Numerical method for determination of the NMR frequency of the single-qubit operation in a silicon-based solid-state quantum computer

A numerical method is introduced to determine the nuclear magnetic resonance frequency of a donor (P-31) doped inside a silicon substrate under the influence of an applied electric field. This phosphorus donor has been suggested for operation as a qubit for the realization of a solid-state scalable quantum computer. The operation of the qubit is achieved by a combination of the rotation of the phosphorus nuclear spin through a globally applied magnetic field and the selection of the phosphorus nucleus through a locally applied electric field. To realize the selection function, it is required to know the relationship between the applied electric field and the change of the nuclear magnetic resonance frequency of phosphorus. In this study, based on the wave functions obtained by the effective-mass theory, we introduce an empirical correction factor to the wave functions at the donor nucleus. Using the corrected wave functions, we formulate a first-order perturbation theory for the perturbed system under the influence of an electric field. In order to calculate the potential distributions inside the silicon and the silicon dioxide layers due to the applied electric field, we use the multilayered Green's functions and solve an integral equation by the moment method. This enables us to consider more realistic, arbitrary shape, and three-dimensional qubit structures. With the calculation of the potential distributions, we have investigated the effects of the thicknesses of silicon and silicon dioxide layers, the relative position of the donor, and the applied electric field on the nuclear magnetic resonance frequency of the donor.

Modulation of channel activity and gadolinium block of MscL by static magnetic fields

The magnetic field of the Earth has for long been known to influence the behaviour and orientation of a variety of living organisms. Experimental studies of the magnetic sense have, however, been impaired by the lack of a plausible cellular and/or molecular mechanism providing meaningful explanation for detection of magnetic fields by these organisms. Recently, mechanosensitive (MS) ion channels have been implied to play a role in magnetoreception. In this study we have investigated the effect of static magnetic fields (SMFs) of moderate intensity on the activity and gadolinium block of MscL, the bacterial MS channel of large conductance, which has served as a model channel to study the basic physical principles of mechanosensory transduction in living cells. In addition to showing that direct application of the magnetic field decreased the activity of the MscL channel, our study demonstrates for the first time that SMFs can reverse the effect of gadolinium, a well-known blocker of MS channels. The results of our study are consistent with a notion that (1) the effects of SMFs on the MscL channels may result from changes in physical properties of the lipid bilayer due to diamagnetic anisotropy of phospholipid molecules and consequently (2) cooperative superdiamagnetism of phospholipid molecules under influence of SMFs could cause displacement of Gd3+ stop ions from the membrane bilayer and thus remove the MscL channel block.

An inverse methodology for high frequency RF head coil design with pre-emphasized B1 field in MRI

An inverse methodology to assist in the design of radio-frequency (RF) head coils for high field MRI application is described in this work. Free space time-harmonic electromagnetic Green's functions and preemphasized B1 field are used to calculate the current density on the coil cylinder. With B1 field preemphasized and lowered in the middle of the RF transverse plane, the calculated current distribution can generate an internal magnetic field that can reduce the EM field/tissue interactions at high frequencies. The current distribution of a head coil operating at 4 T is calculated using inverse methodology with preemphasized B1 fields. FDTD is employed to calculate B1 field and signal intensity inside a homogenous cylindrical phantom and human head. A comparison with conventional RF birdcage coil is reported here and demonstrated that inverse-method designed coil with preemphasized B1 field can help in decreasing the notorious bright region caused by EM field/tissue interactions in the human head images at 4 T.

An equivalent distributed magnetic current based FDTD method for the calculation of e-fields induced by gradient coils in MRI

This paper evaluates a low-frequency FDTD method applied to the problem of induced E-fields/eddy currents in the human body resulting from the pulsed magnetic field gradients in MRI. In this algorithm, a distributed equivalent magnetic current (DEMC) is proposed as the electromagnetic source and is obtained by quasistatic calculation of the empty coil's vector potential or measurements therein. This technique circumvents the discretizing of complicated gradient coil geometries into a mesh of Yee cells, and thereby enables any type of gradient coil modeling or other complex low frequency sources. The proposed method has been verified against an example with an analytical solution. Results are presented showing the spatial distribution of gradient-induced electric fields in a multilayered spherical phantom model and a complete body model.

