An iterative method with error estimators

AbstractIterative methods for the solution of linear systems of equations produce a sequence of approximate solutions. In many applications it is desirable to be able to compute estimates of the norm of the error in the approximate solutions generated and terminate the iterations when the estimates are sufficiently small. This paper presents a new iterative method based on the Lanczos process for the solution of linear systems of equations with a symmetric matrix. The method is designed to allow the computation of estimates of the Euclidean norm of the error in the computed approximate solutions. These estimates are determined by evaluating certain Gauss, anti-Gauss, or Gauss–Radau quadrature rules

Fractal time random walk and subrecoil laser cooling considered as renewal processes with infinite mean waiting times

There exist important stochastic physical processes involving infinite mean waiting times. The mean divergence has dramatic consequences on the process dynamics. Fractal time random walks, a diffusion process, and subrecoil laser cooling, a concentration process, are two such processes that look qualitatively dissimilar. Yet, a unifying treatment of these two processes, which is the topic of this pedagogic paper, can be developed by combining renewal theory with the generalized central limit theorem. This approach enables to derive without technical difficulties the key physical properties and it emphasizes the role of the behaviour of sums with infinite means.Comment: 9 pages, 7 figures, to appear in the Proceedings of Cargese Summer School on "Chaotic dynamics and transport in classical and quantum systems

Enhanced production of propionic acid through acidic hydrolysis by choice of inoculum

BACKGROUND In this study, the enhancement of propionic acid production from a model feedstock mimicking kitchen waste was investigated. For that purpose, two operational runs of a semicontinuous anaerobic hydrolysis reactor were carried out at pH 6.0 ± 0.1 and mesophilic (30 °C) temperature. Two different types of inocula, a mixed microbial culture selected over 24 months for growth on cellulose and a culture contained in goat cheese were compared. RESULTS The results show that the goat cheese inoculum was significantly more efficient for propionic acid (PA) production. The highest propionic acid concentration achieved amounted to 139 mmol L−1 at a yield of 23.3 mg g−1 volatile solids (VS), which was 55% greater than what was achieved with the mixed culture. Furthermore, it was observed that propionic acid production was enhanced by a combination of high hydraulic retention time (HRT) with low organic loading rate (OLR), ensuring sufficient time for complete processing of the complex organic substrates. The fermentation could be kept in a stable process of propionic acid production at HRT of 20 days and a rather low OLR of 11.1 g L−1 day−1 VS. CONCLUSION Our results give a better understanding of PA production in semicontinuous mode, applying optimized process parameters and selecting the adequate microbial community for inoculation. This study provides important information for the improvement of PA production from complex substrates for future industrial application. © 2020 The Authors. Journal of Chemical Technology and Biotechnology published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry (SCI)

Mechanical oscillations of magnetic strips under the influence of external field

This is the final version of the article. Available from EDP Sciences via the DOI in this record.JEMS 2012 – Joint European Magnetic SymposiaBy application of a magnetic field on an amorphous metallic strip, the orientation of magnetization of Weiss domains can be changed. When the strip changes its length, this effect is called magnetostriction. We simulate this effect using a finite element method. In particular we calculate the change of the mechanical resonance frequency of a magnetic platelet as a function of the applied field. This gives a quantitative model of the influence of the applied magnetic field on the effective Young's Modulus of the material. © 2013 Owned by the authors, published by EDP Sciences

Quantum Scattering in Quasi-1D Cylindrical Confinement

Finite size effects alter not only the energy levels of small systems, but can also lead to new effective interactions within these systems. Here the problem of low energy quantum scattering by a spherically symmetric short range potential in the presence of a general cylindrical confinement is investigated. A Green's function formalism is developed which accounts for the full 3D nature of the scattering potential by incorporating all phase-shifts and their couplings. This quasi-1D geometry gives rise to scattering resonances and weakly localized states, whose binding energies and wavefunctions can be systematically calculated. Possible applications include e.g. impurity scattering in ballistic quasi-1D quantum wires in mesoscopic systems and in atomic matter wave guides. In the particular case of parabolic confinement, the present formalism can also be applied to pair collision processes such as two-body interactions. Weakly bound pairs and quasi-molecules induced by the confinement and having zero or higher orbital angular momentum can be predicted, such as p- and d-wave pairings.Comment: Extended version of quant-ph/050319

Ordered and periodic chaos of the bounded one dimensinal multibarrier potential

Numerical analysis indicates that there exists an unexpected new ordered chaos for the bounded one-dimensional multibarrier potential. For certain values of the number of barriers, repeated identical forms (periods) of the wavepackets result upon passing through the multibarrier potential.Comment: 16 pages, 9 figures, 1 Table. Some former text removed and other introduce

Bose-Einstein Condensation in a Surface Micro Trap

Bose-Einstein condensation has been achieved in a magnetic surface micro trap with 4x10^5 87Rb atoms. The strongly anisotropic trapping potential is generated by a microstructure which consists of microfabricated linear copper conductors at a width ranging from 3 to 30 micrometer. After loading a high number of atoms from a pulsed thermal source directly into a magneto-optical trap (MOT) the magnetically stored atoms are transferred into the micro trap by adiabatic transformation of the trapping potential. The complete in vacuo trap design is compatible with ultrahigh vacuum below 2x10^(-11) mbar.Comment: 4 pages, 4 figure

Dipole Blockade and Quantum Information Processing in Mesoscopic Atomic Ensembles

We describe a technique for manipulating quantum information stored in collective states of mesoscopic ensembles. Quantum processing is accomplished by optical excitation into states with strong dipole-dipole interactions. The resulting ``dipole blockade'' can be used to inhibit transitions into all but singly excited collective states. This can be employed for a controlled generation of collective atomic spin states as well as non-classical photonic states and for scalable quantum logic gates. An example involving a cold Rydberg gas is analyzed