KAM-tori near an analytic elliptic fixed point

We study the accumulation of an elliptic fixed point of a real analytic Hamiltonian by quasi-periodic invariant tori. We show that a fixed point with Diophantine frequency vector \o_0 is always accumulated by invariant complex analytic KAM-tori. Indeed, the following alternative holds: If the Birkhoff normal form of the Hamiltonian at the invariant point satisfies a R\"ussmann transversality condition, the fixed point is accumulated by real analytic KAM-tori which cover positive Lebesgue measure in the phase space (in this part it suffices to assume that \o_0 has rationally independent coordinates). If the Birkhoff normal form is degenerate, there exists an analytic subvariety of complex dimension at least $d+1$ passing through 0 that is foliated by complex analytic KAM-tori with frequency $\omega_0$. This is an extension of previous results obtained in \cite{EFK} to the case of an elliptic fixed point

Micro(RNA) Management and Mismanagement of the Islet.

Pancreatic β-cells located within the islets of Langerhans play a central role in metabolic control. The main function of these cells is to produce and secrete insulin in response to a rise in circulating levels of glucose and other nutrients. The release of insufficient insulin to cover the organism needs results in chronic hyperglycemia and diabetes development. β-cells insure a highly specialized task and to efficiently accomplish their function they need to express a specific set of genes. MicroRNAs (miRNAs) are small noncoding RNAs and key regulators of gene expression. Indeed, by partially pairing to specific sequences in the 3' untranslated regions of target mRNAs, each of them can control the translation of hundreds of transcripts. In this review, we focus on few key miRNAs controlling islet function and discuss: their differential expression in Type 2 diabetes (T2D), their regulation by genetic and environmental factors, and their therapeutic potential. Genetic and epigenetic changes or prolonged exposure to hyperglycemia and/or hyperlipidemia can affect the β-cell miRNA expression profile, resulting in impaired β-cell function and survival leading to the development of T2D. Experimental approaches permitting to correct the level of misexpressed miRNAs have been shown to prevent or treat T2D in animal models, suggesting that these small RNAs may become interesting therapeutic targets. However, translation of these experimental findings to the clinics will necessitate the development of innovative strategies allowing safe and specific delivery of compounds modulating the level of the relevant miRNAs to the β-cells

Numerical simulations of the Fourier transformed Vlasov-Maxwell system in higher dimensions --- Theory and applications

We present a review of recent developments of simulations of the Vlasov-Maxwell system of equations using a Fourier transform method in velocity space. In this method, the distribution functions for electrons and ions are Fourier transformed in velocity space, and the resulting set of equations are solved numerically. In the original Vlasov equation, phase mixing may lead to an oscillatory behavior and sharp gradients of the distribution function in velocity space, which is problematic in simulations where it can lead to unphysical electric fields and instabilities and to the recurrence effect where parts of the initial condition recur in the simulation. The particle distribution function is in general smoother in the Fourier transformed velocity space, which is desirable for the numerical approximations. By designing outflow boundary conditions in the Fourier transformed velocity space, the highest oscillating terms are allowed to propagate out through the boundary and are removed from the calculations, thereby strongly reducing the numerical recurrence effect. The outflow boundary conditions in higher dimensions including electromagnetic effects are discussed. The Fourier transform method is also suitable to solve the Fourier transformed Wigner equation, which is the quantum mechanical analogue of the Vlasov equation for classical particles.Comment: 41 pages, 19 figures. To be published in Transport Theory and Statistical Physics. Proceedings of the VLASOVIA 2009 Workshop, CIRM, Luminy, Marseilles, France, 31 August - 4 September 200

Solar coronal electron heating by short-wavelength dispersive shear Alfvén waves

This work was partially supported by the STFC through the Centre for Fundamental Physics (CfFP) at Rutherford Appleton Laboratory, Chilton, Didcot, UK. BE acknowledges support by the Engineering and Physical Sciences Research Council (EPSRC), UK, Grant no EP/M009386/1.The electron heating of the solar coronal plasma has remained one of the most important problems in solar physics. An explanation of the electron heating rests on the identification of the energy source and appropriate physical mechanisms via which the energy can be channelled to the electrons. Our objective here is to present an estimate for the electron heating rate in the presence of finite amplitude short-wavelength (in comparison with the ion gyroradius) dispersive shear Alfven (SWDSA) waves that propagate obliquely to the ambient magnetic field direction in the solar corona. Specifically, it is demonstrated that SWDSA waves can significantly contribute to the solar coronal electron heating via collisionless heating involving SWDSA wave-electron interactions.Publisher PDFPeer reviewe

KAM for the quantum harmonic oscillator

In this paper we prove an abstract KAM theorem for infinite dimensional Hamiltonians systems. This result extends previous works of S.B. Kuksin and J. P\"oschel and uses recent techniques of H. Eliasson and S.B. Kuksin. As an application we show that some 1D nonlinear Schr\"odinger equations with harmonic potential admits many quasi-periodic solutions. In a second application we prove the reducibility of the 1D Schr\"odinger equations with the harmonic potential and a quasi periodic in time potential.Comment: 54 pages. To appear in Comm. Math. Phy

High-quality ion beams by irradiating a nano-structured target with a petawatt laser pulse

We present a novel laser based ion acceleration scheme, where a petawatt circularly polarized laser pulse is shot on an ultra-thin (nano-scale) double-layer target. Our scheme allows the production of high-quality light ion beams with both energy and angular dispersion controllable by the target properties. We show that extraction of all electrons from the target by radiation pressure can lead to a very effective two step acceleration process for light ions if the target is designed correctly. Relativistic protons should be obtainable with pulse powers of a few petawatt. Careful analytical modeling yields estimates for characteristic beam parameters and requirements on the laser pulse quality, in excellent agreement with one and two-dimensional Particle-in Cell simulations.Comment: 18 pages, 7 figures, accepted in New. J. Phy

Predicting delay factors when chipping wood at forest roadside landings

Chipping of bulky biomass assortments at roadside landings is a common and costly step in the biomass-to-energy supply chain. This operation normally involves one chipping unit and one or several transport trucks working together for simultaneous chipping and chip transport to a terminal or end user. Reducing the delay factors in these operations is a relevant ambition for lowering supply costs. A method to estimate organizational delay based on: (1) the capacity ratio between the transport and the chipper, (2) the use of buffer storage, and (3) the number of transport units involved is suggested here. Other delays will also be present, and some of these may relate to the working conditions at the landing. A method to set a landing functionality index based on characteristics of the forest landing is also suggested. A total of 14 roadside chipping operations were assessed and the operators were interviewed to address the impact of machinery configuration and landing characteristics on machine utilization. At most sites, the chipper was the more productive part, and the chipper utilization was to a large extent limited by organizational delay. Still the utilization of the transport units varied between 37 and 97%, of which some 36% of the variation was explained by the landing functionality index. Knowledge from the work presented here should be a good starting point for improving biomass supply planning and supply chain configuration.acceptedVersio

Luminosity Tuning at the Interaction Point

Minimisation of the emittance in a linear collider is not enough to achieve optimal performance. For optimisation of the luminosity, tuning of collision parameters such as angle, offset, waist, etc. is needed, and a fast and reliable tuning signal is required. In this paper tuning knobs are presented, and their optimisation using beamstrahlung as a tuning signal is studied