Im Rahmen der vorliegenden Arbeit ist das am Institut für Kern- und Teilchenphysik der Technischen Universität Dresden entwickelte Monte-Carlo-Strahlungstransportprogramm AMOS für Photonen und Elektronen um einen neuartigen Transportalgorithmus für Neutronen erweitert worden. Für die Modellierung der Wechselwirkungsprozesse werden evaluierte Wirkungsquerschnittsdaten im ENDF-Format verwendet, welche mit einer eigens dafür entwickelten Anwendung für eine effiziente Simulation aufbereitet worden sind. Für eine schnelle Simulation mit hoher Genauigkeit werden die Wirkungsquerschnitte über eine empirisch bestimmte hochaufgelöste Gruppenstruktur gemittelt. Die differentiellen Wirkungsquerschnitte werden für den Transportalgorithmus ins Laborsystem transformiert und linear interpoliert. Das erarbeitete Neutronentransportmodul ist anhand mehrerer Beispielrechnungen getestet und verifiziert worden. Im Vergleich mit vorhandenen Strahlungstransportprogrammen erreicht es bei gleicher Genauigkeit eine deutlich höhere Geschwindigkeit. Sowohl das Programm zur Aufbereitung der Daten als auch der Transportalgorithmus sind im Rahmen dieser Arbeit konzipiert und implementiert worden. Die gute Übereinstimmung der Ergebnisse zeigt, dass das entwickelte Programmsystem eine vollwertige Alternative zu den vorhandenen Lösungen darstellt.

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Solving radiation shielding problems, i.e. deep penetration problems, is a challenging task from both computation time and resource aspects in field of nuclear engineering. This is mainly because of the complexity of the governing equation for neutral particle transport - Linear Boltzmann Equation (LBE). The LBE includes seven independent variables with presence of integral and differential operators. Moreover, the low successive rate of radiation shielding problem is also challenging for solving such problems. In this dissertation, the Detector Response Function (DRF) methodology is proposed and developed for real-time and accurate radiation shielding calculation. The real-time capability of solving radiation shielding problem is very important for: (1) Safety and monitoring of nuclear systems; (2) Nuclear non-proliferation; and (3) Sensitivity study and Uncertainty quantification. Traditionally, the difficulties of solving radiation problem are: (1) Very long computation time using Monte Carlo method; (2) Extremely large memory requirement for deterministic method; and (3) Re-calculations using hybrid method. Among all of them, the hybrid method, typically Monte Carlo + deterministic, is capable of solving radiation shielding problem more efficiently than either Monte Carlo or deterministic methods. However, none of the aforementioned methods are capable of performing "real-time" radiation shielding calculation. Literature survey reveals a number of investigation on improving or developing efficient methods for radiation shielding calculation. These methods can be categorized by: (1) Using variance reduction techniques to improve successive rate of Monte Carlo method; and (2) Developing numerical techniques to improve convergence rate and avoid unphysical behavior for deterministic method. These methods are considered clever and useful for the radiation transport community. However, real-time radiation shielding calculation capability is still missing although the aforementioned advanced methods are able to accelerate the calculation efficiency significantly. In addition, very few methods are "Physics-based" For example, the mean free path of neutrons are typically orders of magnitude smaller than a nuclear system, i.e. nuclear reactor. Each individual neutron will not travel too far before its history is terminated. This is called the "loosely coupled" nature of nuclear systems. In principle, a radiation shielding problem can be potentially decomposed into pieces and solved more efficient. In the DRF methodology, the DRF coefficients are pre-calculated with dependency of several parameters. These coefficients can be directly coupled with radiation source calculated from other code system, i.e. RAPID (Real-time Analysis for Particle transport and In-situ Detection) code system. With this arrangement, detector/dosimeter response can be calculated on the fly. Thus far, the DRF methodology has been incorporated into the RAPID code system, and applied on four different benchmark problems: (1) The GBC-32 Spent Nuclear Fuel (SNF) cask flooded with water with a $^3$He detector placed on the cask surface; (2) The VENUS-3 experimental Reactor Pressure Vessel (RPV) neutron fluence calculation benchmark problem; (3) RPV dosimetry using the Three-Mile Island Unit-1 (TMI-1) commercial reactor; and (4) A Dry storage SNF cask external dosimetry problem. The results show that dosimeter/detector response or dose value calculations