State Power Plant Siting: a Sketch of the Main Features of a Possible Approach

Work on various phases of power plant technology and siting has been underway within the Environmental Quality Laboratory (EQL) at the California Institute of Technology for some time. Of particular relevance to this memorandum, a good deal of effort has been devoted to institutional aspects of the siting process. Our purpose in what follows is to draw from our past work -- and from the discussions and work of others -- a sketch of the major outlines of one possible approach to power plant siting for the state. We hope in doing so to give our present views about the issues and how they might rationally be resolved, not so much to convince as to inform, stimulate fruitful ideas, and help provide the basis for constructive debate. We ourselves are not necessarily wedded to any of the discussion that follows; we find our own minds changing from time to time as we study the problem further or confront sound suggestions from others. Part I of this memorandum briefly outlines the major features of what we see as a fruitful approach to the siting problem. Sections A through E of Part I describe some elements of the approach; Section F sketches the actual siting decision process we suggest, and in doing so shows how the elements play into the process. Section G comments briefly on a suggested role for judicial review. In Part II we attempt to reduce our ideas to a fairly precise outline for a state siting statute, and to deal with certain matters of detail not covered in Part I. Section A of Part II introduces the statutory outline by summarizing each of its provisions; Section B sets forth the outline itself. The Appendix to this memorandum depicts our suggested approach in time-line fashion; it should be helpful in reading and understanding the proposal

Deriving Matrix Concentration Inequalities from Kernel Couplings

This paper derives exponential tail bounds and polynomial moment inequalities for the spectral norm deviation of a random matrix from its mean value. The argument depends on a matrix extension of Stein's method of exchangeable pairs for concentration of measure, as introduced by Chatterjee. Recent work of Mackey et al. uses these techniques to analyze random matrices with additive structure, while the enhancements in this paper cover a wider class of matrix-valued random elements. In particular, these ideas lead to a bounded differences inequality that applies to random matrices constructed from weakly dependent random variables. The proofs require novel trace inequalities that may be of independent interest.Comment: 29 page

Chaotic Mixing in Three Dimensional Porous Media

Under steady flow conditions, the topological complexity inherent to all random 3D porous media imparts complicated flow and transport dynamics. It has been established that this complexity generates persistent chaotic advection via a three-dimensional (3D) fluid mechanical analogue of the baker's map which rapidly accelerates scalar mixing in the presence of molecular diffusion. Hence pore-scale fluid mixing is governed by the interplay between chaotic advection, molecular diffusion and the broad (power-law) distribution of fluid particle travel times which arise from the non-slip condition at pore walls. To understand and quantify mixing in 3D porous media, we consider these processes in a model 3D open porous network and develop a novel stretching continuous time random walk (CTRW) which provides analytic estimates of pore-scale mixing which compare well with direct numerical simulations. We find that chaotic advection inherent to 3D porous media imparts scalar mixing which scales exponentially with longitudinal advection, whereas the topological constraints associated with 2D porous media limits mixing to scale algebraically. These results decipher the role of wide transit time distributions and complex topologies on porous media mixing dynamics, and provide the building blocks for macroscopic models of dilution and mixing which resolve these mechanisms.Comment: 36 page

Localized shear generates three-dimensional transport

Understanding the mechanisms that control three-dimensional (3D) fluid transport is central to many processes including mixing, chemical reaction and biological activity. Here a novel mechanism for 3D transport is uncovered where fluid particles are kicked between streamlines near a localized shear, which occurs in many flows and materials. This results in 3D transport similar to Resonance Induced Dispersion (RID); however, this new mechanism is more rapid and mutually incompatible with RID. We explore its governing impact with both an abstract 2-action flow and a model fluid flow. We show that transitions from one-dimensional (1D) to two-dimensional (2D) and 2D to 3D transport occur based on the relative magnitudes of streamline jumps in two transverse directions.Comment: Copyright 2017 AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishin

Feshbach spectroscopy of an ultracold Rb-Cs mixture

This thesis reports the observation of interspecies Feshbach resonances in an ultracold mixture of Rb and Cs atoms. A versatile combined magnetic and optical potential has been designed and constructed which is capable of bringing both $^{87}\rm{Rb}$ and $^{133}\rm{Cs}$ to degeneracy, and reaching high phase-space density in $^{85}\rm{Rb}$. High phase-space density mixtures are the first step required in the production of ultracold polar molecules, the topic of much current research. The apparatus capitalises on the efficient capture of atoms by a magnetic trap from a magneto-optical trap, and the efficient sympathetic cooling of Cs by Rb therein. Upon transfer to the crossed optical dipole trap condensates in excess of $1\times10^{6}$ $^{87}\rm{Rb}$ atoms and approximately $1\times10^{5}$ $^{133}\rm{Cs}$ atoms are produced after direct evaporation and gravito-magnetic tilting of the potential. The observation of six interspecies $^{87}\rm{Rb}$-$^{133}\rm{Cs}$ Feshbach resonances are reported, three of which had only been predicted theoretically, allowing testing and development of the theoretical model. Furthermore, the extrapolation of this model has predicted numerous Feshbach resonances between $^{85}\rm{Rb}$ and $^{133}\rm{Cs}$, none of which have been experimentally observed prior to this work. The versatile nature of this apparatus is discussed, including the application of the current system to cooling of $^{85}\rm{Rb}$. Initial experiments observed seven interspecies resonances, including a broad s-wave resonance at a magnetic field of $(644\pm2)$ G which is in excellent agreement with the theoretical prediction. Further work has revealed that fourteen Feshbach resonances exist in the 0-700 G magnetic field range between $^{85}\rm{Rb}$ and $^{133}\rm{Cs}$ atoms in the $\left|2,+2\right\rangle$ and $\left|3,+3\right\rangle$ states, respectively. Several of these resonances would be ideal for magneto-association of RbCs molecules, prior to transfer to the rovibrational ground-state

Fiber Optic Temperature Sensors for a Large Electric Power Generator

Fiber optic temperature sensors are excellent candidates for monitoring the temperature along the stator windings of a large electric power generator. Unlike thermocouple thermometers, they are immune to the effects of strong magnetic fields which are present in all power generators. Several different point and line sensors have been evaluated in their ability to resolve temperature and temperature distribution (respectively), as well as their compatibility with the generator environment. The sensor must function inside the generator for long periods of time (up to 25 years) without benefit of recalibration. This constraint has required us to devise methods by which the sensor may remain permanently calibrated. In almost all cases, it is necessary to measure a natural characteristic of a device which is temperature sensitive in order to achieve permanent calibration. This will enable the device to function despite the varying characteristics of the source and detector equipment