A study of magnetic non-linearity and finite length effects in solid iron subjected to a travelling MMF wave

This thesis describes an experimental and analytic study of the effects of magnetic non-linearity and finite length on the loss and field distribution in solid iron due to a travelling mmf wave. In the first half of the thesis, a two-dimensional solution is developed which accounts for the effects of both magnetic non-linearity and eddy-current reaction; this solution is extended, in the second half, to a three-dimensional model. In the two-dimensional solution, new equations for loss and flux/pole are given; these equations contain the primary excitation, the machine parameters and factors describing the shape of the normal B-H curve. The solution applies to machines of any air-gap length. The conditions for maximum loss are defined, and generalised torque/frequency curves are obtained. A relationship between the peripheral component of magnetic field on the surface of the iron and the primary excitation is given. The effects of magnetic non-linearity and finite length are combined analytically by introducing an equivalent constant permeability into a linear three-dimensional analysis. The equivalent constant permeability is defined from the non-linear solution for the two-dimensional magnetic field at the axial centre of the machine to avoid iterative solutions. In the linear three-dimensional analysis, the primary excitation in the passive end-regions of the machine is set equal to zero and the secondary end faces are developed onto the air-gap surface. The analyses, and the assumptions on which they are based, were verified on an experimental machine which consists of a three-phase rotor and alternative solid iron stators, one with copper end rings, and one without copper end rings j the main dimensions of the two stators are identical. Measurements of torque, flux /pole, surface current density and radial power flow were obtained for both stators over a range of frequencies and excitations. Comparison of the measurements on the two stators enabled the individual effects of finite length and saturation to be identified, and the definition of constant equivalent permeability to be verified. The penetration of the peripheral flux into the stator with copper end rings was measured and compared with theoretical penetration curves. Agreement between measured and theoretical results was generally good.

The influence of age on the pattern and flash visual evoked magnetic response (VEMR)

The visual evoked magnetic response (VEMR) was measured over the occipital cortex to pattern and flash stimuli in 86 normal subjects aged 15-86 years. The latency of the major positive component (outgoing magnetic field) to the pattern reversal stimulus (P100M) increased with age, particularly after 55 years, while the amplitude of the P100M decreased more gradually over the lifespan. By contrast, the latency of the major positive component to the flash stimulus (P2M) increased more slowly with age after about 50 years, while its amplitude may have decreased in only a proportion of the elderly subjects. The changes in the P100M with age may reflect senile changes in the eye and optic nerve, e.g. senile miosis, degenerative changes in the retina or geniculostriate deficits. The P2M may be more susceptible to senile changes in the visual cortex. The data suggest that the contrast channels of visual information processing deteriorate more rapidly with age than the luminance channels.

Developments and extensions of Roth's method of double Fourier series with applications to the solution of electromagnetic field problems

The first part of the thesis compares Roth's method with other methods, in particular the method of separation of variables and the finite cosine transform method, for solving certain elliptic partial differential equations arising in practice. In particular we consider the solution of steady state problems associated with insulated conductors in rectangular slots. Roth's method has two main disadvantages namely the slow rate of con­vergence of the double Fourier series and the restrictive form of the allowable boundary conditions. A combined Roth-separation of variables method is derived to remove the restrictions on the form of the boundary conditions and various Chebyshev approximations are used to try to improve the rate of convergence of the series. All the techniques are then applied to the Neumann problem arising from balanced rectangular windings in a transformer window. Roth's method is then extended to deal with problems other than those resulting from static fields. First we consider a rectangular insulated conductor in a rectangular slot when the current is varying sinusoidally with time. An approximate method is also developed and compared with the exact method.The approximation is then used to consider the problem of an insulated conductor in a slot facing an air gap. We also consider the exact method applied to the determination of the eddy-current loss produced in an isolated rectangular conductor by a transverse magnetic field varying sinusoidally with time. The results obtained using Roth's method are critically compared with those obtained by other authors using different methods. The final part of the thesis investigates further the application of Chebyshdev methods to the solution of elliptic partial differential equations; an area where Chebyshev approximations have rarely been used. A poisson equation with a polynomial term is treated first followed by a slot problem in cylindrical geometry.

