004-01-01

    This book is devoted to the applications of probability theory to the theory of nonlinear partial differential equations. More precisely, it is shown that all positive solutions for a class of nonlinear elliptic equations in a domain are described in terms of their traces on the boundary of the domain. The main probabilistic tool is the theory of superdiffusions, which describes a random evolution of a cloud of particles. A substantial enhancement of this theory is presented that can be of interest for everybody who works on applications of probabilistic methods to mathematical analysis.

  8. Analytical solutions for systems of partial differential-algebraic equations.

    Science.gov (United States)

    Benhammouda, Brahim; Vazquez-Leal, Hector

    2014-01-01

    This work presents the application of the power series method (PSM) to find solutions of partial differential-algebraic equations (PDAEs). Two systems of index-one and index-three are solved to show that PSM can provide analytical solutions of PDAEs in convergent series form. What is more, we present the post-treatment of the power series solutions with the Laplace-Padé (LP) resummation method as a useful strategy to find exact solutions. The main advantage of the proposed methodology is that the procedure is based on a few straightforward steps and it does not generate secular terms or depends of a perturbation parameter.

  9. Partial differential equation models in the socio-economic sciences

    KAUST Repository

    Burger, Martin

    2014-10-06

    Mathematical models based on partial differential equations (PDEs) have become an integral part of quantitative analysis in most branches of science and engineering, recently expanding also towards biomedicine and socio-economic sciences. The application of PDEs in the latter is a promising field, but widely quite open and leading to a variety of novel mathematical challenges. In this introductory article of the Theme Issue, we will provide an overview of the field and its recent boosting topics. Moreover, we will put the contributions to the Theme Issue in an appropriate perspective.

  10. Using Partial Differential Equations for Pricing of Goods and Services

    Directory of Open Access Journals (Sweden)

    Traykov Metodi

    2016-06-01

    Full Text Available This article is based on the methodology of comparative analysis, using an innovative approach for pricing of various goods and services. Benchmarking is the continuous search to find and adapt better pricing methods that leading to increased profits. We will consider the numerical solution of partial differential equations, based on Black-Scholes model for pricing of goods and services within European option. Also, we will present formulation and numerical behavior of explicit and implicit methods that can be use in pricing for company assets within European option.

  11. Numerical solution of two-dimensional non-linear partial differential ...

    African Journals Online (AJOL)

    linear partial differential equations using a hybrid method. The solution technique involves discritizing the non-linear system of partial differential equations (PDEs) to obtain a corresponding nonlinear system of algebraic difference equations to be ...

  12. A Priori Regularity of Parabolic Partial Differential Equations

    KAUST Repository

    Berkemeier, Francisco

    2018-05-13

    In this thesis, we consider parabolic partial differential equations such as the heat equation, the Fokker-Planck equation, and the porous media equation. Our aim is to develop methods that provide a priori estimates for solutions with singular initial data. These estimates are obtained by understanding the time decay of norms of solutions. First, we derive regularity results for the heat equation by estimating the decay of Lebesgue norms. Then, we apply similar methods to the Fokker-Planck equation with suitable assumptions on the advection and diffusion. Finally, we conclude by extending our techniques to the porous media equation. The sharpness of our results is confirmed by examining known solutions of these equations. The main contribution of this thesis is the use of functional inequalities to express decay of norms as differential inequalities. These are then combined with ODE methods to deduce estimates for the norms of solutions and their derivatives.

  13. Improved stochastic approximation methods for discretized parabolic partial differential equations

    Science.gov (United States)

    Guiaş, Flavius

    2016-12-01

    We present improvements of the stochastic direct simulation method, a known numerical scheme based on Markov jump processes which is used for approximating solutions of ordinary differential equations. This scheme is suited especially for spatial discretizations of evolution partial differential equations (PDEs). By exploiting the full path simulation of the stochastic method, we use this first approximation as a predictor and construct improved approximations by Picard iterations, Runge-Kutta steps, or a combination. This has as consequence an increased order of convergence. We illustrate the features of the improved method at a standard benchmark problem, a reaction-diffusion equation modeling a combustion process in one space dimension (1D) and two space dimensions (2D).

  14. Numerical methods for stochastic partial differential equations with white noise

    CERN Document Server

    Zhang, Zhongqiang

    2017-01-01

    This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book begins with some motivational and background material in the introductory chapters and is divided into three parts. Part I covers numerical stochastic ordinary differential equations. Here the authors start with numerical methods for SDEs with delay using the Wong-Zakai approximation and finite difference in time. Part II covers temporal white noise. Here the authors consider SPDEs as PDEs driven by white noise, where discretization of white noise (Brownian motion) leads to PDEs with smooth noise, which can then be treated by numerical methods for PDEs. In this part, recursive algorithms based on Wiener chaos expansion and stochastic collocation methods are presented for linear stochastic advection-diffusion-reaction equations. In addition, stochastic Euler equations are exploited as an application of stochastic collocation methods, where a numerical compa...

  15. Variational and potential formulation for stochastic partial differential equations

    International Nuclear Information System (INIS)

    Munoz S, A G; Ojeda, J; Sierra D, P; Soldovieri, T

    2006-01-01

    Recently there has been interest in finding a potential formulation for stochastic partial differential equations (SPDEs). The rationale behind this idea lies in obtaining all the dynamical information of the system under study from one single expression. In this letter we formally provide a general Lagrangian formalism for SPDEs using the Hojman et al method. We show that it is possible to write the corresponding effective potential starting from an s-equivalent Lagrangian, and that this potential is able to reproduce all the dynamics of the system once a special differential operator has been applied. This procedure can be used to study the complete time evolution and spatial inhomogeneities of the system under consideration, and is also suitable for the statistical mechanics description of the problem. (letter to the editor)

  16. Partial wave analysis for folded differential cross sections

    Science.gov (United States)

    Machacek, J. R.; McEachran, R. P.

    2018-03-01

    The value of modified effective range theory (MERT) and the connection between differential cross sections and phase shifts in low-energy electron scattering has long been recognized. Recent experimental techniques involving magnetically confined beams have introduced the concept of folded differential cross sections (FDCS) where the forward (θ ≤ π/2) and backward scattered (θ ≥ π/2) projectiles are unresolved, that is the value measured at the angle θ is the sum of the signal for particles scattered into the angles θ and π - θ. We have developed an alternative approach to MERT in order to analyse low-energy folded differential cross sections for positrons and electrons. This results in a simplified expression for the FDCS when it is expressed in terms of partial waves and thereby enables one to extract the first few phase shifts from a fit to an experimental FDCS at low energies. Thus, this method predicts forward and backward angle scattering (0 to π) using only experimental FDCS data and can be used to determine the total elastic cross section solely from experimental results at low-energy, which are limited in angular range.

  17. Paleomagnetic evidence for a partially differentiated H chondrite parent planetesimal

    Science.gov (United States)

    Bryson, J. F. J.; Weiss, B. P.; Scholl, A.; Getzin, B. L.; Abrahams, J. N. H.; Nimmo, F.

    2016-12-01

    The texture, composition and ages of chondrites have all been used to argue that the parent bodies of these meteorites did not undergo planetary differentiation. Without a core, these planetesimals could not have generated planetary magnetic fields, hence chondrites are predicted to be unmagnetized. Here, we test this hypothesis by applying synchrotron x-ray microscopy to the metallic melt veins in the metamorphosed H chondrite breccia Portales Valley. We find that tetrataenite nanostructures in these veins are uniformly magnetized, suggesting that the H chondrite parent body generated a stable, 10 µT ancient field. We also performed alternating field (AF) demagnetization on bulk silicate-rich portions of Portales Valley, finding that both the large grain size of the metal in these subsamples and the presence of tetrataenite hinder the reliable interpretation of these measurements. Based on 40Ar/39Ar dating and the metallographic cooling rate, we propose that this field inferred from x-ray microscopy was generated 100 Myr after solar system formation and lasted >5 Myr. These properties are consistent with a dynamo field generated by core solidification, implying that the H chondrite parent body was partially differentiated. This conclusion is supported by our analyses of the H4 chondrite Forest Vale, which show that H chondrite magnetization is unlikely to be a relic signature of early nebular or solar wind fields (Getzin et al., this meeting; Oran et al., this meeting). We propose that partial differentiation could result form prolonged accretion over millions of years, possibly in two stages. In this scenario, the earliest accreted material melted from the radioactive decay of abundant 26Al, forming a core and rocky achondritic mantle, while the later accreted material was less metamorphosed, forming an undifferentiated crust. We demonstrate that, with the inclusion of an insulating regolith, the thermal evolution of such a body is consistent with the measured

  18. A concise course on stochastic partial differential equations

    CERN Document Server

    Prévôt, Claudia

    2007-01-01

    These lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. All kinds of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. To keep the technicalities minimal we confine ourselves to the case where the noise term is given by a stochastic integral w.r.t. a cylindrical Wiener process.But all results can be easily generalized to SPDE with more general noises such as, for instance, stochastic integral w.r.t. a continuous local martingale. There are basically three approaches to analyze SPDE: the "martingale measure approach", the "mild solution approach" and the "variational approach". The purpose of these notes is to give a concise and as self-contained as possible an introduction to the "variational approach". A large part of necessary background material, such as definitions and results from the theory of Hilbert spaces, are included in appendices.

  19. Partial differential equations in action from modelling to theory

    CERN Document Server

    Salsa, Sandro

    2016-01-01

    The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background in numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear bo...

  20. Reduced basis methods for partial differential equations an introduction

    CERN Document Server

    Quarteroni, Alfio; Negri, Federico

    2016-01-01

    This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization.  The book presents a general mathematical formulation of RB methods, analyzes their fundamental theoretical properties, discusses the related algorithmic and implementation aspects, and highlights their built-in algebraic and geometric structures.  More specifically, the authors discuss alternative strategies for constructing accurate RB spaces using greedy algorithms and proper orthogonal decomposition techniques, investigate their approximation properties and analyze offline-online decomposition strategies aimed at the reduction of computational complexity. Furthermore, they carry out both a priori and a posteriori error analysis.  The whole mathematical presentation is made more stimulating by the use of representative examp...

  1. Essential partial differential equations analytical and computational aspects

    CERN Document Server

    Griffiths, David F; Silvester, David J

    2015-01-01

    This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and computational approach for these; the qualitative behaviour of solutions being established using classical concepts: maximum principles and energy methods.   Notable inclusions are the treatment of irregularly shaped boundaries, polar coordinates and the use of flux-limiters when approximating hyperbolic conservation laws. The numerical analysis of difference schemes is rigorously developed using discrete maximum principles and discrete Fourier analysis. A novel feature is the inclusion of a chapter containing projects, intended for either individual or group study, that cover a range of topics such as parabolic smoothing, travelling waves, isospectral matrices, and the approximation of multidimensional advection–diffusion problems.   The underlying theory is illustrated by numerous examples and there are around 300 exercises, designed to promote and test unde...

  2. Workload Characterization of CFD Applications Using Partial Differential Equation Solvers

    Science.gov (United States)

    Waheed, Abdul; Yan, Jerry; Saini, Subhash (Technical Monitor)

    1998-01-01

    Workload characterization is used for modeling and evaluating of computing systems at different levels of detail. We present workload characterization for a class of Computational Fluid Dynamics (CFD) applications that solve Partial Differential Equations (PDEs). This workload characterization focuses on three high performance computing platforms: SGI Origin2000, EBM SP-2, a cluster of Intel Pentium Pro bases PCs. We execute extensive measurement-based experiments on these platforms to gather statistics of system resource usage, which results in workload characterization. Our workload characterization approach yields a coarse-grain resource utilization behavior that is being applied for performance modeling and evaluation of distributed high performance metacomputing systems. In addition, this study enhances our understanding of interactions between PDE solver workloads and high performance computing platforms and is useful for tuning these applications.

  3. Nonlinear partial differential equations for scientists and engineers

    CERN Document Server

    Debnath, Lokenath

    1997-01-01

    "An exceptionally complete overview. There are numerous examples and the emphasis is on applications to almost all areas of science and engineering. There is truly something for everyone here. This reviewer feels that it is a very hard act to follow, and recommends it strongly. [This book] is a jewel." ---Applied Mechanics Review (Review of First Edition) This expanded and revised second edition is a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied applications. Building upon the successful material of the first book, this edition contains updated modern examples and applications from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation. Methods and properties of solutions are presented, along with their physical significance, making the book more useful for a diverse readership. Topics and key features: * Thorough coverage of derivation and methods of soluti...

  4. Partial differential equations in action from modelling to theory

    CERN Document Server

    Salsa, Sandro

    2015-01-01

    The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background in numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear bo...

  5. Learning partial differential equations via data discovery and sparse optimization.

    Science.gov (United States)

    Schaeffer, Hayden

    2017-01-01

    We investigate the problem of learning an evolution equation directly from some given data. This work develops a learning algorithm to identify the terms in the underlying partial differential equations and to approximate the coefficients of the terms only using data. The algorithm uses sparse optimization in order to perform feature selection and parameter estimation. The features are data driven in the sense that they are constructed using nonlinear algebraic equations on the spatial derivatives of the data. Several numerical experiments show the proposed method's robustness to data noise and size, its ability to capture the true features of the data, and its capability of performing additional analytics. Examples include shock equations, pattern formation, fluid flow and turbulence, and oscillatory convection.

  6. Optimized difference schemes for multidimensional hyperbolic partial differential equations

    Directory of Open Access Journals (Sweden)

    Adrian Sescu

    2009-04-01

    Full Text Available In numerical solutions to hyperbolic partial differential equations in multidimensions, in addition to dispersion and dissipation errors, there is a grid-related error (referred to as isotropy error or numerical anisotropy that affects the directional dependence of the wave propagation. Difference schemes are mostly analyzed and optimized in one dimension, wherein the anisotropy correction may not be effective enough. In this work, optimized multidimensional difference schemes with arbitrary order of accuracy are designed to have improved isotropy compared to conventional schemes. The derivation is performed based on Taylor series expansion and Fourier analysis. The schemes are restricted to equally-spaced Cartesian grids, so the generalized curvilinear transformation method and Cartesian grid methods are good candidates.

  7. Modeling tree crown dynamics with 3D partial differential equations.

    Science.gov (United States)

    Beyer, Robert; Letort, Véronique; Cournède, Paul-Henry

    2014-01-01

    We characterize a tree's spatial foliage distribution by the local leaf area density. Considering this spatially continuous variable allows to describe the spatiotemporal evolution of the tree crown by means of 3D partial differential equations. These offer a framework to rigorously take locally and adaptively acting effects into account, notably the growth toward light. Biomass production through photosynthesis and the allocation to foliage and wood are readily included in this model framework. The system of equations stands out due to its inherent dynamic property of self-organization and spontaneous adaptation, generating complex behavior from even only a few parameters. The density-based approach yields spatially structured tree crowns without relying on detailed geometry. We present the methodological fundamentals of such a modeling approach and discuss further prospects and applications.

  8. Data-driven discovery of partial differential equations.

    Science.gov (United States)

    Rudy, Samuel H; Brunton, Steven L; Proctor, Joshua L; Kutz, J Nathan

    2017-04-01

    We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg-de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable.

  9. BOOK REVIEW: Partial Differential Equations in General Relativity

    Science.gov (United States)

    Halburd, Rodney G.

    2008-11-01

    Although many books on general relativity contain an overview of the relevant background material from differential geometry, very little attention is usually paid to background material from the theory of differential equations. This is understandable in a first course on relativity but it often limits the kinds of problems that can be studied rigorously. Einstein's field equations lie at the heart of general relativity. They are a system of partial differential equations (PDEs) relating the curvature of spacetime to properties of matter. A central part of most problems in general relativity is to extract information about solutions of these equations. Most standard texts achieve this by studying exact solutions or numerical and analytical approximations. In the book under review, Alan Rendall emphasises the role of rigorous qualitative methods in general relativity. There has long been a need for such a book, giving a broad overview of the relevant background from the theory of partial differential equations, and not just from differential geometry. It should be noted that the book also covers the basic theory of ordinary differential equations. Although there are many good books on the rigorous theory of PDEs, methods related to the Einstein equations deserve special attention, not only because of the complexity and importance of these equations, but because these equations do not fit into any of the standard classes of equations (elliptic, parabolic, hyperbolic) that one typically encounters in a course on PDEs. Even specifying exactly what ones means by a Cauchy problem in general relativity requires considerable care. The main problem here is that the manifold on which the solution is defined is determined by the solution itself. This means that one does not simply define data on a submanifold. Rendall's book gives a good overview of applications and results from the qualitative theory of PDEs to general relativity. It would be impossible to give detailed

  10. Derivation of a macroscale formulation for a class of nonlinear partial differential equations

    International Nuclear Information System (INIS)

    Pantelis, G.

    1995-05-01

    A macroscale formulation is constructed from a system of partial differential equations which govern the microscale dependent variables. The construction is based upon the requirement that the solutions of the macroscale partial differential equations satisfy, in some approximate sense, the system of partial differential equations associated with the microscale. These results are restricted to the class of nonlinear partial differential equations which can be expressed as polynomials of the dependent variables and their partial derivatives up to second order. A linear approximation of transformations of second order contact manifolds is employed. 6 refs

  11. Preconditioning for partial differential equation constrained optimization with control constraints

    KAUST Repository

    Stoll, Martin; Wathen, Andy

    2011-01-01

    Optimal control problems with partial differential equations play an important role in many applications. The inclusion of bound constraints for the control poses a significant additional challenge for optimization methods. In this paper, we propose preconditioners for the saddle point problems that arise when a primal-dual active set method is used. We also show for this method that the same saddle point system can be derived when the method is considered as a semismooth Newton method. In addition, the projected gradient method can be employed to solve optimization problems with simple bounds, and we discuss the efficient solution of the linear systems in question. In the case when an acceleration technique is employed for the projected gradient method, this again yields a semismooth Newton method that is equivalent to the primal-dual active set method. We also consider the Moreau-Yosida regularization method for control constraints and efficient preconditioners for this technique. Numerical results illustrate the competitiveness of these approaches. © 2011 John Wiley & Sons, Ltd.

  12. Grid generation for the solution of partial differential equations

    Science.gov (United States)

    Eiseman, Peter R.; Erlebacher, Gordon

    1989-01-01

    A general survey of grid generators is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstructured meshes. Altogether, the categorization establishes the foundation upon which grid generation techniques are developed. The two primary categories are algebraic techniques and partial differential equation techniques. These are each split into basic parts, and accordingly are individually examined in some detail. In the process, the interrelations between the various parts are accented. From the established background in the primary techniques, consideration is shifted to the topic of interactive grid generation and then to adaptive meshes. The setting for adaptivity is established with a suitable means to monitor severe solution behavior. Adaptive grids are considered first and are followed by adaptive triangular meshes. Then the consideration shifts to the temporal coupling between grid generators and PDE-solvers. To conclude, a reflection upon the discussion, herein, is given.

  13. A hybrid perturbation-Galerkin technique for partial differential equations

    Science.gov (United States)

    Geer, James F.; Anderson, Carl M.

    1990-01-01

    A two-step hybrid perturbation-Galerkin technique for improving the usefulness of perturbation solutions to partial differential equations which contain a parameter is presented and discussed. In the first step of the method, the leading terms in the asymptotic expansion(s) of the solution about one or more values of the perturbation parameter are obtained using standard perturbation methods. In the second step, the perturbation functions obtained in the first step are used as trial functions in a Bubnov-Galerkin approximation. This semi-analytical, semi-numerical hybrid technique appears to overcome some of the drawbacks of the perturbation and Galerkin methods when they are applied by themselves, while combining some of the good features of each. The technique is illustrated first by a simple example. It is then applied to the problem of determining the flow of a slightly compressible fluid past a circular cylinder and to the problem of determining the shape of a free surface due to a sink above the surface. Solutions obtained by the hybrid method are compared with other approximate solutions, and its possible application to certain problems associated with domain decomposition is discussed.

  14. CPDS3, Coupled 3-D Partial Differential Equation Solution

    International Nuclear Information System (INIS)

    Anderson, D.V.; Koniges, A.E.; Shumaker, D.E.

    1992-01-01

    1 - Description of program or function: CPDES3 solves the linear asymmetric matrix equations arising from coupled partial differential equations in three dimensions. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximation employed. CPDES3 allows each spatial operator to have 7, 15, 19, or 27 point stencils, permits general couplings between all of the component PDE's, and automatically generates the matrix structures needed to perform the algorithm. 2 - Method of solution: The resulting sparse matrix equation with a complicated sub-band structure and generally asymmetric is solved by either the preconditioned conjugate gradient (CG) method or the preconditioned bi-conjugate gradient (BCG) algorithm. BCG enjoys faster convergence in most cases but in rare instances diverges. Then, CG iterations must be used. 3 - Restrictions on the complexity of the problem: The discretization of the coupled three-dimensional PDE's and their boundary conditions must result in an operator stencil which fits in the Cray2 memory. In addition, the matrix must possess a reasonable amount of diagonal dominance for the preconditioning technique to be effective

  15. CPDES2, Coupled 2-D Partial Differential Equation Solution

    International Nuclear Information System (INIS)

    Anderson, D.V.; Koniges, A.E.; Shumaker, D.E.

    1992-01-01

    1 - Description of program or function: CPDES2 solves the linear asymmetric equations arising from coupled partial differential equations in two dimensions. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximation employed. CPDES2 allows each spatial operator to have 5 or 9 point stencils, permits general coupling between all of the component PDE's, and automatically generates the matrix structures needed to perform the algorithm. 2 - Method of solution: The resulting sparse matrix equation with a complicated sub-band structure and generally asymmetric is solved by either the preconditioned conjugate gradient (CG) method or the preconditioned bi-conjugate gradient (BCG) algorithm. BCG enjoys faster convergence in most cases but in rare instances diverges. Then, CG iterations must be used. 3 - Restrictions on the complexity of the problem: The discretization of the coupled two-dimensional PDE's and their boundary conditions must result in an operator stencil which fits in the Cray2 memory. In addition, the matrix must possess a reasonable amount of diagonal dominance for the preconditioning technique to be effective

  16. Final Report: Symposium on Adaptive Methods for Partial Differential Equations

    Energy Technology Data Exchange (ETDEWEB)

    Pernice, M.; Johnson, C.R.; Smith, P.J.; Fogelson, A.

    1998-12-10

    OAK-B135 Final Report: Symposium on Adaptive Methods for Partial Differential Equations. Complex physical phenomena often include features that span a wide range of spatial and temporal scales. Accurate simulation of such phenomena can be difficult to obtain, and computations that are under-resolved can even exhibit spurious features. While it is possible to resolve small scale features by increasing the number of grid points, global grid refinement can quickly lead to problems that are intractable, even on the largest available computing facilities. These constraints are particularly severe for three dimensional problems that involve complex physics. One way to achieve the needed resolution is to refine the computational mesh locally, in only those regions where enhanced resolution is required. Adaptive solution methods concentrate computational effort in regions where it is most needed. These methods have been successfully applied to a wide variety of problems in computational science and engineering. Adaptive methods can be difficult to implement, prompting the development of tools and environments to facilitate their use. To ensure that the results of their efforts are useful, algorithm and tool developers must maintain close communication with application specialists. Conversely it remains difficult for application specialists who are unfamiliar with the methods to evaluate the trade-offs between the benefits of enhanced local resolution and the effort needed to implement an adaptive solution method.

  17. Towards information-optimal simulation of partial differential equations.

    Science.gov (United States)

    Leike, Reimar H; Enßlin, Torsten A

    2018-03-01

    Most simulation schemes for partial differential equations (PDEs) focus on minimizing a simple error norm of a discretized version of a field. This paper takes a fundamentally different approach; the discretized field is interpreted as data providing information about a real physical field that is unknown. This information is sought to be conserved by the scheme as the field evolves in time. Such an information theoretic approach to simulation was pursued before by information field dynamics (IFD). In this paper we work out the theory of IFD for nonlinear PDEs in a noiseless Gaussian approximation. The result is an action that can be minimized to obtain an information-optimal simulation scheme. It can be brought into a closed form using field operators to calculate the appearing Gaussian integrals. The resulting simulation schemes are tested numerically in two instances for the Burgers equation. Their accuracy surpasses finite-difference schemes on the same resolution. The IFD scheme, however, has to be correctly informed on the subgrid correlation structure. In certain limiting cases we recover well-known simulation schemes like spectral Fourier-Galerkin methods. We discuss implications of the approximations made.

  18. Preconditioning for partial differential equation constrained optimization with control constraints

    KAUST Repository

    Stoll, Martin

    2011-10-18

    Optimal control problems with partial differential equations play an important role in many applications. The inclusion of bound constraints for the control poses a significant additional challenge for optimization methods. In this paper, we propose preconditioners for the saddle point problems that arise when a primal-dual active set method is used. We also show for this method that the same saddle point system can be derived when the method is considered as a semismooth Newton method. In addition, the projected gradient method can be employed to solve optimization problems with simple bounds, and we discuss the efficient solution of the linear systems in question. In the case when an acceleration technique is employed for the projected gradient method, this again yields a semismooth Newton method that is equivalent to the primal-dual active set method. We also consider the Moreau-Yosida regularization method for control constraints and efficient preconditioners for this technique. Numerical results illustrate the competitiveness of these approaches. © 2011 John Wiley & Sons, Ltd.

  19. Application of Stochastic Partial Differential Equations to Reservoir Property Modelling

    KAUST Repository

    Potsepaev, R.

    2010-09-06

    Existing algorithms of geostatistics for stochastic modelling of reservoir parameters require a mapping (the \\'uvt-transform\\') into the parametric space and reconstruction of a stratigraphic co-ordinate system. The parametric space can be considered to represent a pre-deformed and pre-faulted depositional environment. Existing approximations of this mapping in many cases cause significant distortions to the correlation distances. In this work we propose a coordinate free approach for modelling stochastic textures through the application of stochastic partial differential equations. By avoiding the construction of a uvt-transform and stratigraphic coordinates, one can generate realizations directly in the physical space in the presence of deformations and faults. In particular the solution of the modified Helmholtz equation driven by Gaussian white noise is a zero mean Gaussian stationary random field with exponential correlation function (in 3-D). This equation can be used to generate realizations in parametric space. In order to sample in physical space we introduce a stochastic elliptic PDE with tensor coefficients, where the tensor is related to correlation anisotropy and its variation is physical space.

  20. Partial differential equations an accessible route through theory and applications

    CERN Document Server

    Vasy, András

    2015-01-01

    This text on partial differential equations is intended for readers who want to understand the theoretical underpinnings of modern PDEs in settings that are important for the applications without using extensive analytic tools required by most advanced texts. The assumed mathematical background is at the level of multivariable calculus and basic metric space material, but the latter is recalled as relevant as the text progresses. The key goal of this book is to be mathematically complete without overwhelming the reader, and to develop PDE theory in a manner that reflects how researchers would think about the material. A concrete example is that distribution theory and the concept of weak solutions are introduced early because while these ideas take some time for the students to get used to, they are fundamentally easy and, on the other hand, play a central role in the field. Then, Hilbert spaces that are quite important in the later development are introduced via completions which give essentially all the fea...

  1. Stochastic partial differential equations a modeling, white noise functional approach

    CERN Document Server

    Holden, Helge; Ubøe, Jan; Zhang, Tusheng

    1996-01-01

    This book is based on research that, to a large extent, started around 1990, when a research project on fluid flow in stochastic reservoirs was initiated by a group including some of us with the support of VISTA, a research coopera­ tion between the Norwegian Academy of Science and Letters and Den norske stats oljeselskap A.S. (Statoil). The purpose of the project was to use stochastic partial differential equations (SPDEs) to describe the flow of fluid in a medium where some of the parameters, e.g., the permeability, were stochastic or "noisy". We soon realized that the theory of SPDEs at the time was insufficient to handle such equations. Therefore it became our aim to develop a new mathematically rigorous theory that satisfied the following conditions. 1) The theory should be physically meaningful and realistic, and the corre­ sponding solutions should make sense physically and should be useful in applications. 2) The theory should be general enough to handle many of the interesting SPDEs that occur in r...

  2. PDASAC, Partial Differential Sensitivity Analysis of Stiff System

    International Nuclear Information System (INIS)

    Caracotsios, M.; Stewart, W.E.

    2001-01-01

    1 - Description of program or function: PDASAC solves stiff, nonlinear initial-boundary-value problems in a timelike dimension t and a space dimension x. Plane, circular cylindrical or spherical boundaries can be handled. Mixed-order systems of partial differential and algebraic equations can be analyzed with members of order or 0 or 1 in t, 0, 1 or 2 in x. Parametric sensitivities of the calculated states are computed simultaneously on request, via the Jacobian of the state equations. Initial and boundary conditions are efficiently reconciled. Local error control (in the max-norm or the 2-norm) is provided for the state vector and can include the parametric sensitivities if desired. 2 - Method of solution: The method of lines is used, with a user- selected x-grid and a minimum-bandwidth finite-difference approximations of the x-derivatives. Starting conditions are reconciled with a damped Newton algorithm adapted from Bain and Stewart (1991). Initial step selection is done by the first-order algorithms of Shampine (1987), extended here to differential- algebraic equation systems. The solution is continued with the DASSL predictor-corrector algorithm (Petzold 1983, Brenan et al. 1989) with the initial acceleration phase deleted and with row scaling of the Jacobian added. The predictor and corrector are expressed in divided-difference form, with the fixed-leading-coefficient form of corrector (Jackson and Sacks-Davis 1989; Brenan et al. 1989). Weights for the error tests are updated in each step with the user's tolerances at the predicted state. Sensitivity analysis is performed directly on the corrector equations of Caracotsios and Stewart (1985) and is extended here to the initialization when needed. 3 - Restrictions on the complexity of the problem: This algorithm, like DASSL, performs well on differential-algebraic equation systems of index 0 and 1 but not on higher-index systems; see Brenan et al. (1989). The user assigned the work array lengths and the output

  3. Nonlocal symmetry generators and explicit solutions of some partial differential equations

    International Nuclear Information System (INIS)

    Qin Maochang

    2007-01-01

    The nonlocal symmetry of a partial differential equation is studied in this paper. The partial differential equation written as a conservation law can be transformed into an equivalent system by introducing a suitable potential. The nonlocal symmetry group generators of original partial differential equations can be obtained through their equivalent system. Further, new explicit solutions can be constructed from the newly obtained symmetry generators. The Burgers equation is chosen as an example; many new valuable explicit solutions and nonlocal symmetry generators are presented

  4. Preconditioners based on windowed Fourier frames applied to elliptic partial differential equations

    NARCIS (Netherlands)

    Bhowmik, S.K.; Stolk, C.C.

    2011-01-01

    We investigate the application of windowed Fourier frames to the numerical solution of partial differential equations, focussing on elliptic equations. The action of a partial differential operator (PDO) on a windowed plane wave is close to a multiplication, where the multiplication factor is given

  5. Higher order multi-term time-fractional partial differential equations involving Caputo-Fabrizio derivative

    Directory of Open Access Journals (Sweden)

    Erkinjon Karimov

    2017-10-01

    Full Text Available In this work we discuss higher order multi-term partial differential equation (PDE with the Caputo-Fabrizio fractional derivative in time. Using method of separation of variables, we reduce fractional order partial differential equation to the integer order. We represent explicit solution of formulated problem in particular case by Fourier series.

  6. Higher order multi-term time-fractional partial differential equations involving Caputo-Fabrizio derivative

    OpenAIRE

    Erkinjon Karimov; Sardor Pirnafasov

    2017-01-01

    In this work we discuss higher order multi-term partial differential equation (PDE) with the Caputo-Fabrizio fractional derivative in time. Using method of separation of variables, we reduce fractional order partial differential equation to the integer order. We represent explicit solution of formulated problem in particular case by Fourier series.

  7. Controllability and Stabilization of Bilinear and Semilinear Partial Differential Equations

    DEFF Research Database (Denmark)

    Krishnaswamy, Vijayaraghavan

    The topic of the thesis is the investigation of the question of controllability of weakly nonlinear partial differntial equations. The method is based on the Hilbert Uniqueness Method.......The topic of the thesis is the investigation of the question of controllability of weakly nonlinear partial differntial equations. The method is based on the Hilbert Uniqueness Method....

  8. Analytic Solutions and Resonant Solutions of Hyperbolic Partial Differential Equations

    Science.gov (United States)

    Wagenmaker, Timothy Roger

    This dissertation contains two main subject areas. The first deals with solutions to the wave equation Du/Dt + a Du/Dx = 0, where D/Dt and D/Dx represent partial derivatives and a(t,x) is real valued. The question I studied, which arises in control theory, is whether solutions which are real analytic with respect to the time variable are dense in the space of all solutions. If a is real analytic in t and x, the Cauchy-Kovalevsky Theorem implies that the solutions real analytic in t and x are dense, since it suffices to approximate the initial data by polynomials. The same positive result is valid when a is continuously differentiable and independent of t. This is proved by regularization in time. The hypothesis that a is independent of t cannot be replaced by the weaker assumption that a is real analytic in t, even when it is infinitely smooth. I construct a(t,x) for which the solutions which are analytic in time are automatically periodic in time. In particular these solutions are not dense in the space of all solutions. The second area concerns the resonant interaction of oscillatory waves propagating in a compressible inviscid fluid. An asymptotic description given by Andrew Majda, Rodolfo Rosales, and Maria Schonbek (MRS) involves the genuinely nonlinear quasilinear hyperbolic system Du/Dt + D(uu/2)/Dt + v = 0, Dv/Dt - D(vv/2)/Dt - u = 0. They performed many numerical simulations which indicated that small amplitude solutions of this system tend to evade shock formation, and conjectured that "smooth initial data with a sufficiently small amplitude never develop shocks throughout a long time interval of integration.". I proved that for smooth periodic U(x), V(x) and initial data u(0,x) = epsilonU(x), v(0,x) = epsilonV(x), the solution is smooth for time at least constant times | ln epsilon| /epsilon. This is longer than the lifetime order 1/ epsilon of the solution to the decoupled Burgers equations. The decoupled equation describes nonresonant interaction of

  9. The convergence of the order sequence and the solution function sequence on fractional partial differential equation

    Science.gov (United States)

    Rusyaman, E.; Parmikanti, K.; Chaerani, D.; Asefan; Irianingsih, I.

    2018-03-01

    One of the application of fractional ordinary differential equation is related to the viscoelasticity, i.e., a correlation between the viscosity of fluids and the elasticity of solids. If the solution function develops into function with two or more variables, then its differential equation must be changed into fractional partial differential equation. As the preliminary study for two variables viscoelasticity problem, this paper discusses about convergence analysis of function sequence which is the solution of the homogenous fractional partial differential equation. The method used to solve the problem is Homotopy Analysis Method. The results show that if given two real number sequences (αn) and (βn) which converge to α and β respectively, then the solution function sequences of fractional partial differential equation with order (αn, βn) will also converge to the solution function of fractional partial differential equation with order (α, β).

  10. New Solutions of Three Nonlinear Space- and Time-Fractional Partial Differential Equations in Mathematical Physics

    International Nuclear Information System (INIS)

    Yao Ruo-Xia; Wang Wei; Chen Ting-Hua

    2014-01-01

    Motivated by the widely used ansätz method and starting from the modified Riemann—Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper. (general)

  11. Partial differential equations with variable exponents variational methods and qualitative analysis

    CERN Document Server

    Radulescu, Vicentiu D

    2015-01-01

    Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis provides researchers and graduate students with a thorough introduction to the theory of nonlinear partial differential equations (PDEs) with a variable exponent, particularly those of elliptic type. The book presents the most important variational methods for elliptic PDEs described by nonhomogeneous differential operators and containing one or more power-type nonlinearities with a variable exponent. The authors give a systematic treatment of the basic mathematical theory and constructive meth

  12. Pure soliton solutions of some nonlinear partial differential equations

    International Nuclear Information System (INIS)

    Fuchssteiner, B.

    1977-01-01

    A general approach is given to obtain the system of ordinary differential equations which determines the pure soliton solutions for the class of generalized Korteweg-de Vries equations. This approach also leads to a system of ordinary differential equations for the pure soliton solutions of the sine-Gordon equation. (orig.) [de

  13. Parallels between control PDE's (Partial Differential Equations) and systems of ODE's (Ordinary Differential Equations)

    Science.gov (United States)

    Hunt, L. R.; Villarreal, Ramiro

    1987-01-01

    System theorists understand that the same mathematical objects which determine controllability for nonlinear control systems of ordinary differential equations (ODEs) also determine hypoellipticity for linear partial differentail equations (PDEs). Moreover, almost any study of ODE systems begins with linear systems. It is remarkable that Hormander's paper on hypoellipticity of second order linear p.d.e.'s starts with equations due to Kolmogorov, which are shown to be analogous to the linear PDEs. Eigenvalue placement by state feedback for a controllable linear system can be paralleled for a Kolmogorov equation if an appropriate type of feedback is introduced. Results concerning transformations of nonlinear systems to linear systems are similar to results for transforming a linear PDE to a Kolmogorov equation.

  14. OSCILLATION OF IMPULSIVE HYPERBOLIC PARTIAL DIFFERENTIAL EQUATION WITH DELAY

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    In this paper, oscillation properties of the solutions of impulsive hyperbolic equation with delay are investigated via the method of differential inequalities. Sufficient conditions for oscillations of the solutions are established.

  15. Atmospheres of partially differentiated super-Earth exoplanets

    Science.gov (United States)

    Schaefer, Laura; Sasselov, Dimitar

    2015-11-01

    Terrestrial exoplanets have been discovered in a range of sizes, densities and orbital locations that defy our expectations based upon the Solar System. Planets discovered to date with radii less than ~1.5-1.6 Earth radii all seem to fall on an iso-density curve with the Earth [1]. However, mass and radius determinations, which depend on the known properties of the host star, are not accurate enough to distinguish between a fully differentiated three-layer planet (core, mantle, ocean/atmosphere) and an incompletely differentiated planet [2]. Full differentiation of a planet will depend upon the conditions at the time of accretion, including the abundance of short-lived radioisotopes, which will vary from system to system, as well as the number of giant impacts the planet experiences. Furthermore, separation of metal and silicates at the much larger pressures found inside super-Earths will depend on how the chemistry of these materials change at high pressures. There are therefore hints emerging that not all super-Earths will be fully differentiated. Incomplete differentiation will result in a more reduced mantle oxidation state and may have implications for the composition of an outgassed atmosphere. Here we will present the first results from a chemical equilibrium model of the composition of such an outgassed atmosphere and discuss the possibility of distinguishing between fully and incompletely differentiated planets through atmospheric observations.[1] Rogers, L. 2015. ApJ, 801, 41. [2] Zeng, L. & Sasselov, D. 2013. PASP, 125, 227.

  16. Distilling solid carbonaceous materials

    Energy Technology Data Exchange (ETDEWEB)

    Nielsen, H; Laing, B

    1926-12-04

    In a process of distilling solid carbonaceous materials with by-product recovery, the time factor and the temperature gradient during the distillation period are so controlled that a temperature difference exceeding 150/sup 0/C is avoided between the temperatures at the center and periphery of any suitable size of material or thickness of fuel bed. The material is heated by direct contact with an inert gas, such as water gas, producer gas, or combustion gases, which is passed in counterflow to the material and whose volume is such as to lower the vapor tension or partial pressure of the volatilizable oils and to withdraw the oils without cracking of the oil vapors. The material may be subjected to a preliminary heat treatment by gases containing 2 to 3 percent of free oxygen to reduce its coking properties, and free oxygen may be added either to the heating gases during the heat treatment, or to the retort and heating gases and vapors to polymerize resinous bodies prior to condensation or during condensation and while the oils are still wholly or partially in the vapor state.

  17. Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear partial differential evolution equations of dynamical systems

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    Using functional derivative technique in quantum field theory, the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations. The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynam-ics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new nu-merical algorithm—algebraic dynamics algorithm was proposed for partial differ-ential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.

  18. FORSIM, Solution of Ordinary or Partial Differential Equation with Initial Conditions

    International Nuclear Information System (INIS)

    Carver, M.B.

    1985-01-01

    1 - Description of problem or function: FORSIM is a FORTRAN oriented simulation program which automates the continuous transient solution of systems of ordinary and/or partial differential equations. The user writes his equations in a FORTRAN subroutine, following prescribed rules, and loads this routine along with the executive routines. The executive routines then read in initial data supplied by the user and proceed with the integration. 2 - Method of solution: Partial differential equations are converted to coupled ordinary differential equations by suitable discretization formulae. Integration is done by variable order, variable step-size error controlled algorithms. 3 - Restrictions on the complexity of the problem - Maximum of: 1000 ordinary differential equations

  19. Consistency of direct integral estimator for partially observed systems of ordinary differential equations

    NARCIS (Netherlands)

    Vujačić, Ivan; Dattner, Itai

    In this paper we use the sieve framework to prove consistency of the ‘direct integral estimator’ of parameters for partially observed systems of ordinary differential equations, which are commonly used for modeling dynamic processes.

