Spin-detection in a quantum electromechanical shuttle system

We study the electrical transport of a harmonically bound, single-molecule C-60 shuttle operating in the Coulomb blockade regime, i.e. single electron shuttling. In particular, we examine the dependance of the tunnel current on an ultra-small stationary force exerted on the shuttle. As an example, we consider the force exerted on an endohedral N@C-60 by the magnetic field gradient generated by a nearby nanomagnet. We derive a Hamiltonian for the full shuttle system which includes the metallic contacts, the spatially dependent tunnel couplings to the shuttle, the electronic and motional degrees of freedom of the shuttle itself and a coupling of the shuttle's motion to a phonon bath. We analyse the resulting quantum master equation and find that, due to the exponential dependence of the tunnel probability on the shuttle-contact separation, the current is highly sensitive to very small forces. In particular, we predict that the spin state of the endohedral electrons of N@C-60 in a large magnetic gradient field can be distinguished from the resulting current signals within a few tens of nanoseconds. This effect could prove useful for the detection of the endohedral spin-state of individual paramagnetic molecules such as N@C-60 and P@C-60, or the detection of very small static forces acting on a C-60 shuttle.

The exact sample complexity of PAC-learning problems with unit VC dimension

The Vapnik-Chervonenkis (VC) dimension is a combinatorial measure of a certain class of machine learning problems, which may be used to obtain upper and lower bounds on the number of training examples needed to learn to prescribed levels of accuracy. Most of the known bounds apply to the Probably Approximately Correct (PAC) framework, which is the framework within which we work in this paper. For a learning problem with some known VC dimension, much is known about the order of growth of the sample-size requirement of the problem, as a function of the PAC parameters. The exact value of sample-size requirement is however less well-known, and depends heavily on the particular learning algorithm being used. This is a major obstacle to the practical application of the VC dimension. Hence it is important to know exactly how the sample-size requirement depends on VC dimension, and with that in mind, we describe a general algorithm for learning problems having VC dimension 1. Its sample-size requirement is minimal (as a function of the PAC parameters), and turns out to be the same for all non-trivial learning problems having VC dimension 1. While the method used cannot be naively generalised to higher VC dimension, it suggests that optimal algorithm-dependent bounds may improve substantially on current upper bounds.

Regression with input-dependent noise: A Gaussian process treatment

Gaussian processes provide natural non-parametric prior distributions over regression functions. In this paper we consider regression problems where there is noise on the output, and the variance of the noise depends on the inputs. If we assume that the noise is a smooth function of the inputs, then it is natural to model the noise variance using a second Gaussian process, in addition to the Gaussian process governing the noise-free output value. We show that prior uncertainty about the parameters controlling both processes can be handled and that the posterior distribution of the noise rate can be sampled from using Markov chain Monte Carlo methods. Our results on a synthetic data set give a posterior noise variance that well-approximates the true variance.

Quantification of the relationship between, magnetoencephalographic (MEG) and blood oxygenation dependent (BOLD) images of brain function

Magnetoencephalography (MEG) is the measurement of the magnetic fields generated outside the head by the brain’s electrical activity. The technique offers the promise of high temporal and spatial resolution. There is however an ambiguity in the inversion process of estimating what goes on inside the head from what is measured outside. Other techniques, such as functional Magnetic Resonance Imaging (fMRI) have no such inversion problems yet suffer from poorer temporal resolution. In this study we examined metrics of mutual information and linear correlation between volumetric images from the two modalities. Measures of mutual information reveal a significant, non-linear, relationship between MEG and fMRI datasets across a number of frequency bands.

