Fusion Simulation Project: Integrated Simulation and Optimization of Magnetic Fusion Systems

This is the final report of a panel established as a subcommittee of the U. S. Department of Energy (DOE) Fusion Energy Sciences Committee (FESAC) on Integrated Simulation and Optimization of Magnetic Fusion Systems (ISOFS). The report was requested by the DOE in February 2002 and the approved report was transmitted to the DOE by the FESAC in December 2002. The report addresses the challenge of how to develop fully integrated capability for predicting the performance of externally-controlled systems including turbulent transport, macroscopic stability, wave-particle physics, and multi-phase interfaces.     

Exposure to cigarette promotions and smoking uptake in adolescents: evidence of a dose-response relation

OBJECTIVE: To assess whether a dose-response relation exists between the number of cigarette promotional items (CPIs) owned by an adolescent, and smoking behaviour. DESIGN AND SETTING: Voluntary, self administered survey of 1265 sixth through to 12th grade students (ages 10-19 years), representing 79-95% of all students attending five rural New Hampshire and Vermont public (state funded) schools in October 1996. The association between the number of CPIs owned by students and smoking behaviour was examined using multivariate regression methods. OUTCOME MEASURES: Adjusted odds of being a smoker (>/= 100 cigarettes lifetime) and, among never and experimental smokers, adjusted cumulative odds of having higher levels on a smoking uptake index given the number of CPIs owned. RESULTS: One third of students owned a CPI (n = 406). Among owners, 211 owned one, 82 owned two, 57 owned three, 24 owned four, 23 owned five, and 7 students owned six CPIs. The number of CPIs owned by students was not associated with grade in school but was significantly higher in males, those with poorer school performance, those who perceived high prevalence of peer smoking, and those with higher exposure to peer and family smoking. The more items a student owned, the greater the chances of being a smoker. For example, smoking prevalence was 11.2% for those not owning a CPI, 41.5% for those owning two, 58.5% for those owning four, and 71.4% for those owning six CPIs. The dose-response relation remained after controlling for confounding; compared with those who did not own a CPI, the likelihood of being a smoker was significantly higher for those who owned one CPI, with an adjusted odds ratio (OR) of 2.7 (95% confidence interval (CI) 1.7 to 4.1); OR was 3.4 (95% CI 1.9 to 5.9) for those owning two CPIs, and 8.4 (95% CI 5.0 to 14.2) for those owning three or more CPIs. After excluding smokers, there was a crude dose-response association between CPI ownership and higher rates of experimentation with cigarettes among sixth to ninth graders (ages 11-15 years) only (n = 543). After controlling for confounding influences, the dose-response relation remained, with the likelihood of being higher on the smoking uptake index rising with the number of CPIs owned: one CPI, adjusted cumulative OR 1.7 (95% CI 1.1 to 2.60); two CPIs, OR 2.5 (95% CI 1.2 to 5.1); and three or more CPIs, OR 4.8 (95% CI 1.9 to 12.2). CONCLUSIONS: This study offers evidence of a dose-response relation between the number of CPIs owned by adolescents and higher likelihood of experimental and established smoking. The dose-response relation persists after controlling for confounding influences. These data provide further support of a causal relation between tobacco promotional campaigns and smoking behaviour among adolescents.     

Two mode theory of Bose–Einstein condensates: interferometry and the Josephson model

