An Exactly Solvable Spin Chain Related to Hahn Polynomials

We study a linear spin chain which was originally introduced by Shi et al. [Phys. Rev. A 71 (2005), 032309, 5 pages], for which the coupling strength contains a parameter $\alpha$ and depends on the parity of the chain site. Extending the model by a second parameter $\beta$, it is shown that the single fermion eigenstates of the Hamiltonian can be computed in explicit form. The components of these eigenvectors turn out to be Hahn polynomials with parameters $(\alpha,\beta)$ and $(\alpha+1,\beta-1)$. The construction of the eigenvectors relies on two new difference equations for Hahn polynomials. The explicit knowledge of the eigenstates leads to a closed form expression for the correlation function of the spin chain. We also discuss some aspects of a $q$-extension of this model

Modelling water flow and seasonal soil moisture dynamics in analluvial groundwater-fed wetland

Complex interactions occur in riparian wetlands between groundwater, surface water and climatic conditions. Knowledge of the hydrology of these systems is necessary to understand their functioning and their value and models are a useful and probably essential tool to capture their hydrological complexity. In this study, a 2D-model describing saturated-unsaturated water flow is applied to a transect through a groundwater-fed riparian wetland located along the middle reach of the river Dijle. The transect has high levees close to the river and a depression further into the floodplain. Scaling factors are introduced to describe the variability of soil hydraulic properties along the transect. Preliminary model calculations for one year show a good agreement between model calculations and measurements and demonstrate the capability of the model to capture the internal groundwater dynamics. Seasonal variations in soil moisture are reproduced well by the model thus translating external hydrological boundary conditions to root zone conditions. The model proves to be a promising tool for assessing effects of changes in hydrological boundary conditions on vegetation type distribution and to gain more insight in the highly variable internal flow processes of riparian wetlands.</p> <p style='line-height: 20px;'><b>Keywords: </b>riparian wetland,eco-hydrology, upward seepage, floodplain hydrolog

Deformed su(1,1) Algebra as a Model for Quantum Oscillators

The Lie algebra $\mathfrak{su}(1,1)$ can be deformed by a reflection operator, in such a way that the positive discrete series representations of $\mathfrak{su}(1,1)$ can be extended to representations of this deformed algebra $\mathfrak{su}(1,1)_\gamma$. Just as the positive discrete series representations of $\mathfrak{su}(1,1)$ can be used to model a quantum oscillator with Meixner-Pollaczek polynomials as wave functions, the corresponding representations of $\mathfrak{su}(1,1)_\gamma$ can be utilized to construct models of a quantum oscillator. In this case, the wave functions are expressed in terms of continuous dual Hahn polynomials. We study some properties of these wave functions, and illustrate some features in plots. We also discuss some interesting limits and special cases of the obtained oscillator models

Modelling water flow and seasonal soil moisture dynamics in analluvial groundwater-fed wetland

International audienceComplex interactions occur in riparian wetlands between groundwater, surface water and climatic conditions. Knowledge of the hydrology of these systems is necessary to understand their functioning and their value and models are a useful and probably essential tool to capture their hydrological complexity. In this study, a 2D-model describing saturated-unsaturated water flow is applied to a transect through a groundwater-fed riparian wetland located along the middle reach of the river Dijle. The transect has high levees close to the river and a depression further into the floodplain. Scaling factors are introduced to describe the variability of soil hydraulic properties along the transect. Preliminary model calculations for one year show a good agreement between model calculations and measurements and demonstrate the capability of the model to capture the internal groundwater dynamics. Seasonal variations in soil moisture are reproduced well by the model thus translating external hydrological boundary conditions to root zone conditions. The model proves to be a promising tool for assessing effects of changes in hydrological boundary conditions on vegetation type distribution and to gain more insight in the highly variable internal flow processes of riparian wetlands. Keywords: riparian wetland,eco-hydrology, upward seepage, floodplain hydrolog

Local damage in a 5-harness satin weave composite under static tension, part II: meso-FE modelling

International audienceThis study forms the second part of a paper on the local damage analysis in a thermo-plastic 5-harness satin weave composite under uni-axial static tensile load. The experimental observations of Part I are confronted with the meso-FE simulations. Part II describes the following steps regarding the unit cell meso-FE modeling starting from: 1) Construction of the unit cell geometrical model; 2) Estimation of the homogenized elastic constants of the unit cell using different boundary conditions; 3) Evaluation of the local stress and damage behavior of the unit cell using meso-FE simulations. The aim of the numerical analysis is to investigate the dependency of local ply stress and damage profiles on the adjacent layers of the laminate

Jet pumps for thermoacoustic applications: design guidelines based on a numerical parameter study

