An extended parabolic equation and its application to the calculation of transverse and longitudinal mutual coherence functions in atmospheric turbulence

An extended, wide forward angle scattering version of the parabolic equation is considered and an operator expression for the solution of the generalized nmth moment of the electromagnetic wave field is obtained. Here, 'generalized' connotes the consideration of both the transverse as well as the longitudinal spatial moments of the wave field. A unified solution for the generalized second-order moment, i.e. the mutual coherence function (MCF), is found. The solution is applied to the case of Kolmogorov turbulent fluctuations within the atmosphere. In addition to demonstrating an interesting decaying oscillatory behaviour of the longitudinal MCF in atmospheric turbulence, it is found that the use of the extended parabolic equation yields negligible corrections to the transverse MCF, as calculated from the parabolic equation in the paraxial approximation.     

Introducing Intellectual Property in an Undergraduate Chemistry Curriculum

An exercise that introduces undergraduate chemistry majors to concepts associated with intellectual property is outlined. The assignment includes an introduction to the terminology associated with starting a company based on intellectual property and to nondisclosure agreements. After this, the students write a draft patent application. With over 150,000 United States patents issued annually, the role of intellectual property is prominent and becoming increasingly important in current corporations and in the formation of new businesses, as well as in government and academic settings.     

Applications for Tomographic Technology in Mining,Minerals and Food Engineering

Existing and new applications for tomographic technology using optical, electrical radar and seismic sensing principles are described. It is demonstrated that important similarities link process instrumentation needs in the mineral benefication and food manufacturing sectors. The minerals industries provide a variety of challenging applications for tomography in the development and validation of models associated with acid mine drainage, the stability of mine workings, mineral exploration and other environmental needs such as monitoring landfill sites and groundwater plume dispersion.     

Vibrational modes identify soft spots in a sheared disordered packing

We analyze low-frequency vibrational modes in a two-dimensional, zero-temperature, quasistatically sheared model glass to identify a population of structural "soft spots" where particle rearrangements are initiated. The population of spots evolves slowly compared to the interval between particle rearrangements, and the soft spots are structurally different from the rest of the system. Our results suggest that disordered solids flow via localized rearrangements that tend to occur at soft spots, which are analogous to dislocations in crystalline solids.     

Counterion condensation theory of attraction between like charges in the absence of multivalent counterions

There is abundant experimental evidence suggesting the existence of attractive interactions among identically charged polyelectrolytes in ordinary salt solutions. The presence of multivalent counterions is not required. We review the relevant literature in detail and conclude that it merits more attention than it has received. We discuss also some recent observations of a low ionic strength attraction of negatively charged DNA to the region of a negatively charged glass nanoslit where the floor of the nanoslit meets the walls, again in the absence of multivalent ions. On the theoretical side, it has become clear that purely electrostatic interactions require the presence of multivalent counterions if they are to generate like-charge attraction. Any theory of like-charge attraction in the absence of multivalent counterions must therefore contain a non-electrostatic component. We point out that counterion condensation theory, which has predicted like-charge polyelectrolyte attraction in an intermediate range of distances in ordinary 1:1 salt conditions, contains both electrostatic and non-electrostatic elements. The non-electrostatic component of the theory is the modeling constraint that the counterions fall into two explicit populations, condensed and uncondensed. As reviewed in the paper, this physically motivated constraint is supported by strong experimental evidence. We proceed to offer an explanation of the nanoslit observations by showing in an idealized model that the line of intersection of two intersecting planes is a virtual polyelectrolyte. Since we have previously developed a counterion condensation theory of attraction of two like-charged polyelectrolytes, our suggestion is that the DNA is attracted to the virtual polyelectrolytes that may be located in the nanoslit where floor meets walls. We present the detailed calculations needed to document this suggestion: an extension of previous theory to the case of polyelectrolytes with like but not identical charges; the demonstration of counterion condensation on a plane with bare charge density greater than an explicitly exhibited critical value; a calculation of the free energy of the plane; a calculation of the interaction of a line charge polyelectrolyte with a like-charged plane; and the detailed demonstration that the line of intersection of two planes is a virtual polyelectrolyte.     

Metal-halogen exchange-initiated cyclization of iodo carbonyl compounds

The feasibility of constructing carbocycles through the metal-halogen exchange-initiated cyclization reactions of iodoketones and other carboxyl derivatives has been studied. With saturated primary iodides, cyclization predominates when deactivated ketones are employed.     

Substituted styrene cycloaddition to juglone and derivatives- regiochemical control

No regiochemical directing effects could be attributed to methoxy styrene ring substituents in the cycloaddition of substituted styrene to juglone and its methyl ether. Control of quinone electron distributions, however, led to higher regioselectivity.