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1.
Signal constellations in the hyperbolic plane are provided as an alternative to traditional signal constellations in the Euclidean plane, since channels may actually exist for which the latter signal constellations are not as suitable as the former. A hyperbolic gaussian probability density function, based solely on geometrical considerations, is derived to determine the performance of the hyperbolic signal constellations. Benefits result from an approach conceived in terms of reduced signal-to-noise ratio, needed to achieve a prescribed error rate and equivalent optimum receiver complexity. 相似文献
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《Journal of The Franklin Institute》2022,359(2):1176-1193
The paper describes a novel method of sampled-data in space (spatial variable) nonlinear control of scalar semilinear parabolic and hyperbolic systems with unknown parameters, distributed disturbances and finite number of measurements along the spatial variable. Differently from recent results based on piecewise constant control laws, the proposed one is used piecewise nonlinear functions choosing by designer for providing some properties in the closed-loop system. In particular, we propose several types of functions providing reduced control. The gain design in the control law is found as a solution of linear matrix inequalities with minimum ultimate bound guarantee. The simulations confirm theoretical results and show the efficiency of the proposed control scheme compared with some existing ones. 相似文献
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In this study, we show the importance of extensional rheology, in addition to the shear rheology, in the choice of blood analog solutions intended to be used in vitro for mimicking the microcirculatory system. For this purpose, we compare the flow of a Newtonian fluid and two well-established viscoelastic blood analog polymer solutions through microfluidic channels containing both hyperbolic and abrupt contractions∕expansions. The hyperbolic shape was selected in order to impose a nearly constant strain rate at the centerline of the microchannels and achieve a quasihomogeneous and strong extensional flow often found in features of the human microcirculatory system such as stenoses. The two blood analog fluids used are aqueous solutions of a polyacrylamide (125 ppm w∕w) and of a xanthan gum (500 ppm w∕w), which were characterized rheologically in steady-shear flow using a rotational rheometer and in extension using a capillary breakup extensional rheometer (CaBER). Both blood analogs exhibit a shear-thinning behavior similar to that of whole human blood, but their relaxation times, obtained from CaBER experiments, are substantially different (by one order of magnitude). Visualizations of the flow patterns using streak photography, measurements of the velocity field using microparticle image velocimetry, and pressure-drop measurements were carried out experimentally for a wide range of flow rates. The experimental results were also compared with the numerical simulations of the flow of a Newtonian fluid and a generalized Newtonian fluid with shear-thinning behavior. Our results show that the flow patterns of the two blood analog solutions are considerably different, despite their similar shear rheology. Furthermore, we demonstrate that the elastic properties of the fluid have a major impact on the flow characteristics, with the polyacrylamide solution exhibiting a much stronger elastic character. As such, these properties must be taken into account in the choice or development of analog fluids that are adequate to replicate blood behavior at the microscale. 相似文献
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Presented herein is a detailed analysis of the small, free oscillations of pre- stressed rectangular plates in both pre- and post-buckling ranges. The simply supported plate is stressed either thermally or by the uniaxial in-plane loads on two opposite edges, the other two edges are taken to be either freely movable or immovable, and all the edges are restrained to remain straight. Both the symmetrical and anti-symmetrical small vibration modes superimposed upon both primary- and secondary-buckling, and the coupling among these modes, are studied. A criterion for the existence of coupling is given. Some numerical results are then presented. 相似文献
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《Journal of The Franklin Institute》2019,356(14):7731-7753
