Pulling Pinned Polymers and Unzipping DNA

We study a class of micromanipulation experiments, exemplified by the pulling apart of the two strands of double-stranded DNA (dsDNA). When the pulling force is increased to a critical value, an ``unzipping'' transition occurs. For random DNA sequences with short-ranged correlations, we obtain exact results for the number of monomers liberated and the specific heat, including the critical behavior at the transition. Related systems include a random heteropolymer pulled away from an adsorbing surface and a vortex line in a type II superconductor tilted away from a fragmented columnar defect.Comment: 4 pages, 1 EPS figure; revised references and very brief discussion of order of the transition added; to appear in Phys. Rev. Let

Statistical mechanics of thin spherical shells

We explore how thermal fluctuations affect the mechanics of thin amorphous spherical shells. In flat membranes with a shear modulus, thermal fluctuations increase the bending rigidity and reduce the in-plane elastic moduli in a scale-dependent fashion. This is still true for spherical shells. However, the additional coupling between the shell curvature, the local in-plane stretching modes and the local out-of-plane undulations, leads to novel phenomena. In spherical shells thermal fluctuations produce a radius-dependent negative effective surface tension, equivalent to applying an inward external pressure. By adapting renormalization group calculations to allow for a spherical background curvature, we show that while small spherical shells are stable, sufficiently large shells are crushed by this thermally generated "pressure". Such shells can be stabilized by an outward osmotic pressure, but the effective shell size grows non-linearly with increasing outward pressure, with the same universal power law exponent that characterizes the response of fluctuating flat membranes to a uniform tension.Comment: 16 pages, 6 figure

Survival Probabilities at Spherical Frontiers

Motivated by tumor growth and spatial population genetics, we study the interplay between evolutionary and spatial dynamics at the surfaces of three-dimensional, spherical range expansions. We consider range expansion radii that grow with an arbitrary power-law in time: $R(t)=R_0(1+t/t^*)^{\Theta}$, where $\Theta$ is a growth exponent, $R_0$ is the initial radius, and $t^*$ is a characteristic time for the growth, to be affected by the inflating geometry. We vary the parameters $t^*$ and $\Theta$ to capture a variety of possible growth regimes. Guided by recent results for two-dimensional inflating range expansions, we identify key dimensionless parameters that describe the survival probability of a mutant cell with a small selective advantage arising at the population frontier. Using analytical techniques, we calculate this probability for arbitrary $\Theta$. We compare our results to simulations of linearly inflating expansions ($\Theta=1$ spherical Fisher-Kolmogorov-Petrovsky-Piscunov waves) and treadmilling populations ($\Theta=0$, with cells in the interior removed by apoptosis or a similar process). We find that mutations at linearly inflating fronts have survival probabilities enhanced by factors of 100 or more relative to mutations at treadmilling population frontiers. We also discuss the special properties of "marginally inflating" $(\Theta=1/2)$ expansions.Comment: 35 pages, 11 figures, revised versio

THE ANDEAN PRICE BAND SYSTEM: EFFECTS ON PRICES, PROTECTION AND PRODUCER WELFARE

The Andean Community's Price Band System (APBS), introduced in 1995, had the announced goal of reducing domestic price instability by buffering fluctuations in international prices through use of a variable import tariff. This paper evaluates the effects of the Andean Price Band System on domestic producer price variability, levels of nominal protection and changes in producer welfare. Application is made to four important food products - maize, rice, sugar and milk - in Colombia, Ecuador and Venezuela, from the period 1990 to 1998. The effects of the APBS on producer price variability are analyzed through 1) comparing coefficients of variation of detrended, monthly deseasonalized real prices before and after the harmonization of the APBS in 1995, and 2) variance decomposition of real domestic prices. For Colombia and Ecuador, the APBS is shown to have successfully reduced real price instability below levels of instability which existed prior to its introduction. Real exchange rate instability also decreased sharply in these two countries following introduction of the APBS. In Venezuela, real price instability is shown to have increased following introduction of the APBS, while real exchange rate instability was unchanged. The APBS' effects on producer price protection are examined through estimation of average nominal protection coefficients for the twelve country-commodity combinations identified above before and after the introduction of the APBS. Results show that in all three countries and four virtually all products, the APBS contributed to increased producer protection. Finally, this paper uses a variant of the Newbery-Stiglitz approach to calculate efficiency benefits due to risk reduction among producers and the transfer benefits created by redistributing income among producers, consumers and government. The results show that the risk reduction benefits created by the APBS are small. Similarly, the income transfer effects, though larger, are also low, and both contribute to generally low levels of estimated producer welfare effects. Overall, the paper concludes that the APBS has been of limited usefulness as a policy instrument designed to reduce producer price variability in an economically efficient manner.Andean Community, price band system, agricultural prices, price stabilization, Demand and Price Analysis,