Asymptotic results for renewal risk models with risky investments

We consider a renewal jump-diffusion process, more specifically a renewal insurance risk model with investments in a stock whose price is modeled by a geometric Brownian motion. Using Laplace transforms and regular variation theory, we introduce a transparent and unifying analytic method for investigating the asymptotic behavior of ruin probabilities and related quantities, in models with light- or heavy-tailed jumps, whenever the distribution of the time between jumps has rational Laplace transform

Incremental expansions for Hubbard-Peierls systems

The ground state energies of infinite half-filled Hubbard-Peierls chains are investigated combining incremental expansion with exact diagonalization of finite chain segments. The ground state energy of equidistant infinite Hubbard (Heisenberg) chains is calculated with a relative error of less than $3 \cdot 10^{-3}$ for all values of $U$ using diagonalizations of 12-site (20-site) chain segm ents. For dimerized chains the dimerization order parameter $d$ as a function of the onsite repulsion interaction $U$ has a maximum at nonzero values of $U$, if the electron-phonon coupling $g$ is lower than a critical value $g_c$. The critical value $g_c$ is found with high accuracy to be $g_c=0.69$. For smaller values of $g$ the position of the maximum of $d(U)$ is approximately $3t$, and rapidly tends to zero as $g$ approaches $g_c$ from below. We show how our method can be applied to calculate breathers for the problem of phonon dynamics in Hubbard-Peierls systems.Comment: 4 Pages, 3 Figures, REVTE

On the Navier-Stokes equations with rotating effect and prescribed outflow velocity

We consider the equations of Navier-Stokes modeling viscous fluid flow past a moving or rotating obstacle in $\mathbb{R}^d$ subject to a prescribed velocity condition at infinity. In contrast to previously known results, where the prescribed velocity vector is assumed to be parallel to the axis of rotation, in this paper we are interested in a general outflow velocity. In order to use $L^p$-techniques we introduce a new coordinate system, in which we obtain a non-autonomous partial differential equation with an unbounded drift term. We prove that the linearized problem in $\mathbb{R}^d$ is solved by an evolution system on $L^p_{\sigma}(\mathbb{R}^d)$ for $1<p<\infty$. For this we use results about time-dependent Ornstein-Uhlenbeck operators. Finally, we prove, for $p\geq d$ and initial data $u_0\in L^p_{\sigma}(\mathbb{R}^d)$, the existence of a unique mild solution to the full Navier-Stokes system.Comment: 18 pages, to appear in J. Math. Fluid Mech. (published online first

Space-charge mechanism of aging in ferroelectrics: an exactly solvable two-dimensional model

A mechanism of point defect migration triggered by local depolarization fields is shown to explain some still inexplicable features of aging in acceptor doped ferroelectrics. A drift-diffusion model of the coupled charged defect transport and electrostatic field relaxation within a two-dimensional domain configuration is treated numerically and analytically. Numerical results are given for the emerging internal bias field of about 1 kV/mm which levels off at dopant concentrations well below 1 mol%; the fact, long ago known experimentally but still not explained. For higher defect concentrations a closed solution of the model equations in the drift approximation as well as an explicit formula for the internal bias field is derived revealing the plausible time, temperature and concentration dependencies of aging. The results are compared to those due to the mechanism of orientational reordering of defect dipoles.Comment: 8 pages, 4 figures. accepted to Physical Review

Aging of poled ferroelectric ceramics due to relaxation of random depolarization fields by space-charge accumulation near grain boundaries

Migration of charged point defects triggered by the local random depolarization field is shown to plausibly explain aging of poled ferroelectric ceramics providing reasonable time and acceptor concentration dependences of the emerging internal bias field. The theory is based on the evaluation of the energy of the local depolarization field caused by mismatch of the polarizations of neighbor grains. The kinetics of charge migration assumes presence of mobile oxygen vacancies in the material due to the intentional or unintentional acceptor doping. Satisfactory agreement of the theory with experiment on the Fe-doped lead zirconate titanate is demonstrated.Comment: theory and experiment, 22 pages, 3 figure

Characterising gas behaviour during gas–liquid co-current up-flow in packed beds using magnetic resonance imaging

Magnetic resonance (MR) imaging techniques have been used to study gas phase dynamics during co-current up-flow in a column of inner diameter 43 mm, packed with spherical non-porous elements of diameters of 1.8, 3 and 5 mm. MR measurements of gas hold-up, bubble-size distribution, and bubble-rise velocities were made as a function of flow rate and packing size. Gas and liquid flow rates were studied in the range of 20–250 cm3 s−1 and 0–200 cm3 min−1, respectively. The gas hold-up within the beds was found to increase with gas flow rate, while decreasing with increasing packing size and to a lesser extent with increasing liquid flow rate. The gas hold-up can be separated into a dynamic gas hold-up, only weakly dependent on packing size and associated with bubbles rising up the bed, and a ‘static’ hold-up which refers to locations within the bed associated with temporally-invariant gas hold-up, over the measurement times of 512 s, associated either with gas trapped within the void structure of the bed or with gas channels within the bed. This ‘static’ gas hold-up is strongly dependent on packing size, showing an increase with decreasing packing size. The dynamic gas hold-up is comprised of small bubbles – of order of the packing size – which have rise velocities of 10–40 mm s−1 and which move between the packing elements within the bed, along with much larger bubbles, or agglomerates of bubbles, which move with higher rise velocities (100–300 mm s−1). These ‘larger’ bubbles, which may exist as streams of smaller bubbles or ‘amoeboid’ bubbles, behave as a single large bubble in terms of the observed high rise velocity. Elongation of the bubbles in the direction of flow was observed for all packings.We wish to thank ExxonMobil Research and Engineering Co. and EPSRC Platform Grant (EP/F047991/1) for financial support.This is the author accepted manuscript. The final version is available from Elsevier via http://dx.doi.org/10.1016/j.ces.2016.04.00