Synthesis and evaluation of novel ligands for quantum dot stabilisation and polymerisation studies

This thesis describes the design and synthesis of a variety of functionalised phosphine oxides and sulfides, based on the structure of trioctylphosphine oxide, synthesised for the purpose of surface modification of quantum dots. The ability of the ligands to modify the surface chemistry via displacement of the original hexadecylamine capping layer of quantum dots was evaluated. Finally the surface modified quantum dots were investigated for enhancement in their inherent properties and improved compatibility with the various applications for which they were initially designed. Upon the commencement of research involving quantum dots it became apparent that more information on their behaviour and interaction with the environment was required. The limits of the inherent stability of hexadecylamine capped quantum dots were investigated by exposure to a number of different environments. The effect upon the stability of the quantum dots was monitored by changes in the photoluminescence ability of their cores. Subtle differences between different batches of quantum dots were observed and the necessity to account for these in future applications noted. Lastly the displacement of the original hexadecylamine coating with the "designer" functionalised ligands was evaluated to produce a set of conditions that would result in the best possible surface modification. A general procedure was elucidated however it was discovered that each displacement still required slight adjustment by consideration of the other factors such as the difference in ligand structure and the individuality of the various batches of quantum dots. This thesis also describes a procedure for the addition of a protective layer to the surface of quantum dots by cross-linking the functionalised ligands bound to the surface via an acyclic diene metathesis polymerisation. A detailed description of the problems encountered in the analysis of these materials combined with the use of novel techniques such as diffusion ordered spectroscopy is provided as a means to overcome the limitations encountered. Finally a demonstration of the superior stability, upon exposure to a range of aggressive environments of these protected materials compared with those before cross-linking provided physical proof of the cross-linking process and the advantages of the cross-linking modification. Finally this thesis includes the presentation of initial work into the production of luminescent nanocrystal encoded resin beads for the specific use in solid phase combinatorial chemistry. Demonstration of the successful covalent incorporation of quantum dots into the polymeric matrices of non-functionalised and functionalised resin beads is described. Finally by preliminary work to address and overcome the possible limitations that may be encountered in the production and general employment of these materials in combinatorial techniques is given.

A procedure for determining a spacewise dependent heat source and the initial temperature

The inverse problem of determining a spacewise dependent heat source, together with the initial temperature for the parabolic heat equation, using the usual conditions of the direct problem and information from two supplementary temperature measurements at different instants of time is studied. These spacewise dependent temperature measurements ensure that this inverse problem has a unique solution, despite the solution being unstable, hence the problem is ill-posed. We propose an iterative algorithm for the stable reconstruction of both the initial data and the source based on a sequence of well-posed direct problems for the parabolic heat equation, which are solved at each iteration step using the boundary element method. The instability is overcome by stopping the iterations at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented for a typical benchmark test example, which has the input measured data perturbed by increasing amounts of random noise. The numerical results show that the proposed procedure gives accurate numerical approximations in relatively few iterations.

A variational method for identifying a spacewise-dependent heat source

The inverse problem of determining a spacewise-dependent heat source for the parabolic heat equation using the usual conditions of the direct problem and information from one supplementary temperature measurement at a given instant of time is studied. This spacewise-dependent temperature measurement ensures that this inverse problem has a unique solution, but the solution is unstable and hence the problem is ill-posed. We propose a variational conjugate gradient-type iterative algorithm for the stable reconstruction of the heat source based on a sequence of well-posed direct problems for the parabolic heat equation which are solved at each iteration step using the boundary element method. The instability is overcome by stopping the iterative procedure at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented which have the input measured data perturbed by increasing amounts of random noise. The numerical results show that the proposed procedure yields stable and accurate numerical approximations after only a few iterations.

Determination of a spacewise dependent heat source

This paper investigates the inverse problem of determining a spacewise dependent heat source in the parabolic heat equation using the usual conditions of the direct problem and information from a supplementary temperature measurement at a given single instant of time. The spacewise dependent temperature measurement ensures that the inverse problem has a unique solution, but this solution is unstable, hence the problem is ill-posed. For this inverse problem, we propose an iterative algorithm based on a sequence of well-posed direct problems which are solved at each iteration step using the boundary element method (BEM). The instability is overcome by stopping the iterations at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented for various typical benchmark test examples which have the input measured data perturbed by increasing amounts of random noise.

