FFTW is an implementation of the discrete Fourier transform (DFT) that adapts to the hardware in order to maximize performance. This paper shows that such an approach can yield an implementation that is competitive with hand-optimized libraries, and describes the software structure that makes our current FFTW3 version flexible and adaptive. We further discuss a new algorithm for real-data DFTs of prime size, a new way of implementing DFTs by means of machine-specific single-instruction, multiple-data (SIMD) instructions, and how a special-purpose compiler can derive optimized implementations of the discrete cosine and sine transforms automatically from a DFT algorithm.

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The Design and Implementation of FFTW3

Cell motility in viscous fluids is ubiquitous and affects many biological processes, including reproduction, infection and the marine life ecosystem. Here we review the biophysical and mechanical principles of locomotion at the small scales relevant to cell swimming, tens of micrometers and below. At this scale, inertia is unimportant and the Reynolds number is small. Our emphasis is on the simple physical picture and fundamental flow physics phenomena in this regime. We first give a brief overview of the mechanisms for swimming motility, and of the basic properties of flows at low Reynolds number, paying special attention to aspects most relevant for swimming such as resistance matrices for solid bodies, flow singularities and kinematic requirements for net translation. Then we review classical theoretical work on cell motility, in particular early calculations of swimming kinematics with prescribed stroke and the application of resistive force theory and slender-body theory to flagellar locomotion. After examining the physical means by which flagella are actuated, we outline areas of active research, including hydrodynamic interactions, biological locomotion in complex fluids, the design of small-scale artificial swimmers and the optimization of locomotion strategies. (Some figures in this article are in colour only in the electronic version) This article was invited by Christoph Schmidt.

/pdf/the-hydrodynamics-of-swimming-microorganisms-bonwl3c7w2.pdf

The hydrodynamics of swimming microorganisms

http://repository.ias.ac.in/39608/1/49_pub.pdf

A review of imperative technologies for wastewater treatment I: oxidation technologies at ambient conditions

Domain-specific languages (DSLs) are languages tailored to a specific application domain. They offer substantial gains in expressiveness and ease of use compared with general-purpose programming languages in their domain of application. DSL development is hard, requiring both domain knowledge and language development expertise. Few people have both. Not surprisingly, the decision to develop a DSL is often postponed indefinitely, if considered at all, and most DSLs never get beyond the application library stage.Although many articles have been written on the development of particular DSLs, there is very limited literature on DSL development methodologies and many questions remain regarding when and how to develop a DSL. To aid the DSL developer, we identify patterns in the decision, analysis, design, and implementation phases of DSL development. Our patterns improve and extend earlier work on DSL design patterns. We also discuss domain analysis tools and language development systems that may help to speed up DSL development. Finally, we present a number of open problems.

/pdf/when-and-how-to-develop-domain-specific-languages-29nvxv3ngp.pdf

When and how to develop domain-specific languages

The chemical effects of ultrasound derive primarily from acoustic cavitation. Bubble collapse in liquids results in an enormous concentration of energy from the conversion of the kinetic energy of the liquid motion into heating of the contents of the bubble. The high local temperatures and pressures, combined with extraordinarily rapid cooling, provide a unique means for driving chemical reactions under extreme conditions. A diverse set of applications of ultrasound to enhance chemical reactivity has been explored with important uses in synthetic materials chemistry. For example, the sonochemical decomposition of volatile organometallic precursors in low-volatility solvents produces nanostructured materials in various forms with high catalytic activities. Nanostructured metals, alloys, oxides, carbides and sulfides, nanometer colloids, and nanostructured supported catalysts can all be prepared by this general route. Another important application of sonochemistry in materials chemistry has been the preparation of biomaterials, most notably protein microspheres. Such microspheres have a wide range of biomedical applications, including their use in echo contrast agents for sonography, magnetic resonance imaging, contrast enhancement, and oxygen or drug delivery. Other applications include the modification of polymers and polymer surfaces.

