Charge Transport in one Dimension:Dissipative and Non-Dissipative Space-Charge Limited Currents

We consider charge transport in nanopores where the dielectric constant inside the nanopore is much greater than in the surrounding material, so that the flux of the electric fields due to the charges is almost entirely confined to the nanopore. That means that we may model the electric fields due to charge densities in the nanopore in terms of average properties across the nanopore as solutions of one dimensional Poisson equations. We develop basic equations for an M component system using equations of continuity to relate concentrations to currents, and flux equations relating currents to concentration gradients and conductivities. We then derive simplified scaled versions of the equations. We develop exact solutions for the one component case in a variety of boundary conditions using a Hopf-Cole transformation, Fourier series, and periodic solutions of the Burgers equation. These are compared with a simpler model in which the scaled diffusivity is zero so that all charge motion is driven by the electric field. In this non-dissipative case, recourse to an admissibility condition is utilised to obtain the physically relevant weak solution of a Riemann problem concerning the electric field. It is shown that the admissibility condition is Poynting's theorem.Comment: v2 contains the minor updates and corrections that have been incorporated into the published articl

Induced Gravity on Intersecting Branes

We establish Einstein-Hilbert gravity couplings in the effective action for Intersecting Brane Worlds. The four-dimensional induced Planck mass is determined by calculating graviton scattering amplitudes at one-loop in the string perturbation expansion. We derive a general formula linking the induced Planck mass for N=1 supersymmetric backgrounds directly to the string partition function. We carry out the computation explicitly for simple examples, obtaining analytic expressions.Comment: references added, minor changes to discussion of path integral normalization on page

Neo-Newtonian cosmology: An intermediate step towards General Relativity

Cosmology is a field of physics in which the use of General Relativity theory is indispensable. However, a cosmology based on Newtonian gravity theory for gravity is possible in certain circumstances. The applicability of Newtonian theory can be substantially extended if it is modified in such way that pressure has a more active role as source of the gravitational field. This was done in the neo-Newtonian cosmology. The limitation on the construction of a Newtonian cosmology, and the need for a relativistic theory in cosmology are reviewed. The neo-Newtonian proposal is presented, and its consequences for cosmology are discussed.Comment: 10 pages. Portuguese version submitted to RBE

Modeling the role of constant and time varying recycling delay on an ecological food chain

summary:We consider a mathematical model of nutrient-autotroph-herbivore interaction with nutrient recycling from both autotroph and herbivore. Local and global stability criteria of the model are studied in terms of system parameters. Next we incorporate the time required for recycling of nutrient from herbivore as a constant discrete time delay. The resulting DDE model is analyzed regarding stability and bifurcation aspects. Finally, we assume the recycling delay in the oscillatory form to model the daily variation in nutrient recycling and deduce the stability criteria of the variable delay model. A comparison of the variable delay model with the constant delay one is performed to unearth the biological relevance of oscillating delay in some real world ecological situations. Numerical simulations are done in support of analytical results

Forest Biodiversity Assessment in Peruvian Andean Montane Cloud Forest

Cloud forests are unusual and fragile habitats, being one of the least studied and least understood ecosystems. The tropical Andean dominion is considered one of the most significant places in the world as rega rds biological diversity, with a very high level of endemism. The biodiversity was analysed in an isolated remnant area of a tropical montane cloud forest known as the ?Bosque de Neblina de Cuyas?, in the North of the Peruvian Andean range. Composition, structure and dead wood were measured or estimated. The values obtained were compared with other cloud forests. The study revealed a high level of forest biodiversity, although the level of biodiversity differs from one area to another: in the inner areas, where human pressure is almost inexistent, the biodiversity values increase. The high species richness and the low dominance among species bear testimony to this montane cloud forest as a real enclave of biodiversity