Parametrically excited surface waves: Two-frequency forcing, normal form symmetries, and pattern selection

Motivated by experimental observations of exotic standing wave patterns in the two-frequency Faraday experiment, we investigate the role of normal form symmetries in the pattern selection problem. With forcing frequency components in ratio m/n, where m and n are co-prime integers, there is the possibility that both harmonic and subharmonic waves may lose stability simultaneously, each with a different wavenumber. We focus on this situation and compare the case where the harmonic waves have a longer wavelength than the subharmonic waves with the case where the harmonic waves have a shorter wavelength. We show that in the former case a normal form transformation can be used to remove all quadratic terms from the amplitude equations governing the relevant resonant triad interactions. Thus the role of resonant triads in the pattern selection problem is greatly diminished in this situation. We verify our general results within the example of one-dimensional surface wave solutions of the Zhang-Vinals model of the two-frequency Faraday problem. In one-dimension, a 1:2 spatial resonance takes the place of a resonant triad in our investigation. We find that when the bifurcating modes are in this spatial resonance, it dramatically effects the bifurcation to subharmonic waves in the case of forcing frequencies are in ratio 1/2; this is consistent with the results of Zhang and Vinals. In sharp contrast, we find that when the forcing frequencies are in ratio 2/3, the bifurcation to (sub)harmonic waves is insensitive to the presence of another spatially-resonant bifurcating mode

Wear Testing of a Mechanized Percussion Well Drilling System for Water Access in West Africa

The Mechanized Percussion Well Drilling (MPWD) Collaboratory project is assisting in the development of a mechanized well drilling system for drilling shallow water wells in West Africa. Our client, Mr. Joseph Longenecker with Open Door Development (ODD), desires to make water wells accessible to all in this region, but has experienced difficulty drilling through hard soil layers. To overcome this problem, the MPWD team has worked closely with Mr. Joseph Longenecker to develop a mechanized percussion well drilling rig using a rubber friction wheel drive system that is capable of drilling through these harder layers. Currently, the MPWD team is working to provide recommendations to improve the useful service life of our client’s new, mechanized rig design. The MPWD team’s most recent work includes the design and fabrication of a testing rig to simulate the operation of our client’s full-size rig. The testing rig will allow our team to conduct fatigue testing on a model of the driveline system to analyze the wear patterns on the rubber friction wheel and to estimate its expected service life. The team has also performed a series of finite element analyses on the mast design of our client\u27s rig to evaluate working stresses under static loading and buckling, along with fatigue analysis, to confirm safe operation of the rig and to identify any elements that might require upgrades. Funding for this work provided by The Collaboratory for Strategic Partnerships and Applied Research.https://mosaic.messiah.edu/engr2022/1010/thumbnail.jp

Minimum taxes and repeated tax competition

An agreement about a lower bound for admissible tax rates can reduce the equilibrium tax rate (and thus welfare) in tax competition among fully symmetric countries. This is shown in an infinitely repeated game where the stage game describes the standard tax competition model with source-based taxes and symmetric countries. Repeated interaction may allow countries to sustain cooperation through implicit contracts. Lower bounds on tax rates ('minimum taxes') restrict the ability of countries to punish deviators. This makes cooperation harder to sustain. The introduction of a lower bound on feasible tax rates may thus harm all countries

The Welfare Effects of Attracting Foreign Direct Investment in the Presence of Unemployment

We develop a 2×2×2 model with the following features: (1) one sector is perfectly competitive while the other is oligopolistic; (2) one country has unemployment while the other attains full employment; (3) oligopolists move internationally; and (4) the ownership of each oligopolist is internationally shared. The welfare effects of various tax-cum-subsidies are examined. If the oligopolistic sector is capital intensive, subsidizing the oligopolists' profits, inflows, production or employment is more likely to harm the country. The number of domestically based oligopolists, the volume of domestic demand for the oligopoly-produced commodity, and the country's ownership share of oligopolists also influence the effect

Cross-Border Group-Taxation and Loss-Offset in the EU - An Analysis for CCCTB (Common Consolidated Corporate Tax Base) and Etas (European Tax Allocation System)

The European Commission proposed to replace the currently existing Separate Accounting by an EU-wide tax system based on a Common Consolidated Corporate Tax Base (CCCTB). Besides the CCCTB, there is an alternative tax reform proposal, the European Tax Allocation System (ETAS). In a dynamic capital budgeting model we analyze the impacts of selected loss-offset limitations currently existing in the EU under both concepts on corporate crossborder real investments of MNE. The analyses show that replacing Separate Accounting by either concept can lead to increasing profitability due to cross-border loss compensation. However, if the profitability increases, the study indicates that the main criteria of decisions on location are the tax rate divergences within the EU Member States. High tax rate differentials in the Member States imply significant redistribution of tax payments under CCCTB and ETAS. The results clarify that in both reform proposals tax payment reallocations occur in favor of the holding. National loss-offset limitations and minimum taxation concepts in tendency lose their impact on the profitability under both proposals. However, we found scenarios in which national minimum taxation can encroach upon the group level, although in our model the minimum taxation's impacts seem to be slight. Moreover, we identify harmful paradoxes in ETAS due to the tax credit mechanism. Our results can contribute to the current discussion on corporate group tax harmonization within the EU and other economic zones, e.g. the US, and help to anticipate the tax effects of lossoffset restrictions under the respective tax systems

Cross-Border Acquisitions and Corporate Taxes: Efficiency and Tax Revenues

We find that reduced foreign corporate taxes may lead to inefficient foreign acquisitions if complementarities between foreign and domestic assets are low, and to efficient foreign acquisitions if such complementarities are high. Moreover, with large complementarities, foreign acquisitions can increase domestic tax revenues. The reason is that in the bidding competition between the foreign firms, all benefits from the acquisition, including tax advantages and evaded taxes, are competed away and captured by the domestic seller which, in turn, pays capital gains tax on the proceeds. Technical issues in the tax code, such as the treatment of goodwill deductibility, is also shown to crucially affect the pattern of foreign acquisitions