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 ...

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 ...

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.

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...

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.

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

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

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...

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

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

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.

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.

Abodes for life in carbonaceous asteroids?

Science.gov (United States)

Abramov, Oleg; Mojzsis, Stephen J.

2011-05-01

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

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.

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.

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

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.

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.

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.

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.

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

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

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

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 ...

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

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.

Raman characterization of carbonaceous matter in CONCORDIA Antarctic micrometeorites

Science.gov (United States)

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

2011-09-01

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

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 ...

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...

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...

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.

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.

Pulmonary exposure to carbonaceous nanomaterials and sperm quality

DEFF Research Database (Denmark)

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

2018-01-01

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

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.

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.

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.

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.

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.

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

On radiogenic nature of xenon-X in carbonaceous and LL chondrites

International Nuclear Information System (INIS)

Gerling, Eh.K.

1982-01-01

The nature of Xe-X from the mineral fraction produced during the differential dissolution of carbonaceous and LL chondrites was investigated using literature data on the age of some meteorites and their fractions and quantities of fission 136 Xe contained in them. A graph of lg fission 136 Xe against the age of meteorites was plotted; the decay constant of a hypothetical superheavy nucleus was calculated using the graph and equaled 1x10 - 7 year - 1 . The calculations served as a forcible argument for the radiogenic nature of xenon with 136 and 134 mass in carbonaceous and LL chondrites

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

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

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

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

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

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

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.

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.

Molybdenum isotopic evidence for the origin of chondrules and a distinct genetic heritage of carbonaceous and non-carbonaceous meteorites

Science.gov (United States)

Budde, Gerrit; Burkhardt, Christoph; Brennecka, Gregory A.; Fischer-Gödde, Mario; Kruijer, Thomas S.; Kleine, Thorsten

2016-11-01

Nucleosynthetic isotope anomalies are powerful tracers to determine the provenance of meteorites and their components, and to identify genetic links between these materials. Here we show that chondrules and matrix separated from the Allende CV3 chondrite have complementary nucleosynthetic Mo isotope anomalies. These anomalies result from the enrichment of a presolar carrier enriched in s-process Mo into the matrix, and the corresponding depletion of this carrier in the chondrules. This carrier most likely is a metal and so the uneven distribution of presolar material probably results from metal-silicate fractionation during chondrule formation. The Mo isotope anomalies correlate with those reported for W isotopes on the same samples in an earlier study, suggesting that the isotope variations for both Mo and W are caused by the heterogeneous distribution of the same carrier. The isotopic complementary of chondrules and matrix indicates that both components are genetically linked and formed together from one common reservoir of solar nebula dust. As such, the isotopic data require that most chondrules formed in the solar nebula and are not a product of protoplanetary impacts. Allende chondrules and matrix together with bulk carbonaceous chondrites and some iron meteorites (groups IID, IIIF, and IVB) show uniform excesses in 92Mo, 95Mo, and 97Mo that result from the addition of supernova material to the solar nebula region in which these carbonaceous meteorites formed. Non-carbonaceous meteorites (enstatite and ordinary chondrites as well as most iron meteorites) do not contain this material, demonstrating that two distinct Mo isotope reservoirs co-existed in the early solar nebula that remained spatially separated for several million years. This separation was most likely achieved through the formation of the gas giants, which cleared the disk between the inner and outer solar system regions parental to the non-carbonaceous and carbonaceous meteorites. The Mo isotope

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.

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

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 ...

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

Science.gov (United States)

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

2017-07-01

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

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.

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

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.

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.

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

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

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. 

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.

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.

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

Distilling solid carbonaceous materials

Energy Technology Data Exchange (ETDEWEB)

Nielsen, H; Laing, B

1926-12-04

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

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...

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

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.

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

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,.

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...

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.

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)

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

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.

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

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.

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/

Carbonaceous aerosol at two rural locations in New York State: Characterization and behavior

Science.gov (United States)

Sunder Raman, Ramya; Hopke, Philip K.; Holsen, Thomas M.

2008-06-01

Fine particle samples were collected to determine the chemical constituents in PM2.5 at two rural background sites (Potsdam and Stockton, N. Y.) in the northeastern United States from November 2002 to August 2005. Samples were collected every third day for 24 h with a speciation network sampler. The measured carbonaceous species included thermal-optical organic carbon (OC), elemental carbon (EC), pyrolytic carbon (OP), black carbon (BC), and water-soluble, short-chain (WSSC) organic acids. Concentration time series, autocorrelations, and seasonal variations of the carbonaceous species were examined. During this multiyear period, the contributions of the total carbon (OC + EC) to the measured fine particle mass were 31.2% and 31.1% at Potsdam and Stockton, respectively. The average sum of the WSSC acids carbon accounted for approximately 2.5% of the organic carbon at Potsdam and 3.0% at Stockton. At Potsdam, the seasonal differences in the autocorrelation function (ACF) and partial autocorrelation function (PACF) values for carbonaceous species suggest that secondary formation may be an important contributor to the observed concentrations of species likely to be secondary in origin, particularly during the photochemically active time of the year (May to October). This study also investigated the relationships between carbonaceous species to better understand the behavior of carbonaceous aerosol and to assess the contribution of secondary organic carbon (SOC) to the total organic carbon mass (the EC tracer method was used to estimate SOC). At Potsdam the average SOC contribution to total OC varied between 66% and 72%, while at Stockton it varied between 58% and 64%.

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.

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.

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.

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.

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.

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).

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

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...

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.

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).

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

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

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.

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....

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.)

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 ...

Carbonaceous deposits on naptha reforming catalysts

International Nuclear Information System (INIS)

Redwan, D.S.

1999-01-01

Carbonaceous deposits on naphtha reforming catalysts play a decisive role in limiting process performance. The deposits negatively after catalyst activity, selectivity and the production cycle of a semi regenerative reformer. The magnitude of negative effect of those deposits is directly proportional to their amounts and complexity. Investigations on used reforming catalysts samples reveal that the amount and type (complexity of the chemical nature) of carbonaceous deposits are directly proportional to the catalysts life on stream and the severity of operating conditions. In addition, the combustibility behavior of carbonaceous deposits on the catalyst samples taken from different reformers are found to be different. Optimal carbon removal, for in situ catalyst regeneration, requires the specific conditions be developed, based on the results of well designed and properly performed investigations of the amount and type of carbonaceous deposits. (author)

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.

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

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.)

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 ...

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.

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)

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.

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.

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

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

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.

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

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.

Mild Solutions of Neutral Stochastic Partial Functional Differential Equations

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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.

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)

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

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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.

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.

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.

Carbonaceous electrode materials for supercapacitors.

Science.gov (United States)

Hao, Long; Li, Xianglong; Zhi, Linjie

2013-07-26

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

Global cloud condensation nuclei influenced by carbonaceous combustion aerosol

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D. V. Spracklen

2011-09-01

Full Text Available Black carbon in carbonaceous combustion aerosol warms the climate by absorbing solar radiation, meaning reductions in black carbon emissions are often perceived as an attractive global warming mitigation option. However, carbonaceous combustion aerosol can also act as cloud condensation nuclei (CCN so they also cool the climate by increasing cloud albedo. The net radiative effect of carbonaceous combustion aerosol is uncertain because their contribution to CCN has not been evaluated on the global scale. By combining extensive observations of CCN concentrations with the GLOMAP global aerosol model, we find that the model is biased low (normalised mean bias = −77 % unless carbonaceous combustion aerosol act as CCN. We show that carbonaceous combustion aerosol accounts for more than half (52–64 % of global CCN with the range due to uncertainty in the emitted size distribution of carbonaceous combustion particles. The model predicts that wildfire and pollution (fossil fuel and biofuel carbonaceous combustion aerosol causes a global mean cloud albedo aerosol indirect effect of −0.34 W m⁻², with stronger cooling if we assume smaller particle emission size. We calculate that carbonaceous combustion aerosol from pollution sources cause a global mean aerosol indirect effect of −0.23 W m⁻². The small size of carbonaceous combustion particles from fossil fuel sources means that whilst pollution sources account for only one-third of the emitted mass they cause two-thirds of the cloud albedo aerosol indirect effect that is due to carbonaceous combustion aerosol. This cooling effect must be accounted for, along with other cloud effects not studied here, to ensure that black carbon emissions controls that reduce the high number concentrations of fossil fuel particles have the desired net effect on climate.

Carbonaceous materials in the acid residue from the Orgueil carbonaceous chondrite meteorite

Science.gov (United States)

Garvie, Laurence A. J.; Buseck, Peter R.

2006-04-01

Insoluble organic matter (IOM) dominates the HF/HCl residue of the Orgueil (CI) carbonaceous chondrite meteorite. The IOM is composed primarily of two C-rich particle types. The first has a fluffy texture similar to crumpled tissue paper, and the second type occurs as solid or hollow nanospheres. High-resolution transmission electron microscope (HRTEM) images of the fluffy material show it is poorly ordered, with small, irregularly shaped regions having fringes with 0.34-0.38 nm spacings and locally 0.21 nm cross-fringes. Nanodiamonds occur in the fluffy material. The rounded C-rich particles are common in the residue and their HRTEM images show neither fringes nor nanodiamonds. Both types of carbonaceous materials have a high aromatic component, as revealed by electron energy-loss spectroscopy (EELS), with up to 10 at% substitution by S, N, and O. The average compositions of the fluffy material and nanospheres are C100S1.9N3.7O4.9 and C100S2.4N5.0O3.9, respectively. The structural and chemical heterogeneity of the carbonaceous materials may represent material from multiple sources.

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.

Distilling peat and other carbonaceous matters

Energy Technology Data Exchange (ETDEWEB)

Stones, W B

1850-03-07

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

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

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.

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

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.

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

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.

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...

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

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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.

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…

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.

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

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...

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)

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)

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...

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

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.

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.

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.

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.

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.

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...

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.

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.

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.

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.

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...

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.

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)

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.

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...

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).

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.

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.

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.

Characterization of combustion-generated carbonaceous nanoparticles by size-dependent ultraviolet laser photoionization.

Science.gov (United States)

Commodo, Mario; Sgro, Lee Anne; Minutolo, Patrizia; D'Anna, Andrea

2013-05-16

Photoelectric charging of particles is a powerful tool for online characterization of submicrometer aerosol particles. Indeed photoionization based techniques have high sensitivity and chemical selectivity. Moreover, they yield information on electronic properties of the material and are sensitive to the state of the surface. In the present study the photoionization charging efficiency, i.e., the ratio between the generated positive ions and the corresponding neutral ones, for different classes of flame-generated carbonaceous nanoparticles was measured. The fifth harmonics of a Nd:YAG laser, 213 nm (5.82 eV), was used as an ionization source for the combustion generated nanoparticles, whereas a differential mobility analyzer (DMA) coupled to a Faraday cup electrometer was used for particle classification and detection. Carbonaceous nanoparticles in the nucleation mode, i.e., sizes ranging from 1 to 10 nm, show a photoionization charging efficiency clearly dependent on the flame conditions. In particular, we observed that the richer the flame is, i.e., the higher the equivalent ratio is, the higher the photon charging efficiency is. We hypothesized that such an increase in the photoionization propensity of the carbonaceous nanoparticles from richer flame condition is associated to the presence within the particles of larger aromatic moieties. The results clearly show that photoionization is a powerful diagnostic tool for the physical-chemical characterization of combustion aerosol, and it may lead to further insights into the soot formation mechanism.

Pulmonary exposure to carbonaceous nanomaterials and sperm quality.

Science.gov (United States)

Skovmand, Astrid; Jacobsen Lauvås, Anna; Christensen, Preben; Vogel, Ulla; Sørig Hougaard, Karin; Goericke-Pesch, Sandra

2018-01-31

Semen quality parameters are potentially affected by nanomaterials in several ways: Inhaled nanosized particles are potent inducers of pulmonary inflammation, leading to the release of inflammatory mediators. Small amounts of particles may translocate from the lungs into the lung capillaries, enter the systemic circulation and ultimately reach the testes. Both the inflammatory response and the particles may induce oxidative stress which can directly affect spermatogenesis. Furthermore, spermatogenesis may be indirectly affected by changes in the hormonal milieu as systemic inflammation is a potential modulator of endocrine function. The aim of this study was to investigate the effects of pulmonary exposure to carbonaceous nanomaterials on sperm quality parameters in an experimental mouse model. Effects on sperm quality after pulmonary inflammation induced by carbonaceous nanomaterials were investigated by intratracheally instilling sexually mature male NMRI mice with four different carbonaceous nanomaterials dispersed in nanopure water: graphene oxide (18 μg/mouse/i.t.), Flammruss 101, Printex 90 and SRM1650b (0.1 mg/mouse/i.t. each) weekly for seven consecutive weeks. Pulmonary inflammation was determined by differential cell count in bronchoalveolar lavage fluid. Epididymal sperm concentration and motility were measured by computer-assisted sperm analysis. Epididymal sperm viability and morphological abnormalities were assessed manually using Hoechst 33,342/PI flourescent and Spermac staining, respectively. Epididymal sperm were assessed with regard to sperm DNA integrity (damage). Daily sperm production was measured in the testis, and testosterone levels were measured in blood plasma by ELISA. Neutrophil numbers in the bronchoalveolar fluid showed sustained inflammatory response in the nanoparticle-exposed groups one week after the last instillation. No significant changes in epididymal sperm parameters, daily sperm production or plasma testosterone levels

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

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

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

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

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.

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

International Nuclear Information System (INIS)

Dresner, L.

1990-07-01

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

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

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.

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.

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

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.

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

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.

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.

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

Directory of Open Access Journals (Sweden)

Lingyang Song

2007-04-01

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

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.

Separation of volatile products from solid carbonaceous materials

Energy Technology Data Exchange (ETDEWEB)

White, W W

1915-10-19

A process is set forth for the separation of volatile products from solid carbonaceous materials, in which the vapors produced from the carbonaceous material at higher temperatures and withdrawn into the separate vapor chamber are led in succession through the lower temperature vapors as continuously to deposit their condensible ingredients in the chamber by the action of the successive cooler vapors.

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.

Origin and abundance of water in carbonaceous asteroids

Science.gov (United States)

Marrocchi, Yves; Bekaert, David V.; Piani, Laurette

2018-01-01

The origin and abundance of water accreted by carbonaceous asteroids remains underconstrained, but would provide important information on the dynamic of the protoplanetary disk. Here we report the in situ oxygen isotopic compositions of aqueously formed fayalite grains in the Kaba and Mokoia CV chondrites. CV chondrite bulk, matrix and fayalite O-isotopic compositions define the mass-independent continuous trend (δ17O = 0.84 ± 0.03 × δ18O - 4.25 ± 0.1), which shows that the main process controlling the O-isotopic composition of the CV chondrite parent body is related to isotopic exchange between 16O-rich anhydrous silicates and 17O- and 18O-rich fluid. Similar isotopic behaviors observed in CM, CR and CO chondrites demonstrate the ubiquitous nature of O-isotopic exchange as the main physical process in establishing the O-isotopic features of carbonaceous chondrites, regardless of their alteration degree. Based on these results, we developed a new approach to estimate the abundance of water accreted by carbonaceous chondrites (quantified by the water/rock ratio) with CM (0.3-0.4) ≥ CR (0.1-0.4) ≥ CV (0.1-0.2) > CO (0.01-0.10). The low water/rock ratios and the O-isotopic characteristics of secondary minerals in carbonaceous chondrites indicate they (i) formed in the main asteroid belt and (ii) accreted a locally derived (inner Solar System) water formed near the snowline by condensation from the gas phase. Such results imply low influx of D- and 17O- and 18O-rich water ice grains from the outer part of the Solar System. The latter is likely due to the presence of a Jupiter-induced gap in the protoplanetary disk that limited the inward drift of outer Solar System material at the exception of particles with size lower than 150 μm such as presolar grains. Among carbonaceous chondrites, CV chondrites show O-isotopic features suggesting potential contribution of 17-18O-rich water that may be related to their older accretion relative to other hydrated

Wet, Carbonaceous Asteroids: Altering Minerals, Changing Amino Acids

Science.gov (United States)

Taylor, G. J.

2011-04-01

Many carbonaceous chondrites contain alteration products from water-rock interactions at low temperature and organic compounds. A fascinating fact known for decades is the presence in some of them of an assortment of organic compounds, including amino acids, sometimes called the building blocks of life. Murchison and other CM carbonaceous chondrites contain hundreds of amino acids. Early measurements indicated that the amino acids in carbonaceous chondrites had equal proportions of L- and D-structures, a situation called racemic. This was in sharp contrast to life on Earth, which heavily favors L- forms. However, beginning in 1997, John Cronin and Sandra Pizzarello (Arizona State University) found L- excesses in isovaline and several other amino acids in the Murchison carbonaceous chondrite. In 2009, Daniel Glavin and Jason Dworkin (Astrobiology Analytical Lab, Goddard Space Flight Center) reported the first independent confirmation of L-isovaline excesses in Murchison using a different analytical technique than employed by Cronin and Pizzarello. Inspired by this work, Daniel Glavin, Michael Callahan, Jason Dworkin, and Jamie Elsila (Astrobiology Analytical Lab, Goddard Space Flight Center), have done an extensive study of the abundance and symmetry of amino acids in carbonaceous chondrites that experienced a range of alteration by water in their parent asteroids. The results show that amino acids are more abundant in the less altered meteorites, implying that aqueous processing changes the mix of amino acids. They also confirmed the enrichment in L-structures of some amino acids, especially isovaline, confirming earlier work. The authors suggest that aqueously-altered planetesimals might have seeded the early Earth with nonracemic amino acids, perhaps explaining why life from microorganisms to people use only L- forms to make proteins. The initial imbalance caused by non-biologic processes in wet asteroids might have been amplified by life on Earth. Alternatively

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.

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.

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

Science.gov (United States)

Filimonov, M. Yu.

2017-12-01

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

Pulmonary exposure to carbonaceous nanomaterials and sperm quality

DEFF Research Database (Denmark)

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

2018-01-01

Background: Semen quality parameters are potentially affected by nanomaterials in several ways: Inhaled nanosized particles are potent inducers of pulmonary inflammation, leading to the release of inflammatory mediators. Small amounts of particles may translocate from the lungs into the lung...... inflammation is a potential modulator of endocrine function. The aim of this study was to investigate the effects of pulmonary exposure to carbonaceous nanomaterials on sperm quality parameters in an experimental mouse model.Methods: Effects on sperm quality after pulmonary inflammation induced by carbonaceous...... nanomaterials were investigated by intratracheally instilling sexually mature male NMRI mice with four different carbonaceous nanomaterials dispersed in nanopure water: graphene oxide (18 mu g/mouse/i.t.), Flammruss 101, Printex 90 and SRM1650b (0.1 mg/mouse/i.t. each) weekly for seven consecutive weeks...

Adsorption of dyes onto carbonaceous materials produced from coffee grounds by microwave treatment.

Science.gov (United States)

Hirata, Mizuho; Kawasaki, Naohito; Nakamura, Takeo; Matsumoto, Kazuoki; Kabayama, Mineaki; Tamura, Takamichi; Tanada, Seiki

2002-10-01

Organic wastes have been burned for reclamation. However, they have to be recycled and reused for industrial sustainable development. Carbonaceous materials were produced from coffee grounds by microwave treatment. There are many phenolic hydroxyl and carboxyl groups on the surface of carbonaceous materials. The base consumption of the carbonaceous materials was larger than that of the commercially activated carbon. The carbonaceous materials produced from coffee grounds were applied to the adsorbates for the removal of basic dyes (methylene blue and gentian violet) in wastewater. This result indicated that the adsorption of dyes depended upon the surface polar groups on the carbonaceous materials. Moreover, the Freundlich constants of isotherms for the adsorption of methylene blue and gentian violet onto the carbonaceous materials produced from coffee grounds were greater than those for adsorption onto activated carbon or ceramic activated carbon. The interaction was greatest between the surface or porosity of the carbonaceous materials and methylene blue and gentian violet. The microwave treatment would be useful for the carbonization of organic wastes to save energy.

Spatial and spectral resolution of carbonaceous material from hematite (α-Fe2O3) using multivariate curve resolution-alternating least squares (MCR-ALS) with Raman microspectroscopic mapping: implications for the search for life on Mars.

Science.gov (United States)

Smith, Joseph P; Smith, Frank C; Booksh, Karl S

2017-08-21

The search for evidence of extant or past life on Mars is a primary objective of both the upcoming Mars 2020 rover (NASA) and ExoMars 2020 rover (ESA/Roscosmos) missions. This search will involve the detection and identification of organic molecules and/or carbonaceous material within the Martian surface environment. For the first time on a mission to Mars, the scientific payload for each rover will include a Raman spectrometer, an instrument well-suited for this search. Hematite (α-Fe 2 O 3 ) is a widespread mineral on the Martian surface. The 2LO Raman band of hematite and the Raman D-band of carbonaceous material show spectral overlap, leading to the potential misidentification of hematite as carbonaceous material. Here we report the ability to spatially and spectrally differentiate carbonaceous material from hematite using multivariate curve resolution-alternating least squares (MCR-ALS) applied to Raman microspectroscopic mapping under both 532 nm and 785 nm excitation. For this study, a sample comprised of hematite, carbonaceous material, and substrate-adhesive epoxy in spatially distinct domains was constructed. Principal component analysis (PCA) reveals that both 532 nm and 785 nm excitation produce representative three-phase systems of hematite, carbonaceous material, and substrate-adhesive epoxy in the analyzed sample. MCR-ALS with Raman microspectroscopic mapping using both 532 nm and 785 nm excitation was able to resolve hematite, carbonaceous material, and substrate-adhesive epoxy by generating spatially-resolved chemical maps and corresponding Raman spectra of these spatially distinct chemical species. Moreover, MCR-ALS applied to the combinatorial data sets of 532 nm and 785 nm excitation, which contain hematite and carbonaceous material within the same locations, was able to resolve hematite, carbonaceous material, and substrate-adhesive epoxy. Using multivariate analysis with Raman microspectroscopic mapping, 785 nm excitation more effectively

Treating carbonaceous materials

Energy Technology Data Exchange (ETDEWEB)

Corbett, R L; Corbett, E G

1939-03-21

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

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).

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

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

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...

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...

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...

Preparation and characterization of a new carbonaceous material for electrochemical systems

Directory of Open Access Journals (Sweden)

ZI JI LIN

2010-02-01

Full Text Available A new carbonaceous material was successfully prepared by the py-rolysis of scrap tire rubber at 600 °C under a nitrogen atmosphere. The physical characteristics of the prepared carbonaceous material were studied by scanning electron microscopy (SEM, X-ray powder diffraction (XRD and X-ray photoelectron spectroscopy (XPS. It was proved that the carbonaceous material had a disordered structure and spherical morphology with an average particle size about 100 nm. The prepared carbonaceous material was also used as electrodes in electrochemical systems to examine its electrochemical performances. It was demonstrated that it delivered a lithium insertion capacity of 658 mA h g-1 during the first cycle with a coulombic efficiency of 68 %. Cyclic voltammograms test results showed that a redox reaction occurred during the cycles. The chemical diffusion coefficient based on the impedance diagram was about 10-10 cm2 s-1. The pyrolytic carbonaceous material derived from scrap tire rubber is therefore considered to be a potential anode material in lithium secondary batteries or capacitors. Furthermore, it is advantageous for environmental protection.

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.

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.

