On the transition from ferromagnetism to antiferromagnetism on twofold Cayley tree

A fixed-point conversion theorem which shows the transition from ferromagnetism to antiferromagnetism on twofold Cayley tree is proved. The ferromagnetic and antiferromagnetic maps are shown to be related by an involution and in zero field the stable fixed points of the ferromagnetic map are converted to a stable two-cycle of the antiferromagnetic map. A reduced one-dimensional analysis in zero field yields precisely the same results. © 1992 Società Italiana di Fisica

On the temporal stability of steady-state quasi-1D bubbly cavitating nozzle flow solutions

Quasi-1D unsteady bubbly cavitating nozzle flows are considered by employing a homogeneous bubbly liquid flow model, where the non-linear dynamics of cavitating bubbles is described by a modified Rayleigh–Plesset equation. The various damping mechanisms are considered by a single damping coefficient lumping them together in the form of viscous dissipation and by assuming a polytropic law for the expansion and compression of the gas. The complete system of equations, by appropriate uncoupling, are then reduced to two evolution equations, one for the flow speed and the other for the bubble radius when all damping mechanisms are considered by a single damping coefficient. The evolution equations for the bubble radius and flow speed are then perturbed with respect to flow unsteadiness resulting in a coupled system of linear partial differential equations (PDEs) for the radius and flow speed perturbations. This system of coupled linear PDEs is then cast into an eigenvalue problem and the exact solution of the eigenvalue problem is found by normal mode analysis in the inlet region of the nozzle. Results show that the steady-state cavitating nozzle flow solutions are stable only for perturbations with very small wave numbers. The stable regions of the stability diagram for the inlet region of the nozzle are seen to be broadened by the effect of turbulent wall shear stress

A semiphenomenological droplet model of homogeneous nucleation from the vapor phase

A semiphenomenological droplet model, which corrects for the macroscopic surface tension and monomer-monomer interactions from real gas behavior (second virial coefficient) and for the correlation between the mean surface area of a cluster and the number of molecules constituting the cluster over all ranges of temperature below the critical point, is proposed by modifying Fisher's droplet theory of condensation. A steady-state nucleation rate equation is derived and compared with expansion and diffusion cloud chamber data for a variety of substances. An overall good agreement is achieved for the range of temperatures investigated in contrast to comparison with the classical nucleation rate equation. © 1993 American Institute of Physics

Real gas effects in thermally choked nozzle flows

Real gas effects in condensing nozzle flows are discussed by the virial equation of state truncated after the second virial coefficient. The thermal choking conditions in nozzles previously derived for a perfect condensible vapor are generalized to include real gas effects. For these cases it is shown that the critical amount of heat necessary to thermally choke the flow can be defined explicitly only for the expansion of a pure vapor. © 1994 Birkhäuser Verlag

The mathematical theory of thermal choking in nozzle flows

The mathematical theory of sub- and supercritical nozzle flows is presented by a unified description of integro-algebraic and differential formulations of the flow equations. The critical amount of heat necessary for a thermally choked flow is defined and models which approximate this critical amount of heat are constructed for nozzle flows with both given internal heat source distributions and nonequilibrium condensation. In particular a cubic equation for an estimate of the limiting condensate mass fraction for shock free condensing flows is derived and a criterion for the existence of supercritical condensing flows based on this estimate is established. The necessary and sufficient conditions for thermal choking are then stated. It is shown that the commonly accepted view, which asserts that the flow Mach number reaches unity at thermal choking (known to be not always true in condensing flows), only exhibits a necessary condition for a thermally choked flow. © 1993 Birkhäuser Verlag

Asymptotic solution of transonic nozzle flows with homogeneous condensation. I. Subcritical flows

The one-dimensional (1-D) asymptotic solution of subcritical transonic nozzle flows with nonequilibrium homogeneous condensation is presented. An algorithm based on a local iterative scheme that exhibits the asymptotic solution in distinct condensation zones is developed for transonic moist air expansions under atmospheric supply conditions. Two models that characterize the state of the condensed phase as water drops or ice crystals are employed, together with the classical nucleation theory and Hertz-Knudsen droplet growth law. It is shown that the 1-D asymptotic predictions are in good agreement with the recent static pressure measurements of moist air expansions in relatively slender nozzles when the condensed phase is assumed to consist purely of water drops. © 1993 American Institute of Physics

A Semi-Phenomenological Droplet Model of Homogeneous Nucleation from the Vapor Phase

A semi-phenomenological droplet model, which corrects for the macroscopic surface tension and monomer-monomer interactions from real gas behavior (second virial coefficient) and for the correlation between the mean surface area of a cluster and the number of molecules constituting the cluster over all ranges of temperature below the critical point, is proposed by modifying Fisher's droplet theory of condensation. A steady-state nucleation rate equation is derived and compared with expansion and diffusion cloud chamber data for a variety of substances. An overall good agreement is achieved for the range of temperatures investigated in contrast to comparison with the classical nucleation rate equation

Thermal choking in two-dimensional expansion flows

Two-dimensional supersonic flows with heat addition from given internal sources and/or nonequilibrium condensation are considered. The critical amount of heat necessary to thermally choke the flow is de??ned at any point in the flow ??eld, and the necessary and su??cient conditions for thermal choking are identi??ed from the singularities of the equations of motion along streamlines. In particular, for any practical purposes, it is shown that the flow Mach number reaches unity at any point where the heat added to the flow along the streamline passing through that point reaches the critical value. Thermally choked flows are then identi??ed as those flows where the critical heat along streamlines is exceeded leading to embedded oblique shock waves with a local subsonic flow ??eld downstream