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Sample records for two-dimensional partial differential

  1. 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 ...

  2. 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.

  3. 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.

  4. Weak theorems on differential inequalities for two-dimensional functional differential systems

    Czech Academy of Sciences Publication Activity Database

    Šremr, Jiří

    2008-01-01

    Roč. 65, č. 2 (2008), s. 157-189 ISSN 0032-5155 R&D Projects: GA ČR(CZ) GA201/06/0254 Institutional research plan: CEZ:AV0Z10190503 Keywords : two-dimensional functional differential system * weak theorem on differential inequalities * Volterra operator Subject RIV: BA - General Mathematics

  5. LLUVIA-II: A program for two-dimensional, transient flow through partially saturated porous media

    International Nuclear Information System (INIS)

    Eaton, R.R.; Hopkins, P.L.

    1992-08-01

    LLUVIA-II is a program designed for the efficient solution of two- dimensional transient flow of liquid water through partially saturated, porous media. The code solves Richards equation using the method-of-lines procedure. This document describes the solution procedure employed, input data structure, output, and code verification

  6. Extracting information from two-dimensional electrophoresis gels by partial least squares regression

    DEFF Research Database (Denmark)

    Jessen, Flemming; Lametsch, R.; Bendixen, E.

    2002-01-01

    of all proteins/spots in the gels. In the present study it is demonstrated how information can be extracted by multivariate data analysis. The strategy is based on partial least squares regression followed by variable selection to find proteins that individually or in combination with other proteins vary......Two-dimensional gel electrophoresis (2-DE) produces large amounts of data and extraction of relevant information from these data demands a cautious and time consuming process of spot pattern matching between gels. The classical approach of data analysis is to detect protein markers that appear...... or disappear depending on the experimental conditions. Such biomarkers are found by comparing the relative volumes of individual spots in the individual gels. Multivariate statistical analysis and modelling of 2-DE data for comparison and classification is an alternative approach utilising the combination...

  7. New continual analogs of two-dimensional Toda lattices related with nonlinear integro-differential equations

    International Nuclear Information System (INIS)

    Savel'ev, M.V.

    1988-01-01

    Continual ''extensions'' of two-dimensional Toda lattices are proposed. They are described by integro-differential equations, generally speaking, with singular kernels, depending on new (third) variable. The problem of their integrability on the corresponding class of the initial discrete system solutions is discussed. The latter takes place, in particular, for the kernel coinciding with the causal function

  8. Optimal Control Strategies in a Two Dimensional Differential Game Using Linear Equation under a Perturbed System

    Directory of Open Access Journals (Sweden)

    Musa Danjuma SHEHU

    2008-06-01

    Full Text Available This paper lays emphasis on formulation of two dimensional differential games via optimal control theory and consideration of control systems whose dynamics is described by a system of Ordinary Differential equation in the form of linear equation under the influence of two controls U(. and V(.. Base on this, strategies were constructed. Hence we determine the optimal strategy for a control say U(. under a perturbation generated by the second control V(. within a given manifold M.

  9. 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...

  10. 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

  11. 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

  12. Differentiating Fragmentation Pathways of Cholesterol by Two-Dimensional Fourier Transform Ion Cyclotron Resonance Mass Spectrometry.

    Science.gov (United States)

    van Agthoven, Maria A; Barrow, Mark P; Chiron, Lionel; Coutouly, Marie-Aude; Kilgour, David; Wootton, Christopher A; Wei, Juan; Soulby, Andrew; Delsuc, Marc-André; Rolando, Christian; O'Connor, Peter B

    2015-12-01

    Two-dimensional Fourier transform ion cyclotron resonance mass spectrometry is a data-independent analytical method that records the fragmentation patterns of all the compounds in a sample. This study shows the implementation of atmospheric pressure photoionization with two-dimensional (2D) Fourier transform ion cyclotron resonance mass spectrometry. In the resulting 2D mass spectrum, the fragmentation patterns of the radical and protonated species from cholesterol are differentiated. This study shows the use of fragment ion lines, precursor ion lines, and neutral loss lines in the 2D mass spectrum to determine fragmentation mechanisms of known compounds and to gain information on unknown ion species in the spectrum. In concert with high resolution mass spectrometry, 2D Fourier transform ion cyclotron resonance mass spectrometry can be a useful tool for the structural analysis of small molecules. Graphical Abstract ᅟ.

  13. 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

  14. Two-dimensional differential transform method for solving linear and non-linear Schroedinger equations

    International Nuclear Information System (INIS)

    Ravi Kanth, A.S.V.; Aruna, K.

    2009-01-01

    In this paper, we propose a reliable algorithm to develop exact and approximate solutions for the linear and nonlinear Schroedinger equations. The approach rest mainly on two-dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and nonlinear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. Several illustrative examples are given to demonstrate the effectiveness of the present method.

  15. 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...

  16. Oscillation of two-dimensional linear second-order differential systems

    International Nuclear Information System (INIS)

    Kwong, M.K.; Kaper, H.G.

    1985-01-01

    This article is concerned with the oscillatory behavior at infinity of the solution y: [a, ∞) → R 2 of a system of two second-order differential equations, y''(t) + Q(t) y(t) = 0, t epsilon[a, ∞); Q is a continuous matrix-valued function on [a, ∞) whose values are real symmetric matrices of order 2. It is shown that the solution is oscillatory at infinity if the largest eigenvalue of the matrix integral/sub a//sup t/ Q(s) ds tends to infinity as t → ∞. This proves a conjecture of D. Hinton and R.T. Lewis for the two-dimensional case. Furthermore, it is shown that considerably weaker forms of the condition still suffice for oscillatory behavior at infinity. 7 references

  17. [Establishment of two-dimensional differential gel electrophoresis using cerebrospinal fluid from neurocysticercosis patients].

    Science.gov (United States)

    Li, Jing-Yi; Tian, Xiao-Jun; Huang, Yong; Yang, Yan-Jun; Ma, Qiao-Rong; Xue, Yan-Ping

    2008-06-30

    To establish the method of two-dimensional differential gel electrophoresis and obtain high resolution 2D images from cerebrospinal fluid (CSF) of patients with neurocysticercosis. CSF samples were collected from four patients diagnosed as neurocysticercosis clinically and by ELISA, computed tomography (CT) or magnetic resonance imaging (MRI), and from four healthy subjects without neurological disorders. The CSF samples were precipitated with cold acetone, then pooled by equal amount as patients and controls. The internal standard comprised equal amounts of proteins extracted from both groups. Internal standard, and proteins from the two groups were labeled prior to electrophoresis with spectrally resolvable fluorescent dyes, cyanein dye2 (Cy2), Cy3 and Cy5. Sodium dodecylsulfonate polyacrylamide gel chromatography (SDS-PAGE) and two-dimensional differential in-gel electrophoresis (2-D DIGE) of labeled samples were then run. The differential expressed proteins showed in the images of SDS-PAGE and 2-D DIGE gels scanned with 488 nm, 532 nm and 633 nm wavelength laser were analyzed by ImageQuant and DeCyde 5.0 respectively. Spot detection and quantification was performed for the differential in-gel analysis (DIA) module of DeCyder. Biological variation analysis (BVA) module of DeCyder was matched gel 1 and gel 2 images to provide data on differential protein expression levels between the two groups. The ImageQuant result displayed that the CSF protein was compatible with the dye, and the difference of protein amount was revealed by the difference of fluorescence intensity. DIA indicated that there were 896 and 894 protein dots on gel 1 and gel 2 respectively, and 90% of them were matched each other. BVA showed that there were 55 protein spots with different expressional level between neurocysticercosis and control groups. Protein spots with two-fold increase or decrease were 47 and 8 respectively in neurocysticercosis patients compared with healthy controls. The

  18. 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

  19. 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.

  20. 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

  1. 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

  2. Application of two-dimensional J-resolved nuclear magnetic resonance spectroscopy to differentiation of beer

    International Nuclear Information System (INIS)

    Khatib, Alfi; Wilson, Erica G.; Kim, Hye Kyong; Lefeber, Alfons W.M.; Erkelens, Cornelis; Choi, Young Hae; Verpoorte, Robert

    2006-01-01

    A number of ingredients in beer that directly or indirectly affect its quality require an unbiased wide-spectrum analytical method that allows for the determination of a wide array of compounds for its efficient control. 1 H nuclear magnetic resonance (NMR) spectroscopy is a method that clearly meets this description as the broad range of compounds in beer is detectable. However, the resulting congestion of signals added to the low resolution of 1 H NMR spectra makes the identification of individual components very difficult. Among two-dimensional (2D) NMR techniques that increase the resolution, J-resolved NMR spectra were successfully applied to the analysis of 2-butanol extracts of beer as overlapping signals in 1 H NMR spectra were fully resolved by the additional axis of the coupling constant. Principal component analysis based on the projected J-resolved NMR spectra showed a clear separation between all of the six brands of pilsner beer evaluated in this study. The compounds responsible for the differentiation were identified by 2D NMR spectra including correlated spectroscopy and heteronuclear multiple bond correlation spectra together with J-resolved spectra. They were identified as nucleic acid derivatives (adenine, uridine and xanthine), amino acids (tyrosine and proline), organic acid (succinic and lactic acid), alcohol (tyrosol and isopropanol), cholines and carbohydrates

  3. Differential geometric structures of stream functions: incompressible two-dimensional flow and curvatures

    International Nuclear Information System (INIS)

    Yamasaki, K; Iwayama, T; Yajima, T

    2011-01-01

    The Okubo-Weiss field, frequently used for partitioning incompressible two-dimensional (2D) fluids into coherent and incoherent regions, corresponds to the Gaussian curvature of the stream function. Therefore, we consider the differential geometric structures of stream functions and calculate the Gaussian curvatures of some basic flows. We find the following. (I) The vorticity corresponds to the mean curvature of the stream function. Thus, the stream-function surface for an irrotational flow and that for a parallel shear flow correspond to the minimal surface and a developable surface, respectively. (II) The relationship between the coherency and the magnitude of the vorticity is interpreted by the curvatures. (III) Using the Gaussian curvature, stability of single and double point vortex streets is analyzed. The results of this analysis are compared with the well-known linear stability analysis. (IV) Conformal mapping in fluid mechanics is the physical expression of the geometric fact that the sign of the Gaussian curvature does not change in conformal mapping. These findings suggest that the curvatures of stream functions are useful for understanding the geometric structure of an incompressible 2D flow.

  4. 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...

  5. 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...

  6. On oscillation and nonoscillation of two-dimensional linear differential systems

    Czech Academy of Sciences Publication Activity Database

    Lomtatidze, A.; Šremr, Jiří

    2013-01-01

    Roč. 20, č. 3 (2013), s. 573-600 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : two-dimensional system of linear ODE * oscillation * nonoscillation Subject RIV: BA - General Mathematics Impact factor: 0.340, year: 2013 http://www.degruyter.com/view/j/gmj.2013.20.issue-3/gmj-2013-0025/gmj-2013-0025.xml?format=INT

  7. On oscillation and nonoscillation of two-dimensional linear differential systems

    Czech Academy of Sciences Publication Activity Database

    Lomtatidze, A.; Šremr, Jiří

    2013-01-01

    Roč. 20, č. 3 (2013), s. 573-600 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : two-dimensional system of linear ODE * oscillation * nonoscillation Subject RIV: BA - General Mathematics Impact factor: 0.340, year: 2013 http://www.degruyter.com/view/j/gmj.2013.20.issue-3/gmj-2013-0025/gmj-2013-0025. xml ?format=INT

  8. 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.

  9. 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.

  10. Effect of two dimensional heat conduction within the wall on heat transfer of a tube partially heated on its circumference

    International Nuclear Information System (INIS)

    Satoh, Isao; Kurosaki, Yasuo

    1987-01-01

    This paper dealt with the numerical calculations of the heat transfer of a tube partially heated on its circumference, considering two-dimensional heat conduction within the wall. The contribution of the unheated region of the tube wall to heat tranfer of the heated region was explained by the term of 'fin efficiency of psuedo-fin', it was clarified that the fin efficiency of the unheated region was little affected by the temperature difference between the inner and outer surfaces of the wall, and could be approximated by the fin efficency of a rectangular fin. Both the circumferential and radial heat conductions within the wall affected the temperature difference between the inner and outer surfaces of the heated region; however, the effect of the temperature difference on the circumferentially average Nusselt number could be obtained by using the analytical solution of radially one-dimensional heat conduction. Using these results, a diagram showing the effect of wall conduction on heat transfer, which is useful for designing the circumferentially nonuniformly heated coolant passages, was obtained. (author)

  11. Two Regimes of Bandgap Red Shift and Partial Ambient Retention in Pressure-Treated Two-Dimensional Perovskites

    Energy Technology Data Exchange (ETDEWEB)

    Liu, Gang [Center for High Pressure Science and Technology Advanced Research, Shanghai 201203, China; Geophysical Laboratory, Carnegie Institution of Washington, Washington, DC 20015, United States; Kong, Lingping [Center for High Pressure Science and Technology Advanced Research, Shanghai 201203, China; Geophysical Laboratory, Carnegie Institution of Washington, Washington, DC 20015, United States; Guo, Peijun [Center; Stoumpos, Constantinos C. [Department; Hu, Qingyang [Center for High Pressure Science and Technology Advanced Research, Shanghai 201203, China; Liu, Zhenxian [Geophysical Laboratory, Carnegie Institution of Washington, Washington, DC 20015, United States; Cai, Zhonghou [Advanced; Gosztola, David J. [Center; Mao, Ho-kwang [Center for High Pressure Science and Technology Advanced Research, Shanghai 201203, China; Geophysical Laboratory, Carnegie Institution of Washington, Washington, DC 20015, United States; Kanatzidis, Mercouri G. [Department; Schaller, Richard D. [Center; Department

    2017-10-09

    The discovery of elevated environmental stability in two-dimensional (2D) Ruddlesden–Popper hybrid perovskites represents a significant advance in low-cost, high-efficiency light absorbers. In comparison to 3D counterparts, 2D perovskites of organo-lead-halides exhibit wider, quantum-confined optical bandgaps that reduce the wavelength range of light absorption. Here, we characterize the structural and optical properties of 2D hybrid perovskites as a function of hydrostatic pressure. We observe bandgap narrowing with pressure of 633 meV that is partially retained following pressure release due to an atomic reconfiguration mechanism. We identify two distinct regimes of compression dominated by the softer organic and less compressible inorganic sublattices. Our findings, which also include PL enhancement, correlate well with density functional theory calculations and establish structure–property relationships at the atomic scale. These concepts can be expanded into other hybrid perovskites and suggest that pressure/strain processing could offer a new route to improved materials-by-design in applications.

  12. 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

  13. 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...

  14. 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

  15. Multisoliton formula for completely integrable two-dimensional systems

    International Nuclear Information System (INIS)

    Chudnovsky, D.V.; Chudnovsky, G.V.

    1979-01-01

    For general two-dimensional completely integrable systems, the exact formulae for multisoliton type solutions are given. The formulae are obtained algebrically from solutions of two linear partial differential equations

  16. Negative differential conductance in two-dimensional C-functionalized boronitrene

    KAUST Repository

    Obodo, J T; Obodo, K O; Schwingenschlö gl, Udo

    2015-01-01

    It recently has been demonstrated that the large band gap of boronitrene can be significantly reduced by C functionalization. We show that specific defect configurations even can result in metallicity, raising interest in the material for electronic applications. We thus study the transport properties of C-functionalized boronitrene using the non-equilibrium Green's function formalism. We investigate various zigzag and armchair defect configurations, spanning wide band gap semiconducting to metallic states. Unusual I–V characteristics are found and explained in terms of the energy and bias-dependent transmission coefficient and wavefunction. In particular, we demonstrate negative differential conductance with high peak-to-valley ratios, depending on the details of the substitutional doping, and identify the finite bias effects that are responsible for this behavior.

  17. Negative differential conductance in two-dimensional C-functionalized boronitrene

    KAUST Repository

    Obodo, J T

    2015-09-10

    It recently has been demonstrated that the large band gap of boronitrene can be significantly reduced by C functionalization. We show that specific defect configurations even can result in metallicity, raising interest in the material for electronic applications. We thus study the transport properties of C-functionalized boronitrene using the non-equilibrium Green\\'s function formalism. We investigate various zigzag and armchair defect configurations, spanning wide band gap semiconducting to metallic states. Unusual I–V characteristics are found and explained in terms of the energy and bias-dependent transmission coefficient and wavefunction. In particular, we demonstrate negative differential conductance with high peak-to-valley ratios, depending on the details of the substitutional doping, and identify the finite bias effects that are responsible for this behavior.

  18. 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.

  19. Negative differential resistance observed from vertical p+-n+ junction device with two-dimensional black phosphorous

    Science.gov (United States)

    Lee, Daeyeong; Jang, Young Dae; Kweon, Jaehwan; Ryu, Jungjin; Hwang, Euyheon; Yoo, Won Jong; Samsung-SKKU Graphene/2D Center (SSGC) Collaboration

    A vertical p+-n+ homojunction was fabricated by using black phosphorus (BP) as a van der Waals two-dimensional (2D) material. The top and bottom layers of the materials were doped by chemical dopants of gold chloride (AuCl3) for p-type doping and benzyl viologen (BV) for n-type doping. The negative differential resistance (NDR) effect was clearly observed from the output curves of the fabricated BP vertical devices. The thickness range of the 2D material showing NDR and the peak to valley current ratio of NDR are found to be strongly dependent on doping condition, gate voltage, and BP's degradation level. Furthermore, the carrier transport of the p+-n+ junction was simulated by using density functional theory (DFT) and non-equilibrium Green's function (NEGF). Both the experimental and simulation results confirmed that the NDR is attributed to the band-to-band tunneling (BTBT) across the 2D BP p+-n+ junction, and further quantitative details on the carrier transport in the vertical p+-n+ junction devices were explored, according to the analyses of the measured transfer curves and the DFT simulation results. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (2013R1A2A2A01015516).

  20. Two-dimensional zymography differentiates gelatinase isoforms in stimulated microglial cells and in brain tissues of acute brain injuries.

    Science.gov (United States)

    Chen, Shanyan; Meng, Fanjun; Chen, Zhenzhou; Tomlinson, Brittany N; Wesley, Jennifer M; Sun, Grace Y; Whaley-Connell, Adam T; Sowers, James R; Cui, Jiankun; Gu, Zezong

    2015-01-01

    Excessive activation of gelatinases (MMP-2/-9) is a key cause of detrimental outcomes in neurodegenerative diseases. A single-dimension zymography has been widely used to determine gelatinase expression and activity, but this method is inadequate in resolving complex enzyme isoforms, because gelatinase expression and activity could be modified at transcriptional and posttranslational levels. In this study, we investigated gelatinase isoforms under in vitro and in vivo conditions using two-dimensional (2D) gelatin zymography electrophoresis, a protocol allowing separation of proteins based on isoelectric points (pI) and molecular weights. We observed organomercuric chemical 4-aminophenylmercuric acetate-induced activation of MMP-2 isoforms with variant pI values in the conditioned medium of human fibrosarcoma HT1080 cells. Studies with murine BV-2 microglial cells indicated a series of proform MMP-9 spots separated by variant pI values due to stimulation with lipopolysaccharide (LPS). The MMP-9 pI values were shifted after treatment with alkaline phosphatase, suggesting presence of phosphorylated isoforms due to the proinflammatory stimulation. Similar MMP-9 isoforms with variant pI values in the same molecular weight were also found in mouse brains after ischemic and traumatic brain injuries. In contrast, there was no detectable pI differentiation of MMP-9 in the brains of chronic Zucker obese rats. These results demonstrated effective use of 2D zymography to separate modified MMP isoforms with variant pI values and to detect posttranslational modifications under different pathological conditions.

  1. 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

  2. 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.

  3. 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.

  4. State of the water in crosslinked sulfonated poly(ether ether ketone). Two-dimensional differential scanning calorimetry correlation mapping

    Energy Technology Data Exchange (ETDEWEB)

    Al Lafi, Abdul G. [Department of Chemistry, Atomic Energy Commission, Damascus, P.O. Box 6091 (Syrian Arab Republic); Hay, James N., E-mail: cscientific9@aec.org.sy [The School of Metallurgy and Materials, College of Physical Sciences and Engineering, University of Birmingham, Edgbaston, Birmingham B15 2TT (United Kingdom)

    2015-07-20

    Highlights: • 2D-DSC mapping was applied to analyze the heat flow responses of hydrated crosslinked sPEEK. • Two types of loosely bond water were observed. • The first was bond to the sulfonic acid groups and increased with ion exchange capacity. • The second was attributed to the polar groups introduced by ions irradiation and increased with crosslinking degree. • DSC combined with 2D mapping provides a powerful tool for polymer structural determination. - Abstract: This paper reports the first application of two-dimensional differential scanning calorimetry correlation mapping, 2D-DSC-CM to analyze the heat flow responses of sulphonated poly(ether ether ketone), sPEEK, films having different ion exchange capacity and degrees of crosslinks. With the help of high resolution and high sensitivity of 2D-DSC-CM, it was possible to locate two types of loosely bound water within the structure of crosslinked sPEEK. The first was bound to the sulfonic acid groups and dependent on the ion exchange capacity of the sPEEK. The second was bound to other polar groups, either introduced by irradiation with ions and dependent on the crosslinking degree or present in the polymer such as the carbonyl groups or terminal units. The results suggest that the ability of the sulfonic acid groups in the crosslinked sPEEK membranes to adsorb water molecules is increased by crosslinking, probably due to the better close packing efficiency of the crosslinked samples. DSC combined with 2D correlation mapping provides a fast and powerful tool for polymer structural determination.

