A procedure suggested by Vvedensky for obtaining continuum equations as the coarse-grained limit of discrete models is applied to the restricted solid-on-solid model with both adsorption and desorption. Using an expansion of the master equation, discrete Langevin equations are derived; these agree quantitatively with direct simulation of the model. From these, a continuum differential equation ...

During the spring of 2003, the downstream slope of an embankment dam began to move during an extreme flooding event. The current study was implemented to evaluate the slope stability of the embankment and as a case-study to compare the limit equilibrium and continuum modeling methods. Initially, stability analyses were performed using conservative shear strength of soils estimated from both bor...

The present paper aims at investigating the manner of two dissipative massive scalar fields. Two massive scalar fields that interact with a reservoir were considered and a reservoir was modeled by continuum Klein-Gordon fields. The Lagrangian of the total system was canonically quantized and the dynamics of the system was determined using the Euler-Lagrange equation. Then, the explicit form of the...

Field-theoretic methods are applied to a number of two-dimensional lattice models with Abelian symmetry groups. It is shown, using a vortex + spin-wave decomposition. that the Z, Villain models are related to a class of continuum field theories with analogous duality properties. Fermion operators for these field theories are discussed. In the case of the Ising model, the vortices and spin-waves...

The validity of the traditional plasma continuum is predicated on a hierarchy of scale-lengths, with the Debye length being considered to be effectively unresolvable in the continuum limit. In this article, we revisit the strong magnetic field case in which the Larmor radius is comparable or smaller than the Debye length in the classical plasma, and also for a relativistic plasma. Fresh insight...

This work investigates the breakdown of the continuum relations for diffusion velocity in inert binary gas mixtures. Values of the relative diffusion velocities for components of a gas mixture may be calculated using of Chapman-Enskog theory and occur not only due to concentration gradients, but also pressure and temperature gradients in the flow as described by Hirschfelder. Because Chapman-En...

The main result is that for λ strong limit singular failing the continuum hypothesis (i.e. 2 > λ), a polarized partition theorem holds. § 0. Introduction In the present paper we show a polarized partition theorem for strong limit singular cardinals λ failing the continuum hypothesis. Let us recall the following definition. {jeden} Definition 0.1. For ordinal numbers α1, α2, β1, β2 and a cardina...

We study Γ-convergence of graph-based Ginzburg–Landau functionals, both the limit for zero diffusive interface parameter ε → 0 and the limit for infinite nodes in the graph m→∞. For general graphs we prove that in the limit ε → 0 the graph cut objective function is recovered. We show that the continuum limit of this objective function on 4-regular graphs is related to the total variation semino...

We introduce and solve a generalized 1+1D Lorentzian gravity model in which a certain subclass of baby-universes is allowed, the occurrence of these being governed by a coupling constant β. Combining transfer matrix-, saddle pointand path integral techniques we show that for β < 1 it is possible to take a continuum limit in which the model is described by a 1D quantum Calogero Hamiltonian. The ...

We evaluate for arbitrary even dimensions the classical continuum limit of the lattice axial anomaly defined by the overlap-Dirac operator. Our calculational scheme is simple and systematic. In particular, a powerful topological argument is utilized to determine the value of a lattice integral involved in the calculation. When the Dirac operator is free of species doubling, the classical contin...