Numerical computation of the module of a quadrilateral

The module of a quadrilateral is a positive real number which divides quadrilaterals into conformal equivalence classes. This is an introductory text to the module of a quadrilateral with some historical background and some numerical aspects. This work discusses the following topics: 1. Preliminaries 2. The module of a quadrilateral 3. The Schwarz-Christoffel Mapping 4. Symmetry properties of the module 5. Computational results 6. Other numerical methods Appendices include: Numerical evaluation of the elliptic integrals of the first kind. Matlab programs and scripts and possible topics for future research. Numerical results section covers additive quadrilaterals and the module of a quadrilateral under the movement of one of its vertex.

Evaluation of the Grounding Resistance of Conductors Buried in Steplike Terrain

Availability of land for conventional air-insulated substations is becoming increasingly difficult not only in urban but also in semiurban areas. When the land made available is highly uneven, the associated technoeconomic factors favors the erection of substations on a steplike-formed ground surface and such constructions are in service for more than ten years in some parts of southern India. Noting that the literature on the performance of ground grids in such a construction is rather scarce, the present work was taken up. Evaluation of the performance of earthing elements in steplike ground forms the main goal of the present work. For the numerical evaluation, a suitable boundary-based methodology is employed. This method retains the classical Galerkin approach for the conductors, while the interfaces are replaced by equivalent fictitious surface sources defined over unstructured mesh. Details of the implementation of this numerical method, along with special measures to minimize the computation, are presented. The performance of basic earthing elements, such as the driven rod, counterpoise, and simple grids buried in steplike ground, are analyzed and compared with that for the case with uniform soil surface. It is shown that more than the earthing resistances, the step potentials can get significantly affected.

Evaluation of perforated steel plates as connection in glulam-concrete composite structures

This paper shows the results of an experimental investigation carried out on a connection element of glulam and concrete composite structures, through double-sided push-out shear tests. The connection system was composed of perforated steel plates glued with epoxy adhesive. Five specimens were made and tested under shear forces. This innovative connection system showed an average initial slip modulus equivalent to 339.4 kN/mm. In addition, the connection system was evaluated by means of numerical simulations and the software ANSYS was used for this purpose. The numerical simulations demonstrated good agreement with the experimental data, especially in the regime of elastic-linear behavior of materials. (C) 2011 Elsevier Ltd. All rights reserved.

Fast and accurate numerical solutions in some problems of particle and radiation transport: synthetic acceleration for the method of short characteristics, Doppler-broadened scattering kernel, remote sensing of the cryosphere

The aim of this work is to present various aspects of numerical simulation of particle and radiation transport for industrial and environmental protection applications, to enable the analysis of complex physical processes in a fast, reliable, and efficient way. In the first part we deal with speed-up of numerical simulation of neutron transport for nuclear reactor core analysis. The convergence properties of the source iteration scheme of the Method of Characteristics applied to be heterogeneous structured geometries has been enhanced by means of Boundary Projection Acceleration, enabling the study of 2D and 3D geometries with transport theory without spatial homogenization. The computational performances have been verified with the C5G7 2D and 3D benchmarks, showing a sensible reduction of iterations and CPU time. The second part is devoted to the study of temperature-dependent elastic scattering of neutrons for heavy isotopes near to the thermal zone. A numerical computation of the Doppler convolution of the elastic scattering kernel based on the gas model is presented, for a general energy dependent cross section and scattering law in the center of mass system. The range of integration has been optimized employing a numerical cutoff, allowing a faster numerical evaluation of the convolution integral. Legendre moments of the transfer kernel are subsequently obtained by direct quadrature and a numerical analysis of the convergence is presented. In the third part we focus our attention to remote sensing applications of radiative transfer employed to investigate the Earth's cryosphere. The photon transport equation is applied to simulate reflectivity of glaciers varying the age of the layer of snow or ice, its thickness, the presence or not other underlying layers, the degree of dust included in the snow, creating a framework able to decipher spectral signals collected by orbiting detectors.