  5. Possibility of a two-dimensional spin liquid in CePdAl induced by partial geometric frustration?

    Energy Technology Data Exchange (ETDEWEB)

    Fritsch, V. [Universitaet Augsburg, Institut fuer Physik, Experimentalphysik VI (Germany); Karlsruher Institut fuer Technologie (Germany); Grube, K.; Kittler, W.; Taubenheim, C.; Loehneysen, H. von [Karlsruher Institut fuer Technologie (Germany); Huesges, Z.; Lucas, S.; Stockert, O. [Max-Planck-Institut fuer chemische Physik fester Stoffe, Dresden (Germany); Green, E. [Hochfeldzentrum Dresden-Rossendorf (Germany)

    2015-07-01

    CePdAl crystallizes in the hexagonal ZrNiAl structure, where the magnetic ions form a distorted kagome lattice. At T{sub N} = 2.7 K the onset of antiferromagnetic (AF) order is observed. Neutron scattering experiments revealed a partial frustration in the distorted kagome planes of this structure: two-thirds of the Ce moments form ferromagnetic chains, which are antiferromagnetically coupled, the remaining third do not participate in any long-range order. Along the c-axis the magnetic moments exhibit an amplitude modulation. Accordingly, the kagome planes are stacked on top of each other, resulting in corrugated AF planes parallel to the c-axis formed by the ordered magnetic moments, which are separated by the frustrated moments. It is an intriguing and yet unresolved question if this third of frustrated moments forms a spin liquid state in CePdAl. Based on measurements of specific heat, thermal expansion, magnetization and electrical resistivity we want to discuss this possibility.

  6. 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

  7. 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.

  8. Two-dimensional calculus

    CERN Document Server

    Osserman, Robert

    2011-01-01

    The basic component of several-variable calculus, two-dimensional calculus is vital to mastery of the broader field. This extensive treatment of the subject offers the advantage of a thorough integration of linear algebra and materials, which aids readers in the development of geometric intuition. An introductory chapter presents background information on vectors in the plane, plane curves, and functions of two variables. Subsequent chapters address differentiation, transformations, and integration. Each chapter concludes with problem sets, and answers to selected exercises appear at the end o

  9. 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

  10. Asymptotic behaviour of solutions of real two-dimensional differential system with nonconstant delay in an unstable case

    Directory of Open Access Journals (Sweden)

    J. Kalas

    2012-01-01

    Full Text Available The asymptotic behaviour for the solutions of a real two-dimensional system with a bounded nonconstant delay is studied under the assumption of instability. Our results improve and complement previous results by J. Kalas, where the sufficient conditions assuring the existence of bounded solutions or solutions tending to origin for $t$ approaching infinity are given. The method of investigation is based on the transformation of the considered real system to one equation with complex-valued coefficients. Asymptotic properties of this equation are studied by means of a suitable Lyapunov-Krasovskii functional and by virtue of the Wazewski topological principle.

  11. Exact Solutions for Certain Nonlinear Autonomous Ordinary Differential Equations of the Second Order and Families of Two-Dimensional Autonomous Systems

    Directory of Open Access Journals (Sweden)

    M. P. Markakis

    2010-01-01

    Full Text Available Certain nonlinear autonomous ordinary differential equations of the second order are reduced to Abel equations of the first kind ((Ab-1 equations. Based on the results of a previous work, concerning a closed-form solution of a general (Ab-1 equation, and introducing an arbitrary function, exact one-parameter families of solutions are derived for the original autonomous equations, for the most of which only first integrals (in closed or parametric form have been obtained so far. Two-dimensional autonomous systems of differential equations of the first order, equivalent to the considered herein autonomous forms, are constructed and solved by means of the developed analysis.

  12. 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

  13. 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...

  14. Second invariant for two-dimensional classical super systems

    Indian Academy of Sciences (India)

    Construction of superpotentials for two-dimensional classical super systems (for N. 2) is carried ... extensively used for the case of non-linear partial differential equation by various authors. [3,4–7,12 ..... found to be integrable just by accident.

  15. Two-dimensional gel human protein databases offer a systematic approach to the study of cell proliferation and differentiation

    DEFF Research Database (Denmark)

    Celis, julio E.; Gesser, Borbala; Dejgaard, Kurt

    1989-01-01

    Human cellular protein databases have been established using computer-analyzed 2D gel electrophoresis. These databases, which include information on various properties of proteins, offer a global approach to the study of regulation of cell proliferation and differentiation. Furthermore, thanks...

  16. Solvability conditions for non-local boundary value problems for two-dimensional half-linear differential systems

    Czech Academy of Sciences Publication Activity Database

    Kiguradze, I.; Šremr, Jiří

    2011-01-01

    Roč. 74, č. 17 (2011), s. 6537-6552 ISSN 0362-546X Institutional research plan: CEZ:AV0Z10190503 Keywords : half-linear differential system * non-local boundary value problem * solvability Subject RIV: BA - General Mathematics Impact factor: 1.536, year: 2011 http://www.sciencedirect.com/science/article/pii/S0362546X11004573

  17. Solvability conditions of the Cauchy problem for two-dimensional systems of linear functional differential equations with monotone operators

    Czech Academy of Sciences Publication Activity Database

    Šremr, Jiří

    2007-01-01

    Roč. 132, č. 3 (2007), s. 263-295 ISSN 0862-7959 R&D Projects: GA ČR GP201/04/P183 Institutional research plan: CEZ:AV0Z10190503 Keywords : system of functional differential equations with monotone operators * initial value problem * unique solvability Subject RIV: BA - General Mathematics

  18. Two dimensional gel human protein databases offer a systematic approach to the study of cell proliferation and differentiation

    DEFF Research Database (Denmark)

    Celis, J E; Gesser, B; Dejgaard, K

    1989-01-01

    Human cellular protein databases have been established using computer-analyzed 2D gel electrophoresis. These databases, which include information on various properties of proteins, offer a global approach to the study of regulation of cell proliferation and differentiation. Furthermore, thanks to...

  19. Proteomic analysis of differential protein expression of achilles tendon in a rabbit model by two-dimensional polyacrylamide gel electrophoresis at 21 days postoperation.

    Science.gov (United States)

    Jielile, Jiasharete; Jialili, Ainuer; Sabirhazi, Gulnur; Shawutali, Nuerai; Redati, Darebai; Chen, Jiangtao; Tang, Bin; Bai, Jingping; Aldyarhan, Kayrat

    2011-10-01

    Postoperative early kinesitherapy has been advocated as an optimal method for treating Achilles tendon rupture. However, an insight into the rationale of how early kinesitherapy contributes to healing of Achilles tendon remains to be achieved, and research in the area of proteomic analysis of Achilles tendon has so far been lacking. Forty-two rabbits were randomized into control group, immobilization group, and early motion group, and received postoperative cast immobilization and early motion treatments. Achilles tendon samples were prepared 21 days following microsurgery, and the proteins were separated with two-dimensional polyacrylamide gel electrophoresis. Differentially expressed proteins were first recognized by PDQuest software, and then identified using peptide mass fingerprinting, tandem mass spectrometry, and database searching. A total of 463  ±  12, 511  ±  39, and 513  ±  80 protein spots were successfully detected in the two-dimensional polyacrylamide gels for the Achilles tendon samples of rabbits in the control group, immobilization group, and early motion group, respectively. There were 15, 8, and 9 unique proteins in these three groups, respectively, and some differentially expressed proteins were also identified in each group. It was indicated that some of the differentially expressed proteins were involved in various metabolism pathways and may play an important role in healing of Achilles tendon rupture. Postoperative early kinesitherapy resulted in differentially expressed proteins in ruptured Achilles tendon compared with those treated with postoperative cast immobilization. These differentially expressed proteins may contribute to healing of Achilles tendon rupture through a mechanobiological mechanism due to the application of postoperative early kinesitherapy.

  20. Identification of differentially expressed proteins between human esophageal immortalized and carcinomatous cell lines by two-dimensional electrophoresis and MALDI-TOF-mass spectrometry

    Institute of Scientific and Technical Information of China (English)

    Xing-Dong Xiong; Li-Yan Xu; Zhong-Ying Shen; Wei-Jia Cai; Jian-Min Luo; Ya-Li Han; En-Min Li

    2002-01-01

    AIM: To identify the differentially expressed proteins between the human immortalized esophageal epithelial cell line (SHEE) and the malignant transformed esophageal carcinoma cell line (SHEEC), and to explore new ways for studying esophageal carcinoma associated genes. METHODS: SHEE and SHEEC cell lines were used to separate differentially expressed proteins by two-dimensional electrophoresis/The silver-stained 2-D gels was scanned with EDAS290 digital camera system and analyzed with the PDQuest 6.2 Software. Six spots in which the differentially expressed protein was more obvious were selected and analyzed with matrix-assisted laser desorption/ionization time of flying mass spectrometry (MALDI-TOF-MS).RESULTS: There were 107±4.58 and 115±9.91 protein spots observed in SHEE and SHEEC respectively, and the majority of these spots between the two cell lines matched each other (r=-0.772), only a few were expressed differentially. After analyzed by MALDI-TOF-MS and database search for the six differentially expressed proteins, One new protein as well as other five sequence-known proteins including RNPEP-like protein, human rRNA gene upstream sequence binding transcription factor, uracil DNA glycosylase,Annexin A2 and p300/CBP-associated factor were preliminarily identified.CONCLUSION: These differentially expressed proteins might play an importance role during malignant transformation of SHEEC from SHEE. The identification of these proteins may serve as a new way for studying esophageal carcinoma associated genes.

  1. Two-dimensional errors

    International Nuclear Information System (INIS)

    Anon.

    1991-01-01

    This chapter addresses the extension of previous work in one-dimensional (linear) error theory to two-dimensional error analysis. The topics of the chapter include the definition of two-dimensional error, the probability ellipse, the probability circle, elliptical (circular) error evaluation, the application to position accuracy, and the use of control systems (points) in measurements

  2. 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...

  3. 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

  4. Differentiation of benign from malignant solid breast masses: comparison of two-dimensional and three-dimensional shear-wave elastography.

    Science.gov (United States)

    Lee, Su Hyun; Chang, Jung Min; Kim, Won Hwa; Bae, Min Sun; Cho, Nariya; Yi, Ann; Koo, Hye Ryoung; Kim, Seung Ja; Kim, Jin You; Moon, Woo Kyung

    2013-04-01

    To prospectively compare the diagnostic performances of two-dimensional (2D) and three-dimensional (3D) shear-wave elastography (SWE) for differentiating benign from malignant breast masses. B-mode ultrasound and SWE were performed for 134 consecutive women with 144 breast masses before biopsy. Quantitative elasticity values (maximum and mean elasticity in the stiffest portion of mass, Emax and Emean; lesion-to-fat elasticity ratio, Erat) were measured with both 2D and 3D SWE. The area under the receiver operating characteristic curve (AUC), sensitivity and specificity of B-mode, 2D, 3D SWE and combined data of B-mode and SWE were compared. Sixty-seven of the 144 breast masses (47 %) were malignant. Overall, higher elasticity values of 3D SWE than 2D SWE were noted for both benign and malignant masses. The AUC for 2D and 3D SWE were not significantly different: Emean, 0.938 vs 0.928; Emax, 0.939 vs 0.930; Erat, 0.907 vs 0.871. Either 2D or 3D SWE significantly improved the specificity of B-mode ultrasound from 29.9 % (23 of 77) up to 71.4 % (55 of 77) and 63.6 % (49 of 77) without a significant change in sensitivity. Two-dimensional and 3D SWE performed equally in distinguishing benign from malignant masses and both techniques improved the specificity of B-mode ultrasound.

  5. 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.

  6. 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.

  7. Comparison of liver mitochondrial proteins derived from newborn cloned calves and from cloned adult cattle by two-dimensional differential gel electrophoresis.

    Science.gov (United States)

    Takeda, Kumiko; Tasai, Mariko; Akagi, Satoshi; Watanabe, Shinya; Oe, Mika; Chikuni, Koichi; Ohnishi-Kameyama, Mayumi; Hanada, Hirofumi; Nakamura, Yoshiaki; Tagami, Takahiro; Nirasawa, Keijiro

    2011-04-01

    Aberrant reprogramming of donor somatic cell nuclei may result in many severe problems in animal cloning. The inability to establish functional interactions between donor nucleus and recipient mitochondria is also likely responsible for such a developmental deficiency. However, detailed knowledge of protein expression during somatic cell nuclear transfer (SCNT) in cattle is lacking. In the present study, variations in mitochondrial protein levels between SCNT-derived and control cattle, and from calves derived by artificial insemination were investigated. Mitochondrial fractions were prepared from frozen liver samples and subjected to two-dimensional (2-D) fluorescence differential gel electrophoresis (DIGE) using CyDye™ dyes. Protein expression changes were confirmed with a volume ratio greater than 2.0 (P result implicates mitochondrial-related gene expression in early developmental loss of SCNT embryos. Comparative proteomic analysis represents an important tool for further studies on SCNT animals. Copyright © 2011 Wiley-Liss, Inc.

  8. 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.

  9. Proteomic analysis of halotolerant proteins under high and low salt stress in Dunaliella salina using two-dimensional differential in-gel electrophoresis

    Directory of Open Access Journals (Sweden)

    Yan-Long Jia

    2016-01-01

    Full Text Available Abstract Dunaliella salina, a single-celled marine alga with extreme salt tolerance, is an important model organism for studying fundamental extremophile survival mechanisms and their potential practical applications. In this study, two-dimensional differential in-gel electrophoresis (2D-DIGE was used to investigate the expression of halotolerant proteins under high (3 M NaCl and low (0.75 M NaCl salt concentrations. Matrix-assisted laser desorption ionization time-of-flight mass spectrometry (MALDI-TOF/TOF MS and bioinformatics were used to identify and characterize the differences among proteins. 2D-DIGE analysis revealed 141 protein spots that were significantly differentially expressed between the two salinities. Twenty-four differentially expressed protein spots were successfully identified by MALDI-TOF/TOF MS, including proteins in the following important categories: molecular chaperones, proteins involved in photosynthesis, proteins involved in respiration and proteins involved in amino acid synthesis. Expression levels of these proteins changed in response to the stress conditions, which suggests that they may be involved in the maintenance of intracellular osmotic pressure, cellular stress responses, physiological changes in metabolism, continuation of photosynthetic activity and other aspects of salt stress. The findings of this study enhance our understanding of the function and mechanisms of various proteins in salt stress.

  10. 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

  11. 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...

  12. 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.

  13. 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.

  14. 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....

  15. 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

  16. 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.

  17. 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.

  18. Method translation and full metadata transfer from thermal to differential flow modulated comprehensive two dimensional gas chromatography: Profiling of suspected fragrance allergens.

    Science.gov (United States)

    Cordero, Chiara; Rubiolo, Patrizia; Reichenbach, Stephen E; Carretta, Andrea; Cobelli, Luigi; Giardina, Matthew; Bicchi, Carlo

    2017-01-13

    The possibility to transfer methods from thermal to differential-flow modulated comprehensive two-dimensional gas chromatographic (GC×GC) platforms is of high interest to improve GC×GC flexibility and increase the compatibility of results from different platforms. The principles of method translation are here applied to an original method, developed for a loop-type thermal modulated GC×GC-MS/FID system, suitable for quali-quantitative screening of suspected fragrance allergens. The analysis conditions were translated to a reverse-injection differential flow modulated platform (GC×2GC-MS/FID) with a dual-parallel secondary column and dual detection. The experimental results, for a model mixture of suspected volatile allergens and for raw fragrance mixtures of different composition, confirmed the feasibility of translating methods by preserving 1 D elution order, as well as the relative alignment of resulting 2D peak patterns. A correct translation produced several benefits including an effective transfer of metadata (compound names, MS fragmentation pattern, response factors) by automatic template transformation and matching from the original/reference method to its translated counterpart. The correct translation provided: (a) 2D pattern repeatability, (b) MS fragmentation pattern reliability for identity confirmation, and (c) comparable response factors and quantitation accuracy within a concentration range of three orders of magnitude. The adoption of a narrow bore (i.e. 0.1mm d c ) first-dimension column to operate under close-to-optimal conditions with the differential-flow modulation GC×GC platform was also advantageous in halving the total analysis under the translated conditions. Copyright © 2016 Elsevier B.V. All rights reserved.

  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. 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

  11. Two-dimensional models

    International Nuclear Information System (INIS)

    Schroer, Bert; Freie Universitaet, Berlin

    2005-02-01

    It is not possible to compactly review the overwhelming literature on two-dimensional models in a meaningful way without a specific viewpoint; I have therefore tacitly added to the above title the words 'as theoretical laboratories for general quantum field theory'. I dedicate this contribution to the memory of J. A. Swieca with whom I have shared the passion of exploring 2-dimensional models for almost one decade. A shortened version of this article is intended as a contribution to the project 'Encyclopedia of mathematical physics' and comments, suggestions and critical remarks are welcome. (author)

  12. Two-dimensional ferroelectrics

    Energy Technology Data Exchange (ETDEWEB)

    Blinov, L M; Fridkin, Vladimir M; Palto, Sergei P [A.V. Shubnikov Institute of Crystallography, Russian Academy of Sciences, Moscow, Russian Federaion (Russian Federation); Bune, A V; Dowben, P A; Ducharme, Stephen [Department of Physics and Astronomy, Behlen Laboratory of Physics, Center for Materials Research and Analysis, University of Nebraska-Linkoln, Linkoln, NE (United States)

    2000-03-31

    The investigation of the finite-size effect in ferroelectric crystals and films has been limited by the experimental conditions. The smallest demonstrated ferroelectric crystals had a diameter of {approx}200 A and the thinnest ferroelectric films were {approx}200 A thick, macroscopic sizes on an atomic scale. Langmuir-Blodgett deposition of films one monolayer at a time has produced high quality ferroelectric films as thin as 10 A, made from polyvinylidene fluoride and its copolymers. These ultrathin films permitted the ultimate investigation of finite-size effects on the atomic thickness scale. Langmuir-Blodgett films also revealed the fundamental two-dimensional character of ferroelectricity in these materials by demonstrating that there is no so-called critical thickness; films as thin as two monolayers (1 nm) are ferroelectric, with a transition temperature near that of the bulk material. The films exhibit all the main properties of ferroelectricity with a first-order ferroelectric-paraelectric phase transition: polarization hysteresis (switching); the jump in spontaneous polarization at the phase transition temperature; thermal hysteresis in the polarization; the increase in the transition temperature with applied field; double hysteresis above the phase transition temperature; and the existence of the ferroelectric critical point. The films also exhibit a new phase transition associated with the two-dimensional layers. (reviews of topical problems)

  13. 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...

  14. 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...

  15. 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

  16. 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

  17. 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…

  18. 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 ...

  19. Two-dimensional capillary origami

    Energy Technology Data Exchange (ETDEWEB)

    Brubaker, N.D., E-mail: nbrubaker@math.arizona.edu; Lega, J., E-mail: lega@math.arizona.edu

    2016-01-08

    We describe a global approach to the problem of capillary origami that captures all unfolded equilibrium configurations in the two-dimensional setting where the drop is not required to fully wet the flexible plate. We provide bifurcation diagrams showing the level of encapsulation of each equilibrium configuration as a function of the volume of liquid that it contains, as well as plots representing the energy of each equilibrium branch. These diagrams indicate at what volume level the liquid drop ceases to be attached to the endpoints of the plate, which depends on the value of the contact angle. As in the case of pinned contact points, three different parameter regimes are identified, one of which predicts instantaneous encapsulation for small initial volumes of liquid. - Highlights: • Full solution set of the two-dimensional capillary origami problem. • Fluid does not necessarily wet the entire plate. • Global energy approach provides exact differential equations satisfied by minimizers. • Bifurcation diagrams highlight three different regimes. • Conditions for spontaneous encapsulation are identified.

  20. Two-dimensional capillary origami

    International Nuclear Information System (INIS)

    Brubaker, N.D.; Lega, J.

    2016-01-01

    We describe a global approach to the problem of capillary origami that captures all unfolded equilibrium configurations in the two-dimensional setting where the drop is not required to fully wet the flexible plate. We provide bifurcation diagrams showing the level of encapsulation of each equilibrium configuration as a function of the volume of liquid that it contains, as well as plots representing the energy of each equilibrium branch. These diagrams indicate at what volume level the liquid drop ceases to be attached to the endpoints of the plate, which depends on the value of the contact angle. As in the case of pinned contact points, three different parameter regimes are identified, one of which predicts instantaneous encapsulation for small initial volumes of liquid. - Highlights: • Full solution set of the two-dimensional capillary origami problem. • Fluid does not necessarily wet the entire plate. • Global energy approach provides exact differential equations satisfied by minimizers. • Bifurcation diagrams highlight three different regimes. • Conditions for spontaneous encapsulation are identified.

