Lamellar vector field
In vector calculus, a complex lamellar vector field is a vector field in three dimensions which is orthogonal to its own curl. That is,
\mathbf{F}\cdot (\nabla\times \mathbf{F}) = 0.
Complex lamellar vector fields are precisely those that are normal to a family of surfaces. A special case are irrotational vector fields, satisfying
\nabla\times\mathbf{F}=\mathbf{0}.
An irrotational vector field is locally the gradient of a function, and is therefore orthogonal to the family of level surfaces (the equipotential surfaces). Accordingly, the term lamellar vector field is sometimes used as a synonym for an irrotational vector field. The adjective "lamellar" derives from the noun "lamella", which means a thin layer. The lamellae to which "lamellar flow" refers are the surfaces of constant potential, or in the complex case, the surfaces orthogonal to the vector field.

This is an excerpt from the article Lamellar vector field from the Wikipedia free encyclopedia. A list of authors is available at Wikipedia.
The article Lamellar vector field at en.wikipedia.org was accessed 7 times in the last 30 days. (as of: 08/11/2013)
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Complex lamellar vector field - Wikipedia, the free encyclopedia
In vector calculus, a complex Lamellar vector field is a vector field in three dimensions which is orthogonal to its own curl. That is,. \mathbf{F}\cdot (\nabla\ times ...
en.wikipedia.org/wiki/Complex_lamellar_vector_field
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Conservative vector field - Wikipedia, the free encyclopedia
In vector calculus a conservative vector field is a vector field which is the gradient of a function, known in this context as a scalar potential. Conservative vector ...
en.wikipedia.org/wiki/Conservative_vector_field
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Lamellar vector field - Encyclopedia - The Free Dictionary
Encyclopedia article about Lamellar vector field. Information about Lamellar vector field in the Columbia Encyclopedia, Computer Desktop Encyclopedia, ...
encyclopedia2.thefreedictionary.com/lamellar+vector+field
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Lamellar field - Encyclopedia - The Free Dictionary
Lamellar vector field [lə′mel·ər ′vek·tər ‚fēld]. (mathematics). irrotational vector field. Want to thank TFD for its existence? Tell a friend about us, add a link to this ...
encyclopedia2.thefreedictionary.com/Lamellar+field
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what is lamellar vector field - Winner Science
DEL OPERATOR. Vector differential operator `del' is represented by a symbol \ nabla . Its another name is `nabla'. For three dimensional case, it is defined as.
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Proof of the potential function representation of Complex lamellar ...
Jul 26, 2013 ... Given a continuously differentiable vector field $\bf a$, demonstrate the equivalence (iff) between the requirement that it satisfies ${\bf ...
math.stackexchange.com/questions/452742/proof-of-the-potential-function-representation-of-complex-lamellar-vector-field
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Watch Lamellar Vector Field Video
In vector analysis and in fluid dynamics, a Lamellar vector field is a vector field with no rotational component. That is, if the field is denoted as ...
www.ovguide.com/lamellar-vector-field-9202a8c04000641f800000000025ad2c
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lamellar field | planetmath.org
Oct 11, 2004 ... lamellar field. A vector field F → = F → ⁢ ( x , y , z ) normal-→ F normal-→ F x y z \ vec{F}=\vec{F}(x,\,y,\,z) , defined in an open set D D D of ℝ 3 ...
planetmath.org/lamellarfield
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Irrotational Field: Definition from Answers.com
(mathematics) A vector field whose curl is identically zero; every such field is the gradient of a scalar function. Also known as Lamellar vector field.
www.answers.com/topic/irrotational-vector-field
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Complex lamellar vector field | Facebook
Complex Lamellar vector field. 1 likes · 0 talking about this. See also Beltrami vector field Conservative vector field.
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Lamellar vector field in science
Conservative vector field - Wikipedia, the free encyclopedia
In vector calculus a conservative vector field is a vector field which is the gradient ... Conservative vector fields have the property that the line integral from one point .... Complex Lamellar vector field · Helmholtz decomposition · Laplacian vector field ... D. J. Acheson, Elementary Fluid Dynamics, Oxford University Press (2005).
[PDF]On Complex-lamellar Motion of a Prim Gas. - Department of ...
School of Mathematics, The University of New South W'ales,. Sydney ... to exist only in complex-lamellar motion are then shown by intrinsic geo- .... vector field.
[PDF]COMPUTATIONAL MODELING OF MULTIPLE DOMAIN PATTERN ...
Department of Chemical Engineering, McGill University, ... lamellae equation utilize two coupled field: a non-conserved envelope vector field of the local.
[PDF]on circulation preserving mfd flows with steady streamlines
Department of Mathematics, Faculty of Science, Banaras Hindu University, ... according to a well-known criterion of complex-lamellar vector fields?15 Equation ...
Complex lamellar vector field - Wikipedia, the free encyclopedia
In vector calculus, a complex Lamellar vector field is a vector field in three dimensions which is orthogonal to its own curl. That is,. \mathbf{F}\cdot (\nabla\ times ...
Books on the term Lamellar vector field
Elements of Vorticity Aerodynamics
Elements of Vorticity Aerodynamics
J. C. Wu, 2005
A vector field f is said to be solenoidal if its divergence , V - f , is zero and lamellar if its curl, Vxf, is zero. A solenoidal velocity field V is said to be incompressible and a lamellar velocity field irrotational. In the following discussions, the terms ...
