Regularity and mass conservation for discrete coagulation-fragmentation equations with diffusion

We present a new a-priori estimate for discrete coagulation fragmentation systems with size-dependent diffusion within a bounded, regular domain confined by homogeneous Neumann boundary conditions. Following from a duality argument, this a-priori estimate provides a global L2 bound on the mass density and was previously used, for instance, in the context of reaction-diffusion equations. In this paper we demonstrate two lines of applications for such an estimate: On the one hand, it enables to simplify parts of the known existence theory and allows to show existence of solutions for generalised models involving collision-induced, quadratic fragmentation terms for which the previous existence theory seems difficult to apply. On the other hand and most prominently, it proves mass conservation (and thus the absence of gelation) for almost all the coagulation coefficients for which mass conservation is known to hold true in the space homogeneous case.

A mixed finite element method for nonlinear diffusion equations

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model.

Analysing the innovation process in the EU Integrated Programme, ISAFRUIT

ISAFRUIT is an integrated European Union Project focussed on increasing fruit consumption as a means to improve human health, through evaluating the fruit chain and addressing bottlenecks therein.The innovations which are being developed throughout the ISAFRUIT Project have been analysed to determine both the success factors and the obstacles in reaching the commercialisation stage. Only 9.58% of the deliverables planned within the Project were focussed on developing technological innovations.There is evidence, however, of successes in the development of new innovations arising from the ISAFRUIT Project, with several other potential innovations in the pipeline. Of the technologies identified, 67% are still at the “invention stage”; that is, the stage prior to bridging the so-called “valley of death”, the stage between an invention and an innovation. Those which are considered to have moved over the “valley of death” either had industry partners included in the Project, or had consulted with industry to ensure that the technology was relevant, or met a recognised industry need. Many of the technologies which made less progress did not have the same interactions with industry. A number of other issues were identified which prevented further progress towards innovation. The need for scientists to publish scientific papers, both for their career pathways and to increase their chances of future funding, was identified as one issue, although the filing of patents is now becoming more accepted and recognised. The patenting system is considered complex by many scientists and is not well-understood. Finally, agreements between partners on the sharing of intellectual property rights can cause a delay in the innovation process.

Technological innovation in creative clusters. The case of laser in conservation of artworks in Florence

The field of laser application to the restoration and cleaning of cultural assets is amongst the most thriving developments of recent times. Ablative laser technological systems are able to clean and protect inestimable works of art subject to atmospheric agents and degradation over time. This new technology, which has been developing for the last forty year, is now available to restorers and has received a significant success all over Europe. An important contribution in the process of laser innovation has been carried out in Florence by local actors belonging to a creative cluster. The objects of the analysis are the genesis of this innovation in this local Florentine context, and the relationships among the main actors who have contributed in it. The study investigates how culture can play a part in the generation of ideas and innovations, and which are the creative environments that can favour it. In this context, the issue of laser technologies for the restoration of cultural heritage has been analysed as a case study in the various paths taken by the Creative Capacity of the Culture (CCC).

Trade, firm selection, and innovation: the competition channel

The availability of rich firm-level data sets has recently led researchers to uncover new evidence on the effects of trade liberalization. First, trade openness forces the least productive firms to exit the market. Secondly, it induces surviving firms to increase their innovation efforts and thirdly, it increases the degree of product market competition. In this paper we propose a model aimed at providing a coherent interpretation of these findings. We introducing firm heterogeneity into an innovation-driven growth model, where incumbent firms operating in oligopolistic industries perform cost-reducing innovations. In this framework, trade liberalization leads to higher product market competition, lower markups and higher quantity produced. These changes in markups and quantities, in turn, promote innovation and productivity growth through a direct competition effect, based on the increase in the size of the market, and a selection effect, produced by the reallocation of resources towards more productive firms. Calibrated to match US aggregate and firm-level statistics, the model predicts that a 10 percent reduction in variable trade costs reduces markups by 1:15 percent, firm surviving probabilities by 1 percent, and induces an increase in productivity growth of about 13 percent. More than 90 percent of the trade-induced growth increase can be attributed to the selection effect.

Stabilized Petrov-Galerkin methods for the convection-diffusion-reaction and the Helmholtz equations

