The x¿n-x Plane for Analysis of Certain Second-Order Nonlinear Systems

Analysis of certain second-order nonlinear systems, not easily amenable to the phase-plane methods, and described by either of the following differential equations xÿn-2ÿ+ f(x)xÿ2n+g(x)xÿn+h(x)=0 ÿ+f(x)xÿn+h(x)=0 n≫0 can be effected easily by drawing the entire portrait of trajectories on a new plane; that is, on one of the xÿnÿx planes. Simple equations are given to evaluate time from a trajectory on any of these n planes. Poincaré's fundamental phase plane xÿÿx is conceived of as the simplest case of the general xÿnÿx plane.

Phase-plane techniques for the solution of transient-stability problems

The paper presents a graphical-numerical method for determining the transient stability limits of a two-machine system under the usual assumptions of constant input, no damping and constant voltage behind transient reactance. The method presented is based on the phase-plane criterion,1, 2 in contrast to the usual step-by-step and equal-area methods. For the transient stability limit of a two-machine system, under the assumptions stated, the sum of the kinetic energy and the potential energy, at the instant of fault clearing, should just be equal to the maximum value of the potential energy which the machines can accommodate with the fault cleared. The assumption of constant voltage behind transient reactance is then discarded in favour of the more accurate assumption of constant field flux linkages. Finally, the method is extended to include the effect of field decrement and damping. A number of examples corresponding to each case are worked out, and the results obtained by the proposed method are compared with those obtained by the usual methods.

Approximate synthesis formulas for microstrip line with aperture in ground plane

Approximate closed-form expressions for the propagation characteristics of a microstrip line with a symmetrical aperture in its ground plane are reported in this article. Well-known expressions for the characteristic impedance of a regular microstrip line have been modified to incorporate the effect of this aperture. The accuracy of these expressions for various values of substrate thickness, permittivity and line width has been studied in detail by fullwave simulations. This has been further verified by measurements. These expressions are easier to compute and find immense use in the design of broadband filters, tight couplers, power dividers, transformers, delay lines, and matching circuits. A broadband filter with aperture in ground plane is demonstrated in this article. (c) 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2012.

Minimal triangulation, complementarity and projective planes

Brehm and Kuhnel proved that if M-d is a combinatorial d-manifold with 3d/2 + 3 vertices and \ M-d \ is not homeomorphic to Sd then the combinatorial Morse number of M-d is three and hence d is an element of {0, 2, 4, 8, 16} and \ M-d \ is a manifold like a projective plane in the sense of Eells and Kuiper. We discuss the existence and uniqueness of such combinatorial manifolds. We also present the following result: ''Let M-n(d) be a combinatorial d-manifold with n vertices. M-n(d) satisfies complementarity if and only if d is an element of {0, 2, 4, 8, 16} with n = 3d/2 + 3 and \ M-n(d) \ is a manifold like a projective plane''.

Effect of base dissipation on the granular flow down an inclined plane

The effect of base dissipation on the granular flow down an inclined plane is examined by altering the coefficient of restitution between the moving and base particles in discrete element (DE) simulations. The interaction laws between two moving particles are kept fixed, and the coefficient of restitution (damping constant in the DE simulations) between the base and moving particles are altered to reduce dissipation, and inject energy from the base. The energy injection does result in an increase in the strain rate by up to an order of magnitude, and the temperature by up to two orders of magnitude at the base. However, the volume fraction, strain rate and temperature profiles in the bulk (above about 15 particle diameters from the base) are altered very little by the energy injection at the base. We also examine the variation of h(stop), the minimum height at the cessation of flow, with energy injection from the base. It is found that at a fixed angle of inclination, h(stop) decreases as the energy dissipation at the base decreases.

Changing resonator geometry to boost sound power decouples size and song frequency in a small insect

Despite their small size, some insects, such as crickets, can produce high amplitude mating songs by rubbing their wings together. By exploiting structural resonance for sound radiation, crickets broadcast species-specific songs at a sharply tuned frequency. Such songs enhance the range of signal transmission, contain information about the signaler's quality, and allow mate choice. The production of pure tones requires elaborate structural mechanisms that control and sustain resonance at the species-specific frequency. Tree crickets differ sharply from this scheme. Although they use a resonant system to produce sound, tree crickets can produce high amplitude songs at different frequencies, varying by as much as an octave. Based on an investigation of the driving mechanism and the resonant system, using laser Doppler vibrometry and finite element modeling, we show that it is the distinctive geometry of the crickets' forewings (the resonant system) that is responsible for their capacity to vary frequency. The long, enlarged wings enable the production of high amplitude songs; however, as a mechanical consequence of the high aspect ratio, the resonant structures have multiple resonant modes that are similar in frequency. The drive produced by the singing apparatus cannot, therefore, be locked to a single frequency, and different resonant modes can easily be engaged, allowing individual males to vary the carrier frequency of their songs. Such flexibility in sound production, decoupling body size and song frequency, has important implications for conventional views of mate choice, and offers inspiration for the design of miniature, multifrequency, resonant acoustic radiators.

