Quantitative spectroscopy of superficial turbid media

We report a novel diffuse optical spectroscopy probe design for determining optical properties of superficial volumes of turbid samples. The fiber-based probe employs a highly scattering layer placed in contact with the sample of interest. This layer diffuses photons from a collimated light source before they enter the sample and provides a basis for describing light transported in superficial media by the diffusion approximation. We compare the performance of this modified two-layer diffusion model with Monte Carlo simulations. A set of experiments that demonstrate the feasibility of this method in turbid tissue phantoms is also presented. Optical properties deduced by this approach are in good agreement with those derived by use of a benchmark method for determining optical properties. The average interrogation depth of the probe design investigated here is estimated to be less than 1 mm.     

Multiphoton entanglement concentration and quantum cryptography

Multiphoton states from parametric down-conversion can be entangled both in polarization and photon number. Maximal high-dimensional entanglement can be concentrated postselectively from these states via photon counting. This makes them natural candidates for quantum key distribution, where the presence of more than one photon per detection interval has up to now been considered undesirable. We propose a simple multiphoton cryptography protocol for the case of low losses.     

Differences Between Consecutive Primes

Let p_n be the nth prime. Then this paper is concerned with provingthe following result on the distribution of consecutive primes. The exponent of x in this theorem improves on the work of Heath-Brownwho proved (1) with exponent . Under the Riemann hypothesisone can prove (1) with exponent .The proof of the theorem startswith the Heath-Brown–Linnik identity which leads to aformula giving the number of primes in an interval in termsof coefficients of certain Dirichlet series. I then estimatethe coefficients by using, among other things, the informationwhich can be gained from Montgomery's mean value theorem andHuxley's version of the Hal' asz lemma. Furthermore, by usingfamiliar sieve arguments I am able to discard some of the coefficientsallowing us to gain an improvement over the previous resultof Heath-Brown. 1991 Mathematics Subject Classification: 11N05.     

Alcohols,ethers, carbohydrates,and related compounds. I. The MM4 force field for simple compounds

Simple alcohols and ethers have been studied with the MM4 force field. The structures of 13 molecules have been well fit using the MM4 force field. Moments of inertia have been fit with rms percentage errors as indicated: 18 moments for ethers, 0.28%; 21 moments for alcohols, 0.22%. Rotational barriers and conformational equilibria have also been examined, and the experimental and ab initio results are reproduced substantially better with MM4 than they were with MM3. Much of the improvement comes from the use of additional interaction terms in the force constant matrix, of which the torsion-bend and torsion-torsion are particularly important. Induced dipoles are included in the calculation, and dipole moments are reasonably well fit. It has been possible for the first time to fit conformational energetic data for both open chain and cyclic alcohols (e.g., propanol and cyclohexanol) with the same parameter set. For vibrational spectra, over a total of 82 frequencies, the rms error is 27 cm(-1), as opposed to 38 cm(-1) with MM3. Both the alpha and beta bond shortening resulting from the presence of the electronegative oxygen atom in the molecule are well reproduced. The electronegativity of the oxygen is sufficient that one must also include not only the alpha and beta electronegativity effects on bond lengths, but also on angle distortions, if structures are to be well reproduced. The heats of formation of 32 alcohols and ethers were fit overall to within experimental error (weighted standard deviation error 0.26 kcal/mol).     

In vivo fluorescence spectroscopy of nonmelanoma skin cancer

In vivo and ex vivo tissue autofluorescence (endogenous fluorescence) have been employed to investigate the presence of markers that could be used to detect tissue abnormalities and/or malignancies. We present a study of the autofluorescence of normal skin and tumor in vivo, conducted on 18 patients diagnosed with nonmelanoma skin cancers (NMSC). We observed that both in basal cell carcinomas (BCC) and squamous cell carcinomas (SCC) the endogenous fluorescence due to tryptophan residues was more intense in tumor than in normal tissue, probably due to epidermal thickening and/or hyperproliferation. Conversely, the fluorescence intensity associated with dermal collagen crosslinks was generally lower in tumors than in the surrounding normal tissue, probably because of degradation or erosion of the connective tissue due to enzymes released by the tumor. The decrease of collagen fluorescence in the connective tissue adjacent to the tumor loci was validated by fluorescence imaging on fresh-frozen tissue sections obtained from 33 NMSC excised specimens. Our results suggest that endogenous fluorescence of NMSC, excited in the UV region of the spectrum, has characteristic features that are different from normal tissue and may be exploited for noninvasive diagnostics and for the detection of tumor margins.     

Experimental dynamics of a vortex within a vortex

We report the experimental dynamics of a new two-dimensional (2D) fluid phenomenon that occurs when an intense, pointlike vortex is placed within a diffuse, circular vortex. Our observations, made using strongly magnetized electron columns to model the 2D fluid, support the analysis performed by Jin and Dubin.     

The method of images for regularized Stokeslets

The image system for the method of regularized Stokeslets is developed and implemented. The method uses smooth localized functions to approximate a delta distribution in the derivation of the fluid flow due to a concentrated force. In order to satisfy zero-flow boundary conditions at a plane wall, the method of images derived for a standard (singular) Stokeslet is extended to give exact cancellation of the regularized flow at the wall. As the regularization parameter vanishes, the expressions reduce to the known images for singular Stokeslets. The advantage of the regularized method is that it gives bounded velocity fields even for isolated forces or for distributions of forces along curves. These are useful in the simulation of ciliary beats, flagellar motion, and particle suspensions. The expression relating force and velocity can be inverted to find the forces that generate a given velocity boundary condition. The latter is exemplified by modeling a cilium as a filament moving in a three-dimensional flow. The cilium velocity at various times is constructed from known data and used to determine the force field along the filament. Those forces can then reproduce the flow everywhere. The validity of the method is evaluated by computing the drag on a sphere moving near a wall. Comparisons with known expressions for the drag show that the method gives accurate results for spheres even within a distance from the wall equal to the surface discretization size.     

Reactive scattering of a supersonic oxygen atom beam O + I2

Reactive scattering of O atoms with I₂ molecules has been studied at an initial translational energy E = 43 kJ mol^-1 using a supersonic beam of O atoms seeded in He and E = 18 kJ mol^-1 using O atoms seeded in Ne. Velocity distributions of OI product were measured by cross-correlation time-of-flight analysis. Full contour maps of the differential reaction cross section were obtained which show predominantly rebound scattering at both initial translational energies. Scattering in the forward direction has a product translational energy distribution similar to that predicted for a long-lived collision complex but scattering in the backward direction has a much higher product translational energy. The greater predominance of rebound scattering observed for O + I₂ compared with O + Br₂ may be attributed to the greater exoergicity of the O + I₂ reaction. However, comparison with the O + IBr reaction which exhibits a long-lived collision complex mechanism indicates that the predominance of backward scattering for O + I₂ also arises from diminished forward scattering from larger impact parameter collisions.