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

Acid functionalized, highly dispersed carbonaceous spheres: an effective solid acid for hydrolysis of polysaccharides

International Nuclear Information System (INIS)

Jiang Yijun; Li Xiutao; Cao Quan; Mu Xindong

2011-01-01

Highly dispersed carbonaceous spheres with sulfonic acid groups were successfully prepared from glucose by hydrothermal method. Transmission electron microscopy (TEM) showed the as-synthesized carbonaceous materials were uniform, spherical in shape with an average diameter of about 450 nm. Fourier transform infrared (FT-IR) proved that –SO 3 H, –COOH, OH groups were grafted on the surface of the carbonaceous spheres during the sulfonation. Interestingly, the functionalized carbonaceous spheres exhibited high dispersibility in the polar solvent due to the hydrophilic groups on the surface. The mechanism of the formation for the carbonaceous spheres was also discussed based on the analysis of structure and composition. At last, the functionalized carbonaceous spheres were employed as solid acid to hydrolyze starch and cellulose. By comparison, the as-synthesized catalyst showed considerable high yield of glucose.

Acid functionalized, highly dispersed carbonaceous spheres: an effective solid acid for hydrolysis of polysaccharides

Science.gov (United States)

Jiang, Yijun; Li, Xiutao; Cao, Quan; Mu, Xindong

2011-02-01

Highly dispersed carbonaceous spheres with sulfonic acid groups were successfully prepared from glucose by hydrothermal method. Transmission electron microscopy (TEM) showed the as-synthesized carbonaceous materials were uniform, spherical in shape with an average diameter of about 450 nm. Fourier transform infrared (FT-IR) proved that -SO3H, -COOH, OH groups were grafted on the surface of the carbonaceous spheres during the sulfonation. Interestingly, the functionalized carbonaceous spheres exhibited high dispersibility in the polar solvent due to the hydrophilic groups on the surface. The mechanism of the formation for the carbonaceous spheres was also discussed based on the analysis of structure and composition. At last, the functionalized carbonaceous spheres were employed as solid acid to hydrolyze starch and cellulose. By comparison, the as-synthesized catalyst showed considerable high yield of glucose.

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.)

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

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.

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...

TESTING OF CARBONACEOUS ADSORBENTS FOR REMOVAL OF POLLUTANTS FROM WATER

Directory of Open Access Journals (Sweden)

RAISA NASTAS

2012-03-01

Full Text Available Testing of carbonaceous adsorbents for removal of pollutants from water. Relevant direction for improving of quality of potable water is application of active carbons at various stages of water treatments. This work includes complex research dealing with testing of a broad spectrum of carbonaceous adsorbents for removal of hydrogen sulfide and nitrite ions from water. The role of the surface functional groups of carbonaceous adsorbents, their acid-basic properties, and the influence of the type of impregnated heteroatom (N, O, or metals (Fe, Cu, Ni, on removal of hydrogen sulfide species and nitrite ions have been researched. The efficiency of the catalyst obtained from peach stones by impregnation with Cu2+ ions of oxidized active carbon was established, being recommended for practical purposes to remove the hydrogen sulfide species from the sulfurous ground waters. Comparative analysis of carbonaceous adsorbents reveals the importance of surface chemistry for oxidation of nitrite ions.

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...

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...

Characterization of carbonaceous solids by oxygen chemisorption

Energy Technology Data Exchange (ETDEWEB)

Furimsky, E.; Palmer, A.; Duguay, D.G.; McConnell, D.G.; Henson, D.E.

1988-06-01

Oxygen chemisorption of high and low carbon carbonaceous solids was measured in an electro-microbalance at 200 degrees C in air. A linear correlation between the amount of chemisorbed oxygen and H/C ratio as well as aromaticity was established for the high carbon solids. For the low carbon solids a linear correlation was established between the amount of chemisorbed oxygen and the content of organic matter. Experimental observations are discussed in terms of structural aspects of the solids. Oxygen chemisorption is a suitable technique for a rapid characterization of carbonaceous solids including coal. 15 refs., 7 figs., 3 tabs.

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.

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.

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

Quality evaluation of carbonaceous industrial by-products and its effect on properties of autoclave aerated concrete

Science.gov (United States)

Fomina, E. V.; Lesovik, V. S.; Fomin, A. E.; Kozhukhova, N. I.; Lebedev, M. S.

2018-03-01

Argillite is a carbonaceous industrial by-product that is a potential source in environmentally friendly and source-saving construction industry. In this research, chemical and mineral composition as well as particle size distribution of argillite were studied and used to develop autoclave aerated concrete as partial substitute of quartz sand. Effect of the argillite as a mineral admixture in autoclave aerated concrete was investigated in terms of compressive and tensile strength, density, heat conductivity etc. The obtained results demonstrated an efficiency of argillite as an energy-saving material in autoclave construction composites.

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

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...

Improved process for heating finely divided carbonaceous materials

Energy Technology Data Exchange (ETDEWEB)

1956-08-01

A process for heating finely divided carbonaceous particles by burning a proportion of the carbon consists of passing the carbonaceous material at a temperature above 800/sup 0/F into an upwardly disposed, slender, combustion zone, suspending the particles in an upwardly-moving gas containing free oxygen so that the suspension has a density from 0.1 to 5.0 lb/cu. ft., passing the suspension upwardly through the combustion zone at a velocity of from 5 to 100 ft./sec., and injecting at least one stream of a second gas containing free oxygen at a point in the combustion zone such that at least 50% of the oxygen in the first gas has been consumed by the time the suspension reaches this point. The total quantity of oxygen is chosen so that the finely divided carbonaceous material is heated to a temperature of not less than 1,050/sup 0/F.

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

International Nuclear Information System (INIS)

Lu, Bin

2012-01-01

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

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

The Role of Fe,Ni Metal and Fe,Ni Sulfide Nanoparticles in Catalytic Organic Synthesis in the Early Solar System: Evidence From Carbonaceous Chondrites.

Science.gov (United States)

Brearley, A. J.

2008-12-01

Numerous studies have shown that carbonaceous chondrites contain a wide variety of both soluble and insoluble organic compounds. These compounds formed in a variety of different astrophysical environments including the interstellar medium, the solar nebula and on asteroidal parent bodies. The solid or insoluble organic material (IOM) in carbonaceous chondrites is likely the complex end product of synthesis and processing in all of these environments. Although the bulk chemistry and structure of IOM in carbonaceous chondrites is well understood, important questions remain as to the exact spatial occurrence and distribution of organic material within carbonaceous chondrites. Such information may provide important insights into the possible mechanisms of formation of organic material at the grain scale. We have examined the matrices of three CM carbonaceous chondrites, Y791198, Murchison and ALH81002 using a range of different TEM techniques. Mineralogically, the matrices of these meteorites consist of phyllosilicates and/or amorphous materials associated with sulfides, oxides and carbides. Using energy filtered TEM several distinct occurrences of organic material have been identified, notably associations with nanoparticles of sulfide and carbide. Sulfides have grain sizes that are commonly <100 nm with thin layers of poorly graphitized C (<1 nm) on their surfaces. This carbonaceous layer often contains nitrogen suggesting that it is organic in character. In addition, nanoparticles of Fe,Ni carbides that occur either singly or in clusters are often embedded in carbonaceous material that is also N-bearing. These carbides have experienced partial oxidation to magnetite around their rims. The ubiquitous spatial association between sulfide and carbide nanoparticles and carbonaceous material indicates a genetic relation between these phases. This association can be most readily explained by Fischer-Tropsch-type (FTT) catalysis reactions involving catalytic hydrogenation

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.

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.

Distilling carbonaceous materials

Energy Technology Data Exchange (ETDEWEB)

Griffiths, C A

1924-04-15

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

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.

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.

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)

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...

Carbonaceous material treatment

Energy Technology Data Exchange (ETDEWEB)

Trevor, S R

1939-05-04

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

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.

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

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

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.

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.)

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

The carbonaceous sorbent based on the secondary silica-containing material from oil extraction industry

Science.gov (United States)

Starostina, I. V.; Stolyarov, D. V.; Anichina, Ya N.; Porozhnyuk, E. V.

2018-01-01

The object of research in this work is the silica-containing waste of oil extraction industry - the waste kieselghur (diatomite) sludge from precoat filtering units, used for the purification of vegetable oils from organic impurities. As a result of the thermal modification of the sludge, which contains up to 70% of organic impurities, a finely-dispersed low-porous carbonaceous mineral sorption material is formed. The modification of the sludge particles surface causes the substantial alteration of its physical, chemical, adsorption and structural properties - the organic matter is charred, the particle size is reduced, and on the surface of diatomite particles a carbon layer is formed, which deposits in macropores and partially occludes them. The amount of mesopores is increased, along with the specific surface of the obtained product. The optimal temperature of sludge modification is 500°C. The synthesized carbonaceous material can be used as an adsorbing agent for the purification of wastewater from heavy metal ions. The sorption capacity of Cu2+ ions amounted to 14.2 mg·g-1 and for Ni2+ ions - 17.0 mg·g-1. The obtained values exceed the sorption capacity values of the initial kieselghur, used as a filtering charge, for the researched metal ions.

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

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.

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...

Reversible effects of oxygen partial pressure on genes associated with placental angiogenesis and differentiation in primary-term cytotrophoblast cell culture.

Science.gov (United States)

Debiève, F; Depoix, C; Gruson, D; Hubinont, C

2013-09-01

Timely regulated changes in oxygen partial pressure are important for placental formation. Disturbances could be responsible for pregnancy-related diseases like preeclampsia and intrauterine growth restriction. We aimed to (i) determine the effect of oxygen partial pressure on cytotrophoblast differentiation; (ii) measure mRNA expression and protein secretion from genes associated with placental angiogenesis; and (iii) determine the reversibility of these effects at different oxygen partial pressures. Term cytotrophoblasts were incubated at 21% and 2.5% O2 for 96 hr, or were switched between the two oxygen concentrations after 48 hr. Real-time PCR and enzyme-linked immunosorbent assays (ELISAs) were used to evaluate cell fusion and differentiation, measuring transcript levels for those genes involved in cell fusion and placental angiogenesis, including VEGF, PlGF, VEGFR1, sVEGFR1, sENG, INHA, and GCM1. Cytotrophoblasts underwent fusion and differentiation in 2.5% O2 . PlGF expression was inhibited while sVEGFR1 expression increased. VEGF and sENG mRNA expressions increased in 2.5% compared to 21% O2 , but no protein was detected in the cell supernatants. Finally, GCM1 mRNA expression increased during trophoblast differentiation at 21% O2 , but was inhibited at 2.5% O2 . These mRNA expression effects were reversed by returning the cells to 21% O2 . Thus, low-oxygen partial pressure does not inhibit term-cytotrophoblast cell fusion and differentiation in vitro. Lowering the oxygen partial pressure from 21% to 2.5% caused normal-term trophoblasts to reversibly modify their expression of genes associated with placental angiogenesis. This suggests that modifications observed in pregnancy diseases such as preeclampsia or growth retardation are probably due to an extrinsic effect on trophoblasts. Copyright © 2013 Wiley Periodicals, Inc.

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.

"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.

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.

Baking process of thin plate carbonaceous compact

Energy Technology Data Exchange (ETDEWEB)

Suzuki, Yoshio; Shimada, Toyokazu

1987-06-27

As a production process of a thin plate carbonaceous compact for separator of phosphoric acid fuel cell, there is a process to knead carbonaceous powder and thermosetting resin solution, to form and harden the kneaded material and then to bake, carbonize and graphitize it. However in this baking and carbonization treatment, many thin plate compacts are set in a compiled manner within a heating furnace and receive a heat treatment from their circumference. Since the above compacts to be heated tend generally to be heated from their peripheries, their baked conditions are not homogeneous easily causing the formation of cracks, etc.. As a process to heat and bake homogeneously by removing the above problematical points, this invention offers a process to set in a heating furnace a laminate consisting of the lamination of thin plate carbonaceous compacts and the heat resistant soaking plates which hold the upper and lower ends of the above lamination, to fill the upper and under peripheries of the laminate above with high heat conductive packing material and its side periphery with low heat conductive packing material respectively and to heat and sinter it. In addition, the invention specifies the high and low heat conductive packing materials respectively. (1 fig, 2 tabs)

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.

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

Nebula Scale Mixing Between Non-Carbonaceous and Carbonaceous Chondrite Reservoirs: Testing the Grand Tack Model with Almahata Sitta Stones

Science.gov (United States)

Yin, Q.-Z.; Sanborn, M. E.; Goodrich, C. A.; Zolensky, M.; Fioretti, A. M.; Shaddad, M.; Kohl, I. E.; Young, E. D.

2018-01-01

There is an increasing number of Cr-O-Ti isotope studies that show that solar system materials are divided into two main populations, one carbonaceous chondrite (CC)-like and the other is non-carbonaceous (NCC)-like, with minimal mixing between them attributed to a gap opened in the propoplanetary disk due to Jupiter's formation. The Grand Tack model suggests that there should be a particular time in the disk history when this gap is breached and ensuring a subsequent large-scale mixing between S- and C-type asteroids (inner solar system and outer solar system materials), an idea supported by our recent work on chondrule (Delta)17O-(epsilon)54Cr isotope systematics.

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.

Distilling carbonaceous materials

Energy Technology Data Exchange (ETDEWEB)

Trumble, M J

1925-06-29

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

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.

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.

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

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...

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)

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

Science.gov (United States)

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

2013-01-01

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

The Thermal Properties of CM Carbonaceous Chondrites

Science.gov (United States)

Britt, D. T.; Opeil, C.

2017-12-01

The physical properties of asteroid exploration targets are fundamental parameters for developing models, planning observations, mission operations, reducing operational risk, and interpreting mission results. Until we have returned samples, meteorites represent our "ground truth" for the geological material we expect to interact with, sample, and interpret on the surfaces of asteroids. The physical properties of the volatile-rich carbonaceous chondrites (CI, C2, CM, and CR groups) are of particular interest because of their high resource potential. We have measured the thermal conductivity, heat capacity and thermal expansion of five CM carbonaceous chondrites (Murchison, Murray, Cold Bokkeveld, NWA 7309, Jbilet Winselwan) at low temperatures (5-300 K) to mimic the conditions in the asteroid belt. The mineralogy of these meteorites are dominated by abundant hydrous phyllosilicates, but also contain anhydrous minerals such as olivine and pyroxene found in chondrules. The thermal expansion measurements for all these CMs indicate a substantial increase in meteorite volume as temperature decreases from 230 - 210 K followed by linear contraction below 210 K. Such transitions were unexpected and are not typical for anhydrous carbonaceous chondrites or ordinary chondrites. Our thermal diffusivity results compare well with previous estimates for similar meteorites, where conductivity was derived from diffusivity measurements and modeled heat capacities; our new values are of a higher precision and cover a wider range of temperatures.

Optimal Control Method of Parabolic Partial Differential Equations and Its Application to Heat Transfer Model in Continuous Cast Secondary Cooling Zone

Directory of Open Access Journals (Sweden)

Yuan Wang

2015-01-01

Full Text Available Our work is devoted to a class of optimal control problems of parabolic partial differential equations. Because of the partial differential equations constraints, it is rather difficult to solve the optimization problem. The gradient of the cost function can be found by the adjoint problem approach. Based on the adjoint problem approach, the gradient of cost function is proved to be Lipschitz continuous. An improved conjugate method is applied to solve this optimization problem and this algorithm is proved to be convergent. This method is applied to set-point values in continuous cast secondary cooling zone. Based on the real data in a plant, the simulation experiments show that the method can ensure the steel billet quality. From these experiment results, it is concluded that the improved conjugate gradient algorithm is convergent and the method is effective in optimal control problem of partial differential equations.

On thermodynamics of methane+carbonaceous materials adsorption

KAUST Repository

Rahman, Kazi Afzalur; Chakraborty, Anutosh; Saha, Bidyut Baran; Ng, Kim Choon

2012-01-01

This study presents the theoretical frameworks for the thermodynamic quantities namely the heat of adsorption, specific heat capacity, entropy, and enthalpy for the adsorption of methane onto various carbonaceous materials. The proposed theoretical

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.

An review on geology study of carbonaceous-siliceous-pelitic rock type uranium deposit in China and the strategy for its development

International Nuclear Information System (INIS)

Zhao Fengmin

2009-01-01

Carbonaceous-siliceous-pelitic rock type uranium deposit was founded by Chinese uranium geologist, it refers to the uranium deposit hosted by non or light metamophosed carbonate,siliceous rock, pelitic rock and their intermediates. It is one of the important types uranium deposit in China. A lot of this type deposits have been discovered in China and their temporal-spatial distribution pattern and mineralization features have been basically identified, and the rich experience have layed a good foundation for the future exploration. Although the ore of this type is not favourable economically, it is still available. Because carbonaceous-siliceous-pelitic rock type uranium deposit has great resource potential, metallogenic study and exploration efforts should be projected differentially according to their economic profit so as to meet the uranium resource demand of nuclear power development in China. (authors)

Comets, Carbonaceous Meteorites, and the Origin of the Biosphere

Science.gov (United States)

Hoover, Richard B.

2007-01-01

Evidence for indigenous microfossils in carbonaceous meteorites suggests that the paradigm of the endogenous origin of life on Earth should be reconsidered. It is now widely accepted that comets and carbonaceous meteorites played an important role in the delivery of water, organics and life critical biogenic elements to the early Earth and facilitated the origin and evolution of the Earth's Biosphere. However; the detection of embedded microfossils and mats in carbonaceous meteorites implies that comets and meteorites may have played a direct role in the delivery of intact microorganisms and that the Biosphere may extend far into the Cosmos. Recent space observations have found the nuclei of comets to have very low albedos (approx.0.03) and. these jet-black surfaces become very hot (T approx. 400 K) near perihelion. This paper reviews recent observational data-on comets and suggests that liquid water pools could exist in cavities and fissures between the internal ices and rocks and the exterior carbonaceous crust. The presence of light and liquid water near the surface of the nucleus enhances the possibility that comets could harbor prokaryotic extremophiles (e.g., cyanobacteria) capable of growth over a wide range of temperatures. The hypothesis that comets are the parent bodies of the CI1 and the CM2 carbonaceous meteorites is advanced. Electron microscopy images will be presented showing forms interpreted as indigenous-microfossils embedded' in freshly. fractured interior surfaces of the Orgueil (CI1) and Murchison (CM2) meteorites. These forms are consistent in size and morphologies with known morphotypes of all five orders of Cyanobacteriaceae: Energy Dispersive X-ray Spectroscopy (EDS) elemental data shows that the meteoritic forms have anomalous C/O; C/N; and C/S as compared with modern extremophiles and cyanobacteria. These images and spectral data indicate that the clearly biogenic and embedded remains cannot be interpreted as recent biological

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.

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.

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

Institute of Scientific and Technical Information of China (English)

无

2010-01-01

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

Treating carbonaceous materials

Energy Technology Data Exchange (ETDEWEB)

Pier, M

1929-08-26

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

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...

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)

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)

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

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.

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

International Nuclear Information System (INIS)

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

1991-01-01

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

Carbonaceous aerosols over China--review of observations, emissions, and climate forcing.

Science.gov (United States)

Wang, Linpeng; Zhou, Xuehua; Ma, Yujie; Cao, Zhaoyu; Wu, Ruidong; Wang, Wenxing

2016-01-01

Carbonaceous aerosols have been attracting attention due to the influence on visibility, air quality, and regional climate. Statistical analyses based on concentration levels, spatial-temporal variations, correlations, and organic carbon (OC) to element carbon (EC) ratios from published data of OC and EC in particulate matter (PM2.5 and PM10) were carried out in order to give a carbonaceous aerosol profile in China. The results showed maxima for OC of 29.5 ± 18.2 μg C m(-3) and for EC of 8.4 ± 6.3 μg C m(-3) in winter and minima for OC of 12.9 ± 7.7 μg C m(-3) in summer and for EC of 4.6 ± 2.8 μg C m(-3) in spring. In addition, OC and EC both had higher concentrations in urban than those in rural sites. Carbonaceous aerosol levels in China are about three to seven times higher compared to those in the USA and Europe. OC and EC occupied 20 ± 6 and 7 ± 3% of PM2.5 mass and 17 ± 7 and 5 ± 3% of PM10 mass, respectively, implying that carbonaceous aerosols are the main component of PM, especially OC. Secondary organic carbon (SOC) was a significant portion of PM and contributed 41 ± 26% to OC and 8 ± 6% to PM2.5 mass. The OC/EC ratio was 3.63 ± 1.73, which, along with the good correlation between OC and EC and the OC to EC slope of 2.29, signifies that coal combustion and/or vehicular exhaust is the dominated carbonaceous aerosol source in China. These provide a primary observation-based understanding of carbonaceous aerosol pollution in China and have a great significance in improving the emission inventory and climate forcing evaluation.

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.

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.

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)

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)

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.

Indigenous Carbonaceous Matter in the Nakhla Mars Meteorite

Science.gov (United States)

Clemett, S. J.; Thomas-Keprta, K. L.; Rahman, Z.; Le, L.; Wentworth, S. J.; Gibson, E. K.; McKay, D. S.

2016-01-01

Detailed microanalysis of the Martian meteorite Nakhla has shown there are morphologically distinct carbonaceous features spatially associated with low-T aqueous alteration phases including salts and id-dingsite. A comprehensive suite of analytical instrumentation including optical microscopy, field emission scanning electron microscopy (FESEM), energy dispersive X-ray (EDX) spectroscopy, focused ion beam (FIB) microscopy, transmission electron microscopy (TEM), two-step laser mass spectrometry (mu-L(sup 2)MS), laser mu-Raman spectroscopy, Fourier transform infrared spectroscopy (FTIR), and nanoscale secondary ion mass spectrometry (NanoSIMS) are being used to characterize the carbonaceous matter and host mineralogy. The search for carbonaceous matter on Mars has proved challenging. Viking Landers failed to unambiguously detect simple organics at either of the two landing sites although the Martian surface is estimated to have acquired at least 10(exp15) kg of C as a consequence of meteoritic accretion over the last several Ga. The dearth of organics at the Martian surface has been attributed to various oxidative processes including UV photolysis and peroxide activity. Consequently, investigations of Martian organics need to be focused on the sub-surface regolith where such surface processes are either severely attenuated or absent. Fortuitously since Martian meteorites are derived from buried regolith materials they provide a unique opportunity to study Martian organic geochemistry.

Carbonaceous species in atmospheric aerosols from the Krakow area (Malopolska District: carbonaceous species dry deposition analysis

Directory of Open Access Journals (Sweden)

Szramowiat Katarzyna

2016-01-01

Full Text Available Organic and elemental carbon content in PM10 was studied at three sites in Malopolska District representing the city centre (Krakow, rural/residential (Bialka and residential/industrial environments (Krakow. The PM10 samples were collected during the winter time study. The highest concentrations of carbonaceous species were observed in Skawina (36.9 μg·m-3 of OC and 9.6 μg·m-3 of EC. The lowest OC and EC concentrations were reported in Krakow (15.2 μg·m-3 and 3.9 μg·m-3, respectively. The highest concentration of carbonaceous species and the highest wind velocities in Skawina influenced the highest values of the dry deposition fluxes. Correlations between OC, EC and chemical constituents and meteorological parameters suggest that a Krakow was influenced by local emission sources and temperature inversion occurrence; b Bialka was under the influence of local emission sources and long-range transport of particles; c Skawina was impacted by local emission sources.

