Observers for compressible Navier-Stokes equation

We consider a multi-dimensional model of a compressible fluid in a bounded domain. We want to estimate the density and velocity of the fluid, based on the observations for only velocity. We build an observer exploiting the symmetries of the fluid dynamics laws. Our main result is that for the linearised system with full observations of the velocity field, we can find an observer which converges to the true state of the system at any desired convergence rate for finitely many but arbitrarily large number of Fourier modes. Our one-dimensional numerical results corroborate the results for the linearised, fully observed system, and also show similar convergence for the full nonlinear system and also for the case when the velocity field is observed only over a subdomain

Nonmonotonic dependence of the absolute entropy on temperature in supercooled Stillinger-Weber silicon

Using a recently developed thermodynamic integration method, we compute the precise values of the excess Gibbs free energy (G^e) of the high density liquid (HDL) phase with respect to the crystalline phase at different temperatures (T) in the supercooled region of the Stillinger-Weber (SW) silicon [F. H. Stillinger and T. A. Weber, Phys. Rev. B. 32, 5262 (1985)]. Based on the slope of G^e with respect to T, we find that the absolute entropy of the HDL phase increases as its enthalpy changes from the equilibrium value at T \ge 1065 K to the value corresponding to a non-equilibrium state at 1060 K. We find that the volume distribution in the equilibrium HDL phases become progressively broader as the temperature is reduced to 1060 K, exhibiting van-der-Waals (VDW) loop in the pressure-volume curves. Our results provides insight into the thermodynamic cause of the transition from the HDL phase to the low density phases in SW silicon, observed in earlier studies near 1060 K at zero pressure.Comment: This version is accepted for publication in Journal of Statistical Physics (11 figures, 1 table

The exchange rate and purchasing power parity: extending the theory and tests.

This paper analyzes the exchange rate in a ``no-arbitrage' or ``real business cycle' equilibrium model and provides empirical evidence for this model vis-a-vis PPP. Our contribution is to show, based on a generalization of the equilibrium model of exchange rates, that (i) the test equation linking the exchange rate to fundamentals should allow for international heterogeneity in time preferences or risk attitudes, as well as noise---that is, the model should not be tested as an exact relation; (ii) empirical work should use levels of variables rather than first differences; (iii) tests on the existence of long-run relations should be complemented by tests on the signs of the coefficients; (iv) the specification of the regression should offer demonstrated advantages over alternatives, and the significance tests should not rely on asymptotic distributions; and (v) the tests should steer clear of countries that have imposed, for most of the period, capital restrictions or exchange controls, thus violating the integrated-markets assumption of the model. Our empirical work shows that, as a long-run relation, the generalized model outperforms PPP.Purchasing; Purchasing power; Theory; Equilibrium; Model; International; Risk; Variables; Advantages; Distribution;

U.S. Trade in Information-Intensive Services

Trade in services has increased significantly and the United States has been a leader in services trade. The U.S. not only accounts for the largest share of world trade in private services but also runs a substantial amount of surplus in services trade. One important trend has been the rapid growth of U.S. trade in information-intensive services. This paper examines the growth and patterns in U.S. exports and imports of various information-intensive services. The analysis indicates that trade in business, professional, and technical services; financial services; and insurance has experienced the most rapid growth in recent times. This paper further discusses some of the intuitively plausible explanations for the growth of trade in information-intensive services.

The equilibrium approach to exchange rates: theory and tests.

We characterize the equilibrium exchange rate in a general equilibrium economy without imposing strong restrictions on the output processes, preferences, or commodity market imperfections. The nomial exchange rate is determined by differences in initial wealths - the currencies of richer countries tend to be overvalued, by PPP standards - and by differences of marginal indirect utilities of total nominal spending. Changes in the exchange rate mirror differences in growth rates of real spending weighted by relative risk-aversion (which can be time-varying and can differ across countries), and, in the case of non-homothetic utility functions, differences in inflation rates computed from marginal spending weights. Thus, standard regression or cointegration tests of PPP suffer from missing-variables biases and ignore variations in risk aversions across countries and over time. We also present cointegration test of the homothecy/ CRRA version of the model. When nominal spending is given an independent role (next to prices) in the short-term dynamics, both PPP and the CRRA model become acceptable.Equilibrium; Theory; Trade;