An inviscid model for vortex shedding from a deforming body

An inviscid vortex sheet model is developed in order to study the unsteady separated flow past a two-dimensional deforming body which moves with a prescribed motion in an otherwise quiescent fluid. Following Jones (J Fluid Mech 496, 405–441, 2003) the flow is assumed to comprise of a bound vortex sheet attached to the body and two separate vortex sheets originating at the edges. The complex conjugate velocity potential is expressed explicitly in terms of the bound vortex sheet strength and the edge circulations through a boundary integral representation. It is shown that Kelvin’s circulation theorem, along with the conditions of continuity of the normal velocity across the body and the boundedness of the velocity field, yields a coupled system of equations for the unknown bound vortex sheet strength and the edge circulations. A general numerical treatment is developed for the singular principal value integrals arising in the solution procedure. The model is validated against the results of Jones (J Fluid Mech 496, 405–441, 2003) for computations involving a rigid flat plate and is subsequently applied to the flapping foil experiments of Heathcote et al. (AIAA J, 42, 2196–2204, 2004) in order to predict the thrust coefficient. The utility of the model in simulating aquatic locomotion is also demonstrated, with vortex shedding suppressed at the leading edge of the swimming body.      

A Homological Approach to Two Problems on Finite Sets

We propose a homological approach to two conjectures descended from the Erdös-Ko-Rado Theorem, one due to Chvátal and the other to Frankl and Füredi. We apply the method to reprove, and in one case improve, results of these authors related to their conjectures.     

Testing diffusion processes for non-stationarity

Financial data are often assumed to be generated by diffusions. Using recent results of Fan et al. (J Am Stat Assoc, 102:618–631, 2007; J Financ Econometer, 5:321–357, 2007) and a multiple comparisons procedure created by Benjamini and Hochberg (J R Stat Soc Ser B, 59:289–300, 1995), we develop a test for non-stationarity of a one-dimensional diffusion based on the time inhomogeneity of the diffusion function. The procedure uses a single sample path of the diffusion and involves two estimators, one temporal and one spatial. We first apply the test to simulated data generated from a variety of one-dimensional diffusions. We then apply our test to interest rate data and real exchange rate data. The application to real exchange rate data is of particular interest, since a consequence of the law of one price (or the theory of purchasing power parity) is that real exchange rates should be stationary. With the exception of the GBP/USD real exchange rate, we find evidence that interest rates and real exchange rates are generally non-stationary. The software used to implement the estimation and testing procedure is available on demand and we describe its use in the paper.     

On the maximum number of diagonals of a circuit in a graph

For a graph G, let ?(G) denote the maximum number k such that G contains a circuit with k diagonals.Theorem. For any graph G with minimum valency$\text{n? 3, ?(G) ?}\text{1}\text{2}\text{(n+1)(n-2)}$.If the equality holds and G is connected, then either G is isomorphic to K_n+1 or G is separable and each of its terminal blocks is isomorphic to K_n+1, or K_n+1 with one edge subdivided.     

Matrix characterization of oscillation for double sequences

The notion of oscillation for ordinary sequences was presented by Hurwitz in 1930. Using this notion Agnew and Hurwitz presented regular matrix characterization of the resulting sequence space. The primary goal of this article is to extend this definition to double sequences, which grants us the following definition: the double oscillation of a double sequence of real or complex number is given P-lim sup_{(m,n)→∞;(α,β)→∞}|S _m,n -S _α,β |. Using this concept a matrix characterization of double oscillation sequence space is presented. Other implication and variation shall also be presented.      

The early exercise region for Bermudan options on two underlyings

This paper investigates the early exercise region for Bermudan options on two underlying assets. We present a set of analytical validation results for the early exercise region which can be used as a means of validating pricing techniques. When all strike prices are identical we show the existence of an intersection point such that for any asset price pair below this point early exercise is always optimal. We develop an approximation to this point in the two asset put case. When the strike prices are not all equal, we show that three separate cases exist for the early exercise region. For a Bermudan put on two assets we present these cases and show that there exists a critical point in which the boundaries of the two asset early exercise region bifurcate. Comparisons are drawn between the Bermudan results presented and the corresponding American option results.     

On the stochastic independence properties of hard-core distributions

A probability measurep on the set of matchings in a graph (or, more generally 2-bounded hypergraph) ishard-core if for some : [0,), the probabilityp(M) ofM is proportional to . We show that such distributions enjoy substantial approximate stochastic independence properties. This is based on showing that, withM chosen according to the hard-core distributionp, MP () the matching polytope of , and >0, if the vector ofmarginals, (Pr(AM):A an edge of ), is in (1–) MP (), then the weights (A) are bounded by someA(). This eventually implies, for example, that under the same assumption, with fixed, as the distance betweenA, B tends to infinity.Thought to be of independent interest, our results have already been applied in the resolutions of several questions involving asymptotic behaviour of graphs and hypergraphs (see [14, 16], [11]–[13]).Supported in part by NSFThis work forms part of the author's doctoral dissertation [16]; see also [17]. The author gratefully acknowledges NSERC for partial support in the form of a 1967 Science and Engineering Scholarship.