Linear stochastic neutron transport theory

International Nuclear Information System (INIS)

Lewins, J.

1978-01-01

A new and direct derivation of the Bell-Pal fundamental equation for (low power) neutron stochastic behaviour in the Boltzmann continuum model is given. The development includes correlation of particle emission direction in induced and spontaneous fission. This leads to generalizations of the backward and forward equations for the mean and variance of neutron behaviour. The stochastic importance for neutron transport theory is introduced and related to the conventional deterministic importance. Defining equations and moment equations are derived and shown to be related to the backward fundamental equation with the detector distribution of the operational definition of stochastic importance playing the role of an adjoint source. (author)

Markovian approach: From Ising model to stochastic radiative transfer

International Nuclear Information System (INIS)

Kassianov, E.; Veron, D.

2009-01-01

The origin of the Markovian approach can be traced back to 1906; however, it gained explicit recognition in the last few decades. This overview outlines some important applications of the Markovian approach, which illustrate its immense prestige, respect, and success. These applications include examples in the statistical physics, astronomy, mathematics, computational science and the stochastic transport problem. In particular, the overview highlights important contributions made by Pomraning and Titov to the neutron and radiation transport theory in a stochastic medium with homogeneous statistics. Using simple probabilistic assumptions (Markovian approximation), they have introduced a simplified, but quite realistic, representation of the neutron/radiation transfer through a two-component discrete stochastic mixture. New concepts and methodologies introduced by these two distinguished scientists allow us to generalize the Markovian treatment to the stochastic medium with inhomogeneous statistics and demonstrate its improved predictive performance for the down-welling shortwave fluxes. (authors)

Stochastic models of edge turbulent transport in the thermonuclear reactors

International Nuclear Information System (INIS)

Volchenkov, Dima

2005-01-01

Two-dimensional stochastic model of turbulent transport in the scrape-off layer (SOL) of thermonuclear reactors is considered. Convective instability arisen in the system with respect to perturbations reveals itself in the strong outward bursts of particle density propagating ballistically across the SOL. The criterion of stability for the fluctuations of particle density is formulated. A possibility to stabilize the system depends upon the certain type of plasma waves interactions and the certain scenario of turbulence. A bias of limiter surface would provide a fairly good insulation of chamber walls excepting for the resonant cases. Pdf of the particle flux for the large magnitudes of flux events is modeled with a simple discrete time toy model of I-dimensional random walks concluding at the boundary. The spectra of wandering times feature the pdf of particle flux in the model and qualitatively reproduce the experimental statistics of transport events

Transport stochastic multi-dimensional media

International Nuclear Information System (INIS)

Haran, O.; Shvarts, D.

1996-01-01

Many physical phenomena evolve according to known deterministic rules, but in a stochastic media in which the composition changes in space and time. Examples to such phenomena are heat transfer in turbulent atmosphere with non uniform diffraction coefficients, neutron transfer in boiling coolant of a nuclear reactor and radiation transfer through concrete shields. The results of measurements conducted upon such a media are stochastic by nature, and depend on the specific realization of the media. In the last decade there has been a considerable efforts to describe linear particle transport in one dimensional stochastic media composed of several immiscible materials. However, transport in two or three dimensional stochastic media has been rarely addressed. The important effect in multi-dimensional transport that does not appear in one dimension is the ability to bypass obstacles. The current work is an attempt to quantify this effect. (authors)

Transport stochastic multi-dimensional media

Energy Technology Data Exchange (ETDEWEB)

Haran, O; Shvarts, D [Israel Atomic Energy Commission, Beersheba (Israel). Nuclear Research Center-Negev; Thiberger, R [Ben-Gurion Univ. of the Negev, Beersheba (Israel)

1996-12-01

Many physical phenomena evolve according to known deterministic rules, but in a stochastic media in which the composition changes in space and time. Examples to such phenomena are heat transfer in turbulent atmosphere with non uniform diffraction coefficients, neutron transfer in boiling coolant of a nuclear reactor and radiation transfer through concrete shields. The results of measurements conducted upon such a media are stochastic by nature, and depend on the specific realization of the media. In the last decade there has been a considerable efforts to describe linear particle transport in one dimensional stochastic media composed of several immiscible materials. However, transport in two or three dimensional stochastic media has been rarely addressed. The important effect in multi-dimensional transport that does not appear in one dimension is the ability to bypass obstacles. The current work is an attempt to quantify this effect. (authors).

Stochastic modeling of mass transport in porous media

International Nuclear Information System (INIS)

Lim, Seung Cheol; Lee, Kun Jai

1990-01-01

The stochastic moments analysis technique is developed to investigate radionuclide migration in geologic porous media. The mechanisms for radionuclide transport are assumed to be advection in the micropore, radioactive decay of the species, and sorption on the pore wall. Two covariance functions of groundwater velocity, retardation factor, and concentration are derived to incorporate the geologic parameter uncertainty in porous media of small medium dispersivity. The parametric studies show that the correlation length of groundwater velocity has significant influence on the migration behavior of radionuclide. Macro dispersivity is dominantly affected by the fluctuation of groundwater velocity, while the fluctuation of retardation factor has a considerable effect on the retarded stochastic velocity. The upper estimated concentration evaluated from this stochastic moments analysis can be used as a practical conservative value for the performance assessment of nuclear waste repository

A cavitation model based on Eulerian stochastic fields

Science.gov (United States)

Magagnato, F.; Dumond, J.

2013-12-01

Non-linear phenomena can often be described using probability density functions (pdf) and pdf transport models. Traditionally the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and in particular to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. Firstly, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.

Dynamics of non-holonomic systems with stochastic transport

Science.gov (United States)

Holm, D. D.; Putkaradze, V.

2018-01-01

This paper formulates a variational approach for treating observational uncertainty and/or computational model errors as stochastic transport in dynamical systems governed by action principles under non-holonomic constraints. For this purpose, we derive, analyse and numerically study the example of an unbalanced spherical ball rolling under gravity along a stochastic path. Our approach uses the Hamilton-Pontryagin variational principle, constrained by a stochastic rolling condition, which we show is equivalent to the corresponding stochastic Lagrange-d'Alembert principle. In the example of the rolling ball, the stochasticity represents uncertainty in the observation and/or error in the computational simulation of the angular velocity of rolling. The influence of the stochasticity on the deterministically conserved quantities is investigated both analytically and numerically. Our approach applies to a wide variety of stochastic, non-holonomically constrained systems, because it preserves the mathematical properties inherited from the variational principle.

Stochastic transport processes in discrete biological systems

CERN Document Server

Frehland, Eckart

1982-01-01

These notes are in part based on a course for advanced students in the applications of stochastic processes held in 1978 at the University of Konstanz. These notes contain the results of re­ cent studies on the stochastic description of ion transport through biological membranes. In particular, they serve as an introduction to an unified theory of fluctuations in complex biological transport systems. We emphasize that the subject of this volume is not to introduce the mathematics of stochastic processes but to present a field of theoretical biophysics in which stochastic methods are important. In the last years the study of membrane noise has become an important method in biophysics. Valuable information on the ion transport mechanisms in membranes can be obtained from noise analysis. A number of different processes such as the opening and closing of ion channels have been shown to be sources of the measured current or voltage fluctuations. Bio­ logical 'transport systems can be complex. For example, the tr...

Reconstruction of the solid transport of the river Tiber by a stochastic model

International Nuclear Information System (INIS)

Grimaldi, S.; Magnaldi, S.; Margaritora, G.

1999-01-01

The chronological series of cumulative suspended solids transport observed at Ripetta station in river Tiber (Rome, Italy) is reconstructed on the base of the correlation with the chronological series of liquid discharge, using a TFN (Transfer Function Noise) stochastic model with SARIMA noise. The results are compared with those similar reconstructions based on linear correlation that can be found in literature. Finally, the importance of floods intensity and frequency decrease observed after 1950 at Ripetta station is shown as not negligible aggravation for the decrease solid transport in river Tiber [it

Stochastic forward and inverse groundwater flow and solute transport modeling

NARCIS (Netherlands)

Janssen, G.M.C.M.

2008-01-01

Keywords: calibration, inverse modeling, stochastic modeling, nonlinear biodegradation, stochastic-convective, advective-dispersive, travel time, network design, non-Gaussian distribution, multimodal distribution, representers

This thesis offers three new approaches that contribute

Stochasticity and transport in Hamiltonian systems

International Nuclear Information System (INIS)

MacKay, R.S.; Meiss, J.D.; Percival, I.C.

1983-08-01

The theory of transport in nonlinear dynamics is developed in terms of leaky barriers which remain when invariant tori are destroyed. We describe the organization of stochastic motion by these barriers and give an explanation of long-time correlations in the stochastic regime

Diffusive flux in a model of stochastically gated oxygen transport in insect respiration

Energy Technology Data Exchange (ETDEWEB)

Berezhkovskii, Alexander M. [Mathematical and Statistical Computing Laboratory, Division of Computational Bioscience, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892 (United States); Shvartsman, Stanislav Y. [Department of Chemical and Biological Engineering and Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey 08544 (United States)

2016-05-28

Oxygen delivery to insect tissues is controlled by transport through a branched tubular network that is connected to the atmosphere by valve-like gates, known as spiracles. In certain physiological regimes, the spiracles appear to be randomly switching between open and closed states. Quantitative analysis of this regime leads a reaction-diffusion problem with stochastically switching boundary condition. We derive an expression for the diffusive flux at long times in this problem. Our approach starts with the derivation of the passage probability for a single particle that diffuses between a stochastically gated boundary, which models the opening and closing spiracle, and the perfectly absorbing boundary, which models oxygen absorption by the tissue. This passage probability is then used to derive an expression giving the diffusive flux as a function of the geometric parameters of the tube and characteristic time scales of diffusion and gate dynamics.

Supply Chain Model with Stochastic Lead Time, Trade-Credit Financing, and Transportation Discounts

Directory of Open Access Journals (Sweden)

Sung Jun Kim

2017-01-01

Full Text Available This model extends a two-echelon supply chain model by considering the trade-credit policy, transportations discount to make a coordination mechanism between transportation discounts, trade-credit financing, number of shipments, quality improvement of products, and reduced setup cost in such a way that the total cost of the whole system can be reduced, where the supplier offers trade-credit-period to the buyer. For buyer, the backorder rate is considered as variable. There are two investments to reduce setup cost and to improve quality of products. The model assumes lead time-dependent backorder rate, where the lead time is stochastic in nature. By using the trade-credit policy, the model gives how the credit-period would be determined to achieve the win-win outcome. An iterative algorithm is designed to obtain the global optimum results. Numerical example and sensitivity analysis are given to illustrate the model.

TRANSPORT PROPERTIES FOR REFRIGERANT MIXTURES

Directory of Open Access Journals (Sweden)

V. Geller

2014-06-01

Full Text Available A set of models to predict viscosity and thermal conductivity of refrigerant mixtures is developed. A general model for viscosity and thermal conductivity use the three contributions sum form (the dilute-gas terms, the residual terms, and the liquid terms. The corresponding states model is recommended to predict the dense gas transport properties over a range of reduced density from 0 to 2. It is shown that the RHS model provides the most reliable results for the saturated-liquid and the compressed-liquid transport properties over a range of given temperatures from 0,5 to 0,95.

GRAVITY PIPELINE TRANSPORT FOR HARDENING FILLING MIXTURES

Directory of Open Access Journals (Sweden)

Leonid KROUPNIK

2015-12-01

Full Text Available In underground mining of solid minerals becoming increasingly common development system with stowing hardening mixtures. In this case the natural ore array after it is replaced by an artificial excavation of solidified filling mixture consisting of binder, aggregates and water. Such a mixture is prepared on the surface on special stowing complexes and transported underground at special stowing pipelines. However, it is transported to the horizons of a few kilometers, which requires a sustainable mode of motion of such a mixture in the pipeline. Hardening stowing mixture changes its rheological characteristics over time, which complicates the calculation of the parameters of pipeline transportation. The article suggests a method of determining the initial parameters of such mixtures: the status coefficient, indicator of transportability, coefficient of hydrodynamic resistance to motion of the mixture. These indicators characterize the mixture in terms of the possibility to transport it through pipes. On the basis of these indicators is proposed methodology for calculating the parameters of pipeline transport hardening filling mixtures in drift mode when traffic on the horizontal part of the mixture under pressure column of the mixture in the vertical part of the backfill of the pipeline. This technique allows stable operation is guaranteed to provide pipeline transportation.

Modeling the photochemical attenuation of down-the-drain chemicals during river transport by stochastic methods and field measurements of pharmaceuticals and personal care products.

Science.gov (United States)

Hanamoto, Seiya; Nakada, Norihide; Yamashita, Naoyuki; Tanaka, Hiroaki

2013-01-01

Existing stochastic models for predicting concentrations of down-the-drain chemicals in aquatic environments do not account for the diurnal variation of direct photolysis by sunlight, despite its being an important factor in natural attenuation. To overcome this limitation, we developed a stochastic model incorporating temporal variations in direct photolysis. To verify the model, we measured 57 pharmaceuticals and personal care products (PPCPs) in a 7.6-km stretch of an urban river, and determined their physical and biological properties in laboratory experiments. During transport along the river, 8 PPCPs, including ketoprofen and azithromycin, were attenuated by >20%, mainly owing to direct photolysis and adsorption to sediments. The photolabile PPCPs attenuated significantly in the daytime but persisted in the nighttime. The observations were similar to the values predicted by the photolysis model for the photolabile PPCPs (i.e., ketoprofen, diclofenac and furosemide) but not by the existing model. The stochastic model developed in this study was suggested to be a novel and useful stochastic model for evaluating direct photolysis of down-the-drain chemicals, which occurs during the river transport.

Metaheuristics for the dynamic stochastic dial-a-ride problem with expected return transports.

Science.gov (United States)

Schilde, M; Doerner, K F; Hartl, R F

2011-12-01

The problem of transporting patients or elderly people has been widely studied in literature and is usually modeled as a dial-a-ride problem (DARP). In this paper we analyze the corresponding problem arising in the daily operation of the Austrian Red Cross. This nongovernmental organization is the largest organization performing patient transportation in Austria. The aim is to design vehicle routes to serve partially dynamic transportation requests using a fixed vehicle fleet. Each request requires transportation from a patient's home location to a hospital (outbound request) or back home from the hospital (inbound request). Some of these requests are known in advance. Some requests are dynamic in the sense that they appear during the day without any prior information. Finally, some inbound requests are stochastic. More precisely, with a certain probability each outbound request causes a corresponding inbound request on the same day. Some stochastic information about these return transports is available from historical data. The purpose of this study is to investigate, whether using this information in designing the routes has a significant positive effect on the solution quality. The problem is modeled as a dynamic stochastic dial-a-ride problem with expected return transports. We propose four different modifications of metaheuristic solution approaches for this problem. In detail, we test dynamic versions of variable neighborhood search (VNS) and stochastic VNS (S-VNS) as well as modified versions of the multiple plan approach (MPA) and the multiple scenario approach (MSA). Tests are performed using 12 sets of test instances based on a real road network. Various demand scenarios are generated based on the available real data. Results show that using the stochastic information on return transports leads to average improvements of around 15%. Moreover, improvements of up to 41% can be achieved for some test instances.

Stochastic modeling of phosphorus transport in the Three Gorges Reservoir by incorporating variability associated with the phosphorus partition coefficient

Energy Technology Data Exchange (ETDEWEB)

Huang, Lei; Fang, Hongwei; Xu, Xingya; He, Guojian; Zhang, Xuesong; Reible, Danny

2017-08-01

Phosphorus (P) fate and transport plays a crucial role in the ecology of rivers and reservoirs in which eutrophication is limited by P. A key uncertainty in models used to help manage P in such systems is the partitioning of P to suspended and bed sediments. By analyzing data from field and laboratory experiments, we stochastically characterize the variability of the partition coefficient (Kd) and derive spatio-temporal solutions for P transport in the Three Gorges Reservoir (TGR). We formulate a set of stochastic partial different equations (SPDEs) to simulate P transport by randomly sampling Kd from the measured distributions, to obtain statistical descriptions of the P concentration and retention in the TGR. The correspondence between predicted and observed P concentrations and P retention in the TGR combined with the ability to effectively characterize uncertainty suggests that a model that incorporates the observed variability can better describe P dynamics and more effectively serve as a tool for P management in the system. This study highlights the importance of considering parametric uncertainty in estimating uncertainty/variability associated with simulated P transport.

Variance estimates for transport in stochastic media by means of the master equation

International Nuclear Information System (INIS)

Pautz, S. D.; Franke, B. C.; Prinja, A. K.

2013-01-01

The master equation has been used to examine properties of transport in stochastic media. It has been shown previously that not only may the Levermore-Pomraning (LP) model be derived from the master equation for a description of ensemble-averaged transport quantities, but also that equations describing higher-order statistical moments may be obtained. We examine in greater detail the equations governing the second moments of the distribution of the angular fluxes, from which variances may be computed. We introduce a simple closure for these equations, as well as several models for estimating the variances of derived transport quantities. We revisit previous benchmarks for transport in stochastic media in order to examine the error of these new variance models. We find, not surprisingly, that the errors in these variance estimates are at least as large as the corresponding estimates of the average, and sometimes much larger. We also identify patterns in these variance estimates that may help guide the construction of more accurate models. (authors)

One possible method of mathematical modeling of turbulent transport processes in plasma

International Nuclear Information System (INIS)

Skvortsova, Nina N.; Batanov, German M.; Petrov, Alexander E.; Pshenichnikov, Anton A.; Sarksyan, Karen A.; Kharchev, Nikolay K.; Bening, Vladimir E.; Korolev, Victor Yu.

2003-01-01

It is proposed to use the mathematical modeling of the increments of fluctuating plasma variables to analyzing the probability characteristics of turbulent transport processes in plasma. It is shown that, in plasma of the L-2M stellarator and the TAU-1 linear device, the increments of the process of local fluctuating particle flux are stochastic in nature and their distribution is a scale mixture of Gaussians. (author)

A stochastic solution of the advective transport equation with uncertainty

International Nuclear Information System (INIS)

Williams, M.M.R.

1991-01-01

A model has been developed for calculating the transport of water-borne radionuclides through layers of porous materials, such as rock or clay. The model is based upon a purely advective transport equation, in which the fluid velocity is a random variable, thereby simulating dispersion in a more realistic manner than the ad hoc introduction of a dispersivity. In addition to a random velocity field, which is an observable physical phenomenon, allowance is made for uncertainty in our knowledge of the parameters which enter the equation, e.g. the retardation coefficient. This too, is assumed to be a random variable and contributes to the stochasticity of the resulting partial differential equation of transport. The stochastic differential equation can be solved analytically and then ensemble averages taken over the associated probability distribution of velocity and retardation coefficient. A method based upon a novel form of the central limit theorem of statistics is employed to obtain tractable solutions of a system consisting of many serial legs of varying properties. One interesting conclusion is that the total flux out of a medium is significantly underestimated by using the deterministic solution with an average transit time compared with that from the stochastically averaged solution. The theory is illustrated numerically for a number of physically relevant cases. (author) 8 figs., 4 tabs., 7 refs

AUTOMATIC CALIBRATION OF A STOCHASTIC-LAGRANGIAN TRANSPORT MODEL (SLAM)

Science.gov (United States)

Numerical models are a useful tool in evaluating and designing NAPL remediation systems. Traditional constitutive finite difference and finite element models are complex and expensive to apply. For this reason, this paper presents the application of a simplified stochastic-Lagran...

Stochastic foundations of undulatory transport phenomena: generalized Poisson-Kac processes—part III extensions and applications to kinetic theory and transport

Science.gov (United States)

Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro

2017-08-01

This third part extends the theory of Generalized Poisson-Kac (GPK) processes to nonlinear stochastic models and to a continuum of states. Nonlinearity is treated in two ways: (i) as a dependence of the parameters (intensity of the stochastic velocity, transition rates) of the stochastic perturbation on the state variable, similarly to the case of nonlinear Langevin equations, and (ii) as the dependence of the stochastic microdynamic equations of motion on the statistical description of the process itself (nonlinear Fokker-Planck-Kac models). Several numerical and physical examples illustrate the theory. Gathering nonlinearity and a continuum of states, GPK theory provides a stochastic derivation of the nonlinear Boltzmann equation, furnishing a positive answer to the Kac’s program in kinetic theory. The transition from stochastic microdynamics to transport theory within the framework of the GPK paradigm is also addressed.

