284 research outputs found

    Marching bifurcations

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    Dynamical x-ray diffraction from an icosahedral Al-Pd-Mn quasicrystal

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    Over the past ten years the quality and size of aperiodic crystals has steadily increased. This raises some interesting issues regarding the limitations of structural perfection attainable in non periodic solids. Results from a coherent x-ray diffraction experiment on an icosahedral Al-Pd-Mn quasicrystal, as well as direct evidence of dynamical diffraction of x-rays from quasicrystals are presented. In particular, the anomalous transmission of x-rays (the Borrmann effect), the Borrmann Fan, and Pendellosung fringe patterns have been observed. These measurements show that nearly perfect quasicrystals may be grown to centimeter-size dimensions thus implying the feasibility of performing a large range of measurements based on the study of perfect crystals. In addition, the dynamical theory of diffraction is applicable to the study of aperiodic crystals

    5th EUROMECH nonlinear dynamics conference, August 7-12, 2005 Eindhoven : book of abstracts

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    5th EUROMECH nonlinear dynamics conference, August 7-12, 2005 Eindhoven : book of abstracts

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    A Contemporary Study in the Theory of Traveling-Wave Tubes

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    The traveling-wave tube (TWT) is a widely used amplifier in satellite communications and radar. An electromagnetic signal is fed into one end of the device and is amplified over a distance until it is extracted downstream at the output. The physics behind this spatial amplification of an electromagnetic wave is predicated on the interaction of a linear DC electron beam with the surrounding circuit structure. J. R. Pierce, known as the “father of communications satellites,” was the first to formulate the theory for this beam-circuit interaction, which was since used in other electronic devices such as free-electron lasers, gyrotrons, and Smith-Purcell radiators. In this thesis, we extend the classic Pierce theory in two directions: harmonic generation and the effect of high beam current on both the beam mode and circuit mode. The classical Pierce theory was formulated for a single (fundamental) frequency, same as the input signal. However, in a TWT with an octave bandwidth or greater, in particular the widely used helix TWT, the second harmonic of the input signal may also be within the amplification band and thus may also be generated and amplified. There is no input at this second harmonic frequency. An extension to the Pierce formulation that incorporates the generation of harmonics, including non-uniform taper, will be presented. We show that the second harmonic arises mostly from a newly discovered dynamic synchronous interaction instead of by the kinematic orbital crowding mechanism that is the most dominant harmonic generation mechanism in a klystron. The methodology provided may be applicable to the bi-frequency recirculating planar magnetron and other high-power microwave sources. In beam-circuit interactions, the space-charge effect of the beam is important at high beam currents. In Pierce's TWT theory, this space-charge effect is modeled by the parameter which he called Q in the beam mode. A reliable determination of Q remains elusive for a realistic TWT. In this thesis, the author constructed the first exact small-signal theory of the beam-circuit interaction for the tape helix TWT, from which Q may be unambiguously determined. In the process of doing so, it was discovered that the circuit mode in Pierce's theory must also be modified at high beam current, an aspect overlooked in Pierce’s original analysis. We quantify this circuit mode modification by an entirely new parameter that we call q, introduced here for the first time in TWT theory. For the example using a realistic tape helix TWT, we find that the effect of q is equivalent to a modification of the circuit phase velocity by as much as two percent, which is a significant effect equivalent to a detune of two percent. Lastly, we apply the theory developed for Q and q to a high-power TWT amplifier of current interest, the disk-on-rod TWT. For this configuration, the exact analytical forms of these parameters are extracted from the exact dispersion relation, which the author has also constructed. Comparisons of the numerical solutions to the analytic results to simulations done in ANSYS HFSS, ICEPIC, and MAGIC are made.PHDNuclear Engineering & Radiological SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145994/1/pywong_1.pd

