FDA Express

The main purpose of this book is to present a unified foundation for the development of the basic field equations of nonlocal continuum field theories. To this end, we have relied on the natural extensions of the two fundamental laws of physics to nonlocality: (i) the energy balance law is postulated to remain in global form; and (ii) a material point of the body is considered to be attracted by all points of the body, at all past times. By means of these two natural generalizations of the corresponding local principles, theories of nonlocal elasticity, fluid dynamics, and electromagnetic field theories are formulated that include nonlocality in both space and time (memory-dependence).

More information on this book can be found by the following link: http://link.springer.com/book/10.1007/b97697

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Nonlocal Theory of Material Media

Dominik Rogula

Book Description

The aim of the volume is to sketch the physical and mathematical foundations of the nonlocal theory of material media, its general results, applications, connection with related domains of mechanics, and many questions open for future research. Special attention is paid to the problems of structural defects and boundaries of solids. 　

More information on this book can be found by the following link: http://www.springer.com/physics/classical+continuum+physics/book/978-3-211-81632-5

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Journals

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Applied Mathematics Letters

Volume 36, Pages 1-46

The existence and nonexistence of positive solutions to a discrete fractional boundary value problem with a parameter

Zhen-Lai Han, Yuan-Yuan Pan, Dian-Wu Yang

Study on some qualitative properties for solutions of a certain two-dimensional fractional differential system with Hadamard derivative

Qinghua Ma, Jinwei Wang, Rongnian Wang, Xiaohua Ke

Regularity criteria for the density-dependent Hall-magnetohydrodynamics

Jishan Fan, Tohru Ozawa

Almost automorphic solutions to a Beverton–Holt dynamic equation with survival rate

Toka Diagana

Existence of positive solutions for th-order -Laplacian singular sublinear boundary value problems

Zhongli Wei

Variational approach to impulsive evolution equations

Qing Tang, Juan J. Nieto

Oscillation of fourth order sub-linear differential equations

Miroslav Bartušek, Zuzana Došlá

Sampling inequalities for infinitely smooth radial basis functions and its application to error estimates

Mun Bae Lee, Jungho Yoon

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Journal of Computational and Applied Mathematics

Volume 271, Pages 1-414（selected）(selected)

A modified weak Galerkin finite element method for a class of parabolic problems

Fuzheng Gao, Xiaoshen Wang

A quasi-interpolation scheme for periodic data based on multiquadric trigonometric B-splines

Wenwu Gao, Zongmin Wu

-geometric and -binomial distributions of order

Femin Yalcin, Serkan Eryilmaz

A framework for robust measurement of implied correlation

Daniel Linders, Wim Schoutens

On the completeness of hierarchical tensor-product -splines

Dominik Mokriš, Bert Jüttler, Carlotta Giannelli

A survey on fuzzy fractional variational problems

Omid S. Fard, Maryam Salehi

A coarse space for heterogeneous Helmholtz problems based on the Dirichlet-to-Neumann operator

Lea Conen, Victorita Dolean, Rolf Krause, Frédéric Nataf

A bootstrapping market implied moment matching calibration for models with time-dependent parameters

Florence Guillaume, Wim Schoutens

Transformation techniques and fixed point theories to establish the positive solutions of second order impulsive differential equations

Xuemei Zhang, Meiqiang Feng

A coupled alpha-FEM for dynamic analyses of 2D fluid–solid interaction problems

T. Nguyen-Thoi, P. Phung-Van, S. Nguyen-Hoang, Q. Lieu-Xuan

On Marshall–Olkin type distribution with effect of shock magnitude

Murat Ozkut, Ismihan Bayramoglu (Bairamov)

Local–global model reduction of parameter-dependent, single-phase flow models via balanced truncation

Michael Presho, Anastasiya Protasov, Eduardo Gildin

Parallel subspace correction methods for nearly singular systems

Jinbiao Wu, Hui Zheng

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Paper Highlight
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Exner-Based Master Equation for transport and dispersion of river pebble tracers: Derivation, asymptotic forms, and quantification of nonlocal vertical dispersion

A. Pelosi, G. Parker, R. Schumer and H.-B. Ma

Publication information: A. Pelosi, G. Parker, R. Schumer and H.-B. Ma, Exner-Based Master Equation for transport and dispersion of river pebble tracers: Derivation, asymptotic forms, and quantification of nonlocal vertical dispersion, Journal of Geophysical Research: Earth Surface, 2014, 119(9), 1818–1832.

http://onlinelibrary.wiley.com/doi/10.1002/2014JF003130/abstract

Abstract

Ideas deriving from the standard formulation for continuous time random walk (CTRW) based on the Montroll-Weiss Master Equation (ME) have been recently applied to transport and diffusion of river tracer pebbles. CTRW, accompanied by appropriate probability density functions (PDFs) for walker step length and waiting time, yields asymptotically the standard advection-diffusion equation (ADE) for thin-tailed PDFs and the fractional advection-diffusion equation (fADE) for heavy-tailed PDFs, the latter allowing the possibilities of subdiffusion or superdiffusion. Here we show that the CTRW ME is inappropriate for river pebbles moving as bed load: a deposited particle raises local bed elevation, and an entrained particle lowers it so that particles interact with the “lattice” of the sediment-water interface. We use the Parker-Paola-Leclair framework, which is a probabilistic formulation of the Exner equation of sediment conservation, to develop a new ME for tracer transport and dispersion for alluvial morphodynamics. The formulation is based on the existence of a mean bed elevation averaged over fluctuations. The new ME yields asymptotic forms for ADE and fADE that differ significantly from CTRW. It allows vertical as well as streamwise advection-diffusion. Vertical dispersion is nonlocal but cannot be expressed with fractional derivatives. In order to illustrate the new model, we apply it to the restricted case of vertical dispersion only, with both thin and heavy tails for relevant PDFs. Vertical dispersion shows a subdiffusive behavior.

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Spectral approximations to the fractional integral and derivative

Changpin Li, Fanhai Zeng, Fawang Liu

Publication information: Changpin Li, Fanhai Zeng, Fawang Liu, Spectral approximations to the fractional integral and derivative, Fractional Calculus and Applied Analysis, 2012, 15(3), 383-406.

http://link.springer.com/article/10.2478/s13540-012-0028-x

Abstract

In this paper, the spectral approximations are used to compute the fractional integral and the Caputo derivative. The effective recursive formulae based on the Legendre, Chebyshev and Jacobi polynomials are developed to approximate the fractional integral. And the succinct scheme for approximating the Caputo derivative is also derived. The collocation method is proposed to solve the fractional initial value problems and boundary value problems. Numerical examples are also provided to illustrate the effectiveness of the derived methods.

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The End of This Issue

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