Analogue Models of and for Gravity

Condensed matter systems, such as acoustics in flowing fluids, light in moving dielectrics, or quasiparticles in a moving superfluid, can be used to mimic aspects of general relativity. More precisely these systems (and others) provide experimentally accessible models of curved-space quantum field theory. As such they mimic kinematic aspects of general relativity, though typically they do not mimic the dynamics. Although these analogue models are thereby limited in their ability to duplicate all the effects of Einstein gravity they nevertheless are extremely important—they provide black hole analogues (some of which have already been seen experimentally) and lead to tests of basic principles of curved-space quantum field theory. Currently these tests are still in the realm of gedanken-experiments, but there are plausible candidate models that should lead to laboratory experiments in the not too distant future.     

Two-dimensional high-resolution NMR spectra in matched B(0) and B(1) field gradients

In a recent publication we presented a method to obtain highly resolved NMR spectra in the presence of an inhomogeneous B(0) field with the help of a matched RF gradient. If RF gradient pulses are combined with "ideal" 90 degrees pulses to form inhomogeneous z rotation pulses, the line broadening caused by the B(0) gradient can be refocused, while the full chemical shift information is maintained. This approach is of potential use for NMR spectroscopy in an inhomogeneous magnetic field produced by an "ex-situ" surface spectrometer. In this contribution, we extend this method toward two-dimensional spectroscopy with high resolution in one or both dimensions. Line narrowing in the indirect dimension can be achieved by two types of nutation echoes, thus leading to depth-sensitive NMR spectra with full chemical shift information. If the nutation echo in the indirect dimension is combined with a stroboscopic acquisition using inhomogeneous z-rotation pulses, highly resolved two-dimensional correlation spectra can be obtained in matched field gradients. Finally, we demonstrate that an INEPT coherence transfer from proton to carbon spins is possible in inhomogeneous B(0) fields. Thus, it is possible to obtain one-dimensional (13)C NMR spectra with increased sensitivity and two-dimensional HETCOR spectra in the presence of B(0) gradients of 0.4 mT/cm. These schemes may be of some value for ex-situ NMR analysis of materials and biological systems.     

A correction algorithm for undersampled images using dynamic segmentation and entropy based focus criterion

A post-processing technique is presented for correcting images undersampled in k-space. The method works by taking advantage of the image's background zeros (dynamically segmented through the application of a threshold) to extrapolate the missing k-space samples. The algorithm can produce good quality images from a small set of k-space frequencies with only a few iterations of simple matrix operations, using the image entropy as the focus criterion. It does not require any special patient preparation, extra pulse sequences, complex gradient programming or specialized hardware. This makes it a good candidate for any application that requires short scan times or where only few frequencies can be sampled.     

An electrothermal instability: the influence of albedo boundary conditions on the stationary states of an exactly solvable model

In order to study the effect of partially reflective (albedo) boundary conditions on pattern formation and stability in reaction-diffusion systems, we have analyzed an exactly soluble model of an electrothermal instability: the Ballast resistor. The present results allow a continuous interpolation between the results corresponding to Neumann and Dirichlet boundary conditions, and they allow qualitative changes in the patterns to be followed.     

Determination of the three-dimensional orientation of single molecules

A simple method for real-time determination of the full three-dimensional orientation of the emission dipole of single molecules is presented. Introduction of a pi phase step in the back focal plane of the collector lens breaks the inherent symmetry, allowing the longitudinal dipole component to be measured. Experimental tolerances and the consequence of a nonzero bandwidth emission spectrum are also discussed. The scheme also allows for the longitudinal component of an electric field to be found experimentally.     

Repulsive Gravitation in the Kerr-Newman Field

It is shown that uncharged test particles, released from rest at infinity in the Kerr-Newman field, stop and rebound when the radial coordinate r takes the value r₀ = Q²/(2M). This expression corresponds to the position of a stationary source of the Kerr-Newman field found by the author. It represents the surface of a massive oblate ellipsoid of revolution undergoing rigid rotation. Besides, the magnitude of r₀ guarantees that no violation of causality occurs throughout spacetime. Although the test particles' angular momenta are always zero, they acquire a rotational motion as a consequence of the dragging of inertial frames.     

