A stochastic numerical method is developed for simulation of ﬂows and **particle** **transport** in a 2D layer of porous medium. The hydraulic conductivity is assumed to be a random ﬁeld of a given statistical structure, the ﬂow is modeled in the layer with prescribed boundary conditions. Numerical experiments are carried out by solving the Darcy equation for each sample of the hydraulic conductivity by a direct solver for sparse matrices, and tracking Lagrangian trajectories in the simulated ﬂow. We present and analyze diﬀerent Eulerian and Lagrangian statistical characteristics of the ﬂow such as transverse and longitudinal velocity correlation functions, longitu- dinal dispersion coeﬃcient, and the mean displacement of Lagrangian trajectories. We discuss the eﬀect of long-range correlations of the longitudinal velocities which we have found in our numerical simulations. The related anomalous diﬀusion is also analyzed.

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Physical and Numerical Experiments of Flow and Transport in Heterogeneous Fractured Media: Single Fracture Flow at High Reynolds Numbers, and Reactive Particle Transport Von der Fakultät[r]

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applications. The system of SDEs equations equivalent to the CR **transport** equation can be in- tegrated forward or backward in time, where the latter integration method is more favoured for energetic **particle** **transport** studies, which is the case of cosmic rays. For instance, due to the high stability of the SDEs-based solvers and discrepant approach of calculating the solutions at a number of phase-space points, but not on a specific grid, the time-backward method allows to calculate the probability distribution function to a high precision at the points of interest, without any limitations imposed by the numerical stability condition and the necessity for the highly re- solved computational grid for the entire galaxy ( Strauss and Effenberger , 2017 ). However, quite usually SDEs approach requires a large number of particles, so if the distribution of cosmic rays everywhere in the Galaxy should be considered, which is relevant for the galactic diffuse emission studies, the CR **transport** simulations with SDEs can become computationally demanding ( Kiss- mann , 2017 ). One of the examples of using the SDE-based numerical scheme in CR propagation studies is the Monte-Carlo code CRPropa that simulates the propagation of the ultra-relativistic particles, neglecting their rest-mass, through galactic and extragalactic environment taking into account energy losses and secondary **particle** production originated from the numerous interac- tions, e. g. nuclear decay, electron pair-production, photo-meson production, pion-production, photodisintegration of nuclei with extragalactic background radiation ( Batista et al. , 2015 , 2019 ).

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3 MATHEMATICAL MODEL DEVELOPMENT
3.1 Introduction
This chapter presents a theoretical analysis of **particle** **transport** and hydraulic characteristics in oil-sand and gas-oil-sand multiphase pipe flow systems. The system of governing equations developed to for local and axial distributions of **particle** velocity, hold-up, flux and mass rate; local and axial distributions of slip (critical) velocity; performance and optimal **transport** velocity is based upon a phenomenological description of oil-sand and gas-oil-sand multiphase flow behaviour in a pipe. The mathematical model involves balance equations deduced from macroscopic mass and momentum conservation laws, constitutive models and forces due to drag force, gravitation force, buoyancy force, **particle**-liquid turbulent interaction force, **particle**-**particle** interaction force and **particle**-pipe wall interaction force. The governing equations are solved by fourth order Runge-Kutta numerical method which computational algorithm is implemented in visual basic computer code. The proposed mathematical model provides guidelines in the decision making processes, because it uses optimization techniques to obtain optimal **transport** velocity that prevents sand deposition, minimizes pressure drop, minimizes sand erosion, reduces downtime and cost of maintenance over the life cycle of the production and transfer systems. The computational method is also capable of determining best among various design alternatives.

