2,302,710 research outputs found
Line element in quantum gravity: the examples of DSR and noncommutative geometry
We question the notion of line element in some quantum spaces that are
expected to play a role in quantum gravity, namely non-commutative deformations
of Minkowski spaces. We recall how the implementation of the Leibniz rule
forbids to see some of the infinitesimal deformed Poincare transformations as
good candidates for Noether symmetries. Then we recall the more fundamental
view on the line element proposed in noncommutative geometry, and re-interprete
at this light some previous results on Connes' distance formula.Comment: some references added. Proceedings of the Second Workshop on Quantum
Gravity and Noncommutative Geometry, Universidade Lusofona, Lisbon 22-24
September 200
The shape of the urine stream — from biophysics to diagnostics
We develop a new computational model of capillary-waves in free-jet flows, and apply this to the problem of urological diagnosis in this first ever study of the biophysics behind the characteristic shape of the urine stream as it exits the urethral meatus. The computational fluid dynamics model is used to determine the shape of a liquid jet issuing from a non-axisymmetric orifice as it deforms under the action of surface tension. The computational results are verified with experimental modelling of the urine stream. We find that the shape of the stream can be used as an indicator of both the flow rate and orifice geometry. We performed volunteer trials which showed these fundamental correlations are also observed in vivo for male healthy volunteers and patients undergoing treatment for low flow rate. For healthy volunteers, self estimation of the flow shape provided an accurate estimation of peak flow rate (+-2%). However for the patients, the relationship between shape and flow rate suggested poor meatal opening during voiding. The results show that self measurement of the shape of the urine stream can be a useful diagnostic tool for medical practitioners since it provides a non-invasive method of measuring urine flow rate and urethral dilation
An isoperimetric problem for point interactions
We consider Hamiltonian with point interactions in all
with the same coupling constant, placed at vertices of an equilateral polygon
\PP_N. It is shown that the ground state energy is locally maximized by a
regular polygon. The question whether the maximum is global is reduced to an
interesting geometric problem.Comment: LaTeX 2e, 10 page
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