Solenoidal vector fieldIn vector calculus and differential equations, a divergence free vector field is a vector fieldv with divergence zero at all points in the field: ∇⋅v=0.{\displaystyle abla \cdot \mathbf {v} =0.} In electromagnetic theory, a divergence-free vector field is commonly called a solenoidal vector field, while in hydrodynamics it is commonly called an incompressible vector field, and in mathematical physics it is sometimes called an transverse vector field).
Scalar potentialIn mathematical physics, scalar potential describes the situation where the difference in the potential energies of an object in two different positions depends only on the positions, not upon the path taken by the object in traveling from one position to the other. It is a scalar field in three-space: a directionless value (scalar) that depends only on its location. A familiar example is potential energy due to gravity.
Vector fieldIn vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean spaceRn{\displaystyle \mathbb {R} ^{n}}. A vector field on a plane can be visualized as a collection of arrows with given magnitudes and directions, each attached to a point on the plane. Vector fields often have unit of measurement (for example, metres or kilometres per hour), forming a vector physical quantity.
GradientMultivariate derivative (mathematics) This article needs more citations. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: "Gradient" – news · newspapers · books · scholar · JSTOR (January 2018) (Learn how and when to remove this message) The gradient, represented by the blue arrows, denotes the direction of greatest change of a scalar function.
Curl (mathematics)Circulation density in a vector field Depiction of a two-dimensional vector field with a uniform curl.
DivergenceVector operator in vector calculus The divergence of different vector fields.Conservative vector fieldIn vector calculus, a conservative vector field is a vector field that is the gradient of some function. A conservative vector field has the property that its line integral is path independent; the choice of path between two points does not change the value of the line integral. Path independence of the line integral is equivalent to the vector field under the line integral being conservative.
Fourier transformMathematical transform that expresses a function of time as a function of frequencyThe Fourier transform applied to the waveform of a C majorpianochord (with logarithmic horizontal (frequency) axis). The first three peaks on the left correspond to the fundamental frequencies of the chord (C, E, G).
Hermann von HelmholtzGerman physicist and physiologist (1821–1894) Hermann von HelmholtzForMemRSBornHermann Ludwig Ferdinand Helmholtz(1821-08-31)31 August 1821Potsdam, Province of Brandenburg, Kingdom of Prussia, German ConfederationDied8 September 1894(1894-09-08) (aged 73)Charlottenburg, Kingdom of Prussia, German EmpireEducationMedizinisch-chirurgisches Friedrich-Wilhelm-Institut [de] (MD, 1842)Known for See list Studies in the conservation of energy Helmholtz classical theorem Helmholtz coil Helmholtz condition Helmholtz decomposition Helmholtz equation Helmholtz free energy Helmholtz free entropy Helmholtz layer Helmholtz minimum dissipation theorem Helmholtz motion Helmholtz pitch notation Helmholtz reciprocity Helmholtz resonance Helmholtz temperament Helmholtz's theorems Helmholtz–Kohlrausch effect Helmholtz–Smoluchowski equation Helmholtz–Ellis notation Helmholtz–Thévenin theorem Gibbs–Helmholtz equation Kelvin–Helmholtz instability Smith–Helmholtz invariant Kelvin–Helmholtz mechanism Young–Helmholtz theory Additive synthesis Efference copy Entoptic phenomenon Heat death paradox Hydrodynamic stability Keratometer Ophthalmoscopy Place theory Prism adaptationPure tone Unconscious inference Vortex ring Spouse Anna von Mohl (m. 1861)Children3RelativesAnna Augusta Von Helmholtz-Phelan (grand-niece)AwardsForMemRS (1860)Croonian Medal (1864)Matteucci Medal (1868)Copley Medal (1873)Pour le Mérite (1873)Faraday Lectureship Prize (1881)Albert Medal (1888)Scientific careerFieldsPhysicsPhysiologyWorkplaces University of Königsberg (1849–1855) University of Bonn (1855–1858) University of Heidelberg (1858–1871) University of Berlin (1871–1888) ThesisDe fabrica systematis nervosi evertebratorum (1842)Doctoral advisorJohannes Peter MüllerDoctoral studentsHeinrich HertzGabriel LippmannOtto LummerAlbert A. MichelsonMax PlanckMihajlo PupinFriedrich SchottkyArthur Gordon WebsterMax WienWilhelm WienOther notable studentsÉmile BoutrouxLoránd EötvösJohannes von KriesEdward NicholsHenry Augustus RowlandHans VaihingerWilhelm Wundt Signature Helmholtz's polyphonic siren, Hunterian Museum, Glasgow Hermann Ludwig Ferdinand von Helmholtz (31 August 1821 – 8 September 1894; "von" since 1883) was a German physicist and physician who made significant contributions in several scientific fields, particularly hydrodynamic stability.PhysicsPhysics is the scientific study of matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. It is one of the most fundamental scientific disciplines. A scientist who specializes in the field of physics is called a physicist. Physics is one of the oldest academic disciplines.
MathematicsMathematics is a field of knowledge concerned with abstract concepts such as numbers, geometric shapes, sets, functions, and probabilities. It uses logical reasoning and proof to study and establish their properties, often expressed as theorems, formulas, and equations. Mathematics is used to model and solve problems in science, engineering, technology, economics, and everyday life.
SmoothnessIn mathematical analysis, the smoothness describes the number of times a function can be differentiated without producing discontinuities. The smoothness, or differentiability class, is an integer k{\displaystyle k} such that a function has all derivatives up to order k{\displaystyle k}, and such that all of these derivatives are continuous. One says that such a function has class Ck{\displaystyle C^{k}}.*As an Amazon Associate I earn from qualifying purchases.