Tag Archives: Equations

Stochastic Dynamics by Hans Crauel

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Stochastic Dynamics by Hans Crauel
English | March 26, 1999 | ISBN: 0387985123 | 455 Pages | PDF | 8 MB
Focusing on the mathematical description of stochastic dynamics in discrete as well as in continuous time, this book investigates such dynamical phenomena as perturbations, bifurcations and chaos. It also introduces new ideas for the exploration of infinite dimensional systems, in particular stochastic partial differential equations.

Stochastic Dynamics by Hans Crauel
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“Acoustic Waves: From Microdevices to Helioseismology” ed. by Marco G. Beghi

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"Acoustic Waves: From Microdevices to Helioseismology" ed. by Marco G. Beghi
InTeOpP | 2011 | ISBN: 9533075724 9789533075723 | 665 pages | PDF | 51 MB
This book presents several aspects of the active research ongoing in the field of Acoustic Waves. Theoretical efforts are leading to a deeper understanding of phenomena, also in complicated environments like the solar surface boundary. A whole class of widespread microdevices, including filters and sensors, is based on the behaviour of acoustic waves propagating in thin layers. The search for better performances is driving to new materials for these devices, and to more refined tools for their analysis.

“Acoustic Waves: From Microdevices to Helioseismology” ed. by Marco G. Beghi
Contents
Part 1 Theoretical and Numerical Investigations of Acoustic Waves
1 Analysis of Acoustic Wave in Homogeneous and Inhomogeneous Media Using Finite Element Method
2 Topological Singularities in Acoustic Fields due to Absorption of a Crystal
3 An Operational Approach to the Acoustic Analogy Equations
4 Exact Solutions Expressible in Hyperbolic and Jacobi Elliptic Functions of Some Important Equations of Ion-Acoustic Waves
5 A coustic Wave
Part 2 Acoustic Waves as Investigative Tools
6 Acoustic Waves: A Probe for the Elastic Properties of Films
7 Evaluation Method for Anisotropic Drilling Characteristics of the Formation by Using Acoustic Wave Information
8 Machinery Faults Detection Using Acoustic Emission Signal
9 Compensation of Ultrasound Attenuation in Photoacoustic Imaging
10 Low Frequency Acoustic Devices for Viscoelastic Complex Media Characterization
11 Modeling of Biological Interfacial Processes Using Thickness-Shear Mode Sensors
12 Analysis of Biological Acoustic Waves by Means of the Phase-Sensitivity Technique
13 Photoacoustic Technique Applied to Skin Research: Characterization of Tissue, Topically Applied Products and Transdermal Drug Delivery
14 Acoustic-Gravity Waves in the Ionosphere During Solar Eclipse Events
Part 3 Acoustic Waves as Manipulative Tools
15 Use of Acoustic Waves for Pulsating Water Jet Generation
16 Molecular Desorption by Laser-Driven Acoustic Waves: Analytical Applications and Physical Mechanisms
17 Excitation of Periodical Shock Waves in Solid-State Optical Media (Yb:YAG, Glass) at SBS of Focused Low-Coherent Pump Radiation: Structure Changes, Features of Lasing
18 An Optimal Distribution of Actuatorsin Active Beam Vibration: Some Aspects, Theoretical Considerations
Part 4 Acoustic Wave Based Microdevices
19 Multilayered Structure as a Novel Material for Surface Acoustic Wave Devices: Physical Insight
20 SAW Parameters Analysis and Equivalent Circuit of SAW Device
21 Sources of Third-Order Intermodulation Distortion in Bulk Acoustic Wave Devices: A Phenomenological Approach
22 Shear Mode Piezoelectric Thin Film Resonators
23 Polymer Coated Rayleigh SAW and STW Resonators for Gas Sensor Applications
24 Ultrananocrystalline Diamond as Material for Surface Acoustic Wave Devices
25 Aluminum Nitride (AIN) Film Based Acoustic Devices: Material Synthesis and Device Fabrication
26 Surface Acoustic Wave Devices for Harsh Environment
27 Applications of In-Fiber Acousto-Optic Devices
28 Surface Acoustic Waves and Nano-Electromechanical Systems
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Nonlocal Continuum Field Theories

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Nonlocal Continuum Field Theories
English | Physics, Mechanics | 1. Jule 2002 | ISBN-10: 0387952756 | 376 pages | pdf | 2 mb
Nonlocal continuum field theories are concerned with material bodies whose behavior at any interior point depends on the state of all other points in the body — rather than only on an effective field resulting from these points — in addition to its own state and the state of some calculable external field.

