Excitations of amorphous solid helium

We present neutron scattering measurements of the dynamic structure factor, $S(Q,\omega)$, of amorphous solid helium confined in 47 $\AA$ pore diameter MCM-41 at pressure 48.6 bar. At low temperature, $T$ = 0.05 K, we observe $S(Q,\omega)$ of the confined quantum amorphous solid plus the bulk polycrystalline solid between the MCM-41 powder grains. No liquid-like phonon-roton modes, other sharply defined modes at low energy ($\omega<$ 1.0 meV) or modes unique to a quantum amorphous solid that might suggest superflow are observed. Rather the $S(Q,\omega)$ of confined amorphous and bulk polycrystalline solid appear to be very similar. At higher temperature ($T>$ 1 K), the amorphous solid in the MCM-41 pores melts to a liquid which has a broad $S(Q,\omega)$ peaked near $\omega \simeq$ 0 characteristic of normal liquid $^4$He under pressure. Expressions for the $S(Q,\omega)$ of amorphous and polycrystalline solid helium are presented and compared. In previous measurements of liquid $^4$He confined in MCM-41 at lower pressure the intensity in the liquid roton mode decreases with increasing pressure until the roton vanishes at the solidification pressure (38 bars), consistent with no roton in the solid observed here

Federal mandates by popular demand

This paper proposes a new framework for studying federal mandates regarding public policies in areas such as environmental quality, public health, highway safety, and the provision of local public goods. Voters have single-peaked preferences along a single policy dimension. There are two levels of government, federal and local. The federal level can constrain local policy by mandating a minimum (or maximum) policy. Localities are free to adopt any policy satisfying the constraint imposed by the federal mandate. We show that voters choose federal mandates that are too strict, which leads to excessively severe mandates. We show that similar results can obtain when federal provision of the public-provided good is more efficient than local provision

Transverse Contraction Criteria for Existence, Stability, and Robustness of a Limit Cycle

This paper derives a differential contraction condition for the existence of an orbitally-stable limit cycle in an autonomous system. This transverse contraction condition can be represented as a pointwise linear matrix inequality (LMI), thus allowing convex optimization tools such as sum-of-squares programming to be used to search for certificates of the existence of a stable limit cycle. Many desirable properties of contracting dynamics are extended to this context, including preservation of contraction under a broad class of interconnections. In addition, by introducing the concepts of differential dissipativity and transverse differential dissipativity, contraction and transverse contraction can be established for large scale systems via LMI conditions on component subsystems.Comment: 6 pages, 1 figure. Conference submissio

Output-Feedback Control of Nonlinear Systems using Control Contraction Metrics and Convex Optimization

Control contraction metrics (CCMs) are a new approach to nonlinear control design based on contraction theory. The resulting design problems are expressed as pointwise linear matrix inequalities and are and well-suited to solution via convex optimization. In this paper, we extend the theory on CCMs by showing that a pair of "dual" observer and controller problems can be solved using pointwise linear matrix inequalities, and that when a solution exists a separation principle holds. That is, a stabilizing output-feedback controller can be found. The procedure is demonstrated using a benchmark problem of nonlinear control: the Moore-Greitzer jet engine compressor model.Comment: Conference submissio

Fixed and Flexible Rates: A Renewal of The Debate

The paper reviews the extent to which a decade of analysis and experience has altered thinking about the choice of an exchange rate system. The advantages of flexible rates are viewed to have been exaggerated. They do not permit governments to have permanently higher rates of economic activity at the expense of higher inflation as some thought. Further, the slow speed of adjustment to relative price changes limits the contribution of flexible rates to external adjustment in the short-run, and the degree of insulation from external influences that they provide. Finally, flexible rates tend to be fluctuating rates, and, although there is little empirical evidence so far showing that the fluctuations have had adverse effects on trade and capital flows, the exchange rate instability more than any other factor has led to a certain disillusionment with the floating rate system. Notwithstanding the drawbacks of flexible rates, there will be a continuing need for exchange rate flexibility over the next few years, and some analysis is given of the problems of achieving greater stability under flexible rates or the requisite amount of flexibility under pegged rates.