  20. RECTC/RECTCF, 2. Order Elliptical Partial Differential Equation, Arbitrary Boundary Conditions

    International Nuclear Information System (INIS)

    Hackbusch, W.

    1983-01-01

    1 - Description of problem or function: A general linear elliptical second order partial differential equation on a rectangle with arbitrary boundary conditions is solved. 2 - Method of solution: Multi-grid iteration

  1. The generalized tanh method to obtain exact solutions of nonlinear partial differential equation

    OpenAIRE

    Gómez, César

    2007-01-01

    In this paper, we present the generalized tanh method to obtain exact solutions of nonlinear partial differential equations, and we obtain solitons and exact solutions of some important equations of the mathematical physics.

  2. 3rd International Conference on Particle Systems and Partial Differential Equations

    CERN Document Server

    Soares, Ana

    2016-01-01

    The main focus of this book is on different topics in probability theory, partial differential equations and kinetic theory, presenting some of the latest developments in these fields. It addresses mathematical problems concerning applications in physics, engineering, chemistry and biology that were presented at the Third International Conference on Particle Systems and Partial Differential Equations, held at the University of Minho, Braga, Portugal in December 2014. The purpose of the conference was to bring together prominent researchers working in the fields of particle systems and partial differential equations, providing a venue for them to present their latest findings and discuss their areas of expertise. Further, it was intended to introduce a vast and varied public, including young researchers, to the subject of interacting particle systems, its underlying motivation, and its relation to partial differential equations. This book will appeal to probabilists, analysts and those mathematicians whose wor...

  3. Modulating Function-Based Method for Parameter and Source Estimation of Partial Differential Equations

    KAUST Repository

    Asiri, Sharefa M.

    2017-01-01

    Partial Differential Equations (PDEs) are commonly used to model complex systems that arise for example in biology, engineering, chemistry, and elsewhere. The parameters (or coefficients) and the source of PDE models are often unknown

  4. Intuitive Understanding of Solutions of Partially Differential Equations

    Science.gov (United States)

    Kobayashi, Y.

    2008-01-01

    This article uses diagrams that help the observer see how solutions of the wave equation and heat conduction equation are obtained. The analytical approach cannot necessarily show the mechanisms of the key to the solution without transforming the differential equation into a more convenient form by separation of variables. The visual clues based…

  5. Coverings and the fundamental group for partial differential equations

    NARCIS (Netherlands)

    Igonin, S.

    2003-01-01

    Following I. S. Krasilshchik and A. M. Vinogradov, we regard systems of PDEs as manifolds with involutive distributions and consider their special morphisms called differential coverings, which include constructions like Lax pairs and B\\"acklund transformations in soliton theory. We show that,

  6. Non-linear partial differential equations an algebraic view of generalized solutions

    CERN Document Server

    Rosinger, Elemer E

    1990-01-01

    A massive transition of interest from solving linear partial differential equations to solving nonlinear ones has taken place during the last two or three decades. The availability of better computers has often made numerical experimentations progress faster than the theoretical understanding of nonlinear partial differential equations. The three most important nonlinear phenomena observed so far both experimentally and numerically, and studied theoretically in connection with such equations have been the solitons, shock waves and turbulence or chaotical processes. In many ways, these phenomen

  7. Hyperbolic partial differential equations populations, reactors, tides and waves theory and applications

    CERN Document Server

    Witten, Matthew

    1983-01-01

    Hyperbolic Partial Differential Equations, Volume 1: Population, Reactors, Tides and Waves: Theory and Applications covers three general areas of hyperbolic partial differential equation applications. These areas include problems related to the McKendrick/Von Foerster population equations, other hyperbolic form equations, and the numerical solution.This text is composed of 15 chapters and begins with surveys of age specific population interactions, populations models of diffusion, nonlinear age dependent population growth with harvesting, local and global stability for the nonlinear renewal eq

  8. Modeling Solution of Nonlinear Dispersive Partial Differential Equations using the Marker Method

    International Nuclear Information System (INIS)

    Lewandowski, Jerome L.V.

    2005-01-01

    A new method for the solution of nonlinear dispersive partial differential equations is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details

  9. Analytic continuation of solutions of some nonlinear convolution partial differential equations

    Directory of Open Access Journals (Sweden)

    Hidetoshi Tahara

    2015-01-01

    Full Text Available The paper considers a problem of analytic continuation of solutions of some nonlinear convolution partial differential equations which naturally appear in the summability theory of formal solutions of nonlinear partial differential equations. Under a suitable assumption it is proved that any local holomorphic solution has an analytic extension to a certain sector and its extension has exponential growth when the variable goes to infinity in the sector.

  10. Stepwise Analysis of Differential Item Functioning Based on Multiple-Group Partial Credit Model.

    Science.gov (United States)

    Muraki, Eiji

    1999-01-01

    Extended an Item Response Theory (IRT) method for detection of differential item functioning to the partial credit model and applied the method to simulated data using a stepwise procedure. Then applied the stepwise DIF analysis based on the multiple-group partial credit model to writing trend data from the National Assessment of Educational…

  11. Solving Nonlinear Partial Differential Equations with Maple and Mathematica

    CERN Document Server

    Shingareva, Inna K

    2011-01-01

    The emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple an

  12. RBSDE's with jumps and the related obstacle problems for integral-partial differential equations

    Institute of Scientific and Technical Information of China (English)

    FAN; Yulian

    2006-01-01

    The author proves, when the noise is driven by a Brownian motion and an independent Poisson random measure, the one-dimensional reflected backward stochastic differential equation with a stopping time terminal has a unique solution. And in a Markovian framework, the solution can provide a probabilistic interpretation for the obstacle problem for the integral-partial differential equation.

  13. A direct algebraic method applied to obtain complex solutions of some nonlinear partial differential equations

    International Nuclear Information System (INIS)

    Zhang Huiqun

    2009-01-01

    By using some exact solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct the exact complex solutions for nonlinear partial differential equations. The method is implemented for the NLS equation, a new Hamiltonian amplitude equation, the coupled Schrodinger-KdV equations and the Hirota-Maccari equations. New exact complex solutions are obtained.

  14. Parameter Estimation for Partial Differential Equations by Collage-Based Numerical Approximation

    Directory of Open Access Journals (Sweden)

    Xiaoyan Deng

    2009-01-01

    into a minimization problem of a function of several variables after the partial differential equation is approximated by a differential dynamical system. Then numerical schemes for solving this minimization problem are proposed, including grid approximation and ant colony optimization. The proposed schemes are applied to a parameter estimation problem for the Belousov-Zhabotinskii equation, and the results show that the proposed approximation method is efficient for both linear and nonlinear partial differential equations with respect to unknown parameters. At worst, the presented method provides an excellent starting point for traditional inversion methods that must first select a good starting point.

  15. Multivariate Padé Approximation for Solving Nonlinear Partial Differential Equations of Fractional Order

    Directory of Open Access Journals (Sweden)

    Veyis Turut

    2013-01-01

    Full Text Available Two tecHniques were implemented, the Adomian decomposition method (ADM and multivariate Padé approximation (MPA, for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo sense. First, the fractional differential equation has been solved and converted to power series by Adomian decomposition method (ADM, then power series solution of fractional differential equation was put into multivariate Padé series. Finally, numerical results were compared and presented in tables and figures.

  16. In silico ordinary differential equation/partial differential equation hemodialysis model estimates methadone removal during dialysis

    Science.gov (United States)

    Linares, Oscar A; Schiesser, William E; Fudin, Jeffrey; Pham, Thien C; Bettinger, Jeffrey J; Mathew, Roy O; Daly, Annemarie L

    2015-01-01

    Background There is a need to have a model to study methadone’s losses during hemodialysis to provide informed methadone dose recommendations for the practitioner. Aim To build a one-dimensional (1-D), hollow-fiber geometry, ordinary differential equation (ODE) and partial differential equation (PDE) countercurrent hemodialyzer model (ODE/PDE model). Methodology We conducted a cross-sectional study in silico that evaluated eleven hemodialysis patients. Patients received a ceiling dose of methadone hydrochloride 30 mg/day. Outcome measures included: the total amount of methadone removed during dialysis; methadone’s overall intradialytic mass transfer rate coefficient, km; and, methadone’s removal rate, jME. Each metric was measured at dialysate flow rates of 250 mL/min and 800 mL/min. Results The ODE/PDE model revealed a significant increase in the change of methadone’s mass transfer with increased dialysate flow rate, %Δkm=18.56, P=0.02, N=11. The total amount of methadone mass transferred across the dialyzer membrane with high dialysate flow rate significantly increased (0.042±0.016 versus 0.052±0.019 mg/kg, P=0.02, N=11). This was accompanied by a small significant increase in methadone’s mass transfer rate (0.113±0.002 versus 0.014±0.002 mg/kg/h, P=0.02, N=11). The ODE/PDE model accurately predicted methadone’s removal during dialysis. The absolute value of the prediction errors for methadone’s extraction and throughput were less than 2%. Conclusion ODE/PDE modeling of methadone’s hemodialysis is a new approach to study methadone’s removal, in particular, and opioid removal, in general, in patients with end-stage renal disease on hemodialysis. ODE/PDE modeling accurately quantified the fundamental phenomena of methadone’s mass transfer during hemodialysis. This methodology may lead to development of optimally designed intradialytic opioid treatment protocols, and allow dynamic monitoring of outflow plasma opioid concentrations for model

  17. In silico ordinary differential equation/partial differential equation hemodialysis model estimates methadone removal during dialysis.

    Science.gov (United States)

    Linares, Oscar A; Schiesser, William E; Fudin, Jeffrey; Pham, Thien C; Bettinger, Jeffrey J; Mathew, Roy O; Daly, Annemarie L

    2015-01-01

    There is a need to have a model to study methadone's losses during hemodialysis to provide informed methadone dose recommendations for the practitioner. To build a one-dimensional (1-D), hollow-fiber geometry, ordinary differential equation (ODE) and partial differential equation (PDE) countercurrent hemodialyzer model (ODE/PDE model). We conducted a cross-sectional study in silico that evaluated eleven hemodialysis patients. Patients received a ceiling dose of methadone hydrochloride 30 mg/day. Outcome measures included: the total amount of methadone removed during dialysis; methadone's overall intradialytic mass transfer rate coefficient, km ; and, methadone's removal rate, j ME. Each metric was measured at dialysate flow rates of 250 mL/min and 800 mL/min. The ODE/PDE model revealed a significant increase in the change of methadone's mass transfer with increased dialysate flow rate, %Δkm =18.56, P=0.02, N=11. The total amount of methadone mass transferred across the dialyzer membrane with high dialysate flow rate significantly increased (0.042±0.016 versus 0.052±0.019 mg/kg, P=0.02, N=11). This was accompanied by a small significant increase in methadone's mass transfer rate (0.113±0.002 versus 0.014±0.002 mg/kg/h, P=0.02, N=11). The ODE/PDE model accurately predicted methadone's removal during dialysis. The absolute value of the prediction errors for methadone's extraction and throughput were less than 2%. ODE/PDE modeling of methadone's hemodialysis is a new approach to study methadone's removal, in particular, and opioid removal, in general, in patients with end-stage renal disease on hemodialysis. ODE/PDE modeling accurately quantified the fundamental phenomena of methadone's mass transfer during hemodialysis. This methodology may lead to development of optimally designed intradialytic opioid treatment protocols, and allow dynamic monitoring of outflow plasma opioid concentrations for model predictive control during dialysis in humans.

  18. Multiscale functions, scale dynamics, and applications to partial differential equations

    Science.gov (United States)

    Cresson, Jacky; Pierret, Frédéric

    2016-05-01

    Modeling phenomena from experimental data always begins with a choice of hypothesis on the observed dynamics such as determinism, randomness, and differentiability. Depending on these choices, different behaviors can be observed. The natural question associated to the modeling problem is the following: "With a finite set of data concerning a phenomenon, can we recover its underlying nature? From this problem, we introduce in this paper the definition of multi-scale functions, scale calculus, and scale dynamics based on the time scale calculus [see Bohner, M. and Peterson, A., Dynamic Equations on Time Scales: An Introduction with Applications (Springer Science & Business Media, 2001)] which is used to introduce the notion of scale equations. These definitions will be illustrated on the multi-scale Okamoto's functions. Scale equations are analysed using scale regimes and the notion of asymptotic model for a scale equation under a particular scale regime. The introduced formalism explains why a single scale equation can produce distinct continuous models even if the equation is scale invariant. Typical examples of such equations are given by the scale Euler-Lagrange equation. We illustrate our results using the scale Newton's equation which gives rise to a non-linear diffusion equation or a non-linear Schrödinger equation as asymptotic continuous models depending on the particular fractional scale regime which is considered.

  19. Construction and accuracy of partial differential equation approximations to the chemical master equation.

    Science.gov (United States)

    Grima, Ramon

    2011-11-01

    The mesoscopic description of chemical kinetics, the chemical master equation, can be exactly solved in only a few simple cases. The analytical intractability stems from the discrete character of the equation, and hence considerable effort has been invested in the development of Fokker-Planck equations, second-order partial differential equation approximations to the master equation. We here consider two different types of higher-order partial differential approximations, one derived from the system-size expansion and the other from the Kramers-Moyal expansion, and derive the accuracy of their predictions for chemical reactive networks composed of arbitrary numbers of unimolecular and bimolecular reactions. In particular, we show that the partial differential equation approximation of order Q from the Kramers-Moyal expansion leads to estimates of the mean number of molecules accurate to order Ω(-(2Q-3)/2), of the variance of the fluctuations in the number of molecules accurate to order Ω(-(2Q-5)/2), and of skewness accurate to order Ω(-(Q-2)). We also show that for large Q, the accuracy in the estimates can be matched only by a partial differential equation approximation from the system-size expansion of approximate order 2Q. Hence, we conclude that partial differential approximations based on the Kramers-Moyal expansion generally lead to considerably more accurate estimates in the mean, variance, and skewness than approximations of the same order derived from the system-size expansion.

  20. In silico ordinary differential equation/partial differential equation hemodialysis model estimates methadone removal during dialysis

    Directory of Open Access Journals (Sweden)

    Linares OA

    2015-07-01

    Full Text Available Oscar A Linares,1 William E Schiesser,2 Jeffrey Fudin,3–6 Thien C Pham,6 Jeffrey J Bettinger,6 Roy O Mathew,6 Annemarie L Daly7 1Translational Genomic Medicine Lab, Plymouth Pharmacokinetic Modeling Study Group, Plymouth, MI, 2Department of Chemical and Biomolecular Engineering, Lehigh University, Bethlehem, PA, 3University of Connecticut School of Pharmacy, Storrs, CT, 4Western New England College of Pharmacy, Springfield, MA, 5Albany College of Pharmacy and Health Sciences, Albany, NY, 6Stratton VA Medical Center, Albany, NY, 7Grace Hospice of Ann Arbor, Ann Arbor, MI, USA Background: There is a need to have a model to study methadone’s losses during hemodialysis to provide informed methadone dose recommendations for the practitioner. Aim: To build a one-dimensional (1-D, hollow-fiber geometry, ordinary differential equation (ODE and partial differential equation (PDE countercurrent hemodialyzer model (ODE/PDE model. Methodology: We conducted a cross-sectional study in silico that evaluated eleven hemodialysis patients. Patients received a ceiling dose of methadone hydrochloride 30 mg/day. Outcome measures included: the total amount of methadone removed during dialysis; methadone’s overall intradialytic mass transfer rate coefficient, km; and, methadone’s removal rate, jME. Each metric was measured at dialysate flow rates of 250 mL/min and 800 mL/min. Results: The ODE/PDE model revealed a significant increase in the change of methadone’s mass transfer with increased dialysate flow rate, %Δ km=18.56, P=0.02, N=11. The total amount of methadone mass transferred across the dialyzer membrane with high dialysate flow rate significantly increased (0.042±0.016 versus 0.052±0.019 mg/kg, P=0.02, N=11. This was accompanied by a small significant increase in methadone’s mass transfer rate (0.113±0.002 versus 0.014±0.002 mg/kg/h, P=0.02, N=11. The ODE/PDE model accurately predicted methadone’s removal during dialysis. The absolute value

  1. Mobile point sensors and actuators in the controllability theory of partial differential equations

    CERN Document Server

    Khapalov, Alexander Y

    2017-01-01

    This book presents a concise study of controllability theory of partial differential equations when they are equipped with actuators and/or sensors that are finite dimensional at every moment of time. Based on the author’s extensive research in the area of controllability theory, this monograph specifically focuses on the issues of controllability, observability, and stabilizability for parabolic and hyperbolic partial differential equations. The topics in this book also cover related applied questions such as the problem of localization of unknown pollution sources based on information obtained from point sensors that arise in environmental monitoring. Researchers and graduate students interested in controllability theory of partial differential equations and its applications will find this book to be an invaluable resource to their studies.

  2. Methods for partial differential equations qualitative properties of solutions, phase space analysis, semilinear models

    CERN Document Server

    Ebert, Marcelo R

    2018-01-01

    This book provides an overview of different topics related to the theory of partial differential equations. Selected exercises are included at the end of each chapter to prepare readers for the “research project for beginners” proposed at the end of the book. It is a valuable resource for advanced graduates and undergraduate students who are interested in specializing in this area. The book is organized in five parts: In Part 1 the authors review the basics and the mathematical prerequisites, presenting two of the most fundamental results in the theory of partial differential equations: the Cauchy-Kovalevskaja theorem and Holmgren's uniqueness theorem in its classical and abstract form. It also introduces the method of characteristics in detail and applies this method to the study of Burger's equation. Part 2 focuses on qualitative properties of solutions to basic partial differential equations, explaining the usual properties of solutions to elliptic, parabolic and hyperbolic equations for the archetypes...

  3. ON PARTIAL DIFFERENTIAL AND DIFFERENCE EQUATIONS WITH SYMMETRIES DEPENDING ON ARBITRARY FUNCTIONS

    Directory of Open Access Journals (Sweden)

    Giorgio Gubbiotti

    2016-06-01

    Full Text Available In this note we present some ideas on when Lie symmetries, both point and generalized, can depend on arbitrary functions. We show a few examples, both in partial differential and partial difference equations where this happens. Moreover we show that the infinitesimal generators of generalized symmetries depending on arbitrary functions, both for continuous and discrete equations, effectively play the role of master symmetries.

  4. Soliton solution for nonlinear partial differential equations by cosine-function method

    International Nuclear Information System (INIS)

    Ali, A.H.A.; Soliman, A.A.; Raslan, K.R.

    2007-01-01

    In this Letter, we established a traveling wave solution by using Cosine-function algorithm for nonlinear partial differential equations. The method is used to obtain the exact solutions for five different types of nonlinear partial differential equations such as, general equal width wave equation (GEWE), general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKdV), general improved Korteweg-de Vries equation (GIKdV), and Coupled equal width wave equations (CEWE), which are the important soliton equations

  5. A New Numerical Technique for Solving Systems Of Nonlinear Fractional Partial Differential Equations

    Directory of Open Access Journals (Sweden)

    Mountassir Hamdi Cherif

    2017-11-01

    Full Text Available In this paper, we apply an efficient method called the Aboodh decomposition method to solve systems of nonlinear fractional partial differential equations. This method is a combined form of Aboodh transform with Adomian decomposition method. The theoretical analysis of this investigated for systems of nonlinear fractional partial differential equations is calculated in the explicit form of a power series with easily computable terms. Some examples are given to shows that this method is very efficient and accurate. This method can be applied to solve others nonlinear systems problems.

  6. Formulae and Bounds connected to Optimal Design and Homogenization of Partial Differential Operators and Integral Functionals

    Energy Technology Data Exchange (ETDEWEB)

    Lukkassen, D.

    1996-12-31

    When partial differential equations are set up to model physical processes in strongly heterogeneous materials, effective parameters for heat transfer, electric conductivity etc. are usually required. Averaging methods often lead to convergence problems and in homogenization theory one is therefore led to study how certain integral functionals behave asymptotically. This mathematical doctoral thesis discusses (1) means and bounds connected to homogenization of integral functionals, (2) reiterated homogenization of integral functionals, (3) bounds and homogenization of some particular partial differential operators, (4) applications and further results. 154 refs., 11 figs., 8 tabs.

  7. A boundary value approach for solving three-dimensional elliptic and hyperbolic partial differential equations.

    Science.gov (United States)

    Biala, T A; Jator, S N

    2015-01-01

    In this article, the boundary value method is applied to solve three dimensional elliptic and hyperbolic partial differential equations. The partial derivatives with respect to two of the spatial variables (y, z) are discretized using finite difference approximations to obtain a large system of ordinary differential equations (ODEs) in the third spatial variable (x). Using interpolation and collocation techniques, a continuous scheme is developed and used to obtain discrete methods which are applied via the Block unification approach to obtain approximations to the resulting large system of ODEs. Several test problems are investigated to elucidate the solution process.

  8. Path integral solution of linear second order partial differential equations I: the general construction

    International Nuclear Information System (INIS)

    LaChapelle, J.

    2004-01-01

    A path integral is presented that solves a general class of linear second order partial differential equations with Dirichlet/Neumann boundary conditions. Elementary kernels are constructed for both Dirichlet and Neumann boundary conditions. The general solution can be specialized to solve elliptic, parabolic, and hyperbolic partial differential equations with boundary conditions. This extends the well-known path integral solution of the Schroedinger/diffusion equation in unbounded space. The construction is based on a framework for functional integration introduced by Cartier/DeWitt-Morette

  9. Unified algorithm for partial differential equations and examples of numerical computation

    International Nuclear Information System (INIS)

    Watanabe, Tsuguhiro

    1999-01-01

    A new unified algorithm is proposed to solve partial differential equations which describe nonlinear boundary value problems, eigenvalue problems and time developing boundary value problems. The algorithm is composed of implicit difference scheme and multiple shooting scheme and is named as HIDM (Higher order Implicit Difference Method). A new prototype computer programs for 2-dimensional partial differential equations is constructed and tested successfully to several problems. Extension of the computer programs to 3 or more higher order dimension problems will be easy due to the direct product type difference scheme. (author)

  10. Introductory Applications of Partial Differential Equations With Emphasis on Wave Propagation and Diffusion

    CERN Document Server

    Lamb, George L

    1995-01-01

    INTRODUCTORY APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS. With Emphasis on Wave Propagation and Diffusion. This is the ideal text for students and professionals who have some familiarity with partial differential equations, and who now wish to consolidate and expand their knowledge. Unlike most other texts on this topic, it interweaves prior knowledge of mathematics and physics, especially heat conduction and wave motion, into a presentation that demonstrates their interdependence. The result is a superb teaching text that reinforces the reader's understanding of both mathematics and physic

  11. Numerical solutions of ordinary and partial differential equations in the frequency domain

    International Nuclear Information System (INIS)

    Hazi, G.; Por, G.

    1997-01-01

    Numerical problems during the noise simulation in a nuclear power plant are discussed. The solutions of ordinary and partial differential equations are studied in the frequency domain. Numerical methods by the transfer function method are applied. It is shown that the correctness of the numerical methods is limited for ordinary differential equations in the frequency domain. To overcome the difficulties, step-size selection is suggested. (author)

  12. Modeling biological gradient formation: combining partial differential equations and Petri nets.

    Science.gov (United States)

    Bertens, Laura M F; Kleijn, Jetty; Hille, Sander C; Heiner, Monika; Koutny, Maciej; Verbeek, Fons J

    2016-01-01

    Both Petri nets and differential equations are important modeling tools for biological processes. In this paper we demonstrate how these two modeling techniques can be combined to describe biological gradient formation. Parameters derived from partial differential equation describing the process of gradient formation are incorporated in an abstract Petri net model. The quantitative aspects of the resulting model are validated through a case study of gradient formation in the fruit fly.

  13. A Novel Method for Analytical Solutions of Fractional Partial Differential Equations

    OpenAIRE

    Mehmet Ali Akinlar; Muhammet Kurulay

    2013-01-01

    A new solution technique for analytical solutions of fractional partial differential equations (FPDEs) is presented. The solutions are expressed as a finite sum of a vector type functional. By employing MAPLE software, it is shown that the solutions might be extended to an arbitrary degree which makes the present method not only different from the others in the literature but also quite efficient. The method is applied to special Bagley-Torvik and Diethelm fractional differential equations as...

  14. Numerical and computational analysis of the partial differential equations in hydrocodes and wavecodes

    International Nuclear Information System (INIS)

    Hicks, D.L.; Walsh, R.T.

    1976-06-01

    Discrete methods for the solution of the partial differential equations arising in hydrocodes and wavecodes are presented in a tutorial fashion. By discrete methods is meant, for example, the methods of finite differences, finite elements, discretized characteristics, etc. The concepts of stability, consistency, convergence, order of accuracy, true accuracy, etc., and their relevance to the hydrocodes and wavecodes are discussed

  15. Nonlinear perturbations of systems of partial differential equations with constant coefficients

    Directory of Open Access Journals (Sweden)

    Carmen J. Vanegas

    2000-01-01

    Full Text Available In this article, we show the existence of solutions to boundary-value problems, consisting of nonlinear systems of partial differential equations with constant coefficients. For this purpose, we use the right inverse of an associated operator and a fix point argument. As illustrations, we apply this method to Helmholtz equations and to second order systems of elliptic equations.

  16. Local Fractional Laplace Variational Iteration Method for Solving Linear Partial Differential Equations with Local Fractional Derivative

    Directory of Open Access Journals (Sweden)

    Ai-Min Yang

    2014-01-01

    Full Text Available The local fractional Laplace variational iteration method was applied to solve the linear local fractional partial differential equations. The local fractional Laplace variational iteration method is coupled by the local fractional variational iteration method and Laplace transform. The nondifferentiable approximate solutions are obtained and their graphs are also shown.

  17. Application of partial differential equation modeling of the control/structural dynamics of flexible spacecraft

    Science.gov (United States)

    Taylor, Lawrence W., Jr.; Rajiyah, H.

    1991-01-01

    Partial differential equations for modeling the structural dynamics and control systems of flexible spacecraft are applied here in order to facilitate systems analysis and optimization of these spacecraft. Example applications are given, including the structural dynamics of SCOLE, the Solar Array Flight Experiment, the Mini-MAST truss, and the LACE satellite. The development of related software is briefly addressed.

  18. Functional analytic methods in complex analysis and applications to partial differential equations

    International Nuclear Information System (INIS)

    Mshimba, A.S.A.; Tutschke, W.

    1990-01-01

    The volume contains 24 lectures given at the Workshop on Functional Analytic Methods in Complex Analysis and Applications to Partial Differential Equations held in Trieste, Italy, between 8-19 February 1988, at the ICTP. A separate abstract was prepared for each of these lectures. Refs and figs

  19. Oscillation of certain higher-order neutral partial functional differential equations.

    Science.gov (United States)

    Li, Wei Nian; Sheng, Weihong

    2016-01-01

    In this paper, we study the oscillation of certain higher-order neutral partial functional differential equations with the Robin boundary conditions. Some oscillation criteria are established. Two examples are given to illustrate the main results in the end of this paper.

  20. Parent Ratings of ADHD Symptoms: Generalized Partial Credit Model Analysis of Differential Item Functioning across Gender

    Science.gov (United States)

    Gomez, Rapson

    2012-01-01

    Objective: Generalized partial credit model, which is based on item response theory (IRT), was used to test differential item functioning (DIF) for the "Diagnostic and Statistical Manual of Mental Disorders" (4th ed.), inattention (IA), and hyperactivity/impulsivity (HI) symptoms across boys and girls. Method: To accomplish this, parents completed…

  1. On k-summability of formal solutions for certain partial differential operators with polynomial coefficients

    Directory of Open Access Journals (Sweden)

    Kunio Ichinobe

    2015-01-01

    Full Text Available We study the \\(k\\-summability of divergent formal solutions for the Cauchy problem of certain linear partial differential operators with coefficients which are polynomial in \\(t\\. We employ the method of successive approximation in order to construct the formal solutions and to obtain the properties of analytic continuation of the solutions of convolution equations and their exponential growth estimates.

  2. Multigrid for high dimensional elliptic partial differential equations on non-equidistant grids

    NARCIS (Netherlands)

    bin Zubair, H.; Oosterlee, C.E.; Wienands, R.

    2006-01-01

    This work presents techniques, theory and numbers for multigrid in a general d-dimensional setting. The main focus is the multigrid convergence for high-dimensional partial differential equations (PDEs). As a model problem we have chosen the anisotropic diffusion equation, on a unit hypercube. We

  3. Use of fast Fourier transforms for solving partial differential equations in physics

    CERN Document Server

    Le Bail, R C

    1972-01-01

    The use of fast Fourier techniques for the direct solution of an important class of elliptic, parabolic, and hyperbolic partial differential equations in two dimensions is described. Extensions to higher-order and higher-dimension equations as well as to integrodifferential equations are presented, and several numerical examples with their resulting precision and timing are reported. (12 refs).

  4. Lp Theory for Super-Parabolic Backward Stochastic Partial Differential Equations in the Whole Space

    International Nuclear Information System (INIS)

    Du Kai; Qiu, Jinniao; Tang Shanjian

    2012-01-01

    This paper is concerned with semi-linear backward stochastic partial differential equations (BSPDEs for short) of super-parabolic type. An L p -theory is given for the Cauchy problem of BSPDEs, separately for the case of p∈(1,2] and for the case of p∈(2,∞). A comparison theorem is also addressed.

  5. The modified simplest equation method to look for exact solutions of nonlinear partial differential equations

    OpenAIRE

    Efimova, Olga Yu.

    2010-01-01

    The modification of simplest equation method to look for exact solutions of nonlinear partial differential equations is presented. Using this method we obtain exact solutions of generalized Korteweg-de Vries equation with cubic source and exact solutions of third-order Kudryashov-Sinelshchikov equation describing nonlinear waves in liquids with gas bubbles.

  6. Image denoising using new pixon representation based on fuzzy filtering and partial differential equations

    DEFF Research Database (Denmark)

    Nadernejad, Ehsan; Nikpour, Mohsen

    2012-01-01

    In this paper, we have proposed two extensions to pixon-based image modeling. The first one is using bicubic interpolation instead of bilinear interpolation and the second one is using fuzzy filtering method, aiming to improve the quality of the pixonal image. Finally, partial differential...

  7. Mixed problem with integral boundary condition for a high order mixed type partial differential equation

    OpenAIRE

    M. Denche; A. L. Marhoune

    2003-01-01

    In this paper, we study a mixed problem with integral boundary conditions for a high order partial differential equation of mixed type. We prove the existence and uniqueness of the solution. The proof is based on energy inequality, and on the density of the range of the operator generated by the considered problem.

  8. An approximation theory for nonlinear partial differential equations with applications to identification and control

    Science.gov (United States)

    Banks, H. T.; Kunisch, K.

    1982-01-01

    Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

  9. New model reduction technique for a class of parabolic partial differential equations

    NARCIS (Netherlands)

    Vajta, Miklos

    1991-01-01

    A model reduction (or lumping) technique for a class of parabolic-type partial differential equations is given, and its application is discussed. The frequency response of the temperature distribution in any multilayer solid is developed and given by a matrix expression. The distributed transfer

  10. Introduction to partial differential equations from Fourier series to boundary-value problems

    CERN Document Server

    Broman, Arne

    2010-01-01

    This well-written, advanced-level text introduces students to Fourier analysis and some of its applications. The self-contained treatment covers Fourier series, orthogonal systems, Fourier and Laplace transforms, Bessel functions, and partial differential equations of the first and second orders. Over 260 exercises with solutions reinforce students' grasp of the material. 1970 edition.

  11. Rail-to-rail low-power fully differential OTA utilizing adaptive biasing and partial feedback

    DEFF Research Database (Denmark)

    Tuan Vu, Cao; Wisland, Dag T.; Lande, Tor Sverre

    consumption. The DC-gain of the proposed OTA is improved by adding a partial feedback loop. A Common-Mode Feedback (CMFB) circuit is required for fully differential rail-to-rail operation. Simulations show that the OTA topology has a low stand-by power consumption of 96μW and a high FoM of 3.84 [(V...

  12. A Novel Method for Analytical Solutions of Fractional Partial Differential Equations

    Directory of Open Access Journals (Sweden)

    Mehmet Ali Akinlar

    2013-01-01

    Full Text Available A new solution technique for analytical solutions of fractional partial differential equations (FPDEs is presented. The solutions are expressed as a finite sum of a vector type functional. By employing MAPLE software, it is shown that the solutions might be extended to an arbitrary degree which makes the present method not only different from the others in the literature but also quite efficient. The method is applied to special Bagley-Torvik and Diethelm fractional differential equations as well as a more general fractional differential equation.

  13. Rail-to-rail low-power fully differential OTA utilizing adaptive biasing and partial feedback

    DEFF Research Database (Denmark)

    Tuan Vu, Cao; Wisland, Dag T.; Lande, Tor Sverre

    A fully differential rail-to-rail Operational Transconductance Amplifier (OTA) with improved DC-gain and reduced power consumption is proposed in this paper. By using the adaptive biasing circuit and two differential inputs, a low stand-by current can be obtained together with reduced power...... consumption. The DC-gain of the proposed OTA is improved by adding a partial feedback loop. A Common-Mode Feedback (CMFB) circuit is required for fully differential rail-to-rail operation. Simulations show that the OTA topology has a low stand-by power consumption of 96μW and a high FoM of 3.84 [(V...

  14. Lattice Boltzmann model for high-order nonlinear partial differential equations

    Science.gov (United States)

    Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

    2018-01-01

    In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂tϕ +∑k=1mαk∂xkΠk(ϕ ) =0 (1 ≤k ≤m ≤6 ), αk are constant coefficients, Πk(ϕ ) are some known differential functions of ϕ . As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K (n ,n ) -Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009), 10.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009), 10.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

  15. Lattice Boltzmann model for high-order nonlinear partial differential equations.

    Science.gov (United States)

    Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

    2018-01-01

    In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂_{t}ϕ+∑_{k=1}^{m}α_{k}∂_{x}^{k}Π_{k}(ϕ)=0 (1≤k≤m≤6), α_{k} are constant coefficients, Π_{k}(ϕ) are some known differential functions of ϕ. As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K(n,n)-Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009)1672-179910.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009)PHYADX0378-437110.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

  16. Analytical solutions for coupling fractional partial differential equations with Dirichlet boundary conditions

    Science.gov (United States)

    Ding, Xiao-Li; Nieto, Juan J.

    2017-11-01

    In this paper, we consider the analytical solutions of coupling fractional partial differential equations (FPDEs) with Dirichlet boundary conditions on a finite domain. Firstly, the method of successive approximations is used to obtain the analytical solutions of coupling multi-term time fractional ordinary differential equations. Then, the technique of spectral representation of the fractional Laplacian operator is used to convert the coupling FPDEs to the coupling multi-term time fractional ordinary differential equations. By applying the obtained analytical solutions to the resulting multi-term time fractional ordinary differential equations, the desired analytical solutions of the coupling FPDEs are given. Our results are applied to derive the analytical solutions of some special cases to demonstrate their applicability.

  17. Collage-based approaches for elliptic partial differential equations inverse problems

    Science.gov (United States)

    Yodzis, Michael; Kunze, Herb

    2017-01-01

    The collage method for inverse problems has become well-established in the literature in recent years. Initial work developed a collage theorem, based upon Banach's fixed point theorem, for treating inverse problems for ordinary differential equations (ODEs). Amongst the subsequent work was a generalized collage theorem, based upon the Lax-Milgram representation theorem, useful for treating inverse problems for elliptic partial differential equations (PDEs). Each of these two different approaches can be applied to elliptic PDEs in one space dimension. In this paper, we explore and compare how the two different approaches perform for the estimation of the diffusivity for a steady-state heat equation.

  18. The application of Legendre-tau approximation to parameter identification for delay and partial differential equations

    Science.gov (United States)

    Ito, K.

    1983-01-01

    Approximation schemes based on Legendre-tau approximation are developed for application to parameter identification problem for delay and partial differential equations. The tau method is based on representing the approximate solution as a truncated series of orthonormal functions. The characteristic feature of the Legendre-tau approach is that when the solution to a problem is infinitely differentiable, the rate of convergence is faster than any finite power of 1/N; higher accuracy is thus achieved, making the approach suitable for small N.

  19. Discrete variational derivative method a structure-preserving numerical method for partial differential equations

    CERN Document Server

    Furihata, Daisuke

    2010-01-01

    Nonlinear Partial Differential Equations (PDEs) have become increasingly important in the description of physical phenomena. Unlike Ordinary Differential Equations, PDEs can be used to effectively model multidimensional systems. The methods put forward in Discrete Variational Derivative Method concentrate on a new class of ""structure-preserving numerical equations"" which improves the qualitative behaviour of the PDE solutions and allows for stable computing. The authors have also taken care to present their methods in an accessible manner, which means that the book will be useful to engineer

  20. Partial differential equations II elements of the modern theory equations with constant coefficients

    CERN Document Server

    Shubin, M

    1994-01-01

    This book, the first printing of which was published as Volume 31 of the Encyclopaedia of Mathematical Sciences, contains a survey of the modern theory of general linear partial differential equations and a detailed review of equations with constant coefficients. Readers will be interested in an introduction to microlocal analysis and its applications including singular integral operators, pseudodifferential operators, Fourier integral operators and wavefronts, a survey of the most important results about the mixed problem for hyperbolic equations, a review of asymptotic methods including short wave asymptotics, the Maslov canonical operator and spectral asymptotics, a detailed description of the applications of distribution theory to partial differential equations with constant coefficients including numerous interesting special topics.

  1. Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations

    Science.gov (United States)

    Arqub, Omar Abu; El-Ajou, Ahmad; Momani, Shaher

    2015-07-01

    Building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics, physics, and engineering. In this work, a new analytical technique for constructing and predicting solitary pattern solutions of time-fractional dispersive partial differential equations is proposed based on the generalized Taylor series formula and residual error function. The new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software. For method evaluation and validation, the proposed technique was applied to three different models and compared with some of the well-known methods. The resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct, as well as the prediction of solitary pattern solutions for time-fractional dispersive partial differential equations.

  2. A higher order numerical method for time fractional partial differential equations with nonsmooth data

    Science.gov (United States)

    Xing, Yanyuan; Yan, Yubin

    2018-03-01

    Gao et al. [11] (2014) introduced a numerical scheme to approximate the Caputo fractional derivative with the convergence rate O (k 3 - α), 0 equation is sufficiently smooth, Lv and Xu [20] (2016) proved by using energy method that the corresponding numerical method for solving time fractional partial differential equation has the convergence rate O (k 3 - α), 0 equation has low regularity and in this case the numerical method fails to have the convergence rate O (k 3 - α), 0 quadratic interpolation polynomials. Based on this scheme, we introduce a time discretization scheme to approximate the time fractional partial differential equation and show by using Laplace transform methods that the time discretization scheme has the convergence rate O (k 3 - α), 0 0 for smooth and nonsmooth data in both homogeneous and inhomogeneous cases. Numerical examples are given to show that the theoretical results are consistent with the numerical results.

  3. Parabolic partial differential equations with discrete state-dependent delay: Classical solutions and solution manifold

    Czech Academy of Sciences Publication Activity Database

    Krisztin, T.; Rezunenko, Oleksandr

    2016-01-01

    Roč. 260, č. 5 (2016), s. 4454-4472 ISSN 0022-0396 R&D Projects: GA ČR GAP103/12/2431 Institutional support: RVO:67985556 Keywords : Parabolic partial differential equations * State dependent delay * Solution manifold Subject RIV: BC - Control Systems Theory Impact factor: 1.988, year: 2016 http://library.utia.cas.cz/separaty/2016/AS/rezunenko-0457879.pdf

  4. A Posteriori Finite Element Bounds for Sensitivity Derivatives of Partial-Differential-Equation Outputs. Revised

    Science.gov (United States)

    Lewis, Robert Michael; Patera, Anthony T.; Peraire, Jaume

    1998-01-01

    We present a Neumann-subproblem a posteriori finite element procedure for the efficient and accurate calculation of rigorous, 'constant-free' upper and lower bounds for sensitivity derivatives of functionals of the solutions of partial differential equations. The design motivation for sensitivity derivative error control is discussed; the a posteriori finite element procedure is described; the asymptotic bounding properties and computational complexity of the method are summarized; and illustrative numerical results are presented.

  5. Cellular automata for spatiotemporal pattern formation from reaction–diffusion partial differential equations

    International Nuclear Information System (INIS)

    Ohmori, Shousuke; Yamazaki, Yoshihiro

    2016-01-01

    Ultradiscrete equations are derived from a set of reaction–diffusion partial differential equations, and cellular automaton rules are obtained on the basis of the ultradiscrete equations. Some rules reproduce the dynamical properties of the original reaction–diffusion equations, namely, bistability and pulse annihilation. Furthermore, other rules bring about soliton-like preservation and periodic pulse generation with a pacemaker, which are not obtained from the original reaction–diffusion equations. (author)

  6. Conservation laws for certain time fractional nonlinear systems of partial differential equations

    Science.gov (United States)

    Singla, Komal; Gupta, R. K.

