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Kinetics and mechanism of the interconversion of inverse bicontinuous cubic mesophases
This paper describes time-resolved x-ray diffraction data monitoring the transformation of one inverse bicontinuous cubic mesophase into another, in a hydrated lipid system. The first section of the paper describes a mechanism for the transformation that conserves the topology of the bilayer, based on the work of Charvolin and Sadoc, Fogden and Hyde, and Benedicto and O'Brien in this area. We show a pictorial representation of this mechanism, in terms of both the water channels and the lipid bilayer. The second section describes the experimental results obtained. The system under investigation was 2:1 lauric acid: dilauroylphosphatidylcholine at a hydration of 50% water by weight. A pressure-jump was used to induce a phase transition from the gyroid (Q(II)(G)) to the diamond (Q(II)(D)) bicontinuous cubic mesophase, which was monitored by time-resolved x-ray diffraction. The lattice parameter of both mesophases was found to decrease slightly throughout the transformation, but at the stage where the Q(II)(D) phase first appeared, the ratio of lattice parameters of the two phases was found to be approximately constant for all pressure-jump experiments. The value is consistent with a topology-preserving mechanism. However, the polydomain nature of our sample prevents us from confirming that the specific pathway is that described in the first section of the paper. Our data also reveal signals from two different intermediate structures, one of which we have identified as the inverse hexagonal (H-II) mesophase. We suggest that it plays a role in the transfer of water during the transformation. The rate of the phase transition was found to increase with both temperature and pressure-jump amplitude, and its time scale varied from the order of seconds to minutes, depending on the conditions employed
Radio Astronomical Polarimetry and the Lorentz Group
In radio astronomy the polarimetric properties of radiation are often
modified during propagation and reception. Effects such as Faraday rotation,
receiver cross-talk, and differential amplification act to change the state of
polarized radiation. A general description of such transformations is useful
for the investigation of these effects and for the interpretation and
calibration of polarimetric observations. Such a description is provided by the
Lorentz group, which is intimately related to the transformation properties of
polarized radiation. In this paper the transformations that commonly arise in
radio astronomy are analyzed in the context of this group. This analysis is
then used to construct a model for the propagation and reception of radio
waves. The implications of this model for radio astronomical polarimetry are
discussed.Comment: 10 pages, accepted for publication in Astrophysical Journa
Which diameter and angle rule provides optimal flow patterns in a coronary bifurcation?
The branching angle and diameter ratio in epicardial coronary artery bifurcations are two important determinants of atherogenesis. Murray's cubed diameter law and bifurcation angle have been assumed to yield optimal flows through a bifurcation. In contrast, we have recently shown a 7/3 diameter law (HK diameter model), based on minimum energy hypothesis in an entire tree structure. Here, we derive a bifurcation angle rule corresponding to the HK diameter model and critically evaluate the streamline flow through HK and Murray-type bifurcations. The bifurcations from coronary casts were found to obey the HK diameter model and angle rule much more than Murray's model. A finite element model was used to investigate flow patterns for coronary artery bifurcations of various types. The inlet velocity and pressure boundary conditions were measured by ComboWire. Y-bifurcation of Murray type decreased wall shear stress-WSS (10%-40%) and created an increased oscillatory shear index-OSI in atherosclerosis-prone regions as compared with HK-type bifurcations. The HK-type bifurcations were found to have more optimal flow patterns (i.e., higher WSS and lower OSI) than Murray-type bifurcations which have been traditionally believed to be optimized. This study has implications for changes in bifurcation angles and diameters in percutaneous coronary intervention
Jones-matrix Formalism as a Representation of the Lorentz Group
It is shown that the two-by-two Jones-matrix formalism for polarization
optics is a six-parameter two-by-two representation of the Lorentz group. The
attenuation and phase-shift filters are represented respectively by the
three-parameter rotation subgroup and the three-parameter Lorentz group for two
spatial and one time dimensions. It is noted that the Lorentz group has another
three-parameter subgroup which is like the two-dimensional Euclidean group.
Possible optical filters having this Euclidean symmetry are discussed in
detail. It is shown also that the Jones-matrix formalism can be extended to
some of the non-orthogonal polarization coordinate systems within the framework
of the Lorentz-group representation.Comment: RevTeX, 27 pages, no figures, to be published in J. Opt. Soc. Am.
Propagation of transverse intensity correlations of a two-photon state
The propagation of transverse spatial correlations of photon pairs through
arbitrary first-order linear optical systems is studied experimentally and
theoretically using the fractional Fourier transform. Highly-correlated photon
pairs in an EPR-like state are produced by spontaneous parametric
down-conversion and subject to optical fractional Fourier transform systems. It
is shown that the joint detection probability can display either correlation,
anti-correlation, or no correlation, depending on the sum of the orders
and of the transforms of the down-converted photons. We
present analytical results for the propagation of the perfectly correlated EPR
state, and numerical results for the propagation of the two-photon state
produced from parametric down-conversion. We find good agreement between theory
and experiment.Comment: 9 pages, 7 figures, to appear PR
Stokes Parameters as a Minkowskian Four-vector
It is noted that the Jones-matrix formalism for polarization optics is a
six-parameter two-by-two representation of the Lorentz group. It is shown that
the four independent Stokes parameters form a Minkowskian four-vector, just
like the energy-momentum four-vector in special relativity. The optical filters
are represented by four-by-four Lorentz-transformation matrices. This
four-by-four formalism can deal with partial coherence described by the Stokes
parameters. A four-by-four matrix formulation is given for decoherence effects
on the Stokes parameters, and a possible experiment is proposed. It is shown
also that this Lorentz-group formalism leads to optical filters with a symmetry
property corresponding to that of two-dimensional Euclidean transformations.Comment: RevTeX, 22 pages, no figures, submitted to Phys. Rev.
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