High-Order Dual-Port Quasi-Absorptive Microstrip Coupled-Line Bandpass Filters

In this article, we present the first demonstration of distributed and symmetrical all-band quasi-absorptive filters that can be designed to arbitrarily high orders. The proposed quasi-absorptive filter consists of a bandpass section (reflective-type coupled-line filter) and absorptive sections (a matched resistor in series with a shorted quarter-wavelength transmission line). Through a detailed analysis, we show that the absorptive sections not only eliminate out-of-band reflections but also determine the passband bandwidth (BW). As such, the bandpass section mainly determines the out-of-band roll-off and the order of the filter can be arbitrarily increased without affecting the filter BW by cascading more bandpass sections. A set of 2.45-GHz one-, two-, and three-pole quasi-absorptive microstrip bandpass filters are designed and measured. The filters show simultaneous input and output absorption across both the passband and the stopband. Measurement results agree very well with the simulation and validate the proposed design concept

Entrainment of short-wavelength free-stream vortical disturbances in compressible and incompressible boundary layers

The fundamental difference between continuous modes of the Orr–Sommerfeld/Squire equations and the entrainment of free-stream vortical disturbances (FSVD) into the boundary layer has been investigated in a recent paper (Dong &amp; Wu, J. Fluid Mech., vol. 732, 2013, pp. 616–659). It was shown there that the non-parallel-flow effect plays a leading-order role in the entrainment, and neglecting it at the outset, as is done in the continuous-mode formulation, leads to non-physical features of ‘Fourier entanglement’ and abnormal anisotropy. The analysis, which was for incompressible boundary layers and for FSVD with a characteristic wavelength of the order of the local boundary-layer thickness, is extended in this paper to compressible boundary layers and FSVD with even shorter wavelengths, which are comparable with the width of the so-called edge layer. Non-parallelism remains a leading-order effect in the present scaling, which turns out to be more general in that the equations and solutions in the previous paper are recovered in the appropriate limit. Appropriate asymptotic solutions in the main and edge layers are obtained to characterize the entrainment. It is found that when the Prandtl number \mathit{Pr}<1, free-stream vortical disturbances of relatively low frequency generate very strong temperature fluctuations within the edge layer, leading to formation of thermal streaks. A composite solution, uniformly valid across the entire boundary layer, is constructed, and it can be used in receptivity studies and as inlet conditions for direct numerical simulations of bypass transition. For compressible boundary layers, continuous spectra of the disturbance equations linearized about a parallel base flow exhibit entanglement between vortical and entropy modes, namely, a vortical mode necessarily induces an entropy disturbance in the free stream and vice versa, and this amounts to a further non-physical behaviour. High Reynolds number asymptotic analysis yields the relations between the amplitudes of entangled modes.</jats:p

On the finiteness of the classifying space for the family of virtually cyclic subgroups

Given a group G, we consider its classifying space for the family of virtually cyclic subgroups. We show for many groups, including for example, one-relator groups, acylindrically hyperbolic groups, 3-manifold groups and CAT(0) cube groups, that they do not admit a finite model for this classifying space unless they are virtually cyclic. This settles a conjecture due to Juan-Pineda and Leary for these classes of groups

Asymptotic Behavior of Error Exponents in the Wideband Regime

In this paper, we complement Verd\'{u}'s work on spectral efficiency in the wideband regime by investigating the fundamental tradeoff between rate and bandwidth when a constraint is imposed on the error exponent. Specifically, we consider both AWGN and Rayleigh-fading channels. For the AWGN channel model, the optimal values of $R_z(0)$ and $\dot{R_z}(0)$ are calculated, where $R_z(1/B)$ is the maximum rate at which information can be transmitted over a channel with bandwidth $B/2$ when the error-exponent is constrained to be greater than or equal to $z.$ Based on this calculation, we say that a sequence of input distributions is near optimal if both $R_z(0)$ and $\dot{R_z}(0)$ are achieved. We show that QPSK, a widely-used signaling scheme, is near-optimal within a large class of input distributions for the AWGN channel. Similar results are also established for a fading channel where full CSI is available at the receiver.Comment: 59 pages, 6 figure