Two topics in elementary particle physics. I. Crossing as a group and elimination of exotic channels. II. Real parts of meson-nucleon forward scattering amplitudes.

I. Crossing transformations constitute a group of permutations under which the scattering amplitude is invariant. Using Mandelstem's analyticity, we decompose the amplitude into irreducible representations of this group. The usual quantum numbers, such as isospin or SU(3), are "crossing-invariant". Thus no higher symmetry is generated by crossing itself. However, elimination of certain quantum numbers in intermediate states is not crossing-invariant, and higher symmetries have to be introduced to make it possible. The current literature on exchange degeneracy is a manifestation of this statement. To exemplify application of our analysis, we show how, starting with SU(3) invariance, one can use crossing and the absence of exotic channels to derive the quark-model picture of the tensor nonet. No detailed dynamical input is used.

II. A dispersion relation calculation of the real parts of forward π^±p and K^±p scattering amplitudes is carried out under the assumption of constant total cross sections in the Serpukhov energy range. Comparison with existing experimental results as well as predictions for future high energy experiments are presented and discussed. Electromagnetic effects are found to be too small to account for the expected difference between the π^-p and π⁺p total cross sections at higher energies.

Distributed Optimal Control of Cyber-Physical Systems: Controller Synthesis, Architecture Design and System Identification

The centralized paradigm of a single controller and a single plant upon which modern control theory is built is no longer applicable to modern cyber-physical systems of interest, such as the power-grid, software defined networks or automated highways systems, as these are all large-scale and spatially distributed. Both the scale and the distributed nature of these systems has motivated the decentralization of control schemes into local sub-controllers that measure, exchange and act on locally available subsets of the globally available system information. This decentralization of control logic leads to different decision makers acting on asymmetric information sets, introduces the need for coordination between them, and perhaps not surprisingly makes the resulting optimal control problem much harder to solve. In fact, shortly after such questions were posed, it was realized that seemingly simple decentralized optimal control problems are computationally intractable to solve, with the Wistenhausen counterexample being a famous instance of this phenomenon. Spurred on by this perhaps discouraging result, a concerted 40 year effort to identify tractable classes of distributed optimal control problems culminated in the notion of quadratic invariance, which loosely states that if sub-controllers can exchange information with each other at least as quickly as the effect of their control actions propagates through the plant, then the resulting distributed optimal control problem admits a convex formulation.

The identification of quadratic invariance as an appropriate means of "convexifying" distributed optimal control problems led to a renewed enthusiasm in the controller synthesis community, resulting in a rich set of results over the past decade. The contributions of this thesis can be seen as being a part of this broader family of results, with a particular focus on closing the gap between theory and practice by relaxing or removing assumptions made in the traditional distributed optimal control framework. Our contributions are to the foundational theory of distributed optimal control, and fall under three broad categories, namely controller synthesis, architecture design and system identification.

We begin by providing two novel controller synthesis algorithms. The first is a solution to the distributed H-infinity optimal control problem subject to delay constraints, and provides the only known exact characterization of delay-constrained distributed controllers satisfying an H-infinity norm bound. The second is an explicit dynamic programming solution to a two player LQR state-feedback problem with varying delays. Accommodating varying delays represents an important first step in combining distributed optimal control theory with the area of Networked Control Systems that considers lossy channels in the feedback loop. Our next set of results are concerned with controller architecture design. When designing controllers for large-scale systems, the architectural aspects of the controller such as the placement of actuators, sensors, and the communication links between them can no longer be taken as given -- indeed the task of designing this architecture is now as important as the design of the control laws themselves. To address this task, we formulate the Regularization for Design (RFD) framework, which is a unifying computationally tractable approach, based on the model matching framework and atomic norm regularization, for the simultaneous co-design of a structured optimal controller and the architecture needed to implement it. Our final result is a contribution to distributed system identification. Traditional system identification techniques such as subspace identification are not computationally scalable, and destroy rather than leverage any a priori information about the system's interconnection structure. We argue that in the context of system identification, an essential building block of any scalable algorithm is the ability to estimate local dynamics within a large interconnected system. To that end we propose a promising heuristic for identifying the dynamics of a subsystem that is still connected to a large system. We exploit the fact that the transfer function of the local dynamics is low-order, but full-rank, while the transfer function of the global dynamics is high-order, but low-rank, to formulate this separation task as a nuclear norm minimization problem. Finally, we conclude with a brief discussion of future research directions, with a particular emphasis on how to incorporate the results of this thesis, and those of optimal control theory in general, into a broader theory of dynamics, control and optimization in layered architectures.

