A model of the olfactory bulb and beyond

The olfactory bulb of mammals aids in the discrimination of odors. A mathematical model based on the bulbar anatomy and electrophysiology is described. Simulations of the highly non-linear model produce a 35-60 Hz modulated activity, which is coherent across the bulb. The decision states (for the odor information) in this system can be thought of as stable cycles, rather than as point stable states typical of simpler neuro-computing models. Analysis shows that a group of coupled non-linear oscillators are responsible for the oscillatory activities. The output oscillation pattern of the bulb is determined by the odor input. The model provides a framework in which to understand the transformation between odor input and bulbar output to the olfactory cortex. This model can also be extended to other brain areas such as the hippocampus, thalamus, and neocortex, which show oscillatory neural activities. There is significant correspondence between the model behavior and observed electrophysiology.

It has also been suggested that the olfactory bulb, the first processing center after the sensory cells in the olfactory pathway, plays a role in olfactory adaptation, odor sensitivity enhancement by motivation, and other olfactory psychophysical phenomena. The input from the higher olfactory centers to the inhibitory cells in the bulb are shown to be able to modulate the response, and thus the sensitivity, of the bulb to odor input. It follows that the bulb can decrease its sensitivity to a pre-existing and detected odor (adaptation) while remaining sensitive to new odors, or can increase its sensitivity to discover interesting new odors. Other olfactory psychophysical phenomena such as cross-adaptation are also discussed.

Intense local plasma heating by stopping of ultrashort ultraintense laser pulse in dense plasma

Self-trapping, stopping, and absorption of an ultrashort ultraintense linearly polarized laser pulse in a finite plasma slab of near-critical density is investigated by particle-in-cell simulation. As in the underdense plasma, an electron cavity is created by the pressure of the transmitted part of the light pulse and it traps the latter. Since the background plasma is at near-critical density, no wake plasma oscillation is created. The propagating self-trapped light rapidly comes to a stop inside the slab. Subsequent ion Coulomb explosion of the stopped cavity leads to explosive expulsion of its ions and formation of an extended channel having extremely low plasma density. The energetic Coulomb-exploded ions form shock layers of high density and temperature at the channel boundary. In contrast to a propagating pulse in a lower density plasma, here the energy of the trapped light is deposited onto a stationary and highly localized region of the plasma. This highly localized energy-deposition process can be relevant to the fast ignition scheme of inertial fusion.

Análise das alterações decorrentes do envelhecimento na mecânica respiratória pela técnica de oscilações forçadas

O crescimento do percentual de idosos na população ocorre mundialmente tornando necessário conhecer o impacto do processo de envelhecimento, neste contexto, do sistema respiratório. O desconhecimento do impacto do envelhecimento associado a diferentes graus de exposição a poluentes e a presença de comorbidade(s) dificulta a diagnose das pneumopatias acarretando aos idosos piora da qualidade de vida. São vantagens da Técnica de Oscilações Forçadas (FOT): alto potencial de aplicação em idosos, fácil realização, análise detalhada da mecânica respiratória, desempenho de papel complementar, bem como de alternativa na impossibilidade de realização dos exames tradicionais. Foi realizado um estudo experimental comparativo que objetivou investigar o impacto do envelhecimento no sistema respiratório pela FOT e pela espirometria entre grupos de diferentes faixas etárias, sendo a idade a variável independente e as variáveis dependentes, os parâmetros oscilométricos resistência em regime contínuo (R0) e das vias aéreas centrais (Rm), inclinação da resistência (S), frequência de ressonância (fr), reatância média (Xm), complacência dinâmica (Cdin,sr) e os parâmetros espirométricos (VEF1, CVF, VEF1/CVF e FEF/CVF). Foram realizados entrevista, exame clínico, radiografia torácica, avaliação da mecânica respiratória pela FOT e da função pulmonar pela espirometria. 255 indivíduos com idades entre 20 e 86 anos foram entrevistados. Destes, 175 foram excluídos, restando os 80 voluntários analisados, que foram divididos em 6 grupos de acordo com a faixa etária (A: 20 a 29 anos; B: 30 a 39 anos; C: 40 a 49 anos; D: 50 a 59 anos; E: 60 a 69 anos; F: 70 anos ou mais). Foram utilizados os testes de Shapiro-Wilkins, na avaliação da normalidade dos dados biométricos em cada grupo, Oneway ANOVA, na comparação entre os grupos, e Tukey HSD na comparação entre as classes subjacentes. A análise da associação entre duas variáveis foi realizada inicialmente pela regressão univariada entre os parâmetros oscilométricos, a idade e a altura. A regressão múltipla entre os parâmetros oscilométricos, idade e altura foi realizada em conjunto. Foi realizada a análise de confundimento ou modificação de efeito sobre o parâmetro altura na relação entre a idade e os parâmetros oscilométricos. A correção pelo fator altura foi realizada quando sua análise apresentava fator de confundimento. Quanto aos parâmetros resistivos, não foram observadas alterações em R0 e Rm com o envelhecimento enquanto que o declínio observado em S é discreto e não-significativo. Em relação aos parâmetros reativos, verificouse que Cdin,sr e Xm diminuem enquanto que fr aumenta com o processo de envelhecimento. Todas estas alterações são significativas. Todavia, a diminuição da Cdin,sr não apresenta relação com a idade e sim com a altura, que constituiu modificação do efeito. Nos demais parâmetros oscilométricos, a altura constituiu fator de confundimento. Quanto à espirometria, observou-se declínio significativo do VEF1, do VEF1/CVF e da CVF. O índice FEF/CVF apresentou declínio nãosignificativo. Concluindo, a resistência do sistema respiratório e a complacência dinâmica não se modificam enquanto a homogeneidade do sistema respiratório diminui com o processo de envelhecimento.

