heat equation - translation to russian
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heat equation - translation to russian

PARTIAL DIFFERENTIAL EQUATION FOR DISTRIBUTION OF HEAT IN A GIVEN REGION OVER TIME
Particle diffusion; Heat Diffusion Equation; Heat Diffusion; Heat Conduction Equation; Heat diffusion; Heat flow equation; Solving the heat equation using Fourier series; Applications of the heat equation; Stochastic heat equation
  • Depicted is a numerical solution of the non-homogeneous heat equation. The equation has been solved with 0 initial and boundary conditions and a source term representing a stove top burner.
  • The behavior of temperature when the sides of a 1D rod are at fixed temperatures (in this case, 0.8 and 0 with initial Gaussian distribution). The temperature approaches a linear function because that is the stable solution of the equation: wherever temperature has a nonzero second spatial derivative, the time derivative is nonzero as well.

heat equation         
тепловой баланс
heat conduction equation         
уравнение теплопроводности
heat conduction equation         

строительное дело

уравнение теплопроводности

Definition

Heat
·noun Sexual excitement in animals.
II. Heat ·noun Fermentation.
III. Heat ·noun Animation, as in discourse; ardor; fervency.
IV. Heat ·noun Agitation of mind; inflammation or excitement; exasperation.
V. Heat ·Impf & ·p.p. Heated; as, the iron though heat red-hot.
VI. Heat ·vt To excite or make hot by action or emotion; to make feverish.
VII. Heat ·noun Utmost violence; rage; vehemence; as, the heat of battle or party.
VIII. Heat ·vt To excite ardor in; to rouse to action; to excite to excess; to inflame, as the passions.
IX. Heat ·vt To make hot; to communicate heat to, or cause to grow warm; as, to heat an oven or furnace, an iron, or the like.
X. Heat ·noun A single complete operation of heating, as at a forge or in a furnace; as, to make a horseshoe in a certain number of heats.
XI. Heat ·vi To grow warm or hot by the action of fire or friction, ·etc., or the communication of heat; as, the iron or the water heats slowly.
XII. Heat ·vi To grow warm or hot by fermentation, or the development of heat by chemical action; as, green hay heats in a mow, and manure in the dunghill.
XIII. Heat ·noun A violent action unintermitted; a single effort; a single course in a race that consists of two or more courses; as, he won two heats out of three.
XIV. Heat ·noun High temperature, as distinguished from low temperature, or cold; as, the heat of summer and the cold of winter; heat of the skin or body in fever, ·etc.
XV. Heat ·noun The sensation caused by the force or influence of heat when excessive, or above that which is normal to the human body; the bodily feeling experienced on exposure to fire, the sun's rays, ·etc.; the reverse of cold.
XVI. Heat ·noun Indication of high temperature; appearance, condition, or color of a body, as indicating its temperature; redness; high color; flush; degree of temperature to which something is heated, as indicated by appearance, condition, or otherwise.
XVII. Heat ·noun A force in nature which is recognized in various effects, but especially in the phenomena of fusion and evaporation, and which, as manifested in fire, the sun's rays, mechanical action, chemical combination, ·etc., becomes directly known to us through the sense of feeling. In its nature heat is a mode if motion, being in general a form of molecular disturbance or vibration. It was formerly supposed to be a subtile, imponderable fluid, to which was given the name caloric.

Wikipedia

Heat equation

In mathematics and physics, the heat equation is a certain partial differential equation. Solutions of the heat equation are sometimes known as caloric functions. The theory of the heat equation was first developed by Joseph Fourier in 1822 for the purpose of modeling how a quantity such as heat diffuses through a given region.

As the prototypical parabolic partial differential equation, the heat equation is among the most widely studied topics in pure mathematics, and its analysis is regarded as fundamental to the broader field of partial differential equations. The heat equation can also be considered on Riemannian manifolds, leading to many geometric applications. Following work of Subbaramiah Minakshisundaram and Åke Pleijel, the heat equation is closely related with spectral geometry. A seminal nonlinear variant of the heat equation was introduced to differential geometry by James Eells and Joseph Sampson in 1964, inspiring the introduction of the Ricci flow by Richard Hamilton in 1982 and culminating in the proof of the Poincaré conjecture by Grigori Perelman in 2003. Certain solutions of the heat equation known as heat kernels provide subtle information about the region on which they are defined, as exemplified through their application to the Atiyah–Singer index theorem.

The heat equation, along with variants thereof, is also important in many fields of science and applied mathematics. In probability theory, the heat equation is connected with the study of random walks and Brownian motion via the Fokker–Planck equation. The Black–Scholes equation of financial mathematics is a small variant of the heat equation, and the Schrödinger equation of quantum mechanics can be regarded as a heat equation in imaginary time. In image analysis, the heat equation is sometimes used to resolve pixelation and to identify edges. Following Robert Richtmyer and John von Neumann's introduction of "artificial viscosity" methods, solutions of heat equations have been useful in the mathematical formulation of hydrodynamical shocks. Solutions of the heat equation have also been given much attention in the numerical analysis literature, beginning in the 1950s with work of Jim Douglas, D.W. Peaceman, and Henry Rachford Jr.

What is the Russian for heat equation? Translation of &#39heat equation&#39 to Russian