A FEM model for lifetime prediction of Ancorsteel1000C in rolling contact fatigue

Ancorsteel1000C is commonly used for important components including bearing rollers, gears, connecting rods, wheels and rails; most failures of these components are caused by rolling contact fatigue (RCF). In this study the fatigue damage indicator based on Fatemi-Socie critical plane were determined in a local hot spot area in finite element (FE) model in case of Hertzian stress with zero slip condition. The simulation results compared with respect to experimental data, which is in good agreement. Therefore, this approach can be implemented as a useful tool for lifetime calculations in RCF in the process of structure fatigue design. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A mathematical model for unsteady mixed flows in closed water pipes

We present the formal derivation of a new unidirectional model for unsteady mixed flows in nonuniform closed water pipes.In the case of free surface incompressible flows,the FS-model is formally obtained,using formal asymptotic analysis,which is an extension to more classical shallow water models.In the same way,when the pipe is full,we propose the P-model,which describes the evolution of a compressible inviscid flow,close to gas dynamics equations in a nozzle.In order to cope with the transition between a free surface state and a pressured(i.e.,compressible) state,we propose a mixed model,the PFS-model,taking into account changes of section and slope variation.     

A mathematical model for unemployment

In this paper we have proposed and analyzed a non-linear mathematical model for unemployment by considering three variables, namely the numbers of unemployed, temporarily employed and regularly employed persons. The model is studied using the stability theory of differential equations. It is found that the model has only one equilibrium, which is non-linearly stable under certain conditions. Numerical simulation of the model has been carried out to confirm the analytical results.     

A mathematical model for solute coupled water transport in the production of aqueous humor

A simple mathematical model for the transport of solute and water in the production of aqueous humor by ciliary epithelium in the eye has been developed. The model introduces the intercellular channel, caped with a leaky (porous) tight junction between the layers of non-pigmented ciliary epithelium, as a bisectional channel which consists of two sections: one representing the tight junction which constitutes the blood-aqueous barrier and the other intercellular space with the active solute transport pumps on its lateral surfaces near the junction. The intercellular space and porous tight junction are modeled as electroneutral, uniform, semi-permeable channels of unequal cross-sectional area. Both the cylindrical pore- and rectangular-slit models for the transport through the channels are simultaneously introduced. The approximate analytical solutions to the governing non-linear coupled equations are obtained in normalized forms by employing Segal’s “Isotonic Convection Approximation”. The computational results for the scaled variables are presented through the graphs. The effects of important parameters on the flow/transport produced by (1) the hydrostatic pressure difference alone, (2) the concentration difference alone, and (3) the active transport alone, are examined and discussed. The results of the model may contribute to the present understanding of the mechanisms governing transport processes involved in the aqueous production.     

A mathematical model for asset pricing

Asset price dynamics is studied by using a system of ordinary differential equations which is derived by utilizing a new excess demand function introduced by Caginalp [4] for a market involving more information on demand and supply for a stock rather than their values at a particular price. Derivation is based on the finiteness of assets (rather than assuming unbounded arbitrage) in addition to investment strategies that are based on not only price momentum (trend) but also valuation considerations. For this new model and the older models which were extracted using the classical excess demand function by Caginalp and Balenovich [2] and [3], time evolutions of asset price are compared through numerical simulations.     

A mathematical model for continuous crystallization

J. Banasiak We discuss a mixed‐suspension, mixed‐product removal crystallizer operated at thermodynamic equilibrium. We derive and discuss the mathematical model based on population and mass balance equations and prove local existence and uniqueness of solutions using the method of characteristics. We also discuss the global existence of solutions for continuous and batch mode. Finally, a numerical simulation of a continuous crystallizer in steady state is presented. Copyright © 2015 John Wiley & Sons, Ltd.     

A mathematical model for weighing investments

This model assumes three separate investors each with a set amount of money. The full amount is to be invested in six investments, namely: long‐term bonds, short‐term bonds, treasury bonds, common stock, treasury bills, and commercial paper. The investment is made according to weights assigned to safety of principal, growth, current income, taxable income and volatility. The weights are derived by obtaining pairwise comparison matrices and then using an averaging process.     

A mathematical model for a problem in botany

In this paper, an attempt is made to construct a mathematical model to present a picture of a biological system, namely the evolutionary status of secondary phloem in dicotyledonous plants. In this study 16 parameters have been taken into account. The biological nature of each parameter leads to a mathematical relation and this relationship is exploited to compute a number (conveniently made to lie between 0 and 100) which represents the advance feature of the plant. Thus, given two plants A and B, these computations show whether A is more advanced than B or not. In this communication a set of 18 plants are considered.     