CP and the three pion decay of the K°

The time distribution of the decays of an initially pure K° beam into π+π-π° has been analyzed to determine the complex parameter W (also known as Ƞ^+-° and (x + iy)). The K° beam was produced in a brass target by the interactions of a 2.85 GeV/c π- beam which was generated on an internal target in the Lawrence Radiation Laboratory (LRL) Bevatron. The counters and hodoscopes in the apparatus selected for events with a neutral (K°) produced in the brass target, two charged secondaries passing through a magnet spectrometer and a ɣ-ray shower in a shower hodoscope.

From the 275K apparatus triggers, 148 K → π+π-π° events were isolated. The presence of a ɣ-ray shower in the optical shower chambers and a two-prong vee in the optical spark chambers were devices used to isolate the events. The backgrounds were further reduced by reconstructing the momenta of the two charged secondaries and applying kinematic constraints.

The best fit to the final sample of 148 events distributed between .3 and 7.0 K_S lifetimes gives:

ReW = -.05 ±.17

ImW = +.39 +.35/-.37

This result is consistent with both CPT invariance (ReW = 0) and CP invariance (W = 0). Backgrounds are estimated to be less than 10% and systematic effects have also been estimated to be negligible.

An analysis of the present data on CP violation in this decay mode and other K° decay modes has estimated the phase of ɛ to be 45.3 ± 2.3 degrees. This result is consistent with the super weak theories of CP violation which predicts the phase of ɛ to be 43°. This estimate is in turn used to predict the phase of Ƞ°° to be 48.0 ± 7.9 degrees. This is a substantial improvement on presently available measurements. The largest error in this analysis comes from the present limits on W from the world average of recent experiments. The K → πuʋ mode produces the next largest error. Therefore further experimentation in these modes would be useful.

Photodisintegration of helium-3 at energies between 200 and 600 MEV

We have measured differential cross-sections for the two-body photodisintegration of Helium-3, ɣ + He³ → p + d, between incident photon energies of 200 and 600 MeV, and for center of mass frame angles between 30° and 150°. Both final state particles were detected in arrays of wire spark chambers and scintillation counters; the high momentum particle was analyzed in a magnet spectrometer. The results are interpreted in terms of amplitudes to produce the ∆(1236) resonance in an intermediate state, as well as non-resonant amplitudes. This experiment, together with an (unfinished) experiment on the inverse reaction, p + d → He³ + ɣ, will provide a reciprocity test of time reversal invariance.

洛仑兹脉冲光束的复振幅包络解和复解析信号解的比较研究

使用复振幅包络表示式和复解析信号表示式推导了洛仑兹脉冲光束的传输公式．通过具体数值计算对脉冲光束的复振幅包络解和复解析信号解在不同带宽时的传输进行了对比研究．数值结果表明脉冲光束为窄带时，在传输方向轴中心的一定范围内两种解是一致的，而对于宽带脉冲光束，复振幅包络解在轴中心较近的距离即表现出奇异性，复解析信号解才是符合物理意义的表示式．由数值计算得出了选择脉冲光束研究方法的条件，并从所得公式对复振幅包络解出现奇异性的现象进行了解释．

Charge and spin transport in graphene devices

170 p.

Optical properties of dye-doped zirconia films by spectroscopic ellipsometry

The optical properties of zirconia films doped with rhodamine 6G and oxazine 725 by the sol-gel process were investigated using spectroscopic ellipsometry (SE). Accurate refractive index n and the extinction coefficient k were determined using a three-oscillator classical Lorentz model in the wavelength range of 300-800 nm. The derived refractive index of dye-doped films exhibited anomalous dispersion in the absorption region. Wavelength tunable output lasing action yellow and near-infrared wavelength region was achieved by DFB configuration using zirconia films doped with R6G and oxazine 725. (c) 2006 Elsevier B.V. All rights reserved.