Numerical precision calculations for LHC physics

In dieser Arbeit stelle ich Aspekte zu QCD Berechnungen vor, welche eng verknüpft sind mit der numerischen Auswertung von NLO QCD Amplituden, speziell der entsprechenden Einschleifenbeiträge, und der effizienten Berechnung von damit verbundenen Beschleunigerobservablen. Zwei Themen haben sich in der vorliegenden Arbeit dabei herauskristallisiert, welche den Hauptteil der Arbeit konstituieren. Ein großer Teil konzentriert sich dabei auf das gruppentheoretische Verhalten von Einschleifenamplituden in QCD, um einen Weg zu finden die assoziierten Farbfreiheitsgrade korrekt und effizient zu behandeln. Zu diesem Zweck wird eine neue Herangehensweise eingeführt welche benutzt werden kann, um farbgeordnete Einschleifenpartialamplituden mit mehreren Quark-Antiquark Paaren durch Shufflesummation über zyklisch geordnete primitive Einschleifenamplituden auszudrücken. Ein zweiter großer Teil konzentriert sich auf die lokale Subtraktion von zu Divergenzen führenden Poltermen in primitiven Einschleifenamplituden. Hierbei wurde im Speziellen eine Methode entwickelt, um die primitiven Einchleifenamplituden lokal zu renormieren, welche lokale UV Counterterme und effiziente rekursive Routinen benutzt. Zusammen mit geeigneten lokalen soften und kollinearen Subtraktionstermen wird die Subtraktionsmethode dadurch auf den virtuellen Teil in der Berechnung von NLO Observablen erweitert, was die voll numerische Auswertung der Einschleifenintegrale in den virtuellen Beiträgen der NLO Observablen ermöglicht. Die Methode wurde schließlich erfolgreich auf die Berechnung von NLO Jetraten in Elektron-Positron Annihilation im farbführenden Limes angewandt.

Algorithms for Evaluation of the Wright Function for the Real Arguments’ Values

2000 Math. Subject Classification: 33E12, 65D20, 33F05, 30E15

Computational evaluation of wind loads on low- and highrise buildings

Buildings and other infrastructures located in the coastal regions of the US have a higher level of wind vulnerability. Reducing the increasing property losses and causalities associated with severe windstorms has been the central research focus of the wind engineering community. The present wind engineering toolbox consists of building codes and standards, laboratory experiments, and field measurements. The American Society of Civil Engineers (ASCE) 7 standard provides wind loads only for buildings with common shapes. For complex cases it refers to physical modeling. Although this option can be economically viable for large projects, it is not cost-effective for low-rise residential houses. To circumvent these limitations, a numerical approach based on the techniques of Computational Fluid Dynamics (CFD) has been developed. The recent advance in computing technology and significant developments in turbulence modeling is making numerical evaluation of wind effects a more affordable approach. The present study targeted those cases that are not addressed by the standards. These include wind loads on complex roofs for low-rise buildings, aerodynamics of tall buildings, and effects of complex surrounding buildings. Among all the turbulence models investigated, the large eddy simulation (LES) model performed the best in predicting wind loads. The application of a spatially evolving time-dependent wind velocity field with the relevant turbulence structures at the inlet boundaries was found to be essential. All the results were compared and validated with experimental data. The study also revealed CFD's unique flow visualization and aerodynamic data generation capabilities along with a better understanding of the complex three-dimensional aerodynamics of wind-structure interactions. With the proper modeling that realistically represents the actual turbulent atmospheric boundary layer flow, CFD can offer an economical alternative to the existing wind engineering tools. CFD's easy accessibility is expected to transform the practice of structural design for wind, resulting in more wind-resilient and sustainable systems by encouraging optimal aerodynamic and sustainable structural/building design. Thus, this method will help ensure public safety and reduce economic losses due to wind perils.

Computational Evaluation of Wind Loads on Low- and High- Rise Buildings

Buildings and other infrastructures located in the coastal regions of the US have a higher level of wind vulnerability. Reducing the increasing property losses and causalities associated with severe windstorms has been the central research focus of the wind engineering community. The present wind engineering toolbox consists of building codes and standards, laboratory experiments, and field measurements. The American Society of Civil Engineers (ASCE) 7 standard provides wind loads only for buildings with common shapes. For complex cases it refers to physical modeling. Although this option can be economically viable for large projects, it is not cost-effective for low-rise residential houses. To circumvent these limitations, a numerical approach based on the techniques of Computational Fluid Dynamics (CFD) has been developed. The recent advance in computing technology and significant developments in turbulence modeling is making numerical evaluation of wind effects a more affordable approach. The present study targeted those cases that are not addressed by the standards. These include wind loads on complex roofs for low-rise buildings, aerodynamics of tall buildings, and effects of complex surrounding buildings. Among all the turbulence models investigated, the large eddy simulation (LES) model performed the best in predicting wind loads. The application of a spatially evolving time-dependent wind velocity field with the relevant turbulence structures at the inlet boundaries was found to be essential. All the results were compared and validated with experimental data. The study also revealed CFD’s unique flow visualization and aerodynamic data generation capabilities along with a better understanding of the complex three-dimensional aerodynamics of wind-structure interactions. With the proper modeling that realistically represents the actual turbulent atmospheric boundary layer flow, CFD can offer an economical alternative to the existing wind engineering tools. CFD’s easy accessibility is expected to transform the practice of structural design for wind, resulting in more wind-resilient and sustainable systems by encouraging optimal aerodynamic and sustainable structural/building design. Thus, this method will help ensure public safety and reduce economic losses due to wind perils.

