Phase line

Abstract: The purpose of this paper is to clarify the relationship between the isolated zero points in modulus distribution and the least-squares phase estimation from the phase difference. The concepts of phase and phase difference are reaffirmed. In addition, a necessary condition that makes the least-squares phase estimation feasible is derived by applying the concept of complete observability in estimation theory to the measurement of the phase difference. The occurrence of isolated zero points causes the conventional least-squares phase estimation to fail because the phase difference defined by this concept does not satisfy the necessary condition when isolated zero points occur. This condition also generates a new type of least-squares phase estimation that is feasible for phase retrieval even if zero points exist. One algorithm for realizing this new type of least-squares phase estimation is proposed, and its effectiveness is verified by using computer simulations. Two types of phase unwrapping are also presented: one is the exponential function type; the other results from the proposed least-squares phase-estimation algorithm.

Abstract: The dielectric and thermal properties of a typical antiferroelectric (AFE) material are investigated by minimising numerically the free energy as given by the Kittel model of AFEs. The phase line of second-order phase transitions in the phase diagram is shown to change to a first-order line at the tricritical point T3cp, E3cp. The static dielectric susceptibility and the electrocaloric (EC) effect are calculated as a function of temperature and the applied electric field E. It is found that in a given range of electric fields and temperatures the EC effect has negative values but generally becomes positive above the AFE ordering temperature T0. The dielectric susceptibility shows characteristic peaks at the phase transitions between the field-induced polar and the AFE antipolar phase, and diverges at the tricritical point. We present experimental results for a negative EC effect, which have been obtained by direct EC measurements in PbZrO3 ceramics, and agree qualitatively with the above model.

Abstract: The most general spin model with nearest-neighbour interactions invariant under a global Zp symmetry in two dimensions is considered. Dual transformations are discussed, and the subset of self-dual models is characterised. The phase diagrams for p>or=5 are particularly rich, containing first-order, second-order and infinite-order phase transitions. In particular, the existence of a massless phase similar to the low-temperature phase of the XY model is established.

Abstract: Phase diagrams of binary fluid mixtures have been calculated from the Carnahan–Starling–Redlich–Kwong equation of state in connection with standard quadratic mixing rules. The phase diagrams were classified according to the system of van Konynenburg and Scott and then used to construct global phase diagrams showing the extent of the various phase diagram classes in the space of the parameters of the equation of state. For molecules of equal size, the global phase diagram is rather similar to that of the Redlich–Kwong or the van der Waals equation. For molecules of different sizes, however, a new tricritical line appears. Such a behavior is observed for cubic equations of state only if nonadditive covolumes are assumed. Along this new tricritical line, some unusual phase diagrams involving four‐phase states and high‐density instabilities can be found. The influence of molecular size ratios on the global phase diagrams and the relationship of the equation of state of this work to the ternary symmetric lattice gas and the van der Waals lattice gas are discussed.