  1. Two-dimensional partial-wave analysis of exclusive 190 GeV π-p scattering into the π-π-π+ final state at COMPASS (CERN)

    International Nuclear Information System (INIS)

    Haas, Florian

    2014-01-01

    The dynamics of strong interaction in the regime of low energies, i.e. large distances, is still not understood. Given its simplicity the non-relativistic simple quark model (SQM) describes successfully the observed hadronic spectra. QCD-inspired models, however, predict hadronic states where the gluonic content contributes to the hadron quantum numbers. These so-called hybrids cannot be explained within the SQM. A solid experimental proof of the existence of such systems would be the observation of spin-exotic states, with spin-parity quantum numbers, not allowed in the SQM. The study of mesons, the simplest hadrons, permits to gain insight into the realm of strong interaction where hadrons are the relevant degrees of freedom. The most promising spin-exotic meson candidate is the π 1 (1600), which was claimed in several experiments and in particular in data taken during a previous hadron campaign of the COMPASS experiment. The hadron spectroscopy program of the COMPASS experiment at CERN focuses on the investigation of the light-meson spectrum in order to enlighten this rarely understood regime of strong interaction. During the 2008 data taking an unprecedented statistical precision has been reached in peripheral interactions of 190 GeV/c pions with a proton target leading to the π - π - π + final state. A spin-parity analysis in the kinematical region of the squared fourmomentum transfer 0.1≤t'0≤1.0 GeV 2 /c 2 was carried out based on a model of 88 partial waves up to a total angular momentum of 6. Besides the precise determination of properties of known resonances, a new axial-vector state, the a 1 (1420), was observed for the first time in a mass region where neither model nor lattice calculations predict mesons with this quantum numbers. Noteworthy is the very small intensity of this signal and that it only couples to the f 0 (980) isobar which is assumed to have a large strangeness content. The spin-exotic π 1 (1600) was observed albeit as a

  2. Two-dimensional Radiative Magnetohydrodynamic Simulations of Partial Ionization in the Chromosphere. II. Dynamics and Energetics of the Low Solar Atmosphere

    Energy Technology Data Exchange (ETDEWEB)

    Martínez-Sykora, Juan [Bay Area Environmental Research Institute, Petaluma, CA 94952 (United States); Pontieu, Bart De; Hansteen, Viggo H. [Lockheed Martin Solar and Astrophysics Laboratory, Palo Alto, CA 94304 (United States); Carlsson, Mats; Gudiksen, Boris V. [Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, NO-0315 Oslo (Norway); Nóbrega-Siverio, Daniel, E-mail: juanms@lmsal.com [Instituto de Astrofísica de Canarias, E-38200 La Laguna (Tenerife) (Spain)

    2017-09-20

    We investigate the effects of interactions between ions and neutrals on the chromosphere and overlying corona using 2.5D radiative MHD simulations with the Bifrost code. We have extended the code capabilities implementing ion–neutral interaction effects using the generalized Ohm’s law, i.e., we include the Hall term and the ambipolar diffusion (Pedersen dissipation) in the induction equation. Our models span from the upper convection zone to the corona, with the photosphere, chromosphere, and transition region partially ionized. Our simulations reveal that the interactions between ionized particles and neutral particles have important consequences for the magnetothermodynamics of these modeled layers: (1) ambipolar diffusion increases the temperature in the chromosphere; (2) sporadically the horizontal magnetic field in the photosphere is diffused into the chromosphere, due to the large ambipolar diffusion; (3) ambipolar diffusion concentrates electrical currents, leading to more violent jets and reconnection processes, resulting in (3a) the formation of longer and faster spicules, (3b) heating of plasma during the spicule evolution, and (3c) decoupling of the plasma and magnetic field in spicules. Our results indicate that ambipolar diffusion is a critical ingredient for understanding the magnetothermodynamic properties in the chromosphere and transition region. The numerical simulations have been made publicly available, similar to previous Bifrost simulations. This will allow the community to study realistic numerical simulations with a wider range of magnetic field configurations and physics modules than previously possible.

  3. 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.

  4. 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)

  5. 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)

  6. 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...

  7. Two-dimensional transport of tokamak plasmas

    International Nuclear Information System (INIS)

    Hirshman, S.P.; Jardin, S.C.

    1979-01-01

    A reduced set of two-fluid transport equations is obtained from the conservation equations describing the time evolution of the differential particle number, entropy, and magnetic fluxes in an axisymmetric toroidal plasma with nested magnetic surfaces. Expanding in the small ratio of perpendicular to parallel mobilities and thermal conductivities yields as solubility constraints one-dimensional equations for the surface-averaged thermodynamic variables and magnetic fluxes. Since Ohm's law E +u x B =R', where R' accounts for any nonideal effects, only determines the particle flow relative to the diffusing magnetic surfaces, it is necessary to solve a single two-dimensional generalized differential equation, (partial/partialt) delpsi. (delp - J x B) =0, to find the absolute velocity of a magnetic surface enclosing a fixed toroidal flux. This equation is linear but nonstandard in that it involves flux surface averages of the unknown velocity. Specification of R' and the cross-field ion and electron heat fluxes provides a closed system of equations. A time-dependent coordinate transformation is used to describe the diffusion of plasma quantities through magnetic surfaces of changing shape

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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 ...

  13. The human keratinocyte two-dimensional protein database (update 1994): towards an integrated approach to the study of cell proliferation, differentiation and skin diseases

    DEFF Research Database (Denmark)

    Celis, J E; Rasmussen, H H; Olsen, E

    1994-01-01

    The master two-dimensional (2-D) gel database of human keratinocytes currently lists 3087 cellular proteins (2168 isoelectric focusing, IEF; and 919 none-quilibrium pH gradient electrophoresis, NEPHGE), many of which correspond to posttranslational modifications, 890 polypeptides have been...... in the database. We also report a database of proteins recovered from the medium of noncultured, unfractionated keratinocytes. This database lists 398 polypeptides (309 IEF; 89 NEPHGE) of which 76 have been identified. The aim of the comprehensive databases is to gather, through a systematic study...

  14. 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

  15. 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

  16. 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.

  17. 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 ...

  18. 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...

  19. 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.

  20. 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.

  1. 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

  2. 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

  3. 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.

  4. 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.

  5. 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

  6. 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

  7. 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.

  8. 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,.

  9. 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.

  10. 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.

  11. Analytic energies and wave functions of the two-dimensional Schrodinger equation: ground state of two-dimensional quartic potential and classification of solutions

    Czech Academy of Sciences Publication Activity Database

    Tichý, V.; Kuběna, Aleš Antonín; Skála, L.

    2012-01-01

    Roč. 90, č. 6 (2012), s. 503-513 ISSN 0008-4204 Institutional support: RVO:67985556 Keywords : Schroninger equation * partial differential equation * analytic solution * anharmonic oscilator * double-well Subject RIV: BE - Theoretical Physics Impact factor: 0.902, year: 2012 http://library.utia.cas.cz/separaty/2012/E/kubena-analytic energies and wave functions of the two-dimensional schrodinger equation.pdf

  12. 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

  13. 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.

  14. 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.

  15. Two-dimensional block-based reception for differentially encoded OFDM systems : a study on improved reception techniques for digital audio broadcasting systems

    NARCIS (Netherlands)

    Houtum, van W.J.

    2012-01-01

    Digital audio broadcast (DAB), DAB+ and Terrestrial-Digital Multimedia Broadcasting (T-DMB) systems use multi-carrier modulation (MCM). The principle of MCM in the DAB-family is based on orthogonal frequency division multiplexing (OFDM), for which every subcarrier is modulated by p 4 differentially

  16. 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

  17. Correlation of rocket propulsion fuel properties with chemical composition using comprehensive two-dimensional gas chromatography with time-of-flight mass spectrometry followed by partial least squares regression analysis.

    Science.gov (United States)

    Kehimkar, Benjamin; Hoggard, Jamin C; Marney, Luke C; Billingsley, Matthew C; Fraga, Carlos G; Bruno, Thomas J; Synovec, Robert E

    2014-01-31

    There is an increased need to more fully assess and control the composition of kerosene-based rocket propulsion fuels such as RP-1. In particular, it is critical to make better quantitative connections among the following three attributes: fuel performance (thermal stability, sooting propensity, engine specific impulse, etc.), fuel properties (such as flash point, density, kinematic viscosity, net heat of combustion, and hydrogen content), and the chemical composition of a given fuel, i.e., amounts of specific chemical compounds and compound classes present in a fuel as a result of feedstock blending and/or processing. Recent efforts in predicting fuel chemical and physical behavior through modeling put greater emphasis on attaining detailed and accurate fuel properties and fuel composition information. Often, one-dimensional gas chromatography (GC) combined with mass spectrometry (MS) is employed to provide chemical composition information. Building on approaches that used GC-MS, but to glean substantially more chemical information from these complex fuels, we recently studied the use of comprehensive two dimensional (2D) gas chromatography combined with time-of-flight mass spectrometry (GC×GC-TOFMS) using a "reversed column" format: RTX-wax column for the first dimension, and a RTX-1 column for the second dimension. In this report, by applying chemometric data analysis, specifically partial least-squares (PLS) regression analysis, we are able to readily model (and correlate) the chemical compositional information provided by use of GC×GC-TOFMS to RP-1 fuel property information such as density, kinematic viscosity, net heat of combustion, and so on. Furthermore, we readily identified compounds that contribute significantly to measured differences in fuel properties based on results from the PLS models. We anticipate this new chemical analysis strategy will have broad implications for the development of high fidelity composition-property models, leading to an

  18. Two-dimensional NMR spectrometry

    International Nuclear Information System (INIS)

    Farrar, T.C.

    1987-01-01

    This article is the second in a two-part series. In part one (ANALYTICAL CHEMISTRY, May 15) the authors discussed one-dimensional nuclear magnetic resonance (NMR) spectra and some relatively advanced nuclear spin gymnastics experiments that provide a capability for selective sensitivity enhancements. In this article and overview and some applications of two-dimensional NMR experiments are presented. These powerful experiments are important complements to the one-dimensional experiments. As in the more sophisticated one-dimensional experiments, the two-dimensional experiments involve three distinct time periods: a preparation period, t 0 ; an evolution period, t 1 ; and a detection period, t 2

  19. Quasi-two-dimensional holography

    International Nuclear Information System (INIS)

    Kutzner, J.; Erhard, A.; Wuestenberg, H.; Zimpfer, J.

    1980-01-01

    The acoustical holography with numerical reconstruction by area scanning is memory- and time-intensive. With the experiences by the linear holography we tried to derive a scanning for the evaluating of the two-dimensional flaw-sizes. In most practical cases it is sufficient to determine the exact depth extension of a flaw, whereas the accuracy of the length extension is less critical. For this reason the applicability of the so-called quasi-two-dimensional holography is appropriate. The used sound field given by special probes is divergent in the inclined plane and light focussed in the perpendicular plane using cylindrical lenses. (orig.) [de

  20. 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.

  1. Differential Proteomics Identification of HSP90 as Potential Serum Biomarker in Hepatocellular Carcinoma by Two-dimensional Electrophoresis and Mass Spectrometry

    Directory of Open Access Journals (Sweden)

    Yiyi Sun

    2010-03-01

    Full Text Available The aim of the current study is to identify the potential biomarkers involved in Hepatocellular carcinoma (HCC carcinogenesis. A comparative proteomics approach was utilized to identify the differentially expressed proteins in the serum of 10 HCC patients and 10 controls. A total of 12 significantly altered proteins were identified by mass spectrometry. Of the 12 proteins identified, HSP90 was one of the most significantly altered proteins and its over-expression in the serum of 20 HCC patients was confirmed using ELISA analysis. The observations suggest that HSP90 might be a potential biomarker for early diagnosis, prognosis, and monitoring in the therapy of HCC. This work demonstrates that a comprehensive strategy of proteomic identification combined with further validation should be adopted in the field of cancer biomarker discovery.

  2. 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

  3. 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.

  4. Two-dimensional metamaterial optics

    International Nuclear Information System (INIS)

    Smolyaninov, I I

    2010-01-01

    While three-dimensional photonic metamaterials are difficult to fabricate, many new concepts and ideas in the metamaterial optics can be realized in two spatial dimensions using planar optics of surface plasmon polaritons. In this paper we review recent progress in this direction. Two-dimensional photonic crystals, hyperbolic metamaterials, and plasmonic focusing devices are demonstrated and used in novel microscopy and waveguiding schemes

  5. Proteomic analysis by two-dimensional differential in gel electrophoresis (2D DIGE) of the early response of Pisum sativum to Orobanche crenata.

    Science.gov (United States)

    Castillejo, Ma Ángeles; Fernández-Aparicio, Mónica; Rubiales, Diego

    2012-01-01

    Crenate broomrape (Orobanche crenata) is considered to be the major constraint for legume crops in Mediterranean countries. Strategies of control have been developed, but only marginal successes have been achieved. For the efficient control of the parasite, a better understanding of its interaction and associated resistance mechanisms at the molecular level is required. The pea response to this parasitic plant and the molecular basis of the resistance was studied using a proteomic approach based on 2D DIGE and MALDI-MSMS analysis. For this purpose, two genotypes showing different levels of resistance to O. crenata, as well as three time points (21, 25, and 30 d after inoculation) have been compared. Multivariate statistical analysis identified 43 differential protein spots under the experimental conditions (genotypes/treatments), 22 of which were identified using a combination of peptide mass fingerprinting (PMF) and MSMS fragmentation. Most of the proteins identified were metabolic and stress-related proteins and a high percentage of them (86%) matched with specific proteins of legume species. The behaviour pattern of the identified proteins suggests the existence of defence mechanisms operating during the early stages of infection that differed in both genotypes. Among these, several proteins were identified with protease activity which could play an important role in preventing the penetration and connection to the vascular system of the parasite. Our data are discussed and compared with those previously obtained in pea and Medicago truncatula.

  6. 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.

  7. 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

  8. 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.

  9. 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 ...

  10. 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.

  11. 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.

  12. 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.

  13. 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

  14. 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.

  15. 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.)

  16. 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

  17. 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)

  18. 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. 

  19. 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 ...

  20. Two-dimensional flexible nanoelectronics

    Science.gov (United States)

    Akinwande, Deji; Petrone, Nicholas; Hone, James

    2014-12-01

    2014/2015 represents the tenth anniversary of modern graphene research. Over this decade, graphene has proven to be attractive for thin-film transistors owing to its remarkable electronic, optical, mechanical and thermal properties. Even its major drawback--zero bandgap--has resulted in something positive: a resurgence of interest in two-dimensional semiconductors, such as dichalcogenides and buckled nanomaterials with sizeable bandgaps. With the discovery of hexagonal boron nitride as an ideal dielectric, the materials are now in place to advance integrated flexible nanoelectronics, which uniquely take advantage of the unmatched portfolio of properties of two-dimensional crystals, beyond the capability of conventional thin films for ubiquitous flexible systems.

  1. Two-dimensional topological photonics

    Science.gov (United States)

    Khanikaev, Alexander B.; Shvets, Gennady

    2017-12-01

    Originating from the studies of two-dimensional condensed-matter states, the concept of topological order has recently been expanded to other fields of physics and engineering, particularly optics and photonics. Topological photonic structures have already overturned some of the traditional views on wave propagation and manipulation. The application of topological concepts to guided wave propagation has enabled novel photonic devices, such as reflection-free sharply bent waveguides, robust delay lines, spin-polarized switches and non-reciprocal devices. Discrete degrees of freedom, widely used in condensed-matter physics, such as spin and valley, are now entering the realm of photonics. In this Review, we summarize the latest advances in this highly dynamic field, with special emphasis on the experimental work on two-dimensional photonic topological structures.

  2. Two-dimensional thermofield bosonization

    International Nuclear Information System (INIS)

    Amaral, R.L.P.G.; Belvedere, L.V.; Rothe, K.D.

    2005-01-01

    The main objective of this paper was to obtain an operator realization for the bosonization of fermions in 1 + 1 dimensions, at finite, non-zero temperature T. This is achieved in the framework of the real-time formalism of Thermofield Dynamics. Formally, the results parallel those of the T = 0 case. The well-known two-dimensional Fermion-Boson correspondences at zero temperature are shown to hold also at finite temperature. To emphasize the usefulness of the operator realization for handling a large class of two-dimensional quantum field-theoretic problems, we contrast this global approach with the cumbersome calculation of the fermion-current two-point function in the imaginary-time formalism and real-time formalisms. The calculations also illustrate the very different ways in which the transmutation from Fermi-Dirac to Bose-Einstein statistics is realized

  3. Two-dimensional critical phenomena

    International Nuclear Information System (INIS)

    Saleur, H.

    1987-09-01

    Two dimensional critical systems are studied using transformation to free fields and conformal invariance methods. The relations between the two approaches are also studied. The analytical results obtained generally depend on universality hypotheses or on renormalization group trajectories which are not established rigorously, so numerical verifications, mainly using the transfer matrix approach, are presented. The exact determination of critical exponents; the partition functions of critical models on toruses; and results as the critical point is approached are discussed [fr

  4. Two dimensional unstable scar statistics.

    Energy Technology Data Exchange (ETDEWEB)

    Warne, Larry Kevin; Jorgenson, Roy Eberhardt; Kotulski, Joseph Daniel; Lee, Kelvin S. H. (ITT Industries/AES Los Angeles, CA)

    2006-12-01

    This report examines the localization of time harmonic high frequency modal fields in two dimensional cavities along periodic paths between opposing sides of the cavity. The cases where these orbits lead to unstable localized modes are known as scars. This paper examines the enhancements for these unstable orbits when the opposing mirrors are both convex and concave. In the latter case the construction includes the treatment of interior foci.

  5. Finding two-dimensional peaks

    International Nuclear Information System (INIS)

    Silagadze, Z.K.

    2007-01-01

    Two-dimensional generalization of the original peak finding algorithm suggested earlier is given. The ideology of the algorithm emerged from the well-known quantum mechanical tunneling property which enables small bodies to penetrate through narrow potential barriers. We merge this 'quantum' ideology with the philosophy of Particle Swarm Optimization to get the global optimization algorithm which can be called Quantum Swarm Optimization. The functionality of the newborn algorithm is tested on some benchmark optimization problems

  6. 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/

  7. Two dimensional infinite conformal symmetry

    International Nuclear Information System (INIS)

    Mohanta, N.N.; Tripathy, K.C.

    1993-01-01

    The invariant discontinuous (discrete) conformal transformation groups, namely the Kleinian and Fuchsian groups Gamma (with an arbitrary signature) of H (the Poincare upper half-plane l) and the unit disc Delta are explicitly constructed from the fundamental domain D. The Riemann surface with signatures of Gamma and conformally invariant automorphic forms (functions) with Peterson scalar product are discussed. The functor, where the category of complex Hilbert spaces spanned by the space of cusp forms constitutes the two dimensional conformal field theory. (Author) 7 refs

  8. Two-dimensional liquid chromatography

    DEFF Research Database (Denmark)

    Græsbøll, Rune

    -dimensional separation space. Optimization of gradients in online RP×RP is more difficult than in normal HPLC as a result of the increased number of parameters and their influence on each other. Modeling the coverage of the compounds across the two-dimensional chromatogram as a result of a change in gradients could...... be used for optimization purposes, and reduce the time spend on optimization. In this thesis (chapter 6), and manuscript B, a measure of the coverage of the compounds in the twodimensional separation space is defined. It is then shown that this measure can be modeled for changes in the gradient in both...

  9. 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

  10. 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...

  11. 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...

  12. 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

  13. 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.

  14. 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)

  15. 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...

  16. 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.

  17. 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

  18. Two dimensional solid state NMR

    International Nuclear Information System (INIS)

    Kentgens, A.P.M.

    1987-01-01

    This thesis illustrates, by discussing some existing and newly developed 2D solid state experiments, that two-dimensional NMR of solids is a useful and important extension of NMR techniques. Chapter 1 gives an overview of spin interactions and averaging techniques important in solid state NMR. As 2D NMR is already an established technique in solutions, only the basics of two dimensional NMR are presented in chapter 2, with an emphasis on the aspects important for solid spectra. The following chapters discuss the theoretical background and applications of specific 2D solid state experiments. An application of 2D-J resolved NMR, analogous to J-resolved spectroscopy in solutions, to natural rubber is given in chapter 3. In chapter 4 the anisotropic chemical shift is mapped out against the heteronuclear dipolar interaction to obtain information about the orientation of the shielding tensor in poly-(oxymethylene). Chapter 5 concentrates on the study of super-slow molecular motions in polymers using a variant of the 2D exchange experiment developed by us. Finally chapter 6 discusses a new experiment, 2D nutation NMR, which makes it possible to study the quadrupole interaction of half-integer spins. 230 refs.; 48 figs.; 8 tabs

  19. Two-dimensional turbulent convection

    Science.gov (United States)

    Mazzino, Andrea

    2017-11-01

    We present an overview of the most relevant, and sometimes contrasting, theoretical approaches to Rayleigh-Taylor and mean-gradient-forced Rayleigh-Bénard two-dimensional turbulence together with numerical and experimental evidences for their support. The main aim of this overview is to emphasize that, despite the different character of these two systems, especially in relation to their steadiness/unsteadiness, turbulent fluctuations are well described by the same scaling relationships originated from the Bolgiano balance. The latter states that inertial terms and buoyancy terms balance at small scales giving rise to an inverse kinetic energy cascade. The main difference with respect to the inverse energy cascade in hydrodynamic turbulence [R. H. Kraichnan, "Inertial ranges in two-dimensional turbulence," Phys. Fluids 10, 1417 (1967)] is that the rate of cascade of kinetic energy here is not constant along the inertial range of scales. Thanks to the absence of physical boundaries, the two systems here investigated turned out to be a natural physical realization of the Kraichnan scaling regime hitherto associated with the elusive "ultimate state of thermal convection" [R. H. Kraichnan, "Turbulent thermal convection at arbitrary Prandtl number," Phys. Fluids 5, 1374-1389 (1962)].

