Is the Tsallis entropy stable?

The question of whether the Tsallis entropy is Lesche-stable is revisited. It is argued that when physical averages are computed with the escort probabilities, the correct application of the concept of Lesche-stability requires use of the escort probabilities. As a consequence, as shown here, the Tsallis entropy is unstable but the thermodynamic averages are stable. We further show that Lesche stability as well as thermodynamic stability can be obtained if the homogeneous entropy is used as the basis of the formulation of non-extensive thermodynamics. In this approach, the escort distribution arises naturally as a secondary structure.Comment: 6 page

PPl 15: The First Brown Dwarf Spectroscopic Binary

PPl 15 is the first object to have been confirmed as a brown dwarf by the lithium test (in 1995), though its inferred mass was very close to the substellar limit. It is a member of the Pleiades open cluster. Its position in a cluster color-magnitude diagram suggested that it might be binary, and preliminary indications that it is a double-lined spectroscopic binary were reported by us in 1997. Here we report on the results of a consecutive week of Keck HIRES observations of this system, which yield its orbit. It has a period of about 5.8 days, and an eccentricity of 0.4+/-0.05. The rotation of the stars is slow for this class of objects. Because the system luminosity is divided between 2 objects with a mass ratio of 0.85, this renders each of them an incontrovertible brown dwarf, with masses between 60-70 jupiters. We show that component B is a little redder than A by studying their wavelength-dependent line ratios, and that this variation is compatible with the mass ratio. We confirm that the system has lithium, but cannot support the original conclusion that it is depleted (which would be surprising, given the new masses). This is a system of very close objects which, if they had combined, would have produced a low mass star. We discuss the implications of this discovery for the theories of binary formation and formation of very low mass objects.Comment: Latex, 18 pages, 4 figures, submitted to Astron.

The Public Resource Management Game

Use of public resources for private economic gain is a longstanding, contested political issue. Public resources generate benefits beyond commodity uses, including recreation, environmental and ecological conservation and preservation, and existence and aesthetic values. We analyze this problem using a dynamic resource use game. Low use fees let commodity users capture more of the marginal benefit from private use. This increases the incentive to comply with government regulations. Optimal contracts therefore include public use fees that are lower than private rates. The optimal policy also includes random monitoring to prevent strategic learning and cheating on the use agreements and to avoid wasteful efforts to disguise noncompliant behavior. An optimal policy also includes a penalty for cheating beyond terminating the use contract. This penalty must be large enough that the commodity user who would gain the most from noncompliance experiences a negative expected net return.Renewable resources, public resources policy, optimal contracts

The impact of population-based faecal occult blood test screening on colorectal cancer mortality:a matched cohort study

BACKGROUND: Randomised trials show reduced colorectal cancer (CRC) mortality with faecal occult blood testing (FOBT). This outcome is now examined in a routine, population-based, screening programme. METHODS: Three biennial rounds of the UK CRC screening pilot were completed in Scotland (2000–2007) before the roll out of a national programme. All residents (50–69 years) in the three pilot Health Boards were invited for screening. They received a FOBT test by post to complete at home and return for analysis. Positive tests were followed up with colonoscopy. Controls, selected from non-pilot Health Boards, were matched by age, gender, and deprivation and assigned the invitation date of matched invitee. Follow-up was from invitation date to 31 December 2009 or date of death if earlier. RESULTS: There were 379 655 people in each group (median age 55.6 years, 51.6% male). Participation was 60.6%. There were 961 (0.25%) CRC deaths in invitees, 1056 (0.28%) in controls, rate ratio (RR) 0.90 (95% confidence interval (CI) 0.83–0.99) overall and 0.73 (95% CI 0.65–0.82) for participants. Non-participants had increased CRC mortality compared with controls, RR 1.21 (95% CI 1.06–1.38). CONCLUSION: There was a 10% relative reduction in CRC mortality in a routine screening programme, rising to 27% in participants

