The Generation of Fullerenes

We describe an efficient new algorithm for the generation of fullerenes. Our implementation of this algorithm is more than 3.5 times faster than the previously fastest generator for fullerenes -- fullgen -- and the first program since fullgen to be useful for more than 100 vertices. We also note a programming error in fullgen that caused problems for 136 or more vertices. We tabulate the numbers of fullerenes and IPR fullerenes up to 400 vertices. We also check up to 316 vertices a conjecture of Barnette that cubic planar graphs with maximum face size 6 are hamiltonian and verify that the smallest counterexample to the spiral conjecture has 380 vertices.Comment: 21 pages; added a not

Economic analysis of condition monitoring systems for offshore wind turbine sub-systems

The use of condition monitoring systems on wind turbines has increased dramatically in recent times. However, their use is mostly restricted to vibration based monitoring systems for the gearbox, generator and drive train. There are many forms and types of condition monitoring systems now available for wind turbines. A survey of commercially available condition monitoring systems and their associated costs has been undertaken for the blades, drive train and tower. This paper considers what value can be obtained from these systems if they are used correctly. This is achieved by running simulations on an operations and maintenance model for a 20 year life cycle wind farm. The model uses Hidden Markov Models to represent both the actual system state and the observed state. The costs for system failures are derived, as are possible reductions in these costs due to early detection. Various scenarios are simulated including the addition of condition monitoring systems to the drive train and blade and tower monitoring. Finally, the efficacy of these systems is examined and its effect on operation costs

Dynamics of quantum systems

A relation between the eigenvalues of an effective Hamilton operator and the poles of the $S$ matrix is derived which holds for isolated as well as for overlapping resonance states. The system may be a many-particle quantum system with two-body forces between the constituents or it may be a quantum billiard without any two-body forces. Avoided crossings of discrete states as well as of resonance states are traced back to the existence of branch points in the complex plane. Under certain conditions, these branch points appear as double poles of the $S$ matrix. They influence the dynamics of open as well as of closed quantum systems. The dynamics of the two-level system is studied in detail analytically as well as numerically.Comment: 21 pages 7 figure

Geometric Phases and Multiple Degeneracies in Harmonic Resonators

In a recent experiment Lauber et al. have deformed cyclically a microwave resonator and have measured the adiabatic normal-mode wavefunctions for each shape along the path of deformation. The nontrivial observed cyclic phases around a 3-fold degeneracy were accounted for by Manolopoulos and Child within an approximate theory. However, open-path geometrical phases disagree with experiment. By solving exactly the problem, we find unsuspected extra degeneracies around the multiple one that account for the measured phase changes throughout the path. It turns out that proliferation of additional degeneracies around a multiple one is a common feature of quantum mechanics.Comment: 4 pages, 4 figures. Accepted in Phys. Rev. Let

Topological Phases near a Triple Degeneracy

We study the pattern of three state topological phases that appear in systems with real Hamiltonians and wave functions. We give a simple geometric construction for representing these phases. We then apply our results to understand previous work on three state phases. We point out that the ``mirror symmetry'' of wave functions noticed in microwave experiments can be simply understood in our framework.Comment: 4 pages, 1 figure, to appear in Phys. Rev. Let

Off-Diagonal Geometric Phases

We investigate the adiabatic evolution of a set of non-degenerate eigenstates of a parameterized Hamiltonian. Their relative phase change can be related to geometric measurable quantities that extend the familiar concept of Berry phase to the evolution of more than one state. We present several physical systems where these concepts can be applied, including an experiment on microwave cavities for which off-diagonal phases can be determined from published data.Comment: 5 pages 2 figures - RevTeX. Revised version including geometrical interpretatio

Proton-counting radiography for proton therapy: a proof of principle using CMOS APS technology

Despite the early recognition of the potential of proton imaging to assist proton therapy (Cormack 1963 J. Appl. Phys. 34 2722), the modality is still removed from clinical practice, with various approaches in development. For proton-counting radiography applications such as computed tomography (CT), the water-equivalent-path-length that each proton has travelled through an imaged object must be inferred. Typically, scintillator-based technology has been used in various energy/range telescope designs. Here we propose a very different alternative of using radiation-hard CMOS active pixel sensor technology. The ability of such a sensor to resolve the passage of individual protons in a therapy beam has not been previously shown. Here, such capability is demonstrated using a 36 MeV cyclotron beam (University of Birmingham Cyclotron, Birmingham, UK) and a 200 MeV clinical radiotherapy beam (iThemba LABS, Cape Town, SA). The feasibility of tracking individual protons through multiple CMOS layers is also demonstrated using a two-layer stack of sensors. The chief advantages of this solution are the spatial discrimination of events intrinsic to pixelated sensors, combined with the potential provision of information on both the range and residual energy of a proton. The challenges in developing a practical system are discussed

The variable phase method used to calculate and correct scattering lengths

It is shown that the scattering length can be obtained by solving a Riccati equation derived from variable phase theory. Two methods of solving it are presented. The equation is used to predict how long-range interactions influence the scattering length, and upper and lower bounds on the scattering length are determined. The predictions are compared with others and it is shown how they may be obtained from secular perturbation theory.Comment: 7 pages including 3 figure