Nonlocal Continuum Field Theories
nonlocal continuum field theories are concerned with material bodies whose behavior at any interior point depends on the state of all other points in the body — rather than only on an effective field resulting from these points — in addition to its own state and the state of some calculable external field. Nonlocal field theory extends classical field theory by describing the responses of points within the medium by functionals rather than functions (the "constitutive relations" of classical field theory). Such considerations are already well known in solid-state physics, where the nonlocal interactions between the atoms are prevalent in determining the properties of the material. The tools developed for crystalline materials, however, do not lend themselves to analyzing amorphous materials, or materials in which imperfections are a major part of the structure. Nonlocal continuum theories, by contrast, can describe these materials faithfully at scales down to the lattice parameter. This book presents a unified approach to field theories for elastic solids, viscous fluids, and heat-conducting electromagnetic solids and fluids that include nonlocal effects in both space and time (memory effects). The solutions to the field equations agree remarkably well with atomic theories and experimental observations.
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Nonlinear Waves in Elastic Crystals

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Nonlinear Waves in Elastic Crystals
English | Physics, Mathematics | January 2000 | ISBN-10: 0198534841 | 320 pages | Djvu | 3.2 mb
The mathematical modelling of changing structures in materials is of increasing importance to industry where applications of the theory are found in subjects as diverse as aerospace and medicine.

Nonlinear Waves in Elastic Crystals
This book deals with aspects of the nonlinear dynamics of deformable ordered solids (known as elastic crystals) where the nonlinear effects combine or compete with each other. Physical and mathematical models are discused and computational aspects are also included. Different models are considered – on discrete as well as continuum scales – applying heat, electricity, or magnetism to the crystal structure and these are analysed using the equations of rational mechanics. In this way the student is introduced to the important equations of nonlinear science that describe shock waves, solitons and chaos and also the non-exactly integrable systems or partial differential equations. A large number of problems and examples are included, many taken from recent research and involving both one-dimensional and two-dimensional problems as well as some coupled degress of freedom.
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Classical Electromagnetism via Relativity

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W. G. V. Rosser, "Classical Electromagnetism via Relativity"
1968 | pages: 302 | ISBN: 0408433000, 1489962581 | DJVU | 2,3 mb

Classical Electromagnetism via Relativity
One of the arts of teaching is to attack a problem from a different point of view, if the conventional approach has not been fully appreciated. This often helps the class to appreciate the conventional approach more fully. Maxwell's equations are generally introduced during a long course on electromagnetism, in which the correct interpretations and experimental bases of Maxwell's equations are sometimes obscured by the large amount of time of necessity devoted to the important applications of individual laws. The displacement 'current' is often introduced in a way that gives the wrong impression of its role in contemporary electromagnetic theory. There have been refinements of interpretation since Maxwell's time, particularly following the abandonment of the ether theories and the introduction of the theory of relativity. This is particularly true of the displacement 'current'. In this monograph, Maxwell's equations are approached from a different point of view from the conventional approach, namely using Coulomb's law and the transformations of the theory of special relativity. This approach illustrates the essential unity of Maxwell's equations, and the modern interpretation of the various terms in Maxwell's equations. It is the reverse of the historical approach, since the theory of special relativity arose out of optics and electromagnetism.
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The Weyl Operator and its Generalization

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The Weyl Operator and its Generalization (Pseudo-Differential Operators) by Leon Cohen
English | 2012-12-12 | ISBN: 3034802935 | PDF | 171 pages | 0,9 MB

The Weyl Operator and its Generalization
The discovery of quantum mechanics in the years 1925-1930 necessitated the consideration of associating ordinary functions with non-commuting operators. Methods were proposed by Born/Jordan, Kirkwood, and Weyl. Sometime later, Moyal saw the connection between the Weyl rule and the Wigner distribution, which had been proposed by Wigner in 1932 as a way of doing quantum statistical mechanics. The basic idea of associating functions with operators has since been generalized and developed to a high degree. It has found several application fields, including quantum mechanics, pseudo-differential operators, time-frequency analysis, quantum optics, wave propagation, differential equations, image processing, radar, and sonar. This book aims at bringing together the results from the above mentioned fields in a unified manner and showing the reader how the methods have been applied. A wide audience is addressed, particularly students and researchers who want to obtain an up-to-date working knowledge of the field. The mathematics is accessible to the uninitiated reader and is presented in a straightforward manner.
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Handbook of Industrial Engineering Equations, Formulas, and Calculations (Industrial Innovation Series)