Image Quotient Set Transforms in Segmentation Problems

Image content interpretation is much dependent on segmentations efficiency. Requirements for the image recognition applications lead to a nessesity to create models of new type, which will provide some adaptation between law-level image processing, when images are segmented into disjoint regions and features are extracted from each region, and high-level analysis, using obtained set of all features for making decisions. Such analysis requires some a priori information, measurable region properties, heuristics, and plausibility of computational inference. Sometimes to produce reliable true conclusion simultaneous processing of several partitions is desired. In this paper a set of operations with obtained image segmentation and a nested partitions metric are introduced.

On a Direct Approach to the Solution of Inverse Optical Problems

The evaluation from experimental data, of physical quantities, which enter into the electromagnetic Maxwell equations, is described as inverse optical problem. The functional relations between the dependent and independent variables are of transcendental character and numeric procedures for evaluation of the unknowns are largely used. Herein, we discuss a direct approach to the solution, illustrated by a specific example of determination of thin films optical constants from spectrophotometric data. New algorithm is proposed for the parameters evaluation, which does not need an initial guess of the unknowns and does not use iterative procedures. Thus we overcome the intrinsic deficiency of minimization techniques, such as gradient search methods, Simplex methods, etc. The price of it is a need of more computing power, but our algorithm is easily implemented in structures such as grid clusters. We show the advantages of this approach and its potential for generalization to other inverse optical problems.

First-Order Conditions for Optimization Problems with Quasiconvex Inequality Constraints

2000 Mathematics Subject Classification: 90C46, 90C26, 26B25, 49J52.

Remarks on blow up time for solutions of a nonlinear diffusion system with time dependent coefficients

2000 Mathematics Subject Classification: 35K55, 35K60.

Activated escape from polarization pulling in fibre Raman amplifiers

Fluctuation-induced escape (FIE) from a metastable state with probability controlled by external force is a process inherent in many physical phenomena such as diffusion in crystals, protein folding, activated chemical reactions etc. [1-3]. In this work we present a novel example of FIE problem, considering a very practical nonlinear system recently emerged in the area of fibre telecommunications. Unlike the standard FIE problems where noise is time-dependent, in fibre Raman amplifier (FRA) the role of noise is played by frozen fluctuations of parameters (random birefringence) along the fibre span which result from the breaking of cylindrical symmetry during the fibre drawing [4-6]. The role of periodic forcing in this problem is played by the periodic fibre spinning, leading to key model that is formally similar to the time-domain equations for periodically forced escape [1-3]. © 2011 IEEE.

A method of fundamental solutions for radially symmetric and axisymmetric backward heat conduction problems

We propose and investigate an application of the method of fundamental solutions (MFS) to the radially symmetric and axisymmetric backward heat conduction problem (BHCP) in a solid or hollow cylinder. In the BHCP, the initial temperature is to be determined from the temperature measurements at a later time. This is an inverse and ill-posed problem, and we employ and generalize the MFS regularization approach [B.T. Johansson and D. Lesnic, A method of fundamental solutions for transient heat conduction, Eng. Anal. Boundary Elements 32 (2008), pp. 697–703] for the time-dependent heat equation to obtain a stable and accurate numerical approximation with small computational cost.

Quantum dot materials for terahertz generation applications

Compact and tunable semiconductor terahertz sources providing direct electrical control, efficient operation at room temperatures and device integration opportunities are of great interest at the present time. One of the most well-established techniques for terahertz generation utilises photoconductive antennas driven by ultrafast pulsed or dual wavelength continuous wave laser systems, though some limitations, such as confined optical wavelength pumping range and thermal breakdown, still exist. The use of quantum dot-based semiconductor materials, having unique carrier dynamics and material properties, can help to overcome limitations and enable efficient optical-to-terahertz signal conversion at room temperatures. Here we discuss the construction of novel and versatile terahertz transceiver systems based on quantum dot semiconductor devices. Configurable, energy-dependent optical and electronic characteristics of quantum-dot-based semiconductors are described, and the resonant response to optical pump wavelength is revealed. Terahertz signal generation and detection at energies that resonantly excite only the implanted quantum dots opens the potential for using compact quantum dot-based semiconductor lasers as pump sources. Proof-of-concept experiments are demonstrated here that show quantum dot-based samples to have higher optical pump damage thresholds and reduced carrier lifetime with increasing pump power.