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EN
There have been significant developments in clinical, experimental, and theoretical approaches to understand the biomechanics of tumor cells and immune cells. Cytotoxic T lymphocytes (CTLs) are regarded as a major antitumor mechanism of immune cells. Mathematical modeling of tumor growth is an important and useful tool to observe and understand clinical phenomena analytically. This work develops a novel two-variable mathematical model to describe the interaction of tumor cells and CTLs. The designed model is providing an integrated framework to investigate the complexity of tumor progression and answer clinical questions that cannot always be reached with experimental tools. The parameters of the model are estimated from experimental study and stability analysis of the model is performed through nullclines. A global sensitivity analysis is also performed to check the uncertainty of the parameters. The results of numerical simulations of the model support the importance of the CTLs and demonstrate that CTLs can eliminate small tumors. The proposed model provides efficacious information to study and demonstrate the complex dynamics of breast cancer.
EN
Knowledge about complex physical phenomena used in the casting process simulation requires continuous complementary research and improvement in mathematical modeling. The basic mathematical model taking into account only thermal phenomena often becomes insufficient to analyze the process of metal solidification, therefore more complex models are formulated, which include coupled heat-flow phenomena, mechanical or shrinkage phenomena. However, such models significantly complicate and lengthen numerical simulations; therefore the work is limited only to the analysis of coupled thermal and flow phenomena. The mathematical description consists then of a system of Navier-Stokes differential equations, flow continuity and energy. The finite element method was used to numerically modeling this problem. In computer simulations, the impact of liquid metal movements on the alloy solidification process in the casting-riser system was assessed, which was the purpose of this work, and the locations of possible shrinkage defects were pointed out, trying to ensure the right supply conditions for the casting to be free from these defects.
EN
Aim: The aim of the experiments was to check if different jet fans with similar parameters had a similar air flow profile. The study was also aimed at testing whether normal and reverse flow direction have the same profile. Next, the obtained results of velocity distribution along the airflow axis were compared with the results of numerical analysis carried out using tools commonly applied in Poland. Project and methods: The study involved three jet fans (W1 and W3 were manufactured as reversible units, W2 was a unidirectional device). The tests were conducted in two empty warehouses to investigate airflow velocity. The measurements were performed along the axis of the fans and at additional specific points. The first measurement point was located at the fan inlet plane. The following measurements were conducted at 0.6-meter intervals at a distance of 3.6 m from the fans and at 1.2-meter intervals at a distance from 3.6 m to 24.0 m from the fan. The velocity at each measurement point was determined as the average of a 10-second measurement. The velocity measurements were conducted using an ultrasonic anemometer – Windmaster Pro. At the second stage of the study, CFD analysis was performed. Two models were devised in both Ansys Fluent and FDS. Each CFD model presented a single fan in warehouses. Models included the actual position of the fan, doors, columns and joists. Different settings and different sizes of the computational mesh were used in CFD simulation. Results: The study resulted in an air profile along three different jet fans. Velocity profiles in normal and reverse directions were compared. Significant differences were found between airflows for normal and reverse directions. Additionally, it was possible to compare the obtained results in real scale and a CFD simulation performed in the ANSYS FLUENT 13, FDS 5.5.3 and FDS 6. Some of the CFD simulations provided a good similarity of airflow profiles in CFD and real tests, while others did not. Thus, the study showed which settings provided the best results. Conclusions: Each of the tested fans is characterised by a different airflow distribution. The velocity distribution profile is different for the normal and reverse direction in the studied reversible fans despite the same air stream blown in both directions. The performed analyses show that CFD programs can solve velocity correctly, but this requires good settings.
PL
4
Rail vehicle model motion analysis on curved track with vertical irregularity
EN
The properties of a classic railway track largely depend on the properties of the subgrade, which is most often a natural creation. Atmospheric phenomena (e.g. temperature changes, heavy rainfall) can locally reduce the elasticity of the subgrade and create conditions conducive to permanent track deformation. One of the most common forms of atrack fragment destruction is the loss of foundation support (one or several neighbouring sleepers) resulting from the indentation of the ballast material in the subgrade. The pressure ofavehicle passing through a damaged section of the track causes the so-called dynamic track irregularity. The impact of dynamic track vertical irregularity on the values of wheel-rail contact forces of a passing vehicle was investigated. The model of thepassenger wagon-track system was cre-ated using the VI-Rail tool. The vehicle motion on curves with different values of track radius and superelevations was investigated. Vertical track irregularities occur on the internal rail only. The lengths of the track irregularity correspond to one, two or three sleepers unsupported on one side. The test results are presented in the form of diagrams and referred to applicable standards and regulations.