A critical assessment of the finite element method for calculating electric and magnetic fields

The present dissertation is concerned with the determination of the magnetic field distribution in ma[.rnetic electron lenses by means of the finite element method. In the differential form of this method a Poisson type equation is solved by numerical methods over a finite boundary. Previous methods of adapting this procedure to the requirements of digital computers have restricted its use to computers of extremely large core size. It is shown that by reformulating the boundary conditions, a considerable reduction in core store can be achieved for a given accuracy of field distribution. The magnetic field distribution of a lens may also be calculated by the integral form of the finite element rnethod. This eliminates boundary problems mentioned but introduces other difficulties. After a careful analysis of both methods it has proved possible to combine the advantages of both in a .new approach to the problem which may be called the 'differential-integral' finite element method. The application of this method to the determination of the magnetic field distribution of some new types of magnetic lenses is described. In the course of the work considerable re-programming of standard programs was necessary in order to reduce the core store requirements to a minimum.

The electron optical limits of performance of single-polepiece magnetic electron lenses

The thesis is concerned with the electron properties of single-polepiece magnetic electron lenses especially under conditions of extreme polepiece saturation. The electron optical properties are first analysed under conditions of high polepiece permeability. From this analysis, a general idea can be obtained of the important parameters that affect ultimate lens performance. In addition, useful information is obtained concerning the design of improved lenses operating under conditions of extreme polepiece saturation, for example at flux densities of the order of 10 Tesla. It is shown that in a single-polepiece lens , the position and shape of the lens exciting coil plays an important role. In particular, the maximum permissible current density in the windings,rather than the properties of the iron, can set a limit to lens performance. This factor was therefore investigated in some detail. The axial field distribution of a single-polepiece lens, unlike that of a conventional lens, is highly asymmetrical. There are therefore two possible physical arrangements of the lens with respect to the incoming electron beam. In general these two orientations will result in different aberration coefficients. This feature has also been investigated in some detail. Single-pole piece lenses are thus considerably more complicated electron- optically than conventional double polepiece lenses. In particular, the absence of the usual second polepiece causes most of the axial magnetic flux density distribution to lie outside the body of the lens. This can have many advantages in electron microscopy but it creates problems in calculating the magnetic field distribution. In particular, presently available computer programs are liable to be considerably in error when applied to such structures. It was therefore necessary to find independent ways of checking the field calculations. Furthermore, if the polepiece is allowed to saturate, much more calculation is involved since the field distribution becomes a non-linear function of the lens excitation. In searching for optimum lens designs, care was therefore taken to ensure that the coil was placed in the optimum position. If this condition is satisfied there seems to be no theoretical limit to the maximum flux density that can be attained at the polepiece tip. However , under iron saturation condition, some broadening of the axial field distribution will take place, thereby changing the lens aberrations . Extensive calculations were therefore made to find the minimum spherical and chromatic aberration coefficients . The focal properties of such lens designs are presented and compared with the best conventional double-polepiece lenses presently available.

Fabrication of magnetic drug-loaded polymeric composite nanofibres and their drug release characteristics

Magnetic polymer nanofibres intended for drug delivery have been designed and fabricated by electrospinning. Magnetite (Fe3O4) nanoparticles were successfully incorporated into electrospun nanofibre composites of two cellulose derivatives, dehydroxypropyl methyl cellulose phthalate (HPMCP) and cellulose acetate (CA), while indomethacin (IDN) and aspirin have been used as model drugs. The morphology of the neat and magnetic drug-loaded electrospun fibres and the release characteristics of the drugs in artificial intestinal juice were investigated. It was found that both types of electrospun composite nanofibres containing magnetite nanoparticles showed superparamagnetism at room temperature, and their saturation magnetisation and morphology depend on the Fe3O4 nanoparticle content. Furthermore, the presence of the magnetite nanoparticles did not affect the drug release profiles of the nanofibrous devices. The feasibility of controlled drug release to a target area of treatment under the guidance of an external magnetic field has also been demonstrated, showing the viability of the concept of magnetic drug-loaded polymeric composite nanofibres for magneto-chemotherapy.