Transition due to base roughness in a dense granular flow down an inclined plane

Particle simulations based on the discrete element method are used to examine the effect of base roughness on the granular flow down an inclined plane. The base is composed of a random configuration of fixed particles, and the base roughness is decreased by decreasing the ratio of diameters of the base and moving particles. A discontinuous transition from a disordered to an ordered flow state is observed when the ratio of diameters of base and moving particles is decreased below a critical value. The ordered flowing state consists of hexagonally close packed layers of particles sliding over each other. The ordered state is denser (higher volume fraction) and has a lower coordination number than the disordered state, and there are discontinuous changes in both the volume fraction and the coordination number at transition. The Bagnold law, which states that the stress is proportional to the square of the strain rate, is valid in both states. However, the Bagnold coefficients in the ordered flowing state are lower, by more than two orders of magnitude, in comparison to those of the disordered state. The critical ratio of base and moving particle diameters is independent of the angle of inclination, and varies very little when the height of the flowing layer is doubled from about 35 to about 70 particle diameters. While flow in the disordered state ceases when the angle of inclination decreases below 20 degrees, there is flow in the ordered state at lower angles of inclination upto 14 degrees. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4710543]

Conflict-Free Coloring for Rectangle Ranges Using O(n.382) Colors

Given a set of points P ⊆ R2, a conflict-free coloring of P w.r.t. rectangle ranges is an assignment of colors to points of P, such that each nonempty axisparallel rectangle T in the plane contains a point whose color is distinct from all other points in P ∩ T . This notion has been the subject of recent interest and is motivated by frequency assignment in wireless cellular networks: one naturally would like to minimize the number of frequencies (colors) assigned to base stations (points) such that within any range (for instance, rectangle), there is no interference. We show that any set of n points in R2 can be conflict-free colored with O(nβ∗+o(1)) colors in expected polynomial time, where β∗ = 3−√5 2 < 0.382.

Influence of stack geometry and resonator length on the performance of thermoacoustic engine

Thermoacoustic engines convert heat energy into high amplitude sound waves, which is used to drive thermoacoustic refrigerator or pulse tube cryocoolers by replacing the mechanical pistons such as compressors. The increasing interest in thermoacoustic technology is of its potentiality of no exotic materials, low cost and high reliability compared to vapor compression refrigeration systems. The experimental setup has been built based on the linear thermoacoustic model and some simple design parameters. The engines produce acoustic energy at the temperature difference of 325-450 K imposed along the stack of the system. This work illustrates the influence of stack parameters such as plate thickness (PT) and plate spacing (PS) with resonator length on the performance of thermoacoustic engine, which are measured in terms of onset temperature difference, resonance frequency and pressure amplitude using air as a working fluid. The results obtained from the experiments are in good agreement with the theoretical results from DeltaEc. (C) 2012 Elsevier Ltd. All rights reserved.

Current transport in nonpolar a-plane InN/GaN eterostructures Schottky junction

The temperature dependent current transport properties of nonpolar a-plane (11 2 0) InN/GaN heterostructure Schottky junction were investigated. The barrier height ( b) and ideally factor (η) estimated from the thermionic emission (TE) model were found to be temperature dependent in nature. The conventional Richardson plot of the ln(I s/T 2) versus 1/kT has two regions: the first region (150-300 K) and the second region (350-500 K). The values of Richardson constant (A +) obtained from this plot are found to be lower than the theoretical value of n-type GaN. The variation in the barrier heights was explained by a double Gaussian distribution with mean barrier height values ( b ) of 1.17 and 0.69 eV with standard deviation (� s) of 0.17 and 0.098 V, respectively. The modified Richardson plot in the temperature range 350-500 K gives the Richardson constant which is close to the theoretical value of n-type GaN. Hence, the current mechanism is explained by TE by assuming the Gaussian distribution of barrier height. At low temperature 150-300 K, the absence of temperature dependent tunneling parameters indicates the tunneling assisted current transport mechanism. © 2012 American Institute of Physics.

PIV study on the dimple mid-plane of a narrow rectangular channel with dimples applied to one wall

This paper presents an investigation of the fluid flow in the fully developed portion of a rectangular channel (Aspect Ratio of 2) with dimples applied to one wall at channel Reynolds numbers of 20,000, 30,000, and 40,000. The dimples are applied in a staggered-row, racetrack configuration. Results for three different dimple geometries are presented: a large dimple, small dimple, and double dimple. Heat transfer and aerodynamic results from preceding works are presented in Nusselt number and friction factor augmentation plots as determined experimentally. Using particle image velocimetry, the region near the dimple feature is studied in detail in the location of the entrainment and ejection of vortical packets into and out of the dimple; the downstream wake region behind each dimple is also studied to examine the effects of the local flow phenomenon that result in improved heat transfer in the areas of the channel wall not occupied by a feature. The focus of the paper is to examine the secondary flows in these dimpled channels in order to support the previously presented heat transfer trends. The flow visualization is also intended to improve the understanding of the flow disturbances in a dimpled channel; a better understanding of these effects would lead the development of more effective channel cooling designs. Copyright © 2011 by ASME.

Methane and carbon dioxide adsorption on edge-functionalized graphene: a comparative DFT study

With a view towards optimizing gas storage and separation in crystalline and disordered nanoporous carbon-based materials, we use ab initio density functional theory calculations to explore the effect of chemical functionalization on gas binding to exposed edges within model carbon nanostructures. We test the geometry, energetics, and charge distribution of in-plane and out-of-plane binding of CO2 and CH4 to model zigzag graphene nanoribbons edge-functionalized with COOH, OH, NH2, H2PO3, NO2, and CH3. Although different choices for the exchange-correlation functional lead to a spread of values for the binding energy, trends across the functional groups are largely preserved for each choice, as are the final orientations of the adsorbed gas molecules. We find binding of CO2 to exceed that of CH4 by roughly a factor of two. However, the two gases follow very similar trends with changes in the attached functional group, despite different molecular symmetries. Our results indicate that the presence of NH2, H2PO3, NO2, and COOH functional groups can significantly enhance gas binding, making the edges potentially viable binding sites in materials with high concentrations of edge carbons. To first order, in-plane binding strength correlates with the larger permanent and induced dipole moments on these groups. Implications for tailoring carbon structures for increased gas uptake and improved CO2/CH4 selectivity are discussed. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4736568]