We have investigated the formation of denuded zones during epitaxial growth on surfaces exhibiting anisotropic diffusion of adparticles, such as Si(001)-231, using Monte Carlo simulations and a continuum model. In both the simulations, which were mainly for low-temperature cases ~small critical clusters!, and the continuum model, appropriate for high-temperature cases ~large critical clusters!,...

We explore thermal fluctuations of thin planar membranes with a frozen spatially varying background metric and a shear modulus. We focus on a special class of D-dimensional "warped membranes" embedded in a d-dimensional space with d ≥ D + 1 and a preferred height profile characterized by quenched random Gaussian variables {h(α)(q)}, α = D + 1,...,d, in Fourier space with zero mean and a power-l...

In quantum field theory, the vacuum action is subject to renormalization and to the renormalization group running. Consequently, the “cosmological constant” is not a constant, still less should be zero. In this paper we continue with previous work, and derive the contributions of the light particles to the running of the cosmological and gravitational constants in the Standard Model, from the c...

This paper concerns moment and tail probability inequalities and the strong law of large numbers for U-statistics with nonnegative or symmetrized kernels and their multisample and decoupled versions. SubBernoulli functions are used to obtain the moment and tail probability inequalities, which are then used to obtain necessary and sufficient conditions for the almost sure convergence to zero of ...

Empirical studies indicate that the exponents governing the scaling of plant respiration rates (R) with respect to biomass (M) numerically vary between three-fourth for adult plants and 1.0 for seedlings and saplings and are affected by nitrogen (N) and phosphorus (P) content. However, whether the scaling of R with respect to M (or N and P) varies among different phylogenetic groups (e.g., gymn...

In quantum field theory the parameters of the vacuum action are subject to renormalization group running. In particular, the “cosmological constant” is not a constant in a quantum field theory context, still less should be zero. In this paper we continue with previous work, and derive the particle contributions to the running of the cosmological and gravitational constants in the framework of t...

We propose a class of microstructurally informed models for the linear elastic mechanical behaviour of cross-linked polymer networks such as the actin cytoskeleton. Salient features of the models include the possibility to represent anisotropic mechanical behaviour resulting from anisotropic filament distributions, and a power law scaling of the mechanical properties with the filament density. ...

We have used scaling kinetics and the concept of kinetic competence to elucidate the role of hemeproteins OmcA and MtrC in iron reduction by Shewanella oneidensis MR-1. Second-order rate constants for OmcA and MtrC were determined by single-turnover experiments. For soluble iron species, a stopped-flow apparatus was used, and for the less reactive iron oxide goethite, a conventional spectrophot...

We consider a family of Gagliardo-Nirenberg-Sobolev interpolation inequalities which interpolate between Sobolev’s inequality and the logarithmic Sobolev inequality, with optimal constants. The difference of the two terms in the interpolation inequalities (written with optimal constant) measures a distance to the manifold of the optimal functions. We give an explicit estimate of the remainder t...