Since being postulated more than a decade ago, inerters have been successfully employed to enhance the dynamic performance of mechanical systems in several applications. Their ability to lend a high dynamic mass presence to systems that employ them with only a relatively small static device mass makes them unique among mechanical elements. This study explores the mechanical wave manipulation characteristics of nonlinear inertant acoustic metamaterial (NLIAM) configurations using analysis and simulations for their one-dimensional discrete element lattice representations. Firstly, based on notional concepts for nonlinear inertant devices, potential frequency-dependent and acceleration-dependent nonlinear inertant models are identified. Using an effective mass model for the NLIAM with frequency-dependent inertance in the local resonator attachment, the dispersion characteristics of inverse square law and power law inertance models are examined and contrasted with those for an acoustic metamaterial with frequency invariant inertance. While a tuned inverse square law inertance model ensures the existence of a band gap over almost the entire frequency bandwidth of interest even encompassing the extremely low frequency regime, the low and high frequency limits for this inertance law would not be realizable in practice. A potentially more practical power law approximation is proposed and shown to deliver a widening of the band gap by more than 100% towards frequencies below the lower bound of the band gap for the acoustic metamaterial with frequency invariant inertance. Further, drawing inspiration from the Duffing-type stiffness, an acceleration-dependent cubically nonlinear inertance model is proposed. First order corrections to the dispersion characteristics are obtained for an NLIAM with acceleration-dependent inertance using a perturbation approach. For weakly nonlinear cases, excitation amplitude-activated shifts in the dispersion curves are found to enable this NLIAM to act as a passive adaptive filter for mechanical waves based solely on their excitation amplitude. Practical manifestations of such NLIAM could therefore provide a means to realize extraordinary wave manipulation capabilities especially suitable for low frequency structural dynamic applications. 相似文献
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《Journal of The Franklin Institute》2001,338(2-3):171-185
In this paper, we announce our recent results on the asymptotic and spectral analysis of the model of an aircraft wing in a subsonic air flow. This model has been developed in the Flight Systems Research Center of UCLA and is presented in the works by Balakrishnan. The model is governed by a system of two coupled integro-differential equations and a two-parameter family of boundary conditions modeling the action of the self-straining actuators. The differential parts of the above equations form a coupled linear hyperbolic system; the integral parts are of the convolution type. We provide the spectral asymptotics for the eigenfrequencies of the system (or aeroelastic modes) and the asymptotical approximations for the corresponding eigenfunctions (or the mode shapes). Based on the asymptotical results, we (a) state that the set of the mode shapes is complete in the energy space; (b) construct a system which is biorthogonal to the set of the mode shapes in the case when there might be multiple aeroelastic modes; and (c) show that the mode shapes form a Riesz basis in the energy space. 相似文献
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Two-dimensional spatial manipulation of microparticles in continuous flows in acoustofluidic systems
Lu Gao C. Wyatt Shields IV Leah M. Johnson Steven W. Graves Benjamin B. Yellen Gabriel P. López 《Biomicrofluidics》2015,9(1)
We report a modeling and experimental study of techniques to acoustically focus particles flowing through a microfluidic channel. Our theoretical model differs from prior works in that we solve an approximate 2-D wave transmission model that accounts for wave propagation in both the solid and fluid phases. Our simulations indicate that particles can be effectively focused at driving frequencies as high as 10% off of the resonant condition. This conclusion is supported by experiments on the acoustic focusing of particles in nearly square microchannels, which are studied for different flow rates, driving frequencies and placements of the lead zirconate titanate transducer, either underneath the microchannel or underneath a parallel trough. The relative acoustic potential energy and the resultant velocity fields for particles with positive acoustic contrast coefficients are estimated in the 2-D limit. Confocal microscopy was used to observe the spatial distribution of the flowing microparticles in three dimensions. Through these studies, we show that a single driving frequency from a single piezoelectric actuator can induce the 2-D concentration of particles in a microchannel with a nearly square cross section, and we correlate these behaviors with theoretical predictions. We also show that it is possible to control the extent of focusing of the microparticles, and that it is possible to decouple the focusing of microparticles in the vertical direction from the lateral direction in rectangular channels with anisotropic cross sections. This study provides guidelines to design and operate microchip-based acoustofluidic devices for precise control over the spatial arrangement of microparticles for applications such as flow cytometry and cellular sorting. 相似文献
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RUDENBERG R 《Journal of The Franklin Institute》1948,246(5):377-408