Stochastic foundations of undulatory transport phenomena: generalized Poisson–Kac processes—part III extensions and applications to kinetic theory and transport

International Nuclear Information System (INIS)

Giona, Massimiliano; Brasiello, Antonio; Crescitelli, Silvestro

2017-01-01

This third part extends the theory of Generalized Poisson–Kac (GPK) processes to nonlinear stochastic models and to a continuum of states. Nonlinearity is treated in two ways: (i) as a dependence of the parameters (intensity of the stochastic velocity, transition rates) of the stochastic perturbation on the state variable, similarly to the case of nonlinear Langevin equations, and (ii) as the dependence of the stochastic microdynamic equations of motion on the statistical description of the process itself (nonlinear Fokker–Planck–Kac models). Several numerical and physical examples illustrate the theory. Gathering nonlinearity and a continuum of states, GPK theory provides a stochastic derivation of the nonlinear Boltzmann equation, furnishing a positive answer to the Kac’s program in kinetic theory. The transition from stochastic microdynamics to transport theory within the framework of the GPK paradigm is also addressed. (paper)

Stochastic line motion and stochastic flux conservation for nonideal hydromagnetic models

International Nuclear Information System (INIS)

Eyink, Gregory L.

2009-01-01

We prove that smooth solutions of nonideal (viscous and resistive) incompressible magnetohydrodynamic (MHD) equations satisfy a stochastic law of flux conservation. This property implies that the magnetic flux through a surface is equal to the average of the magnetic fluxes through an ensemble of surfaces advected backward in time by the plasma velocity perturbed with a random white noise. Our result is an analog of the well-known Alfven theorem of ideal MHD and is valid for any value of the magnetic Prandtl number. A second stochastic conservation law is shown to hold at unit Prandtl number, a random version of the generalized Kelvin theorem derived by Bekenstein and Oron for ideal MHD. These stochastic conservation laws are not only shown to be consequences of the nonideal MHD equations but are proved in fact to be equivalent to those equations. We derive similar results for two more refined hydromagnetic models, Hall MHD and the two-fluid plasma model, still assuming incompressible velocities and isotropic transport coefficients. Finally, we use these results to discuss briefly the infinite-Reynolds-number limit of hydromagnetic turbulence and to support the conjecture that flux conservation remains stochastic in that limit.

Heat transfer analysis of porous media receiver with different transport and thermophysical models using mixture as feeding gas

International Nuclear Information System (INIS)

Wang, Fuqiang; Tan, Jianyu; Wang, Zhiqiang

2014-01-01

Highlights: • Using local thermal non-equilibrium model to solve heat transfer of porous media. • CH 4 /H 2 O mixture is adopted as feeding gas of porous media receiver. • Radiative transfer equation between porous strut is solved by Rosseland approximation. • Transport and thermophysical models not included in Fluent are programmed by UDFs. • Variations of model on thermal performance of porous media receiver are studied. - Abstract: The local thermal non-equilibrium model is adopted to solve the steady state heat and mass transfer problems of porous media solar receiver. The fluid entrance surface is subjected to concentrated solar radiation, and CH 4 /H 2 O mixture is adopted as feeding gas. The radiative heat transfer equation between porous strut is solved by Rosseland approximation. The impacts of variation in transport and thermophysical characteristics model of gas mixture on thermal performance of porous media receiver are investigated. The transport and thermophysical characteristics models which are not included in software Fluent are programmed by user defined functions (UDFs). The numerical results indicate that models of momentum source term for porous media receiver have significant impact on pressure drop and static pressure distribution, and the radiative heat transfer cannot be omitted during the thermal performance analysis of porous media receiver

Stochastic porous media modeling and high-resolution schemes for numerical simulation of subsurface immiscible fluid flow transport

Science.gov (United States)

Brantson, Eric Thompson; Ju, Binshan; Wu, Dan; Gyan, Patricia Semwaah

2018-04-01

This paper proposes stochastic petroleum porous media modeling for immiscible fluid flow simulation using Dykstra-Parson coefficient (V DP) and autocorrelation lengths to generate 2D stochastic permeability values which were also used to generate porosity fields through a linear interpolation technique based on Carman-Kozeny equation. The proposed method of permeability field generation in this study was compared to turning bands method (TBM) and uniform sampling randomization method (USRM). On the other hand, many studies have also reported that, upstream mobility weighting schemes, commonly used in conventional numerical reservoir simulators do not accurately capture immiscible displacement shocks and discontinuities through stochastically generated porous media. This can be attributed to high level of numerical smearing in first-order schemes, oftentimes misinterpreted as subsurface geological features. Therefore, this work employs high-resolution schemes of SUPERBEE flux limiter, weighted essentially non-oscillatory scheme (WENO), and monotone upstream-centered schemes for conservation laws (MUSCL) to accurately capture immiscible fluid flow transport in stochastic porous media. The high-order schemes results match well with Buckley Leverett (BL) analytical solution without any non-oscillatory solutions. The governing fluid flow equations were solved numerically using simultaneous solution (SS) technique, sequential solution (SEQ) technique and iterative implicit pressure and explicit saturation (IMPES) technique which produce acceptable numerical stability and convergence rate. A comparative and numerical examples study of flow transport through the proposed method, TBM and USRM permeability fields revealed detailed subsurface instabilities with their corresponding ultimate recovery factors. Also, the impact of autocorrelation lengths on immiscible fluid flow transport were analyzed and quantified. A finite number of lines used in the TBM resulted into visual

Calculation of Transport Coefficients in Dense Plasma Mixtures

Science.gov (United States)

Haxhimali, T.; Cabot, W. H.; Caspersen, K. J.; Greenough, J.; Miller, P. L.; Rudd, R. E.; Schwegler, E. R.

2011-10-01

We use classical molecular dynamics (MD) to estimate species diffusivity and viscosity in mixed dense plasmas. The Yukawa potential is used to describe the screened Coulomb interaction between the ions. This potential has been used widely, providing the basis for models of dense stellar materials, inertial confined plasmas, and colloidal particles in electrolytes. We calculate transport coefficients in equilibrium simulations using the Green- Kubo relation over a range of thermodynamic conditions including the viscosity and the self - diffusivity for each component of the mixture. The interdiffusivity (or mutual diffusivity) can then be related to the self-diffusivities by using a generalization of the Darken equation. We have also employed non-equilibrium MD to estimate interdiffusivity during the broadening of the interface between two regions each with a high concentration of either species. Here we present results for an asymmetric mixture between Ar and H. These can easily be extended to other plasma mixtures. A main motivation for this study is to develop accurate transport models that can be incorporated into the hydrodynamic codes to study hydrodynamic instabilities. We use classical molecular dynamics (MD) to estimate species diffusivity and viscosity in mixed dense plasmas. The Yukawa potential is used to describe the screened Coulomb interaction between the ions. This potential has been used widely, providing the basis for models of dense stellar materials, inertial confined plasmas, and colloidal particles in electrolytes. We calculate transport coefficients in equilibrium simulations using the Green- Kubo relation over a range of thermodynamic conditions including the viscosity and the self - diffusivity for each component of the mixture. The interdiffusivity (or mutual diffusivity) can then be related to the self-diffusivities by using a generalization of the Darken equation. We have also employed non-equilibrium MD to estimate interdiffusivity during

Robust transport by multiple motors with nonlinear force–velocity relations and stochastic load sharing

International Nuclear Information System (INIS)

Kunwar, Ambarish; Mogilner, Alexander

2010-01-01

Transport by processive molecular motors plays an important role in many cell biological phenomena. In many cases, motors work together to transport cargos in the cell, so it is important to understand the mechanics of the multiple motors. Based on earlier modeling efforts, here we study effects of nonlinear force–velocity relations and stochastic load sharing on multiple motor transport. We find that when two or three motors transport the cargo, then the nonlinear and stochastic effects compensate so that the mechanical properties of the transport are robust. Similarly, the transport is insensitive to compliance of the cargo-motor links. Furthermore, the rate of movement against moderate loads is not improved by increasing the small number of motors. When the motor number is greater than 4, correlations between the motors become negligible, and the earlier analytical mean-field theory of the multiple motor transport holds. We predict that the effective diffusion of the cargo driven by the multiple motors under load increases by an order of magnitude compared to that for the single motor. Finally, our simulations predict that the stochastic effects are responsible for a significant dispersion of velocities generated by the 'tug-of-war' of the multiple opposing motors

ParPor: Particles in Pores. Stochastic Modeling of Polydisperse Transport

DEFF Research Database (Denmark)

Yuan, Hao

2010-01-01

Liquid flow containing particles in the different types of porous media appear in a large variety of practically important industrial and natural processes. The project aims at developing a stochastic model for the deep bed filtration process in which the polydisperse suspension flow...... in the polydisperse porous media. Instead of the traditional parabolic Advection-Dispersion Equation (ADE) the novel elliptic PDE based on the Continuous Time Random Walk is adopted for the particle size kinetics. The pore kinetics is either described by the stochastic size exclusion mechanism or the incomplete pore...

Revisiting the cape cod bacteria injection experiment using a stochastic modeling approach

Science.gov (United States)

Maxwell, R.M.; Welty, C.; Harvey, R.W.

2007-01-01

Bromide and resting-cell bacteria tracer tests conducted in a sandy aquifer at the U.S. Geological Survey Cape Cod site in 1987 were reinterpreted using a three-dimensional stochastic approach. Bacteria transport was coupled to colloid filtration theory through functional dependence of local-scale colloid transport parameters upon hydraulic conductivity and seepage velocity in a stochastic advection - dispersion/attachment - detachment model. Geostatistical information on the hydraulic conductivity (K) field that was unavailable at the time of the original test was utilized as input. Using geostatistical parameters, a groundwater flow and particle-tracking model of conservative solute transport was calibrated to the bromide-tracer breakthrough data. An optimization routine was employed over 100 realizations to adjust the mean and variance ofthe natural-logarithm of hydraulic conductivity (InK) field to achieve best fit of a simulated, average bromide breakthrough curve. A stochastic particle-tracking model for the bacteria was run without adjustments to the local-scale colloid transport parameters. Good predictions of mean bacteria breakthrough were achieved using several approaches for modeling components of the system. Simulations incorporating the recent Tufenkji and Elimelech (Environ. Sci. Technol. 2004, 38, 529-536) correlation equation for estimating single collector efficiency were compared to those using the older Rajagopalan and Tien (AIChE J. 1976, 22, 523-533) model. Both appeared to work equally well at predicting mean bacteria breakthrough using a constant mean bacteria diameter for this set of field conditions. Simulations using a distribution of bacterial cell diameters available from original field notes yielded a slight improvement in the model and data agreement compared to simulations using an average bacterial diameter. The stochastic approach based on estimates of local-scale parameters for the bacteria-transport process reasonably captured

Stochastic transport models for mixing in variable-density turbulence

Science.gov (United States)

Bakosi, J.; Ristorcelli, J. R.

2011-11-01

In variable-density (VD) turbulent mixing, where very-different- density materials coexist, the density fluctuations can be an order of magnitude larger than their mean. Density fluctuations are non-negligible in the inertia terms of the Navier-Stokes equation which has both quadratic and cubic nonlinearities. Very different mixing rates of different materials give rise to large differential accelerations and some fundamentally new physics that is not seen in constant-density turbulence. In VD flows material mixing is active in a sense far stronger than that applied in the Boussinesq approximation of buoyantly-driven flows: the mass fraction fluctuations are coupled to each other and to the fluid momentum. Statistical modeling of VD mixing requires accounting for basic constraints that are not important in the small-density-fluctuation passive-scalar-mixing approximation: the unit-sum of mass fractions, bounded sample space, and the highly skewed nature of the probability densities become essential. We derive a transport equation for the joint probability of mass fractions, equivalent to a system of stochastic differential equations, that is consistent with VD mixing in multi-component turbulence and consistently reduces to passive scalar mixing in constant-density flows.

Transport of radionuclides in stochastic media. Pt. 1: The quasi-asymptotic approximation

International Nuclear Information System (INIS)

Devooght, J.; Smidts, O.F.

1996-01-01

A three-dimensional quasi-asymptotic approximate equation is developed for the transport of radionuclides in a stochastic velocity field. This approximation is derived from an integro-differential equation of transport in stochastic media, commonly encountered in hydrogeology. The quasi-asymptotic equation turns out to be a generalised Telegrapher's equation as found by Williams in the particular context of fractured media. We obtain the Telegrapher's equation without specifying the causes responsible for the random velocity field. Our model may thus be applied in porous media as well as in fractured media. We give the developments leading to the analytical solution of the three-dimensional Telegrapher's equation for constant parameters. This solution is then visualised for a source in the form of a square wave. (Author)

Comparison of stochastic models in Monte Carlo simulation of coated particle fuels

International Nuclear Information System (INIS)

Yu Hui; Nam Zin Cho

2013-01-01

There is growing interest worldwide in very high temperature gas cooled reactors as candidates for next generation reactor systems. For design and analysis of such reactors with double heterogeneity introduced by the coated particle fuels that are randomly distributed in graphite pebbles, stochastic transport models are becoming essential. Several models were reported in the literature, such as coarse lattice models, fine lattice stochastic (FLS) models, random sequential addition (RSA) models, metropolis models. The principles and performance of these stochastic models are described and compared in this paper. Compared with the usual fixed lattice methods, sub-FLS modeling allows more realistic stochastic distribution of fuel particles and thus results in more accurate criticality calculation. Compared with the basic RSA method, sub-FLS modeling requires simpler and more efficient overlapping checking procedure. (authors)

A new approach to stochastic transport via the functional Volterra expansion

International Nuclear Information System (INIS)

Ziya Akcasu, A.; Corngold, N.

2005-01-01

In this paper we present a new algorithm (FDA) for the calculation of the mean and the variance of the flux in stochastic transport when the transport equation contains a spatially random parameter θ(r), such as the density of the medium. The approach is based on the renormalized functional Volterra expansion of the flux around its mean. The attractive feature of the approach is that it explicitly displays the functional dependence of the flux on the products of θ(r i ), and hence enables one to take ensemble averages directly to calculate the moments of the flux in terms of the correlation functions of the underlying random process. The renormalized deterministic transport equation for the mean flux has been obtained to the second order in θ(r), and a functional relationship between the variance and the mean flux has been derived to calculate the variance to this order. The feasibility and accuracy of FDA has been demonstrated in the case of stochastic diffusion, using the diffusion equation with a spatially random diffusion coefficient. The connection of FDA with the well-established approximation schemes in the field of stochastic linear differential equations, such as the Bourret approximation, developed by Van Kampen using cumulant expansion, and by Terwiel using projection operator formalism, which has recently been extended to stochastic transport by Corngold. We hope that FDA's potential will be explored numerically in more realistic applications of the stochastic transport. (authors)

A random walk approach to stochastic neutron transport

International Nuclear Information System (INIS)

Mulatier, Clelia de

2015-01-01

One of the key goals of nuclear reactor physics is to determine the distribution of the neutron population within a reactor core. This population indeed fluctuates due to the stochastic nature of the interactions of the neutrons with the nuclei of the surrounding medium: scattering, emission of neutrons from fission events and capture by nuclear absorption. Due to these physical mechanisms, the stochastic process performed by neutrons is a branching random walk. For most applications, the neutron population considered is very large, and all physical observables related to its behaviour, such as the heat production due to fissions, are well characterised by their average values. Generally, these mean quantities are governed by the classical neutron transport equation, called linear Boltzmann equation. During my PhD, using tools from branching random walks and anomalous diffusion, I have tackled two aspects of neutron transport that cannot be approached by the linear Boltzmann equation. First, thanks to the Feynman-Kac backward formalism, I have characterised the phenomenon of 'neutron clustering' that has been highlighted for low-density configuration of neutrons and results from strong fluctuations in space and time of the neutron population. Then, I focused on several properties of anomalous (non-exponential) transport, that can model neutron transport in strongly heterogeneous and disordered media, such as pebble-bed reactors. One of the novel aspects of this work is that problems are treated in the presence of boundaries. Indeed, even though real systems are finite (confined geometries), most of previously existing results were obtained for infinite systems. (author) [fr

Stochastic neuron models

CERN Document Server

Greenwood, Priscilla E

2016-01-01

This book describes a large number of open problems in the theory of stochastic neural systems, with the aim of enticing probabilists to work on them. This includes problems arising from stochastic models of individual neurons as well as those arising from stochastic models of the activities of small and large networks of interconnected neurons. The necessary neuroscience background to these problems is outlined within the text, so readers can grasp the context in which they arise. This book will be useful for graduate students and instructors providing material and references for applying probability to stochastic neuron modeling. Methods and results are presented, but the emphasis is on questions where additional stochastic analysis may contribute neuroscience insight. An extensive bibliography is included. Dr. Priscilla E. Greenwood is a Professor Emerita in the Department of Mathematics at the University of British Columbia. Dr. Lawrence M. Ward is a Professor in the Department of Psychology and the Brain...

Applications of stochastic models to solute transport in fractured rocks

International Nuclear Information System (INIS)

Gelhar, L.W.

1987-01-01

A stochastic theory for flow and solute transport in a single variable aperture fracture bounded by sorbing porous matrix into which solutes may diffuse, is developed using a perturbation approximation and spectral solution techniques which assume local statistical homogeneity. The theory predicts that the effective aperture of the fracture for mean solute displacement will be larger than the aperture required to calculate the large-scale flow resistance of the fracture. This ratio of apertures is a function of the variance of the logarithm of the apertures. The theory also predicts the macrodispersion coefficient for large-scale transport in the fracture. The resulting macrodispersivity is proportional to the variance of the logaperture and to its correlation scale. When variable surface sorption is included, it is found that the macrodispersivity is increased significantly, in some cases more than an order of magnitude. It is also shown that the effective retardation coefficient for the sorptively heterogeneous fracture is found by simply taking the arithmetic mean of the local surface sorption coefficient. Matrix diffusion is also shown to increase the fracture macrodispesivity at very large times. A reexamination of the results of four different field tracer tests in crystalline rock in Sweden and Canada shows aperture ratios and dispersivities that are consistent with the stochastic theory. The variance of the natural logarithm of the aperture is found to be in the range of 3 to 6 and the correlation scales for logaperture ranges from .2 to 1.2 meters. Detailed recommendations for additional field investigations at scales ranging from a few meters up to a kilometer are presented. (orig.)

Microbial and Organic Fine Particle Transport Dynamics in Streams - a Combined Experimental and Stochastic Modeling Approach

Science.gov (United States)

Drummond, Jen; Davies-Colley, Rob; Stott, Rebecca; Sukias, James; Nagels, John; Sharp, Alice; Packman, Aaron

2014-05-01

Transport dynamics of microbial cells and organic fine particles are important to stream ecology and biogeochemistry. Cells and particles continuously deposit and resuspend during downstream transport owing to a variety of processes including gravitational settling, interactions with in-stream structures or biofilms at the sediment-water interface, and hyporheic exchange and filtration within underlying sediments. Deposited cells and particles are also resuspended following increases in streamflow. Fine particle retention influences biogeochemical processing of substrates and nutrients (C, N, P), while remobilization of pathogenic microbes during flood events presents a hazard to downstream uses such as water supplies and recreation. We are conducting studies to gain insights into the dynamics of fine particles and microbes in streams, with a campaign of experiments and modeling. The results improve understanding of fine sediment transport, carbon cycling, nutrient spiraling, and microbial hazards in streams. We developed a stochastic model to describe the transport and retention of fine particles and microbes in rivers that accounts for hyporheic exchange and transport through porewaters, reversible filtration within the streambed, and microbial inactivation in the water column and subsurface. This model framework is an advance over previous work in that it incorporates detailed transport and retention processes that are amenable to measurement. Solute, particle, and microbial transport were observed both locally within sediment and at the whole-stream scale. A multi-tracer whole-stream injection experiment compared the transport and retention of a conservative solute, fluorescent fine particles, and the fecal indicator bacterium Escherichia coli. Retention occurred within both the underlying sediment bed and stands of submerged macrophytes. The results demonstrate that the combination of local measurements, whole-stream tracer experiments, and advanced modeling

Stochastic biomathematical models with applications to neuronal modeling

CERN Document Server

Batzel, Jerry; Ditlevsen, Susanne

2013-01-01

Stochastic biomathematical models are becoming increasingly important as new light is shed on the role of noise in living systems. In certain biological systems, stochastic effects may even enhance a signal, thus providing a biological motivation for the noise observed in living systems. Recent advances in stochastic analysis and increasing computing power facilitate the analysis of more biophysically realistic models, and this book provides researchers in computational neuroscience and stochastic systems with an overview of recent developments. Key concepts are developed in chapters written by experts in their respective fields. Topics include: one-dimensional homogeneous diffusions and their boundary behavior, large deviation theory and its application in stochastic neurobiological models, a review of mathematical methods for stochastic neuronal integrate-and-fire models, stochastic partial differential equation models in neurobiology, and stochastic modeling of spreading cortical depression.

