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[en] The hypergeometric function method naturally provides the analytic expressions of scalar integrals from concerned Feynman diagrams in some connected regions of independent kinematic variables, also presents the systems of homogeneous linear partial differential equations satisfied by the corresponding scalar integrals. Taking examples of the one-loop and massless functions, as well as the scalar integrals of two-loop vacuum and sunset diagrams, we verify our expressions coinciding with the well-known results of literatures. Based on the multiple hypergeometric functions of independent kinematic variables, the systems of homogeneous linear partial differential equations satisfied by the mentioned scalar integrals are established. Using the calculus of variations, one recognizes the system of linear partial differential equations as stationary conditions of a functional under some given restrictions, which is the cornerstone to perform the continuation of the scalar integrals to whole kinematic domains numerically with the finite element methods. In principle this method can be used to evaluate the scalar integrals of any Feynman diagrams.
[en] A novel, hierarchical Haar wavelet basis is introduced and used to discretise the angular dimension of the Boltzmann transport equation. This is used in conjunction with a finite element subgrid scale method. This combination is then validated using two steady-state radiation transport problems, namely a 2D dogleg-duct shielding problem and the 2D C5MOX OECD/NEA benchmark. It is shown that the scheme has many similarities to a traditional equal weighted discrete ordinates () angular discretisation, but the strong motivation for our hierarchical Haar wavelet method is the potential for adapting in angle in a simple fashion through elimination of redundant wavelets. Initial investigations of this adaptive approach are presented for a shielding and criticality eigenvalue example. It is shown that a 60% reduction in the number of angles needed on most spatial nodes - and rising up to 90% on nodes located in high streaming areas - can be attained without adversely affecting the accuracy of the solution.
[en] Authors discuss the problem of mathematical modeling of the stationary heat transfer process in a multilayer medium possessing a cylindrical symmetry. For modeling, the matrix method and the Bers' method of generalized powers were used together. The proposed method has many applications. A more general spatial problem is also briefly considered. In solving this problem, the methods are used together with the classical Fourier method
[ru]В работе рассмотрена задача математического моделирования стационарного процесса теплопереноса в многослойной среде, обладающей цилиндрической симметрией. Для моделирования использованы матричный метод и метод обобщенных степеней Берса. Также кратко рассмотрена и более общая пространственная задача. При ее решении указанные методы применяются совместно с классическим методом Фурье
[en] A new generalized perturbation theory (GPT) equation is derived applying the comprehensive mathematical framework (C-Framework) for Monte Carlo (Mc) eigenvalue calculations. The new GPT equation no longer limits the type of a target response in its application, in contrast to the conventional generalized perturbation theory that has a limited application to the GPT-allowable target response only. It is shown that the new GPT equations are exactly the same as the conventional GPT counterparts for GPT-allowable types of response such as the standard Mc tally and the effective multiplication factor. It is also shown that the new GPT equation can deal with absolute reaction rate and equilibrium xenon concentration which is not GPT-allowable responses. (Author)
[en] It is very important and sometimes even vital to maintain reliability of industrial structures. High quality control during production and structural health monitoring (SHM) in exploitation provides reliable functioning of large, massive and remote structures, like wind generators, pipelines, power line posts, etc. This paper introduces a complex of technological and methodical solutions for SHM and diagnostics of industrial structures, including those that are actuated by periodic forces. Solutions were verified on a wind generator scaled model with integrated system of piezo-film deformation sensors. Simultaneous and multi-patch Operational Modal Analysis (OMA) approaches were implemented as methodical means for structural diagnostics and monitoring. Specially designed data processing algorithms provide objective evaluation of structural state modification. (paper)
[en] The search process is used in various activities performed both online and offline, many algorithms that can be used to perform the search process one of which is a hash search algorithm, search process with hash search algorithm used in this study using double hashing technique where the data will be formed into the table with same length and then search, the results of this study indicate that the search process with double hashing technique allows faster searching than the usual search techniques, this research allows to search the solution by dividing the value into the main table and overflow table so that the search process is expected faster than the data stacked in the form of one table and collision data could avoided. (paper)
