37,322 research outputs found
Signal conditioner for potentiometer type transducers
Low cost method is described for signal conditioning of pot-type transducers utilizing printed circuitry. Conditioner fits into standard rack, accommodates 56 channels, and can be operated by one attendant
Phase Transitions in "Small" systems
Traditionally, phase transitions are defined in the thermodynamic limit only.
We discuss how phase transitions of first order (with phase separation and
surface tension), continuous transitions and (multi)-critical points can be
seen and classified for small systems. Boltzmann defines the entropy as the
logarithm of the area W(E,N)=e^S(E,N) of the surface in the mechanical N-body
phase space at total energy E. The topology of the curvature determinant D(E,N)
of S(E,N) allows the classification of phase transitions without taking the
thermodynamic limit. The first calculation of the entire entropy surface S(E,N)
for the diluted Potts model (ordinary (q=3)-Potts model plus vacancies) on a
50*50 square lattice is shown. The regions in {E,N} where D>0 correspond to
pure phases, ordered resp. disordered, and D<0 represent transitions of first
order with phase separation and ``surface tension''. These regions are bordered
by a line with D=0. A line of continuous transitions starts at the critical
point of the ordinary (q=3)-Potts model and runs down to a branching point P_m.
Along this line \nabla D vanishes in the direction of the eigenvector v_1 of D
with the largest eigen-value \lambda_1\approx 0. It characterizes a maximum of
the largest eigenvalue \lambda_1. This corresponds to a critical line where the
transition is continuous and the surface tension disappears. Here the
neighboring phases are indistinguishable. The region where two or more lines
with D=0 cross is the region of the (multi)-critical point. The micro-canonical
ensemble allows to put these phenomena entirely on the level of mechanics.Comment: 21 pages,Latex, 12 eps figure
Phase Transitions in "Small" Systems - A Challenge for Thermodynamics
Traditionally, phase transitions are defined in the thermodynamic limit only.
We propose a new formulation of equilibrium thermo-dynamics that is based
entirely on mechanics and reflects just the {\em geometry and topology} of the
N-body phase-space as function of the conserved quantities, energy, particle
number and others. This allows to define thermo-statistics {\em without the use
of the thermodynamic limit}, to apply it to ``Small'' systems as well and to
define phase transitions unambiguously also there. ``Small'' systems are
systems where the linear dimension is of the characteristic range of the
interaction between the particles. Also astrophysical systems are ``Small'' in
this sense. Boltzmann defines the entropy as the logarithm of the area
of the surface in the mechanical N-body phase space at
total energy E. The topology of S(E,N) or more precisely, of the curvature
determinant allows the classification of phase
transitions {\em without taking the thermodynamic limit}. The topology gives
further a simple and transparent definition of the {\em order parameter.}
Attention: Boltzmann's entropy S(E) as defined here is different from the
information entropy and can even be non-extensive and convex.Comment: 8 pages, 4 figures, Invited paper for CRIS200
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