    2017-12-01

    In this study, an extension of the concept of nonlinear self-adjointness and Noether operators is proposed for calculating conserved vectors of the time fractional nonlinear systems of partial differential equations. In our recent work (J Math Phys 2016; 57: 101504), by proposing the symmetry approach for time fractional systems, the Lie symmetries for some fractional nonlinear systems have been derived. In this paper, the obtained infinitesimal generators are used to find conservation laws for the corresponding fractional systems.

  7. Scale-invariant solutions to partial differential equations of fractional order with a moving boundary condition

    International Nuclear Information System (INIS)

    Li Xicheng; Xu Mingyu; Wang Shaowei

    2008-01-01

    In this paper, we give similarity solutions of partial differential equations of fractional order with a moving boundary condition. The solutions are given in terms of a generalized Wright function. The time-fractional Caputo derivative and two types of space-fractional derivatives are considered. The scale-invariant variable and the form of the solution of the moving boundary are obtained by the Lie group analysis. A comparison between the solutions corresponding to two types of fractional derivative is also given

  8. On the solution of elliptic partial differential equations on regions with corners

    International Nuclear Information System (INIS)

    Serkh, Kirill; Rokhlin, Vladimir

    2016-01-01

    In this paper we investigate the solution of boundary value problems on polygonal domains for elliptic partial differential equations. We observe that when the problems are formulated as the boundary integral equations of classical potential theory, the solutions are representable by series of elementary functions. In addition to being analytically perspicuous, the resulting expressions lend themselves to the construction of accurate and efficient numerical algorithms. The results are illustrated by a number of numerical examples.

  9. Study of coupled nonlinear partial differential equations for finding exact analytical solutions.

    Science.gov (United States)

    Khan, Kamruzzaman; Akbar, M Ali; Koppelaar, H

    2015-07-01

    Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G'/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd-Sokolov-Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics.

  10. Existence of pseudo almost periodic solutions for a class of partial functional differential equations

    Directory of Open Access Journals (Sweden)

    Hui-Sheng Ding

    2013-04-01

    Full Text Available In this paper, we first introduce a new class of pseudo almost periodic type functions and investigate some properties of pseudo almost periodic type functions; and then we discuss the existence of pseudo almost periodic solutions to the class of abstract partial functional differential equations $x'(t=Ax(t+f(t,x_t$ with finite delay in a Banach space X.

  11. Taguchi method for partial differential equations with application in tumor growth.

    Science.gov (United States)

    Ilea, M; Turnea, M; Rotariu, M; Arotăriţei, D; Popescu, Marilena

    2014-01-01

    The growth of tumors is a highly complex process. To describe this process, mathematical models are needed. A variety of partial differential mathematical models for tumor growth have been developed and studied. Most of those models are based on the reaction-diffusion equations and mass conservation law. A variety of modeling strategies have been developed, each focusing on tumor growth. Systems of time-dependent partial differential equations occur in many branches of applied mathematics. The vast majority of mathematical models in tumor growth are formulated in terms of partial differential equations. We propose a mathematical model for the interactions between these three cancer cell populations. The Taguchi methods are widely used by quality engineering scientists to compare the effects of multiple variables, together with their interactions, with a simple and manageable experimental design. In Taguchi's design of experiments, variation is more interesting to study than the average. First, Taguchi methods are utilized to search for the significant factors and the optimal level combination of parameters. Except the three parameters levels, other factors levels other factors levels would not be considered. Second, cutting parameters namely, cutting speed, depth of cut, and feed rate are designed using the Taguchi method. Finally, the adequacy of the developed mathematical model is proved by ANOVA. According to the results of ANOVA, since the percentage contribution of the combined error is as small. Many mathematical models can be quantitatively characterized by partial differential equations. The use of MATLAB and Taguchi method in this article illustrates the important role of informatics in research in mathematical modeling. The study of tumor growth cells is an exciting and important topic in cancer research and will profit considerably from theoretical input. Interpret these results to be a permanent collaboration between math's and medical oncologists.

  12. The Adomian decomposition method for solving partial differential equations of fractal order in finite domains

    Energy Technology Data Exchange (ETDEWEB)

    El-Sayed, A.M.A. [Faculty of Science University of Alexandria (Egypt)]. E-mail: amasyed@hotmail.com; Gaber, M. [Faculty of Education Al-Arish, Suez Canal University (Egypt)]. E-mail: mghf408@hotmail.com

    2006-11-20

    The Adomian decomposition method has been successively used to find the explicit and numerical solutions of the time fractional partial differential equations. A different examples of special interest with fractional time and space derivatives of order {alpha}, 0<{alpha}=<1 are considered and solved by means of Adomian decomposition method. The behaviour of Adomian solutions and the effects of different values of {alpha} are shown graphically for some examples.

  13. Analytical Solutions for Systems of Singular Partial Differential-Algebraic Equations

    Directory of Open Access Journals (Sweden)

    U. Filobello-Nino

    2015-01-01

    Full Text Available This paper proposes power series method (PSM in order to find solutions for singular partial differential-algebraic equations (SPDAEs. We will solve three examples to show that PSM method can be used to search for analytical solutions of SPDAEs. What is more, we will see that, in some cases, Padé posttreatment, besides enlarging the domain of convergence, may be employed in order to get the exact solution from the truncated series solutions of PSM.

  14. Study of coupled nonlinear partial differential equations for finding exact analytical solutions

    Science.gov (United States)

    Khan, Kamruzzaman; Akbar, M. Ali; Koppelaar, H.

    2015-01-01

    Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G′/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd–Sokolov–Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics. PMID:26587256

  15. Baecklund transformations and zero-curvature representations of systems of partial differential equations

    International Nuclear Information System (INIS)

    Brandt, F.

    1993-01-01

    It is shown that Baecklund transformations (BTs) and zero-curvature representations (ZCRs) of systems of partial differential equations (PDEs) are closely related. The connection is established by nonlinear representations of the symmetry group underlying the ZCR which induce gauge transformations relating different BTs. This connection is used to construct BTs from ZCRs (and vice versa). Furthermore a procedure is outlined which allows a systematic search for ZCRs of a given system of PDEs. (orig.)

  16. Explicit finite difference predictor and convex corrector with applications to hyperbolic partial differential equations

    Science.gov (United States)

    Dey, C.; Dey, S. K.

    1983-01-01

    An explicit finite difference scheme consisting of a predictor and a corrector has been developed and applied to solve some hyperbolic partial differential equations (PDEs). The corrector is a convex-type function which is applied at each time level and at each mesh point. It consists of a parameter which may be estimated such that for larger time steps the algorithm should remain stable and generate a fast speed of convergence to the steady-state solution. Some examples have been given.

  17. Semi-groups of operators and some of their applications to partial differential equations

    International Nuclear Information System (INIS)

    Kisynski, J.

    1976-01-01

    Basic notions and theorems of the theory of one-parameter semi-groups of linear operators are given, illustrated by some examples concerned with linear partial differential operators. For brevity, some important and widely developed parts of the semi-group theory such as the general theory of holomorphic semi-groups or the theory of temporally inhomogeneous evolution equations are omitted. This omission includes also the very important application of semi-groups to investigating stochastic processes. (author)

  18. New finite volume methods for approximating partial differential equations on arbitrary meshes

    International Nuclear Information System (INIS)

    Hermeline, F.

    2008-12-01

    This dissertation presents some new methods of finite volume type for approximating partial differential equations on arbitrary meshes. The main idea lies in solving twice the problem to be dealt with. One addresses the elliptic equations with variable (anisotropic, antisymmetric, discontinuous) coefficients, the parabolic linear or non linear equations (heat equation, radiative diffusion, magnetic diffusion with Hall effect), the wave type equations (Maxwell, acoustics), the elasticity and Stokes'equations. Numerous numerical experiments show the good behaviour of this type of method. (author)

  19. An Accurate Approximate-Analytical Technique for Solving Time-Fractional Partial Differential Equations

    Directory of Open Access Journals (Sweden)

    M. Bishehniasar

    2017-01-01

    Full Text Available The demand of many scientific areas for the usage of fractional partial differential equations (FPDEs to explain their real-world systems has been broadly identified. The solutions may portray dynamical behaviors of various particles such as chemicals and cells. The desire of obtaining approximate solutions to treat these equations aims to overcome the mathematical complexity of modeling the relevant phenomena in nature. This research proposes a promising approximate-analytical scheme that is an accurate technique for solving a variety of noninteger partial differential equations (PDEs. The proposed strategy is based on approximating the derivative of fractional-order and reducing the problem to the corresponding partial differential equation (PDE. Afterwards, the approximating PDE is solved by using a separation-variables technique. The method can be simply applied to nonhomogeneous problems and is proficient to diminish the span of computational cost as well as achieving an approximate-analytical solution that is in excellent concurrence with the exact solution of the original problem. In addition and to demonstrate the efficiency of the method, it compares with two finite difference methods including a nonstandard finite difference (NSFD method and standard finite difference (SFD technique, which are popular in the literature for solving engineering problems.

  20. Discontinuous Galerkin finite element methods for hyperbolic nonconservative partial differential equations

    International Nuclear Information System (INIS)

    Rhebergen, S.; Bokhove, O.; Vegt, J.J.W. van der

    2008-01-01

    We present space- and space-time discontinuous Galerkin finite element (DGFEM) formulations for systems containing nonconservative products, such as occur in dispersed multiphase flow equations. The main criterium we pose on the weak formulation is that if the system of nonconservative partial differential equations can be transformed into conservative form, then the formulation must reduce to that for conservative systems. Standard DGFEM formulations cannot be applied to nonconservative systems of partial differential equations. We therefore introduce the theory of weak solutions for nonconservative products into the DGFEM formulation leading to the new question how to define the path connecting left and right states across a discontinuity. The effect of different paths on the numerical solution is investigated and found to be small. We also introduce a new numerical flux that is able to deal with nonconservative products. Our scheme is applied to two different systems of partial differential equations. First, we consider the shallow water equations, where topography leads to nonconservative products, in which the known, possibly discontinuous, topography is formally taken as an unknown in the system. Second, we consider a simplification of a depth-averaged two-phase flow model which contains more intrinsic nonconservative products

  1. A new RBF-Trefftz meshless method for partial differential equations

    International Nuclear Information System (INIS)

    Cao Leilei; Zhao Ning; Qin Qinghua

    2010-01-01

    Based on the radial basis functions (RBF) and T-Trefftz solution, this paper presents a new meshless method for numerically solving various partial differential equation systems. First, the analog equation method (AEM) is used to convert the original patial differential equation to an equivalent Poisson's equation. Then, the radial basis functions (RBF) are employed to approxiamate the inhomogeneous term, while the homogeneous solution is obtained by linear combination of a set of T-Trefftz solutions. The present scheme, named RBF-Trefftz has the advantage over the fundamental solution (MFS) method due to the use of nonsingular T-Trefftz solution rather than singular fundamental solutions, so it does not require the artificial boundary. The application and efficiency of the proposed method are validated through several examples which include different type of differential equations, such as Laplace equation, Hellmholtz equation, convectin-diffusion equation and time-dependent equation.

  2. Abodes for life in carbonaceous asteroids?

    Science.gov (United States)

    Abramov, Oleg; Mojzsis, Stephen J.

    2011-05-01

    Thermal evolution models for carbonaceous asteroids that use new data for permeability, pore volume, and water circulation as input parameters provide a window into what are arguably the earliest habitable environments in the Solar System. Plausible models of the Murchison meteorite (CM) parent body show that to first-order, conditions suitable for the stability of liquid water, and thus pre- or post-biotic chemistry, could have persisted within these asteroids for tens of Myr. In particular, our modeling results indicate that a 200-km carbonaceous asteroid with a 40% initial ice content takes almost 60 Myr to cool completely, with habitable temperatures being maintained for ˜24 Myr in the center. Yet, there are a number of indications that even with the requisite liquid water, thermal energy sources to drive chemical gradients, and abundant organic "building blocks" deemed necessary criteria for life, carbonaceous asteroids were intrinsically unfavorable sites for biopoesis. These controls include different degrees of exothermal mineral hydration reactions that boost internal warming but effectively remove liquid water from the system, rapid (1-10 mm yr -1) inward migration of internal habitable volumes in most models, and limitations imposed by low permeabilities and small pore sizes in primitive undifferentiated carbonaceous asteroids. Our results do not preclude the existence of habitable conditions on larger, possibly differentiated objects such as Ceres and the Themis family asteroids due to presumed longer, more intense heating and possible long-lived water reservoirs.

  3. Carbonaceous material treatment

    Energy Technology Data Exchange (ETDEWEB)

    Trevor, S R

    1939-05-04

    To separate and collect for use the component parts of carbonaceous materials, they are fed to superimposed connected vertical or substantially vertical chambers, located over a furnace, the flue gases from which pass to space or spaces of a casing surrounding the superimposed chambers. Pipes are provided so that part or whole of the gases may be passed through the chambers. Take-off pipes are connected to expansion chambers, through which the gases pass to condenser coils and separating tanks.

  4. Treating carbonaceous materials

    Energy Technology Data Exchange (ETDEWEB)

    Corbett, R L; Corbett, E G

    1939-03-21

    A process is given for the production of aliphatic compounds by heat treatment of carbonaceous material. The latter are impregnated with a dilute solution of a catalyst, such as chromium copper or nickel acetate or nitrate, or ammonium or urea acetate and subjected to destructive distillation in a retort in the presence of a reducing gas and steam, at a pressure not greater than fifteen atmospheres.

  5. Distilling carbonaceous materials

    Energy Technology Data Exchange (ETDEWEB)

    Griffiths, C A

    1924-04-15

    In apparatus of the kind set forth for distilling solid carbonaceous materials, a rotary retort in the form of a tubular, hollow cylindrical, or other similar hollow body, of small diameter, having a thin wall is provided to which the heat is applied externally, with means operative within it adapted, not only for cleaning the internal wall of the retort but also for distributing the heat throughout the mass of materials under treatment, substantially as described.

  6. Workshop on Recent Trends in Complex Methods for Partial Differential Equations

    CERN Document Server

    Celebi, A; Tutschke, Wolfgang

    1999-01-01

    This volume is a collection of manscripts mainly originating from talks and lectures given at the Workshop on Recent Trends in Complex Methods for Par­ tial Differential Equations held from July 6 to 10, 1998 at the Middle East Technical University in Ankara, Turkey, sponsored by The Scientific and Tech­ nical Research Council of Turkey and the Middle East Technical University. This workshop is a continuation oftwo workshops from 1988 and 1993 at the In­ ternational Centre for Theoretical Physics in Trieste, Italy entitled Functional analytic Methods in Complex Analysis and Applications to Partial Differential Equations. Since classical complex analysis of one and several variables has a long tra­ dition it is of high level. But most of its basic problems are solved nowadays so that within the last few decades it has lost more and more attention. The area of complex and functional analytic methods in partial differential equations, however, is still a growing and flourishing field, in particular as these ...

  7. Total, partial and differential ionization cross sections in proton-hydrogen collisions at low energy

    Energy Technology Data Exchange (ETDEWEB)

    Zou, Shiyang [Graduate University for Advanced Studies, School of Mathematical and Physical Science, Toki, Gifu (Japan); Pichl, Lukas [University of Aizu, Foundation of Computer Science Laboratory, Aizuwakamatsu, Fukushima (Japan); Kimura, Mineo [Yamaguchi Univ., Graduate School of Science and Engineering, Ube, Yamaguchi (Japan); Kato, Takako [National Inst. for Fusion Science, Toki, Gifu (Japan)

    2003-01-01

    Single-differential, partial and total ionization cross sections for the proton-hydrogen collision system at low energy range (0.1-10 keV/amu) are determined by using the electron translation factor corrected molecular-orbital close-coupling method. Full convergence of ionization cross sections as a function of H{sub 2}{sup +} molecular basis size is achieved by including up to 10 bound states, and 11 continuum partial waves. The present cross sections are in an excellent agreement with the recent experiments of Shah et al., but decrease more rapidly than the cross sections measured by Pieksma et al. with decreasing energy. The calculated cross section data are included in this report. (author)

  8. On mixed derivatives type high dimensional multi-term fractional partial differential equations approximate solutions

    Science.gov (United States)

    Talib, Imran; Belgacem, Fethi Bin Muhammad; Asif, Naseer Ahmad; Khalil, Hammad

    2017-01-01

    In this research article, we derive and analyze an efficient spectral method based on the operational matrices of three dimensional orthogonal Jacobi polynomials to solve numerically the mixed partial derivatives type multi-terms high dimensions generalized class of fractional order partial differential equations. We transform the considered fractional order problem to an easily solvable algebraic equations with the aid of the operational matrices. Being easily solvable, the associated algebraic system leads to finding the solution of the problem. Some test problems are considered to confirm the accuracy and validity of the proposed numerical method. The convergence of the method is ensured by comparing our Matlab software simulations based obtained results with the exact solutions in the literature, yielding negligible errors. Moreover, comparative results discussed in the literature are extended and improved in this study.

  9. Differentiation of mucosal disease from partial development of the paranasal sinuses in pediatric patients

    International Nuclear Information System (INIS)

    Duerinckx, A.J.; Whyte, A.M.; Lufkin, R.B.; Hall, T.R.; Kangarloo, H.

    1988-01-01

    On magnetic resonance (MR) images of pediatric patients, sinus mucosal disease may have an appearance similar to that of the normal partially developed sinus, leading to an increase in the number of patients labeled as having incidental sinusitis. The paranasal sinuses were retrospectively evaluated in 27 infants and children aged 0-11 years undergoing brain MR imaging for indications both unrelated and related to sinus disease. The authors developed criteria for grading paranasal sinus development and mucosal disease. Incidental mucosal disease is not uncommon, occurring in 28% of patients aged 0-7 years. In children under 3 years of age, inflammatory mucosal thickening and marrow surrounding the partially developed sinus have a high signal on many MR sequences and may be confused. Recognition of the low-intensity peripheral cortical margin of the sinus and awareness of the stages of normal sinus development allow differentiation

  10. ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing

    KAUST Repository

    Calatroni, Luca

    2013-08-01

    We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H -1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation.

  11. Survey of the status of finite element methods for partial differential equations

    Science.gov (United States)

    Temam, Roger

    1986-01-01

    The finite element methods (FEM) have proved to be a powerful technique for the solution of boundary value problems associated with partial differential equations of either elliptic, parabolic, or hyperbolic type. They also have a good potential for utilization on parallel computers particularly in relation to the concept of domain decomposition. This report is intended as an introduction to the FEM for the nonspecialist. It contains a survey which is totally nonexhaustive, and it also contains as an illustration, a report on some new results concerning two specific applications, namely a free boundary fluid-structure interaction problem and the Euler equations for inviscid flows.

  12. Building bridges connections and challenges in modern approaches to numerical partial differential equations

    CERN Document Server

    Brezzi, Franco; Cangiani, Andrea; Georgoulis, Emmanuil

    2016-01-01

    This volume contains contributed survey papers from the main speakers at the LMS/EPSRC Symposium “Building bridges: connections and challenges in modern approaches to numerical partial differential equations”. This meeting took place in July 8-16, 2014, and its main purpose was to gather specialists in emerging areas of numerical PDEs, and explore the connections between the different approaches. The type of contributions ranges from the theoretical foundations of these new techniques, to the applications of them, to new general frameworks and unified approaches that can cover one, or more than one, of these emerging techniques.

  13. ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing

    KAUST Repository

    Calatroni, Luca; Dü ring, Bertram; Schö nlieb, Carola-Bibiane

    2013-01-01

    We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H -1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation.

  14. New Generalized Hyperbolic Functions to Find New Exact Solutions of the Nonlinear Partial Differential Equations

    Directory of Open Access Journals (Sweden)

    Yusuf Pandir

    2013-01-01

    Full Text Available We firstly give some new functions called generalized hyperbolic functions. By the using of the generalized hyperbolic functions, new kinds of transformations are defined to discover the exact approximate solutions of nonlinear partial differential equations. Based on the generalized hyperbolic function transformation of the generalized KdV equation and the coupled equal width wave equations (CEWE, we find new exact solutions of two equations and analyze the properties of them by taking different parameter values of the generalized hyperbolic functions. We think that these solutions are very important to explain some physical phenomena.

  15. Simple equation method for nonlinear partial differential equations and its applications

    Directory of Open Access Journals (Sweden)

    Taher A. Nofal

    2016-04-01

    Full Text Available In this article, we focus on the exact solution of the some nonlinear partial differential equations (NLPDEs such as, Kodomtsev–Petviashvili (KP equation, the (2 + 1-dimensional breaking soliton equation and the modified generalized Vakhnenko equation by using the simple equation method. In the simple equation method the trial condition is the Bernoulli equation or the Riccati equation. It has been shown that the method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering problems.

  16. 2013 CIME Course Vector-valued Partial Differential Equations and Applications

    CERN Document Server

    Marcellini, Paolo

    2017-01-01

    Collating different aspects of Vector-valued Partial Differential Equations and Applications, this volume is based on the 2013 CIME Course with the same name which took place at Cetraro, Italy, under the scientific direction of John Ball and Paolo Marcellini. It contains the following contributions: The pullback equation (Bernard Dacorogna), The stability of the isoperimetric inequality (Nicola Fusco), Mathematical problems in thin elastic sheets: scaling limits, packing, crumpling and singularities (Stefan Müller), and Aspects of PDEs related to fluid flows (Vladimir Sverák). These lectures are addressed to graduate students and researchers in the field.

  17. Parametric Borel summability for some semilinear system of partial differential equations

    Directory of Open Access Journals (Sweden)

    Hiroshi Yamazawa

    2015-01-01

    Full Text Available In this paper we study the Borel summability of formal solutions with a parameter of first order semilinear system of partial differential equations with \\(n\\ independent variables. In [Singular perturbation of linear systems with a regular singularity, J. Dynam. Control. Syst. 8 (2002, 313-322], Balser and Kostov proved the Borel summability of formal solutions with respect to a singular perturbation parameter for a linear equation with one independent variable. We shall extend their results to a semilinear system of equations with general independent variables.

  18. A New Fractional Projective Riccati Equation Method for Solving Fractional Partial Differential Equations

    International Nuclear Information System (INIS)

    Feng Qing-Hua

    2014-01-01

    In this paper, a new fractional projective Riccati equation method is proposed to establish exact solutions for fractional partial differential equations in the sense of modified Riemann—Liouville derivative. This method can be seen as the fractional version of the known projective Riccati equation method. For illustrating the validity of this method, we apply this method to solve the space-time fractional Whitham—Broer—Kaup (WBK) equations and the nonlinear fractional Sharma—Tasso—Olever (STO) equation, and as a result, some new exact solutions for them are obtained. (general)

  19. Solution of Nonlinear Partial Differential Equations by New Laplace Variational Iteration Method

    Directory of Open Access Journals (Sweden)

    Eman M. A. Hilal

    2014-01-01

    Full Text Available The aim of this study is to give a good strategy for solving some linear and nonlinear partial differential equations in engineering and physics fields, by combining Laplace transform and the modified variational iteration method. This method is based on the variational iteration method, Laplace transforms, and convolution integral, introducing an alternative Laplace correction functional and expressing the integral as a convolution. Some examples in physical engineering are provided to illustrate the simplicity and reliability of this method. The solutions of these examples are contingent only on the initial conditions.

  20. A lattice Boltzmann model with an amending function for simulating nonlinear partial differential equations

    International Nuclear Information System (INIS)

    Lin-Jie, Chen; Chang-Feng, Ma

    2010-01-01

    This paper proposes a lattice Boltzmann model with an amending function for one-dimensional nonlinear partial differential equations (NPDEs) in the form u t + αuu x + βu n u x + γu xx + δu xxx + ζu xxxx = 0. This model is different from existing models because it lets the time step be equivalent to the square of the space step and derives higher accuracy and nonlinear terms in NPDEs. With the Chapman–Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The numerical results agree well with the analytical solutions. (general)

  1. Analytical solutions to time-fractional partial differential equations in a two-dimensional multilayer annulus

    Science.gov (United States)

    Chen, Shanzhen; Jiang, Xiaoyun

    2012-08-01

    In this paper, analytical solutions to time-fractional partial differential equations in a multi-layer annulus are presented. The final solutions are obtained in terms of Mittag-Leffler function by using the finite integral transform technique and Laplace transform technique. In addition, the classical diffusion equation (α=1), the Helmholtz equation (α→0) and the wave equation (α=2) are discussed as special cases. Finally, an illustrative example problem for the three-layer semi-circular annular region is solved and numerical results are presented graphically for various kind of order of fractional derivative.

  2. The Spectral/hp-Finite Element Method for Partial Differential Equations

    DEFF Research Database (Denmark)

    Engsig-Karup, Allan Peter

    2009-01-01

    dimensions. In the course the chosen programming environment is Matlab, however, this is by no means a necessary requirement. The mathematical level needed to grasp the details of this set of notes requires an elementary background in mathematical analysis and linear algebra. Each chapter is supplemented......This set of lecture notes provides an elementary introduction to both the classical Finite Element Method (FEM) and the extended Spectral/$hp$-Finite Element Method for solving Partial Differential Equations (PDEs). Many problems in science and engineering can be formulated mathematically...

  3. First-order systems of linear partial differential equations: normal forms, canonical systems, transform methods

    Directory of Open Access Journals (Sweden)

    Heinz Toparkus

    2014-04-01

    Full Text Available In this paper we consider first-order systems with constant coefficients for two real-valued functions of two real variables. This is both a problem in itself, as well as an alternative view of the classical linear partial differential equations of second order with constant coefficients. The classification of the systems is done using elementary methods of linear algebra. Each type presents its special canonical form in the associated characteristic coordinate system. Then you can formulate initial value problems in appropriate basic areas, and you can try to achieve a solution of these problems by means of transform methods.

  4. Student Solutions Manual to Boundary Value Problems and Partial Differential Equations

    CERN Document Server

    Powers, David L

    2005-01-01

    This student solutions manual accompanies the text, Boundary Value Problems and Partial Differential Equations, 5e. The SSM is available in print via PDF or electronically, and provides the student with the detailed solutions of the odd-numbered problems contained throughout the book.Provides students with exercises that skillfully illustrate the techniques used in the text to solve science and engineering problemsNearly 900 exercises ranging in difficulty from basic drills to advanced problem-solving exercisesMany exercises based on current engineering applications

  5. Distribution of the Discretization and Algebraic Error in Numerical Solution of Partial Differential Equations

    Czech Academy of Sciences Publication Activity Database

    Papež, Jan; Liesen, J.; Strakoš, Z.

    2014-01-01

    Roč. 449, 15 May (2014), s. 89-114 ISSN 0024-3795 R&D Projects: GA AV ČR IAA100300802; GA ČR GA201/09/0917 Grant - others:GA MŠk(CZ) LL1202; GA UK(CZ) 695612 Institutional support: RVO:67985807 Keywords : numerical solution of partial differential equations * finite element method * adaptivity * a posteriori error analysis * discretization error * algebra ic error * spatial distribution of the error Subject RIV: BA - General Mathematics Impact factor: 0.939, year: 2014

  6. "Real-Time Optical Laboratory Linear Algebra Solution Of Partial Differential Equations"

    Science.gov (United States)

    Casasent, David; Jackson, James

    1986-03-01

    A Space Integrating (SI) Optical Linear Algebra Processor (OLAP) employing space and frequency-multiplexing, new partitioning and data flow, and achieving high accuracy performance with a non base-2 number system is described. Laboratory data on the performance of this system and the solution of parabolic Partial Differential Equations (PDEs) is provided. A multi-processor OLAP system is also described for the first time. It use in the solution of multiple banded matrices that frequently arise is then discussed. The utility and flexibility of this processor compared to digital systolic architectures should be apparent.

  7. Mathematical Methods for Engineers and Scientists 3 Fourier Analysis, Partial Differential Equations and Variational Methods

    CERN Document Server

    Tang, Kwong-Tin

    2007-01-01

    Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow. Numerous clearly stated, completely worked out examples together with carefully selected problem sets with answers are used to enhance students' understanding and manipulative skill. The goal is to make students comfortable and confident in using advanced mathematical tools in junior, senior, and beginning graduate courses.

  8. Maillet type theorem for singular first order nonlinear partial differential equations of totally characteristic type. Part II

    Directory of Open Access Journals (Sweden)

    Akira Shirai

    2015-01-01

    Full Text Available In this paper, we study the following nonlinear first order partial differential equation: \\[f(t,x,u,\\partial_t u,\\partial_x u=0\\quad\\text{with}\\quad u(0,x\\equiv 0.\\] The purpose of this paper is to determine the estimate of Gevrey order under the condition that the equation is singular of a totally characteristic type. The Gevrey order is indicated by the rate of divergence of a formal power series. This paper is a continuation of the previous papers [Convergence of formal solutions of singular first order nonlinear partial differential equations of totally characteristic type, Funkcial. Ekvac. 45 (2002, 187-208] and [Maillet type theorem for singular first order nonlinear partial differential equations of totally characteristic type, Surikaiseki Kenkyujo Kokyuroku, Kyoto University 1431 (2005, 94-106]. Especially the last-mentioned paper is regarded as part I of this paper.

  9. Partial differential equation-based localization of a monopole source from a circular array.

    Science.gov (United States)

    Ando, Shigeru; Nara, Takaaki; Levy, Tsukassa

    2013-10-01

    Wave source localization from a sensor array has long been the most active research topics in both theory and application. In this paper, an explicit and time-domain inversion method for the direction and distance of a monopole source from a circular array is proposed. The approach is based on a mathematical technique, the weighted integral method, for signal/source parameter estimation. It begins with an exact form of the source-constraint partial differential equation that describes the unilateral propagation of wide-band waves from a single source, and leads to exact algebraic equations that include circular Fourier coefficients (phase mode measurements) as their coefficients. From them, nearly closed-form, single-shot and multishot algorithms are obtained that is suitable for use with band-pass/differential filter banks. Numerical evaluation and several experimental results obtained using a 16-element circular microphone array are presented to verify the validity of the proposed method.

  10. Analytical approach to linear fractional partial differential equations arising in fluid mechanics

    International Nuclear Information System (INIS)

    Momani, Shaher; Odibat, Zaid

    2006-01-01

    In this Letter, we implement relatively new analytical techniques, the variational iteration method and the Adomian decomposition method, for solving linear fractional partial differential equations arising in fluid mechanics. The fractional derivatives are described in the Caputo sense. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of fractional differential equations. In these methods, the solution takes the form of a convergent series with easily computable components. The corresponding solutions of the integer order equations are found to follow as special cases of those of fractional order equations. Some numerical examples are presented to illustrate the efficiency and reliability of the two methods

  11. An Efficient Numerical Approach for Solving Nonlinear Coupled Hyperbolic Partial Differential Equations with Nonlocal Conditions

    Directory of Open Access Journals (Sweden)

    A. H. Bhrawy

    2014-01-01

    Full Text Available One of the most important advantages of collocation method is the possibility of dealing with nonlinear partial differential equations (PDEs as well as PDEs with variable coefficients. A numerical solution based on a Jacobi collocation method is extended to solve nonlinear coupled hyperbolic PDEs with variable coefficients subject to initial-boundary nonlocal conservation conditions. This approach, based on Jacobi polynomials and Gauss-Lobatto quadrature integration, reduces solving the nonlinear coupled hyperbolic PDEs with variable coefficients to a system of nonlinear ordinary differential equation which is far easier to solve. In fact, we deal with initial-boundary coupled hyperbolic PDEs with variable coefficients as well as initial-nonlocal conditions. Using triangular, soliton, and exponential-triangular solutions as exact solutions, the obtained results show that the proposed numerical algorithm is efficient and very accurate.

  12. Matrix-oriented implementation for the numerical solution of the partial differential equations governing flows and transport in porous media

    KAUST Repository

    Sun, Shuyu; Salama, Amgad; El-Amin, Mohamed

    2012-01-01

    In this paper we introduce a new technique for the numerical solution of the various partial differential equations governing flow and transport phenomena in porous media. This method is proposed to be used in high level programming languages like

  13. Modulating functions-based method for parameters and source estimation in one-dimensional partial differential equations

    KAUST Repository

    Asiri, Sharefa M.; Laleg-Kirati, Taous-Meriem

    2016-01-01

    In this paper, modulating functions-based method is proposed for estimating space–time-dependent unknowns in one-dimensional partial differential equations. The proposed method simplifies the problem into a system of algebraic equations linear

  14. From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Angstmann, C.N.; Donnelly, I.C. [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia); Henry, B.I., E-mail: B.Henry@unsw.edu.au [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia); Jacobs, B.A. [School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050 (South Africa); DST–NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) (South Africa); Langlands, T.A.M. [Department of Mathematics and Computing, University of Southern Queensland, Toowoomba QLD 4350 (Australia); Nichols, J.A. [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia)

    2016-02-15

    We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also show that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.

  15. Treating carbonaceous materials

    Energy Technology Data Exchange (ETDEWEB)

    Pier, M

    1929-08-26

    To separate the constituents or conversion products, which are liquid or which liquefy when heated, from solid distillable carbonaceous materials such as coals, oil shales, or other bituminous substances, the initial materials are subjected to a destructive hydrogenation under mild conditions so that the formation of benzines is substantially avoided, after which the material is subjected to an extraction treatment with solvents. The constituents of high boiling point range, suitable for the production of lubricating oils and solid paraffins, obtained by the said destructive hydrogenation are separated off before or/and after the said extraction treatment.

  16. Distilling carbonaceous materials

    Energy Technology Data Exchange (ETDEWEB)

    Trumble, M J

    1925-06-29

    Carbonaceous materials such as coal, oil shale, peat, or wood are destructively distilled while being subjected to the action of superheated steam and hydrogen, the latter being provided by dissociating a part of the superheated steam. The materials are charged into a retort heated by a burner and superheated steam and hydrogen are passed in by a pipe and nozzles. The distillates enter a dust extractor through openings and escape through openings shielded by cones into an outlet pipe leading to condensers. The dust which settles in the bottom of the apparatus is periodically removed.

  17. ICM: an Integrated Compartment Method for numerically solving partial differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Yeh, G.T.

    1981-05-01

    An integrated compartment method (ICM) is proposed to construct a set of algebraic equations from a system of partial differential equations. The ICM combines the utility of integral formulation of finite element approach, the simplicity of interpolation of finite difference approximation, and the flexibility of compartment analyses. The integral formulation eases the treatment of boundary conditions, in particular, the Neumann-type boundary conditions. The simplicity of interpolation provides great economy in computation. The flexibility of discretization with irregular compartments of various shapes and sizes offers advantages in resolving complex boundaries enclosing compound regions of interest. The basic procedures of ICM are first to discretize the region of interest into compartments, then to apply three integral theorems of vectors to transform the volume integral to the surface integral, and finally to use interpolation to relate the interfacial values in terms of compartment values to close the system. The Navier-Stokes equations are used as an example of how to derive the corresponding ICM alogrithm for a given set of partial differential equations. Because of the structure of the algorithm, the basic computer program remains the same for cases in one-, two-, or three-dimensional problems.

  18. Solution of Fractional Partial Differential Equations in Fluid Mechanics by Extension of Some Iterative Method

    Directory of Open Access Journals (Sweden)

    A. A. Hemeda

    2013-01-01

    Full Text Available An extension of the so-called new iterative method (NIM has been used to handle linear and nonlinear fractional partial differential equations. The main property of the method lies in its flexibility and ability to solve nonlinear equations accurately and conveniently. Therefore, a general framework of the NIM is presented for analytical treatment of fractional partial differential equations in fluid mechanics. The fractional derivatives are described in the Caputo sense. Numerical illustrations that include the fractional wave equation, fractional Burgers equation, fractional KdV equation, fractional Klein-Gordon equation, and fractional Boussinesq-like equation are investigated to show the pertinent features of the technique. Comparison of the results obtained by the NIM with those obtained by both Adomian decomposition method (ADM and the variational iteration method (VIM reveals that the NIM is very effective and convenient. The basic idea described in this paper is expected to be further employed to solve other similar linear and nonlinear problems in fractional calculus.

  19. A model and variance reduction method for computing statistical outputs of stochastic elliptic partial differential equations

    International Nuclear Information System (INIS)

    Vidal-Codina, F.; Nguyen, N.C.; Giles, M.B.; Peraire, J.

    2015-01-01

    We present a model and variance reduction method for the fast and reliable computation of statistical outputs of stochastic elliptic partial differential equations. Our method consists of three main ingredients: (1) the hybridizable discontinuous Galerkin (HDG) discretization of elliptic partial differential equations (PDEs), which allows us to obtain high-order accurate solutions of the governing PDE; (2) the reduced basis method for a new HDG discretization of the underlying PDE to enable real-time solution of the parameterized PDE in the presence of stochastic parameters; and (3) a multilevel variance reduction method that exploits the statistical correlation among the different reduced basis approximations and the high-fidelity HDG discretization to accelerate the convergence of the Monte Carlo simulations. The multilevel variance reduction method provides efficient computation of the statistical outputs by shifting most of the computational burden from the high-fidelity HDG approximation to the reduced basis approximations. Furthermore, we develop a posteriori error estimates for our approximations of the statistical outputs. Based on these error estimates, we propose an algorithm for optimally choosing both the dimensions of the reduced basis approximations and the sizes of Monte Carlo samples to achieve a given error tolerance. We provide numerical examples to demonstrate the performance of the proposed method

  20. 4th International Conference on Particle Systems and Partial Differential Equations

    CERN Document Server

    Soares, Ana

    2017-01-01

    'This book addresses mathematical problems motivated by various applications in physics, engineering, chemistry and biology. It gathers the lecture notes from the mini-course presented by Jean-Christophe Mourrat on the construction of the various stochastic “basic” terms involved in the formulation of the dynamic Ö4  theory in three space dimensions, as well as selected contributions presented at the fourth meeting on Particle Systems and PDEs, which was held at the University of Minho’s Centre of Mathematics in December 2015. The purpose of the conference was to bring together prominent researchers working in the fields of particle systems and partial differential equations, offering them a forum to present their recent results and discuss their topics of expertise. The meeting was also intended to present to a vast and varied public, including young researchers, the area of interacting particle systems, its underlying motivation, and its relation to partial differential equations.  The book w...

  1. Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations

    Directory of Open Access Journals (Sweden)

    Vladimir P. Gerdt

    2006-05-01

    Full Text Available In this paper we present an algorithmic approach to the generation of fully conservative difference schemes for linear partial differential equations. The approach is based on enlargement of the equations in their integral conservation law form by extra integral relations between unknown functions and their derivatives, and on discretization of the obtained system. The structure of the discrete system depends on numerical approximation methods for the integrals occurring in the enlarged system. As a result of the discretization, a system of linear polynomial difference equations is derived for the unknown functions and their partial derivatives. A difference scheme is constructed by elimination of all the partial derivatives. The elimination can be achieved by selecting a proper elimination ranking and by computing a Gröbner basis of the linear difference ideal generated by the polynomials in the discrete system. For these purposes we use the difference form of Janet-like Gröbner bases and their implementation in Maple. As illustration of the described methods and algorithms, we construct a number of difference schemes for Burgers and Falkowich-Karman equations and discuss their numerical properties.

  2. A linearizing transformation for the Korteweg-de Vries equation; generalizations to higher-dimensional nonlinear partial differential equations

    NARCIS (Netherlands)

    Dorren, H.J.S.