This topical review provides an overview of the key theoretical features of Bose–Einstein condensates (BECs) in cold atomic gases at near zero temperature in the situation where all the bosons occupy at most two single particle states or modes. This situation applies to single-component BECs in double well trap potentials and to two-component BEC in single well trap potentials, such as occur when BEC are used in interferometry experiments. The Hamiltonian is introduced in terms of field operators and mode expansions are restricted to a total of two modes. Spin operators and their eigenstates are introduced as the fundamental basis states for describing the two-mode N boson quantum system. The spin states have a macroscopic angular momentum quantum number of N/2 and the magnetic quantum number k specifies the relative number of bosons in the two modes. The treatment presented involves an extensive use of angular momentum theory, including unitary rotation operators. Important states of the two-mode system such as binomial or coherent states, relative phase eigenstates are discussed. Boson position measurements are specified via quantum correlation functions, and the use of these functions in describing coherence properties, interference patterns and fragmentation effects in BECs is presented. The Bloch vector is defined and related to the quantum correlation functions, with quantum fluctuations of the Bloch vector being treated in terms of the covariance matrix. Applications to important two-mode states are made. Spin squeezing is discussed. Based on applying variational principles, the general dynamical behaviour of the two-mode BEC is determined via generalised Gross–Pitaevskii equations for the modes and matrix mechanics equations for the probability amplitudes of the relative number basis states, the mode and amplitude equations being coupled and self-consistent. The single mode equations are also presented. The Hamiltonian is written in terms of the spin operators and the Josephson Hamiltonian obtained as a simplification in which the dynamical behaviour of the mode functions is ignored – for the one-component case the mode functions are also required to be localised and separate. Coefficients in the Josephson Hamiltonian describe tunneling/intercomponent coupling, asymmetry and collisions and these are defined via integrals involving the mode functions. The Josephson model involves using the Josephson Hamiltonian to give simple predictions of the energy states and dynamical behaviour of the two-mode system, dynamical effects on the mode functions being ignored. The three regimes – Rabi, Josephson and Fock are described, and the energy states obtained for the Fock and Rabi regimes. Dynamical behaviour treatments based on the Josephson model are outlined. In the situation where all bosons are in the same single particle state, semi-classical Bloch equations are derived and their solutions given in terms of elliptic functions. The quantum regime is treated using matrix mechanics equations for the probability amplitudes. Two representative applications of the Josephson model dynamics are treated, with graphs showing the results of numerical work being displayed. The first is in describing Heisenberg limited BEC interferometry for a single-component BEC in a double well, the treatment showing collapses and revivals in the probability distribution for the relative phase. The second treats Ramsey interferometry for a two-component BEC in a single well, the study revealing that oscillations of the Bloch vector collapse and revive, with the Bloch vector's departure from the Bloch sphere during the collapse period revealing that the BEC has fragmented. In both cases collisions cause the dephasing effects that result in the collapse, revival phenomena. The review ends with a brief outline of phase space and other approaches that extend the treatment beyond the two-mode theory, enabling decoherence effects associated with bosons in non-condensate modes to be studied. A summary of the review contents is included. Detailed mathematical derivations are included in several appendices, available as online supplementary material.     

Field quantization,photons and non-Hermitean modes

Field quantization in unstable optical systems is treated by expanding the vector potential in terms of non-Hermitean (Fox-Li) modes. We define non-Hermitean modes and their adjoints in both the cavity and external regions and make use of the important bi-orthogonality relationships that exist within each mode set. We employ a standard canonical quantization procedure involving the introduction of generalized coordinates and momenta for the electromagnetic (EM) field. Three-dimensional systems are treated, making use of the paraxial and monochromaticity approximations for the cavity non-Hermitean modes. We show that the quantum EM field is equivalent to a set of quantum harmonic oscillators (QHOs), associated with either the cavity or the external region non-Hermitean modes, and thus confirming the validity of the photon model in unstable optical systems. Unlike in the conventional (Hermitean mode) case, the annihilation and creation operators we define for each QHO are not Hermitean adjoints. It is shown that the quantum Hamiltonian for the EM field is the sum of non-commuting cavity and external region contributions, each of which can be expressed as a sum of independent QHO Hamiltonians for each non-Hermitean mode, except that the external field Hamiltonian also includes a coupling term responsible for external non-Hermitean mode photon exchange processes. The non-commutativity of certain cavity and external region annihilation and creation operators is associated with cavity energy gain and loss processes, and may be described in terms of surface integrals involving cavity and external region non-Hermitean mode functions on the cavity-external region boundary. Using the essential states approach and the rotating wave approximation, our results are applied to the spontaneous decay of a two-level atom inside an unstable cavity. We find that atomic transitions leading to cavity non-Hermitean mode photon absorption are associated with a different coupling constant to that for transitions leading to photon emission, a feature consequent on the use of non-Hermitean mode functions. We show that under certain conditions the spontaneous decay rate is enhanced by the Petermann factor.     