EARLY GUIDANCE FOR ASSIGNING DISTRIBUTION PARAMETERS TO GEOCHEMICAL INPUT TERMS TO STOCHASTIC TRANSPORT MODELS

International Nuclear Information System (INIS)

Kaplan, D; Margaret Millings, M

2006-01-01

Stochastic modeling is being used in the Performance Assessment program to provide a probabilistic estimate of the range of risk that buried waste may pose. The objective of this task was to provide early guidance for stochastic modelers for the selection of the range and distribution (e.g., normal, log-normal) of distribution coefficients (K d ) and solubility values (K sp ) to be used in modeling subsurface radionuclide transport in E- and Z-Area on the Savannah River Site (SRS). Due to the project's schedule, some modeling had to be started prior to collecting the necessary field and laboratory data needed to fully populate these models. For the interim, the project will rely on literature values and some statistical analyses of literature data as inputs. Based on statistical analyses of some literature sorption tests, the following early guidance was provided: (1) Set the range to an order of magnitude for radionuclides with K d values >1000 mL/g and to a factor of two for K d values of sp values -6 M and to a factor of two for K d values of >10 -6 M. This decision is based on the literature. (3) The distribution of K d values with a mean >1000 mL/g will be log-normally distributed. Those with a K d value <1000 mL/g will be assigned a normal distribution. This is based on statistical analysis of non-site-specific data. Results from on-going site-specific field/laboratory research involving E-Area sediments will supersede this guidance; these results are expected in 2007

Determinant of flexible Parametric Estimation of Mixture Cure ...

African Journals Online (AJOL)

PROF. OLIVER OSUAGWA

2015-12-01

Dec 1, 2015 ... Suitability of four parametric mixture cure models were considered namely; Log .... regression analysis which relies on the ... The parameter of mixture cure fraction model was ..... Stochastic Models of Tumor Latency and Their.

Anomalous transport regimes in a stochastic advection-diffusion model

International Nuclear Information System (INIS)

Dranikov, I.L.; Kondratenko, P.S.; Matveev, L.V.

2004-01-01

A general solution to the stochastic advection-diffusion problem is obtained for a fractal medium with long-range correlated spatial fluctuations. A particular transport regime is determined by two basic parameters: the exponent 2h of power-law decay of the two-point velocity correlation function and the mean advection velocity u. The values of these parameters corresponding to anomalous diffusion are determined, and anomalous behavior of the tracer distribution is analyzed for various combinations of u and h. The tracer concentration is shown to decrease exponentially at large distances, whereas power-law decay is predicted by fractional differential equations. Equations that describe the essential characteristics of the solution are written in terms of coupled space-time fractional differential operators. The analysis relies on a diagrammatic technique and makes use of scale-invariant properties of the medium

Parameters of Solidifying Mixtures Transporting at Underground Ore Mining

Directory of Open Access Journals (Sweden)

Golik Vladimir

2017-01-01

Full Text Available The article is devoted to the problem of providing mining enterprises with solidifying filling mixtures at underground mining. The results of analytical studies using the data of foreign and domestic practice of solidifying mixtures delivery to stopes are given. On the basis of experimental practice the parameters of transportation of solidifying filling mixtures are given with an increase in their quality due to the effect of vibration in the pipeline. The mechanism of the delivery process and the procedure for determining the parameters of the forced oscillations of the pipeline, the characteristics of the transporting processes, the rigidity of the elastic elements of pipeline section supports and the magnitude of vibrator’ driving force are detailed. It is determined that the quality of solidifying filling mixtures can be increased due to the rational use of technical resources during the transportation of mixtures, and as a result the mixtures are characterized by a more even distribution of the aggregate. The algorithm for calculating the parameters of the pipe vibro-transport of solidifying filling mixtures can be in demand in the design of mineral deposits underground mining technology.

Parameters of Solidifying Mixtures Transporting at Underground Ore Mining

Science.gov (United States)

Golik, Vladimir; Dmitrak, Yury

2017-11-01

The article is devoted to the problem of providing mining enterprises with solidifying filling mixtures at underground mining. The results of analytical studies using the data of foreign and domestic practice of solidifying mixtures delivery to stopes are given. On the basis of experimental practice the parameters of transportation of solidifying filling mixtures are given with an increase in their quality due to the effect of vibration in the pipeline. The mechanism of the delivery process and the procedure for determining the parameters of the forced oscillations of the pipeline, the characteristics of the transporting processes, the rigidity of the elastic elements of pipeline section supports and the magnitude of vibrator' driving force are detailed. It is determined that the quality of solidifying filling mixtures can be increased due to the rational use of technical resources during the transportation of mixtures, and as a result the mixtures are characterized by a more even distribution of the aggregate. The algorithm for calculating the parameters of the pipe vibro-transport of solidifying filling mixtures can be in demand in the design of mineral deposits underground mining technology.

Abstracts of the symposium on unsaturated flow and transport modeling

International Nuclear Information System (INIS)

1982-03-01

Abstract titles are: Recent developments in modeling variably saturated flow and transport; Unsaturated flow modeling as applied to field problems; Coupled heat and moisture transport in unsaturated soils; Influence of climatic parameters on movement of radionuclides in a multilayered saturated-unsaturated media; Modeling water and solute transport in soil containing roots; Simulation of consolidation in partially saturated soil materials; modeling of water and solute transport in unsaturated heterogeneous fields; Fluid dynamics and mass transfer in variably-saturated porous media; Solute transport through soils; One-dimensional analytical transport modeling; Convective transport of ideal tracers in unsaturated soils; Chemical transport in macropore-mesopore media under partially saturated conditions; Influence of the tension-saturated zone on contaminant migration in shallow water regimes; Influence of the spatial distribution of velocities in porous media on the form of solute transport; Stochastic vs deterministic models for solute movement in the field; and Stochastic analysis of flow and solute transport

Sea Outfall Design Based on a Stochastic Transport/Dispersion Model

DEFF Research Database (Denmark)

Larsen, Torben

1983-01-01

/dispersion phenomena can easily be modelled by the stochastic approach without going into advanced methods as finite differences or elements. The advantage of this approach is the simple programming and Iow need of computer memory. The disadvantage could be the need for excessive computing time.......This paper describes a numerical model of the dilution and disappearance of sewage discharged to the coastal zone. The model is based on the Monte Carlo (or random walk) principle. A cloud of particles is released at discrete time steps and the 3-dimensional path of every particle is simulated...

Stochastic modeling concepts in groundwater and risk assessment: potential application to marine problems

International Nuclear Information System (INIS)

Hamed, Maged M.

2000-01-01

Parameter uncertainty is ubiquitous in marine environmental processes. Failure to account for this uncertainty may lead to erroneous results, and may have significant environmental and economic ramifications. Stochastic modeling of oil spill transport and fate is, therefore, central in the development of an oil spill contingency plan for new oil and gas projects. Over the past twenty years, several stochastic modeling tools have been developed for modeling parameter uncertainty, including the spectral, perturbation, and simulation methods. In this work we explore the application of a new stochastic methodology, the first-order reliability method (FORM), in oil spill modeling. FORM was originally developed in the structural reliability field and has been recently applied to various environmental problems. The method has many appealing features that makes it a powerful tool for modeling complex environmental systems. The theory of FORM is presented, identifying the features that distinguish the method from other stochastic tools. Different formulations to the reliability-based stochastic oil spill modeling are presented in a decision-analytic context. (Author)

Stochastic Still Water Response Model

DEFF Research Database (Denmark)

Friis-Hansen, Peter; Ditlevsen, Ove Dalager

2002-01-01

In this study a stochastic field model for the still water loading is formulated where the statistics (mean value, standard deviation, and correlation) of the sectional forces are obtained by integration of the load field over the relevant part of the ship structure. The objective of the model is...... out that an important parameter of the stochastic cargo field model is the mean number of containers delivered by each customer.......In this study a stochastic field model for the still water loading is formulated where the statistics (mean value, standard deviation, and correlation) of the sectional forces are obtained by integration of the load field over the relevant part of the ship structure. The objective of the model...... is to establish the stochastic load field conditional on a given draft and trim of the vessel. The model contributes to a realistic modelling of the stochastic load processes to be used in a reliability evaluation of the ship hull. Emphasis is given to container vessels. The formulation of the model for obtaining...

Neutron stochastic transport theory with delayed neutrons

International Nuclear Information System (INIS)

Munoz-Cobo, J.L.; Verdu, G.

1987-01-01

From the stochastic transport theory with delayed neutrons, the Boltzmann transport equation with delayed neutrons for the average flux emerges in a natural way without recourse to any approximation. From this theory a general expression is obtained for the Feynman Y-function when delayed neutrons are included. The single mode approximation for the particular case of a subcritical assembly is developed, and it is shown that Y-function reduces to the familiar expression quoted in many books, when delayed neutrons are not considered, and spatial and source effects are not included. (author)

Maximal stochastic transport in the Lorenz equations

Energy Technology Data Exchange (ETDEWEB)

Agarwal, Sahil, E-mail: sahil.agarwal@yale.edu [Program in Applied Mathematics, Yale University, New Haven (United States); Wettlaufer, J.S., E-mail: john.wettlaufer@yale.edu [Program in Applied Mathematics, Yale University, New Haven (United States); Departments of Geology & Geophysics, Mathematics and Physics, Yale University, New Haven (United States); Mathematical Institute, University of Oxford, Oxford (United Kingdom); Nordita, Royal Institute of Technology and Stockholm University, Stockholm (Sweden)

2016-01-08

We calculate the stochastic upper bounds for the Lorenz equations using an extension of the background method. In analogy with Rayleigh–Bénard convection the upper bounds are for heat transport versus Rayleigh number. As might be expected, the stochastic upper bounds are larger than the deterministic counterpart of Souza and Doering [1], but their variation with noise amplitude exhibits interesting behavior. Below the transition to chaotic dynamics the upper bounds increase monotonically with noise amplitude. However, in the chaotic regime this monotonicity depends on the number of realizations in the ensemble; at a particular Rayleigh number the bound may increase or decrease with noise amplitude. The origin of this behavior is the coupling between the noise and unstable periodic orbits, the degree of which depends on the degree to which the ensemble represents the ergodic set. This is confirmed by examining the close returns plots of the full solutions to the stochastic equations and the numerical convergence of the noise correlations. The numerical convergence of both the ensemble and time averages of the noise correlations is sufficiently slow that it is the limiting aspect of the realization of these bounds. Finally, we note that the full solutions of the stochastic equations demonstrate that the effect of noise is equivalent to the effect of chaos.

Multi-choice stochastic transportation problem involving general form of distributions.

Science.gov (United States)

Quddoos, Abdul; Ull Hasan, Md Gulzar; Khalid, Mohammad Masood

2014-01-01

Many authors have presented studies of multi-choice stochastic transportation problem (MCSTP) where availability and demand parameters follow a particular probability distribution (such as exponential, weibull, cauchy or extreme value). In this paper an MCSTP is considered where availability and demand parameters follow general form of distribution and a generalized equivalent deterministic model (GMCSTP) of MCSTP is obtained. It is also shown that all previous models obtained by different authors can be deduced with the help of GMCSTP. MCSTP with pareto, power function or burr-XII distributions are also considered and equivalent deterministic models are obtained. To illustrate the proposed model two numerical examples are presented and solved using LINGO 13.0 software package.

Stochastic transport in complex systems from molecules to vehicles

CERN Document Server

Schadschneider, Andreas; Nishinari, Katsuhiro

2011-01-01

What is common between a motor protein, an ant and a vehicle? Each can be modelled as a"self-propelled particle"whose forward movement can be hindered by another in front of it. Traffic flow of such interacting driven"particles"has become an active area of interdisciplinary research involving physics, civil engineering and computer science. We present a unified pedagogical introduction to the analytical and computational methods which are currently used for studying such complex systems far from equilibrium. We also review a number of applications ranging from intra-cellular molecular motor transport in living systems to ant trails and vehicular traffic. Researchers working on complex systems, in general, and on classical stochastic transport, in particular, will find the pedagogical style, scholarly critical overview and extensive list of references extremely useful.

ODE constrained mixture modelling: a method for unraveling subpopulation structures and dynamics.

Directory of Open Access Journals (Sweden)

Jan Hasenauer

2014-07-01

Full Text Available Functional cell-to-cell variability is ubiquitous in multicellular organisms as well as bacterial populations. Even genetically identical cells of the same cell type can respond differently to identical stimuli. Methods have been developed to analyse heterogeneous populations, e.g., mixture models and stochastic population models. The available methods are, however, either incapable of simultaneously analysing different experimental conditions or are computationally demanding and difficult to apply. Furthermore, they do not account for biological information available in the literature. To overcome disadvantages of existing methods, we combine mixture models and ordinary differential equation (ODE models. The ODE models provide a mechanistic description of the underlying processes while mixture models provide an easy way to capture variability. In a simulation study, we show that the class of ODE constrained mixture models can unravel the subpopulation structure and determine the sources of cell-to-cell variability. In addition, the method provides reliable estimates for kinetic rates and subpopulation characteristics. We use ODE constrained mixture modelling to study NGF-induced Erk1/2 phosphorylation in primary sensory neurones, a process relevant in inflammatory and neuropathic pain. We propose a mechanistic pathway model for this process and reconstructed static and dynamical subpopulation characteristics across experimental conditions. We validate the model predictions experimentally, which verifies the capabilities of ODE constrained mixture models. These results illustrate that ODE constrained mixture models can reveal novel mechanistic insights and possess a high sensitivity.

ODE constrained mixture modelling: a method for unraveling subpopulation structures and dynamics.

Science.gov (United States)

Hasenauer, Jan; Hasenauer, Christine; Hucho, Tim; Theis, Fabian J

2014-07-01

Functional cell-to-cell variability is ubiquitous in multicellular organisms as well as bacterial populations. Even genetically identical cells of the same cell type can respond differently to identical stimuli. Methods have been developed to analyse heterogeneous populations, e.g., mixture models and stochastic population models. The available methods are, however, either incapable of simultaneously analysing different experimental conditions or are computationally demanding and difficult to apply. Furthermore, they do not account for biological information available in the literature. To overcome disadvantages of existing methods, we combine mixture models and ordinary differential equation (ODE) models. The ODE models provide a mechanistic description of the underlying processes while mixture models provide an easy way to capture variability. In a simulation study, we show that the class of ODE constrained mixture models can unravel the subpopulation structure and determine the sources of cell-to-cell variability. In addition, the method provides reliable estimates for kinetic rates and subpopulation characteristics. We use ODE constrained mixture modelling to study NGF-induced Erk1/2 phosphorylation in primary sensory neurones, a process relevant in inflammatory and neuropathic pain. We propose a mechanistic pathway model for this process and reconstructed static and dynamical subpopulation characteristics across experimental conditions. We validate the model predictions experimentally, which verifies the capabilities of ODE constrained mixture models. These results illustrate that ODE constrained mixture models can reveal novel mechanistic insights and possess a high sensitivity.

A review on fuzzy and stochastic extensions of the multi index transportation problem

Directory of Open Access Journals (Sweden)

Singh Sungeeta

2017-01-01

Full Text Available The classical transportation problem (having source and destination as indices deals with the objective of minimizing a single criterion, i.e. cost of transporting a commodity. Additional indices such as commodities and modes of transport led to the Multi Index transportation problem. An additional fixed cost, independent of the units transported, led to the Multi Index Fixed Charge transportation problem. Criteria other than cost (such as time, profit etc. led to the Multi Index Bi-criteria transportation problem. The application of fuzzy and stochastic concept in the above transportation problems would enable researchers to not only introduce real life uncertainties but also obtain solutions of these transportation problems. The review article presents an organized study of the Multi Index transportation problem and its fuzzy and stochastic extensions till today, and aims to help researchers working with complex transportation problems.

Stochastic models of intracellular transport

KAUST Repository

Bressloff, Paul C.; Newby, Jay M.

2013-01-01

mechanisms for intracellular transport: passive diffusion and motor-driven active transport. Diffusive transport can be formulated in terms of the motion of an overdamped Brownian particle. On the other hand, active transport requires chemical energy, usually

Considerations when ranking stochastically modeled oil sands resource models for mining applications

Energy Technology Data Exchange (ETDEWEB)

Etris, E.L. [Society of Petroleum Engineers, Canadian Section, Calgary, AB (Canada)]|[Petro-Canada, Calgary, AB (Canada); Idris, Y.; Hunter, A.C. [Petro-Canada, Calgary, AB (Canada)

2008-10-15

Alberta's Athabasca oil sands deposit has been targeted as a major resource for development. Bitumen recovery operations fall into 2 categories, namely mining and in situ operations. Mining recovery is done above ground level and consists of open pit digging, disaggregation of the bitumen-saturated sediment through crushing followed by pipeline transport in a water-based slurry and then separation of oil, water and sediment. In situ recovery consists of drilling wells and stimulating the oil sands in the subsurface with a thermal treatment to reduce the viscosity of the bitumen and allow it to come to the surface. Steam assisted gravity drainage (SAGD) is the most popular thermal treatment currently in use. Resource models that simulate the recovery process are needed for both mining and in situ recovery operations. Both types can benefit from the advantages of a stochastic modeling process for resource model building and uncertainty evaluation. Stochastic modeling provides a realistic geology and allows for multiple realizations, which mining operations can use to evaluate the variability of recoverable bitumen volumes and develop mine plans accordingly. This paper described the processes of stochastic modelling and of determining the appropriate single realization for mine planning as applied to the Fort Hills oil sands mine which is currently in the early planning stage. The modeling exercise was used to estimate the in-place resource and quantify the uncertainty in resource volumes. The stochastic models were checked against those generated from conventional methods to identify any differences and to make the appropriate adaptations. 13 refs., 3 tabs., 16 figs.

Modelling of diesel spray flame under engine-like conditions using an accelerated eulerian stochastic fields method: A convergence study of the number of stochastic fields

OpenAIRE

Pang, Kar Mun; Jangi, Mehdi; Bai, X.-S.; Schramm, Jesper; Walther, Jens Honore

2016-01-01

The use of transported Probability Density Function(PDF) methods allows a single model to compute the autoignition, premixed mode and diffusion flame of diesel combustion under engine-like conditions [1,2]. The Lagrangian particle based transported PDF models have been validated across a wide range of conditions [2,3]. Alternatively, the transported PDF model can also be formulated in the Eulerian framework[4]. The Eulerian PDF is commonly known as the Eulerian Stochastic Fields (ESF) model. ...

Research on nonlinear stochastic dynamical price model

International Nuclear Information System (INIS)

Li Jiaorui; Xu Wei; Xie Wenxian; Ren Zhengzheng

2008-01-01

In consideration of many uncertain factors existing in economic system, nonlinear stochastic dynamical price model which is subjected to Gaussian white noise excitation is proposed based on deterministic model. One-dimensional averaged Ito stochastic differential equation for the model is derived by using the stochastic averaging method, and applied to investigate the stability of the trivial solution and the first-passage failure of the stochastic price model. The stochastic price model and the methods presented in this paper are verified by numerical studies

Alternative Asymmetric Stochastic Volatility Models

NARCIS (Netherlands)

M. Asai (Manabu); M.J. McAleer (Michael)

2010-01-01

textabstractThe stochastic volatility model usually incorporates asymmetric effects by introducing the negative correlation between the innovations in returns and volatility. In this paper, we propose a new asymmetric stochastic volatility model, based on the leverage and size effects. The model is

Algorithm for the Stochastic Generalized Transportation Problem

Directory of Open Access Journals (Sweden)

Marcin Anholcer

2012-01-01

Full Text Available The equalization method for the stochastic generalized transportation problem has been presented. The algorithm allows us to find the optimal solution to the problem of minimizing the expected total cost in the generalized transportation problem with random demand. After a short introduction and literature review, the algorithm is presented. It is a version of the method proposed by the author for the nonlinear generalized transportation problem. It is shown that this version of the method generates a sequence of solutions convergent to the KKT point. This guarantees the global optimality of the obtained solution, as the expected cost functions are convex and twice differentiable. The computational experiments performed for test problems of reasonable size show that the method is fast. (original abstract

A stochastic multiscale framework for modeling flow through random heterogeneous porous media

International Nuclear Information System (INIS)

Ganapathysubramanian, B.; Zabaras, N.