    1998-01-01

    It is shown that the Korteweg–de Vries (KdV) equation can be transformed into an ordinary linear partial differential equation in the wave number domain. Explicit solutions of the KdV equation can be obtained by subsequently solving this linear differential equation and by applying a cascade of

  3. Uniqueness of global quasi-classical solutions of the Cauchy problems for first-order nonlinear partial differential equations

    International Nuclear Information System (INIS)

    Tran Duc Van

    1994-01-01

    The notion of global quasi-classical solutions of the Cauchy problems for first-order nonlinear partial differential equations is presented, some uniqueness theorems and a stability result are established by the method based on the theory of differential inclusions. In particular, the answer to an open problem of S.N. Kruzhkov is given. (author). 10 refs, 1 fig

  4. Advanced Topics in Computational Partial Differential Equations: Numerical Methods and Diffpack Programming

    International Nuclear Information System (INIS)

    Katsaounis, T D

    2005-01-01

    The scope of this book is to present well known simple and advanced numerical methods for solving partial differential equations (PDEs) and how to implement these methods using the programming environment of the software package Diffpack. A basic background in PDEs and numerical methods is required by the potential reader. Further, a basic knowledge of the finite element method and its implementation in one and two space dimensions is required. The authors claim that no prior knowledge of the package Diffpack is required, which is true, but the reader should be at least familiar with an object oriented programming language like C++ in order to better comprehend the programming environment of Diffpack. Certainly, a prior knowledge or usage of Diffpack would be a great advantage to the reader. The book consists of 15 chapters, each one written by one or more authors. Each chapter is basically divided into two parts: the first part is about mathematical models described by PDEs and numerical methods to solve these models and the second part describes how to implement the numerical methods using the programming environment of Diffpack. Each chapter closes with a list of references on its subject. The first nine chapters cover well known numerical methods for solving the basic types of PDEs. Further, programming techniques on the serial as well as on the parallel implementation of numerical methods are also included in these chapters. The last five chapters are dedicated to applications, modelled by PDEs, in a variety of fields. In summary, the book focuses on the computational and implementational issues involved in solving partial differential equations. The potential reader should have a basic knowledge of PDEs and the finite difference and finite element methods. The examples presented are solved within the programming framework of Diffpack and the reader should have prior experience with the particular software in order to take full advantage of the book. Overall

  5. Reciprocal links among differential parenting, perceived partiality, and self-worth: a three-wave longitudinal study.

    Science.gov (United States)

    Shebloski, Barbara; Conger, Katherine J; Widaman, Keith F

    2005-12-01

    This study examined reciprocal links between parental differential treatment, siblings' perception of partiality, and self-worth with 3 waves of data from 384 adolescent sibling dyads. Results suggest that birth-order status was significantly associated with self-worth and perception of maternal and paternal differential treatment. There was a consistent across-time effect of self-worth on perception of parental partiality for later born siblings, but not earlier born siblings, and a consistent effect of differential treatment on perception of partiality for earlier born but not later born siblings. The results contribute new insight into the associations between perception of differential parenting and adolescents' adjustment and the role of birth order. Copyright 2006 APA, all rights reserved).

  6. Basis adaptation and domain decomposition for steady-state partial differential equations with random coefficients

    Energy Technology Data Exchange (ETDEWEB)

    Tipireddy, R.; Stinis, P.; Tartakovsky, A. M.

    2017-12-01

    We present a novel approach for solving steady-state stochastic partial differential equations (PDEs) with high-dimensional random parameter space. The proposed approach combines spatial domain decomposition with basis adaptation for each subdomain. The basis adaptation is used to address the curse of dimensionality by constructing an accurate low-dimensional representation of the stochastic PDE solution (probability density function and/or its leading statistical moments) in each subdomain. Restricting the basis adaptation to a specific subdomain affords finding a locally accurate solution. Then, the solutions from all of the subdomains are stitched together to provide a global solution. We support our construction with numerical experiments for a steady-state diffusion equation with a random spatially dependent coefficient. Our results show that highly accurate global solutions can be obtained with significantly reduced computational costs.

  7. Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models.

    Science.gov (United States)

    Shah, A A; Xing, W W; Triantafyllidis, V

    2017-04-01

    In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach.

  8. Computable Error Estimates for Finite Element Approximations of Elliptic Partial Differential Equations with Rough Stochastic Data

    KAUST Repository

    Hall, Eric Joseph

    2016-12-08

    We derive computable error estimates for finite element approximations of linear elliptic partial differential equations with rough stochastic coefficients. In this setting, the exact solutions contain high frequency content that standard a posteriori error estimates fail to capture. We propose goal-oriented estimates, based on local error indicators, for the pathwise Galerkin and expected quadrature errors committed in standard, continuous, piecewise linear finite element approximations. Derived using easily validated assumptions, these novel estimates can be computed at a relatively low cost and have applications to subsurface flow problems in geophysics where the conductivities are assumed to have lognormal distributions with low regularity. Our theory is supported by numerical experiments on test problems in one and two dimensions.

  9. Partial differential equations of first order and their applications to physics

    CERN Document Server

    López, Gustavo

    2012-01-01

    This book tries to point out the mathematical importance of the Partial Differential Equations of First Order (PDEFO) in Physics and Applied Sciences. The intention is to provide mathematicians with a wide view of the applications of this branch in physics, and to give physicists and applied scientists a powerful tool for solving some problems appearing in Classical Mechanics, Quantum Mechanics, Optics, and General Relativity. This book is intended for senior or first year graduate students in mathematics, physics, or engineering curricula. This book is unique in the sense that it covers the applications of PDEFO in several branches of applied mathematics, and fills the theoretical gap between the formal mathematical presentation of the theory and the pure applied tool to physical problems that are contained in other books. Improvements made in this second edition include corrected typographical errors; rewritten text to improve the flow and enrich the material; added exercises in all chapters; new applicati...

  10. On Direct Transformation Approach to Asymptotical Analytical Solutions of Perturbed Partial Differential Equation

    International Nuclear Information System (INIS)

    Liu Hongzhun; Pan Zuliang; Li Peng

    2006-01-01

    In this article, we will derive an equality, where the Taylor series expansion around ε = 0 for any asymptotical analytical solution of the perturbed partial differential equation (PDE) with perturbing parameter ε must be admitted. By making use of the equality, we may obtain a transformation, which directly map the analytical solutions of a given unperturbed PDE to the asymptotical analytical solutions of the corresponding perturbed one. The notion of Lie-Baecklund symmetries is introduced in order to obtain more transformations. Hence, we can directly create more transformations in virtue of known Lie-Baecklund symmetries and recursion operators of corresponding unperturbed equation. The perturbed Burgers equation and the perturbed Korteweg-de Vries (KdV) equation are used as examples.

  11. An ansatz for solving nonlinear partial differential equations in mathematical physics.

    Science.gov (United States)

    Akbar, M Ali; Ali, Norhashidah Hj Mohd

    2016-01-01

    In this article, we introduce an ansatz involving exact traveling wave solutions to nonlinear partial differential equations. To obtain wave solutions using direct method, the choice of an appropriate ansatz is of great importance. We apply this ansatz to examine new and further general traveling wave solutions to the (1+1)-dimensional modified Benjamin-Bona-Mahony equation. Abundant traveling wave solutions are derived including solitons, singular solitons, periodic solutions and general solitary wave solutions. The solutions emphasize the nobility of this ansatz in providing distinct solutions to various tangible phenomena in nonlinear science and engineering. The ansatz could be more efficient tool to deal with higher dimensional nonlinear evolution equations which frequently arise in many real world physical problems.

  12. A dynamical regularization algorithm for solving inverse source problems of elliptic partial differential equations

    Science.gov (United States)

    Zhang, Ye; Gong, Rongfang; Cheng, Xiaoliang; Gulliksson, Mårten

    2018-06-01

    This study considers the inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary data. The unknown source term is to be determined by additional boundary conditions. Unlike the existing methods found in the literature, which usually employ the first-order in time gradient-like system (such as the steepest descent methods) for numerically solving the regularized optimization problem with a fixed regularization parameter, we propose a novel method with a second-order in time dissipative gradient-like system and a dynamical selected regularization parameter. A damped symplectic scheme is proposed for the numerical solution. Theoretical analysis is given for both the continuous model and the numerical algorithm. Several numerical examples are provided to show the robustness of the proposed algorithm.

  13. Isostable reduction with applications to time-dependent partial differential equations.

    Science.gov (United States)

    Wilson, Dan; Moehlis, Jeff

    2016-07-01

    Isostables and isostable reduction, analogous to isochrons and phase reduction for oscillatory systems, are useful in the study of nonlinear equations which asymptotically approach a stationary solution. In this work, we present a general method for isostable reduction of partial differential equations, with the potential power to reduce the dimensionality of a nonlinear system from infinity to 1. We illustrate the utility of this reduction by applying it to two different models with biological relevance. In the first example, isostable reduction of the Fokker-Planck equation provides the necessary framework to design a simple control strategy to desynchronize a population of pathologically synchronized oscillatory neurons, as might be relevant to Parkinson's disease. Another example analyzes a nonlinear reaction-diffusion equation with relevance to action potential propagation in a cardiac system.

  14. Rapid Fourier space solution of linear partial integro-differential equations in toroidal magnetic confinement geometries

    International Nuclear Information System (INIS)

    McMillan, B.F.; Jolliet, S.; Tran, T.M.; Villard, L.; Bottino, A.; Angelino, P.

    2010-01-01

    Fluctuating quantities in magnetic confinement geometries often inherit a strong anisotropy along the field lines. One technique for describing these structures is the use of a certain set of Fourier components on the tori of nested flux surfaces. We describe an implementation of this approach for solving partial differential equations, like Poisson's equation, where a different set of Fourier components may be chosen on each surface according to the changing safety factor profile. Allowing the resolved components to change to follow the anisotropy significantly reduces the total number of degrees of freedom in the description. This can permit large gains in computational performance. We describe, in particular, how this approach can be applied to rapidly solve the gyrokinetic Poisson equation in a particle code, ORB5 (Jolliet et al. (2007) [5]), with a regular (non-field-aligned) mesh. (authors)

  15. Harmonic analysis, partial differential equations and applications in honor of Richard L. Wheeden

    CERN Document Server

    Franchi, Bruno; Lu, Guozhen; Perez, Carlos; Sawyer, Eric

    2017-01-01

    This is a collection of contributed papers by many eminent Harmonic Analysts and specialists of Partial Differential equations. The papers focus on weighted norm equalities for singular integrals, focusing wave equations, degenerate elliptic equations, Navier-Stokes flow in two dimensions and Poincare-Sobolev inequalities in the setting of metric spaces equipped with measures among others. Many topics considered in this volume stem from the interests of Richard L. Wheeden whose contributions to Potential Theory, singular integral theory and degenerate elliptic PDE theory this volume honors. Luis Caffarelli, Sagun Chanillo, Bruno Franchi, Cristian Guttierez, Xiaojun Huang, Carlos Kenig, Ermanno Lanconelli, Eric Sawyer and Alexander Volberg, are some of the many contributors to this volume. .

  16. Elliptic–hyperbolic partial differential equations a mini-course in geometric and quasilinear methods

    CERN Document Server

    Otway, Thomas H

    2015-01-01

    This text is a concise introduction to the partial differential equations which change from elliptic to hyperbolic type across a smooth hypersurface of their domain. These are becoming increasingly important in diverse sub-fields of both applied mathematics and engineering, for example:   • The heating of fusion plasmas by electromagnetic waves • The behaviour of light near a caustic • Extremal surfaces in the space of special relativity • The formation of rapids; transonic and multiphase fluid flow • The dynamics of certain models for elastic structures • The shape of industrial surfaces such as windshields and airfoils • Pathologies of traffic flow • Harmonic fields in extended projective space   They also arise in models for the early universe, for cosmic acceleration, and for possible violation of causality in the interiors of certain compact stars. Within the past 25 years, they have become central to the isometric embedding of Riemannian manifolds and the prescription of Gauss curvatur...

  17. Mathematical and numerical methods for partial differential equations applications for engineering sciences

    CERN Document Server

    Chaskalovic, Joël

    2014-01-01

    This self-tutorial offers a concise yet thorough introduction into the mathematical analysis of approximation methods for partial differential equation. A particular emphasis is put on finite element methods. The unique approach first summarizes and outlines the finite-element mathematics in general and then, in the second and major part, formulates problem examples that clearly demonstrate the techniques of functional analysis via numerous and diverse exercises. The solutions of the problems are given directly afterwards. Using this approach, the author motivates and encourages the reader to actively acquire the knowledge of finite- element methods instead of passively absorbing the material, as in most standard textbooks. This English edition is based on the Finite Element Methods for Engineering Sciences by Joel Chaskalovic

  18. A Table Lookup Method for Exact Analytical Solutions of Nonlinear Fractional Partial Differential Equations

    Directory of Open Access Journals (Sweden)

    Ji Juan-Juan

    2017-01-01

    Full Text Available A table lookup method for solving nonlinear fractional partial differential equations (fPDEs is proposed in this paper. Looking up the corresponding tables, we can quickly obtain the exact analytical solutions of fPDEs by using this method. To illustrate the validity of the method, we apply it to construct the exact analytical solutions of four nonlinear fPDEs, namely, the time fractional simplified MCH equation, the space-time fractional combined KdV-mKdV equation, the (2+1-dimensional time fractional Zoomeron equation, and the space-time fractional ZKBBM equation. As a result, many new types of exact analytical solutions are obtained including triangular periodic solution, hyperbolic function solution, singular solution, multiple solitary wave solution, and Jacobi elliptic function solution.

  19. Stable multi-domain spectral penalty methods for fractional partial differential equations

    Science.gov (United States)

    Xu, Qinwu; Hesthaven, Jan S.

    2014-01-01

    We propose stable multi-domain spectral penalty methods suitable for solving fractional partial differential equations with fractional derivatives of any order. First, a high order discretization is proposed to approximate fractional derivatives of any order on any given grids based on orthogonal polynomials. The approximation order is analyzed and verified through numerical examples. Based on the discrete fractional derivative, we introduce stable multi-domain spectral penalty methods for solving fractional advection and diffusion equations. The equations are discretized in each sub-domain separately and the global schemes are obtained by weakly imposed boundary and interface conditions through a penalty term. Stability of the schemes are analyzed and numerical examples based on both uniform and nonuniform grids are considered to highlight the flexibility and high accuracy of the proposed schemes.

  20. Partial differential equations for self-organization in cellular and developmental biology

    International Nuclear Information System (INIS)

    Baker, R E; Gaffney, E A; Maini, P K

    2008-01-01

    Understanding the mechanisms governing and regulating the emergence of structure and heterogeneity within cellular systems, such as the developing embryo, represents a multiscale challenge typifying current integrative biology research, namely, explaining the macroscale behaviour of a system from microscale dynamics. This review will focus upon modelling how cell-based dynamics orchestrate the emergence of higher level structure. After surveying representative biological examples and the models used to describe them, we will assess how developments at the scale of molecular biology have impacted on current theoretical frameworks, and the new modelling opportunities that are emerging as a result. We shall restrict our survey of mathematical approaches to partial differential equations and the tools required for their analysis. We will discuss the gap between the modelling abstraction and biological reality, the challenges this presents and highlight some open problems in the field. (invited article)

  1. Treating carbonaceous materials

    Energy Technology Data Exchange (ETDEWEB)

    Kelly, T D

    1927-07-29

    Coal, lignite, shale, peat, or like carbonaceous material is heated at 70 to 300/sup 0/C with an alkaline solution of sodium, potassium, or ammonium oleate and aluminum sulfate is added in order to solidify the oleate. The solid material is separated and molded or shaped or disintegrated for use as a pigment or mixed with rubber or similar compounds such as solidified, oxidized or polymerized oils in making building blocks or tiles, tires, footwear, or other resilient material. It may be distilled with water or steam in a retort to make gas, or in porous condition can be burnt. The liquid products may be subjected to fractional distillation or mixed with bitumen, resin or oils or materials such as clay, red oxide, or barytes to give colour or body in the manufacture of waterproof heatproof dressings which may be made quick-drying by the addition of ammonia, or for mixing with or spreading over stones or on roads or concrete.

  2. An odor interaction model of binary odorant mixtures by a partial differential equation method.

    Science.gov (United States)

    Yan, Luchun; Liu, Jiemin; Wang, Guihua; Wu, Chuandong

    2014-07-09

    A novel odor interaction model was proposed for binary mixtures of benzene and substituted benzenes by a partial differential equation (PDE) method. Based on the measurement method (tangent-intercept method) of partial molar volume, original parameters of corresponding formulas were reasonably displaced by perceptual measures. By these substitutions, it was possible to relate a mixture's odor intensity to the individual odorant's relative odor activity value (OAV). Several binary mixtures of benzene and substituted benzenes were respectively tested to establish the PDE models. The obtained results showed that the PDE model provided an easily interpretable method relating individual components to their joint odor intensity. Besides, both predictive performance and feasibility of the PDE model were proved well through a series of odor intensity matching tests. If combining the PDE model with portable gas detectors or on-line monitoring systems, olfactory evaluation of odor intensity will be achieved by instruments instead of odor assessors. Many disadvantages (e.g., expense on a fixed number of odor assessors) also will be successfully avoided. Thus, the PDE model is predicted to be helpful to the monitoring and management of odor pollutions.

  3. A Differential Evolution Based MPPT Method for Photovoltaic Modules under Partial Shading Conditions

    Directory of Open Access Journals (Sweden)

    Kok Soon Tey

    2014-01-01

    Full Text Available Partially shaded photovoltaic (PV modules have multiple peaks in the power-voltage (P-V characteristic curve and conventional maximum power point tracking (MPPT algorithm, such as perturbation and observation (P&O, which is unable to track the global maximum power point (GMPP accurately due to its localized search space. Therefore, this paper proposes a differential evolution (DE based optimization algorithm to provide the globalized search space to track the GMPP. The direction of mutation in the DE algorithm is modified to ensure that the mutation always converges to the best solution among all the particles in the generation. This helps to provide the rapid convergence of the algorithm. Simulation of the proposed PV system is carried out in PSIM and the results are compared to P&O algorithm. In the hardware implementation, a high step-up DC-DC converter is employed to verify the proposed algorithm experimentally on partial shading conditions, load variation, and solar intensity variation. The experimental results show that the proposed algorithm is able to converge to the GMPP within 1.2 seconds with higher efficiency than P&O.

  4. An Odor Interaction Model of Binary Odorant Mixtures by a Partial Differential Equation Method

    Directory of Open Access Journals (Sweden)

    Luchun Yan

    2014-07-01

    Full Text Available A novel odor interaction model was proposed for binary mixtures of benzene and substituted benzenes by a partial differential equation (PDE method. Based on the measurement method (tangent-intercept method of partial molar volume, original parameters of corresponding formulas were reasonably displaced by perceptual measures. By these substitutions, it was possible to relate a mixture’s odor intensity to the individual odorant’s relative odor activity value (OAV. Several binary mixtures of benzene and substituted benzenes were respectively tested to establish the PDE models. The obtained results showed that the PDE model provided an easily interpretable method relating individual components to their joint odor intensity. Besides, both predictive performance and feasibility of the PDE model were proved well through a series of odor intensity matching tests. If combining the PDE model with portable gas detectors or on-line monitoring systems, olfactory evaluation of odor intensity will be achieved by instruments instead of odor assessors. Many disadvantages (e.g., expense on a fixed number of odor assessors also will be successfully avoided. Thus, the PDE model is predicted to be helpful to the monitoring and management of odor pollutions.

  5. Solutions to an advanced functional partial differential equation of the pantograph type.

    Science.gov (United States)

    Zaidi, Ali A; Van Brunt, B; Wake, G C

    2015-07-08

    A model for cells structured by size undergoing growth and division leads to an initial boundary value problem that involves a first-order linear partial differential equation with a functional term. Here, size can be interpreted as DNA content or mass. It has been observed experimentally and shown analytically that solutions for arbitrary initial cell distributions are asymptotic as time goes to infinity to a certain solution called the steady size distribution. The full solution to the problem for arbitrary initial distributions, however, is elusive owing to the presence of the functional term and the paucity of solution techniques for such problems. In this paper, we derive a solution to the problem for arbitrary initial cell distributions. The method employed exploits the hyperbolic character of the underlying differential operator, and the advanced nature of the functional argument to reduce the problem to a sequence of simple Cauchy problems. The existence of solutions for arbitrary initial distributions is established along with uniqueness. The asymptotic relationship with the steady size distribution is established, and because the solution is known explicitly, higher-order terms in the asymptotics can be readily obtained.

  6. DISPL-1, 2. Order Nonlinear Partial Differential Equation System Solution for Kinetics Diffusion Problems

    International Nuclear Information System (INIS)

    Leaf, G.K.; Minkoff, M.

    1982-01-01

    1 - Description of problem or function: DISPL1 is a software package for solving second-order nonlinear systems of partial differential equations including parabolic, elliptic, hyperbolic, and some mixed types. The package is designed primarily for chemical kinetics- diffusion problems, although not limited to these problems. Fairly general nonlinear boundary conditions are allowed as well as inter- face conditions for problems in an inhomogeneous medium. The spatial domain is one- or two-dimensional with rectangular Cartesian, cylindrical, or spherical (in one dimension only) geometry. 2 - Method of solution: The numerical method is based on the use of Galerkin's procedure combined with the use of B-Splines (C.W.R. de-Boor's B-spline package) to generate a system of ordinary differential equations. These equations are solved by a sophisticated ODE software package which is a modified version of Hindmarsh's GEAR package, NESC Abstract 592. 3 - Restrictions on the complexity of the problem: The spatial domain must be rectangular with sides parallel to the coordinate geometry. Cross derivative terms are not permitted in the PDE. The order of the B-Splines is at most 12. Other parameters such as the number of mesh points in each coordinate direction, the number of PDE's etc. are set in a macro table used by the MORTRAn2 preprocessor in generating the object code

  7. XMDS2: Fast, scalable simulation of coupled stochastic partial differential equations

    Science.gov (United States)

    Dennis, Graham R.; Hope, Joseph J.; Johnsson, Mattias T.

    2013-01-01

    XMDS2 is a cross-platform, GPL-licensed, open source package for numerically integrating initial value problems that range from a single ordinary differential equation up to systems of coupled stochastic partial differential equations. The equations are described in a high-level XML-based script, and the package generates low-level optionally parallelised C++ code for the efficient solution of those equations. It combines the advantages of high-level simulations, namely fast and low-error development, with the speed, portability and scalability of hand-written code. XMDS2 is a complete redesign of the XMDS package, and features support for a much wider problem space while also producing faster code. Program summaryProgram title: XMDS2 Catalogue identifier: AENK_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENK_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 2 No. of lines in distributed program, including test data, etc.: 872490 No. of bytes in distributed program, including test data, etc.: 45522370 Distribution format: tar.gz Programming language: Python and C++. Computer: Any computer with a Unix-like system, a C++ compiler and Python. Operating system: Any Unix-like system; developed under Mac OS X and GNU/Linux. RAM: Problem dependent (roughly 50 bytes per grid point) Classification: 4.3, 6.5. External routines: The external libraries required are problem-dependent. Uses FFTW3 Fourier transforms (used only for FFT-based spectral methods), dSFMT random number generation (used only for stochastic problems), MPI message-passing interface (used only for distributed problems), HDF5, GNU Scientific Library (used only for Bessel-based spectral methods) and a BLAS implementation (used only for non-FFT-based spectral methods). Nature of problem: General coupled initial-value stochastic partial differential equations. Solution method: Spectral method

  8. Asymptotic behavior of solutions of diffusion-like partial differential equations invariant to a family of affine groups

    International Nuclear Information System (INIS)

    Dresner, L.

    1990-07-01

    This report deals with the asymptotic behavior of certain solutions of partial differential equations in one dependent and two independent variables (call them c, z, and t, respectively). The partial differential equations are invariant to one-parameter families of one-parameter affine groups of the form: c' = λ α c, t' = λ β t, z' = λz, where λ is the group parameter that labels the individual transformations and α and β are parameters that label groups of the family. The parameters α and β are connected by a linear relation, Mα + Nβ = L, where M, N, and L are numbers determined by the structure of the partial differential equation. It is shown that when L/M and N/M are L/M t -N/M for large z or small t. Some practical applications of this result are discussed. 8 refs

  9. Three tesla magnetic resonance imaging of the anterior cruciate ligament of the knee: can we differentiate complete from partial tears?

    Energy Technology Data Exchange (ETDEWEB)

    Dyck, Pieter van; Gielen, Jan L.; Parizel, Paul M. [University Hospital Antwerp and University of Antwerp, Department of Radiology, Antwerp (Edegem) (Belgium); Vanhoenacker, Filip M. [University Hospital Antwerp and University of Antwerp, Department of Radiology, Antwerp (Edegem) (Belgium); AZ St-Maarten Duffel/Mechelen, Department of Radiology, Duffel (Belgium); Dossche, Lieven; Gestel, Jozef van [University Hospital Antwerp and University of Antwerp, Department of Orthopedics, Antwerp (Edegem) (Belgium); Wouters, Kristien [University Hospital Antwerp and University of Antwerp, Department of Scientific Coordination and Biostatistics, Antwerp (Edegem) (Belgium)

    2011-06-15

    To determine the ability of 3.0T magnetic resonance (MR) imaging to identify partial tears of the anterior cruciate ligament (ACL) and to allow distinction of complete from partial ACL tears. One hundred seventy-two patients were prospectively studied by 3.0T MR imaging and arthroscopy in our institution. MR images were interpreted in consensus by two experienced reviewers, and the ACL was diagnosed as being normal, partially torn, or completely torn. Diagnostic accuracy of 3.0T MR for the detection of both complete and partial tears of the ACL was calculated using arthroscopy as the standard of reference. There were 132 patients with an intact ACL, 17 had a partial, and 23 had a complete tear of the ACL seen at arthroscopy. Sensitivity, specificity, and accuracy of 3.0T MR for complete ACL tears were 83, 99, and 97%, respectively, and, for partial ACL tears, 77, 97, and 95%, respectively. Five of 40 ACL lesions (13%) could not correctly be identified as complete or partial ACL tears. MR imaging at 3.0T represents a highly accurate method for identifying tears of the ACL. However, differentiation between complete and partial ACL tears and identification of partial tears of this ligament remains difficult, even at 3.0T. (orig.)

  10. Three tesla magnetic resonance imaging of the anterior cruciate ligament of the knee: can we differentiate complete from partial tears?

    International Nuclear Information System (INIS)

    Dyck, Pieter van; Gielen, Jan L.; Parizel, Paul M.; Vanhoenacker, Filip M.; Dossche, Lieven; Gestel, Jozef van; Wouters, Kristien

    2011-01-01

    To determine the ability of 3.0T magnetic resonance (MR) imaging to identify partial tears of the anterior cruciate ligament (ACL) and to allow distinction of complete from partial ACL tears. One hundred seventy-two patients were prospectively studied by 3.0T MR imaging and arthroscopy in our institution. MR images were interpreted in consensus by two experienced reviewers, and the ACL was diagnosed as being normal, partially torn, or completely torn. Diagnostic accuracy of 3.0T MR for the detection of both complete and partial tears of the ACL was calculated using arthroscopy as the standard of reference. There were 132 patients with an intact ACL, 17 had a partial, and 23 had a complete tear of the ACL seen at arthroscopy. Sensitivity, specificity, and accuracy of 3.0T MR for complete ACL tears were 83, 99, and 97%, respectively, and, for partial ACL tears, 77, 97, and 95%, respectively. Five of 40 ACL lesions (13%) could not correctly be identified as complete or partial ACL tears. MR imaging at 3.0T represents a highly accurate method for identifying tears of the ACL. However, differentiation between complete and partial ACL tears and identification of partial tears of this ligament remains difficult, even at 3.0T. (orig.)

  11. Tracer kinetics: Modelling by partial differential equations of inhomogeneous compartments with age-dependent elimination rates. Pt. 2

    International Nuclear Information System (INIS)

    Winkler, E.

    1991-01-01

    The general theory of inhomogeneous compartments with age-dependent elimination rates is illustrated by examples. Mathematically, it turns out that models consisting of partial differential equations include ordinary, delayed and integro-differential equations, a general fact which is treated here in the context of linear tracer kinetics. The examples include standard compartments as a degenerate case, systems of standard compartments (compartment blocks), models resulting in special residence time distributions, models with pipes, and systems with heterogeneous particles. (orig./BBR) [de

  12. Computation of Green function of the Schroedinger-like partial differential equations by the numerical functional integration

    International Nuclear Information System (INIS)

    Lobanov, Yu.Yu.; Shahbagian, R.R.; Zhidkov, E.P.

    1991-01-01

    A new method for numerical solution of the boundary problem for Schroedinger-like partial differential equations in R n is elaborated. The method is based on representation of multidimensional Green function in the form of multiple functional integral and on the use of approximation formulas which are constructed for such integrals. The convergence of approximations to the exact value is proved, the remainder of the formulas is estimated. Method reduces the initial differential problem to quadratures. 16 refs.; 7 tabs

  13. Distilling solid carbonaceous materials

    Energy Technology Data Exchange (ETDEWEB)

    Nielsen, H; Laing, B

    1926-12-04

    In the distillation of solid carbonaceous materials with by-product recovery by direct heating with a gas such as water gas, producer gas, or combustion gas which is passed in counter-flow to the materials, the volume of the gas used is such as to lower the vapor tension of the volatiles to enable the oil vapor to be liberated at temperatures not exceeding 450 to 500/sup 0/C and so that the gaseous mixture may be cooled to from 80 to 100/sup 0/C without causing the highest boiling oil fraction to condense. Coking coals may be subjected to a preliminary heat treatment with gases containing an oxygen content of from 2 to 8 percent to reduce their coking properties, and oxygen may be added to the heating gases to assist the polymerization of resinous bodies. Lubricating oil may be obtained by treating the primary oil with caustic soda to remove tar acids, refining the residue with sulfuric acid, distilling off 25 percent of the refined oil and passing the remainder through a filter press at -5/sup 0/C to extract the paraffin wax. The residue of wax-free oil is distilled to yield a lubricating oil which at normal temperatures has a static coefficient of friction of from .1 to .185. Other specifications are referred to.

  14. Carbonaceous Survivability on Impact

    Science.gov (United States)

    Bunch, T. E.; Becker, Luann; Morrison, David (Technical Monitor)

    1994-01-01

    In order to gain knowledge about the potential contributions of comets and cosmic dust to the origin of life on Earth, we need to explore the survivability of their potential organic compounds on impact and the formation of secondary products that may have arisen from the chaotic events sustained by the carriers as they fell to Earth. We have performed a series of hypervelocity impact experiments using carbon-bearing impactors (diamond, graphite, kerogens, PAH crystals, and Murchison and Nogoya meteorites) into Al plate targets at velocities - 6 km/s. Estimated peak shock pressures probably did not exceed 120 GPa and peak shock temperatures were probably less than 4000 K for times of nano- to microsecs. Nominal crater dia. are less than one mm. The most significant results of these experiments are the preservation of the higher mass PAHs (e. g., pyrene relative to napthalene) and the formation of additional alkylated PAHs. We have also examined the residues of polystyrene projectiles impacted by a microparticle accelerator into targets at velocities up to 15 km/s. This talk will discuss the results of these experiments and their implications with respect to the survival of carbonaceous deliverables to early Earth. The prospects of survivability of organic molecules on "intact" capture of cosmic dust in space via soft: and hard cosmic dust collectors will also be discussed.

  15. Distilling carbonaceous materials

    Energy Technology Data Exchange (ETDEWEB)

    Garrow, J R

    1921-04-16

    To obtain an increased yield of by-products such as oils, ammonia, and gas from coal, oil shale, wood, peat, and the like by low and medium temperature processes, the requisite quantity of hot producer gas from a gas producer, is caused to travel, without ignition, through the material as it passes in a continuous manner through the retort so that the sensible heat of the producer gas is utilized to produce distillation of the carbonaceous material, the gases passing to a condenser, absorption apparatus, and an ammonia absorber respectively. In a two-stage method of treatment of materials such as peat or the like, separate supplies of producer gas are utilized for a preliminary drying operation and for the distillation of the material, the drying receptacle and the retort being joined together to render the process continuous. The gas from the drying receptacle may be mixed with the combined producer and retort gas from the retort, after the hydrocarbon oils have deen removed therefrom.

  16. Distillation of carbonaceous material

    Energy Technology Data Exchange (ETDEWEB)

    Ainscow, J W.H.

    1936-10-03

    To recover hydrocarbon products by distillation of carbonaceous material in a plurality of horizontal zones maintained at different temperatures, a retort has a plurality of superimposed (3) retort chambers, the uppermost being in communication at one end with a hopper and at the other end through coupled junction not shown with one end of the next lower chamber, whose opposite end communicates with lowermost chamber, the other end of which has a sealed discharge passage, tank, and conveyor not shown. Each retort chamber has stirring and conveying means consisting of helical blades (2) attached to radial arms on shaft mounted in water cooled bearings and driven through suitably mounted sprocket wheels and chains not shown. Each retort chamber has a gas dome, with pyrometer tube, and off-take connected to a common main opening into a dust eliminator which in turn connects with a plurality of vertical condensation towers of known construction, maintained at different temperatures by means of steam from a superheater not shown situated in one retort chamber. The retort heating gases pass from the furnace via zig-zag, (three) baffles under and around each retort chamber to a flue not shown.

  17. Distilling carbonaceous materials

    Energy Technology Data Exchange (ETDEWEB)

    Ironside, T G

    1921-09-01

    In the distillation of carbonaceous material such as shale, coal, lignite, wood or liquid hydrocarbons, the material is mixed with a heated granular substance such as sand which supplies the necessary heat. The shale or the like, which may be preheated, is fed from a hopper by a worm conveyer to a tube leading into a retort, and the heated granular material such as sand is supplied from a jacketed container through a tube. On the lower end of a rotary shaft are radial arms to which are fixed angularly disposed blades which serve to mix the shale and hot sand and deliver the residue to a central discharge pipe closed at the bottom by a conical valve which opens when the weight of the superimposed material is sufficient. The distillates are taken off by an outlet. Steam vapor or gas may be supplied to the retort, preferably through a hollow shaft leading to hollow stirrers perforated to permit of the gas passing into the material. The retort may be externally heated by hot gases in the space surrounding the retort, and the latter may be divided by horizontal floors so that the material is caused to funnel from the periphery to the center of the floor, then through a central opening on to the floor next below, and from the center to the periphery of this floor, and so on.

  18. A model reduction approach to numerical inversion for a parabolic partial differential equation

    International Nuclear Information System (INIS)

    Borcea, Liliana; Druskin, Vladimir; Zaslavsky, Mikhail; Mamonov, Alexander V

    2014-01-01

    We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where the unknown is the subsurface electrical resistivity and the data are time resolved surface measurements of the magnetic field. The algorithm presented in this paper considers inversion in one and two dimensions. The reduced model is obtained with rational interpolation in the frequency (Laplace) domain and a rational Krylov subspace projection method. It amounts to a nonlinear mapping from the function space of the unknown resistivity to the small dimensional space of the parameters of the reduced model. We use this mapping as a nonlinear preconditioner for the Gauss–Newton iterative solution of the inverse problem. The advantage of the inversion algorithm is twofold. First, the nonlinear preconditioner resolves most of the nonlinearity of the problem. Thus the iterations are less likely to get stuck in local minima and the convergence is fast. Second, the inversion is computationally efficient because it avoids repeated accurate simulations of the time-domain response. We study the stability of the inversion algorithm for various rational Krylov subspaces, and assess its performance with numerical experiments. (paper)

  19. A model reduction approach to numerical inversion for a parabolic partial differential equation

    Science.gov (United States)

    Borcea, Liliana; Druskin, Vladimir; Mamonov, Alexander V.; Zaslavsky, Mikhail

    2014-12-01

    We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where the unknown is the subsurface electrical resistivity and the data are time resolved surface measurements of the magnetic field. The algorithm presented in this paper considers inversion in one and two dimensions. The reduced model is obtained with rational interpolation in the frequency (Laplace) domain and a rational Krylov subspace projection method. It amounts to a nonlinear mapping from the function space of the unknown resistivity to the small dimensional space of the parameters of the reduced model. We use this mapping as a nonlinear preconditioner for the Gauss-Newton iterative solution of the inverse problem. The advantage of the inversion algorithm is twofold. First, the nonlinear preconditioner resolves most of the nonlinearity of the problem. Thus the iterations are less likely to get stuck in local minima and the convergence is fast. Second, the inversion is computationally efficient because it avoids repeated accurate simulations of the time-domain response. We study the stability of the inversion algorithm for various rational Krylov subspaces, and assess its performance with numerical experiments.

  20. Partial differential equation techniques for analysing animal movement: A comparison of different methods.

    Science.gov (United States)

    Wang, Yi-Shan; Potts, Jonathan R

    2017-03-07

    Recent advances in animal tracking have allowed us to uncover the drivers of movement in unprecedented detail. This has enabled modellers to construct ever more realistic models of animal movement, which aid in uncovering detailed patterns of space use in animal populations. Partial differential equations (PDEs) provide a popular tool for mathematically analysing such models. However, their construction often relies on simplifying assumptions which may greatly affect the model outcomes. Here, we analyse the effect of various PDE approximations on the analysis of some simple movement models, including a biased random walk, central-place foraging processes and movement in heterogeneous landscapes. Perhaps the most commonly-used PDE method dates back to a seminal paper of Patlak from 1953. However, our results show that this can be a very poor approximation in even quite simple models. On the other hand, more recent methods, based on transport equation formalisms, can provide more accurate results, as long as the kernel describing the animal's movement is sufficiently smooth. When the movement kernel is not smooth, we show that both the older and newer methods can lead to quantitatively misleading results. Our detailed analysis will aid future researchers in the appropriate choice of PDE approximation for analysing models of animal movement. Copyright © 2017 Elsevier Ltd. All rights reserved.

  1. Research on odor interaction between aldehyde compounds via a partial differential equation (PDE) model.

    Science.gov (United States)

    Yan, Luchun; Liu, Jiemin; Qu, Chen; Gu, Xingye; Zhao, Xia

    2015-01-28

    In order to explore the odor interaction of binary odor mixtures, a series of odor intensity evaluation tests were performed using both individual components and binary mixtures of aldehydes. Based on the linear relation between the logarithm of odor activity value and odor intensity of individual substances, the relationship between concentrations of individual constituents and their joint odor intensity was investigated by employing a partial differential equation (PDE) model. The obtained results showed that the binary odor interaction was mainly influenced by the mixing ratio of two constituents, but not the concentration level of an odor sample. Besides, an extended PDE model was also proposed on the basis of the above experiments. Through a series of odor intensity matching tests for several different binary odor mixtures, the extended PDE model was proved effective at odor intensity prediction. Furthermore, odorants of the same chemical group and similar odor type exhibited similar characteristics in the binary odor interaction. The overall results suggested that the PDE model is a more interpretable way of demonstrating the odor interactions of binary odor mixtures.

  2. Solving variational problems and partial differential equations that map between manifolds via the closest point method

    Science.gov (United States)

    King, Nathan D.; Ruuth, Steven J.

    2017-05-01

    Maps from a source manifold M to a target manifold N appear in liquid crystals, color image enhancement, texture mapping, brain mapping, and many other areas. A numerical framework to solve variational problems and partial differential equations (PDEs) that map between manifolds is introduced within this paper. Our approach, the closest point method for manifold mapping, reduces the problem of solving a constrained PDE between manifolds M and N to the simpler problems of solving a PDE on M and projecting to the closest points on N. In our approach, an embedding PDE is formulated in the embedding space using closest point representations of M and N. This enables the use of standard Cartesian numerics for general manifolds that are open or closed, with or without orientation, and of any codimension. An algorithm is presented for the important example of harmonic maps and generalized to a broader class of PDEs, which includes p-harmonic maps. Improved efficiency and robustness are observed in convergence studies relative to the level set embedding methods. Harmonic and p-harmonic maps are computed for a variety of numerical examples. In these examples, we denoise texture maps, diffuse random maps between general manifolds, and enhance color images.

  3. Mesh refinement and numerical sensitivity analysis for parameter calibration of partial differential equations

    Science.gov (United States)

    Becker, Roland; Vexler, Boris

    2005-06-01

    We consider the calibration of parameters in physical models described by partial differential equations. This task is formulated as a constrained optimization problem with a cost functional of least squares type using information obtained from measurements. An important issue in the numerical solution of this type of problem is the control of the errors introduced, first, by discretization of the equations describing the physical model, and second, by measurement errors or other perturbations. Our strategy is as follows: we suppose that the user defines an interest functional I, which might depend on both the state variable and the parameters and which represents the goal of the computation. First, we propose an a posteriori error estimator which measures the error with respect to this functional. This error estimator is used in an adaptive algorithm to construct economic meshes by local mesh refinement. The proposed estimator requires the solution of an auxiliary linear equation. Second, we address the question of sensitivity. Applying similar techniques as before, we derive quantities which describe the influence of small changes in the measurements on the value of the interest functional. These numbers, which we call relative condition numbers, give additional information on the problem under consideration. They can be computed by means of the solution of the auxiliary problem determined before. Finally, we demonstrate our approach at hand of a parameter calibration problem for a model flow problem.

  4. Statistical mechanics of normal grain growth in one dimension: A partial integro-differential equation model

    International Nuclear Information System (INIS)

    Ng, Felix S.L.

    2016-01-01

    We develop a statistical-mechanical model of one-dimensional normal grain growth that does not require any drift-velocity parameterization for grain size, such as used in the continuity equation of traditional mean-field theories. The model tracks the population by considering grain sizes in neighbour pairs; the probability of a pair having neighbours of certain sizes is determined by the size-frequency distribution of all pairs. Accordingly, the evolution obeys a partial integro-differential equation (PIDE) over ‘grain size versus neighbour grain size’ space, so that the grain-size distribution is a projection of the PIDE's solution. This model, which is applicable before as well as after statistically self-similar grain growth has been reached, shows that the traditional continuity equation is invalid outside this state. During statistically self-similar growth, the PIDE correctly predicts the coarsening rate, invariant grain-size distribution and spatial grain size correlations observed in direct simulations. The PIDE is then reducible to the standard continuity equation, and we derive an explicit expression for the drift velocity. It should be possible to formulate similar parameterization-free models of normal grain growth in two and three dimensions.