线性共蒸法制备渐变折射率薄膜的光学特性分析

利用德鲁德理论和洛伦兹一洛伦茨理论，从介电常数分析人手，探讨了混合介质膜的折射率表达式，给出利用双源共蒸法镀制的渐变折射率薄膜在混合介质膜的总沉积速率恒定、两种膜料的单分子大小近似相等和沉积速率均为线性变化时的折射率表达式；从正变和负变、单周期和多周期、不同的周期数和不同的单周期厚度几个方面对渐变折射率薄膜的光学特性进行了模拟分析和讨论；对渐变折射率薄膜的实现、应用以及实验制备中有待进一步解决和处理的问题进行了讨论。

Propiedades radiativas y ópticas de una herramienta de corte compuesta por nitruro de boro cúbico

Se ha medido la emisividad espectral (2,5-25 micras) normal de una herramienta de corte industrial, compuesta en un 55% por nitruro de boro cúbico (cBN), en el rango de temperaturas 200-1000 ºC. La emisividad medida muestra un comportamiento suavemente descendente al aumentar la longitud de onda, propio de metales, con un descenso pronunciado alrededor de 9 micras. Este valle se corresponde con la emisividad calculada para el cBN cúbico puro en la literatura, que sin embargo no exhibe el comportamiento metálico medido. Así mismo, se observa que la emisividad espectral es esencialmente independiente de la temperatura, aunque no así la emisividad total. Los resultados experimentales para el cBN puro indican que la reflectividad de dicho compuesto se puede explicar satisfactoriamente mediante un modelo de Lorentz para dieléctricos, mientras que el ajuste teórico de la reflectividad medida para la herramienta de corte necesita incluir una contribución del modelo de Drude para explicar el comportamiento metálico observado. Este modelo combinado se ajusta razonablemente bien a las medidas, y revela que la herramienta de corte se comporta como un semiconductor degenerado, con una alta densidad de portadores libres. Además, permite realizar una estimación teórica de sus constantes ópticas. Por último, se ha realizado un estudio sobre la medida y el control de la temperatura de la muestra, empleando distintos métodos de unión termopar.

Uso de espinores na investigação do limite de Karlhede para ondas pp

Neste trabalho foi feito um estudo do limite de Karlhede para ondas pp. Para este fim, uma revisão rigorosa de Geometria Diferencial foi apresentada numa abordagem independente de sistemas de coordenadas. Além da abordagem usual, a curvatura de uma variedade riemanniana foi reescrita usando os formalismos de referenciais, formas diferenciais e espinores do grupo de Lorentz. O problema de equivalência para geometrias riemannianas foi formulado e as peculiaridades de sua aplicação é a Relatividade Geral são delineadas. O limite teórico de Karlhede para espaços-tempo de vácuo de tipo Petrov N foi apresentado. Esse limite é estudado na prática usando técnicas espinores e as condições para sua existência são resolvidas sem a introdução de sistemas de coordenadas.

Review of size- and age-dependence in batch spawning: implications for stock assessment of fish species exhibiting indeterminate fecundity

Most assessments of fish stocks use some measure of the reproductive potential of a population, such as spawning biomass. However, the correlation between spawning biomass and reproductive potential is not always strong, and it likely is weakest in the tropics and subtropics, where species tend to exhibit indeterminate fecundity and release eggs in batches over a protracted spawning season. In such cases, computing annual reproductive output requires estimates of batch fecundity and the annual number of batches—the latter subject to spawning frequency and duration of spawning season. Batch fecundity is commonly measured by age (or size), but these other variables are not. Without the relevant data, the annual number of batches is assumed to be invariant across age. We reviewed the literature and found that this default assumption lacks empirical support because both spawning duration and spawning frequency generally increase with age or size. We demonstrate effects of this assumption on measures of reproductive value and spawning potential ratio, a metric commonly used to gauge stock status. Model applications showed substantial sensitivity to age dependence in the annual number of batches. If the annual number of batches increases with age but is incorrectly assumed to be constant, stock assessment models would tend to overestimate the biological reference points used for setting harvest rates. This study underscores the need to better understand the age- or size-dependent contrast in the annual number of batches, and we conclude that, for species without evidence to support invariance, the default assumption should be replaced with one that accounts for age- or size-dependence.

