Nonlinear Analysis: Real World Applications

Stringent emission regulations combined with customer demands for improved fuel economy and performance have forced the automotive industry to consider more advanced powertrain configurations than standard port-fuel injected gasoline engines. Modern state-of-the-art powertrain systems may combine several power sources (internal combustion engines, electric motors, fuel cells, etc.) and various exhaust aftertreatment devices (catalytic converters, lean NOx traps, particulate filters, etc.) in addition to conventional engine subsystems such as turbochargers and exhaust gas recirculation. The determination of the way in which these systems need to be operated to meet driver's torque demand, performance and fuel economy expectations while satisfying federal emission regulations is a complex and a multiobjective optimal control problem. This paper reviews some of the approaches to this problem in the context of two case studies

This study was conducted aimed at providing a sustainable multi-objective model of supply chain location, inventory, routing under uncertainty with a passive defense approach, in which the Upgral model was first introduced to the world. The Upgral Paradigm is an integrated model for the location-inventory-routing problem in a four-level supply chain where parameters such as demand, facility cost and inventory costs are taken into account uncertain as triangular fuzzy numbers (TFNs). In this study, the characteristics and capabilities of passive defense in the supply chain, such as "logistical flow rate", "backup path security", "the possibility of resource and equipment deployment", and the dispersion principle were considered for location to increase the resilience of supply chain. The model was solved using Whale Optimization Algorithm (WOA) and NSGA-II meta-heuristic algorithm. First, a four-objective mathematical model was proposed for the problem t...

The stability of the motion of an oscillator with a periodically time-varying mass is under consideration. The key idea is that an adequate change of variables leads to a newtonian equation, where classical stability techniques can be applied: Floquet theory for the linear oscillator, KAM method in the nonlinear case. To illustrate this general idea, first we have generalized the results of [W.T. van Horssen, A.K. Abramian, Hartono, On the free vibrations of an oscillator with a periodically time-varying mass, J. Sound Vibration 298 (2006) 1166–1172] to the forced case; second, for a weakly forced Duffing’s oscillator with variable mass, the stability in the nonlinear sense is proved by showing that the first twist coefficient is not zero.

The proliferation of heterogeneous data sources of semantic knowledge base intensifies the need of anautomatic instance matching technique. However, the efficiency of instance matching is often influenced bythe weight of a property associated to instances. Automatic weight generation is a non-trivial, however animportant task in instance matching technique. Therefore,identifying an appropriate metric for generatingweight for a property automatically is nevertheless a formidable task. In this paper, we investigate anapproach of generating weights automatically by considering hypotheses: (1) the weight of a property isdirectly proportional to the ratio of the number of its distinct values to the number of instances contain the property, and (2) the weight is also proportional to the ratio of the number of distinct values of a propertyto the number of instances in a training dataset. The basic intuition behind the use of our approach is theclassical theory of information content that infrequent words are more informative than frequent ones. Our mathematical model derives a metric for generating property weights automatically, which is applied ininstance matching system to produce re-conciliated instances efficiently. Our experiments and evaluationsshow the effectiveness of our proposed metric of automatic weight generation for properties in an instancematching technique

The problem dealing with the two-dimensional flow of an incompressible viscoelastic Maxwell fluid past an infinite porous plate is investigated. It is assumed that the suction velocity is normal to the plate and oscillates about a mean value. The external free-stream velocity varies periodically in time. The resulting differential equation subject to the relevant boundary and initial conditions is numerically solved by means of a numerical technique, in which a coordinate transformation is employed to transform the semi-infinite physical space to a bounded computational domain. The effects of various values of the emerging parameters, e.g. the elasticity parameter, the oscillation amplitude and frequency of the external flow and the suction velocity, on the time series of velocity, especially on the boundary-layer structure near the plate, are discussed. The nature of the shear stress engendered due to the flow is also investigated.