We discuss a statistical variant of Ruzsa's covering lemma and use it to show that if G is an Abelian group of bounded exponent and A in G has |A+A| < K|A| then the subgroup generated by A has size at most exp(O(K log^22K))|A|, where the constant in the big-O depends on the exponent of the group only.

Tom Sanders

We show that if f is an injection from an n-dimensional Boolean cube (considered as an additive group) to a group of prime order then the probability that f(x+y)=f(x)+f(y) is O(2^{-n/11}).

Tom Sanders

We show that if A is a finite set of integers then it has a subset S of size \log^{1+c} |A| (c>0 absolute) such that s+s' is never in A when s and s' are distinct elements of S.

Tom Sanders

We show that if G is a group and A is a finite subset of G with |A^2| < K|A|, then for all k there is a symmetric neighbourhood of the identity S with S^k a subset of A^2A^{-2} and |S| > exp(-K^{O(k)})|A|.

Tom Sanders

In this paper we present a hybridizable discontinuous Galerkin method for the time-dependent Navier-Stokes equations coupled to the quasi-static poroelasticity equations via interface conditions. We determine a bound on the data that guarantees stability and well-posedness of the fully discrete problem and prove a priori error estimates. A numerical example confirms our analysis.

Aycil Cesmelioglu Jeonghun J. Lee Sander Rhebergen

We introduce and analyze a coupled hybridizable discontinuous Galerkin/discontinuous Galerkin (HDG/DG) method for porous media in which we allow fully and partly immersed faults, and faults that separate the domain into two disjoint subdomains. We prove well-posedness and present an a priori error analysis of the discretization. Numerical examples verify our analysis.

Aycil Cesmelioglu Miroslav Kuchta Jeonghun J. Lee Sander Rhebergen

At luminosities above ~10^{11} L_sun, infrared galaxies become the dominant population of extragalactic objects in the local Universe (z < 0.5), being more numerous than optically selected starburst and Seyfert galaxies, and QSOs at comparable bolometric luminosity. At the highest luminosities, ultraluminous infrared galaxies (ULIGs: L_ir > 10^{12} L_sun), outnumber optically selected QSOs by a factor of ~1.5-2. All of the nearest ULIGs (z < 0.1) appear to be advanced mergers that are powered by both a circumnuclear starburst and AGN, both of which are fueled by an enormous concentration of molecular gas (~10^{10} M_sun) that has been funneled into the merger nucleus. ULIGs may represent a primary stage in the formation of massive black holes and elliptical galaxy cores. The intense circumnuclear starburst that accompanies the ULIG phase may also represent a primary stage in the formation of globular clusters, and the metal enrichment of the intergalactic medium by gas and dust expelled from the nucleus due to the combined forces of supernova explosions and powerful stellar winds.

D. B. Sanders J. A. Surace C. M. Ishida

Elliptic flow has been measured by the BRAHMS experiment as a function of transverse momentum and pseudorapidity for the Au+Au reaction at sqrt[s_{NN}] = 200 GeV. Identified-particle v2 (eta, pt) values were obtained with the two BRAHMS spectrometers at pseudorapidities eta approximately equal to 0, 1, and 3.4. The results show that the differential v2(eta, pt) values for a given particle type are essentially constant over the covered pseudorapidity range. It is suggested that the dominant cause of the observed fall-off of the integral v2 values going away from mid-rapidity is a corresponding softening of the particle spectra .

S. J. Sanders

We report numerical calculations of the concentration of interstitials in hard-sphere crystals. We find that, in a three-dimensional fcc hard-sphere crystal at the melting point, the concentration of interstitials is 2 * 10^-8. This is some three orders of magnitude lower than the concentration of vacancies. A simple, analytical estimate yields a value that is in fair agreement with the numerical results.

Sander Pronk Daan Frenkel

For a prime p and natural number n with p greater than or equal to n, we establish the existence of a non-functorial one-to-one correspondence between isomorphism classes of groups of order p^n whose derived subgroup has exponent dividing p, and isomorphism classes of nilpotent p^n-element Lie algebras L over the truncated polynomial ring F_p[T]/(T^n) in which T[L,L]=0.

Paul J. Sanders