Relaxation time for a parametric family of zero-range processes

Deterministic and Monte Carlo methods are regularly employed to conduct lattice calculations. Monte Carlo methods can effectively model a large range of complex geometries and, compared to deterministic methods, they have the major advantage of reducing systematic errors and are computationally effective when integral quantities such as effective multiplication factor or reactivity are calculated. In contrast, deterministic methods do introduce discretization approximations but usually require shorter computation times than Monte Carlo methods when detailed flux and reaction-rate solutions are sought. This work compares the results of the deterministic code DRAGON to the Monte Carlo code Serpent in the calculation of the reactivity effects for a pressurized heavy water reactor (PHWR) lattice cell containing a 37-element, natural uranium fuel bundle with heavy water coolant and moderator. The reactivity effects are determined for changes to the coolant, moderator, and fuel temperatures and to the coolant and moderator densities for zero-burnup, mid-burnup [3750 MWd/t(U)] and discharge burnup [7500 MWd/t(U)] fuel. It is found that the overall trend in the reactivity effects calculated using DRAGON match those calculated using Serpent for the burnup cases considered. However, differences that exceed the amount attributable to statistical error have been found for some reactivity effects, particularly for perturbations to coolant and moderator density and fuel temperature.

Information gap decision theory with risk aversion strategy for robust planning of hybrid photovoltaic/wind/battery storage system in distribution networks considering uncertainty

If you have ever given up on a nuclear criticality calculation and terminated it because it took so long to converge, you might find this thesis of interest. The author develops three methods for improving the fission source convergence in nuclear criticality calculations for physical systems with high dominance ratios for which convergence is slow. The Fission Matrix Acceleration Method and the Fission Diffusion Synthetic Acceleration (FDSA) Method are acceleration methods that speed fission source convergence for both Monte Carlo and deterministic methods. The third method is a hybrid Monte Carlo method that also converges for difficult problems where the unaccelerated Monte Carlo method fails. The author tested the feasibility of all three methods in a test bed consisting of idealized problems. He has successfully accelerated fission source convergence in both deterministic and Monte Carlo criticality calculations. By filtering statistical noise, he has incorporated deterministic attributes into the Monte Carlo calculations in order to speed their source convergence. He has used both the fission matrix and a diffusion approximation to perform unbiased accelerations. The Fission Matrix Acceleration method has been implemented in the production code MCNP and successfully applied to a real problem. When the unaccelerated calculations are unable to converge to the correct solution, they cannot be accelerated in an unbiased fashion. A Hybrid Monte Carlo method weds Monte Carlo and a modified diffusion calculation to overcome these deficiencies. The Hybrid method additionally possesses reduced statistical errors.

We discuss statics and dynamics of condensation in a zero-range process with compartments of limited sizes. For the symmetric dynamics the stationary state has a factorized form. For the asymmetric dynamics the steady state factorizes only for special hopping rules which allow for overjumps of fully occupied compartments. In the limit of large system size the grand canonical analysis is exact also in a condensed phase, and for a broader class of hopping rates as compared to the previously studied systems with infinite compartments. The dynamics of condensation exhibits dynamical self-blocking, which significantly prolongs relaxation times. These general features are illustrated with a concrete example: an inhomogeneous system with hopping rates that result in Bose-Einstein-like condensations.

In this thesis a new method for the analysis of power transients in a nuclear reactor is developed, which is more accurate than the present state-of-the-art methods. Transient analysis is important tool when designing nuclear reactors, since they predict the behaviour of a reactor during changing conditions, such as a control-rod movement, induced by an operator, or an accident scenario. The current methods for transient analysis apply deterministic solvers to calculate the neutronic response, but not only do these deterministic solvers always need to discretise the problem, they also often apply more fundamental approximations such as homogenization or diffusion. Therefore a stochastic method is needed, which only has a statistical uncertainty. A challenge for applying the Monte Carlo method on transient analysis, is the different types of particles which must be simulated in a single simulation. It is common for a neutronics calculation to simulate the prompt neutrons, however the simulation of precursors is new. The main challenge when simulating precursors lies in their long lifetime, which is seconds, whereas the prompt neutrons have a lifetime of microseconds. This has been solved by dividing the transient problem into time intervals and forcing the precursors to produce a delayed neutron is all time intervals. This will ensure prompt-neutron chains in all intervals. The prompt neutrons will form prompt-neutron chains, which poses another challenge for the Monte Carlo method. The chain length of these prompt neutrons varies a lot and the can also split into many branches, which averages out in a real power reactor, but is difficult to simulate on a computer. To improve the chain-length statistics, a new variance reduction technique is developed, which dictates that a single neutron will emerge from each interaction. This emerging neutron can be the result of a scattering event or a fission event. Finally, a dynamic simulation scheme, which can run in parallel, has been devised, simulating all time intervals consecutively. Also, a method for sampling the initial conditions is created and this scheme is implemented in a purpose-built Monte Carlo code and in a general-purpose Monte Carlo code. The two codes have been tested in several cases and they behave as expected, agreeing with deterministic method where expected, but deviating when the deterministic methods are no longer valid. In order to simulate realistic transients in a power reactor, feedback has to be taken into account. To achieve this, the dynamic Monte Carlo method has been coupled to a thermal-hydraulics code, using an explicit scheme. The results of this coupled simulation are compared to a state-of-the-art coupled diffusion calculation in a NURISP-benchmark calculation and the results agree well, except for a small deviation towards the end. The exact source of this deviation should be further investigated, but the difference is small, when realising that there is already a deviation in the steady-state results. The results demonstrate the feasibility of performing a fully dynamic transient analysis, using only Monte Carlo for the neutronics part of the calculation. Transients can now be calculated, with detailed modelling of any complex geometry and with continuous energy, which is especially useful for newly developed reactor types and one-of-a-kind research reactors.