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In addition, there has been relatively little use of advanced experimental flow measurement techniques application to study **particle** **transport** in gas-oil multiphase flow conditions. These techniques such as electrical capacitance tomography (ECT), nuclear magnetic resonance imaging (MRI) pulsed ultrasonic Doppler velocimetry (PDA), **particle** image velocimetry (PIV), **particle** tracking velocimetry (PTV), Laser Doppler velocimetry (LDA) flows in fluidized beds and high speed charged couple device (CCD) tracking techniques are established methods which have been deployed to visualize, elucidate and analyze multiphase flows in fluidized beds and bubble columns (Fan et. al. 2002, 2003, 2004, 2005). They have numerous advantages over the existing methods (direct sampling probe, stop watch, quick-closing valves and particles collection) because of their non-invasive character. The fast response and valuable insight into the physical mechanisms controlling sand **particle** **transport** in gas-oil multiphase pipe flow justify the choice of CCD measuring technique for this study. The advantage of CCD imaging technique is its feasibility in practice that gives adequate results of both visualization and quantitative measurements can be obtained by a conventional high speed CCD camera coupled to a video system which is easily facilitated in laboratory and quite cheap. However, it needs a very good computer program algorithm for image processing and calculation of local solid **particle** velocity, holdup, flux and mass rate.

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Furthermore, I developed a modeling framework, built upon the experimental evi- dence on cellular truck behaviour, that connects the relative dynamics and interactions arising at the truck scale with the actual **particle** **transport** dynamics. In fact, numerical simulations of the proposed model successfully reproduced the phenomenology of the cell-cargo system, while enabling the prediction of the **transport** properties of cellular trucks over larger spatial and temporal scales. The theoretical analysis provided a deeper understanding of the role of cell-cargo interaction on mass **transport**, unveiling in particular how the long-time **transport** efficiency is governed by the interplay between the persistence time of cell polarity and time scales of the relative dynamics stemming from cell-cargo interaction. Interestingly, the model predicts the existence of an optimal cargo size, enhancing the diffusivity of cellular trucks; this is in line with previous independent experimental data, which appeared rather counterintuitive and had no explanation prior to this study.

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Strong offshore **transport** of particles at 25.5°S may be favored by a distinct inward turn of the outer shelf break between 24°S and 25°S (Fig. 2.1). This morphological feature should lead to an extension of the southward flowing central water undercurrent across the shelf break and an associated **transport** of particles towards the upper slope area. It is noteworthy that shelf break stations 1 and 2 on HT and 10 on T1 have an equally strong BNL of about 50 m thickness as station 16 at T2, while there is no indication of intense offshore **transport** at the two northern transects. Therefore we assume that the material suspended in the northern area represents an additional source for the intensive INL at T2. Another indication for the importance of the poleward undercurrent regarding **particle** **transport** is the strength of the oxygen minimum zone. The low oxygen content of the central waters at 150 to 400 m depth at T2 suggests, that the SACW may still be strong at this transect, although its influence should generally decrease to the south (Fig. 2.5). Intense microbial degradation processes on the high **particle** content at T2 and especially in the shelf break INL obviously intensify the oxygen minimum zone. The poleward undercurrent has not been described any further to the south, indicating that its **particle** load is deposited in this area, contributing to the slope depth depot center. This scenario is consistent with an equatorward directed friction between the undercurrent and the seabed, causing seaward Ekman **transport** of bottom waters over the outer shelf (Smith 1995). The assumed mass **transport** from the north to the south can also be derived from the distribution of the TOC-content in surficial sediments (Fig. 2.8), further supported by data of Inthorn et al. (subm.-a, in press; chapters 3 and 4) showing the highest massflux into the sediment and the highest sedimentation rates of the continental slope at the depocenter location.