using the DRF methodology are all within $2sigma$ relative statistical uncertainties of MCNP5 + CADIS (Consistent Adjoint Driven Importance Sampling) standard fixed-source calculation. The DRF methodology only requires order of seconds for the dosimeter/detector response or dose value calculations using 1 processor if the DRF coefficients are appropriately prepared. The DRF coefficients can be reused without re-calculations when a model configuration is changed. In contrast, the standard MCNP5 calculations typically require more than an hour using 8 processors, even using the CADIS methodology. The DRF methodology has enabled the capability of real-time radiation shielding calculation. The radiation transport community can be greatly benefited by the development of DRF methodology. Users can easily utilize the DRF methodology to perform parametric studies, sensitivity studies, and uncertainty quantifications. The DRF methodology can be applied on various radiation shielding problems, such as nuclear system monitoring and medical radiation facilities. The appropriate procedure of DRF methodology and necessary parameters on DRF coefficient dependency will be discussed in detail in this dissertation. / Doctor of Philosophy / Since the beginning of nuclear era, enormous amount of radiation applications have been proposed, developed, and applied in our daily life. The radiation is useful and beneficial when they are under control. However, there will be some "unwanted radiation" from these applications, which have to be shielded. For this, radiation shielding has become a very important task. To effectively shield the unwanted radiations, studying the thickness and design of the shields is important. Instead of directly performing experiments, computation is a more affordable and safer approach. The radiation shielding computation is typically an extremely difffficult task due to very limited "communication" between the radiation within the shield and detector outside the shield. In general, it is impractical to simulate the radiation shielding problems directly because the extremely expensive computation resources. Most of interactions of radiation are within the shield while we are only interested in how many of them penetrate through the shield. This is typically called "deep penetration" problems in the radiation transport community.

This thesis reports our work on transport related problems in mesoscopic physics using analytical as well as numerical techniques. Some of the problems we studied are: effect of interactions and static impurities on the conductance of a ballistic quantum wire[1], aspects of quantum charge pumping [2, 3, 4], DC and AC conductivity of a (dissipative) quantum Hall (edge) line junctions[5, 6], and junctions of three or more Luttinger liquid (LL)quantum wires[7]. This thesis begins with an introductory chapter which gives a brief glimpse of the underlying physical systems and the ideas and techniques used in our studies. In most of the problems we will look at the physical effects caused by e-e interactions and static scattering processes. In the second chapter we study the effects of a static impurity and interactions on the conductance of a 1D-quantum wire numerically. We use the non-equilibrium Green’s function (NEGF) formalism along with a self-consistent Hartree-Fock approximation to numerically study the effects of a single impurity and interactions between the electrons (with and without spin) on the conductance of a quantum wire [1]. We study the variation of the conductance with the wire length, temperature and the strength of the impurity and electron-electron interactions. We find our numerical results to be in agreement with the results obtained from the weak interaction RG analysis. We also discover that bound states produce large density deviations at short distances and have an appreciable effect on the conductance which is not captured by the renormalization group analysis. In the third chapter we use the equations of motion (EOM) for the density matrix and Floquet scattering theory to study different aspects of charge pumping of non-interacting electrons in a one-dimensional system. We study the effects of the pumping frequency, amplitude, band filling and finite bias on the charge pumped per cycle, and the spectra of the charge and energy currents in the leads[2]. The EOM method works for all values of parameters, and gives the complete time-dependences of the current and charge at any site of the system. In particular we study a system with oscillating impurities at several sites and our results agree with Floquet and adiabatic theory where these are applicable, and provides support for a mechanism proposed elsewhere for charge pumping by a traveling potential wave in such systems. For non-adiabatic and strong pumping, the charge