Mathematical & Computational Physics
6 terms
Genetic Algorithms
Mathematical & Computational Physics
Stochastic Heuristic Optimization
A search heuristic optimization method inspired by natural biological evolution that iteratively evolves candidate solutions toward optimal physics configurations.
Evolutionary Operators: Selection, Crossover, Mutation
Gradient
Mathematical & Computational Physics
[Scalar Field Unit] / m
A vector operator that points in the direction of the greatest rate of increase of a scalar field, with magnitude equal to that maximum rate of change.
∇f = (∂f/∂x) î + (∂f/∂y) ĵ + (∂f/∂z) k̂
Gradient Descent
Mathematical & Computational Physics
Iterative Optimization Method
An iterative first-order optimization algorithm for finding local minima of a differentiable scalar objective function by taking steps proportional to the negative gradient.
x_(k+1) = x_k - α ∇f(x_k)
Green's Function
Mathematical & Computational Physics
Impulse Response Function
An impulse response function used to solve inhomogeneous linear differential equations subject to specified boundary conditions.
L G(x, x') = δ(x - x'), y(x) = ∫ G(x, x') f(x') dx'
Green's Theorem
Mathematical & Computational Physics
2D Vector Integral Theorem
A 2D vector calculus theorem relating a line integral around a simple closed curve C to a double area integral over the enclosed plane region D.
∮_C (L dx + M dy) = ∬_D ((∂M/∂x) - (∂L/∂y)) dx dy
Group Theory
Mathematical & Computational Physics
Symmetry Groups (SO(3), SU(2), SU(3))
The mathematical study of groups and algebraic symmetry structures.
Group Axioms: Closure, Associativity, Identity, Inverse