Modified face seal for positive film stiffness

The film stiffness of a face seal is improved without increasing the sealing and dam area by using an apparatus which includes a primary seal ring in the form of a nose piece. A spring forces a sealing surface on the seal ring into sealing contact with a seat to form a face seal. A circumferential clearance seal is formed in series with this face seal by a lip on the piece. The width of the surface of the lip is substantially the same as the width of the sealing surface on the face seal and the clearance between the surface on the lip and the shaft is substantially the same as the spacing between the face sealing surfaces on the face seal when the shaft is rotating. The circumferential clearance seal restricts the flow of fluid from a main cavity to an intermediate cavity with a resulting pressure drop. The hydrostatic opening face is strongly dependent on the face seal clearance, and the desired axial stiffness is achieved

Dilution Jet Behavior in the Turn Section of a Reverse Flow Combuster

Measurements of the temperature field produced by a single jet and a row of dilution jets issued into a reverse flow combustor are presented. The temperature measurements are presented in the form of consecutive normalized temperature profiles, and jet trajectories. Single jet trajectories were swept toward the inner wall of the turn, whether injection was from the inner or outer wall. This behavior is explained by the radially inward velocity component necessary to support irrotational flow through the turn. Comparison between experimental results and model calculations showed poor agreement due to the model's not including the radial velocity component. A widely spaced row of jets produced trajectories similar to single jets at similar test conditions, but as spacing ratio was reduced, penetration was reduced to the point where the dilution jet flow attached to the wall

Dilution jets in accelerated cross flows

Results of flow visualization experiments and measurements of the temperature field produced by a single jet and a row of dilution jets issued into a reverse flow combustor are presented. The flow in such combustors is typified by transverse and longitudinal acceleration during the passage through its bending section. The flow visualization experiments are designed to examine the separate effects of longitudinal and transverse acceleration on the jet trajectory and spreading rate. A model describing a dense single jet in a lighter accelerating cross flow is developed. The model is based on integral conservation equations, including the pressure terms appropriate to accelerating flows. It uses a modified entrainment correlation obtained from previous experiments of a jet in a cross stream. The flow visualization results are compared with the model calculations in terms of trajectories and spreading rates. Each experiment is typified by a set of three parameters: momentum ratio, density ratio and the densimetric Froude number

Notes on bordered Floer homology

This is a survey of bordered Heegaard Floer homology, an extension of the Heegaard Floer invariant HF-hat to 3-manifolds with boundary. Emphasis is placed on how bordered Heegaard Floer homology can be used for computations.Comment: 73 pages, 29 figures. Based on lectures at the Contact and Symplectic Topology Summer School in Budapest, July 2012. v2: Fixed many small typo

Quantum Analogue Computing

We briefly review what a quantum computer is, what it promises to do for us, and why it is so hard to build one. Among the first applications anticipated to bear fruit is quantum simulation of quantum systems. While most quantum computation is an extension of classical digital computation, quantum simulation differs fundamentally in how the data is encoded in the quantum computer. To perform a quantum simulation, the Hilbert space of the system to be simulated is mapped directly onto the Hilbert space of the (logical) qubits in the quantum computer. This type of direct correspondence is how data is encoded in a classical analogue computer. There is no binary encoding, and increasing precision becomes exponentially costly: an extra bit of precision doubles the size of the computer. This has important consequences for both the precision and error correction requirements of quantum simulation, and significant open questions remain about its practicality. It also means that the quantum version of analogue computers, continuous variable quantum computers (CVQC) becomes an equally efficient architecture for quantum simulation. Lessons from past use of classical analogue computers can help us to build better quantum simulators in future.Comment: 10 pages, to appear in the Visions 2010 issue of Phil. Trans. Roy. Soc.

Quadratic Word Equations with Length Constraints, Counter Systems, and Presburger Arithmetic with Divisibility

Word equations are a crucial element in the theoretical foundation of constraint solving over strings, which have received a lot of attention in recent years. A word equation relates two words over string variables and constants. Its solution amounts to a function mapping variables to constant strings that equate the left and right hand sides of the equation. While the problem of solving word equations is decidable, the decidability of the problem of solving a word equation with a length constraint (i.e., a constraint relating the lengths of words in the word equation) has remained a long-standing open problem. In this paper, we focus on the subclass of quadratic word equations, i.e., in which each variable occurs at most twice. We first show that the length abstractions of solutions to quadratic word equations are in general not Presburger-definable. We then describe a class of counter systems with Presburger transition relations which capture the length abstraction of a quadratic word equation with regular constraints. We provide an encoding of the effect of a simple loop of the counter systems in the theory of existential Presburger Arithmetic with divisibility (PAD). Since PAD is decidable, we get a decision procedure for quadratic words equations with length constraints for which the associated counter system is \emph{flat} (i.e., all nodes belong to at most one cycle). We show a decidability result (in fact, also an NP algorithm with a PAD oracle) for a recently proposed NP-complete fragment of word equations called regular-oriented word equations, together with length constraints. Decidability holds when the constraints are additionally extended with regular constraints with a 1-weak control structure.Comment: 18 page

