Capacitors can radiate - some consequences of the two-capacitor problem with radiation

We fill a gap in the arguments of Boykin et al [American Journal of Physics, Vol 70 No. 4, pp 415-420 (2002)] by not invoking an electric current loop (i.e. magnetic dipole model) to account for the radiation energy loss, since an obvious corollary of their results is that the capacitors should radiate directly even if the connecting wires are shrunk to zero length. That this is so is shown here by a direct derivation of capacitor radiation using an oscillating electric dipole radiator model for the capacitors as well as the alternative less widely known magnetic 'charge' current loop representation for an electric dipole [see for example "Electromagnetic Waves" by S.A.Schlekunoff, van Nostrand (1948)]. Implications for Electromagnetic Compliance (EMC) issues as well as novel antenna designs further motivate the purpose of this paper.Comment: 5 Pages with No figure

Majorana fermions emerging from magnetic nanoparticles on a superconductor without spin-orbit coupling

There exists a variety of proposals to transform a conventional s-wave superconductor into a topological superconductor, supporting Majorana fermion mid-gap states. A necessary ingredient of these proposals is strong spin-orbit coupling. Here we propose an alternative system consisting of a one-dimensional chain of magnetic nanoparticles on a superconducting substrate. No spin-orbit coupling in the superconductor is needed. We calculate the topological quantum number of a chain of finite length, including the competing effects of disorder in the orientation of the magnetic moments and in the hopping energies, to identify the transition into the topologically nontrivial state (with Majorana fermions at the end points of the chain).Comment: 7 pages, 5 figure

Low-cost CMOS Neurological Sensor Array

Current methods used to study neural communication have not been able to achieve both good spatial and temporal resolution of recordings. There are two ways to record synaptic potentials from nerve endings: recordings using single or dual intracellular or extra cellular metal electrodes give good temporal resolution but poor spatial resolution, and recording activity with fluorescent dyes gives good spatial resolution but poor temporal resolution. Such medical research activity in the area of neurological signal detection has thus identified a requirement for the design of a CMOS circuit that contains an array of independent sensors. As both spatial and temporal distribution of acquired data is required in this application, the circuit must be capable of continuous measurement of synaptic potentials from an array of points on a tissue sample, with a 10 µm separation between sensor points.The major requirement for the circuit is that it is capable of sensing synaptic potentials of the order of several mV, with a resolution of 0.05 mV. For data recording purposes, the circuit must amplify these synaptic potentials and digitise them together with their locations in the sensor array. Finally, the circuit must be biologically inert, to avoid specimen deterioration.This paper presents the design of a prototype single-chip circuit, which provides a 6 x 3 array of independent synaptic potential sensors. The signal from each of the sensors is amplified and time-multiplexed into an on-chip A/D converter. The circuit provides an 8-bit synaptic potential value, together with an 8-bit field containing array location and trigger signals suitable for external data acquisition instrumentation.Our test circuit is implemented in a low-cost 0.5 um, 5 V CMOS process. The fabricated die is mounted in a standard 40 pin DIP ceramic package, with no lid to allow direct contact of the die surface with the tissue sample. The only post-processing step required for these packages is to encapsulate the exposed bond wires to ensure that the device is biologically inert. No further processing of the silicon die is required. Both the circuit design and the chip performance will be presented in the seminar

The Van der Waals interaction of the hydrogen molecule - an exact local energy density functional

We verify that the van der Waals interaction and hence all dispersion interactions for the hydrogen molecule given by: W"= -{A/R^6}-{B/R^8}-{C/R^10}- ..., in which R is the internuclear separation, are exactly soluble. The constants A=6.4990267..., B=124.3990835 ... and C=1135.2140398... (in Hartree units) first obtained approximately by Pauling and Beach (PB) [1] using a linear variational method, can be shown to be obtainable to any desired accuracy via our exact solution. In addition we shall show that a local energy density functional can be obtained, whose variational solution rederives the exact solution for this problem. This demonstrates explicitly that a static local density functional theory exists for this system. We conclude with remarks about generalising the method to other hydrogenic systems and also to helium.Comment: 11 pages, 13 figures and 28 reference