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periods from t = 3 to 7 s. This supports the hypothesis that filamentary **transport** forms the density shoulder in the scrape-off layer as observed by Li-BES. Furthermore, in both periods a phase with reduced filament frequency and amplitude can be observed indicating a toroidal asymmetry. Comparing this pattern between all the available Langmuir probes on the outer divertor (see left plots in figures 6.15 and 6.16) shows that the phase of reduced filament frequency and amplitude can be observed in all probes in the scrape- off layer (not in the private flux region, probe 8ua1 ), though, in each probe with a different time shift. This can be explained by the fact that Langmuir probes mounted at different radial positions are connected via the open field lines with different toroidal positions on the midplane. Field lines in contact with each Langmuir probe can be traced up until they intersect with the horizontal plane on which the reflectometry data was taken, which observed the toroidally asymmetric density fluctuations (see figure 6.18). The Langmuir probe data was then mapped onto α at this intersection point on the right- hand plots of figures 6.15 and 6.16. Plotted against α, the reduced intermittency occurs at approximately the same phase at around α = 0.5 π. However, the width of the phase with reduced intermittency is not constant in all probes and also not always exactly centered around α = 0.5 π. Furthermore, this comparison can just be made for fluctuations of up to 11 kHz due to measurement constraints of the Langmuir probes. Nevertheless, the toroidal asymmetry was strongest at low frequencies making a comparison reasonable. In addition to the toroidal asymmetry, a sudden drop in density fluctuation amplitude can be observed between probe 8ua8 and 8ua9. These probes are approximately separated by the magnetic flux surface with ρ pol = 1.075 (see figure 6.17), which is about where the density shoulder ends (see figure 6.13). Hence, the filaments creating the density shoulder might be responsible for the intermittent density and fluctuations measured with Langmuir probes on the divertor. These measurements suggest a causal relationship between **particle** flux events (e. g. filaments) observed at different radial positions on the divertor target, the formation of a toroidally asymmetric density shoulder in the scrape-off layer and density fluctuations at corresponding toroidal positions in the steep gradient region. Therefore, these observations demonstrate how **particle** **transport** is associated with the observed toroidally asymmetric density fluctuations related to the magnetic perturbation field.

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3.2 Geant4 Toolkit
Geometry and tracking (Geant4) is a toolkit for the simulation of the passage of particles through matter [Geant4, 2012]. The toolkit, in C++, makes building applications flexible and versatile. Its areas of application include high energy, nuclear and accelerator physics, as well as studies in medical and space science. Geant4 propagates particles - elementary particles and ions, both stable and unstable - through any geometrical arrangement of material. Many different models area available in Geant4, that have been derived from the domains of **particle**, nuclear and atomic physics [Geant4, 2010]. Electromagnetic pro- cesses such as bremsstrahlung, delta ray production, pair-production, Compton scattering, photo-absorption and multiple scattering are well described. In the area of nuclear and hadronic interactions, simulations are shaped either through data-driven (neutron data) or theoretical models (binary cascade) or both. The high precision neutron model (Neu- tron HP) to describe low energy neutrons (<20 MeV) depends on an evaluated neutron data library (G4NDL) for cross sections, angular distributions and final state information.

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“Dosimetric veriﬁcation in water of a Monte Carlo treatment planning tool for proton, helium, carbon and oxygen ion beams at the Heidelberg Ion Beam Therapy Center”.. “Biophysical modeli[r]

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The relativistic **particle** motion in a constant B -field is ideal to asses the approx- imation characteristics in situations where high order derivatives with respect to the relativistic velocity are necessary for the TE method. In order to get quanti- tative insight in the approximation properties for this case, we perform the usual convergence study which confirm that all formal orders of the TE schemes are met experimentally. Also the second order Boris LF integrator which is due to its special construction - namely, the decoupling of the electrical and magnetic force contribution and the resulting conservation properties for B -field rotation - also the benchmark for such kind of problems. The comparison between the high order (4,5 and 6) TE and RK schemes reveals that their experimental order of conver- gence nearly coincide for the present class of problems what was not observed in the previous numerical experiments. Furthermore, we once again found out that the TE schemes of order four to six are more efficient than their multi-stage RK counterparts when the coupling with 1000 particles to the full PIC exist.

