tions. Bootstrap has found many applications in engineering field, including artificial neural networks, biomedical engineering, environmental engineering, image processing, and radar and sonar signal processing. Basic concepts of the bootstrap are summarized in each section as a step-by-step algorithm for ease of implementation. Most of the applications are taken from the signal processing literature. The principles of the bootstrap are introduced in Chapter 2. Both the nonparametric and parametric bootstrap procedures are explained. Babu and Singh (1984) have demonstrated that in general, these two procedures behave similarly for pivotal (Studentized) statistics. The fact that the bootstrap is not the solution for all of the problems has been known to statistics community for a long time; however, this fact is rarely touched on in the manuscripts meant for practitioners. It was first observed by Babu (1984) that the bootstrap does not work in the infinite variance case. Bootstrap Techniques for Signal Processing explains the limitations of bootstrap method with an example. I especially liked the presentation style. The basic results are stated without proofs; however, the application of each result is presented as a simple step-by-step process, easy for nonstatisticians to follow. The bootstrap procedures, such as moving block bootstrap for dependent data, along with applications to autoregressive models and for estimation of power spectral density, are also presented in Chapter 2. Signal detection in the presence of noise is generally formulated as a testing of hypothesis problem. Chapter 3 introduces principles of bootstrap hypothesis testing. The topics are introduced with interesting real life examples. Flow charts, typical in engineering literature, are used to aid explanations of the bootstrap hypothesis testing procedures. The bootstrap leads to second-order correction due to pivoting; this improvement in the results due to pivoting is also explained. In the second part of Chapter 3, signal processing is treated as a regression problem. The performance of the bootstrap for matched filters as well as constant false-alarm rate matched filters is also illustrated. Chapters 2 and 3 focus on estimation problems. Chapter 4 introduces bootstrap methods used in model selection. Due to the inherent structure of the subject matter, this chapter may be difficult for nonstatisticians to follow. Chapter 5 is the most impressive chapter in the book, especially from the standpoint of statisticians. It provides real data bootstrap applications to illustrate the theory covered in the earlier chapters. These include applications to optimal sensor placement for knock detection and land-mine detection. The authors also provide a MATLAB toolbox comprising frequently used routines. Overall, this is a very useful handbook for engineers, especially those working in signal processing.

Probability and Random Processes

The dynamics and stability of thin liquid films have fascinated scientists over many decades: the observations of regular wave patterns in film flows down a windowpane or along guttering, the patterning of dewetting droplets, and the fingering of viscous flows down a slope are all examples that are familiar in daily life. Thin film flows occur over a wide range of length scales and are central to numerous areas of engineering, geophysics, and biophysics; these include nanofluidics and microfluidics, coating flows, intensive processing, lava flows, dynamics of continental ice sheets, tear-film rupture, and surfactant replacement therapy. These flows have attracted considerable attention in the literature, which have resulted in many significant developments in experimental, analytical, and numerical research in this area. These include advances in understanding dewetting, thermocapillary- and surfactant-driven films, falling films and films flowing over structured, compliant, and rapidly rotating substrates, and evaporating films as well as those manipulated via use of electric fields to produce nanoscale patterns. These developments are reviewed in this paper and open problems and exciting research avenues in this thriving area of fluid mechanics are also highlighted.

Dynamics and stability of thin liquid films

We discuss the deformation of a curved interface between solid phases, assuming small strains in the bulk phases and neglecting accretion at the interfaces. Such assumptions are relevant to the deformation of solid microstructures when atomic diffusion and the formation of defects such as dislocations are negligible. We base our theory on a constitutive equation giving the (excess) free energy ψ of the interface when the interfacial limits of the displacement fields in the abutting phases as well as the limits of the displacement gradients are known. Using general considerations of frame invariance, we show that ψ can depend on these quantities at most through: firstly the normal and tangential components of the jump in displacement at the interface (stretch and slip), secondly the average of the projected strain in the tangent plane (average tangential strain), thirdly the tangential component of the jump in the projected displacement gradient at the interface (relative tangential strain and rel...

