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Everything about Continuity equation
Equation describing the transport of some quantity
A continuity equation or transport equation is an equation that describes the transport of some quantity. It is particularly simple and powerful when applied to a conserved quantity, but it can be generalized to apply to any extensive quantity. Since mass, energy, momentum, electric charge and other natural quantities are conserved under their respective appropriate conditions, a variety of physical phenomena may be described using continuity equations. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Continuity equationA 5-minute orientation
- Skim a recent paper: Enhanced resolution of the continuity equation in explicit weakly compressible SPH simulations of incompressible free‐surface fluid flowsInfluential work since 2022
- Pick up a classic book: Elementary Flight Dynamics with an Introduction to Bifurcation and Continuation MethodsThe most-reprinted book on the subject
- Read the landmark paper: A new integral equation formalism for the polarizable continuum model: Theoretical background and applications to isotropic and anisotropic dielectricsCited 6,823 times
- Go sideways: Probability currentA closely related topic
- Go sideways: Charge conservationA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
A new integral equation formalism for the polarizable continuum model: Theoretical background and applications to isotropic and anisotropic dielectrics
An equation for continuous chaos
Continuity of solutions of a singular parabolic equation
FRAM—Nonlinear damping algorithms for the continuity equation
On the F2-layer continuity equation
Non-renormalized solutions to the continuity equation
Continuity Estimates for the Monge–Ampère Equation
A quantitative theory for the continuity equation
🆕 Influential since 2022
Enhanced resolution of the continuity equation in explicit weakly compressible SPH simulations of incompressible free‐surface fluid flows
Evaluation of accuracy for Bernardi equation in estimating heat generation rate for continuous and pulse-discharge protocols in LFP and NMC based Li-ion batteries
Continuity equation for the flow of Fisher information in wave scattering
Enhanced schemes for resolution of the continuity equation in projection-based SPH
Existence and continuity results for Kirchhoff parabolic equation with Caputo–Fabrizio operator
📚 Books worth reading
Elementary Flight Dynamics with an Introduction to Bifurcation and Continuation MethodsNandan K. Sinha, N. Ananthkrishnan · 2013
Solution of Ordinary Differential Equations by Continuous GroupsGeorge Emanuel · 2000- 📕Die Werke WiposWipo · 1915
An introduction to the Lie theory of one-parameter groupsCohen, Abraham · 1911
Continuous symmetries, Lie algebras, differential equations, and computer algebraW.-H Steeb · 1996
Introduction to numerical continuation methodsEugene L. Allgower, Kurt Georg · 1987
Continuous flows in the planeAnatole Beck · 1974
Problems of nonlinear deformationĖduard Ivanovich Grigoli͡uk, E.I. Grigolyuk · 1991
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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