On the Geometric Principles of Surface Growth

We introduce a new equation describing epitaxial growth processes. This equation is derived from a simple variational geometric principle and it has a straightforward interpretation in terms of continuum and microscopic physics. It is also able to reproduce the critical behavior already observed, mound formation and mass conservation, but however does not fit a divergence form as the most commonly spread models of conserved surface growth. This formulation allows us to connect the results of the dynamic renormalization group analysis with intuitive geometric principles, whose generic character may well allow them to describe surface growth and other phenomena in different areas of physics

On the spectrum of nonrelativistic AdS/CFT

We develop a Hamiltonian picture for a family of models of nonrelativistic AdS/CFT duality. The Schrodinger group is realized via the conformal quantum mechanics of De Alfaro, Fubini and Furlan in the holographic direction. We show that most physical requirements, including the introduction of harmonic traps, can be realized with exact AdS metrics, but without any need for exotic matter sectors in the bulk dynamics. This Hamiltonian picture can be used to compare directly with many-body spectra of fermions at unitarity on harmonic traps, thereby providing a direct physical interpretation of the holographic radial coordinate for these systems. Finally, we add some speculations on the dynamical generation of mass gaps in the AdS description, the resulting quasiparticle spectra, and the analog of `deconfining' phase transitions that may occur.Comment: 20 pages and 1 figure; typos corrected, references added; references added, minor changes matching published versio

Geometrical approach to tumor growth

Tumor growth has a number of features in common with a physical process known as molecular beam epitaxy. Both growth processes are characterized by the constraint of growth development to the body border, and surface diffusion of cells/particles at the growing edge. However, tumor growth implies an approximate spherical symmetry that makes necessary a geometrical treatment of the growth equations. The basic model was introduced in a former article [C. Escudero, Phys. Rev. E 73, 020902(R) (2006)], and in the present work we extend our analysis and try to shed light on the possible geometrical principles that drive tumor growth. We present two-dimensional models that reproduce the experimental observations, and analyse the unexplored three-dimensional case, for which new conclusions on tumor growth are derived

World trends in fertilizer use and projections to 2020

Fertilizers have played an important role in increased crop production, especially in cereal yields, and will continue to be a cornerstone of the science-based agriculture required to feed the expanding world population. Fertilizers replenish the nutrients removed from soils by harvested crops, encourage adoption of high-yielding varieties, and increase biomass in the nutrient-poor soils of the tropics. Bumb and Baanante trace fertilizer use until the 1990s as well as production and price trends. Finally they propose projected trends in use, requirements, and production. The authors conclude that, overall, a conducive and stable policy environment, including macroeconomic stability, price incentives, credit availability, efficient organizational arrangements, research and extension support, regulatory frameworks, and environmental monitoring, will be essential to promote environmentally friendly growth in fertilizer use and supply to 2020.Fertilizers. ,Crops Economic aspects. ,Cereal crops. ,Environmental protection. ,