A mathematical model for impulse resistance welding

We present a mathematical model of impulse resistance welding. It accounts for electrical, thermal and mechanical effects, which are non‐linearly coupled by the balance laws, constitutive equations and boundary conditions. The electrical effects of the weld machine are incorporated by a discrete oscillator circuit which is coupled to the field equations by a boundary condition. We prove the existence of weak solutions for a slightly simplified model which however still covers most of its essential features, e.g. the quadratic Joule heat term and a quadratic term due to non‐elastic energy dissipation. We discuss the numerical implementation in a 2D setting, present some numerical results and conclude with some remarks on future research. Copyright © 2003 John Wiley & Sons, Ltd.     

A graphic model for imaging of mathematical formulas

Translated from Vychislitel'nye Kompleksy i Modelirovanie Slozhnykh Sistem, pp. 39–46, Moscow State University, 1989.     

A mathematical model for fungal development in heterogeneous environments

A mathematical model for the development of fungal mycelia in heterogeneous environmental conditions is presented. The validity of this model is tested by comparison of numerical simulations with experimental observations.     

A simple mathematical model for seasonal planktonic blooms

We show how the inclusion of the defense strategy by different species can alter the prediction of simple models. One of the defense strategy by the phytoplankton population against their grazer is the release of toxic chemicals. In turn the zooplankton population reduces there predation rate over toxin producing phytoplankton (TPP) to protect themselves from those toxic chemicals. Thus, when the level of toxicity is high, the grazing pressure is low and when the level of toxicity is low or when the toxin is absent, the grazing pressure is high. Here we have considered a TPP–zooplankton system where the rate of toxin liberation and the predation rate vary with zooplankton abundance. We observe that our proposed model has the potential to show different dynamical behaviour that are similar to that seen in real‐world situations. Further, we consider three different functional forms for the distribution of the toxins and compare them using latin hypercube sampling technique and found that the functional forms seem to have no effect in determining the final outcome of the system. Copyright © 2009 John Wiley & Sons, Ltd.     

A mathematical model for a capacity reservation contract

It is common practice in many industries to use a replenishment contract with a mechanism of capacity reservation. In this paper, we focus on a multi-period capacity reservation contract practiced between a buyer, who buys a single type of product and sells it to end-customers, and two or more heterogeneous suppliers, who produce and replenish the product as agreed upon contractually.In this paper, a mathematical model including several key features of a real contract is developed for a single supplier situation from the buyer’s perspective. It is then extended to a multiple supplier model for a system in which there are several heterogeneous suppliers with different capacities and prices. A rolling-horizon implementation strategy is suggested for the efficient application of the models. Extensive computational experiments demonstrate that the model and strategy can produce cost effective contractual terms for the buyer within a few seconds.     

A mathematical framework for a crowd motion model

In a previous paper, we proposed a model for crowd motion, together with a numerical algorithm, especially designed to handle highly packed situations. This model rests on two principles: We first define a spontaneous velocity which corresponds to the velocity each individual would like to have in the absence of other people; The actual velocity is then computed as the projection of the spontaneous velocity onto the set of admissible velocities (i.e. velocities which do not violate the non-overlapping constraint). We describe here the underlying mathematical framework, and we explain how recent results by J.F. Edmond and L. Thibault on the sweeping process in the prox-regular case can be adapted to handle this situation, in terms of well-posedness as well as convergence of the numerical algorithm. To cite this article: B. Maury, J. Venel, C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

Computation of the lifetime of metal cathode coatings

We propose a method of computing the service time of protective coatings as functions of the geometric and physical characteristics of the aggressive medium-coating-base system. The method is based on representing the destruction process as a series of successive time stages. We analyze the possibility of loss of protective properties of a metallic cathode covering both as a consequence of mechanical failure and as a result of flaking.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 24–34.     

A mathematical model for personalized advertisement in virtual reality environments

We consider a personalized advertisement assignment problem faced by the manager of a virtual reality environment. In this online environment, users log in/out, and they spend time in different virtual locations while they are online. Every time a user visits a new virtual location, the site manager can show the ad of an advertiser. At the end of a fixed time horizon, the manager collects revenues from all of the advertisers, and the total revenue depends on the number of ads of different advertisers she displays to different users. In this setup, the objective of the manager is to find an optimal dynamic ad display policy in order to maximize her expected revenue. In the current paper, we formulate this problem as a continuous time stochastic optimization problem in which the actions of users are represented with two-state Markov processes and the manager makes display decisions at the transition times of these processes. To our best knowledge, no formal stochastic model and rigorous analysis has been given for this practical problem. Such a model and its analysis are the major contributions of this paper along with an optimal solution.