Increasing lens voltage, higher than the incident electron voltage, at first blocks the beam and then converts the electron lens into a curved mirror, the focal properties of which are analyzed.The embodiment of hyperbolic lenses is discussed by means of the boundary conditions which may be rigorously or approximately satisfied in actual designs. The effects of lateral apertures and windows on the imaging qualities of the field are considered in detail.Expressions are derived for velocity-, angular- and aperture-defects, the latter being merely a surface effect of the hyperbolic field. They all depend on a few parameters only of the lens field and are relatively small in magnitude. An experi- mental verification of the field structure with partial compensation of the defects shows favorable imaging qualities.Two-dimensional fields, constituting electron cylinder lenses, are considered in a similar way, leading to analogous formulations for the cardinal properties. 相似文献
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Mont Hubbard 《Journal of The Franklin Institute》1979,308(4):405-421
Bond graphs are used to generate the equations of motion of a whirling flywheel. The formulation is shown to be a natural one when control forces and moments are included for active control of the whirling modes. Critical frequencies are interpreted as rotational speeds at which non-zero equilibrium configurations exist for displacements (as opposed to the more familiar momenta) and arise when the system dynamics matrix of the complete whirl motion has two zero eigenvalues. In addition, oscillatory modes corresponding to non-zero eigenvalues are examined. Time simulations and other numerical results are given for an example flywheel system which has been proposed for electric utility energy storage. 相似文献
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The thermal conductivity of two-dimensional materials, such as graphene, typically decreases when tensile strain is applied, which softens their phonon modes. Here, we report an anomalous strain effect on the thermal conductivity of monolayer silicene, a representative low-buckled two-dimensional (LB-2D) material. ReaxFF-based molecular dynamics simulations are performed to show that biaxially stretched monolayer silicene exhibits a remarkable increase in thermal conductivity, by as much as 10 times the freestanding value, with increasing applied strain in the range of [0, 0.1], which is attributed to increased contributions from long-wavelength phonons. A further increase in strain in the range of [0.11, 0.18] results in a plateau of the thermal conductivity in an oscillatory manner, governed by a unique dynamic bonding behavior under extreme loading. This anomalous effect reveals new physical insights into the thermal properties of LB-2D materials and may provide some guidelines for designing heat management and energy conversion devices based on such materials. 相似文献
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Frequency dependent dynamic properties from resonant column and cyclic triaxial tests 总被引：1，自引：0，他引：1
The resonant column (RC) and cyclic triaxial (CT) devices are commonly used for the measurement of soils’ dynamic properties. The results of these tests do not agree when extrapolated to similar strain levels. The main objectives of this paper are to evaluate the effect of excitation frequency on the dynamic properties of soils, and to provide a methodology to reconcile shear modulus values obtained from RC and CT tests. The effect of frequency on the dynamic properties is evaluated using the new non-resonance (NR) method in the RC device and CT tests. Sand specimens with varying percentages of bentonite-water mixture and a clay specimen are tested. The results obtained from RC tests utilizing the NR method indicate significant change in shear modulus with frequency. The extrapolation of shear modulus from the conventional RC results to shear strains used in CT is significantly overestimated. The extrapolations improved when the results were corrected for frequency effect inferred from the NR method. 相似文献
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设计并加工测试了一种高效率的中心频率220GHz的模式转换器,将矩形波导的TE10模式转换为圆波导的TE01模式。使用三维仿真软件CST进行模拟设计,在保证一定带宽的基础上,以减少噪声模式激励、提高转换效率为标准进行优化。模拟结果显示,中心频率220GHz时最大转换效率达到99%以上,转换效率98.5%以上的绝对带宽达到4GHz。实验结果表明该模式转换器对TE10-TE01的转换性能已达到工程应用要求。 相似文献
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Wei Liu 《Journal of The Franklin Institute》2011,348(9):2556-2569
A novel design of the frequency invariant beamformer based on a rectangular array is proposed with two unique features: there are no taped delay-lines (TDLs) or any other temporal processing involved and the resultant beamformer has a full 360° azimuth angle coverage. This leads to a wideband beamformer with complex-valued coefficients and its implementation is not as straightforward as the traditional ones. Depending on whether the input signal is complex-valued or real-valued, special arrangements and structures are required for its effective implementation. Several design examples are provided with a satisfactory frequency invariant property. Two sets of implementation results are given based on both simulations and data collected by a planar microphone array system. 相似文献