Laboratory Experiments on the Low-temperature Formation of Carbonaceous Grains in the ISM

Science.gov (United States)

Fulvio, Daniele; Góbi, Sándor; Jäger, Cornelia; Kereszturi, Ákos; Henning, Thomas

2017-11-01

The life cycle of cosmic dust grains is far from being understood and the origin and evolution of interstellar medium (ISM) grains is still under debate. In the ISM, the cosmic dust destruction rate is faster than the production rate by stellar sources. However, observations of ISM refractory matter suggest that to maintain a steady amount of cosmic grains, some supplementary production mechanism takes place. In this context, we aimed to study possible reformation mechanisms of cosmic grains taking place at low temperature directly in the ISM. The low-temperature condensation of carbonaceous materials has been investigated in experiments mimicking the ISM conditions. Gas-phase carbonaceous precursors created by laser ablation of graphite were forced to accrete on cold substrates (T ≈ 10 K) representing surviving dust grains. The growing and evolution of the condensing carbonaceous precursors have been monitored by MIR and UV spectroscopy under a number of experimental scenarios. For the first time, the possibility to form ISM carbonaceous grains in situ is demonstrated. The condensation process is governed by carbon chains that first condense into small carbon clusters and finally into more stable carbonaceous materials, of which structural characteristics are comparable to the material formed in gas-phase condensation experiments at very high temperature. We also show that the so-formed fullerene-like carbonaceous material is transformed into a more ordered material under VUV processing. The cold condensation mechanisms discussed here can give fundamental clues to fully understand the balance between the timescale for dust injection, destruction, and reformation in the ISM.

Microwave assisted synthesis of luminescent carbonaceous nanoparticles from silk fibroin for bioimaging.

Science.gov (United States)

Gao, Hongzhi; Teng, Choon Peng; Huang, Donghong; Xu, Wanqing; Zheng, Chaohui; Chen, Yisong; Liu, Minghuan; Yang, Da-Peng; Lin, Ming; Li, Zibiao; Ye, Enyi

2017-11-01

Bombyx mori silk as a natural protein based biopolymer with high nitrogen content, is abundant and sustainable because of its mass product all over the world per year. In this study, we developed a facile and fast microwave-assisted synthesis of luminescent carbonaceous nanoparticles using Bombyx mori silk fibroin and silk solution as the precursors. As a result, the obtained carbonaceous nanoparticles exhibit a photoluminescence quantum yield of ~20%, high stability, low cytotoxicity, high biocompatibility. Most importantly, we successfully demonstrated bioimaging using these luminescent carbonaceous nanoparticles with excitation dependent luminescence. In addition, the microwave-assisted hydrothermal method can be extended to convert other biomass into functional nanomaterials. Copyright © 2017 Elsevier B.V. All rights reserved.

Evaluation of early Archean volcaniclastic and volcanic flow rocks as possible sites for carbonaceous fossil microbes.

Science.gov (United States)

Walsh, Maud M

2004-01-01

Sedimentary rocks have traditionally been the focus of the search for Archean microfossils; the Earth's oldest fossil bacteria are associated with carbonaceous matter in sedimentary cherts in greenstone belts in the eastern Pilbara block of Western Australia and Barberton greenstone belt of South Africa. Reports of possible fossils in a martian meteorite composed of igneous rock and the discovery of modern bacteria associated with basalts have stimulated a new look at Archean volcanic rocks as possible sites for fossil microbes. This study examines silicified volcaniclastic rocks, near-surface altered volcanic flow rocks, and associated stromatolite- like structures from the Archean Barberton greenstone belt to evaluate their potential for the preservation of carbonaceous fossils. Detrital carbonaceous particles are widely admixed with current-deposited debris. Carbonaceous matter is also present in altered volcanic flow rocks as sparse particles in silica veins that appear to be fed by overlying carbonaceous chert layers. Neither microfossils nor mat-like material was identified in the altered volcanic rocks or adjacent stromatolite-like structures. Ancient volcanic flow and volcaniclastic rocks are not promising sites for carbonaceous fossil preservation.

Carbonaceous Aerosols in Fine Particulate Matter of Santiago Metropolitan Area, Chile

Science.gov (United States)

Toro Araya, Richard; Flocchini, Robert; Morales Segura, Rául G. E.; Leiva Guzmán, Manuel A.

2014-01-01

Measurements of carbonaceous aerosols in South American cities are limited, and most existing data are of short term and limited to only a few locations. For 6 years (2002–2007), concentrations of fine particulate matter and organic and elemental carbon were measured continuously in the capital of Chile. The contribution of carbonaceous aerosols to the primary and secondary fractions was estimated at three different sampling sites and in the warm and cool seasons. The results demonstrate that there are significant differences in the levels in both the cold (March to August) and warm (September to February) seasons at all sites studied. The percent contribution of total carbonaceous aerosol fine particulate matter was greater in the cool season (53 ± 41%) than in the warm season (44 ± 18%). On average, the secondary organic carbon in the city corresponded to 29% of the total organic carbon. In cold periods, this proportion may reach an average of 38%. A comparison of the results with the air quality standards for fine particulate matter indicates that the total carbonaceous fraction alone exceeds the World Health Organization standard (10 µg/m3) and the United States Environmental Protection Agency standard (15 µg/m3) for fine particulate matter. PMID:24587753

Carbonaceous Aerosols in Fine Particulate Matter of Santiago Metropolitan Area, Chile

Directory of Open Access Journals (Sweden)

Richard Toro Araya

2014-01-01

Full Text Available Measurements of carbonaceous aerosols in South American cities are limited, and most existing data are of short term and limited to only a few locations. For 6 years (2002–2007, concentrations of fine particulate matter and organic and elemental carbon were measured continuously in the capital of Chile. The contribution of carbonaceous aerosols to the primary and secondary fractions was estimated at three different sampling sites and in the warm and cool seasons. The results demonstrate that there are significant differences in the levels in both the cold (March to August and warm (September to February seasons at all sites studied. The percent contribution of total carbonaceous aerosol fine particulate matter was greater in the cool season (53 ± 41% than in the warm season (44 ± 18%. On average, the secondary organic carbon in the city corresponded to 29% of the total organic carbon. In cold periods, this proportion may reach an average of 38%. A comparison of the results with the air quality standards for fine particulate matter indicates that the total carbonaceous fraction alone exceeds the World Health Organization standard (10 µg/m3 and the United States Environmental Protection Agency standard (15 µg/m3 for fine particulate matter.

Carbonaceous aerosols in fine particulate matter of Santiago Metropolitan Area, Chile.

Science.gov (United States)

Toro Araya, Richard; Flocchini, Robert; Morales Segura, Rául G E; Leiva Guzmán, Manuel A

2014-01-01

Measurements of carbonaceous aerosols in South American cities are limited, and most existing data are of short term and limited to only a few locations. For 6 years (2002-2007), concentrations of fine particulate matter and organic and elemental carbon were measured continuously in the capital of Chile. The contribution of carbonaceous aerosols to the primary and secondary fractions was estimated at three different sampling sites and in the warm and cool seasons. The results demonstrate that there are significant differences in the levels in both the cold (March to August) and warm (September to February) seasons at all sites studied. The percent contribution of total carbonaceous aerosol fine particulate matter was greater in the cool season (53 ± 41%) than in the warm season (44 ± 18%). On average, the secondary organic carbon in the city corresponded to 29% of the total organic carbon. In cold periods, this proportion may reach an average of 38%. A comparison of the results with the air quality standards for fine particulate matter indicates that the total carbonaceous fraction alone exceeds the World Health Organization standard (10 µg/m(3)) and the United States Environmental Protection Agency standard (15 µg/m(3)) for fine particulate matter.

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

KAUST Repository

Piret, Cé cile

2012-01-01

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

Treating distillable carbonaceous materials with hydrocarbon gases, etc

Energy Technology Data Exchange (ETDEWEB)

1935-12-04

A process is described for the treatment of distillable carbonaceous materials with hydrogen gases in the presence of hydrogen halides to recover valuable hydrocarbon products, characterized by the stable halide forming the treating medium for the hot-test gasesous product of this treatment with hydrogen gases in combination with an alkaline metal or alkaline earth, able to be decomposed by an inorganic acid soluble in water, capable of driving off hydrogen halide from their salts and also with salts of ammonia of the mentioned inorganic acids, the halide being converted into halide of ammonia and halogen, and the ammonia halide or hydrogen halide being returned to the process alone or together with the feed of carbonaceous materials with which it began.

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.

Radiocarbon: nature's tracer for carbonaceous pollutants

International Nuclear Information System (INIS)

Currie, L.A.; Klouda, G.A.; Gerlach, R.W.

1982-01-01

Recent developments in radiocarbon dating techniques have made it feasible to determine 14 C/ 12 C ratios in samples containing milligram or even microgram quantities of carbon. As a result, it has become practicable to apply these techniques to the study of trace gases and particles in the atmosphere, as a means of resolving anthropogenic from natural source components. Interpretation of 14 C data is straightforward: biospheric carbon (such as vegetation) is alive with a 14 C/ 12 C ratio of about 1.5 x 10 -12 , whereas fossil carbon is dead. Beyond this dichotomous classification it becomes very interesting to combine the isotopic data with concurrent chemical data, as well as spatial and temporal distributions, in order to infer the strengths of specific sources of carbonaceous pollutants. A brief review will be presented of our program on atmospheric gases and carbonaceous particles. For the latter, we have assayed individual chemical and size fractions, and samples collected in urban, rural, and remote locales. The biogenic carbon fraction - presumably from wood-burning - ranged from 10% to 100% for the urban samples analyzed

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.

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.

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.

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…

Carbowaste: treatment and disposal of irradiated graphite and other carbonaceous waste

International Nuclear Information System (INIS)

Von Lensa, W.; Rizzato, C.; Baginski, K.; Banford, A.W.; Bradbury, D.; Goodwin, J.; Grambow, B.; Grave, M.J.; Jones, A.N.; Laurent, G.; Pina, G.; Vulpius, D.

2014-01-01

The European Project on 'Treatment and Disposal of Irradiated Graphite and other Carbonaceous Waste (CARBOWASTE)' addressed the retrieval, characterization, treatment, reuse and disposal of irradiated graphite with the following main results: - I-graphite waste features significantly depend on the specific manufacture process, on the operational conditions in the nuclear reactor (neutron dose, atmosphere, temperature etc.) and on radiolytic oxidation leading to partial releases of activation products and precursors during operation. - The neutron activation process generates significant recoil energies breaking pre-existing chemical bonds resulting in dislocations of activation products and new chemical compounds. - Most activation products exist in different chemical forms and at different locations. - I-graphite can be partly purified by thermal and chemical treatment processes leaving more leach-resistant waste products. - Leach tests and preliminary performance analyses show that i-graphite can be safely disposed of in a wide range of disposal systems, after appropriate treatment and/or conditioning. (authors)

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 ...

Explosive Characteristics of Carbonaceous Nanoparticles

Science.gov (United States)

Turkevich, Leonid; Fernback, Joseph; Dastidar, Ashok

2013-03-01

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

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.

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...

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...

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

International Nuclear Information System (INIS)

Winkler, E.

1991-01-01

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

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.

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

OpenAIRE

Denche, M.; Marhoune, A. L.

2001-01-01

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

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.

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.

Fungal-Transformation of Surrogate Sulphides and Carbonaceous ...

African Journals Online (AJOL)

In the recovery of gold from refractory gold ores, pretreatment is required to decompose sulphides and liberate occluded gold before cyanidation, and to deactivate carbonaceous matter and prevent it from adsorbing dissolved gold. Until the past three decades, most commercial pretreatment processes had been by abiotic ...

High resolution TEM of chondritic carbonaceous matter: Metamorphic evolution and heterogeneity

Science.gov (United States)

Le Guillou, Corentin; Rouzaud, Jean-Noël.; Bonal, Lydie; Quirico, Eric; Derenne, Sylvie; Remusat, Laurent

2012-03-01

The insoluble carbonaceous matter from 12 chondrites (CI, CM, CO, CV, EH, and UOC), was characterized by high resolution transmission electron microscopy (HRTEM). Besides ubiquitous nanoglobules, the insoluble organic matter from petrologic type 1 and 2 chondrites and Semarkona (LL 3.0) is composed of a highly disordered polyaromatic component. No structural differences were observed between these IOMs, in agreement with the limited thermal metamorphism they all experienced. In chondrites of petrologic type >3.0, the evolution of the IOM is controlled by the extent of thermal metamorphism. The polyaromatic layers, shorter than 1 nm in petrologic type ≤3.0 chondrites, grow up to sizes between 5 and 10 nm in petrologic type >3.6 chondrites, contributing to the increase of the degree of structural order. In addition, we find rare, but ubiquitous onion-like carbons, which may be the product of nanodiamond graphitization. The insoluble carbonaceous matter of the enstatite chondrite Sahara 97096 (EH 3) is different from the other meteorites studied here. It is more heterogeneous and displays a high abundance of graphitized particles. This may be the result of a mixture between (1) the disordered carbon located in the matrix, and (2) catalytic graphitized phases associated with metal, potentially originating from partial melting events. The structural and nanostructural evolution are similar in all IOMs. This suggests that the structure of the accreted precursors and the parent body conditions of their secondary thermal modifications (temperature, duration, and pressure) were similar. The limited degree of organization of the most metamorphosed IOMs compared with terrestrial rocks submitted to similar temperature suggests that the conditions are not favorable to graphitization processes, due to the chemical nature of the precursor or the lack of confinement pressure.

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

CERN Document Server

Bove, Antonio; Murthy, MK Venkatesha

2009-01-01

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

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.

Slurry burner for mixture of carbonaceous material and water

Science.gov (United States)

Nodd, D.G.; Walker, R.J.

1985-11-05

The present invention is intended to overcome the limitations of the prior art by providing a fuel burner particularly adapted for the combustion of carbonaceous material-water slurries which includes a stationary high pressure tip-emulsion atomizer which directs a uniform fuel into a shearing air flow as the carbonaceous material-water slurry is directed into a combustion chamber, inhibits the collection of unburned fuel upon and within the atomizer, reduces the slurry to a collection of fine particles upon discharge into the combustion chamber, and regulates the operating temperature of the burner as well as primary air flow about the burner and into the combustion chamber for improved combustion efficiency, no atomizer plugging and enhanced flame stability.

Apparatus for the distillation of coal, shale or other carbonaceous materials

Energy Technology Data Exchange (ETDEWEB)

Wilson, P

1932-02-16

The design consists of a retort having a series of joined closed superheated sections each having a heavier gas delivery port therefrom leading to an outlet pipe in combination with a condenser, means above and on said sections comprising a series of hoppers in communication with a common feed hopper for carbonaceous materials to be distilled. An air tight cover for said feed hopper and intermediate rotatable valve control are provided. Means are provided for said carbonaceous material between said hoppers and said sections and adjacent means having lighter gas ports to a pipe also in communication with said condenser. A series of exit hoppers are located below such sections and means for feeding preheated gas through the exit hoppers to the material to be distilled are provided. A rotatable valve control means associated with the exit hoppers for discharging spent carbonaceous materials to separate water sealed outlets to a tank located below the apparatus.

Carbonaceous Asteroid Volatile Recovery (CAVoR) system, Phase II

Data.gov (United States)

National Aeronautics and Space Administration — The Carbonaceous Asteroid Volatile Recovery (CAVoR) system produces water and hydrogen-rich syngas for propellant production, life support consumables, and...

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)

Retorts for distilling carbonaceous material

Energy Technology Data Exchange (ETDEWEB)

Lutz, H E

1921-09-12

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

MRI differential diagnosis of complete and partial tears of the anterior cruciate ligament of the knee: the usefulness of oblique coronal T2-weighted image

International Nuclear Information System (INIS)

Lee, Seo Young; Shim, Jae Chan; Lee, Ghi Jai; Bang, Sun Woo; Ryu, Seok Jong; Kim, Ho Kyun; Kim, Jeong Seok

2002-01-01

To assess the usefulness of T2-weighted oblique coronal MR imaging (T2OCI) in the differential diagnosis of complete and partial tears of the anterior cruciate ligament (ACL) of the knee. Thirty-three patients with ACL tear (16 complete and 17 partial tears), comfirmed by arthroscopy, were included in this study. Conventional MR imaging and T2OCI were performed, and the findings were retrospectively reviewed by two radiologists in terms of continuity, shape, axis and internal signal intensity of the ligament. Each finding was tested if there were stastistically significant differences in its prevalence between partial and complete tears. The diagnostic accuracy of T2OCI and conventional MR imaging in the detection of partial and complete tears of the ACL were compared. Conventional MR imaging revealed no statistically significant finding for differential diagnosis of complete and partial ACL tears. The reliable and statistically significant (p<0.001) findings of T2OCI were complete discontinuity of the ligament in cases involving complete ACL tears (14 of 16 complete tears and 2 of 17 partial tears) and the preservation of the band form for partial ACL tears (2 of 16 complete tears and 15 of 17 partial tears). The accuracy of T2OCI and conventional MR imaging was 88% and 70%, respectively. When ACL injury is vague on conventional MR images, a modality which is more useful in the differential diagnosis of partial and complete tears of the ACL, and in predicting the site of a tear, is T2-weighted oblique coronal imaging

Carbonaceous Aerosol Characterization during 2016 KOR-US 2016

Science.gov (United States)

Rodriguez, B.; Santos, G. M.; Sanchez, D.; Jeong, D.; Czimczik, C. I.; Kim, S.

2017-12-01

Atmospheric carbonaceous aerosols are a major component of fine particulate matter and assume important roles in Earth's climate and human health. Because atmospheric carbonaceous aerosols exist as a continuum ranging from small, light-scattering organic carbon (OC), to highly-condensed, light-absorbing elemental carbon (EC) they have contrasting effects on interaction with incoming and outgoing radiation, cloud formation, and snow/ice albedo. By strengthening our understanding of the relative contribution and sources of OC and EC we will be able to further describe aerosol formation and mixing at the regional level. To understand the relative anthropogenic and biogenic contributions to carbonaceous aerosol, 12 PM10 aerosols samples were collected on quartz fiber filters at the Mt. Taewha Research Forest in South Korea during the KORUS-AQ 2016 campaign over periods of 24-48 hours with a high-volume air sampler. Analysis of bulk C and N concentrations and absorption properties of filter extracts interspersed with HYSPLIT model results indicated that continental outflow across the Yellow Sea in enriched in bulk nitrogen loading and enhanced bulk absorptive properties of the aerosols. Bulk radiocarbon analysis also indicated enriched values in all samples indicating contamination from a nuclear power plant or the combustion of biomedical waste nearby. Here, we aim to investigate further the chemical characterization of VOCs adsorbed unto the aerosol through TD-GC-TOFMS. With this dataset we aim to determine the relative contribution of anthropogenic and biogenic aerosols by utilizing specific chemical tracers for source apportionment.

Tunable atomic force microscopy bias lithography on electron beam induced carbonaceous platforms

Directory of Open Access Journals (Sweden)

Narendra Kurra

2013-09-01

Full Text Available Tunable local electrochemical and physical modifications on the carbonaceous platforms are achieved using Atomic force microscope (AFM bias lithography. These carbonaceous platforms are produced on Si substrate by the technique called electron beam induced carbonaceous deposition (EBICD. EBICD is composed of functionalized carbon species, confirmed through X-ray photoelectron spectroscopy (XPS analysis. AFM bias lithography in tapping mode with a positive tip bias resulted in the nucleation of attoliter water on the EBICD surface under moderate humidity conditions (45%. While the lithography in the contact mode with a negative tip bias caused the electrochemical modifications such as anodic oxidation and etching of the EBICD under moderate (45% and higher (60% humidity conditions respectively. Finally, reversible charge patterns are created on these EBICD surfaces under low (30% humidity conditions and investigated by means of electrostatic force microscopy (EFM.

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.

Series expansion solutions for the multi-term time and space fractional partial differential equations in two- and three-dimensions

Science.gov (United States)

Ye, H.; Liu, F.; Turner, I.; Anh, V.; Burrage, K.

2013-09-01

Fractional partial differential equations with more than one fractional derivative in time describe some important physical phenomena, such as the telegraph equation, the power law wave equation, or the Szabo wave equation. In this paper, we consider two- and three-dimensional multi-term time and space fractional partial differential equations. The multi-term time-fractional derivative is defined in the Caputo sense, whose order belongs to the interval (1,2],(2,3],(3,4] or (0, m], and the space-fractional derivative is referred to as the fractional Laplacian form. We derive series expansion solutions based on a spectral representation of the Laplacian operator on a bounded region. Some applications are given for the two- and three-dimensional telegraph equation, power law wave equation and Szabo wave equation.

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.

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.

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

Cloud albedo increase from carbonaceous aerosol

Directory of Open Access Journals (Sweden)

W. R. Leaitch

2010-08-01

Full Text Available Airborne measurements from two consecutive days, analysed with the aid of an aerosol-adiabatic cloud parcel model, are used to study the effect of carbonaceous aerosol particles on the reflectivity of sunlight by water clouds. The measurements, including aerosol chemistry, aerosol microphysics, cloud microphysics, cloud gust velocities and cloud light extinction, were made below, in and above stratocumulus over the northwest Atlantic Ocean. On the first day, the history of the below-cloud fine particle aerosol was marine and the fine particle sulphate and organic carbon mass concentrations measured at cloud base were 2.4 μg m⁻³ and 0.9 μg m⁻³ respectively. On the second day, the below-cloud aerosol was continentally influenced and the fine particle sulphate and organic carbon mass concentrations were 2.3 μg m⁻³ and 2.6 μg m⁻³ respectively. Over the range 0.06–0.8 μm diameter, the shapes of the below-cloud size distributions were similar on both days and the number concentrations were approximately a factor of two higher on the second day. The cloud droplet number concentrations (CDNC on the second day were approximately three times higher than the CDNC measured on the first day. Using the parcel model to separate the influence of the differences in gust velocities, we estimate from the vertically integrated cloud light scattering measurements a 6% increase in the cloud albedo principally due to the increase in the carbonaceous components on the second day. Assuming no additional absorption by this aerosol, a 6% albedo increase translates to a local daytime radiative cooling of ∼12 W m⁻². This result provides observational evidence that the role of anthropogenic carbonaceous components in the cloud albedo effect can be much larger than that of anthropogenic sulphate, as some global simulations have indicated.

Gasoline cars produce more carbonaceous particulate matter than modern filter-equipped diesel cars.

Science.gov (United States)

Platt, S M; El Haddad, I; Pieber, S M; Zardini, A A; Suarez-Bertoa, R; Clairotte, M; Daellenbach, K R; Huang, R-J; Slowik, J G; Hellebust, S; Temime-Roussel, B; Marchand, N; de Gouw, J; Jimenez, J L; Hayes, P L; Robinson, A L; Baltensperger, U; Astorga, C; Prévôt, A S H

2017-07-13

Carbonaceous particulate matter (PM), comprising black carbon (BC), primary organic aerosol (POA) and secondary organic aerosol (SOA, from atmospheric aging of precursors), is a highly toxic vehicle exhaust component. Therefore, understanding vehicle pollution requires knowledge of both primary emissions, and how these emissions age in the atmosphere. We provide a systematic examination of carbonaceous PM emissions and parameterisation of SOA formation from modern diesel and gasoline cars at different temperatures (22, -7 °C) during controlled laboratory experiments. Carbonaceous PM emission and SOA formation is markedly higher from gasoline than diesel particle filter (DPF) and catalyst-equipped diesel cars, more so at -7 °C, contrasting with nitrogen oxides (NO X ). Higher SOA formation from gasoline cars and primary emission reductions for diesels implies gasoline cars will increasingly dominate vehicular total carbonaceous PM, though older non-DPF-equipped diesels will continue to dominate the primary fraction for some time. Supported by state-of-the-art source apportionment of ambient fossil fuel derived PM, our results show that whether gasoline or diesel cars are more polluting depends on the pollutant in question, i.e. that diesel cars are not necessarily worse polluters than gasoline cars.

