A Krylov subspace algorithm for evaluating the phi-functions appearing in exponential integrators

We develop an algorithm for computing the solution of a large system of linear ordinary differential equations (ODEs) with polynomial inhomogeneity. This is equivalent to computing the action of a certain matrix function on the vector representing the initial condition. The matrix function is a linear combination of the matrix exponential and other functions related to the exponential (the so-called phi-functions). Such computations are the major computational burden in the implementation of exponential integrators, which can solve general ODEs. Our approach is to compute the action of the matrix function by constructing a Krylov subspace using Arnoldi or Lanczos iteration and projecting the function on this subspace. This is combined with time-stepping to prevent the Krylov subspace from growing too large. The algorithm is fully adaptive: it varies both the size of the time steps and the dimension of the Krylov subspace to reach the required accuracy. We implement this algorithm in the Matlab function phipm and we give instructions on how to obtain and use this function. Various numerical experiments show that the phipm function is often significantly more efficient than the state-of-the-art.Comment: 20 pages, 3 colour figures, code available from http://www.maths.leeds.ac.uk/~jitse/software.html . v2: Various changes to improve presentation as suggested by the refere

Homogeneous bubble nucleation limit of mercury under the normal working conditions of the planned European Spallation Source

In spallation neutron sources, liquid mercury is the subject of big thermal and pressure shocks, upon adsorbing the proton beam. These changes can cause unstable bubbles in the liquid, which can damage the structural material. While there are methods to deal with the pressure shock, the local temperature shock cannot be avoided. In our paper we calculated the work of the critical cluster formation (i.e. for mercury micro-bubbles) together with the rate of their formation (nucleation rate). It is shown that the homogeneous nucleation rates are very low even after adsorbing several proton pulses, therefore the probability of temperature induced homogeneous bubble nucleation is negligible.Comment: 22 Pages, 11 figures, one of them is colour, we plan to publish it in Eur. Phys. J.

Association between genetic variants in the Coenzyme Q10 metabolism and Coenzyme Q10 status in humans

<p>Abstract</p> <p>Background</p> <p>Coenzyme Q₁₀(CoQ₁₀) is essential for mitochondrial energy production and serves as an antioxidants in extra mitochondrial membranes. The genetics of primary CoQ₁₀deficiency has been described in several studies, whereas the influence of common genetic variants on CoQ₁₀status is largely unknown. Here we tested for non-synonymous single-nucleotidepolymorphisms (SNP) in genes involved in the biosynthesis (CoQ3^G272S, CoQ6^M406V, CoQ7^M103T), reduction (NQO1^P187S, NQO2^L47F) and metabolism (apoE3/4) of CoQ₁₀and their association with CoQ₁₀status. For this purpose, CoQ₁₀serum levels of 54 healthy male volunteers were determined before (T₀) and after a 14 days supplementation (T₁₄) with 150 mg/d of the reduced form of CoQ₁₀.</p> <p>Findings</p> <p>At T₀, the CoQ₁₀level of heterozygous NQO1^P187Scarriers were significantly lower than homozygous S/S carriers (0.93 ± 0.25 μM versus 1.34 ± 0.42 μM, p = 0.044). For this polymorphism a structure homology-based method (PolyPhen) revealed a possibly damaging effect on NQO1 protein activity. Furthermore, CoQ₁₀plasma levels were significantly increased in apoE4/E4 genotype after supplementation in comparison to apoE2/E3 genotype (5.93 ± 0.151 μM versus 4.38 ± 0.792 μM, p = 0.034). Likewise heterozygous CoQ3^G272Scarriers had higher CoQ₁₀plasma levels at T₁₄compared to G/G carriers but this difference did not reach significance (5.30 ± 0.96 μM versus 4.42 ± 1.67 μM, p = 0.082).</p> <p>Conclusions</p> <p>In conclusion, our pilot study provides evidence that NQO1^P187Sand apoE polymorphisms influence CoQ₁₀status in humans.</p

Split Ring Resonator Experiment - Simulation Results

FLUTE (Ferninfrarot Linac- Und Test-Experiment) is a compact linac-based test facility for accelerator and diagnostics R&D. An example for a new accelerator diagnostics tool currently studied at FLUTE is the split-ring-resonator (SRR) experiment, which aims to measure the longitudinal bunch profile of fs-scale electron bunches. Laser-generated THz radiation is used to excite a high frequency oscillating electromagnetic field in the SRR. Particles passing through the SRR gap are time-dependently deflected in the vertical plane, which allows a vertical streaking of an electron bunch. This principle allows a diagnosis of the longitudinal bunch profile in the femtosecond time domain and will be tested at FLUTE. This contribution presents an overview of the SRR experiment and the results of various tracking simulations for different scenarios as a function of laser pulse length and bunch charge. Based on these results possible working points for the experiments at FLUTE will be proposed

A condensed matter interpretation of SM fermions and gauge fields

We present the bundle Aff(3) x C x /(R^3), with a geometric Dirac equation on it, as a three-dimensional geometric interpretation of the SM fermions. Each C x /(R^3) describes an electroweak doublet. The Dirac equation has a doubler-free staggered spatial discretization on the lattice space Aff(3) x C (Z^3). This space allows a simple physical interpretation as a phase space of a lattice of cells in R^3. We find the SM SU(3)_c x SU(2)_L x U(1)_Y action on Aff(3) x C x /(R^3) to be a maximal anomaly-free special gauge action preserving E(3) symmetry and symplectic structure, which can be constructed using two simple types of gauge-like lattice fields: Wilson gauge fields and correction terms for lattice deformations. The lattice fermion fields we propose to quantize as low energy states of a canonical quantum theory with Z_2-degenerated vacuum state. We construct anticommuting fermion operators for the resulting Z_2-valued (spin) field theory. A metric theory of gravity compatible with this model is presented too.Comment: Minimal modifications in comparison with the published versio

Detailed Analysis of Transverse Emittance of the FLUTE Electron Bunch

The com­pact and ver­sa­tile lin­ear ac­cel­er­a­tor-based test fa­cil­ity FLUTE (Fer­n­in­frarot Linac- Und Test-Ex­per­i­ment) is op­er­ated at KIT. Its pri­mary goal is to serve as a plat­form for a va­ri­ety of ac­cel­er­a­tor R\&D stud­ies like the gen­er­a­tion of strong ul­tra-short ter­a­hertz pulses. The am­pli­tude of the gen­er­ated co­her­ent THz pulses is pro­por­tional to the square num­ber of par­ti­cles in the bunch. With the trans­verse emit­tance a mea­sure for the trans­verse par­ti­cle den­sity can be de­ter­mined. It is there­fore a vital pa­ra­me­ter in the op­ti­miza­tion for op­er­a­tion. In a sys­tem­atic study, the trans­verse emit­tance of the elec­tron beam was mea­sured in the FLUTE in­jec­tor. A de­tailed analy­sis con­sid­ers dif­fer­ent in­flu­ences such as the bunch charge and com­pares this with par­ti­cle track­ing sim­u­la­tions car­ried out with ASTRA. In this con­tri­bu­tion, the key find­ings of this analy­sis are dis­cussed

The Simplicial Ricci Tensor

The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The 3-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The 4-dimensional Ric is the Einstein tensor for such spacetimes. More recently the Ric was used by Hamilton to define a non-linear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincare conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher-dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area -- an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimension.Comment: 19 pages, 2 figure