Multimode radiation from an unflanged, semi-infinite circular duct with uniform flow.

Multimode sound radiation from an unflanged, semi-infinite, rigid-walled circular duct with uniform subsonic mean flow everywhere is investigated theoretically. The multimode directivity depends on the amplitude and directivity function of each individual cut-on mode. The amplitude of each mode is expressed as a function of cut-on ratio for a uniform distribution of incoherent monopoles, a uniform distribution of incoherent axial dipoles, and for equal power per mode. The directivity function of each mode is obtained by applying a Lorentz transformation to the zero-flow directivity function, which is given by a Wiener-Hopf solution. This exact numerical result is compared to an analytic solution, valid in the high-frequency limit, for multimode directivity with uniform flow. The high-frequency asymptotic solution is derived assuming total transmission of power at the open end of the duct, and gives the multimode directivity function with flow in the forward arc for a general family of mode amplitude distribution functions. At high frequencies the agreement between the exact and asymptotic solutions is shown to be excellent.

Face recognition from video

In spite of over two decades of intense research, illumination and pose invariance remain prohibitively challenging aspects of face recognition for most practical applications. The objective of this work is to recognize faces using video sequences both for training and recognition input, in a realistic, unconstrained setup in which lighting, pose and user motion pattern have a wide variability and face images are of low resolution. In particular there are three areas of novelty: (i) we show how a photometric model of image formation can be combined with a statistical model of generic face appearance variation, learnt offline, to generalize in the presence of extreme illumination changes; (ii) we use the smoothness of geodesically local appearance manifold structure and a robust same-identity likelihood to achieve invariance to unseen head poses; and (iii) we introduce an accurate video sequence "reillumination" algorithm to achieve robustness to face motion patterns in video. We describe a fully automatic recognition system based on the proposed method and an extensive evaluation on 171 individuals and over 1300 video sequences with extreme illumination, pose and head motion variation. On this challenging data set our system consistently demonstrated a nearly perfect recognition rate (over 99.7%), significantly outperforming state-of-the-art commercial software and methods from the literature. © Springer-Verlag Berlin Heidelberg 2006.

High frequency multimode radiation from ducts with flow

Multimode sound radiation from hard-walled semi-infinite ducts with uniform subsonic flow is investigated theoretically. An analytic expression, valid in the high frequency limit, is derived for the multimode directivity function in the forward arc for a general family of mode distribution functions. The multimode directivity depends on the amplitude and directivity function of each individual mode. The amplitude of each mode is expressed as a function of cut-off ratio for a uniform distribution of incoherent monopoles, a uniform distribution of incoherent axial dipoles and for equal power per mode. The modes' directivity functions are obtained analytically by applying a Lorentz transformation to the zero flow solution. The analytic formula for the multimode directivity with flow is derived assuming total transmission of power at the open-end of the duct. This formula is compared to the exact numerical result for an unflanged duct, computed utilizing a Wiener-Hopf solution. The agreement is shown to be excellent. Copyright © 2008 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Fem modeling of periodic arrays of multi-walled carbon nanotubes

Multiwalled carbon nanotubes display dielectric properties similar to those of graphite, which can be calculated using the well known Drude-Lorentz model. However, most computational softwares lack the capacity to directly incorporate this model into the simulations. We present the finite element modeling of optical propagation through periodic arrays of multiwalled carbon nanotubes. The dielectric function of nanotubes was incorporated into the model by using polynomial curve fitting technique. The computational analysis revealed interesting metamaterial filtering effects displayed by the highly dense square lattice arrays of carbon nanotubes, having lattice constants of the order few hundred nanometers. The curve fitting results for the dielectric function can also be used for simulating other interesting optical applications based on nanotube arrays.