  5. High-order asynchrony-tolerant finite difference schemes for partial differential equations

    Science.gov (United States)

    Aditya, Konduri; Donzis, Diego A.

    2017-12-01

    Synchronizations of processing elements (PEs) in massively parallel simulations, which arise due to communication or load imbalances between PEs, significantly affect the scalability of scientific applications. We have recently proposed a method based on finite-difference schemes to solve partial differential equations in an asynchronous fashion - synchronization between PEs is relaxed at a mathematical level. While standard schemes can maintain their stability in the presence of asynchrony, their accuracy is drastically affected. In this work, we present a general methodology to derive asynchrony-tolerant (AT) finite difference schemes of arbitrary order of accuracy, which can maintain their accuracy when synchronizations are relaxed. We show that there are several choices available in selecting a stencil to derive these schemes and discuss their effect on numerical and computational performance. We provide a simple classification of schemes based on the stencil and derive schemes that are representative of different classes. Their numerical error is rigorously analyzed within a statistical framework to obtain the overall accuracy of the solution. Results from numerical experiments are used to validate the performance of the schemes.

  6. Patch Similarity Modulus and Difference Curvature Based Fourth-Order Partial Differential Equation for Image Denoising

    Directory of Open Access Journals (Sweden)

    Yunjiao Bai

    2015-01-01

    Full Text Available The traditional fourth-order nonlinear diffusion denoising model suffers the isolated speckles and the loss of fine details in the processed image. For this reason, a new fourth-order partial differential equation based on the patch similarity modulus and the difference curvature is proposed for image denoising. First, based on the intensity similarity of neighbor pixels, this paper presents a new edge indicator called patch similarity modulus, which is strongly robust to noise. Furthermore, the difference curvature which can effectively distinguish between edges and noise is incorporated into the denoising algorithm to determine the diffusion process by adaptively adjusting the size of the diffusion coefficient. The experimental results show that the proposed algorithm can not only preserve edges and texture details, but also avoid isolated speckles and staircase effect while filtering out noise. And the proposed algorithm has a better performance for the images with abundant details. Additionally, the subjective visual quality and objective evaluation index of the denoised image obtained by the proposed algorithm are higher than the ones from the related methods.

  7. A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data

    KAUST Repository

    Babuška, Ivo; Nobile, Fabio; Tempone, Raul

    2010-01-01

    This work proposes and analyzes a stochastic collocation method for solving elliptic partial differential equations with random coefficients and forcing terms. These input data are assumed to depend on a finite number of random variables. The method consists of a Galerkin approximation in space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space, and naturally leads to the solution of uncoupled deterministic problems as in the Monte Carlo approach. It treats easily a wide range of situations, such as input data that depend nonlinearly on the random variables, diffusivity coefficients with unbounded second moments, and random variables that are correlated or even unbounded. We provide a rigorous convergence analysis and demonstrate exponential convergence of the “probability error” with respect to the number of Gauss points in each direction of the probability space, under some regularity assumptions on the random input data. Numerical examples show the effectiveness of the method. Finally, we include a section with developments posterior to the original publication of this work. There we review sparse grid stochastic collocation methods, which are effective collocation strategies for problems that depend on a moderately large number of random variables.

  8. The solids-flux theory--confirmation and extension by using partial differential equations.

    Science.gov (United States)

    Diehl, Stefan

    2008-12-01

    The solids-flux theory has been used for half a century as a tool for estimating concentration and fluxes in the design and operation of secondary settling tanks during stationary conditions. The flux theory means that the conservation of mass is used in one dimension together with the batch-settling flux function according to the Kynch assumption. The flux theory results correspond to stationary solutions of a partial differential equation, a conservation law, with discontinuous coefficients modelling the continuous-sedimentation process in one dimension. The mathematical analysis of such an equation is intricate, partly since it cannot be interpreted in the classical sense. Recent results, however, make it possible to partly confirm and extend the previous flux theory statements, partly draw new conclusions also on the dynamic behaviour and the possibilities and limitations for control. We use here a single example of an ideal settling tank and a given batch-settling flux in a whole series of calculations. The mathematical results are adapted towards the application and many of them are conveniently presented in terms of operating charts.

  9. Partial differential equation-based approach for empirical mode decomposition: application on image analysis.

    Science.gov (United States)

    Niang, Oumar; Thioune, Abdoulaye; El Gueirea, Mouhamed Cheikh; Deléchelle, Eric; Lemoine, Jacques

    2012-09-01

    The major problem with the empirical mode decomposition (EMD) algorithm is its lack of a theoretical framework. So, it is difficult to characterize and evaluate this approach. In this paper, we propose, in the 2-D case, the use of an alternative implementation to the algorithmic definition of the so-called "sifting process" used in the original Huang's EMD method. This approach, especially based on partial differential equations (PDEs), was presented by Niang in previous works, in 2005 and 2007, and relies on a nonlinear diffusion-based filtering process to solve the mean envelope estimation problem. In the 1-D case, the efficiency of the PDE-based method, compared to the original EMD algorithmic version, was also illustrated in a recent paper. Recently, several 2-D extensions of the EMD method have been proposed. Despite some effort, 2-D versions for EMD appear poorly performing and are very time consuming. So in this paper, an extension to the 2-D space of the PDE-based approach is extensively described. This approach has been applied in cases of both signal and image decomposition. The obtained results confirm the usefulness of the new PDE-based sifting process for the decomposition of various kinds of data. Some results have been provided in the case of image decomposition. The effectiveness of the approach encourages its use in a number of signal and image applications such as denoising, detrending, or texture analysis.

  10. Fast solution of elliptic partial differential equations using linear combinations of plane waves.

    Science.gov (United States)

    Pérez-Jordá, José M

    2016-02-01

    Given an arbitrary elliptic partial differential equation (PDE), a procedure for obtaining its solution is proposed based on the method of Ritz: the solution is written as a linear combination of plane waves and the coefficients are obtained by variational minimization. The PDE to be solved is cast as a system of linear equations Ax=b, where the matrix A is not sparse, which prevents the straightforward application of standard iterative methods in order to solve it. This sparseness problem can be circumvented by means of a recursive bisection approach based on the fast Fourier transform, which makes it possible to implement fast versions of some stationary iterative methods (such as Gauss-Seidel) consuming O(NlogN) memory and executing an iteration in O(Nlog(2)N) time, N being the number of plane waves used. In a similar way, fast versions of Krylov subspace methods and multigrid methods can also be implemented. These procedures are tested on Poisson's equation expressed in adaptive coordinates. It is found that the best results are obtained with the GMRES method using a multigrid preconditioner with Gauss-Seidel relaxation steps.

  11. Advances in phase space analysis of partial differential equations in honor of Ferruccio Colombini's 60th birthday

    CERN Document Server

    Bove, Antonio; Murthy, MK Venkatesha

    2009-01-01

    This collection of original articles and surveys addresses the recent advances in linear and nonlinear aspects of the theory of partial differential equations. The key topics include operators as "sums of squares" of real and complex vector fields, nonlinear evolution equations, local solvability, and hyperbolic questions.

  12. Issues in developing parallel iterative algorithms for solving partial differential equations on a (transputer-based) distributed parallel computing system

    International Nuclear Information System (INIS)

    Rajagopalan, S.; Jethra, A.; Khare, A.N.; Ghodgaonkar, M.D.; Srivenkateshan, R.; Menon, S.V.G.

    1990-01-01

    Issues relating to implementing iterative procedures, for numerical solution of elliptic partial differential equations, on a distributed parallel computing system are discussed. Preliminary investigations show that a speed-up of about 3.85 is achievable on a four transputer pipeline network. (author). 2 figs., 3 a ppendixes., 7 refs

  13. Dimensional analysis to transform the differential equations in partial derivates in the theory of heat transmission into ordinary ones

    International Nuclear Information System (INIS)

    Diaz Sanchidrian, C.

    1989-01-01

    The present paper applies dimensional analysis with spatial discrimination to transform the differential equations in partial derivatives developed in the theory of heat transmission into ordinary ones. The effectivity of the method is comparable to that methods based in transformations of uni or multiparametric groups, with the advantage of being more direct and simple. (Author)

  14. The orthogonal gradients method: A radial basis functions method for solving partial differential equations on arbitrary surfaces

    KAUST Repository

    Piret, Cé cile

    2012-01-01

    Much work has been done on reconstructing arbitrary surfaces using the radial basis function (RBF) method, but one can hardly find any work done on the use of RBFs to solve partial differential equations (PDEs) on arbitrary surfaces. In this paper

  15. Mixed problem with nonlocal boundary conditions for a third-order partial differential equation of mixed type

    OpenAIRE

    Denche, M.; Marhoune, A. L.

    2001-01-01

    We study a mixed problem with integral boundary conditions for a third-order partial differential equation of mixed type. We prove the existence and uniqueness of the solution. The proof is based on two-sided a priori estimates and on the density of the range of the operator generated by the considered problem.

  16. Bäcklund transformation of fractional Riccati equation and its applications to nonlinear fractional partial differential equations

    International Nuclear Information System (INIS)

    Lu, Bin

    2012-01-01

    In this Letter, the fractional derivatives in the sense of modified Riemann–Liouville derivative and the Bäcklund transformation of fractional Riccati equation are employed for constructing the exact solutions of nonlinear fractional partial differential equations. The power of this manageable method is presented by applying it to several examples. This approach can also be applied to other nonlinear fractional differential equations. -- Highlights: ► Backlund transformation of fractional Riccati equation is presented. ► A new method for solving nonlinear fractional differential equations is proposed. ► Three important fractional differential equations are solved successfully. ► Some new exact solutions of the fractional differential equations are obtained.

  17. A Simple Differential Modulation Scheme for Quasi-Orthogonal Space-Time Block Codes with Partial Transmit Diversity

    Directory of Open Access Journals (Sweden)

    Lingyang Song

    2007-04-01

    Full Text Available We report a simple differential modulation scheme for quasi-orthogonal space-time block codes. A new class of quasi-orthogonal coding structures that can provide partial transmit diversity is presented for various numbers of transmit antennas. Differential encoding and decoding can be simplified for differential Alamouti-like codes by grouping the signals in the transmitted matrix and decoupling the detection of data symbols, respectively. The new scheme can achieve constant amplitude of transmitted signals, and avoid signal constellation expansion; in addition it has a linear signal detector with very low complexity. Simulation results show that these partial-diversity codes can provide very useful results at low SNR for current communication systems. Extension to more than four transmit antennas is also considered.

  18. On new classes of solutions of nonlinear partial differential equations in the form of convergent special series

    Science.gov (United States)

    Filimonov, M. Yu.

    2017-12-01

    The method of special series with recursively calculated coefficients is used to solve nonlinear partial differential equations. The recurrence of finding the coefficients of the series is achieved due to a special choice of functions, in powers of which the solution is expanded in a series. We obtain a sequence of linear partial differential equations to find the coefficients of the series constructed. In many cases, one can deal with a sequence of linear ordinary differential equations. We construct classes of solutions in the form of convergent series for a certain class of nonlinear evolution equations. A new class of solutions of generalized Boussinesque equation with an arbitrary function in the form of a convergent series is constructed.

  19. Implementation of geomechanical models for engineered clay barriers in multi-physic partial differential equation solvers

    International Nuclear Information System (INIS)

    Navarro, V.; Alonso, J.; Asensio, L.; Yustres, A.; Pintado, X.

    2012-01-01

    Document available in extended abstract form only. The use of numerical methods, especially the Finite Element Method (FEM), for solving boundary problems in Unsaturated Soil Mechanics has experienced significant progress. Several codes, both built mainly for research purposes and commercial software, are now available. In the last years, Multi-physic Partial Differentiation Equation Solvers (MPDES) have turned out to be an interesting proposal. In this family of solvers, the user defines the governing equations and the behaviour models, generally using a computer algebra environment. The code automatically assembles and solves the equation systems, saving the user having to redefine the structures of memory storage or to implement solver algorithms. The user can focus on the definition of the physics of the problem, while it is possible to couple virtually any physical or chemical process that can be described by a PDE. This can be done, for instance, in COMSOL Multiphysics (CM). Nonetheless, the versatility of CM is compromised by the impossibility to implement models with variables defined by implicit functions. Elasto-plastic models involve an implicit coupling among stress increments, plastic strains and plastic variables increments. For this reason, they cannot be implemented in CM in a straightforward way. This means a very relevant limitation for the use of this tool in the analysis of geomechanical boundary value problems. In this work, a strategy to overcome this problem using the multi-physics concept is presented. A mixed method is proposed, considering the constitutive stresses, the pre-consolidation pressure and the plastic variables as main unknowns of the model. Mixed methods usually present stability problems. However, the algorithmics present in CM include several numerical strategies to minimise this kind of problems. Besides, CM is based on the application of the FEM with Lagrange multipliers, an approach that significantly contributes stability

  20. Sparse grid spectral methods for the numerical solution of partial differential equations with periodic boundary conditions

    International Nuclear Information System (INIS)

    Kupka, F.

    1997-11-01

    This thesis deals with the extension of sparse grid techniques to spectral methods for the solution of partial differential equations with periodic boundary conditions. A review on boundary and initial-boundary value problems and a discussion on numerical resolution is used to motivate this research. Spectral methods are introduced by projection techniques, and by three model problems: the stationary and the transient Helmholtz equations, and the linear advection equation. The approximation theory on the hyperbolic cross is reviewed and its close relation to sparse grids is demonstrated. This approach extends to non-periodic problems. Various Sobolev spaces with dominant mixed derivative are introduced to provide error estimates for Fourier approximation and interpolation on the hyperbolic cross and on sparse grids by means of Sobolev norms. The theorems are immediately applicable to the stability and convergence analysis of sparse grid spectral methods. This is explicitly demonstrated for the three model problems. A variant of the von Neumann condition is introduced to simplify the stability analysis of the time-dependent model problems. The discrete Fourier transformation on sparse grids is discussed together with its software implementation. Results on numerical experiments are used to illustrate the performance of the new method with respect to the smoothness properties of each example. The potential of the method in mathematical modelling is estimated and generalizations to other sparse grid methods are suggested. The appendix includes a complete Fortran90 program to solve the linear advection equation by the sparse grid Fourier collocation method and a third-order Runge-Kutta routine for integration in time. (author)

  1. A hybrid algorithm for coupling partial differential equation and compartment-based dynamics.

    Science.gov (United States)

    Harrison, Jonathan U; Yates, Christian A

    2016-09-01

    Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing particle numbers. An alternative description of many of these systems can be derived in the diffusive limit as a deterministic, continuum system of partial differential equations (PDEs). Although the numerical solution of such PDEs is, in general, much more efficient than the full stochastic simulation, the deterministic continuum description is generally not valid when copy numbers are low and stochastic effects dominate. Therefore, to take advantage of the benefits of both of these types of models, each of which may be appropriate in different parts of a spatial domain, we have developed an algorithm that can be used to couple these two types of model together. This hybrid coupling algorithm uses an overlap region between the two modelling regimes. By coupling fluxes at one end of the interface and using a concentration-matching condition at the other end, we ensure that mass is appropriately transferred between PDE- and compartment-based regimes. Our methodology gives notable reductions in simulation time in comparison with using a fully stochastic model, while maintaining the important stochastic features of the system and providing detail in appropriate areas of the domain. We test our hybrid methodology robustly by applying it to several biologically motivated problems including diffusion and morphogen gradient formation. Our analysis shows that the resulting error is small, unbiased and does not grow over time. © 2016 The Authors.

  2. Highly Scalable Asynchronous Computing Method for Partial Differential Equations: A Path Towards Exascale

    Science.gov (United States)

    Konduri, Aditya

    Many natural and engineering systems are governed by nonlinear partial differential equations (PDEs) which result in a multiscale phenomena, e.g. turbulent flows. Numerical simulations of these problems are computationally very expensive and demand for extreme levels of parallelism. At realistic conditions, simulations are being carried out on massively parallel computers with hundreds of thousands of processing elements (PEs). It has been observed that communication between PEs as well as their synchronization at these extreme scales take up a significant portion of the total simulation time and result in poor scalability of codes. This issue is likely to pose a bottleneck in scalability of codes on future Exascale systems. In this work, we propose an asynchronous computing algorithm based on widely used finite difference methods to solve PDEs in which synchronization between PEs due to communication is relaxed at a mathematical level. We show that while stability is conserved when schemes are used asynchronously, accuracy is greatly degraded. Since message arrivals at PEs are random processes, so is the behavior of the error. We propose a new statistical framework in which we show that average errors drop always to first-order regardless of the original scheme. We propose new asynchrony-tolerant schemes that maintain accuracy when synchronization is relaxed. The quality of the solution is shown to depend, not only on the physical phenomena and numerical schemes, but also on the characteristics of the computing machine. A novel algorithm using remote memory access communications has been developed to demonstrate excellent scalability of the method for large-scale computing. Finally, we present a path to extend this method in solving complex multi-scale problems on Exascale machines.

  3. Iterative Observer-based Estimation Algorithms for Steady-State Elliptic Partial Differential Equation Systems

    KAUST Repository

    Majeed, Muhammad Usman

    2017-07-19

    Steady-state elliptic partial differential equations (PDEs) are frequently used to model a diverse range of physical phenomena. The source and boundary data estimation problems for such PDE systems are of prime interest in various engineering disciplines including biomedical engineering, mechanics of materials and earth sciences. Almost all existing solution strategies for such problems can be broadly classified as optimization-based techniques, which are computationally heavy especially when the problems are formulated on higher dimensional space domains. However, in this dissertation, feedback based state estimation algorithms, known as state observers, are developed to solve such steady-state problems using one of the space variables as time-like. In this regard, first, an iterative observer algorithm is developed that sweeps over regular-shaped domains and solves boundary estimation problems for steady-state Laplace equation. It is well-known that source and boundary estimation problems for the elliptic PDEs are highly sensitive to noise in the data. For this, an optimal iterative observer algorithm, which is a robust counterpart of the iterative observer, is presented to tackle the ill-posedness due to noise. The iterative observer algorithm and the optimal iterative algorithm are then used to solve source localization and estimation problems for Poisson equation for noise-free and noisy data cases respectively. Next, a divide and conquer approach is developed for three-dimensional domains with two congruent parallel surfaces to solve the boundary and the source data estimation problems for the steady-state Laplace and Poisson kind of systems respectively. Theoretical results are shown using a functional analysis framework, and consistent numerical simulation results are presented for several test cases using finite difference discretization schemes.

  4. High-order fractional partial differential equation transform for molecular surface construction.

    Science.gov (United States)

    Hu, Langhua; Chen, Duan; Wei, Guo-Wei

    2013-01-01

    Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model

  5. Ionic diffusion through confined geometries: from Langevin equations to partial differential equations

    International Nuclear Information System (INIS)

    Nadler, Boaz; Schuss, Zeev; Singer, Amit; Eisenberg, R S

    2004-01-01

    Ionic diffusion through and near small domains is of considerable importance in molecular biophysics in applications such as permeation through protein channels and diffusion near the charged active sites of macromolecules. The motion of the ions in these settings depends on the specific nanoscale geometry and charge distribution in and near the domain, so standard continuum type approaches have obvious limitations. The standard machinery of equilibrium statistical mechanics includes microscopic details, but is also not applicable, because these systems are usually not in equilibrium due to concentration gradients and to the presence of an external applied potential, which drive a non-vanishing stationary current through the system. We present a stochastic molecular model for the diffusive motion of interacting particles in an external field of force and a derivation of effective partial differential equations and their boundary conditions that describe the stationary non-equilibrium system. The interactions can include electrostatic, Lennard-Jones and other pairwise forces. The analysis yields a new type of Poisson-Nernst-Planck equations, that involves conditional and unconditional charge densities and potentials. The conditional charge densities are the non-equilibrium analogues of the well studied pair correlation functions of equilibrium statistical physics. Our proposed theory is an extension of equilibrium statistical mechanics of simple fluids to stationary non-equilibrium problems. The proposed system of equations differs from the standard Poisson-Nernst-Planck system in two important aspects. First, the force term depends on conditional densities and thus on the finite size of ions, and second, it contains the dielectric boundary force on a discrete ion near dielectric interfaces. Recently, various authors have shown that both of these terms are important for diffusion through confined geometries in the context of ion channels

  6. Carbonaceous electrode materials for supercapacitors.

    Science.gov (United States)

    Hao, Long; Li, Xianglong; Zhi, Linjie

    2013-07-26

    Supercapacitors have been widely studied around the world in recent years, due to their excellent power density and long cycle life. As the most frequently used electrode materials for supercapacitors, carbonaceous materials attract more and more attention. However, their relatively low energy density still holds back the widespread application. Up to now, various strategies have been developed to figure out this problem. This research news summarizes the recent advances in improving the supercapacitor performance of carbonaceous materials, including the incorporation of heteroatoms and the pore size effect (subnanopores' contribution). In addition, a new class of carbonaceous materials, porous organic networks (PONs) has been managed into the supercapacitor field, which promises great potential in not only improving the supercapacitor performances, but also unraveling the related mechanisms. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  7. Approximate Solutions of Nonlinear Partial Differential Equations by Modified q-Homotopy Analysis Method

    Directory of Open Access Journals (Sweden)

    Shaheed N. Huseen

    2013-01-01

    Full Text Available A modified q-homotopy analysis method (mq-HAM was proposed for solving nth-order nonlinear differential equations. This method improves the convergence of the series solution in the nHAM which was proposed in (see Hassan and El-Tawil 2011, 2012. The proposed method provides an approximate solution by rewriting the nth-order nonlinear differential equation in the form of n first-order differential equations. The solution of these n differential equations is obtained as a power series solution. This scheme is tested on two nonlinear exactly solvable differential equations. The results demonstrate the reliability and efficiency of the algorithm developed.

  8. BOOK REVIEW: Advanced Topics in Computational Partial Differential Equations: Numerical Methods and Diffpack Programming

    Science.gov (United States)

    Katsaounis, T. D.

    2005-02-01

    The scope of this book is to present well known simple and advanced numerical methods for solving partial differential equations (PDEs) and how to implement these methods using the programming environment of the software package Diffpack. A basic background in PDEs and numerical methods is required by the potential reader. Further, a basic knowledge of the finite element method and its implementation in one and two space dimensions is required. The authors claim that no prior knowledge of the package Diffpack is required, which is true, but the reader should be at least familiar with an object oriented programming language like C++ in order to better comprehend the programming environment of Diffpack. Certainly, a prior knowledge or usage of Diffpack would be a great advantage to the reader. The book consists of 15 chapters, each one written by one or more authors. Each chapter is basically divided into two parts: the first part is about mathematical models described by PDEs and numerical methods to solve these models and the second part describes how to implement the numerical methods using the programming environment of Diffpack. Each chapter closes with a list of references on its subject. The first nine chapters cover well known numerical methods for solving the basic types of PDEs. Further, programming techniques on the serial as well as on the parallel implementation of numerical methods are also included in these chapters. The last five chapters are dedicated to applications, modelled by PDEs, in a variety of fields. The first chapter is an introduction to parallel processing. It covers fundamentals of parallel processing in a simple and concrete way and no prior knowledge of the subject is required. Examples of parallel implementation of basic linear algebra operations are presented using the Message Passing Interface (MPI) programming environment. Here, some knowledge of MPI routines is required by the reader. Examples solving in parallel simple PDEs using

  9. A Solution Space for a System of Null-State Partial Differential Equations: Part 1

    Science.gov (United States)

    Flores, Steven M.; Kleban, Peter

    2015-01-01

    This article is the first of four that completely and rigorously characterize a solution space for a homogeneous system of 2 N + 3 linear partial differential equations (PDEs) in 2 N variables that arises in conformal field theory (CFT) and multiple Schramm-Löwner evolution (SLE). In CFT, these are null-state equations and conformal Ward identities. They govern partition functions for the continuum limit of a statistical cluster or loop-gas model, such as percolation, or more generally the Potts models and O( n) models, at the statistical mechanical critical point. (SLE partition functions also satisfy these equations.) For such a lattice model in a polygon with its 2 N sides exhibiting a free/fixed side-alternating boundary condition , this partition function is proportional to the CFT correlation function where the w i are the vertices of and where is a one-leg corner operator. (Partition functions for "crossing events" in which clusters join the fixed sides of in some specified connectivity are linear combinations of such correlation functions.) When conformally mapped onto the upper half-plane, methods of CFT show that this correlation function satisfies the system of PDEs that we consider. In this first article, we use methods of analysis to prove that the dimension of this solution space is no more than C N , the Nth Catalan number. While our motivations are based in CFT, our proofs are completely rigorous. This proof is contained entirely within this article, except for the proof of Lemma 14, which constitutes the second article (Flores and Kleban, in Commun Math Phys, arXiv:1404.0035, 2014). In the third article (Flores and Kleban, in Commun Math Phys, arXiv:1303.7182, 2013), we use the results of this article to prove that the solution space of this system of PDEs has dimension C N and is spanned by solutions constructed with the CFT Coulomb gas (contour integral) formalism. In the fourth article (Flores and Kleban, in Commun Math Phys, arXiv:1405

  10. A Solution Space for a System of Null-State Partial Differential Equations: Part 2

    Science.gov (United States)

    Flores, Steven M.; Kleban, Peter

    2015-01-01

    This article is the second of four that completely and rigorously characterize a solution space for a homogeneous system of 2 N + 3 linear partial differential equations in 2 N variables that arises in conformal field theory (CFT) and multiple Schramm-Löwner evolution (SLE). The system comprises 2 N null-state equations and three conformal Ward identities which govern CFT correlation functions of 2 N one-leg boundary operators. In the first article (Flores and Kleban, Commun Math Phys, arXiv:1212.2301, 2012), we use methods of analysis and linear algebra to prove that dim , with C N the Nth Catalan number. The analysis of that article is complete except for the proof of a lemma that it invokes. The purpose of this article is to provide that proof. The lemma states that if every interval among ( x 2, x 3), ( x 3, x 4),…,( x 2 N-1, x 2 N ) is a two-leg interval of (defined in Flores and Kleban, Commun Math Phys, arXiv:1212.2301, 2012), then F vanishes. Proving this lemma by contradiction, we show that the existence of such a nonzero function implies the existence of a non-vanishing CFT two-point function involving primary operators with different conformal weights, an impossibility. This proof (which is rigorous in spite of our occasional reference to CFT) involves two different types of estimates, those that give the asymptotic behavior of F as the length of one interval vanishes, and those that give this behavior as the lengths of two intervals vanish simultaneously. We derive these estimates by using Green functions to rewrite certain null-state PDEs as integral equations, combining other null-state PDEs to obtain Schauder interior estimates, and then repeatedly integrating the integral equations with these estimates until we obtain optimal bounds. Estimates in which two interval lengths vanish simultaneously divide into two cases: two adjacent intervals and two non-adjacent intervals. The analysis of the latter case is similar to that for one vanishing

  11. A Solution Space for a System of Null-State Partial Differential Equations: Part 4

    Science.gov (United States)

    Flores, Steven M.; Kleban, Peter

    2015-01-01

    This article is the last of four that completely and rigorously characterize a solution space for a homogeneous system of 2 N + 3 linear partial differential equations in 2 N variables that arises in conformal field theory (CFT) and multiple Schramm-Löwner evolution (SLE). The system comprises 2 N null-state equations and three conformal Ward identities that govern CFT correlation functions of 2 N one-leg boundary operators. In the first two articles (Flores and Kleban in Commun Math Phys, 2012; Flores and Kleban, in Commun Math Phys, 2014), we use methods of analysis and linear algebra to prove that dim , with C N the Nth Catalan number. Using these results in the third article (Flores and Kleban, in Commun Math Phys, 2013), we prove that dim and is spanned by (real-valued) solutions constructed with the Coulomb gas (contour integral) formalism of CFT. In this article, we use these results to prove some facts concerning the solution space . First, we show that each of its elements equals a sum of at most two distinct Frobenius series in powers of the difference between two adjacent points (unless is odd, in which case a logarithmic term may appear). This establishes an important element in the operator product expansion for one-leg boundary operators, assumed in CFT. We also identify particular elements of , which we call connectivity weights, and exploit their special properties to conjecture a formula for the probability that the curves of a multiple-SLE process join in a particular connectivity. This leads to new formulas for crossing probabilities of critical lattice models inside polygons with a free/fixed side-alternating boundary condition, which we derive in Flores et al. (Partition functions and crossing probabilities for critical systems inside polygons, in preparation). Finally, we propose a reason for why the exceptional speeds [certain values that appeared in the analysis of the Coulomb gas solutions in Flores and Kleban (Commun Math Phys, 2013)] and

  12. A Solution Space for a System of Null-State Partial Differential Equations: Part 3

    Science.gov (United States)

    Flores, Steven M.; Kleban, Peter

    2015-01-01

    This article is the third of four that completely and rigorously characterize a solution space for a homogeneous system of 2 N + 3 linear partial differential equations (PDEs) in 2 N variables that arises in conformal field theory (CFT) and multiple Schramm-Löwner evolution (SLE κ ). The system comprises 2 N null-state equations and three conformal Ward identities that govern CFT correlation functions of 2 N one-leg boundary operators. In the first two articles (Flores and Kleban, in Commun Math Phys, arXiv:1212.2301, 2012; Commun Math Phys, arXiv:1404.0035, 2014), we use methods of analysis and linear algebra to prove that dim , with C N the Nth Catalan number. Extending these results, we prove in this article that dim and entirely consists of (real-valued) solutions constructed with the CFT Coulomb gas (contour integral) formalism. In order to prove this claim, we show that a certain set of C N such solutions is linearly independent. Because the formulas for these solutions are complicated, we prove linear independence indirectly. We use the linear injective map of Lemma 15 in Flores and Kleban (Commun Math Phys, arXiv:1212.2301, 2012) to send each solution of the mentioned set to a vector in , whose components we find as inner products of elements in a Temperley-Lieb algebra. We gather these vectors together as columns of a symmetric matrix, with the form of a meander matrix. If the determinant of this matrix does not vanish, then the set of C N Coulomb gas solutions is linearly independent. And if this determinant does vanish, then we construct an alternative set of C N Coulomb gas solutions and follow a similar procedure to show that this set is linearly independent. The latter situation is closely related to CFT minimal models. We emphasize that, although the system of PDEs arises in CFT in away that is typically non-rigorous, our treatment of this system here and in Flores and Kleban (Commun Math Phys, arXiv:1212.2301, 2012; Commun Math Phys, arXiv:1404

  13. Stochastic Partial Differential Equation Solver for Hydroacoustic Modeling: Improvements to Paracousti Sound Propagation Solver

    Science.gov (United States)

    Preston, L. A.

    2017-12-01

    Marine hydrokinetic (MHK) devices offer a clean, renewable alternative energy source for the future. Responsible utilization of MHK devices, however, requires that the effects of acoustic noise produced by these devices on marine life and marine-related human activities be well understood. Paracousti is a 3-D full waveform acoustic modeling suite that can accurately propagate MHK noise signals in the complex bathymetry found in the near-shore to open ocean environment and considers real properties of the seabed, water column, and air-surface interface. However, this is a deterministic simulation that assumes the environment and source are exactly known. In reality, environmental and source characteristics are often only known in a statistical sense. Thus, to fully characterize the expected noise levels within the marine environment, this uncertainty in environmental and source factors should be incorporated into the acoustic simulations. One method is to use Monte Carlo (MC) techniques where simulation results from a large number of deterministic solutions are aggregated to provide statistical properties of the output signal. However, MC methods can be computationally prohibitive since they can require tens of thousands or more simulations to build up an accurate representation of those statistical properties. An alternative method, using the technique of stochastic partial differential equations (SPDE), allows computation of the statistical properties of output signals at a small fraction of the computational cost of MC. We are developing a SPDE solver for the 3-D acoustic wave propagation problem called Paracousti-UQ to help regulators and operators assess the statistical properties of environmental noise produced by MHK devices. In this presentation, we present the SPDE method and compare statistical distributions of simulated acoustic signals in simple models to MC simulations to show the accuracy and efficiency of the SPDE method. Sandia National Laboratories

  14. A deterministic partial differential equation model for dose calculation in electron radiotherapy.

    Science.gov (United States)

    Duclous, R; Dubroca, B; Frank, M

    2010-07-07

    High-energy ionizing radiation is a prominent modality for the treatment of many cancers. The approaches to electron dose calculation can be categorized into semi-empirical models (e.g. Fermi-Eyges, convolution-superposition) and probabilistic methods (e.g.Monte Carlo). A third approach to dose calculation has only recently attracted attention in the medical physics community. This approach is based on the deterministic kinetic equations of radiative transfer. We derive a macroscopic partial differential equation model for electron transport in tissue. This model involves an angular closure in the phase space. It is exact for the free streaming and the isotropic regime. We solve it numerically by a newly developed HLLC scheme based on Berthon et al (2007 J. Sci. Comput. 31 347-89) that exactly preserves the key properties of the analytical solution on the discrete level. We discuss several test cases taken from the medical physics literature. A test case with an academic Henyey-Greenstein scattering kernel is considered. We compare our model to a benchmark discrete ordinate solution. A simplified model of electron interactions with tissue is employed to compute the dose of an electron beam in a water phantom, and a case of irradiation of the vertebral column. Here our model is compared to the PENELOPE Monte Carlo code. In the academic example, the fluences computed with the new model and a benchmark result differ by less than 1%. The depths at half maximum differ by less than 0.6%. In the two comparisons with Monte Carlo, our model gives qualitatively reasonable dose distributions. Due to the crude interaction model, these so far do not have the accuracy needed in clinical practice. However, the new model has a computational cost that is less than one-tenth of the cost of a Monte Carlo simulation. In addition, simulations can be set up in a similar way as a Monte Carlo simulation. If more detailed effects such as coupled electron-photon transport, bremsstrahlung

  15. 3D early embryogenesis image filtering by nonlinear partial differential equations.

    Science.gov (United States)

    Krivá, Z; Mikula, K; Peyriéras, N; Rizzi, B; Sarti, A; Stasová, O

    2010-08-01

    We present nonlinear diffusion equations, numerical schemes to solve them and their application for filtering 3D images obtained from laser scanning microscopy (LSM) of living zebrafish embryos, with a goal to identify the optimal filtering method and its parameters. In the large scale applications dealing with analysis of 3D+time embryogenesis images, an important objective is a correct detection of the number and position of cell nuclei yielding the spatio-temporal cell lineage tree of embryogenesis. The filtering is the first and necessary step of the image analysis chain and must lead to correct results, removing the noise, sharpening the nuclei edges and correcting the acquisition errors related to spuriously connected subregions. In this paper we study such properties for the regularized Perona-Malik model and for the generalized mean curvature flow equations in the level-set formulation. A comparison with other nonlinear diffusion filters, like tensor anisotropic diffusion and Beltrami flow, is also included. All numerical schemes are based on the same discretization principles, i.e. finite volume method in space and semi-implicit scheme in time, for solving nonlinear partial differential equations. These numerical schemes are unconditionally stable, fast and naturally parallelizable. The filtering results are evaluated and compared first using the Mean Hausdorff distance between a gold standard and different isosurfaces of original and filtered data. Then, the number of isosurface connected components in a region of interest (ROI) detected in original and after the filtering is compared with the corresponding correct number of nuclei in the gold standard. Such analysis proves the robustness and reliability of the edge preserving nonlinear diffusion filtering for this type of data and lead to finding the optimal filtering parameters for the studied models and numerical schemes. Further comparisons consist in ability of splitting the very close objects which

  16. A deterministic partial differential equation model for dose calculation in electron radiotherapy

    Science.gov (United States)

    Duclous, R.; Dubroca, B.; Frank, M.

    2010-07-01

    High-energy ionizing radiation is a prominent modality for the treatment of many cancers. The approaches to electron dose calculation can be categorized into semi-empirical models (e.g. Fermi-Eyges, convolution-superposition) and probabilistic methods (e.g. Monte Carlo). A third approach to dose calculation has only recently attracted attention in the medical physics community. This approach is based on the deterministic kinetic equations of radiative transfer. We derive a macroscopic partial differential equation model for electron transport in tissue. This model involves an angular closure in the phase space. It is exact for the free streaming and the isotropic regime. We solve it numerically by a newly developed HLLC scheme based on Berthon et al (2007 J. Sci. Comput. 31 347-89) that exactly preserves the key properties of the analytical solution on the discrete level. We discuss several test cases taken from the medical physics literature. A test case with an academic Henyey-Greenstein scattering kernel is considered. We compare our model to a benchmark discrete ordinate solution. A simplified model of electron interactions with tissue is employed to compute the dose of an electron beam in a water phantom, and a case of irradiation of the vertebral column. Here our model is compared to the PENELOPE Monte Carlo code. In the academic example, the fluences computed with the new model and a benchmark result differ by less than 1%. The depths at half maximum differ by less than 0.6%. In the two comparisons with Monte Carlo, our model gives qualitatively reasonable dose distributions. Due to the crude interaction model, these so far do not have the accuracy needed in clinical practice. However, the new model has a computational cost that is less than one-tenth of the cost of a Monte Carlo simulation. In addition, simulations can be set up in a similar way as a Monte Carlo simulation. If more detailed effects such as coupled electron-photon transport, bremsstrahlung

  17. Modulating Function-Based Method for Parameter and Source Estimation of Partial Differential Equations

    KAUST Repository

    Asiri, Sharefa M.

    2017-10-08

    Partial Differential Equations (PDEs) are commonly used to model complex systems that arise for example in biology, engineering, chemistry, and elsewhere. The parameters (or coefficients) and the source of PDE models are often unknown and are estimated from available measurements. Despite its importance, solving the estimation problem is mathematically and numerically challenging and especially when the measurements are corrupted by noise, which is often the case. Various methods have been proposed to solve estimation problems in PDEs which can be classified into optimization methods and recursive methods. The optimization methods are usually heavy computationally, especially when the number of unknowns is large. In addition, they are sensitive to the initial guess and stop condition, and they suffer from the lack of robustness to noise. Recursive methods, such as observer-based approaches, are limited by their dependence on some structural properties such as observability and identifiability which might be lost when approximating the PDE numerically. Moreover, most of these methods provide asymptotic estimates which might not be useful for control applications for example. An alternative non-asymptotic approach with less computational burden has been proposed in engineering fields based on the so-called modulating functions. In this dissertation, we propose to mathematically and numerically analyze the modulating functions based approaches. We also propose to extend these approaches to different situations. The contributions of this thesis are as follows. (i) Provide a mathematical analysis of the modulating function-based method (MFBM) which includes: its well-posedness, statistical properties, and estimation errors. (ii) Provide a numerical analysis of the MFBM through some estimation problems, and study the sensitivity of the method to the modulating functions\\' parameters. (iii) Propose an effective algorithm for selecting the method\\'s design parameters

  18. Equivalent construction of the infinitesimal time translation operator in algebraic dynamics algorithm for partial differential evolution equation

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    We give an equivalent construction of the infinitesimal time translation operator for partial differential evolution equation in the algebraic dynamics algorithm proposed by Shun-Jin Wang and his students. Our construction involves only simple partial differentials and avoids the derivative terms of δ function which appear in the course of computation by means of Wang-Zhang operator. We prove Wang’s equivalent theorem which says that our construction and Wang-Zhang’s are equivalent. We use our construction to deal with several typical equations such as nonlinear advection equation, Burgers equation, nonlinear Schrodinger equation, KdV equation and sine-Gordon equation, and obtain at least second order approximate solutions to them. These equations include the cases of real and complex field variables and the cases of the first and the second order time derivatives.

  19. Polynomial chaos methods for hyperbolic partial differential equations numerical techniques for fluid dynamics problems in the presence of uncertainties

    CERN Document Server

    Pettersson, Mass Per; Nordström, Jan

    2015-01-01

    This monograph presents computational techniques and numerical analysis to study conservation laws under uncertainty using the stochastic Galerkin formulation. With the continual growth of computer power, these methods are becoming increasingly popular as an alternative to more classical sampling-based techniques. The approach described in the text takes advantage of stochastic Galerkin projections applied to the original conservation laws to produce a large system of modified partial differential equations, the solutions to which directly provide a full statistical characterization of the effect of uncertainties. Polynomial Chaos Methods of Hyperbolic Partial Differential Equations focuses on the analysis of stochastic Galerkin systems obtained for linear and non-linear convection-diffusion equations and for a systems of conservation laws; a detailed well-posedness and accuracy analysis is presented to enable the design of robust and stable numerical methods. The exposition is restricted to one spatial dime...