2009-01-01

Flow through porous media is ubiquitous, occurring from large geological scales down to the microscopic scales. Several critical engineering phenomena like contaminant spread, nuclear waste disposal and oil recovery rely on accurate analysis and prediction of these multiscale phenomena. Such analysis is complicated by inherent uncertainties as well as the limited information available to characterize the system. Any realistic modeling of these transport phenomena has to resolve two key issues: (i) the multi-length scale variations in permeability that these systems exhibit, and (ii) the inherently limited information available to quantify these property variations that necessitates posing these phenomena as stochastic processes. A stochastic variational multiscale formulation is developed to incorporate uncertain multiscale features. A stochastic analogue to a mixed multiscale finite element framework is used to formulate the physical stochastic multiscale process. Recent developments in linear and non-linear model reduction techniques are used to convert the limited information available about the permeability variation into a viable stochastic input model. An adaptive sparse grid collocation strategy is used to efficiently solve the resulting stochastic partial differential equations (SPDEs). The framework is applied to analyze flow through random heterogeneous media when only limited statistics about the permeability variation are given

Applications of stochastic models and geostatistical analyses to study sources and spatial patterns of soil heavy metals in a metalliferous industrial district of China

Energy Technology Data Exchange (ETDEWEB)

Zhong, Buqing; Liang, Tao, E-mail: liangt@igsnrr.ac.cn; Wang, Lingqing; Li, Kexin

2014-08-15

An extensive soil survey was conducted to study pollution sources and delineate contamination of heavy metals in one of the metalliferous industrial bases, in the karst areas of southwest China. A total of 597 topsoil samples were collected and the concentrations of five heavy metals, namely Cd, As (metalloid), Pb, Hg and Cr were analyzed. Stochastic models including a conditional inference tree (CIT) and a finite mixture distribution model (FMDM) were applied to identify the sources and partition the contribution from natural and anthropogenic sources for heavy metal in topsoils of the study area. Regression trees for Cd, As, Pb and Hg were proved to depend mostly on indicators of anthropogenic activities such as industrial type and distance from urban area, while the regression tree for Cr was found to be mainly influenced by the geogenic characteristics. The FMDM analysis showed that the geometric means of modeled background values for Cd, As, Pb, Hg and Cr were close to their background values previously reported in the study area, while the contamination of Cd and Hg were widespread in the study area, imposing potentially detrimental effects on organisms through the food chain. Finally, the probabilities of single and multiple heavy metals exceeding the threshold values derived from the FMDM were estimated using indicator kriging (IK) and multivariate indicator kriging (MVIK). The high probabilities exceeding the thresholds of heavy metals were associated with metalliferous production and atmospheric deposition of heavy metals transported from the urban and industrial areas. Geostatistics coupled with stochastic models provide an effective way to delineate multiple heavy metal pollution to facilitate improved environmental management. - Highlights: • Conditional inference tree can identify variables controlling metal distribution. • Finite mixture distribution model can partition natural and anthropogenic sources. • Geostatistics with stochastic models

Applications of stochastic models and geostatistical analyses to study sources and spatial patterns of soil heavy metals in a metalliferous industrial district of China

International Nuclear Information System (INIS)

Zhong, Buqing; Liang, Tao; Wang, Lingqing; Li, Kexin

2014-01-01

An extensive soil survey was conducted to study pollution sources and delineate contamination of heavy metals in one of the metalliferous industrial bases, in the karst areas of southwest China. A total of 597 topsoil samples were collected and the concentrations of five heavy metals, namely Cd, As (metalloid), Pb, Hg and Cr were analyzed. Stochastic models including a conditional inference tree (CIT) and a finite mixture distribution model (FMDM) were applied to identify the sources and partition the contribution from natural and anthropogenic sources for heavy metal in topsoils of the study area. Regression trees for Cd, As, Pb and Hg were proved to depend mostly on indicators of anthropogenic activities such as industrial type and distance from urban area, while the regression tree for Cr was found to be mainly influenced by the geogenic characteristics. The FMDM analysis showed that the geometric means of modeled background values for Cd, As, Pb, Hg and Cr were close to their background values previously reported in the study area, while the contamination of Cd and Hg were widespread in the study area, imposing potentially detrimental effects on organisms through the food chain. Finally, the probabilities of single and multiple heavy metals exceeding the threshold values derived from the FMDM were estimated using indicator kriging (IK) and multivariate indicator kriging (MVIK). The high probabilities exceeding the thresholds of heavy metals were associated with metalliferous production and atmospheric deposition of heavy metals transported from the urban and industrial areas. Geostatistics coupled with stochastic models provide an effective way to delineate multiple heavy metal pollution to facilitate improved environmental management. - Highlights: • Conditional inference tree can identify variables controlling metal distribution. • Finite mixture distribution model can partition natural and anthropogenic sources. • Geostatistics with stochastic models

Stochasticity Modeling in Memristors

KAUST Repository

Naous, Rawan

2015-10-26

Diverse models have been proposed over the past years to explain the exhibiting behavior of memristors, the fourth fundamental circuit element. The models varied in complexity ranging from a description of physical mechanisms to a more generalized mathematical modeling. Nonetheless, stochasticity, a widespread observed phenomenon, has been immensely overlooked from the modeling perspective. This inherent variability within the operation of the memristor is a vital feature for the integration of this nonlinear device into the stochastic electronics realm of study. In this paper, experimentally observed innate stochasticity is modeled in a circuit compatible format. The model proposed is generic and could be incorporated into variants of threshold-based memristor models in which apparent variations in the output hysteresis convey the switching threshold shift. Further application as a noise injection alternative paves the way for novel approaches in the fields of neuromorphic engineering circuits design. On the other hand, extra caution needs to be paid to variability intolerant digital designs based on non-deterministic memristor logic.

Stochasticity Modeling in Memristors

KAUST Repository

Naous, Rawan; Al-Shedivat, Maruan; Salama, Khaled N.

2015-01-01

Diverse models have been proposed over the past years to explain the exhibiting behavior of memristors, the fourth fundamental circuit element. The models varied in complexity ranging from a description of physical mechanisms to a more generalized mathematical modeling. Nonetheless, stochasticity, a widespread observed phenomenon, has been immensely overlooked from the modeling perspective. This inherent variability within the operation of the memristor is a vital feature for the integration of this nonlinear device into the stochastic electronics realm of study. In this paper, experimentally observed innate stochasticity is modeled in a circuit compatible format. The model proposed is generic and could be incorporated into variants of threshold-based memristor models in which apparent variations in the output hysteresis convey the switching threshold shift. Further application as a noise injection alternative paves the way for novel approaches in the fields of neuromorphic engineering circuits design. On the other hand, extra caution needs to be paid to variability intolerant digital designs based on non-deterministic memristor logic.

Stochastic interpretation of the advection-diffusion equation and its relevance to bed load transport

Science.gov (United States)

Ancey, C.; Bohorquez, P.; Heyman, J.

2015-12-01

The advection-diffusion equation is one of the most widespread equations in physics. It arises quite often in the context of sediment transport, e.g., for describing time and space variations in the particle activity (the solid volume of particles in motion per unit streambed area). Phenomenological laws are usually sufficient to derive this equation and interpret its terms. Stochastic models can also be used to derive it, with the significant advantage that they provide information on the statistical properties of particle activity. These models are quite useful when sediment transport exhibits large fluctuations (typically at low transport rates), making the measurement of mean values difficult. Among these stochastic models, the most common approach consists of random walk models. For instance, they have been used to model the random displacement of tracers in rivers. Here we explore an alternative approach, which involves monitoring the evolution of the number of particles moving within an array of cells of finite length. Birth-death Markov processes are well suited to this objective. While the topic has been explored in detail for diffusion-reaction systems, the treatment of advection has received no attention. We therefore look into the possibility of deriving the advection-diffusion equation (with a source term) within the framework of birth-death Markov processes. We show that in the continuum limit (when the cell size becomes vanishingly small), we can derive an advection-diffusion equation for particle activity. Yet while this derivation is formally valid in the continuum limit, it runs into difficulty in practical applications involving cells or meshes of finite length. Indeed, within our stochastic framework, particle advection produces nonlocal effects, which are more or less significant depending on the cell size and particle velocity. Albeit nonlocal, these effects look like (local) diffusion and add to the intrinsic particle diffusion (dispersal due

THE IMPACT OF COMPETITIVENESS ON TRADE EFFICIENCY: THE ASIAN EXPERIENCE BY USING THE STOCHASTIC FRONTIER GRAVITY MODEL

Directory of Open Access Journals (Sweden)

Memduh Alper Demir

2017-12-01

Full Text Available The purpose of this study is to examine the bilateral machinery and transport equipment trade efficiency of selected fourteen Asian countries by applying stochastic frontier gravity model. These selected countries have the top machinery and transport equipment trade (both export and import volumes in Asia. The model we use includes variables such as income, market size of trading partners, distance, common culture, common border, common language and global economic crisis similar to earlier studies using the stochastic frontier gravity models. Our work, however, includes an extra variable called normalized revealed comparative advantage (NRCA index additionally. The NRCA index is comparable across commodity, country and time. Thus, the NRCA index is calculated and then included in our stochastic frontier gravity model to see the impact of competitiveness (here measured by the NRCA index on the efficiency of trade.

A stochastic optimization approach to reduce greenhouse gas emissions from buildings and transportation

International Nuclear Information System (INIS)

Karan, Ebrahim; Asadi, Somayeh; Ntaimo, Lewis

2016-01-01

The magnitude of building- and transportation-related GHG (greenhouse gas) emissions makes the adoption of all-EVs (electric vehicles) powered with renewable power as one of the most effective strategies to reduce emission of GHGs. This paper formulates the problem of GHG mitigation strategy under uncertain conditions and optimizes the strategies in which EVs are powered by solar energy. Under a pre-specified budget, the objective is to determine the type of EV and power generation capacity of the solar system in such a way as to maximize GHG emissions reductions. The model supports the three primary solar systems: off-grid, grid-tied, and hybrid. First, a stochastic optimization model using probability distributions of stochastic variables and EV and solar system specifications is developed. The model is then validated by comparing the estimated values of the optimal strategies and actual values. It is found that the mitigation strategies in which EVs are powered by a hybrid solar system lead to the best cost-expected reduction of CO_2 emissions ratio. The results show an accuracy of about 4% for mitigation strategies in which EVs are powered by a grid-tied or hybrid solar system and 11% when applied to estimate the CO_2 emissions reductions of an off-grid system. - Highlights: • The problem of GHG mitigation is formulated as a stochastic optimization problem. • The objective is to maximize CO_2 emissions reductions within a specified budget. • The stochastic model is validated using actual data. • The results show an estimation accuracy of 4–11%.

A mixture theory model of fluid and solute transport in the microvasculature of normal and malignant tissues. I. Theory.

Science.gov (United States)

Schuff, M M; Gore, J P; Nauman, E A

2013-05-01

In order to better understand the mechanisms governing transport of drugs, nanoparticle-based treatments, and therapeutic biomolecules, and the role of the various physiological parameters, a number of mathematical models have previously been proposed. The limitations of the existing transport models indicate the need for a comprehensive model that includes transport in the vessel lumen, the vessel wall, and the interstitial space and considers the effects of the solute concentration on fluid flow. In this study, a general model to describe the transient distribution of fluid and multiple solutes at the microvascular level was developed using mixture theory. The model captures the experimentally observed dependence of the hydraulic permeability coefficient of the capillary wall on the concentration of solutes present in the capillary wall and the surrounding tissue. Additionally, the model demonstrates that transport phenomena across the capillary wall and in the interstitium are related to the solute concentration as well as the hydrostatic pressure. The model is used in a companion paper to examine fluid and solute transport for the simplified case of an axisymmetric geometry with no solid deformation or interconversion of mass.

Multi-Period Natural Gas Market Modeling. Applications, Stochastic Extensions and Solution Approaches

International Nuclear Information System (INIS)

Egging, R.G.

2010-11-01

This dissertation develops deterministic and stochastic multi-period mixed complementarity problems (MCP) for the global natural gas market, as well as solution approaches for large-scale stochastic MCP. The deterministic model is unique in the combination of the level of detail of the actors in the natural gas markets and the transport options, the detailed regional and global coverage, the multi-period approach with endogenous capacity expansions for transportation and storage infrastructure, the seasonal variation in demand and the representation of market power according to Nash-Cournot theory. The model is applied to several scenarios for the natural gas market that cover the formation of a cartel by the members of the Gas Exporting Countries Forum, a low availability of unconventional gas in the United States, and cost reductions in long-distance gas transportation. The results provide insights in how different regions are affected by various developments, in terms of production, consumption, traded volumes, prices and profits of market participants. The stochastic MCP is developed and applied to a global natural gas market problem with four scenarios for a time horizon until 2050 with nineteen regions and containing 78,768 variables. The scenarios vary in the possibility of a gas market cartel formation and varying depletion rates of gas reserves in the major gas importing regions. Outcomes for hedging decisions of market participants show some significant shifts in the timing and location of infrastructure investments, thereby affecting local market situations. A first application of Benders decomposition (BD) is presented to solve a large-scale stochastic MCP for the global gas market with many hundreds of first-stage capacity expansion variables and market players exerting various levels of market power. The largest problem solved successfully using BD contained 47,373 variables of which 763 first-stage variables, however using BD did not result in

Stochastic analysis of transport of conservative solutes in caisson experiments

International Nuclear Information System (INIS)

Dagan, G.

1995-01-01

The Los Alamos National Laboratory has conducted in the past a series of experiments of transport of conservative and reactive solutes. The experimental setup and the experimental results are presented in a series of reports. The main aim of the experiments was to validate models of transport of solutes in unsaturated flow at the caisson intermediate scale, which is much larger than the one pertaining to laboratory columns. First attempts to analyze the experimental results were by one-dimensional convective-dispersion models. These models could not explain the observed solute breakthrough curves and particularly the large solute dispersion in the caisson effluent Since there were some question marks about the uniformity of water distribution at the caisson top, the transport experiments were repeated under conditions of saturated flow. In these experiments constant heads were applied at the top and the bottom of the caisson and the number of concentration monitoring stations was quadrupled. The analysis of the measurements by the same one-dimensional model indicated clearly that the fitted dispersivity is much larger than the pore-sole dispersivity and that it grows with the distance in an approximately linear fashion. This led to the conclusion, raised before, that transport in the caisson is dominated by heterogeneity effects, i.e. by spatial variability of the material Such effects cannot be captured by traditional one-dimensional models. In order to account for the effect of heterogeneity, the saturated flow experiments have been analyzed by using stochastic transport modeling. The apparent linear growth of dispersivity with distance suggested that the system behaves like a stratified one. Consequently, the model of Dagan and Bresier has been adopted in order to interpret concentration measurements. In this simple model the caisson is viewed as a bundle of columns of different permeabilities, which are characterized by a p.d.f. (probability denasity function)

Evaluation of the reliability of transport networks based on the stochastic flow of moving objects

International Nuclear Information System (INIS)

Wu Weiwei; Ning, Angelika; Ning Xuanxi

2008-01-01

In transport networks, human beings are moving objects whose moving direction is stochastic in emergency situations. Based on this idea, a new model-stochastic moving network (SMN) is proposed. It is different from binary-state networks and stochastic-flow networks. The flow of SMNs has multiple-saturated states, that correspond to different flow values in each arc. In this paper, we try to evaluate the system reliability, defined as the probability that the saturated flow of the network is not less than a given demand d. Based on this new model, we obtain the flow probability distribution of every arc by simulation. An algorithm based on the blocking cutset of the SMN is proposed to evaluate the network reliability. An example is used to show how to calculate the corresponding reliabilities for different given demands of the SMN. Simulation experiments of different size were made and the system reliability precision was calculated. The precision of simulation results also discussed

Development of a Stochastically-driven, Forward Predictive Performance Model for PEMFCs

Science.gov (United States)

Harvey, David Benjamin Paul

A one-dimensional multi-scale coupled, transient, and mechanistic performance model for a PEMFC membrane electrode assembly has been developed. The model explicitly includes each of the 5 layers within a membrane electrode assembly and solves for the transport of charge, heat, mass, species, dissolved water, and liquid water. Key features of the model include the use of a multi-step implementation of the HOR reaction on the anode, agglomerate catalyst sub-models for both the anode and cathode catalyst layers, a unique approach that links the composition of the catalyst layer to key properties within the agglomerate model and the implementation of a stochastic input-based approach for component material properties. The model employs a new methodology for validation using statistically varying input parameters and statistically-based experimental performance data; this model represents the first stochastic input driven unit cell performance model. The stochastic input driven performance model was used to identify optimal ionomer content within the cathode catalyst layer, demonstrate the role of material variation in potential low performing MEA materials, provide explanation for the performance of low-Pt loaded MEAs, and investigate the validity of transient-sweep experimental diagnostic methods.

Stochastic modelling of turbulent combustion for design optimization of gas turbine combustors

Science.gov (United States)

Mehanna Ismail, Mohammed Ali

The present work covers the development and the implementation of an efficient algorithm for the design optimization of gas turbine combustors. The purpose is to explore the possibilities and indicate constructive suggestions for optimization techniques as alternative methods for designing gas turbine combustors. The algorithm is general to the extent that no constraints are imposed on the combustion phenomena or on the combustor configuration. The optimization problem is broken down into two elementary problems: the first is the optimum search algorithm, and the second is the turbulent combustion model used to determine the combustor performance parameters. These performance parameters constitute the objective and physical constraints in the optimization problem formulation. The examination of both turbulent combustion phenomena and the gas turbine design process suggests that the turbulent combustion model represents a crucial part of the optimization algorithm. The basic requirements needed for a turbulent combustion model to be successfully used in a practical optimization algorithm are discussed. In principle, the combustion model should comply with the conflicting requirements of high fidelity, robustness and computational efficiency. To that end, the problem of turbulent combustion is discussed and the current state of the art of turbulent combustion modelling is reviewed. According to this review, turbulent combustion models based on the composition PDF transport equation are found to be good candidates for application in the present context. However, these models are computationally expensive. To overcome this difficulty, two different models based on the composition PDF transport equation were developed: an improved Lagrangian Monte Carlo composition PDF algorithm and the generalized stochastic reactor model. Improvements in the Lagrangian Monte Carlo composition PDF model performance and its computational efficiency were achieved through the

Stochastic models: theory and simulation.

Energy Technology Data Exchange (ETDEWEB)

Field, Richard V., Jr.

2008-03-01

Many problems in applied science and engineering involve physical phenomena that behave randomly in time and/or space. Examples are diverse and include turbulent flow over an aircraft wing, Earth climatology, material microstructure, and the financial markets. Mathematical models for these random phenomena are referred to as stochastic processes and/or random fields, and Monte Carlo simulation is the only general-purpose tool for solving problems of this type. The use of Monte Carlo simulation requires methods and algorithms to generate samples of the appropriate stochastic model; these samples then become inputs and/or boundary conditions to established deterministic simulation codes. While numerous algorithms and tools currently exist to generate samples of simple random variables and vectors, no cohesive simulation tool yet exists for generating samples of stochastic processes and/or random fields. There are two objectives of this report. First, we provide some theoretical background on stochastic processes and random fields that can be used to model phenomena that are random in space and/or time. Second, we provide simple algorithms that can be used to generate independent samples of general stochastic models. The theory and simulation of random variables and vectors is also reviewed for completeness.

Transport Properties of operational gas mixtures used at LHC

CERN Document Server

Assran, Yasser

2011-01-01

This report summarizes some useful data on the transport characteristics of gas mixtures which are required for detection of charged particles in gas detectors. We try to replace Freon used for RPC detector in the CMS experiment with another gas while maintaining the good properties of the Freon gas mixture unchanged. We try to switch to freonless gas mixture because Freon is not a green gas, it is very expensive and its availability is decreasing. Noble gases like Ar, He, Ne and Xe (with some quenchers like carbon dioxide, methane, ethane and isobutene) are investigated. Transport parameters like drift velocity, diffusion, Townsend coefficient, attachment coefficient and Lorentz angle are computed using Garfield software for different gas mixtures and compared with experimental data.

Modelling radionuclide transport in the geosphere: a review of the models available

International Nuclear Information System (INIS)

Cacas, M.C.; Cordier, E.; Coudrain-Ribstein, A.; Fargue, D.; Goblet, P.; Jamet, Ph.; Ledoux, E.; Marsily, G. de; Vinsot, A.; Brun, Ch.; Cernes, A.; Jacquier, Ph.; Lewi, J.; Priem, Th.