5
EN
As part of the work, the error level of simulations of uniform optical-fibre Bragg gratings was determined using the transition matrix method. The errors were established by comparing the transmission characteristics of the structures obtained by simulation with the corresponding characteristics arrived at experimentally. To compile these objects, elementary properties of the characteristics were specified, also affecting the applications of Bragg gratings, and compared with each other. The level of error in determining each of these features was estimated. Relationships were also found between the size of the physical properties of Bragg gratings and the level of errors obtained. Based on the findings, the correctness of the simulation of structures with the said method was verified, giving satisfying results.
EN
A numerical method is presented for a mathematical model which describes the frictional contact between a thermo-electro-elastic body and a conductive foundation. The contact is described by Signorini’s conditions and Tresca’s friction law including electrical and ther- mal conductivity conditions. Our aim is to present a detailed description of the numerical modelling of the problem. To this end, we introduce a discrete scheme based on the finite element method. Under some regularity assumptions imposed on the true solution, optimal order error estimates are derived for the linear element solution. This theoretical result is illustrated numerically.
PL
Przedstawiono wpływ planowanego stopnia Siarzewo na Wiśle na dynamikę lodu w obszarze powyżej i poniżej stopnia. Do tego celu zaimplementowano model matematyczny i przeprowadzono symulacje numeryczne dla różnych scenariuszy. Obliczenia służyły do wyznaczeniu trasy spływu lodu przez zbiornik i poniżej zbiornika oraz sił z jakimi lód będzie oddziaływał na brzegi i dno rzeki oraz projektowane na zbiorniku wyspy. Badaniami objęto odcinek Wisły pomiędzy istniejącym stopniem wodnym Włocławek (km 674,850) a km 715.
EN
The article presents the impact of the planned Siarzewo dam on the ice dynamics upstream and downstream of the barrage. Mathematical model was implemented to the study area and the results of numerical simulations for different scenarios were used to achieve the goal. The calculations were used to determine the ice flow through the reservoir and downstream of the dam. The forces caused by the dynamic ice impact on river banks, riverbed and the shore of islands planned on the reservoir were also calculated. The research covers the Vistula section between the Im 678,850 (the existing Włocławek dam) and km 715,000.
EN
Due to the longer distance of moving the crew to the workplace in hard coal mines, the possibility of increasing the maximum permissible speed of suspended monorails was considered. To ensure an adequate level of safety, decelerations affecting the crew in the case of emergency braking in various travelling conditions were analysed. The computational model was verified based on the results of the bench tests on a dedicated test track. The article presents a comparison of results of numerical calculations with measurements at the test stand, and results of numerical simulations in relation to the criterial states that could not be checked at the test stand as well as the analysis of overloads that affect the crew during the emergency braking. These overloads have a significant impact on safety of the operator and passengers, and their determination and analysis may be the basis for assessing the degree of safety as well as for the development of guidelines for designing the additional equipment for the operator's cabs and passenger cars, i.e. components increasing their safety.
PL
W związku z wydłużającym się czasem dojazdu załogi do miejsca pracy w kopalniach węgla kamiennego, rozważana jest możliwość zwiększenia maksymalnej dopuszczalnej prędkości jazdy kolejek podwieszonych. W celu zapewnienia odpowiedniego poziomu bezpieczeństwa, przeprowadzono analizy opóźnień oddziałujących na załogę w sytuacji awaryjnego hamowania w odniesieniu do różnych stanów kryterialnych. Model obliczeniowy został zweryfikowany w oparciu o wyniki badań stanowiskowych, przeprowadzonych na dedykowanym torze testowym. W artykule przedstawiono porównanie wyników obliczeń numerycznych oraz zmierzonych na stanowisku badawczym oraz wyniki symulacji numerycznych w odniesieniu do stanów kryterialnych, których nie można było sprawdzić na stanowisku badawczym, oraz przedstawiono analizę przeciążeń, jakie oddziałują na załogę w sytuacji awaryjnego hamowania. Wartości te mają duży wpływ na bezpieczeństwo operatora i pasażerów, a ich wyznaczenie i analiza może stanowić podstawę do oceny stopnia bezpieczeństwa oraz wytyczne do zaprojektowania dodatkowego wyposażenia kabin operatora i wozów pasażerskich, w postaci elementów zwiększających bezpieczeństwo ich użytkowania.
