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Sample deformation mechanism map for a hypothetical material. Here there are three main regions: plasticity, power law creep, and diffusional flow. A deformation mechanism map is a way of representing the dominant deformation mechanism in a material loaded under a given set of conditions. The technique is applicable to all crystalline materials ...
The explicit form of a covariant transformation is best introduced with the transformation properties of the derivative of a function. Consider a scalar function f (like the temperature at a location in a space) defined on a set of points p, identifiable in a given coordinate system , =,, … (such a collection is called a manifold).
A plot of Lorenz' strange attractor for values ρ=28, σ = 10, β = 8/3. The butterfly effect or sensitive dependence on initial conditions is the property of a dynamical system that, starting from any of various arbitrarily close alternative initial conditions on the attractor, the iterated points will become arbitrarily spread out from each other.
A more modern interpretation of the physical content of the original principle of general covariance is that the Lie group GL 4 (R) is a fundamental "external" symmetry of the world. Other symmetries, including "internal" symmetries based on compact groups , now play a major role in fundamental physical theories.
Various forms of metamorphism exist, including regional, contact, hydrothermal, shock, and dynamic metamorphism. These differ in the characteristic temperatures, pressures, and rate at which they take place and in the extent to which reactive fluids are involved.
Energy transformation, also known as energy conversion, is the process of changing energy from one form to another. [1] In physics , energy is a quantity that provides the capacity to perform work (e.g. lifting an object) or provides heat .
Phase transitions (phase changes) that help describe polymorphism include polymorphic transitions as well as melting and vaporization transitions. According to IUPAC, a polymorphic transition is "A reversible transition of a solid crystalline phase at a certain temperature and pressure (the inversion point) to another phase of the same chemical composition with a different crystal structure."
Sinusoids are an important type of periodic function, because realistic signals are often modeled as the summation of many sinusoids of different frequencies and different amplitudes (for example, with a Fourier series or transform). Understanding what aliasing does to the individual sinusoids is useful in understanding what happens to their sum.