Controlled non uniform random generation of decomposable structures

Consider a class of decomposable combinatorial structures, using different types of atoms \Atoms = \{\At_1,\ldots ,\At_{|{\Atoms}|}\}. We address the random generation of such structures with respect to a size $n$ and a targeted distribution in $k$ of its \emph{distinguished} atoms. We consider two variations on this problem. In the first alternative, the targeted distribution is given by $k$ real numbers \TargFreq_1, \ldots, \TargFreq_k such that 0 < \TargFreq_i < 1 for all $i$ and \TargFreq_1+\cdots+\TargFreq_k \leq 1. We aim to generate random structures among the whole set of structures of a given size $n$, in such a way that the {\em expected} frequency of any distinguished atom \At_i equals \TargFreq_i. We address this problem by weighting the atoms with a $k$-tuple \Weights of real-valued weights, inducing a weighted distribution over the set of structures of size $n$. We first adapt the classical recursive random generation scheme into an algorithm taking \bigO{n^{1+o(1)}+mn\log{n}} arithmetic operations to draw $m$ structures from the \Weights-weighted distribution. Secondly, we address the analytical computation of weights such that the targeted frequencies are achieved asymptotically, i. e. for large values of $n$. We derive systems of functional equations whose resolution gives an explicit relationship between \Weights and \TargFreq_1, \ldots, \TargFreq_k. Lastly, we give an algorithm in \bigO{k n^4} for the inverse problem, {\it i.e.} computing the frequencies associated with a given $k$-tuple \Weights of weights, and an optimized version in \bigO{k n^2} in the case of context-free languages. This allows for a heuristic resolution of the weights/frequencies relationship suitable for complex specifications. In the second alternative, the targeted distribution is given by a $k$ natural numbers $n_1, \ldots, n_k$ such that $n_1+\cdots+n_k+r=n$ where $r \geq 0$ is the number of undistinguished atoms. The structures must be generated uniformly among the set of structures of size $n$ that contain {\em exactly} $n_i$ atoms \At_i ($1 \leq i \leq k$). We give a \bigO{r^2\prod_{i=1}^k n_i^2 +m n k \log n} algorithm for generating $m$ structures, which simplifies into a \bigO{r\prod_{i=1}^k n_i +m n} for regular specifications

Derivation of an optimal directivity pattern for sweet spot widening in stereo sound reproduction

In this paper the correction of the degradation of the stereophonic illusion during sound reproduction due to off-center listening is investigated. The main idea is that the directivity pattern of a loudspeaker array should have a well-defined shape such that a good stereo reproduction is achieved in a large listening area. Therefore, a mathematical description to derive an optimal directivity pattern lopt that achieves sweet spot widening in a large listening area for stereophonic sound applications is described. This optimal directivity pattern is based on parametrized time/intensity trading data coming from psycho-acoustic experiments within a wide listening area. After the study, the required digital FIR filters are determined by means of a least-squares optimization method for a given stereo base setup (two pair of drivers for the loudspeaker arrays and 2.5-m distance between loudspeakers), which radiate sound in a broad range of listening positions in accordance with the derived lopt. Informal listening tests have shown that the lopt worked as predicted by the theoretical simulations. They also demonstrated the correct central sound localization for speech and music for a number of listening positions. This application is referred to as "Position-Independent (PI) stereo.

Ultrasonic attenuation measurements at very high SNR: correlation, information theory and performance

This paper describes a system for ultrasonic wave attenuation measurements which is based on pseudo-random binary codes as transmission signals combined with on-the-fly correlation for received signal detection. The apparatus can receive signals in the nanovolt range against a noise background in the order of hundreds of microvolts and an analogue to digital convertor (ADC) bit-step also in the order of hundreds of microvolts. Very high signal to noise ratios (SNRs) are achieved without recourse to coherent averaging with its associated requirement for high sampling times. The system works by a process of dithering – in which very low amplitude received signals enter the dynamic range of the ADC by 'riding' on electronic noise at the system input. The amplitude of this 'useful noise' has to be chosen with care for an optimised design. The process of optimisation is explained on the basis of classical information theory and is achieved through a simple noise model. The performance of the system is examined for different transmitted code lengths and gain settings in the receiver chain. Experimental results are shown to verify the expected operation when the system is applied to a very highly attenuating material – an aerated slurry