Quenched carbonaceous composite (QCC): a likely candidate for interstellar grains

International Nuclear Information System (INIS)

Sakata, A.; Wada, S.; Tanabe, T.; Onaka, T.

1984-01-01

The authors have recently reported that a carbonaceous composite synthesized from a hydrocarbon plasma shows an extinction property quite resembling the observed average interstellar extinction curve around the 220 nm hump. This composite is synthesized by quenching the excited gas ejecting from a plasma of methane gas, so it is called 'quenched carbonaceous composite' or 'QCC'. A recent study of QCC in the infrared region has shown that QCC can also account for some of the unidentified bands in the infrared region detected in several celestial objects. These results suggest that most of the pronounced features of the interstellar grains originate from substances whose major constituent is carbon. (author)

Carbonaceous aerosols from prescribed burning of a boreal forest ecosystem

International Nuclear Information System (INIS)

Mazurek, M.A.; Cofer, W.R. III; Levine, J.S.

1991-01-01

Smoke aerosol and background aerosol particles were collected from the controlled burning of boreal forest where vegetation species and relative mass distributions are known. Chemical mass balances were constructed for the total mass of carbonaceous aerosol particles emitted during the prescribed burn. In addition, a carbonaceous species inventory was developed for aerosol particles presnt under background, smoldering, and full-fire conditions; the production of organic carbon and elemental carbon particles is noted for these two fire regimes. Distributions of the solvent-soluble organic components of the sampled aerosols were generated to identify molecular properties that can be traced to unburned and pyrolyzed materials present in the boreal forest fuels

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.

Extraterrestrial Nucleobases in Carbonaceous Chondrites

Science.gov (United States)

Martins, Z.; Botta, O.; Fogel, M.; Sephton, M.; Glavin, D.; Watson, J.; Dworkin, J.; Schwartz, A.; Ehrenfreund, P.

Nucleobases in Carbonaceous Chondrites Z. Martins (1), O. Botta (2), M. L. Fogel (3), M. A. Sephton (4), D. P. Glavin (2), J. S. Watson (5), J. P. Dworkin (2), A. W. Schwartz (6) and P. Ehrenfreund (1,6). (1) Astrobiology Laboratory, Leiden Institute of Chemistry, Leiden, The Netherlands, (2) NASA Goddard Space Flight Center, Goddard Center for Astrobiology, Greenbelt, MD, USA, (3) GL, Carnegie Institution of Washington, Washington DC, USA, (4) Impacts and Astromaterials Research Centre, Department of Earth Science and Engineering, South Kensington Campus, Imperial College, London, UK, (5) Planetary and Space Sciences Research Institute, The Open University, Walton Hall, Milton Keynes, UK, (6) Radboud University Nijmegen, Nijmegen, The Netherlands. E-mail: z.martins@chem.leidenuniv.nl/Phone:+31715274440 Nucleobases are crucial compounds in terrestrial biochemistry, because they are key components of DNA and RNA. Carbonaceous meteorites have been analyzed for nucleobases by different research groups [1-5]. However, significant quantitative and qualitative differences were observed, leading to the controversial about the origin of these nucleobases. In order to establish the origin of these compounds in carbonaceous chondrites and to assess the plausibility of their exogenous delivery to the early Earth, we have performed formic acid extraction of samples of the Murchison meteorite [6], followed by an extensive purification procedure, analysis and quantification by high-performance liquid chromatography with UV absorption detection and gas chromatography-mass spectrometry. Our results were qualitatively consistent with previous results [3, 4], but showed significant quantitative differences. Compound specific carbon isotope values were obtained, using gas chromatography-combustion- isotope ratio mass spectrometry. A soil sample collected in the proximity of the Murchison meteorite fall site was subjected to the same extraction, purification and analysis procedure

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.

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.

Sorption characteristics and mechanisms of organic contaminant to carbonaceous biosorbents in aqueous solution

Institute of Scientific and Technical Information of China (English)

2008-01-01

A series of carbonaceous biosorbents was prepared by pyrolyzing pine needles,a model biomass,at various temperatures (100-700℃) under an oxygen-limited condition for 6h. The elemental composi-tions and the specific surface areas (BET-N2) of the biosorbents were analyzed. Sorption properties of 4-nitrotoluene to the biosorbents and their mechanisms were investigated,and then correlated with the structures of the biosorbents. The result shows that with the increase of the pyrolytic temperature,the aromaticity of the carbonaceous biosorbents increases dramatically and the polarity (the (N+O)/C atomic ratio) decreases sharply. Correspondingly,conformations of the organic matter in the biosor-bents transform gradually from a "soft-state" to a "hard-state" and the specific surface areas of the resultant biosorbents extend rapidly. The sorption isotherms fit well with the Freundlich equation. The regression parameters (i.e.,N and lgKf) are linearly related to the aromaticity indices (the H/C atomic ratio). Contributions of adsorption and partition to total sorption of the carbonaceous biosorbents are quantified. The adsorption of the carbonaceous biosorbents increases quickly with the increase of the pyrolytic temperature. The saturated adsorption amounts (Qmax) increase linearly with the increase of the specific surface areas (SA) of the biosorbents. For the carbonaceous biosorbents with hard-state carbon,the calculated normalized-Qmax values by SA are comparable to the theoretical estimation (2.45 μmol/m2). In comparison,for the carbonaceous sorbents with soft-state carbon,the calculated nor-malized-Qmax values by SA are much higher than the theoretical estimation. The partition coefficients (Kom) increase with the decrease of the polarity of the biosorbents,reaching a maximum,and then de-crease sharply with further decreasing the polarity,suggesting that partition mechanism be dominated by the compatibility and accessibility of the sorbent medium with organic

Sorption characteristics and mechanisms of organic contaminant to carbonaceous biosorbents in aqueous solution

Institute of Scientific and Technical Information of China (English)

CHEN BaoLiang; ZHOU DanDan; ZHU LiZhong; SHEN XueYou

2008-01-01

A series of carbonaceous biosorbents was prepared by pyrolyzing pine needles, a model biomass, at various temperatures (100-700℃) under an oxygen-limited condition for 6 h. The elemental composi-tions and the specific surface areas (BET-N2) of the biosorbents were analyzed. Sorption properties of 4-nitrotoluene to the biosorbents and their mechanisms were investigated, and then correlated with the structures of the biosorbents. The result shows that with the increase of the pyrolytic temperature, the sromaticity of the carbonaceous biosorbents increases dramatically and the polarity (the (N+O)/C atomic ratio) decreases sharply. Correspondingly, conformations of the organic matter in the biosor-bents transform gradually from a "soft-state" to a "hard-state" and the specific surface areas of the resultant biosorbents extend rapidly. The sorption isotherms fit well with the Freundlich equation. The regression parameters (I.e., N and IgKf) are linearly related to the aromaticity indices (the H/C atomic ratio). Contributions of adsorption and partition to total sorption of the carbonaceous biosorbents are quantified. The adsorption of the carbonaceous biosorbents increases quickly with the increase of the pyrolytic temperature. The saturated adsorption amounts (Qmax) increase linearly with the increase of the specific surface areas (SA) of the biosorbents. For the carbonaceous biosorbents with hard-state carbon, the calculated normalized-Qmax values by SA are comparable to the theoretical estimation (2.45 μmol/m2). In comparison, for the carbonaceous sorbents with soft-state carbon, the calculated nor-malized-Qmax values by SA are much higher than the theoretical estimation. The partition coefficients (Kom) increase with the decrease of the polarity of the biosorbents, reaching a maximum, and then de-crease sharply with further decreasing the polarity, suggesting that partition mechanism be dominated by the compatibility and accessibility of the sorbent medium with

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

Ore-forming environment and ore-forming system of carbonaceous-siliceous-pelitic rock type uranium deposit in China

International Nuclear Information System (INIS)

Qi Fucheng; Zhang Zilong; Li Zhixing; He Zhongbo; Wang Wenquan

2012-01-01

It is proposed that there are four types of ore-forming systems about carbonaceous-siliceous-pelitic rock type uranium deposit in China based on systematic study on structural environment and distribution regularity of uraniferous construction of marine carbonaceous-siliceous-pelitic rock in China: continental margin rift valley ore-forming systems, continental margin rifting deep fracture zone ore-forming systems, landmass boundary borderland basin ore-forming systems and epicontinental mobile belt downfaulted aulacogen ore-forming systems. It is propounded definitely that it is controlled by margin rift valley ore-forming systems and continental margin rifting deep fracture zone ore-forming systems for large-scale uranium mineralization of carbonaceous-siliceous-pelitic rock type uranium deposit in China, which is also controlled by uraniferous marine carbonaceous-siliceous-pelitic rock construction made up of silicalite, siliceous phosphorite and carbonaceous-siliceous-pelitic rock, which settled down accompany with submarine backwash and sub marine volcanic eruption in margin rift valley and continental margin rifting mineralizing environment. Continental mar gin rift valley and continental margin rifting thermal sedimentation or exhalation sedimentation is the mechanism of forming large-scale uraniferous marine carbonaceous-siliceous-pelitic rock construction Early Palaeozoic Era in China or large-scale uranium-polymetallic mineralization. (authors)

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

OpenAIRE

Pirnapasov, Sardor; Karimov, Erkinjon

2017-01-01

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

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.

Effects of chemical functional groups on elemental mercury adsorption on carbonaceous surfaces

Energy Technology Data Exchange (ETDEWEB)

Liu Jing, E-mail: liujing27@mail.hust.edu.cn [State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074 (China); Cheney, Marcos A. [Department of Natural Sciences, University of Maryland Eastern Shore, Princess Anne, MD 21853 (United States); Wu Fan; Li Meng [State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074 (China)

2011-02-15

A systematic theoretical study using density functional theory is performed to provide molecular-level understanding of the effects of chemical functional groups on mercury adsorption on carbonaceous surfaces. The zigzag and armchair edges were used in modeling the carbonaceous surfaces to simulate different adsorption sites. The edge atoms on the upper side of the models are unsaturated to simulate active sites. All calculations (optimizations, energies, and frequencies) were made at B3PW91 density functional theory level, using RCEP60VDZ basis set for mercury and 6-31G(d) pople basis set for other atoms. The results indicate that the embedding of halogen atom can increase the activity of its neighboring site which in turn increases the adsorption capacity of the carbonaceous surface for Hg{sup 0}. The adsorption belongs to chemisorptions, which is in good agreement with the experimental results. For the effects of oxygen functional groups, lactone, carbonyl and semiquinone favor Hg{sup 0} adsorption because they increase the neighboring site's activity for mercury adsorption. On the contrary, phenol and carboxyl functional groups show a physisorption of Hg{sup 0}, and reduce Hg capture. This result can explain the seemingly conflicting experimental results reported in the literature concerning the influence of oxygen functional groups on mercury adsorption on carbonaceous surface.

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

Science.gov (United States)

Xu, Qinwu; Hesthaven, Jan S.

2014-01-01

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

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

Proto-Planetary Disk Chemistry Recorded by D-Rich Organic Radicals in Carbonaceous Chondrites

OpenAIRE

Remusat, Laurent; Robert, François; Meibom, Anders; Mostefaoui, Smail; Delpoux, Olivier; Binet, Laurent; Gourier, Didier; Derenne, Sylvie

2009-01-01

Insoluble organic matter (IOM) in primitive carbonaceous meteorites has preserved its chemical composition and isotopic heterogeneity since the solar system formed ~4.567 billion years ago. We have identified the carrier moieties of isotopically anomalous hydrogen in IOM isolated from the Orgueil carbonaceous chondrite. Data from high spatial resolution, quantitative isotopic NanoSIMS mapping of Orgueil IOM combined with data from electron paramagnetic resonance spectroscopy reveals that orga...

A Mudball Model for the Evolution of Carbonaceous Asteroids

Science.gov (United States)

Travis, B. J.; Bland, P. A.

2018-05-01

We simulation the evolution of carbonaceous chondrite parent bodies from initially unconsolidated aggregations of rock grains and ice crystals. Application of the numerical model MAGHNUM to evolution of CM type planetesimals and Ceres is described.

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.

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...

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.

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

KAUST Repository

Asiri, Sharefa M.

2016-10-20

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

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.

Process of treating carbonaceous substances

Energy Technology Data Exchange (ETDEWEB)

1938-12-16

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

Template-free synthesis of multifunctional carbonaceous microcone forests

Science.gov (United States)

Wang, Qiang; Yang, Lei; Dai, Bing; Bai, Jie; Yang, Zhenhuai; Guo, Shuai; He, Yurong; Han, Jiecai; Zhu, Jiaqi

2018-01-01

Forests of vertically aligned carbonaceous microcones are fabricated directly on a nickel mesh by microwave-plasma-assisted chemical vapor deposition. The microstructure is formed through a simple one-step process involving self-assembly. The fabricated composite exhibits superhydrophobicity and superoleophilicity as well as low density, owing to which it floats on water and can be used for the in-situ separation of oil from water at the oil/water interface. Furthermore, the composite exhibits pH responsivity, and its water permeability can be varied simply by altering the pH of the aqueous solution. In addition, the composite is suitable for use as an electrode material for supercapacitors owing to its large geometric surface area, porous structure, and superior electrical properties, which allow for fast ion and electron transportation. Thus, this composite consisting of forests of vertically aligned carbonaceous microcones on a nickel mesh is expected to find use in a wide range of fields and applications, including in environmental cleanup, flow switches, and energy storage devices.

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.

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

Science.gov (United States)

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

2015-07-08

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

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

CERN Document Server

Pettersson, Mass Per; Nordström, Jan

2015-01-01

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

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.

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

International Nuclear Information System (INIS)

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

2008-01-01

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

Influence of hydrothermal carbonization and treatment by microwave on morphology of carbonaceous materials obtained from lignin

International Nuclear Information System (INIS)

Oliveira, I.B.; Barin, G.B.; Barreto, L.S.; Santos, M.C.G.

2014-01-01

The conversion of biomass into carbon materials with special morphologies via hydrothermal carbonization presents itself as a potential route for the use of renewable precursors in obtaining carbonaceous structures. In the present study the influence of the hydrothermal carbonization (250 ° C / 4 h) followed by microwave treatment (1-2-4 hours at 25 and 40 mL) in morphology and structure of lignin. The samples were analyzed by X-ray diffraction and scanning electron microscopy. The plaque morphology of lignin was preserved during the hydrothermal process. However, when treated by microwave can be observed partial dissolution of lignin leading to the formation of microspheres on the surface. XRD presence of an amorphous halo 2θ = 23 ° attributed to the (002) network of the amorphous carbon was observed. (author)

Biomass-derived carbonaceous materials as components in wood briquettes

Energy Technology Data Exchange (ETDEWEB)

Stengl, S.; Koch, C.; Stadlbauer, E.A.; Scheer, J. [Univ. of Applied Sciences, THM Campus Giessen, Giessen (Germany); Weber, B. [Instituto de Ingenieria de la Universidad Nacional Autonoma de Mexico (UNAM), Coyoacan (Mexico); Strohal, U.; Fey, J. [Strohal Anlagenbau, Staufenberg (Germany)

2012-11-01

The present paper describes a briquette composed of a substantial amount of wooden biomass and up to 35% of carbonaceous materials derived from biogenic residues. The cellulosic component may be a mixture of any wooden residue. Suitable substrates for the carbonaceous fraction are vegetation wastes from land management or agriculture. Depending on physical and chemical nature of the substrate, Hydrothermal Carbonisation (HTC) or Low Temperature Conversion (LTC) may be used to produce the carbonaceous part of the briquette. HTC turns wet biomass at temperatures around 200 deg C in an autoclave into lignite whereas LTC treatment at 400 deg C and atmospheric pressure produces black coal. This is manifested by a molar ratio of 0.1 {<=} H/C (LTC) {<=} 0.7; 0.05{<=} O/C (LTC) {<=} 0.4 and 0.7 < H/C (HTC) <1.5 ; 0.2< O/C (HTC) < 0.5. Solid state {sup 13}C-NMR confirms these findings showing a strong absorption band for sp{sup 2}-hybridized carbon atoms at chemical shifts of 100 ppm und 165 ppm for LTC biochar. Depending on the substrate, HTC gives rise to an increase in the specific calorific value (MJ/kg) by a factor of {Psi} {approx} 1.2 - 1.4; LTC by 1.5 - 1.8. In addition ash melting points are significantly increased; in case of wheat straw by about 200 deg C. Compacted products may have a cylindrical or rectangular profile.

Source apportionment of carbonaceous aerosol in southern Sweden

Directory of Open Access Journals (Sweden)

J. Genberg

2011-11-01

Full Text Available A one-year study was performed at the Vavihill background station in southern Sweden to estimate the anthropogenic contribution to the carbonaceous aerosol. Weekly samples of the particulate matter PM₁₀ were collected on quartz filters, and the amounts of organic carbon, elemental carbon, radiocarbon (¹⁴C and levoglucosan were measured. This approach enabled source apportionment of the total carbon in the PM₁₀ fraction using the concentration ratios of the sources. The sources considered in this study were emissions from the combustion of fossil fuels and biomass, as well as biogenic sources. During the summer, the carbonaceous aerosol mass was dominated by compounds of biogenic origin (80%, which are associated with biogenic primary and secondary organic aerosols. During the winter months, biomass combustion (32% and fossil fuel combustion (28% were the main contributors to the carbonaceous aerosol. Elemental carbon concentrations in winter were about twice as large as during summer, and can be attributed to biomass combustion, probably from domestic wood burning. The contribution of fossil fuels to elemental carbon was stable throughout the year, although the fossil contribution to organic carbon increased during the winter. Thus, the organic aerosol originated mainly from natural sources during the summer and from anthropogenic sources during the winter. The result of this source apportionment was compared with results from the EMEP MSC-W chemical transport model. The model and measurements were generally consistent for total atmospheric organic carbon, however, the contribution of the sources varied substantially. E.g. the biomass burning contributions of OC were underestimated by the model by a factor of 2.2 compared to the measurements.

Immobilization of pentachlorophenol in soil using carbonaceous material amendments

Energy Technology Data Exchange (ETDEWEB)

Wen Bei [State Key Laboratory of Environmental Chemistry and Ecotoxicology, Research Center for Eco-Environmental Sciences, Chinese Academy of Sciences, Shuangqing Road, Haidian District, Beijing 100085 (China)], E-mail: bwen@rcees.ac.cn; Li Ruijuan; Zhang Shuzhen [State Key Laboratory of Environmental Chemistry and Ecotoxicology, Research Center for Eco-Environmental Sciences, Chinese Academy of Sciences, Shuangqing Road, Haidian District, Beijing 100085 (China); Shan Xiaoquan [State Key Laboratory of Environmental Chemistry and Ecotoxicology, Research Center for Eco-Environmental Sciences, Chinese Academy of Sciences, Shuangqing Road, Haidian District, Beijing 100085 (China)], E-mail: xiaoquan@rcees.ac.cn; Fang Jing; Xiao Ke [State Key Laboratory of Environmental Chemistry and Ecotoxicology, Research Center for Eco-Environmental Sciences, Chinese Academy of Sciences, Shuangqing Road, Haidian District, Beijing 100085 (China); Khan, Shahamat U. [Department of Chemistry and Biochemistry, MSN 3E2, George Mason University, 4400 University Drive, Fairfax, VA 22030-4444 (United States)

2009-03-15

In this study, three pentachlorophenol (PCP) laboratory-spiked and one field-contaminated soil were amended with 2.0% char, humic acid (HA) and peat, respectively. The amended soils were aged for either 7 or 250 days. After amendment, CaCl{sub 2} extractability of PCP was significantly decreased. Desorption kinetics indicated that the proposed amendment could lead to a strong binding and slow desorption of PCP in soils. Amendment with char reduced the bioaccumulation factor (BAF) of PCP most significantly for earthworms (Eisenia fetida) in all soils studied. The results of both physicochemical and biological tests suggested that amendment reduced PCP bioavailability quickly and enduringly, implying that carbonaceous material amendment, especially char amendment, was a potentially attractive in situ remediation method for sequestration of PCP in contaminated soil. - Carbonaceous material amendment was a potential in situ remediation method for pentachlorophenol contaminated soil.

Origin and nature of carbonaceous material in the galaxy

Energy Technology Data Exchange (ETDEWEB)

Hoyle, F; Wickramasinghe, N C [University Coll. of South Wales and Monmouthshire, Cardiff (UK)

1977-12-22

It is stated that astronomers generally believe that the carbonaceous material emerging from stars must be in the form of graphite, the most stable condensed form of carbon, and that such emergence must be confined to situations where the C/O ratio exceeds unity, such as in the atmospheres of carbon stars. It is argued here, however, that whilst this state of affairs remains valid for mass flows from stars of sufficiently low surface temperatures, it is not correct for low density flows from stars with colour temperatures approximately > 4,000 K (or for oscillatory stars with colour temperatures that go above 4,000 K for a portion of their cycle). In the latter case it is shown that carbonaceous material comprised mainly of polysaccharides will be able to condense. Implications for the origin of life on the Earth are discussed.

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

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

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

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.

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

Modeling and analytical simulation of a smouldering carbonaceous ...

African Journals Online (AJOL)

Modeling and analytical simulation of a smouldering carbonaceous rod. A.A. Mohammed, R.O. Olayiwola, M Eseyin, A.A. Wachin. Abstract. Modeling of pyrolysis and combustion in a smouldering fuel bed requires the solution of flow, heat and mass transfer through porous media. This paper presents an analytical method ...

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

The analysis of creep characteristics of the surrounding rock of the carbonaceous rock tunnel based on Singh-Mitchell model

Science.gov (United States)

Luo, Junhui; Mi, Decai; Ye, Qiongyao; Deng, Shengqiang; Zeng, Fuquan; Zeng, Yongjun

2018-01-01

Carbonaceous rock has the characteristics of easy disintegration, softening, swelling and environmental sensitivity, which belongs to soft surrounding rock, and the deformation during excavation and long-term stability of the surrounding rock of carbonaceous rock tunnel are common problems in the construction of carbonaceous rock tunnel. According to the above, the Monitor and measure the displacement, temperature and osmotic pressure of the surrounding carbonaceous rock of the tunnel of Guangxi Hebai highway. Then it based on the obtaining data to study the creep mechanism of surrounding rock using Singh-Mitchell model and predict the deformation of surrounding rock before the tunnel is operation. The results show that the Singh-Mitchell creep model can effectively analyse and predict the deformation development law of surrounding rock of tunnel without considering temperature and osmotic pressure, it can provide reference for the construction of carbonaceous rock tunnel and the measures to prevent and reinforce it..

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

Science.gov (United States)

Zia, Haider

2017-06-01

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

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

Science.gov (United States)

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

2005-12-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2011-06-15

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

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

International Nuclear Information System (INIS)

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

2011-01-01

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

Microporous carbonaceous adsorbents for CO2 separation via selective adsorption

KAUST Repository

Zhao, Yunfeng

2015-01-01

Selective adsorption of CO2 has important implications for many energy and environment-related processes, which require the separation of CO2 from other gases (e.g. N2 and CH4) with high uptakes and selectivity. The development of high-performance adsorbents is one of the most promising solutions to the success of these processes. The present review is focused on the state-of-the-art of carbon-based (carbonaceous) adsorbents, covering microporous inorganic carbons and microporous organic polymers, with emphasis on the correlation between their textural and compositional properties and their CO2 adsorption/separation performance. Special attention is given to the most recently developed materials that were not covered in previous reviews. We summarize various effective strategies (N-doping, surface functionalization, extra-framework ions, molecular design, and pore size engineering) for enhancing the CO2 adsorption capacity and selectivity of carbonaceous adsorbents. Our discussion focuses on CO2/N2 separation and CO2/CH4 separation, while including an introduction to the methods and criteria used for evaluating the performance of the adsorbents. Critical issues and challenges regarding the development of high-performance adsorbents as well as some overlooked facts and misconceptions are also discussed, with the aim of providing important insights into the design of novel carbonaceous porous materials for various selective adsorption based applications. This journal is © The Royal Society of Chemistry.