9
Analizy epidemiologiczne w środowisku MATLAB/Octave
PL
W artykule skonstruowano proste modele matematyczne rozprzestrzeniania się chorób zakaźnych oparte na równaniach różniczkowych oraz automatach komórkowych. Na przykładzie modeli SIS i SIR zilustrowano praktyczne zastosowanie pojęć matematycznych nauczanych w toku studiów. Za pomocą symulacji komputerowych, do których użyto pakietów matematycznych MATLAB i Octave, uzyskano wizualizacje tempa rozwoju danej choroby oraz zasięgu epidemii. Ponadto przedstawiono informacje o zastosowaniu e-technologii w kształceniu studentów.
EN
Epidemiology is a branch of medicine that studies the causes, development and spread of infectious diseases, as well as other large-scale diseases in human societies. Information about infectious diseases helps to control the health problem of the society and enables research of the outbreak of an epidemic. In our article, we construct simple mathematical models of the spread of infections: the model of a disease with no immunity against re-infection (SIS model) and the model including such an effect (SIR model). Moreover, we present numerical simulations in MATLAB and Octave, which illustrate the rate and extent of disease epidemics. In addition, information on the use of e-technologies in the education of students is presented.
PL
W artykule przedstawiono koncepcję możliwości zwiększenia zdolności penetracji pocisku podkalibrowego z penetratorem wykonanym ze spieku na osnowie wolframowej poprzez zastosowanie materiałów o zmiennych właściwościach mechanicznych penetratora w poszczególnych jego segmentach. Na podstawie przeglądu literatury problemu określono wpływ dodatków stopowych w spiekach na osnowie wolframowej na wybrane parametry wytrzymałościowe, następnie wykonano analizy numeryczne procesu penetracji płyty stalowej przez penetrator segmentowy dla wybranych konfiguracji materiałów konstrukcyjnych segmentów penetratora. W podsumowaniu przedstawiono możliwości modyfikacji struktury spieków na osnowie wolframowej, które mogą mieć decydujący wpływ na zwiększenie zdolności penetracji.
EN
The paper describes a concept of increasing the penetration capacities of kinetic antitank projectiles, having a penetrator made of a tungsten based sinter, through the application of materials with variable mechanical characteristics for penetrator’s particular segments. The influence of alloy additions on some strength parameters for the tungsten based sinters were assessed by using the literature data, and in the next step by numerical analyses of steel plate penetration process calculated for selected configurations of structural materials of penetrator segments. The summary describes some possibilities for modification of the structure of tungsten based sinters which may decisively improve the penetrating capacities.
EN
This article presents results of an analysis of impact of a designed discharge of contaminated water into the Dead Vistula (Wisła Martwa) in the region of the Isthmus (Przesmyk) with the aim of determination of a possible effect of the pollution onto protected areas of Natura 2000 (bird habitats and sites, especially the Bird Paradise – Ptasi Raj) nature reserve. The analysis was conducted on the basis of the two-dimensional modelling of unsteady transport of non-degradable dissolved matter. To this end, a numerical model of a section of the Dead Vistula was worked out. Four scenarios of hydro-dynamical conditions (2 – for average weather conditions and 2 – for stormy weather conditions) were selected. To solving the equation of pollution migration the finite volumes method (MOS) was applied. Two localizations of contaminated water discharge outlet were considered, namely: the first from the side of Siennicki Bridge before the Isthmus and the other in the section of the Brave Vistula (Wisła Śmiała) downstream the Isthmus. The obtained results made it possible to assess positively the first localization of the designed discharge outlet. In the other case there is a fear that at unfavourable hydro-meteorological conditions a water pollution may happen over Natura 2000 protected areas.
12
On certain modification of age-dependent predator-prey model
EN
This work proposes a new model of coexistence of a predator population with a population of prey. In works [5] and [7] it is assumed that the number of prey aged x eaten by predators aged y is directly proportional to the number of prey aged x and the number of predators aged y. This paper presents a more general model. First of all, the dependency is functional, i.e. the chances of being eaten are affected by the structure of the whole population. In addition, this dependence is not bili near because the predator, after satisfying its hunger, will give up the hunt for prey.
