The Expansion Method, Mathematical Modeling, and Spatial Econometrics

AbstractChaotic mixing by oscillating a Stokeslet in a circular Hele-Shaw microffluidic device is presented in this article. Mathematical modeling for the induced flow motions by moving a Stokeslet along the x-axis is derived using Fourier expansion method. The solution is formulated in terms of the velocity stream function. The model is then used to explore different stirring dynamics as function of the Stokeslet parameters. For instance, the effects of using various oscillation amplitudes and force strengths are investigated. Mixing patterns using Poincaré maps are obtained numerically and have been used to characterize the mixing efficiency. Results have shown that, for a given Stokeslet’s strength, efficient mixing can be obtained when small oscillation amplitudes are used. The present mixing platform is expected to be useful for many of biomicrofluidic applications.

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Mathematical Modeling of Dusty-Gas Boundary Layers

Applied Mechanics Reviews ◽

10.1115/1.3101716 ◽

1997 ◽

Vol 50 (6) ◽

pp. 357-370 ◽

Cited By ~ 26

Author(s):

A. N. Osiptsov

Keyword(s):

Mathematical Modeling ◽

Boundary Layers ◽

Expansion Method ◽

Heat Fluxes ◽

Matched Asymptotic Expansion ◽

Dusty Gas ◽

Two Phase ◽

Flat Surfaces ◽

Laminar Boundary Layers ◽

Further Development

This article reviews the state of the art in the mathematical modeling of dusty-gas laminar boundary layers in the framework of the two-fluid approach. Main attention is paid to the strict formulation of the two-phase boundary layer approximation, using the matched asymptotic expansion method. The low and high-velocity boundary layers both on curve and flat surfaces are considered. The particle accumulation in the boundary layers and the effects of particles on the friction and heat fluxes are examined. Important advances in the field of study are summarized and the areas deserving further development are discussed. This review article has 107 references.

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Electron Scattering in Solids

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100133618 ◽

1990 ◽

Vol 48 (2) ◽

pp. 4-5

Author(s):

Ryuichi Shimizu ◽

Ze-Jun Ding

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Angular Distribution ◽

Elastic Scattering ◽

Electron Scattering ◽

Cross Sections ◽

Expansion Method ◽

Electron Excitation ◽

Partial Wave Expansion ◽

Backscattered Electrons

Monte Carlo simulation has been becoming most powerful tool to describe the electron scattering in solids, leading to more comprehensive understanding of the complicated mechanism of generation of various types of signals for microbeam analysis.The present paper proposes a practical model for the Monte Carlo simulation of scattering processes of a penetrating electron and the generation of the slow secondaries in solids. The model is based on the combined use of Gryzinski’s inner-shell electron excitation function and the dielectric function for taking into account the valence electron contribution in inelastic scattering processes, while the cross-sections derived by partial wave expansion method are used for describing elastic scattering processes. An improvement of the use of this elastic scattering cross-section can be seen in the success to describe the anisotropy of angular distribution of elastically backscattered electrons from Au in low energy region, shown in Fig.l. Fig.l(a) shows the elastic cross-sections of 600 eV electron for single Au-atom, clearly indicating that the angular distribution is no more smooth as expected from Rutherford scattering formula, but has the socalled lobes appearing at the large scattering angle.

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An empirical review of gambling expansion and gambling-related harm

SUCHT - Zeitschrift für Wissenschaft und Praxis / Journal of Addiction Research and Practice ◽

10.1024/0939-5911/a000563 ◽

2018 ◽

Vol 64 (5-6) ◽

pp. 295-306 ◽

Cited By ~ 8

Author(s):

Debi A. LaPlante ◽

Heather M. Gray ◽

Pat M. Williams ◽

Sarah E. Nelson

Keyword(s):

Literature Review ◽

Peer Review ◽

Empirical Data ◽

Empirical Studies ◽

Expansion Method ◽

Responsible Gambling ◽

Review Literature ◽

Evidence Based ◽

Empirical Comparison ◽

Related Harm

Abstract. Aims: To discuss and review the latest research related to gambling expansion. Method: We completed a literature review and empirical comparison of peer reviewed findings related to gambling expansion and subsequent gambling-related changes among the population. Results: Although gambling expansion is associated with changes in gambling and gambling-related problems, empirical studies suggest that these effects are mixed and the available literature is limited. For example, the peer review literature suggests that most post-expansion gambling outcomes (i. e., 22 of 34 possible expansion outcomes; 64.7 %) indicate no observable change or a decrease in gambling outcomes, and a minority (i. e., 12 of 34 possible expansion outcomes; 35.3 %) indicate an increase in gambling outcomes. Conclusions: Empirical data related to gambling expansion suggests that its effects are more complex than frequently considered; however, evidence-based intervention might help prepare jurisdictions to deal with potential consequences. Jurisdictions can develop and evaluate responsible gambling programs to try to mitigate the impacts of expanded gambling.

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