Tensors

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Data Analysis Biaxial Tensile Tests Different stress and strain definitions have been used to study the biomechanics of soft tissue [24]. The 2nd Piola-Kirchhoff stress and Green strain definitions have been employed in this study, which are described briefly in the following. The Green strain tensor is defined as E=1/2(F^T F-1), where F is the gradient deformation tensor. For the case of in-plane biaxial stretching in directions 1 and 2, the Green strain in these directions can be written as E_i=(λ_i^2-1)/2,=(〖〖(L〗_i/L_i0)〗^2-1)/2,i=1,2, with λi (i=1, 2, 3) the stretch values in the deformed equilibrium configuration and L_i and L_i0 the length between gauge marks in the deformed and initial configurations, respectively. The 2nd-Piola Kirchhoff stress tensor, denoted by S, is a symmetric tensor relating force to areas in the reference configuration. By assuming the specimens as rectangular plates with uniform thicknesses subjected to axial loads on their edges and with no shear stresses, the stresses in directions 1 and 2 are given by S_1=F_11/(A_1^0 λ_1 )=F_11/(A_1^0 √(2E_1+1)),〖 and S〗_2=F_22/(A_2^0 λ_2 )=F_22/(A_2^0 √(2E_2+1)), Eq. 3 where A_1^0 and A_2^0 are the initial areas, and F11 and F22 are…

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2. In “Remaing Yamato, Remaking Japan: Space Battleship Yamato and SF Anime” by Baryon Tensor Posadas, I am going to focus on the fetishization of anime and Techno-Orientalism characterized in the article. The transition from non-national to national qualities of anime in the age of globalization generated significant tension. Initially, when Japanese anime was imported into foreign markets from 1970s to 1980s, the ethnic quality was perceived as “too Japanese” to the subject – the Western or…

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the fluid temperature, is the nanoparticle volume fraction, is the Brownian diffusion coefficient, is the thermophoretic diffusion coefficient, is the specific heat of the nanoparticle material, is the fluid thermal diffusivity, is the fluid temperature at the initial state , is the velocity vector components in the and directions and is the time. The overall density of the nanofluid is given by [22] . …

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includes a field equation for gravity, which consists of three terms: two tensors that represent space-time and the energy-momentum tensor. The energy momentum tensor represents the matter and energy in the universe which bends space-time to produce gravity (lecture 1). His equation is seen in Figure 1. Figure 1 On the right side of the equation is the matter and energy tensor and, on the left, are the two space-time terms (lecture 1). Despite the incredible paradigm shift this equation and…

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the electrically conducting fluids. Plasmas, salt water, liquid metals and electrolytes are its examples. The equations, which define MHD are a combination of the Navier-Stokes equations of fluid dynamics and Maxwell's calculations of electromagnetism. 2.9 Continuity equation In physics, a continuity equation is an equation that defines the passage of some quantity. Since mass, energy, momentum, electric charge and other natural quantities are conserved under their respective appropriate…

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A “field” associates a physical quantity with a position. It may be time dependent. For example, T(r ⃗,t ) can represent the spatial and time-dependent temperature and ρ(r ⃗,t ) the density. These are examples of scalar valued fields. On the other hand, force or flux are examples of vector valued fields. Furthermore, stress is an example of a rank-two tensor field. Material Point notion If we consider a body with volume ”V” which separates parts of a physical space with its surface “A”, the…

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Positron emission tomography (PET): is an anatomically based measurement that utilizes small radioactive tracers that are able to identify and determine glucose and metabolic levels within the organs of the body. This type of tomography could be used in a concussion assessment to determine the metabolic activities and glucose levels of the brain, as these levels are important and often become altered following a concussion. Functional magnetic resonance imaging (fMRI): is an anatomically…

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Head Trauma has recently become a great concern in the medical field and especially encircling the medical field with ties to sports. Concussions have become an injury that the medical world has become very aware of and very cautious of because of the effects of them. A concussion is “a traumatic brain injury caused by a bump, blow or jolt to the head…damaging the brain cells and creating a chemical change in the brain” (United States Department of Health, 2015). A study, published in the Indian…

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quadrangular in shape and has a broad origin at the lateral surface of the ilium posterior to the linea glutea posterior, and along the dorsal surface of lower sacrum and the lateral surface of the coccyx to the external surface of the sacrotuberous ligament. There is also attachment to fascia overlying the gluteal medius muscle and between the ilium and sacrum, to fascia covering the erector spinae muscle. It covers diagonally downwards and laterally towards the femur. The upper two thirds…

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Some forms are common to males, some forms are common to females, and some are common to both, male and female. This new study was by researchers led by Daphna Joel. Joel tried to be as comprehensive as possible. Using sets of brain images, the research group measured the volume of gray matter and white matter in the brain of over 1400 people. They also studied data from images of diffusion tensors. The data from diffusion tensor imaging showed how areas of white matter extend throughout the…

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