Two-photon two-color nuclear magnetic resonance

Two-photon excitation has recently been demonstrated to be a practical means of exciting nuclear magnetic resonance (NMR) signals by radio-frequency (rf) irradiation at half the normal resonance frequency. In this work, two-photon excitation is treated with average Hamiltonian theory and shown to be a consequence of higher order terms in the Magnus expansion. It is shown that the excitation condition may be satisfied not only with rf at half resonance, but also with two independent rf fields, where the two frequencies sum to or differ by the resonance frequency. The technique is demonstrated by observation of proton NMR signals at 400 MHz while simultaneously exciting at 30 and 370 MHz. Advantages of this so-called two-color excitation, such as a dramatic increase in nutation rate over half-frequency excitation, along with a variety potential applications are discussed.     

Two contradictory conjectures concerning Carmichael numbers

Erdos conjectured that there are Carmichael numbers up to , whereas Shanks was skeptical as to whether one might even find an up to which there are more than Carmichael numbers. Alford, Granville and Pomerance showed that there are more than Carmichael numbers up to , and gave arguments which even convinced Shanks (in person-to-person discussions) that Erdos must be correct. Nonetheless, Shanks's skepticism stemmed from an appropriate analysis of the data available to him (and his reasoning is still borne out by Pinch's extended new data), and so we herein derive conjectures that are consistent with Shanks's observations, while fitting in with the viewpoint of Erdos and the results of Alford, Granville and Pomerance.

     

State-Space Based Approach to Particle Creation in Spatially Uniform Electric Fields

Our formalism, described recently in (C. E. Dolby and S. F. Gull, Ann. Phys.293 (2001), 189-214.) is applied to the study of particle creation in spatially uniform electric fields, concentrating on the cases of a time-invariant electric field and a so-called adiabatic electric field. Several problems are resolved by incorporating the Bogoliubov coefficient approach and the tunnelling approach into a single consistent, gauge invariant formulation. The value of a time-dependent particle interpretation is demonstrated by presenting a coherent account of the time-development of the particle creation process, in which the particles are created with small momentum (in the frame of the electric field) and are then accelerated by the electric field to make up the bulge of created particles predicted by asymptotic calculations [2, 3]. An initial state comprising one particle is also considered, and its evolution is described as being the sum of two contributions: the sea of current produced by the evolved vacuum and the extra current arising from the initial particle state.     

Stereocontrolled [3 + 2] annulations with arene chromium tricarbonyl complexes: construction of spirocyclic compounds related to fredericamycin A

[reaction: see text] An efficient method has been developed for the stereocontrolled construction of polycyclic and spirocyclic compounds, including the spirocyclic core of the antitumor agent fredericamycin A. The strategy involves a one-pot aldol addition/Brook rearrangement/cyclization sequence beginning from arene chromium tricarbonyl complexes and can formally be described as a [3 + 2] annulation.     

Enhanced regioselectivity of Yang photocyclization in the crystalline state

[reaction: see text] In contrast to the solution state, where Yang photocyclization of ketones of general structure 1 leads to equal amounts of cyclobutanols 2 and 3 (by abstraction of HA and HB, respectively), irradiation in the crystalline state is much more regioselective, favoring either 2 or 3 depending on the nature of the substituent X. X-ray crystallography and molecular mechanics calculations reveal the source of this remarkable solid-state regioselectivity.     

Noise Corrections to Stochastic Trace Formulas

We review studies of an evolution operator for a discrete Langevin equation with a strongly hyperbolic classical dynamics and a Gaussian noise. The leading eigenvalue of yields a physically measurable property of the dynamical system, the escape rate from the repeller. The spectrum of the evolution operator in the weak noise limit can be computed in several ways. A method using a local matrix representation of the operator allows to push the corrections to the escape rate up to order eight in the noise expansion parameter. These corrections then appear to form a divergent series. Actually, via a cumulant expansion, they relate to analogous divergent series for other quantities, the traces of the evolution operators ⁿ. Using an integral representation of the evolution operator , we then investigate the high order corrections to the latter traces. Their asymptotic behavior is found to be controlled by sub-dominant saddle points previously neglected in the perturbative expansion, and to be ultimately described by a kind of trace formula.     

