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Method of directly defining the inverse mapping applied to prostate cancer immunotherapy --Mathematical model

International Journal of Biomathematics 2018年第5期11卷 233-254页

作者： Ophir Nave Miriam Elbaz Department of Mathematics Jerusalem College of Technology (JCT) Hava'ad Haleumi 21 Jerusalem Israel

In this paper, we apply the method of directly defining the inverse mapping introduced by Liao and Zhao [On the method of directly defining inverse mapping for nonlinear differential equations, Numer. Algorithms 72（4）（2016） 989-1020] to the problem of prostate cancer immunotherapy. We extend this method in two directions： first, we apply the method to a system of nonlinear ordinary differential equation, and second, we propose a new technique for finding the base functions in the considered algorithm.

关键词： Nonlinear system of differential equations prostate cancer numerical simulations cancer immunotherapy asymptotic analysis.

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Elastic-plastic growth of plane stress mode Ⅱ cracks in power law hardening solids

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Progress in Natural Science:Materials International 2003年第1期 33-40页

作者： PAN Hao(Central Iron and Steel Research Institute, Beijing 100081, China)

Abstract The asymptotic analysis.of near tip field of plane stress mode II cracks growing quasi-statically in steadiness in power lawhardening solids has been performed. Attention was focused on the behavior of the asymptotic solutions as hardening exponent n → ∞.Analytical expressions of the dominant terms of velocities and now factor in centered fan sectors were obtained by expanding them in seriesof the small parameter s = 2/(n - 1). Results show that, as n→∞, all the expressions of dominant terms of quantities in near tip fieldtend to their corresponding ones for elastic-perfectly plastic materials. The effect of hardening exponent n on the angular variations ofstresses in near tip field is very weak. analysis.and discussion that related to plane stress mode Ⅰ crack problem is given in appendix forcomparison with results for mode Ⅱ.

关键词： crack growth hardening solids plane stress mode Ⅱ mode Ⅰ asymptotic analysis.

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On Near-Wall Limiting Behaviors of Low-Reynolds-Number Reynolds-Stress Models

On Near-Wall Limiting Behaviors of Low-Reynolds-Number Reyno...

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第四届海峡两岸计算流体力学学术研讨会

作者： Sergey N. YAKOVENKO and Keh-Chin CHANG Department of Aeronautics and Astronautics, National Cheng Kung University, Tainan, Taiwan

＜正＞ A new approach is proposed to resolve the unbalance contradiction found during checking near-wall behavior of modeled second-moment equations. In addition to presentation of sought functions as the expansions in terms of y but excluding the condition stemmed from the continuity equation for fluctuation velocity, it solves directly the approximate equations at small y values. The present analysis.shows that orders of the major terms of expansions for vertical normal and shear stresses found in the grid-independent LRN RSM models are smaller than those of the conventional expansions.

关键词： Reynolds-stress model Channel flow asymptotic analysis.

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