An introductory example: the uniform static field

2021 ◽  
pp. 27-31
Author(s):  
Andrew M. Steane
Keyword(s):  
Static Field ◽  
Exact Calculation ◽  
Christoffel Symbols ◽  
Physical Effects ◽  
Curvature Tensors

This chapter discusses some physical effects related to two simple metrics: the RIndler metric and the uniform static field. The purpose is to illustrate the methods by applying them in an exact calculation which is not too taxing. The Christoffel symbols and curvature tensors are obtained, and some example geodesics are calculated. The force experienced by a fisherman fishing in the RIndler metric is calculated.

RELATIONS OF TWO TRANSVERSAL SUBMANIFOLDS AND GLOBAL MANIFOLD

2001 ◽  
Vol 16 (21) ◽  
pp. 3535-3551 ◽  
Author(s):  
GUO-HONG YANG ◽  
SHI-XIANG FENG ◽  
GUANG-JIONG NI ◽  
YI-SHI DUAN
Keyword(s):  
Tangent Vector ◽  
Second Fundamental Form ◽  
Momentum Tensor ◽  
Matter Field ◽  
The Other ◽  
Inner Product ◽  
Normal Vector ◽  
Riemann Geometry ◽  
Christoffel Symbols ◽  
Curvature Tensors

In Riemann geometry, the relations of two transversal submanifolds and global manifold are discussed without any concrete models. By replacing the normal vector of a submanifold with the tangent vector of another submanifold, the metric tensors, Christoffel symbols and curvature tensors of the three manifolds are connected at the intersection points of the two submanifolds. When the inner product of the two tangent vectors of submanifolds vanishes, some corollaries of these relations give the most important second fundamental form and Gauss–Codazzi equation in the conventional submanifold theory. As a special case, the global manifold which is Euclidean is considered. It is pointed out that, in order to obtain the nonzero energy–momentum tensor of matter field in a submanifold, there must be the contributions of the above inner product and the other submanifold. Generally speaking, a submanifold is closely related to the matter fields of the other submanifold and the two submanifolds affect each other through the above inner product.

Modeling Vibration-Induced Tire-Pavement Interaction Noise in the Mid-frequency Range

2020 ◽  
Author(s):  
Sterling McBride ◽  
Ricardo Burdisso ◽  
Corina Sandu
Keyword(s):  
Sound Intensity ◽  
Element Model ◽  
Dominant Frequency ◽  
Contact Forces ◽  
Surface Velocity ◽  
New Wave ◽  
Normal Surface ◽  
Radiated Noise ◽  
Physical Effects ◽  
Effects Of Rotation

ABSTRACT Tire-pavement interaction noise (TPIN) is one of the main sources of exterior noise produced by vehicles traveling at greater than 50 kph. The dominant frequency content is typically within 500–1500 Hz. Structural tire vibrations are among the principal TPIN mechanisms. In this work, the structure of the tire is modeled and a new wave propagation solution to find its response is proposed. Multiple physical effects are accounted for in the formulation. In an effort to analyze the effects of curvature, a flat plate and a cylindrical shell model are presented. Orthotropic and nonuniform structural properties along the tire's transversal direction are included to account for differences between its sidewalls and belt. Finally, the effects of rotation and inflation pressure are also included in the formulation. Modeled frequency response functions are analyzed and validated. In addition, a new frequency-domain formulation is presented for the computation of input tread pattern contact forces. Finally, the rolling tire's normal surface velocity response is coupled with a boundary element model to demonstrate the radiated noise at the leading and trailing edge locations. These results are then compared with experimental data measured with an on-board sound intensity system.

Orderly exact calculation of integrals of products of functions by the method of tenzor products of functionals

2019 ◽  
pp. 94-99
Author(s):  
Nurlan Temirgaliyev ◽  
◽  
Sabit Sarypbekovich Kudaibergenov ◽  
Nurlan Zhumabaevich Nauryzbayev ◽  
◽  
...  
Keyword(s):  
Exact Calculation

NUMERICAL STUDY OF DETONATION PROPAGATION IN VISCOUS TURBULENT FLOW IN A DUCT

2020 ◽  
Author(s):  
V. A. SABELNIKOV ◽  
◽  
V. V. VLASENKO ◽  
S. BAKHNE ◽  
S. S. MOLEV ◽  
...  
Keyword(s):  
Complex Geometry ◽  
Numerical Study ◽  
Navier Stokes ◽  
Detonation Waves ◽  
Detonation Propagation ◽  
Eddy Simulation ◽  
Detonation Structure ◽  
Classical Studies ◽  
Large Eddy ◽  
Physical Effects

Gasdynamics of detonation waves was widely studied within last hundred years - analytically, experimentally, and numerically. The majority of classical studies of the XX century were concentrated on inviscid aspects of detonation structure and propagation. There was a widespread opinion that detonation is such a fast phenomenon that viscous e¨ects should have insigni¦cant in§uence on its propagation. When the era of calculations based on the Reynolds-averaged Navier- Stokes (RANS) and large eddy simulation approaches came into effect, researchers pounced on practical problems with complex geometry and with the interaction of many physical effects. There is only a limited number of works studying the in§uence of viscosity on detonation propagation in supersonic §ows in ducts (i. e., in the presence of boundary layers).

Holomorphically projective mappings between generalized m-parabolic Kähler manifolds

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4865-4873 ◽  
Author(s):  
Milos Petrovic
Keyword(s):  
Linear Systems ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Covariant Derivatives ◽  
Linearly Independent ◽  
Non Linear ◽  
Non Linear Systems ◽  
Curvature Tensors ◽  
Derivatives Of

Generalized m-parabolic K?hler manifolds are defined and holomorphically projective mappings between such manifolds have been considered. Two non-linear systems of PDE?s in covariant derivatives of the first and second kind for the existence of such mappings are given. Also, relations between five linearly independent curvature tensors of generalized m-parabolic K?hler manifolds with respect to these mappings are examined.

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