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Dimitris S. Sophianopoulos 《Journal of The Franklin Institute》2007,344(5):463-488
The nonlinear buckling and postbuckling behavior of rectangular plates in symmetric and antisymmetric modes is re-examined, in the context of Bifurcation and Catastrophe Theories, using a two-degrees-of-freedom model, which has been adopted for the same purpose in the pioneer literature. At first the perfect system is dealt with in detail, symbolically utilizing the exact as well as the approximate equilibrium equations, the latter being products of a universal unfolding of the original total potential energy function. Conditions for the existence of remote secondary bifurcations are fully assessed and the stability of critical states is determined, revealing sudden qualitative changes in the postbuckling response of the perfect system, which have been also reported for the actual continuous structural system—the rectangular plate—using the von Kárman equations. Thereafter, the imperfection sensitivity is dealt with, introducing symmetric as well as asymmetric imperfections, considered as individual or consecutive perturbations of the perfect system. It is found that symmetry breaking bifurcations give birth to complicated cusp singularities, which may lead to unexpected jumps from one to two-mode remote postbuckling behavior. Finally, considering the general case of random imperfections, higher order two-mode singularities are revealed, mainly of the double-cusp catastrophe type, which have been also discovered in the postbuckling response of rectangular plates, a fact validating the choice of the foregoing nonlinear simulation. 相似文献
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《Journal of The Franklin Institute》2022,359(18):10578-10601
In this paper, a distributed control architecture is presented for addressing the cooperative perimeter surveillance of rectangular areas for multi-agent system whose dynamics is described by double integrator models subject to exogenous bounded disturbances. In particular, a novel methodology to generate proper state trajectories of a swarm of agents is provided and then exploited as references for the underlying model predictive controllers bank. Specifically, the swarm is first driven along the perimeter of a rectangular strip and next imposed to enter a given containment region while remaining simultaneously outside a forbidden region around a prescribed target. Steady-state conditions are analyzed and sufficient conditions derived in terms of the control law parameters. Simulation results put in light the main properties of the control architecture that is designed to adequately switch between two different distributed algorithms in order to guarantee constraints satisfaction within the capturing region despite any disturbance realization. 相似文献
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The need for cell and particle sorting in human health care and biotechnology applications is undeniable. Inertial microfluidics has proven to be an effective cell and particle sorting technology in many of these applications. Still, only a limited understanding of the underlying physics of particle migration is currently available due to the complex inertial and impact forces arising from particle–particle and particle–wall interactions. Thus, even though it would likely enable significant advances in the field, very few studies have tried to simulate particle-laden flows in inertial microfluidic devices. To address this, this study proposes new codes (solved in OpenFOAM software) that capture all the salient inertial forces, including the four-way coupling between the conveying fluid and the suspended particles traveling a spiral microchannel. Additionally, these simulations are relatively (computationally) inexpensive since the arbitrary Lagrangian–Eulerian formulation allows the fluid elements to be much larger than the particles. In this study, simulations were conducted for two different spiral microchannel cross sections (e.g., rectangular and trapezoidal) for comparison against previously published experimental results. The results indicate good agreement with experiments in terms of (monodisperse) particle focusing positions, and the codes can readily be extended to simulate two different particle types. This new numerical approach is significant because it opens the door to rapid geometric and flow rate optimization in order to improve the efficiency and purity of cell and particle sorting in biotechnology applications. 相似文献
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研究地质流体的物理化学性质和地球化学行为是地球系统科学研究所面对的挑战性课题之一。与诸如实验和物理化学建模等传统研究方法相比，分子水平上的计算机模拟在解决极端条件下流体体系物理化学性质方面表现出明显的优势，成为定量研究地球内部不同层圈中地质流体特点及其作用规律的有效途径。本论文简要介绍了我们把计算机模拟技术应用到地质流体研究中的成果，主要可概括为：（1）利用蒙特卡罗计算机模拟方法，我们成功地模拟了地质流体体系相平衡和相变，取得了与实验一致的结果，从而在计算机上实现了相平衡研究，与花费昂贵的实验相比具有方法学上的先进性；（2）通过分子动力学模拟研究水的物理化学性质，我们把水的PVT数据从实验所允许的温压范围（温度小于1873.15 K、压力低于5万大气压）扩展到2000 K、20万大气压，并提出了一个适用于宽广温压条件下的状态方程；（3）通过分子动力学和蒙特卡罗模拟，我们建立了一个CO2分子模型，它能同时准确预测CO2的各种物理化学性质和行为（PVT性质、相平衡、潜热、结构性质和动力学性质）；（4）通过分子动力学模拟研究氯化锂在溶液中的离子水化和缔合性质，我们得到了与实验和量子力学模拟一致的结果，与此同时还揭示了离子水化和缔合过程的微观机制。 相似文献