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"This book collects recent developments in nonlinear and complex systems. It provides up-to-date theoretic developments and new techniques based on a nonlinear dynamical systems approach that can be used to model and understand complex behavior in nonlinear dynamical systems. It covers symmetry groups, conservation laws, risk reduction management, barriers in Hamiltonian systems, and synchronization and chaotic transient. Illustrating mathematical modeling applications to nonlinear physics and nonlinear engineering, the book is ideal for academic and industrial researchers concerned with machinery and controls, manufacturing, and controls.· Introduces new concepts for understanding and modeling complex systems;· Explains risk reduction management in complex systems;· Examines the symmetry group approach to understanding complex systems;· Illustrates the relation between transient chaos and crises."

"Mathematical modeling he ability to apply mathematical concepts and techniques to real-life systems as expanded considerably over the last decades, making it impossible to cover all of its aspects in one course or textbook. Continuum Modeling in the Physical Sciences provides an extensive exposition of the general principles and methods of this growing field with a focus on applications in the natural sciences. The authors present a thorough treatment of mathematical modeling from the elementary level to more advanced concepts.Most of the chapters are devoted to a discussion of central issues such as dimensional analysis, conservation principles, balance laws, constitutive relations, stability, robustness, and variational methods, and are accompanied by numerous real-life examples. Readers will benefit from the exercises placed throughout the text and the Challenging Problems sections found at the ends of several chapters. The last chapter is devoted to extensively worked-out case studies in polymer dynamics, fiber spinning, water waves, and waveguide optics."

"Interfacial fluid mechanics: a mathematical modeling approach provides an introduction to mathematical models of viscous flow used in rapidly developing fields of microfluidics and microscale heat transfer. The basic physical effects are first introduced in the context of simple configurations and their relative importance in typical microscale applications is discussed. Then, several configurations of importance to microfluidics, most notably thin films/droplets on substrates and confined bubbles, are discussed in detail. Topics from current research on electrokinetic phenomena, liquid flow near structured solid surfaces,evaporation/condensation, and surfactant phenomena are discussed in the later chapters."

"ABSTRAKPenyebaran HIV dapat dimodelkan dengan menggunakan pendekatan deterministik kedalam sistem persamaan diferensial biasa tidak linier berdimensi tujuh, pada skripsi ini dibuat model matematika penyebaran HIV dengan intervensi ART. Pada model sederhana yaitu ketika tidak dilakukan intervensi ART, titik keseimbangan bebas penyakit dan titik keseimbangan endemik dapat ditentukan secara analitik dengan basic reproduction number. Kriteria kestabilan lokal dari titik keseimbangan bebas penyakit dan titik keseimbangan endemik dapat dianalisis. Titik keseimbangan endemik ada ketika nilai basic reproduction number lebih besar dari satu. Berdasarkan analisis sensitivitas dari basic reproduction number pada model lengkap model dengan intervensi ART , dengan memperbesar laju intervensi ART pada manusia yang terinfeksi HIV akan menurunkan basic reproduction number. Simulasi numerik dilakukan untuk menganalisis pengaruh intervensi ART dalam mengurangi total manusia terinfeksi selama periode intervensi.

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ABSTRACTHIV spreads can be modeled using a deterministic approach into a seven dimensional nonlinear ordinary differential equation, in this thesis establish a mathematical model for the spread of HIV with an intervention of ART treatment. In a simplified model, when no ART treatment implemented, disease free and the endemic equilibrium points were established analytically along with the basic reproduction number. The local stability criteria of disease free equilibrium and the existing criteria of endemic equilibrium analyzed. The endemic equilibrium exists when basic reproduction number is larger than one. From the sensitivity analysis of basic reproduction number of the complete model model with ART treatment , the enlarging number of the infected human who following the ART treatment program will reduce basic reproduction number. The numerical simulation of the autonomous system to show how treatment intervention of ART impacts the reduction of the infected population during intervention time period."

"This book explains the hypoplastic modelling framework. It is divided into two parts, the first of which is devoted to principles of hypoplasticity. First, the basic features of soils mechanical behaviour are introduced, namely non-linearity and asymptotic properties. These features are then incorporated into simple one-dimensional hypoplastic equations for compression and shear. Subsequently, a hypoplastic equivalent of the Modified Cam-Clay model is developed in 2D space using stress and strain invariants to demonstrate key similarities and differences between elasto-plastic and hypoplastic formulations. Lastly, the mathematical structure of hypoplastic models is explained by tracing their historical development, from the early trial-and-error models to more recent approaches. In turn, Part II introduces specific hypoplastic models for soils. First, two reference models for sand and clay are defined. After summarising their mathematical formulations, calibration procedures are described and discussed. Subsequently, more advanced modelling approaches are covered: the intergranular strain concept incorporating the effects of small strain stiffness and cyclic loading, viscohypoplasticity for predicting rate effects, soil structure to represent structured and bonded materials and soil anisotropy. The book concludes with a description of partial saturation and thermal effects: topics that are increasingly important to the disciplines of energy and environmental geotechnics.Selecting a constitutive model and its parameters is often the most important and yet challenging part of any numerical analysis in geotechnical engineering. Hypoplasticity involves a specific class of soil constitutive models, which are described in detail here. The book offers an essential resource, both for model users who need a more advanced model for their geotechnical calculations and are mainly interested in parameter calibration procedures, and for model developers who are seeking a comprehensive understanding of the mathematical structure of hypoplasticity."

"This book presents recent developments in nonlinear dynamics with an emphasis on complex systems. The volume illustrates new methods to characterize the solutions of nonlinear dynamics associated with complex systems. This book contains the following topics: new solutions of the functional equations, optimization algorithm for traveling salesman problem, fractals, control, fractional calculus models, fractional discretization, local fractional partial differential equations and their applications, and solutions of fractional kinetic equations."

"The book develops a descriptive mathematical model articulated through continuum mechanics concepts for these non-Newtonian, viscoelastic fluids and turbulent flows. Each complex fluid and flow is examined in this continuum context as well as in combination with the turbulent flow of viscoelastic fluids. Some details are also explored via kinetic theory, especially viscoelastic fluids and their treatment with the Boltzmann equation. Both solution and modeling strategies for turbulent flows are laid out using continuum concepts, including a description of constructing polynomial representations and accounting for non-inertial and curvature effects."