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 ?
Increasing the paste phase volume will lead to the increase of the number micro-pores inside the mix's matrix, hence, increasing water absorption [7].
It minimizes the uncertainty in the rinsing phase volume in order to carry out the measurement, and it also prevents the repeated rinsing in order to separate the dye derivative component from the adsorbent phase.
In the two-phase model, S depends on the amorphous phase volume fraction [[phi].
Flow fields within the continuous phase are disrupted around dispersed droplets, and so the emulsion viscosity rises with increasing dispersed phase volume fraction.
The effect of the dispersed phase volume fraction ([phi]) on the DSD of aqueous PU dispersions is also examined to understand the fundamental characteristics that result from the high shear mixing.
X-ray video images, provide quantitative phase volume, phase density, and elemental composition data by phase, as well as dispersed solid phase and phase boundary detection.
It's possible to influence the rheological properties by modifying the length of the hyphae and their relative phase volume in the formulation.
which is none other than the function of the phase volume fraction in the annulus.
The phase volume ratio, [PHI], can be estimated from the triangular phase diagram by the tie line and lever rule (11), as shown in Fig.
1 contains more than 20,000 diagrams previously published in phase volumes produced as part of the ACerS-NIST Phase Equilibria Diagrams Program: Volumes I through XIV; Annuals 91, 92 and 93; High Tc Superconductors I & II; Zirconium & Zirconia Systems; and Electronic Ceramics.