The northern part of INDIA is most vulnerable in failure of slopes due to hill region with complex geology, high-intensity rainfall and frequently occurrence of earthquakes. The stability of slopes has traditionally analyzed using deterministic methods. But uncertainty plays major role in geotechnical engineering. the probabilistic characterization of uncertainties in input variables for the assessment of slope stability is very helpful. In this paper, the safety of slope using deterministic and probabilistic methods under static and pseudo-static loads is carried for Lungchok landslide which is in south district of Sikkim state, India. The Factor of safety calculated by deterministic cannot represent the stability of slope exactly as it is limited to the single value of parameters. The stability of slope is independent of single soil parameter but dependent on random process with distribution of soil parameters. Rather than the conventional factor of safety against the sliding failure the probability of sliding failure is most useful. The stability of slope is analyzed using two approaches deterministic and probabilistic analysis under the effects of static and pseudo static forces. The deterministic approach with Morgenstern Price limit equilibrium method and the probabilistic approach with Monte Carlo simulation have been performed for the stability analysis of Lungchok landslide using Geo-Studio Software. The dependence and efficiency of the probabilistic strategies in the investigation of slope stability was highlighted in this paper.

Occurrence of aflatoxin M 1 and exposure assessment in Catalonia (Spain)

Vibrations of fuel assemblies are an important issue in the safe operation of nuclear reactors, because they can challenge the integrity of the fuel with potential for radioactive releases. Reactor neutron noise-based techniques for monitoring vibrations are valuable for core diagnostic since they are not intrusive and make use of ordinary neutron flux measurements from ex-core and in-core detectors. The application of these techniques involves the solution of inverse problems that require numerical simulations capable of estimating the reactor neutron noise, given a model of the vibrations. For this purpose, several novel reactor neutron noise solvers have been developed in the CORTEX project using either Monte Carlo or deterministic methods, such as the discrete ordinates method, the method of characteristics, and the diffusion approximation. In the current work, these solvers have been scrutinized by computing the neutron noise induced by vibrations of one or multiple fuel pins in a simplified UOX fuel assembly benchmark, via proper variations of macroscopic neutron cross sections. The comparison of these neutron noise solutions obtained from the different methods shows novel insights into the simulation of neutron noise induced by mechanical vibrations, such as the challenges posed by the Monte Carlo method, the impact of the angular discretization on the application of the discrete ordinates method, and the accuracy of the diffusion approximation assessed via the higher-order neutron transport methods.

Adaptive Monte Carlo methods for solving hyperbolic telegraph equation

PageRank is one of the principle criteria according to which Google ranks Web pages. PageRank can be interpreted as a frequency of visiting a Web page by a random surfer, and thus it reflects the popularity of a Web page. Google computes the PageRank using the power iteration method, which requires about one week of intensive computations. In the present work we propose and analyze Monte Carlo‐type methods for the PageRank computation. There are several advantages of the probabilistic Monte Carlo methods over the deterministic power iteration method: Monte Carlo methods already provide good estimation of the PageRank for relatively important pages after one iteration; Monte Carlo methods have natural parallel implementation; and finally, Monte Carlo methods allow one to perform continuous update of the PageRank as the structure of the Web changes.

