We provide a complete description of the giant component of the Erdős-Rényi random graph G(n, p) as soon as it emerges from the scaling window, i.e., for p = (1 + ε)/n where εn → ∞ and ε = o(1). Our description is particularly simple for ε = o(n), where the giant component C1 is contiguous with the following model (i.e., every graph property that holds with high probability for this model also ...

This report presents algorithms for finding large matchings in the streaming model. In this model, applicable when dealing with massive graphs, edges are streamed-in in some arbitrary order rather than residing in randomly accessible memory. For ε > 0, we achieve a 1/(1+ε) approximation for maximum cardinality matching and a 1/(2+ε) approximation to maximum weighted matching. Both algorithms us...

The T ∗ ε integral was calculated numerically along an extending, tunneling crack front in an 8 mm thick, aluminum three-point bend (3PB) specimen, using a numerical model driven by experimentally obtained surface displacements. The model provided input to a contour integration for the T ∗ ε integral, via the Equivalent Domain Integral (EDI) method with incremental plasticity. Validity of the a...

This paper is concerned with a class of singular equations modeling the combustion of premixed gas in periodic media. The model involves two parameters: the period of the medium |L| and a singular parameter ε related to the activation energy. The existence of pulsating travelling fronts for fixed ε and |L| was proved by H. Berestycki and F. Hamel in [BH]. In the present paper, we investigate th...

A non-premixed coaxial oxy-fuel turbulent flame was studied numerically with standard and realizable k-ε turbulence model and a comparison was made between them. The governing equations were solved by finite volume approach and were discretized using the second order upwind scheme. The presumed β-PDF model was applied to model turbulence-combustion interaction. The discrete ordinate radiation h...

A new robust method to extract the specific shear viscosity (η/s)(QGP) of a quark-gluon plasma (QGP) at temperatures T(c) < T ≲ 2T(c) from the centrality dependence of the eccentricity-scaled elliptic flow v2/ε measured in ultrarelativistic heavy-ion collisions is presented. Coupling viscous fluid dynamics for the QGP with a microscopic transport model for hadronic freeze-out we find for 200 A ...

In this paper which is an extended version of an article submitted to the Finite Volumes for Complex Applications V conference, we design a finite-volume based numerical scheme for the solution of the nonlinear balance equations of RNG variants of the well-known k − ε model and the v − f system encountered in the k − ε− v − f model which can be seen as an extension of first order turbulence mod...

We show that, contrary to the flavour mixing amplitude q/p, both Re(ε) and Im(ε) are observable quantities, where ε is the phase-convention-independent CP mixing. We consider semileptonic B d decays from a CP tag and build appropriate time-dependent asymmetries to separate out Re(ε) and Im(ε). " Indirect " CP violation would have in Im(ε)/(1 + |ε| 2) its most prominent manifestation in the B-sy...

In this paper we consider the pricing of Chicago Board Options Exchange Volatility Index (VIX) options in rough Bergomi model. setting, VIX random variable is defined by one-dimensional integral exponential a Gaussian process with correlated increments. Hence, approximate samples can be constructed via discretization and simulation vector. A Monte Carlo estimator based on rectangle scheme exact...