  20. 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.

  1. 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.

  2. 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.

  3. 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

  4. On a method of construction of exact solutions for equations of two-dimensional hydrodynamics of incompressible liquids

    International Nuclear Information System (INIS)

    Yurov, A.V.; Yurova, A.A.

    2006-01-01

    The simple algebraic method for construction of exact solutions of two-dimensional hydrodynamic equations of incompressible flow is proposed. This method can be applied both to nonviscous flow (Euler equations) and to viscous flow (Navier-Stokes equations). In the case of nonviscous flow, the problem is reduced to sequential solving of three linear partial differential equations. In the case of viscous flow, the Navier-Stokes equations are reduced to three linear partial differential equations and one differential equation of the first order [ru

  5. 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

  6. Two-dimensional quantum repeaters

    Science.gov (United States)

    Wallnöfer, J.; Zwerger, M.; Muschik, C.; Sangouard, N.; Dür, W.

    2016-11-01

    The endeavor to develop quantum networks gave rise to a rapidly developing field with far-reaching applications such as secure communication and the realization of distributed computing tasks. This ultimately calls for the creation of flexible multiuser structures that allow for quantum communication between arbitrary pairs of parties in the network and facilitate also multiuser applications. To address this challenge, we propose a two-dimensional quantum repeater architecture to establish long-distance entanglement shared between multiple communication partners in the presence of channel noise and imperfect local control operations. The scheme is based on the creation of self-similar multiqubit entanglement structures at growing scale, where variants of entanglement swapping and multiparty entanglement purification are combined to create high-fidelity entangled states. We show how such networks can be implemented using trapped ions in cavities.

  7. Finite elements for partial differential equations: An introductory survey

    International Nuclear Information System (INIS)

    Succi, S.

    1988-03-01

    After presentation of the basic ideas behind the theory of the Finite Element Method, the application of the method to three equations of particular interest in Physics and Engineering is discussed in some detail, namely, a one-dimensional Sturm-Liouville problem, a two-dimensional linear Fokker-Planck equation and a two-dimensional nonlinear Navier-Stokes equation. 6 refs, 8 figs

  8. 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.

  9. 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...

  10. 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

  11. 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.

  12. 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.

  13. 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.)

  14. 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.

  15. 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

  16. 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

  17. 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

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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).

  4. 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...

  5. 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)

  6. Equilibrium: two-dimensional configurations

    International Nuclear Information System (INIS)

    Anon.

    1987-01-01

    In Chapter 6, the problem of toroidal force balance is addressed in the simplest, nontrivial two-dimensional geometry, that of an axisymmetric torus. A derivation is presented of the Grad-Shafranov equation, the basic equation describing axisymmetric toroidal equilibrium. The solutions to equations provide a complete description of ideal MHD equilibria: radial pressure balance, toroidal force balance, equilibrium Beta limits, rotational transform, shear, magnetic wall, etc. A wide number of configurations are accurately modeled by the Grad-Shafranov equation. Among them are all types of tokamaks, the spheromak, the reversed field pinch, and toroidal multipoles. An important aspect of the analysis is the use of asymptotic expansions, with an inverse aspect ratio serving as the expansion parameter. In addition, an equation similar to the Grad-Shafranov equation, but for helically symmetric equilibria, is presented. This equation represents the leading-order description low-Beta and high-Beta stellarators, heliacs, and the Elmo bumpy torus. The solutions all correspond to infinitely long straight helices. Bending such a configuration into a torus requires a full three-dimensional calculation and is discussed in Chapter 7

  7. A Novel Machine Learning Strategy Based on Two-Dimensional Numerical Models in Financial Engineering

    Directory of Open Access Journals (Sweden)

    Qingzhen Xu

    2013-01-01

    Full Text Available Machine learning is the most commonly used technique to address larger and more complex tasks by analyzing the most relevant information already present in databases. In order to better predict the future trend of the index, this paper proposes a two-dimensional numerical model for machine learning to simulate major U.S. stock market index and uses a nonlinear implicit finite-difference method to find numerical solutions of the two-dimensional simulation model. The proposed machine learning method uses partial differential equations to predict the stock market and can be extensively used to accelerate large-scale data processing on the history database. The experimental results show that the proposed algorithm reduces the prediction error and improves forecasting precision.

  8. 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.

  9. 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

  10. 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.

  11. 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...

  12. 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...

  13. 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...

  14. 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.

  15. 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...

  16. 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...

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. Numerical model for two-dimensional hydrodynamics and energy transport. [VECTRA code

    Energy Technology Data Exchange (ETDEWEB)

    Trent, D.S.

    1973-06-01

    The theoretical basis and computational procedure of the VECTRA computer program are presented. VECTRA (Vorticity-Energy Code for TRansport Analysis) is designed for applying numerical simulation to a broad range of intake/discharge flows in conjunction with power plant hydrological evaluation. The code computational procedure is based on finite-difference approximation of the vorticity-stream function partial differential equations which govern steady flow momentum transport of two-dimensional, incompressible, viscous fluids in conjunction with the transport of heat and other constituents.

  2. Whitham modulation theory for the two-dimensional Benjamin-Ono equation.

    Science.gov (United States)

    Ablowitz, Mark; Biondini, Gino; Wang, Qiao

    2017-09-01

    Whitham modulation theory for the two-dimensional Benjamin-Ono (2DBO) equation is presented. A system of five quasilinear first-order partial differential equations is derived. The system describes modulations of the traveling wave solutions of the 2DBO equation. These equations are transformed to a singularity-free hydrodynamic-like system referred to here as the 2DBO-Whitham system. Exact reductions of this system are discussed, the formulation of initial value problems is considered, and the system is used to study the transverse stability of traveling wave solutions of the 2DBO equation.

  3. 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

  4. 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

  5. Exterior calculus and two-dimensional supersymmetric models

    International Nuclear Information System (INIS)

    Sciuto, S.

    1980-01-01

    An important property of the calculus of differential forms on superspace is pointed out, and an economical way to treat the linear problem associated with certain supersymmetric two-dimensional models is discussed. A generalization of the super sine-Gordon model is proposed; its bosonic limit is a new model whose associate linear set has an SU(3) structure. (orig.)

  6. Mass relations for two-dimensional classical configurations

    International Nuclear Information System (INIS)

    Tataru-Mihai, P.

    1980-01-01

    Using the two-dimensional sigma-nonlinear models as a framework mass relations for classical configurations of instanton/soliton type are derived. Our results suggest an interesting differential-geometric interpretation of the mass of a classical configuration in terms of the topological characteristics of an associated manifold. (orig.)

  7. A comprehensive two-dimensional gel protein database of noncultured unfractionated normal human epidermal keratinocytes: towards an integrated approach to the study of cell proliferation, differentiation and skin diseases

    DEFF Research Database (Denmark)

    Celis, J E; Madsen, Peder; Rasmussen, H H

    1991-01-01

    A two-dimensional (2-D) gel database of cellular proteins from noncultured, unfractionated normal human epidermal keratinocytes has been established. A total of 2651 [35S]methionine-labeled cellular proteins (1868 isoelectric focusing, 783 nonequilibrium pH gradient electrophoresis) were resolved...

  8. Two-dimensional grating guided-mode resonance tunable filter.

    Science.gov (United States)

    Kuo, Wen-Kai; Hsu, Che-Jung

    2017-11-27

    A two-dimensional (2D) grating guided-mode resonance (GMR) tunable filter is experimentally demonstrated using a low-cost two-step nanoimprinting technology with a one-dimensional (1D) grating polydimethylsiloxane mold. For the first nanoimprinting, we precisely control the UV LED irradiation dosage and demold the device when the UV glue is partially cured and the 1D grating mold is then rotated by three different angles, 30°, 60°, and 90°, for the second nanoimprinting to obtain 2D grating structures with different crossing angles. A high-refractive-index film ZnO is then coated on the surface of the grating structure to form the GMR filter devices. The simulation and experimental results demonstrate that the passband central wavelength of the filter can be tuned by rotating the device to change azimuth angle of the incident light. We compare these three 2D GMR filters with differential crossing angles and find that the filter device with a crossing angle of 60° exhibits the best performance. The tunable range of its central wavelength is 668-742 nm when the azimuth angle varies from 30° to 90°.

  9. Topology optimization of two-dimensional waveguides

    DEFF Research Database (Denmark)

    Jensen, Jakob Søndergaard; Sigmund, Ole

    2003-01-01

    In this work we use the method of topology optimization to design two-dimensional waveguides with low transmission loss.......In this work we use the method of topology optimization to design two-dimensional waveguides with low transmission loss....

  10. 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.

  11. 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.

  12. 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.

  13. 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

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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...

  19. 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...

  20. 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

  1. 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

  2. The construction of a two-dimensional reproducing kernel function and its application in a biomedical model.

    Science.gov (United States)

    Guo, Qi; Shen, Shu-Ting

    2016-04-29

    There are two major classes of cardiac tissue models: the ionic model and the FitzHugh-Nagumo model. During computer simulation, each model entails solving a system of complex ordinary differential equations and a partial differential equation with non-flux boundary conditions. The reproducing kernel method possesses significant applications in solving partial differential equations. The derivative of the reproducing kernel function is a wavelet function, which has local properties and sensitivities to singularity. Therefore, study on the application of reproducing kernel would be advantageous. Applying new mathematical theory to the numerical solution of the ventricular muscle model so as to improve its precision in comparison with other methods at present. A two-dimensional reproducing kernel function inspace is constructed and applied in computing the solution of two-dimensional cardiac tissue model by means of the difference method through time and the reproducing kernel method through space. Compared with other methods, this method holds several advantages such as high accuracy in computing solutions, insensitivity to different time steps and a slow propagation speed of error. It is suitable for disorderly scattered node systems without meshing, and can arbitrarily change the location and density of the solution on different time layers. The reproducing kernel method has higher solution accuracy and stability in the solutions of the two-dimensional cardiac tissue model.

  3. Piezoelectricity in Two-Dimensional Materials

    KAUST Repository

    Wu, Tao; Zhang, Hua

    2015-01-01

    Powering up 2D materials: Recent experimental studies confirmed the existence of piezoelectricity - the conversion of mechanical stress into electricity - in two-dimensional single-layer MoS2 nanosheets. The results represent a milestone towards

  4. Construction of two-dimensional quantum chromodynamics

    Energy Technology Data Exchange (ETDEWEB)

    Klimek, S.; Kondracki, W.

    1987-12-01

    We present a sketch of the construction of the functional measure for the SU(2) quantum chromodynamics with one generation of fermions in two-dimensional space-time. The method is based on a detailed analysis of Wilson loops.

  5. Development of Two-Dimensional NMR

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 20; Issue 11. Development of Two-Dimensional NMR: Strucure Determination of Biomolecules in Solution. Anil Kumar. General Article Volume 20 Issue 11 November 2015 pp 995-1002 ...

  6. Phase transitions in two-dimensional systems

    International Nuclear Information System (INIS)

    Salinas, S.R.A.

    1983-01-01

    Some experiences are related using synchrotron radiation beams, to characterize solid-liquid (fusion) and commensurate solid-uncommensurate solid transitions in two-dimensional systems. Some ideas involved in the modern theories of two-dimensional fusion are shortly exposed. The systems treated consist of noble gases (Kr,Ar,Xe) adsorbed in the basal plane of graphite and thin films formed by some liquid crystal shells. (L.C.) [pt

  7. 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

  8. 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.

  9. 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.

  10. 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....

  11. 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

  12. 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).

  13. 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)

  14. 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

  15. 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

  16. 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.

  17. Two-dimensional nuclear magnetic resonance spectroscopy

    International Nuclear Information System (INIS)

    Bax, A.; Lerner, L.

    1986-01-01

    Great spectral simplification can be obtained by spreading the conventional one-dimensional nuclear magnetic resonance (NMR) spectrum in two independent frequency dimensions. This so-called two-dimensional NMR spectroscopy removes spectral overlap, facilitates spectral assignment, and provides a wealth of additional information. For example, conformational information related to interproton distances is available from resonance intensities in certain types of two-dimensional experiments. Another method generates 1 H NMR spectra of a preselected fragment of the molecule, suppressing resonances from other regions and greatly simplifying spectral appearance. Two-dimensional NMR spectroscopy can also be applied to the study of 13 C and 15 N, not only providing valuable connectivity information but also improving sensitivity of 13 C and 15 N detection by up to two orders of magnitude. 45 references, 10 figures

  18. Explorative data analysis of two-dimensional electrophoresis gels

    DEFF Research Database (Denmark)

    Schultz, J.; Gottlieb, D.M.; Petersen, Marianne Kjerstine

    2004-01-01

    of gels is presented. First, an approach is demonstrated in which no prior knowledge of the separated proteins is used. Alignment of the gels followed by a simple transformation of data makes it possible to analyze the gels in an automated explorative manner by principal component analysis, to determine......Methods for classification of two-dimensional (2-DE) electrophoresis gels based on multivariate data analysis are demonstrated. Two-dimensional gels of ten wheat varieties are analyzed and it is demonstrated how to classify the wheat varieties in two qualities and a method for initial screening...... if the gels should be further analyzed. A more detailed approach is done by analyzing spot volume lists by principal components analysis and partial least square regression. The use of spot volume data offers a mean to investigate the spot pattern and link the classified protein patterns to distinct spots...

  19. Two-dimensional x-ray diffraction

    CERN Document Server

    He, Bob B

    2009-01-01

    Written by one of the pioneers of 2D X-Ray Diffraction, this useful guide covers the fundamentals, experimental methods and applications of two-dimensional x-ray diffraction, including geometry convention, x-ray source and optics, two-dimensional detectors, diffraction data interpretation, and configurations for various applications, such as phase identification, texture, stress, microstructure analysis, crystallinity, thin film analysis and combinatorial screening. Experimental examples in materials research, pharmaceuticals, and forensics are also given. This presents a key resource to resea

  20. Equivalence of two-dimensional gravities

    International Nuclear Information System (INIS)

    Mohammedi, N.

    1990-01-01

    The authors find the relationship between the Jackiw-Teitelboim model of two-dimensional gravity and the SL(2,R) induced gravity. These are shown to be related to a two-dimensional gauge theory obtained by dimensionally reducing the Chern-Simons action of the 2 + 1 dimensional gravity. The authors present an explicit solution to the equations of motion of the auxiliary field of the Jackiw-Teitelboim model in the light-cone gauge. A renormalization of the cosmological constant is also given

  1. 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.

  2. 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.

  3. Network patterns in exponentially growing two-dimensional biofilms

    Science.gov (United States)

    Zachreson, Cameron; Yap, Xinhui; Gloag, Erin S.; Shimoni, Raz; Whitchurch, Cynthia B.; Toth, Milos

    2017-10-01

    Anisotropic collective patterns occur frequently in the morphogenesis of two-dimensional biofilms. These patterns are often attributed to growth regulation mechanisms and differentiation based on gradients of diffusing nutrients and signaling molecules. Here, we employ a model of bacterial growth dynamics to show that even in the absence of growth regulation or differentiation, confinement by an enclosing medium such as agar can itself lead to stable pattern formation over time scales that are employed in experiments. The underlying mechanism relies on path formation through physical deformation of the enclosing environment.

  4. Analytical simulation of two dimensional advection dispersion ...

    African Journals Online (AJOL)

    The study was designed to investigate the analytical simulation of two dimensional advection dispersion equation of contaminant transport. The steady state flow condition of the contaminant transport where inorganic contaminants in aqueous waste solutions are disposed of at the land surface where it would migrate ...

  5. Analytical Simulation of Two Dimensional Advection Dispersion ...

    African Journals Online (AJOL)

    ADOWIE PERE

    ABSTRACT: The study was designed to investigate the analytical simulation of two dimensional advection dispersion equation of contaminant transport. The steady state flow condition of the contaminant transport where inorganic contaminants in aqueous waste solutions are disposed of at the land surface where it would ...

  6. Sums of two-dimensional spectral triples

    DEFF Research Database (Denmark)

    Christensen, Erik; Ivan, Cristina

    2007-01-01

    construct a sum of two dimensional modules which reflects some aspects of the topological dimensions of the compact metric space, but this will only give the metric back approximately. At the end we make an explicit computation of the last module for the unit interval in. The metric is recovered exactly...

  7. Stability of two-dimensional vorticity filaments

    International Nuclear Information System (INIS)

    Elhmaidi, D.; Provenzale, A.; Lili, T.; Babiano, A.

    2004-01-01

    We discuss the results of a numerical study on the stability of two-dimensional vorticity filaments around a circular vortex. We illustrate how the stability of the filaments depends on the balance between the strain associated with the far field of the vortex and the local vorticity of the filament, and we discuss an empirical criterion for filament stability

  8. Two-Dimensional Motions of Rockets

    Science.gov (United States)

    Kang, Yoonhwan; Bae, Saebyok

    2007-01-01

    We analyse the two-dimensional motions of the rockets for various types of rocket thrusts, the air friction and the gravitation by using a suitable representation of the rocket equation and the numerical calculation. The slope shapes of the rocket trajectories are discussed for the three types of rocket engines. Unlike the projectile motions, the…

  9. Two-dimensional microstrip detector for neutrons

    Energy Technology Data Exchange (ETDEWEB)

    Oed, A [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France)

    1997-04-01

    Because of their robust design, gas microstrip detectors, which were developed at ILL, can be assembled relatively quickly, provided the prefabricated components are available. At the beginning of 1996, orders were received for the construction of three two-dimensional neutron detectors. These detectors have been completed. The detectors are outlined below. (author). 2 refs.

  10. Conformal invariance and two-dimensional physics

    International Nuclear Information System (INIS)

    Zuber, J.B.

    1993-01-01

    Actually, physicists and mathematicians are very interested in conformal invariance: geometric transformations which keep angles. This symmetry is very important for two-dimensional systems as phase transitions, string theory or node mathematics. In this article, the author presents the conformal invariance and explains its usefulness

  11. Matching Two-dimensional Gel Electrophoresis' Spots

    DEFF Research Database (Denmark)

    Dos Anjos, António; AL-Tam, Faroq; Shahbazkia, Hamid Reza

    2012-01-01

    This paper describes an approach for matching Two-Dimensional Electrophoresis (2-DE) gels' spots, involving the use of image registration. The number of false positive matches produced by the proposed approach is small, when compared to academic and commercial state-of-the-art approaches. This ar...

  12. Two-dimensional membranes in motion

    NARCIS (Netherlands)

    Davidovikj, D.

    2018-01-01

    This thesis revolves around nanomechanical membranes made of suspended two - dimensional materials. Chapters 1-3 give an introduction to the field of 2D-based nanomechanical devices together with an overview of the underlying physics and the measurementtools used in subsequent chapters. The research

  13. Extended Polymorphism of Two-Dimensional Material

    NARCIS (Netherlands)

    Yoshida, Masaro; Ye, Jianting; Zhang, Yijin; Imai, Yasuhiko; Kimura, Shigeru; Fujiwara, Akihiko; Nishizaki, Terukazu; Kobayashi, Norio; Nakano, Masaki; Iwasa, Yoshihiro

    When controlling electronic properties of bulk materials, we usually assume that the basic crystal structure is fixed. However, in two-dimensional (2D) materials, atomic structure or to functionalize their properties. Various polymorphs can exist in transition metal dichalcogenides (TMDCs) from

  14. Piezoelectricity in Two-Dimensional Materials

    KAUST Repository

    Wu, Tao

    2015-02-25

    Powering up 2D materials: Recent experimental studies confirmed the existence of piezoelectricity - the conversion of mechanical stress into electricity - in two-dimensional single-layer MoS2 nanosheets. The results represent a milestone towards embedding low-dimensional materials into future disruptive technologies. © 2015 Wiley-VCH Verlag GmbH & Co. KGaA.

  15. 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

  16. 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.

  17. 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

  18. 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.

  19. 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

  20. 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.

  1. 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...

  2. 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

  3. 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…

  4. 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,

  5. 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

  6. 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

  7. 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

  8. 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.

  9. Solving Two -Dimensional Diffusion Equations with Nonlocal Boundary Conditions by a Special Class of Padé Approximants

    Directory of Open Access Journals (Sweden)

    Mohammad Siddique

    2010-08-01

    Full Text Available Parabolic partial differential equations with nonlocal boundary conditions arise in modeling of a wide range of important application areas such as chemical diffusion, thermoelasticity, heat conduction process, control theory and medicine science. In this paper, we present the implementation of positivity- preserving Padé numerical schemes to the two-dimensional diffusion equation with nonlocal time dependent boundary condition. We successfully implemented these numerical schemes for both Homogeneous and Inhomogeneous cases. The numerical results show that these Padé approximation based numerical schemes are quite accurate and easily implemented.

