3,648 research outputs found
Syzygies of torsion bundles and the geometry of the level l modular variety over M_g
We formulate, and in some cases prove, three statements concerning the purity
or, more generally the naturality of the resolution of various rings one can
attach to a generic curve of genus g and a torsion point of order l in its
Jacobian. These statements can be viewed an analogues of Green's Conjecture and
we verify them computationally for bounded genus. We then compute the
cohomology class of the corresponding non-vanishing locus in the moduli space
R_{g,l} of twisted level l curves of genus g and use this to derive results
about the birational geometry of R_{g, l}. For instance, we prove that R_{g,3}
is a variety of general type when g>11 and the Kodaira dimension of R_{11,3} is
greater than or equal to 19. In the last section we explain probabilistically
the unexpected failure of the Prym-Green conjecture in genus 8 and level 2.Comment: 35 pages, appeared in Invent Math. We correct an inaccuracy in the
statement of Prop 2.
Construction of equilibrium networks with an energy function
We construct equilibrium networks by introducing an energy function depending
on the degree of each node as well as the product of neighboring degrees. With
this topological energy function, networks constitute a canonical ensemble,
which follows the Boltzmann distribution for given temperature. It is observed
that the system undergoes a topological phase transition from a random network
to a star or a fully-connected network as the temperature is lowered. Both
mean-field analysis and numerical simulations reveal strong first-order phase
transitions at temperatures which decrease logarithmically with the system
size. Quantitative discrepancies of the simulation results from the mean-field
prediction are discussed in view of the strong first-order nature.Comment: To appear in J. Phys.
Nonlinear preferential rewiring in fixed-size networks as a diffusion process
We present an evolving network model in which the total numbers of nodes and
edges are conserved, but in which edges are continuously rewired according to
nonlinear preferential detachment and reattachment. Assuming power-law kernels
with exponents alpha and beta, the stationary states the degree distributions
evolve towards exhibit a second order phase transition - from relatively
homogeneous to highly heterogeneous (with the emergence of starlike structures)
at alpha = beta. Temporal evolution of the distribution in this critical regime
is shown to follow a nonlinear diffusion equation, arriving at either pure or
mixed power-laws, of exponents -alpha and 1-alpha
Effect of high hydrostatic pressure treatments on volatiles of berry purées
High hydrostatic pressure (HHP) technology, as a promising alternative of thermal-treatment and chemical preservatives, can be used to produce minimally processed foods. It has the advantage of affecting only non-covalent bonds of macromolecules in foods, and thus preserves nutritional components, taste, and flavour exceptionally well. However, HHP also influences enzymatic reactions of food. Although some of these changes are often beneficial, monitoring the potential effects of high pressure treatments — especially in the field of product and technology development — is essential. The aim of this study was to point out some parameters of high hydrostatic pressure technique (pressure, temperature, build-up time, holding time, number of cycles) that can substantially impact the sensory properties of treated products
Food security and sustainability - chances and limitations of agriculture
The increasing population of the world may induce various problems. There are two major fields; food security and adequate fresh water supply, which are predominant for all Global economic structures. On the other hand all activities implemented in favour of meeting the demand of the population, increase the ecological footprint and may risk sustainability of both mankind and its environment. The present study deals with an assessment of future trends on the basis of the present state of alimentation. Agriculture has a basic role in providing food for the human race. All sort of activities of that are in relation with the environment and at the same time they are driven by economic and social aspects. Sustainable agriculture can only be implemented if agricultural production can be run in an environment which is socially bearable, and economically viable. The scheme has to take into consideration that the society has to be equitable economically continuously. Whenever any of these interrelations cannot be manifested, the whole system may turn to be non-sustainable, or inefficient regarding food security
Heat storage in alloy transformations
The feasibility of using metal alloys as thermal energy storage media was determined. The following major elements were studied: (1) identification of congruently transforming alloys and thermochemical property measurements; (2) development of a precise and convenient method for measuring volume change during phase transformation and thermal expansion coefficients; (3) development of a numerical modeling routine for calculating heat flow in cylindrical heat exchangers containing phase change materials; and (4) identification of materials that could be used to contain the metal alloys. Several eutectic alloys and ternary intermetallic phases were determined. A method employing X-ray absorption techniques was developed to determine the coefficients of thermal expansion of both the solid and liquid phases and the volume change during phase transformation from data obtained during one continuous experimental test. The method and apparatus are discussed and the experimental results are presented. The development of the numerical modeling method is presented and results are discussed for both salt and metal alloy phase change media
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