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

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.

Disequilibrium Dynamics with Inventories and Anticipatory Price-Setting:Some Impirical Results

The basic assumption of this paper is an attempt to be specific about price formation while retaining a fixed-price, quantity-constrained equilibration in the short-run. The second theme of this paper is the role of inventories in macrodynamics a topic of long-recognized importance, but one which has not received much attention within the disequilibrium literature. We will analyze how the level of inventories interacts with the level of prices and wages, and how the spillover effects in a fixed-price equilibrium produce certain testable characteristics in macro time series data. We will argue that these can be used to discriminate between a model of the type we study and the analogous flexible-price system. In section 2 we set out the basic model and discuss its assumptions. Section 3 derives the short-run quantity-constrained equilibrium as it depends on initial inventory stocks and on the random disturbances within the period. Section 4 presents, for comparison purposes, the analogous results under conditions of full price flexibility after these shocks are realized. Sections 5 and 6 are the heart of the paper. We first derive the probabilistic nature of the equilibrium as it depends upon the underlying stochastic disturbances. The probabilities of different types of quantity constrained equilibria can be compared. Then, we use these results to present the dynamics of inventory behavior and the statistical relationships between real wages, inventories and employment. We emphasize the possibility of using this type of analysis to test the disequilibrium hypothesis with anticipatory pricing, against the market-clearing assumptions.