Novel Methods for Determining Effective Interactions for the Nuclear Shell Model

The Contractor Renormalization (CORE) method is applied in combination with modern effective-theory techniques to the nuclear many-body problem. A one-dimensional--yet ``realistic''--nucleon-nucleon potential is introduced to test these novel ideas. It is found that the magnitude of ``model-space'' (CORE) corrections diminishes considerably when an effective potential that eliminates the hard-momentum components of the potential is first introduced. As a result, accurate predictions for the ground-state energy of the there-body system are made with relatively little computational effort when both techniques are used in a complementary fashion.Comment: 14 pages, 5 figures and 2 tabl

Density Functional Theory of Inhomogeneous Liquids: II. A Fundamental Measure Approach

Previously, it has been shown that the direct correlation function for a Lennard-Jones fluid could be modeled by a sum of that for hard-spheres, a mean-field tail and a simple linear correction in the core region constructed so as to reproduce the (known) bulk equation of state of the fluid(Lutsko, JCP 127, 054701 (2007)). Here, this model is combined with ideas from Fundamental Measure Theory to construct a density functional theory for the free energy. The theory is shown to accurately describe a range of inhomogeneous conditions including the liquid-vapor interface, the fluid in contact with a hard wall and a fluid confined in a slit pore. The theory gives quantitatively accurate predictions for the surface tension, including its dependence on the potential cutoff. It also obeys two important exact conditions: that relating the direct correlation function to the functional derivative of the free energy with respect to density, and the wall theorem.Comment: to appear in J. Chem. Phy

Quantum transport in carbon nanotubes

Carbon nanotubes are a versatile material in which many aspects of condensed matter physics come together. Recent discoveries, enabled by sophisticated fabrication, have uncovered new phenomena that completely change our understanding of transport in these devices, especially the role of the spin and valley degrees of freedom. This review describes the modern understanding of transport through nanotube devices. Unlike conventional semiconductors, electrons in nanotubes have two angular momentum quantum numbers, arising from spin and from valley freedom. We focus on the interplay between the two. In single quantum dots defined in short lengths of nanotube, the energy levels associated with each degree of freedom, and the spin-orbit coupling between them, are revealed by Coulomb blockade spectroscopy. In double quantum dots, the combination of quantum numbers modifies the selection rules of Pauli blockade. This can be exploited to read out spin and valley qubits, and to measure the decay of these states through coupling to nuclear spins and phonons. A second unique property of carbon nanotubes is that the combination of valley freedom and electron-electron interactions in one dimension strongly modifies their transport behaviour. Interaction between electrons inside and outside a quantum dot is manifested in SU(4) Kondo behavior and level renormalization. Interaction within a dot leads to Wigner molecules and more complex correlated states. This review takes an experimental perspective informed by recent advances in theory. As well as the well-understood overall picture, we also state clearly open questions for the field. These advances position nanotubes as a leading system for the study of spin and valley physics in one dimension where electronic disorder and hyperfine interaction can both be reduced to a very low level.Comment: In press at Reviews of Modern Physics. 68 pages, 55 figure

Gas-Liquid Nucleation in Two Dimensional System

We study the nucleation of the liquid phase from a supersaturated vapor in two dimensions (2D). Using different Monte Carlo simulation methods, we calculate the free energy barrier for nucleation, the line tension and also investigate the size and shape of the critical nucleus. The study is carried out at an intermediate level of supersaturation(away from the spinodal limit). In 2D, a large cut-off in the truncation of the Lennard-Jones (LJ) potential is required to obtain converged results, whereas low cut-off (say, $2.5\sigma$ is generally sufficient in three dimensional studies, where $\sigma$ is the LJ diameter) leads to a substantial error in the values of line tension, nucleation barrier and characteristics of the critical cluster. It is found that in 2D, the classical nucleation theory (CNT) fails to provide a reliable estimate of the free energy barrier. It underestimates the barrier by as much as 70% at the saturation-ratio S=1.1 (defined as S=P/PC, where PC is the coexistence pressure at reduced temperature $T^{\star}= 0.427$). Interestingly, CNT has been found to overestimate the nucleation free energy barrier in three dimensional (3D)systems near the triple point. In fact, the agreement with CNT is worse in 2D than in 3D. Moreover, the existing theoretical estimate of the line tension overestimates the value significantly.Comment: 24 pages, 8 figure