Evaluation of the CELL-DYN® 3500 haematology instrument for the analysis of the mouse and rat blood

The objective of this study was to evaluate the performance of the CELL-DYN® 3500 for rat and mouse blood analysis in a routine environment. The WBC (white blood cells), RBC (red blood cells), PLT (platelets) counts and the WBC differential were determined. In addition, the following aspects were studied: within-run precision, day-to-day precision, biasfree paired difference precision; extended ranges of linearity for RBC, HCT (haematocrit), WBC, PLT; carry-over, the fffect of blood ageing, cell stability with different anticoagulants; and the normal ranges, the out of range flagging and some typical pathology cases. The CELL-DYN® 3500 is a multiparameter flow cytometer which counts and differentiates WBC, based on the principle of multi-angle polarised light scatter separation. RBC and PLT are determined by the impedance method. The WBC count is evaluated by both, optical and impedance methods. Reference methods used were according to the ICSH recommendations on blood cell analysis, including manual counts of WBC and platelets, a centrifugal microhaematocrit method and a haemoglobin measurement by spectrophotometry using the WHO haemoglobin standard. All cell counts were compared with the results obtained by our routine blood cell analyser (Contraves AL820), and the WBC differential was compared with the manual microscopic differentiation of the 400 WBC (200 cells differentiated by two technicians). The following coefficients of variation were obtained: within-run precision was 1.2% and 2.7% for WBC; 1.0% and 1.0% for RBC; 1.3% and 0.9% for haematocrit; 2.1% and 2.7% for platelets (rats and mice respectively). Day-to-day precision was performed using human trilevel control blood, and the CVs were found to be <1.7% for WBC, <1.4% for RBC, <1.2% for haemoglobin and <6.3% for platelets. The following ranges of measurement were found to be linear in the rat: WBC: 0.10-20.20×103/μl; RBC: 0.016-14.3×106/μl; haemoglobin: 0.08-26.8 g/dl; haematocrit: 5.0%-77%; platelets: 14.0-1670.0×103/μl. Equal ranges were observed for mouse blood. Carry-over in rat blood was found to be 0.12% for WBC, 0.05% for RBC, 0.15% for haemoglobin and 0.46% for platelets. In mice, similar carry-over results were obtained. The correlation coefficients (Pearson, correlation coefficient) between the CELL-DYN® 3500 and Contraves AL 820 using linear regression analysis were as follows: 0.988 and 0.997 for WBC; 0.986 and 0.920 for RBC; 0.995 and 0.984 for haemoglobin; 0.958 and 0.85 for haematocrit; 0.958 and 0.963 for platelets, for rats and mice, respectively. Correlation coefficients between the CELL-DYN® 3500 and the manual differential of NEU (neutrophils) and LYM (lymphocytes) were higher than 0.8 in rats and higher than 0.9 in mice. Due to the relatively low absolute counts of MONO (monocytes), EOS (eosinophils) and BASO (basophils), only moderate correlation of methods was found. The CELL-DYN® 3500 was judged to be reliable, accurate and easy-to-use for counting and identifying normal and most of the pathological blood specimens obtained from mice and rats. By using the CELL-DYN® 3500, the time for blood sample analysis can be shortened significantly and provides extensive opportunities to characterise pathological sample

Driving the atom by atomic fluorescence: analytic results for the power and noise spectra

We study how the spectral properties of resonance fluorescence propagate through a two-atom system. Within the weak-driving-field approximation we find that, as we go from one atom to the next, the power spectrum exhibits both sub-natural linewidth narrowing and large asymmetries while the spectrum of squeezing narrows but remains otherwise unchanged. Analytical results for the observed spectral features of the fluorescence are provided and their origin is thoroughly discussed.Comment: 13 pages, 5 figures; to be published in Phys. Rev. A Changed title and conten

Turbulent Supersonic/Hypersonic Heating Correlations for Open and Closed Cavities

Supersonic/hypersonic laminar heating correlations that were developed for damage assessment analysis of atmospheric re-entry vehicles have been modified and extended to cover fully-turbulent conditions over rectangular cavity geometries that are aligned with the local velocity. Turbulent boundary layer properties were computationally determined and used to develop the cavity geometry parametrics and to correlate experimental closed cavity heating data to yield new relationships for the floor-averaged and centerline endwall peak-heating augmentation. With the form of the closed-cavity correlations established, historical data were used to develop new correlations for turbulent open-cavity heating