Condições mecânicas do sistema respiratório em adultos com fibrose cística: estudo pela espirometria, pletismografia e técnica de oscilações forçadas

A fibrose cística (FC) é a doença autossômica recessiva mais comum na população branca que leva à redução na expectativa de vida. A doença pulmonar é a maior causa de morbidade e mortalidade. A relevância do presente estudo se dá diante de alguns fatores: aumento drástico da sobrevida média nos últimos 60 anos na FC, a fisiopatologia pulmonar não é bem compreendida, ausência de estudos reportados na literatura, até o momento, utilizando a técnica de oscilações forçadas (TOF) exclusivamente em adultos com FC. Assim sendo os objetivos deste estudo são: analisar as alterações da mecânica respiratória em adultos com FC através da espirometria, pletismografia e TOF; correlacionar os resultados da TOF aos espirométricos e pletismográficos e avaliar a sensibilidade e especificidade da TOF nestes indivíduos. É um estudo de corte transversal descritivo, no qual foram analisados dois grupos de indivíduos: controle (n=23) e FC (n=27). Os resultados foram expressos através média desvio-padrão. As técnicas funcionais respiratórias foram realizadas na seguinte sequência: TOF, espirometria, pletismografia. Na pletismografia foram avaliados os parâmetros: CPT (capacidade pulmonar total), CRF (capacidade residual funcional) e VR (volume residual), CRF/CPT e VR/CPT, resistência (Rva) e condutância específica das vias aéreas (SGva). Na espirometria: volume expiratório forçado no primeiro segundo (VEF1), capacidade vital forçada (CVF), fluxo expiratório entre 25% e 75% (FEF25%-75%) da CVF (FEF25%-75%) e razões VEF1/CVF (%) e FEF/CVF (%). Na TOF: propriedades resistivas do sistema respiratório- R0 (resistência no intercepto), Rm (resistência média) e S (inclinação da reta de resistência) e propriedades reativas: Cdin,sr (complacência dinâmica do sistema respiratório), Xm (reatância média), frequência de ressonância (fr); e o módulo da impedância em 4 Hz (׀Zrs4Hz׀). Na espirometria o distúrbio ventilatório obstrutivo (DVO) com CVF reduzida foi predominante, com marcante redução do FEF25%-75% no grupo FC (p<0,0001) em relação ao controle. Na pletismografia: destacou-se a elevação de VR, na presença de CPT normal e elevação da Rva e redução da SGva no grupo FC. Alterações da TOF ocorridas no grupo FC em relação ao controle: aumento de R0 e Rm (p<0,0001) e fr (p<0,0002), relacionados à obstrução das vias aéreas; redução de S (p<0,0006), Xm (p<0,0001) associadas à não-homogeneidade do sistema respiratório e Cdin,sr (p<0,0001), relacionada à redução da complacência pulmonar; aumento do módulo da impedância em 4 Hz (׀Zrs4Hz׀) (representando a carga mecânica total do sistema respiratório) resultante da interação das demais alterações da TOF citadas. Os parâmetros da TOF apresentaram correlações muito boas com a espirometria e moderadas com a pletismografia. Rm foi o único parâmetro que não se relacionou com nenhuma destas técnicas. A sensibilidade e especificidade da TOF em adultos com FC apresentaram valores elevados, sobretudo nos parâmetros reativos, em especial, Xm (85,2% e 73,9% respectivamente e área sob a curva de 0,86).