Simulation studies of permeation through two-dimensional ideal polymer networks

We study the diffusion process through an ideal polymer network, using numerical methods. Polymers are modeled by random walks on the bonds of a two-dimensional square lattice. Molecules occupy the lattice cells and may jump to the nearest-neighbor cells, with probability determined by the occupation of the bond separating the two cells. Subjected to a concentration gradient across the system, a constant average current flows in the steady state. Its behavior appears to be a non-trivial function of polymer length, mass density and temperature, for which we offer qualitative explanations.Comment: 8 pages, 4 figure

Electrokinetic behavior of two touching inhomogeneous biological cells and colloidal particles: Effects of multipolar interactions

We present a theory to investigate electro-kinetic behavior, namely, electrorotation and dielectrophoresis under alternating current (AC) applied fields for a pair of touching inhomogeneous colloidal particles and biological cells. These inhomogeneous particles are treated as graded ones with physically motivated model dielectric and conductivity profiles. The mutual polarization interaction between the particles yields a change in their respective dipole moments, and hence in the AC electrokinetic spectra. The multipolar interactions between polarized particles are accurately captured by the multiple images method. In the point-dipole limit, our theory reproduces the known results. We find that the multipolar interactions as well as the spatial fluctuations inside the particles can affect the AC electrokinetic spectra significantly.Comment: Revised version with minor changes: References added and discussion extende

Bethe ansatz for the SU(4) extension of the Hubbard Model

We apply the nested algebraic Bethe ansatz method to solve the eigenvalue problem for the SU(4) extension of the Hubbard model. The Hamiltonian is equivalent to the SU(4) graded permutation operator. The graded Yang-Baxter equation and the graded Quantum Inverse Scattering Method are used to obtain the eigenvalue of the SU(4) extension of the Hubbard model.Comment: Latex file, 12 page

Transversality of Electromagnetic Waves in the Calculus-Based Introductory Physics Course

Introductory calculus-based physics textbooks state that electromagnetic waves are transverse and list many of their properties, but most such textbooks do not bring forth arguments why this is so. Both physical and theoretical arguments are at a level appropriate for students of courses based on such books, and could be readily used by instructors of such courses. Here, we discuss two physical arguments (based on polarization experiments and on lack of monopole electromagnetic radiation), and the full argument for the transversality of (plane) electromagnetic waves based on the integral Maxwell equations. We also show, at a level appropriate for the introductory course, why the electric and magnetic fields in a wave are in phase and the relation of their magnitudes.Comment: 10 pages, 6 figure

Electrorotation of a pair of spherical particles

We present a theoretical study of electrorotation (ER) of two spherical particles under the action of a rotating electric field. When the two particles approach and finally touch, the mutual polarization interaction between the particles leads to a change in the dipole moment of the individual particle and hence the ER spectrum, as compared to that of the well-separated particles. The mutual polarization effects are captured by the method of multiple images. From the theoretical analysis, we find that the mutual polarization effects can change the characteristic frequency at which the maximum angular velocity of electrorotation occurs. The numerical results can be understood in the spectral representation theory.Comment: Minor revisions; accepted by Phys. Rev.

NMR studies of Successive Phase Transitions in Na0.5CoO2 and K0.5CoO2

59Co- and 23Na-NMR measurements have been carried out on polycrystalline and c-axis aligned samples of Na0.5CoO2, which exhibits successive transitions at temperatures T = 87 K (= Tc1) and T = 53 K (= Tc2). 59Co-NMR has also been carried out on c-axis aligned crystallites of K0.5CoO2 with similar successive transitions at Tc1 ~ 60 K and Tc2 ~ 20 K. For Na0.5CoO2, two sets of three NMR lines of 23Na nuclei explained by considering the quadrupolar frequencies nuQ ~1.32 and 1.40 MHz have been observed above Tc1, as is expected from the crystalline structure. Rather complicated but characteristic variation of the 23Na-NMR spectra has been observed with varying T through the transition temperatures, and the internal fields at two crystallographically distinct Na sites are discussed on the basis of the magnetic structures reported previously. The internal fields at two distinct Co sites observed below Tc1 and the 591/T1-T curves of Na0.5CoO2 and K0.5CoO2 are also discussed in a comparative way.Comment: 7 pages, 10 figures, submitted to J. Phys. Soc. Jpn, correction is made in right colum of p6 (35th line) as K0.5CoO2-->Na0.5CoO