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

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.

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)

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.

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.

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

Directory of Open Access Journals (Sweden)

Hasibun Naher

2012-01-01

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

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

Directory of Open Access Journals (Sweden)

Kok Soon Tey

2014-01-01

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

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

International Nuclear Information System (INIS)

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

1990-01-01

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

Mineralized remains of morphotypes of filamentous cyanobacteria in carbonaceous meteorites

Science.gov (United States)

Hoover, Richard B.

2005-09-01

The quest for conclusive evidence of microfossils in meteorites has been elusive. Abiotic microstructures, mineral grains, and even coating artifacts may mimic unicellular bacteria, archaea and nanobacteria with simple spherical or rod morphologies (i.e., cocci, diplococci, bacilli, etc.). This is not the case for the larger and more complex microorganisms, colonies and microbial consortia and ecosystems. Microfossils of algae, cyanobacteria, and cyanobacterial and microbial mats have been recognized and described from many of the most ancient rocks on Earth. The filamentous cyanobacteria and sulphur-bacteria have very distinctive size ranges, complex and recognizable morphologies and visibly differentiated cellular microstructures. The taphonomic modes of fossilization and the life habits and processes of these microorganisms often result in distinctive chemical biosignatures associated with carbonization, silicification, calcification, phosphatization and metal-binding properties of their cell-walls, trichomes, sheaths and extracellular polymeric substances (EPS). Valid biogenicity is provided by the combination of a suite of known biogenic elements (that differ from the meteorite matrix) found in direct association with recognizable and distinct biological features and microstructures (e.g., uniseriate or multiseriate filaments, trichomes, sheaths and cells of proper size/size range); specialized cells (e.g., basal or apical cells, hormogonia, akinetes, and heterocysts); and evidence of growth characteristics (e.g., spiral filaments, robust or thin sheaths, laminated sheaths, true or false branching of trichomes, tapered or uniform filaments) and evidence of locomotion (e.g. emergent cells and trichomes, coiling hormogonia, and hollow or flattened and twisted sheaths). Since 1997 we have conducted Environmental and Field Emission Scanning Electron Microscopy (ESEM and FESEM) studies of freshly fractured interior surfaces of carbonaceous meteorites, terrestrial

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.

Characteristics and sources of carbonaceous aerosols from Shanghai, China

Science.gov (United States)

Cao, J.-J.; Zhu, C.-S.; Tie, X.-X.; Geng, F.-H.; Xu, H.-M.; Ho, S. S. H.; Wang, G.-H.; Han, Y.-M.; Ho, K.-F.

2013-01-01

An intensive investigation of carbonaceous PM2.5 and TSP (total suspended particles) from Pudong (China) was conducted as part of the MIRAGE-Shanghai (Megacities Impact on Regional and Global Environment) experiment in 2009. Data for organic and elemental carbon (OC and EC), organic species, including C17 to C40 n-alkanes and 17 polycyclic aromatic hydrocarbons (PAHs), and stable carbon isotopes OC (δ13COC) and EC (δ13CEC) were used to evaluate the aerosols' temporal variations and identify presumptive sources. High OC/EC ratios indicated a large fraction of secondary organic aerosol (SOA); high char/soot ratios indicated stronger contributions to EC from motor vehicles and coal combustion than biomass burning. Diagnostic ratios of PAHs indicated that much of the SOA was produced via coal combustion. Isotope abundances (δ13COC = -24.5 ± 0.8‰ and δ13CEC = -25.1 ± 0.6‰) indicated that fossil fuels were the most important source for carbonaceous PM2.5 (particulate matter less than 2.5 micrometers in diameter), with lesser impacts from biomass burning and natural sources. An EC tracer system and isotope mass balance calculations showed that the relative contributions to total carbon from coal combustion, motor vehicle exhaust, and SOA were 41%, 21%, and 31%; other primary sources such as marine, soil and biogenic emissions contributed 7%. Combined analyses of OC and EC, n-alkanes and PAHs, and stable carbon isotopes provide a new way to apportion the sources of carbonaceous particles.

Improvements in or relating to process for the production of fuel gas from a carbonaceous solid

Energy Technology Data Exchange (ETDEWEB)

1952-12-03

A process was designed for the generation of fuel gas from a solid carbonaceous fuel containing volatilizable constituents, which comprises admixing the solid carbonaceous fuel in particle form with sufficient water to form a fluid suspension, passing the suspension through a heating zone at an elevated temperature such that substantially all of the water is vaporized, thereby forming a dispersion of coal in steam and causing the dispersion to attain a velocity of at least 60 ft. per second to shatter the particles of coal by collision, passing the resulting dispersion into a fluidized bed of solid carbonaceous material in a methanization zone into contact with carbon monoxide and hydrogen at a temperature within the range of from 900/sup 0/ to 1,800/sup 0/F whereby carbon monoxide and hydrogen are converted to methane and volatilizable constituents of the solid carbonaceous material are distilled therefrom, withdrawing carbonaceous material from the methanization zone and passing it into contact with oxygen and steam in dilute phase in a gasification zone maintained at a temperature within the range of 2,000/sup 0/ to about 3,000/sup 0/F, passing the resulting gases comprising carbon monoxide and hydrogen from the gasification zone into the methanization zone as the source of carbon monoxide and hydrogen, and discharging the gaseous products of the methanization zone as the raw-product fuel gas.

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.

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...

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. .

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.

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.

THREE-POINT BACKWARD FINITE DIFFERENCE METHOD FOR SOLVING A SYSTEM OF MIXED HYPERBOLIC-PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS. (R825549C019)

Science.gov (United States)

A three-point backward finite-difference method has been derived for a system of mixed hyperbolic¯¯parabolic (convection¯¯diffusion) partial differential equations (mixed PDEs). The method resorts to the three-point backward differenci...

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...

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.

Carbonaceous aerosols from prescribed burning of a boreal forest ecosystem

International Nuclear Information System (INIS)

Mazurek, M.A.; Cofer, W.R. III; Levine, J.S.

1990-10-01

The identity and ambient mass concentrations of radiatively important carbonaceous aerosols were measured for a boreal forest prescribed burn conducted in northern Ontario, CAN in August 1989. Nonsize-segregated airborne particles were collected for smoldering-fire and full-fire conditions using a helicopter sampling platform. Total carbon (TC), organic carbon (OC) and elemental carbon (EC) were measured. Smoke plume mass concentrations of the OC and EC particles were greatest for full-fire conditions and had ranges of 1.560 to 2.160 mg/m -1 (OC) and 0.120 to 0.160 mg/m -3 (EC) with OC:EC ratios of 10 to 18, respectively. Smoldering fire conditions showed smoke plume OC and EC levels of 0.570--1.030 mg/m -3 (OC) and 0.006--0.050 mg/m -3 (EC) and much higher ratios of OC:EC (21 to 95). These aerosol data indicate the formation of EC particles is greatest during full-fire combustion of boreal forest material relative to smoldering combustion. However, EC particles comprise a minor fraction of the particulate carbon smoke aerosols for both full-fire and smoldering conditions; the major component of carbonaceous smoke aerosols emitted during the prescribed burn is OC. Overall, the OC and EC in-plume smoke aerosol data show nonuniform production of these particles during various stages of the prescribed burn, and major differences in the type of carbonaceous aerosol that is generated (OC versus EC)

Laboratory study of carbonaceous dust and molecules of astrochemical interest

International Nuclear Information System (INIS)

Cataldo, F; Garcia-Hernandez, D A; Manchado, A; Kwok, S

2016-01-01

In this paper are reviewed some research works dedicated to the study of carbonaceous dust and molecules of astrochemical interest. First of all it is discussed the carbon arc through which it is possible to produce carbon soot and fullerenes under helium but also many other different products just changing the arcing conditions. For example, when the carbon arc is struck in an hydrocarbon solvent it is possible to produce and trap polyynes in the solvent. Monocyanopolyynes and dicyanopolyynes can be produced as well by selecting the appropriate conditions. Amorphous carbon soot or partially graphitized carbon black can be produced with the carbon arc. Fullerenes were found in space thanks to the reference infrared spectra and the absorption cross sections which were determined in laboratory. Fullerenes are readily reactive with hydrogen yielding fulleranes the hydrogenated fullerenes. Furthermore fullerenes react with PAHs and with iron carbonyl yielding adducts. All these fullerene derivatives were synthesized and their reference spectra recorded in laboratory. It was proposed that petroleum fractions can be used as model substrates in the explanation of the carriers of the AIB (Aromatic Infrared Bands) observed in protoplanetary and planetary nebulae and the UIE (Unidentified Infrared Bands) found in the interstellar medium. (paper)

Distilling carbonaceous materials

Energy Technology Data Exchange (ETDEWEB)

Garrow, J R

1921-04-16

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

Treating carbonaceous materials

Energy Technology Data Exchange (ETDEWEB)

Kelly, T D

1927-07-29

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

Evolution of carbonaceous chondrite parent bodies: Insights into cometary nuclei

International Nuclear Information System (INIS)

McSween, H.Y. Jr.

1989-01-01

It is thought that cometary samples will comprise the most primitive materials that are able to be sampled. Although parent body alteration of such samples would not necessarily detract from scientists' interest in them, the possibility exists that modification processes may have affected cometary nuclei. Inferences about the kinds of modifications that might be encountered can be drawn from data on the evolution of carbonaceous chondrite parent bodies. Observations suggest that, of all the classes of chondrites, these meteorites are most applicable to the study of comets. If the proportion of possible internal heat sources such as Al-26 in cometary materials are similar to those in chondrites, and if the time scale of comet accretion was fast enough to permit incorporation of live radionuclides, comets might have had early thermal histories somewhat like those of carbonaceous chondrite parent bodies

Antarctic carbonaceous chondrites - New opportunities for research

Science.gov (United States)

McSween, Harry Y., Jr.

An account is given of the types of carbonaceous meteorites available in the Antarctic collections of the U.S. and Japan. In the case of the collection for Victoria Land and Queen Maud Land, all known classes for meteorites except C1 are present; available pairing data, though limited, are indicative of the presence of many different falls. Thus far, attention has been focused on the largest meteorites. Most samples, however, are small.

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.

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

Science.gov (United States)

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

2008-10-01

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

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

Science.gov (United States)

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

2010-05-01

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

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.

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

International Nuclear Information System (INIS)

Diaz Sanchidrian, C.

1989-01-01

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

Everyone Wins: A Mars-Impact Origin for Carbonaceous Phobos and Deimos

Science.gov (United States)

Fries, M.; Welzenbach, L.; Steele, A.

2016-01-01

Discussions of Phobos' and Deimos' origin(s) tend to feature an orthogonally opposed pair of observations: dynamical studies which favor coalescence of the moons from an orbital debris ring arising from a large impact on Mars; and reflectance spectroscopy of the moons that indicate a carbonaceous composition that is not consistent with Martian surface materials. One way to reconcile this discrepancy is to consider the option of a Mars-impact origin for Phobos and Deimos, followed by surficial decoration of carbon-rich materials by interplanetary dust particles (IDP). The moons experience a high IDP flux because of their location in Mars' gravity well. Calculations show that accreted carbon is sufficient to produce a surface with reflectance spectra resembling carbonaceous chondrites.

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

Science.gov (United States)

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

2017-04-01

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

Pressure hydrogenation of solid carbonaceous material

Energy Technology Data Exchange (ETDEWEB)

Pier, M; Kroenig, W

1942-09-28

A process is described for the continuous pressure hydrogenation of solid, nonfusible carbonaceous material, such as coal, oil shale, or peat, in a pasted condition, characterized in that the charge is heated in a known way under pressure, together with water, nearly to the reaction temperature, then it is led into a pressure vessel, whose volume amounts to 20 to 40% of the usual reaction space without any change at the same temperature, and the charge then goes through the reaction vessel, after which its temperature is raised to the reaction height.

Sub-micrometer refractory carbonaceous particles in the polar stratosphere

Science.gov (United States)

Schütze, Katharina; Wilson, James Charles; Weinbruch, Stephan; Benker, Nathalie; Ebert, Martin; Günther, Gebhard; Weigel, Ralf; Borrmann, Stephan

2017-10-01

Eleven particle samples collected in the polar stratosphere during SOLVE (SAGE III Ozone loss and validation experiment) from January until March 2000 were characterized in detail by high-resolution transmission and scanning electron microscopy (TEM/SEM) combined with energy-dispersive X-ray microanalysis. A total of 4202 particles (TEM = 3872; SEM = 330) were analyzed from these samples, which were collected mostly inside the polar vortex in the altitude range between 17.3 and 19.9 km. Particles that were volatile in the microscope beams contained ammonium sulfates and hydrogen sulfates and dominated the samples. Some particles with diameters ranging from 20 to 830 nm were refractory in the electron beams. Carbonaceous particles containing additional elements to C and O comprised from 72 to 100 % of the refractory particles. The rest were internal mixtures of these materials with sulfates. The median number mixing ratio of the refractory particles, expressed in units of particles per milligram of air, was 1.1 (mg air)-1 and varied between 0.65 and 2.3 (mg air)-1. Most of the refractory carbonaceous particles are completely amorphous, a few of the particles are partly ordered with a graphene sheet separation distance of 0.37 ± 0.06 nm (mean value ± standard deviation). Carbon and oxygen are the only detected major elements with an atomic O/C ratio of 0.11 ± 0.07. Minor elements observed include Si, S, Fe, Cr and Ni with the following atomic ratios relative to C: Si/C: 0.010 ± 0.011; S/C: 0.0007 ± 0.0015; Fe/C: 0.0052 ± 0.0074; Cr/C: 0.0012 ± 0.0017; Ni/C: 0.0006 ± 0.0011 (all mean values ± standard deviation).High-resolution element distribution images reveal that the minor elements are distributed within the carbonaceous matrix; i.e., heterogeneous inclusions are not observed. No difference in size, nanostructure and elemental composition was found between particles collected inside and outside the polar vortex. Based on chemistry and nanostructure

Impact of anthropogenic emissions and open biomass burning on regional carbonaceous aerosols in South China

Energy Technology Data Exchange (ETDEWEB)

Zhang Gan, E-mail: zhanggan@gig.ac.c [State Key Laboratory of Organic Geochemistry, Guangzhou Institute of Geochemistry, Chinese Academy of Sciences, Guangzhou 510640 (China); Li Jun [State Key Laboratory of Organic Geochemistry, Guangzhou Institute of Geochemistry, Chinese Academy of Sciences, Guangzhou 510640 (China); Li Xiangdong [Department of Civil and Structural Engineering, Hong Kong Polytechnic University, Hung Hom, Kowloon (Hong Kong); Xu Yue; Guo Lingli [State Key Laboratory of Organic Geochemistry, Guangzhou Institute of Geochemistry, Chinese Academy of Sciences, Guangzhou 510640 (China); Tang Jianhui [Yantai Institute of Coastal Zone Research, Chinese Academy of Sciences, Yantai 264003 (China); Lee, Celine S.L. [Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon (Hong Kong); Liu Xiang [State Key Laboratory of Organic Geochemistry, Guangzhou Institute of Geochemistry, Chinese Academy of Sciences, Guangzhou 510640 (China); Chen Yingjun [Yantai Institute of Coastal Zone Research, Chinese Academy of Sciences, Yantai 264003 (China)

2010-11-15

Carbonaceous aerosols were studied at three background sites in south and southwest China. Hok Tsui in Hong Kong had the highest concentrations of carbonaceous aerosols (OC = 8.7 {+-} 4.5 {mu}g/m{sup 3}, EC = 2.5 {+-} 1.9 {mu}g/m{sup 3}) among the three sites, and Jianfeng Mountains in Hainan Island (OC = 5.8 {+-} 2.6 {mu}g/m{sup 3}, EC = 0.8 {+-} 0.4 {mu}g/m{sup 3}) and Tengchong mountain over the east edge of the Tibetan Plateau (OC = 4.8 {+-} 4.0 {mu}g/m{sup 3}, EC = 0.5 {+-} 0.4 {mu}g/m{sup 3}) showed similar concentration levels. Distinct seasonal patterns with higher concentrations during the winter, and lower concentrations during the summertime were observed, which may be caused by the changes of the regional emissions, and monsoon effects. The industrial and vehicular emissions in East, Southeast and South China, and the regional open biomass burning in the Indo-Myanmar region of Asia were probably the two major potential sources for carbonaceous matters in this region. - Anthropogenic emissions in China and open biomass burning in the Indo-Myanmar region were the two major potential sources for carbonaceous matters in South China region.

Impact of anthropogenic emissions and open biomass burning on regional carbonaceous aerosols in South China

International Nuclear Information System (INIS)

Zhang Gan; Li Jun; Li Xiangdong; Xu Yue; Guo Lingli; Tang Jianhui; Lee, Celine S.L.; Liu Xiang; Chen Yingjun

2010-01-01

Carbonaceous aerosols were studied at three background sites in south and southwest China. Hok Tsui in Hong Kong had the highest concentrations of carbonaceous aerosols (OC = 8.7 ± 4.5 μg/m 3 , EC = 2.5 ± 1.9 μg/m 3 ) among the three sites, and Jianfeng Mountains in Hainan Island (OC = 5.8 ± 2.6 μg/m 3 , EC = 0.8 ± 0.4 μg/m 3 ) and Tengchong mountain over the east edge of the Tibetan Plateau (OC = 4.8 ± 4.0 μg/m 3 , EC = 0.5 ± 0.4 μg/m 3 ) showed similar concentration levels. Distinct seasonal patterns with higher concentrations during the winter, and lower concentrations during the summertime were observed, which may be caused by the changes of the regional emissions, and monsoon effects. The industrial and vehicular emissions in East, Southeast and South China, and the regional open biomass burning in the Indo-Myanmar region of Asia were probably the two major potential sources for carbonaceous matters in this region. - Anthropogenic emissions in China and open biomass burning in the Indo-Myanmar region were the two major potential sources for carbonaceous matters in South China region.

Sorption of ionizable and ionic organic compounds to biochar, activated carbon and other carbonaceous materials.

Science.gov (United States)

Kah, Melanie; Sigmund, Gabriel; Xiao, Feng; Hofmann, Thilo

2017-11-01

The sorption of ionic and ionizable organic compounds (IOCs) (e.g., pharmaceuticals and pesticides) on carbonaceous materials plays an important role in governing the fate, transport and bioavailability of IOCs. The paradigms previously established for the sorption of neutral organic compounds do not always apply to IOCs and the importance of accounting for the particular sorption behavior of IOCs is being increasingly recognized. This review presents the current state of knowledge and summarizes the recent advances on the sorption of IOCs to carbonaceous sorbents. A broad range of sorbents were considered to evaluate the possibility to read across between fields of research that are often considered in isolation (e.g., carbon nanotubes, graphene, biochar, and activated carbon). Mechanisms relevant to IOCs sorption on carbonaceous sorbents are discussed and critically evaluated, with special attention being given to emerging sorption mechanisms including low-barrier, charge-assisted hydrogen bonds and cation-π assisted π-π interactions. The key role played by some environmental factors is also discussed, with a particular focus on pH and ionic strength. Overall the review reveals significant advances in our understanding of the interactions between IOCs and carbonaceous sorbents. In addition, knowledge gaps are identified and priorities for future research are suggested. Copyright © 2017 Elsevier Ltd. All rights reserved.

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.

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.

Preg-robbing of Gold by Carbonaceous Materials Encountered in ...

African Journals Online (AJOL)

Processing of gold from refractory ores containing carbonaceous materials (CM) poses challenges due to the ability of the CM to preg-rob dissolved gold. Depending on the type and maturity of CM encountered, preg-robbing of aurocyanide ion can lead to reduction in gold recovery ranging from a few percentages to more ...

Carbonaceous particle record in lake sediments from the Arctic and other remote areas of the northern hemisphere

International Nuclear Information System (INIS)

Rose, N.L.

1995-01-01

Lake sediments, including spheroidal carbonaceous particles produced by high temperature combustion of fossil fuels, contain a record of lake, catchment and atmospheric deposition history. The spatial and temporal distributions of these particles can indicate the extent to which a single lake or a region has been contaminated by airborne pollutants (e.g. sulfur, polycyclic aromatic hydrocarbons (PAHs)) derived from fossil fuels. The carbonaceous particle records of two Arctic lakes, Shuonijavr and Stepanovichjarvi, close to local pollution sources on the Kola Peninsula, Russia, are compared with the record of a remote lake on Svalbard and with mid-latitude remote mountain lakes in Europe and Asia. Although, Shuonijavr and Stepanovichjarvi show relatively high levels of contamination, as expected, the presence of carbonaceous particles at all of the remote sites studied suggests there is a hemispherical background of these particles. Other less remote mountain lakes in Europe have been found to contain significant concentrations of particles and these may represent regional deposition patterns. Carbonaceous particle analysis may provide an effective assessment of whether a lake site is receiving local, regional or background levels of deposition

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

Science.gov (United States)

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

2014-07-09

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

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

Directory of Open Access Journals (Sweden)

Luchun Yan

2014-07-01

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

Processes for liquefying carbonaceous feedstocks and related compositions

Energy Technology Data Exchange (ETDEWEB)

MacDonnell, Frederick M.; Dennis, Brian H.; Billo, Richard E.; Priest, John W.

2017-02-28

Methods for the conversion of lignites, subbituminous coals and other carbonaceous feedstocks into synthetic oils, including oils with properties similar to light weight sweet crude oil using a solvent derived from hydrogenating oil produced by pyrolyzing lignite are set forth herein. Such methods may be conducted, for example, under mild operating conditions with a low cost stoichiometric co-reagent and/or a disposable conversion agent.

Hydrocarbon oils from carbonaceous material

Energy Technology Data Exchange (ETDEWEB)

Fletcher, J

1943-01-28

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

Regional variation of carbonaceous aerosols from space and simulations

Science.gov (United States)

Mukai, Sonoyo; Sano, Itaru; Nakata, Makiko; Kokhanovsky, Alexander

2017-04-01

Satellite remote sensing provides us with a systematic monitoring in a global scale. As such, aerosol observation via satellites is known to be useful and effective. However, before attempting to retrieve aerosol properties from satellite data, the efficient algorithms for aerosol retrieval need to be considered. The characteristics and distributions of atmospheric aerosols are known to be complicated, owing to both natural factors and human activities. It is known that the biomass burning aerosols generated by the large-scale forest fires and burn agriculture have influenced the severity of air pollution. Nevertheless the biomass burning episodes increase due to global warming and climate change and vice versa. It is worth noting that the near ultra violet (NUV) measurements are helpful for the detection of carbonaceous particles, which are the main component of aerosols from biomass burning. In this work, improved retrieval algorithms for biomass burning aerosols are shown by using the measurements observed by GLI and POLDER-2 on Japanese short term mission ADEOS-2 in 2003. The GLI sensor has 380nm channel. For detection of biomass burning episodes, the aerosol optical thickness of carbonaceous aerosols simulated with the numerical model simulations (SPRINTARS) is available as well as fire products from satellite imagery. Moreover the algorithm using shorter wavelength data is available for detection of absorbing aerosols. An algorithm based on the combined use of near-UV and violet data has been introduced in our previous work with ADEOS (Advanced Earth Observing Satellite) -2 /GLI measurements [1]. It is well known that biomass burning plume is a seasonal phenomenon peculiar to a particular region. Hence, the mass concentrations of aerosols are frequently governed with spatial and/or temporal variations of biomass burning plumes. Accordingly the satellite data sets for our present study are adopted from the view points of investigation of regional and seasonal

Hydrogen ion-driven permeation in carbonaceous films

International Nuclear Information System (INIS)

Anderl, R.A.; Holland, D.F.; Longhurst, G.R.