Horizontal Bloch line motion in magnetic bubble materials

The purpose of this work is to extend experimental and theoretical understanding of horizontal Bloch line (HBL) motion in magnetic bubble materials. The present theory of HBL motion is reviewed, and then extended to include transient effects in which the internal domain wall structure changes with time. This is accomplished by numerically solving the equations of motion for the internal azimuthal angle ɸ and the wall position q as functions of z, the coordinate perpendicular to the thin-film material, and time. The effects of HBL's on domain wall motion are investigated by comparing results from wall oscillation experiments with those from the theory. In these experiments, a bias field pulse is used to make a step change in equilibrium position of either bubble or stripe domain walls, and the wall response is measured by using transient photography. During the initial response, the dynamic wall structure closely resembles the initial static structure. The wall accelerates to a relatively high velocity (≈20 m/sec), resulting in a short (≈22 nsec ) section of initial rapid motion. An HBL gradually forms near one of the film surfaces as a result of local dynamic properties, and moves along the wall surface toward the film center. The presence of this structure produces low-frequency, triangular-shaped oscillations in which the experimental wall velocity is nearly constant, v_s≈ 5-8 m/sec. If the HBL reaches the opposite surface, i.e., if the average internal angle reaches an integer multiple of π, the momentum stored in the HBL is lost, and the wall chirality is reversed. This results in abrupt transitions to overdamped motion and changes in wall chirality, which are observed as a function of bias pulse amplitude. The pulse amplitude at which the n^th punch- through occurs just as the wall reaches equilibrium is given within 0.2 0e by H_n = (2v_sH'/γ)^1/2 • (nπ)^1/2 + H_sv), where H' is the effective field gradient from the surrounding domains, and H_sv is a small (less than 0.03 0e), effective drag field. Observations of wall oscillation in the presence of in-plane fields parallel to the wall show that HBL formation is suppressed by fields greater than about 40 0e (≈2πM_s), resulting in the high-frequency, sinusoidal oscillations associated with a simple internal wall structure.

A study of a new electromechanical energy conversion process using superconducting frequency modulated resonators

Experimental demonstrations and theoretical analyses of a new electromechanical energy conversion process which is made feasible only by the unique properties of superconductors are presented in this dissertation. This energy conversion process is characterized by a highly efficient direct energy transformation from microwave energy into mechanical energy or vice versa and can be achieved at high power level. It is an application of a well established physical principle known as the adiabatic theorem (Boltzmann-Ehrenfest theorem) and in this case time dependent superconducting boundaries provide the necessary interface between the microwave energy on one hand and the mechanical work on the other. The mechanism which brings about the conversion is another known phenomenon - the Doppler effect. The resonant frequency of a superconducting resonator undergoes continuous infinitesimal shifts when the resonator boundaries are adiabatically changed in time by an external mechanical mechanism. These small frequency shifts can accumulate coherently over an extended period of time to produce a macroscopic shift when the resonator remains resonantly excited throughout this process. In addition, the electromagnetic energy in s ide the resonator which is proportional to the oscillation frequency is al so accordingly changed so that a direct conversion between electromagnetic and mechanical energies takes place. The intrinsically high efficiency of this process is due to the electromechanical interactions involved in the conversion rather than a process of thermodynamic nature and therefore is not limited by the thermodynamic value.

A highly reentrant superconducting resonator resonating in the range of 90 to 160 MHz was used for demonstrating this new conversion technique. The resonant frequency was mechanically modulated at a rate of two kilohertz. Experimental results showed that the time evolution of the electromagnetic energy inside this frequency modulated (FM) superconducting resonator indeed behaved as predicted and thus demonstrated the unique features of this process. A proposed usage of FM superconducting resonators as electromechanical energy conversion devices is given along with some practical design considerations. This device seems to be very promising in producing high power (~10W/cm^3) microwave energy at 10 - 30 GHz.

Weakly coupled FM resonator system is also analytically studied for its potential applications. This system shows an interesting switching characteristic with which the spatial distribution of microwave energies can be manipulated by external means. It was found that if the modulation was properly applied, a high degree (>95%) of unidirectional energy transfer from one resonator to the other could be accomplished. Applications of this characteristic to fabricate high efficiency energy switching devices and high power microwave pulse generators are also found feasible with present superconducting technology.