[en] Inherently UWB (Ultra Wideband) communication systems comes with interference problem with some if the existing narrowband communication systems. These bands are stopped with the help of band-stop filter in order to reduce electromagnetic interference However, the complexity and limitations are increased due to these filters, hence this solution is turned down in those applications where design complications and complexity is of concern. Introducing various slots of specific shapes and exact dimensions however, have solved this issue for the researchers around the world. This paper presents a hexagonal PMA (Printed Monopole Antenna) with triple stop bands. The antenna is used for UWB application. The antenna is stopped the WiMAX (Worldwide Interoperability for Microwave Access), WLAN (Wireless Local Area Network) and ITU (International Telecommunication Union) bands. The antenna dimensions are 30x28x16 mm3. FR4 is used between ground and radiating patch with relative permittivity of 4.4. The VSWR (Voltage Standing Wave Ratio) is less than 2 between 3-11 GHz except WiMAX (3.1-3.7 GHz), WLAN (5.1-5.8 GHz) and the ITU frequency band (7.95-8.4 GHz). The antenna is design in CST software. (author)
[en] The degrees of freedom (DOF) in standard ensemble-based data assimilation is limited by the ensemble size. Successful assimilation of a data set with large information content (IC) therefore requires that the DOF is sufficiently large. A too small number of DOF with respect to the IC may result in ensemble collapse, or at least in unwarranted uncertainty reduction in the estimation results. In this situation, one has two options to restore a proper balance between the DOF and the IC: to increase the DOF or to decrease the IC. Spatially dense data sets typically have a large IC. Within subsurface applications, inverted time-lapse seismic data used for reservoir history matching is an example of a spatially dense data set. Such data are considered to have great potential due to their large IC, but they also contain errors that are challenging to characterize properly. The computational cost of running the forward simulations for reservoir history matching with any kind of data is large for field cases, such that a moderately large ensemble size is standard. Realization of the potential in seismic data for ensemble-based reservoir history matching is therefore not straightforward, not only because of the unknown character of the associated data errors, but also due to the imbalance between a large IC and a too small number of DOF. Distance-based localization is often applied to increase the DOF but is example specific and involves cumbersome implementation work. We consider methods to obtain a proper balance between the IC and the DOF when assimilating inverted seismic data for reservoir history matching. To decrease the IC, we consider three ways to reduce the influence of the data space; subspace pseudo inversion, data coarsening, and a novel way of performing front extraction. To increase the DOF, we consider coarse-scale simulation, which allows for an increase in the DOF by increasing the ensemble size without increasing the total computational cost. We also consider a combination of decreasing the IC and increasing the DOF by proposing a novel method consisting of a combination of data coarsening and coarse-scale simulation. The methods were compared on one small and one moderately large example with seismic bulk-velocity fields at four assimilation times as data. The size of the examples allows for calculation of a reference solution obtained with standard ensemble-based data assimilation methodology and an unrealistically large ensemble size. With the reference solution as the yardstick with which the quality of other methods are measured, we find that the novel method combining data coarsening and coarse-scale simulations gave the best results. With very restricted computational resources available, this was the only method that gave satisfactory results.
[en] Methods to simulate facies (or categorical) fields are numerous. However, calibration of simulated facies fields to large-scale or dynamic data still remains an important challenge due to the discrete nature of the fields, the non-linearity of the response with respect to the facies fields, and the non-derivability of the objective function used in calibration. A new gradual deformation method (GDM) is presented and tested for the calibration of facies realizations obtained by patch-multipoint simulation (MPS). The proposed method borrows ideas from pluriGaussian simulation, evolutionary algorithms, and GDM. Various test cases are considered: proportion maps, section of seismic amplitudes, inlet to outlet travel time along the shortest path, and water-cut curves obtained with a flow simulator. Both conditional/unconditional MPS simulations and 2D/3D problems are considered. In all studied test cases, the new GDM approach has provided excellent calibration to the target variables. The method is general as it can be used in conjunction with any facies simulator.