PL
Praca niniejsza proponuje nowy model koegzystencji populacji drapieżcy z populacją ofiar. W pracach [5] i [7] założono, że liczba ofiar w wieku x zjadanych przez drapieżcę w wieku y jest wprost proporcjonalna do liczby ofiar w wieku x i do liczby drapieżców w wieku y. W niniejszej pracy zaprezentowany jest ogólniejszy model. Przede wszystkim zależność jest funkcjonalna, czyli na szanse zjedzenia ma wpływ struktura całej populacji. Poza tym zależność ta nie jest dwuliniowa, gdyż drapieżca po zaspokojeniu głodu zrezygnuje z polowania na ofiary.
PL
W artykule przedstawiono wyniki analizy numerycznej plastycznego płynięcia metalu podczas odkształcania w ławie przepychowej sześciowalcowej. Dane do symulacji numerycznych przyjęto na przykładzie jednego z zakładów produkujących rury bez szwu. Analizę przeprowadzono dla walcowania rury surowej D=115 mm o grubości ścianki 5 mm. Badania przeprowadzono przy użyciu programu Forge 2011®. Uzyskane wyniki pozwoliły na opracowanie numerycznego modelu płynięcia metalu podczas odkształcania w ławie przepychowej sześciowalcowej.
EN
The article presents the results of the numerical analysis of the plastic flow of metal during deformation in a pivotal plural pivot. Data for numerical simulations was adopted on the example of one of the plants producing seamless tubes. The analysis was carried out for rolling the crude tube D=115 mm with a wall thickness of 5 mm. The research was carried out using the Forge 2011® program. The results allowed us to develop a numerical model of metal flow during deformation in a six-high bench pusher.
EN
The paper presents the problems in selecting the fiber shape in numerical strength analysis for wood-polymer composites. For this purpose numerical analysis of the uniaxial tensile test for the wood-polymer composite sample was performed. Variable geometry of the fiber model was used. The fiber orientation data were obtained using Autodesk Moldflow Insight 2016 software. Micromechanical calculations based on homogenization methods were performed using Digimat FE commercial code. The results of the numerical simulations were compared with the experiment ones. To manufacture the WP composite, Moplen HP 648T polypropylene (PP) from Basell Orlen Polyolefins was used as the polymer matrix. As the filler 10 vol.% Lignocel C120 wood fiber manufactured by JRS - J. RETTENMAIER & Söhne Company was used. Adhesion promoter P613 by Dupont was used as well. A Dr Boy 55E injection molding machine was used to produce the test specimens. It was noted that the selection of the fiber shape has a significant impact on the consistency of the obtained results and consequently on compliance with the experiment ones. Fiber location calculations were performed for each geometry type available in the Digimat software. The most consistent results for numerical homogenization (Digimat FE) are associated with the choice of a curved cylinder shape of fiber. This may be due to the greatest convergence of the orientation tensor value received from the numerical simulation of the injection molding process during its transformations to the representative volume element model. In addition, this result may be due to the fact that the curved cylinder type of geometry is characterized by the most variable shape due to the degree of curvature. This reflects the real, non-standard problems to determine the shape of the wood fiber in the polymer matrix.
PL
Przedstawiono problematykę wyboru geometrii włókna w numerycznej analizie wytrzymałościowej kompozytu typu drewno-polimer. W tym celu przeprowadzono symulację próby jednoosiowego rozciągania dla próbek wykonanych z kompozytu polimerowo-drzewnego. Badano zmienną geometrię włókna, gdzie dane dotyczące orientacji włókien otrzymano z użyciem programu Autodesk Moldflow Insight 2016. Obliczenia mikromechaniczne opierające się na metodach homogenizacji przeprowadzono z użyciem programu Digimat FE. Wyniki otrzymane w symulacjach numerycznych porównano z eksperymentem. Stwierdzono, że dobór geometrii włókna w analizach numerycznych ma istotny wpływ na otrzymane wyniki, a w konsekwencji zgodność z eksperymentem.
EN
In contemporary high-pressure die casting foundries, the mastery of each sequence in the production cycle is more and more important. In the paper, an example of virtual analysis of gearbox casting from Al alloy will be presented. It includes a large variety of parameters, as follows: choosing of appropriate foundry technology, calculation of computer simulation of casting process which takes into account the filling process of cold chamber and filling of cavity, model description of three phases in high-pressure die casting, flow of molten metal, solidification, formation of stress and deformations. Additionally, the optimization of cooling and heating systems will be compared with calculated volume defects, dimensions of castings and their deformations with experimentally obtained values.
