Convergence to equilibrium for the discrete coagulation-fragmentation equations with detailed balance

Under the condition of detailed balance and some additional restrictions on the size of the coefficients, we identify the equilibrium distribution to which solutions of the discrete coagulation-fragmentation system of equations converge for large times, thus showing that there is a critical mass which marks a change in the behavior of the solutions. This was previously known only for particular cases as the generalized Becker-D\"oring equations. Our proof is based on an inequality between the entropy and the entropy production which also gives some information on the rate of convergence to equilibrium for solutions under the critical mass.Comment: 28 page

Next--to--Leading Order Corrections to Meson Masses in the Heavy Quark Effective Theory

We use the QCD sum rule approach to calculate the splitting between vector and pseudoscalar mesons containing one light and one heavy quark, and the kinetic energy of the heavy quark. Our result for the splitting induced by the chromomagnetic interaction agrees to the experimental data on charm and beauty mesons. For the matrix element of the kinetic energy operator, we obtain the value $K=-(0.60\pm 0.10)\, {\rm GeV}^2$.Comment: 33 ps., PS figures included, requires REVTEX.3 and psfig, TUM-T31-42/93/R (additional contribution to kinetic energy taken into account, marginal changes in the results

Explicit results for all orders of the epsilon-expansion of certain massive and massless diagrams

An arbitrary term of the epsilon-expansion of dimensionally regulated off-shell massless one-loop three-point Feynman diagram is expressed in terms of log-sine integrals related to the polylogarithms. Using magic connection between these diagrams and two-loop massive vacuum diagrams, the epsilon-expansion of the latter is also obtained, for arbitrary values of the masses. The problem of analytic continuation is also discussed.Comment: 8 pages, late

Semileptonic D decay into scalar mesons: a QCD sum rule approach

Semileptonic decays of D-mesons into scalar hadronic states are investigated. Two extreme cases are considered: a) the meson decays directly into an uncorrelated scalar state of two two mesons and b) the decay proceeds via resonance formation. QCD sum rules including instanton contributions are used to calculate total and differential decay rates under the two assumptions.Comment: 18 pages, 9 figures, e-mail: [email protected]

Public rules about using and owning real estate in Cuba

The discussion on urban land continues to be absent in most of the specialized Cuban literature about planning and economic policies, despite its relevance. In very thorough essays about the present challenges and future development of the Cuban economy, nothing is said about the need for adequate public land policies and the implementation of public value capture mechanisms as part of the economic development of the country. The issue is complex, there is a void of almost half a century of not dealing with land value, but these reasons are not sufficient to justify the continued lack of vision in this direction, all the more when the Cuban cities are in desperate need to reverse the deterioration and stagnation that affects them. The Cuban state determines the general rules under which citizens and organisations may own and use real estate. These are rules about property rights and about the limitations - in compliance with aspects such as state security, environmental and heritage protection, economic development, social equity and human and civil rights – on exercising those rights. In doing this, the Cuban state is no different from other states: most states make such rules and enforce them when necessary. What is particular to Cuba is the content of those rules. In particular, the Cuban state has the monopoly to perform land development and management. There are public institutions to plan and deal with all of these aspects, and there are no recognised real estate markets in the country. Another important aspect is the utmost importance given to planning. But in spite of this, Cuban urban planners have rarely been certain of what will be built and where. The main reason for this may be that, despite the numerous master plans to study and anticipate development trends, most of the decisions ultimately involve top officials who envision the projects and establish the investment priorities according to the public interests or needs and the historical moment, irrespective of the plans. This article intends to give a clear picture of how things are done in the public sector, how the administration works, and under which legal framework. I will look at the physical planning system and its importance in the location and implementation of land use, investment projects and housing programs, and at the legal procedures that include licenses for construction, demolition, habitat and other licenses for heritage conservation and redevelopment. I will analyze the difficulties faced by the Cuban planning and legal system with respect to land and urban development, in the attempt to understand the limits imposed by the government on land and urban development, and I will explore to what extent those limits are to blame for the increasing irregularities and violations at all levels of the formal procedures for land and property. I will also introduce the public and personal rights concerning housing, buying and selling, permutes, donations and other tenure alternatives; and clarify the civil responsibilities, namely types of ownership, properties, property registers and so forth in order to expose the opportunities and accessibility of the system but also its limitations

Interaction of CO2 laser-modified nylon with osteoblast cells in relation to wettability

It has been amply demonstrated previously that CO2 lasers hold the ability to surface modify various polymers. In addition, it has been observed that these surface enhancements can augment the biomimetic nature of the laser irradiated materials. This research has employed a CO2 laser marker to produce trench and hatch topographical patterns with peak heights of around 1 μm on the surface of nylon 6,6. The patterns generated have been analysed using white light interferometery, optical microscopy and X-ray photoelectron spectroscopy was employed to determine the surface oxygen content. Contact angle measurements were used to characterize each sample in terms of wettability. Generally, it was seen that as a result of laser processing the contact angle, surface roughness and surface oxygen content increased whilst the apparent polar and total surface energies decreased. The increase in contact angle and reduction in surface energy components was found to be on account of a mixed intermediate state wetting regime owing to the change in roughness due to the induced topographical patterns. To determine the biomimetic nature of the modified and as-received control samples each one was seeded with 2×104 cells/ml normal human osteoblast cells and observed after periods of 24 hours and 4 days using optical microscopy and SEM to determine mean cell cover densities and variations in cell morphology. In addition a haeymocytometer was used to show that the cell count for the laser patterned samples had increased by up to a factor of 1.5 compared to the as-received control sample after 4 days of incubation. Significantly, it was determined that all laser-induced patterns gave rise to better cell response in comparison to the as-received control sample studied due to increased preferential cell growth on those surfaces with increased surface roughness