Transport and health in China : recent collaborative research relating to vehicle factors and pollution

The nature of the transport system contributes to public health outcomes in a range of ways. The clearest contribution to public health is in the area of traffic crashes, because of their direct impact on individual death and disability and their direct costs to the health system. Other papers in this conference address these issues. This paper outlines some collaborative research between the Centre for Accident Research and Road Safety - Queensland (CARRS-Q) at QUT and Chinese researchers in areas that have indirect health impacts. Heavy vehicle dynamics: The integrity of the road surface influences crash risk, with ruts, pot-holes and other forms of road damage contributing to increased crash risks. The great majority of damage to the road surface from vehicles is caused by heavy trucks and buses, rather than cars or smaller vehicles. In some cases this damage is due to deliberate overloading, but in other cases it is due to vehicle suspension characteristics that lead to occasional high loads on particular wheels. Together with a visiting researcher and his colleagues, we have used both Queensland and Chinese data to model vehicle suspension systems that reduce the level of load, and hence the level of road damage and resulting crash risk(1-5). Toll worker exposure to vehicle emissions: The increasing construction of highways in China has also involved construction of a large number of toll roads. Tollbooth workers are potentially exposed to high levels of pollutants from vehicles, however the extent of this exposure and how it relates to standards for exposure are not well known. In a study led by a visiting researcher, we conducted a study to model these levels of exposure for a tollbooth in China(6). Noise pollution: The increasing presence of high speed roads in China has contributed to an increase in noise levels. In this collaborative study we modelled noise levels associated with a freeway widening near a university campus, and measures to reduce the noise(7). Along with these areas of research, there are many other areas of transport with health implications that are worthy of exploration. Traffic, noise and pollution contribute to a difficult environment for pedestrians, especially in an ageing society where there are health benefits to increasing physical activity. By building on collaborations such as those outlined, there is potential for a contribution to improved public health by addressing transport issues such as vehicle factors and pollution, and extending the research to other areas of travel activity. 1. Chen, Y., He, J., King, M., Chen, W. and Zhang, W. (2014). Stiffness-damping matching method of an ECAS system based on LQG control. Journal of Central South University, 21:439-446. DOI: 10.1007/s1177101419579 2. Chen, Y., He, J., King, M., Feng, Z. and Chang, W. (2013). Comparison of two suspension control strategies for multi-axle heavy truck. Journal of Central South University, 20(2): 550-562. 3. Chen, Y., He, J., King, M., Chen, W. and Zhang, W. (2013). Effect of driving conditions and suspension parameters on dynamic load-sharing of longitudinal-connected air suspensions. Science China Technological Sciences, 56(3): 666-676. DOI: 10.1007/s11431-012-5091-3 4. Chen, Y., He., J., King, M., Chen, W. and Zhang, W. (2013). Model development and dynamic load-sharing analysis of longitudinal-connected air suspensions. Strojniški Vestnik - Journal of Mechanical Engineering, 59(1):14-24. 5. Chen, Y., He, J., King, M., Liu, H. and Zhang, W. (2013). Dynamic load-sharing of longitudinal-connected air suspensions of a tri-axle semi-trailer. Proceedings of Transportation Research Board Annual Conference, Washington DC, 13-17 January 2013, paper no. 13-1117. 6. He, J., Qi, Z., Hang, W., King, M., and Zhao, C. (2011). Numerical evaluation of pollutant dispersion at a toll plaza based on system dynamics and Computational Fluid Dynamics models. Transportation Research Part C, 19(2011):510-520. 7. Zhang, C., He, J., Wang, Z., Yin, R. and King, M. (2013). Assessment of traffic noise level before and after freeway widening using traffic microsimulation and a refined classic noise prediction method. Proceedings of Transportation Research Board Annual Conference, Washington DC, 13-17 January 2013, paper no. 13-2016.

Effects of environment on surface-wave characteristics of a dielectric-coated conductor .4.

The problem of excitation of 11zultilayercd-graded-dielectric-coatedc onductor by a magnetic ring source is fornzulated in the ,form of a contour integrul which is rolved by using the method of steepest descent. Numerical evaluation of launching efiiency shows that high value of about 90 percent can be attained by choosing proper dimensions of the launcher with respect to the dimension of the surface wave line.