EN
Scale modelling should be a very useful strategy for the design of lunar structures. Preventing structural damages in the lunar environment is crucial and scale models are helpful to achieve this aim. The size of these models must be scaled to take into account the different gravitational levels. Since the lunar gravity acceleration is about one-sixth of the terrestrial one, it follows that the models on Earth will be very smaller than the prototype to be realized on the Moon. This strategy will represent an opportunity for engineers working on lunar structure design, provided that the errors, both computational and experimental, related to the change of scale are quantified, allowing reliable extension of the physical scale modeling results to the prototype. In this work, a three-dimensional finite element analysis of walls retaining lunar regolith backfill is described and discussed, in order to provide preliminary results, which can guide a future experimental investigation based on physical scale-modelling. In particular, computational errors related to the scale effects are assessed, with respect to a virtual prototype of the lunar geotechnical structure, and compared with errors from other sources of discrepancy, like the adopted constitutive model, the variability of the geotechnical parameters and the calculation section used in the 3D analysis. The results seem to suggest the soundness of this strategy of modelling and are likely to encourage new research, both numerical and experimental, supporting the structure serviceability assessment.
PL
Modelowano skutki termiczne oddziaływania pola elektromagnetycznego (współczynnik SAR w modelu numerycznym człowieka) emitowanego przez czytniki RFID z zakresu HF o różnych zasięgach odczytu. Stwierdzono możliwość występowania wartości SAR przekraczających limity narażenia ludności przy czytnikach o zasięgach odczytu przekraczających 100 cm. Wyniki badań mogą być pomocne w minimalizacji zagrożeń elektromagnetycznych podczas użytkowania czytników RFID z zakresu HF.
EN
Thermal effects of exposure to electromagnetic field (SAR values inside numerical model) emitted by RFID HF desktop readers of various reading ranges were modelled. SAR values exceeding general public limits were found near readers with reading ranges exceeding 100 cm. Investigation results may be helpful in minimizing electromagnetic hazards while use of RFID HF readers.
EN
The article presents the experiment’s results of the lifeboat model lowered with an initial speed and then released to fall onto a flat water surface. The purpose of the research is to determine the trajectory of the vertical boat motion and describe it with a mathematical model. This is closely related to determining the damping factor since the vertical motion is damped and the lifeboat gets balanced and stops moving after some time. The procedure of selecting parameters in the mathematical model to adjust to the results of the experiment was described in details. The summary describes the imperfections of the presented damping model and their probable causes.
19
EN
The analyzes were aimed at demonstrating the influence of parameters describing the deformation of the structure on the uncertainty of critical force, and the impact of technological imperfections on stress uncertainty in compression conditions. In a linear buckling analysis, the problem is considered only for the initial, permanent state of the stiffness matrix. In the case of demonstrating the influence of initial deformations on the behavior of the structure under load, it is necessary to visualize changes in stiffness over time. To this end, a non-linear MES analysis was carried out, which will take into account local changes in the stiffness of the model through a gradual increase in the load. Thus, the difference in stiffness is taken into account, which in the linear problem is infinite. The analysis was used to examine the local and global sensitivity of the parameters describing: plating thickness as well as deformation caused by the technological process on the stress value reduced by Huber hypothesis, and the value of normal stress. To take into account the influence of non-specified values of the magnitude of geometric deviations, and their simultaneous influence on the range of obtained results, the Experimental Planning Method and the Surface Method of Answers were used.
PL
Przedstawiono koncepcję narzędzia do wspomagania symulacji numerycznych wypadków przy pracy. Narzędzie jest nakładką na darmowy program graficzny Blender, w której do wykonywania symulacji numerycznych wykorzystano pakiet MADYMO. Jego zastosowanie znacząco przyspiesza proces modelowania sceny, a w przyszłości planowane jest również zautomatyzowanie procesu poszukiwania najbardziej prawdopodobnego przebiegu wypadku. Dostarczy to wielu informacji o potencjalnych zagrożeniach i – z dużym prawdopodobieństwem – przyczyni się do powstania nowych środków bezpieczeństwa. W artykule opisano narzędzie i zaprezentowano jegowstępne możliwości.
EN
Proposed is a concept of a new tool for supporting numerical simulations of occupational accidents. Such tool, in form of add-on for graphics software called Blender, uses MADYMO package to execute simulations. It provides fast and intuitive way of modeling accidents scenes without a need of particular knowledge in simulation physics. In the future, it will also implement an auto-search algorithm for the most possible course of event throughout any given state space. Hopefully, it will allow to recognize potential risks and create new ways of preventing injuries. This paper describes the tool, and presents early results of its possibilities.
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