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We investigate the role of topological defects in the zero-temperature transition in an n-component quantum rotor with ferromagnetic interaction on a d-dimensional lattice close to dϭ1,nϭ2. The topological defects in the present problem are identified with higher-dimensional classical defects arising in the imaginary time classical action of the quantum rotor. In the same spirit as in Cardy and Hamber ͓Phys. Rev. Lett. 45, 499 ͑1980͔͒, we use the analyticity of the renormalization-group equations. In the (d,n) plane, there is a line passing through (1,2) across which the critical exponents are nonanalytic. As expected a clear d→(dϩ1) correspondence is seen between the quantum and equivalent classical transitions.

A closed-form approximant is proposed for the dynamic scaling function that characterizes the behavior of the wave-numberdependent diffusion of the order-parameter fluctuations in a fluid near a critical point. The expression contains two parameters that determine the expected behavior of the diffusion coefficient in the hydrodynamic and in the nonlocal critical limits. The proposed scaling function yields an accurate representation of our recent experimental data for the 3methylpentane and nitroethane mixture near the critical mixing point with parameter values that are in good agreement with the values predicted from theory. the last 10 mK from the critical temperature and the effect on the actual value deduced for the diffusion coefficient remains small.In a previous paper we demonstrated that the experimental decay-rate data are consistent with the predictions of the mode-coupling theory for dynamic critical phenomena. ' For that purpose we solved two coupled integral 28 1567 1983 The American Physical Society 1568 BURSTYN, SENGERS, BHATTACHARJEE, AND FERRELL 28

No abstract

A wave equation for a time-dependent perturbation about the steady shallow-water solution emulates the metric an acoustic white hole, even upon the incorporation of nonlinearity in the lowest order. A standing wave in the sub-critical region of the flow is stabilised by viscosity, and the resulting time scale for the amplitude decay helps in providing a scaling argument for the formation of the hydraulic jump. A standing wave in the super-critical region, on the other hand, displays an unstable character, which, although somewhat mitigated by viscosity, needs nonlinear effects to be saturated. A travelling wave moving upstream from the sub-critical region, destabilises the flow in the vicinity of the jump, for which experimental support has been given.

The spherically symmetric stationary transonic (Bondi) flow is considered a classic example of an accretion flow. This flow, however, is along a separatrix, which is usually not physically realizable. We demonstrate, using a pedagogical example, that it is the dynamics which selects the transonic flow.

Following the ideas of Herzfeld, Rice, Fixman, and Mistura, we are able to establish the adiabatic temperature oscillations as the sole origin of the critical attenuation and dispersion near the consolute point of a binary liquid. Special attention is given to the scaling function F(Q) for the attenuation normalized to its consolute-point value, where Q is the frequency, scaled by the relaxation rate of the fluid. By imposing some general conditions, we are led to the empirical function F(Q)=(1+Q ' ),whi ch is in excellent agreement with the data of Garland and Sanchez. By including a new hydrodynamic effect, we find that the frequency scale is also in accord with experiment.

Abstract. In the presence of viscosity the hydraulic jump in one dimension is seen to be a first-order transition. A scaling relation for the position of the jump has been determined by applying an averaging technique on the stationary hydrodynamic equations. This gives a linear height profile before the jump, as well as a clear dependence of the magnitude of the jump on the outer boundary condition. The importance of viscosity in the jump formation has been convincingly established, and its physical basis has been understood by a time-dependent analysis of the flow equations. In doing so, a very close correspondence has been revealed between a perturbation equation for the flow rate and the metric of an acoustic white hole. We finally provide experimental support for our heuristically developed theory.