Anomalous population of 10^{10}He states in reactions with 11^{11}Li

Structure with the lowest energy observed in the $^{10}$He spectrum populated in the proton knockout reaction with $^{11}$Li beam has a peak at $1.2-1.5$ MeV. This peak is usually interpreted as a resonant $0^+$ ground state of $^{10}$He. Our theoretical calculations indicate that this peak is likely to be a pileup of $1^-$, $0^+$, and $2^+$ excitations with very similar shapes. %We predict a very specific nature of the $1^-$ excitation in $^{10}$He. Moreover, the ``soft'' $1^-$ excitation appears to be the lowest one in energy. Such an anomalous continuum response is traced to the halo structure of $^{11}$Li providing extreme low energy shift to all the expected continuum excitations. Competitions of the initial state structure (ISS) and the final state interaction (FSI) effects on the spectrum and three-body correlations in $^{10}$He are discussed. Analogous effect of the extreme low-energy shift could also be expected in other cases of $2n$ emitters populated in reactions with halo nuclei. Simplified example of the $^{10}$He spectrum in $\alpha$ knockout from $^{14}$Be, is given. We also discuss limits on the properties of $^{9}$He stemming from the observed $^{10}$He spectrum.Comment: 10 pages, 13 figure

Scattering Theory for Jacobi Operators with Steplike Quasi-Periodic Background

We develop direct and inverse scattering theory for Jacobi operators with steplike quasi-periodic finite-gap background in the same isospectral class. We derive the corresponding Gel'fand-Levitan-Marchenko equation and find minimal scattering data which determine the perturbed operator uniquely. In addition, we show how the transmission coefficients can be reconstructed from the eigenvalues and one of the reflection coefficients.Comment: 14 page

Scattering theory with finite-gap backgrounds: Transformation operators and characteristic properties of scattering data

We develop direct and inverse scattering theory for Jacobi operators (doubly infinite second order difference operators) with steplike coefficients which are asymptotically close to different finite-gap quasi-periodic coefficients on different sides. We give necessary and sufficient conditions for the scattering data in the case of perturbations with finite second (or higher) moment.Comment: 23 page

Wildland fire propagation modeling: fire-spotting parametrisation and energy balance

Present research concerns the physical background of a wild-fire propagation model based on the split of the front motion into two parts - drifting and fluctuating. The drifting part is solved by the level set method and the fluctuating part describes turbulence and fire-spotting. These phenomena have a random nature and can be modeled as a stochastic process with the appropriate probability density function. Thus, wildland fire propagation results to be described by a nonlinear partial differential equation (PDE) of the reaction-diffusion type. A numerical study of the effects of the atmospheric stability on wildfire propagation is performed through its effects on fire-spotting. Moreover, it is shown that the solution of the PDE as an indicator function allows to construct the energy balance equation in terms of the temperature.PhD Grant "La Caixa 2014

Wildland fire propagation modelling

Wildfire propagation modelling is a challenging problem due to its complex multi-scale multi-physics nature. This process can be described by a reaction- diffusion equation based on the energy balance principle. Alternative technique is the so-called level-set method (LSM), used in wildfire modelling as well as in many other fields. In the present study a methodology for fire propagation modelling that reconciles these approaches is proposed. This methodology is distinguishable and significant from both academical and industrial point of view because of the inclusion of the ran- dom effects by preserving the existing algorithms and direct implementation as a post-processing numerical routine. The random behaviour of the fire front is caused, for example, by the turbulence and the fire-spotting phenomenon. A probability density function (PDF) is employed in order to describe the random process. In earlier studies it has been shown that new independent ignitions can increase the rate of spread (ROS) of fire and therefore should be carefully studied. In this respect, a physical parametrization of the fire-spotting distribution was proposed. Special attention in the present study is paid to the atmospheric stability conditions. The parametrization proposed in previous works is completed by the multiple fire-spotting modelling. Afterwards special attention is paid to the study of uniqueness of the PDF and consistency with the energy balance equation. Numerical results and discussions complete the study.PhD grant ”La Caixa 2014

Concurent multi-scale physical parametrization of fire-spotting: A study on the role of macro- and meso-scale characteristics of the system

The strong impact of wildfires in terms of lives and homes lost and of damage to ecosystems, calls for an urgent improvement in the risk management. The aim of the present research is the improvement of these software codes by proposing a complete physical characterization of fire-spotting within an approach that is ready to be implemented as a post-processing routine of standard outputs. The main feature of the proposed method is that the effects of random fluctuations are included in a way that preserves the existing structure of the operational and industrial codes and can be implemented directly. The operational code WRF-SFIRE have been used to test the proposed post-processing routine. Results show the suitability of the approach for simulating random effects due to turbulent convection and fire-spotting, which are cases not resolved by standard operational codes. Results of simulations including response analysis with test cases are shown and discussed.PhD grant "La Caixa 2014

Exact quantum master equation for a molecular aggregate coupled to a harmonic bath

We consider a molecular aggregate consisting of $N$ identical monomers. Each monomer comprises two electronic levels and a single harmonic mode. The monomers interact with each other via dipole-dipole forces. The monomer vibrational modes are bilinearly coupled to a bath of harmonic oscillators. This is a prototypical model for the description of coherent exciton transport, from quantum dots to photosynthetic antennae. We derive an exact quantum master equation for such systems. Computationally, the master equation may be useful for the testing of various approximations employed in theories of quantum transport. Physically, it offers a plausible explanation of the origins of long-lived coherent optical responses of molecular aggregates in dissipative environments

Spectrum of cosmic rays, produced in supernova remnants

Nonlinear kinetic theory of cosmic ray (CR) acceleration in supernova remnants is employed to calculate CR spectra. The magnetic field in SNRs is assumed to be significantly amplified by the efficiently accelerating nuclear CR component. It is shown that the calculated CR spectra agree in a satisfactory way with the existing measurements up to the energy $10^{17}$ eV. The power law spectrum of protons extends up to the energy $3\times 10^{15}$ eV with a subsequent exponential cutoff. It gives a natural explanation for the observed knee in the Galactic CR spectrum. The maximum energy of the accelerated nuclei is proportional to their charge number $Z$. Therefore the break in the Galactic CR spectrum is the result of the contribution of progressively heavier species in the overall CR spectrum so that at $10^{17}$ eV the CR spectrum is dominated by iron group nuclei. It is shown that this component plus a suitably chosen extragalactic CR component can give a consistent description for the entire Galactic CR spectrum.Comment: 4 pages with emulateapj, 3 figures, accepted for publication in the Astrophysical Journal Letter

Trace Formulas in Connection with Scattering Theory for Quasi-Periodic Background

We investigate trace formulas for Jacobi operators which are trace class perturbations of quasi-periodic finite-gap operators using Krein's spectral shift theory. In particular we establish the conserved quantities for the solutions of the Toda hierarchy in this class.Comment: 7 page