A deterministic and Monte Carlo coupling method for PWR cavity radiation streaming calculation

Semiquantitative fat fraction estimation using 2-point Dixon sequences is widely used in whole-body (WB) MR imaging for malignant bone disease but is biased by relaxation times. Understanding this bias requires water- and fat-specific relaxometry data in normal-appearing marrow and lesions. This study measured bone marrow relaxation times in healthy volunteers and WB-MRI patients using MRS at 3T. Five healthy female volunteers (mean age 38.0 ± 2.5 years) and 24 patients with malignant bone disease undergoing clinical WB-MRI (13 male; mean age 67.7 ± 9.7 years; primary cancers: breast = 5, melanoma = 1, multiple myeloma = 8, prostate = 10) underwent variable inversion/echo time STEAM and 3D gradient echo fat-water imaging. MRS water and fat peaks were fitted to determine T1, T2, R2* (from linewidths) and proton density fat fraction (PDFF). Scan-rescan repeatability of MRS parameters was assessed in volunteers. Lesions were classified by disease state according to clinical reports and segmented in Dixon imaging data for comparison of fat fraction estimates with MRS. Repeatability was evaluated using coefficients of variation. Summary statistics (mean, standard deviation and range) were reported; exploratory inferential statistics were also determined with normality (Shapiro-Wilk) and variance (Levene's) tests before one-way ANOVA and Tukey's comparisons (p < 0.05). Monte-Carlo simulations assessed relaxation bias on PDFF. All quantitative MRS parameters were repeatable (coefficient of variation < 10%). Water T1 and T2 were most sensitive to disease state in patients, ranging from 1121 to 2206 and from 15 to 71 ms respectively, and were demonstrated to substantially affect 2-point Dixon fat fraction estimates with Monte-Carlo simulation. Imaging PDFF achieves closer agreement with MRS PDFF than 2-point Dixon methods. These findings remain preliminary due to the small sample size, but they suggest value in future studies with larger cohorts evaluating water relaxation times or PDFF in malignant bone disease.

A system of generalized hydrodynamic equations is derived from Boltzmann's transport equation for semiconductors without the assumption of a parabolic band structure. After some simplifications these equations can be arranged in such a way that their structure is similar to that of the well-known conventional ones. For this purpose the quantity carrier temperature is redefined and five relaxation times have to be introduced instead of the two in use so far, in order to take nonparabolicity into account. For all quantities of interest results from Monte Carlo simulation are presented for silicon with an impurity concentration of up to 10/sup 18/ cm/sup -3/ and an electric field of up to 200 kV/cm. They show that two of the five relaxation times are not distinguishable; hence, for silicon at room temperature the number of relaxation times can be reduced to four. Considerable deviations from results derived under the assumption of a parabolic band structure demonstrate the necessity of this generalized hydrodynamic model. The new hydrodynamic model is applied to a n-channel LDD MOSFET with a 0.5- mu m channel length. The results agree well with the results of Monte Carlo device simulation. >

A new pulsed nuclear magnetic resonance (NMR) logging tool, known as the CMR* Combinable Magnetic Resonance tool, is being used worldwide. During the CMR tool development phase, one challenge was to design a robust and economical data acquisition and signal processing scheme for the hundreds or thousands of spin-echo amplitudes that can be acquired during the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence. This challenge was met by developing a new signal processing and associated downhole data compression algorithm. Data compression is essential to reducing the processing times so that formation T2-distributions can be estimated in real time. Compression of the digital data is possible, without loss of information, because the linear dependency of the NMR measurement kernels results in gross redundancy of the measured spin-echo amplitudes. An attractive feature of the algorithm described in this paper is that the compression can be performed in the downhole tool, thus substantially reducing the telemetry requirements. The raw spin echoes can also be sent uphole and made available for additional processing. Logs of CMR porosity, free-fluid porosity, mean relaxation time and rock permeability are computed from the estimated T2-distributions. The accuracy and precision of the CMR log outputs are demonstrated by repetitive Monte Carlo computer simulations in which noisy, synthetic spin-echo amplitudes are generated from known T2-distributions and then processed to obtain log outputs. Monte Carlo simulations are used to elucidate CMR log responses in typical clean sand, shaly sand, and carbonate rocks. The relative insensitivity of the measurements to short relaxation times (e.g., those less than a few milliseconds) is discussed and used to explain the differences between CMR log porosity and "total" formation porosity in shaly formations. We show that CMR porosity is an "effective porosity" that does not include clay bound water and microporosity having relaxation times less than a few milliseconds. We give examples of statistical fluctuations that can occur on estimated T2-distributions to assist log analysts in recognizing artifacts that are not indicative of actual reservoir rock properties. Field logs that display many of the features of CMR log responses revealed by the simulations are also presented.

A bead‐spring off‐lattice model of a polymer chain with repulsive interactions among repeating units confined into straight tubes of various cross sections, DT2, is studied by Monte Carlo simulation. We are also varying the chain length from N = 16 to 128 and the strength of a short‐range attractive interaction between the repeating units and the walls of the tube. Longitudinal and perpendicular static linear dimensions of the chains are analyzed, as well as the density profile of repeating units across the tube. These data are interpreted in terms of scaling concepts describing the crossover between three‐dimensional and quasi‐one‐dimensional chain conformations and the adsorption transition of chains at flat infinite walls, respectively. We also study the time‐dependent mean‐square displacements of repeating units and obtain various relaxation times. It is shown that both relaxation times scaling proportional to N2 and to N3 play a role in the reptative motion of the chain in the tubes.