Using multiple random walk simulation in short-term grade models

Resolving diffusion in clay minerals at different time scales: Combination of experimental and modeling approaches

The numerical simulation of random walks is considered using the Monte Carlo method proposed by Janse van Rensburg (1987). The algorithm is tested and then generalised to generate Edwards random walk (1965). The renormalised masses of the Edwards model (which corresponds to an N to 0, g0 mod phi 2 mod 2 theory) are calculated and the results are compared with those obtained from a simple perturbation theory calculation for small values of the bare coupling constant. The efficiency of this algorithm is discussed and compared with an alternative approach.

Dynamic processes leading to natural disasters often translate into random walks in state spaces which are inhomogeneous in transport characteristics. In other words, such random walks will behave differently in different parts of a network which would have different values for transport properties (\(d\!\!f\) and dw if using methods from Chap. 4). Thus, for such networks the application of \(\textit{MFPT}\) calculation methods introduced in Chap. 4 along with many other methods described in literature are not straight forward. This chapter proposes that using the novel concept of dividing the node distribution into patches/clusters known as network primitives (NPs) where all nodes within each primitive share common transport variables, and adopting a ‘hop-wise’ approach to calculate \(\textit{MFPT}\) between any source and target pair as an extension to the methods described under Chap. 4, can be a viable solution for predicting \(\textit{MFPT}\) for random walks in inhomogeneous networks. This methodology’s potential is demonstrated through simulated random walks and with a case study using the dataset of past cyclone tracks over the North Atlantic Ocean. The predictions using the presented method are compared to real data averages and predictions assuming homogeneous transport properties.

Adaptive time stepping algorithm for Lagrangian transport models: Theory and idealised test cases

Random walk models are often used to interpret experimental observations of the motion of biological cells and molecules. A key aim in applying a random walk model to mimic an in vitro experiment is to estimate the Fickian diffusivity (or Fickian diffusion coefficient), D. However, many in vivo experiments are complicated by the fact that the motion of cells and molecules is hindered by the presence of obstacles. Crowded transport processes have been modeled using repeated stochastic simulations in which a motile agent undergoes a random walk on a lattice that is populated by immobile obstacles. Early studies considered the most straightforward case in which the motile agent and the obstacles are the same size. More recent studies considered stochastic random walk simulations describing the motion of an agent through an environment populated by obstacles of different shapes and sizes. Here, we build on previous simulation studies by analyzing a general class of lattice-based random walk models with agents and obstacles of various shapes and sizes. Our analysis provides exact calculations of the Fickian diffusivity, allowing us to draw conclusions about the role of the size, shape and density of the obstacles, as well as examining the role of the size and shape of the motile agent. Since our analysis is exact, we calculate D directly without the need for random walk simulations. In summary, we find that the shape, size and density of obstacles has a major influence on the exact Fickian diffusivity. Furthermore, our results indicate that the difference in diffusivity for symmetric and asymmetric obstacles is significant.

Fernandez, C, Pascual, J.J., Piquer, O., Bias, E. and Cervera, C. 2008. Milk production prediction of dairy goats using multiple component systems models. J. Appl. Anim. Res., 34: 127–132. To predict milk production in dairy goats using multiple component systems models, a homogenous group of 34 dairy goats within a commercial farm (Excamur, S.L.) was used. During 5 months lactation period body weight and dry matter intake were recorded and a multiple component system model was developed. The training models are characterized by an expanding set of management options such as feed intake, energy digestibility, locomotion energy expenditure and maintenance. Total milk yield during lactation by goat was simulated. Milk yield (MY) from a group of 10 goats (from literature) and the MY obtained at the present trial were used to validate the multiple component simulation models. An r of 0.93 was obtained between MY observed and predicted with the multiple component system. Therefore, the multiple component simulation models at the present work are useful to predict MY in Murciano-Granadina goat during lactation when total mixed ration was used to feed the animals.