We present two new stabilized high-resolution numerical methods for the convection–diffusion–reaction (CDR) and the Helmholtz equations respectively. The work embarks upon a priori analysis of some consistency recovery procedures for some stabilization methods belonging to the Petrov–Galerkin framework. It was found that the use of some standard practices (e.g. M-Matrices theory) for the design of essentially non-oscillatory numerical methods is not feasible when consistency recovery methods are employed. Hence, with respect to convective stabilization, such recovery methods are not preferred. Next, we present the design of a high-resolution Petrov–Galerkin (HRPG) method for the 1D CDR problem. The problem is studied from a fresh point of view, including practical implications on the formulation of the maximum principle, M-Matrices theory, monotonicity and total variation diminishing (TVD) finite volume schemes. The current method is next in line to earlier methods that may be viewed as an upwinding plus a discontinuity-capturing operator. Finally, some remarks are made on the extension of the HRPG method to multidimensions. Next, we present a new numerical scheme for the Helmholtz equation resulting in quasi-exact solutions. The focus is on the approximation of the solution to the Helmholtz equation in the interior of the domain using compact stencils. Piecewise linear/bilinear polynomial interpolation are considered on a structured mesh/grid. The only a priori requirement is to provide a mesh/grid resolution of at least eight elements per wavelength. No stabilization parameters are involved in the definition of the scheme. The scheme consists of taking the average of the equation stencils obtained by the standard Galerkin finite element method and the classical finite difference method. Dispersion analysis in 1D and 2D illustrate the quasi-exact properties of this scheme. Finally, some remarks are made on the extension of the scheme to unstructured meshes by designing a method within the Petrov–Galerkin framework.

A geometric mechanism of diffusion: Rigorous verification in a priori unstable Hamiltonian systems

In this paper we consider a representative a priori unstable Hamiltonian system with 2+1/2 degrees of freedom, to which we apply the geometric mechanism for diffusion introduced in the paper Delshams et al., Mem.Amer.Math. Soc. 2006, and generalized in Delshams and Huguet, Nonlinearity 2009, and provide explicit, concrete and easily verifiable conditions for the existence of diffusing orbits. The simplification of the hypotheses allows us to perform explicitly the computations along the proof, which contribute to present in an easily understandable way the geometric mechanism of diffusion. In particular, we fully describe the construction of the scattering map and the combination of two types of dynamics on a normally hyperbolic invariant manifold.

Product differentiation, competitive pressure and the effects of innovation on the success and survivability of firms in oligopoly markets

In a recent paper Tishler and Milstein (2009) fi…nd that increased competition may increase aggregate R&D spending while market output decreases. Therefore, they obtain the surprising result that R&D spending is excessive when competition becomes intense. Their result is based on the standard linear demand function for differentiated products introduced by Bowley (1924) where decreased product differentiation is interpreted as more competitive pressure. In this paper I show that at an aggregate level this interpretation is problematic because equilibrium effects are dominated by a demand reduction effect. A slight modifi…cation of the standard demand function eliminates this effect. For the Tishler and Milstein (2009) setting it is shown that then increased competition increases both R&D spending and aggregate market output. Therefore, at least for consumers, more intense competition increases welfare. Journal of Economic Literature Classi…fication Numbers: D43, L1, O3. Keywords: Oligopoly markets, Product differentiation, Competitive pressure.

Patent policy, patent pools, and the accumulation of claims in sequential innovation

We present a dynamic model where the accumulation of patents generates an increasing number of claims on sequential innovation. We compare innovation activity under three regimes -patents, no-patents, and patent pools- and find that none of them can reach the first best. We find that the first best can be reached through a decentralized tax-subsidy mechanism, by which innovators receive a subsidy when they innovate, and are taxed with subsequent innovations. This finding implies that optimal transfers work in the exact opposite way as traditional patents. Finally, we consider patents of finite duration and determine the optimal patent length.

In vitro Comparison of Disk Diffusion and Agar Dilution Antibiotic Susceptibility Test Methods for Neisseria gonorrhoeae

At present, most Neisseria gonorrhoeae testing is done with ß-lactamase and agar dilution tests with common therapeutic agents. Generally, in bacteriological diagnosis laboratories in Argentina, study of antibiotic susceptibility of N.gonorrhoeae is based on ß-lactamase determination and agar dilution method with common therapeutic agents. The National Committee for Clinical Laboratory Standards (NCCLS) has recently described a disk diffusion test that produces results comparable to the reference agar dilution method for antibiotic susceptibility of N.gonorrhoeae, using a dispersion diagram for analyzing the correlation between both techniques. We obtained 57 gonococcal isolates from patients attending a clinic for sexually transmitted diseases in Tucumán, Argentina. Antibiotic susceptibility tests using agar dilution and disk diffusion techniques were compared. The established NCCLS interpretive criteria for both susceptibility methods appeared to be applicable to domestic gonococcal strains. The correlation between the MIC's and the zones of inhibition was studied for penicillin, ampicillin, cefoxitin, spectinomycin, cefotaxime, cephaloridine, cephalexin, tetracycline, norfloxacin and kanamycin. Dispersion diagrams showed a high correlation between both methods.

On Lundh's percolation diffusion

A collection of spherical obstacles in the unit ball in Euclidean space is said to be avoidable for Brownian motion if there is a positive probability that Brownian motion diffusing from some point in the ball will avoid all the obstacles and reach the boundary of the ball. The centres of the spherical obstacles are generated according to a Poisson point process while the radius of an obstacle is a deterministic function. If avoidable configurations are generated with positive probability Lundh calls this percolation diffusion. An integral condition for percolation diffusion is derived in terms of the intensity of the point process and the function that determines the radii of the obstacles.