An Even Sterner Review: Introducing Relative Prices into the Discounting Debate

The Stern Review has had a major influence on the policy discussion on climate change. One reason is that the report has raised the estimated cost of unmitigated climate damages by an order of magnitude compared to most earlier estimates, leading to a call for strong and urgent action on climate change. Not surprisingly, severe criticism has been levied against the report by authors who think that these results hinge mainly on the use of a discount rate that is too low. Here we discuss the Ramsey rule for the discount rates and its implications for the economics of climate change. While we find no strong objections to the discounting assumptions adopted in the Stern Review, our main point is that the conclusions reached in the review can be justified on other grounds than by using a low discount rate. We argue that nonmarket damages from climate change are probably underestimated and that future scarcities that will be induced by the changing composition of the economy and climate change should lead to rising relative prices for certain goods and services, raising the estimated damage of climate change and counteracting the effect of discounting. We build our analysis on earlier research (Hoel and Sterner 2007) that has shown that the Ramsey discounting formula is somewhat modified in a two-sector economy with differential growth rates. Most importantly, such a model is characterized by changing relative prices, something that has major implications for a correct valuation of future climate damages. We introduce these results into a slightly modified version of the DICE model (Nordhaus 1994) and find that taking relative prices into account can have as large an effect on economically warranted abatement levels as can a low discount rate.discounting, relative prices, Ramsey, climate damage

Nanodroplets on rough hydrophilic and hydrophobic surfaces

We present results of Molecular Dynamics (MD) calculations on the behavior of liquid nanodroplets on rough hydrophobic and hydrophilic solid surfaces. On hydrophobic surfaces, the contact angle for nanodroplets depends strongly on the root mean square roughness amplitude, but it is nearly independent of the fractal dimension of the surface. Since increasing the fractal dimension increases the short-wavelength roughness, while the long-wavelength roughness is almost unchanged, we conclude that for hydrophobic interactions the short-wavelength (atomistic) roughness is not very important. We show that the nanodroplet is in a Cassie-like state. For rough hydrophobic surfaces, there is no contact angle hysteresis due to strong thermal fluctuations, which occur at the liquid-solid interface on the nanoscale. On hydrophilic surfaces, however, there is strong contact angle hysteresis due to higher energy barrier. These findings may be very important for the development of artificially biomimetic superhydrophobic surfaces.Comment: 15 pages, 25 figures. Minimal changes with respect to the previous one. A few small improvements, references updated, added the reference to the published paper. Previous work on the same subject: arXiv:cond-mat/060405

A multiscale Molecular Dynamics approach to Contact Mechanics

The friction and adhesion between elastic bodies are strongly influenced by the roughness of the surfaces in contact. Here we develop a multiscale molecular dynamics approach to contact mechanics, which can be used also when the surfaces have roughness on many different length-scales, e.g., for self affine fractal surfaces. As an illustration we consider the contact between randomly rough surfaces, and show that the contact area varies linearly with the load for small load. We also analyze the contact morphology and the pressure distribution at different magnification, both with and without adhesion. The calculations are compared with analytical contact mechanics models based on continuum mechanics.Comment: Format Revtex4, two columns, 13 pages, 19 pictures. Submitted for publication in the European Physical Journal E. Third revision with minimal changes: Corrected a few mistypin

Sealing is at the Origin of Rubber Slipping on Wet Roads

Loss of braking power and rubber skidding on a wet road is still an open physics problem, since neither the hydrodynamical effects nor the loss of surface adhesion that are sometimes blamed really manage to explain the 20-30% observed loss of low speed tire-road friction. Here we advance a novel mechanism based on sealing of water-filled substrate pools by the rubber. The sealed-in water effectively smoothens the substrate, thus reducing the viscoelastic dissipation in bulk rubber induced by surface asperities, well established as a major friction contribution. Starting with the measured spectrum of asperities one can calculate the water-smoothened spectrum and from that the predicted friction reduction, which is of the right magnitude. The theory is directly supported by fresh tire-asphalt friction data.Comment: 5 pages, 4 figures. Published on Nature Materials (November 7th 2004