  20. NATO Advanced Research Workshop on Approximation by Solutions of Partial Differential Equations, Quadrature Formulae, and Related Topics

    CERN Document Server

    Goldstein, M; Haussmann, W; Hayman, W; Rogge, L

    1992-01-01

    This volume consists of the proceedings of the NATO Advanced Research Workshop on Approximation by Solutions of Partial Differential Equations, Quadrature Formulae, and Related Topics, which was held at Hanstholm, Denmark. These proceedings include the main invited talks and contributed papers given during the workshop. The aim of these lectures was to present a selection of results of the latest research in the field. In addition to covering topics in approximation by solutions of partial differential equations and quadrature formulae, this volume is also concerned with related areas, such as Gaussian quadratures, the Pompelu problem, rational approximation to the Fresnel integral, boundary correspondence of univalent harmonic mappings, the application of the Hilbert transform in two dimensional aerodynamics, finely open sets in the limit set of a finitely generated Kleinian group, scattering theory, harmonic and maximal measures for rational functions and the solution of the classical Dirichlet problem. In ...

  1. Distilling peat and other carbonaceous matters

    Energy Technology Data Exchange (ETDEWEB)

    Stones, W B

    1850-03-07

    Improvements in treating peat and other carbonaceous and ligneous matters, so as to obtain products therefrom are disclosed. These improvements consist, first, of a machine for compressing and partially drying peat. The unpressed peat is put into boxes and these into frames which are passed through between the bowls of a machine resembling a pair of squeezers. Secondly, consists in distilling, at a temperature of, say 700/sup 0/F, the compressed peat, with or without the addition of tar or fatty matter in retorts, and condensing the vapors in a series of vessels, arranged after the manner of Wolfe's bottles. The resulting charcoal may be extinguished by passing carbonic acid through it while in an air-tight box or chamber, and it may then be compressed into bricks, and used for locomotives and other purposes.

  2. New Traveling Wave Solutions of the Higher Dimensional Nonlinear Partial Differential Equation by the Exp-Function Method

    Directory of Open Access Journals (Sweden)

    Hasibun Naher

    2012-01-01

    Full Text Available We construct new analytical solutions of the (3+1-dimensional modified KdV-Zakharov-Kuznetsev equation by the Exp-function method. Plentiful exact traveling wave solutions with arbitrary parameters are effectively obtained by the method. The obtained results show that the Exp-function method is effective and straightforward mathematical tool for searching analytical solutions with arbitrary parameters of higher-dimensional nonlinear partial differential equation.

  3. Algebraic aspects of evolution partial differential equation arising in the study of constant elasticity of variance model from financial mathematics

    Science.gov (United States)

    Motsepa, Tanki; Aziz, Taha; Fatima, Aeeman; Khalique, Chaudry Masood

    2018-03-01

    The optimal investment-consumption problem under the constant elasticity of variance (CEV) model is investigated from the perspective of Lie group analysis. The Lie symmetry group of the evolution partial differential equation describing the CEV model is derived. The Lie point symmetries are then used to obtain an exact solution of the governing model satisfying a standard terminal condition. Finally, we construct conservation laws of the underlying equation using the general theorem on conservation laws.

  4. On a higher order multi-term time-fractional partial differential equation involving Caputo-Fabrizio derivative

    OpenAIRE

    Pirnapasov, Sardor; Karimov, Erkinjon

    2017-01-01

    In the present work we discuss higher order multi-term partial differential equation (PDE) with the Caputo-Fabrizio fractional derivative in time. We investigate a boundary value problem for fractional heat equation involving higher order Caputo-Fabrizio derivatives in time-variable. Using method of separation of variables and integration by parts, we reduce fractional order PDE to the integer order. We represent explicit solution of formulated problem in particular case by Fourier series.

  5. Using the phase-space imager to analyze partially coherent imaging systems: bright-field, phase contrast, differential interference contrast, differential phase contrast, and spiral phase contrast

    Science.gov (United States)

    Mehta, Shalin B.; Sheppard, Colin J. R.

    2010-05-01

    Various methods that use large illumination aperture (i.e. partially coherent illumination) have been developed for making transparent (i.e. phase) specimens visible. These methods were developed to provide qualitative contrast rather than quantitative measurement-coherent illumination has been relied upon for quantitative phase analysis. Partially coherent illumination has some important advantages over coherent illumination and can be used for measurement of the specimen's phase distribution. However, quantitative analysis and image computation in partially coherent systems have not been explored fully due to the lack of a general, physically insightful and computationally efficient model of image formation. We have developed a phase-space model that satisfies these requirements. In this paper, we employ this model (called the phase-space imager) to elucidate five different partially coherent systems mentioned in the title. We compute images of an optical fiber under these systems and verify some of them with experimental images. These results and simulated images of a general phase profile are used to compare the contrast and the resolution of the imaging systems. We show that, for quantitative phase imaging of a thin specimen with matched illumination, differential phase contrast offers linear transfer of specimen information to the image. We also show that the edge enhancement properties of spiral phase contrast are compromised significantly as the coherence of illumination is reduced. The results demonstrate that the phase-space imager model provides a useful framework for analysis, calibration, and design of partially coherent imaging methods.

  6. Introduction to partial differential equations for scientists and engineers using Mathematica

    CERN Document Server

    Adzievski, Kuzman

    2013-01-01

    Fourier Series The Fourier Series of a Periodic Function Convergence of Fourier Series Integration and Differentiation of Fourier Series Fourier Sine and Fourier Cosine Series Mathematica Projects Integral TransformsThe Fourier Transform and Elementary Properties Inversion Formula of the Fourier Transform Convolution Property of the Fourier TransformThe Laplace Transform and Elementary Properties Differentiation and Integration of the Laplace Transform Heaviside and Dirac Delta Functions Convolution Property of the Laplace Transform Solution of Differential Equations by the Integral Transforms

  7. A three operator split-step method covering a larger set of non-linear partial differential equations

    Science.gov (United States)

    Zia, Haider

    2017-06-01

    This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a notable example being the generalized derivative non-linear Schrödinger equation that arises in non-linear optics with self-steepening terms. These differential equations feature terms that were previously inaccessible to model accurately with low computational resources. The new method maintains a 3rd order error even with these additional terms and models the equation in all three spatial dimensions and time. The class of non-linear differential equations that this method applies to is shown. The method is fully derived and implementation of the method in the split-step architecture is shown. This paper lays the mathematical ground work for an upcoming paper employing this method in white-light generation simulations in bulk material.

  8. Retorts for distilling carbonaceous material

    Energy Technology Data Exchange (ETDEWEB)

    Lutz, H E

    1921-09-12

    A retort for distilling carbonaceous material is described in which a mass of such material is retained in a pocket formed between an outer wall and an internal wall which is perforated to permit the free escape of distilled products, the retorts having heating means that directly heat the retort but are so related to the pocket that the material therein is heated indirectly and simultaneously from all sides entirely by heat conducted thereto by the walls.

  9. A Contraction Fixed Point Theorem in Partially Ordered Metric Spaces and Application to Fractional Differential Equations

    Directory of Open Access Journals (Sweden)

    Xiangbing Zhou

    2012-01-01

    Full Text Available We generalize a fixed point theorem in partially ordered complete metric spaces in the study of A. Amini-Harandi and H. Emami (2010. We also give an application on the existence and uniqueness of the positive solution of a multipoint boundary value problem with fractional derivatives.

  10. Discontinuous Galerkin finite element methods for hyperbolic nonconservative partial differential equations

    NARCIS (Netherlands)

    Rhebergen, Sander; Bokhove, Onno; van der Vegt, Jacobus J.W.

    We present space- and space-time discontinuous Galerkin finite element (DGFEM) formulations for systems containing nonconservative products, such as occur in dispersed multiphase flow equations. The main criterium we pose on the formulation is that if the system of nonconservative partial

  11. Discontinuous Galerkin finite element methods for hyperbolic nonconservative partial differential equations

    NARCIS (Netherlands)

    Rhebergen, Sander; Bokhove, Onno; van der Vegt, Jacobus J.W.

    2008-01-01

    We present space- and space-time discontinuous Galerkin finite element (DGFEM) formulations for systems containing nonconservative products, such as occur in dispersed multiphase flow equations. The main criterium we pose on the weak formulation is that if the system of nonconservative partial

  12. Raman characterization of carbonaceous matter in CONCORDIA Antarctic micrometeorites

    Science.gov (United States)

    Dobricǎ, E.; Engrand, C.; Quirico, E.; Montagnac, G.; Duprat, J.

    2011-09-01

    Abstract- We report a multi-wavelength Raman spectroscopy study of carbonaceous matter in 38 Antarctic micrometeorites (AMMs) from the 2006 CONCORDIA collection. The particles were selected as a function of their degree of thermal alteration developed during the deceleration in the atmosphere. These samples range from unmelted (fine-grained—Fg; ultracarbonaceous—UCAMMs) to partially melted AMMs (scorias—Sc) and completely melted particles (cosmic spherules—CS). More than half of the analyzed AMMs contain a substantial amount of polyaromatic carbonaceous matter with a high degree of disorder. The proportion of particles where carbon is not detected increase from the Fg to the Fg-Sc and to the Sc-AMMs, and no carbon is detected in CS. In addition, the spectral characteristics of the G and D bands of the carbonaceous matter in Sc-AMMs plot apart from the trend formed by the data from Fg-AMMs and UCAMMs. These results suggest that oxidation processes occurred during the deceleration of the particles in the atmosphere. In Fg-AMMs and UCAMMs, the spectral characteristics of the G and D bands reveal the high degree of disorder of the carbonaceous matter, precluding a long duration thermal metamorphism on the parent body and suggesting that AMMs have a connection with C1-C2 chondrites. The Raman parameters of the deuterium-rich carbonaceous matter of UCAMMs do not differ from that of Fg-AMMs. Using a 244 nm excitation, we detected the cyanide (-CN) functional group for the first time in a UCAMM, reinforcing the likely cometary origin of this type of micrometeorites.

  13. Nonlinear self-adjointness, conservation laws, and the construction of solutions of partial differential equations using conservation laws

    International Nuclear Information System (INIS)

    Ibragimov, N Kh; Avdonina, E D

    2013-01-01

    The method of nonlinear self-adjointness, which was recently developed by the first author, gives a generalization of Noether's theorem. This new method significantly extends approaches to constructing conservation laws associated with symmetries, since it does not require the existence of a Lagrangian. In particular, it can be applied to any linear equations and any nonlinear equations that possess at least one local conservation law. The present paper provides a brief survey of results on conservation laws which have been obtained by this method and published mostly in recent preprints of the authors, along with a method for constructing exact solutions of systems of partial differential equations with the use of conservation laws. In most cases the solutions obtained by the method of conservation laws cannot be found as invariant or partially invariant solutions. Bibliography: 23 titles

  14. On the strong solution of a class of partial differential equations that arise in the pricing of mortgage backed securities

    KAUST Repository

    Parshad, Rana; Bayazit, Derviş; Barlow, Nathaniel S.; Prasad, V. Ramchandra

    2011-01-01

    We consider a reduced form pricing model for mortgage backed securities, formulated as a non-linear partial differential equation. We prove that the model possesses a weak solution. We then show that under additional regularity assumptions on the initial data, we also have a mild solution. This mild solution is shown to be a strong solution via further regularity arguments. We also numerically solve the reduced model via a Fourier spectral method. Lastly, we compare our numerical solution to real market data. We observe interestingly that the reduced model captures a number of recent market trends in this data, that have escaped previous models.

  15. On the removal of boundary errors caused by Runge-Kutta integration of non-linear partial differential equations

    Science.gov (United States)

    Abarbanel, Saul; Gottlieb, David; Carpenter, Mark H.

    1994-01-01

    It has been previously shown that the temporal integration of hyperbolic partial differential equations (PDE's) may, because of boundary conditions, lead to deterioration of accuracy of the solution. A procedure for removal of this error in the linear case has been established previously. In the present paper we consider hyperbolic (PDE's) (linear and non-linear) whose boundary treatment is done via the SAT-procedure. A methodology is present for recovery of the full order of accuracy, and has been applied to the case of a 4th order explicit finite difference scheme.

  16. Numerical Solution of the Fractional Partial Differential Equations by the Two-Dimensional Fractional-Order Legendre Functions

    Directory of Open Access Journals (Sweden)

    Fukang Yin

    2013-01-01

    Full Text Available A numerical method is presented to obtain the approximate solutions of the fractional partial differential equations (FPDEs. The basic idea of this method is to achieve the approximate solutions in a generalized expansion form of two-dimensional fractional-order Legendre functions (2D-FLFs. The operational matrices of integration and derivative for 2D-FLFs are first derived. Then, by these matrices, a system of algebraic equations is obtained from FPDEs. Hence, by solving this system, the unknown 2D-FLFs coefficients can be computed. Three examples are discussed to demonstrate the validity and applicability of the proposed method.

  17. Modulating functions-based method for parameters and source estimation in one-dimensional partial differential equations

    KAUST Repository

    Asiri, Sharefa M.

    2016-10-20

    In this paper, modulating functions-based method is proposed for estimating space–time-dependent unknowns in one-dimensional partial differential equations. The proposed method simplifies the problem into a system of algebraic equations linear in unknown parameters. The well-posedness of the modulating functions-based solution is proved. The wave and the fifth-order KdV equations are used as examples to show the effectiveness of the proposed method in both noise-free and noisy cases.

  18. Second-order oriented partial-differential equations for denoising in electronic-speckle-pattern interferometry fringes.

    Science.gov (United States)

    Tang, Chen; Han, Lin; Ren, Hongwei; Zhou, Dongjian; Chang, Yiming; Wang, Xiaohang; Cui, Xiaolong

    2008-10-01

    We derive the second-order oriented partial-differential equations (PDEs) for denoising in electronic-speckle-pattern interferometry fringe patterns from two points of view. The first is based on variational methods, and the second is based on controlling diffusion direction. Our oriented PDE models make the diffusion along only the fringe orientation. The main advantage of our filtering method, based on oriented PDE models, is that it is very easy to implement compared with the published filtering methods along the fringe orientation. We demonstrate the performance of our oriented PDE models via application to two computer-simulated and experimentally obtained speckle fringes and compare with related PDE models.

  19. The Distinct Genetics of Carbonaceous and Non-Carbonaceous Meteorites Inferred from Molybdenum Isotopes

    Science.gov (United States)

    Budde, G.; Burkhardt, C.; Kleine, T.

    2017-07-01

    Mo isotope systematics manifest a fundamental dichotomy in the genetic heritage of carbonaceous and non-carbonaceous meteorites. We discuss its implications in light of the most recent literature data and new isotope data for primitive achondrites.

  20. The orthogonal gradients method: A radial basis functions method for solving partial differential equations on arbitrary surfaces

    KAUST Repository

    Piret, Cécile

    2012-05-01

    Much work has been done on reconstructing arbitrary surfaces using the radial basis function (RBF) method, but one can hardly find any work done on the use of RBFs to solve partial differential equations (PDEs) on arbitrary surfaces. In this paper, we investigate methods to solve PDEs on arbitrary stationary surfaces embedded in . R3 using the RBF method. We present three RBF-based methods that easily discretize surface differential operators. We take advantage of the meshfree character of RBFs, which give us a high accuracy and the flexibility to represent the most complex geometries in any dimension. Two out of the three methods, which we call the orthogonal gradients (OGr) methods are the result of our work and are hereby presented for the first time. © 2012 Elsevier Inc.

  1. INERTIAL MANIFOLDS FOR NONAUTONOMOUS SEMILINEAR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH TIME DELAYS

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    The present paper deals with the long-time behavior of a class of nonautonomous retarded semilinear parabolic differential equations. When the time delays are small enough and the spectral gap conditions hold, the inertial manifolds of the nonautonomous retard parabolic equations are constructed by using the Lyapunov-Perron method.

  2. Reduced basis ANOVA methods for partial differential equations with high-dimensional random inputs

    Energy Technology Data Exchange (ETDEWEB)

    Liao, Qifeng, E-mail: liaoqf@shanghaitech.edu.cn [School of Information Science and Technology, ShanghaiTech University, Shanghai 200031 (China); Lin, Guang, E-mail: guanglin@purdue.edu [Department of Mathematics & School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907 (United States)

    2016-07-15

    In this paper we present a reduced basis ANOVA approach for partial deferential equations (PDEs) with random inputs. The ANOVA method combined with stochastic collocation methods provides model reduction in high-dimensional parameter space through decomposing high-dimensional inputs into unions of low-dimensional inputs. In this work, to further reduce the computational cost, we investigate spatial low-rank structures in the ANOVA-collocation method, and develop efficient spatial model reduction techniques using hierarchically generated reduced bases. We present a general mathematical framework of the methodology, validate its accuracy and demonstrate its efficiency with numerical experiments.

  3. Semigroup Approach to Semilinear Partial Functional Differential Equations with Infinite Delay

    Directory of Open Access Journals (Sweden)

    Hassane Bouzahir

    2007-02-01

    Full Text Available We describe a semigroup of abstract semilinear functional differential equations with infinite delay by the use of the Crandall Liggett theorem. We suppose that the linear part is not necessarily densely defined but satisfies the resolvent estimates of the Hille-Yosida theorem. We clarify the properties of the phase space ensuring equivalence between the equation under investigation and the nonlinear semigroup.

  4. Combination of oriented partial differential equation and shearlet transform for denoising in electronic speckle pattern interferometry fringe patterns.

    Science.gov (United States)

    Xu, Wenjun; Tang, Chen; Gu, Fan; Cheng, Jiajia

    2017-04-01

    It is a key step to remove the massive speckle noise in electronic speckle pattern interferometry (ESPI) fringe patterns. In the spatial-domain filtering methods, oriented partial differential equations have been demonstrated to be a powerful tool. In the transform-domain filtering methods, the shearlet transform is a state-of-the-art method. In this paper, we propose a filtering method for ESPI fringe patterns denoising, which is a combination of second-order oriented partial differential equation (SOOPDE) and the shearlet transform, named SOOPDE-Shearlet. Here, the shearlet transform is introduced into the ESPI fringe patterns denoising for the first time. This combination takes advantage of the fact that the spatial-domain filtering method SOOPDE and the transform-domain filtering method shearlet transform benefit from each other. We test the proposed SOOPDE-Shearlet on five experimentally obtained ESPI fringe patterns with poor quality and compare our method with SOOPDE, shearlet transform, windowed Fourier filtering (WFF), and coherence-enhancing diffusion (CEDPDE). Among them, WFF and CEDPDE are the state-of-the-art methods for ESPI fringe patterns denoising in transform domain and spatial domain, respectively. The experimental results have demonstrated the good performance of the proposed SOOPDE-Shearlet.

  5. Survival of partially differentiated mouse embryonic stem cells in the scala media of the guinea pig cochlea.

    Science.gov (United States)

    Hildebrand, Michael S; Dahl, Hans-Henrik M; Hardman, Jennifer; Coleman, Bryony; Shepherd, Robert K; de Silva, Michelle G

    2005-12-01

    The low regenerative capacity of the hair cells of the mammalian inner ear is a major obstacle for functional recovery following sensorineural hearing loss. A potential treatment is to replace damaged tissue by transplantation of stem cells. To test this approach, undifferentiated and partially differentiated mouse embryonic stem (ES) cells were delivered into the scala media of the deafened guinea pig cochlea. Transplanted cells survived in the scala media for a postoperative period of at least nine weeks, evidenced by histochemical and direct fluorescent detection of enhanced green fluorescent protein (EGFP). Transplanted cells were discovered near the spiral ligament and stria vascularis in the endolymph fluid of the scala media. In some cases, cells were observed close to the damaged organ of Corti structure. There was no evidence of significant immunological rejection of the implanted ES cells despite the absence of immunosuppression. Our surgical approach allowed efficient delivery of ES cells to the scala media while preserving the delicate structures of the cochlea. This is the first report of the survival of partially differentiated ES cells in the scala media of the mammalian cochlea, and it provides support for the potential of cell-based therapies for sensorineural hearing impairment.

  6. Differential effects of total and partial sleep deprivation on salivary factors in Wistar rats.

    Science.gov (United States)

    Lasisi, Dr T J; Shittu, S T; Meludu, C C; Salami, A A

    2017-01-01

    Aim of this study was to investigate the effects of sleep deprivation on salivary factors in rats. Animals were randomly assigned into three groups of 6 animals each as control, total sleep deprivation (TSD) and partial sleep deprivation (PSD) groups. The multiple platform method was used to induce partial and total sleep deprivation for 7days. On the 8th day, stimulated saliva samples were collected for the analysis of salivary lag time, flow rate, salivary amylase activity, immunoglobulin A secretion rate and corticosterone levels using ELISA and standard kinetic enzyme assay. Data were analyzed using ANOVA with Dunnett T3 post hoc tests. Salivary flow rate reduced significantly in the TSD group compared with the PSD group as well as the control group (p=0.01). The secretion rate of salivary IgA was significantly reduced in the TSD group compared with the control group (p=0.04). Salivary amylase activity was significantly elevated in the TSD group compared with the PSD group as well as control group (psalivary lag time and levels of corticosterone among the groups. These findings suggest that total sleep deprivation is associated with reduced salivary flow rate and secretion rate of IgA as well as elevated levels of salivary amylase activity in rats. However, sleep recovery of four hours in the PSD group produced ameliorative effects on the impaired functions of salivary glands. Copyright © 2016 Elsevier Ltd. All rights reserved.

  7. Hydrocarbon oils from carbonaceous material

    Energy Technology Data Exchange (ETDEWEB)

    Fletcher, J

    1943-01-28

    Carbonaceous material is subjected to gradually increasing temperature in a retort and the gases and vapours are drawn off through four pipes according to their temperature and are passed respectively to a separate bubble tower or a fractionation column. The condensate and overhead from each bubble tower are refluxed in the bubble tower into which the gases and vapours of the next succeeding higher temperature are passed and the condensates and overheads from the bubble tower into which gases and vapours at the highest of the lower temperatures are passed are refluxed in the fractionation column. The waste products of combustion pass to a boiler for generating steam for the fractional plant.

  8. Process of treating carbonaceous substances

    Energy Technology Data Exchange (ETDEWEB)

    1938-12-16

    A process is described of removing halogens or halogen compounds (or both) from the products which form when carbonaceous substances are treated thermally in the presence of halogens or halogen compounds, consisting of passing the reaction products at the same temperature with a substance able to fix halogens or acid halides through an apparatus included between the receiver and the heat exchanger, which contains, in a relatively restricted space, internal elements obliquely disposed in relation to the direction of the flow, stretched in this direction and constituted preferably of helicoidal passages.

  9. Pulmonary exposure to carbonaceous nanomaterials and sperm quality

    DEFF Research Database (Denmark)

    Skovmand, Astrid; Lauvas, Anna Jacobsen; Christensen, Preben

    2018-01-01

    . Pulmonary inflammation was determined by differential cell count in bronchoalveolar lavage fluid. Epididymal sperm concentration and motility were measured by computer-assisted sperm analysis. Epididymal sperm viability and morphological abnormalities were assessed manually using Hoechst 33,342/PI...... inflammation is a potential modulator of endocrine function. The aim of this study was to investigate the effects of pulmonary exposure to carbonaceous nanomaterials on sperm quality parameters in an experimental mouse model.Methods: Effects on sperm quality after pulmonary inflammation induced by carbonaceous...... flourescent and Spermac staining, respectively. Epididymal sperm were assessed with regard to sperm DNA integrity (damage). Daily sperm production was measured in the testis, and testosterone levels were measured in blood plasma by ELISA.Results: Neutrophil numbers in the bronchoalveolar fluid showed...

  10. Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics.

    Science.gov (United States)

    Cotter, C J; Gottwald, G A; Holm, D D

    2017-09-01

    In Holm (Holm 2015 Proc. R. Soc. A 471 , 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.

  11. Operational method of solution of linear non-integer ordinary and partial differential equations.

    Science.gov (United States)

    Zhukovsky, K V

    2016-01-01

    We propose operational method with recourse to generalized forms of orthogonal polynomials for solution of a variety of differential equations of mathematical physics. Operational definitions of generalized families of orthogonal polynomials are used in this context. Integral transforms and the operational exponent together with some special functions are also employed in the solutions. The examples of solution of physical problems, related to such problems as the heat propagation in various models, evolutional processes, Black-Scholes-like equations etc. are demonstrated by the operational technique.

  12. Exact solutions and transformation properties of nonlinear partial differential equations from general relativity

    International Nuclear Information System (INIS)

    Fischer, E.

    1977-01-01

    Various families of exact solutions to the Einstein and Einstein--Maxwell field equations of general relativity are treated for situations of sufficient symmetry that only two independent variables arise. The mathematical problem then reduces to consideration of sets of two coupled nonlinear differential equations. The physical situations in which such equations arise include: the external gravitational field of an axisymmetric, uncharged steadily rotating body, cylindrical gravitational waves with two degrees of freedom, colliding plane gravitational waves, the external gravitational and electromagnetic fields of a static, charged axisymmetric body, and colliding plane electromagnetic and gravitational waves. Through the introduction of suitable potentials and coordinate transformations, a formalism is presented which treats all these problems simultaneously. These transformations and potentials may be used to generate new solutions to the Einstein--Maxwell equations from solutions to the vacuum Einstein equations, and vice-versa. The calculus of differential forms is used as a tool for generation of similarity solutions and generalized similarity solutions. It is further used to find the invariance group of the equations; this in turn leads to various finite transformations that give new, physically distinct solutions from old. Some of the above results are then generalized to the case of three independent variables

  13. Explosive Characteristics of Carbonaceous Nanoparticles

    Science.gov (United States)

    Turkevich, Leonid; Fernback, Joseph; Dastidar, Ashok

    2013-03-01

    Explosion testing has been performed on 20 codes of carbonaceous particles. These include SWCNTs (single-walled carbon nanotubes), MWCNTs (multi-walled carbon nanotubes), CNFs (carbon nanofibers), graphene, diamond, fullerene, carbon blacks and graphites. Explosion screening was performed in a 20 L explosion chamber (ASTM E1226-10 protocol), at a (dilute) concentration of 500 g/m3, using a 5 kJ ignition source. Time traces of overpressure were recorded. Samples exhibited overpressures of 5-7 bar, and deflagration index KSt = V1/3 (dp/pt)max ~ 10 - 80 bar-m/s, which places these materials in European Dust Explosion Class St-1 (similar to cotton and wood dust). There was minimal variation between these different materials. The explosive characteristics of these carbonaceous powders are uncorrelated with particle size (BET specific surface area). Additional tests were performed on selected materials to identify minimum explosive concentration [MEC]. These materials exhibit MEC ~ 101 -102 g/m3 (lower than the MEC for coals). The concentration scans confirm that the earlier screening was performed under fuel-rich conditions (i.e. the maximum over-pressure and deflagration index exceed the screening values); e.g. the true fullerene KSt ~ 200 bar-m/s, placing it borderline St-1/St-2. Work supported through the NIOSH Nanotechnology Research Center (NTRC)

  14. The large discretization step method for time-dependent partial differential equations

    Science.gov (United States)

    Haras, Zigo; Taasan, Shlomo

    1995-01-01

    A new method for the acceleration of linear and nonlinear time dependent calculations is presented. It is based on the Large Discretization Step (LDS) approximation, defined in this work, which employs an extended system of low accuracy schemes to approximate a high accuracy discrete approximation to a time dependent differential operator. Error bounds on such approximations are derived. These approximations are efficiently implemented in the LDS methods for linear and nonlinear hyperbolic equations, presented here. In these algorithms the high and low accuracy schemes are interpreted as the same discretization of a time dependent operator on fine and coarse grids, respectively. Thus, a system of correction terms and corresponding equations are derived and solved on the coarse grid to yield the fine grid accuracy. These terms are initialized by visiting the fine grid once in many coarse grid time steps. The resulting methods are very general, simple to implement and may be used to accelerate many existing time marching schemes.

  15. Differential Diptera succession patterns onto partially burned and unburned pig carrion in southeastern Brazil

    Directory of Open Access Journals (Sweden)

    J Oliveira-Costa

    Full Text Available In the present contribution we compared the entomological succession pattern of a burned carcass with that of an unburned one. For that, we used domestic pig carcasses and focused on Calliphoridae, Muscidae and Sarcophagidae flies, because they are the ones most commonly used in Postmortem Interval estimates. Adult and immature flies were collected daily. A total of 27 species and 2,498 specimens were collected, 1,295 specimens of 26 species from the partially burned carcass and 1,203 specimens of 22 species from the control carcass (unburned. The species composition in the two samples differed, and the results of the similarity measures were 0.875 by Sorensen and 0.756 by Bray-Curtis index. The results obtained for both carcasses also differ with respect to the decomposition process, indicating that the post mortem interval would be underestimated if the entomological succession pattern observed for a carcass under normal conditions was applied to a carbonized carcass.

  16. The analysis of linear partial differential operators I distribution theory and Fourier analysis

    CERN Document Server

    Hörmander, Lars

    2003-01-01

    The main change in this edition is the inclusion of exercises with answers and hints. This is meant to emphasize that this volume has been written as a general course in modern analysis on a graduate student level and not only as the beginning of a specialized course in partial differen­ tial equations. In particular, it could also serve as an introduction to harmonic analysis. Exercises are given primarily to the sections of gen­ eral interest; there are none to the last two chapters. Most of the exercises are just routine problems meant to give some familiarity with standard use of the tools introduced in the text. Others are extensions of the theory presented there. As a rule rather complete though brief solutions are then given in the answers and hints. To a large extent the exercises have been taken over from courses or examinations given by Anders Melin or myself at the University of Lund. I am grateful to Anders Melin for letting me use the problems originating from him and for numerous valuable comm...

  17. Differentiation of partial acylglycerols derived from different animal fats by EA-IRMS and GCMS techniques

    Energy Technology Data Exchange (ETDEWEB)

    Nina Naquiah, A.N.; Marikkar, J.M.N.; Shuhaimi, M.

    2016-07-01

    A study was carried out to compare partial acylglycerols of lard with those of chicken fat, beef fat and mutton fat using Gas Chromatography Mass Spectrometry (GC-MS) and Elemental Analysis–Isotope Ratio Mass Spectrometry (EA-IRMS). Mono- (MAG) and di-(DAG) acylglycerols of animal fats were prepared according to a chemical glycerolysis method and isolated using column chromatography. The fatty acid composition and δ13C carbon isotope ratio of MAG and DAG derived from individual animal fat were determined separately to establish their identity characteristics. The results showed that the δ13C values of MAG and DAG of lard were significantly different from those of MAG and DAG derived from chicken fat, beef fat and mutton fat. According to the loading plots based on a principle component analysis (PCA), fatty acids namely stearic, oleic and linoleic were the most discriminating parameters to distinctly identify MAG and DAG derived from different animal fats. This demonstrated that the EA-IRMS and the PCA of fatty acid data have considerable potential for discriminating MAG and DAG derived from lard from other animal fats for Halal authentication purposes. (Author)

  18. Tracer kinetics: Modelling by partial differential equations of inhomogeneous compartments with age-dependent elimination rates. Pt. 1

    International Nuclear Information System (INIS)

    Winkler, E.

    1991-01-01

    Mathematical models in tracer kinetics are usually based on ordinary differential equations which correspond to a system of kinetically homogeneous compartments (standard compartments). A generalization is possible by the admission of inhomogeneities in the behaviour of the elements belonging to a compartment. The important special case of the age-dependence of elimination rates is treated in its deterministic version. It leads to partial different equations (i.e., systems with distributed coefficients) with the 'age' or the 'residence time' of an element of the compartment as a variable additional to 'time'. The basic equations for one generalized compartment and for systems of such compartments are given together with their general solutions. (orig.) [de

  19. An Equation-Type Approach for the Numerical Solution of the Partial Differential Equations Governing Transport Phenomena in Porous Media

    KAUST Repository

    Sun, Shuyu; Salama, Amgad; El-Amin, Mohamed

    2012-01-01

    A new technique for the numerical solution of the partial differential equations governing transport phenomena in porous media is introduced. In this technique, the governing equations as depicted from the physics of the problem are used without extra manipulations. In other words, there is no need to reduce the number of governing equations by some sort of mathematical manipulations. This technique enables the separation of the physics part of the problem and the solver part, which makes coding more robust and could be used in several other applications with little or no modifications (e.g., multi-phase flow in porous media). In this method, one abandons the need to construct the coefficient matrix for the pressure equation. Alternatively, the coefficients are automatically generated within the solver routine. We show examples of using this technique to solving several flow problems in porous media.

  20. A Sequential, Implicit, Wavelet-Based Solver for Multi-Scale Time-Dependent Partial Differential Equations

    Directory of Open Access Journals (Sweden)

    Donald A. McLaren

    2013-04-01

    Full Text Available This paper describes and tests a wavelet-based implicit numerical method for solving partial differential equations. Intended for problems with localized small-scale interactions, the method exploits the form of the wavelet decomposition to divide the implicit system created by the time-discretization into multiple smaller systems that can be solved sequentially. Included is a test on a basic non-linear problem, with both the results of the test, and the time required to calculate them, compared with control results based on a single system with fine resolution. The method is then tested on a non-trivial problem, its computational time and accuracy checked against control results. In both tests, it was found that the method requires less computational expense than the control. Furthermore, the method showed convergence towards the fine resolution control results.

  1. An Equation-Type Approach for the Numerical Solution of the Partial Differential Equations Governing Transport Phenomena in Porous Media

    KAUST Repository

    Sun, Shuyu

    2012-06-02

    A new technique for the numerical solution of the partial differential equations governing transport phenomena in porous media is introduced. In this technique, the governing equations as depicted from the physics of the problem are used without extra manipulations. In other words, there is no need to reduce the number of governing equations by some sort of mathematical manipulations. This technique enables the separation of the physics part of the problem and the solver part, which makes coding more robust and could be used in several other applications with little or no modifications (e.g., multi-phase flow in porous media). In this method, one abandons the need to construct the coefficient matrix for the pressure equation. Alternatively, the coefficients are automatically generated within the solver routine. We show examples of using this technique to solving several flow problems in porous media.

  2. Symbolic computation of exact solutions expressible in rational formal hyperbolic and elliptic functions for nonlinear partial differential equations

    International Nuclear Information System (INIS)

    Wang Qi; Chen Yong

    2007-01-01

    With the aid of symbolic computation, some algorithms are presented for the rational expansion methods, which lead to closed-form solutions of nonlinear partial differential equations (PDEs). The new algorithms are given to find exact rational formal polynomial solutions of PDEs in terms of Jacobi elliptic functions, solutions of the Riccati equation and solutions of the generalized Riccati equation. They can be implemented in symbolic computation system Maple. As applications of the methods, we choose some nonlinear PDEs to illustrate the methods. As a result, we not only can successfully obtain the solutions found by most existing Jacobi elliptic function methods and Tanh-methods, but also find other new and more general solutions at the same time

  3. A meshless scheme for partial differential equations based on multiquadric trigonometric B-spline quasi-interpolation

    International Nuclear Information System (INIS)

    Gao Wen-Wu; Wang Zhi-Gang

    2014-01-01

    Based on the multiquadric trigonometric B-spline quasi-interpolant, this paper proposes a meshless scheme for some partial differential equations whose solutions are periodic with respect to the spatial variable. This scheme takes into account the periodicity of the analytic solution by using derivatives of a periodic quasi-interpolant (multiquadric trigonometric B-spline quasi-interpolant) to approximate the spatial derivatives of the equations. Thus, it overcomes the difficulties of the previous schemes based on quasi-interpolation (requiring some additional boundary conditions and yielding unwanted high-order discontinuous points at the boundaries in the spatial domain). Moreover, the scheme also overcomes the difficulty of the meshless collocation methods (i.e., yielding a notorious ill-conditioned linear system of equations for large collocation points). The numerical examples that are presented at the end of the paper show that the scheme provides excellent approximations to the analytic solutions. (general)

  4. Automating Embedded Analysis Capabilities and Managing Software Complexity in Multiphysics Simulation, Part II: Application to Partial Differential Equations

    Directory of Open Access Journals (Sweden)

    Roger P. Pawlowski

    2012-01-01

    Full Text Available A template-based generic programming approach was presented in Part I of this series of papers [Sci. Program. 20 (2012, 197–219] that separates the development effort of programming a physical model from that of computing additional quantities, such as derivatives, needed for embedded analysis algorithms. In this paper, we describe the implementation details for using the template-based generic programming approach for simulation and analysis of partial differential equations (PDEs. We detail several of the hurdles that we have encountered, and some of the software infrastructure developed to overcome them. We end with a demonstration where we present shape optimization and uncertainty quantification results for a 3D PDE application.

  5. The fifth-order partial differential equation for the description of the α + β Fermi-Pasta-Ulam model

    Science.gov (United States)

    Kudryashov, Nikolay A.; Volkov, Alexandr K.

    2017-01-01

    We study a new nonlinear partial differential equation of the fifth order for the description of perturbations in the Fermi-Pasta-Ulam mass chain. This fifth-order equation is an expansion of the Gardner equation for the description of the Fermi-Pasta-Ulam model. We use the potential of interaction between neighbouring masses with both quadratic and cubic terms. The equation is derived using the continuous limit. Unlike the previous works, we take into account higher order terms in the Taylor series expansions. We investigate the equation using the Painlevé approach. We show that the equation does not pass the Painlevé test and can not be integrated by the inverse scattering transform. We use the logistic function method and the Laurent expansion method to find travelling wave solutions of the fifth-order equation. We use the pseudospectral method for the numerical simulation of wave processes, described by the equation.

  6. A partial differential equation model and its reduction to an ordinary differential equation model for prostate tumor growth under intermittent hormone therapy.

    Science.gov (United States)

    Tao, Youshan; Guo, Qian; Aihara, Kazuyuki

    2014-10-01

    Hormonal therapy with androgen suppression is a common treatment for advanced prostate tumors. The emergence of androgen-independent cells, however, leads to a tumor relapse under a condition of long-term androgen deprivation. Clinical trials suggest that intermittent androgen suppression (IAS) with alternating on- and off-treatment periods can delay the relapse when compared with continuous androgen suppression (CAS). In this paper, we propose a mathematical model for prostate tumor growth under IAS therapy. The model elucidates initial hormone sensitivity, an eventual relapse of a tumor under CAS therapy, and a delay of a relapse under IAS therapy, which are due to the coexistence of androgen-dependent cells, androgen-independent cells resulting from reversible changes by adaptation, and androgen-independent cells resulting from irreversible changes by genetic mutations. The model is formulated as a free boundary problem of partial differential equations that describe the evolution of populations of the abovementioned three types of cells during on-treatment periods and off-treatment periods. Moreover, the model can be transformed into a piecewise linear ordinary differential equation model by introducing three new volume variables, and the study of the resulting model may help to devise optimal IAS schedules.

  7. Extraterrestrial Nucleobases in Carbonaceous Chondrites

    Science.gov (United States)

    Martins, Z.; Botta, O.; Fogel, M.; Sephton, M.; Glavin, D.; Watson, J.; Dworkin, J.; Schwartz, A.; Ehrenfreund, P.

    Nucleobases in Carbonaceous Chondrites Z. Martins (1), O. Botta (2), M. L. Fogel (3), M. A. Sephton (4), D. P. Glavin (2), J. S. Watson (5), J. P. Dworkin (2), A. W. Schwartz (6) and P. Ehrenfreund (1,6). (1) Astrobiology Laboratory, Leiden Institute of Chemistry, Leiden, The Netherlands, (2) NASA Goddard Space Flight Center, Goddard Center for Astrobiology, Greenbelt, MD, USA, (3) GL, Carnegie Institution of Washington, Washington DC, USA, (4) Impacts and Astromaterials Research Centre, Department of Earth Science and Engineering, South Kensington Campus, Imperial College, London, UK, (5) Planetary and Space Sciences Research Institute, The Open University, Walton Hall, Milton Keynes, UK, (6) Radboud University Nijmegen, Nijmegen, The Netherlands. E-mail: z.martins@chem.leidenuniv.nl/Phone:+31715274440 Nucleobases are crucial compounds in terrestrial biochemistry, because they are key components of DNA and RNA. Carbonaceous meteorites have been analyzed for nucleobases by different research groups [1-5]. However, significant quantitative and qualitative differences were observed, leading to the controversial about the origin of these nucleobases. In order to establish the origin of these compounds in carbonaceous chondrites and to assess the plausibility of their exogenous delivery to the early Earth, we have performed formic acid extraction of samples of the Murchison meteorite [6], followed by an extensive purification procedure, analysis and quantification by high-performance liquid chromatography with UV absorption detection and gas chromatography-mass spectrometry. Our results were qualitatively consistent with previous results [3, 4], but showed significant quantitative differences. Compound specific carbon isotope values were obtained, using gas chromatography-combustion- isotope ratio mass spectrometry. A soil sample collected in the proximity of the Murchison meteorite fall site was subjected to the same extraction, purification and analysis procedure

  8. Organic Chemistry of Carbonaceous Meteorites

    Science.gov (United States)

    Cronin, John R.

