scholarly journals The scaling equation of state of the three-dimensional O(N) universality class:

2005 ◽  
Vol 140 ◽  
pp. 808-810 ◽  
Author(s):  
Agostino Butti ◽  
Francesco Parisen Toldin ◽  
Andrea Pelissetto ◽  
Ettore Vicari
Keyword(s):  
Equation Of State ◽  
Three Dimensional ◽  
Universality Class ◽  
Scaling Equation

scholarly journals The scaling equation of state of the 3-D O(4) universality class

2003 ◽  
Vol 2003 (07) ◽  
pp. 029-029 ◽  
Author(s):  
Francesco Parisen Toldin ◽  
Andrea Pelissetto ◽  
Ettore Vicari
Keyword(s):  
Equation Of State ◽  
Universality Class ◽  
Scaling Equation

scholarly journals Critical exponents and equation of state of the three-dimensional Heisenberg universality class

2002 ◽  
Vol 65 (14) ◽  
Author(s):  
Massimo Campostrini ◽  
Martin Hasenbusch ◽  
Andrea Pelissetto ◽  
Paolo Rossi ◽  
Ettore Vicari
Keyword(s):  
Equation Of State ◽  
Critical Exponents ◽  
Three Dimensional ◽  
Universality Class

Analysis of Single- and Two-Phase Flows in Turbopump Inducers

1967 ◽  
Vol 89 (4) ◽  
pp. 577-586 ◽  
Author(s):  
P. Cooper
Keyword(s):  
Equation Of State ◽  
Flow Field ◽  
Thermal Effects ◽  
Single Phase ◽  
Fluid Pressure ◽  
Three Dimensional ◽  
Pressure Rise ◽  
Recent Theory ◽  
Two Phase ◽  
Overall Efficiency

A model is developed for analytically determining pump inducer performance in both the single-phase and cavitating flow regimes. An equation of state for vaporizing flow is used in an approximate, three-dimensional analysis of the flow field. The method accounts for losses and yields internal distributions of fluid pressure, velocity, and density together with the resulting overall efficiency and pressure rise. The results of calculated performance of two sample inducers are presented. Comparison with recent theory for fluid thermal effects on suction head requirements is made with the aid of a resulting dimensionless vaporization parameter.

A nonparametric scaling equation of state for fluids with inclusion of asymmetry

2009 ◽  
Vol 109 (2) ◽  
pp. 262-268 ◽  
Author(s):  
P. P. Bezverkhiĭ ◽  
V. G. Martynets ◽  
É. V. Matizen
Keyword(s):  
Equation Of State ◽  
Scaling Equation

scholarly journals Critical flow and dissipation in a quasi–one-dimensional superfluid

2015 ◽  
Vol 1 (4) ◽  
pp. e1400222 ◽  
Author(s):  
Pierre-François Duc ◽  
Michel Savard ◽  
Matei Petrescu ◽  
Bernd Rosenow ◽  
Adrian Del Maestro ◽  
...  
Keyword(s):  
Power Law ◽  
Capillary Flow ◽  
Three Dimensional ◽  
Universality Class ◽  
Superfluid State ◽  
One Dimensional ◽  
Flow Experiment ◽  
20 Nm ◽  
Bulk Behavior ◽  
Superfluid Velocity

In one of the most celebrated examples of the theory of universal critical phenomena, the phase transition to the superfluid state of 4He belongs to the same three-dimensional (3D) O(2) universality class as the onset of ferromagnetism in a lattice of classical spins with XY symmetry. Below the transition, the superfluid density ρs and superfluid velocity vs increase as a power law of temperature described by a universal critical exponent that is constrained to be identical by scale invariance. As the dimensionality is reduced toward 1D, it is expected that enhanced thermal and quantum fluctuations preclude long-range order, thereby inhibiting superfluidity. We have measured the flow rate of liquid helium and deduced its superfluid velocity in a capillary flow experiment occurring in single 30-nm-long nanopores with radii ranging down from 20 to 3 nm. As the pore size is reduced toward the 1D limit, we observe the following: (i) a suppression of the pressure dependence of the superfluid velocity; (ii) a temperature dependence of vs that surprisingly can be well-fitted by a power law with a single exponent over a broad range of temperatures; and (iii) decreasing critical velocities as a function of decreasing radius for channel sizes below R ≃ 20 nm, in stark contrast with what is observed in micrometer-sized channels. We interpret these deviations from bulk behavior as signaling the crossover to a quasi-1D state, whereby the size of a critical topological defect is cut off by the channel radius.

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