and energy currents are found to have a marked asymmetry between the two leads, and pumping can work even against a substantial bias. We also study one-parameter charge pumping in a system where an oscillating potential is applied at one site while a static potential is applied in a different region [3]. Using Floquet scattering theory, we calculate the current up to second order in the oscillation amplitude and exactly in the oscillation frequency. For low frequency, the charge pumped per cycle is proportional to the frequency and therefore vanishes in the adiabatic limit. If the static potential has a bound state, we find that such a state has a significant effect on the pumped charge if the oscillating potential can excite the bound state into the continuum states or vice versa. In the fourth chapter we study the current produced in a Tomonaga-Luttinger liquid (TLL) by an applied bias and by weak, point-like impurity potentials which are oscillating in time[4]. We use bosonization to perturbatively calculate the current up to second order in the impurity potentials. In the regime of small bias and low pumping frequency, both the DC and AC components of the current have power law dependences on the bias and pumping frequencies with an exponent 2K−1 for spinless electrons, where Kis the interaction parameter. For K<1/2, the current grows large for special values of the bias. For non-interacting electrons with K= 1, our results agree with those obtained using Floquet scattering theory for Dirac fermions. We also discuss the cases of extended impurities and of spin-1/2 electrons. In chapter five, we present a microscopic model for a line junction formed by counter or co-propagating single mode quantum Halledges corresponding to different filling factors and calculate the DC [5] and AC[6] conductivity of the system in the diffusive transport regime. The ends of the line junction can be described by two possible current splitting matrices which are dictated by the conditions of both lack of dissipation and the existence of chiral commutation relations between the outgoing bosonic fields. Tunneling between the two edges of the line junction then leads to a microscopic understanding of a phenomenological description of line junctions introduced by Wen. The effect of density-density interactions between the two edges is considered exactly, and renormalization group (RG) ideas are used to study how the tunneling parameter changes with the length scale. The RG analysis leads to a power law variation of the conductance of the line junction with the temperature (or other energy scales) and the line junction may exhibit metallic or insulating phase depending on the strength of the interactions. Our results can be tested in bent quantum Hall systems fabricated recently. In chapter six, we study a junction of several Luttinger Liquid (LL) wires. We use bosonization with delayed evaluation of boundary conditions for our study. We first study the fixed points of the system and discuss RG flow of various fixed points under switching of different ‘tunneling’ operators at the junction. Then We study the DC conductivity, AC conductivity and noise due to tunneling operators at the junction (perturbative).We also study the tunneling density of states of a junction of three Tomonaga-Luttinger liquid quantum wires[7]. and find an anomalous enhancement in the TDOS for certain fixed points even with repulsive e-e interactions.

This work is concerned with the theoretical description of the Scanning Gate Microscopy (SGM) in general and with solving particular models of the quantum point contact (QPC) nanostructure, analytically and numerically. SGM is an experimental technique, which measures the conductance of a nanostructure, while a charged AFM tip is scanned above its surface. It gives many interesting results, such as lobed and branched images, interference fringes and a chequerboard pattern. A generally applicable theory, allowing for unambiguous interpretation of the results, is still missing. Using the Lippman-Schwinger scattering theory, we have developed a perturbative description of non-invasive SGM signal. First and second order expressions are given, pertaining to the ramp- and plateau-regions of the conductance curve. The maps of time-reversal invariant (TRI) systems, tuned to the lowest conductance plateau, are related to the Fermi-energy charge density. In a TRI system with a four-fold spatial symmetry and very wide leads, the map is also related to the current density, on any plateau. We present and discuss the maps calculated for two analytically solvable models of the QPC and maps obtained numerically, with Recursive Green Function method, pointing to the experimental features they reproduce and to the fundamental difficulties in obtaining good plateau tuning which they reveal.

