``Weather'' Records: Musings on Cold Days after a Long Hot Indian Summer

We present a simple, pedagogical introduction to the statistics of extreme values. Motivated by a string of record high temperatures in December 1998, we consider the distribution, averages and lifetimes for a simplified model of such ``records.'' Our ``data'' are sequences of independent random numbers all of which are generated from the same probability distribution. A remarkable universality emerges: a number of results, including the lifetime histogram, are universal, that is, independent of the underlying distribution.Comment: 14 pages, 3 figures. Invited paper for American Journal of Physic

Convection cells induced by spontaneous symmetry breaking

Ubiquitous in nature, convection cells are a clear signature of systems out-of-equilibrium. Typically, they are driven by external forces, like gravity (in combination with temperature gradients) or shear. In this article, we show the existence of such cells in possibly the simplest system, one that involves only a temperature gradient. In particular, we consider an Ising lattice gas on a square lattice, in contact with two thermal reservoirs, one at infinite temperature and another at $T$. When this system settles into a non-equilibrium stationary state, many interesting phenomena exist. One of these is the emergence of convection cells, driven by spontaneous symmetry breaking when $T$ is set below the critical temperature.Comment: published version, 2 figures, 5 page

The effect of demographic changes on saving for life cycle motives in developing countries

If developing countries follow the same paths that industrialized countries have followed, saving for retirement will initially become more important as the population growth rate declines. To calculate the potential importance of life-cycle savings (saving for retirement), the paper presents a simulation model that translates demographic projections into savings-rate projections. It simulated aggregate rates for life-cycle savings for Brazil, China, Korea, Mexico, Nigeria, Pakistan and Turkey. The savings rates increase 5 or 6 percentage points when the last baby boomers enter the work force and begin to save after their children leave home. The effect on life-cycle savings is dramatic; the effect on total savings rates which are often three or four times as high, is not. Simulated life-cycle savings rates peak at an absolute 10 percent or less in all cases. The patterns of these projections seem robust with regard to assumptions about productivity growth, interest rates, and age-specific participation in the labor force.Banks&Banking Reform,Environmental Economics&Policies,Economic Theory&Research,Health Monitoring&Evaluation,Inequality

Borrowing, resource transfers, and external shocks to developing countries : historical and counterfactual

Since the late 1970's the buildup and servicing of external debt has dominated the economic situation in many developing countries. This paper gathers some statistical evidence on the magnitude of lending and repayment and on the question of whether repayment reduces the resources available for development. The evidence largely confirms commonly held beliefs. Although most debtor countries have made net transfers of resources to creditors, middle-income countries that have not had to reschedule their debts have averaged smaller net transfers than those that did reschedule. Adverse changes in terms of trade since 1978 accounted for most of the debt buildup in many non-oil developing countries. The mostly favorable terms of trade for oil exporters, on the other hand, gave them large gains that could have more than covered the losses of the oil importing developing countries. Heavy borrowing by oil exporters during favorable times seems to have been a major factor in precipitating the debt crisis. Since the debt crisis, the highly indebted countries have greatly increased their official borrowing. Increased official lending might help the resource balance and domestic investment of lower-income countries more than those of middle-income countries with high commercial debts.Environmental Economics&Policies,Economic Theory&Research,Banks&Banking Reform,Strategic Debt Management,Financial Intermediation

Dynamic scaling in vacancy-mediated disordering

We consider the disordering dynamics of an interacting binary alloy with a small admixture of vacancies which mediate atom-atom exchanges. Starting from a perfectly phase-segregated state, the system is rapidly heated to a temperature in the disordered phase. A suitable disorder parameter, namely, the number of broken bonds, is monitored as a function of time. Using Monte Carlo simulations and a coarse-grained field theory, we show that the late stages of this process exhibit dynamic scaling, characterized by a set of scaling functions and exponents. We discuss the universality of these exponents and comment on some subtleties in the early stages of the disordering process.Comment: 15 pages, 6 figure

Extraordinary variability and sharp transitions in a maximally frustrated dynamic network

Using Monte Carlo and analytic techniques, we study a minimal dynamic network involving two populations of nodes, characterized by different preferred degrees. Reminiscent of introverts and extroverts in a population, one set of nodes, labeled \textit{introverts} ($I$), prefers fewer contacts (a lower degree) than the other, labeled \textit{extroverts} ($E$). As a starting point, we consider an \textit{extreme} case, in which an $I$ simply cuts one of its links at random when chosen for updating, while an $E$ adds a link to a random unconnected individual (node). The model has only two control parameters, namely, the number of nodes in each group, $N_{I}$ and $N_{E}$). In the steady state, only the number of crosslinks between the two groups fluctuates, with remarkable properties: Its average ($X$) remains very close to 0 for all $N_{I}>N_{E}$ or near its maximum ($\mathcal{N}\equiv N_{I}N_{E}$) if $N_{I}<N_{E}$. At the transition ($N_{I}=N_{E}$), the fraction $X/\mathcal{N}$ wanders across a substantial part of $[0,1]$, much like a pure random walk. Mapping this system to an Ising model with spin-flip dynamics and unusual long-range interactions, we note that such fluctuations are far greater than those displayed in either first or second order transitions of the latter. Thus, we refer to the case here as an `extraordinary transition.' Thanks to the restoration of detailed balance and the existence of a `Hamiltonian,' several qualitative aspects of these remarkable phenomena can be understood analytically.Comment: 6 pages, 3 figures, accepted for publication in EP