scholarly journals Divergence and Curl of COVID19 Spreading in the Lower Peninsula of Michigan

2021 ◽  
Vol 15 (1) ◽  
pp. 32
Author(s):  
Yanshuo Wang
Keyword(s):  
Vector Field ◽  
Scalar Field ◽  
Volume Density ◽  
Volume Flux ◽  
Wayne County ◽  
The Third ◽  
Clockwise Direction ◽  
Kent County ◽  
Lower Peninsula ◽  
Circulation Dynamics

This paper explores the COVID19 transmission pattern and circulation dynamics in the Euclidean space at the lower peninsula of Michigan by using the divergence and curl concept in vector field. The COVID19 transmission volume flux can be calculated for each county by using vector divergence. The results shows Wayne county had the highest divergence (162660), the Kent county had the second highest divergence (152540), and the Saginaw county had the third highest divergence (103240), the divergence is positive which means the COVID19 virus was transmitted from these counties to other places. The results also shows Monroe county had the lowest divergence (-187843), the Allegan county had the second lowest number in divergence (-90824), the divergence is negative which means the COVID19 virus was transmitted from other places to these counties. The circulation of the virus is also calculated by using vector curl. The positive curl means that the virus has circulated in a counter-clockwise direction, and the negative curl means the virus has circulated in a clockwise direction. The divergence is an operator of the COVID19 transmission vector field, which produces a scalar field giving the quantity of the transmission vector field’s source at each location. The COVID19 spreading volume density of the outward flux of transmission field is represented by divergence around a given location. The curl is an operator of the COVID19 transmission field, which describes the circulation of a transmission vector field. The curl at a location in COVID19 transmission field is represented by a vector whose length and direction denote the magnitude and axis of the maximum circulation. The curl of a transmission field is formally defined as the circulation density at each location of COVID19 transmission field.

scholarly journals Divergence and Curl of COVID19 Spreading in Lower Peninsula of Michigan

2021 ◽  
Author(s):  
Yanshuo Wang
Keyword(s):  
Data Analysis ◽  
Vector Field ◽  
Scalar Field ◽  
Volume Density ◽  
Volume Flux ◽  
Lower Peninsula

Abstract Divergence and Curl concept in vector field is applied to the COVID19 spreading data for Lower Peninsula of Michigan State, U.S.A. The Divergence is an operator of COVID19 transmission vector field, which produces a scalar field giving the quantity of transmission vector field’s source at each location. The COVID19 spreading volume density of the outward flux of transmission field is represented by divergence around a given location. The Curl is an operator of COVID19 transmission field, which describes the circulation of a transmission vector field. The Curl at a location in COVID19 transmission field is represented by a vector whose length and direction denote the magnitude and axis of the maximum circulation. The curl of a transmission field is formally defined as the circulation density at each location of COVID19 transmission field. From data analysis of divergence of curl of Lower Michigan Peninsula, the COVID19 transmission volume flux and circulation can be identified for each County. Summary: This paper is to use vector Divergence and Curl concept to apply to COVID19 confirmed cases in Lower Peninsula of Michigan, U.S.A.

scholarly journals On the anisotropy of the turbulent passive scalar in the presence of a mean scalar gradient

2014 ◽  
Vol 744 ◽  
pp. 38-64 ◽  
Author(s):  
Wouter J. T. Bos
Keyword(s):  
Vector Field ◽  
Scalar Field ◽  
Time Scale ◽  
Correlation Time ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Second Order ◽  
Third Order ◽  
The Third ◽  
Order Quantities

AbstractWe investigate the origin of the scalar gradient skewness in isotropic turbulence on which a mean scalar gradient is imposed. The problem of the advection of an anisotropic scalar field is reformulated in terms of the advection of an isotropic vector field. For this field, triadic closure equations are derived. It is shown how the scaling of the scalar gradient skewness depends on the choice of the time scale used for the Lagrangian decorrelation of the vector field. The persistent anisotropy in the small scales for the third-order statistics is shown to be perfectly compatible with Corrsin–Obukhov scaling for second-order quantities, since second- and third-order scalar quantities are governed by a different triad correlation time scale. Whereas the inertial range dynamics of second-order scalar quantities is governed by the Lagrangian velocity correlation time, the third-order quantities remain correlated over a time related to the large-scale dynamics of the scalar field. It is argued that this time is determined by the average time it takes for a fluid particle to travel between ramp-cliff scalar structures.

