Spiral and Taylor vortex fronts and pulses in axial through-flow

The influence of an axial through-flow on the spatiotemporal growth behavior of different vortex structures in the Taylor-Couette system with radius ratio eta=0.5 is determined. The Navier Stokes equations (NSE) linearized around the basic Couette-Poiseuille flow are solved numerically with a shooting method in a wide range of through-flow strengths Re and different rates of co- and counterrotating cylinders for toroidally closed vortices with azimuthal wave number m=0 and for spiral vortex flow with m=+1 and m=-1. For each of these three different vortex varieties we have investigated (i) axially extended vortex structures, (ii) axially localized vortex pulses, and (iii) vortex fronts. The complex dispersion relations of the linearized NSE for vortex modes with the three different m are evaluated for real axial wave numbers for (i) and over the plane of complex axial wave numbers for (ii,iii). We have also determined the Ginzburg-Landau amplitude equation (GLE) approximation in order to analyze its predictions for the vortex stuctures (ii,iii). Critical bifurcation thresholds for extended vortex structures are evaluated. The boundaries between absolute and convective instability of the basic state for vortex pulses are determined with a saddle-point analysis of the dispersion relations. Finally, the linearly selected front behavior of growing vortex structures is investigated. For the two front intensity profiles (increasing in positive or negative axial direction) we have determined front velocities, axial growth rates, and the wave numbers and frequencies of the unfolding vortex patterns with azimuthal wave numbers m=0, +1, -1, respectively.Comment: 15 pages, 9 figure

Wave-number dependence of the transitions between traveling and standing vortex waves and their mixed states in the Taylor-Couette system

Previous numerical investigations of the stability and bifurcation properties of different nonlinear combination structures of spiral vortices in a counterrotating Taylor-Couette system that were done for fixed axial wavelengths are supplemented by exploring the dependence of the vortex phenomena waves on their wavelength. This yields information about the experimental and numerical accessability of the various bifurcation scenarios. Also backwards bifurcating standing waves with oscillating amplitudes of the constituent traveling waves are found.Comment: 4 pages, 5 figure

The men who weren't even there: Legislative voting with absentees

Voting power in voting situations is measured by the probability of changing decisions by altering the cast 'yes' or 'no' votes. Recently this analysis has been extended by strategic abstention. Abstention, just as 'yes' or 'no' votes can change decisions. This theory is often applied to weighted voting situations, where voters can cast multiple votes. Measuring the power of a party in a national assembly seems to fit this model, but in fact its power comprises of votes of individual representatives each having a single vote. These representatives may vote yes or no, or may abstain, but in some cases they are not even there to vote. We look at absentees not due to a conscious decision, but due to illness, for instance. Formally voters will be absent, say, ill, with a certain probability and only present otherwise. As in general not all voters will be present, a thin majority may quickly melt away making a coalition that is winning in theory a losing one in practice. A simple model allows us to differentiate between winning and more winning and losing and less losing coalitions reected by a voting game that is not any more simple. We use data from Scotland, Hungary and a number of other countries both to illustrate the relation of theoretical and effective power and show our results working in the practice.a priori voting power; power index; being absent from voting; minority; Shapley-Shubik index; Shapley value

Home values and firm behaviour

The homes of those in charge of firms are an important source of finance for ongoing businesses. We use firm level accounting data, transaction level house price data and loan level residential mortgage data from the UK to show that a £1 increase in the value of the residential real estate of a firm’s directors increases the firm’s investment and wage bill by £0.03 each. These effects run through smaller firms and are similar in booms and busts. In aggregate, the homes of firm directors are worth 80% of GDP. Using this, a back of the envelope calculation suggests that a 1% increase in real estate prices leads, through this channel, to up to a 0.28% rise in business investment and a 0.08% rise in total wages paid. We complement this with evidence on how a firm responds to changes in the value of its own corporate real estate; we find that, in aggregate, the residential real estate of directors is at least as important for activity. We use an estimated general equilibrium model to quantify the importance of both types of real estate for the propagation of shocks to the macroeconomy

Bifurcation of standing waves into a pair of oppositely traveling waves with oscillating amplitudes caused by a three-mode interaction

A novel flow state consisting of two oppositely travelling waves (TWs) with oscillating amplitudes has been found in the counterrotating Taylor-Couette system by full numerical simulations. This structure bifurcates out of axially standing waves that are nonlinear superpositions of left and right handed spiral vortex waves with equal time-independent amplitudes. Beyond a critical driving the two spiral TW modes start to oscillate in counterphase due to a Hopf bifurcation. The trigger for this bifurcation is provided by a nonlinearly excited mode of different symmetry than the spiral TWs. A three-mode coupled amplitude equation model is presented that captures this bifurcation scenario. The mode-coupling between two symmetry degenerate critical modes and a nonlinearly excited one that is contained in the model can be expected to occur in other structure forming systems as well.Comment: 4 pages, 5 figure

Waveform Approach for Assessing Conformity of CISPR 16-1-1 Measuring Receivers

An alternative approach for assessing the conformity of electromagnetic interference measuring receivers with respect to the baseline CISPR 16-1-1 requirements is proposed. The method’s core is based on the generation of digitally synthesized complex waveforms comprising multisine excitation signals and modulated pulses. The superposition of multiple narrowband reference signals populating the standard frequency bands allows for a single-stage evaluation of the receiver’s voltage accuracy and frequency selectivity. Moreover, characterizing the response of the weighting detectors using modulated pulses is more repeatable and less restrictive than the conventional approach. This methodology significantly reduces the amount of time required to complete the verification of the receiver’s baseline magnitudes, because time-domain measurements enable a broadband assessment while the typical calibration methodology follows the time-consuming narrow band frequency sweep scheme. Since the reference signals are generated using arbitrary waveform generators, they can be easily reproduced from a standard numerical vector. For different test receivers, the results of such assessment are presented in the 9 kHz–1 GHz frequency range. Finally, a discussion on the measurement uncertainty of this methodology for assessing measuring receivers is given.Postprint (author's final draft

The residential collateral channel

We present evidence on a new macroeconomic channel which we call the residential collateral channel. Through this channel, an increase in real estate prices expands firm activity by enabling company directors to utilise their residential property as a source of funds for their business. This channel is a key determinant of investment and job creation, with a £1 increase in the combined residential collateral of a firm’s directors estimated to increase the firm’s investment by £0.02 and total wage costs by £0.02. To show this, we use a unique combination of UK datasets including firm-level accounting data matched with transaction-level house price data and loan-level residential mortgage data. The aggregate value of residential collateral held by company directors (around 70% of GDP) suggests that this channel has important macroeconomic effects. We complement this with further evidence on the corporate collateral channel whereby an increase in real estate prices directly expands firm activity by enabling businesses to borrow more against their corporate real estate. An estimated general equilibrium model with collateral constrained firms is used to quantify the aggregate effects of both channels

Competition between Traveling Fluid Waves of Left and Right Spiral Vortices and Their Different Amplitude Combinations

Stability, bifurcation properties, and the spatiotemporal behavior of different nonlinear combination structures of spiral vortices in the counter rotating Taylor-Couette system are investigated by full numerical simulations and by coupled amplitude equation approximations. Stable cross-spiral structures with continuously varying content of left and right spiral modes are found. They provide a stability transferring connection between the initially stable, axially counter propagating wave states of pure spirals and the axially standing waves of so-called ribbons that become stable slightly further away from onset of vortex flow.Comment: 4 pages, 5 figure