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4302 results in General and Classical Physics

Page 14 of 216

  • 1 - Mass Conservation and the Continuity Equation

  • Justin W. Garvin, University of Iowa
  • Book:
    A Student's Guide to the Navier-Stokes Equations
    Published online:
    10 March 2023
    Print publication:
    09 February 2023, pp 1-31

  • Summary

    This chapter serves as an introduction to the concept of conservation and how conservation principles are used in fluid mechanics. The conservation principle is then applied to mass and an equation known as the continuity equation is developed. Various mathematical operations such as the dot product, the divergence, and the divergence theorem are introduced along the way. The continuity equation is discussed and the idea of an incompressible flow is introduced. Some examples using mass conservation are also given.

  • 6 - Nondimensionalization and Scaling

  • Justin W. Garvin, University of Iowa
  • Book:
    A Student's Guide to the Navier-Stokes Equations
    Published online:
    10 March 2023
    Print publication:
    09 February 2023, pp 182-219

  • Summary

    In this chapter, a concept known as scaling is introduced. Scaling (also known as nondimensionalization) is essentially a form of dimensional analysis. Dimensional analysis is a general term used to describe a means of analyzing a system based off the units of the problem (e.g. kilogram for mass, kelvin for temperature, meter for length, coulomb for electric change, etc.). The concepts of this chapter, while not entirely about the fluid equations per se, is arguably the most useful in understanding the various concepts of fluid mechanics. In addition, the concepts discussed within this chapter can be extended to other areas of physics, particularly areas that are heavily reliant on differential equations (which is most of physics and engineering).

  • 11 - Numerical methods

  • Richard C. Fernow, Formerly Brookhaven National Laboratory
  • Book:
    Principles of Magnetostatics
    Published online:
    04 November 2022
    Print publication:
    09 February 2023, pp 245-273
    • Chapter
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  • 5 - The Energy Equation and a Discussion on Diffusion and Advection

  • Justin W. Garvin, University of Iowa
  • Book:
    A Student's Guide to the Navier-Stokes Equations
    Published online:
    10 March 2023
    Print publication:
    09 February 2023, pp 124-181

  • Summary

    In addition to the continuity equation, there is another very important equation that is often employed alongside the Navier–Stokes equations: the energy equation. The energy equation is required to fully describe compressible flows. This chapter guides the student through the development of the energy equation, which can be an intimidating equation. A discussion on diffusion and its interplay with advection is also included, leading to the idea of a boundary layer. The chapter ends with the addition of the energy equation in shear-driven and pressure-driven flows.

  • 6 - Iron–dominant transverse fields

  • Richard C. Fernow, Formerly Brookhaven National Laboratory
  • Book:
    Principles of Magnetostatics
    Published online:
    04 November 2022
    Print publication:
    09 February 2023, pp 150-164
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  • 5 - Complex analysis of transverse fields

  • Richard C. Fernow, Formerly Brookhaven National Laboratory
  • Book:
    Principles of Magnetostatics
    Published online:
    04 November 2022
    Print publication:
    09 February 2023, pp 108-149
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  • Preface

  • Richard C. Fernow, Formerly Brookhaven National Laboratory
  • Book:
    Principles of Magnetostatics
    Published online:
    04 November 2022
    Print publication:
    09 February 2023, pp ix-xii
    • Chapter
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  • 2 - Magnetic materials

  • Richard C. Fernow, Formerly Brookhaven National Laboratory
  • Book:
    Principles of Magnetostatics
    Published online:
    04 November 2022
    Print publication:
    09 February 2023, pp 23-38
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  • 3 - Potential theory

  • Richard C. Fernow, Formerly Brookhaven National Laboratory
  • Book:
    Principles of Magnetostatics
    Published online:
    04 November 2022
    Print publication:
    09 February 2023, pp 39-70
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  • Index

  • Richard C. Fernow, Formerly Brookhaven National Laboratory
  • Book:
    Principles of Magnetostatics
    Published online:
    04 November 2022
    Print publication:
    09 February 2023, pp 297-302
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  • Frontmatter

  • Richard C. Fernow, Formerly Brookhaven National Laboratory
  • Book:
    Principles of Magnetostatics
    Published online:
    04 November 2022
    Print publication:
    09 February 2023, pp i-iv
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  • 9 - Permanent magnets

  • Richard C. Fernow, Formerly Brookhaven National Laboratory
  • Book:
    Principles of Magnetostatics
    Published online:
    04 November 2022
    Print publication:
    09 February 2023, pp 211-228
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  • Appendices

  • Richard C. Fernow, Formerly Brookhaven National Laboratory
  • Book:
    Principles of Magnetostatics
    Published online:
    04 November 2022
    Print publication:
    09 February 2023, pp 274-296
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Principles of Magnetostatics
  • Richard C. Fernow
  • Published online:
    04 November 2022
    Print publication:
    09 February 2023
  • Magnetostatics, the mathematical theory that describes the forces and fields resulting from the steady flow of electrical currents, has a long history. By capturing the basic concepts, and building towards the computation of magnetic fields, this book is a self-contained discussion of the major subjects in magnetostatics. Overviews of Maxwell's equations, the Poisson equation, and boundary value problems pave the way for dealing with fields from transverse, axial and periodic magnetic arrangements and assemblies of permanent magnets. Examples from accelerator and beam physics give up-to-date context to the theory. Both complex contour integration and numerical techniques for calculating magnetic fields are discussed in detail with plentiful examples. Theoretical and practical information on carefully selected topics make this a one-stop reference for magnet designers, as well as for physics and electrical engineering undergraduate students. This title, first published in 2016, has been reissued as an Open Access publication on Cambridge Core.

Page 14 of 216