*Eaton E. Lattman, Thomas D. Grant, and Edward H. Snell*

- Published in print:
- 2018
- Published Online:
- September 2018
- ISBN:
- 9780199670871
- eISBN:
- 9780191749575
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199670871.003.0008
- Subject:
- Physics, Soft Matter / Biological Physics

Thic chapter describes some of the processes that are often carried out within specific data processing software associated with an instrument but are invisible to the user. It is useful to be aware ...
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Thic chapter describes some of the processes that are often carried out within specific data processing software associated with an instrument but are invisible to the user. It is useful to be aware of them. These include dealing with detector artifacts and limitations, and the integration of the signal from a two-dimensional image to produce a one-dimensional scattering profile, among other steps.Less

Thic chapter describes some of the processes that are often carried out within specific data processing software associated with an instrument but are invisible to the user. It is useful to be aware of them. These include dealing with detector artifacts and limitations, and the integration of the signal from a two-dimensional image to produce a one-dimensional scattering profile, among other steps.

*Eaton E. Lattman, Thomas D. Grant, and Edward H. Snell*

- Published in print:
- 2018
- Published Online:
- September 2018
- ISBN:
- 9780199670871
- eISBN:
- 9780191749575
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199670871.003.0006
- Subject:
- Physics, Soft Matter / Biological Physics

Extracting information from scattering data is very sensitive to the quality of the data. In this chapter data quality characterization is described, including initial data processing procedures to ...
More

Extracting information from scattering data is very sensitive to the quality of the data. In this chapter data quality characterization is described, including initial data processing procedures to alert the user to potential data quality issues. Accurate buffer subtraction is crucial for correct modeling and analysis of SAS data, and mechanisms for identifying buffer subtraction errors are discussed. Examining SAS parameters such as a function of concentration or exposure is very useful for identifying concentration dependent artifacts or radiation damage that, if unnoticed, can be very detrimental to further analysis, including misinterpreting the results and drawing erroneous conclusions. SAS is often used for analyzing flexible molecules in solution that may be difficult to study with other structural techniques. Qualitative and quantitative assessments of flexibility are described.Less

Extracting information from scattering data is very sensitive to the quality of the data. In this chapter data quality characterization is described, including initial data processing procedures to alert the user to potential data quality issues. Accurate buffer subtraction is crucial for correct modeling and analysis of SAS data, and mechanisms for identifying buffer subtraction errors are discussed. Examining SAS parameters such as a function of concentration or exposure is very useful for identifying concentration dependent artifacts or radiation damage that, if unnoticed, can be very detrimental to further analysis, including misinterpreting the results and drawing erroneous conclusions. SAS is often used for analyzing flexible molecules in solution that may be difficult to study with other structural techniques. Qualitative and quantitative assessments of flexibility are described.

*Joseph F. Boudreau and Eric S. Swanson*

- Published in print:
- 2017
- Published Online:
- February 2018
- ISBN:
- 9780198708636
- eISBN:
- 9780191858598
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198708636.003.0005
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses the numerous applications of numerical quadrature (integration) in classical mechanics, in semiclassical approaches to quantum mechanics, and in statistical mechanics; and then ...
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This chapter discusses the numerous applications of numerical quadrature (integration) in classical mechanics, in semiclassical approaches to quantum mechanics, and in statistical mechanics; and then describes several ways of implementing integration in C++, for both proper and improper integrals. Various algorithms are described and analyzed, including simple classical quadrature algorithms as well as those enhanced with speedups and convergence tests. Classical orthogonal polynomials, whose properties are reviewed, are the basis of a sophisticated technique known as Gaussian integration. Practical implementations require the roots of these polynomials, so an algorithm for finding them from three-term recurrence relations is presented. On the computational side, the concept of polymorphism is introduced and exploited (prior to the detailed treatment later in the text). The nondimensionalization of physical problems, which is a common and important means of simplifying a problem, is discussed using Compton scattering and the Schrödinger equation as an example.Less

This chapter discusses the numerous applications of numerical quadrature (integration) in classical mechanics, in semiclassical approaches to quantum mechanics, and in statistical mechanics; and then describes several ways of implementing integration in C++, for both proper and improper integrals. Various algorithms are described and analyzed, including simple classical quadrature algorithms as well as those enhanced with speedups and convergence tests. Classical orthogonal polynomials, whose properties are reviewed, are the basis of a sophisticated technique known as Gaussian integration. Practical implementations require the roots of these polynomials, so an algorithm for finding them from three-term recurrence relations is presented. On the computational side, the concept of polymorphism is introduced and exploited (prior to the detailed treatment later in the text). The nondimensionalization of physical problems, which is a common and important means of simplifying a problem, is discussed using Compton scattering and the Schrödinger equation as an example.