Mixed-mode interface toughness of wafer-level Cu-Cu bonds using asymmetric chevron test

Characterization of interfacial adhesion is critical for the development of wafer bonding processes to manufacture microsystems with high yield and reliability. It is imperative that the test method used in such adhesion studies corresponds to the loading conditions present during processing and operation of the devices. In most applications in which wafers and die are bonded, the interface experiences a combination of shear and normal loading (i.e. mixed-mode loading) with the relative magnitude of the Mode I and II components varying in different scenarios. In the current work, the toughness of Cu-Cu thermocompression bonds, which are of interest for the fabrication of three-dimensional integrated circuits, is analyzed using a bonded chevron specimen with layers of different thickness that allows for the application of interfacial loading with variable mode mixity. The phase angle (a function of the degree of mode mixity at the interface) is varied from 0° to 24° by changing the layer thickness ratio from 1 to 0.48. The Cu-Cu bond toughness increases from 2.68 to 10.1 J/m², as the loading is changed from Mode I (pure tension) to a loading with a phase angle of 24°. The energy of plastic dissipation increases with increasing mode mixity, resulting in the enhanced interface toughness. The Mode I toughness of Cu-Cu bonds is minimally affected by plasticity, and therefore, provides the closest estimate of the interfacial work of fracture under the bonding conditions employed.     

Raman spectral signatures of mouse mammary tissue and associated lymph nodes: normal,tumor and mastitis

Raman spectroscopy involves the interaction of light with the molecular vibrations and therefore can provide information about molecular structure, tissue composition and changes in its environment. We explored whether Raman spectroscopy can reliably distinguish mammary tumors from normal mammary tissues and other pathological states in mice. We analyzed a large number of Raman spectra from the tumor and normal mammary glands of mice injected with 4T1 tumor cells, which were collected using a high‐resolution (less than 4 cm⁻¹) Raman spectrometer at a fixed (785 nm) laser excitation wavelength and with 60 mW of laser power. The spectra of normal and tumor mammary glands showed consistent differences in the intensity of certain Raman bands and loss of some bands in the tumor spectra. Multivariate statistical methods—principal component analysis (PCA) and discriminant functional analysis (DFA)—were used to separate the data into different groups of mammary tumors, mastitis, lymph nodes contralateral and tumor‐cell‐injected sides, and normal contralateral and tumor‐cell‐injected sides. We demonstrate that this spectroscopic technique has the feasibility of discriminating tumor and mastitis from normal tissues and other pathological states in a short period of time and may detect tumor transformation earlier than the standard histological examination stage. Copyright © 2006 John Wiley & Sons, Ltd.     

A robust method for automated background subtraction of tissue fluorescence

This paper introduces a new robust method for the removal of background tissue fluorescence from Raman spectra. Raman spectra consist of noise, fluorescence and Raman scattering. In order to extract the Raman scattering, both noise and background fluorescence must be removed, ideally without human intervention and preserving the original data. We describe the rationale behind our robust background subtraction method, determine the parameters of the method and validate it using a Raman phantom against other methods currently used. We also statistically compare the methods using the residual mean square (RMS) with a fluorescence‐to‐signal (F/S) ratio ranging from 0.1 to 1000. The method, ‘adaptive minmax’, chooses the subtraction method based on the F/S ratio. It uses multiple fits of different orders to maximize each polynomial fit. The results show that the adaptive minmax method was significantly better than any single polynomial fit across all F/S ratios. This method can be implemented as part of a modular automated real‐time diagnostic in vivo Raman system. Copyright © 2007 John Wiley & Sons, Ltd.     

Casimir Energy in Astrophysics: Gamma-Ray Bursts from QED Vacuum Transitions

Motivated by analogous applications to sonoluminescence, neutron stars mergers are examined in the context of Schwinger's dynamical Casimir effect. When the dielectric properties of the QED vacuum are altered through the introduction of dense matter, energy shifts in the zero-point fluctuations can appear as photon bursts at gamma-ray frequencies. The amount of radiation depends upon the properties and amount of matter in motion and the suddenness of the transition. It is shown that the dynamical Casimir effect can convert sufficient energy of neutron star mergers into gamma rays. Using information extracted from simulations of matter flow in neutron star mergers by Ruffert and Janka, we estimate that the total Casimir energy released can exceed 10 ⁵³ ergs in gamma-ray frequencies. The Casimir energy approach is capable of explaining the most energetic gamma-ray bursts.