Robert W. Brown

We study the orientation in a uniform magnetic field of rod-like anisotropic biofluid crystals with an easy plane that makes an oblique angle with the crystal’s c-axis. For a sufficiently strong field, these crystalline rods orient themselves such that the crystal’s easy plane is parallel to the magnetic field, the rod’s direction being defined as the direction of the crystal’s c-axis. As the rod rotates about the crystal’s hard axis there will therefore be a range of angles that the rod makes with the magnetic field. We detail this behavior by first providing illustrations of hemozoin crystals at various orientations. These illustrations clearly demonstrate that the orientation angle that the crystalline rod makes with respect to the magnetic field varies from about 30° to 150°. We also derive an analytical expression for the probability density function for the orientation angle. We find that the orientation angles are not uniformly distributed between the limits of 30° and 150°, but rather tend to cluster near these limits. This suggests experimental tests and addresses confusion about the rod orientation found in past literature. The relevance to other anisotropic biofluid crystals, such as those produced by gout, is also discussed.

We have designed, developed and evaluated an innovative portable magneto-optical detector (MOD) in which a light beam with variable polarization passes through a fluid sample immersed in a variable magnetic field. The light intensity is measured downstream along the forward scattering direction. The field is turned on and off through the in-and-out motion of nearby permanent magnets. As a result, for sufficiently magnetically and optically anisotropic samples, the optical absorption is sensitive to changes in the light polarization. Both detection and characterization applications are therefore available. For instance, both the degree of malaria infection can be measured and hemozoin crystalline properties can be studied. We present experimental results for synthetic hemozoin, and describe them in terms of the basic physics and chemistry underlying the correlations of the directions of the external magnetic field and the light beam polarization. We connect this work to a commercialized product for malaria detection and compare it to other magneto-optical instruments and methods. We conduct tests of absorption parameters, the electric polarizability tensor, and we discuss the connection to magnetic and electric dipole moments.

Coaxial cables commonly used to connect radio-frequency (RF) coil arrays with the control console of an MRI scanner are susceptible to electromagnetic coupling. As the number of RF channels increases, such coupling could result in severe heating and pose a safety concern. Non-conductive transmission solutions based on fiber-optic cables are considered to be one of the alternatives but are limited by the high dynamic range (>80 dB) of typical MRI signals. A new digital fiber-optic transmission system based on delta–sigma modulation (DSM) is developed to address this problem. A DSM-based optical link is prototyped using off-the-shelf components and bench-tested at different signal oversampling rates (OSRs). An end-to-end dynamic range (DR) of 81 dB, which is sufficient for typical MRI signals, is obtained over a bandwidth of 200 kHz, which corresponds to OSR = 50. A fully integrated custom fourth-order continuous-time DSM is designed in 180 nm CMOS technology to enable transmission of full-bandwidth MRI signals (up to 1 MHz) with an adequate DR. Initial electrical test results from this custom chip are also presented.

Color-factor symmetry is used to derive a KLT-type relation for tree-level QCD amplitudes containing gluons and an arbitrary number of massive or massless quark-antiquark pairs, generalizing the expression for Yang-Mills amplitudes originally postulated by Bern, De Freitas, and Wong. An explicit expression is given for all amplitudes with two or fewer quark-antiquark pairs in terms of the (modified) momentum kernel. We also introduce the bicolor scalar theory, the “zeroth copy” of QCD, containing massless biadjoint scalars and massive bifundamental scalars, generalizing the biadjoint scalar theory of Cachazo, He, and Yuan. We derive KLT-type relations for tree-level amplitudes of biadjoint and bicolor theories using the color-factor symmetry possessed by these theories.

Color-factor symmetry is used to derive a KLT-type relation for tree-level QCD amplitudes containing gluons and an arbitrary number of massive or massless quark-antiquark pairs, generalizing the expression for Yang-Mills amplitudes originally postulated by Bern, De Freitas, and Wong. An explicit expression is given for all amplitudes with two or fewer quark-antiquark pairs in terms of the (modified) momentum kernel. We also introduce the bicolor scalar theory, the "zeroth copy" of QCD, containing massless biadjoint scalars and massive bifundamental scalars, generalizing the biadjoint scalar theory of Cachazo, He, and Yuan. We derive KLT-type relations for tree-level amplitudes of biadjoint and bicolor theories using the color-factor symmetry possessed by these theories.

We introduce a new set of symmetries obeyed by tree-level gauge-theory amplitudes involving at least one gluon. The symmetry acts as a momentum-dependent shift on the color factors of the amplitude. Using the radiation vertex expansion, we prove the invariance under this color-factor shift of the $n$-gluon amplitude, as well as amplitudes involving massless or massive particles in an arbitrary representation of the gauge group with spin zero, one-half, or one. The Bern-Carrasco-Johansson relations are a direct consequence of this symmetry. We also introduce the cubic vertex expansion of an amplitude, and use it to derive a generalized-gauge-invariant constraint on the kinematic numerators of the amplitude. We show that the amplitudes of the bi-adjoint scalar theory are invariant under the color-factor symmetry, and use this to derive the null eigenvectors of the propagator matrix. We generalize the color-factor shift to loop level, and prove the invariance under this shift of one-loop $n$-gluon amplitudes in any theory that admits a color-kinematic-dual representation of numerators. We show that the one-loop color-factor symmetry implies known relations among the integrands of one-loop color-ordered amplitudes.