  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. The Penalty Cost Functional for the Two-Dimensional

    Directory of Open Access Journals (Sweden)

    Victor Onomza WAZIRI

    2006-07-01

    Full Text Available This paper constructs the penalty cost functional for optimizing the two-dimensional control operator of the energized wave equation. In some multiplier methods such as the Lagrange multipliers and Pontrygean maximum principle, the cost of merging the constraint equation to the integral quadratic objective functional to obtain an unconstraint equation is normally guessed or obtained from the first partial derivatives of the unconstrained equation. The Extended Conjugate Gradient Method (ECGM necessitates that the penalty cost be sequentially obtained algebraically. The ECGM problem contains a functional which is completely given in terms of state and time spatial dependent variables.

  12. Two-dimensional confinement of heavy fermions

    International Nuclear Information System (INIS)

    Shishido, Hiroaki; Shibauchi, Takasada; Matsuda, Yuji; Terashima, Takahito

    2010-01-01

    Metallic systems with the strongest electron correlations are realized in certain rare-earth and actinide compounds whose physics are dominated by f-electrons. These materials are known as heavy fermions, so called because the effective mass of the conduction electrons is enhanced via correlation effects up to as much as several hundreds times the free electron mass. To date the electronic structure of all heavy-fermion compounds is essentially three-dimensional. Here we report on the first realization of a two-dimensional heavy-fermion system, where the dimensionality is adjusted in a controllable fashion by fabricating heterostructures using molecular beam epitaxy. The two-dimensional heavy fermion system displays striking deviations from the standard Fermi liquid low-temperature electronic properties. (author)

  13. Two-dimensional sensitivity calculation code: SENSETWO

    International Nuclear Information System (INIS)

    Yamauchi, Michinori; Nakayama, Mitsuo; Minami, Kazuyoshi; Seki, Yasushi; Iida, Hiromasa.

    1979-05-01

    A SENSETWO code for the calculation of cross section sensitivities with a two-dimensional model has been developed, on the basis of first order perturbation theory. It uses forward neutron and/or gamma-ray fluxes and adjoint fluxes obtained by two-dimensional discrete ordinates code TWOTRAN-II. The data and informations of cross sections, geometry, nuclide density, response functions, etc. are transmitted to SENSETWO by the dump magnetic tape made in TWOTRAN calculations. The required input for SENSETWO calculations is thus very simple. The SENSETWO yields as printed output the cross section sensitivities for each coarse mesh zone and for each energy group, as well as the plotted output of sensitivity profiles specified by the input. A special feature of the code is that it also calculates the reaction rate with the response function used as the adjoint source in TWOTRAN adjoint calculation and the calculated forward flux from the TWOTRAN forward calculation. (author)

  14. Two-dimensional ranking of Wikipedia articles

    Science.gov (United States)

    Zhirov, A. O.; Zhirov, O. V.; Shepelyansky, D. L.

    2010-10-01

    The Library of Babel, described by Jorge Luis Borges, stores an enormous amount of information. The Library exists ab aeterno. Wikipedia, a free online encyclopaedia, becomes a modern analogue of such a Library. Information retrieval and ranking of Wikipedia articles become the challenge of modern society. While PageRank highlights very well known nodes with many ingoing links, CheiRank highlights very communicative nodes with many outgoing links. In this way the ranking becomes two-dimensional. Using CheiRank and PageRank we analyze the properties of two-dimensional ranking of all Wikipedia English articles and show that it gives their reliable classification with rich and nontrivial features. Detailed studies are done for countries, universities, personalities, physicists, chess players, Dow-Jones companies and other categories.

  15. Toward two-dimensional search engines

    International Nuclear Information System (INIS)

    Ermann, L; Shepelyansky, D L; Chepelianskii, A D

    2012-01-01

    We study the statistical properties of various directed networks using ranking of their nodes based on the dominant vectors of the Google matrix known as PageRank and CheiRank. On average PageRank orders nodes proportionally to a number of ingoing links, while CheiRank orders nodes proportionally to a number of outgoing links. In this way, the ranking of nodes becomes two dimensional which paves the way for the development of two-dimensional search engines of a new type. Statistical properties of information flow on the PageRank–CheiRank plane are analyzed for networks of British, French and Italian universities, Wikipedia, Linux Kernel, gene regulation and other networks. A special emphasis is done for British universities networks using the large database publicly available in the UK. Methods of spam links control are also analyzed. (paper)

  16. Acoustic phonon emission by two dimensional plasmons

    International Nuclear Information System (INIS)

    Mishonov, T.M.

    1990-06-01

    Acoustic wave emission of the two dimensional plasmons in a semiconductor or superconductor microstructure is investigated by using the phenomenological deformation potential within the jellium model. The plasmons are excited by the external electromagnetic (e.m.) field. The power conversion coefficient of e.m. energy into acoustic wave energy is also estimated. It is shown, the coherent transformation has a sharp resonance at the plasmon frequency of the two dimensional electron gas (2DEG). The incoherent transformation of the e.m. energy is generated by ohmic dissipation of 2DEG. The method proposed for coherent phonon beam generation can be very effective for high mobility 2DEG and for thin superconducting layers if the plasmon frequency ω is smaller than the superconducting gap 2Δ. (author). 21 refs, 1 fig

  17. Confined catalysis under two-dimensional materials

    OpenAIRE

    Li, Haobo; Xiao, Jianping; Fu, Qiang; Bao, Xinhe

    2017-01-01

    Small spaces in nanoreactors may have big implications in chemistry, because the chemical nature of molecules and reactions within the nanospaces can be changed significantly due to the nanoconfinement effect. Two-dimensional (2D) nanoreactor formed under 2D materials can provide a well-defined model system to explore the confined catalysis. We demonstrate a general tendency for weakened surface adsorption under the confinement of graphene overlayer, illustrating the feasible modulation of su...

  18. Two-Dimensional Extreme Learning Machine

    Directory of Open Access Journals (Sweden)

    Bo Jia

    2015-01-01

    (BP networks. However, like many other methods, ELM is originally proposed to handle vector pattern while nonvector patterns in real applications need to be explored, such as image data. We propose the two-dimensional extreme learning machine (2DELM based on the very natural idea to deal with matrix data directly. Unlike original ELM which handles vectors, 2DELM take the matrices as input features without vectorization. Empirical studies on several real image datasets show the efficiency and effectiveness of the algorithm.

  19. Superintegrability on the two dimensional hyperboloid

    International Nuclear Information System (INIS)

    Akopyan, E.; Pogosyan, G.S.; Kalnins, E.G.; Miller, W. Jr

    1998-01-01

    This work is devoted to the investigation of the quantum mechanical systems on the two dimensional hyperboloid which admit separation of variables in at least two coordinate systems. Here we consider two potentials introduced in a paper of C.P.Boyer, E.G.Kalnins and P.Winternitz, which haven't been studied yet. An example of an interbasis expansion is given and the structure of the quadratic algebra generated by the integrals of motion is carried out

  20. Two-dimensional Kagome photonic bandgap waveguide

    DEFF Research Database (Denmark)

    Nielsen, Jens Bo; Søndergaard, Thomas; Libori, Stig E. Barkou

    2000-01-01

    The transverse-magnetic photonic-bandgap-guidance properties are investigated for a planar two-dimensional (2-D) Kagome waveguide configuration using a full-vectorial plane-wave-expansion method. Single-moded well-localized low-index guided modes are found. The localization of the optical modes...... is investigated with respect to the width of the 2-D Kagome waveguide, and the number of modes existing for specific frequencies and waveguide widths is mapped out....

  1. The finite element solution of two-dimensional transverse magnetic scattering problems on the connection machine

    International Nuclear Information System (INIS)

    Hutchinson, S.; Costillo, S.; Dalton, K.; Hensel, E.

    1990-01-01

    A study is conducted of the finite element solution of the partial differential equations governing two-dimensional electromagnetic field scattering problems on a SIMD computer. A nodal assembly technique is introduced which maps a single node to a single processor. The physical domain is first discretized in parallel to yield the node locations of an O-grid mesh. Next, the system of equations is assembled and then solved in parallel using a conjugate gradient algorithm for complex-valued, non-symmetric, non-positive definite systems. Using this technique and Thinking Machines Corporation's Connection Machine-2 (CM-2), problems with more than 250k nodes are solved. Results of electromagnetic scattering, governed by the 2-d scalar Hemoholtz wave equations are presented in this paper. Solutions are demonstrated for a wide range of objects. A summary of performance data is given for the set of test problems

  2. Mechanical exfoliation of two-dimensional materials

    Science.gov (United States)

    Gao, Enlai; Lin, Shao-Zhen; Qin, Zhao; Buehler, Markus J.; Feng, Xi-Qiao; Xu, Zhiping

    2018-06-01

    Two-dimensional materials such as graphene and transition metal dichalcogenides have been identified and drawn much attention over the last few years for their unique structural and electronic properties. However, their rise begins only after these materials are successfully isolated from their layered assemblies or adhesive substrates into individual monolayers. Mechanical exfoliation and transfer are the most successful techniques to obtain high-quality single- or few-layer nanocrystals from their native multi-layer structures or their substrate for growth, which involves interfacial peeling and intralayer tearing processes that are controlled by material properties, geometry and the kinetics of exfoliation. This procedure is rationalized in this work through theoretical analysis and atomistic simulations. We propose a criterion to assess the feasibility for the exfoliation of two-dimensional sheets from an adhesive substrate without fracturing itself, and explore the effects of material and interface properties, as well as the geometrical, kinetic factors on the peeling behaviors and the torn morphology. This multi-scale approach elucidates the microscopic mechanism of the mechanical processes, offering predictive models and tools for the design of experimental procedures to obtain single- or few-layer two-dimensional materials and structures.

  3. 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

  4. 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.

  5. 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.

  6. Two-dimensional magnetohydrodynamic equilibria with flow and studies of equilibria fluctuations

    International Nuclear Information System (INIS)

    Agim, Y.Z.

    1989-08-01

    A set of reduced ideal MHD equations is derived to investigate equilibria of plasmas with mass flow in general two-dimensional geometry. These equations provide a means of investigating the effects of flow on self-consistent equilibria in a number of new two-dimensional configurations such as helically symmetric configurations with helical axis, which are relevant to stellarators, as well as axisymmetric configurations. It is found that as in the axisymmetric case, general two-dimensional flow equilibria are governed by a second-order quasi-linear partial differential equation for a magnetic flux function, which is coupled to a Bernoulli-type equation for the density. The equation for the magnetic flux function becomes hyperbolic at certain critical flow speeds which follow from its characteristic equation. When the equation is hyperbolic, shock phenomena may exist. As a particular example, unidirectional flow along the lines of symmetry is considered. In this case, the equation mentioned above is always elliptic. An exact solution for the case of helically symmetric unidirectional flow is found and studied to determine flow effects on the magnetic topology. In second part of this thesis, magnetic fluctuations due to the thermally excited MHD waves are investigated using fluid and kinetic models to describe stable, uniform, compressible plasma in the range above the drift wave frequency and below the ion cyclotron frequency. It is shown that the fluid model with resistivity yields spectral densities which are roughly Lorentzian, exhibit equipartition with no apparent cutoff in wavenumber space and a Bohm-type diffusion coefficient. Under certain conditions, the ensuing transport may be comparable to classical values. For a phenomenological cutoff imposed on the spectrum, the typical fluctuating-to-equilibrium magnetic field ratio is found to be of the order of 10 -10

  7. Modeling of thin-walled structures interacting with acoustic media as constrained two-dimensional continua

    Science.gov (United States)

    Rabinskiy, L. N.; Zhavoronok, S. I.

    2018-04-01

    The transient interaction of acoustic media and elastic shells is considered on the basis of the transition function approach. The three-dimensional hyperbolic initial boundary-value problem is reduced to a two-dimensional problem of shell theory with integral operators approximating the acoustic medium effect on the shell dynamics. The kernels of these integral operators are determined by the elementary solution of the problem of acoustic waves diffraction at a rigid obstacle with the same boundary shape as the wetted shell surface. The closed-form elementary solution for arbitrary convex obstacles can be obtained at the initial interaction stages on the background of the so-called “thin layer hypothesis”. Thus, the shell–wave interaction model defined by integro-differential dynamic equations with analytically determined kernels of integral operators becomes hence two-dimensional but nonlocal in time. On the other hand, the initial interaction stage results in localized dynamic loadings and consequently in complex strain and stress states that require higher-order shell theories. Here the modified theory of I.N.Vekua–A.A.Amosov-type is formulated in terms of analytical continuum dynamics. The shell model is constructed on a two-dimensional manifold within a set of field variables, Lagrangian density, and constraint equations following from the boundary conditions “shifted” from the shell faces to its base surface. Such an approach allows one to construct consistent low-order shell models within a unified formal hierarchy. The equations of the N th-order shell theory are singularly perturbed and contain second-order partial derivatives with respect to time and surface coordinates whereas the numerical integration of systems of first-order equations is more efficient. Such systems can be obtained as Hamilton–de Donder–Weyl-type equations for the Lagrangian dynamical system. The Hamiltonian formulation of the elementary N th-order shell theory is

  8. 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.

  9. 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.

  10. 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

  11. 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.

  12. 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.

  13. Vector (two-dimensional) magnetic phenomena

    International Nuclear Information System (INIS)

    Enokizono, Masato

    2002-01-01

    In this paper, some interesting phenomena were described from the viewpoint of two-dimensional magnetic property, which is reworded with the vector magnetic property. It shows imperfection of conventional magnetic property and some interested phenomena were discovered, too. We found magnetic materials had the strong nonlinearity both magnitude and spatial phase due to the relationship between the magnetic field strength H-vector and the magnetic flux density B-vector. Therefore, magnetic properties should be defined as the vector relationship. Furthermore, the new Barukhausen signal was observed under rotating flux. (Author)

  14. Two-dimensional Semiconductor-Superconductor Hybrids

    DEFF Research Database (Denmark)

    Suominen, Henri Juhani

    This thesis investigates hybrid two-dimensional semiconductor-superconductor (Sm-S) devices and presents a new material platform exhibiting intimate Sm-S coupling straight out of the box. Starting with the conventional approach, we investigate coupling superconductors to buried quantum well....... To overcome these issues we integrate the superconductor directly into the semiconducting material growth stack, depositing it in-situ in a molecular beam epitaxy system under high vacuum. We present a number of experiments on these hybrid heterostructures, demonstrating near unity interface transparency...

  15. Optimized two-dimensional Sn transport (BISTRO)

    International Nuclear Information System (INIS)

    Palmiotti, G.; Salvatores, M.; Gho, C.

    1990-01-01

    This paper reports on an S n two-dimensional transport module developed for the French fast reactor code system CCRR to optimize algorithms in order to obtain the best performance in terms of computational time. A form of diffusion synthetic acceleration was adopted, and a special effort was made to solve the associated diffusion equation efficiently. The improvements in the algorithms, along with the use of an efficient programming language, led to a significant gain in computational time with respect to the DOT code

  16. Binding energy of two-dimensional biexcitons

    DEFF Research Database (Denmark)

    Singh, Jai; Birkedal, Dan; Vadim, Lyssenko

    1996-01-01

    Using a model structure for a two-dimensional (2D) biexciton confined in a quantum well, it is shown that the form of the Hamiltonian of the 2D biexciton reduces into that of an exciton. The binding energies and Bohr radii of a 2D biexciton in its various internal energy states are derived...... analytically using the fractional dimension approach. The ratio of the binding energy of a 2D biexciton to that of a 2D exciton is found to be 0.228, which agrees very well with the recent experimental value. The results of our approach are compared with those of earlier theories....

  17. Airy beams on two dimensional materials

    Science.gov (United States)

    Imran, Muhammad; Li, Rujiang; Jiang, Yuyu; Lin, Xiao; Zheng, Bin; Dehdashti, Shahram; Xu, Zhiwei; Wang, Huaping

    2018-05-01

    We propose that quasi-transverse-magnetic (quasi-TM) Airy beams can be supported on two dimensional (2D) materials. By taking graphene as a typical example, the solution of quasi-TM Airy beams is studied under the paraxial approximation. The analytical field intensity in a bilayer graphene-based planar plasmonic waveguide is confirmed by the simulation results. Due to the tunability of the chemical potential of graphene, the self-accelerating behavior of the quasi-TM Airy beam can be steered effectively. 2D materials thus provide a good platform to investigate the propagation of Airy beams.

  18. Two-dimensional heat flow apparatus

    Science.gov (United States)

    McDougall, Patrick; Ayars, Eric

    2014-06-01

    We have created an apparatus to quantitatively measure two-dimensional heat flow in a metal plate using a grid of temperature sensors read by a microcontroller. Real-time temperature data are collected from the microcontroller by a computer for comparison with a computational model of the heat equation. The microcontroller-based sensor array allows previously unavailable levels of precision at very low cost, and the combination of measurement and modeling makes for an excellent apparatus for the advanced undergraduate laboratory course.

  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. Efficient two-dimensional magnetotellurics modelling using implicitly ...

    Indian Academy of Sciences (India)

    (MT)), based on eigenmode approach to solve the relevant partial differential equation, for forward com- putation of .... Further, the application of integral boundary condition at the ..... Financial support given (to KK) by Ministry of Human ...

  1. 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.

  2. Decoherence in two-dimensional quantum walks

    International Nuclear Information System (INIS)

    Oliveira, A. C.; Portugal, R.; Donangelo, R.

    2006-01-01

    We analyze the decoherence in quantum walks in two-dimensional lattices generated by broken-link-type noise. In this type of decoherence, the links of the lattice are randomly broken with some given constant probability. We obtain the evolution equation for a quantum walker moving on two-dimensional (2D) lattices subject to this noise, and we point out how to generalize for lattices in more dimensions. In the nonsymmetric case, when the probability of breaking links in one direction is different from the probability in the perpendicular direction, we have obtained a nontrivial result. If one fixes the link-breaking probability in one direction, and gradually increases the probability in the other direction from 0 to 1, the decoherence initially increases until it reaches a maximum value, and then it decreases. This means that, in some cases, one can increase the noise level and still obtain more coherence. Physically, this can be explained as a transition from a decoherent 2D walk to a coherent 1D walk

  3. Study of two-dimensional interchange turbulence

    International Nuclear Information System (INIS)

    Sugama, Hideo; Wakatani, Masahiro.

    1990-04-01

    An eddy viscosity model describing enstrophy transfer in two-dimensional turbulence is presented. This model is similar to that of Canuto et al. and provides an equation for the energy spectral function F(k) as a function of the energy input rate to the system per unit wavenumber, γ s (k). In the enstrophy-transfer inertial range, F(k)∝ k -3 is predicted by the model. The eddy viscosity model is applied to the interchange turbulence of a plasma in shearless magnetic field. Numerical simulation of the two-dimensional interchange turbulence demonstrates that the energy spectrum in the high wavenumber region is well described by this model. The turbulent transport driven by the interchange turbulence is expressed in terms of the Nusselt number Nu, the Rayleigh number Ra and Prantl number Pr in the same manner as that of thermal convection problem. When we use the linear growth rate for γ s (k), our theoretical model predicts that Nu ∝ (Ra·Pr) 1/2 for a constant background pressure gradient and Nu ∝ (Ra·Pr) 1/3 for a self-consistent background pressure profile with the stress-free slip boundary conditions. The latter agrees with our numerical result showing Nu ∝ Ra 1/3 . (author)

  4. Two-Dimensional Theory of Scientific Representation

    Directory of Open Access Journals (Sweden)

    A Yaghmaie

    2013-03-01

    Full Text Available Scientific representation is an interesting topic for philosophers of science, many of whom have recently explored it from different points of view. There are currently two competing approaches to the issue: cognitive and non-cognitive, and each of them claims its own merits over the other. This article tries to provide a hybrid theory of scientific representation, called Two-Dimensional Theory of Scientific Representation, which has the merits of the two accounts and is free of their shortcomings. To do this, we will argue that although scientific representation needs to use the notion of intentionality, such a notion is defined and realized in a simply structural form contrary to what cognitive approach says about intentionality. After a short introduction, the second part of the paper is devoted to introducing theories of scientific representation briefly. In the third part, the structural accounts of representation will be criticized. The next step is to introduce the two-dimensional theory which involves two key components: fixing and structural fitness. It will be argued that fitness is an objective and non-intentional relation, while fixing is intentional.

  5. 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

  6. 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.

  7. 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...

  8. 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.

  9. 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

  10. 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.

  11. 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.

  12. 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.

  13. 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

  14. 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)

  15. 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

  16. Two-dimensional simulation of sintering process

    International Nuclear Information System (INIS)

    Vasconcelos, Vanderley de; Pinto, Lucio Carlos Martins; Vasconcelos, Wander L.