1989-01-01

This paper presents the results of investigations into the permeation properties of amorphous carbonaceous, a-C:H, films produced by plasmachemical deposition techniques. Carbonaceous films on iron substrates with thickness ranging from 60 nm to 110 nm were subjected to high fluence implantations with mass analyzed D 3 + ions with energies ranging from 600 eV to 3000 eV and fluxes ranging from 5x10 14 D/cm 2 s to 5x10 15 D/cm 2 s, respectively. Deuterium re-emission upstream, deuterium permeation downstream and secondary ions sputtered from the implantation surface were measured as a function of implantation fluence for specimens at 420 K. The present studies indicate that the a-C:H film permeability is directly related to the time, hence the fluence, required to achieve isotopic replacement and saturation of the deuterium ion beam atoms stopped in the implant region. Once the deuterium saturation level is achieved in the layer, a significant fraction of the implanting ions can result in permeation. For the present experiment, this permeation factor was much higher than that for uncoated iron specimens subjected to similar beam conditions. Carbon sputter yields of 0.008-0.01 C/D were determined in this work for 1000-eV to 400-eV deuterium ions incident on a-C:H films. (orig.)

Hydrogen ion-driven permeation in carbonaceous films

Energy Technology Data Exchange (ETDEWEB)

Anderl, R.A.; Holland, D.F.; Longhurst, G.R.

1989-04-01

This paper presents the results of investigations into the permeation properties of amorphous carbonaceous, a-C:H, films produced by plasmachemical deposition techniques. Carbonaceous films on iron substrates with thickness ranging from 60 nm to 110 nm were subjected to high fluence implantations with mass analyzed D/sub 3//sup +/ ions with energies ranging from 600 eV to 3000 eV and fluxes ranging from 5x10/sup 14/ D/cm/sup 2/ s to 5x10/sup 15/ D/cm/sup 2/ s, respectively. Deuterium re-emission upstream, deuterium permeation downstream and secondary ions sputtered from the implantation surface were measured as a function of implantation fluence for specimens at 420 K. The present studies indicate that the a-C:H film permeability is directly related to the time, hence the fluence, required to achieve isotopic replacement and saturation of the deuterium ion beam atoms stopped in the implant region. Once the deuterium saturation level is achieved in the layer, a significant fraction of the implanting ions can result in permeation. For the present experiment, this permeation factor was much higher than that for uncoated iron specimens subjected to similar beam conditions. Carbon sputter yields of 0.008-0.01 C/D were determined in this work for 1000-eV to 400-eV deuterium ions incident on a-C:H films. (orig.).

Hydrogen ion-driven permeation in carbonaceous films

Science.gov (United States)

Anderl, R. A.; Holland, D. F.; Longhurst, G. R.

1989-04-01

This paper presents the results of investigations into the permeation properties of amorphous carbonaceous, a-C: H, films produced by plasmachemical deposition techniques. Carbonaceous films on iron substrates with thickness ranging from 60 nm to 110 nm were subjected to high fluence implantations with mass analyzed D +3 ions with energies ranging from 600 eV to 3000 eV and fluxes ranging from 5 × 10 14D/ cm2 s to 5 × 10 15D/ cm2 s, respectively. Deuterium re-emission upstream, deuterium permeation downstream and secondary ions sputtered from the implantation surface were measured as a function of implantation fluence for specimens at 420 K. The present studies indicate that the a-C : H film permeability is directly related to the time, hence the fluence, required to achieve isotopic replacement and saturation of the deuterium ion beam atoms stopped in the implant region. Once the deuterium saturation level is achieved in the layer, a significant fraction of the implanting ions can result in permeation. For the present experiment, this permeation factor was much higher than that for uncoated iron specimens subjected to similar beam conditions. Carbon sputter yields of 0.008-0.01 C/D were determined in this work for 1000-eV to 400-eV deuterium ions incident on a-C : H films.

A dual origin for water in carbonaceous asteroids revealed by CM chondrites

Science.gov (United States)

Piani, Laurette; Yurimoto, Hisayoshi; Remusat, Laurent

2018-04-01

Carbonaceous asteroids represent the principal source of water in the inner Solar System and might correspond to the main contributors for the delivery of water to Earth. Hydrogen isotopes in water-bearing primitive meteorites, for example carbonaceous chondrites, constitute a unique tool for deciphering the sources of water reservoirs at the time of asteroid formation. However, fine-scale isotopic measurements are required to unravel the effects of parent-body processes on the pre-accretion isotopic distributions. Here, we report in situ micrometre-scale analyses of hydrogen isotopes in six CM-type carbonaceous chondrites, revealing a dominant deuterium-poor water component (δD = -350 ± 40‰) mixed with deuterium-rich organic matter. We suggest that this deuterium-poor water corresponds to a ubiquitous water reservoir in the inner protoplanetary disk. A deuterium-rich water signature has been preserved in the least altered part of the Paris chondrite (δDParis ≥ -69 ± 163‰) in hydrated phases possibly present in the CM rock before alteration. The presence of the deuterium-enriched water signature in Paris might indicate that transfers of ice from the outer to the inner Solar System were significant within the first million years of the history of the Solar System.

Characteristics and sources of carbonaceous aerosols from Shanghai, China

Directory of Open Access Journals (Sweden)

J.-J. Cao

2013-01-01

Full Text Available An intensive investigation of carbonaceous PM_2.5 and TSP (total suspended particles from Pudong (China was conducted as part of the MIRAGE-Shanghai (Megacities Impact on Regional and Global Environment experiment in 2009. Data for organic and elemental carbon (OC and EC, organic species, including C17 to C40 n-alkanes and 17 polycyclic aromatic hydrocarbons (PAHs, and stable carbon isotopes OC (δ¹³C_OC and EC (δ¹³C_EC were used to evaluate the aerosols' temporal variations and identify presumptive sources. High OC/EC ratios indicated a large fraction of secondary organic aerosol (SOA; high char/soot ratios indicated stronger contributions to EC from motor vehicles and coal combustion than biomass burning. Diagnostic ratios of PAHs indicated that much of the SOA was produced via coal combustion. Isotope abundances (δ¹³C_OC = −24.5 ± 0.8‰ and δ¹³C_EC = −25.1 ± 0.6‰ indicated that fossil fuels were the most important source for carbonaceous PM_2.5 (particulate matter less than 2.5 micrometers in diameter, with lesser impacts from biomass burning and natural sources. An EC tracer system and isotope mass balance calculations showed that the relative contributions to total carbon from coal combustion, motor vehicle exhaust, and SOA were 41%, 21%, and 31%; other primary sources such as marine, soil and biogenic emissions contributed 7%. Combined analyses of OC and EC, n-alkanes and PAHs, and stable carbon isotopes provide a new way to apportion the sources of carbonaceous particles.

Preparation of a Sulfonated Carbonaceous Material from Lignosulfonate and Its Usefulness as an Esterification Catalyst

Directory of Open Access Journals (Sweden)

Duckhee Lee

2013-07-01

Full Text Available Sulfonated carbonaceous material useful as a solid acid catalyst was prepared from lignosulfonate, a waste of the paper-making industry sulfite pulping process, and characterized by 13C-NMR, FT-IR, TGA, SEM and elemental analysis, etc. The sulfonic acid group density and total density of all acid groups in the sulfonated carbonaceous material was determined by titration to be 1.24 mmol/g and 5.90 mmol/g, respectively. Its catalytic activity in the esterification of cyclohexanecarboxylic acid with anhydrous ethanol was shown to be comparable to that of the ionic exchange resin Amberlyst-15, when they were used in the same amount. In the meantime, the sulfonic acid group was found to be leached out by 26%–29% after it was exposed to hot water (95 °C for 5 h. The catalytic usefulness of the prepared carbonaceous material was investigated by performing esterifications.

Ethanol and other oxygenateds from low grade carbonaceous resources

Energy Technology Data Exchange (ETDEWEB)

Joo, O.S.; Jung, K.D.; Han, S.H. [Korea Institute of Science and Technology, Seoul (Korea, Democratic People`s Republic of)] [and others

1995-12-31

Anhydrous ethanol and other oxygenates of C2 up can be produced quite competitively from low grade carbonaceous resources in high yield via gasification, methanol synthesis, carbonylation of methanol an hydrogenation consecutively. Gas phase carbonylation of methanol to form methyl acetate is the key step for the whole process. Methyl acetate can be produced very selectively in one step gas phase reaction on a fixed bed column reactor with GHSV over 5,000. The consecutive hydrogenation of methyl or ethyl acetate produce anhydrous ethanol in high purity. It is also attempted to co-produce methanol and DME in IGCC, in which low grade carbonaceous resources are used as energy sources, and the surplus power and pre-power gas can be stored in liquid form of methanol and DME during base load time. Further integration of C2 up oxygenate production with IGCC can improve its economics. The attempt of above extensive technology integration can generate significant industrial profitability as well as reduce the environmental complication related with massive energy consumption.

Heavy-ion irradiation induced diamond formation in carbonaceous materials

International Nuclear Information System (INIS)

Daulton, T. L.

1999-01-01

The basic mechanisms of metastable phase formation produced under highly non-equilibrium thermodynamic conditions within high-energy particle tracks are investigated. In particular, the possible formation of diamond by heavy-ion irradiation of graphite at ambient temperature is examined. This work was motivated, in part, by earlier studies which discovered nanometer-grain polycrystalline diamond aggregates of submicron-size in uranium-rich carbonaceous mineral assemblages of Precambrian age. It was proposed that the radioactive decay of uranium formed diamond in the fission particle tracks produced in the carbonaceous minerals. To test the hypothesis that nanodiamonds can form by ion irradiation, fine-grain polycrystalline graphite sheets were irradiated with 400 MeV Kr ions. The ion irradiated graphite (and unirradiated graphite control) were then subjected to acid dissolution treatments to remove the graphite and isolate any diamonds that were produced. The acid residues were then characterized by analytical and high-resolution transmission electron microscopy. The acid residues of the ion-irradiated graphite were found to contain ppm concentrations of nanodiamonds, suggesting that ion irradiation of bulk graphite at ambient temperature can produce diamond

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

KAUST Repository

Piret, Cécile

2012-05-01

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

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

International Nuclear Information System (INIS)

Ibragimov, N Kh; Avdonina, E D

2013-01-01

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

Low-temperature catalytic conversion of carbonaceous materials

Directory of Open Access Journals (Sweden)

Tabakaev Roman B.

2015-01-01

Full Text Available Laws of the rate of carbon conversion in steam atmosphere at a temperature in modes of the catalytic low-temperature treatment of peat, brown coal, semi-coke from peat and brown coal are obtained by experiments. Increasing of the rate of carbon conversion in temperature range up to 500 °C is achieved by using of catalysts. The possibility of using results is associated with the burners, a working zone of which is porous filling from carbonaceous particles.

Destructive hydrogenation of carbonaceous material, etc

Energy Technology Data Exchange (ETDEWEB)

1938-07-30

A process is described for the destructive hydrogenation of solid distillable carbonaceous material, consisting of mixing the raw material in a paste by means of a mixture practically free from asphalt, from an oil obtained initially from the products coming out of the reaction space as vapor, particularly heavy oil, and oils obtained by pushing just to the state of pitch or coke the distillation of all the products which come out of the reaction space in any state but the vapor and which restrain some of the raw material intact and part of the products.

Functionalization of biomass carbonaceous aerogels: selective preparation of MnO2@CA composites for supercapacitors.

Science.gov (United States)

Ren, Yumei; Xu, Qun; Zhang, Jianmin; Yang, Hongxia; Wang, Bo; Yang, Daoyuan; Hu, Junhua; Liu, Zhimin

2014-06-25

Functionalized porous carbon materials with hierarchical structure and developed porosity coming from natural and renewable biomass have been attracting tremendous attention recently. In this work, we present a facile and scalable method to synthesize MnO2 loaded carbonaceous aerogel (MnO2@CA) composites via the hydrothermal carbonaceous (HTC) process. We employ two reaction systems of the mixed metal ion precursors to study the optimal selective adsorption and further reaction of MnO2 precursor on CA. Our experimental results show that the system containing KMnO4 and Na2S2O3·5H2O exhibits better electrochemical properties compared with the reaction system of MnSO4·H2O and (NH4)2S2O8. For the former, the obtained MnO2@CA displays the specific capacitance of 123.5 F·g(-1). The enhanced supercapacitance of MnO2@CA nanocomposites could be ascribed to both electrochemical contributions of the loaded MnO2 nanoparticles and the porous structure of three-dimensional carbonaceous aerogels. This study not only indicates that it is vital for the reaction systems to match with porous carbonaceous materials, but also offers a new fabrication strategy to prepare lightweight and high-performance materials that can be used in energy storage devices.

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

Science.gov (United States)

Aditya, Konduri; Donzis, Diego A.

2017-12-01

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

The strategic value of partial vertical integration

OpenAIRE

Fiocco, Raffaele

2014-01-01

We investigate the strategic incentives for partial vertical integration, namely, partial ownership agreements between manufacturers and retailers, when retailers privately know their costs and engage in differentiated good price competition. The partial misalignment between the profit objectives within a partially integrated manufacturer-retailer hierarchy entails a higher retail price than under full integration. This `information vertical effect' translates into an opposite ...

Review of the technology for solar gasification of carbonaceous materials

International Nuclear Information System (INIS)

Epstein, M.; Spiewak, I.; Funken, K.H.; Ortner, J.

1994-01-01

Research has demonstrated the feasibility of solar assisted gasification of carbonaceous materials to form synthesis gas (syngas). The potential feedstocks range from natural gas, residual oil, biomass, and oil-shale to coal. The expected advantages of such processing are yields of syngas with calorific values above those of the carbonaceous feedstocks, syngas quality suited to production of hydrogen, methanol or bulk Fischer-Tropsch fuels, and the ability to process low-grade and waste materials with essentially no emissions to atmosphere other than small amounts of CO 2 . The review provides some background on solar receiver concepts to reach the high temperatures needed for syngas production, the basic chemistry involved, covers applicable experiments that have been reported with solar inputs and with conventional heating, heat transfer processes, process and energy balances, and cost analysis. Approximately 80 references are cited. The authors present their views on the most promising approaches to solar-assisted gasification, the technology development required, and the ultimate benefits of such development and commercialization

A fast direct method for block triangular Toeplitz-like with tri-diagonal block systems from time-fractional partial differential equations

Science.gov (United States)

Ke, Rihuan; Ng, Michael K.; Sun, Hai-Wei

2015-12-01

In this paper, we study the block lower triangular Toeplitz-like with tri-diagonal blocks system which arises from the time-fractional partial differential equation. Existing fast numerical solver (e.g., fast approximate inversion method) cannot handle such linear system as the main diagonal blocks are different. The main contribution of this paper is to propose a fast direct method for solving this linear system, and to illustrate that the proposed method is much faster than the classical block forward substitution method for solving this linear system. Our idea is based on the divide-and-conquer strategy and together with the fast Fourier transforms for calculating Toeplitz matrix-vector multiplication. The complexity needs O (MNlog2 ⁡ M) arithmetic operations, where M is the number of blocks (the number of time steps) in the system and N is the size (number of spatial grid points) of each block. Numerical examples from the finite difference discretization of time-fractional partial differential equations are also given to demonstrate the efficiency of the proposed method.

Sub-micrometer refractory carbonaceous particles in the polar stratosphere

Directory of Open Access Journals (Sweden)

K. Schütze

2017-10-01

Full Text Available Eleven particle samples collected in the polar stratosphere during SOLVE (SAGE III Ozone loss and validation experiment from January until March 2000 were characterized in detail by high-resolution transmission and scanning electron microscopy (TEM/SEM combined with energy-dispersive X-ray microanalysis. A total of 4202 particles (TEM  =  3872; SEM  =  330 were analyzed from these samples, which were collected mostly inside the polar vortex in the altitude range between 17.3 and 19.9 km. Particles that were volatile in the microscope beams contained ammonium sulfates and hydrogen sulfates and dominated the samples. Some particles with diameters ranging from 20 to 830 nm were refractory in the electron beams. Carbonaceous particles containing additional elements to C and O comprised from 72 to 100 % of the refractory particles. The rest were internal mixtures of these materials with sulfates. The median number mixing ratio of the refractory particles, expressed in units of particles per milligram of air, was 1.1 (mg air−1 and varied between 0.65 and 2.3 (mg air−1. Most of the refractory carbonaceous particles are completely amorphous, a few of the particles are partly ordered with a graphene sheet separation distance of 0.37 ± 0.06 nm (mean value ± standard deviation. Carbon and oxygen are the only detected major elements with an atomic O∕C ratio of 0.11 ± 0.07. Minor elements observed include Si, S, Fe, Cr and Ni with the following atomic ratios relative to C: Si∕C: 0.010 ± 0.011; S∕C: 0.0007 ± 0.0015; Fe∕C: 0.0052 ± 0.0074; Cr∕C: 0.0012 ± 0.0017; Ni∕C: 0.0006 ± 0.0011 (all mean values ± standard deviation.High-resolution element distribution images reveal that the minor elements are distributed within the carbonaceous matrix; i.e., heterogeneous inclusions are not observed. No difference in size, nanostructure and elemental composition was found between

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

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.

Distillation of solid carbonaceous material

Energy Technology Data Exchange (ETDEWEB)

Burney, C D

1918-08-31

A method of distilling carbonaceous material at low or moderate temperatures is described in which the main supply of gases for heating the material under treatment is generated in a combustion chamber located externally of the retort chamber from which combustion chamber the gases are withdrawn and passed under control through hollow elements located within the retort chamber in such manner as to insure the production of the desired temperature gradient along the length of the retort, the said elements being so constructed that they serve to bring the heating gases into indirect contact with the material undergoing treatment while also moving the material progressively through the retort in the opposite direction to that in which the heating gases flow.

Organic free radicals and micropores in solid graphitic carbonaceous matter at the Oklo natural fission reactors, Gabon

International Nuclear Information System (INIS)

Rigali, M.J.; Nagy, B.

1997-01-01

The presence, concentration, and distribution of organic free radicals as well as their association with specific surface areas and microporosities help characterize the evolution and behavior of the Oklo carbonaceous matter. Such information is necessary in order to evaluate uranium mineralization, liquid bitumen solidification, and radio nuclide containment at Oklo. In the Oklo ore deposits and natural fission reactors carbonaceous matter is often referred to as solid graphitic bitumen. The carbonaceous parts of the natural reactors may contain as much as 65.9% organic C by weight in heterogeneous distribution within the clay-rich matrix. The solid carbonaceous matter immobilized small uraninite crystals and some fission products enclosed in this uraninite and thereby facilitated radio nuclide containment in the reactors. Hence, the Oklo natural fission reactors are currently the subjects of detailed studies because they may be useful analogues to support performance assessment of radio nuclide containment at anthropogenic radioactive waste repository sites. Seven carbonaceous matter rich samples from the 1968 ± 50 Ma old natural fission reactors and the associated Oklo uranium ore deposit were studied by electron spin resonance (ESR) spectroscopy and by measurements of specific surface areas (BET method). Humic acid, fulvic acid, and fully crystalline graphite standards were also examined by ESR spectroscopy for comparison with the Oklo solid graphitic bitumens. With one exception, the ancient Oklo bitumens have higher organic free radical concentrations than the modem humic and fulvic acid samples. The presence of carbon free radicals in the graphite standard could not be determined due to the conductivity of this material. 72 refs., 7 figs., 1 tab

Composition and sources of carbonaceous aerosols in Northern Europe during winter

NARCIS (Netherlands)

Glasius, M.; Hansen, A.M.K.; Claeys, M.; Henzing, J.S.; Jedynska, A.D.; Kasper-Giebl, A.; Kistler, M.; Kristensen, K.; Martinsson, J.; Maenhaut, W.; Nøjgaard, J.K.; Spindler, G.; Stenström, K.E.; Swietlicki, E.; Szidat, S.; Simpson, D.; Yttri, K.E.

2018-01-01

Sources of elemental carbon (EC) and organic carbon (OC) in atmospheric aerosols (carbonaceous aerosols) were investigated by collection of weekly aerosol filter samples at six background sites in Northern Europe (Birkenes, Norway; Vavihill, Sweden; Risoe, Denmark; Cabauw and Rotterdam in The

A comparison of numerical solutions of partial differential equations with probabilistic and possibilistic parameters for the quantification of uncertainty in subsurface solute transport.

Science.gov (United States)

Zhang, Kejiang; Achari, Gopal; Li, Hua

2009-11-03

Traditionally, uncertainty in parameters are represented as probabilistic distributions and incorporated into groundwater flow and contaminant transport models. With the advent of newer uncertainty theories, it is now understood that stochastic methods cannot properly represent non random uncertainties. In the groundwater flow and contaminant transport equations, uncertainty in some parameters may be random, whereas those of others may be non random. The objective of this paper is to develop a fuzzy-stochastic partial differential equation (FSPDE) model to simulate conditions where both random and non random uncertainties are involved in groundwater flow and solute transport. Three potential solution techniques namely, (a) transforming a probability distribution to a possibility distribution (Method I) then a FSPDE becomes a fuzzy partial differential equation (FPDE), (b) transforming a possibility distribution to a probability distribution (Method II) and then a FSPDE becomes a stochastic partial differential equation (SPDE), and (c) the combination of Monte Carlo methods and FPDE solution techniques (Method III) are proposed and compared. The effects of these three methods on the predictive results are investigated by using two case studies. The results show that the predictions obtained from Method II is a specific case of that got from Method I. When an exact probabilistic result is needed, Method II is suggested. As the loss or gain of information during a probability-possibility (or vice versa) transformation cannot be quantified, their influences on the predictive results is not known. Thus, Method III should probably be preferred for risk assessments.

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.

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

Directory of Open Access Journals (Sweden)

Ji Juan-Juan

2017-01-01

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

Adsorption of perfluoroalkyl acids by carbonaceous adsorbents: Effect of carbon surface chemistry

International Nuclear Information System (INIS)

Zhi, Yue; Liu, Jinxia

2015-01-01

Adsorption by carbonaceous sorbents is among the most feasible processes to remove perfluorooctane sulfonic (PFOS) and carboxylic acids (PFOA) from drinking and ground waters. However, carbon surface chemistry, which has long been recognized essential for dictating performance of such sorbents, has never been considered for PFOS and PFOA adsorption. Thus, the role of surface chemistry was systematically investigated using sorbents with a wide range in precursor material, pore structure, and surface chemistry. Sorbent surface chemistry overwhelmed physical properties in controlling the extent of uptake. The adsorption affinity was positively correlated carbon surface basicity, suggesting that high acid neutralizing or anion exchange capacity was critical for substantial uptake of PFOS and PFOA. Carbon polarity or hydrophobicity had insignificant impact on the extent of adsorption. Synthetic polymer-based Ambersorb and activated carbon fibers were more effective than activated carbon made of natural materials in removing PFOS and PFOA from aqueous solutions. - Highlights: • Adsorption of PFOS and PFOA by ten carbonaceous adsorbents were compared. • Surface chemistry of the adsorbents controlled adsorption affinity. • Carbon surface basicity was positively correlated with the extent of PFOS and PFOA uptake. • Carbon polarity or hydrophobicity was not correlated with adsorption affinity. • Synthetic polymer-based adsorbents were more effective in removing PFOS and PFOA. - Carbon surface basicity is the primary factor that influences adsorption affinity of the carbonaceous sorbents for perfluorooctane sulfonic and carboxylic acids

Carbonaceous aerosol characteristics over Delhi in Northern India: Seasonal variability and possible sources

Science.gov (United States)

Srivastava, Atul Kumar; Bisht, Ds; Tiwari, S.

