Computational Methods And Models

This volume addresses challenges and solutions in transport and mobility of people and goods with respect to environment, safety, security and socio–economics issues, exploring advanced computational research work and the latest innovations in transport.

This volume addresses challenges and solutions in transport and mobility of people and goods with respect to environment, safety, security and socio–economics issues, exploring advanced computational research work and the latest innovations in transport.

Density functional theory (DFT) provides the most widely used models for simulating molecules and materials based on the fundamental laws of quantum mechanics. It plays a central role in a huge spectrum of applications in chemistry, physics, and materials science.Quantum mechanics describes a system of N interacting particles in the physical 3-dimensional space by a partial differential equation in 3N spatial variables. The standard numerical methods thus incur an exponential increase of computational effort with N, a phenomenon known as the curse of dimensionality; in practice these methods already fail beyond N=2.

Microcirculation is a key area of interest within the realms of biology and medicine. As a vital discipline, microcirculatory biology forms a significant part of established medical fields like cardiovascular medicine and oncology, and is increasingly relevant in emerging fields such as neuroscience. With its multifaceted nature, the study of microcirculation has evolved from basic observations and experiments to embrace cutting-edge imaging technologies, quantitative methods, and the power of data science. This volume brings together a series of insightful chapters that highlight the latest trends in modeling microcirculation. It casts a spotlight on the vital role of microcirculation in brain function modeling and the innovative applications of microvascular models in oncology. Readers will be introduced to state-of-the-art methodologies of microcirculation modeling. A key focus is on mixed-dimensional models, mathematical methods adept at describing complex interactions within lower dimensional manifolds. Each chapter thoughtfully navigates the mathematical, computational, and practical challenges of these approaches, underscoring their effectiveness in capturing the essence of microcirculation. This book offers a window into the latest advancements and methodologies that are shaping the future of this vital field.

The considerable influence of inherent uncertainties on structural behavior has led the engineering community to recognize the importance of a stochastic approach to structural problems. Issues related to uncertainty quantification and its influence on the reliability of the computational models are continuously gaining in significance. In particular, the problems of dynamic response analysis and reliability assessment of structures with uncertain system and excitation parameters have been the subject of continuous research over the last two decades as a result of the increasing availability of powerful computing resources and technology.

This book offers a collection of 17 scientific papers about the computational modeling of fracture. Some of the manuscripts propose new computational methods and/or how to improve existing cutting edge methods for fracture. These contributions can be classified into two categories: 1. Methods which treat the crack as strong discontinuity such as peridynamics, scaled boundary elements or specific versions of the smoothed finite element methods applied to fracture and 2.

Around the world, liberalization and privatization in the electricity industry have lead to increased competition among utilities. At the same time, utilities are now exposed more than ever to risk and uncertainties, which they cannot pass on to their customers through price increases as in a regulated environment. Especially electricity-generating companies have to face volatile wholesale prices, fuel price uncertainty, limited long-term hedging possibilities and huge, to a large extent, sunk investments.

This book presents a collection of original research papers from the 2nd International Conference on Mathematical and Related Sciences, held in Antalya, Turkey, on 27 – 30 April 2019 and sponsored/supported by Düzce University, Turkey; the University of Jordan; and the Institute of Applied Mathematics, Baku State University, Azerbaijan.

Contemporary macroeconomics is built upon microeconomic principles, with its most recent advance featuring dynamic stochastic general equilibrium models. The textbook by Heer and Maußner acquaints readers with the essential computational techniques required to tackle these models and employ them for quantitative analysis. This third edition maintains the structure of the second, dividing the content into three separate parts dedicated to representative agent models, heterogeneous agent models, and numerical methods. At the same time, every chapter has been revised and two entirely new chapters have been added.