    1996-01-01

    The results of two-dimensional simulations are directly applied to systems in which one of the dimensions is much smaller than the others, and to sections of three dimensional models. Moreover, these simulations are the first step of the analysis of more complex three-dimensional systems. In this work, two basic features of the sintering process are studied: the types of particle size distributions related to the powder production processes and the evolution of geometric parameters of the resultant microstructures during the solid-state sintering. Random packing of equal spheres is considered in the sintering simulation. The packing algorithm does not take into account the interactive forces between the particles. The used sintering algorithm causes the densification of the particle set. (author)

  17. Two dimensional generalizations of the Newcomb equation

    International Nuclear Information System (INIS)

    Dewar, R.L.; Pletzer, A.

    1989-11-01

    The Bineau reduction to scalar form of the equation governing ideal, zero frequency linearized displacements from a hydromagnetic equilibrium possessing a continuous symmetry is performed in 'universal coordinates', applicable to both the toroidal and helical cases. The resulting generalized Newcomb equation (GNE) has in general a more complicated form than the corresponding one dimensional equation obtained by Newcomb in the case of circular cylindrical symmetry, but in this cylindrical case , the equation can be transformed to that of Newcomb. In the two dimensional case there is a transformation which leaves the form of the GNE invariant and simplifies the Frobenius expansion about a rational surface, especially in the limit of zero pressure gradient. The Frobenius expansions about a mode rational surface is developed and the connection with Hamiltonian transformation theory is shown. 17 refs

  18. Pressure of two-dimensional Yukawa liquids

    International Nuclear Information System (INIS)

    Feng, Yan; Wang, Lei; Tian, Wen-de; Goree, J; Liu, Bin

    2016-01-01

    A simple analytic expression for the pressure of a two-dimensional Yukawa liquid is found by fitting results from a molecular dynamics simulation. The results verify that the pressure can be written as the sum of a potential term which is a simple multiple of the Coulomb potential energy at a distance of the Wigner–Seitz radius, and a kinetic term which is a multiple of the one for an ideal gas. Dimensionless coefficients for each of these terms are found empirically, by fitting. The resulting analytic expression, with its empirically determined coefficients, is plotted as isochores, or curves of constant area. These results should be applicable to monolayer dusty plasmas. (paper)

  19. Two dimensional nanomaterials for flexible supercapacitors.

    Science.gov (United States)

    Peng, Xu; Peng, Lele; Wu, Changzheng; Xie, Yi

    2014-05-21

    Flexible supercapacitors, as one of most promising emerging energy storage devices, are of great interest owing to their high power density with great mechanical compliance, making them very suitable as power back-ups for future stretchable electronics. Two-dimensional (2D) nanomaterials, including the quasi-2D graphene and inorganic graphene-like materials (IGMs), have been greatly explored to providing huge potential for the development of flexible supercapacitors with higher electrochemical performance. This review article is devoted to recent progresses in engineering 2D nanomaterials for flexible supercapacitors, which survey the evolution of electrode materials, recent developments in 2D nanomaterials and their hybrid nanostructures with regulated electrical properties, and the new planar configurations of flexible supercapacitors. Furthermore, a brief discussion on future directions, challenges and opportunities in this fascinating area is also provided.

  20. Geometrical aspects of solvable two dimensional models

    International Nuclear Information System (INIS)

    Tanaka, K.

    1989-01-01

    It was noted that there is a connection between the non-linear two-dimensional (2D) models and the scalar curvature r, i.e., when r = -2 the equations of motion of the Liouville and sine-Gordon models were obtained. Further, solutions of various classical nonlinear 2D models can be obtained from the condition that the appropriate curvature two form Ω = 0, which suggests that these models are closely related. This relation is explored further in the classical version by obtaining the equations of motion from the evolution equations, the infinite number of conserved quantities, and the common central charge. The Poisson brackets of the solvable 2D models are specified by the Virasoro algebra. 21 refs

  1. Two-dimensional materials for ultrafast lasers

    International Nuclear Information System (INIS)

    Wang Fengqiu

    2017-01-01

    As the fundamental optical properties and novel photophysics of graphene and related two-dimensional (2D) crystals are being extensively investigated and revealed, a range of potential applications in optical and optoelectronic devices have been proposed and demonstrated. Of the many possibilities, the use of 2D materials as broadband, cost-effective and versatile ultrafast optical switches (or saturable absorbers) for short-pulsed lasers constitutes a rapidly developing field with not only a good number of publications, but also a promising prospect for commercial exploitation. This review primarily focuses on the recent development of pulsed lasers based on several representative 2D materials. The comparative advantages of these materials are discussed, and challenges to practical exploitation, which represent good future directions of research, are laid out. (paper)

  2. Two-dimensional phase fraction charts

    International Nuclear Information System (INIS)

    Morral, J.E.

    1984-01-01

    A phase fraction chart is a graphical representation of the amount of each phase present in a system as a function of temperature, composition or other variable. Examples are phase fraction versus temperature charts used to characterize specific alloys and as a teaching tool in elementary texts, and Schaeffler diagrams used to predict the amount of ferrite in stainless steel welds. Isothermal-transformation diagrams (TTT diagrams) are examples that give phase (or microconstituent) amount versus temperature and time. The purpose of this communication is to discuss the properties of two-dimensional phase fraction charts in more general terms than have been reported before. It is shown that they can represent multi-component, multiphase equilibria in a way which is easier to read and which contains more information than the isotherms and isopleths of multi-component phase diagrams

  3. Two-dimensional motions of rockets

    International Nuclear Information System (INIS)

    Kang, Yoonhwan; Bae, Saebyok

    2007-01-01

    We analyse the two-dimensional motions of the rockets for various types of rocket thrusts, the air friction and the gravitation by using a suitable representation of the rocket equation and the numerical calculation. The slope shapes of the rocket trajectories are discussed for the three types of rocket engines. Unlike the projectile motions, the descending parts of the trajectories tend to be gentler and straighter slopes than the ascending parts for relatively large launching angles due to the non-vanishing thrusts. We discuss the ranges, the maximum altitudes and the engine performances of the rockets. It seems that the exponential fuel exhaustion can be the most potent engine for the longest and highest flights

  4. Two dimensional NMR studies of polysaccharides

    International Nuclear Information System (INIS)

    Byrd, R.A.; Egan, W.; Summers, M.F.

    1987-01-01

    Polysaccharides are very important components in the immune response system. Capsular polysaccharides and lipopolysaccharides occupy cell surface sites of bacteria, play key roles in recognition and some have been used to develop vaccines. Consequently, the ability to determine chemical structures of these systems is vital to an understanding of their immunogenic action. The authors have been utilizing recently developed two-dimensional homonuclear and heteronuclear correlation spectroscopy for unambiguous assignment and structure determination of a number of polysaccharides. In particular, the 1 H-detected heteronuclear correlation experiments are essential to the rapid and sensitive determination of these structures. Linkage sites are determined by independent polarization transfer experiments and multiple quantum correlation experiments. These methods permit the complete structure determination on very small amounts of the polysaccharides. They present the results of a number of structural determinations and discuss the limits of these experiments in terms of their applications to polysaccharides

  5. Two-Dimensional Homogeneous Fermi Gases

    Science.gov (United States)

    Hueck, Klaus; Luick, Niclas; Sobirey, Lennart; Siegl, Jonas; Lompe, Thomas; Moritz, Henning

    2018-02-01

    We report on the experimental realization of homogeneous two-dimensional (2D) Fermi gases trapped in a box potential. In contrast to harmonically trapped gases, these homogeneous 2D systems are ideally suited to probe local as well as nonlocal properties of strongly interacting many-body systems. As a first benchmark experiment, we use a local probe to measure the density of a noninteracting 2D Fermi gas as a function of the chemical potential and find excellent agreement with the corresponding equation of state. We then perform matter wave focusing to extract the momentum distribution of the system and directly observe Pauli blocking in a near unity occupation of momentum states. Finally, we measure the momentum distribution of an interacting homogeneous 2D gas in the crossover between attractively interacting fermions and bosonic dimers.

  6. Two-dimensional electroacoustic waves in silicene

    Science.gov (United States)

    Zhukov, Alexander V.; Bouffanais, Roland; Konobeeva, Natalia N.; Belonenko, Mikhail B.

    2018-01-01

    In this letter, we investigate the propagation of two-dimensional electromagnetic waves in a piezoelectric medium built upon silicene. Ultrashort optical pulses of Gaussian form are considered to probe this medium. On the basis of Maxwell's equations supplemented with the wave equation for the medium's displacement vector, we obtain the effective governing equation for the vector potential associated with the electromagnetic field, as well as the component of the displacement vector. The dependence of the pulse shape on the bandgap in silicene and the piezoelectric coefficient of the medium was analyzed, thereby revealing a nontrivial triadic interplay between the characteristics of the pulse dynamics, the electronic properties of silicene, and the electrically induced mechanical vibrations of the medium. In particular, we uncovered the possibility for an amplification of the pulse amplitude through the tuning of the piezoelectric coefficient. This property could potentially offer promising prospects for the development of amplification devices for the optoelectronics industry.

  7. Versatile two-dimensional transition metal dichalcogenides

    DEFF Research Database (Denmark)

    Canulescu, Stela; Affannoukoué, Kévin; Döbeli, Max

    ), a strategy for the fabrication of 2D heterostructures must be developed. Here we demonstrate a novel approach for the bottom-up synthesis of TMDC monolayers, namely Pulsed Laser Deposition (PLD) combined with a sulfur evaporation beam. PLD relies on the use of a pulsed laser (ns pulse duration) to induce...... material transfer from a solid source (such as a sintered target of MoS2) to a substrate (such as Si or sapphire). The deposition rate in PLD is typically much less than a monolayer per pulse, meaning that the number of MLs can be controlled by a careful selection of the number of laser pulses......Two-dimensional transition metal dichalcogenides (2D-TMDCs), such as MoS2, have emerged as a new class of semiconducting materials with distinct optical and electrical properties. The availability of 2D-TMDCs with distinct band gaps allows for unlimited combinations of TMDC monolayers (MLs...

  8. Two-dimensional heterostructures for energy storage

    Energy Technology Data Exchange (ETDEWEB)

    Gogotsi, Yury G. [Drexel Univ., Philadelphia, PA (United States); Pomerantseva, Ekaterina [Drexel Univ., Philadelphia, PA (United States)

    2017-06-12

    Two-dimensional (2D) materials provide slit-shaped ion diffusion channels that enable fast movement of lithium and other ions. However, electronic conductivity, the number of intercalation sites, and stability during extended cycling are also crucial for building high-performance energy storage devices. While individual 2D materials, such as graphene, show some of the required properties, none of them can offer all properties needed to maximize energy density, power density, and cycle life. Here we argue that stacking different 2D materials into heterostructured architectures opens an opportunity to construct electrodes that would combine the advantages of the individual building blocks while eliminating the associated shortcomings. We discuss characteristics of common 2D materials and provide examples of 2D heterostructured electrodes that showed new phenomena leading to superior electrochemical performance. As a result, we also consider electrode fabrication approaches and finally outline future steps to create 2D heterostructured electrodes that could greatly expand current energy storage technologies.

  9. Two-dimensional fourier transform spectrometer

    Science.gov (United States)

    DeFlores, Lauren; Tokmakoff, Andrei

    2013-09-03

    The present invention relates to a system and methods for acquiring two-dimensional Fourier transform (2D FT) spectra. Overlap of a collinear pulse pair and probe induce a molecular response which is collected by spectral dispersion of the signal modulated probe beam. Simultaneous collection of the molecular response, pulse timing and characteristics permit real time phasing and rapid acquisition of spectra. Full spectra are acquired as a function of pulse pair timings and numerically transformed to achieve the full frequency-frequency spectrum. This method demonstrates the ability to acquire information on molecular dynamics, couplings and structure in a simple apparatus. Multi-dimensional methods can be used for diagnostic and analytical measurements in the biological, biomedical, and chemical fields.

  10. Equivalency of two-dimensional algebras

    International Nuclear Information System (INIS)

    Santos, Gildemar Carneiro dos; Pomponet Filho, Balbino Jose S.

    2011-01-01

    Full text: Let us consider a vector z = xi + yj over the field of real numbers, whose basis (i,j) satisfy a given algebra. Any property of this algebra will be reflected in any function of z, so we can state that the knowledge of the properties of an algebra leads to more general conclusions than the knowledge of the properties of a function. However structural properties of an algebra do not change when this algebra suffers a linear transformation, though the structural constants defining this algebra do change. We say that two algebras are equivalent to each other whenever they are related by a linear transformation. In this case, we have found that some relations between the structural constants are sufficient to recognize whether or not an algebra is equivalent to another. In spite that the basis transform linearly, the structural constants change like a third order tensor, but some combinations of these tensors result in a linear transformation, allowing to write the entries of the transformation matrix as function of the structural constants. Eventually, a systematic way to find the transformation matrix between these equivalent algebras is obtained. In this sense, we have performed the thorough classification of associative commutative two-dimensional algebras, and find that even non-division algebra may be helpful in solving non-linear dynamic systems. The Mandelbrot set was used to have a pictorial view of each algebra, since equivalent algebras result in the same pattern. Presently we have succeeded in classifying some non-associative two-dimensional algebras, a task more difficult than for associative one. (author)

  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. Two-Dimensional Impact Reconstruction Method for Rail Defect Inspection

    Directory of Open Access Journals (Sweden)

    Jie Zhao

    2014-01-01

    Full Text Available The safety of train operating is seriously menaced by the rail defects, so it is of great significance to inspect rail defects dynamically while the train is operating. This paper presents a two-dimensional impact reconstruction method to realize the on-line inspection of rail defects. The proposed method utilizes preprocessing technology to convert time domain vertical vibration signals acquired by wireless sensor network to space signals. The modern time-frequency analysis method is improved to reconstruct the obtained multisensor information. Then, the image fusion processing technology based on spectrum threshold processing and node color labeling is proposed to reduce the noise, and blank the periodic impact signal caused by rail joints and locomotive running gear. This method can convert the aperiodic impact signals caused by rail defects to partial periodic impact signals, and locate the rail defects. An application indicates that the two-dimensional impact reconstruction method could display the impact caused by rail defects obviously, and is an effective on-line rail defects inspection method.

  15. 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

  16. 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.

  17. 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.

  18. 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.

  19. 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

  20. 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.

  1. 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…

  2. 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.

  3. 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

  4. 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).

  5. 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.

  6. 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.

  7. 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...

  8. 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.

  9. 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.

  10. 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

  11. 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.

  12. 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...

  13. 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.

  14. 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...

  15. Two-dimensional electronic spectroscopy with birefringent wedges

    Energy Technology Data Exchange (ETDEWEB)

    Réhault, Julien; Maiuri, Margherita; Oriana, Aurelio; Cerullo, Giulio [IFN-CNR, Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano (Italy)

    2014-12-15

    We present a simple experimental setup for performing two-dimensional (2D) electronic spectroscopy in the partially collinear pump-probe geometry. The setup uses a sequence of birefringent wedges to create and delay a pair of phase-locked, collinear pump pulses, with extremely high phase stability and reproducibility. Continuous delay scanning is possible without any active stabilization or position tracking, and allows to record rapidly and easily 2D spectra. The setup works over a broad spectral range from the ultraviolet to the near-IR, it is compatible with few-optical-cycle pulses and can be easily reconfigured to two-colour operation. A simple method for scattering suppression is also introduced. As a proof of principle, we present degenerate and two-color 2D spectra of the light-harvesting complex 1 of purple bacteria.

  16. Electronic Transport in Two-Dimensional Materials

    Science.gov (United States)

    Sangwan, Vinod K.; Hersam, Mark C.

    2018-04-01

    Two-dimensional (2D) materials have captured the attention of the scientific community due to the wide range of unique properties at nanometer-scale thicknesses. While significant exploratory research in 2D materials has been achieved, the understanding of 2D electronic transport and carrier dynamics remains in a nascent stage. Furthermore, because prior review articles have provided general overviews of 2D materials or specifically focused on charge transport in graphene, here we instead highlight charge transport mechanisms in post-graphene 2D materials, with particular emphasis on transition metal dichalcogenides and black phosphorus. For these systems, we delineate the intricacies of electronic transport, including band structure control with thickness and external fields, valley polarization, scattering mechanisms, electrical contacts, and doping. In addition, electronic interactions between 2D materials are considered in the form of van der Waals heterojunctions and composite films. This review concludes with a perspective on the most promising future directions in this fast-evolving field.

  17. Stress distribution in two-dimensional silos

    Science.gov (United States)

    Blanco-Rodríguez, Rodolfo; Pérez-Ángel, Gabriel

    2018-01-01

    Simulations of a polydispersed two-dimensional silo were performed using molecular dynamics, with different numbers of grains reaching up to 64 000, verifying numerically the model derived by Janssen and also the main assumption that the walls carry part of the weight due to the static friction between grains with themselves and those with the silo's walls. We vary the friction coefficient, the radii dispersity, the silo width, and the size of grains. We find that the Janssen's model becomes less relevant as the the silo width increases since the behavior of the stresses becomes more hydrostatic. Likewise, we get the normal and tangential stress distribution on the walls evidencing the existence of points of maximum stress. We also obtained the stress matrix with which we observe zones of concentration of load, located always at a height around two thirds of the granular columns. Finally, we observe that the size of the grains affects the distribution of stresses, increasing the weight on the bottom and reducing the normal stress on the walls, as the grains are made smaller (for the same total mass of the granulate), giving again a more hydrostatic and therefore less Janssen-type behavior for the weight of the column.

  18. Asymptotics for Two-dimensional Atoms

    DEFF Research Database (Denmark)

    Nam, Phan Thanh; Portmann, Fabian; Solovej, Jan Philip

    2012-01-01

    We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge $Z>0$ and $N$ quantum electrons of charge -1 is $E(N,Z)=-{1/2}Z^2\\ln Z+(E^{\\TF}(\\lambda)+{1/2}c^{\\rm H})Z^2+o(Z^2)$ when $Z\\to \\infty$ and $N/Z\\to \\lambda$, where $E^{\\TF}(\\lambd......We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge $Z>0$ and $N$ quantum electrons of charge -1 is $E(N,Z)=-{1/2}Z^2\\ln Z+(E^{\\TF}(\\lambda)+{1/2}c^{\\rm H})Z^2+o(Z^2)$ when $Z\\to \\infty$ and $N/Z\\to \\lambda$, where $E......^{\\TF}(\\lambda)$ is given by a Thomas-Fermi type variational problem and $c^{\\rm H}\\approx -2.2339$ is an explicit constant. We also show that the radius of a two-dimensional neutral atom is unbounded when $Z\\to \\infty$, which is contrary to the expected behavior of three-dimensional atoms....

  19. Seismic isolation of two dimensional periodic foundations

    International Nuclear Information System (INIS)

    Yan, Y.; Mo, Y. L.; Laskar, A.; Cheng, Z.; Shi, Z.; Menq, F.; Tang, Y.

    2014-01-01

    Phononic crystal is now used to control acoustic waves. When the crystal goes to a larger scale, it is called periodic structure. The band gaps of the periodic structure can be reduced to range from 0.5 Hz to 50 Hz. Therefore, the periodic structure has potential applications in seismic wave reflection. In civil engineering, the periodic structure can be served as the foundation of upper structure. This type of foundation consisting of periodic structure is called periodic foundation. When the frequency of seismic waves falls into the band gaps of the periodic foundation, the seismic wave can be blocked. Field experiments of a scaled two dimensional (2D) periodic foundation with an upper structure were conducted to verify the band gap effects. Test results showed the 2D periodic foundation can effectively reduce the response of the upper structure for excitations with frequencies within the frequency band gaps. When the experimental and the finite element analysis results are compared, they agree well with each other, indicating that 2D periodic foundation is a feasible way of reducing seismic vibrations.

  20. Two-dimensional topological photonic systems

    Science.gov (United States)

    Sun, Xiao-Chen; He, Cheng; Liu, Xiao-Ping; Lu, Ming-Hui; Zhu, Shi-Ning; Chen, Yan-Feng

    2017-09-01

    The topological phase of matter, originally proposed and first demonstrated in fermionic electronic systems, has drawn considerable research attention in the past decades due to its robust transport of edge states and its potential with respect to future quantum information, communication, and computation. Recently, searching for such a unique material phase in bosonic systems has become a hot research topic worldwide. So far, many bosonic topological models and methods for realizing them have been discovered in photonic systems, acoustic systems, mechanical systems, etc. These discoveries have certainly yielded vast opportunities in designing material phases and related properties in the topological domain. In this review, we first focus on some of the representative photonic topological models and employ the underlying Dirac model to analyze the edge states and geometric phase. On the basis of these models, three common types of two-dimensional topological photonic systems are discussed: 1) photonic quantum Hall effect with broken time-reversal symmetry; 2) photonic topological insulator and the associated pseudo-time-reversal symmetry-protected mechanism; 3) time/space periodically modulated photonic Floquet topological insulator. Finally, we provide a summary and extension of this emerging field, including a brief introduction to the Weyl point in three-dimensional systems.

  1. Turbulent equipartitions in two dimensional drift convection

    International Nuclear Information System (INIS)

    Isichenko, M.B.; Yankov, V.V.

