8,876 research outputs found
A map for heavy inertial particles in fluid flows
We introduce a map which reproduces qualitatively many fundamental properties
of the dynamics of heavy particles in fluid flows. These include a uniform rate
of decrease of volume in phase space, a slow-manifold effective dynamics when
the single parameter (analogous of the Stokes number) approaches zero, the
possibility of fold caustics in the "velocity field", and a minimum, as a
function of , of the Lyapunov (Kaplan-Yorke) dimension of the attractor
where particles accumulate.Comment: 10 pages, 5 figure
The fractional volatility model : no-arbitrage, leverage and completeness
When the volatility process is driven by fractional noise one obtains a model which is consistent with the empirical market data. Depending on whether the stochasticity generators of log-price and volatility are independent or are the same, two versions of the model are obtained with different leverage behaviors. Here, the no-arbitrage and completeness properties of the models are rigorously studied
Büchwald-Hartwig reaction applied to synthesis of new luminescent liquid crystal triarylamines derived from isoxazoles
© 2015 Taylor & Francis Group, LLC. The present work describes the synthesis and characterization of novel series of triarylamines isoxazoles (TAA) addressed to the organic photovoltaic materials. Diarylisoxazoles were synthesized by sequential [3+2] 1,3-dipolar cycloaddition reaction between arylnitrile oxides and selected arylalkenes followed by MnO2-oxidation. Isoxazoles were coupled to diarylamines by Büchwald-Hartwig reaction to afford desired compounds 6a-k. Some TAA display liquid-crystalline behaviour and UV-Vis absorption and fluorescence emission were analysed for all samples of TAA 6a-k
Linear Form of 3-scale Relativity Algebra and the Relevance of Stability
We show that the algebra of the recently proposed Triply Special Relativity
can be brought to a linear (ie, Lie) form by a correct identification of its
generators. The resulting Lie algebra is the stable form proposed by Vilela
Mendes a decade ago, itself a reapparition of Yang's algebra, dating from 1947.
As a corollary we assure that, within the Lie algebra framework, there is no
Quadruply Special Relativity.Comment: 5 page
Stratification of the orbit space in gauge theories. The role of nongeneric strata
Gauge theory is a theory with constraints and, for that reason, the space of
physical states is not a manifold but a stratified space (orbifold) with
singularities. The classification of strata for smooth (and generalized)
connections is reviewed as well as the formulation of the physical space as the
zero set of a momentum map. Several important features of nongeneric strata are
discussed and new results are presented suggesting an important role for these
strata as concentrators of the measure in ground state functionals and as a
source of multiple structures in low-lying excitations.Comment: 22 pages Latex, 1 figur
Geometry, stochastic calculus and quantum fields in a non-commutative space-time
The algebras of non-relativistic and of classical mechanics are unstable
algebraic structures. Their deformation towards stable structures leads,
respectively, to relativity and to quantum mechanics. Likewise, the combined
relativistic quantum mechanics algebra is also unstable. Its stabilization
requires the non-commutativity of the space-time coordinates and the existence
of a fundamental length constant. The new relativistic quantum mechanics
algebra has important consequences on the geometry of space-time, on quantum
stochastic calculus and on the construction of quantum fields. Some of these
effects are studied in this paper.Comment: 36 pages Latex, 1 eps figur
Stability Analysis of a Hybrid Cellular Automaton Model of Cell Colony Growth
Cell colonies of bacteria, tumour cells and fungi, under nutrient limited
growth conditions, exhibit complex branched growth patterns. In order to
investigate this phenomenon we present a simple hybrid cellular automaton model
of cell colony growth. In the model the growth of the colony is limited by a
nutrient that is consumed by the cells and which inhibits cell division if it
falls below a certain threshold. Using this model we have investigated how the
nutrient consumption rate of the cells affects the growth dynamics of the
colony. We found that for low consumption rates the colony takes on a Eden-like
morphology, while for higher consumption rates the morphology of the colony is
branched with a fractal geometry. These findings are in agreement with previous
results, but the simplicity of the model presented here allows for a linear
stability analysis of the system. By observing that the local growth of the
colony is proportional to the flux of the nutrient we derive an approximate
dispersion relation for the growth of the colony interface. This dispersion
relation shows that the stability of the growth depends on how far the nutrient
penetrates into the colony. For low nutrient consumption rates the penetration
distance is large, which stabilises the growth, while for high consumption
rates the penetration distance is small, which leads to unstable branched
growth. When the penetration distance vanishes the dispersion relation is
reduced to the one describing Laplacian growth without ultra-violet
regularisation. The dispersion relation was verified by measuring how the
average branch width depends on the consumption rate of the cells and shows
good agreement between theory and simulations.Comment: 8 pages, 6 figure
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