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Applied Mathematical Sciences)
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Applied Mathematical Sciences)
John Guckenheimer and Philip Holmes, 2002
An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations an...
Mathematical Methods Oscillations Waves
Mathematical Methods Oscillations Waves
1 1.14 : Give a brief account of line, surface and volume integral of vector. What do you understand by lamellar and non-lamellar fields ? Line Integral : Let us consider, a curve AB in any vector field. The vector at any point P of the curve AB  ...
ELECTROMAGNETISM: Theory and Applications
ELECTROMAGNETISM: Theory and Applications
ASHUTOSH PRAMANIK, 2008
i i as _i as Z dx dy dy dx = 0 {= V X (VS)} (0.69) This is a vector identity and is the characteristic of a lamellar field, that is, the line integral of the scalar function S around any closed path is zero. Note that the scalar S is the scalar potential of the  ...
Vector Analysis Versus Vector Calculus (Universitext)
Vector Analysis Versus Vector Calculus (Universitext)
Antonio Galbis and Manuel Maestre, 2012
The aim of this book is to facilitate the use of Stokes' Theorem in applications. The text takes a differential geometric point of view and provides for the student a bridge between pure and applied mathematics by carefully building a formal rigorous development of the topic and following this through to concrete applications in two and three ...
Advances in Chemical Physics, Modern Nonlinear Optics
Advances in Chemical Physics, Modern Nonlinear Optics
Myron W. Evans, 2004
As argued by Reed [4], the Beltrami vector field originated in hydrodynamics and is force-free. It is one of the three basic types of field: solenoidal, complex lamellar, and Beltrami. These vector fields originated in hydrodynamics and describe ...
Electromagnetic Fields in Cavities: Deterministic and Statistical Theories (IEEE Press Series on Electromagnetic...
Electromagnetic Fields in Cavities: Deterministic and Statistical Theories (IEEE Press Series on Electromagnetic...
David A. Hill, 2009
A thorough and rigorous analysis of electromagnetic fields in cavitiesThis book offers a comprehensive analysis of electromagnetic fields in cavities of general shapes and properties.Part One covers classical deterministic methods to conclude resonant frequencies, modal fields, and cavity losses; quality factor; mode bandwidth; and the excitation o...
Methods of Applied Mathematics for Engineers and Scientists
Methods of Applied Mathematics for Engineers and Scientists
Tomas B. Co, 2013
However, there are situations in which the curl is perpendicular to the vector field. If y - (V X y) I 0, then X is known as a complex Lamellar vector field. An example of a complex Lamellar vector field is X: vx(x'y)§.x+vy(x'y)§y+0§1 Conversely, ...
Incompressible Flow
Incompressible Flow
Ronald L. Panton, 2013
The most teachable book on incompressible flow— now fully revised, updated, and expandedIncompressible Flow, Fourth Edition is the updated and revised edition of Ronald Panton's classic text. It continues a respected tradition of providing the most comprehensive coverage of the subject in an exceptionally clear, unified, and carefully paced in...
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Lamellar vector field
Del operator and gradient
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The Profound Significance of the B(3) Field | Dr. Myron Evans
The profound significance of the B(3) field is that it introduces into electrodynamics a higher topology. The B(3) field is reviewed for example by Donald Reed, in "Advances in Chemical Physics", volume 119(3), pp. 532 ff., published by Wiley Interscience in 2001 as a special topical issue called "Modern Non-Linear Optics". Reed describes how Cartan's…
atomicprecision.wordpress.com/2009/11/11/the-profound-significance-of-the-b3-field/
25-Lecture Course: Multivariable Calculus (UC Berkeley) | Virtual-Lectures
Multivariable calculus is also known as “multivariate calculus”. This is the extension of calculus in one variable to calculus in more than one variable.
virtual-lectures.com/25-lecture-course-multivariable-calculus-uc-berkeley/
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Arthritis Research & Therapy | Full text | Disruption of the thrombospondin-2 gene alters lamellar morphology but does not permit vascularization of the adult mouse lumbar disc
The biological basis for the avascular state of the intervertebral disc is not well understood. Previous work has suggested that the presence of thrombospondin-1 (TSP-1), a matricellular protein, in the outer annulus reflects a role for this protein in conferring an avascular status to the disc. In the present study we have examined thrombospondin-2 (TSP-2), a matricellular protein with recognized anti-angiogenic activity in vivo and in vitro.
arthritis-research.com/content/10/4/r96
Backreaction: The Casimir Effect
When asked about experiments that confirm quantum field theory, most people think about the Lamb-shift, Compton scattering, decay rates or particle cross-sections. The most stunning experiment for me however is the Casimir effect.
backreaction.blogspot.com/2007/11/casimir-effect.html
Demicellization of Polyethylene Oxide in Water Solution under Static Magnetic Field Exposure Studied by FTIR Spectroscopy
Advances in Physical Chemistry is a peer-reviewed, open access journal that publishes original research articles as well as review articles in all areas of physical chemistry.
www.hindawi.com/journals/apc/2013/485865/
Wiley: Incompressible Flow, 4th Edition - Ronald L. Panton
www.wiley.com/WileyCDA/WileyTitle/productCd-1118013433.html
PLOS ONE: The ELBA Force Field for Coarse-Grain Modeling of Lipid Membranes
PLOS ONE: an inclusive, peer-reviewed, open-access resource from the PUBLIC LIBRARY OF SCIENCE. Reports of well-performed scientific studies from all disciplines freely available to the whole world.
www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0028637
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