Mathematics
The mathematics physics is written in: 72 concepts — operators, transforms, equations and theorems behind the laws.
All concepts →Analysis · 22
exponential growth 23A process where a quantity increases at a rate proportional to its current value.
power law 12A mathematical relationship where one quantity varies as a power of another, often used to describe spectra.
uniform convergence 11Uniform convergence is a mode of convergence where the rate of convergence is independent of the point.
logarithm 7A mathematical function that is the inverse of exponentiation, used here to linearize brightness-distance relations.
derivative 6A derivative measures the rate at which a function changes with respect to a variable.
Fourier series 5A Fourier series is a mathematical expansion of periodic functions into a sum of sine and cosine waves.
limit 4A limit is the value that a function or sequence approaches as the input or index approaches some point.
cosineA trigonometric function, the complement of sine, describing a smooth periodic oscillation.
integralAn integral is a mathematical object that generalizes the concept of area under a curve.
sinesine — from formula anatomy
Algebra and operators · 16
group theory 28Symmetry analysis used to classify magnetic order and altermagnetic spin-splitting.
commutator 25An operator measuring the non-commutativity of two quantum operators, here of a scalar field.
group 15A group is a mathematical structure defined by a set and an operation satisfying closure, associativity, identity, and invertibility.
tensor 12A tensor is a mathematical object that generalizes scalars, vectors, and matrices to higher dimensions.
elliptic curve 11An elliptic curve is a smooth, projective algebraic curve of genus one with a specified base point.
ring 10A ring is an algebraic structure with two binary operations satisfying certain axioms.
zeta function 6The zeta function is a complex function whose zeros are connected to the distribution of prime numbers.
modular form 5A modular form is a complex analytic function that transforms in a specific way under the action of a discrete group.
category 4A category is a mathematical structure consisting of objects and morphisms that relate them.
Lie groupA Lie group is a mathematical group that is also a smooth manifold with continuous symmetry operations.
eigenvalueAn eigenvalue is a scalar associated with a linear transformation that satisfies a specific equation.
Spaces and geometry · 10
topology 49Topology is a mathematical study of properties preserved under continuous deformations like knots and surfaces.
Hilbert space 32A Hilbert space is a complete vector space with an inner product, used in quantum mechanics to describe states.
homotopy 27Homotopy is a mathematical concept classifying continuous deformations of shapes, applied to material elasticity and quantum fields.
symplectic geometry 26Symplectic geometry is a mathematical framework describing Hamiltonian dynamics and phase space structures in physics.
fractal 17A fractal is a geometric shape exhibiting self-similarity at various scales, often found in natural and cosmological structures.
knots 14A knot is a closed curve in space that cannot be untangled without cutting, often studied in topology and physics.
manifold 12A manifold is a mathematical space that locally resembles Euclidean space near each point.
differential form 10A differential form is a mathematical object used to express integration over manifolds and describe physical quantities like flux.
Banach space 5A Banach space is a complete normed vector space that allows infinite-dimensional averaging operations.
Randomness · 7
maximum likelihood 39A statistical method for estimating parameters by maximizing the likelihood function.
Markov chain 24A Markov chain is a stochastic process where future states depend only on the present state, not on past events.
Gaussian distribution 23A probability distribution characterized by a bell-shaped curve, often used to model random fluctuations.
random variable 15A variable whose possible values are numerical outcomes of a random phenomenon.
covariance matrix 9A covariance matrix is a matrix that describes the variance and covariance of multiple variables.
random matrix 7A random matrix is a matrix with entries drawn from probability distributions, used to model complex systems and spectra.
Foundations and computation · 4
functional analysis 20Functional analysis is the study of vector spaces and operators, often involving infinite-dimensional spaces and averaging processes.
hubbard model 12A mathematical model describing how electrons hop between lattice sites and repel each other.
axiom of choice 7The axiom of choice is a mathematical principle asserting that from any collection of non-empty sets, one can select an element from each set.
Turing machine 4A Turing machine is an abstract computational model that manipulates symbols on a tape.
Other · 13
ENSO 222A coupled ocean-atmosphere phenomenon in the tropical Pacific characterized by irregular sea surface temperature and pressure variations.
Indian Ocean Dipole 45A coupled ocean-atmosphere mode in the tropical Indian Ocean with opposing sea surface temperature anomalies in east and west.
annual cycle 32The yearly periodic variation in a climate variable, often driven by Earth's orbital position.
koopman operator 27A linear operator acting on observable functions, advancing them along the flow of a dynamical system.
rmse 25Root mean square error, a metric measuring the average magnitude of prediction errors.
rossby wave 17A large-scale planetary wave whose restoring force is the variation of Coriolis parameter with latitude.
Hurst exponent 8A dimensionless measure of long-term memory and self-similarity in a time series, indicating persistence or anti-persistence.
ornstein uhlenbeck process 8A stationary Gaussian process defined by a linear stochastic differential equation with mean-reverting drift.
rotation number 8A measure of the average rotation angle per iteration of a circle map.