Correlating and predicting the air infiltration through the cracks of suspended timber floors

This paper shows that the visible gap length may be used as a physical parameter when correlating pressure difference to volume flow rate (or air velocity) through the cracks between floorboards and can be termed the Equivalent Crack Length. The crack widths, which previously have been determined separately from the edge effect coefficient and the laminar flow coefficient, were significantly different. When analysed graphically they can be shown to correlate by an empirical relationship. A generalised equation is proposed that, in conjunction with the empirical relationship, allows predictions to be made of the volume flow rate through the cracks between floorboards for a known pressure difference

Comparison of 3D computation and experiment for non-axisymmetric nozzles

Three dimensional solutions of a single expansion ramp nozzle are computed with the existing PARC computer code by solving the full Navier-Stokes equations. The computations are performed to simulate the non-axisymmetric nozzle flowfield in both the internal/external expansion regions and the exhaust plume in a quiescent ambient environment. Two different configurations of the nozzle at a pressure ratio NPR = 10 are examined. Numerical results of laminar flows are presented, and the wall pressure distributions are compared with the experimental data

Cusp-scaling behavior in fractal dimension of chaotic scattering

A topological bifurcation in chaotic scattering is characterized by a sudden change in the topology of the infinite set of unstable periodic orbits embedded in the underlying chaotic invariant set. We uncover a scaling law for the fractal dimension of the chaotic set for such a bifurcation. Our analysis and numerical computations in both two- and three-degrees-of-freedom systems suggest a striking feature associated with these subtle bifurcations: the dimension typically exhibits a sharp, cusplike local minimum at the bifurcation.Comment: 4 pages, 4 figures, Revte

Spectrins in Axonal Cytoskeletons: Dynamics Revealed by Extensions and Fluctuations

The macroscopic properties, the properties of individual components and how those components interact with each other are three important aspects of a composited structure. An understanding of the interplay between them is essential in the study of complex systems. Using axonal cytoskeleton as an example system, here we perform a theoretical study of slender structures that can be coarse-grained as a simple smooth 3-dimensional curve. We first present a generic model for such systems based on the fundamental theorem of curves. We use this generic model to demonstrate the applicability of the well-known worm-like chain (WLC) model to the network level and investigate the situation when the system is stretched by strong forces (weakly bending limit). We specifically studied recent experimental observations that revealed the hitherto unknown periodic cytoskeleton structure of axons and measured the longitudinal fluctuations. Instead of focusing on single molecules, we apply analytical results from the WLC model to both single molecule and network levels and focus on the relations between extensions and fluctuations. We show how this approach introduces constraints to possible local dynamics of the spectrin tetramers in the axonal cytoskeleton and finally suggests simple but self-consistent dynamics of spectrins in which the spectrins in one spatial period of axons fluctuate in-sync.Comment: 18 pages, 4 figure

How strong are the Rossby vortices?

The Rossby wave instability, associated with density bumps in differentially rotating discs, may arise in several different astrophysical contexts, such as galactic or protoplanetary discs. While the linear phase of the instability has been well studied, the nonlinear evolution and especially the saturation phase remain poorly understood. In this paper, we test the non-linear saturation mechanism analogous to that derived for wave-particle interaction in plasma physics. To this end we perform global numerical simulations of the evolution of the instability in a two-dimensional disc. We confirm the physical mechanism for the instability saturation and show that the maximum amplitude of vorticity can be estimated as twice the linear growth rate of the instability. We provide an empirical fitting formula for this growth rate for various parameters of the density bump. We also investigate the effects of the azimuthal mode number of the instability and the energy leakage in the spiral density waves. Finally, we show that our results can be extrapolated to 3D discs.Comment: Accepted for publication in MNRA

Amortized Rotation Cost in AVL Trees

An AVL tree is the original type of balanced binary search tree. An insertion in an $n$-node AVL tree takes at most two rotations, but a deletion in an $n$-node AVL tree can take $\Theta(\log n)$. A natural question is whether deletions can take many rotations not only in the worst case but in the amortized case as well. A sequence of $n$ successive deletions in an $n$-node tree takes $O(n)$ rotations, but what happens when insertions are intermixed with deletions? Heaupler, Sen, and Tarjan conjectured that alternating insertions and deletions in an $n$-node AVL tree can cause each deletion to do $\Omega(\log n)$ rotations, but they provided no construction to justify their claim. We provide such a construction: we show that, for infinitely many $n$, there is a set $E$ of {\it expensive} $n$-node AVL trees with the property that, given any tree in $E$, deleting a certain leaf and then reinserting it produces a tree in $E$, with the deletion having done $\Theta(\log n)$ rotations. One can do an arbitrary number of such expensive deletion-insertion pairs. The difficulty in obtaining such a construction is that in general the tree produced by an expensive deletion-insertion pair is not the original tree. Indeed, if the trees in $E$ have even height $k$, $2^{k/2}$ deletion-insertion pairs are required to reproduce the original tree

Improved Memoryless RNS Forward Converter Based on the Periodicity of Residues

The residue number system (RNS) is suitable for DSP architectures because of its ability to perform fast carry-free arithmetic. However, this advantage is over-shadowed by the complexity involved in the conversion of numbers between binary and RNS representations. Although the reverse conversion (RNS to binary) is more complex, the forward transformation is not simple either. Most forward converters make use of look-up tables (memory). Recently, a memoryless forward converter architecture for arbitrary moduli sets was proposed by Premkumar in 2002. In this paper, we present an extension to that architecture which results in 44% less hardware for parallel conversion and achieves 43% improvement in speed for serial conversions. It makes use of the periodicity properties of residues obtained using modular exponentiation

Thrifty Viability and Traditional Mortgage Lending: A Simultaneous Equations Analysis of the Risk-Return Trade-Off

A number of studies have argued that the thrift industry is not viable as it is presently structured and regulated because mortgage yields are inadequate to cover interest and operating costs. This hypothesis suggests that observed profitability is primarily the result of the tendency of the industry to "ride" the yield curve by borrowing short and lending long. To evaluate this argument, we construct a simultaneous-equations model of thrift risk (maturity gap positions) and return (net interest margin). We find support for the notion that the industry could not be reasonably profitable if it did not take on significant interest-rate risk. For instance, a zero gap position produces a return on assets of only 19 basis points and a return on equity of only 4%. We also estimate the amount of interest-rate risk the industry can employ to increase returns on equity and assets. Our estimates show that over 50% of thrift profits earned during this period are the result of negative gap positions and interest-rate speculation. As earlier research shows, changes in regulations affecting thrift asset and liability choices can be counterproductive.