Regularization of the stress-energy tensor for vector and scalar particles propagating in a general backgroud metric : Stephen L. Adler, Judy Lieberman, and Yee Jack Ng . The Institute for Advanced Study, Princeton, New Jersey 08540doi:10.1016/0003-4916(77)90253-6...
Stress is directed on the interior surface of the object. It can be directed either along the longitudinal axis or in all directions of the body. Is stress a vector or scalar? Stress is a vector quantity. Why is stress called a tensor? Stress is called a tensor because despite being a ...
Whereas pressure is a scalar, stress is a vector, as it must have direction as well as quantity. The symbol of stress is σ. When a force is loaded on a material, it will deform. Deformation is defined as work and involves energy. However, there is more than one type of stress, e...
That is, the notation for the stress field can be described in the form of a scalar (zero rank), vector (first rank) or a matrix (second rank). Tensors have special properties in that they must obey certain "rules" for transformation. Based on my experience, it is necessary...
withanddenoting the scalar and vector part of the quaternionqof unit norm. The inverse rotation ofqis given by the conjugation defined as. The rotation of a pointaroundbyto the pointis (2) A sequence of two consecutive Euler rotationsfollowed byassociated withandcan be expressed as a single ...
[ 24 ]. in four dimensions, the four point function of scalar operators of the stress-tensor multiplet for \({\mathcal {n}}=4\) theories was analysed in [ 8 , 25 ]. they found that using bootstrap constraint a particular operator spectrum is singled out. it was conjectured that ...
A number of dynamic variants of the modulated gradient model (MGM) for the sub-grid scale (SGS) stress tensor and the SGS scalar flux vector are developed and evaluated a posteriori in large eddy simulations of neutral and stably stratified turbulent channel flow. Two dynamic procedures are eval...
{\nu }F^2)\), wheref,Fare test functions on a globally hyperbolic Lorentzian manifoldMsuch that\(F\equiv 1\)on\(\textrm{supp}(f)\)and\(t^{\mu }\)is any smooth time-like vector field. This stress tensor bound essentially takes the form of a new kind ofquantum energy inequality(...
Force is a vector. It can be split between normal and shear forces across and along a plane as shown in Fig. 1.1. For the structures with a finite surface, the concept of stress is introduced where the force divided by the area is the stress. The normal stress is the normal force div...
Among many statistics, dispersion, which denotes how scattered or spread out a data group is, is an effective tool to quantify the amount of variability. However, dispersion measures are commonly only used for scalar and vector data, and it is not yet clear what robust scalar-valued measures ...