Building retrofit procedures play a crucial role in improving the energy performance and economic indicators of a building. In this context, an energy audit is typically recommended, but it is seldom used as a comprehensive approach due to the complexity and associated costs. This article aims to conduct a holistic energy audit approach for a university building in Malaysia, with the objective of diagnosing energy efficiency deficiencies, identifying areas of energy waste and proposing practical retrofit measures accordingly. The approach involved multiple stages, including measurements, surveys and simulation work. Eight energy-saving measures were proposed, targeting improvements in envelope elements, cooling and lighting systems, and operation and control. The Design-Builder software was utilized for energy simulation, assessing the annual energy savings. Economic evaluation indices, such as net present value and simple payback period, were used to assess the economic feasibility of the measures. The results demonstrated significant potential for energy reduction, with each measure achieving annual energy reductions ranging from 2% to 18%, and a cumulative impact of 41% on annual energy consumption when combined. The investment payback period for the energy-saving measures varied from 0.8 to 8.9 years, with a payback period of 3.9 years for the combined energy-saving measures. Furthermore, the net present value was positive, indicating the economic feasibility of investing in the proposed energy-saving measures. These findings provide valuable energy-saving opportunities that can be applied to improve similar buildings on the university campus.

We consider a discrete-time random walk on a one-dimensional lattice with space- and time-dependent random jump probabilities, known as the beta random walk. We are interested in the probability that, for a given realization of the jump probabilities (a sample), a walker starting at the origin at time t=0 is at position beyond ξsqrt[T/2] at time T. This probability fluctuates from sample to sample and we study the large-deviation rate function, which characterizes the tails of its distribution at large time T≫1. It is argued that, up to a simple rescaling, this rate function is identical to the one recently obtained exactly by two of the authors for the continuum version of the model. That continuum model also appears in the macroscopic fluctuation theory of a class of lattice gases, e.g., in the so-called KMP model of heat transfer. An extensive numerical simulation of the beta random walk, based on an importance sampling algorithm, is found in good agreement with the detailed analytical predictions. A first-order transition in the tilted measure, predicted to occur in the continuum model, is also observed in the numerics.

High-speed simulation of discrete dynamic probabilistic systems

Uncertainty quantification of structural and geotechnical parameter by geostatistical simulations applied to a stability analysis case study with limited exploration data

Contemporarily, the random walk is widely applied in the field of finance, suggests that the history stock price has no relation or impact on the stock price tomorrow, i.e., the direction the of stock price is entirely random and unpredictable. This paper investigates random walk simulation in Finance based on the information retrieval and literature review. According to the analysis, if one holds the strong belief in the random walk theory, well-perform ETH or portfolio strongly relevant to core Index (e.g., S and P 500, Nasdaq) will be a proper choice for investors. Otherwise, if one holds that the price movements are inherit connected instead of random variation, statistic evaluation (also known as technical analysis) can be applied to earn with extra returns via time-selection trading actively and positively. Based on enough trials, this paper will try to explore the nature and patterns of random process, which sheds light on future stock price prediction and explanation.

Each year, unexpected large precipitations around the world lead to huge flooding but unexpected shortage of precipitations around the world lead to severe droughts. Both cause heavy casualties in human and domestic animal lives and dramatic losses in properties. The patterns of these irregular precipitations are closely related to the hydrological ecosystem. The big data mining provides an opportunity to find out the patterns of precipitations. In this study, we applied the random walk model to simulate the annual precipitation in 46 Asian capitals for the 20^thcentury. The results show that the random walk simulations are workable, suggesting the underlined mechanism for the precipitations.

We study the linear large-n behaviour of the average number of distinct sites S(n) visited by a random walker after n steps on a large random graph. An expression for the graph topology-dependent prefactor B in S(n) = Bn is proposed. We use generating function techniques to relate this prefactor to the graph adjacency matrix and then devise message-passing equations to calculate its value. Numerical simulations are performed to evaluate the agreement between the message passing predictions and random walk simulations on random graphs. Scaling with system size and average graph connectivity are also analysed.