    1995-01-01

    Unlike the thermodynamic equipartition of energy in conservative systems, turbulent equipartitions (TEP) describe strongly non-equilibrium systems such as turbulent plasmas. In turbulent systems, energy is no longer a good invariant, but one can utilize the conservation of other quantities, such as adiabatic invariants, frozen-in magnetic flux, entropy, or combination thereof, in order to derive new, turbulent quasi-equilibria. These TEP equilibria assume various forms, but in general they sustain spatially inhomogeneous distributions of the usual thermodynamic quantities such as density or temperature. This mechanism explains the effects of particle and energy pinch in tokamaks. The analysis of the relaxed states caused by turbulent mixing is based on the existence of Lagrangian invariants (quantities constant along fluid-particle or other orbits). A turbulent equipartition corresponds to the spatially uniform distribution of relevant Lagrangian invariants. The existence of such turbulent equilibria is demonstrated in the simple model of two dimensional electrostatically turbulent plasma in an inhomogeneous magnetic field. The turbulence is prescribed, and the turbulent transport is assumed to be much stronger than the classical collisional transport. The simplicity of the model makes it possible to derive the equations describing the relaxation to the TEP state in several limits

  2. Radiation effects on two-dimensional materials

    Energy Technology Data Exchange (ETDEWEB)

    Walker, R.C. II; Robinson, J.A. [Department of Materials Science, Penn State, University Park, PA (United States); Center for Two-Dimensional Layered Materials, Penn State, University Park, PA (United States); Shi, T. [Department of Mechanical and Nuclear Engineering, Penn State, University Park, PA (United States); Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI (United States); Silva, E.C. [GlobalFoundries, Malta, NY (United States); Jovanovic, I. [Department of Nuclear Engineering and Radiological Sciences, University of Michigan, Ann Arbor, MI (United States)

    2016-12-15

    The effects of electromagnetic and particle irradiation on two-dimensional materials (2DMs) are discussed in this review. Radiation creates defects that impact the structure and electronic performance of materials. Determining the impact of these defects is important for developing 2DM-based devices for use in high-radiation environments, such as space or nuclear reactors. As such, most experimental studies have been focused on determining total ionizing dose damage to 2DMs and devices. Total dose experiments using X-rays, gamma rays, electrons, protons, and heavy ions are summarized in this review. We briefly discuss the possibility of investigating single event effects in 2DMs based on initial ion beam irradiation experiments and the development of 2DM-based integrated circuits. Additionally, beneficial uses of irradiation such as ion implantation to dope materials or electron-beam and helium-beam etching to shape materials have begun to be used on 2DMs and are reviewed as well. For non-ionizing radiation, such as low-energy photons, we review the literature on 2DM-based photo-detection from terahertz to UV. The majority of photo-detecting devices operate in the visible and UV range, and for this reason they are the focus of this review. However, we review the progress in developing 2DMs for detecting infrared and terahertz radiation. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  3. Buckled two-dimensional Xene sheets.

    Science.gov (United States)

    Molle, Alessandro; Goldberger, Joshua; Houssa, Michel; Xu, Yong; Zhang, Shou-Cheng; Akinwande, Deji

    2017-02-01

    Silicene, germanene and stanene are part of a monoelemental class of two-dimensional (2D) crystals termed 2D-Xenes (X = Si, Ge, Sn and so on) which, together with their ligand-functionalized derivatives referred to as Xanes, are comprised of group IVA atoms arranged in a honeycomb lattice - similar to graphene but with varying degrees of buckling. Their electronic structure ranges from trivial insulators, to semiconductors with tunable gaps, to semi-metallic, depending on the substrate, chemical functionalization and strain. More than a dozen different topological insulator states are predicted to emerge, including the quantum spin Hall state at room temperature, which, if realized, would enable new classes of nanoelectronic and spintronic devices, such as the topological field-effect transistor. The electronic structure can be tuned, for example, by changing the group IVA element, the degree of spin-orbit coupling, the functionalization chemistry or the substrate, making the 2D-Xene systems promising multifunctional 2D materials for nanotechnology. This Perspective highlights the current state of the art and future opportunities in the manipulation and stability of these materials, their functions and applications, and novel device concepts.

  4. Two-dimensional neutron scintillation detector with optimal gamma discrimination

    International Nuclear Information System (INIS)

    Kanyo, M.; Reinartz, R.; Schelten, J.; Mueller, K.D.

    1993-01-01

    The gamma sensitivity of a two-dimensional scintillation neutron detector based on position sensitive photomultipliers (Hamamatsu R2387 PM) has been minimized by a digital differential discrimination unit. Since the photomultiplier gain is position-dependent by ±25% a discrimination unit was developed where digital upper and lower discrimination levels are set due to the position-dependent photomultiplier gain obtained from calibration measurements. By this method narrow discriminator windows can be used to reduce the gamma background drastically without effecting the neutron sensitivity of the detector. The new discrimination method and its performance tested by neutron measurements will be described. Experimental results concerning spatial resolution and γ-sensitivity are presented

  5. Discrete formulation for two-dimensional multigroup neutron diffusion equations

    Energy Technology Data Exchange (ETDEWEB)

    Vosoughi, Naser E-mail: vosoughi@mehr.sharif.edu; Salehi, Ali A.; Shahriari, Majid

    2003-02-01

    The objective of this paper is to introduce a new numerical method for neutronic calculation in a reactor core. This method can produce the final finite form of the neutron diffusion equation by classifying the neutronic variables and using two kinds of cell complexes without starting from the conventional differential form of the neutron diffusion equation. The method with linear interpolation produces the same convergence as the linear continuous finite element method. The quadratic interpolation is proven; the convergence order depends on the shape of the dual cell. The maximum convergence order is achieved by choosing the dual cell based on two Gauss' points. The accuracy of the method was examined with a well-known IAEA two-dimensional benchmark problem. The numerical results demonstrate the effectiveness of the new method.

  6. Discrete formulation for two-dimensional multigroup neutron diffusion equations

    International Nuclear Information System (INIS)

    Vosoughi, Naser; Salehi, Ali A.; Shahriari, Majid

    2003-01-01

    The objective of this paper is to introduce a new numerical method for neutronic calculation in a reactor core. This method can produce the final finite form of the neutron diffusion equation by classifying the neutronic variables and using two kinds of cell complexes without starting from the conventional differential form of the neutron diffusion equation. The method with linear interpolation produces the same convergence as the linear continuous finite element method. The quadratic interpolation is proven; the convergence order depends on the shape of the dual cell. The maximum convergence order is achieved by choosing the dual cell based on two Gauss' points. The accuracy of the method was examined with a well-known IAEA two-dimensional benchmark problem. The numerical results demonstrate the effectiveness of the new method

  7. 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.

  8. 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.

  9. Two-dimensional boundary-value problem for ion-ion diffusion

    International Nuclear Information System (INIS)

    Tuszewski, M.; Lichtenberg, A.J.

    1977-01-01

    Like-particle diffusion is usually negligible compared with unlike-particle diffusion because it is two orders higher in spatial derivatives. When the ratio of the ion gyroradius to the plasma transverse dimension is of the order of the fourth root of the mass ratio, previous one-dimensional analysis indicated that like-particle diffusion is significant. A two-dimensional boundary-value problem for ion-ion diffusion is investigated. Numerical solutions are found with models for which the nonlinear partial differential equation reduces to an ordinary fourth-order differential equation. These solutions indicate that the ion-ion losses are higher by a factor of six for a slab geometry, and by a factor of four for circular geometry, than estimated from dimensional analysis. The solutions are applied to a multiple mirror experiment stabilized with a quadrupole magnetic field which generates highly elliptical flux surfaces. It is found that the ion-ion losses dominate the electron-ion losses and that these classical radial losses contribute to a significant decrease of plasma lifetime, in qualitiative agreement with the experimental results

  10. 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.

  11. 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.

  12. 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.

  13. 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

  14. Two-dimensional vibrational-electronic spectroscopy

    Science.gov (United States)

    Courtney, Trevor L.; Fox, Zachary W.; Slenkamp, Karla M.; Khalil, Munira

    2015-10-01

    Two-dimensional vibrational-electronic (2D VE) spectroscopy is a femtosecond Fourier transform (FT) third-order nonlinear technique that creates a link between existing 2D FT spectroscopies in the vibrational and electronic regions of the spectrum. 2D VE spectroscopy enables a direct measurement of infrared (IR) and electronic dipole moment cross terms by utilizing mid-IR pump and optical probe fields that are resonant with vibrational and electronic transitions, respectively, in a sample of interest. We detail this newly developed 2D VE spectroscopy experiment and outline the information contained in a 2D VE spectrum. We then use this technique and its single-pump counterpart (1D VE) to probe the vibrational-electronic couplings between high frequency cyanide stretching vibrations (νCN) and either a ligand-to-metal charge transfer transition ([FeIII(CN)6]3- dissolved in formamide) or a metal-to-metal charge transfer (MMCT) transition ([(CN)5FeIICNRuIII(NH3)5]- dissolved in formamide). The 2D VE spectra of both molecules reveal peaks resulting from coupled high- and low-frequency vibrational modes to the charge transfer transition. The time-evolving amplitudes and positions of the peaks in the 2D VE spectra report on coherent and incoherent vibrational energy transfer dynamics among the coupled vibrational modes and the charge transfer transition. The selectivity of 2D VE spectroscopy to vibronic processes is evidenced from the selective coupling of specific νCN modes to the MMCT transition in the mixed valence complex. The lineshapes in 2D VE spectra report on the correlation of the frequency fluctuations between the coupled vibrational and electronic frequencies in the mixed valence complex which has a time scale of 1 ps. The details and results of this study confirm the versatility of 2D VE spectroscopy and its applicability to probe how vibrations modulate charge and energy transfer in a wide range of complex molecular, material, and biological systems.

  15. Two-dimensional silica opens new perspectives

    Science.gov (United States)

    Büchner, Christin; Heyde, Markus

    2017-12-01

    In recent years, silica films have emerged as a novel class of two-dimensional (2D) materials. Several groups succeeded in epitaxial growth of ultrathin SiO2 layers using different growth methods and various substrates. The structures consist of tetrahedral [SiO4] building blocks in two mirror symmetrical planes, connected via oxygen bridges. This arrangement is called a silica bilayer as it is the thinnest 2D arrangement with the stoichiometry SiO2 known today. With all bonds saturated within the nano-sheet, the interaction with the substrate is based on van der Waals forces. Complex ring networks are observed, including hexagonal honeycomb lattices, point defects and domain boundaries, as well as amorphous domains. The network structures are highly tuneable through variation of the substrate, deposition parameters, cooling procedure, introducing dopants or intercalating small species. The amorphous networks and structural defects were resolved with atomic resolution microscopy and modeled with density functional theory and molecular dynamics. Such data contribute to our understanding of the formation and characteristic motifs of glassy systems. Growth studies and doping with other chemical elements reveal ways to tune ring sizes and defects as well as chemical reactivities. The pristine films have been utilized as molecular sieves and for confining molecules in nanocatalysis. Post growth hydroxylation can be used to tweak the reactivity as well. The electronic properties of silica bilayers are favourable for using silica as insulators in 2D material stacks. Due to the fully saturated atomic structure, the bilayer interacts weakly with the substrate and can be described as quasi-freestanding. Recently, a mm-scale film transfer under structure retention has been demonstrated. The chemical and mechanical stability of silica bilayers is very promising for technological applications in 2D heterostacks. Due to the impact of this bilayer system for glass science

  16. Two-dimensional vibrational-electronic spectroscopy

    Energy Technology Data Exchange (ETDEWEB)

    Courtney, Trevor L.; Fox, Zachary W.; Slenkamp, Karla M.; Khalil, Munira, E-mail: mkhalil@uw.edu [Department of Chemistry, University of Washington, Box 351700, Seattle, Washington 98195 (United States)

    2015-10-21

    Two-dimensional vibrational-electronic (2D VE) spectroscopy is a femtosecond Fourier transform (FT) third-order nonlinear technique that creates a link between existing 2D FT spectroscopies in the vibrational and electronic regions of the spectrum. 2D VE spectroscopy enables a direct measurement of infrared (IR) and electronic dipole moment cross terms by utilizing mid-IR pump and optical probe fields that are resonant with vibrational and electronic transitions, respectively, in a sample of interest. We detail this newly developed 2D VE spectroscopy experiment and outline the information contained in a 2D VE spectrum. We then use this technique and its single-pump counterpart (1D VE) to probe the vibrational-electronic couplings between high frequency cyanide stretching vibrations (ν{sub CN}) and either a ligand-to-metal charge transfer transition ([Fe{sup III}(CN){sub 6}]{sup 3−} dissolved in formamide) or a metal-to-metal charge transfer (MMCT) transition ([(CN){sub 5}Fe{sup II}CNRu{sup III}(NH{sub 3}){sub 5}]{sup −} dissolved in formamide). The 2D VE spectra of both molecules reveal peaks resulting from coupled high- and low-frequency vibrational modes to the charge transfer transition. The time-evolving amplitudes and positions of the peaks in the 2D VE spectra report on coherent and incoherent vibrational energy transfer dynamics among the coupled vibrational modes and the charge transfer transition. The selectivity of 2D VE spectroscopy to vibronic processes is evidenced from the selective coupling of specific ν{sub CN} modes to the MMCT transition in the mixed valence complex. The lineshapes in 2D VE spectra report on the correlation of the frequency fluctuations between the coupled vibrational and electronic frequencies in the mixed valence complex which has a time scale of 1 ps. The details and results of this study confirm the versatility of 2D VE spectroscopy and its applicability to probe how vibrations modulate charge and energy transfer in a

  17. 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.

  18. 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.

  19. 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.

  20. 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

  1. 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.

  2. 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)

  3. 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.

  4. 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

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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

  12. 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.)

  13. 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.

  14. 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)

  15. 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)

  16. 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.

  17. 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

  18. One class of meromorphic solutions of general two-dimensional nonlinear equations, connected with the algebraic inverse scattering method.

    Science.gov (United States)

    Chudnovsky, D V

    1978-09-01

    For systems of nonlinear equations having the form [L(n) - ( partial differential/ partial differentialt), L(m) - ( partial differential/ partial differentialy)] = 0 the class of meromorphic solutions obtained from the linear equations [Formula: see text] is presented.

  19. Two-dimensional exactly and completely integrable dynamic systems (Monopoles, instantons, dual models, relativistic strings, Lund-Regge model, generalized Toda lattice, etc)

    International Nuclear Information System (INIS)

    Leznov, A.N.; Saveliev, M.V.

    1982-01-01

    An investigation of two-dimensional exactly and completely integrable dynamical systems associated with the local part of an arbitrary Lie algebra g whose grading is consistent with an arbitrary integral embedding of 3d-subalgebra in g has been carried out. The corresponding systems of nonlinear partial differential equations of the second order h been constructed in an explicit form and their genral solutions in the sense of a Goursat problem have been obtained. A method for the construction of a wide class of infinite-dimensional Lie algebras of finite growth has been proposed

  20. 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.

  1. Lie algebra contractions on two-dimensional hyperboloid

    International Nuclear Information System (INIS)

    Pogosyan, G. S.; Yakhno, A.

    2010-01-01

    The Inoenue-Wigner contraction from the SO(2, 1) group to the Euclidean E(2) and E(1, 1) group is used to relate the separation of variables in Laplace-Beltrami (Helmholtz) equations for the four corresponding two-dimensional homogeneous spaces: two-dimensional hyperboloids and two-dimensional Euclidean and pseudo-Euclidean spaces. We show how the nine systems of coordinates on the two-dimensional hyperboloids contracted to the four systems of coordinates on E 2 and eight on E 1,1 . The text was submitted by the authors in English.

  2. General method and exact solutions to a generalized variable-coefficient two-dimensional KdV equation

    International Nuclear Information System (INIS)

    Chen, Yong; Shanghai Jiao-Tong Univ., Shangai; Chinese Academy of sciences, Beijing

    2005-01-01

    A general method to uniformly construct exact solutions in terms of special function of nonlinear partial differential equations is presented by means of a more general ansatz and symbolic computation. Making use of the general method, we can successfully obtain the solutions found by the method proposed by Fan (J. Phys. A., 36 (2003) 7009) and find other new and more general solutions, which include polynomial solutions, exponential solutions, rational solutions, triangular periodic wave solution, soliton solutions, soliton-like solutions and Jacobi, Weierstrass doubly periodic wave solutions. A general variable-coefficient two-dimensional KdV equation is chosen to illustrate the method. As a result, some new exact soliton-like solutions are obtained. planets. The numerical results are given in tables. The results are discussed in the conclusion

  3. 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 ...

  4. A Galleria Boundary Element Method for two-dimensional nonlinear magnetostatics

    Science.gov (United States)

    Brovont, Aaron D.

    The Boundary Element Method (BEM) is a numerical technique for solving partial differential equations that is used broadly among the engineering disciplines. The main advantage of this method is that one needs only to mesh the boundary of a solution domain. A key drawback is the myriad of integrals that must be evaluated to populate the full system matrix. To this day these integrals have been evaluated using numerical quadrature. In this research, a Galerkin formulation of the BEM is derived and implemented to solve two-dimensional magnetostatic problems with a focus on accurate, rapid computation. To this end, exact, closed-form solutions have been derived for all the integrals comprising the system matrix as well as those required to compute fields in post-processing; the need for numerical integration has been eliminated. It is shown that calculation of the system matrix elements using analytical solutions is 15-20 times faster than with numerical integration of similar accuracy. Furthermore, through the example analysis of a c-core inductor, it is demonstrated that the present BEM formulation is a competitive alternative to the Finite Element Method (FEM) for linear magnetostatic analysis. Finally, the BEM formulation is extended to analyze nonlinear magnetostatic problems via the Dual Reciprocity Method (DRBEM). It is shown that a coarse, meshless analysis using the DRBEM is able to achieve RMS error of 3-6% compared to a commercial FEM package in lightly saturated conditions.

  5. Ferromagnetism in the two-dimensional periodic Anderson model

    International Nuclear Information System (INIS)

    Batista, C. D.; Bonca, J.; Gubernatis, J. E.

    2001-01-01

    Using the constrained-path Monte Carlo method, we studied the magnetic properties of the two-dimensional periodic Anderson model for electron fillings between 1/4 and 1/2. We also derived two effective low-energy theories to assist in interpreting the numerical results. For 1/4 filling, we found that the system can be a Mott or a charge-transfer insulator, depending on the relative values of the Coulomb interaction and the charge-transfer gap between the two noninteracting bands. The insulator may be a paramagnet or antiferromagnet. We concentrated on the effect of electron doping on these insulating phases. Upon doping we obtained a partially saturated ferromagnetic phase for low concentrations of conduction electrons. If the system were a charge-transfer insulator, we would find that the ferromagnetism is induced by the well-known Ruderman-Kittel-Kasuya-Yosida interaction. However, we found a novel correlated hopping mechanism inducing the ferromagnetism in the region where the nondoped system is a Mott insulator. Our regions of ferromagnetism spanned a much smaller doping range than suggested by recent slave boson and dynamical mean-field theory calculations, but they were consistent with that obtained by density-matrix renormalization group calculations of the one-dimensional periodic Anderson model

  6. 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)

  7. 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.

  8. 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

  9. Beginning Introductory Physics with Two-Dimensional Motion

    Science.gov (United States)

    Huggins, Elisha

    2009-01-01

    During the session on "Introductory College Physics Textbooks" at the 2007 Summer Meeting of the AAPT, there was a brief discussion about whether introductory physics should begin with one-dimensional motion or two-dimensional motion. Here we present the case that by starting with two-dimensional motion, we are able to introduce a considerable…

  10. Two-dimensional black holes and non-commutative spaces

    International Nuclear Information System (INIS)

    Sadeghi, J.

    2008-01-01

    We study the effects of non-commutative spaces on two-dimensional black hole. The event horizon of two-dimensional black hole is obtained in non-commutative space up to second order of perturbative calculations. A lower limit for the non-commutativity parameter is also obtained. The observer in that limit in contrast to commutative case see two horizon

  11. Solution of the two-dimensional spectral factorization problem

    Science.gov (United States)

    Lawton, W. M.

    1985-01-01

    An approximation theorem is proven which solves a classic problem in two-dimensional (2-D) filter theory. The theorem shows that any continuous two-dimensional spectrum can be uniformly approximated by the squared modulus of a recursively stable finite trigonometric polynomial supported on a nonsymmetric half-plane.

  12. Two-dimensional Navier-Stokes turbulence in bounded domains

    NARCIS (Netherlands)

    Clercx, H.J.H.; van Heijst, G.J.F.

    In this review we will discuss recent experimental and numerical results of quasi-two-dimensional decaying and forced Navier–Stokes turbulence in bounded domains. We will give a concise overview of developments in two-dimensional turbulence research, with emphasis on the progress made during the

  13. Two-dimensional Navier-Stokes turbulence in bounded domains

    NARCIS (Netherlands)

    Clercx, H.J.H.; Heijst, van G.J.F.

    2009-01-01

    In this review we will discuss recent experimental and numerical results of quasi-two-dimensional decaying and forced Navier–Stokes turbulence in bounded domains. We will give a concise overview of developments in two-dimensional turbulence research, with emphasis on the progress made during the

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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)

  3. 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.

  4. 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)

  5. 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...

  6. 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.

  7. 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

  8. 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

  9. "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.

  10. 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.

  11. 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.

  12. 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.

  13. 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

  14. 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.