    Numerical tools for computational design of acoustic metamaterials

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    The notion of metamaterials as artificially engineered structures designed to obtain specific material properties, typically unachievable in naturally occurring materials, has captured the attention of the scientific and industrial communities. Among the broad range of applications for such kind of materials, in the field of acoustics, the possibility of creating materials capable of efficiently attenuating noise in target frequency ranges is of utmost importance for a lot of industrial areas. In this context, the so-called locally resonant acoustic metamaterials (LRAMs) can play an important role, as their internal topology can be designed to exhibit huge levels of attenuation in specific frequency regions by taking advantage of internal resonance modes. With a proper, optimized topological design, LRAMs can be used, for instance, to build lightweight and thin noise insulation panels that operate in a low-frequency regime, where standard solutions for effectively attenuating the noise sources require dense and thick materials. Given the importance of the topological structure in obtaining the desired properties in acoustic metamaterials, the use of novel numerical techniques can be exploited to cre-ate a set of computational tools aimed at the analysis and design of optimized solutions. These are based on three fundamental pillars: (1) the multiscale homogenization of complex material structures in the microscale to get a set of effective properties capa-ble of describing the material behavior in the macroscale, (2) the model-order reduc-tion techniques, which are used to decrease the computational cost of heavy computa-tions while still maintaining a sufficient degree of accuracy, and (3) the topology optimi-zation methods that can be employed to obtain optimal configurations with a given set of constraints and a target material behavior. This set of computational tools can be applied to design acoustic metamaterials that are both efficient and practical, i.e. they behave according to their design specifications and can be produced easily, for in-stance, making use of novel additive manufacturing techniques.La concepció dels metamaterials com a estructures dissenyades artificialment amb l’objectiu d’obtenir un conjunt de propietats que no són assolibles en materials de manera natural, ha captat l’atenció de les comunitats científiques i industrials. Dins de l’ampli ventall d’aplicacions que se’ls pot donar als metamaterials, si ens centrem en el camp de l’acústica, la possibilitat de crear un material capaç d’atenuar de manera efectiva sorolls en rangs de freqüència concrets és de gran interès en multitud d’indústries. En aquest context, els anomenats “locally resonant acoustic metamaterials” (LRAMs) destaquen per la possibilitat de dissenyar la seva topologia interna per tal que produeixin elevats nivells d’atenuació en regions concretes de l’espectre de freqüències. Amb un disseny topològic òptim, els LRAMs poden servir, per exemple, per a la construcció de panells lleugers aïllants de soroll, que operin en rangs de freqüències baixos, en els quals la solució clàssica requereix de materials d’elevada densitat i espessor. Donada la importància de l’estructura topològica dels metamaterials acústics en l’obtenció de les propietats desitjades, resulta convenient l’ús de mètodes numèrics punters per al desenvolupament d’un conjunt d’eines computacionals que tinguin per objectiu l’anàlisi i el disseny de solucions òptimes. Tals eines es fonamenten en tres pilars: (1) la homogeneïtzació multiescala d’estructures de material complexes a una escala micro que derivi en l’obtenció de propietats efectives que permetin descriure el comportament del material a una escala macro, (2) tècniques de reducció per minimitzar l’esforç computacional mantenint nivells de precisió suficients i (3) mètodes d’optimització topològica emprats per a l’obtenció de configuracions òptimes donat un conjunt de restriccions i unes propietats de material objectiu. Aquestes eines computacionals es poden aplicar al disseny de metamaterials acústics que resultin eficients i pràctics a la vegada, és a dir, que es comportin segons les especificacions de disseny i siguin fàcilment fabricables, per exemple, mitjançant tècniques punteres d’impressió 3D