The unique physical properties of nanomaterials, attributed to the combined effects of their size, shape, and composition, have sparked significant interest in the field of nanotechnology. Fabrication of nanodevices using nanomaterials as building-blocks are underway to enable novel technological applications. A fundamental understanding on the structure-property relationships and the mechanism of synthesizing nanomaterials with tailored physical properties is critical for a rationale design of functional nanodevices. In this thesis, molecular simulations that employ a detailed atomistic description of the nanoscopic structures were used to understand the structure-transport property relationships in two novel classes of porous nanomaterials, namely, polymer/porous inorganic layered nanocomposite materials and single-walled metal oxide nanotubes, and provide predictions for the design of nanodevices using these nanomaterials. We employed molecular dynamics to study transport of gas molecules (in particular He, H2, N2 and O2) through a polydimethylsiloxane/porous layered silicate (AMH-3) nanocomposite membrane material as a function of its composition. Gas separation performance of the nanocomposite was found to be substantially enhanced for H2/N2 and H2/O2 compared to pure polymeric material due to the molecular sieving effect of AMH-3, suggesting the possibility of developing a new class of superior separation devices. We also developed force field parameters for layered aluminophosphates that are emerging as potential inorganic layers for construction of nanocomposite materials. We presented preliminary work on developing Transition State Approach-Monte Carlo simulation method for calculating gas transport properties of nanocomposite materials. We investigated in detail the diameter control phenomenon in single-walled metal oxide nanotubes using molecular dynamics simulations and demonstrated the existence of a thermodynamic 'handle' for tuning the nanotube diameters and derived a unique correlation between nanotube energy, composition, and diameter to precisely predict nanotube diameters. Finally, using a combination of molecular dynamics, monte carlo and sorption experiments, we investigated adsorption and diffusion properties of water in single-walled aluminosilicate nanotubes. We predicted high water fluxes in these nanotubes, due to short lengths, hydrophilic interior and near-bulk-water diffusivities. Overall, my research represents two examples of the progress in developing a predictive basis for the design and analysis of nanostructures for applications in separations, nanofluidics, and fuel cell technology.

Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro / A formulação explícita matricial desenvolvida nesta tese de doutorado foi proposta visando ser uma alternativa na solução de Problemas Inversos de estimativa de propriedades radiativas em meios participantes homogêneos unidimensionais usando a Equação de Transferência Radiativa para modelar a interação da radiação com o meio participante. A equação de transporte é formulada em forma matricial e o domínio angular é discretizado usando conceitos do método de ordenadas discretas e a expansão da função de fase do espalhamento anisotrópico em uma série de polinômios de Legendre. A formulação proposta consiste em uma formulação explícita para o problema inverso. Um arranjo apropriado das condições de contorno prescritas (fluxos incidentes) e dos fluxos emergentes nos contornos de uma placa permitem o cálculo direto do operador de transmissão, do operador albedo e do operador de colisão. A partir do operador de colisão calculado são obtidos os valores estimados dos coeficientes de extinção total e de espalhamento. São apresentadas as formulações para problemas em regime estacionário e em regime transiente, bem como os resultados para alguns casos-teste. / The explicit matrix formulation developed in the present thesis has been proposed as an alternative for the solution of Inverse Problems for radiative properties estimation in one-dimensional homogeneous participating media using Radiative transfer equation for the modeling of the radiation interaction with the participating medium. This transport equation is formulated in a matrix form and the angular domain is discretized using concepts of the discrete ordinates methods and the expansion of the function of phase function of anisotropic scattering in a series of Legendre polynomial. The formulation proposed consists on an explicit formulation for the inverse problem. An adequate assembly of the prescribed boundary conditions (incidents flux) and of the emerging flux at the boundaries of the slab allows the direct computation of the transmission, albedo and collision operators. From the computed collision operator estimated values for total extinction and scattering coefficients are obtained. The formulations for steady state and transient situations are presented, as well as test case results.