1990-01-01

Over the last twelve years, several models have been developed to simulate the transport of radionuclides in the environment of a radioactive waste repository: - continuous equivalent porous media flow and transport models using the finite element method in 1, 2 or 3 dimensions and taking into account various coupled mechanisms; - discontinuous stochastic fracture network models in 3 dimensions representing flow, transport, matrix diffusion, heat flow and mechanical stress; - geochemical models representing interactions between transported elements and a solid matrix; - transport process models coupling non dominant phenomena such as thermo-diffusion or thermo-gravitation. This paper reviews the role that each of these models can play in safety analyses. 3 refs [fr

Gaussian Mixture Random Coefficient model based framework for SHM in structures with time-dependent dynamics under uncertainty

Science.gov (United States)

Avendaño-Valencia, Luis David; Fassois, Spilios D.

2017-12-01

The problem of vibration-based damage diagnosis in structures characterized by time-dependent dynamics under significant environmental and/or operational uncertainty is considered. A stochastic framework consisting of a Gaussian Mixture Random Coefficient model of the uncertain time-dependent dynamics under each structural health state, proper estimation methods, and Bayesian or minimum distance type decision making, is postulated. The Random Coefficient (RC) time-dependent stochastic model with coefficients following a multivariate Gaussian Mixture Model (GMM) allows for significant flexibility in uncertainty representation. Certain of the model parameters are estimated via a simple procedure which is founded on the related Multiple Model (MM) concept, while the GMM weights are explicitly estimated for optimizing damage diagnostic performance. The postulated framework is demonstrated via damage detection in a simple simulated model of a quarter-car active suspension with time-dependent dynamics and considerable uncertainty on the payload. Comparisons with a simpler Gaussian RC model based method are also presented, with the postulated framework shown to be capable of offering considerable improvement in diagnostic performance.

Public Transportation Hub Location with Stochastic Demand: An Improved Approach Based on Multiple Attribute Group Decision-Making

Directory of Open Access Journals (Sweden)

Sen Liu

2015-01-01

Full Text Available Urban public transportation hubs are the key nodes of the public transportation system. The location of such hubs is a combinatorial problem. Many factors can affect the decision-making of location, including both quantitative and qualitative factors; however, most current research focuses solely on either the quantitative or the qualitative factors. Little has been done to combine these two approaches. To fulfill this gap in the research, this paper proposes a novel approach to the public transportation hub location problem, which takes both quantitative and qualitative factors into account. In this paper, an improved multiple attribute group decision-making (MAGDM method based on TOPSIS (Technique for Order Preference by Similarity to Ideal Solution and deviation is proposed to convert the qualitative factors of each hub into quantitative evaluation values. A location model with stochastic passenger flows is then established based on the above evaluation values. Finally, stochastic programming theory is applied to solve the model and to determine the location result. A numerical study shows that this approach is applicable and effective.

Stochastic Optimization of Wind Turbine Power Factor Using Stochastic Model of Wind Power

DEFF Research Database (Denmark)

Chen, Peiyuan; Siano, Pierluigi; Bak-Jensen, Birgitte

2010-01-01

This paper proposes a stochastic optimization algorithm that aims to minimize the expectation of the system power losses by controlling wind turbine (WT) power factors. This objective of the optimization is subject to the probability constraints of bus voltage and line current requirements....... The optimization algorithm utilizes the stochastic models of wind power generation (WPG) and load demand to take into account their stochastic variation. The stochastic model of WPG is developed on the basis of a limited autoregressive integrated moving average (LARIMA) model by introducing a crosscorrelation...... structure to the LARIMA model. The proposed stochastic optimization is carried out on a 69-bus distribution system. Simulation results confirm that, under various combinations of WPG and load demand, the system power losses are considerably reduced with the optimal setting of WT power factor as compared...

Stochastic diffusion models for substitutable technological innovations

NARCIS (Netherlands)

Wang, L.; Hu, B.; Yu, X.

2004-01-01

Based on the analysis of firms' stochastic adoption behaviour, this paper first points out the necessity to build more practical stochastic models. And then, stochastic evolutionary models are built for substitutable innovation diffusion system. Finally, through the computer simulation of the

Method of model reduction and multifidelity models for solute transport in random layered porous media

Energy Technology Data Exchange (ETDEWEB)

Xu, Zhijie; Tartakovsky, Alexandre M.

2017-09-01

This work presents a hierarchical model for solute transport in bounded layered porous media with random permeability. The model generalizes the Taylor-Aris dispersion theory to stochastic transport in random layered porous media with a known velocity covariance function. In the hierarchical model, we represent (random) concentration in terms of its cross-sectional average and a variation function. We derive a one-dimensional stochastic advection-dispersion-type equation for the average concentration and a stochastic Poisson equation for the variation function, as well as expressions for the effective velocity and dispersion coefficient. We observe that velocity fluctuations enhance dispersion in a non-monotonic fashion: the dispersion initially increases with correlation length λ, reaches a maximum, and decreases to zero at infinity. Maximum enhancement can be obtained at the correlation length about 0.25 the size of the porous media perpendicular to flow.

Double diffusivity model under stochastic forcing

Science.gov (United States)

Chattopadhyay, Amit K.; Aifantis, Elias C.

2017-05-01

The "double diffusivity" model was proposed in the late 1970s, and reworked in the early 1980s, as a continuum counterpart to existing discrete models of diffusion corresponding to high diffusivity paths, such as grain boundaries and dislocation lines. It was later rejuvenated in the 1990s to interpret experimental results on diffusion in polycrystalline and nanocrystalline specimens where grain boundaries and triple grain boundary junctions act as high diffusivity paths. Technically, the model pans out as a system of coupled Fick-type diffusion equations to represent "regular" and "high" diffusivity paths with "source terms" accounting for the mass exchange between the two paths. The model remit was extended by analogy to describe flow in porous media with double porosity, as well as to model heat conduction in media with two nonequilibrium local temperature baths, e.g., ion and electron baths. Uncoupling of the two partial differential equations leads to a higher-ordered diffusion equation, solutions of which could be obtained in terms of classical diffusion equation solutions. Similar equations could also be derived within an "internal length" gradient (ILG) mechanics formulation applied to diffusion problems, i.e., by introducing nonlocal effects, together with inertia and viscosity, in a mechanics based formulation of diffusion theory. While being remarkably successful in studies related to various aspects of transport in inhomogeneous media with deterministic microstructures and nanostructures, its implications in the presence of stochasticity have not yet been considered. This issue becomes particularly important in the case of diffusion in nanopolycrystals whose deterministic ILG-based theoretical calculations predict a relaxation time that is only about one-tenth of the actual experimentally verified time scale. This article provides the "missing link" in this estimation by adding a vital element in the ILG structure, that of stochasticity, that takes into

Sequential neural models with stochastic layers

DEFF Research Database (Denmark)

Fraccaro, Marco; Sønderby, Søren Kaae; Paquet, Ulrich

2016-01-01

How can we efficiently propagate uncertainty in a latent state representation with recurrent neural networks? This paper introduces stochastic recurrent neural networks which glue a deterministic recurrent neural network and a state space model together to form a stochastic and sequential neural...... generative model. The clear separation of deterministic and stochastic layers allows a structured variational inference network to track the factorization of the model's posterior distribution. By retaining both the nonlinear recursive structure of a recurrent neural network and averaging over...

Numerical Simulation of the Heston Model under Stochastic Correlation

Directory of Open Access Journals (Sweden)

Long Teng

2017-12-01

Full Text Available Stochastic correlation models have become increasingly important in financial markets. In order to be able to price vanilla options in stochastic volatility and correlation models, in this work, we study the extension of the Heston model by imposing stochastic correlations driven by a stochastic differential equation. We discuss the efficient algorithms for the extended Heston model by incorporating stochastic correlations. Our numerical experiments show that the proposed algorithms can efficiently provide highly accurate results for the extended Heston by including stochastic correlations. By investigating the effect of stochastic correlations on the implied volatility, we find that the performance of the Heston model can be proved by including stochastic correlations.

Multi-period natural gas market modeling Applications, stochastic extensions and solution approaches

Science.gov (United States)

Egging, Rudolf Gerardus

This dissertation develops deterministic and stochastic multi-period mixed complementarity problems (MCP) for the global natural gas market, as well as solution approaches for large-scale stochastic MCP. The deterministic model is unique in the combination of the level of detail of the actors in the natural gas markets and the transport options, the detailed regional and global coverage, the multi-period approach with endogenous capacity expansions for transportation and storage infrastructure, the seasonal variation in demand and the representation of market power according to Nash-Cournot theory. The model is applied to several scenarios for the natural gas market that cover the formation of a cartel by the members of the Gas Exporting Countries Forum, a low availability of unconventional gas in the United States, and cost reductions in long-distance gas transportation. 1 The results provide insights in how different regions are affected by various developments, in terms of production, consumption, traded volumes, prices and profits of market participants. The stochastic MCP is developed and applied to a global natural gas market problem with four scenarios for a time horizon until 2050 with nineteen regions and containing 78,768 variables. The scenarios vary in the possibility of a gas market cartel formation and varying depletion rates of gas reserves in the major gas importing regions. Outcomes for hedging decisions of market participants show some significant shifts in the timing and location of infrastructure investments, thereby affecting local market situations. A first application of Benders decomposition (BD) is presented to solve a large-scale stochastic MCP for the global gas market with many hundreds of first-stage capacity expansion variables and market players exerting various levels of market power. The largest problem solved successfully using BD contained 47,373 variables of which 763 first-stage variables, however using BD did not result in

Comparison of analytical transport and stochastic solutions for neutron slowing down in an infinite medium

International Nuclear Information System (INIS)

Jahshan, S.N.; Wemple, C.A.; Ganapol, B.D.

1993-01-01

A comparison of the numerical solutions of the transport equation describing the steady neutron slowing down in an infinite medium with constant cross sections is made with stochastic solutions obtained from tracking successive neutron histories in the same medium. The transport equation solution is obtained using a numerical Laplace transform inversion algorithm. The basis for the algorithm is an evaluation of the Bromwich integral without analytical continuation. Neither the transport nor the stochastic solution is limited in the number of scattering species allowed. The medium may contain an absorption component as well. (orig.)

Modeling and analysis of stochastic systems

CERN Document Server

Kulkarni, Vidyadhar G

2011-01-01

Based on the author's more than 25 years of teaching experience, Modeling and Analysis of Stochastic Systems, Second Edition covers the most important classes of stochastic processes used in the modeling of diverse systems, from supply chains and inventory systems to genetics and biological systems. For each class of stochastic process, the text includes its definition, characterization, applications, transient and limiting behavior, first passage times, and cost/reward models. Along with reorganizing the material, this edition revises and adds new exercises and examples. New to the second edi

Uncertainty calculation in transport models and forecasts

DEFF Research Database (Denmark)

Manzo, Stefano; Prato, Carlo Giacomo

Transport projects and policy evaluations are often based on transport model output, i.e. traffic flows and derived effects. However, literature has shown that there is often a considerable difference between forecasted and observed traffic flows. This difference causes misallocation of (public...... implemented by using an approach based on stochastic techniques (Monte Carlo simulation and Bootstrap re-sampling) or scenario analysis combined with model sensitivity tests. Two transport models are used as case studies: the Næstved model and the Danish National Transport Model. 3 The first paper...... in a four-stage transport model related to different variable distributions (to be used in a Monte Carlo simulation procedure), assignment procedures and levels of congestion, at both the link and the network level. The analysis used as case study the Næstved model, referring to the Danish town of Næstved2...

Modelling Cow Behaviour Using Stochastic Automata

DEFF Research Database (Denmark)

Jónsson, Ragnar Ingi

This report covers an initial study on the modelling of cow behaviour using stochastic automata with the aim of detecting lameness. Lameness in cows is a serious problem that needs to be dealt with because it results in less profitable production units and in reduced quality of life...... for the affected livestock. By featuring training data consisting of measurements of cow activity, three different models are obtained, namely an autonomous stochastic automaton, a stochastic automaton with coinciding state and output and an autonomous stochastic automaton with coinciding state and output, all...... of which describe the cows' activity in the two regarded behavioural scenarios, non-lame and lame. Using the experimental measurement data the different behavioural relations for the two regarded behavioural scenarios are assessed. The three models comprise activity within last hour, activity within last...

Plasma transport in stochastic magnetic fields. I. General considerations and test particle transport

International Nuclear Information System (INIS)

Krommes, J.A.; Kleva, R.G.; Oberman, C.

1978-05-01

A systematic theory is developed for the computation of electron transport in stochastic magnetic fields. Small scale magnetic perturbations arising, for example, from finite-β micro-instabilities are assumed to destroy the flux surfaces of a standard tokamak equilibrium. Because the magnetic lines then wander in a volume, electron radial flux is enhanced due to the rapid particle transport along as well as across the lines. By treating the magnetic lines as random variables, it is possible to develop a kinetic equation for the electron distribution function. This is solved approximately to yield the diffusion coefficient

Plasma transport in stochastic magnetic fields. I. General considerations and test particle transport

Energy Technology Data Exchange (ETDEWEB)

Krommes, J.A.; Kleva, R.G.; Oberman, C.

1978-05-01

A systematic theory is developed for the computation of electron transport in stochastic magnetic fields. Small scale magnetic perturbations arising, for example, from finite-..beta.. micro-instabilities are assumed to destroy the flux surfaces of a standard tokamak equilibrium. Because the magnetic lines then wander in a volume, electron radial flux is enhanced due to the rapid particle transport along as well as across the lines. By treating the magnetic lines as random variables, it is possible to develop a kinetic equation for the electron distribution function. This is solved approximately to yield the diffusion coefficient.

Electricity price modeling with stochastic time change

International Nuclear Information System (INIS)

Borovkova, Svetlana; Schmeck, Maren Diane

2017-01-01

In this paper, we develop a novel approach to electricity price modeling, based on the powerful technique of stochastic time change. This technique allows us to incorporate the characteristic features of electricity prices (such as seasonal volatility, time varying mean reversion and seasonally occurring price spikes) into the model in an elegant and economically justifiable way. The stochastic time change introduces stochastic as well as deterministic (e.g., seasonal) features in the price process' volatility and in the jump component. We specify the base process as a mean reverting jump diffusion and the time change as an absolutely continuous stochastic process with seasonal component. The activity rate of the stochastic time change can be related to the factors that influence supply and demand. Here we use the temperature as a proxy for the demand and hence, as the driving factor of the stochastic time change, and show that this choice leads to realistic price paths. We derive properties of the resulting price process and develop the model calibration procedure. We calibrate the model to the historical EEX power prices and apply it to generating realistic price paths by Monte Carlo simulations. We show that the simulated price process matches the distributional characteristics of the observed electricity prices in periods of both high and low demand. - Highlights: • We develop a novel approach to electricity price modeling, based on the powerful technique of stochastic time change. • We incorporate the characteristic features of electricity prices, such as seasonal volatility and spikes into the model. • We use the temperature as a proxy for the demand and hence, as the driving factor of the stochastic time change • We derive properties of the resulting price process and develop the model calibration procedure. • We calibrate the model to the historical EEX power prices and apply it to generating realistic price paths.

Stochastic volatility and stochastic leverage

DEFF Research Database (Denmark)

Veraart, Almut; Veraart, Luitgard A. M.

This paper proposes the new concept of stochastic leverage in stochastic volatility models. Stochastic leverage refers to a stochastic process which replaces the classical constant correlation parameter between the asset return and the stochastic volatility process. We provide a systematic...... treatment of stochastic leverage and propose to model the stochastic leverage effect explicitly, e.g. by means of a linear transformation of a Jacobi process. Such models are both analytically tractable and allow for a direct economic interpretation. In particular, we propose two new stochastic volatility...... models which allow for a stochastic leverage effect: the generalised Heston model and the generalised Barndorff-Nielsen & Shephard model. We investigate the impact of a stochastic leverage effect in the risk neutral world by focusing on implied volatilities generated by option prices derived from our new...

Stochastic models of cell motility

DEFF Research Database (Denmark)

Gradinaru, Cristian

2012-01-01

Cell motility and migration are central to the development and maintenance of multicellular organisms, and errors during this process can lead to major diseases. Consequently, the mechanisms and phenomenology of cell motility are currently under intense study. In recent years, a new...... interdisciplinary field focusing on the study of biological processes at the nanoscale level, with a range of technological applications in medicine and biological research, has emerged. The work presented in this thesis is at the interface of cell biology, image processing, and stochastic modeling. The stochastic...... models introduced here are based on persistent random motion, which I apply to real-life studies of cell motility on flat and nanostructured surfaces. These models aim to predict the time-dependent position of cell centroids in a stochastic manner, and conversely determine directly from experimental...

Stochastic Modelling of Hydrologic Systems

DEFF Research Database (Denmark)

Jonsdottir, Harpa

2007-01-01

In this PhD project several stochastic modelling methods are studied and applied on various subjects in hydrology. The research was prepared at Informatics and Mathematical Modelling at the Technical University of Denmark. The thesis is divided into two parts. The first part contains...... an introduction and an overview of the papers published. Then an introduction to basic concepts in hydrology along with a description of hydrological data is given. Finally an introduction to stochastic modelling is given. The second part contains the research papers. In the research papers the stochastic methods...... are described, as at the time of publication these methods represent new contribution to hydrology. The second part also contains additional description of software used and a brief introduction to stiff systems. The system in one of the papers is stiff....

Stochasticity and determinism in models of hematopoiesis.

Science.gov (United States)

Kimmel, Marek

2014-01-01

This chapter represents a novel view of modeling in hematopoiesis, synthesizing both deterministic and stochastic approaches. Whereas the stochastic models work in situations where chance dominates, for example when the number of cells is small, or under random mutations, the deterministic models are more important for large-scale, normal hematopoiesis. New types of models are on the horizon. These models attempt to account for distributed environments such as hematopoietic niches and their impact on dynamics. Mixed effects of such structures and chance events are largely unknown and constitute both a challenge and promise for modeling. Our discussion is presented under the separate headings of deterministic and stochastic modeling; however, the connections between both are frequently mentioned. Four case studies are included to elucidate important examples. We also include a primer of deterministic and stochastic dynamics for the reader's use.

Models for microtubule cargo transport coupling the Langevin equation to stochastic stepping motor dynamics: Caring about fluctuations.

Science.gov (United States)

Bouzat, Sebastián

2016-01-01

One-dimensional models coupling a Langevin equation for the cargo position to stochastic stepping dynamics for the motors constitute a relevant framework for analyzing multiple-motor microtubule transport. In this work we explore the consistence of these models focusing on the effects of the thermal noise. We study how to define consistent stepping and detachment rates for the motors as functions of the local forces acting on them in such a way that the cargo velocity and run-time match previously specified functions of the external load, which are set on the base of experimental results. We show that due to the influence of the thermal fluctuations this is not a trivial problem, even for the single-motor case. As a solution, we propose a motor stepping dynamics which considers memory on the motor force. This model leads to better results for single-motor transport than the approaches previously considered in the literature. Moreover, it gives a much better prediction for the stall force of the two-motor case, highly compatible with the experimental findings. We also analyze the fast fluctuations of the cargo position and the influence of the viscosity, comparing the proposed model to the standard one, and we show how the differences on the single-motor dynamics propagate to the multiple motor situations. Finally, we find that the one-dimensional character of the models impede an appropriate description of the fast fluctuations of the cargo position at small loads. We show how this problem can be solved by considering two-dimensional models.

Revisiting Temporal Markov Chains for Continuum modeling of Transport in Porous Media

Science.gov (United States)

Delgoshaie, A. H.; Jenny, P.; Tchelepi, H.

