This work compares the performance of two Lagrangian turbulent particle dispersion models: the standard model (e.g., that presented in Sommerfeld et al. (1993)), in which the fluctuating fluid velocity experienced by the particle is composed of two components, one correlated with the previous time step and a second one randomly sampled from a Wiener process, and the model proposed by Minier and...

Dispersion in labor and factor productivity across firms is large and persistent, large flows of workers move across firms, and worker reallocation is an important source of productivity growth. The purpose of the paper is to provide a formal explanation for these observations that clarifies the role of worker reallocation as a source of productivity growth. Specifically, we study a modified ve...

A one-parameter family of smooth hypersurfaces {Mt} ⊂ R flows by mean curvature if zt = H(z) = ∆Mtz , (0.1) where z are coordinates on R and H = −Hn is the mean curvature vector. In this note, we prove sharp gradient and area estimates for graphs flowing by mean curvature. Thus, each Mt is assumed to be the graph of a function u(·, t). So, if z = (x, y) with x ∈ R, then Mt is given by y = u(x, ...

This paper establishes the proper notation and precise interpretation for Laplacian flows on simplicial complexes. In particular, we have shown how to interpret these flows as time-varying discrete differential forms that converge to harmonic forms. The stability properties of the corresponding dynamical system are shown to be related to the topological structure of the underlying simplicial co...

In this paper, some time-dependent flows of a non-Newtonian fluid between two side walls over a plane wall are investigated. The following three problems have been studied: (i) flow due to an oscillating plate, (ii) flow due to an accelerating plate, and (iii) flow due to applied constant stress. The explicit expressions for the velocity field are determined by using the integral transforms. Th...

The functional verification landscape has changed beyond all recognition over the last 10 years, and while design paradigms have become mature and stable, verification methodologies and technologies have continued to evolve with new flows and tools being invented. Against this rapidly changing background, designs have been steadily growing to gigascale dimensions, with more intellectual propert...

Recent progress in simulating the properties of interfacial water at hard hydrophobic and hydrophilic surfaces is reviewed and compared to results for the air/water interface. The authors discuss static properties such as the equilibrium contact angle, the depletion layer thickness, and the orientation of interfacial water molecules. Relations between these properties, e.g., the relation betwee...

The throughflow level of approximation still remains an important tool for designing turbomachines [2] even though 3-D calculations are used more and more early in the design process. The throughflow models heavily rely on empirical inputs such as 2-D correlations or end-wall loss models. This feature has shown to be efficient but lack of generality. Two-dimensional empirical correlations are a...

There is a gap in the proof of Lemma VII.4 in [1]. We present an alternative proof of Theorem B (C 1 Ω-stable vector fields satisfy Axiom A) in [1]. The novel and essential part in the proof of the stability and Ω-stability conjectures for flows is the connecting lemma introduced in [1]. A mistake in the proof of the last conjecture was pointed out to me by Toyoshiba [5], who later also provide...

We consider the equations governing multicomponent reactive flows derived from the kinetic theory of dilute polyatomic reactive gas mixtures. It was shown in [2] that there exists a generalized entropy which allows to derive a symmetric conservative form of the system. In the framework of Kawashima’s and Shizuta’s theory, we had recast the resulting system into a normal form, that is, in the fo...