Applications of ultrasound to materials chemistry

The present study examines the flow past slender bodies possessing finite centre-line curvature in a viscous, incompressible fluid without any appreciable inertia effects. We consider slender bodies having arbitrary centre-line configurations, circular transverse cross-sections, and longitudinal cross-sections which are approximately elliptic close to the body ends (i.e. prolate-spheroidal body ends). The no-slip boundary condition on the body surface is satisfied, using a convenient stepwise procedure, to higher orders in the slenderness parameter (e) than has previously been possible. In fact, the boundary condition is satisfied up to an error term of O(e2) by distributing appropriate stokeslets, potential doublets, rotlets, sources, stresslets and quadrupoles on the body centre-line. The methods used here produce an integral equation valid along the entire body length, including the ends, whose solution determines the stokeslet strength or equivalently the force per unit length up to a term of O(e2). The O(e2) correction to the stokeslet strength is also found. The theory is used to examine the motion of a partial torus and a helix of finite length. For helical bodies comparisons are made between the present theory and the resistive-force theory using the force coefficients of Gray & Hancock and Lighthill. For the motion considered the Gray & Hancock force coefficients generally underestimate the force per unit length, whereas Lighthill's coefficients provide good agreement except in the vicinity of the body ends.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112080000687

An improved slender-body theory for Stokes flow

In this investigation the creeping flow due to the motion of a liquid drop or a bubble in another immiscible fluid is examined when the interface is partially covered by a stagnant layer of surfactant. The associated boundary-value problem involves mixed boundary conditions at the interface, which lead to a set of dual series equations. An inversion of these equations yields the exact solution to the stagnant cap problem.Several useful results are obtained in closed form. Among these are the expressions for the drag force, the difference between the maximum and the minimum interfacial tensions, and the amount of adsorbed surfactant. A shifting of the centre of the internal vortex is observed.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112083000130

Stokes flow past bubbles and drops partially coated with thin films. Part 1. Stagnant cap of surfactant film – exact solution

We discuss the design and implementation of a compiler that translates formulas representing signal processing transforms into efficient C or Fortran programs. The formulas are represented in a language that we call SPL, an acronym from Signal Processing Language. The compiler is a component of the SPIRAL system which makes use of formula transformations and intelligent search strategies to automatically generate optimized digital signal processing (DSP) libraries. After a discussion of the translation and optimization techniques implemented in the compiler, we use SPL formulations of the fast Fourier transform (FFT) to evaluate the compiler. Our results show that SPIRAL, which can be used to implement many classes of algorithms, produces programs that perform as well as “hard-wired” systems like FFTW.

/pdf/spl-a-language-and-compiler-for-dsp-algorithms-1ccqfrenbf.pdf

SPL: a language and compiler for DSP algorithms

In order to elucidate the general Stokes flow characteristics present for slender bodies of finite centre-line curvature the singularity method for Stokes flow has been employed to construct solutions to the flow past a slender torus. The symmetry of the geometry and absence of ends has made a highly accurate analysis possible. The no-slip boundary condition on the body surface is satisfied up to an error term of O(E^2 ln E), where E is the slenderness parameter (ratio of cross-sectional radius to centre-line radius). This degree of accuracy makes it possible to determine the force per unit length experienced by the torus up to a term of O(E^2). A comparison is made between the force coefficients of the slender torus to those of a straight slender body to illustrate the large differences that may occur as a result of the finite centre-line curvature.

/pdf/hydromechanics-of-low-reynolds-number-flow-part-5-motion-of-2mj0nnmsea.pdf

Robert E. Johnson

Papers

An improved slender-body theory for Stokes flow

Stokes flow past bubbles and drops partially coated with thin films. Part 1. Stagnant cap of surfactant film – exact solution

SPL: a language and compiler for DSP algorithms

Hydromechanics of low-Reynolds-number flow. Part 5. Motion of a slender torus

Fluid Mechanics of Compound Multiphase Drops and Bubbles