    2001-01-01

    Chiral and carbon-isotopic analyses of isovaline have been carried out on numerous samples of the Murchison and one sample of the Murray carbonaceous chondrite. The isovaline was found to be heterogeneous with regard to enantiomeric excess (ee) both between samples and within a single Murchison sample. L-Excesses ranging from 0 to 15% were observed. The isovaline delta(sup 13) C was found to be about +18%. No evidence was obtained suggesting terrestrial contamination in the more abundant L-enantiomer. A correlation was observed between isovaline (also alpha - aminoisobutyric acid) concentration and PCP content of five CM chondrites. It is suggested that isovaline, along with other meteoritic a-methyl amino acids with ee, are of presolar origin. The possible formation of ee in extraterrestrial amino acids by exposure to circularly polarized light or by magnetochiral photochemistry is discussed. Key words: Murchison meteorite, Murray meteorite, amino acids, isovaline, chirality, carbon isotopes, PCP.

  9. Distillation of solid carbonaceous material

    Energy Technology Data Exchange (ETDEWEB)

    Burney, C D

    1918-08-31

    A method of distilling carbonaceous material at low or moderate temperatures is described in which the main supply of gases for heating the material under treatment is generated in a combustion chamber located externally of the retort chamber from which combustion chamber the gases are withdrawn and passed under control through hollow elements located within the retort chamber in such manner as to insure the production of the desired temperature gradient along the length of the retort, the said elements being so constructed that they serve to bring the heating gases into indirect contact with the material undergoing treatment while also moving the material progressively through the retort in the opposite direction to that in which the heating gases flow.

  10. Differentiation of partial acylglycerols derived from different animal fats by EA-IRMS and GCMS techniques

    Directory of Open Access Journals (Sweden)

    Nina Naquiah, A. N.

    2016-06-01

    Full Text Available A study was carried out to compare partial acylglycerols of lard with those of chicken fat, beef fat and mutton fat using Gas Chromatography Mass Spectrometry (GC-MS and Elemental Analysis–Isotope Ratio Mass Spectrometry (EA-IRMS. Mono- (MAG and di-(DAG acylglycerols of animal fats were prepared according to a chemical glycerolysis method and isolated using column chromatography. The fatty acid composition and δ13C carbon isotope ratio of MAG and DAG derived from individual animal fat were determined separately to establish their identity characteristics. The results showed that the δ13C values of MAG and DAG of lard were significantly different from those of MAG and DAG derived from chicken fat, beef fat and mutton fat. According to the loading plots based on a principle component analysis (PCA, fatty acids namely stearic, oleic and linoleic were the most discriminating parameters to distinctly identify MAG and DAG derived from different animal fats. This demonstrated that the EA-IRMS and the PCA of fatty acid data have considerable potential for discriminating MAG and DAG derived from lard from other animal fats for Halal authentication purposes.Se realizó un estudio para comparar acilgliceroles parciales de la manteca de cerdo con las de grasa de pollo, grasa de vacuno y grasa de cordero utilizando cromatografía de gases-espectrometría de masas (GC-MS y análisis elemental de Isótopos-Espectrometría de Masas (EA-IRMS. Los mono- (MAG y di- (DAG acilgliceroles de grasas animales se prepararon mediante un método de glicerolisis química y se aislaron mediante cromatografía en columna. La composición de ácidos grasos y la relación isotópica de carbono δ13C de los MAG y DAG de las grasas de animales se determinan por separado para establecer sus características de identidad. Los resultados mostraron que los valores de δ13C de MAG y DAG de la manteca de cerdo fue significativamente diferente de los de MAG y DAG derivados de grasa

  11. Optimal Control Method of Parabolic Partial Differential Equations and Its Application to Heat Transfer Model in Continuous Cast Secondary Cooling Zone

    Directory of Open Access Journals (Sweden)

    Yuan Wang

    2015-01-01

    Full Text Available Our work is devoted to a class of optimal control problems of parabolic partial differential equations. Because of the partial differential equations constraints, it is rather difficult to solve the optimization problem. The gradient of the cost function can be found by the adjoint problem approach. Based on the adjoint problem approach, the gradient of cost function is proved to be Lipschitz continuous. An improved conjugate method is applied to solve this optimization problem and this algorithm is proved to be convergent. This method is applied to set-point values in continuous cast secondary cooling zone. Based on the real data in a plant, the simulation experiments show that the method can ensure the steel billet quality. From these experiment results, it is concluded that the improved conjugate gradient algorithm is convergent and the method is effective in optimal control problem of partial differential equations.

  12. MRI differential diagnosis of complete and partial tears of the anterior cruciate ligament of the knee: the usefulness of oblique coronal T2-weighted image

    International Nuclear Information System (INIS)

    Lee, Seo Young; Shim, Jae Chan; Lee, Ghi Jai; Bang, Sun Woo; Ryu, Seok Jong; Kim, Ho Kyun; Kim, Jeong Seok

    2002-01-01

    To assess the usefulness of T2-weighted oblique coronal MR imaging (T2OCI) in the differential diagnosis of complete and partial tears of the anterior cruciate ligament (ACL) of the knee. Thirty-three patients with ACL tear (16 complete and 17 partial tears), comfirmed by arthroscopy, were included in this study. Conventional MR imaging and T2OCI were performed, and the findings were retrospectively reviewed by two radiologists in terms of continuity, shape, axis and internal signal intensity of the ligament. Each finding was tested if there were stastistically significant differences in its prevalence between partial and complete tears. The diagnostic accuracy of T2OCI and conventional MR imaging in the detection of partial and complete tears of the ACL were compared. Conventional MR imaging revealed no statistically significant finding for differential diagnosis of complete and partial ACL tears. The reliable and statistically significant (p<0.001) findings of T2OCI were complete discontinuity of the ligament in cases involving complete ACL tears (14 of 16 complete tears and 2 of 17 partial tears) and the preservation of the band form for partial ACL tears (2 of 16 complete tears and 15 of 17 partial tears). The accuracy of T2OCI and conventional MR imaging was 88% and 70%, respectively. When ACL injury is vague on conventional MR images, a modality which is more useful in the differential diagnosis of partial and complete tears of the ACL, and in predicting the site of a tear, is T2-weighted oblique coronal imaging

  13. Carbonaceous deposits on naptha reforming catalysts

    International Nuclear Information System (INIS)

    Redwan, D.S.

    1999-01-01

    Carbonaceous deposits on naphtha reforming catalysts play a decisive role in limiting process performance. The deposits negatively after catalyst activity, selectivity and the production cycle of a semi regenerative reformer. The magnitude of negative effect of those deposits is directly proportional to their amounts and complexity. Investigations on used reforming catalysts samples reveal that the amount and type (complexity of the chemical nature) of carbonaceous deposits are directly proportional to the catalysts life on stream and the severity of operating conditions. In addition, the combustibility behavior of carbonaceous deposits on the catalyst samples taken from different reformers are found to be different. Optimal carbon removal, for in situ catalyst regeneration, requires the specific conditions be developed, based on the results of well designed and properly performed investigations of the amount and type of carbonaceous deposits. (author)

  14. Comparison of Laser Doppler Imaging (LDI) and clinical assessment in differentiating between superficial and deep partial thickness burn wounds.

    Science.gov (United States)

    Jan, Saadia Nosheen; Khan, Farid Ahmed; Bashir, Muhammad Mustehsan; Nasir, Muneeb; Ansari, Hamid Hussain; Shami, Hussan Birkhez; Nazir, Umer; Hanif, Asif; Sohail, Muhammad

    2018-03-01

    To compare the accuracy of Laser Doppler Imaging (LDI) and clinical assessment in differentiating between superficial and deep partial thickness burns to decide whether early tangential excision and grafting or conservative management should be employed to optimize burn and patient management. March 2015 to November 2016. Ninety two wounds in 34 patients reporting within 5days of less than 40% burn surface area were included. Unstable patients, pregnant females and those who expired were excluded. The wounds were clinically assessed and LDI done concomitantly Plastic Surgeons blinded to each other's findings. Wound appearance, color, blanching, pain, hair follicle dislodgement were the clinical parameters that distinguished between superficial and deep partial thickness burns. On day 21, the wounds were again assessed for the presence of healing by the same plastic surgeons. The findings were correlated with the initial findings on LDI and clinical assessment and the results statistically analyzed. The data of 92 burn wounds was analyzed using SPSS (ver. 17). Clinical assessment correctly identified the depth of 75 and LDI 83 wounds, giving diagnostic accuracies of 81.52% and 90.21% respectively. The sensitivity of clinical assessment was 81% and of LDI 92.75%, whereas the specificity was 82% for both. The positive predictive value was 93% for clinical assessment and 94% for LDI while the negative predictive value was 59% and 79% respectively. Predictive accuracy of LDI was found to be better than clinical assessment in the prediction of wound healing, the gold standard for wound healing being 21 days. As such it can prove to be a reliable and viable cost effective alternative per se to clinical assessment. Copyright © 2017 Elsevier Ltd and ISBI. All rights reserved.

  15. Applied partial differential equations

    CERN Document Server

    Logan, J David

    2015-01-01

    This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs.  Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory. The concise treatment of the subject is maintained in this third edition covering all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. In this third edition, text remains intimately tied to applications in heat transfer, wave motion, biological systems, and a variety other topics in pure and applied science. The text offers flexibility to instructors who, for example, may wish to insert topics from biology or numerical methods at any time in the course. The exposition is presented in a friendly, easy-to-read, style, with mathematical ideas motivated from physical problems. Many exercises and worked e...

  16. Partial differential equations

    Indian Academy of Sciences (India)

    prehensive paper [14] on degenerate elliptic equa- tions with special ... An analysis of the leading term shows it to be the solution of a ... true in all space dimensions. One of the ... Pisa, Serie IV 15 No. 3,. 453–465. ..... the method is its ability to make the construction ..... type formula for sub and super solution; Adv. Diff. Eq.

  17. Wave Partial Differential Equation

    OpenAIRE

    Szöllös, Alexandr

    2009-01-01

    Práce se zabývá diferenciálními rovnicemi, jejich využitím při analýze     vedení, experimenty s vedením a možnou akcelerací výpočtu v GPU  s využitím prostředí nVidia CUDA. This work deals with diffrential equations, with the possibility     of using them for analysis of the line and the possibility     of accelerating the computations in GPU using nVidia CUDA. C

  18. Stochastic partial differential equations

    CERN Document Server

    Lototsky, Sergey V

    2017-01-01

    Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and perhaps even to formulate and prove a few new ones. Most of the material could be covered in about 40 hours of lectures, as long as not too much time is spent on the general discussion of stochastic analysis in infinite dimensions. As the subject of SPDEs is currently making the transition from the research level to that of a graduate or even undergraduate course, the book attempts to present enough exercise material to fill potential exams and homework assignments. Exercises appear throughout and are usually directly connected ...

  19. Applied partial differential equations

    CERN Document Server

    DuChateau, Paul

    2012-01-01

    Book focuses mainly on boundary-value and initial-boundary-value problems on spatially bounded and on unbounded domains; integral transforms; uniqueness and continuous dependence on data, first-order equations, and more. Numerous exercises included.

  20. Partial differential equation methods for stochastic dynamic optimization: an application to wind power generation with energy storage.

    Science.gov (United States)

    Johnson, Paul; Howell, Sydney; Duck, Peter

    2017-08-13

    A mixed financial/physical partial differential equation (PDE) can optimize the joint earnings of a single wind power generator (WPG) and a generic energy storage device (ESD). Physically, the PDE includes constraints on the ESD's capacity, efficiency and maximum speeds of charge and discharge. There is a mean-reverting daily stochastic cycle for WPG power output. Physically, energy can only be produced or delivered at finite rates. All suppliers must commit hourly to a finite rate of delivery C , which is a continuous control variable that is changed hourly. Financially, we assume heavy 'system balancing' penalties in continuous time, for deviations of output rate from the commitment C Also, the electricity spot price follows a mean-reverting stochastic cycle with a strong evening peak, when system balancing penalties also peak. Hence the economic goal of the WPG plus ESD, at each decision point, is to maximize expected net present value (NPV) of all earnings (arbitrage) minus the NPV of all expected system balancing penalties, along all financially/physically feasible future paths through state space. Given the capital costs for the various combinations of the physical parameters, the design and operating rules for a WPG plus ESD in a finite market may be jointly optimizable.This article is part of the themed issue 'Energy management: flexibility, risk and optimization'. © 2017 The Author(s).

  1. Spatial and temporal accuracy of asynchrony-tolerant finite difference schemes for partial differential equations at extreme scales

    Science.gov (United States)

    Kumari, Komal; Donzis, Diego

    2017-11-01

    Highly resolved computational simulations on massively parallel machines are critical in understanding the physics of a vast number of complex phenomena in nature governed by partial differential equations. Simulations at extreme levels of parallelism present many challenges with communication between processing elements (PEs) being a major bottleneck. In order to fully exploit the computational power of exascale machines one needs to devise numerical schemes that relax global synchronizations across PEs. This asynchronous computations, however, have a degrading effect on the accuracy of standard numerical schemes.We have developed asynchrony-tolerant (AT) schemes that maintain order of accuracy despite relaxed communications. We show, analytically and numerically, that these schemes retain their numerical properties with multi-step higher order temporal Runge-Kutta schemes. We also show that for a range of optimized parameters,the computation time and error for AT schemes is less than their synchronous counterpart. Stability of the AT schemes which depends upon history and random nature of delays, are also discussed. Support from NSF is gratefully acknowledged.

  2. Exploring the interplay of resilience and energy consumption for a task-based partial differential equations preconditioner

    KAUST Repository

    Rizzi, F.; Morris, K.; Sargsyan, K.; Mycek, P.; Safta, C.; Le Maî tre, O.; Knio, Omar; Debusschere, B.J.

    2017-01-01

    We discuss algorithm-based resilience to silent data corruptions (SDCs) in a task-based domain-decomposition preconditioner for partial differential equations (PDEs). The algorithm exploits a reformulation of the PDE as a sampling problem, followed by a solution update through data manipulation that is resilient to SDCs. The implementation is based on a server-client model where all state information is held by the servers, while clients are designed solely as computational units. Scalability tests run up to ∼ 51K cores show a parallel efficiency greater than 90%. We use a 2D elliptic PDE and a fault model based on random single and double bit-flip to demonstrate the resilience of the application to synthetically injected SDC. We discuss two fault scenarios: one based on the corruption of all data of a target task, and the other involving the corruption of a single data point. We show that for our application, given the test problem considered, a four-fold increase in the number of faults only yields a 2% change in the overhead to overcome their presence, from 7% to 9%. We then discuss potential savings in energy consumption via dynamic voltage/frequency scaling, and its interplay with fault-rates, and application overhead.

  3. Exploring the interplay of resilience and energy consumption for a task-based partial differential equations preconditioner

    KAUST Repository

    Rizzi, F.

    2017-05-25

    We discuss algorithm-based resilience to silent data corruptions (SDCs) in a task-based domain-decomposition preconditioner for partial differential equations (PDEs). The algorithm exploits a reformulation of the PDE as a sampling problem, followed by a solution update through data manipulation that is resilient to SDCs. The implementation is based on a server-client model where all state information is held by the servers, while clients are designed solely as computational units. Scalability tests run up to ∼ 51K cores show a parallel efficiency greater than 90%. We use a 2D elliptic PDE and a fault model based on random single and double bit-flip to demonstrate the resilience of the application to synthetically injected SDC. We discuss two fault scenarios: one based on the corruption of all data of a target task, and the other involving the corruption of a single data point. We show that for our application, given the test problem considered, a four-fold increase in the number of faults only yields a 2% change in the overhead to overcome their presence, from 7% to 9%. We then discuss potential savings in energy consumption via dynamic voltage/frequency scaling, and its interplay with fault-rates, and application overhead.

  4. Dual-shaped offset reflector antenna designs from solutions of the geometrical optics first-order partial differential equations

    Science.gov (United States)

    Galindo-Israel, V.; Imbriale, W.; Shogen, K.; Mittra, R.

    1990-01-01

    In obtaining solutions to the first-order nonlinear partial differential equations (PDEs) for synthesizing offset dual-shaped reflectors, it is found that previously observed computational problems can be avoided if the integration of the PDEs is started from an inner projected perimeter and integrated outward rather than starting from an outer projected perimeter and integrating inward. This procedure, however, introduces a new parameter, the main reflector inner perimeter radius p(o), when given a subreflector inner angle 0(o). Furthermore, a desired outer projected perimeter (e.g., a circle) is no longer guaranteed. Stability of the integration is maintained if some of the initial parameters are determined first from an approximate solution to the PDEs. A one-, two-, or three-parameter optimization algorithm can then be used to obtain a best set of parameters yielding a close fit to the desired projected outer rim. Good low cross-polarization mapping functions are also obtained. These methods are illustrated by synthesis of a high-gain offset-shaped Cassegrainian antenna and a low-noise offset-shaped Gregorian antenna.

  5. Matrix-oriented implementation for the numerical solution of the partial differential equations governing flows and transport in porous media

    KAUST Repository

    Sun, Shuyu

    2012-09-01

    In this paper we introduce a new technique for the numerical solution of the various partial differential equations governing flow and transport phenomena in porous media. This method is proposed to be used in high level programming languages like MATLAB, Python, etc., which show to be more efficient for certain mathematical operations than for others. The proposed technique utilizes those operations in which these programming languages are efficient the most and keeps away as much as possible from those inefficient, time-consuming operations. In particular, this technique is based on the minimization of using multiple indices looping operations by reshaping the unknown variables into one-dimensional column vectors and performing the numerical operations using shifting matrices. The cell-centered information as well as the face-centered information are shifted to the adjacent face-center and cell-center, respectively. This enables the difference equations to be done for all the cells at once using matrix operations rather than within loops. Furthermore, for results post-processing, the face-center information can further be mapped to the physical grid nodes for contour plotting and stream lines constructions. In this work we apply this technique to flow and transport phenomena in porous media. © 2012 Elsevier Ltd.

  6. THREE-POINT BACKWARD FINITE DIFFERENCE METHOD FOR SOLVING A SYSTEM OF MIXED HYPERBOLIC-PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS. (R825549C019)

    Science.gov (United States)

    A three-point backward finite-difference method has been derived for a system of mixed hyperbolic¯¯parabolic (convection¯¯diffusion) partial differential equations (mixed PDEs). The method resorts to the three-point backward differenci...

  7. On radiogenic nature of xenon-X in carbonaceous and LL chondrites

    International Nuclear Information System (INIS)

    Gerling, Eh.K.

    1982-01-01

    The nature of Xe-X from the mineral fraction produced during the differential dissolution of carbonaceous and LL chondrites was investigated using literature data on the age of some meteorites and their fractions and quantities of fission 136 Xe contained in them. A graph of lg fission 136 Xe against the age of meteorites was plotted; the decay constant of a hypothetical superheavy nucleus was calculated using the graph and equaled 1x10 - 7 year - 1 . The calculations served as a forcible argument for the radiogenic nature of xenon with 136 and 134 mass in carbonaceous and LL chondrites

  8. Molybdenum isotopic evidence for the origin of chondrules and a distinct genetic heritage of carbonaceous and non-carbonaceous meteorites

    Science.gov (United States)

    Budde, Gerrit; Burkhardt, Christoph; Brennecka, Gregory A.; Fischer-Gödde, Mario; Kruijer, Thomas S.; Kleine, Thorsten

    2016-11-01

    Nucleosynthetic isotope anomalies are powerful tracers to determine the provenance of meteorites and their components, and to identify genetic links between these materials. Here we show that chondrules and matrix separated from the Allende CV3 chondrite have complementary nucleosynthetic Mo isotope anomalies. These anomalies result from the enrichment of a presolar carrier enriched in s-process Mo into the matrix, and the corresponding depletion of this carrier in the chondrules. This carrier most likely is a metal and so the uneven distribution of presolar material probably results from metal-silicate fractionation during chondrule formation. The Mo isotope anomalies correlate with those reported for W isotopes on the same samples in an earlier study, suggesting that the isotope variations for both Mo and W are caused by the heterogeneous distribution of the same carrier. The isotopic complementary of chondrules and matrix indicates that both components are genetically linked and formed together from one common reservoir of solar nebula dust. As such, the isotopic data require that most chondrules formed in the solar nebula and are not a product of protoplanetary impacts. Allende chondrules and matrix together with bulk carbonaceous chondrites and some iron meteorites (groups IID, IIIF, and IVB) show uniform excesses in 92Mo, 95Mo, and 97Mo that result from the addition of supernova material to the solar nebula region in which these carbonaceous meteorites formed. Non-carbonaceous meteorites (enstatite and ordinary chondrites as well as most iron meteorites) do not contain this material, demonstrating that two distinct Mo isotope reservoirs co-existed in the early solar nebula that remained spatially separated for several million years. This separation was most likely achieved through the formation of the gas giants, which cleared the disk between the inner and outer solar system regions parental to the non-carbonaceous and carbonaceous meteorites. The Mo isotope

  9. Reversible effects of oxygen partial pressure on genes associated with placental angiogenesis and differentiation in primary-term cytotrophoblast cell culture.

    Science.gov (United States)

    Debiève, F; Depoix, C; Gruson, D; Hubinont, C

    2013-09-01

    Timely regulated changes in oxygen partial pressure are important for placental formation. Disturbances could be responsible for pregnancy-related diseases like preeclampsia and intrauterine growth restriction. We aimed to (i) determine the effect of oxygen partial pressure on cytotrophoblast differentiation; (ii) measure mRNA expression and protein secretion from genes associated with placental angiogenesis; and (iii) determine the reversibility of these effects at different oxygen partial pressures. Term cytotrophoblasts were incubated at 21% and 2.5% O2 for 96 hr, or were switched between the two oxygen concentrations after 48 hr. Real-time PCR and enzyme-linked immunosorbent assays (ELISAs) were used to evaluate cell fusion and differentiation, measuring transcript levels for those genes involved in cell fusion and placental angiogenesis, including VEGF, PlGF, VEGFR1, sVEGFR1, sENG, INHA, and GCM1. Cytotrophoblasts underwent fusion and differentiation in 2.5% O2 . PlGF expression was inhibited while sVEGFR1 expression increased. VEGF and sENG mRNA expressions increased in 2.5% compared to 21% O2 , but no protein was detected in the cell supernatants. Finally, GCM1 mRNA expression increased during trophoblast differentiation at 21% O2 , but was inhibited at 2.5% O2 . These mRNA expression effects were reversed by returning the cells to 21% O2 . Thus, low-oxygen partial pressure does not inhibit term-cytotrophoblast cell fusion and differentiation in vitro. Lowering the oxygen partial pressure from 21% to 2.5% caused normal-term trophoblasts to reversibly modify their expression of genes associated with placental angiogenesis. This suggests that modifications observed in pregnancy diseases such as preeclampsia or growth retardation are probably due to an extrinsic effect on trophoblasts. Copyright © 2013 Wiley Periodicals, Inc.

  10. An experimental detrending approach to attributing change of pan evaporation in comparison with the traditional partial differential method

    Science.gov (United States)

    Wang, Tingting; Sun, Fubao; Xia, Jun; Liu, Wenbin; Sang, Yanfang

    2017-04-01

    In predicting how droughts and hydrological cycles would change in a warming climate, change of atmospheric evaporative demand measured by pan evaporation (Epan) is one crucial element to be understood. Over the last decade, the derived partial differential (PD) form of the PenPan equation is a prevailing attribution approach to attributing changes to Epan worldwide. However, the independency among climatic variables required by the PD approach cannot be met using long term observations. Here we designed a series of numerical experiments to attribute changes of Epan over China by detrending each climatic variable, i.e., an experimental detrending approach, to address the inter-correlation among climate variables, and made comparison with the traditional PD method. The results show that the detrending approach is superior not only to a complicate system with multi-variables and mixing algorithm like aerodynamic component (Ep,A) and Epan, but also to a simple case like radiative component (Ep,R), when compared with traditional PD method. The major reason for this is the strong and significant inter-correlation of input meteorological forcing. Very similar and fine attributing results have been achieved based on detrending approach and PD method after eliminating the inter-correlation of input through a randomize approach. The contribution of Rh and Ta in net radiation and thus Ep,R, which has been overlooked based on the PD method but successfully detected by detrending approach, provides some explanation to the comparing results. We adopted the control run from the detrending approach and applied it to made adjustment of PD method. Much improvement has been made and thus proven this adjustment an effective way in attributing changes to Epan. Hence, the detrending approach and the adjusted PD method are well recommended in attributing changes in hydrological models to better understand and predict water and energy cycle.

  11. Acute versus chronic partial sleep deprivation in middle-aged people: differential effect on performance and sleepiness.

    Science.gov (United States)

    Philip, Pierre; Sagaspe, Patricia; Prague, Mélanie; Tassi, Patricia; Capelli, Aurore; Bioulac, Bernard; Commenges, Daniel; Taillard, Jacques

    2012-07-01

    To evaluate the effects of acute sleep deprivation and chronic sleep restriction on vigilance, performance, and self-perception of sleepiness. Habitual night followed by 1 night of total sleep loss (acute sleep deprivation) or 5 consecutive nights of 4 hr of sleep (chronic sleep restriction) and recovery night. Eighteen healthy middle-aged male participants (age [(± standard deviation] = 49.7 ± 2.6 yr, range 46-55 yr). Multiple sleep latency test trials, Karolinska Sleepiness Scale scores, simple reaction time test (lapses and 10% fastest reaction times), and nocturnal polysomnography data were recorded. Objective and subjective sleepiness increased immediately in response to sleep restriction. Sleep latencies after the second and third nights of sleep restriction reached levels equivalent to those observed after acute sleep deprivation, whereas Karolinska Sleepiness Scale scores did not reach these levels. Lapse occurrence increased after the second day of sleep restriction and reached levels equivalent to those observed after acute sleep deprivation. A statistical model revealed that sleepiness and lapses did not progressively worsen across days of sleep restriction. Ten percent fastest reaction times (i.e., optimal alertness) were not affected by acute or chronic sleep deprivation. Recovery to baseline levels of alertness and performance occurred after 8-hr recovery night. In middle-aged study participants, sleep restriction induced a high increase in sleep propensity but adaptation to chronic sleep restriction occurred beyond day 3 of restriction. This sleepiness attenuation was underestimated by the participants. One recovery night restores daytime sleepiness and cognitive performance deficits induced by acute or chronic sleep deprivation. Philip P; Sagaspe P; Prague M; Tassi P; Capelli A; Bioulac B; Commenges D; Taillard J. Acute versus chronic partial sleep deprivation in middle-aged people: differential effect on performance and sleepiness. SLEEP 2012;35(7):997-1002.

  12. Pulmonary exposure to carbonaceous nanomaterials and sperm quality.

    Science.gov (United States)

    Skovmand, Astrid; Jacobsen Lauvås, Anna; Christensen, Preben; Vogel, Ulla; Sørig Hougaard, Karin; Goericke-Pesch, Sandra

    2018-01-31

    Semen quality parameters are potentially affected by nanomaterials in several ways: Inhaled nanosized particles are potent inducers of pulmonary inflammation, leading to the release of inflammatory mediators. Small amounts of particles may translocate from the lungs into the lung capillaries, enter the systemic circulation and ultimately reach the testes. Both the inflammatory response and the particles may induce oxidative stress which can directly affect spermatogenesis. Furthermore, spermatogenesis may be indirectly affected by changes in the hormonal milieu as systemic inflammation is a potential modulator of endocrine function. The aim of this study was to investigate the effects of pulmonary exposure to carbonaceous nanomaterials on sperm quality parameters in an experimental mouse model. Effects on sperm quality after pulmonary inflammation induced by carbonaceous nanomaterials were investigated by intratracheally instilling sexually mature male NMRI mice with four different carbonaceous nanomaterials dispersed in nanopure water: graphene oxide (18 μg/mouse/i.t.), Flammruss 101, Printex 90 and SRM1650b (0.1 mg/mouse/i.t. each) weekly for seven consecutive weeks. Pulmonary inflammation was determined by differential cell count in bronchoalveolar lavage fluid. Epididymal sperm concentration and motility were measured by computer-assisted sperm analysis. Epididymal sperm viability and morphological abnormalities were assessed manually using Hoechst 33,342/PI flourescent and Spermac staining, respectively. Epididymal sperm were assessed with regard to sperm DNA integrity (damage). Daily sperm production was measured in the testis, and testosterone levels were measured in blood plasma by ELISA. Neutrophil numbers in the bronchoalveolar fluid showed sustained inflammatory response in the nanoparticle-exposed groups one week after the last instillation. No significant changes in epididymal sperm parameters, daily sperm production or plasma testosterone levels

  13. Characterization of carbonaceous solids by oxygen chemisorption

    Energy Technology Data Exchange (ETDEWEB)

    Furimsky, E.; Palmer, A.; Duguay, D.G.; McConnell, D.G.; Henson, D.E.

    1988-06-01

    Oxygen chemisorption of high and low carbon carbonaceous solids was measured in an electro-microbalance at 200 degrees C in air. A linear correlation between the amount of chemisorbed oxygen and H/C ratio as well as aromaticity was established for the high carbon solids. For the low carbon solids a linear correlation was established between the amount of chemisorbed oxygen and the content of organic matter. Experimental observations are discussed in terms of structural aspects of the solids. Oxygen chemisorption is a suitable technique for a rapid characterization of carbonaceous solids including coal. 15 refs., 7 figs., 3 tabs.

  14. Methods for constructing exact solutions of partial differential equations mathematical and analytical techniques with applications to engineering

    CERN Document Server

    Meleshko, Sergey V

    2005-01-01

    Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.

  15. The pseudo-compartment method for coupling partial differential equation and compartment-based models of diffusion.

    Science.gov (United States)

    Yates, Christian A; Flegg, Mark B

    2015-05-06

    Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs), which assumes there are sufficient densities of particles that a continuum approximation is valid. However, owing to recent advances in computational power, the simulation and therefore postulation, of computationally intensive individual-based models has become a popular way to investigate the effects of noise in reaction-diffusion systems in which regions of low copy numbers exist. The specific stochastic models with which we shall be concerned in this manuscript are referred to as 'compartment-based' or 'on-lattice'. These models are characterized by a discretization of the computational domain into a grid/lattice of 'compartments'. Within each compartment, particles are assumed to be well mixed and are permitted to react with other particles within their compartment or to transfer between neighbouring compartments. Stochastic models provide accuracy, but at the cost of significant computational resources. For models that have regions of both low and high concentrations, it is often desirable, for reasons of efficiency, to employ coupled multi-scale modelling paradigms. In this work, we develop two hybrid algorithms in which a PDE in one region of the domain is coupled to a compartment-based model in the other. Rather than attempting to balance average fluxes, our algorithms answer a more fundamental question: 'how are individual particles transported between the vastly different model descriptions?' First, we present an algorithm derived by carefully redefining the continuous PDE concentration as a probability distribution. While this first algorithm shows very strong convergence to analytical solutions of test problems, it can be cumbersome to simulate. Our second algorithm is a simplified and more efficient implementation of

  16. Series expansion solutions for the multi-term time and space fractional partial differential equations in two- and three-dimensions

    Science.gov (United States)

    Ye, H.; Liu, F.; Turner, I.; Anh, V.; Burrage, K.

    2013-09-01

    Fractional partial differential equations with more than one fractional derivative in time describe some important physical phenomena, such as the telegraph equation, the power law wave equation, or the Szabo wave equation. In this paper, we consider two- and three-dimensional multi-term time and space fractional partial differential equations. The multi-term time-fractional derivative is defined in the Caputo sense, whose order belongs to the interval (1,2],(2,3],(3,4] or (0, m], and the space-fractional derivative is referred to as the fractional Laplacian form. We derive series expansion solutions based on a spectral representation of the Laplacian operator on a bounded region. Some applications are given for the two- and three-dimensional telegraph equation, power law wave equation and Szabo wave equation.

  17. A comparison of numerical solutions of partial differential equations with probabilistic and possibilistic parameters for the quantification of uncertainty in subsurface solute transport.

    Science.gov (United States)

    Zhang, Kejiang; Achari, Gopal; Li, Hua

    2009-11-03

    Traditionally, uncertainty in parameters are represented as probabilistic distributions and incorporated into groundwater flow and contaminant transport models. With the advent of newer uncertainty theories, it is now understood that stochastic methods cannot properly represent non random uncertainties. In the groundwater flow and contaminant transport equations, uncertainty in some parameters may be random, whereas those of others may be non random. The objective of this paper is to develop a fuzzy-stochastic partial differential equation (FSPDE) model to simulate conditions where both random and non random uncertainties are involved in groundwater flow and solute transport. Three potential solution techniques namely, (a) transforming a probability distribution to a possibility distribution (Method I) then a FSPDE becomes a fuzzy partial differential equation (FPDE), (b) transforming a possibility distribution to a probability distribution (Method II) and then a FSPDE becomes a stochastic partial differential equation (SPDE), and (c) the combination of Monte Carlo methods and FPDE solution techniques (Method III) are proposed and compared. The effects of these three methods on the predictive results are investigated by using two case studies. The results show that the predictions obtained from Method II is a specific case of that got from Method I. When an exact probabilistic result is needed, Method II is suggested. As the loss or gain of information during a probability-possibility (or vice versa) transformation cannot be quantified, their influences on the predictive results is not known. Thus, Method III should probably be preferred for risk assessments.

  18. Normal differential renal function does not indicate a normal kidney after partial ureteropelvic obstruction and subsequent relief in 2-week-old piglets

    Energy Technology Data Exchange (ETDEWEB)

    Dissing, Thomas H.; Mikkelsen, Mette Marie; Pedersen, Michael; Froekiaer, Joergen; Djurhuus, Jens Christian [University of Aarhus, Institute of Clinical Medicine, Aarhus (Denmark); Eskild-Jensen, Anni [Aarhus University Hospital, Department of Nuclear Medicine, Aarhus Sygehus, Aarhus (Denmark); Gordon, Isky [University College London, Institute of Child Health, London (United Kingdom); University College London, Radiology and Physics Unit, Institute of Child Health, London (United Kingdom)

    2008-09-15

    We investigated the functional consequences of relieving ureteric obstruction in young pigs with experimental hydronephrosis (HN) induced by partial unilateral ureteropelvic obstruction. Three groups of animals were followed from the age of 2 weeks to the age of 14 weeks: Eight animals had severe or grades 3-4 HN throughout the study. Six animals had relief of the obstruction after 4 weeks. Six animals received sham operations at both ages. Morphological and functional examinations were performed at age 6 weeks and again at age 14 weeks and consisted of magnetic resonance imaging (MRI), technetium-diethylenetriaminepentaaceticacid ({sup 99m}Tc-DTPA) renography, renal technetium-dimercaptosuccinicacid ({sup 99m}Tc-DMSA) scintigraphy, and glomerular filtration rate (GFR) measurement. After relief of the partial obstruction, there was reduction of the pelvic diameter and improvement of urinary drainage. Global and relative kidney function was not significantly affected by either obstruction or its relief. Renal {sup 99m}Tc-DMSA scintigraphy showed a change in both the appearance of the kidney and a change in the distribution within kidneys even after relief of obstruction. This study shows that partial ureteric obstruction in young pigs may be associated with little effect on global and differential kidney function. However, even after relief of HN, the distribution of {sup 99m}Tc-DMSA in the kidney remains abnormal suggesting that a normal differential renal function may not represent a normal kidney. (orig.)

  19. Lactobacillus strain diversity based on partial hsp60 gene sequences and design of PCR-restriction fragment length polymorphism assays for species identification and differentiation.

    Science.gov (United States)

    Blaiotta, Giuseppe; Fusco, Vincenzina; Ercolini, Danilo; Aponte, Maria; Pepe, Olimpia; Villani, Francesco

    2008-01-01

    A phylogenetic tree showing diversities among 116 partial (499-bp) Lactobacillus hsp60 (groEL, encoding a 60-kDa heat shock protein) nucleotide sequences was obtained and compared to those previously described for 16S rRNA and tuf gene sequences. The topology of the tree produced in this study showed a Lactobacillus species distribution similar, but not identical, to those previously reported. However, according to the most recent systematic studies, a clear differentiation of 43 single-species clusters was detected/identified among the sequences analyzed. The slightly higher variability of the hsp60 nucleotide sequences than of the 16S rRNA sequences offers better opportunities to design or develop molecular assays allowing identification and differentiation of either distant or very closely related Lactobacillus species. Therefore, our results suggest that hsp60 can be considered an excellent molecular marker for inferring the taxonomy and phylogeny of members of the genus Lactobacillus and that the chosen primers can be used in a simple PCR procedure allowing the direct sequencing of the hsp60 fragments. Moreover, in this study we performed a computer-aided restriction endonuclease analysis of all 499-bp hsp60 partial sequences and we showed that the PCR-restriction fragment length polymorphism (RFLP) patterns obtainable by using both endonucleases AluI and TacI (in separate reactions) can allow identification and differentiation of all 43 Lactobacillus species considered, with the exception of the pair L. plantarum/L. pentosus. However, the latter species can be differentiated by further analysis with Sau3AI or MseI. The hsp60 PCR-RFLP approach was efficiently applied to identify and to differentiate a total of 110 wild Lactobacillus strains (including closely related species, such as L. casei and L. rhamnosus or L. plantarum and L. pentosus) isolated from cheese and dry-fermented sausages.

  20. Antarctic carbonaceous chondrites - New opportunities for research

    Science.gov (United States)

    McSween, Harry Y., Jr.

    An account is given of the types of carbonaceous meteorites available in the Antarctic collections of the U.S. and Japan. In the case of the collection for Victoria Land and Queen Maud Land, all known classes for meteorites except C1 are present; available pairing data, though limited, are indicative of the presence of many different falls. Thus far, attention has been focused on the largest meteorites. Most samples, however, are small.

  1. Carbonaceous aerosol at two rural locations in New York State: Characterization and behavior

    Science.gov (United States)

    Sunder Raman, Ramya; Hopke, Philip K.; Holsen, Thomas M.

    2008-06-01

    Fine particle samples were collected to determine the chemical constituents in PM2.5 at two rural background sites (Potsdam and Stockton, N. Y.) in the northeastern United States from November 2002 to August 2005. Samples were collected every third day for 24 h with a speciation network sampler. The measured carbonaceous species included thermal-optical organic carbon (OC), elemental carbon (EC), pyrolytic carbon (OP), black carbon (BC), and water-soluble, short-chain (WSSC) organic acids. Concentration time series, autocorrelations, and seasonal variations of the carbonaceous species were examined. During this multiyear period, the contributions of the total carbon (OC + EC) to the measured fine particle mass were 31.2% and 31.1% at Potsdam and Stockton, respectively. The average sum of the WSSC acids carbon accounted for approximately 2.5% of the organic carbon at Potsdam and 3.0% at Stockton. At Potsdam, the seasonal differences in the autocorrelation function (ACF) and partial autocorrelation function (PACF) values for carbonaceous species suggest that secondary formation may be an important contributor to the observed concentrations of species likely to be secondary in origin, particularly during the photochemically active time of the year (May to October). This study also investigated the relationships between carbonaceous species to better understand the behavior of carbonaceous aerosol and to assess the contribution of secondary organic carbon (SOC) to the total organic carbon mass (the EC tracer method was used to estimate SOC). At Potsdam the average SOC contribution to total OC varied between 66% and 72%, while at Stockton it varied between 58% and 64%.

  2. Baking process of thin plate carbonaceous compact

    Energy Technology Data Exchange (ETDEWEB)

    Suzuki, Yoshio; Shimada, Toyokazu

    1987-06-27

    As a production process of a thin plate carbonaceous compact for separator of phosphoric acid fuel cell, there is a process to knead carbonaceous powder and thermosetting resin solution, to form and harden the kneaded material and then to bake, carbonize and graphitize it. However in this baking and carbonization treatment, many thin plate compacts are set in a compiled manner within a heating furnace and receive a heat treatment from their circumference. Since the above compacts to be heated tend generally to be heated from their peripheries, their baked conditions are not homogeneous easily causing the formation of cracks, etc.. As a process to heat and bake homogeneously by removing the above problematical points, this invention offers a process to set in a heating furnace a laminate consisting of the lamination of thin plate carbonaceous compacts and the heat resistant soaking plates which hold the upper and lower ends of the above lamination, to fill the upper and under peripheries of the laminate above with high heat conductive packing material and its side periphery with low heat conductive packing material respectively and to heat and sinter it. In addition, the invention specifies the high and low heat conductive packing materials respectively. (1 fig, 2 tabs)

  3. The Thermal Properties of CM Carbonaceous Chondrites

    Science.gov (United States)

    Britt, D. T.; Opeil, C.

