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 ?
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.
These methods are relied on the identification of attractors VSOCH in phase volume for one cluster and for another.
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].
vii) Robustness of the method: by introducing small changes in the mobile phase composition, development distance, mobile phase volume, and duration of chamber saturation, the effects on the results were examined.
The influences of effective parameters such as salt (type and amount), water-miscible organic solvent, phase volume, equilibration time, centrifugation time and pH of sample solution were all studied and optimized.
The pressures observed upon filling the sample chamber, then discharging the displaced gas into a second empty chamber allow computation of the sample solid phase volume.
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.
The obtained results can be used for investigating of the measurement of solid phase volume flow transporting by fluid.
d*] is the average disperse phase volume conditioned to the presence of the disperse phase centered at (x, t) and the integration surface, [S.
In the two-phase model, S depends on the amorphous phase volume fraction [[phi].
An authentication system using a correlator that correlates an input with a reference wherein at least one of the input and reference comprises a phase volume mask having structures, preferably points, that are each less than about six microns in size and can have an aspect ratio (AR) greater than 1:1 so as to produce a phase encoded random pattern having millions of combinations in a mask that is as small as one square millimeter.
Flow fields within the continuous phase are disrupted around dispersed droplets, and so the emulsion viscosity rises with increasing dispersed phase volume fraction.