On The Distribution Of Digits in Dyadic Expansions

We estimate the Hausdorff dimension of certain Borel sets determined in dyadic expansion by products of r successive digits.     

A space–time approach to multi-gluon loop computations in QCD: an application to effective action terms

The applicability of the space–time formulation of the gluonic sector of QCD in terms of the Polyakov worldline path integral, via the use of the background field gauge fixing method, is extended to multi-gluon loop configurations. Relevant master formulas are derived for the computation of effective action terms.     

On the Hausdorff dimension of rademacher Riesz products

We give a formula for the Hausdorff dimension of fractals which are the support of certain Riesz-product type measures.     

Zig zag symmetry in AdS/CFT duality

The validity of the Bianchi identity, which is intimately connected with the zig zag symmetry, is established, for piecewise continuous contours, in the context of Polakov’s gauge field–string connection in the large ’t Hooft coupling limit, according to which the chromoelectric ‘string’ propagates in five dimensions with its ends attached on a Wilson loop in four dimensions. An explicit check in the wavy line approximation is presented.     

Multiscale Haar Orthonormal Matrices with the Corresponding Riesz Products and a Characterization of Cantor-Type Languages

We introduce a class of multiscale orthonormal matrices H(m) of order m×m, m = 2, 3,... . For m = 2 ^N, N = 1, 2,..., we get the well known Haar wavelet system. The term "multiscale" indicates that the construction of H(m) is achieved in different scales by an iteration process, determined through the prime integer factorization of m and by repetitive dilation and translation operations on matrices. The new Haar transforms allow us to detect the underlying ergodic structures on a class of Cantor-type sets or languages. We give a sufficient condition on finite data of lengthm, or step functions determined on the intervals [k/m, (k + 1)/m) , k = 0,...,m − 1 of [0, 1), to be written as a Riesz-type product in terms of the rows of H(m). This allows us to approximate in the weak-* topology continuous measures by Riesz-type products.     

Density profiles and solvation forces for a Yukawa fluid in a slit pore

The effect of varying wall-particle and particle-particle interactions on the density profiles near a single wall and the solvation forces between two walls immersed in a fluid of particles is investigated by grand canonical Monte Carlo simulations. Attractive and repulsive particle-particle and particle-wall interactions are modeled by a versatile hard-core Yukawa form. These simulation results are compared to theoretical calculations using the hypernetted chain integral equation technique, as well as with fundamental measure density functional theory (DFT), where particle-particle interactions are either treated as a first order perturbation using the radial distribution function or else with a DFT based on the direct-correlation function. All three theoretical approaches reproduce the main trends fairly well, but exhibit inconsistent accuracy, particularly for attractive particle-particle interactions. We show that the wall-particle and particle-particle attractions can couple together to induce a nonlinear enhancement of the adsorption and a related "repulsion through attraction" effect for the effective wall-wall forces. We also investigate the phenomenon of bridging, where an attractive wall-particle interaction induces strongly attractive solvation forces.