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We compare above approximations for the first **transport** coefficient of protons scattered at water molecules. Figure 1.26 illustrates the different approaches. Although small deviations appear for smaller energies, the analytic formulas of Mott (eqs. (1.48)) and Li/Petrasso (eqs. (1.49)) are close to each other. This is due to the fact that the largest contribution in both models is the Coulomb interaction of protons with an atom of atomic number Z = 10. As cross sections from the ENDF database additionally include important nuclear interactions they show significant differences. The **transport** coefficient for oxygen, computed by simply neglecting the H1-term σ H1 p in (1.52), is much closer to the analytic expressions for large energies. On the contrary, taking p-p collisions into account by a linear combination of hydrogen and oxygen cross sections leads to the opposite behavior: Values for growing energies above 10 MeV increasingly deviate from results calculated by the Mott- or Li/Petrasso-formula.

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This study focuses on the grain size-dependent distribution of natural radionuclides in marine sediments and their application for tracing **particle** **transport** in the ocean. Large proportions of particulate matter experience lateral **transport** pathways before the ultimate burial in the marine sediments. The lateral displacement of particles includes long distance advection within the water column prior to initial deposition and the **transport** within deep and bottom waters following resuspension by bottom currents. Lateral **transport** is widely recognized as an important mode of delivery of organic matter across continental margins and to the abyssal plains of the oceans. Distinguishing between diﬀerent modes of **particle** **transport** is therefore an integral part of those studies that focus on the fate of organic matter within marine reservoirs as part of the global carbon cycle. Biogeochemical cycles in the modern and past oceans can be traced by using diﬀerent naturally occurring isotopes including cosmogenic isotopes (e.g. 3 He, 26 Al, 10 Be) and U-series isotopes (e.g. 230 Th, 234 Th, 231 Pa, 210 Po, 210 Pb) covering a wide range

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In this paper, we concentrate on the numerical aspects of the stripping of a galaxy’s gas as it interacts with the ICM. Agertz et al. (2007) has recently shown that the popu- lar smoothed **particle** hydrodynamics (SPH) technique has problems to properly account for fluid instabilities, prompting significant concerns about a possible unphysical suppres- sion of stripping processes. In a recent study (Heß and Springel 2010) we have therefore proposed a new ‘Voronoi **particle** hydrodynamics’ (VPH) method that improves on the widely used SPH technique (Lucy 1977b; Gingold and Monaghan 1977; Larson 1978) in several respects. By employing a Voronoi tessellation for the local density estimate, a consistent decomposition of the simulation volume is achieved, contact discontinuities can be resolved much more sharply, and a ‘surface tension’ effect across them is avoided. Our preliminary tests of VPH based on the ‘blob-test’ of Agertz et al. (2007) already suggested that stripping is more efficient in VPH compared with SPH. Here we shall investigate this in more detail using more realistic set-ups that mimic galaxy evolution processes. In addi- tion to the two **particle**-based Lagrangian schemes for hydrodynamics, SPH and VPH, we will also carry out comparison simulations with the moving-mesh code AREPO (Springel 2010a). Whereas AREPO uses a Voronoi tessellation as well, this code employs an entirely different methodology for fluid dynamics, based on a finite volume Godunov scheme that calculates hydrodynamical fluxes with a Riemann solver across mesh boundaries. The com- parison of this diverse set of three numerical methods is useful to understand and quantify the systematic uncertainties of the different methods.

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accuracy. In the past many different drag force correlations have been proposed for the flow through random monodis- perse assemblies of spheres for varying solids volume frac- tions and Reynolds numbers based on PR-DNS where the particles are assumed to be rigid [2–7]. Only recently it has been questioned whether these static correlations are also accurate for freely moving particles, which are ubiquitous in industrial applications. By performing PR-DNS Tang et al. [8] and Huang et al. [9] have shown that **particle** velocity fluctuations increase the interphase drag at intermediate Reynolds numbers and proposed drag correlations based on the systems’ granular temperature, which is a measure for the ensemble-averaged **particle** velocity fluctuations. Rubin- stein et al. [10], on the other hand, concluded from **particle**- resolved lattice Boltzmann (LB) simulations that in low Reynolds number flows drag forces are lowered by the abil- ity of mobile particles to adjust to the surrounding fluid flow and proposed a Stokes number dependent drag corre- lation for the Stokes regime that takes into account the sol- id-fluid density ratio. Tavanashad et al. [11] also used LB simulations to study the effect of **particle** velocity fluctua- tions for varying density ratios at Re = 20 and found that

