The discrete fragmentation equations : semigroups, compactness and asynchronous exponential growth

In this paper we present a class of fragmentation semigroups which are compact in a scale of spaces defined in terms of finite higher moments. We use this compactness result to analyse the long time behaviour of such semigroups and, in particular, to prove that they have the asynchronous growth property. We note that, despite compactness, this growth property is not automatic as the fragmentation semigroups are not irreducible

TRÓJWYMIAROWA WIZUALIZACJA STRUKTUR PRZEPŁYWÓW DWUFAZOWYCH PRZY UŻYCIU ELEKTRYCZNEJ TOMOGRAFII POJEMNOŚCIOWEJ – ALGORYTMY I OPROGRAMOWANIE

This paper presents the software for comprehensive processing and visualization of 2D and 3D electrical tomography data. The system name as TomoKIS Studio has been developed in the frame of DENIDIA international research project and has been improved in the frame of Polish Ministry of Science and Higher Education Project no 4664/B/T02/2010/38. This software is worldwide unique because it simultaneously integrates the process of tomographic data acquisition, numerical FEM modeling and tomographic images reconstruction. The software can be adapted to specific industrial applications, particularly to monitoring and diagnosis of two-phase flows. The software architecture is composed of independent modules. Their combination offers calibration, configuration and full-duplex communication with any tomographic acquisition system with known and open communication protocol. The other major features are: online data acquisition and processing, online and offline 2D/3D images linear and nonlinear reconstruction and visualization as well as raw data and tomograms processing. Another important ability is 2D/3D ECT sensor construction using FEM modeling. The presented software is supported with the multi-core GPU technology and parallel computing using Nvidia CUDA technology.W artykule autorzy przedstawiają środowisko komputerowe do kompleksowego przetwarzania i wizualizacji tomograficznych danych pomiarowych. Oprogramowanie  TomoKIS Studio powstało w Instytucie Informatyki Stosowanej PŁ w ramach projektu DENIDIA i zostało rozwinięte w ramach projektu MNiSW nr 4664/B/T02/2010/38. Zbudowane oprogramowanie jest unikalne w skali światowej, gdyż integruje w sobie proces pozyskiwania danych pomiarowych, modelowanie numeryczne oraz proces konstruowania obrazów tomograficznych, z możliwością adaptacji dla różnych aplikacji przemysłowych, w szczególności dla potrzeb monitorowania i diagnostyki przepływów dwufazowych gaz-ciecz. Architektura aplikacji oparta jest na zestawie niezależnych modułów, które pozwalają na w pełni dwukierunkową komunikacją, konfigurację oraz kalibrację dowolnego urządzenia tomografii elektrycznej z otwartym protokołem pomiarowym, akwizycję i przetwarzanie danych pomiarowych on-line, liniową oraz nieliniową rekonstrukcję obrazów 2D i 3D w czasie rzeczywistym, a także wizualizację surowych danych pomiarowych i tomogramów. Istotnym elementem systemu jest moduł numerycznego modelowania czujników pojemnościowych wykorzystujący metodę elementów skończonych, oparty na autorskich algorytmach generowania siatek MES komputerowych modeli czujników pojemnościowych. Architektura prezentowanego systemu została zaprojektowana przy użyciu obliczeń równoległych na procesorach graficznych, z wykorzystaniem technologii Nvidia CUDA

Coagulation and fragmentation processes with evolving size and shape profiles : a semigroup approach

We investigate a class of bivariate coagulation-fragmentation equations. These equations describe the evolution of a system of particles that are characterised not only by a discrete size variable but also by a shape variable which can be either discrete or continuous. Existence and uniqueness of strong solutions to the associated abstract Cauchy problems are established by using the theory of substochastic semigroups of operators

Fundamental aspects related to sediment transport in sandy coasts

Marine sediment transport processes occur mainly in coastal areas, where the presence of waves and slowly varying currents is the main hydrodynamic feature. Several processes taking place at different time and space scales are involved. On the inner shelf, waves generate turbulence next to the bed largely responsible for sediment resuspension. Over the bottom boundary layer, mean currents control horizontal motion of suspended sediment while the falling of grains is compensated by the upwards diffusion resulting from the turbulent motion close to the bed . Here, the total stress depends on the waves' and currents' varying contributions, whose degree of non-linearity remains unknown for the moment (Soulsby, 1993). Due to the complexity of the governing processes, technological limitations and lack of knowledge on several aspects, mainly related to the involved physics, most of the existing models do not consider certain mechanisms as wave-related mass transport or bed roughness effects on near-bed flows. Nevertheless, to understand the fundamental aspects of sediment transport some (often non-linear) relationships involved in morphodynamic processes should not be overlooked. Parallel and interactive development of physical and numerical experiments is a powerful tool to improve our understanding of previously investigated and new matters and to advance our ability to measure particular processes. Experiments at full scale have been done in the Deltaflume2 in order to improve the knowledge of sediment transport under waves. Furthermore, a smaller wave-current flume at Flanders Hydraulics is used. At this moment the flume and the various instruments are being tested and the hydrodynamics of the interaction of waves and currents are studied. In a later phase also sediments will be introduced. In addition, a set of numerical models has been selected to simulate processes taking place at several time and space scales. Vertical 1D and 2D models are used to reproduce wave-current flow close to a sandy bed and to model sediment-turbulence interaction. These detailed models are very demanding in terms of computer time. The use of 2D horizontal flow models, spectral wave and transport models, is more realistic for the study of the hydrodynamics and sediment transport in larger areas. Spatial and temporal variations of currents, sediment distribution along the water column and bed roughness related energy dissipation, control sediment deposition, entrainment and transport at various scales. The progressive parameterisation of processes at a smaller scale for the use in models at a larger scale forms the synergy between the different models. It is seen as one of the main goals of this project

Linear chaos for the Quick-Thinking-Driver model

The final publication is available at Springer via http://dx.doi.org/10.1007/s00233-015-9704-6In recent years, the topic of car-following has experimented an increased importance in traffic engineering and safety research. This has become a very interesting topic because of the development of driverless cars (Google driverless cars, http://en.wikipedia.org/wiki/Google_driverless_car).Driving models which describe the interaction between adjacent vehicles in the same lane have a big interest in simulation modeling, such as the Quick-Thinking-Driver model. A non-linear version of it can be given using the logistic map, and then chaos appears. We show that an infinite-dimensional version of the linear model presents a chaotic behaviour using the same approach as for studying chaos of death models of cell growth.The authors were supported by a grant from the FPU program of MEC and MEC Project MTM2013-47093-P.Conejero, JA.; Murillo Arcila, M.; Seoane-Sepúlveda, JB. (2016). 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Integral representation of the linear Boltzmann operator for granular gas dynamics with applications

We investigate the properties of the collision operator associated to the linear Boltzmann equation for dissipative hard-spheres arising in granular gas dynamics. We establish that, as in the case of non-dissipative interactions, the gain collision operator is an integral operator whose kernel is made explicit. One deduces from this result a complete picture of the spectrum of the collision operator in an Hilbert space setting, generalizing results from T. Carleman to granular gases. In the same way, we obtain from this integral representation of the gain operator that the semigroup in L^1(\R \times \R,\d \x \otimes \d\v) associated to the linear Boltzmann equation for dissipative hard spheres is honest generalizing known results from the first author.Comment: 19 pages, to appear in Journal of Statistical Physic