    2017-12-01

    The physical properties of asteroid exploration targets are fundamental parameters for developing models, planning observations, mission operations, reducing operational risk, and interpreting mission results. Until we have returned samples, meteorites represent our "ground truth" for the geological material we expect to interact with, sample, and interpret on the surfaces of asteroids. The physical properties of the volatile-rich carbonaceous chondrites (CI, C2, CM, and CR groups) are of particular interest because of their high resource potential. We have measured the thermal conductivity, heat capacity and thermal expansion of five CM carbonaceous chondrites (Murchison, Murray, Cold Bokkeveld, NWA 7309, Jbilet Winselwan) at low temperatures (5-300 K) to mimic the conditions in the asteroid belt. The mineralogy of these meteorites are dominated by abundant hydrous phyllosilicates, but also contain anhydrous minerals such as olivine and pyroxene found in chondrules. The thermal expansion measurements for all these CMs indicate a substantial increase in meteorite volume as temperature decreases from 230 - 210 K followed by linear contraction below 210 K. Such transitions were unexpected and are not typical for anhydrous carbonaceous chondrites or ordinary chondrites. Our thermal diffusivity results compare well with previous estimates for similar meteorites, where conductivity was derived from diffusivity measurements and modeled heat capacities; our new values are of a higher precision and cover a wider range of temperatures.

  4. Effect of runway training on rat brain tyrosine hydroxylase: differential effect of continuous and partial reinforcement schedules.

    Science.gov (United States)

    Boarder, M R; Feldon, J; Gray, J A; Fillenz, M

    1979-12-01

    Previous experiments have implicated ascending noradrenergic systems in the development of the behavioural responses to different patterns of reward. In this report food deprived male Sprague--Dawley rats were trained to run a straight alley for good reward on a continuous reinforcement (CRF) or a partial reinforcement (PRF) schedule. Tyrosine hydroxylase measured in a partially solubilized preparation from hippocampus and hypothalamus at the end of acquisition was not different from controls, indicating that enzyme induction does not occur during either training schedules. However, hippocampal synaptosomal tyrosine hydroxylation rates from the CRF group was significantly higher than from either the PRF group or the handled controls. This indicates that at the end of the acquisition schedule the noradrenergic projection to hippocampus was more active in the CRF group than with the PRF group or the handled control.

  5. Differential mode EMI filter design for ultra high efficiency partial parallel isolated full-bridge boost converter

    DEFF Research Database (Denmark)

    Makda, Ishtiyaq Ahmed; Nymand, M.

    2013-01-01

    for such application, it calls for a carefully optimized EMI filter which is designed and implemented in this work. Moreover, the negative input impedance of the regulated converter is extremely low; well-designed filter damping branch is also included. Differential mode noise is analyzed analytically for a 3KW/400V...

  6. On a partial differential equation method for determining the free energies and coexisting phase compositions of ternary mixtures from light scattering data.

    Science.gov (United States)

    Ross, David S; Thurston, George M; Lutzer, Carl V

    2008-08-14

    In this paper we present a method for determining the free energies of ternary mixtures from light scattering data. We use an approximation that is appropriate for liquid mixtures, which we formulate as a second-order nonlinear partial differential equation. This partial differential equation (PDE) relates the Hessian of the intensive free energy to the efficiency of light scattering in the forward direction. This basic equation applies in regions of the phase diagram in which the mixtures are thermodynamically stable. In regions in which the mixtures are unstable or metastable, the appropriate PDE is the nonlinear equation for the convex hull. We formulate this equation along with continuity conditions for the transition between the two equations at cloud point loci. We show how to discretize this problem to obtain a finite-difference approximation to it, and we present an iterative method for solving the discretized problem. We present the results of calculations that were done with a computer program that implements our method. These calculations show that our method is capable of reconstructing test free energy functions from simulated light scattering data. If the cloud point loci are known, the method also finds the tie lines and tie triangles that describe thermodynamic equilibrium between two or among three liquid phases. A robust method for solving this PDE problem, such as the one presented here, can be a basis for optical, noninvasive means of characterizing the thermodynamics of multicomponent mixtures.

  7. A fast direct method for block triangular Toeplitz-like with tri-diagonal block systems from time-fractional partial differential equations

    Science.gov (United States)

    Ke, Rihuan; Ng, Michael K.; Sun, Hai-Wei

    2015-12-01

    In this paper, we study the block lower triangular Toeplitz-like with tri-diagonal blocks system which arises from the time-fractional partial differential equation. Existing fast numerical solver (e.g., fast approximate inversion method) cannot handle such linear system as the main diagonal blocks are different. The main contribution of this paper is to propose a fast direct method for solving this linear system, and to illustrate that the proposed method is much faster than the classical block forward substitution method for solving this linear system. Our idea is based on the divide-and-conquer strategy and together with the fast Fourier transforms for calculating Toeplitz matrix-vector multiplication. The complexity needs O (MNlog2 ⁡ M) arithmetic operations, where M is the number of blocks (the number of time steps) in the system and N is the size (number of spatial grid points) of each block. Numerical examples from the finite difference discretization of time-fractional partial differential equations are also given to demonstrate the efficiency of the proposed method.

  8. 16S partial gene mitochondrial DNA and internal transcribed spacers ribosomal DNA as differential markers of Trichuris discolor populations.

    Science.gov (United States)

    Callejón, R; Halajian, A; de Rojas, M; Marrugal, A; Guevara, D; Cutillas, C

    2012-05-25

    Comparative morphological, biometrical and molecular studies of Trichuris discolor isolated from Bos taurus from Spain and Iran was carried out. Furthermore, Trichuris ovis isolated from B. taurus and Capra hircus from Spain has been, molecularly, analyzed. Morphological studies revealed clear differences between T. ovis and T. discolor isolated from B. taurus but differences were not observed between populations of T. discolor isolated from different geographical regions. Nevertheless, the molecular studies based on the amplification and sequencing of the internal transcribed spacers 1 and 2 ribosomal DNA and 16S partial gene mitochondrial DNA showed clear differences between both populations of T. discolor from Spain and Iran suggesting two cryptic species. Phylogenetic studies corroborated these data. Thus, phylogenetic trees based on ITS1, ITS2 and 16S partial gene sequences showed that individuals of T. discolor from B. taurus from Iran clustered together and separated, with high bootstrap values, of T. discolor isolated from B. taurus from Spain, while populations of T. ovis from B. taurus and C. hircus from Spain clustered together but separated with high bootstrap values of both populations of T. discolor. Furthermore, a comparative phylogenetic study has been carried out with the ITS1and ITS2 sequences of Trichuris species from different hosts. Three clades were observed: the first clustered all the species of Trichuris parasitizing herbivores (T. discolor, T. ovis, Trichuris leporis and Trichuris skrjabini), the second clustered all the species of Trichuris parasitizing omnivores (Trichuris trichiura and Trichuris suis) and finally, the third clustered species of Trichuris parasitizing carnivores (Trichuris muris, Trichuris arvicolae and Trichuris vulpis). Copyright © 2011 Elsevier B.V. All rights reserved.

  9. Pressure hydrogenation of solid carbonaceous material

    Energy Technology Data Exchange (ETDEWEB)

    Pier, M; Kroenig, W

    1942-09-28

    A process is described for the continuous pressure hydrogenation of solid, nonfusible carbonaceous material, such as coal, oil shale, or peat, in a pasted condition, characterized in that the charge is heated in a known way under pressure, together with water, nearly to the reaction temperature, then it is led into a pressure vessel, whose volume amounts to 20 to 40% of the usual reaction space without any change at the same temperature, and the charge then goes through the reaction vessel, after which its temperature is raised to the reaction height.

  10. Destructive hydrogenation of carbonaceous material, etc

    Energy Technology Data Exchange (ETDEWEB)

    1938-07-30

    A process is described for the destructive hydrogenation of solid distillable carbonaceous material, consisting of mixing the raw material in a paste by means of a mixture practically free from asphalt, from an oil obtained initially from the products coming out of the reaction space as vapor, particularly heavy oil, and oils obtained by pushing just to the state of pitch or coke the distillation of all the products which come out of the reaction space in any state but the vapor and which restrain some of the raw material intact and part of the products.

  11. Traveling wave solutions to some nonlinear fractional partial differential equations through the rational (G′/G-expansion method

    Directory of Open Access Journals (Sweden)

    Tarikul Islam

    2018-03-01

    Full Text Available In this article, the analytical solutions to the space-time fractional foam drainage equation and the space-time fractional symmetric regularized long wave (SRLW equation are successfully examined by the recently established rational (G′/G-expansion method. The suggested equations are reduced into the nonlinear ordinary differential equations with the aid of the fractional complex transform. Consequently, the theories of the ordinary differential equations are implemented effectively. Three types closed form traveling wave solutions, such as hyperbolic function, trigonometric function and rational, are constructed by using the suggested method in the sense of conformable fractional derivative. The obtained solutions might be significant to analyze the depth and spacing of parallel subsurface drain and small-amplitude long wave on the surface of the water in a channel. It is observed that the performance of the rational (G′/G-expansion method is reliable and will be used to establish new general closed form solutions for any other NPDEs of fractional order.

  12. A method based on the Jacobi tau approximation for solving multi-term time-space fractional partial differential equations

    Science.gov (United States)

    Bhrawy, A. H.; Zaky, M. A.

    2015-01-01

    In this paper, we propose and analyze an efficient operational formulation of spectral tau method for multi-term time-space fractional differential equation with Dirichlet boundary conditions. The shifted Jacobi operational matrices of Riemann-Liouville fractional integral, left-sided and right-sided Caputo fractional derivatives are presented. By using these operational matrices, we propose a shifted Jacobi tau method for both temporal and spatial discretizations, which allows us to present an efficient spectral method for solving such problem. Furthermore, the error is estimated and the proposed method has reasonable convergence rates in spatial and temporal discretizations. In addition, some known spectral tau approximations can be derived as special cases from our algorithm if we suitably choose the corresponding special cases of Jacobi parameters θ and ϑ. Finally, in order to demonstrate its accuracy, we compare our method with those reported in the literature.

  13. Separation of volatile products from solid carbonaceous materials

    Energy Technology Data Exchange (ETDEWEB)

    White, W W

    1915-10-19

    A process is set forth for the separation of volatile products from solid carbonaceous materials, in which the vapors produced from the carbonaceous material at higher temperatures and withdrawn into the separate vapor chamber are led in succession through the lower temperature vapors as continuously to deposit their condensible ingredients in the chamber by the action of the successive cooler vapors.

  14. Simulation, optimal control and parametric sensitivity analysis of a molten carbonate fuel cell using a partial differential algebraic dynamic equation system; Simulation, Optimale Steuerung und Sensitivitaetsanalyse einer Schmelzkarbonat-Brennstoffzelle mithilfe eines partiellen differential-algebraischen dynamischen Gleichungssystems

    Energy Technology Data Exchange (ETDEWEB)

    Sternberg, K

    2007-02-08

    Molten carbonate fuel cells (MCFCs) allow an efficient and environmentally friendly energy production by converting the chemical energy contained in the fuel gas in virtue of electro-chemical reactions. In order to predict the effect of the electro-chemical reactions and to control the dynamical behavior of the fuel cell a mathematical model has to be found. The molten carbonate fuel cell (MCFC) can indeed be described by a highly complex,large scale, semi-linear system of partial differential algebraic equations. This system includes a reaction-diffusion-equation of parabolic type, several reaction-transport-equations of hyperbolic type, several ordinary differential equations and finally a system of integro-differential algebraic equations which describes the nonlinear non-standard boundary conditions for the entire partial differential algebraic equation system (PDAE-system). The existence of an analytical or the computability of a numerical solution for this high-dimensional PDAE-system depends on the kind of the differential equations and their special characteristics. Apart from theoretical investigations, the real process has to be controlled, more precisely optimally controlled. Hence, on the basis of the PDAE-system an optimal control problem is set up, whose analytical and numerical solvability is closely linked to the solvability of the PDAE-system. Moreover the solution of that optimal control problem is made more difficult by inaccuracies in the underlying database, which does not supply sufficiently accurate values for the model parameters. Therefore the optimal control problem must also be investigated with respect to small disturbances of model parameters. The aim of this work is to analyze the relevant dynamic behavior of MCFCs and to develop concepts for their optimal process control. Therefore this work is concerned with the simulation, the optimal control and the sensitivity analysis of a mathematical model for MCDCs, which can be characterized

  15. Radiocarbon: nature's tracer for carbonaceous pollutants

    International Nuclear Information System (INIS)

    Currie, L.A.; Klouda, G.A.; Gerlach, R.W.

    1982-01-01

    Recent developments in radiocarbon dating techniques have made it feasible to determine 14 C/ 12 C ratios in samples containing milligram or even microgram quantities of carbon. As a result, it has become practicable to apply these techniques to the study of trace gases and particles in the atmosphere, as a means of resolving anthropogenic from natural source components. Interpretation of 14 C data is straightforward: biospheric carbon (such as vegetation) is alive with a 14 C/ 12 C ratio of about 1.5 x 10 -12 , whereas fossil carbon is dead. Beyond this dichotomous classification it becomes very interesting to combine the isotopic data with concurrent chemical data, as well as spatial and temporal distributions, in order to infer the strengths of specific sources of carbonaceous pollutants. A brief review will be presented of our program on atmospheric gases and carbonaceous particles. For the latter, we have assayed individual chemical and size fractions, and samples collected in urban, rural, and remote locales. The biogenic carbon fraction - presumably from wood-burning - ranged from 10% to 100% for the urban samples analyzed

  16. Partial coupling and differential regulation of biologically and photochemically labile dissolved organic carbon across boreal aquatic networks

    Science.gov (United States)

    Lapierre, J.-F.; del Giorgio, P. A.

    2014-10-01

    continental watersheds resulted in a partial coupling of those carbon pools in natural freshwaters, despite fundamental contrasts in terms of their composition and regulation.

  17. Partial coupling and differential regulation of biologically and photo-chemically labile dissolved organic carbon across boreal aquatic networks

    Science.gov (United States)

    Lapierre, J.-F.; del Giorgio, P. A.

    2014-05-01

    Despite the rapidly increasing volume of research on the biological and photochemical degradation of DOC in aquatic environments, little is known on the large-scale patterns in biologically and photo-chemically degradable DOC (Bd-DOC and Pd-DOC, respectively) in continental watersheds, and on the links that exist between these two key properties that greatly influence the flow of carbon from continents to oceans. Here we explore the patterns of Bd- and Pd-DOC across hundreds of boreal lakes, rivers and wetlands spanning a large range of system trophy and terrestrial influence, and compared the drivers of these two reactive pools of DOC at the landscape level. Using standardized incubations of natural waters, we found that the concentrations of Bd- and Pd-DOC co-varied across all systems studied but were nevertheless related to different pools of dissolved organic matter (DOM, identified by fluorescence analyses) in ambient waters. A combination of nutrients and protein-like DOM explained nearly half of the variation in Bd-DOC, whereas Pd-DOC was exclusively predicted by DOM optical properties, consistent with the photochemical degradability of specific fluorescent DOM (FDOM) pools that we experimentally determined. The concentrations of colored DOM (CDOM), a proxy of terrestrial influence, almost entirely accounted for the observed relationship between FDOM and the concentrations of both Bd- and Pd-DOC. The concentrations of CDOM and of the putative bio-labile fluorescence component shifted from complete decoupling in clear-water environments to strong coupling in browner streams and wetlands. This suggests a baseline autochthonous Bd-DOC pool fuelled by internal production that is gradually overwhelmed by land-derived Bd-DOC as terrestrial influence increases across landscape gradients. The importance of land as a major source of both biologically and photo-chemically degradable DOC for continental watersheds resulted in a partial coupling of those carbon pools in

  18. Retinal genes are differentially expressed in areas of primary versus secondary degeneration following partial optic nerve injury.

    Directory of Open Access Journals (Sweden)

    Wissam Chiha

    Full Text Available Partial transection (PT of the optic nerve is an established experimental model of secondary degeneration in the central nervous system. After a dorsal transection, retinal ganglion cells (RGCs with axons in ventral optic nerve are intact but vulnerable to secondary degeneration, whereas RGCs in dorsal retina with dorsal axons are affected by primary and secondary injuries. Using microarray, we quantified gene expression changes in dorsal and ventral retina at 1 and 7 days post PT, to characterize pathogenic pathways linked to primary and secondary degeneration.In comparison to uninjured retina Cryba1, Cryba2 and Crygs, were significantly downregulated in injured dorsal retina at days 1 and 7. While Ecel1, Timp1, Mt2A and CD74, which are associated with reducing excitotoxicity, oxidative stress and inflammation, were significantly upregulated. Genes associated with oxygen binding pathways, immune responses, cytokine receptor activity and apoptosis were enriched in dorsal retina at day 1 after PT. Oxygen binding and apoptosis remained enriched at day 7, as were pathways involved in extracellular matrix modification. Fewer changes were observed in ventral retina at day 1 after PT, most associated with the regulation of protein homodimerization activity. By day 7, apoptosis, matrix organization and signal transduction pathways were enriched. Discriminant analysis was also performed for specific functional gene groups to compare expression intensities at each time point. Altered expression of selected genes (ATF3, GFAP, Ecel1, TIMP1, Tp53 and proteins (GFAP, ECEL1 and ATF3 were semi-quantitatively assessed by qRT-PCR and immunohistochemistry respectively.There was an acute and complex primary injury response in dorsal retina indicative of a dynamic interaction between neuroprotective and neurodegenerative events; ventral retina vulnerable to secondary degeneration showed a delayed injury response. Both primary and secondary injury resulted in the

  19. CPDES2: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in two dimensions

    Science.gov (United States)

    Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

    1988-11-01

    Many physical problems require the solution of coupled partial differential equations on two-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES2 allows each spatial operator to have 5 or 9 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect indices which is vectorizable on some of the newer scientific computers.

  20. Inclusion of exact exchange in the noniterative partial-differential-equation method of electron-molecule scattering - Application to e-N2

    Science.gov (United States)

    Weatherford, C. A.; Onda, K.; Temkin, A.

    1985-01-01

    The noniterative partial-differential-equation (PDE) approach to electron-molecule scattering of Onda and Temkin (1983) is modified to account for the effects of exchange explicitly. The exchange equation is reduced to a set of inhomogeneous equations containing no integral terms and solved noniteratively in a difference form; a method for propagating the solution to large values of r is described; the changes in the polarization potential of the original PDE method required by the inclusion of exact static exchange are indicated; and the results of computations for e-N2 scattering in the fixed-nuclei approximation are presented in tables and graphs and compared with previous calculations and experimental data. Better agreement is obtained using the modified PDE method.

  1. Colon cancer metastasis to the mandibular gingiva with partial occult squamous differentiation: A case report and literature review.

    Science.gov (United States)

    Ren, Quan-Guang; Huang, Tao; Yang, Sheng-Li; Hu, Jian-Li

    2017-02-01

    Metastasis is the primary cause of death among patients with colon cancer. However, the number of available studies regarding oral cavity metastases from colon cancer is currently limited. We herein report an unusual case of a 60-year-old male patient who developed an oral cavity metastasis from colon cancer. A total of 12 clinical case studies reporting colon cancer metastases to the mandibular gingival region were also reviewed, with the aim to elucidate the clinical and pathological characteristics of this disease entity in order to improve clinical diagnosis and treatment. It was demonstrated that patients with oral cavity metastases from colon cancer were predominantly in the sixth or seventh decades of life. The mandible was the main site of metastatic tumors to the oral cavity, while the occurrence of gingival metastases was comparatively rare. Moreover, the diagnoses of an oral metastatic tumor and primary colon cancer were often synchronous and were frequently accompanied with metastases to other organs. Several key aspects were suggested that should be accounted for when diagnosing colon cancer patients, including focusing attention to oral symptoms when examining cancer patients, utilizing a multidisciplinary approach for differential diagnosis and utilizing postoperative pathological examination to accurately diagnose the type of tumor and optimize the efficacy of treatment.

  2. Global cloud condensation nuclei influenced by carbonaceous combustion aerosol

    Directory of Open Access Journals (Sweden)

    D. V. Spracklen

    2011-09-01

    Full Text Available Black carbon in carbonaceous combustion aerosol warms the climate by absorbing solar radiation, meaning reductions in black carbon emissions are often perceived as an attractive global warming mitigation option. However, carbonaceous combustion aerosol can also act as cloud condensation nuclei (CCN so they also cool the climate by increasing cloud albedo. The net radiative effect of carbonaceous combustion aerosol is uncertain because their contribution to CCN has not been evaluated on the global scale. By combining extensive observations of CCN concentrations with the GLOMAP global aerosol model, we find that the model is biased low (normalised mean bias = −77 % unless carbonaceous combustion aerosol act as CCN. We show that carbonaceous combustion aerosol accounts for more than half (52–64 % of global CCN with the range due to uncertainty in the emitted size distribution of carbonaceous combustion particles. The model predicts that wildfire and pollution (fossil fuel and biofuel carbonaceous combustion aerosol causes a global mean cloud albedo aerosol indirect effect of −0.34 W m−2, with stronger cooling if we assume smaller particle emission size. We calculate that carbonaceous combustion aerosol from pollution sources cause a global mean aerosol indirect effect of −0.23 W m−2. The small size of carbonaceous combustion particles from fossil fuel sources means that whilst pollution sources account for only one-third of the emitted mass they cause two-thirds of the cloud albedo aerosol indirect effect that is due to carbonaceous combustion aerosol. This cooling effect must be accounted for, along with other cloud effects not studied here, to ensure that black carbon emissions controls that reduce the high number concentrations of fossil fuel particles have the desired net effect on climate.

  3. Tandem differential mobility analysis-mass spectrometry reveals partial gas-phase collapse of the GroEL complex.

    Science.gov (United States)

    Hogan, Christopher J; Ruotolo, Brandon T; Robinson, Carol V; Fernandez de la Mora, Juan

    2011-04-07

    A parallel-plate differential mobility analyzer and a time-of-flight mass spectrometer (DMA-MS) are used in series to measure true mobility in dry atmospheric pressure air for mass-resolved electrosprayed GroEL tetradecamers (14-mers; ~800 kDa). Narrow mobility peaks are found (2.6-2.9% fwhm); hence, precise mobilities can be obtained for these ions without collisional activation, just following their generation by electrospray ionization. In contrast to previous studies, two conformers are found with mobilities (Z) differing by ~5% at charge state z ~ 79. By extrapolating to small z, a common mobility/charge ratio Z(0)/z = 0.0117 cm(2) V(-1) s(-1) is found for both conformers. When interpreted as if the GroEL ion surface were smooth and the gas molecule-protein collisions were perfectly elastic and specular, this mobility yields an experimental collision cross section, Ω, 11% smaller than in an earlier measurement, and close to the cross section, A(C,crystal), expected for the crystal structure (determined by a geometric approximation). However, the similarity between Ω and A(C,crystal) does not imply a coincidence between the native and gas-phase structures. The nonideal nature of protein-gas molecule collisions introduces a drag enhancement factor, ξ = 1.36, with which the true cross section A(C) is related to Ω via A(C) = Ω/ξ. Therefore, A(C) for GroEL 14-mer ions determined by DMA measurements is 0.69A(C,crystal). The factor 1.36 used here is based on the experimental Stokes-Millikan equation, as well as on prior and new numerical modeling accounting for multiple scattering events via exact hard-sphere scattering calculations. Therefore, we conclude that the gas-phase structure of the GroEL complex as electrosprayed is substantially more compact than the corresponding X-ray crystal structure.

  4. Laboratory study of carbonaceous dust and molecules of astrochemical interest

    International Nuclear Information System (INIS)

    Cataldo, F; Garcia-Hernandez, D A; Manchado, A; Kwok, S

    2016-01-01

    In this paper are reviewed some research works dedicated to the study of carbonaceous dust and molecules of astrochemical interest. First of all it is discussed the carbon arc through which it is possible to produce carbon soot and fullerenes under helium but also many other different products just changing the arcing conditions. For example, when the carbon arc is struck in an hydrocarbon solvent it is possible to produce and trap polyynes in the solvent. Monocyanopolyynes and dicyanopolyynes can be produced as well by selecting the appropriate conditions. Amorphous carbon soot or partially graphitized carbon black can be produced with the carbon arc. Fullerenes were found in space thanks to the reference infrared spectra and the absorption cross sections which were determined in laboratory. Fullerenes are readily reactive with hydrogen yielding fulleranes the hydrogenated fullerenes. Furthermore fullerenes react with PAHs and with iron carbonyl yielding adducts. All these fullerene derivatives were synthesized and their reference spectra recorded in laboratory. It was proposed that petroleum fractions can be used as model substrates in the explanation of the carriers of the AIB (Aromatic Infrared Bands) observed in protoplanetary and planetary nebulae and the UIE (Unidentified Infrared Bands) found in the interstellar medium. (paper)

  5. Cloud albedo increase from carbonaceous aerosol

    Directory of Open Access Journals (Sweden)

    W. R. Leaitch

    2010-08-01

    Full Text Available Airborne measurements from two consecutive days, analysed with the aid of an aerosol-adiabatic cloud parcel model, are used to study the effect of carbonaceous aerosol particles on the reflectivity of sunlight by water clouds. The measurements, including aerosol chemistry, aerosol microphysics, cloud microphysics, cloud gust velocities and cloud light extinction, were made below, in and above stratocumulus over the northwest Atlantic Ocean. On the first day, the history of the below-cloud fine particle aerosol was marine and the fine particle sulphate and organic carbon mass concentrations measured at cloud base were 2.4 μg m−3 and 0.9 μg m−3 respectively. On the second day, the below-cloud aerosol was continentally influenced and the fine particle sulphate and organic carbon mass concentrations were 2.3 μg m−3 and 2.6 μg m−3 respectively. Over the range 0.06–0.8 μm diameter, the shapes of the below-cloud size distributions were similar on both days and the number concentrations were approximately a factor of two higher on the second day. The cloud droplet number concentrations (CDNC on the second day were approximately three times higher than the CDNC measured on the first day. Using the parcel model to separate the influence of the differences in gust velocities, we estimate from the vertically integrated cloud light scattering measurements a 6% increase in the cloud albedo principally due to the increase in the carbonaceous components on the second day. Assuming no additional absorption by this aerosol, a 6% albedo increase translates to a local daytime radiative cooling of ∼12 W m−2. This result provides observational evidence that the role of anthropogenic carbonaceous components in the cloud albedo effect can be much larger than that of anthropogenic sulphate, as some global simulations have indicated.

  6. Characterization of combustion-generated carbonaceous nanoparticles by size-dependent ultraviolet laser photoionization.

    Science.gov (United States)

    Commodo, Mario; Sgro, Lee Anne; Minutolo, Patrizia; D'Anna, Andrea

    2013-05-16

    Photoelectric charging of particles is a powerful tool for online characterization of submicrometer aerosol particles. Indeed photoionization based techniques have high sensitivity and chemical selectivity. Moreover, they yield information on electronic properties of the material and are sensitive to the state of the surface. In the present study the photoionization charging efficiency, i.e., the ratio between the generated positive ions and the corresponding neutral ones, for different classes of flame-generated carbonaceous nanoparticles was measured. The fifth harmonics of a Nd:YAG laser, 213 nm (5.82 eV), was used as an ionization source for the combustion generated nanoparticles, whereas a differential mobility analyzer (DMA) coupled to a Faraday cup electrometer was used for particle classification and detection. Carbonaceous nanoparticles in the nucleation mode, i.e., sizes ranging from 1 to 10 nm, show a photoionization charging efficiency clearly dependent on the flame conditions. In particular, we observed that the richer the flame is, i.e., the higher the equivalent ratio is, the higher the photon charging efficiency is. We hypothesized that such an increase in the photoionization propensity of the carbonaceous nanoparticles from richer flame condition is associated to the presence within the particles of larger aromatic moieties. The results clearly show that photoionization is a powerful diagnostic tool for the physical-chemical characterization of combustion aerosol, and it may lead to further insights into the soot formation mechanism.

  7. Carbonaceous materials in the acid residue from the Orgueil carbonaceous chondrite meteorite

    Science.gov (United States)

    Garvie, Laurence A. J.; Buseck, Peter R.

    2006-04-01

    Insoluble organic matter (IOM) dominates the HF/HCl residue of the Orgueil (CI) carbonaceous chondrite meteorite. The IOM is composed primarily of two C-rich particle types. The first has a fluffy texture similar to crumpled tissue paper, and the second type occurs as solid or hollow nanospheres. High-resolution transmission electron microscope (HRTEM) images of the fluffy material show it is poorly ordered, with small, irregularly shaped regions having fringes with 0.34-0.38 nm spacings and locally 0.21 nm cross-fringes. Nanodiamonds occur in the fluffy material. The rounded C-rich particles are common in the residue and their HRTEM images show neither fringes nor nanodiamonds. Both types of carbonaceous materials have a high aromatic component, as revealed by electron energy-loss spectroscopy (EELS), with up to 10 at% substitution by S, N, and O. The average compositions of the fluffy material and nanospheres are C100S1.9N3.7O4.9 and C100S2.4N5.0O3.9, respectively. The structural and chemical heterogeneity of the carbonaceous materials may represent material from multiple sources.

  8. Reactions on carbonaceous materials with hydrogenating gases

    Energy Technology Data Exchange (ETDEWEB)

    Pier, M; Simon, W; Kronig, W

    1933-02-08

    A process is given for the production of valuable hydrocarbons by treatment of distillable carbonaceous materials with added hydrogenating gases under pressure in contact with catalysts. The process comprises adding to the initial materials before or during the said treatment organic sulphonic acids together with metals of groups 4 to 8 of the periodic system or compounds thereof, or free organic carboxylic acids which when inorganic salts are simultaneously present do not combine therewith to form complex ansolvo acids, or acid salts of strong acids or acid salts of heavy metals, lithium, magnesium, and aluminum, with the exception of aluminum hydrosilicates, or inorganic oxygen containing acids of sulfur or nitrogen or the anhydrides of said inorganic oxygen-containing acids.

  9. Extracting solid carbonaceous materials with solvents

    Energy Technology Data Exchange (ETDEWEB)

    1936-02-08

    Solvent extraction of solid carbonaceous materials is performed in the presence of powdered catalysts together with alkaline substances. Oxides of nickel or iron or nickel nitrate have been used together with caustic soda or potash solutions or milk of lime. Solvents used include benzenes, middle oils, tars, tetrahydronaphthalene. The extraction is performed at 200 to 500/sup 0/C under pressures of 20 to 200 atm. Finely ground peat was dried and mixed with milk of lime and nickel nitrate and an equal quantity of middle oil. The mixture was heated for 3 h at 380/sup 0/C at 90 atm. 88.5% of the peat was extracted. In a similar treatment brown coal was impregnated with solutions of caustic soda and ferric chloride.

  10. Carbonaceous matter in the Pomozhan deposit

    Energy Technology Data Exchange (ETDEWEB)

    Piatek, G

    1979-01-01

    Carbonaceous matter (CM), encountered in the Pomozhan deposit, is coordinate to dolomitic-illitic clay, filling caverns in ore-bearing dolomites. The CM represents a disperse mass with particle sizes up to 2 mm, having a color from dark brown to black. The reflectivity (0.35-0.42%) and classification assignment of the CM to macerals of the vitrinite or dopplerinite group were determined by micropetrographic methods. CM belonging to the type of humic coals, transitional from brown to bituminous coals is an epigenetic formation. Its accumulation in the regions of the Ol'kush ore deposits occurred in the Triassic-Cretaceous or Cenozoic interval. Liassic coal of the Zavertse region or Helvetian coal of Khomentuv and Tarnobzheg could be the source of the CM.

  11. Destructive hydrogenation of carbonaceous materials, etc

    Energy Technology Data Exchange (ETDEWEB)

    1938-02-15

    A process is described for the destructive hydrogenation continuously of solid and infusible carbonaceous substances, consisting of heating the charge to the same temperature as the added hydrogen, under a pressure essentially equal to that of the reaction, from the first to at least 300/sup 0/C, but not more than 440/sup 0/C, while passing the heated charge through a zone the contents of which are equal to about 20 per cent to 40 per cent of that of the reaction space, maintaining the charge for a certain time at the temperature without sensible change in the pressure, then reheating the charge to at least the temperature to prime the reaction and finally to introduce the charge into the reaction space.

  12. Photolytic process for gasification of carbonaceous material

    International Nuclear Information System (INIS)

    Zenty, S.

    1979-01-01

    Process and apparatus are disclosed for converting carbon dioxide to carbon monoxide by subjecting the carbon dioxide to radiation in the presence of carbonaceous material such as coal to form carbon monoxide. The preferred form of radiation is solar energy, and the process is preferably carried out in an atmosphere essentially free of oxygen. The invention also includes subjecting carbon monoxide to radiation to form purified carbon and useful heat energy. The two procedures can be combined into a single process for converting solar or other energy into useful thermal energy with the production of useful products. The reactor apparatus is specifically designed to carry out the radiation-induced conversions. Coal can be desulfurized and its caking characteristics altered by solar radiation in the presence of suitable gases. 3 figures

  13. Mineralized remains of morphotypes of filamentous cyanobacteria in carbonaceous meteorites

    Science.gov (United States)

    Hoover, Richard B.

    2005-09-01

    The quest for conclusive evidence of microfossils in meteorites has been elusive. Abiotic microstructures, mineral grains, and even coating artifacts may mimic unicellular bacteria, archaea and nanobacteria with simple spherical or rod morphologies (i.e., cocci, diplococci, bacilli, etc.). This is not the case for the larger and more complex microorganisms, colonies and microbial consortia and ecosystems. Microfossils of algae, cyanobacteria, and cyanobacterial and microbial mats have been recognized and described from many of the most ancient rocks on Earth. The filamentous cyanobacteria and sulphur-bacteria have very distinctive size ranges, complex and recognizable morphologies and visibly differentiated cellular microstructures. The taphonomic modes of fossilization and the life habits and processes of these microorganisms often result in distinctive chemical biosignatures associated with carbonization, silicification, calcification, phosphatization and metal-binding properties of their cell-walls, trichomes, sheaths and extracellular polymeric substances (EPS). Valid biogenicity is provided by the combination of a suite of known biogenic elements (that differ from the meteorite matrix) found in direct association with recognizable and distinct biological features and microstructures (e.g., uniseriate or multiseriate filaments, trichomes, sheaths and cells of proper size/size range); specialized cells (e.g., basal or apical cells, hormogonia, akinetes, and heterocysts); and evidence of growth characteristics (e.g., spiral filaments, robust or thin sheaths, laminated sheaths, true or false branching of trichomes, tapered or uniform filaments) and evidence of locomotion (e.g. emergent cells and trichomes, coiling hormogonia, and hollow or flattened and twisted sheaths). Since 1997 we have conducted Environmental and Field Emission Scanning Electron Microscopy (ESEM and FESEM) studies of freshly fractured interior surfaces of carbonaceous meteorites, terrestrial

  14. A Mudball Model for the Evolution of Carbonaceous Asteroids

    Science.gov (United States)

    Travis, B. J.; Bland, P. A.

    2018-05-01

    We simulation the evolution of carbonaceous chondrite parent bodies from initially unconsolidated aggregations of rock grains and ice crystals. Application of the numerical model MAGHNUM to evolution of CM type planetesimals and Ceres is described.

  15. On thermodynamics of methane+carbonaceous materials adsorption

    KAUST Repository

    Rahman, Kazi Afzalur; Chakraborty, Anutosh; Saha, Bidyut Baran; Ng, Kim Choon

    2012-01-01

    This study presents the theoretical frameworks for the thermodynamic quantities namely the heat of adsorption, specific heat capacity, entropy, and enthalpy for the adsorption of methane onto various carbonaceous materials. The proposed theoretical

  16. Carbonaceous Asteroid Volatile Recovery (CAVoR) system, Phase II

    Data.gov (United States)

    National Aeronautics and Space Administration — The Carbonaceous Asteroid Volatile Recovery (CAVoR) system produces water and hydrogen-rich syngas for propellant production, life support consumables, and...

  17. TESTING OF CARBONACEOUS ADSORBENTS FOR REMOVAL OF POLLUTANTS FROM WATER

    Directory of Open Access Journals (Sweden)

    RAISA NASTAS

    2012-03-01

    Full Text Available Testing of carbonaceous adsorbents for removal of pollutants from water. Relevant direction for improving of quality of potable water is application of active carbons at various stages of water treatments. This work includes complex research dealing with testing of a broad spectrum of carbonaceous adsorbents for removal of hydrogen sulfide and nitrite ions from water. The role of the surface functional groups of carbonaceous adsorbents, their acid-basic properties, and the influence of the type of impregnated heteroatom (N, O, or metals (Fe, Cu, Ni, on removal of hydrogen sulfide species and nitrite ions have been researched. The efficiency of the catalyst obtained from peach stones by impregnation with Cu2+ ions of oxidized active carbon was established, being recommended for practical purposes to remove the hydrogen sulfide species from the sulfurous ground waters. Comparative analysis of carbonaceous adsorbents reveals the importance of surface chemistry for oxidation of nitrite ions.

  18. Visual and semiquantitative analysis of 18F-fluorodeoxyglucose positron emission tomography using a partial-ring tomograph without attenuation correction to differentiate benign and malignant pulmonary nodules

    International Nuclear Information System (INIS)

    Skehan, S.J.; Coates, G.; Otero, C.; O'Donovan, N.; Pelling, M.; Nahmias, C.

    2001-01-01

    Many studies have reported the use of attenuation-corrected positron emission tomography with 18 F-fluorodeoxyglucose (FDG PET) with full-ring tomographs to differentiate between benign and malignant pulmonary nodules. We sought to evaluate FDG PET using a partial-ring tomograph without attenuation correction. A retrospective review of PET images from 77 patients (range 38-84 years of age) with proven benign or malignant pulmonary nodules was undertaken. All images were obtained using a Siemens/CTI ECAT ART tomograph, without attenuation correction, after 185 MBq 18 F-FDG was injected. Images were visually graded on a 5-point scale from 'definitely malignant' to 'definitely benign,' and lesion-to-background (LB) ratios were calculated using region of interest analysis. Visual and semiquantitative analyses were compared using receiver operating characteristic analysis. Twenty lesions were benign and 57 were malignant. The mean LB ratio for benign lesions was 1.5 (range 1.0-5.7) and for malignant lesions 5.7 (range 1.2-14.1) (p < 0.001). The area under the ROC curve for LB ratio analysis was 0.95, and for visual analysis 0.91 (p = 0.39). The optimal cut-off ratio with LB ratio analysis was 1.8, giving a sensitivity of 95% and a specificity of 85%. For lesions thought to be 'definitely malignant' on visual analysis, the sensitivity was 93% and the specificity 85%. Three proven infective lesions were rated as malignant by both techniques (LB ratio 2.6-5.7). FDG PET without attenuation correction is accurate for differentiating between benign and malignant lung nodules. Results using simple LB ratios without attenuation correction compare favourably with the published sensitivity and specificity for standard uptake ratios. Visual analysis is equally accurate. (author)

  19. Lectures on partial differential equations

    CERN Document Server

    Petrovsky, I G

    1992-01-01

    Graduate-level exposition by noted Russian mathematician offers rigorous, transparent, highly readable coverage of classification of equations, hyperbolic equations, elliptic equations and parabolic equations. Wealth of commentary and insight invaluable for deepening understanding of problems considered in text. Translated from the Russian by A. Shenitzer.

  20. Carbonaceous aerosols in Norwegian urban areas

    Directory of Open Access Journals (Sweden)

    K. E. Yttri

    2009-03-01

    Full Text Available Little is known regarding levels and source strength of carbonaceous aerosols in Scandinavia. In the present study, ambient aerosol (PM10 and PM2.5 concentrations of elemental carbon (EC, organic carbon (OC, water-insoluble organic carbon (WINSOC, and water-soluble organic carbon (WSOC are reported for a curbside site, an urban background site, and a suburban site in Norway in order to investigate their spatial and seasonal variations. Aerosol filter samples were collected using tandem filter sampling to correct for the positive sampling artefact introduced by volatile and semivolatile OC. Analyses were performed using the thermal optical transmission (TOT instrument from Sunset Lab Inc., which corrects for charring during analysis. Finally, we estimated the relative contribution of OC from wood burning based on the samples content of levoglucosan.

    Levels of EC varied by more than one order of magnitude between sites, likely due to the higher impact of vehicular traffic at the curbside and the urban background sites. In winter, the level of particulate organic carbon (OCp at the suburban site was equal to (for PM10 or even higher (for PM2.5 than the levels observed at the curbside and the urban background sites. This finding was attributed to the impact of residential wood burning at the suburban site in winter, which was confirmed by a high mean concentration of levoglucosan (407 ng m−3. This finding indicates that exposure to primary combustion derived OCp could be equally high in residential areas as in a city center. It is demonstrated that OCp from wood burning (OCwood accounted for almost all OCp at the suburban site in winter, allowing a new estimate of the ratio TCp/levoglucosan for both PM10 and PM2.5. Particulate carbonaceous material (PCM