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Energetic, charged particles elicit an orchestrated DNA damage response (DDR) during their traversal through healthy tissues and tumors. Complex DNA damage formation, after exposure to high linear energy transfer (LET) charged particles, results in DNA repair foci formation, which begins within seconds. More protein modifications occur after high-LET, compared with low-LET, irradiation. Charged-**particle** exposure activates several transcription factors that are cytoprotective or cytodestructive, or that upregulate cytokine and chemokine expression, and are involved in bystander signaling. Molecular signaling for a survival or death decision in different tumor types and healthy tissues should be studied as prerequisite for shaping sensitizing and protective strategies. Long-term signaling and gene expression changes were found in various tissues of animals exposed to charged particles, and elucidation of their role in chronic and late effects of charged-**particle** therapy will help to develop effective preventive measures.

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Electron **transport** measurement
Electron **transport** activity was m easured in terms of oxygen evolution in a Clark-type oxygen electrode. The reaction mixture in 1 ml contained; 100 m M sucrose, 10 m M NaCl, 5 m M MgCl2 and 20 m M M E S -N aO H (pH 6.5). Fresh ethanolic solu tion of DCBQ was used at rate saturating concen tration (400 [ i m ) as electron acceptor. C are was taken not to exceed the ethanol concentration more than 1% in the reaction mixture. All assays were carried out at 25 °C under rate saturating light intensity (1500 j.iE m "2 s_1). The Chi concen tration in the reaction mixture was m aintained at 10 [ig m l-1. As when required, Ca2+ was added to the reaction mixture from 1 m stock solution of

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Konkreter soll die Musik in Form eines Partikelsystems visualisiert werden, welches sich bei ruhiger Musik langsam bewegt und umgekehrt bei hektischer Musik sich schnell b[r]

neglect a certain number of frames allows one to flexibly choose the timebase. By varation of the frame overleap it is possible to adjust the range of **particle** velocities which can be recorded. Very slow particles rolling on the bottom of the micro- channel can thus be made visible (Fig. 4 - yellow marks).

Reddington, C. L., Carslaw, K. S., Spracklen, D. V., Frontoso, M. G., Collins, L., Merikanto, J., Minikin, A., Hamburger, T., Coe, H., Kulmala, M., Aalto, P., Flentje, H., Plass-Dülmer, C., Bir- mili, W., Wiedensohler, A., Wehner, B., Tuch, T., Sonntag, A., O’Dowd, C. D., Jennings, S. G., Dupuy, R., Baltensperger, U., Weingartner, E., Hansson, H.-C., Tunved, P., Laj, P., Sellegri, K., Boulon, J., Putaud, J.-P., Gruening, C., Swietlicki, E., Roldin, P., Henzing, J. S., Moerman, M., Mihalopoulos, N., Kouvarakis, G., Ždímal, V., Zíková, N., Marinoni, A., Bonasoni, P., and Duchi, R.: Primary versus secondary contributions to **particle** number concentrations in the European boundary layer, Atmos. Chem. Phys., 11, 12007–12036, doi:10.5194/acp-11-12007-2011, 2011. Sihto, S.-L., Kulmala, M., Kerminen, V.-M., Dal Maso, M., Petäjä, T., Riipinen, I., Korhonen, H., Arnold, F., Janson, R., Boy, M., Laaksonen, A., and Lehtinen, K. E. J.: Atmospheric sulphuric acid and aerosol formation: implications from atmospheric mea- surements for nucleation and early growth mechanisms, At- mos. Chem. Phys., 6, 4079–4091, doi:10.5194/acp-6-4079-2006, 2006.

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