Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients

A broad class of exact self-similar solutions to the nonlinear Schr?dinger equation (NLSE) with distributed dispersion, nonlinearity, and gain or loss has been found. Appropriate solitary wave solutions applying to propagation in optical fibers and optical fiber amplifiers with these distributed parameters have also been studied. These solutions exist for physically realistic dispersion and nonlinearity profiles in a fiber with anomalous group velocity dispersion. They correspond either to compressing or spreading solitary pulses which maintain a linear chirp or to chirped oscillatory solutions. The stability of these solutions has been confirmed by numerical simulations of the NLSE.     

On the Structure and Flow Processes in the Capillary Fringe of Phreatic Aquifers

The water distribution in the capillary fringe (CF) reflects the interaction of a strongly wetting fluid in a heterogeneous porous medium. Field profiles of gravimetric water content of the CF for a 30m deep, sandy, phreatic aquifer in Israel are critically analyzed in the context of the possible wetting and drainage processes in these sediments. A highly plausible explanation of the profiles is based on the spatial configuration of the CF surface determined from a model of the movement of water within the porous medium. The structural types of CF that can arise from a number of competing pore-scale displacement mechanisms, in the presence of gravity, are characterized by the model. We differentiate between two generic types of CF structures: a tenuous invasion-percolation type and a compact type. Flow, in response to a horizontal pressure gradient, associated with each structure is analyzed. Our interpretation of the field data supports the compact structure with a spatial variation in the height of the CF surface, above the water table, on the order of 1m. In this compact structure horizontal flow is characterized by stagnant regions in the CF above a critical height h _c and flow only for regions below h _c . The field water content (at h _c ) may be used to predict the onset of lateral water flow in the CF.     

Investigation of biological reactor designs for treatment of methanol and thiodiglycol waste streams

Applied Biochemistry and Biotechnology - Biological reactor designs for the degradation of the toxic compounds methanol and thiodiglycol are compared to determine the smallest volume. Both...     

Prime flows in topological dynamics

We present some results in topological dynamics and number theory. The number-theoretical results are estimates of the rates of convergence of sequences {fx26-1}, wherena is irrational,a is taken mod 1, and 0<β<1. One of these results is used to construct a homorphismT of a compact metric spaceX such that the minimal flow (X, T) had no nontrivial homomorphic images, i.e. is a prime flow. We define an infinite family of such flows, and describe other interesting properties of these flows. The research of all of the authors was supported by NSF Grant 28071.     

Detection of monobasic phosphorus acid esters by conversion to cholinesterase inhibitors

Many monobasic acids of quinquevalent phosphorus form cholinesterase inhibitors when exposed to ketene. Based upon this finding, a sensitive test to detect the presence of these compounds on filter paper has been developed. Seventeen out of nineteen of these acids tested gave positive results. Negative results obtained with the remaining two are attributable to steric factors or to the high hydrolysis rate of the acetylated product. Only one of eighteen phosphorus compounds other than the monobasic acids examined, namely n-butylphosphonic acid, gave a positive test; an explanation is offered to account for this exception.     

A method for the structural determination of cannabichromene metabolites by mass spectrometry

Ready identification of hydroxy metabolites of cannabichromene (CBC) by mass spectrometry of their trimethylsilyl derivatives is prevented by the dominant fragmentation to give a substituted chromenyl ion; this suppresses ions diagnostic of the position of metabolic hydroxylation. To overcome this difficulty, metabolites were hydrogenated over a rhodium/alumina catalyst to reduce the double bond responsible for chromenyl ion formation and to redirect the fragmentation to the site of metabolic attack. This resulted in the production of abundant diagnostic fragment ions enabling all monohydroxy-CBCs to be readily identified.