2017-12-01

The transport of fluids in porous media is dominated by flow­-field heterogeneity resulting from the underlying permeability field. Due to the high uncertainty in the permeability field, many realizations of the reference geological model are used to describe the statistics of the transport phenomena in a Monte Carlo (MC) framework. There has been strong interest in working with stochastic formulations of the transport that are different from the standard MC approach. Several stochastic models based on a velocity process for tracer particle trajectories have been proposed. Previous studies have shown that for high variances of the log-conductivity, the stochastic models need to account for correlations between consecutive velocity transitions to predict dispersion accurately. The correlated velocity models proposed in the literature can be divided into two general classes of temporal and spatial Markov models. Temporal Markov models have been applied successfully to tracer transport in both the longitudinal and transverse directions. These temporal models are Stochastic Differential Equations (SDEs) with very specific drift and diffusion terms tailored for a specific permeability correlation structure. The drift and diffusion functions devised for a certain setup would not necessarily be suitable for a different scenario, (e.g., a different permeability correlation structure). The spatial Markov models are simple discrete Markov chains that do not require case specific assumptions. However, transverse spreading of contaminant plumes has not been successfully modeled with the available correlated spatial models. Here, we propose a temporal discrete Markov chain to model both the longitudinal and transverse dispersion in a two-dimensional domain. We demonstrate that these temporal Markov models are valid for different correlation structures without modification. Similar to the temporal SDEs, the proposed model respects the limited asymptotic transverse spreading of

Compressible cavitation with stochastic field method

Science.gov (United States)

Class, Andreas; Dumond, Julien

2012-11-01

Non-linear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally the simulation of pdf transport requires Monte-Carlo codes based on Lagrange particles or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic field method solving pdf transport based on Euler fields has been proposed which eliminates the necessity to mix Euler and Lagrange techniques or prescribed pdf assumptions. In the present work, part of the PhD Design and analysis of a Passive Outflow Reducer relying on cavitation, a first application of the stochastic field method to multi-phase flow and in particular to cavitating flow is presented. The application considered is a nozzle subjected to high velocity flow so that sheet cavitation is observed near the nozzle surface in the divergent section. It is demonstrated that the stochastic field formulation captures the wide range of pdf shapes present at different locations. The method is compatible with finite-volume codes where all existing physical models available for Lagrange techniques, presumed pdf or binning methods can be easily extended to the stochastic field formulation.

Stochastic Models of Polymer Systems

Science.gov (United States)

2016-01-01

Distribution Unlimited Final Report: Stochastic Models of Polymer Systems The views, opinions and/or findings contained in this report are those of the...ADDRESS. Princeton University PO Box 0036 87 Prospect Avenue - 2nd floor Princeton, NJ 08544 -2020 14-Mar-2014 ABSTRACT Number of Papers published in...peer-reviewed journals: Number of Papers published in non peer-reviewed journals: Final Report: Stochastic Models of Polymer Systems Report Title

CAM Stochastic Volatility Model for Option Pricing

Directory of Open Access Journals (Sweden)

Wanwan Huang

2016-01-01

Full Text Available The coupled additive and multiplicative (CAM noises model is a stochastic volatility model for derivative pricing. Unlike the other stochastic volatility models in the literature, the CAM model uses two Brownian motions, one multiplicative and one additive, to model the volatility process. We provide empirical evidence that suggests a nontrivial relationship between the kurtosis and skewness of asset prices and that the CAM model is able to capture this relationship, whereas the traditional stochastic volatility models cannot. We introduce a control variate method and Monte Carlo estimators for some of the sensitivities (Greeks of the model. We also derive an approximation for the characteristic function of the model.

Enhanced bulk conductivity and bipolar transport in mixtures of MoOx and organic hole transport materials

International Nuclear Information System (INIS)

Tian, Baolin; Ban, Dayan; Aziz, Hany

2013-01-01

We study the conductivity of thin films of molybdenum oxide (MoO x ) mixed with an organic hole transport material, such as N,N′-bis(naphthalen-1-yl)-N,N′-bis (phenyl)benzidine or 4′,4″-tri(N-carbazolyl)triphenylamine, in lateral test devices. Contrary to previous reports, the conductivity of the mixture is found to exceed that of neat MoO x , exhibiting ∼ 5 orders of magnitude higher conductivity in comparison to the neat films. Studies also show that the mixing enhances both hole and electron transport. The higher conductivity may be attributed to a higher concentration of “free” carriers in the mixture, as a result of the formation of a charge transfer complex between the MoO x and the hole transport material. The findings shed light on the potential of hybrid composites of inorganic and organic materials in realizing enhanced conductivity. - Highlights: • We investigate the conductivity of mixtures of MoO x and hole transport material (HTM). • Materials are studied in lateral devices instead of conventional vertical devices. • Mixing MoO x with HTM brings > 5 orders of magnitude increase in bulk conductivity. • The mixture of MoO x and HTM enhances both hole and electron transport

Electron transport in the stochastic fields of RFP ZT-40M

International Nuclear Information System (INIS)

Punjabi, A.; Verma, A.; Kim, Myung-Hee; Boozer, A.

1991-01-01

In this paper, we use our newly developed Monte Carlo Method to study the transport of electrons in stochastic magnetic fields of the device RFP ZT4OM. The results of this calculation will be compared with the Rechester-Rosenbluth scaling

Stochastic calculations for radiation risk assessment: a Monte-Carlo approach to the simulation of radiocesium transport in the pasture-cow-milk food chain

Energy Technology Data Exchange (ETDEWEB)

Mathies, M; Eisfeld, K; Paretzke, H; Wirth, E [Gesellschaft fuer Strahlen- und Umweltforschung m.b.H. Muenchen, Neuherberg (Germany, F.R.). Inst. fuer Strahlenschutz

1981-05-01

The effects of introducing probability distributions of the parameters in radionuclide transport models are investigated. Results from a Monte-Carlo simulation were presented for the transport of /sup 137/Cs via the pasture-cow-milk pathway, taking into the account the uncertainties and naturally occurring fluctuations in the rate constants. The results of the stochastic model calculations characterize the activity concentrations at a given time t and provide a great deal more information for analysis of the environmental transport of radionuclides than deterministic calculations in which the variation of parameters is not taken into consideration. Moreover the stochastic model permits an estimate of the variation of the physico-chemical behaviour of radionuclides in the environment in a more realistic way than by using only the highest transfer coefficients in deterministic approaches, which can lead to non-realistic overestimates of the probability with which high activity levels will be encountered.

Modeling stochasticity and robustness in gene regulatory networks.

Science.gov (United States)

Garg, Abhishek; Mohanram, Kartik; Di Cara, Alessandro; De Micheli, Giovanni; Xenarios, Ioannis

2009-06-15

Understanding gene regulation in biological processes and modeling the robustness of underlying regulatory networks is an important problem that is currently being addressed by computational systems biologists. Lately, there has been a renewed interest in Boolean modeling techniques for gene regulatory networks (GRNs). However, due to their deterministic nature, it is often difficult to identify whether these modeling approaches are robust to the addition of stochastic noise that is widespread in gene regulatory processes. Stochasticity in Boolean models of GRNs has been addressed relatively sparingly in the past, mainly by flipping the expression of genes between different expression levels with a predefined probability. This stochasticity in nodes (SIN) model leads to over representation of noise in GRNs and hence non-correspondence with biological observations. In this article, we introduce the stochasticity in functions (SIF) model for simulating stochasticity in Boolean models of GRNs. By providing biological motivation behind the use of the SIF model and applying it to the T-helper and T-cell activation networks, we show that the SIF model provides more biologically robust results than the existing SIN model of stochasticity in GRNs. Algorithms are made available under our Boolean modeling toolbox, GenYsis. The software binaries can be downloaded from http://si2.epfl.ch/ approximately garg/genysis.html.

Stochastic models in reliability and maintenance

CERN Document Server

2002-01-01

Our daily lives can be maintained by the high-technology systems. Computer systems are typical examples of such systems. We can enjoy our modern lives by using many computer systems. Much more importantly, we have to maintain such systems without failure, but cannot predict when such systems will fail and how to fix such systems without delay. A stochastic process is a set of outcomes of a random experiment indexed by time, and is one of the key tools needed to analyze the future behavior quantitatively. Reliability and maintainability technologies are of great interest and importance to the maintenance of such systems. Many mathematical models have been and will be proposed to describe reliability and maintainability systems by using the stochastic processes. The theme of this book is "Stochastic Models in Reliability and Main­ tainability. " This book consists of 12 chapters on the theme above from the different viewpoints of stochastic modeling. Chapter 1 is devoted to "Renewal Processes," under which cla...

Stochastic approach and fluctuation theorem for charge transport in diodes

Science.gov (United States)

Gu, Jiayin; Gaspard, Pierre

2018-05-01

A stochastic approach for charge transport in diodes is developed in consistency with the laws of electricity, thermodynamics, and microreversibility. In this approach, the electron and hole densities are ruled by diffusion-reaction stochastic partial differential equations and the electric field generated by the charges is determined with the Poisson equation. These equations are discretized in space for the numerical simulations of the mean density profiles, the mean electric potential, and the current-voltage characteristics. Moreover, the full counting statistics of the carrier current and the measured total current including the contribution of the displacement current are investigated. On the basis of local detailed balance, the fluctuation theorem is shown to hold for both currents.

The multivariate supOU stochastic volatility model

DEFF Research Database (Denmark)

Barndorff-Nielsen, Ole; Stelzer, Robert

Using positive semidefinite supOU (superposition of Ornstein-Uhlenbeck type) processes to describe the volatility, we introduce a multivariate stochastic volatility model for financial data which is capable of modelling long range dependence effects. The finiteness of moments and the second order...... structure of the volatility, the log returns, as well as their "squares" are discussed in detail. Moreover, we give several examples in which long memory effects occur and study how the model as well as the simple Ornstein-Uhlenbeck type stochastic volatility model behave under linear transformations....... In particular, the models are shown to be preserved under invertible linear transformations. Finally, we discuss how (sup)OU stochastic volatility models can be combined with a factor modelling approach....

A Fractionally Integrated Wishart Stochastic Volatility Model

NARCIS (Netherlands)

M. Asai (Manabu); M.J. McAleer (Michael)

2013-01-01

textabstractThere has recently been growing interest in modeling and estimating alternative continuous time multivariate stochastic volatility models. We propose a continuous time fractionally integrated Wishart stochastic volatility (FIWSV) process. We derive the conditional Laplace transform of

A stochastic SIS epidemic model with vaccination

Science.gov (United States)

Cao, Boqiang; Shan, Meijing; Zhang, Qimin; Wang, Weiming

2017-11-01

In this paper, we investigate the basic features of an SIS type infectious disease model with varying population size and vaccinations in presence of environment noise. By applying the Markov semigroup theory, we propose a stochastic reproduction number R0s which can be seen as a threshold parameter to utilize in identifying the stochastic extinction and persistence: If R0s disease-free absorbing set for the stochastic epidemic model, which implies that disease dies out with probability one; while if R0s > 1, under some mild extra conditions, the SDE model has an endemic stationary distribution which results in the stochastic persistence of the infectious disease. The most interesting finding is that large environmental noise can suppress the outbreak of the disease.

Development of random geometry capability in RMC code for stochastic media analysis

International Nuclear Information System (INIS)

Liu, Shichang; She, Ding; Liang, Jin-gang; Wang, Kan

2015-01-01

Highlights: • Monte Carlo method plays an important role in modeling of particle transport in random media. • Three stochastic geometry modeling methods have been developed in RMC. • The stochastic effects of the randomly dispersed fuel particles are analyzed. • Investigation of accuracy and efficiency of three methods has been carried out. • All the methods are effective, and explicit modeling is regarded as the best choice. - Abstract: Simulation of particle transport in random media poses a challenge for traditional deterministic transport methods, due to the significant effects of spatial and energy self-shielding. Monte Carlo method plays an important role in accurate simulation of random media, owing to its flexible geometry modeling and the use of continuous-energy nuclear cross sections. Three stochastic geometry modeling methods including Random Lattice Method, Chord Length Sampling and explicit modeling approach with mesh acceleration technique, have been developed in RMC to simulate the particle transport in the dispersed fuels. The verifications of the accuracy and the investigations of the calculation efficiency have been carried out. The stochastic effects of the randomly dispersed fuel particles are also analyzed. The results show that all three stochastic geometry modeling methods can account for the effects of the random dispersion of fuel particles, and the explicit modeling method can be regarded as the best choice

Transport coefficients of hard-sphere mixtures: Theory and Monte Carlo molecular-dynamics calculations for an isotopic mixture

International Nuclear Information System (INIS)

Erpenbeck, J.J.

1989-01-01

The thermal transport properties of mixtures can be formulated in a number of ways, depending on the choice of driving forces for the transport of heat and matter, without violating the Onsager conditions. Here we treat transport in mixtures based on the driving forces -del ln T and -T del(μ/sub a//T), with T the temperature and μ/sub a/ the specific chemical potential, to obtain the Green-Kubo expressions and the Enskog theory for the corresponding transport coefficients which seem most amenable to molecular-dynamics evaluation. The transport properties of a hard-sphere mixture (mass ratio of 0.1, diameter ratio of 1.0, at a volume of three times close-packed volume), calculated by a Monte Carlo, molecular-dynamics method based on the Green-Kubo formulas, are compared with the predictions of the Enskog theory. The long-time behavior of the Green-Kubo time-correlation functions for shear viscosity, thermal conductivity, thermal diffusion, and mutual diffusion are found to be in good agreement with the predictions of mode-coupling theory. Except for viscosity, the contribution of the long-time tails to the transport coefficients is found to be significant. We obtain values, relative to Enskog, of 1.016 +- 0.007 for shear viscosity, 1.218 +- 0.009 for thermal conductivity, 1.267 +- 0.026 for thermal diffusion, and 1.117 +- 0.008 for mutual diffusion

Population stochastic modelling (PSM)--an R package for mixed-effects models based on stochastic differential equations.

Science.gov (United States)

Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode; Overgaard, Rune Viig; Madsen, Henrik

2009-06-01

The extension from ordinary to stochastic differential equations (SDEs) in pharmacokinetic and pharmacodynamic (PK/PD) modelling is an emerging field and has been motivated in a number of articles [N.R. Kristensen, H. Madsen, S.H. Ingwersen, Using stochastic differential equations for PK/PD model development, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 109-141; C.W. Tornøe, R.V. Overgaard, H. Agersø, H.A. Nielsen, H. Madsen, E.N. Jonsson, Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations, Pharm. Res. 22 (August(8)) (2005) 1247-1258; R.V. Overgaard, N. Jonsson, C.W. Tornøe, H. Madsen, Non-linear mixed-effects models with stochastic differential equations: implementation of an estimation algorithm, J. Pharmacokinet. Pharmacodyn. 32 (February(1)) (2005) 85-107; U. Picchini, S. Ditlevsen, A. De Gaetano, Maximum likelihood estimation of a time-inhomogeneous stochastic differential model of glucose dynamics, Math. Med. Biol. 25 (June(2)) (2008) 141-155]. PK/PD models are traditionally based ordinary differential equations (ODEs) with an observation link that incorporates noise. This state-space formulation only allows for observation noise and not for system noise. Extending to SDEs allows for a Wiener noise component in the system equations. This additional noise component enables handling of autocorrelated residuals originating from natural variation or systematic model error. Autocorrelated residuals are often partly ignored in PK/PD modelling although violating the hypothesis for many standard statistical tests. This article presents a package for the statistical program R that is able to handle SDEs in a mixed-effects setting. The estimation method implemented is the FOCE(1) approximation to the population likelihood which is generated from the individual likelihoods that are approximated using the Extended Kalman Filter's one-step predictions.

Consistent Stochastic Modelling of Meteocean Design Parameters

DEFF Research Database (Denmark)

Sørensen, John Dalsgaard; Sterndorff, M. J.

2000-01-01

Consistent stochastic models of metocean design parameters and their directional dependencies are essential for reliability assessment of offshore structures. In this paper a stochastic model for the annual maximum values of the significant wave height, and the associated wind velocity, current...

Stochastic linear programming models, theory, and computation

CERN Document Server

Kall, Peter

2011-01-01

This new edition of Stochastic Linear Programming: Models, Theory and Computation has been brought completely up to date, either dealing with or at least referring to new material on models and methods, including DEA with stochastic outputs modeled via constraints on special risk functions (generalizing chance constraints, ICC’s and CVaR constraints), material on Sharpe-ratio, and Asset Liability Management models involving CVaR in a multi-stage setup. To facilitate use as a text, exercises are included throughout the book, and web access is provided to a student version of the authors’ SLP-IOR software. Additionally, the authors have updated the Guide to Available Software, and they have included newer algorithms and modeling systems for SLP. The book is thus suitable as a text for advanced courses in stochastic optimization, and as a reference to the field. From Reviews of the First Edition: "The book presents a comprehensive study of stochastic linear optimization problems and their applications. … T...

Stochastic Wake Modelling Based on POD Analysis

Directory of Open Access Journals (Sweden)

David Bastine

2018-03-01

Full Text Available In this work, large eddy simulation data is analysed to investigate a new stochastic modeling approach for the wake of a wind turbine. The data is generated by the large eddy simulation (LES model PALM combined with an actuator disk with rotation representing the turbine. After applying a proper orthogonal decomposition (POD, three different stochastic models for the weighting coefficients of the POD modes are deduced resulting in three different wake models. Their performance is investigated mainly on the basis of aeroelastic simulations of a wind turbine in the wake. Three different load cases and their statistical characteristics are compared for the original LES, truncated PODs and the stochastic wake models including different numbers of POD modes. It is shown that approximately six POD modes are enough to capture the load dynamics on large temporal scales. Modeling the weighting coefficients as independent stochastic processes leads to similar load characteristics as in the case of the truncated POD. To complete this simplified wake description, we show evidence that the small-scale dynamics can be captured by adding to our model a homogeneous turbulent field. In this way, we present a procedure to derive stochastic wake models from costly computational fluid dynamics (CFD calculations or elaborated experimental investigations. These numerically efficient models provide the added value of possible long-term studies. Depending on the aspects of interest, different minimalized models may be obtained.

Fractional diffusion models of transport in magnetically confined plasmas

International Nuclear Information System (INIS)

Castillo-Negrete, D. del; Carreras, B. A.; Lynch, V. E.

2005-01-01

Experimental and theoretical evidence suggests that transport in magnetically confined fusion plasmas deviates from the standard diffusion paradigm. Some examples include the confinement time scaling in L-mode plasmas, rapid pulse propagation phenomena, and inward transport in off-axis fueling experiments. The limitations of the diffusion paradigm can be traced back to the restrictive assumptions in which it is based. In particular, Fick's law, one of the cornerstones of diffusive transport, assumes that the fluxes only depend on local quantities, i. e. the spatial gradient of the field (s). another key issue is the Markovian assumption that neglects memory effects. Also, at a microscopic level, standard diffusion assumes and underlying Gaussian, uncorrelated stochastic process (i. e. a Brownian random walk) with well defined characteristic spatio-temporal scales. Motivated by the need to develop models of non-diffusive transport, we discuss here a class of transport models base on the use of fractional derivative operators. The models incorporates in a unified way non-Fickian transport, non-Markovian processes or memory effects, and non-diffusive scaling. At a microscopic level, the models describe an underlying stochastic process without characteristic spatio-temporal scales that generalizes the Brownian random walk. As a concrete case study to motivate and test the model, we consider transport of tracers in three-dimensional, pressure-gradient-driven turbulence. We show that in this system transport is non-diffusive and cannot be described in the context of the standard diffusion parading. In particular, the probability density function (pdf) of the radial displacements of tracers is strongly non-Gaussian with algebraic decaying tails, and the moments of the tracer displacements exhibit super-diffusive scaling. there is quantitative agreement between the turbulence transport calculations and the proposed fractional diffusion model. In particular, the model

Fluctuation theory for transport properties in multicomponent mixtures: thermodiffusion and heat conductivity

DEFF Research Database (Denmark)

Shapiro, Alexander

2004-01-01

The theory of transport properties in multicomponent gas and liquid mixtures, which was previously developed for diffusion coefficients, is extended onto thermodiffusion coefficients and heat conductivities. The derivation of the expressions for transport properties is based on the general statis...... of the heat conductivity coefficient for ideal gas. (C) 2003 Elsevier B.V. All rights reserved.......The theory of transport properties in multicomponent gas and liquid mixtures, which was previously developed for diffusion coefficients, is extended onto thermodiffusion coefficients and heat conductivities. The derivation of the expressions for transport properties is based on the general...

Stochastic stability and bifurcation in a macroeconomic model

International Nuclear Information System (INIS)

Li Wei; Xu Wei; Zhao Junfeng; Jin Yanfei

2007-01-01

On the basis of the work of Goodwin and Puu, a new business cycle model subject to a stochastically parametric excitation is derived in this paper. At first, we reduce the model to a one-dimensional diffusion process by applying the stochastic averaging method of quasi-nonintegrable Hamiltonian system. Secondly, we utilize the methods of Lyapunov exponent and boundary classification associated with diffusion process respectively to analyze the stochastic stability of the trivial solution of system. The numerical results obtained illustrate that the trivial solution of system must be globally stable if it is locally stable in the state space. Thirdly, we explore the stochastic Hopf bifurcation of the business cycle model according to the qualitative changes in stationary probability density of system response. It is concluded that the stochastic Hopf bifurcation occurs at two critical parametric values. Finally, some explanations are given in a simply way on the potential applications of stochastic stability and bifurcation analysis

Population stochastic modelling (PSM)-An R package for mixed-effects models based on stochastic differential equations

DEFF Research Database (Denmark)

Klim, Søren; Mortensen, Stig Bousgaard; Kristensen, Niels Rode

2009-01-01

are often partly ignored in PK/PD modelling although violating the hypothesis for many standard statistical tests. This article presents a package for the statistical program R that is able to handle SDEs in a mixed-effects setting. The estimation method implemented is the FOCE1 approximation......The extension from ordinary to stochastic differential equations (SDEs) in pharmacokinetic and pharmacodynamic (PK/PD) modelling is an emerging field and has been motivated in a number of articles [N.R. Kristensen, H. Madsen, S.H. Ingwersen, Using stochastic differential equations for PK/PD model...... development, J. Pharmacokinet. Pharmacodyn. 32 (February(l)) (2005) 109-141; C.W. Tornoe, R.V Overgaard, H. Agerso, H.A. Nielsen, H. Madsen, E.N. Jonsson, Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations, Pharm. Res. 22 (August(8...

