Phase Volume

Phase Volume

 

the volume in phase space. For a mechanical system with N degrees of freedom, the elementary phase volume is equal to dpdq = dpldq1 . . . dpNdqN, where q1, . . .,qN are the generalized coordinates and p1, . . .,pN are the generalized momenta of the system. The phase volume of a finite phase region G is equal to the 2N-dimensional integral Gdpdq. If the system is described by Hamilton’s equations of motion, then the system’s phase volume remains constant when the system moves (Liouville’s theorem). This makes it possible to introduce normalized distribution functions in phase space.

References in periodicals archive ?
The total volume of emulsion, V is comprised of the dispersed phase volume, [V.sub.d] and the continuous phase volume, [V.sub.c].
[phi] is a phase volume number with the relation equation of [[phi].sub.L] + [[phi].sub.S] = 1, in which the subscripts L and S represent the liquid and solid phases, respectively, while i and k are the tensor coordinates.
where: y is ratio of removed part of the substance to its whole amount that was in the cake before washing, The value is in interval 0-1, Na is ratio of washing liquid volume to solid phase volume, this characterizes usage of washing liquid, [c.sub.0] is concentration of the scrubbed components in the bath, [c.sub.p] is the initial concentration of the scrubbed components in the solid phase (filtration cake), [C.sub.0] is dimensionless concentration of the scrubbed components in the bath.
The analysis of the XRD data involved fitting the diffraction peaks with a series of Lorentzians to extract lattice parameter, crystallite size, and phase volume.
Due to the fact that there were only two types of seepage fluids in the fractured rock pores, the water phase volume fraction [Y.sub.1] and sand phase volume fraction [Y.sub.2] met the following conditions:
The choice of methanol volume in the ultrasonic extraction process requires two aspects: on one hand, there is a need for sufficient methanol to facilitate the extraction of the OPPs from the wheat sample as much as possible; on the other hand, a suitable volume of methanol is required to better disperse the ionic liquid in the DLLME to obtain a suitable deposition phase volume for subsequent injection analysis.
A change of the conformation of hemoglobin hematoporphyrin (both cytoplasmic and membrane-bound) is may be interconnected with changes in the morphometric indicators of erythrocytes (erythrocyte surface area, phase height, phase volume, and hemoglobin distribution).
Here [phi] (dimensionless) denotes the phase volume fraction, [rho] (kg/[m.sup.3]) is the density, and u (m/s) is the velocity of each phase.
Because the absorption coefficient [epsilon]([[lambda].sub.UV]) is expected to depend on the ambient temperature and gas density, comparisons of estimated vapor phase volume fractions generated by the different injectors under different ambient conditions would be of questionable value.
Firm phase volume of earthworks 64 880 m3 road surface 2850 m2, EP collector 250 to 500 1550 m, EU collector 200 1510 m, collector aep 150f 240 m, 250f fire protection 1110 m.