Electronic friction and liquid-flow-induced voltage in nanotubes

A recent exciting experiment by Ghosh et al. reported that the flow of an ion-containing liquid such as water through bundles of single-walled carbon nanotubes induces a voltage in the nanotubes that grows logarithmically with the flow velocity v0. We propose an explanation for this observation. Assuming that the liquid molecules nearest the nanotube form a 2D solid-like monolayer pinned through the adsorbed ions to the nanotubes, the monolayer sliding will occur by elastic loading followed by local yield (stick-slip). The drifting adsorbed ions produce a voltage in the nanotube through electronic friction against free electrons inside the nanotube. Thermally excited jumps over force-biased barriers, well-known in stick-slip, can explain the logarithmic voltage growth with flow velocity. We estimate the short circuit current and the internal resistance of the nanotube voltage generator.Comment: 8 pages, 3 figures; published on PRB (http://link.aps.org/abstract/PRB/v69/e235410) and on the Virtual Journal of Nanoscale Science and Technology (http://www.vjnano.org, July 14, 2002, Vol. 10, Iss. 2

Influence of surface roughness on superhydrophobicity

Superhydrophobic surfaces, with liquid contact angle theta greater than 150 degree, have important practical applications ranging from self-cleaning window glasses, paints, and fabrics to low-friction surfaces. Many biological surfaces, such as the lotus leaf, have hierarchically structured surface roughness which is optimized for superhydrophobicity through natural selection. Here we present a molecular dynamics study of liquid droplets in contact with self-affine fractal surfaces. Our results indicate that the contact angle for nanodroplets depends strongly on the root-mean-square surface roughness amplitude but is nearly independent of the fractal dimension D_f of the surface.Comment: 5 Pages, 6 figures. Minimal changes with respect to the previous versio

How do liquids confined at the nanoscale influence adhesion?

Liquids play an important role in adhesion and sliding friction. They behave as lubricants in human bodies especially in the joints. However, in many biological attachment systems they acts like adhesives, e.g. facilitating insects to move on ceilings or vertical walls. Here we use molecular dynamics to study how liquids confined at the nanoscale influence the adhesion between solid bodies with smooth and rough surfaces. We show that a monolayer of liquid may strongly affect the adhesion.Comment: 5 pages, 9 color figures. Some figures are in Postscript Level 3 format. Minimal changes with respect to the previous version. Added doi and reference to the published article also inside the pape

Impact of molecular structure on the lubricant squeeze-out between curved surfaces with long range elasticity

The properties of butane (C4H10) lubricants confined between two approaching solids are investigated by a model that accounts for the curvature and elastic properties of the solid surfaces. We consider the linear n-butane and the branched iso-butane. For the linear molecule, well defined molecular layers develop in the lubricant film when the width is of the order of a few atomic diameters. The branched iso-butane forms more disordered structures which permit it to stay liquid-like at smaller surface separations. During squeezing the solvation forces show oscillations corresponding to the width of a molecule. At low speeds (< 0.1 m/s) the last layers of iso-butane are squeezed out before those of n-butane. Since the (interfacial) squeezing velocity in most practical applications is very low when the lubricant layer has molecular thickness, one expects n-butane to be a better boundary lubricant than iso-butane. N-butane possessing a slightly lower viscosity at high pressures, our result refutes the view that squeeze out should be harder for higher viscosities, on the other hand our results are consistent with wear experiments in which n-butane were shown to protect steel surfaces better than iso-butane.Comment: 7 pages, 10 figures, format revtex. Submitted to J. Chem. Phy

PCN46 EPOIETIN ALPHA TREATMENT FOR CANCER PATIENTS WITH CHEMOTHERAPY INDUCED ANAEMIA–A COSTEFFECTIVENESS ANALYSIS FOR SWEDEN

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