Black hole in balance with dark matter

2020 ◽  
Vol 35 (02n03) ◽  
pp. 2040050
Author(s):  
Boris E. Meierovich
Keyword(s):  
Black Hole ◽  
Dark Matter ◽  
Phase Equilibrium ◽  
Vector Field ◽  
Scalar Field ◽  
Total Mass ◽  
Metric Tensor ◽  
Static Solutions ◽  
Tensor Formula ◽  
Galaxy Rotation Curves

Equilibrium of a gravitating scalar field inside a black hole compressed to the state of a boson matter, in balance with a longitudinal vector field (dark matter) from outside is considered. Analytical consideration, confirmed numerically, shows that there exist static solutions of Einstein’s equations with arbitrary high total mass of a black hole, where the component of the metric tensor [Formula: see text] changes its sign twice. The balance of the energy-momentum tensors of the scalar field and the longitudinal vector field at the interface ensures the equilibrium of these phases. Considering a gravitating scalar field as an example, the internal structure of a black hole is revealed. Its phase equilibrium with the longitudinal vector field, describing dark matter on the periphery of a galaxy, determines the dependence of the velocity on the plateau of galaxy rotation curves on the mass of a black hole, located in the center of a galaxy.

LOCALIZATION OF MATTERS ON A NON-Z2-SYMMETRIC THICK BRANE

2010 ◽  
Vol 25 (07) ◽  
pp. 511-523
Author(s):  
JUN LIANG ◽  
YI-SHI DUAN
Keyword(s):  
Vector Field ◽  
Scalar Field ◽  
Yukawa Coupling ◽  
Spinor Field ◽  
Zero Mode ◽  
Parallel Transport ◽  
Type Coupling ◽  
Matter Fields

We study localization of various matter fields on a non-Z2-symmetric scalar thick brane in a pure geometric Weyl integrable manifold in which variations in the length of vectors during parallel transport are allowed and a geometric scalar field is involved in its formulation. It is shown that, for spin 0 scalar field, the massless zero mode can be normalized on the brane. Spin 1 vector field cannot be normalized on the brane. And there is no spinor field which can be trapped on the brane for the case of no Yukawa-type coupling. By introducing the appropriate Yukawa coupling, the left or right chiral fermionic zero mode can be localized on the brane.

Phenomenological approach to the viable nonmetric relativistic scalar 4-vector theory of gravitation

1995 ◽  
Vol 73 (3-4) ◽  
pp. 187-192 ◽  
Author(s):  
Alexander A. Vlasov
Keyword(s):  
Vector Field ◽  
Scalar Field ◽  
Gravitational Radiation ◽  
Phenomenological Approach ◽  
Gravitational Theory ◽  
Nonlinear Scalar Field ◽  
Minkowski Space Time ◽  
Vector Theory ◽  
Theory Of Gravitation ◽  
Relativistic Gravitational Theory

Contrary to the hypothesis that every viable theory of gravitation must be the metric one, this paper presents the example of nonmetric relativistic gravitational theory on the basis of Minkowski space-time, where the gravitation is described by a mixture of the nonlinear scalar field and the linear 4-vector field, compatible with all the known post-Newtonian gravitational tests, with tests on gravitational radiation from binary pulsar PSR 1913 + 16 and with the ordinary cosmological notions.

A note on generalized Robertson–Walker space-times

2016 ◽  
Vol 13 (06) ◽  
pp. 1650079 ◽  
Author(s):  
Carlo Alberto Mantica ◽  
Young Jin Suh ◽  
Uday Chand De
Keyword(s):  
Vector Field ◽  
Scalar Field ◽  
Perfect Fluid ◽  
Curvature Tensor ◽  
Weyl Tensor ◽  
Space Time ◽  
Stiff Matter ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Mass Less Scalar Field

A generalized Robertson–Walker (GRW) space-time is the generalization of the classical Robertson–Walker space-time. In the present paper, we show that a Ricci simple manifold with vanishing divergence of the conformal curvature tensor admits a proper concircular vector field and it is necessarily a GRW space-time. Further, we show that a stiff matter perfect fluid space-time or a mass-less scalar field with time-like gradient and with divergence-free Weyl tensor are GRW space-times.

scholarly journals Solutions of the second and fourth Painlevé equations, I

1997 ◽  
Vol 148 ◽  
pp. 151-198 ◽  
Author(s):  
Hiroshi Umemura ◽  
Humihiko Watanabe
Keyword(s):  
Vector Field ◽  
Differential Equations ◽  
Painlevé Equations ◽  
Necessary Condition ◽  
Hamiltonian Vector Field ◽  
Rigorous Proof ◽  
Painleve Equations ◽  
Algebraic Differential Equations ◽  
The Third ◽  
Principal Ideals

