There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Statistics for Spatial Data.

关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

In this chapter, we will restrict our attention to the ferrites and a few other closely related materials. The great interest in ferrites stems from their unique combination of a spontaneous magnetization and a high electrical resistivity. The observed magnetization results from the difference in the magnetizations of two non-equivalent sub-lattices of the magnetic ions in the crystal structure. Materials of this type should strictly be designated as “ferrimagnetic” and in some respects are more closely related to anti-ferromagnetic substances than they are to ferromagnetics in which the magnetization results from the parallel alignment of all the magnetic moments present. We shall not adhere to this special nomenclature except to emphasize effects, which are due to the existence of the sub-lattices.

Ferromagnetic materials

This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.

Coverage control for mobile sensing networks

The field of uncertainty quantification is evolving rapidly because of increasing emphasis on models that require quantified uncertainties for large-scale applications, novel algorithm development, and new computational architectures that facilitate implementation of these algorithms. Uncertainty Quantification: Theory, Implementation, and Applications provides readers with the basic concepts, theory, and algorithms necessary to quantify input and response uncertainties for simulation models arising in a broad range of disciplines. The book begins with a detailed discussion of applications where uncertainty quantification is critical for both scientific understanding and policy. It then covers concepts from probability and statistics, parameter selection techniques, frequentist and Bayesian model calibration, propagation of uncertainties, quantification of model discrepancy, surrogate model construction, and local and global sensitivity analysis. The author maintains a complementary web page where readers can find data used in the exercises and other supplementary material. Uncertainty Quantification: Theory, Implementation, and Applications includes a large number of definitions and examples that use a suite of relatively simple models to illustrate concepts; numerous references to current and open research issues; and exercises that illustrate basic concepts and guide readers through the numerical implementation of algorithms for prototypical problems. It also features a wide range of applications, including weather and climate models, subsurface hydrology and geology models, nuclear power plant design, and models for biological phenomena, along with recent advances and topics that have appeared in the research literature within the last 15 years, including aspects of Bayesian model calibration, surrogate model development, parameter selection techniques, and global sensitivity analysis. Audience: The text is intended for advanced undergraduates, graduate students, and researchers in mathematics, statistics, operations research, computer science, biology, science, and engineering. It can be used as a textbook for one- or two-semester courses on uncertainty quantification or as a resource for researchers in a wide array of disciplines. A basic knowledge of probability, linear algebra, ordinary and partial differential equations, and introductory numerical analysis techniques is assumed. Contents: Chapter 1: Introduction; Chapter 2: Large-Scale Applications; Chapter 3: Prototypical Models; Chapter 4: Fundamentals of Probability, Random Processes, and Statistics; Chapter 5: Representation of Random Inputs; Chapter 6: Parameter Selection Techniques; Chapter 7: Frequentist Techniques for Parameter Estimation; Chapter 8: Bayesian Techniques for Parameter Estimation; Chapter 9: Uncertainty Propagation in Models; Chapter 10: Stochastic Spectral Methods; Chapter 11: Sparse Grid Quadrature and Interpolation Techniques; Chapter 12: Prediction in the Presence of Model Discrepancy; Chapter 13: Surrogate Models; Chapter 14: Local Sensitivity Analysis; Chapter 15: Global Sensitivity Analysis; Appendix A: Concepts from Functional Analysis; Bibliography; Index

Uncertainty Quantification: Theory, Implementation, and Applications

A curtain having an integral tie-back arrangement includes a piece of flexible material, part of which is fixed to the curtain for providing a channel from one of its vertical edges to the other of its vertical edges. An elongated flexible member which extends through the channel is fixed at one end to one of the vertical edges. As a result, if the free end of the elongated flexible member is pulled, the curtain is shirred along its width. The flexible material supports a device having a circular loop and an S-shaped section to which the elongated flexible member may be frictionally tied so as to support the shirred curtain. After the curtain is hung, the loop may be coupled to a nail on its window, thereby supporting the tie-back arrangement.

Smart Material Systems: Model Development

Smart Materials Technology and Control Applications. Modeling Aspects of Shells, Plates and Beams. Patch Contributions to Structural Equations. Well-Posedness of Abstract Structural Models. Estimation of Parameters and Inverse Problems. Damage Detection in Smart Material Structures. Infinite Dimensional Control and Galerkin Approximation. Implementation of Finite-Dimensional Compensators. Modeling and Control in Coupled Systems. Bibliography. Notation. Index.

Smart material structures: Modeling, estimation, and control

This paper addresses the modeling of strains generated by magnetostrictive transducers in response to applied magnetic fields. The measured strains depend on both the rotation of moments within the material in response to the field and the elastic properties of the material. The magnetic behavior is characterized by considering the Jiles-Atherton mean field theory for ferromagnetic hysteresis in combination with a quadratic moment rotation model for magnetostriction. Elastic properties must be incorporated to account for the dynamics of the material as it vibrates. This is modeled by force balancing, which yields a wave equation with magnetostrictive inputs. The validity of the resulting transducer model is illustrated by comparison with experimental data.

/pdf/structural-magnetic-strain-model-for-magnetostrictive-44q7q0znrl.pdf

Structural magnetic strain model for magnetostrictive transducers

This paper addresses the modeling of hysteresis in magnetostrictive transducers in the context of control applications that require an accurate characterization of the relation between input currents and strains output by the transducer. This relation typically exhibits significant nonlinearities and hysteresis because of inherent properties of magnetostrictive materials. The characterization considered here is based on the Jiles-Atherton mean field model for ferromagnetic hysteresis in combination with a quadratic moment rotation model for magnetostriction. As demonstrated by comparison with experimental data, the magnetization model very adequately quantifies both major and minor loops under various operating conditions. The combined model can then be used to accurately characterize output strains at moderate drive levels. The advantages of this model lie in the small number (six) of required parameters and its flexibility under a variety of operating conditions.

/pdf/energy-based-hysteresis-model-for-magnetostrictive-3vdmazgb9r.pdf

Ralph C. Smith

Papers

Uncertainty Quantification: Theory, Implementation, and Applications

Smart Material Systems: Model Development

Smart material structures: Modeling, estimation, and control

Structural magnetic strain model for magnetostrictive transducers

Energy-based hysteresis model for magnetostrictive transducers