a region of space under the influence of some vector quantity, such as magnetic field strength, in which the quantity takes a unique vector value at every point of the region
vector field in American English
noun
Math & Physics
a region, domain, set, etc., with a vector assigned at each point; vector function
Examples of 'vector field' in a sentence
vector field
We provide the existence and multiplicity results using the vector field rotation theory.
A. Gritsans, F. Sadyrbaev, I. Yermachenko 2016, 'Dirichlet Boundary Value Problem for the Second Order Asymptotically Linear System',International Journal of Differential Equationshttp://dx.doi.org/10.1155/2016/5676217. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
We consider two types of interactions, linear and nonlinear in the vector field.
André Amado, Zahra Haghani, Azadeh Mohammadi, Shahab Shahidi 2017, 'Quantum corrections to the generalized Proca theory via a matter field', Physics Letters Bhttp://www.sciencedirect.com/science/article/pii/S0370269317305166. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
The position vector field plays important roles in physics, in particular in mechanics.
Bang-Yen Chen 2017, 'Euclidean Submanifolds via Tangential Components of Their Position Vector Fields',Mathematicshttps://www.mdpi.com/2227-7390/5/4/51. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
In this paper, we consider the localization of vector field in three formulations.
Masafumi Higuchi, Shin'ichi Nojiri 2017, 'Localization of vector field on dynamical domain wall', Physics Letters Bhttp://www.sciencedirect.com/science/article/pii/S0370269317300229. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Two singular straight lines are found in the associated topological vector field.
Lina Zhang, Tao Song 2015, 'Traveling Wave Solutions of a Generalized Camassa-Holm Equation: A Dynamical SystemApproach', Mathematical Problems in Engineeringhttp://dx.doi.org/10.1155/2015/610979. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
The terrain without coordinate information was reconstructed by iterating the vector field.
Xu Xinchao, Zhen Ying, Wang Guobin, Zhou Peixi, Li Hang, Lee Mengying 2015, 'Terrain reconstruction based on descent images for the Chang’e III landing area',Journal of Engineering Science and Technology Reviewhttp://www.jestr.org/downloads/Volume8Issue4/fulltext8492015.pdf. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Each output spectral line represents the amplitude of the vector field at a specific frequency.
Bellan Diego 2014, 'Noise Propagation in Multiple-Input ADC-Based Measurement Systems', Measurement Science Reviewhttp://www.degruyter.com/view/j/msr.2014.14.issue-6/msr-2014-0041/msr-2014-0041.xml?format=INT. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
A multi-resolution scheme significantly reduces the searching time, and provides a smooth motion vector field.
S. Usama, B. Šimák 2002, 'A Low-complexity Wavelet Based Algorithm for Inter-frame Image Prediction', Acta Polytechnicahttps://ojs.cvut.cz/ojs/index.php/ap/article/view/326. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
We also give a geometric interpretation to it by means of a specially defined vector field.
P. Kotko, A. M. Stasto 2017, 'Wilson lines in the MHV action', Journal of High Energy Physicshttp://link.springer.com/article/10.1007/JHEP09(2017)047. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Once corresponding regions in both images were found, a displacement vector field representing the local deformation was computed.
Michael Figl, Rainer Hoffmann, Marcus Kaar, Johann Hummel 2019, 'Deformable registration of 3D ultrasound volumes using automatic landmark generation',PLOS ONE10.1371/journal.pone.0213004. Retrieved from PLOS CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)