8,235 research outputs found
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
Quantifying Equivocation for Finite Blocklength Wiretap Codes
This paper presents a new technique for providing the analysis and comparison
of wiretap codes in the small blocklength regime over the binary erasure
wiretap channel. A major result is the development of Monte Carlo strategies
for quantifying a code's equivocation, which mirrors techniques used to analyze
normal error correcting codes. For this paper, we limit our analysis to
coset-based wiretap codes, and make several comparisons of different code
families at small and medium blocklengths. Our results indicate that there are
security advantages to using specific codes when using small to medium
blocklengths.Comment: Submitted to ICC 201
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
Measurement of the double-ss decay half-life and search for the neutrinoless double-ss decay of Ca-48 with the NEMO-3 detector
Neutrinoless double-β decay is a powerful probe of lepton number violating processes that may arise from Majorana terms in neutrino masses, or from supersymmetric, left-right symmetric, and other extensions of the Standard Model. Of the candidate isotopes for the observation of this process, 48Ca has the highest Qββ -value, resulting in decays with energies significantly above most naturally occurring backgrounds. The nucleus also lends itself to precise matrix element calculations within the nuclear shell model. We present the world's best measurement of the two-neutrino double-β decay of 48Ca, obtained by the NEMO-3 collaboration using 5.25 yr of data recorded with a 6.99 g sample of isotope, yielding ≈ 150 events with a signal to background ratio larger than 3. Neutrinoless modes of double-β decay are also investigated, with no evidence of new physics. Furthermore, these results indicate that two-neutrino double-β decay would be the main source of background for similar future searches using 48Ca with significantly larger exposures
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
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