Data from a mineral deposit are commonly obtained by core drilling. This kind of sampling involves high costs, limiting the number of drill holes. Additional holes should be located to bring the maximum benefit. The benefit can be evaluated by various ways and must take into account the goals of sampling. This article presents a case study where the deposit has been sampled and the new drillings must be added to reduce the uncertainty about a transfer function, Net Present Value (NPV) of the mining project. There are basically two ways to choose locations where new drillings should be placed for cases where the aim of sampling is to reduce uncertainty about a global function: the addition of new drillings outlining a quasi regular grid with previously collected drillings or the addition of new drillings on the locations of high uncertainty about the attribute of interest (or the attribute that is considered most influential in the transfer function). The performances of these patterns on reducing the uncertainty measured by the function selected are compared. The results point out that the most efficient pattern relates to the distribution (histogram) of the uncertainty about the attribute of interest. Thus, the choice of which sampling pattern should be adopted varies depending on data distribution and its influence on the transfer function.

Increased demand for natural gas in Venezuela has led to an intensified search for additional supply from mature oil fields in Eastern Venezuela. The search has involved the ranking of oil reservoirs that could be converted to gas producing reservoirs. Unreliable reservoir and historical production data introduced high uncertainties to the ranking based on gas reserves only. A fuzzy model was therefore constructed and used for ranking 45 reservoirs. Eight input variables were used to evaluate each of the reservoirs. The variables included remaining petroleum reserves, remaining gas reserves, gas cap volume, oil production per psi, gas production per psi, flow capacity, storage capacity and the distance to existing gas transmission lines. Membership functions were developed for each variable and 20 fuzzy rules were used to capture the non-linear relationship amongst the input and output variables. The output variable was represented by 5 membership functions and presented in a 0 - 1 range after defuzzification. The reservoirs were then ranked on the basis of their output range values. The results from the fuzzy model were compared to those obtained from a conventional methodology using a Decision Tree - Monte Carlo model. In this conventional model, the 8 input variables were normalized and represented as events in a decision tree. The variables were then weighted by using Monte Carlo simulation to generate the mean probability of each event occurring. A rolling netback calculation produced an output value for each reservoir. The output values were used to rank the 45 reservoirs. The paper concludes that although the two models handled the uncertainties of the impact of the 8 input variables on the output variable, the fuzzy model best capture the vagueness in the non-linear relationships between these variables. Introduction Venezuela has 147.5 TCF of gas reserves with 91% as associated gas and the remaining 9% as non-associated gas. In the Eastern part of the country, gas reserves are about 105 TCF with over 94% as associated gas. Gas demand is 1.92 BCF per day with a 7.5% annual growth rate. There is an on-going intensive search for gas to enhance the national gas supply. This search involved the conversion of mature oil reservoirs to gas producing reservoirs. Budget constraints limited the number of mature reservoirs that could be converted. Therefore, the reservoirs were ranked on the basis of Remaining Gas Reserves and the top ranked reservoirs were assumed to have the best gas opportunities. However, there was a high degree of uncertainty with the gas data. Furthermore, some of the reservoirs with large Remaining Gas Reserves had very low reservoir pressure and flow capacity. Others were located very far from any gas pipelines and surface infrastructure. There was therefore a need to use more sophisticated methods to rank the reservoirs. Conventional ranking techniques include the Net Present Value (NPV), the Internal Rate of Return (IRR), the Expected Monetary Value (EMV), Value of Information (VOI) and hydrocarbon volume such as the Remaining Gas Reserves. 1 Moore and Tucker 2 used NPV and the Economic Chance Factor to rank exploration opportunities. Zammerilli 3 used the EMV to rank horizontal well locations in tight, naturally fractured reservoirs. Variables such as reservoir pressure, net thickness, success ratio, well length, drainage area, azimuth, well radius and topography were fixed at the beginning of the project. Variables like gas price and drilling costs were allowed to vary. Kelkar 4 also used EMV to rank independent projects in the presence of uncertainties. Demirmen 5 used Decision Tree and the Value of Information (VOI) analyses for screening and ranking subsurface appraisal projects. VOI captures uncertainties arising from volumetric parameters and hydrocarbon quality parameters. Gottardi et al 6 gave a good summary of the new conventional tools for ranking R & D projects using multivariate analysis.