The scaling behavior of nonlocal surface growth equations are analyzed using a Flory-type approach introduced by Hentschel and Family [Phys. Rev. Lett. 66 (1991) 1982]. The growth equations studied include the nonlocal Kardar–Parisi–Zhang, nonlocal Sun–Guo–Grant, and nonlocal Lai–Das...

The scaling behaviors of the anisotropic nonlocal Kardar–Parisi–Zhang equation are studied by the scaling analysis method introduced by Hentschel and Family. The scaling exponents in both the weak- and strong-coupling regions are obtained, respectively. The scaling exponents in weak-coupling...

Using standard calculus, explicit formulas for the one-dimensional continuous and discrete homotopy operators are derived. It is shown that these formulas are equivalent to those in terms of Euler operators obtained from the variational complex.

Jiang et al. (Jiang, Y.Q., Wong, S.C., Ho, H.W., Zhang, P., Liu, R.X., Sumalee, A., 2011. A dynamic traffic assignment model for a continuum transportation system. Transportation Research Part B 45 (2), 343–363) proposed a predictive continuum dynamic user-optimaDUO-l to investigate the...

We will develop and study synchronised material flow with the help of fluid dynamics. After discussing the empirical relevance of synchronised material flow we develop a deterministic supply chain model. Unlike similar approaches, this model is not based on some quasi steady-state assumptions...

This paper presents an approximation formula for the overflow probability for GI/GI/c(N) queues in terms of a queue-length distribution for the corresponding GI/GI/c(\infty ) queues, where N is the total capacity of the system. The approximation is based on the conservation law, and on...

We implement and assess several statistical methods for rough surface morphology characterization, which can largely be divided into two classes. The first class is based on estimation of two-point, quadratic statistical functions and includes: estimates of the sample autocovariance function,...

In surface growth simulations, usually the substrate is initially considered smooth with no roughness. But as known in reality, many substrates in nature are initially rough. In this article, we study the sensitivity of dynamic scaling of different models on rough substrates generated by...

The spreading of a small mercury droplet (150μm) on thin gold films is studied, using an optical microscope enhanced with a differential interference contrast system. The growing interfaces are analyzed in order to determine the roughness (α) and growth (β) exponents. For gold film thickness...

We study two models for competitive deposition and evaporation of particles from rough surfaces. The process of deposition is carried out for two models, one according to the ballistic deposition (BD) and the other according to the random deposition with a surface relaxation (RDSR). The process...