Femtosecond laser inscribed Bragg sensor in Terfenol-D coated optical fibre with ablated microslot for the detection of static magnetic fields

A novel device for the detection and characterisation of static magnetic fields is presented. It consists of a femtosecond laser inscribed fibre Bragg grating (FBG) that is incorporated into an optical fibre with a femtosecond laser micromachined slot. The symmetry of the fibre is broken by the micro-slot, producing non-uniform strain across the fibre cross section. The sensing region is coated with Terfenol-D making the device sensitive to static magnetic fields, whereas the symmetry breaking results in a vectorial sensor for the detection of magnetic fields as low as 0.046 mT with a resolution of ±0.3mT in transmission and ±0.7mT in reflection. The sensor output is directly wavelength encoded from the FBG filtering, leading to simple demodulation through the monitoring of wavelength shifts that result as the fibre structure changes shape in response to the external magnetic field. The use of a femtosecond laser to both inscribe the FBG and micro-machine the slot in a single stage, prior to coating the device, significantly simplifies the sensor fabrication.

Femtosecond laser inscribed Bragg sensor in Terfenol-D coated optical fibre with ablated microslot for the detection of static magnetic fields

A novel device for the detection and characterisation of static magnetic fields is presented. It consists of a femtosecond laser inscribed fibre Bragg grating (FBG) that is incorporated into an optical fibre with a femtosecond laser micromachined slot. The symmetry of the fibre is broken by the micro-slot, producing non-uniform strain across the fibre cross section. The sensing region is coated with Terfenol-D making the device sensitive to static magnetic fields, whereas the symmetry breaking results in a vectorial sensor for the detection of magnetic fields as low as 0.046 mT with a resolution of ±0.3mT in transmission and ±0.7mT in reflection. The sensor output is directly wavelength encoded from the FBG filtering, leading to simple demodulation through the monitoring of wavelength shifts that result as the fibre structure changes shape in response to the external magnetic field. The use of a femtosecond laser to both inscribe the FBG and micro-machine the slot in a single stage, prior to coating the device, significantly simplifies the sensor fabrication.

Direct observation of R...R distances in rare-earth (R) phosphate glasses by magnetic difference neutron diffraction

A magnetic difference neutron diffraction study of a rare-earth (Tb) phosphate glass has revealed exclusively the Tb...Tb distances. The difference between data taken with and without an applied magnetic field of 4 T shows Tb...Tb pairwise atomic correlations at 3.9 and 6.4 A, respectively, with relative coordination numbers of 1:14. The first distance arises when two Tb3+ ions share a common oxygen neighbor, and indicates a clustering of rare-earth ions. The second distance arises when two Tb3+ ions are coordinated to different oxygens in the same PO4 group, in a near-linear arrangement.

Dynamical Resonances and SSF Singularities for a Magnetic Schrödinger Operator

We consider the Hamiltonian H of a 3D spinless non-relativistic quantum particle subject to parallel constant magnetic and non-constant electric field. The operator H has infinitely many eigenvalues of infinite multiplicity embedded in its continuous spectrum. We perturb H by appropriate scalar potentials V and investigate the transformation of these embedded eigenvalues into resonances. First, we assume that the electric potentials are dilation-analytic with respect to the variable along the magnetic field, and obtain an asymptotic expansion of the resonances as the coupling constant ϰ of the perturbation tends to zero. Further, under the assumption that the Fermi Golden Rule holds true, we deduce estimates for the time evolution of the resonance states with and without analyticity assumptions; in the second case we obtain these results as a corollary of suitable Mourre estimates and a recent article of Cattaneo, Graf and Hunziker [11]. Next, we describe sets of perturbations V for which the Fermi Golden Rule is valid at each embedded eigenvalue of H; these sets turn out to be dense in various suitable topologies. Finally, we assume that V decays fast enough at infinity and is of definite sign, introduce the Krein spectral shift function for the operator pair (H+V, H), and study its singularities at the energies which coincide with eigenvalues of infinite multiplicity of the unperturbed operator H.

Fiber optic sensing of magnetic fields utilizing femtosecond laser sculpted microslots and long period gratings coated with Terfenol-D

Fiber optic sensors are fabricated for detecting static magnetic fields. The sensors consist of a UV inscribed long period grating with two 50 micron long microslots. The microslots are fabricated using the femtosecond laser based inscribe and etch technique. The microslots and the fiber surface are coated with a magnetostrictive material Terfenol-D. A spectral sensitivity of 1.15 pm/mT was measured in transmission with a working resolution of ±0.2 mT for a static magnetic field strength below 10 mT. These devices also present a different response when the spatial orientation of the fiber was adjusted relative to the magnetic field lines.