AbstractA rigorous proof of the irreducibility of the second and fourth Painlevé equations is given by applying Umemura’s theory on algebraic differential equations ([26], [27], [28]) to the two equations. The proof consists of two parts: to determine a necessary condition for the parameters of the existence of principal ideals invariant under the Hamiltonian vector field; to determine the principal invariant ideals for a parameter where the principal invariant ideals exist. Our method is released from complicated calculation, and applicable to the proof of the irreducibility of the third, fifth and sixth equation (e.g. [32]).

ASPECTS OF HADRONS AT FINITE BARYONIC DENSITY

2007 ◽  
Vol 16 (09) ◽  
pp. 2830-2833 ◽  
Author(s):  
FÁBIO L. BRAGHIN
Keyword(s):  
Vector Field ◽  
Scalar Field ◽  
Ground State ◽  
Sigma Model ◽  
Dynamical Symmetry ◽  
Linear Sigma Model ◽  
Baryonic Density ◽  
The Stability ◽  
Classical Vector ◽  
Symmetry Breakings

The linear sigma model at finite baryonic density with a massive classical vector field is investigated considering that all the bosonic fields develop non zero expected classical values, eventually corresponding to dynamical symmetry breakings. The densities involving baryons are calculated using the solutions of the Dirac equation coupled to the classical vector and scalar field. The stability and ground state conditions are analyzed with particular (variational-like) prescriptions. Some aspects of relevance for states containing anti-hadrons and also for the restoration of chiral symmetry are discussed.

scholarly journals On Calculation of the First Integrals for Three-dimensional ODE Systems

2019 ◽  
pp. 11-21
Author(s):  
A. V. Kavinov
Keyword(s):  
Vector Field ◽  
General Solution ◽  
Nonlinear Dynamical Systems ◽  
First Integral ◽  
First Integrals ◽  
Third Order ◽  
The Third ◽  
Ode System ◽  
Special Cases ◽  
Ode Systems

The search for solutions of nonlinear stationary systems of ordinary differential equations (ODE) is sometimes very complicated. It is not always possible to obtain a general solution in an analytical form. As a consequence, a qualitative theory of nonlinear dynamical systems has been developed. Its methods allow us to investigate the properties of solutions without finding a general solution. Numerical methods of investigation are also widely used.In the case when it is impossible to find an analytically general solution of the ODE system, sometimes, nevertheless, it is possible to find its first integral. There is a number of known results that make it possible to obtain the first integral for certain special cases.The article deals with the method for obtaining the first integrals of ODE systems of the third order, based on the fact of integrability of the involutive distribution.The method proposed in the paper allows us to obtain the first integral of a nonlinear ODE system of the third order in the case when a vector field, which generates an involutive distribution of dimension 2 together with the vector field of the right-hand side of a given ODE system, is known. In this case, the solution of a certain sequence of Cauchy problems allows us to construct a level surface of the function of the first integral containing the given point of the state space of the system. Using the method of least squares, in a number of cases it is possible to obtain an analytic expression for the first integral.The article gives examples of the method application to two ODE systems, namely to a simple nonlinear third-order system and to the Lorentz system with special parameter values. The article shows how the first integrals can be obtained analytically using the method developed for the two systems mentioned above.

scholarly journals Iterative Smoothing of Field Data in Spherical Meshes

2010 ◽  
Author(s):  
Luis Ibanez ◽  
B.t. thomas Yeo ◽  
Polina Golland
Keyword(s):  
Vector Field ◽  
Scalar Field ◽  
Input Data ◽  
Field Data ◽  
Source Code ◽  
Fundamental Principle ◽  
Mesh Smoothing ◽  
Output Data ◽  
Scientific Publications

This document describes a contribution to the Insight Toolkit intended to smooth the values of Field data associated with the nodes of a Spherical Mesh. The Mesh Smoothing filters contributed here do not modify the geometry or the topology of the Mesh. They act only upon the pixel data values associated with the nodes. Two filters are presented, one that smooths scalar field data, and a second one that smooths vector field data. This paper is accompanied with the source code, input data, parameters and output data that we used for validating the algorithm described in this paper. This adheres to the fundamental principle that scientific publications must facilitate reproducibility of the reported results.

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