Conselho Nacional de Desenvolvimento Científico e Tecnológico / Nesta dissertação o método espectronodal SD-SGF-CN, cf. spectral diamond spectral Green's function - constant nodal, é utilizado para a determinação dos fluxos angulares médios nas faces dos nodos homogeneizados em domínio heterogêneo. Utilizando esses resultados, desenvolvemos um algoritmo para a reconstrução intranodal da solução numérica visto que, em cálculos de malha grossa, soluções numéricas mais localizadas não são geradas. Resultados numéricos são apresentados para ilustrar a precisão do algoritmo desenvolvido. / In this dissertation the spectral nodal method SD-SGF-CN, cf. spectral diamond spectral Green's function - constant nodal, is used to determine the angular fluxes averaged along the edges of the homogenized nodes in heterogeneous domains. Using these results, we developed an algorithm for the reconstruction of the node-edge average angular fluxes within the nodes of the spatial grid set up on the domain, since more localized numerical solutions are not generated by coarse-mesh numerical methods. Numerical results are presented to illustrate the accuracy of the algorithm we offer.

Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro / A formulação explícita matricial desenvolvida nesta tese de doutorado foi proposta visando ser uma alternativa na solução de Problemas Inversos de estimativa de propriedades radiativas em meios participantes homogêneos unidimensionais usando a Equação de Transferência Radiativa para modelar a interação da radiação com o meio participante. A equação de transporte é formulada em forma matricial e o domínio angular é discretizado usando conceitos do método de ordenadas discretas e a expansão da função de fase do espalhamento anisotrópico em uma série de polinômios de Legendre. A formulação proposta consiste em uma formulação explícita para o problema inverso. Um arranjo apropriado das condições de contorno prescritas (fluxos incidentes) e dos fluxos emergentes nos contornos de uma placa permitem o cálculo direto do operador de transmissão, do operador albedo e do operador de colisão. A partir do operador de colisão calculado são obtidos os valores estimados dos coeficientes de extinção total e de espalhamento. São apresentadas as formulações para problemas em regime estacionário e em regime transiente, bem como os resultados para alguns casos-teste. / The explicit matrix formulation developed in the present thesis has been proposed as an alternative for the solution of Inverse Problems for radiative properties estimation in one-dimensional homogeneous participating media using Radiative transfer equation for the modeling of the radiation interaction with the participating medium. This transport equation is formulated in a matrix form and the angular domain is discretized using concepts of the discrete ordinates methods and the expansion of the function of phase function of anisotropic scattering in a series of Legendre polynomial. The formulation proposed consists on an explicit formulation for the inverse problem. An adequate assembly of the prescribed boundary conditions (incidents flux) and of the emerging flux at the boundaries of the slab allows the direct computation of the transmission, albedo and collision operators. From the computed collision operator estimated values for total extinction and scattering coefficients are obtained. The formulations for steady state and transient situations are presented, as well as test case results.

Conselho Nacional de Desenvolvimento Científico e Tecnológico / Nesta dissertação o método espectronodal SD-SGF-CN, cf. spectral diamond spectral Green's function - constant nodal, é utilizado para a determinação dos fluxos angulares médios nas faces dos nodos homogeneizados em domínio heterogêneo. Utilizando esses resultados, desenvolvemos um algoritmo para a reconstrução intranodal da solução numérica visto que, em cálculos de malha grossa, soluções numéricas mais localizadas não são geradas. Resultados numéricos são apresentados para ilustrar a precisão do algoritmo desenvolvido. / In this dissertation the spectral nodal method SD-SGF-CN, cf. spectral diamond spectral Green's function - constant nodal, is used to determine the angular fluxes averaged along the edges of the homogenized nodes in heterogeneous domains. Using these results, we developed an algorithm for the reconstruction of the node-edge average angular fluxes within the nodes of the spatial grid set up on the domain, since more localized numerical solutions are not generated by coarse-mesh numerical methods. Numerical results are presented to illustrate the accuracy of the algorithm we offer.