The contact angle in inviscid fluid mechanics

We show that in general, the specification of a contact angle condition at the contact line in inviscid fluid motions is incompatible with the classical field equations and boundary conditions generally applicable to them. The limited conditions under which such a specification is permissible are derived; however, these include cases where the static meniscus is not flat. In view of this situation, the status of the many `solutions' in the literature which prescribe a contact angle in potential flows comes into question. We suggest that these solutions which attempt to incorporate a phenomenological, but incompatible, condition are in some, imprecise sense `weak-type solutions'; they satisfy or are likely to satisfy, at least in the limit, the governing equations and boundary conditions everywhere except in the neighbourhood of the contact line. We discuss the implications of the result for the analysis of inviscid flows with free surfaces.Comment: 13 pages, no figures, no table

Kinetic Theory of Transient Condensation and Evaporation at a Plane Surface

The phenomenon of transient condensation onto, or evaporation from, a liquid sheet in contact with its pure vapor is treated from a kinetic theory viewpoint. The Maxwell moment method is used to formulate the detailed transient problem. A steady surface mass flux rate exists for times large in comparison with the collision time, that is, in the continuum regime, and explicit formulas are given for this limit. The complete gasdynamic field, however, is nonsteady for all times. The calculations are carried out utilizing four moments, and the effects of incorporating additional moments are negligible. Finally, the analysis is extended to incorporate imperfect mass and temperature accommodation. Examination of the transient solution and a matched asymptotic "quasisteady" solution shows that the gasdynamic field consists of a diffusion process near the liquid surface coupled through an expansion or compression wave to the constant far field state

Exact Haldane mapping for all SS and super universality in spin chains

The low energy dynamics of the anti-ferromagnetic Heisenberg spin $S$ chain in the semiclassical limit $S\to\infty$ is known to map onto the O(3) nonlinear $\sigma$ model with a $\theta$ term in 1+1 dimension. Guided by the underlying dual symmetry of the spin chain, as well as the recently established topological significance of "dangling edge spins," we report an {\em exact} mapping onto the O(3) model that avoids the conventional large $S$ approximation altogether. Our new methodology demonstrates all the super universal features of the $\theta$ angle concept that previously arose in the theory of the quantum Hall effect. It explains why Haldane's original ideas remarkably yield the correct answer in spite of the fundamental complications that generally exist in the idea of semiclassical expansions

Spectral reflectance measurements of a virus host model

A technique has been developed to detect the characteristic spectral signatures of healthy and infected St. Augustine grass. It is possible to predict the coverage of the infected area provided ground truth coverage shows positive St. Augustine grass turf. Qualitative measurements from photographs of plants in the blue and red regions with polarization show that light reflected from healthy plants is more strongly polarized than that from diseased plants. Photographs taken through the blue Wratten 47 filter in conjuction with a polarizer show an excellent differentiation. A large photographic difference also appears in the red region. Much smaller differences were noted in the 540 to 550 nm region. Although the intensity in the near-IR region is much higher than the visible region of the spectrum, differences in the healthy and diseased plants' reflectance were quite small

A computational model for three-dimensional incompressible wall jets with large cross flow

A computational model for the flow field of three dimensional incompressible wall jets prototypic of thrust augmenting ejectors with large cross flow is presented. The formulation employs boundary layer equations in an orthogonal curvilinear coordinate system. Simulation of laminar as well as turbulen wall jets is reported. Quantification of jet spreading, jet growth, nominal separation, and jet shrink effects due to corss flow are discussed

SARAS: a precision system for measurement of the Cosmic Radio Background and signatures from the Epoch of Reionization

SARAS is a correlation spectrometer purpose designed for precision measurements of the cosmic radio background and faint features in the sky spectrum at long wavelengths that arise from redshifted 21-cm from gas in the reionization epoch. SARAS operates in the octave band 87.5-175 MHz. We present herein the system design arguing for a complex correlation spectrometer concept. The SARAS design concept provides a differential measurement between the antenna temperature and that of an internal reference termination, with measurements in switched system states allowing for cancellation of additive contaminants from a large part of the signal flow path including the digital spectrometer. A switched noise injection scheme provides absolute spectral calibration. Additionally, we argue for an electrically small frequency-independent antenna over an absorber ground. Various critical design features that aid in avoidance of systematics and in providing calibration products for the parametrization of other unavoidable systematics are described and the rationale discussed. The signal flow and processing is analyzed and the response to noise temperatures of the antenna, reference termination and amplifiers is computed. Multi-path propagation arising from internal reflections are considered in the analysis, which includes a harmonic series of internal reflections. We opine that the SARAS design concept is advantageous for precision measurement of the absolute cosmic radio background spectrum; therefore, the design features and analysis methods presented here are expected to serve as a basis for implementations tailored to measurements of a multiplicity of features in the background sky at long wavelengths, which may arise from events in the dark ages and subsequent reionization era.Comment: 49 pages, 17 figure