scholarly journals Variational Problem Involving Operator Curl in a Multiconnected Domain

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Junichi Aramaki
Keyword(s):  
Variational Problem ◽  
Minimization Problem ◽  
Vector Fields ◽  
Three Dimensional ◽  
Tangential Component ◽  
Multiconnected Domain

We shall study the problem of minimizing a functional involving the curl of vector fields in a three-dimensional, bounded multiconnected domain with prescribed tangential component on the boundary. The paper is an extension of L2 minimization problem of the curl of vector fields. We shall prove the existence and the estimate of minimizers of more general functional which contains Lp norm of the curl of vector fields.

Minimizing the Lp norm of the curl of vector fields in a multi-connected domain

2017 ◽  
Vol 28 (01) ◽  
pp. 1750004
Author(s):  
Junichi Aramaki
Keyword(s):  
Connected Domain ◽  
Vector Fields ◽  
Three Dimensional ◽  
Tangential Component ◽  
Lp Norm ◽  
Existence Of Minimizers

We study the problem of minimizing the [Formula: see text] norm of the curl of vector fields in a three-dimensional, bounded multi-connected domain with a prescribed tangential component on the boundary. We then prove the existence of minimizers and estimate them.

Limit cycles of three-dimensional polynomial vector fields

Nonlinearity ◽  
2004 ◽  
Vol 18 (1) ◽  
pp. 175-209 ◽  
Author(s):  
Marcin Bobie ski ◽  
Henryk o a dek
Keyword(s):  
Limit Cycles ◽  
Vector Fields ◽  
Three Dimensional ◽  
Polynomial Vector ◽  
Polynomial Vector Fields

Reconstructing Three-Dimensional Fluid Velocity Vector Fields from Acoustic Transmission Measurements

1977 ◽  
pp. 307-326 ◽  
Author(s):  
S. A. Johnson ◽  
J. F. Greenleaf ◽  
C. R. Hansen ◽  
W. F. Samayoa ◽  
M. Tanaka ◽  
...  
Keyword(s):  
Velocity Vector ◽  
Vector Fields ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Acoustic Transmission ◽  
Transmission Measurements

Unitary vector fields are Fermi–Walker transported along Rytov–Legendre curves

2015 ◽  
Vol 12 (10) ◽  
pp. 1550111 ◽  
Author(s):  
Mircea Crasmareanu ◽  
Camelia Frigioiu
Keyword(s):  
Vector Field ◽  
Vector Fields ◽  
Killing Vector ◽  
Three Dimensional ◽  
Ricci Soliton ◽  
Conformal Killing ◽  
Space Forms ◽  
Potential Vector ◽  
Legendre Curves ◽  
Complex Space Forms

Fix ξ a unitary vector field on a Riemannian manifold M and γ a non-geodesic Frenet curve on M satisfying the Rytov law of polarization optics. We prove in these conditions that γ is a Legendre curve for ξ if and only if the γ-Fermi–Walker covariant derivative of ξ vanishes. The cases when γ is circle or helix as well as ξ is (conformal) Killing vector filed or potential vector field of a Ricci soliton are analyzed and an example involving a three-dimensional warped metric is provided. We discuss also K-(para)contact, particularly (para)Sasakian, manifolds and hypersurfaces in complex space forms.

Twelve Limit Cycles in 3D Quadratic Vector Fields with Z3 Symmetry

2018 ◽  
Vol 28 (11) ◽  
pp. 1850139 ◽  
Author(s):  
Laigang Guo ◽  
Pei Yu ◽  
Yufu Chen
Keyword(s):  
Limit Cycles ◽  
Vector Fields ◽  
Center Manifold ◽  
Three Dimensional ◽  
Center Manifold Theory ◽  
Normal Form Theory ◽  
Quadratic Vector Fields ◽  
Fine Focus ◽  
Form Theory ◽  
Manifold Theory

This paper is concerned with the number of limit cycles bifurcating in three-dimensional quadratic vector fields with [Formula: see text] symmetry. The system under consideration has three fine focus points which are symmetric about the [Formula: see text]-axis. Center manifold theory and normal form theory are applied to prove the existence of 12 limit cycles with [Formula: see text]–[Formula: see text]–[Formula: see text] distribution in the neighborhood of three singular points. This is a new lower bound on the number of limit cycles in three-dimensional quadratic systems.

scholarly journals On the symmetries of three-dimensional generalized symmetric spaces

2021 ◽  
Vol 13(62) (2) ◽  
pp. 451-462
Author(s):  
Lakehal Belarbi
Keyword(s):  
Symmetric Spaces ◽  
Vector Fields ◽  
Killing Vector ◽  
Three Dimensional ◽  
Riemannian Metric ◽  
Killing Vector Fields ◽  
Generalized Symmetric Space ◽  
Generalized Symmetric Spaces ◽  
Full Classification

In this work we consider the three-dimensional generalized symmetric space, equipped with the left-invariant pseudo-Riemannian metric. We determine Killing vector fields and affine vectors fields. Also we obtain a full classification of Ricci, curvature and matter collineations

scholarly journals ARBTools: A Tricubic Spline Interpolator for Three-Dimensional Scalar or Vector Fields

2019 ◽  
Author(s):  
Paul Walker ◽  
Ulrich Krohn ◽  
Carty David
Keyword(s):  
Magnetic Field ◽  
Vector Field ◽  
Vector Fields ◽  
Three Dimensional ◽  
Spline Method ◽  
Particle Trajectories ◽  
The Core ◽  
Numerical Integrators ◽  
Data Points ◽  
System Requirements

ARBTools is a Python library containing a Lekien-Marsden type tricubic spline method for interpolating three-dimensional scalar or vector fields presented as a set of discrete data points on a regular cuboid grid. ARBTools was developed for simulations of magnetic molecular traps, in which the magnitude, gradient and vector components of a magnetic field are required. Numerical integrators for solving particle trajectories are included, but the core interpolator can be used for any scalar or vector field. The only additional system requirements are NumPy.

Unique Normal Form and the Associated Coefficients for a Class of Three-Dimensional Nilpotent Vector Fields

2017 ◽  
Vol 27 (14) ◽  
pp. 1750224
Author(s):  
Jing Li ◽  
Liying Kou ◽  
Duo Wang ◽  
Wei Zhang
Keyword(s):  
Normal Form ◽  
Vector Fields ◽  
Three Dimensional ◽  
Recursive Formula ◽  
Higher Order ◽  
Dimensional Vector ◽  
Symbolic Calculations

In this paper, we mainly focus on the unique normal form for a class of three-dimensional vector fields via the method of transformation with parameters. A general explicit recursive formula is derived to compute the higher order normal form and the associated coefficients, which can be achieved easily by symbolic calculations. To illustrate the efficiency of the approach, a comparison of our result with others is also presented.

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