Densitometer Patent

Measuring density of single and two-phase cryogenic fluids in rocket fuel tank

Fibrational induction rules for initial algebras

This paper provides an induction rule that can be used to prove properties of data structures whose types are inductive, i.e., are carriers of initial algebras of functors. Our results are semantic in nature and are inspired by Hermida and Jacobs’ elegant algebraic formulation of induction for polynomial data types. Our contribution is to derive, under slightly different assumptions, an induction rule that is generic over all inductive types, polynomial or not. Our induction rule is generic over the kinds of properties to be proved as well: like Hermida and Jacobs, we work in a general fibrational setting and so can accommodate very general notions of properties on inductive types rather than just those of particular syntactic forms. We establish the correctness of our generic induction rule by reducing induction to iteration. We show how our rule can be instantiated to give induction rules for the data types of rose trees, finite hereditary sets, and hyperfunctions. The former lies outside the scope of Hermida and Jacobs’ work because it is not polynomial; as far as we are aware, no induction rules have been known to exist for the latter two in a general fibrational framework. Our instantiation for hyperfunctions underscores the value of working in the general fibrational setting since this data type cannot be interpreted as a set

Instrument continuously measures density of flowing fluids

Electromechanical densitometer continuously measures the densities of either single-phase or two-phase flowing cryogenic fluids. Measurement is made on actual flow. The instrument operates on the principle that the mass of any vibrating system is a primary factor in determining the dynamic characteristics of the system

Combinatorial models of rigidity and renormalization

We first introduce the percolation problems associated with the graph theoretical concepts of $(k,l)$-sparsity, and make contact with the physical concepts of ordinary and rigidity percolation. We then devise a renormalization transformation for $(k,l)$-percolation problems, and investigate its domain of validity. In particular, we show that it allows an exact solution of $(k,l)$-percolation problems on hierarchical graphs, for $k\leq l<2k$. We introduce and solve by renormalization such a model, which has the interesting feature of showing both ordinary percolation and rigidity percolation phase transitions, depending on the values of the parameters.Comment: 22 pages, 6 figure

Finite element analysis of gradient coil deformation and vibration in NMR microscopy

Resolution degradation due to gradient coil deformation and vibration in NMR microscopy is investigated using finite element analysis. From the analysis, deformations due to the Lorentz force can be as large as 1-10 μm depending on the gradient strength and coil frame material. Thus, these deformations can be one of the major resolution limiting factors in NMR microscopy. Coil vibration, which depends on the input current waveform and resolution degradation due to time-variant deformation and time-invariant deformation are investigated by numerical simulations

Experimental Demonstration of a Quantum Circuit using Linear Optics Gates

One of the main advantages of an optical approach to quantum computing is the fact that optical fibers can be used to connect the logic and memory devices to form useful circuits, in analogy with the wires of a conventional computer. Here we describe an experimental demonstration of a simple quantum circuit of that kind in which two probabilistic exclusive-OR (XOR) logic gates were combined to calculate the parity of three input qubits.Comment: v2 is final PRA versio

Variation of proton flux profiles with the observer's latitude in simulated gradual SEP events

We study the variation of the shape of the proton intensity-time profiles in simulated gradual Solar Energetic Particle (SEP) events with the relative observer's position in space with respect to the main direction of propagation of an interplanetary (IP) shock. Using a three-dimensional (3D) magnetohydrodynamic (MHD) code to simulate such a shock, we determine the evolution of the downstream-to-upstream ratios of the plasma variables at its front. Under the assumption of an existing relation between the normalized ratio in speed across the shock front and the injection rate of shock-accelerated particles, we model the transport of the particles and we obtain the proton flux profiles to be measured by a grid of 18 virtual observers located at 0.4 and 1.0 AU, with different latitudes and longitudes with respect to the shock nose. The differences among flux profiles are the result of the way each observer establishes a magnetic connection with the shock front, and we find that changes in the observer's latitude may result in intensity changes of up to one order of magnitude at both radial distances considered here. The peak intensity variation with the radial distance for the pair of observers located at the same angular position is also derived. This is the first time that the latitudinal dependence of the peak intensity with the observer's heliocentric radial distance has been quantified within the framework of gradual SEP event simulations.Comment: 20 pages, 6 Figures, 2 Table

Indexed induction and coinduction, fibrationally.

This paper extends the fibrational approach to induction and coinduction pioneered by Hermida and Jacobs, and developed by the current authors, in two key directions. First, we present a sound coinduction rule for any data type arising as the final coalgebra of a functor, thus relaxing Hermida and Jacobs’ restriction to polynomial data types. For this we introduce the notion of a quotient category with equality (QCE), which both abstracts the standard notion of a fibration of relations constructed from a given fibration, and plays a role in the theory of coinduction dual to that of a comprehension category with unit (CCU) in the theory of induction. Second, we show that indexed inductive and coinductive types also admit sound induction and coinduction rules. Indexed data types often arise as initial algebras and final coalgebras of functors on slice categories, so our key technical results give sufficent conditions under which we can construct, from a CCU (QCE) U : E -> B, a fibration with base B/I that models indexing by I and is also a CCU (QCE)