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An object being pushed together, such as a crumpled sponge, is subject to compressive stress and may undergo shortening. [1] [2] The greater the force and the smaller the cross-sectional area of the body on which it acts, the greater the stress. Stress has dimension of force per area, with SI units of newtons per square meter (N/m 2) or pascal ...
Its components are known as Beltrami stress functions. is the Levi-Civita pseudotensor, with all values equal to zero except those in which the indices are not repeated. For a set of non-repeating indices the component value will be +1 for even permutations of the indices, and -1 for odd permutations.
Mathematical physics is concerned with "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". 1. List of mathematical topics in classical mechanics; List of mathematical topics in quantum theory
The force's vector components are also three in number. Thus, 3 × 3, or 9 components are required to describe the stress at this cube-shaped infinitesimal segment. Within the bounds of this solid is a whole mass of varying stress quantities, each requiring 9 quantities to describe. Thus, a second-order tensor is needed.
Lefschetz theorem on (1,1)-classes (algebraic geometry) Local invariant cycle theorem (algebraic geometry) Malgrange–Zerner theorem (complex analysis) Newlander–Niremberg theorem (differential geometry) Remmert–Stein theorem (complex analysis) Riemann singularity theorem (algebraic geometry) Skoda–El Mir theorem (complex geometry)
Invariant (physics) Momentum. Cauchy momentum equation; Energy. Conservation of energy and the First law of thermodynamics; Conservative system; Conserved quantity. Some kinds of helicity are conserved in dissipationless limit: hydrodynamical helicity, magnetic helicity, cross-helicity. Principle of mutability; Conservation law of the Stress ...
The following is a list of notable unsolved problems grouped into broad areas of physics. [1]Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result.
The stress due to shear force is maximum along the neutral axis of the beam (when the width of the beam, t, is constant along the cross section of the beam; otherwise an integral involving the first moment and the beam's width needs to be evaluated for the particular cross section), and the maximum tensile stress is at either the top or bottom ...