energy integral

energy integral

[′en·ər·jē ′in·tə·grəl]
(mechanics)
A constant of integration resulting from integration of Newton's second law of motion in the case of a conservative force; equal to the sum of the kinetic energy of the particle and the potential energy of the force acting on it.
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The KED model universe incorporates an additive, [p.sub.2] = -[[rho].sub.2][c.sup.2]/3, to the equation of state that describes the total energy integral, often treated as a special case of 'quintessence'.
In the paper (Sapar, 1964) a number of analytical formulae, including for the universe with matter, radiation, and the kinetic energy integral in the flat space, were derived.
Summing up, in our model universe dark matter and dark energy have been replaced by a single and well understood physical parameter--the total energy integral in the space.
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the energy integral of the Brownian particle and dx = 1/N [[PI].sub.t] dx(t) is symbolically a product of Lebesgue measures dx(t) and N is a normalized constant.
Similar to (1.1) we consider the following energy integral:
Then we see that the above one-loop energy integral of the photon gives the mass-energy parameter [omega] of electron which gives the mass m of electron.
In this article, a higher-order system of dispersive evolution equations and the associated energy integral are used to study the energy balance across an undular bore.
The energy contained in a control volume of unit width above the interval [[x.sub.1], [x.sub.2]] is given by the energy integral E(h, u) associated with the shallow-water system (2).
In the next section we will derive a dispersive system of partial differential equations along with the corresponding energy integral. In Section 3, a finite difference method for solving the dispersive system is put forward.
If we prescribe a point charge (3D delta-function) then the energy integral will be infinite.
The importance of null Lagrangians is highlighted by of recent research in the calculus of variations (polyconvex energy integrals), nonlinear PDEs (compensated compactness), geometric function theory (quasiconformal deformations) and some areas of applied mathematics: nonlinear elasticity, material science and crystals (rank-one connections).
Features Package features include: direct import of complex parts from SolidWorks and other 3D CAD programmes; representation of self-consistent saturation effects in any soft magnetic material; interactive graphical utility Magwinder to build complex drive coils; MagView postprocessor capabilities which include high-quality 2D and 3D plots, interactive point and scan calculations and automatic force and energy integrals.
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