URDME: a modular framework for stochastic simulation of reaction-transport processes in complex geometries.

Science.gov (United States)

Drawert, Brian; Engblom, Stefan; Hellander, Andreas

2012-06-22

Experiments in silico using stochastic reaction-diffusion models have emerged as an important tool in molecular systems biology. Designing computational software for such applications poses several challenges. Firstly, realistic lattice-based modeling for biological applications requires a consistent way of handling complex geometries, including curved inner- and outer boundaries. Secondly, spatiotemporal stochastic simulations are computationally expensive due to the fast time scales of individual reaction- and diffusion events when compared to the biological phenomena of actual interest. We therefore argue that simulation software needs to be both computationally efficient, employing sophisticated algorithms, yet in the same time flexible in order to meet present and future needs of increasingly complex biological modeling. We have developed URDME, a flexible software framework for general stochastic reaction-transport modeling and simulation. URDME uses Unstructured triangular and tetrahedral meshes to resolve general geometries, and relies on the Reaction-Diffusion Master Equation formalism to model the processes under study. An interface to a mature geometry and mesh handling external software (Comsol Multiphysics) provides for a stable and interactive environment for model construction. The core simulation routines are logically separated from the model building interface and written in a low-level language for computational efficiency. The connection to the geometry handling software is realized via a Matlab interface which facilitates script computing, data management, and post-processing. For practitioners, the software therefore behaves much as an interactive Matlab toolbox. At the same time, it is possible to modify and extend URDME with newly developed simulation routines. Since the overall design effectively hides the complexity of managing the geometry and meshes, this means that newly developed methods may be tested in a realistic setting already at

A Generic Model for Prediction of Separation Performance of Olefin/Paraffin Mixture by Glassy Polymer Membranes

Directory of Open Access Journals (Sweden)

A.A. Ghoreyshi

2008-02-01

Full Text Available The separation of olefin/paraffin mixtures is an important process in petrochemical industries, which is traditionally performed by low temperature distillation with a high-energy consumption, or complex extractive distillationand adsorption techniques. Membrane separation process is emerging as an alternative for traditional separation processes with respect to low energy and simple operation. Investigations made by various researchers on polymeric membranes it is found that special glassy polymers render them as suitable materials for olefin/paraffin mixture separation. In this regard, having some knowledge on the possible transport mechanism of these processes would play a significant role in their design and applications. In this study, separation behavior of olefin/paraffin mixtures through glassy polymers was modeled by three different approaches: the so-called dual transport model, the basic adsorption-diffusion theory and the general Maxwell-Stefan formulation. The systems chosen to validate the developed transport models are separation of ethane-ethylene mixture by 6FDA-6FpDA polyimide membrane and propane-propylene mixture by 6FDA-TrMPD polyimide membrane for which the individual sorption and permeation data are available in the literature. Acritical examination of dual transport model shows that this model fails clearly to predict even the proper trend for selectivities. The adjustment of pemeabilities by accounting for the contribution of non-selective bulk flow in the transport model introduced no improvement in the predictability of the model. The modeling results based on the basic adsorption-diffusion theory revealed that in this approach only using mixed permeability data, an acceptable result is attainable which fades out the advantages of predictibility of multicomponent separation performance from pure component data. Finally, the results obtained from the model developed based on Maxwell-Stefan formulation approach show a

Electron transport in the stochastic fields of the reversed-field pinch

International Nuclear Information System (INIS)

Kim, M.-H.; Punjabi, A.

1996-01-01

We employ the Monte Carlo method for the calculation of anomalous transport developed by Punjabi and Boozer to calculate the particle diffusion coefficient for electrons in the stochastic magnetic fields of the reversed-field pinch (RFP). In the Monte Carlo calculations represented here, the transport mechanism is the loss of magnetic surfaces due to resistive perturbations. The equilibrium magnetic fields are represented by the Bessel function model for the RFP. The diffusion coefficient D is calculated as a function of a, the amplitude of the perturbation. We see three regimes as the amplitude of the tearing modes is increased: the Rechester-Rosenbluth regime where D scales as a 2 ; the anomalous regime where D scales more rapidly than a 2 ; and the Mynick-Krommes regime where D scales more slowly than a 2 . Inclusion of the effects of loop voltage on the particle drift orbits in the RFP does not affect the intervals in the amplitude a where these regimes operate. (Author)

Stochastic volatility models and Kelvin waves

Science.gov (United States)

Lipton, Alex; Sepp, Artur

2008-08-01

We use stochastic volatility models to describe the evolution of an asset price, its instantaneous volatility and its realized volatility. In particular, we concentrate on the Stein and Stein model (SSM) (1991) for the stochastic asset volatility and the Heston model (HM) (1993) for the stochastic asset variance. By construction, the volatility is not sign definite in SSM and is non-negative in HM. It is well known that both models produce closed-form expressions for the prices of vanilla option via the Lewis-Lipton formula. However, the numerical pricing of exotic options by means of the finite difference and Monte Carlo methods is much more complex for HM than for SSM. Until now, this complexity was considered to be an acceptable price to pay for ensuring that the asset volatility is non-negative. We argue that having negative stochastic volatility is a psychological rather than financial or mathematical problem, and advocate using SSM rather than HM in most applications. We extend SSM by adding volatility jumps and obtain a closed-form expression for the density of the asset price and its realized volatility. We also show that the current method of choice for solving pricing problems with stochastic volatility (via the affine ansatz for the Fourier-transformed density function) can be traced back to the Kelvin method designed in the 19th century for studying wave motion problems arising in fluid dynamics.

Stochastic volatility models and Kelvin waves

International Nuclear Information System (INIS)

Lipton, Alex; Sepp, Artur

2008-01-01

We use stochastic volatility models to describe the evolution of an asset price, its instantaneous volatility and its realized volatility. In particular, we concentrate on the Stein and Stein model (SSM) (1991) for the stochastic asset volatility and the Heston model (HM) (1993) for the stochastic asset variance. By construction, the volatility is not sign definite in SSM and is non-negative in HM. It is well known that both models produce closed-form expressions for the prices of vanilla option via the Lewis-Lipton formula. However, the numerical pricing of exotic options by means of the finite difference and Monte Carlo methods is much more complex for HM than for SSM. Until now, this complexity was considered to be an acceptable price to pay for ensuring that the asset volatility is non-negative. We argue that having negative stochastic volatility is a psychological rather than financial or mathematical problem, and advocate using SSM rather than HM in most applications. We extend SSM by adding volatility jumps and obtain a closed-form expression for the density of the asset price and its realized volatility. We also show that the current method of choice for solving pricing problems with stochastic volatility (via the affine ansatz for the Fourier-transformed density function) can be traced back to the Kelvin method designed in the 19th century for studying wave motion problems arising in fluid dynamics

Stochastic volatility models and Kelvin waves

Energy Technology Data Exchange (ETDEWEB)

Lipton, Alex [Merrill Lynch, Mlfc Main, 2 King Edward Street, London EC1A 1HQ (United Kingdom); Sepp, Artur [Merrill Lynch, 4 World Financial Center, New York, NY 10080 (United States)], E-mail: Alex_Lipton@ml.com, E-mail: Artur_Sepp@ml.com

2008-08-29

We use stochastic volatility models to describe the evolution of an asset price, its instantaneous volatility and its realized volatility. In particular, we concentrate on the Stein and Stein model (SSM) (1991) for the stochastic asset volatility and the Heston model (HM) (1993) for the stochastic asset variance. By construction, the volatility is not sign definite in SSM and is non-negative in HM. It is well known that both models produce closed-form expressions for the prices of vanilla option via the Lewis-Lipton formula. However, the numerical pricing of exotic options by means of the finite difference and Monte Carlo methods is much more complex for HM than for SSM. Until now, this complexity was considered to be an acceptable price to pay for ensuring that the asset volatility is non-negative. We argue that having negative stochastic volatility is a psychological rather than financial or mathematical problem, and advocate using SSM rather than HM in most applications. We extend SSM by adding volatility jumps and obtain a closed-form expression for the density of the asset price and its realized volatility. We also show that the current method of choice for solving pricing problems with stochastic volatility (via the affine ansatz for the Fourier-transformed density function) can be traced back to the Kelvin method designed in the 19th century for studying wave motion problems arising in fluid dynamics.

Stochastic Modelling Of The Repairable System

Directory of Open Access Journals (Sweden)

Andrzejczak Karol

2015-11-01

Full Text Available All reliability models consisting of random time factors form stochastic processes. In this paper we recall the definitions of the most common point processes which are used for modelling of repairable systems. Particularly this paper presents stochastic processes as examples of reliability systems for the support of the maintenance related decisions. We consider the simplest one-unit system with a negligible repair or replacement time, i.e., the unit is operating and is repaired or replaced at failure, where the time required for repair and replacement is negligible. When the repair or replacement is completed, the unit becomes as good as new and resumes operation. The stochastic modelling of recoverable systems constitutes an excellent method of supporting maintenance related decision-making processes and enables their more rational use.

Hybrid approaches for multiple-species stochastic reaction–diffusion models

International Nuclear Information System (INIS)

Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K.; Byrne, Helen

2015-01-01

Reaction–diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction–diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model. - Highlights: • A novel hybrid stochastic/deterministic reaction–diffusion simulation method is given. • Can massively speed up stochastic simulations while preserving stochastic effects. • Can handle multiple reacting species. • Can handle moving boundaries

Hybrid approaches for multiple-species stochastic reaction–diffusion models

Energy Technology Data Exchange (ETDEWEB)

Spill, Fabian, E-mail: fspill@bu.edu [Department of Biomedical Engineering, Boston University, 44 Cummington Street, Boston, MA 02215 (United States); Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 (United States); Guerrero, Pilar [Department of Mathematics, University College London, Gower Street, London WC1E 6BT (United Kingdom); Alarcon, Tomas [Centre de Recerca Matematica, Campus de Bellaterra, Edifici C, 08193 Bellaterra (Barcelona) (Spain); Departament de Matemàtiques, Universitat Atonòma de Barcelona, 08193 Bellaterra (Barcelona) (Spain); Maini, Philip K. [Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG (United Kingdom); Byrne, Helen [Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX2 6GG (United Kingdom); Computational Biology Group, Department of Computer Science, University of Oxford, Oxford OX1 3QD (United Kingdom)

2015-10-15

Reaction–diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction–diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model. - Highlights: • A novel hybrid stochastic/deterministic reaction–diffusion simulation method is given. • Can massively speed up stochastic simulations while preserving stochastic effects. • Can handle multiple reacting species. • Can handle moving boundaries.

Infinite-degree-corrected stochastic block model

DEFF Research Database (Denmark)

Herlau, Tue; Schmidt, Mikkel Nørgaard; Mørup, Morten

2014-01-01

In stochastic block models, which are among the most prominent statistical models for cluster analysis of complex networks, clusters are defined as groups of nodes with statistically similar link probabilities within and between groups. A recent extension by Karrer and Newman [Karrer and Newman...... corrected stochastic block model as a nonparametric Bayesian model, incorporating a parameter to control the amount of degree correction that can then be inferred from data. Additionally, our formulation yields principled ways of inferring the number of groups as well as predicting missing links...

A Stochastic Model for Malaria Transmission Dynamics

Directory of Open Access Journals (Sweden)

Rachel Waema Mbogo

2018-01-01

Full Text Available Malaria is one of the three most dangerous infectious diseases worldwide (along with HIV/AIDS and tuberculosis. In this paper we compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in malaria transmission dynamics. Relationships between the basic reproduction number for malaria transmission dynamics between humans and mosquitoes and the extinction thresholds of corresponding continuous-time Markov chain models are derived under certain assumptions. The stochastic model is formulated using the continuous-time discrete state Galton-Watson branching process (CTDSGWbp. The reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or die out. Thresholds for disease extinction from stochastic models contribute crucial knowledge on disease control and elimination and mitigation of infectious diseases. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that malaria outbreak is more likely if the disease is introduced by infected mosquitoes as opposed to infected humans. These insights demonstrate the importance of a policy or intervention focusing on controlling the infected mosquito population if the control of malaria is to be realized.

Stochastic modeling and analysis of telecoms networks

CERN Document Server

Decreusefond, Laurent

2012-01-01

This book addresses the stochastic modeling of telecommunication networks, introducing the main mathematical tools for that purpose, such as Markov processes, real and spatial point processes and stochastic recursions, and presenting a wide list of results on stability, performances and comparison of systems.The authors propose a comprehensive mathematical construction of the foundations of stochastic network theory: Markov chains, continuous time Markov chains are extensively studied using an original martingale-based approach. A complete presentation of stochastic recursions from an

A stochastic model of enzyme kinetics

Science.gov (United States)

Stefanini, Marianne; Newman, Timothy; McKane, Alan

2003-10-01

Enzyme kinetics is generally modeled by deterministic rate equations, and in the simplest case leads to the well-known Michaelis-Menten equation. It is plausible that stochastic effects will play an important role at low enzyme concentrations. We have addressed this by constructing a simple stochastic model which can be exactly solved in the steady-state. Throughout a wide range of parameter values Michaelis-Menten dynamics is replaced by a new and simple theoretical result.

A stochastic model of particle dispersion in turbulent reacting gaseous environments

Science.gov (United States)

Sun, Guangyuan; Lignell, David; Hewson, John

2012-11-01

We are performing fundamental studies of dispersive transport and time-temperature histories of Lagrangian particles in turbulent reacting flows. The particle-flow statistics including the full particle temperature PDF are of interest. A challenge in modeling particle motions is the accurate prediction of fine-scale aerosol-fluid interactions. A computationally affordable stochastic modeling approach, one-dimensional turbulence (ODT), is a proven method that captures the full range of length and time scales, and provides detailed statistics of fine-scale turbulent-particle mixing and transport. Limited results of particle transport in ODT have been reported in non-reacting flow. Here, we extend ODT to particle transport in reacting flow. The results of particle transport in three flow configurations are presented: channel flow, homogeneous isotropic turbulence, and jet flames. We investigate the functional dependence of the statistics of particle-flow interactions including (1) parametric study with varying temperatures, Reynolds numbers, and particle Stokes numbers; (2) particle temperature histories and PDFs; (3) time scale and the sensitivity of initial and boundary conditions. Flow statistics are compared to both experimental measurements and DNS data.

Synthetic Sediments and Stochastic Groundwater Hydrology

Science.gov (United States)

Wilson, J. L.

2002-12-01

For over twenty years the groundwater community has pursued the somewhat elusive goal of describing the effects of aquifer heterogeneity on subsurface flow and chemical transport. While small perturbation stochastic moment methods have significantly advanced theoretical understanding, why is it that stochastic applications use instead simulations of flow and transport through multiple realizations of synthetic geology? Allan Gutjahr was a principle proponent of the Fast Fourier Transform method for the synthetic generation of aquifer properties and recently explored new, more geologically sound, synthetic methods based on multi-scale Markov random fields. Focusing on sedimentary aquifers, how has the state-of-the-art of synthetic generation changed and what new developments can be expected, for example, to deal with issues like conceptual model uncertainty, the differences between measurement and modeling scales, and subgrid scale variability? What will it take to get stochastic methods, whether based on moments, multiple realizations, or some other approach, into widespread application?

Stochastic Control - External Models

DEFF Research Database (Denmark)

Poulsen, Niels Kjølstad

2005-01-01

This note is devoted to control of stochastic systems described in discrete time. We are concerned with external descriptions or transfer function model, where we have a dynamic model for the input output relation only (i.e.. no direct internal information). The methods are based on LTI systems...

Stochastic dynamic modeling of regular and slow earthquakes

Science.gov (United States)

Aso, N.; Ando, R.; Ide, S.

2017-12-01

Both regular and slow earthquakes are slip phenomena on plate boundaries and are simulated by a (quasi-)dynamic modeling [Liu and Rice, 2005]. In these numerical simulations, spatial heterogeneity is usually considered not only for explaining real physical properties but also for evaluating the stability of the calculations or the sensitivity of the results on the condition. However, even though we discretize the model space with small grids, heterogeneity at smaller scales than the grid size is not considered in the models with deterministic governing equations. To evaluate the effect of heterogeneity at the smaller scales we need to consider stochastic interactions between slip and stress in a dynamic modeling. Tidal stress is known to trigger or affect both regular and slow earthquakes [Yabe et al., 2015; Ide et al., 2016], and such an external force with fluctuation can also be considered as a stochastic external force. A healing process of faults may also be stochastic, so we introduce stochastic friction law. In the present study, we propose a stochastic dynamic model to explain both regular and slow earthquakes. We solve mode III problem, which corresponds to the rupture propagation along the strike direction. We use BIEM (boundary integral equation method) scheme to simulate slip evolution, but we add stochastic perturbations in the governing equations, which is usually written in a deterministic manner. As the simplest type of perturbations, we adopt Gaussian deviations in the formulation of the slip-stress kernel, external force, and friction. By increasing the amplitude of perturbations of the slip-stress kernel, we reproduce complicated rupture process of regular earthquakes including unilateral and bilateral ruptures. By perturbing external force, we reproduce slow rupture propagation at a scale of km/day. The slow propagation generated by a combination of fast interaction at S-wave velocity is analogous to the kinetic theory of gasses: thermal

Intermittency inhibited by transport: An exactly solvable model

Science.gov (United States)

Zanette, Damián H.

1994-04-01

Transport is incorporated in a discrete-time stochastic model of a system undergoing autocatalytic reactions of the type A-->2A and A-->0, whose population field is known to exhibit spatiotemporal intermittency. The temporal evolution is exactly solved, and it is shown that if the transport process is strong enough, intermittency is inhibited. This inhibition is nonuniform, in the sense that, as transport is strengthened, low-order population moments are affected before the high-order ones. Numerical simulations are presented to support the analytical results.

Stochastic Watershed Models for Risk Based Decision Making

Science.gov (United States)

Vogel, R. M.

2017-12-01

Over half a century ago, the Harvard Water Program introduced the field of operational or synthetic hydrology providing stochastic streamflow models (SSMs), which could generate ensembles of synthetic streamflow traces useful for hydrologic risk management. The application of SSMs, based on streamflow observations alone, revolutionized water resources planning activities, yet has fallen out of favor due, in part, to their inability to account for the now nearly ubiquitous anthropogenic influences on streamflow. This commentary advances the modern equivalent of SSMs, termed `stochastic watershed models' (SWMs) useful as input to nearly all modern risk based water resource decision making approaches. SWMs are deterministic watershed models implemented using stochastic meteorological series, model parameters and model errors, to generate ensembles of streamflow traces that represent the variability in possible future streamflows. SWMs combine deterministic watershed models, which are ideally suited to accounting for anthropogenic influences, with recent developments in uncertainty analysis and principles of stochastic simulation

Dynamics of a Stochastic Intraguild Predation Model

Directory of Open Access Journals (Sweden)

Zejing Xing

2016-04-01

Full Text Available Intraguild predation (IGP is a widespread ecological phenomenon which occurs when one predator species attacks another predator species with which it competes for a shared prey species. The objective of this paper is to study the dynamical properties of a stochastic intraguild predation model. We analyze stochastic persistence and extinction of the stochastic IGP model containing five cases and establish the sufficient criteria for global asymptotic stability of the positive solutions. This study shows that it is possible for the coexistence of three species under the influence of environmental noise, and that the noise may have a positive effect for IGP species. A stationary distribution of the stochastic IGP model is established and it has the ergodic property, suggesting that the time average of population size with the development of time is equal to the stationary distribution in space. Finally, we show that our results may be extended to two well-known biological systems: food chains and exploitative competition.

