Singular 0/1-matrices, and the hyperplanes spanned by random 0/1-vectors

Let $P(d)$ be the probability that a random 0/1-matrix of size $d \times d$ is singular, and let $E(d)$ be the expected number of 0/1-vectors in the linear subspace spanned by d-1 random independent 0/1-vectors. (So $E(d)$ is the expected number of cube vertices on a random affine hyperplane spanned by vertices of the cube.) We prove that bounds on $P(d)$ are equivalent to bounds on $E(d)$: $$P(d) = (2^{-d} E(d) + \frac{d^2}{2^{d+1}}) (1 + o(1)).$$ We also report about computational experiments pertaining to these numbers.Comment: 9 page

Possibilities of using the ultrasonic wave transmission method to estimate initial setting time of cement paste

In this paper, the applicability of the ultrasonic wave transmission method to estimate the initial setting time of an arbitrary cement paste is discussed. Ultrasonic pulse velocity measurements were fully automated and measured continuously. The Vicar Needle Test was used in order to determine the initial setting time of cement pastes. Different cement pastes were prepared in order to check the influence of the water/cement ratio, type of cement, curing temperature, cement fineness, and some clinker compositions, on the relationship between the initial setting time and ultrasonic pulse velocity. It was found that the initial setting time of an arbitrary cement paste can be estimated very accurately by the time the first inflection point appears on the ultrasonic pulse velocity curve. Moreover, it can be estimated quite accurately by the time the ultrasonic pulse velocity reaches a fixed value, close to the value of the ultrasonic pulse velocity in water

On the Expressivity and Applicability of Model Representation Formalisms

A number of first-order calculi employ an explicit model representation formalism for automated reasoning and for detecting satisfiability. Many of these formalisms can represent infinite Herbrand models. The first-order fragment of monadic, shallow, linear, Horn (MSLH) clauses, is such a formalism used in the approximation refinement calculus. Our first result is a finite model property for MSLH clause sets. Therefore, MSLH clause sets cannot represent models of clause sets with inherently infinite models. Through a translation to tree automata, we further show that this limitation also applies to the linear fragments of implicit generalizations, which is the formalism used in the model-evolution calculus, to atoms with disequality constraints, the formalisms used in the non-redundant clause learning calculus (NRCL), and to atoms with membership constraints, a formalism used for example in decision procedures for algebraic data types. Although these formalisms cannot represent models of clause sets with inherently infinite models, through an additional approximation step they can. This is our second main result. For clause sets including the definition of an equivalence relation with the help of an additional, novel approximation, called reflexive relation splitting, the approximation refinement calculus can automatically show satisfiability through the MSLH clause set formalism

A phase-field-crystal approach to critical nuclei

We investigate a phase-field-crystal model for homogeneous nucleation. Instead of solving the time evolution of a density field towards equilibrium we use a String Method to identify saddle points in phase space. The saddle points allow to obtain the nucleation barrier and the critical nucleus. The advantage of using the phase-field-crystal model for this task is its ability to resolve atomistic effects. The obtained results indicate different properties of the critical nucleus compared with bulk crystals and show a detailed description of the nucleation process.Comment: 12 pages, 5 figures, submitte

A methodology for exploiting parallelism in the finite element process

A methodology is described for developing a parallel system using a top down approach taking into account the requirements of the user. Substructuring, a popular technique in structural analysis, is used to illustrate this approach

Solution of partial differential equations on vector and parallel computers

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed

Design, development and use of the finite element machine

Some of the considerations that went into the design of the Finite Element Machine, a research asynchronous parallel computer are described. The present status of the system is also discussed along with some indication of the type of results that were obtained

A bibliography on parallel and vector numerical algorithms

This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also

Cold fronts in cool core clusters

Cold fronts have been detected both in merging and in cool core clusters, where little or no sign of a merging event is present. A systematic search of sharp surface brightness discontinuities performed on a sample of 62 galaxy clusters observed with XMM-Newton shows that cold fronts are a common feature in galaxy clusters. Indeed most (if not all) of the nearby clusters (z < 0.04) host a cold front. Understanding the origin and the nature of a such frequent phenomenon is clearly important. To gain insight on the nature of cold fronts in cool core clusters we have undertaken a systematic study of all contact discontinuities detected in our sample, measuring surface brightness, temperature and when possible abundance profiles across the fronts. We measure the Mach numbers for the cold fronts finding values which range from 0.2 to 0.9; we also detect a discontinuities in the metal profile of some clusters.Comment: 6 pages, 3 figures, for proceedings of "Heating vs. Cooling in Galaxies and Clusters of Galaxies," eds H. Boehringer, P. Schuecker, G. W. Pratt & A. Finoguenov, in Springer-Verlag series "ESO Astrophysics Symposia.

On the temporal Wilson loop in the Hamiltonian approach in Coulomb gauge

We investigate the temporal Wilson loop using the Hamiltonian approach to Yang-Mills theory. In simple cases such as the Abelian theory or the non-Abelian theory in (1+1) dimensions, the known results can be reproduced using unitary transformations to take care of time evolution. We show how Coulomb gauge can be used for an alternative solution if the exact ground state wave functional is known. In the most interesting case of Yang-Mills theory in (3+1) dimensions, the vacuum wave functional is not known, but recent variational approaches in Coulomb gauge give a decent approximation. We use this formulation to compute the temporal Wilson loop and find that the Wilson and Coulomb string tension agree within our approximation scheme. Possible improvements of these findings are briefly discussed.Comment: 24 pages, 4 eps-figures; new version matches published on