A Systematic Extended Iterative Solution for QCD

An outline is given of an extended perturbative solution of Euclidean QCD which systematically accounts for a class of nonperturbative effects, while allowing renormalization by the perturbative counterterms. Proper vertices Gamma are approximated by a double sequence Gamma[r,p], with r the degree of rational approximation w.r.t. the QCD mass scale Lambda, nonanalytic in the coupling g, and p the order of perturbative corrections in g-squared, calculated from Gamma[r,0] - rather than from the perturbative Feynman rules Gamma(0)(pert) - as a starting point. The mechanism allowing the nonperturbative terms to reproduce themselves in the Dyson-Schwinger equations preserves perturbative renormalizability and is tied to the divergence structure of the theory. As a result, it restricts the self-consistency problem for the Gamma[r,0] rigorously - i.e. without decoupling approximations - to the superficially divergent vertices. An interesting aspect of the scheme is that rational-function sequences for the propagators allow subsequences describing short-lived excitations. The method is calculational, in that it allows known techniques of loop computation to be used while dealing with integrands of truly nonperturbative content.Comment: 48 pages (figures included). Scope of replacement: correction of a technical defect; no changes in conten

The energy dependence of the hard exclusive diffractive processes in pQCD as the function of momentum transfer

We predict the dependence on energy of photo(electro) production processes: $\gamma(\gamma^*)+p\to V+ X$ with large rapidity gap at small x and large momentum $-t$ transferred to $V$ in pQCD. Here V is a heavy quarkonium ($J/\psi, \Upsilon$) or longitudinally polarized light vector meson (in the electroproduction processes), etc. In the kinematics of HERA we calculate the dependence on energy of cross sections of these processes as the function of momentum transfer $t$, photon virtuality $Q^2$ and/or quarkonium mass. In the kinematical region $Q_0^2\le -t\ll Q^2+M^2_V$ the nontrivial energy dependence of the cross section for the vector meson production due to the photon scattering off a parton follows within QCD from the summing of the double logarithmic terms. In the second regime $-t\ge Q^2+M^2_V$ within DGLAP approximation in all orders of perturbation theory the $q\bar q - {\rm parton}$ elastic cross section is energy independent. We show that the correct account of the double logarithmic terms and of the gluon radiation including kinematical constraints removes the disagreement between pQCD calculations and recent HERA experimental data. The explicit formula for the dependence of the differential cross section$\displaystyle{\frac{d^2\sigma}{dtdx_J}}$ of these processes on $s_{\gamma^*N}$ is obtained. We show that perturbative Pomeron type behavior may reveal itself only at energies significantly larger than those available at HERA. In addition we evaluate the energy dependence of DCVS processes.Comment: 22 pages, 4 figure

The spread of epidemic disease on networks

The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the so-called susceptible/infective/removed (SIR) models can be solved exactly on a wide variety of networks. In addition to the standard but unrealistic case of fixed infectiveness time and fixed and uncorrelated probability of transmission between all pairs of individuals, we solve cases in which times and probabilities are non-uniform and correlated. We also consider one simple case of an epidemic in a structured population, that of a sexually transmitted disease in a population divided into men and women. We confirm the correctness of our exact solutions with numerical simulations of SIR epidemics on networks.Comment: 12 pages, 3 figure

Randomly Crosslinked Macromolecular Systems: Vulcanisation Transition to and Properties of the Amorphous Solid State

As Charles Goodyear discovered in 1839, when he first vulcanised rubber, a macromolecular liquid is transformed into a solid when a sufficient density of permanent crosslinks is introduced at random. At this continuous equi- librium phase transition, the liquid state, in which all macromolecules are delocalised, is transformed into a solid state, in which a nonzero fraction of macromolecules have spontaneously become localised. This solid state is a most unusual one: localisation occurs about mean positions that are distributed homogeneously and randomly, and to an extent that varies randomly from monomer to monomer. Thus, the solid state emerging at the vulcanisation transition is an equilibrium amorphous solid state: it is properly viewed as a solid state that bears the same relationship to the liquid and crystalline states as the spin glass state of certain magnetic systems bears to the paramagnetic and ferromagnetic states, in the sense that, like the spin glass state, it is diagnosed by a subtle order parameter. In this review we give a detailed exposition of a theoretical approach to the physical properties of systems of randomly, permanently crosslinked macromolecules. Our primary focus is on the equilibrium properties of such systems, especially in the regime of Goodyear's vulcanisation transition.Comment: Review Article, REVTEX, 58 pages, 3 PostScript figure