1976 step in the Pacific climate: forty environmental changes between 1968-1975 and 1977-1984

Examination of 40 time series of multidisciplinary environmental variables from the Pacific Ocean and the Americas, collected in 1968 to 1984, demonstrated the remarkable consistency of a major climate-related, step-like change in 1976. To combine the 40 variables (e.g., air and water temperatures, Southern Oscillation, chlorophyll, geese, salmon, crabs, glaciers, atmospheric dust, coral, carbon dioxide, winds, ice cover, Bering Strait transport) into a single time series, standard variants of individual annual values (subtracting the mean and dividing by a standard deviation) were averaged. Analysis of the resulting time series showed that the single step in 1976, separating the 1968-1975 period from the 1977-1984 period, accounted for 89% of variance within the composite time series. Apparently, one of the Earth's large ecosystems occasionally undergoes large abrupt shifts.

较高阶非线性抽运-探测过程中的空间效应

在飞秒抽运一探测光谱技术中，空间分辨的探测光信号反映了在不同空间位置的材料的非线性效应。当抽运光强度增大时，探测光信号中会出现明显的高阶特别是五阶非线性效应。利用劈裂算子方法直接解决了一维非线性传播方程的问题。在数值模拟中，研究了在不同抽运强度和位置下的抽运一探测过程中的五阶非线性效应。在足够高的抽运场下，探测信号出现清晰的振荡，显示了三阶和五阶非线性效应之间的干涉。当空间位置离抽运场中心足够远时，五阶比三阶非线性效应的衰减快得多，对其物理机制和趋势进行了定性的讨论。

Nanofabrication for On-Chip Optical Levitation, Atom-Trapping, and Superconducting Quantum Circuits

Researchers have spent decades refining and improving their methods for fabricating smaller, finer-tuned, higher-quality nanoscale optical elements with the goal of making more sensitive and accurate measurements of the world around them using optics. Quantum optics has been a well-established tool of choice in making these increasingly sensitive measurements which have repeatedly pushed the limits on the accuracy of measurement set forth by quantum mechanics. A recent development in quantum optics has been a creative integration of robust, high-quality, and well-established macroscopic experimental systems with highly-engineerable on-chip nanoscale oscillators fabricated in cleanrooms. However, merging large systems with nanoscale oscillators often require them to have extremely high aspect-ratios, which make them extremely delicate and difficult to fabricate with an "experimentally reasonable" repeatability, yield and high quality. In this work we give an overview of our research, which focused on microscopic oscillators which are coupled with macroscopic optical cavities towards the goal of cooling them to their motional ground state in room temperature environments. The quality factor of a mechanical resonator is an important figure of merit for various sensing applications and observing quantum behavior. We demonstrated a technique for pushing the quality factor of a micromechanical resonator beyond conventional material and fabrication limits by using an optical field to stiffen and trap a particular motional mode of a nanoscale oscillator. Optical forces increase the oscillation frequency by storing most of the mechanical energy in a nearly loss-less optical potential, thereby strongly diluting the effects of material dissipation. By placing a 130 nm thick SiO₂ pendulum in an optical standing wave, we achieve an increase in the pendulum center-of-mass frequency from 6.2 to 145 kHz. The corresponding quality factor increases 50-fold from its intrinsic value to a final value of Q_m = 5.8(1.1) x 10⁵, representing more than an order of magnitude improvement over the conventional limits of SiO₂ for a pendulum geometry. Our technique may enable new opportunities for mechanical sensing and facilitate observations of quantum behavior in this class of mechanical systems. We then give a detailed overview of the techniques used to produce high-aspect-ratio nanostructures with applications in a wide range of quantum optics experiments. The ability to fabricate such nanodevices with high precision opens the door to a vast array of experiments which integrate macroscopic optical setups with lithographically engineered nanodevices. Coupled with atom-trapping experiments in the Kimble Lab, we use these techniques to realize a new waveguide chip designed to address ultra-cold atoms along lithographically patterned nanobeams which have large atom-photon coupling and near 4π Steradian optical access for cooling and trapping atoms. We describe a fully integrated and scalable design where cold atoms are spatially overlapped with the nanostring cavities in order to observe a resonant optical depth of d₀ ≈ 0.15. The nanodevice illuminates new possibilities for integrating atoms into photonic circuits and engineering quantum states of atoms and light on a microscopic scale. We then describe our work with superconducting microwave resonators coupled to a phononic cavity towards the goal of building an integrated device for quantum-limited microwave-to-optical wavelength conversion. We give an overview of our characterizations of several types of substrates for fabricating a low-loss high-frequency electromechanical system. We describe our electromechanical system fabricated on a Si₃N₄ membrane which consists of a 12 GHz superconducting LC resonator coupled capacitively to the high frequency localized modes of a phononic nanobeam. Using our suspended membrane geometry we isolate our system from substrates with significant loss tangents, drastically reducing the parasitic capacitance of our superconducting circuit to ≈ 2.5$ fF. This opens up a number of possibilities in making a new class of low-loss high-frequency electromechanics with relatively large electromechanical coupling. We present our substrate studies, fabrication methods, and device characterization.

