Early time behavior of the order parameter coupled to a conserved density: A study in a semi-infinite geometry

We study the short time behavior of the order parameter coupled to a conserved field in semi-infinite geometry. The short time exponent, obtained by solving the one loop differential equations for the conserved density and the order parameter, agrees with the prediction from a scaling argument based on short distance expansion. The scaling analysis further shows that this exponent satisfies a scaling relation similar to that known in the case of a nonconserved order parameter without any coupling.Comment: 5 pages, latex, no figure

On the SL(2,Z) Covariant World-Sheet Action with Sources

We analyse various world-sheet properties of the $SL(2,Z)$ covariant type IIB string action by coupling it with $SL(2,Z)$ covariant source.Comment: 8 pages, harvmac, minor changes, journal versio

Polymers with Randomness: Phases and Phase Transitions

We discuss various aspects of the randomly interacting directed polymers with emphasis on the phases and phase transition. We also discuss the behaviour of overlaps of directed paths in a random medium.Comment: Invited talk at StatPhys, Calcutta 1995, to appear in Physica A; REVTEX, 2 figures on request (email: [email protected]

Robust Cyclical Growth

The stability of cyclical growth within the context of a model in Matsuyama (1999) is examined.It is shown that but for an extreme situation, the two-cycles are unique and a range of parameter values which imply the stability of such cyclical growth is derived. The growth enhancing property of 2-cycles are shown to be retained by any cycle; the results of simulation exercises carried out are reported to show that for very wide range of parameter values, such cyclical growth paths are stable and thus robustness of the conclusions are established. Finally, the configuration of parameters for which the dynamics exhibits complicated (chaotic) behavior is also identified.

Global Stability Conditions on the Plane

The paper considers price adjustment on the plane and derives global stability conditions for such dynamics. First, we examine the well-known Scarf Example, to obtain and analyze a global stability condition for this case. Next, for a general class of excess demand functions, a set of conditions is identified which guarantee not only convergence to some equilibrium but also robustness of these properties.