37,470 research outputs found
Shaping an ultracold atomic soliton in a travelling wave laser beam
An ultracold wave packet of bosonic atoms loaded into a travelling laser wave
may form a many-atom soliton.This is disturbed by a homogeneous force field,
for example by the inevitable gravitation. The wave packet is accelerated and
therefore the laser frequency appears to be chirped in the rest frame of the
atoms. We derive the effective nonlinear Schr\"odinger equation. It shows a
time dependent nonlinearity coefficient which amounts to a damping or
antidamping, respectively. The accelerated packet solution remains a soliton
which changes its shape adiabatically. Similarly, an active shaping can be
obtained in the force-free case by chirping the laser frequency thus
representing a way of coherent control of the soliton form. The experimental
consequences are discussed.Comment: 5 pages, Latex, to published in Europhys. Let
Cell cycle regulation of p34cdc2 kinase activity in Physarum polycephalum
The regulation of the mitotic histone H1 kinase activity has been analyzed during the naturally synchronous cell cycle of Physarum polycephalum plasmodia. The universal binding property of the p13suc1 Schizosaccharomyces pombe gene product was used to precipitate and assay the cdc2 histone H1 kinase activity. The kinase activity peaks at the beginning of metaphase and its decline, which requires protein synthesis, appears to be an early event during the metaphase process. Microtubular poisons, temperature shifts and DNA synthesis inhibitors were used to perturb cell cycle regulatory pathways and characterize their effects on cdc2 kinase activation. Our results suggest that the full activation of the mitotic kinase requires at least two successive triggering signals involving microtubular components and DNA synthesis
Ill-posedness of degenerate dispersive equations
In this article we provide numerical and analytical evidence that some
degenerate dispersive partial differential equations are ill-posed.
Specifically we study the K(2,2) equation and
the "degenerate Airy" equation . For K(2,2) our results are
computational in nature: we conduct a series of numerical simulations which
demonstrate that data which is very small in can be of unit size at a
fixed time which is independent of the data's size. For the degenerate Airy
equation, our results are fully rigorous: we prove the existence of a compactly
supported self-similar solution which, when combined with certain scaling
invariances, implies ill-posedness (also in )
Exploiting Chordality in Optimization Algorithms for Model Predictive Control
In this chapter we show that chordal structure can be used to devise
efficient optimization methods for many common model predictive control
problems. The chordal structure is used both for computing search directions
efficiently as well as for distributing all the other computations in an
interior-point method for solving the problem. The chordal structure can stem
both from the sequential nature of the problem as well as from distributed
formulations of the problem related to scenario trees or other formulations.
The framework enables efficient parallel computations.Comment: arXiv admin note: text overlap with arXiv:1502.0638
Full-time dynamics of modulational instability in spinor Bose-Einstein condensates
We describe the full-time dynamics of modulational instability in F=1 spinor
Bose-Einstein condensates for the case of the integrable three-component model
associated with the matrix nonlinear Schroedinger equation. We obtain an exact
homoclinic solution of this model by employing the dressing method which we
generalize to the case of the higher-rank projectors. This homoclinic solution
describes the development of modulational instability beyond the linear regime,
and we show that the modulational instability demonstrates the reversal
property when the growth of the modulation amplitude is changed by its
exponential decay.Comment: 6 pages, 2 figures, text slightly extended, a reference adde
Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism
This essay examines the philosophical significance of -logic in Zermelo-Fraenkel set theory with choice (ZFC). The duality between coalgebra and algebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras. The modal profile of -logical validity can then be countenanced within a coalgebraic logic, and -logical validity can be defined via deterministic automata. I argue that the philosophical significance of the foregoing is two-fold. First, because the epistemic and modal profiles of -logical validity correspond to those of second-order logical consequence, -logical validity is genuinely logical, and thus vindicates a neo-logicist conception of mathematical truth in the set-theoretic multiverse. Second, the foregoing provides a modal-computational account of the interpretation of mathematical vocabulary, adducing in favor of a realist conception of the cumulative hierarchy of sets
Aging of the Nonlinear Optical Susceptibility of colloidal solutions
Using Z-scan and dynamic light scattering measurements we investigate the
nonlinear optics response of a colloidal solution undergoing dynamics slowing
down with age. We study the high optical nonlinearity of an organic dye
(Rhodamine B) dispersed in a water-clay (Laponite) solution, at different clay
concentrations (2.0 wt% - 2.6 wt%), experiencing the gelation process. We
determine the clay platelets self diffusion coefficient and, by its comparison
with the structural relaxation time, we conclude that the gelation process
proceeds through the structuring of interconnecting clay platelets network
rather than through clusters growth and aggregation.Comment: 4 figures, 4 page
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