Industrial Mathematics from SpringerOpen

Finding the optimal opening time of harvesting farmed fishery resources

As an application of mathematics to engineering problems, this paper formulates a simple optimal stopping problem to decide the opening time of harvesting farmed fishery resources that maximizes an economic objective function. A sufficient condition for unique existence of the internal optimal opening time is provided and its concrete mathematical analysis is carried out. Comparative statics of the optimal opening time clearly reveals its dependence on the parameters of the farming environment. The problem is finally applied to analyzing management of a commercially important fishery resource in Japan.

Hidekazu Yoshioka and Yuta Yaegashi

Gas turbine modeling using adaptive fuzzy neural network approach based on measured data classification

The use of gas turbines is widespread in several industries such as; hydrocarbons, aerospace, power generation. However, despite to their many advantages, they are subject to multiple exploitation problem that need to be solved. Indeed, the purpose of the present paper is to develop mathematical models of this industrial system using an adaptive fuzzy neural network inference system. Where the knowledge variables in this complex system are determined from the real time input/output data measurements collected from the plant of the examined gas turbine. It is obvious that the advantage of the neuro-fuzzy modeling is to obtain robust model, which enable a decomposition of a complex system into a set of linear subsystems. On the other side, by focusing on the membership functions for residual generator to get consistent settings based on the used data structure classification and selection, where the main goal is to obtain a robust system information to ensure the supervision of the examined gas turbine.

Abdelhafid Benyounes, Ahmed Hafaifa, Abdellah Kouzou, and Mouloud Guemana

Credit, funding, margin, and capital valuation adjustments for bilateral portfolios

We apply to the concrete setup of a bank engaged into bilateral trade portfolios the XVA theoretical framework of (Albanese and Crépey 2017), whereby so-called contra-liabilities and cost of capital are charged by the bank to its clients, on top of the fair valuation of counterparty risk, in order to account for the incompleteness of this risk. The transfer of the residual reserve credit capital from shareholders to creditors at bank default results in a unilateral CVA, consistent with the regulatory requirement that capital should not diminish as an effect of the sole deterioration of the bank credit spread. Our funding cost for variation margin (FVA) is defined asymmetrically since there is no benefit in holding excess capital in the future. Capital is fungible as a source of funding for variation margin, causing a material FVA reduction. We introduce a specialist initial margin lending scheme that drastically reduces the funding cost for initial margin (MVA). Our capital valuation adjustment (KVA) is defined as a risk premium, i.e. the cost of remunerating shareholder capital at risk at some hurdle rate.

Claudio Albanese, Simone Caenazzo, and Stéphane Crépey

Coffee extraction kinetics in a well mixed system

The extraction of coffee solubles from roasted and ground coffee is a complex operation, the understanding of which is key to the brewing of high quality coffee. This complexity stems from the fact that brewing of coffee is achieved through a wide variety of techniques each of which depends on a large number of process variables. In this paper, we consider a recent, experimentally validated model of coffee extraction, which describes extraction from a coffee bed using a double porosity model. The model incorporates dissolution and transport of coffee in the coffee bed. The model was shown to accurately describe extraction of coffee solubles from grains in two situations: extraction from a dilute suspension of coffee grains and extraction from a packed coffee bed. The full model equations can only be solved numerically. In this work we consider asymptotic solutions, based on the dominant mechanisms, in the case of coffee extraction from a dilute suspension of coffee grains. Extraction in this well mixed system, can be described by a set of ordinary differential equations. This allows analysis of the extraction kinetics from the coffee grains independent of transport processes associated with flow through packed coffee beds. Coffee extraction for an individual grain is controlled by two processes: a rapid dissolution of coffee from the grain surfaces in conjunction with a much slower diffusion of coffee through the tortuous intragranular pore network to the grain surfaces. Utilising a small parameter resulting from the ratio of these two timescales, we construct asymptotic solutions using the method of matched asymptotic expansions. The asymptotic solutions are compared with numerical solutions and data from coffee extraction experiments. The asymptotic solutions depend on a small number of dimensionless parameters, so the solutions facilitate quick investigation of the influence of various process parameters on the coffee extraction curves.

Kevin M Moroney, William T Lee, Stephen BG O’Brien, Freek Suijver, and Johan Marra