The oscillatory flow through tapered cylindrical tube sections (jet pumps) is characterized by a numerical parameter study. The shape of a jet pump results in asymmetric hydrodynamic end effects which cause a time-averaged pressure drop to occur under oscillatory flow conditions. Hence, jet pumps are used as streaming suppressors in closed-loop thermoacoustic devices. A two-dimensional axisymmetric computational fluid dynamics model is used to calculate the performance of a large number of conical jet pump geometries in terms of time-averaged pressure drop and acoustic power dissipation. The investigated geometrical parameters include the jet pump length, taper angle, waist diameter and waist curvature. In correspondence with previous work, four flow regimes are observed which characterize the jet pump performance and dimensionless parameters are introduced to scale the performance of the various jet pump geometries. The simulation results are compared to an existing quasi-steady theory and it is shown that this theory is only applicable in a small operation region. Based on the scaling parameters, an optimum operation region is defined and design guidelines are proposed which can be directly used for future jet pump design.Comment: The following article has been accepted by the Journal of the Acoustical Society of America. After it is published, it will be found at http://scitation.aip.org/JAS

Quantum communication and state transfer in spin chains

We investigate the time evolution of a single spin excitation state in certain linear spin chains, as a model for quantum communication. We consider first the simplest possible spin chain, where the spin chain data (the nearest neighbour interaction strengths and the magnetic field strengths) are constant throughout the chain. The time evolution of a single spin state is determined, and this time evolution is illustrated by means of an animation. Some years ago it was discovered that when the spin chain data are of a special form so-called perfect state transfer takes place. These special spin chain data can be linked to the Jacobi matrix entries of Krawtchouk polynomials or dual Hahn polynomials. We discuss here the case related to Krawtchouk polynomials, and illustrate the possibility of perfect state transfer by an animation showing the time evolution of the spin chain from an initial single spin state. Very recently, these ideas were extended to discrete orthogonal polynomials of q-hypergeometric type. Here, a remarkable result is a new analytic model where perfect state transfer is achieved: this is when the spin chain data are related to the Jacobi matrix of q-Krawtchouk polynomials. This case is discussed here, and again illustrated by means of an animation

A numerical investigation on the vortex formation and flow separation of the oscillatory flow in jet pumps

A two-dimensional computational fluid dynamics model is used to predict the oscillatory flow through a tapered cylindrical tube section (jet pump) placed in a larger outer tube. Due to the shape of the jet pump, there will exist an asymmetry in the hydrodynamic end effects which will cause a time-averaged pressure drop to occur that can be used to cancel Gedeon streaming in a closed-loop thermoacoustic device. The performance of two jet pump geometries with different taper angles is investigated. A specific time-domain impedance boundary condition is implemented in order to simulate traveling acoustic wave conditions. It is shown that by scaling the acoustic displacement amplitude to the jet pump dimensions, similar minor losses are observed independent of the jet pump geometry. Four different flow regimes are distinguished and the observed flow phenomena are related to the jet pump performance. The simulated jet pump performance is compared to an existing quasi-steady approximation which is shown to only be valid for small displacement amplitudes compared to the jet pump length.Comment: The following article has been accepted by the Journal of the Acoustical Society of America. After it is published, it will be found at: http://scitation.aip.org/JAS

Sensitivity and specificity of detection methods for erythropoietin doping in cyclists

Recombinant human erythropoietin (rHuEPO) is used as doping a substance. Anti-doping efforts include urine and blood testing and monitoring the athlete biological passport (ABP). As data on the performance of these methods are incomplete, this study aimed to evaluate the performance of two common urine assays and the ABP. In a randomized, double-blinded, placebo-controlled trial, 48 trained cyclists received a mean dose of 6000 IU rHuEPO (epoetin beta) or placebo by weekly injection for eight weeks. Seven timed urine and blood samples were collected per subject. Urine samples were analyzed by sarcosyl-PAGE and isoelectric focusing methods in the accredited DoCoLab in Ghent. A selection of samples, including any with false presumptive findings, underwent a second sarcosyl-PAGE confirmation analysis. Hematological parameters were used to construct a module similar to the ABP and analyzed by two evaluators from an Athlete Passport Management Unit. Sensitivity of the sarcosyl-PAGE and isoelectric focusing assays for the detection of erythropoietin abuse were 63.8% and 58.6%, respectively, with a false presumptive finding rate of 4.3% and 6%. None of the false presumptive findings tested positive in the confirmation analysis. Sensitivity was highest between 2 and 6 days after dosing, and dropped rapidly outside this window. Sensitivity of the ABP was 91.3%. Specificity of the urine assays was high; however, the detection window of rHuEPO was narrow, leading to questionable sensitivity. The ABP, integrating longitudinal data, is more sensitive, but there are still subjects that evade detection. Combining these methods might improve performance, but will not resolve all observed shortcomings