A general theory of curved deformable interfaces in solids at equilibrium

This study develops a gradient theory of single-crystal plasticity that accounts for geometrically necessary dislocations. The theory is based on classical crystalline kinematics; classical macroforces; microforces for each slip system consistent with a microforce balance; a mechanical version of the second law that includes, via the microforces, work performed during slip; a rate-independent constitutive theory that includes dependences on a tensorial measure of geometrically necessary dislocations. The microforce balances are shown to be equivalent to nonlocal yield conditions for the individual slip systems. The field equations consist of the yield conditions coupled to the standard macroscopic force balance; these are supplemented by classical macroscopic boundary conditions in conjunction with nonstandard boundary conditions associated with slip. As an aid to solution, a weak (virtual power) formulation of the nonlocal yield conditions is derived. To make contact with classical dislocation theory, the microstresses are shown to represent counterparts of the Peach–Koehler force on a single dislocation.

A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations

Microencapsulated healing agents that possess adequate strength, long shelf-life and excellent bonding to the host material are required for self-healing materials. Urea-formaldehyde microcapsules containing dicyclopentadiene were prepared by in situ polymerization in an oil-in-water emulsion that meet these requirements for self-healing epoxy. Microcapsules of 10-1000 microm in diameter were produced by appropriate selection of agitation rate in the range of 200-2000 rpm. A linear relation exists between log(mean diameter) and log(agitation rate). Surface morphology and shell wall thickness were investigated by optical and electron microscopy. Microcapsules are composed of a smooth 160-220 nm inner membrane and a rough, porous outer surface of agglomerated urea-formaldehyde nanoparticles. Surface morphology is influenced by pH of the reacting emulsion and interfacial surface area at the core-water interface. High yields (80-90%) of a free flowing powder of spherical microcapsules were produced with a fill content of 83-92 wt% as determined by CHN analysis.

/pdf/in-situ-poly-urea-formaldehyde-microencapsulation-of-4p1ii8jlau.pdf

In situ poly(urea-formaldehyde) microencapsulation of dicyclopentadiene

We develop a general theory of geometrically necessary dislocations based on the decomposition F=FeFp. The incompatibility of Fe and that of Fp are characterized by a single tensor G giving the Burgers vector, measured and reckoned per unit area in the microstructural (intermediate) configuration. We show that G may be expressed in terms of Fp and the referential curl of Fp, or equivalently in terms of Fe−1 and the spatial curl of Fe−1. We derive explicit relations for G in terms of Euler angles for a rigid-plastic material and — without neglecting elastic strains — for strict plane strain and strict anti-plane shear. We discuss the relationship between G and the distortion of microstructural planes. We show that kinematics alone yields a balance law for the transport of geometrically necessary dislocations.

On the characterization of geometrically necessary dislocations in finite plasticity

We establish transport relations for integrals over evolving fluid interfaces. These relations make it possible to localize integral balance laws over non-material interfaces separating fluid phases and, therefore, obtain associated interface conditions in differential form.

/pdf/transport-relations-for-surface-integrals-arising-in-the-2up2mjqykl.pdf

Transport relations for surface integrals arising in the formulation of balance laws for evolving fluid interfaces

http://www.math.cmu.edu/CNA/Publications/publications2002/005abs/02-CNA-005.pdf

Geometrically necessary dislocations in viscoplastic single crystals and bicrystals undergoing small deformations

Incoherent phase transitions are more difficult to treat than their coherent counterparts The interface, which appears as a single surface in the deformed configuration, is represented in its undeformed state by a separate surface in each phase This leads to a rich but detailed kinematics, one in which defects such as vacancies and dislocations are generated by the moving interface In this paper we develop a complete theory of incoherent phase transitions in the presence of deformation and mass transport, with phase interface structured by energy and stress The final results are a complete set of interface conditions for an evolving incoherent interface

The dynamics of solid-solid phase transitions 2. Incoherent interfaces

We discuss some properties of surfaces in whose unit normal vector has constant angle with an assigned direction field. The constant-angle condition can be rewritten as a Hamilton–Jacobi equation correlating the surface and the direction field. We focus on examples motivated by the physics of interfaces in liquid crystals and of layered fluids, and examine some properties of the constant-angle surfaces when the direction field is singular along a line (disclination) or at a point (hedgehog). We also show how our results may be used to study the shape of disclination cores.

/pdf/constant-angle-surfaces-in-liquid-crystals-13zabufd0k.pdf

Paolo Cermelli

Papers

On the characterization of geometrically necessary dislocations in finite plasticity

Transport relations for surface integrals arising in the formulation of balance laws for evolving fluid interfaces

Geometrically necessary dislocations in viscoplastic single crystals and bicrystals undergoing small deformations

The dynamics of solid-solid phase transitions 2. Incoherent interfaces

Constant-angle surfaces in liquid crystals