Carbonaceous aerosols have been the focus of extensive studies during the last decade due to its significant impacts on human health, visibility and climate change. As per Asian regions are concerned, aerosols in south-Asia are gaining considerable importance because of their potential impacts on regional climate, yet their possible sources are poorly understood. Semi-continuous measurements of organic carbon (OC) and elemental carbon (EC) and continuous measurements of black carbon (BC) aerosols were conducted simultaneously at Delhi during the period from January 2011 to May 2012. Delhi is the capital city of India and one of the densely populated and industrialized urban megacities in Asia, located at the Ganga basin in the northern part of India. Being highly polluted region, mass concentrations of OC, EC and BC over Delhi were found to vary from about 6-92 mug m (-3) (mean: 23±16 mug m (-3) ), 3-38 mug m (-3) (mean: 11±7 mug m (-3) ) and 1-24 mug m (-3) (mean: 7±5 mug m (-3) ), respectively during the entire measurement period, with about two times higher concentration during winter as compared to summer. A significant correlation between OC and EC (R=0.95, n=232) and relatively lower OC/EC ratio (range: 1.0-3.6; mean: 2.2±0.5) suggest fossil fuel emission as a dominant source of carbonaceous aerosols over the station. The average mass concentration of EC was found about 38% higher than BC during the study period, which is interestingly different as reported at other locations over Ganga basin. We also determined the associated optical properties of carbonaceous species (e.g. absorption coefficient and mass absorption efficiency) over the station. Significant loading of carbonaceous species over such regions emphasize an urgent need to focus on air quality management and proper impact assessment on health perspective.

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.

Preparing patterned carbonaceous nanostructures directly by overexposure of PMMA using electron-beam lithography

Energy Technology Data Exchange (ETDEWEB)

Duan Huigao; Zhao Jianguo; Zhang Yongzhe; Xie Erqing [School of Physical Science and Technology, Lanzhou University, Lanzhou 730000 (China); Han Li [Institute of Electrical Engineering, Chinese Academy of Sciences, Beijing 100190 (China)], E-mail: duanhg@gmail.com, E-mail: xieeq@lzu.edu.cn

2009-04-01

The overexposure process of poly(methyl methacrylate) (PMMA) was studied in detail using electron-beam lithography. It was found that PMMA films could be directly patterned without development due to the electron-beam-induced collapse of PMMA macromolecular chains. By analyzing the evolution of surface morphologies and compositions of the overexposed PMMA films, it was also found that the transformation of PMMA from positive to negative resist was a carbonization process, so patterned carbonaceous nanostructures could be prepared directly by overexposure of PMMA using electron-beam lithography. This simple one-step process for directly obtaining patterned carbonaceous nanostructures has promising potential application as a tool to make masks and templates, nanoelectrodes, and building blocks for MEMS and nanophotonic devices.

PCB congener sorption to carbonaceous sediment components: Macroscopic comparison and characterization of sorption kinetics and mechanism

International Nuclear Information System (INIS)

Choi, Hyeok; Al-Abed, Souhail R.

2009-01-01

Sorption of polychlorinated biphenyls (PCBs) to sediment is a key process in determining their mobility, bioavailability, and chemical decomposition in aquatic environments. In order to examine the validity of currently used interpretation approaches for PCBs sorption, comparative results on 2-chlorobiphenyl sorption to carbonaceous components in sediments (activated carbon, carbon black, coal, soot, graphite, flyash, wood) were macroscopically correlated with the structural, morphological, crystallographic, and compositional properties of the carbonaceous components. Since the Freundlich sorption constant, K F (L kg -1 ) spanned several orders of magnitude, ranging from log K F of 6.13-5.27 for activated carbon, 5.04 for carbon black, 3.83 for coal to 3.08 for wood, organic carbon partitioning approach should be more specifically categorized, considering the various forms, nature and origins of organic carbon in sediment. Sorption rate constants and fraction parameters, which were numerically defined from empirical kinetic model with fast and slow sorption fractions, were closely related to the physicochemical properties of the carbonaceous components. Sorption interpretation approaches with a specific property and viewpoint, such as organic carbon partitioning, soot carbon distribution, or surface area correlation, did not properly explain the overall results on sorption capacity, fast and slow sorption kinetics, and partitioning coefficient. It is also important to emphasize the heterogeneous nature of sediment and the difficulties of encompassing the partitioning among its carbonaceous components.

PCB congener sorption to carbonaceous sediment components: Macroscopic comparison and characterization of sorption kinetics and mechanism

Energy Technology Data Exchange (ETDEWEB)

Choi, Hyeok [National Risk Management Research Laboratory, U.S. Environmental Protection Agency, 26 West Martin Luther King Drive, Cincinnati, OH 45268 (United States); Al-Abed, Souhail R., E-mail: al-abed.souhail@epa.gov [National Risk Management Research Laboratory, U.S. Environmental Protection Agency, 26 West Martin Luther King Drive, Cincinnati, OH 45268 (United States)

2009-06-15

Sorption of polychlorinated biphenyls (PCBs) to sediment is a key process in determining their mobility, bioavailability, and chemical decomposition in aquatic environments. In order to examine the validity of currently used interpretation approaches for PCBs sorption, comparative results on 2-chlorobiphenyl sorption to carbonaceous components in sediments (activated carbon, carbon black, coal, soot, graphite, flyash, wood) were macroscopically correlated with the structural, morphological, crystallographic, and compositional properties of the carbonaceous components. Since the Freundlich sorption constant, K{sub F} (L kg{sup -1}) spanned several orders of magnitude, ranging from log K{sub F} of 6.13-5.27 for activated carbon, 5.04 for carbon black, 3.83 for coal to 3.08 for wood, organic carbon partitioning approach should be more specifically categorized, considering the various forms, nature and origins of organic carbon in sediment. Sorption rate constants and fraction parameters, which were numerically defined from empirical kinetic model with fast and slow sorption fractions, were closely related to the physicochemical properties of the carbonaceous components. Sorption interpretation approaches with a specific property and viewpoint, such as organic carbon partitioning, soot carbon distribution, or surface area correlation, did not properly explain the overall results on sorption capacity, fast and slow sorption kinetics, and partitioning coefficient. It is also important to emphasize the heterogeneous nature of sediment and the difficulties of encompassing the partitioning among its carbonaceous components.

AFM measurements of adhesive forces between carbonaceous particles and the substrates

Energy Technology Data Exchange (ETDEWEB)

Zhang, Tianqi [Institute of Nuclear and New Energy Technology of Tsinghua University, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Beijing 100084 (China); Peng, Wei, E-mail: pengwei@tsinghua.edu.cn [Institute of Nuclear and New Energy Technology of Tsinghua University, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Beijing 100084 (China); Shen, Ke [Institute of Nuclear and New Energy Technology of Tsinghua University, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Beijing 100084 (China); Yu, Suyuan, E-mail: suyuan@tsinghua.edu.cn [Center for Combustion Energy, Key Laboratory for Thermal Science and Power Engineering of Ministry of Educations, Department of Thermal Engineering, Tsinghua University, Beijing 100084 (China)

2015-11-15

Highlights: • Adhesive force of spherical carbonaceous particle MCMBs and HTR-10 graphite matrix debris were measured for the first time. • The measured equivalent works of adhesion were much smaller than the ideal values. • The shape factor and the particle morphology reduce the adhesive force. • The adhesion effect does not change directly with the asperity size. - Abstract: Graphite dust is carbonaceous particles generated during operation of High Temperature Gas-Cooled Reactors (HTR). Graphite dust resuspension is the key behavior associated with HTR source term analyses and environmental safety assessment. The adhesive force is the key factor that determines the resuspension rate. The present study used an atomic force microscope (AFM) to measure the adhesive force between a single carbonaceous particle and the substrate. The measurements were performed on mica, graphite IG110 and Inconel 800H. The prepared “probe cantilevers” were mesocarbon microbeads (MCMB), fuel element debris from HTR-10 and graphite NBG18. The equivalent work of adhesion was derived from the measured adhesive force and calculated based on substrate profile approximation and the JKR theoretical model. The measured work was smaller than the ideal work of adhesion, most likely due to the rough particle morphology and the rough substrate surface. Additionally, a shape factor imposes a constraint on the lateral deformation of the particles. Furthermore, surface roughness could reduce the adhesive force some depending on the particle size. Once the particle was too small to be trapped into a trough, the adhesive force would not be further reduced.

AFM measurements of adhesive forces between carbonaceous particles and the substrates

International Nuclear Information System (INIS)

Zhang, Tianqi; Peng, Wei; Shen, Ke; Yu, Suyuan

2015-01-01

Highlights: • Adhesive force of spherical carbonaceous particle MCMBs and HTR-10 graphite matrix debris were measured for the first time. • The measured equivalent works of adhesion were much smaller than the ideal values. • The shape factor and the particle morphology reduce the adhesive force. • The adhesion effect does not change directly with the asperity size. - Abstract: Graphite dust is carbonaceous particles generated during operation of High Temperature Gas-Cooled Reactors (HTR). Graphite dust resuspension is the key behavior associated with HTR source term analyses and environmental safety assessment. The adhesive force is the key factor that determines the resuspension rate. The present study used an atomic force microscope (AFM) to measure the adhesive force between a single carbonaceous particle and the substrate. The measurements were performed on mica, graphite IG110 and Inconel 800H. The prepared “probe cantilevers” were mesocarbon microbeads (MCMB), fuel element debris from HTR-10 and graphite NBG18. The equivalent work of adhesion was derived from the measured adhesive force and calculated based on substrate profile approximation and the JKR theoretical model. The measured work was smaller than the ideal work of adhesion, most likely due to the rough particle morphology and the rough substrate surface. Additionally, a shape factor imposes a constraint on the lateral deformation of the particles. Furthermore, surface roughness could reduce the adhesive force some depending on the particle size. Once the particle was too small to be trapped into a trough, the adhesive force would not be further reduced.

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

Science.gov (United States)

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

1994-01-01

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

A partial differential equation model and its reduction to an ordinary differential equation model for prostate tumor growth under intermittent hormone therapy.

Science.gov (United States)

Tao, Youshan; Guo, Qian; Aihara, Kazuyuki

2014-10-01

Hormonal therapy with androgen suppression is a common treatment for advanced prostate tumors. The emergence of androgen-independent cells, however, leads to a tumor relapse under a condition of long-term androgen deprivation. Clinical trials suggest that intermittent androgen suppression (IAS) with alternating on- and off-treatment periods can delay the relapse when compared with continuous androgen suppression (CAS). In this paper, we propose a mathematical model for prostate tumor growth under IAS therapy. The model elucidates initial hormone sensitivity, an eventual relapse of a tumor under CAS therapy, and a delay of a relapse under IAS therapy, which are due to the coexistence of androgen-dependent cells, androgen-independent cells resulting from reversible changes by adaptation, and androgen-independent cells resulting from irreversible changes by genetic mutations. The model is formulated as a free boundary problem of partial differential equations that describe the evolution of populations of the abovementioned three types of cells during on-treatment periods and off-treatment periods. Moreover, the model can be transformed into a piecewise linear ordinary differential equation model by introducing three new volume variables, and the study of the resulting model may help to devise optimal IAS schedules.

Conditions of formation for carbonaceous silicites of the continental margins

Energy Technology Data Exchange (ETDEWEB)

Bazhenova, O.K.

1986-06-01

Carbonaceous silicites occur in virtually all systems in Phanerozoic folded regions. They are of practical interest as concentrators of silver, molybdenum, vanadium, and nickel and as source and occasionally reservoir beds for petroleum. Some small oil pools occur in them in basins in Japan (Niigata and Akita), California, and East Sakhalin. Recently, interest has increased because a major pool was discovered in silicites of the Monterey formation: Point Arguello Hueso in the offshore part of the Santa Maria basin. Here the authors consider carbonaceous silicates in the western part of the Pacific active margin, which include Silurian and Devonian phthanites in the Mongolia-Okhotsk belt, and Triassic and Jurassic phthanites in the Sikhote-Alin area, although these rocks are of fairly local occurrence in the section. The authors have examined silicites in Kamchatka, Sakhalin, and Chukotka: diatomites, tuff-diatomites, and opokas, together with their recrystallized analogs. They occur in the Paleogene, but they are most abundant in the Miocene and Pliocene, as well as in the Jurassic, Cretaceous, and Eocene, particularly in the Miocene of California and Japan. 16 references.

Selective reduction of nitric oxide over Cu/ZSM-5: The role of oxygen in suppressing catalyst deactivation by carbonaceous deposits

Energy Technology Data Exchange (ETDEWEB)

d' Itri, Julie L; Sachtler, Wolfgang M.H. [V.N. Ipatieff Laboratory, Center for Catalysis and Surface Science, Departments of Chemical Engineering and Chemistry, Northwestern University, Evanston, IL (United States)

1993-06-15

The role of oxygen in the selective reduction of nitrogen monoxide by either propane or propene over 'excessively' ion-exchanged Cu/ZSM-5 has been studied. In a wide temperature region and in the absence of additives such as steam, propane is a more effective reductant than propene; with propane and in the presence of oxygen reduction of nitric oxide to nitrogen approaches 100% above 600 K. The difference in effectiveness is due to the different degree of catalyst deactivation by carbonaceous deposits: more carbonaceous material is deposited from propene than from propane. Temperature-programmed oxidation shows that above 600 K the rate of oxidation of carbonaceous deposits by oxygen is significant. The amount of such carbonaceous deposits is, therefore, lower when catalytic tests above 600 K are done in the presence of oxygen. At very high temperatures, the in situ volatilization of the deposits by reaction with oxygen keeps the catalyst surface clean in the steady state of nitric oxide reduction.

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.

Enantiomer excesses of rare and common sugar derivatives in carbonaceous meteorites

Science.gov (United States)

Cooper, George; Rios, Andro C.

2016-06-01

Biological polymers such as nucleic acids and proteins are constructed of only one—the d or l—of the two possible nonsuperimposable mirror images (enantiomers) of selected organic compounds. However, before the advent of life, it is generally assumed that chemical reactions produced 50:50 (racemic) mixtures of enantiomers, as evidenced by common abiotic laboratory syntheses. Carbonaceous meteorites contain clues to prebiotic chemistry because they preserve a record of some of the Solar System’s earliest (˜4.5 Gy) chemical and physical processes. In multiple carbonaceous meteorites, we show that both rare and common sugar monoacids (aldonic acids) contain significant excesses of the d enantiomer, whereas other (comparable) sugar acids and sugar alcohols are racemic. Although the proposed origins of such excesses are still tentative, the findings imply that meteoritic compounds and/or the processes that operated on meteoritic precursors may have played an ancient role in the enantiomer composition of life’s carbohydrate-related biopolymers.

Enantiomer excesses of rare and common sugar derivatives in carbonaceous meteorites.

Science.gov (United States)

Cooper, George; Rios, Andro C

2016-06-14

Biological polymers such as nucleic acids and proteins are constructed of only one-the d or l-of the two possible nonsuperimposable mirror images (enantiomers) of selected organic compounds. However, before the advent of life, it is generally assumed that chemical reactions produced 50:50 (racemic) mixtures of enantiomers, as evidenced by common abiotic laboratory syntheses. Carbonaceous meteorites contain clues to prebiotic chemistry because they preserve a record of some of the Solar System's earliest (∼4.5 Gy) chemical and physical processes. In multiple carbonaceous meteorites, we show that both rare and common sugar monoacids (aldonic acids) contain significant excesses of the d enantiomer, whereas other (comparable) sugar acids and sugar alcohols are racemic. Although the proposed origins of such excesses are still tentative, the findings imply that meteoritic compounds and/or the processes that operated on meteoritic precursors may have played an ancient role in the enantiomer composition of life's carbohydrate-related biopolymers.

Source apportionment of atmospheric carbonaceous particulate matter based on the radiocarbon

International Nuclear Information System (INIS)

Guang-hua Wang; You-shi Zeng; Jian Yao; Yuan Qian; Ke Liu; Wei Liu; Yan Li; Yu Huang; University of South China, Hunan

2013-01-01

A method was established to quantitatively estimate sources of atmospheric carbonaceous matter, using a combination of radiocarbon technology, linear regression of organic carbon (OC) -K + and elemental carbon (EC) tracer method. Fractional contributions of fossil fuels, biomass burning, biogenic secondary organic carbon (BSOC) and soil dust to the atmospheric size-resolved carbonaceous matters in Shanghai suburb were estimated using this new method. The fossil carbon contributed most of the OC in particles smaller than 0.49 μm, and its fraction decreased with the increase of particle size. Biomass burning contributed 17-28 % to the OC. The BSOC contributed comparable proportions to the OC in particles smaller than 3.0 μm with the biomass burning, but larger in the particles lager than 3.0 μm. The soil dust contributed least fraction to the OC of each size with a proportion of 2-13 %. The biomass burning and fossil sources shared comparable fraction of the EC in all size range. (author)

Mineralogy and Textural Characteristics of Fine-grained Rims in the Yamato 791198 CM2 Carbonaceous Chondrite: Constraints on the Location of Aqueous Alteration

Science.gov (United States)

Chizmadia, Lysa J.; Brearley, Adrian J.

2003-01-01

Carbonaceous chondrites provide important clues into the nature of physical and chemical processes in the early solar system. A question of key importance concerns the role of water in solar nebular and asteroidal processes. The effects of water on primary mineral assemblages have been widely recognized in chondritic meteorites, especially the CI and CM carbonaceous chondrites. These meteorites have undergone extensive aqueous alteration that occurred prior to their arrival on Earth. In the case of the CM chondrites, this alteration has resulted in the partial to complete replacement of the primary nebular phases with secondary alteration phases. Considerable controversy exists as to the exact location where the alteration of the CM chondrites occurred. Several textural lines of evidence have been cited in support of aqueous alteration prior to the accretion of the final parent asteroid. An important line of evidence to support this hypothesis is the dis-equilibrium nature of fine-grained rims and matrix materials. [2] also noted the juxtaposition of micron-sized Fe-Ni metal grains and apparently unaltered chondrule glass against hydrated rim silicates. Conversely, there is a large body of evidence in favor of parent body alteration such as the occurrence of undisturbed Fe-rich aureoles and the systematic redistribution of elemental components over millimeters, e.g., Mg(+2) into the matrix and Fe(+2) into chondrules etc.

Liquefaction of solid carbonaceous material with catalyst recycle

Science.gov (United States)

Gupta, Avinash; Greene, Marvin I.

1992-01-01

In the two stage liquefaction of a carbonaceous solid such as coal wherein coal is liquefied in a first stage in the presence of a liquefaction solvent and the first stage effluent is hydrogenated in the presence of a supported hydrogenation catalyst in a second stage, catalyst which has been previously employed in the second stage and comminuted to a particle size distribution equivalent to 100% passing through U.S. 100 Mesh, is passed to the first stage to improve the overall operation.

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.

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

Science.gov (United States)

Diehl, Stefan

2008-12-01

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

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...

A Sequential, Implicit, Wavelet-Based Solver for Multi-Scale Time-Dependent Partial Differential Equations

Directory of Open Access Journals (Sweden)

Donald A. McLaren

2013-04-01

Full Text Available This paper describes and tests a wavelet-based implicit numerical method for solving partial differential equations. Intended for problems with localized small-scale interactions, the method exploits the form of the wavelet decomposition to divide the implicit system created by the time-discretization into multiple smaller systems that can be solved sequentially. Included is a test on a basic non-linear problem, with both the results of the test, and the time required to calculate them, compared with control results based on a single system with fine resolution. The method is then tested on a non-trivial problem, its computational time and accuracy checked against control results. In both tests, it was found that the method requires less computational expense than the control. Furthermore, the method showed convergence towards the fine resolution control results.

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....

Comets as parent bodies of CI1 carbonaceous meteorites and possible habitats of ice-microbes

Science.gov (United States)

Wickramasinghe, N. Chandra; Wickramasinghe, Janaki T.; Wallis, Jamie; Hoover, Richard B.; Rozanov, Alexei Y.

2011-10-01

Recent studies of comets and cometary dust have confirmed the presence of biologically relevant organic molecules along with clay minerals and water ice. It is also now well established by deuterium/hydrogen ratios that the CI1 carbonaceous meteorites contain indigenous extraterrestrial water. The evidence of extensive aqueous alteration of the minerals in these meteorites led to the hypothesis that water-bearing asteroids or comets represent the parent bodies of the CI1 (and perhaps CM2) carbonaceous meteorites. These meteorites have also been shown to possess a diverse array of complex organics and chiral and morphological biomarkers. Stable isotope studies by numerous independent investigators have conclusively established that the complex organics found in these meteorites are both indigenous and extraterrestrial in nature. Although the origin of these organics is still unknown, some researchers have suggested that they originated by unknown abiotic mechanisms and may have played a role in the delivery of chiral biomolecules and the origin of life on Early Earth. In this paper we review these results and investigate the thermal history of comets. We show that permanent as well as transient domains of liquid water can be maintained on a comet under a plausible set of assumptions. With each perihelion passage of a comet volatiles are preferentially released, and during millions of such passages the comet could shed crustal debris that may survive transit through the Earth's atmosphere as a carbonaceous meteorite. We review the current state of knowledge of comets and carbonaceous meteorites. We also present the results of recent studies on the long-term viability of terrestrial ice-microbiota encased in ancient glacial ice and permafrost. We suggest that the conditions which have been observed to prevail on many comets do not preclude either survivability (or even the active metabolism and growth) of many types of eukaryotic and prokaryotic microbial

Comets as Parent Bodies of CI1 Carbonaceous Meteorites and Possible Habitats of Ice-Microbiota

Science.gov (United States)

Wickramasinghe, N. Chandra; Wallis, Daryl H.; Rozanov, Alexei Yu.; Hoover, Richard B.

2011-01-01

Recent studies of comets and cometary dust have confirmed the presence of biologically relevant organic molecules along with clay minerals and water ice. It is also now well established by deuterium/hydrogen ratios that the CI1 carbonaceous meteorites contain indigenous extraterrestrial water. The evidence of extensive aqueous alteration of the minerals in these meteorites led to the hypothesis that water-bearing asteroids or comets represent the parent bodies of the CI1 (and perhaps CM2) carbonaceous meteorites. These meteorites have also been shown to possess a diverse array of complex organics and chiral and morphological biomarkers. Stable isotope studies by numerous independent investigators have conclusively established that the complex organics found in these meteorites are both indigenous and extraterrestrial in nature. Although the origin of these organics is still unknown, some researchers have suggested that they originated by unknown abiotic mechanisms and may have played a role in the delivery of chiral biomolecules and the origin of life on Early Earth. In this paper we review these results and investigate the thermal history of comets. We show that permanent as well as transient domains of liquid water can be maintained on a comet under a plausible set of assumptions. With each perihelion passage of a comet volatiles are preferentially released, and during millions of such passages the comet could shed crustal debris that may survive transit through the Earth s atmosphere as a carbonaceous meteorite. We review the current state of knowledge of comets and carbonaceous meteorites. We also present the results of recent studies on the long-term viability of terrestrial ice-microbiota encased in ancient glacial ice and permafrost. We suggest that the conditions which have been observed to prevail on many comets do not preclude either survivability (or even the active metabolism and growth) of many types of eukaryotic and prokaryotic microbial

Sources of carbonaceous aerosol in the Amazon basin

Directory of Open Access Journals (Sweden)

S. Gilardoni

2011-03-01

Full Text Available The quantification of sources of carbonaceous aerosol is important to understand their atmospheric concentrations and regulating processes and to study possible effects on climate and air quality, in addition to develop mitigation strategies.