  15. Surface and Interface Engineering of Organometallic and Two Dimensional Semiconductor

    Science.gov (United States)

    Park, Jun Hong

    For over half a century, inorganic Si and III-V materials have led the modern semiconductor industry, expanding to logic transistor and optoelectronic applications. However, these inorganic materials have faced two different fundamental limitations, flexibility for wearable applications and scaling limitation as logic transistors. As a result, the organic and two dimensional have been studied intentionally for various fields. In the present dissertation, three different studies will be presented with followed order; (1) the chemical response of organic semiconductor in NO2 exposure. (2) The surface and stability of WSe2 in ambient air. (3) Deposition of dielectric on two dimensional materials using organometallic seeding layer. The organic molecules rely on the van der Waals interaction during growth of thin films, contrast to covalent bond inorganic semiconductors. Therefore, the morphology and electronic property at surface of organic semiconductor in micro scale is more sensitive to change in gaseous conditions. In addition, metal phthalocyanine, which is one of organic semiconductor materials, change their electronic property as reaction with gaseous analytes, suggesting as potential chemical sensing platforms. In the present part, the growth behavior of metal phthalocyanine and surface response to gaseous condition will be elucidated using scanning tunneling microscopy (STM). In second part, the surface of layered transition metal dichalcogenides and their chemical response to exposure ambient air will be investigated, using STM. Layered transition metal dichalcogenides (TMDs) have attracted widespread attention in the scientific community for electronic device applications because improved electrostatic gate control and suppression of short channel leakage resulted from their atomic thin body. To fabricate the transistor based on TMDs, TMDs should be exposed to ambient conditions, while the effect of air exposure has not been understood fully. In this part

  16. 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

  17. 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

  18. 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.

  19. Two-dimensional steady unsaturated flow through embedded elliptical layers

    Science.gov (United States)

    Bakker, Mark; Nieber, John L.

    2004-12-01

    New analytic element solutions are presented for unsaturated, two-dimensional steady flow in vertical planes that include nonoverlapping impermeable elliptical layers and elliptical inhomogeneities. The hydraulic conductivity, which is represented by an exponential function of the pressure head, differs between the inside and outside of an elliptical inhomogeneity; both the saturated hydraulic conductivity and water retention parameters are allowed to differ between the inside and outside. The Richards equation is transformed, through the Kirchhoff transformation and a second standard transformation, into the modified Helmholtz equation. Analytic element solutions are obtained through separation of variables in elliptical coordinates. The resulting equations for the Kirchhoff potential consist of infinite sums of products of exponentials and modified Mathieu functions. In practical applications the series are truncated but still fulfill the differential equation exactly; boundary conditions are met approximately but up to machine accuracy, provided that enough terms are used. The pressure head, saturation, and flow may be computed analytically at any point in the vadose zone. Examples are given of the shadowing effect of an impermeable elliptical layer in a uniform flow field and funnel-type flow between two elliptical inhomogeneities. The presented solutions may be applied to study transport processes in vadose zones containing many impermeable elliptical layers or elliptical inhomogeneities.

  20. Fractional calculus phenomenology in two-dimensional plasma models

    Science.gov (United States)

    Gustafson, Kyle; Del Castillo Negrete, Diego; Dorland, Bill

    2006-10-01

    Transport processes in confined plasmas for fusion experiments, such as ITER, are not well-understood at the basic level of fully nonlinear, three-dimensional kinetic physics. Turbulent transport is invoked to describe the observed levels in tokamaks, which are orders of magnitude greater than the theoretical predictions. Recent results show the ability of a non-diffusive transport model to describe numerical observations of turbulent transport. For example, resistive MHD modeling of tracer particle transport in pressure-gradient driven turbulence for a three-dimensional plasma reveals that the superdiffusive (2̂˜t^α where α> 1) radial transport in this system is described quantitatively by a fractional diffusion equation Fractional calculus is a generalization involving integro-differential operators, which naturally describe non-local behaviors. Our previous work showed the quantitative agreement of special fractional diffusion equation solutions with numerical tracer particle flows in time-dependent linearized dynamics of the Hasegawa-Mima equation (for poloidal transport in a two-dimensional cold-ion plasma). In pursuit of a fractional diffusion model for transport in a gyrokinetic plasma, we now present numerical results from tracer particle transport in the nonlinear Hasegawa-Mima equation and a planar gyrokinetic model. Finite Larmor radius effects will be discussed. D. del Castillo Negrete, et al, Phys. Rev. Lett. 94, 065003 (2005).

  1. 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.

  2. 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.

  3. 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

  4. 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...

  5. Optimizing separations in online comprehensive two-dimensional liquid chromatography.

    Science.gov (United States)

    Pirok, Bob W J; Gargano, Andrea F G; Schoenmakers, Peter J

    2018-01-01

    Online comprehensive two-dimensional liquid chromatography has become an attractive option for the analysis of complex nonvolatile samples found in various fields (e.g. environmental studies, food, life, and polymer sciences). Two-dimensional liquid chromatography complements the highly popular hyphenated systems that combine liquid chromatography with mass spectrometry. Two-dimensional liquid chromatography is also applied to the analysis of samples that are not compatible with mass spectrometry (e.g. high-molecular-weight polymers), providing important information on the distribution of the sample components along chemical dimensions (molecular weight, charge, lipophilicity, stereochemistry, etc.). Also, in comparison with conventional one-dimensional liquid chromatography, two-dimensional liquid chromatography provides a greater separation power (peak capacity). Because of the additional selectivity and higher peak capacity, the combination of two-dimensional liquid chromatography with mass spectrometry allows for simpler mixtures of compounds to be introduced in the ion source at any given time, improving quantitative analysis by reducing matrix effects. In this review, we summarize the rationale and principles of two-dimensional liquid chromatography experiments, describe advantages and disadvantages of combining different selectivities and discuss strategies to improve the quality of two-dimensional liquid chromatography separations. © 2017 The Authors. Journal of Separation Science published by WILEY-VCH Verlag GmbH & Co. KGaA.

  6. 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.

  7. Exploring two-dimensional electron gases with two-dimensional Fourier transform spectroscopy

    Energy Technology Data Exchange (ETDEWEB)

    Paul, J.; Dey, P.; Karaiskaj, D., E-mail: karaiskaj@usf.edu [Department of Physics, University of South Florida, 4202 East Fowler Ave., Tampa, Florida 33620 (United States); Tokumoto, T.; Hilton, D. J. [Department of Physics, University of Alabama at Birmingham, Birmingham, Alabama 35294 (United States); Reno, J. L. [CINT, Sandia National Laboratories, Albuquerque, New Mexico 87185 (United States)

    2014-10-07

    The dephasing of the Fermi edge singularity excitations in two modulation doped single quantum wells of 12 nm and 18 nm thickness and in-well carrier concentration of ∼4 × 10{sup 11} cm{sup −2} was carefully measured using spectrally resolved four-wave mixing (FWM) and two-dimensional Fourier transform (2DFT) spectroscopy. Although the absorption at the Fermi edge is broad at this doping level, the spectrally resolved FWM shows narrow resonances. Two peaks are observed separated by the heavy hole/light hole energy splitting. Temperature dependent “rephasing” (S{sub 1}) 2DFT spectra show a rapid linear increase of the homogeneous linewidth with temperature. The dephasing rate increases faster with temperature in the narrower 12 nm quantum well, likely due to an increased carrier-phonon scattering rate. The S{sub 1} 2DFT spectra were measured using co-linear, cross-linear, and co-circular polarizations. Distinct 2DFT lineshapes were observed for co-linear and cross-linear polarizations, suggesting the existence of polarization dependent contributions. The “two-quantum coherence” (S{sub 3}) 2DFT spectra for the 12 nm quantum well show a single peak for both co-linear and co-circular polarizations.

  8. Functional inks and printing of two-dimensional materials.

    Science.gov (United States)

    Hu, Guohua; Kang, Joohoon; Ng, Leonard W T; Zhu, Xiaoxi; Howe, Richard C T; Jones, Christopher G; Hersam, Mark C; Hasan, Tawfique

    2018-05-08

    Graphene and related two-dimensional materials provide an ideal platform for next generation disruptive technologies and applications. Exploiting these solution-processed two-dimensional materials in printing can accelerate this development by allowing additive patterning on both rigid and conformable substrates for flexible device design and large-scale, high-speed, cost-effective manufacturing. In this review, we summarise the current progress on ink formulation of two-dimensional materials and the printable applications enabled by them. We also present our perspectives on their research and technological future prospects.

  9. Third sound in one and two dimensional modulated structures

    International Nuclear Information System (INIS)

    Komuro, T.; Kawashima, H., Shirahama, K.; Kono, K.

    1996-01-01

    An experimental technique is developed to study acoustic transmission in one and two dimensional modulated structures by employing third sound of a superfluid helium film. In particular, the Penrose lattice, which is a two dimensional quasiperiodic structure, is studied. In two dimensions, the scattering of third sound is weaker than in one dimension. Nevertheless, the authors find that the transmission spectrum in the Penrose lattice, which is a two dimensional prototype of the quasicrystal, is observable if the helium film thickness is chosen around 5 atomic layers. The transmission spectra in the Penrose lattice are explained in terms of dynamical theory of diffraction

  10. ONE-DIMENSIONAL AND TWO-DIMENSIONAL LEADERSHIP STYLES

    Directory of Open Access Journals (Sweden)

    Nikola Stefanović

    2007-06-01

    Full Text Available In order to motivate their group members to perform certain tasks, leaders use different leadership styles. These styles are based on leaders' backgrounds, knowledge, values, experiences, and expectations. The one-dimensional styles, used by many world leaders, are autocratic and democratic styles. These styles lie on the two opposite sides of the leadership spectrum. In order to precisely define the leadership styles on the spectrum between the autocratic leadership style and the democratic leadership style, leadership theory researchers use two dimensional matrices. The two-dimensional matrices define leadership styles on the basis of different parameters. By using these parameters, one can identify two-dimensional styles.

  11. 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

  12. 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

  13. Mean-field description of ultracold bosons on disordered two-dimensional optical lattices

    International Nuclear Information System (INIS)

    Buonsante, Pierfrancesco; Massel, Francesco; Penna, Vittorio; Vezzani, Alessandro

    2007-01-01

    In the present communication, we describe the properties induced by disorder on an ultracold gas of bosonic atoms loaded into a two-dimensional optical lattice with global confinement ensured by a parabolic potential. Our analysis is centred on the spatial distribution of the various phases, focusing particularly on the superfluid properties of the system as a function of external parameters and disorder amplitude. In particular, it is shown how disorder can suppress superfluidity, while partially preserving the system coherence. (fast track communication)

  14. Two-dimensional electronic femtosecond stimulated Raman spectroscopy

    Directory of Open Access Journals (Sweden)

    Ogilvie J.P.

    2013-03-01

    Full Text Available We report two-dimensional electronic spectroscopy with a femtosecond stimulated Raman scattering probe. The method reveals correlations between excitation energy and excited state vibrational structure following photoexcitation. We demonstrate the method in rhodamine 6G.

  15. Micromachined two dimensional resistor arrays for determination of gas parameters

    NARCIS (Netherlands)

    van Baar, J.J.J.; Verwey, Willem B.; Dijkstra, Mindert; Dijkstra, Marcel; Wiegerink, Remco J.; Lammerink, Theodorus S.J.; Krijnen, Gijsbertus J.M.; Elwenspoek, Michael Curt

    A resistive sensor array is presented for two dimensional temperature distribution measurements in a micromachined flow channel. This allows simultaneous measurement of flow velocity and fluid parameters, like thermal conductivity, diffusion coefficient and viscosity. More general advantages of

  16. Generalized similarity method in unsteady two-dimensional MHD ...

    African Journals Online (AJOL)

    user

    International Journal of Engineering, Science and Technology. Vol. 1, No. 1, 2009 ... temperature two-dimensional MHD laminar boundary layer of incompressible fluid. ...... Φ η is Blasius solution for stationary boundary layer on the plate,. ( ). 0.

  17. 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

  18. 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).

  19. Topological aspect of disclinations in two-dimensional crystals

    International Nuclear Information System (INIS)

    Wei-Kai, Qi; Tao, Zhu; Yong, Chen; Ji-Rong, Ren

    2009-01-01

    By using topological current theory, this paper studies the inner topological structure of disclinations during the melting of two-dimensional systems. From two-dimensional elasticity theory, it finds that there are topological currents for topological defects in homogeneous equation. The evolution of disclinations is studied, and the branch conditions for generating, annihilating, crossing, splitting and merging of disclinations are given. (the physics of elementary particles and fields)

  20. Structures of two-dimensional three-body systems

    International Nuclear Information System (INIS)

    Ruan, W.Y.; Liu, Y.Y.; Bao, C.G.

    1996-01-01

    Features of the structure of L = 0 states of a two-dimensional three-body model system have been investigated. Three types of permutation symmetry of the spatial part, namely symmetric, antisymmetric, and mixed, have been considered. A comparison has been made between the two-dimensional system and the corresponding three-dimensional one. The effect of symmetry on microscopic structures is emphasized. (author)

  1. Study on two-dimensional induced signal readout of MRPC

    International Nuclear Information System (INIS)

    Wu Yucheng; Yue Qian; Li Yuanjing; Ye Jin; Cheng Jianping; Wang Yi; Li Jin

    2012-01-01

    A kind of two-dimensional readout electrode structure for the induced signal readout of MRPC has been studied in both simulation and experiments. Several MRPC prototypes are produced and a series of test experiments have been done to compare with the result of simulation, in order to verify the simulation model. The experiment results are in good agreement with those of simulation. This method will be used to design the two-dimensional signal readout mode of MRPC in the future work.

  2. Controlled Interactions between Two Dimensional Layered Inorganic Nanosheets and Polymers

    Science.gov (United States)

    2016-06-15

    AFRL-AFOSR-JP-TR-2016-0071 Controlled Interactions between Two Dimensional Layered Inorganic Nanosheets and Polymers Cheolmin Park YONSEI UNIVERSITY...Interactions between Two Dimensional Layered Inorganic Nanosheets and Polymers 5a.  CONTRACT NUMBER 5b.  GRANT NUMBER FA2386-14-1-4054 5c.  PROGRAM ELEMENT...prospects for a variety of emerging applications in a broad range of fields, such as electronics, energy conversion and storage, catalysis and polymer

  3. The theory of critical phenomena in two-dimensional systems

    International Nuclear Information System (INIS)

    Olvera de la C, M.

    1981-01-01

    An exposition of the theory of critical phenomena in two-dimensional physical systems is presented. The first six chapters deal with the mean field theory of critical phenomena, scale invariance of the thermodynamic functions, Kadanoff's spin block construction, Wilson's renormalization group treatment of critical phenomena in configuration space, and the two-dimensional Ising model on a triangular lattice. The second part of this work is made of four chapters devoted to the application of the ideas expounded in the first part to the discussion of critical phenomena in superfluid films, two-dimensional crystals and the two-dimensional XY model of magnetic systems. Chapters seven to ten are devoted to the following subjects: analysis of long range order in one, two, and three-dimensional physical systems. Topological defects in the XY model, in superfluid films and in two-dimensional crystals. The Thouless-Kosterlitz iterated mean field theory of the dipole gas. The renormalization group treatment of the XY model, superfluid films and two-dimensional crystal. (author)

  4. Two-dimensional multifractal cross-correlation analysis

    International Nuclear Information System (INIS)

    Xi, Caiping; Zhang, Shuning; Xiong, Gang; Zhao, Huichang; Yang, Yonghong

    2017-01-01

    Highlights: • We study the mathematical models of 2D-MFXPF, 2D-MFXDFA and 2D-MFXDMA. • Present the definition of the two-dimensional N 2 -partitioned multiplicative cascading process. • Do the comparative analysis of 2D-MC by 2D-MFXPF, 2D-MFXDFA and 2D-MFXDMA. • Provide a reference on the choice and parameter settings of these methods in practice. - Abstract: There are a number of situations in which several signals are simultaneously recorded in complex systems, which exhibit long-term power-law cross-correlations. This paper presents two-dimensional multifractal cross-correlation analysis based on the partition function (2D-MFXPF), two-dimensional multifractal cross-correlation analysis based on the detrended fluctuation analysis (2D-MFXDFA) and two-dimensional multifractal cross-correlation analysis based on the detrended moving average analysis (2D-MFXDMA). We apply these methods to pairs of two-dimensional multiplicative cascades (2D-MC) to do a comparative study. Then, we apply the two-dimensional multifractal cross-correlation analysis based on the detrended fluctuation analysis (2D-MFXDFA) to real images and unveil intriguing multifractality in the cross correlations of the material structures. At last, we give the main conclusions and provide a valuable reference on how to choose the multifractal algorithms in the potential applications in the field of SAR image classification and detection.

  5. Two-Dimensional Materials for Sensing: Graphene and Beyond

    Directory of Open Access Journals (Sweden)

    Seba Sara Varghese

    2015-09-01

    Full Text Available Two-dimensional materials have attracted great scientific attention due to their unusual and fascinating properties for use in electronics, spintronics, photovoltaics, medicine, composites, etc. Graphene, transition metal dichalcogenides such as MoS2, phosphorene, etc., which belong to the family of two-dimensional materials, have shown great promise for gas sensing applications due to their high surface-to-volume ratio, low noise and sensitivity of electronic properties to the changes in the surroundings. Two-dimensional nanostructured semiconducting metal oxide based gas sensors have also been recognized as successful gas detection devices. This review aims to provide the latest advancements in the field of gas sensors based on various two-dimensional materials with the main focus on sensor performance metrics such as sensitivity, specificity, detection limit, response time, and reversibility. Both experimental and theoretical studies on the gas sensing properties of graphene and other two-dimensional materials beyond graphene are also discussed. The article concludes with the current challenges and future prospects for two-dimensional materials in gas sensor applications.

  6. Symmetry of the homogeneous linear partial differential equations and seperation of variables

    International Nuclear Information System (INIS)

    Gegelia, D.T.; Markovski, B.L.

    1990-01-01

    The general interplay between dynamical symmetry of LPDE and the problem of variables splitting is analyzed. The existence of symmetry is only a necessary condition for separation of variables. The necessary and sufficient conditions for two-dimensional second-order LPDE are explicitly found in an appropriate coordinate system. The proposed construction can be straight forwardly extended for higher dimensions too. 8 refs

  7. Stable multiple-layer stationary solutions of a semilinear parabolic equation in two-dimensional domains

    Directory of Open Access Journals (Sweden)

    Arnaldo Simal do Nascimento

    1997-12-01

    Full Text Available We use $Gamma$--convergence to prove existence of stable multiple--layer stationary solutions (stable patterns to the reaction--diffusion equation. $$ eqalign{ {partial v_varepsilon over partial t} =& varepsilon^2, hbox{div}, (k_1(xabla v_varepsilon + k_2(x(v_varepsilon -alpha(Beta-v_varepsilon (v_varepsilon -gamma_varepsilon(x,,hbox{ in }Omegaimes{Bbb R}^+ cr &v_varepsilon(x,0 = v_0 quad {partial v_varepsilon over partial widehat{n}} = 0,, quadhbox{ for } xin partialOmega,, t >0,.} $$ Given nested simple closed curves in ${Bbb R}^2$, we give sufficient conditions on their curvature so that the reaction--diffusion problem possesses a family of stable patterns. In particular, we extend to two-dimensional domains and to a spatially inhomogeneous source term, a previous result by Yanagida and Miyata.

  8. Segregation in quasi-two-dimensional granular systems

    International Nuclear Information System (INIS)

    Rivas, Nicolas; Cordero, Patricio; Soto, Rodrigo; Risso, Dino

    2011-01-01

    Segregation for two granular species is studied numerically in a vertically vibrated quasi-two-dimensional (quasi-2D) box. The height of the box is smaller than two particle diameters so that particles are limited to a submonolayer. Two cases are considered: grains that differ in their density but have equal size, and grains that have equal density but different diameters, while keeping the quasi-2D condition. It is observed that in both cases, for vibration frequencies beyond a certain threshold-which depends on the density or diameter ratios-segregation takes place in the lateral directions. In the quasi-2D geometry, gravity does not play a direct role in the in-plane dynamics and gravity does not point to the segregation directions; hence, several known segregation mechanisms that rely on gravity are discarded. The segregation we observe is dominated by a lack of equipartition between the two species; the light particles exert a larger pressure than the heavier ones, inducing the latter to form clusters. This energy difference in the horizontal direction is due to the existence of a fixed point characterized by vertical motion and hence vanishing horizontal energy. Heavier and bigger grains are more rapidly attracted to the fixed point and the perturbations are less efficient in taking them off the fixed point when compared to the lighter grains. As a consequence, heavier and bigger grains have less horizontal agitation than lighter ones. Although limited by finite size effects, the simulations suggest that the two cases we consider differ in the transition character: one is continuous and the other is discontinuous. In the cases where grains differ in mass on varying the control parameter, partial segregation is first observed, presenting many clusters of heavier particles. Eventually, a global cluster is formed with impurities; namely lighter particles are present inside. The transition looks continuous when characterized by several segregation order

  9. 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.

  10. 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.

  11. 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.

  12. 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...

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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)

  18. 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. .

  19. 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...

  20. 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