Stopping power of gases for heavy ions

Pulse-height and time-of-flight methods have been used to measure the electronic stopping cross sections for projectiles of ¹²C, ¹⁶O, ¹⁹F, ²³Na, ²⁴Mg, and ²⁷Al, slowing in helium, neon, argon, krypton, and xenon. The ion energies were in the range 185 keV ≤ E ≤ 2560 keV.

A semiempirical calculation of the electronic stopping cross section for projectiles with atomic numbers between 6 and 13 passing through the inert gases has been performed using a modification of the Firsov model. Using Hartree-Slater-Fock orbitals, and summing over the losses for the individual charge states of the projectiles, good agreement has been obtained with the experimental data. The main features of the stopping cross section seen in the data, such as the Z₁ oscillation and the variation of the velocity dependence on Z₁ and Z₂, are present in the calculation. The inclusion of a modified form of the Bethe-Bloch formula as an additional term allows the increase of the velocity dependence for projectile velocities above v_o to be reproduced in the calculation.

Fiber-optic integration and efficient detection schemes for optomechanical resonators

With the advent of the laser in the year 1960, the field of optics experienced a renaissance from what was considered to be a dull, solved subject to an active area of development, with applications and discoveries which are yet to be exhausted 55 years later. Light is now nearly ubiquitous not only in cutting-edge research in physics, chemistry, and biology, but also in modern technology and infrastructure. One quality of light, that of the imparted radiation pressure force upon reflection from an object, has attracted intense interest from researchers seeking to precisely monitor and control the motional degrees of freedom of an object using light. These optomechanical interactions have inspired myriad proposals, ranging from quantum memories and transducers in quantum information networks to precision metrology of classical forces. Alongside advances in micro- and nano-fabrication, the burgeoning field of optomechanics has yielded a class of highly engineered systems designed to produce strong interactions between light and motion.

Optomechanical crystals are one such system in which the patterning of periodic holes in thin dielectric films traps both light and sound waves to a micro-scale volume. These devices feature strong radiation pressure coupling between high-quality optical cavity modes and internal nanomechanical resonances. Whether for applications in the quantum or classical domain, the utility of optomechanical crystals hinges on the degree to which light radiating from the device, having interacted with mechanical motion, can be collected and detected in an experimental apparatus consisting of conventional optical components such as lenses and optical fibers. While several efficient methods of optical coupling exist to meet this task, most are unsuitable for the cryogenic or vacuum integration required for many applications. The first portion of this dissertation will detail the development of robust and efficient methods of optically coupling optomechanical resonators to optical fibers, with an emphasis on fabrication processes and optical characterization.

I will then proceed to describe a few experiments enabled by the fiber couplers. The first studies the performance of an optomechanical resonator as a precise sensor for continuous position measurement. The sensitivity of the measurement, limited by the detection efficiency of intracavity photons, is compared to the standard quantum limit imposed by the quantum properties of the laser probe light. The added noise of the measurement is seen to fall within a factor of 3 of the standard quantum limit, representing an order of magnitude improvement over previous experiments utilizing optomechanical crystals, and matching the performance of similar measurements in the microwave domain.

The next experiment uses single photon counting to detect individual phonon emission and absorption events within the nanomechanical oscillator. The scattering of laser light from mechanical motion produces correlated photon-phonon pairs, and detection of the emitted photon corresponds to an effective phonon counting scheme. In the process of scattering, the coherence properties of the mechanical oscillation are mapped onto the reflected light. Intensity interferometry of the reflected light then allows measurement of the temporal coherence of the acoustic field. These correlations are measured for a range of experimental conditions, including the optomechanical amplification of the mechanics to a self-oscillation regime, and comparisons are drawn to a laser system for phonons. Finally, prospects for using phonon counting and intensity interferometry to produce non-classical mechanical states are detailed following recent proposals in literature.