Excitation energy transfer from a fluorophore to single-walled carbon nanotubes

We study the process of electronic excitation energy transfer from a fluorophore to the electronic energy levels of a single-walled carbon nanotube. The matrix element for the energy transfer involves the Coulombic interaction between the transition densities on the donor and the acceptor. In the Foumlrster approach, this is approximated as the interaction between the corresponding transition dipoles. For energy transfer from a dye to a nanotube, one can use the dipole approximation for the dye, but not for the nanotube. We have therefore calculated the rate using an approach that avoids the dipole approximation for the nanotube. We find that for the metallic nanotubes, the rate has an exponential dependence if the energy that is to be transferred, h is less than a threshold and a d(-5) dependence otherwise. The threshold is the minimum energy required for a transition other than the k(i,perpendicular to)=0 and l=0 transition. Our numerical evaluation of the rate of energy transfer from the dye pyrene to a (5,5) carbon nanotube, which is metallic leads to a distance of similar to 165 A degrees up to which energy transfer is appreciable. For the case of transfer to semiconducting carbon nanotubes, apart from the process of transfer to the electronic energy levels within the one electron picture, we also consider the possibility of energy transfer to the lowest possible excitonic state. Transfer to semiconducting carbon nanotubes is possible only if>=epsilon(g)-epsilon(b). The long range behavior of the rate of transfer has been found to have a d(-5) dependence if h >=epsilon(g). But, when the emission energy of the fluorophore is in the range epsilon(g)>h >=epsilon(g)-epsilon(b), the rate has an exponential dependence on the distance. For the case of transfer from pyrene to the semiconducting (6,4) carbon nanotube, energy transfer is found to be appreciable up to a distance of similar to 175 A degrees.

Molecular theory of dielectric relaxation in a dense binary dipolar liquid

A molecular theory of dielectric relaxation in a dense binary dipolar liquid is presented. The theory takes into account the effects of intra- and interspecies intermolecular interactions. It is shown that the relaxation is, in general, nonexponential. In certain limits, we recover the biexponential form traditionally used to analyze the experimental data of dielectric relaxation in a binary mixture. However, the relaxation times are widely different from the prediction of the noninteracting rotational diffusion model of Debye for a binary system. Detailed numerical evaluation of the frequency-dependent dielectric function epsilon-(omega) is carried out by using the known analytic solution of the mean spherical approximation (MSA) model for the two-particle direct correlation function for a polar mixture. A microscopic expression for both wave vector (k) and frequency (omega) dependent dielectric function, epsilon-(k,omega), of a binary mixture is also presented. The theoretical predictions on epsilon-(omega) (= epsilon-(k = 0, omega)) have been compared with the available experimental results. In particular, the present theory offers a molecular explanation of the phenomenon of fusing of the two relaxation channels of the neat liquids, observed by Schallamach many years ago.

Relationship between microscopic and macroscopic orientational relaxation times in polar liquids

Microscopic relations between single-particle orientational relaxation time (T, ) , dielectric relaxation time ( T ~ )a,n d many-body orientational relaxation time ( T ~o)f a dipolar liquid are derived. We show that both T~ and T~ are influenced significantly by many-body effects. In the present theory, these many-body effects enter through the anisotropic part of the two-particle direct correlation function of the polar liquid. We use mean-spherical approximation (MSA) for dipolar hard spheres for explicit numerical evaluation of the relaxation times. We find that, although the dipolar correlation function is biexponential, the frequency-dependent dielectric constant is of simple Debye form, with T~ equal to the transverse polarization relaxation time. The microscopic T~ falls in between Debye and Onsager-Glarum expressions at large values of the static dielectric constant.

Biorthogonal series method for Oseen type flows

A biorthogonal series method is developed to solve Oseen type flow problems. The theory leads to a new set of eigenfunctions for a specific class of linear non-selfadjoint operators containing the biharmonic one. These eigenfunctions differ from those given earlier in the literature for the biharmonic operator. The method is applied to the problem of thermocapillary flow in a cylindrical liquid bridge of finite length with axial through flow. Flow and temperature distributions are obtained at leading order of an expansion for small surface tension Reynolds number and Prandtl number. Another related problem considered is that of cylindrical cavity flow. Solutions for both cases are presented in terms of biorthogonal series. The effect of axial through flow on velocity and temperature fields is discussed by numerical evaluation of the truncated analytical series. The presence of axial through flow not only convectively shifts the vortices induced by surface forces in the direction of the through flow, but also moves their centers toward the outer cylindrical boundary. This process can lead to significantly asymmetric flow structures.