In the framework of the European Integrated Project on Aerosol Cloud Climate Interactions (EUCAARI fine (D_p < 2.5 μm and coarse (2.5 μm < D_p <10 μm aerosol particles were sampled from February to June (wet season and from August to September (dry season 2008 in the central Amazon basin. The mass of fine particles averaged 2.4 μg m⁻³ during the wet season and 4.2 μg m⁻³ during the dry season. The average coarse aerosol mass concentration during wet and dry periods was 7.9 and 7.6 μg m⁻³, respectively. The overall chemical composition of fine and coarse mass did not show any seasonality with the largest fraction of fine and coarse aerosol mass explained by organic carbon (OC; the average OC to mass ratio was 0.4 and 0.6 in fine and coarse aerosol modes, respectively. The mass absorbing cross section of soot was determined by comparison of elemental carbon and light absorption coefficient measurements and it was equal to 4.7 m² g⁻¹ at 637 nm. Carbon aerosol sources were identified by Positive Matrix Factorization (PMF analysis of thermograms: 44% of fine total carbon mass was assigned to biomass burning, 43% to secondary organic aerosol (SOA, and 13% to volatile species that are difficult to apportion. In the coarse mode, primary biogenic aerosol particles (PBAP dominated the carbonaceous aerosol mass. The results confirmed the importance of PBAP in forested areas.

The source apportionment results were employed to evaluate the ability of global chemistry transport models to simulate carbonaceous aerosol sources in a regional tropical background site. The comparison showed an overestimation

Carbon isotope analysis of carbonaceous compounds in Puget Sound and Lake Washington

International Nuclear Information System (INIS)

Swanson, J.R.

1980-01-01

A new method has been developed and tested for determining chronological profiles of organic pollutants. This method, Carbon Isotope Analysis (CIA), involves measurements of 12 C, 13 C and 14 C in carbonaceous compounds found in layers of sediment. Lipids, total aliphatic hydrocarbons (TAHs) and polycyclic aromatic hydrocarbons (PAHs) are separated from kg quantities of sediment. Large Soxhlet extractors are used to remove the extractable organics, using ultra-pure benzene-methanol solution and having an extraction efficiency of about 86% for compounds with boiling points higher than n-tetradecane (n-C 14 ). The basic steps in compound separation include freeze-drying, extraction, fractionation, column chromatography and evaporation. Isolating the TAH and PAH fractions is accomplished by eluting samples from Sephadex and alumina/silica-gel columns. The amount of each fraction recovered is determined by converting the hydrocarbons to carbon dioxide and measuring this gas manometrically. Variations in 12 C and 13 C abundances for carbonaceous compounds are primarily due to thermodynamic, photosynthetic and metabolic fractionation processes. Thus, the source of a particular organic compound can often be determined by measuring its 13 C/ 12 C ratio. Combining the information from both the 13 C analysis and 14 C analysis makes source identification more certain. In addition, this investigation reviews carbon isotopic data and carbon cycling and analyzes organic pollution in two limited ecosystems (Puget Sound and Lake Washington). Specifically, distinct carbonaceous species are analyzed for pollution in sediments of Lake Washington, Elliott Bay, Commencement Bay, central Puget Sound and northern Puget Sound near the Cherry Point oil refineries

Characterization and performance of carbonaceous materials obtained from exhausted sludges for the anaerobic biodecolorization of the azo dye Acid Orange II

Energy Technology Data Exchange (ETDEWEB)

Athalathil, S.; Stüber, F.; Bengoa, C.; Font, J. [Departament d’Enginyeria Quimica, ETSEQ, Universitat Rovira i Virgili, Av. Paisos Catalans 26, 43007 Tarragona, Catalunya (Spain); Fortuny, A. [Departament d’Enginyeria Quimica, EPSEVG, Universitat Politecnica de Catalunya, Av. Victor Balaguer s/n, 08800 Vilanova i la Geltru, Catalunya (Spain); Fabregat, A., E-mail: azael.fabregat@urv.cat [Departament d’Enginyeria Quimica, ETSEQ, Universitat Rovira i Virgili, Av. Paisos Catalans 26, 43007 Tarragona, Catalunya (Spain)

2014-02-01

Graphical abstract: - Highlights: • Carbonaceous materials were prepared from exhausted sludge materials. • High surface area and good physicochemical properties were achieved. • Utilization of waste sludge materials and mixed anaerobic cultures were used in a continuous anaerobic UPBR system (upflow packed bed biological reactor). • Effective treatment of dye contaminated wastewater in a cheapest and environmental friendly method was demonstrated. - Abstract: This work presents the preliminary study of new carbonaceous materials (CMs) obtained from exhausted sludge, their use in the heterogeneous anaerobic process of biodecolorization of azo dyes and the comparison of their performance with one commercial active carbon. The preparation of carbonaceous materials was conducted through chemical activation and carbonization. Chemical activation was carried out through impregnation of sludge-exhausted materials with ZnCl{sub 2} and the activation by means of carbonization at different temperatures (400, 600 and 800 °C). Their physicochemical and surface characteristics were also investigated. Sludge based carbonaceous (SBC) materials SBC400, SBC600 and SBC800 present values of 13.0, 111.3 and 202.0 m{sup 2}/g of surface area. Biodecolorization levels of 76% were achieved for SBC600 and 86% for SBC800 at space time (τ) of 1.0 min, similar to that obtained with commercial activated carbons in the continuous anaerobic up-flow packed bed reactor (UPBR). The experimental data fit well to the first order kinetic model and equilibrium data are well represented by the Langmuir isotherm model. Carbonaceous materials show high level of biodecolorization even at very short space times. Results indicate that carbonaceous materials prepared from sludge-exhausted materials have outstanding textural properties and significant degradation capacity for treating textile effluents.

Acid/base bifunctional carbonaceous nanomaterial with large surface area: Preparation, characterization, and adsorption properties for cationic and anionic compounds

Energy Technology Data Exchange (ETDEWEB)

Li, Kai; Ma, Chun–Fang; Ling, Yuan; Li, Meng [Department of Chemistry, Faculty of Material Science and Chemistry, China University of Geosciences, Wuhan 430074 (China); Gao, Qiang, E-mail: gaoqiang@cug.edu.cn [Department of Chemistry, Faculty of Material Science and Chemistry, China University of Geosciences, Wuhan 430074 (China); Engineering Research Center of Nano-Geo Materials of Ministry of Education, China University of Geosciences, Wuhan 430074 (China); Luo, Wen–Jun, E-mail: heartnohome@yahoo.com.cn [Department of Chemistry, Faculty of Material Science and Chemistry, China University of Geosciences, Wuhan 430074 (China)

2015-07-15

Nanostructured carbonaceous materials are extremely important in the nano field, yet developing simple, mild, and “green” methods that can make such materials possess large surface area and rich functional groups on their surfaces still remains a considerable challenge. Herein, a one-pot and environment-friendly method, i.e., thermal treatment (180 °C; 18 h) of water mixed with glucose and chitosan (CTS), has been proposed. The resultant carbonaceous nanomaterials were characterized by field emitting scanning electron microscope, N{sub 2} adsorption/desorption, Fourier transform infrared spectroscope, X-ray photoelectron spectroscopy, and zeta-potential analysis. It was found that, in contrast to the conventional hydrothermally carbonized product from pure glucose, with low surface area (9.3 m{sup 2} g{sup −1}) and pore volume (0.016 cm{sup 3} g{sup −1}), the CTS-added carbonaceous products showed satisfactory textural parameters (surface area and pore volume up to 254 m{sup 2} g{sup −1} and 0.701 cm{sup 3} g{sup −1}, respectively). Moreover, it was also interestingly found that these CTS-added carbonaceous products possessed both acidic (–COOH) and basic (–NH{sub 2}) groups on their surfaces. Taking the advantages of large surface area and –COOH/–NH{sub 2} bifunctional surface, the carbonaceous nanomaterials exhibited excellent performance for adsorptions of cationic compound (i.e., methylene blue) at pH 10 and anionic compound (i.e., acid red 18) at pH 2, respectively. This work not only provides a simple and green route to prepare acid/base bifunctional carbonaceous nanomaterials with large surface area but also well demonstrates their potential for application in adsorption. - Highlights: • A simple and green method was proposed to prepare carbon nanomaterials. • The carbon product showed acid/base bifunctional surface with large surface area. • The carbon material could efficiently adsorb both cationic and anionic compounds.

Inner Surface Chirality of Single-Handed Twisted Carbonaceous Tubular Nanoribbons.

Science.gov (United States)

Liu, Dan; Li, Baozong; Guo, Yongmin; Li, Yi; Yang, Yonggang

2015-11-01

Single-handed twisted 4,4'-biphenylene-bridged polybissilsesquioxane tubular nanoribbons and single-layered nanoribbons were prepared by tuning the water/ethanol volume ratio in the reaction mixture at pH = 11.6 through a supramolecular templating approach. The single-layered nanoribbons were formed by shrinking tubular nanoribbons after the removal of the templates. In addition, solvent-induced handedness inversion was achieved. The handedness of the polybissilsesquioxanes could be controlled by changing the ethanol/water volume ratio in the reaction mixture. After carbonization at 900 °C for 4.0 h and removal of silica, single-handed twisted carbonaceous tubular nanoribbons and single-layered nanoribbons with micropores in the walls were obtained. X-ray diffraction and Raman spectroscopy analyses indicated that the carbon is predominantly amorphous. The circular dichroism spectra show that the twisted tubular nanoribbons exhibit optical activity, while the twisted single-layered nanoribbons do not. The results shown here indicate that chirality is transferred from the organic self-assemblies to the inner surfaces of the 4,4'-biphenylene-bridged polybissilsesquioxane tubular nanoribbons and subsequently to those of the carbonaceous tubular nanoribbons. © 2015 Wiley Periodicals, Inc.

Extracting solid carbonaceous materials with solvents

Energy Technology Data Exchange (ETDEWEB)

1936-02-08

Solvent extraction of solid carbonaceous materials is performed in the presence of powdered catalysts together with alkaline substances. Oxides of nickel or iron or nickel nitrate have been used together with caustic soda or potash solutions or milk of lime. Solvents used include benzenes, middle oils, tars, tetrahydronaphthalene. The extraction is performed at 200 to 500/sup 0/C under pressures of 20 to 200 atm. Finely ground peat was dried and mixed with milk of lime and nickel nitrate and an equal quantity of middle oil. The mixture was heated for 3 h at 380/sup 0/C at 90 atm. 88.5% of the peat was extracted. In a similar treatment brown coal was impregnated with solutions of caustic soda and ferric chloride.

Destructive hydrogenation of carbonaceous materials, etc

Energy Technology Data Exchange (ETDEWEB)

1938-02-15

A process is described for the destructive hydrogenation continuously of solid and infusible carbonaceous substances, consisting of heating the charge to the same temperature as the added hydrogen, under a pressure essentially equal to that of the reaction, from the first to at least 300/sup 0/C, but not more than 440/sup 0/C, while passing the heated charge through a zone the contents of which are equal to about 20 per cent to 40 per cent of that of the reaction space, maintaining the charge for a certain time at the temperature without sensible change in the pressure, then reheating the charge to at least the temperature to prime the reaction and finally to introduce the charge into the reaction space.

Carbonaceous matter in the Pomozhan deposit

Energy Technology Data Exchange (ETDEWEB)

Piatek, G

1979-01-01

Carbonaceous matter (CM), encountered in the Pomozhan deposit, is coordinate to dolomitic-illitic clay, filling caverns in ore-bearing dolomites. The CM represents a disperse mass with particle sizes up to 2 mm, having a color from dark brown to black. The reflectivity (0.35-0.42%) and classification assignment of the CM to macerals of the vitrinite or dopplerinite group were determined by micropetrographic methods. CM belonging to the type of humic coals, transitional from brown to bituminous coals is an epigenetic formation. Its accumulation in the regions of the Ol'kush ore deposits occurred in the Triassic-Cretaceous or Cenozoic interval. Liassic coal of the Zavertse region or Helvetian coal of Khomentuv and Tarnobzheg could be the source of the CM.

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

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.

Solution of differential equations by application of transformation groups

Science.gov (United States)

Driskell, C. N., Jr.; Gallaher, L. J.; Martin, R. H., Jr.

1968-01-01

Report applies transformation groups to the solution of systems of ordinary differential equations and partial differential equations. Lies theorem finds an integrating factor for appropriate invariance group or groups can be found and can be extended to partial differential equations.

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

Science.gov (United States)

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

2018-03-01

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

The chemical structure of the insoluble organic matter from carbonaceous meteorites

Science.gov (United States)

Derenne, S.; Robert, F.

2008-09-01

Carbonaceous chondrites are the most primitive objects of the solar system. They contain substantial amounts of carbon (up to 3%), mostly occurring in macromolecular insoluble organic matter (IOM). This IOM is generally considered as a record of interstellar synthesis and may contain precursors of prebiotic molecules possibly deposited on earth by meteoritic bombardments. For these reasons, chondritic IOM has been raising interest for long and it is therefore of special interest to decipher its chemical structure. It is now well established that the chemical structure of this macromolecular material is based on aromatic moieties linked by short aliphatic chains and comprising substantial amounts of heteroatoms. However, its precise chemical structure could only be recently specified. The aim of this presentation is to propose a molecular model for the chemical structure of IOM isolated from non-metamorphosed carbonaceous chondrites. This model is derived from a large set of data obtained through a combination of techniques including various spectrocopies, high resolution transmission electron microscopy (HRTEM) and chemical and thermal degradations. Cosmochemical implications of such a structure will also be discussed.

Effects of day-of-week trends and vehicle types on PM{sub 2.5}-bounded carbonaceous compositions

Energy Technology Data Exchange (ETDEWEB)

Pongpiachan, Siwatt, E-mail: pongpiajun@gmail.com [NIDA Center for Research & Development of Disaster Prevention & Management, School of Social and Environmental Development, National Institute of Development Administration (NIDA), 118 Moo 3, Sereethai Road, Klong-Chan, Bangkapi, Bangkok 10240 (Thailand); SKLLQG, Institute of Earth Environment, Chinese Academy of Sciences (IEECAS), Xi' an 710075 (China); Kositanont, Charnwit [Department of Microbiology, Faculty of Sciences, Chulalongkorn University, Bangkok 10330 (Thailand); Palakun, Jittree [Faculty of Education, Valaya Alongkorn Rajabhat University under the Royal Patronage (VRU), No.1 Moo 20, Phaholyothin Road, Klong luang, Pathumthani 13180 (Thailand); Liu, Suixin; Ho, Kin Fai; Cao, Junji [SKLLQG, Institute of Earth Environment, Chinese Academy of Sciences (IEECAS), Xi' an 710075 (China)

2015-11-01

Carbonaceous compositions of PM{sub 2.5} were measured in the heart of Bangkok from 17th November 2010 to 19th January 2012, and a data set of 94 samples was constructed. Effects of day-of-week trends and vehicle types on PM{sub 2.5}-bound TC, OC, and EC were carefully investigated. In this study, OC was the most important contributor to the total PM{sub 2.5} mass concentration. The average PM{sub 2.5}-bound OC content measured at CHAOS (18.8 ± 9.18 μg m{sup −3}) was approximately 11 times higher than at Chaumont, Switzerland (1.7 μg m{sup −3}), but approximately five times lower than at Xi'an, China (93.0 μg m{sup −3}). The application of diagnostic binary ratios of OC/EC and estimations of secondary organic carbon (SOC) coupled with autocorrelation plots (Box and Jenkins) highlight the enhanced impacts of traffic emissions, especially from diesel vehicles, on PM{sub 2.5}-bound carbonaceous compositions on weekdays relative to weekends. Hierarchical cluster analysis (HCA) coupled with principal component analysis (PCA) underline the importance of diesel emissions as the primary contributors of carbonaceous aerosols, particularly during weekdays. - Highlights: • Traffic emissions play an important role in governing OC and EC during weekdays. • Time series analysis shows the existence of day-of-week trends of OC and EC. • Diesel vehicles are the main contributors of carbonaceous compositions.

Normal differential renal function does not indicate a normal kidney after partial ureteropelvic obstruction and subsequent relief in 2-week-old piglets

Energy Technology Data Exchange (ETDEWEB)

Dissing, Thomas H.; Mikkelsen, Mette Marie; Pedersen, Michael; Froekiaer, Joergen; Djurhuus, Jens Christian [University of Aarhus, Institute of Clinical Medicine, Aarhus (Denmark); Eskild-Jensen, Anni [Aarhus University Hospital, Department of Nuclear Medicine, Aarhus Sygehus, Aarhus (Denmark); Gordon, Isky [University College London, Institute of Child Health, London (United Kingdom); University College London, Radiology and Physics Unit, Institute of Child Health, London (United Kingdom)

2008-09-15

We investigated the functional consequences of relieving ureteric obstruction in young pigs with experimental hydronephrosis (HN) induced by partial unilateral ureteropelvic obstruction. Three groups of animals were followed from the age of 2 weeks to the age of 14 weeks: Eight animals had severe or grades 3-4 HN throughout the study. Six animals had relief of the obstruction after 4 weeks. Six animals received sham operations at both ages. Morphological and functional examinations were performed at age 6 weeks and again at age 14 weeks and consisted of magnetic resonance imaging (MRI), technetium-diethylenetriaminepentaaceticacid ({sup 99m}Tc-DTPA) renography, renal technetium-dimercaptosuccinicacid ({sup 99m}Tc-DMSA) scintigraphy, and glomerular filtration rate (GFR) measurement. After relief of the partial obstruction, there was reduction of the pelvic diameter and improvement of urinary drainage. Global and relative kidney function was not significantly affected by either obstruction or its relief. Renal {sup 99m}Tc-DMSA scintigraphy showed a change in both the appearance of the kidney and a change in the distribution within kidneys even after relief of obstruction. This study shows that partial ureteric obstruction in young pigs may be associated with little effect on global and differential kidney function. However, even after relief of HN, the distribution of {sup 99m}Tc-DMSA in the kidney remains abnormal suggesting that a normal differential renal function may not represent a normal kidney. (orig.)

Automatic differentiation bibliography

Energy Technology Data Exchange (ETDEWEB)

Corliss, G.F. [comp.

1992-07-01

This is a bibliography of work related to automatic differentiation. Automatic differentiation is a technique for the fast, accurate propagation of derivative values using the chain rule. It is neither symbolic nor numeric. Automatic differentiation is a fundamental tool for scientific computation, with applications in optimization, nonlinear equations, nonlinear least squares approximation, stiff ordinary differential equation, partial differential equations, continuation methods, and sensitivity analysis. This report is an updated version of the bibliography which originally appeared in Automatic Differentiation of Algorithms: Theory, Implementation, and Application.

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

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

Atmospheric carbonaceous aerosols from Indo-Gangetic Plain and Central Himalaya: impact of anthropogenic sources.

Science.gov (United States)

Ram, Kirpa; Sarin, M M

2015-01-15

In the present-day scenario of growing anthropogenic activities, carbonaceous aerosols contribute significantly (∼20-70%) to the total atmospheric particulate matter mass and, thus, have immense potential to influence the Earth's radiation budget and climate on a regional to global scale. In addition, formation of secondary organic aerosols is being increasingly recognized as an important process in contributing to the air-pollution and poor visibility over urban regions. It is, thus, essential to study atmospheric concentrations of carbonaceous species (EC, OC and WSOC), their mixing state and absorption properties on a regional scale. This paper presents the comprehensive data on emission sources, chemical characteristics and optical properties of carbonaceous aerosols from selected urban sites in the Indo-Gangetic Plain (IGP) and from a high-altitude location in the central Himalaya. The mass concentrations of OC, EC and WSOC exhibit large spatio-temporal variability in the IGP. This is attributed to seasonally varying emissions from post-harvest agricultural-waste burning, their source strength, boundary layer dynamics and secondary aerosol formation. The high concentrations of OC and SO4(2-), and their characteristic high mass scattering efficiency, contribute significantly to the aerosol optical depth and scattering coefficient. This has implications to the assessment of single scattering albedo and aerosol radiative forcing on a regional scale. Copyright © 2014 Elsevier Ltd. All rights reserved.

Distinct Purine Distribution in Carbonaceous Chondrites

Science.gov (United States)

Callahan, Michael P.; Smith, Karen E.; Cleaves, Henderson J.; Ruzicka, Josef; Stern, Jennifer C.; Glavin, Daniel P.; House, Christopher H.; Dworkin, Jason P.

2011-01-01

Carbonaceous chondrite meteorites are known to contain a diverse suite of organic compounds, many of which are essential components of biochemistry. Amino acids, which are the monomers of proteins, have been extensively studied in such meteorites (e.g. Botta and Bada 2002; Pizzarello et aI., 2006). The origin of amino acids in meteorites has been firmly established as extraterrestrial based on their detection typically as racemic mixtures of amino acids, the presence of many non-protein amino acids, and non-terrestrial values for compound-specific deuterium, carbon, and nitrogen isotopic measurements. In contrast to amino acids, nucleobases in meteorites have been far less studied. Nucleobases are substituted one-ring (pyrimidine) or two-ring (purine) nitrogen heterocyclic compounds and serve as the information carriers of nucleic acids and in numerous coenzymes. All of the purines (adenine, guanine, hypoxanthine, and xanthine) and pyrimidines (uracil) previously reported in meteorites are biologically common and could be interpreted as the result of terrestrial contamination (e.g. van del' Velden and Schwartz, 1974.) Unlike other meteoritic organics, there have been no observations of stochastic molecular diversity of purines and pyrimidines in meteorites, which has been a criterion for establishing extraterrestrial origin. Maltins et al. (2008) performed compound-specific stable carbon isotope measurements for uracil and xanthine in the Murchison meteorite. They assigned a non-terrestrial origin for these nucleobases; however, the possibility that interfering indigenous molecules (e.g. carboxylic acids) contributed to the 13C-enriched isotope values for these nucleobases cannot be completely ruled out. Thus, the origin of these meteoritic nucleobases has never been established unequivocally. Here we report on our investigation of extracts of II different carbonaceous chondrites covering various petrographic types (Cl, CM, and CR) and degrees of aqueous alteration

Characterization of Chiral Carbonaceous Nanotubes Prepared from Four Coiled Tubular 4,4'-biphenylene-silica Nanoribbons

Directory of Open Access Journals (Sweden)

Shuwei Lin

2014-04-01

Full Text Available Four dipeptides derived from phenylalanine were synthesized, which can self-assemble into twisted nanoribbon in deionized water. The handedness of the organic self-assemblies was controlled by the chirality of the phenylalanine at the terminals. Coiled 4,4'-biphenylene bridged polybissilsesquioxane tubular nanoribbons were prepared using the organic self-assemblies as the templates. The circular dichroism spectra indicated that the biphenylene rings preferred to twist in one-handedness within the walls of the samples. After carbonization and removal of silica, single-handed coiled carbonaceous tubular nanoribbons were obtained. The Raman spectra indicated that the carbon was amorphous. The diffuse reflectance circular dichroism spectra indicated the tubular carbonaceous nanoribbons exhibited optical activity.