Decoherence rates in large-scale quantum computers and macroscopic quantum systems

Markovian regime decoherence effects in quantum computers are studied in terms of the fidelity for the situation where the number of qubits N becomes large. A general expression giving the decoherence time scale in terms of Markovian relaxation elements and expectation values of products of system fluctuation operators is obtained, which could also be applied to study decoherence in other macroscopic systems such as Bose condensates and superconductors. A standard circuit model quantum computer involving three-state lambda system ionic qubits is considered, with qubits localized around well-separated positions via trapping potentials. The centre of mass vibrations of the qubits act as a reservoir. Coherent one and two qubit gating processes are controlled by time-dependent localized classical electromagnetic fields that address specific qubits, the two qubit gating processes being facilitated by a cavity mode ancilla, which permits state interchange between qubits. With a suitable choice of parameters, it is found that the decoherence time can be made essentially independent of N.     

Weighted fourier series representation and its application to quantifying the amount of gray matter

We present a novel weighted Fourier series (WFS) representation for cortical surfaces. The WFS representation is a data smoothing technique that provides the explicit smooth functional estimation of unknown cortical boundary as a linear combination of basis functions. The basic properties of the representation are investigated in connection with a self-adjoint partial differential equation and the traditional spherical harmonic (SPHARM) representation. To reduce steep computational requirements, a new iterative residual fitting (IRF) algorithm is developed. Its computational and numerical implementation issues are discussed in detail. The computer codes are also available at http://www.stat.wisc.edu/-mchung/softwares/weighted.SPHARM/weighted-SPHARM.html. As an illustration, the WFS is applied i n quantifying the amount ofgray matter in a group of high functioning autistic subjects. Within the WFS framework, cortical thickness and gray matter density are computed and compared.     

Directing substrate morphology via self-assembly: ligand-mediated scission of gallium-indium microspheres to the nanoscale

We have developed a facile method for the construction of liquid-phase eutectic gallium-indium (EGaIn) alloy nanoparticles. Particle formation is directed by molecular self-assembly and assisted by sonication. As the bulk liquid alloy is ultrasonically dispersed, fast thiolate self-assembly at the EGaIn interface protects the material against oxidation. The choice of self-assembled monolayer ligand directs the ultimate size reduction in the material; strongly interacting molecules induce surface strain and assist particle cleavage to the nanoscale. Transmission electron microscopy images and diffraction analyses reveal that the nanoscale particles are in an amorphous or liquid phase, with no observed faceting. The particles exhibit strong absorption in the ultraviolet (～200 nm), consistent with the gallium surface plasmon resonance, but dependent on the nature of the particle ligand shell.     

Superior fatigue crack growth resistance, irreversibility, and fatigue crack growth–microstructure relationship of nanocrystalline alloys

While previous studies have reported that nanocrystalline materials exhibit poor resistance to fatigue crack growth (FCG), the electro-deposited nanocrystalline Ni–Co alloys tested in this paper show superior resistance to FCG. The high damage tolerance of our alloy is attributed to the following: alloying with Co, low internal stresses resulting in stability of the microstructure, and a combination of high strength and ductility. The high density of grain boundaries interact with the dislocations emitted from the crack tip, which impedes FCG, as predicted by the present model and measured experimentally by digital image correlation. Further, the addition of Co increases the strength of the material by refining the grain size, reducing the fraction of low angle grain boundaries, and reducing the stacking fault energy of the material, thereby increasing the prevalence of twinning. The microstructure is stabilized by minimizing the internal stress during a stress relief heat treatment following the electro-deposition process. As a result grain growth does not occur during deformation, leaving dislocation-mediated plasticity as the primary deformation mechanism. The low internal stresses and nanoscale twins preserve the ductility of the material, thereby reaching a balance between strength and ductility, which results in a superior resistance to FCG.