Electrochromism accompanying ferroelectric domain inversion in congruent RuO2 : LiNbO3 crystal

Electrochromic phenomena accompanying the ferroelectric domain inversion in congruent RuO2-doped z-cut LiNbO3 crystals at room temperature are observed in experiments. During the electric poling process, the electrochromism accompanies the ferroelectric domain inversion simultaneously in the same poled area. The electrochromism is completely reversible when the domain is inverted from the reverse direction. The influences of electric field and annealing conditions on domain inversion and electrochromism are also discussed. We propose the reasonable assumption that charge redistribution within the crystal structure caused by domain inversion is the source for electrochemically oxidation and reduction of Ru ion to produce the electrochromic effect. (c) 2005 Optical Society of America.

Dielectric recovery of short A-C arcs between low-boiling-point electrodes

The re-ignition characteristics (variation of re-ignition voltage with time after current zero) of short alternating current arcs between plane brass electrodes in air were studied by observing the average re-ignition voltages on the screen of a cathode-ray oscilloscope and controlling the rates of rise of voltage by varying the shunting capacitance and hence the natural period of oscillation of the reactors used to limit the current. The shape of these characteristics and the effects on them of varying the electrode separation, air pressure, and current strength were determined.

The results show that short arc spaces recover dielectric strength in two distinct stages. The first stage agrees in shape and magnitude with a previously developed theory that all voltage is concentrated across a partially deionized space charge layer which increases its breakdown voltage with diminishing density of ionization in the field-tree space. The second stage appears to follow complete deionization by the electric field due to displacement of the field-free region by the space charge layer, its magnitude and shape appearing to be due simply to increase in gas density due to cooling. Temperatures calculated from this second stage and ion densities determined from the first stage by means of the space charge equation and an extrapolation of the temperature curve are consistent with recent measurements of arc value by other methods. Analysis or the decrease with time of the apparent ion density shows that diffusion alone is adequate to explain the results and that volume recombination is not. The effects on the characteristics of variations in the parameters investigated are found to be in accord with previous results and with the theory if deionization mainly by diffusion be assumed.

Study of oscillatory behavior of recording process arising from electron-hole competition in strongly oxidized LiNbO3 : Ce : Cu

We have investigated ultraviolet (UV) photorefractive effect of lithium niobate doubly doped with Ce and Cu. It is found the diffraction efficiency shows oscillating behavior Under UV-1ight-recording. A model in which electrons and holes can be excited from impurity centers in the UV region is proposed to study the oscillatory behavior of the diffraction efficiency. Oil the basis of the material equations and the coupled-wave equations, we found that the oscillatory behavior is due to the oscillation of the relative spatial phase shift Phi. And the electron-hole competition may cause the oscillation of the relative spatial phase shift. A switch point from electron grating to hole grating is chosen to realize nonvolatile readout by a red light with high sensitivity (0.4 cm/J). (c) 2005 Elsevier GmbH. All rights reserved.

Behavior of spherical particles at low Reynolds numbers in a fluctuating translational flow

The behavior of spheres in non-steady translational flow has been studied experimentally for values of Reynolds number from 0.2 to 3000. The aim of the work was to improve our qualitative understanding of particle transport in turbulent gaseous media, a process of extreme importance in power plants and energy transfer mechanisms.

Particles, subjected to sinusoidal oscillations parallel to the direction of steady translation, were found to have changes in average drag coefficient depending upon their translational Reynolds number, the density ratio, and the dimensionless frequency and amplitude of the oscillations. When the Reynolds number based on sphere diameter was less than 200, the oscillation had negligible effect on the average particle drag.

For Reynolds numbers exceeding 300, the coefficient of the mean drag was increased significantly in a particular frequency range. For example, at a Reynolds number of 3000, a 25 per cent increase in drag coefficient can be produced with an amplitude of oscillation of only 2 per cent of the sphere diameter, providing the frequency is near the frequency at which vortices would be shed in a steady flow at the mean speed. Flow visualization shows that over a wide range of frequencies, the vortex shedding frequency locks in to the oscillation frequency. Maximum effect at the natural frequency and lock-in show that a non-linear interaction between wake vortex shedding and the oscillation is responsible for the increase in drag.