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Handbook of Industrial Engineering Equations, Formulas, and Calculations (Industrial Innovation Series) by Adedeji B. Badiru
English | 2010 | ISBN: 1420076272 | 426 Pages | PDF | 2 MB
The first handbook to focus exclusively on industrial engineering calculations with a correlation to applications, Handbook of Industrial Engineering Equations, Formulas, and Calculations contains a general collection of the mathematical equations often used in the practice of industrial engineering.

Handbook of Industrial Engineering Equations, Formulas, and Calculations (Industrial Innovation Series)
Many books cover individual areas of engineering and some cover all areas, but none covers industrial engineering specifically, nor do they highlight topics such as project management, materials, and systems engineering from an integrated viewpoint. Written by acclaimed researchers and authors, this concise reference marries theory and practice, making it a versatile and flexible resource. Succinctly formatted for functionality, the book presents: Basic Math Calculations Engineering Math Calculations Production Engineering Calculations Engineering Economics Calculations Ergonomics Calculations Facility Layout Calculations Production Sequencing and Scheduling Calculations Systems Engineering Calculations Data Engineering Calculations Project Engineering Calculations Simulation and Statistical Equations It has been said that engineers make things while industrial engineers make things better . To make something better requires an understanding of its basic characteristics and the underlying equations and calculations that facilitate that understanding. To do this, however, you don't have to be computational experts; you just have to know where to get the computational resources that are needed. This book elucidates the underlying equations that facilitate the understanding required to improve design processes, continuously improving the answer to the age-old question: What is the best way to do a job?
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Phase-Space Optics: Fundamentals and Applications

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Phase-Space Optics: Fundamentals and Applications
English | Physics, Optics | 18. August 2009 | ISBN-10: 0071597980 | 393 pages | pdf | 3 mb
A comprehensive cross section of phase-space optics This definitive volume highlights an elegant, unified approach to optical rays, waves, and system design using cutting-edge phase-space techniques.

Phase-Space Optics: Fundamentals and Applications
details theoretical concepts of phase space as well as novel engineering applications in specific disciplines. This authoritative guide includes full coverage of sampling, superresolution imaging, and the phase-space interpretation of ultrafast optics. Work with Wigner optics, analyze phase-space equations, develop wave propagation models, and gain a new understanding of optical sources and systems. Discover how to: Describe optical phenomena using Wigner and ambiguity functions Perform phase-space rotations using ray transformation matrices Influence the trade-off between pupil size and depth of field Analyze and design optical signals using the Radon-Wigner transform Accomplish superresolution by squeezing phase space Interpret the intimate relationship between radiometry and coherence Use basic algebra to discover self-imaging, Fresnel diffraction, and the Talbot effect Develop discrete models, sampling criteria, and interpolation formulae Work with ultrafast processes and complex space-time structures
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Mathematics for Economics and Finance: Methods and Modelling

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Martin Anthony, Norman Biggs, "Mathematics for Economics and Finance: Methods and Modelling"
1996 | ISBN-10: 0521551137, 0521559138 | 410 pages | PDF | 12 MB

Mathematics for Economics and Finance: Methods and Modelling
Mathematics has become indispensable in the modelling of economics, finance, business and management. Without expecting any particular background of the reader, this book covers the following mathematical topics, with frequent reference to applications in economics and finance: functions, graphs and equations, recurrences (difference equations), differentiation, exponentials and logarithms, optimisation, partial differentiation, optimisation in several variables, vectors and matrices, linear equations, Lagrange multipliers, integration, first-order and second-order differential equations. The stress is on the relation of maths to economics, and this is illustrated with copious examples and exercises to foster depth of understanding. Each chapter has three parts: the main text, a section of further worked examples and a summary of the chapter together with a selection of problems for the reader to attempt. For students of economics, mathematics, or both, this book provides an introduction to mathematical methods in economics and finance that will be welcomed for its clarity and breadth.
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