347 research outputs found
On cyclic branched coverings of prime knots
We prove that a prime knot K is not determined by its p-fold cyclic branched
cover for at most two odd primes p. Moreover, we show that for a given odd
prime p, the p-fold cyclic branched cover of a prime knot K is the p-fold
cyclic branched cover of at most one more knot K' non equivalent to K. To prove
the main theorem, a result concerning the symmetries of knots is also obtained.
This latter result can be interpreted as a characterisation of the trivial
knot.Comment: 28 pages, 2 figure
Run-and-tumble particles in speckle fields
The random energy landscapes developed by speckle fields can be used to
confine and manipulate a large number of micro-particles with a single laser
beam. By means of molecular dynamics simulations, we investigate the static and
dynamic properties of an active suspension of swimming bacteria embedded into
speckle patterns. Looking at the correlation of the density fluctuations and
the equilibrium density profiles, we observe a crossover phenomenon when the
forces exerted by the speckles are equal to the bacteria's propulsion
Design and Performance of a 500 V Pulse Amplifier for the Chopper of the CERN Superonducting H LINAC (SPL)
The Superconducting H- Linac under study at CERN requires a high performance 3 MeV chopper. The pulse amplifier driving the chopper structure has to provide 500 V on 50 W, with rise and fall times below 2 ns at a repetition rate as high as 45 MHz. After analysis of the limiting parameters, potential solutions are described. The detailed design of the selected solution is presented, together with the actual performance of the prototype
Effective run-and-tumble dynamics of bacteria baths
{\it E. coli} bacteria swim in straight runs interrupted by sudden
reorientation events called tumbles. The resulting random walks give rise to
density fluctuations that can be derived analytically in the limit of non
interacting particles or equivalently of very low concentrations. However, in
situations of practical interest, the concentration of bacteria is always large
enough to make interactions an important factor. Using molecular dynamics
simulations, we study the dynamic structure factor of a model bacterial bath
for increasing values of densities. We show that it is possible to reproduce
the dynamics of density fluctuations in the system using a free run-and-tumble
model with effective fitting parameters. We discuss the dependence of these
parameters, e.g., the tumbling rate, tumbling time and self-propulsion
velocity, on the density of the bath
First-passage time of run-and-tumble particles
We solve the problem of first-passage time for run-and-tumble particles in
one dimension. Exact expression is derived for the mean first-passage time in
the general case, considering external force-fields and chemotactic-fields,
giving rise to space dependent swim-speed and tumble rate. Agreement between
theoretical formulae and numerical simulations is obtained in the analyzed case
studies -- constant and sinusoidal force fields, constant gradient chemotactic
field. Reported findings can be useful to get insights into very different
phenomena involving active particles, such as bacterial motion in external
fields, intracellular transport, cell migration, animal foraging
- âŠ