    Numerical tools for computational design of acoustic metamaterials

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    Tesi en modalitat de compendi de publicacionsThe notion of metamaterials as artificially engineered structures designed to obtain specific material properties, typically unachievable in naturally occurring materials, has captured the attention of the scientific and industrial communities. Among the broad range of applications for such kind of materials, in the field of acoustics, the possibility of creating materials capable of efficiently attenuating noise in target frequency ranges is of utmost importance for a lot of industrial areas. In this context, the so-called locally resonant acoustic metamaterials (LRAMs) can play an important role, as their internal topology can be designed to exhibit huge levels of attenuation in specific frequency regions by taking advantage of internal resonance modes. With a proper, optimized topological design, LRAMs can be used, for instance, to build lightweight and thin noise insulation panels that operate in a low-frequency regime, where standard solutions for effectively attenuating the noise sources require dense and thick materials. Given the importance of the topological structure in obtaining the desired properties in acoustic metamaterials, the use of novel numerical techniques can be exploited to cre-ate a set of computational tools aimed at the analysis and design of optimized solutions. These are based on three fundamental pillars: (1) the multiscale homogenization of complex material structures in the microscale to get a set of effective properties capa-ble of describing the material behavior in the macroscale, (2) the model-order reduc-tion techniques, which are used to decrease the computational cost of heavy computa-tions while still maintaining a sufficient degree of accuracy, and (3) the topology optimi-zation methods that can be employed to obtain optimal configurations with a given set of constraints and a target material behavior. This set of computational tools can be applied to design acoustic metamaterials that are both efficient and practical, i.e. they behave according to their design specifications and can be produced easily, for in-stance, making use of novel additive manufacturing techniques.La concepció dels metamaterials com a estructures dissenyades artificialment amb l’objectiu d’obtenir un conjunt de propietats que no són assolibles en materials de manera natural, ha captat l’atenció de les comunitats científiques i industrials. Dins de l’ampli ventall d’aplicacions que se’ls pot donar als metamaterials, si ens centrem en el camp de l’acústica, la possibilitat de crear un material capaç d’atenuar de manera efectiva sorolls en rangs de freqüència concrets és de gran interès en multitud d’indústries. En aquest context, els anomenats “locally resonant acoustic metamaterials” (LRAMs) destaquen per la possibilitat de dissenyar la seva topologia interna per tal que produeixin elevats nivells d’atenuació en regions concretes de l’espectre de freqüències. Amb un disseny topològic òptim, els LRAMs poden servir, per exemple, per a la construcció de panells lleugers aïllants de soroll, que operin en rangs de freqüències baixos, en els quals la solució clàssica requereix de materials d’elevada densitat i espessor. Donada la importància de l’estructura topològica dels metamaterials acústics en l’obtenció de les propietats desitjades, resulta convenient l’ús de mètodes numèrics punters per al desenvolupament d’un conjunt d’eines computacionals que tinguin per objectiu l’anàlisi i el disseny de solucions òptimes. Tals eines es fonamenten en tres pilars: (1) la homogeneïtzació multiescala d’estructures de material complexes a una escala micro que derivi en l’obtenció de propietats efectives que permetin descriure el comportament del material a una escala macro, (2) tècniques de reducció per minimitzar l’esforç computacional mantenint nivells de precisió suficients i (3) mètodes d’optimització topològica emprats per a l’obtenció de configuracions òptimes donat un conjunt de restriccions i unes propietats de material objectiu. Aquestes eines computacionals es poden aplicar al disseny de metamaterials acústics que resultin eficients i pràctics a la vegada, és a dir, que es comportin segons les especificacions de disseny i siguin fàcilment fabricables, per exemple, mitjançant tècniques punteres d’impressió 3D.Postprint (published version

    Properties of point defects on single crystalline MgO(100) films

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    WAVE PROPAGATION IN TENSEGRITY AND PERIODIC STRUCTURES

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    This dissertation focuses on the development of the fundamental understanding of the dynamic behavior of assemblies of periodic arrays of tensegrity unit cells (along one and two directions). The ultimate aim of the dissertation is to capitalize on the attractive attributes of tensegrity structures with the unique characteristics of periodic structures, which stem from their ability to impede the propagation of disturbances that fall within certain frequency bands (known as stop bands or bandgaps). A successful implementation of such periodic/tensegrity structures is envisioned to extend the usefulness of tensegrity to vibration isolation problems, as well as to the synthesis of tunable acoustic and elastic wave filters, in both the frequency and spatial domains. In this dissertation, numerical analysis of the statics and kinematics of icosahedron tensegrity cells are developed. The developed relationships are utilized to conceive one- and two-dimensional periodic arrays by appropriate stacking of icosahedron tensegrity cells. Alternative configurations for the periodic tensegrity arrays are considered for improved band gap characteristics, and a novel design for a periodic, tensegrity-based damper/vibration isolator is presented and demonstrated. Particular emphasis is placed here on investigating and demonstrating some of the very interesting elastic properties of the periodic/tensegrity structures. Among these properties is the ratio of the bulk modulus to the shear modulus which are shown to be on the order of 1000. These values are two orders of magnitude higher than any naturally-occurring bulk material, suggesting that the viable potential of the periodic/tensegrity structures as suitable candidates for the synthesis of practical and realizable “pentamode” metamaterials, with many potential applications in the novel areas of acoustic and elastic cloaking where the proposed periodic/tensegrity structures act as liquids to ensure proper impedance matching

    Kinematics and Dynamics of Roller Chain Drives

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