Optically detected nuclear magnetic resonance at the sub-micron scale

Nuclear magnetic resonance is arguably one of the most powerful techniques available today to characterize diverse systems. However, the low sensitivity of the standard detection method constrains the applicability of this technique to samples having effective dimensions not less than a few microns. Here, we propose a novel scheme and device for the indirect detection of the nuclear spin signal at a submicroscopic scale. This approach--for which the name Dipolar Field Microscopy is suggested--is based on the manipulation of the long-range nuclear dipolar interaction created between the sample and a semiconductor tip located close to its surface. After a preparation interval, the local magnetization of the sample is used to modulate the nuclear magnetization in the semiconductor tip, which, in turn is determined by an optical inspection. Based on results previously reported, it is shown that, in principle, images and/or localized high-resolution spectra of the sample can be retrieved with spatial resolution proportional to the size of the tip.     

Investigating directed influences between activated brain areas in a motor-response task using fMRI

Localization of cognitive processes is a strength of functional neuroimaging. However, information about functional interactions between brain areas is crucial for a deeper understanding of brain function. We applied vector autoregressive modeling in the context of Granger causality as a method to analyze directed connectivity in a standard event-related fMRI study using a simple auditory-motor paradigm. The basic idea is to use temporal information in stochastic time series of a brain region in order to predict signal time courses in other brain regions. Thus, we predicted that the method should demonstrate causal influence of the auditory cortex and the supplementary motor area (SMA) on primary motor cortex. Eleven right-handed healthy female subjects were instructed to press a ball with either their left or their right hand when hearing the command "left" or "right" in the scanner. Influence to the left motor cortex was found from bilateral auditory cortex as well as from the SMA in 9 of 11 subjects. Granger causality to the right motor cortex existed from bilateral auditory cortex in 5 and from SMA in 6 subjects. Granger causality to the SMA existed from right auditory cortex in 7 subjects and from left auditory cortex in 8 subjects. Our findings in a simple task show that even under suboptimal circumstances (a relatively long TR of 2440 ms), Granger causality can be a useful tool to explore effective connectivity. Temporally optimized scanning should increase that potential.     

Synthesis and magnetic characterization of cobalt-substituted ferrite (CoxFe3−xO4) nanoparticles

Cobalt-substituted ferrite nanoparticles were synthesized with a narrow size distribution using reverse micelles formed in the system water/AOT/isooctane. Fe:Co ratios of 3:1, 4:1, and 5:1 were used in the synthesis, obtaining cobalt-substituted ferrites (Co_xFe_3−xO₄) and some indication of γ-Fe₃O₄ when 4:1 and 5:1 Fe:Co ratios were used. Inductively coupled plasma mass spectroscopy (ICP-MS) verified the presence of cobalt in all samples. Fourier transform infrared (FTIR) showed bands at ∼560 and ∼400 cm⁻¹, characteristic of the metal–oxygen bond in ferrites. Transmission electron microscopy showed that the number median diameter of the particles was ∼3 nm with a geometric deviation of ∼0.2. X-ray diffraction (XRD) confirmed the inverse spinel structure typical of ferrites with a lattice parameter of a=8.388 Å for Co_0.61Fe_0.39O₄, which is near that of CoFe₂O₄ (a=8.394 Å). Magnetic properties were determined using a superconducting quantum interference device (SQUID). Coercivities higher than 8 kOe were observed at 5 K, whereas at 300 K the particles showed superparamagnetic behavior. The anisotropy constant was determined based on the Debye model for a magnetic dipole in an oscillating field and an expression relating χ′ and the temperature of the in-phase susceptibility peak. Anisotropy constant values in the order of ∼10⁶ erg/cm³ were determined using the Debye model, whereas anisotropy constants in the order of ∼10⁷ erg/cm³ were calculated assuming Ωτ=1 at the temperature peak of the in-phase component of the susceptibility curve as commonly done in the literature. Our analysis demonstrates that the assumption Ωτ=1 at the temperature peak of χ′ is rigorously incorrect.     

Paraxial designing of planar waveguide variable-index focusing elements: Part 2—lenses of elliptical symmetry

A paraxial ray-optics formalism proposed for designing radially symmetric variable-index lenses is extended to the case of lenses of elliptical symmetry of the index profile.