Effective Relative Permeabilities and Capillary Pressure for One-Dimensional Heterogeneous Media

The paper presents an analytical construction of effective two-phase parameters for one-dimensional heterogeneous porous media, and studies their properties. We base the computation of effective parameters on analytical solutions for steady-state saturation distributions. Special care has to be taken with respect to saturation and pressure discontinuities at the interface between different rocks. The ensuing effective relative permeabilities and effective capillary pressure will be functions of rate, flow direction, fluid viscosities, and spatial scale of the heterogeneities.The applicability of the effective parameters in dynamic displacement situations is studied by comparing fine-gridded simulations in heterogeneous media with simulations in their homogeneous (effective) counterparts. Performance is quite satisfactory, even with strong fronts present. Also, we report computations studying the applicability of capillary limit parameters outside the strict limit.     

Composition of recursions and nonlinear complexity of periodic binary sequences

We investigate further the new approach towards the classification of periodic binary sequences into nonlinear complexity classes that commenced in the paper by Petrides and Mykkeltveit (Proceedings of SETA’06 international conference on sequences and their applications, 2006). Nonlinear complexity was first introduced by Jansen (Investigations on nonlinear streamcipher systems: construction and evaluation methods, PhD thesis, 1989) and several attempts have since been made to make it of more practical cryptographic interest. In this direction, we will follow with this article. In particular we perform composition of the recursions found in the (2006) article which are related to nonlinear complexity, and prove some of its missing results. Studying the properties of the composition operation for a certain type of recursions is an alternative to study all possible recursions, as required for completing the above mentioned classification. A complete classification will allow, amongst other things, construction of statistical tests to assess the cryptographic strength of binary sequences used in stream ciphers.     

A Proof of Simmons' Conjecture

An open problem posed by Simmons is whether two given permutations of the vertices of the deBruijn graph have the same cycle structure, or not. We present a solution to this problem and find the complete cycle structure.     

The weight distribution of irreducible cyclic codes with block lengths n1((q1−1)N)

We study the weight distribution of irreducible cyclic (n, k) codeswith block lengths n = n₁((q¹ ? 1)/N), where N|q ? 1, gcd(n₁,N) = 1, and gcd(l,N) = 1. We present the weight enumerator polynomial, A(z), when k = n₁l, k = (n₁ ? 1)l, and k = 2l. We also show how to find A(z) in general by studying the generator matrix of an (n₁, m) linear code, $\text{V}{}^1{}_{\mathrm{d}}$ over GF(q^d) where d = gcd (ord_n1(q), l). Specifically we study A(z) when $\text{V}{}^1{}_{\mathrm{d}}$ is a maximum distance separable code, a maximal shiftregister code, and a semiprimitive code. We tabulate some numbers A_μ which completely determine the weight distributionof any irreducible cyclic (n₁(2¹ ? 1), k) code over GF(2) for all n₁ ? 17.