Stochastic Modeling of Traffic Air Pollution

DEFF Research Database (Denmark)

Thoft-Christensen, Palle

2014-01-01

In this paper, modeling of traffic air pollution is discussed with special reference to infrastructures. A number of subjects related to health effects of air pollution and the different types of pollutants are briefly presented. A simple model for estimating the social cost of traffic related air...... and using simple Monte Carlo techniques to obtain a stochastic estimate of the costs of traffic air pollution for infrastructures....... pollution is derived. Several authors have published papers on this very complicated subject, but no stochastic modelling procedure have obtained general acceptance. The subject is discussed basis of a deterministic model. However, it is straightforward to modify this model to include uncertain parameters...

Stochastic modelling of turbulence

DEFF Research Database (Denmark)

Sørensen, Emil Hedevang Lohse

previously been shown to be closely connected to the energy dissipation. The incorporation of the small scale dynamics into the spatial model opens the door to a fully fledged stochastic model of turbulence. Concerning the interaction of wind and wind turbine, a new method is proposed to extract wind turbine...

The stochastic nuclide transport model for buffer/backfill materials

International Nuclear Information System (INIS)

Ma Liping; Han Yongguo

2014-01-01

Currently, study on nuclide migration law in geological disposal repository of high level waste is assumed buffer/backfill layer to be continuous medium, utilized the continuity equation, equation of state, the equations of motion, etc, formed a set of theory and method to estimate nuclide concentration distribution in buffer/backfill layer, and provided an important basis for nuclide migration rules of repository. However, it is necessary to study the buffer/backfill layer microstructure and subtly describe the pore structure and fracture system of the buffer/backfill layer, and reflect the changes in connectivity and in different directions of the buffer/backfill layer. Through using random field theory, the nuclide transport for the buffer/backfill layer in geological disposal repository of nuclear waste is described in the paper. This paper mainly includes that, t represents the time, ξ t ⊂ Z d = d represents the integer lattice, Z represents collectivity integers, d = l, 2, 3, for instance, d = 2, Z d = {(m, n) : m, n ∈ Z} the state point of ξ t is typically considered to be occupied by the nuclide concentration values of the buffer/backfill layer, ξ t also represents random set in the diagram of two dimensional integer lattice, namely, t ∈ [0, T], {ξ t ,0 ≤ t ≤ ⊂ T} Consequently, according to the stochastic process obtained above, the changes of the nuclide concentration values of the buffer/backfill layer or the buffer/backfill laboratory materials in the repository with the time can be known. (authors)

Modeling Phase Equilibria for Acid Gas Mixtures using the Cubic-Plus-Association Equation of State. 3. Applications Relevant to Liquid or Supercritical CO2 Transport

DEFF Research Database (Denmark)

Tsivintzelis, Ioannis; Ali, Shahid; Kontogeorgis, Georgios

2014-01-01

density data for both CO2 and CO2–water and for vapor–liquid equilibrium for mixtures of CO2 with various compounds present in transport systems. In all of these cases we consider various possibilities for modeling CO2 (inert, self-associating using two-, three-, and four sites) and the possibility......The CPA (cubic-plus-association) equation of state is applied in this work to a wide range of systems of relevance to CO2 transport. Both phase equilibria and densities over extensive temperature and pressure ranges are considered. More specifically in this study we first evaluate CPA against......” for applying CPA to acid gas mixtures. The overall conclusion is that CPA performs satisfactorily; the model in most cases correlates well binary data and predicts with good accuracy multicomponent vapor–liquid equilibria. Among the various approaches investigated, the best ones are when cross association...

Efficient decomposition and linearization methods for the stochastic transportation problem

International Nuclear Information System (INIS)

Holmberg, K.

1993-01-01

The stochastic transportation problem can be formulated as a convex transportation problem with nonlinear objective function and linear constraints. We compare several different methods based on decomposition techniques and linearization techniques for this problem, trying to find the most efficient method or combination of methods. We discuss and test a separable programming approach, the Frank-Wolfe method with and without modifications, the new technique of mean value cross decomposition and the more well known Lagrangian relaxation with subgradient optimization, as well as combinations of these approaches. Computational tests are presented, indicating that some new combination methods are quite efficient for large scale problems. (authors) (27 refs.)

Pore-Scale Hydrodynamics in a Progressively Bioclogged Three-Dimensional Porous Medium: 3-D Particle Tracking Experiments and Stochastic Transport Modeling

Science.gov (United States)

Carrel, M.; Morales, V. L.; Dentz, M.; Derlon, N.; Morgenroth, E.; Holzner, M.

2018-03-01

Biofilms are ubiquitous bacterial communities that grow in various porous media including soils, trickling, and sand filters. In these environments, they play a central role in services ranging from degradation of pollutants to water purification. Biofilms dynamically change the pore structure of the medium through selective clogging of pores, a process known as bioclogging. This affects how solutes are transported and spread through the porous matrix, but the temporal changes to transport behavior during bioclogging are not well understood. To address this uncertainty, we experimentally study the hydrodynamic changes of a transparent 3-D porous medium as it experiences progressive bioclogging. Statistical analyses of the system's hydrodynamics at four time points of bioclogging (0, 24, 36, and 48 h in the exponential growth phase) reveal exponential increases in both average and variance of the flow velocity, as well as its correlation length. Measurements for spreading, as mean-squared displacements, are found to be non-Fickian and more intensely superdiffusive with progressive bioclogging, indicating the formation of preferential flow pathways and stagnation zones. A gamma distribution describes well the Lagrangian velocity distributions and provides parameters that quantify changes to the flow, which evolves from a parallel pore arrangement under unclogged conditions, toward a more serial arrangement with increasing clogging. Exponentially evolving hydrodynamic metrics agree with an exponential bacterial growth phase and are used to parameterize a correlated continuous time random walk model with a stochastic velocity relaxation. The model accurately reproduces transport observations and can be used to resolve transport behavior at intermediate time points within the exponential growth phase considered.

A hybrid algorithm for stochastic single-source capacitated facility location problem with service level requirements

Directory of Open Access Journals (Sweden)

Hosseinali Salemi

2016-04-01

Full Text Available Facility location models are observed in many diverse areas such as communication networks, transportation, and distribution systems planning. They play significant role in supply chain and operations management and are one of the main well-known topics in strategic agenda of contemporary manufacturing and service companies accompanied by long-lasting effects. We define a new approach for solving stochastic single source capacitated facility location problem (SSSCFLP. Customers with stochastic demand are assigned to set of capacitated facilities that are selected to serve them. It is demonstrated that problem can be transformed to deterministic Single Source Capacitated Facility Location Problem (SSCFLP for Poisson demand distribution. A hybrid algorithm which combines Lagrangian heuristic with adjusted mixture of Ant colony and Genetic optimization is proposed to find lower and upper bounds for this problem. Computational results of various instances with distinct properties indicate that proposed solving approach is efficient.

Approximate models for broken clouds in stochastic radiative transfer theory

International Nuclear Information System (INIS)

Doicu, Adrian; Efremenko, Dmitry S.; Loyola, Diego; Trautmann, Thomas

2014-01-01

This paper presents approximate models in stochastic radiative transfer theory. The independent column approximation and its modified version with a solar source computed in a full three-dimensional atmosphere are formulated in a stochastic framework and for arbitrary cloud statistics. The nth-order stochastic models describing the independent column approximations are equivalent to the nth-order stochastic models for the original radiance fields in which the gradient vectors are neglected. Fast approximate models are further derived on the basis of zeroth-order stochastic models and the independent column approximation. The so-called “internal mixing” models assume a combination of the optical properties of the cloud and the clear sky, while the “external mixing” models assume a combination of the radiances corresponding to completely overcast and clear skies. A consistent treatment of internal and external mixing models is provided, and a new parameterization of the closure coefficient in the effective thickness approximation is given. An efficient computation of the closure coefficient for internal mixing models, using a previously derived vector stochastic model as a reference, is also presented. Equipped with appropriate look-up tables for the closure coefficient, these models can easily be integrated into operational trace gas retrieval systems that exploit absorption features in the near-IR solar spectrum. - Highlights: • Independent column approximation in a stochastic setting. • Fast internal and external mixing models for total and diffuse radiances. • Efficient optimization of internal mixing models to match reference models

Parameter estimation in stochastic rainfall-runoff models

DEFF Research Database (Denmark)

Jonsdottir, Harpa; Madsen, Henrik; Palsson, Olafur Petur

2006-01-01

A parameter estimation method for stochastic rainfall-runoff models is presented. The model considered in the paper is a conceptual stochastic model, formulated in continuous-discrete state space form. The model is small and a fully automatic optimization is, therefore, possible for estimating all...... the parameter values are optimal for simulation or prediction. The data originates from Iceland and the model is designed for Icelandic conditions, including a snow routine for mountainous areas. The model demands only two input data series, precipitation and temperature and one output data series...

Test models for improving filtering with model errors through stochastic parameter estimation

International Nuclear Information System (INIS)

Gershgorin, B.; Harlim, J.; Majda, A.J.

2010-01-01

The filtering skill for turbulent signals from nature is often limited by model errors created by utilizing an imperfect model for filtering. Updating the parameters in the imperfect model through stochastic parameter estimation is one way to increase filtering skill and model performance. Here a suite of stringent test models for filtering with stochastic parameter estimation is developed based on the Stochastic Parameterization Extended Kalman Filter (SPEKF). These new SPEKF-algorithms systematically correct both multiplicative and additive biases and involve exact formulas for propagating the mean and covariance including the parameters in the test model. A comprehensive study is presented of robust parameter regimes for increasing filtering skill through stochastic parameter estimation for turbulent signals as the observation time and observation noise are varied and even when the forcing is incorrectly specified. The results here provide useful guidelines for filtering turbulent signals in more complex systems with significant model errors.

Interlocking-induced stiffness in stochastically microcracked materials beyond the transport percolation threshold

Science.gov (United States)

Picu, R. C.; Pal, A.; Lupulescu, M. V.

2016-04-01

We study the mechanical behavior of two-dimensional, stochastically microcracked continua in the range of crack densities close to, and above, the transport percolation threshold. We show that these materials retain stiffness up to crack densities much larger than the transport percolation threshold due to topological interlocking of sample subdomains. Even with a linear constitutive law for the continuum, the mechanical behavior becomes nonlinear in the range of crack densities bounded by the transport and stiffness percolation thresholds. The effect is due to the fractal nature of the fragmentation process and is not linked to the roughness of individual cracks.

Recommended direct simulation Monte Carlo collision model parameters for modeling ionized air transport processes

Energy Technology Data Exchange (ETDEWEB)

Swaminathan-Gopalan, Krishnan; Stephani, Kelly A., E-mail: ksteph@illinois.edu [Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 (United States)

2016-02-15

A systematic approach for calibrating the direct simulation Monte Carlo (DSMC) collision model parameters to achieve consistency in the transport processes is presented. The DSMC collision cross section model parameters are calibrated for high temperature atmospheric conditions by matching the collision integrals from DSMC against ab initio based collision integrals that are currently employed in the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) and Data Parallel Line Relaxation (DPLR) high temperature computational fluid dynamics solvers. The DSMC parameter values are computed for the widely used Variable Hard Sphere (VHS) and the Variable Soft Sphere (VSS) models using the collision-specific pairing approach. The recommended best-fit VHS/VSS parameter values are provided over a temperature range of 1000-20 000 K for a thirteen-species ionized air mixture. Use of the VSS model is necessary to achieve consistency in transport processes of ionized gases. The agreement of the VSS model transport properties with the transport properties as determined by the ab initio collision integral fits was found to be within 6% in the entire temperature range, regardless of the composition of the mixture. The recommended model parameter values can be readily applied to any gas mixture involving binary collisional interactions between the chemical species presented for the specified temperature range.

Modelling and application of stochastic processes

CERN Document Server

1986-01-01

The subject of modelling and application of stochastic processes is too vast to be exhausted in a single volume. In this book, attention is focused on a small subset of this vast subject. The primary emphasis is on realization and approximation of stochastic systems. Recently there has been considerable interest in the stochastic realization problem, and hence, an attempt has been made here to collect in one place some of the more recent approaches and algorithms for solving the stochastic realiza­ tion problem. Various different approaches for realizing linear minimum-phase systems, linear nonminimum-phase systems, and bilinear systems are presented. These approaches range from time-domain methods to spectral-domain methods. An overview of the chapter contents briefly describes these approaches. Also, in most of these chapters special attention is given to the problem of developing numerically ef­ ficient algorithms for obtaining reduced-order (approximate) stochastic realizations. On the application side,...

A study on the stochastic model for nuclide transport in the fractured porous rock using continuous time Markov process

International Nuclear Information System (INIS)

Lee, Youn Myoung

1995-02-01

As a newly approaching model, a stochastic model using continuous time Markov process for nuclide decay chain transport of arbitrary length in the fractured porous rock medium has been proposed, by which the need for solving a set of partial differential equations corresponding to various sets of side conditions can be avoided. Once the single planar fracture in the rock matrix is represented by a series of finite number of compartments having region wise constant parameter values in them, the medium is continuous in view of various processes associated with nuclide transport but discrete in medium space and such geologic system is assumed to have Markov property, since the Markov process requires that only the present value of the time dependent random variable be known to determine the future value of random variable, nuclide transport in the medium can then be modeled as a continuous time Markov process. Processes that are involved in nuclide transport are advective transport due to groundwater flow, diffusion into the rock matrix, adsorption onto the wall of the fracture and within the pores in the rock matrix, and radioactive decay chain. The transition probabilities for nuclide from the transition intensities between and out of the compartments are represented utilizing Chapman-Kolmogorov equation, through which the expectation and the variance of nuclide distribution for each compartment or the fractured rock medium can be obtained. Some comparisons between Markov process model developed in this work and available analytical solutions for one-dimensional layered porous medium, fractured medium with rock matrix diffusion, and porous medium considering three member nuclide decay chain without rock matrix diffusion have been made showing comparatively good agreement for all cases. To verify the model developed in this work another comparative study was also made by fitting the experimental data obtained with NaLS and uranine running in the artificial fractured

12th Workshop on Stochastic Models, Statistics and Their Applications

CERN Document Server

Rafajłowicz, Ewaryst; Szajowski, Krzysztof

2015-01-01

This volume presents the latest advances and trends in stochastic models and related statistical procedures. Selected peer-reviewed contributions focus on statistical inference, quality control, change-point analysis and detection, empirical processes, time series analysis, survival analysis and reliability, statistics for stochastic processes, big data in technology and the sciences, statistical genetics, experiment design, and stochastic models in engineering. Stochastic models and related statistical procedures play an important part in furthering our understanding of the challenging problems currently arising in areas of application such as the natural sciences, information technology, engineering, image analysis, genetics, energy and finance, to name but a few. This collection arises from the 12th Workshop on Stochastic Models, Statistics and Their Applications, Wroclaw, Poland.

Effects of flavonoid mixtures on the transport of 2-amino-1-methyl-6-phenylimidazo[4,5-b]pyridine (PhIP) through Caco-2 monolayers: An in vitro and kinetic modeling approach to predict the combined effects on transporter inhibition

NARCIS (Netherlands)

Schutte, M.E.; Boersma, M.G.; Verhallen, D.A.M.; Groten, J.P.; Rietjens, I.M.C.M.

2008-01-01

This study describes and kinetically models the effect of flavonoid mixtures on PhIP transport through Caco-2 monolayers. Previously it was shown that quercetin, luteolin, naringenin and myricetin increase the apical to basolateral PhIP transport in Caco-2 monolayers. In this study, apigenin was

Effect of chemical degradation on fluxes of reactive compounds – a study with a stochastic Lagrangian transport model

Directory of Open Access Journals (Sweden)

J. Rinne

2012-06-01

Full Text Available In the analyses of VOC fluxes measured above plant canopies, one usually assumes the flux above canopy to equal the exchange at the surface. Thus one assumes the chemical degradation to be much slower than the turbulent transport. We used a stochastic Lagrangian transport model in which the chemical degradation was described as first order decay in order to study the effect of the chemical degradation on above canopy fluxes of chemically reactive species. With the model we explored the sensitivity of the ratio of the above canopy flux to the surface emission on several parameters such as chemical lifetime of the compound, friction velocity, stability, and canopy density. Our results show that friction velocity and chemical lifetime affected the loss during transport the most. The canopy density had a significant effect if the chemically reactive compound was emitted from the forest floor. We used the results of the simulations together with oxidant data measured during HUMPPA-COPEC-2010 campaign at a Scots pine site to estimate the effect of the chemistry on fluxes of three typical biogenic VOCs, isoprene, α-pinene, and β-caryophyllene. Of these, the chemical degradation had a major effect on the fluxes of the most reactive species β-caryophyllene, while the fluxes of α-pinene were affected during nighttime. For these two compounds representing the mono- and sesquiterpenes groups, the effect of chemical degradation had also a significant diurnal cycle with the highest chemical loss at night. The different day and night time loss terms need to be accounted for, when measured fluxes of reactive compounds are used to reveal relations between primary emission and environmental parameters.

Constraining Stochastic Parametrisation Schemes Using High-Resolution Model Simulations

Science.gov (United States)

Christensen, H. M.; Dawson, A.; Palmer, T.

2017-12-01

Stochastic parametrisations are used in weather and climate models as a physically motivated way to represent model error due to unresolved processes. Designing new stochastic schemes has been the target of much innovative research over the last decade. While a focus has been on developing physically motivated approaches, many successful stochastic parametrisation schemes are very simple, such as the European Centre for Medium-Range Weather Forecasts (ECMWF) multiplicative scheme `Stochastically Perturbed Parametrisation Tendencies' (SPPT). The SPPT scheme improves the skill of probabilistic weather and seasonal forecasts, and so is widely used. However, little work has focused on assessing the physical basis of the SPPT scheme. We address this matter by using high-resolution model simulations to explicitly measure the `error' in the parametrised tendency that SPPT seeks to represent. The high resolution simulations are first coarse-grained to the desired forecast model resolution before they are used to produce initial conditions and forcing data needed to drive the ECMWF Single Column Model (SCM). By comparing SCM forecast tendencies with the evolution of the high resolution model, we can measure the `error' in the forecast tendencies. In this way, we provide justification for the multiplicative nature of SPPT, and for the temporal and spatial scales of the stochastic perturbations. However, we also identify issues with the SPPT scheme. It is therefore hoped these measurements will improve both holistic and process based approaches to stochastic parametrisation. Figure caption: Instantaneous snapshot of the optimal SPPT stochastic perturbation, derived by comparing high-resolution simulations with a low resolution forecast model.

Hybrid approaches for multiple-species stochastic reaction-diffusion models

Science.gov (United States)

Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K.; Byrne, Helen

2015-10-01

Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.

Hybrid approaches for multiple-species stochastic reaction-diffusion models.

KAUST Repository

Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K; Byrne, Helen

2015-01-01

Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.

Hybrid approaches for multiple-species stochastic reaction-diffusion models.

KAUST Repository

Spill, Fabian

2015-10-01

Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.

Multistage stochastic optimization

CERN Document Server

Pflug, Georg Ch

2014-01-01

Multistage stochastic optimization problems appear in many ways in finance, insurance, energy production and trading, logistics and transportation, among other areas. They describe decision situations under uncertainty and with a longer planning horizon. This book contains a comprehensive treatment of today’s state of the art in multistage stochastic optimization.  It covers the mathematical backgrounds of approximation theory as well as numerous practical algorithms and examples for the generation and handling of scenario trees. A special emphasis is put on estimation and bounding of the modeling error using novel distance concepts, on time consistency and the role of model ambiguity in the decision process. An extensive treatment of examples from electricity production, asset liability management and inventory control concludes the book

A stochastic modeling of recurrent measles epidemic | Kassem ...

African Journals Online (AJOL)

A simple stochastic mathematical model is developed and investigated for the dynamics of measles epidemic. The model, which is a multi-dimensional diffusion process, includes susceptible individuals, latent (exposed), infected and removed individuals. Stochastic effects are assumed to arise in the process of infection of ...

Stochastic Feedforward Control Technique

Science.gov (United States)

Halyo, Nesim

1990-01-01

Class of commanded trajectories modeled as stochastic process. Advanced Transport Operating Systems (ATOPS) research and development program conducted by NASA Langley Research Center aimed at developing capabilities for increases in capacities of airports, safe and accurate flight in adverse weather conditions including shear, winds, avoidance of wake vortexes, and reduced consumption of fuel. Advances in techniques for design of modern controls and increased capabilities of digital flight computers coupled with accurate guidance information from Microwave Landing System (MLS). Stochastic feedforward control technique developed within context of ATOPS program.

Stochastic quantization for the axial model

International Nuclear Information System (INIS)

Farina, C.; Montani, H.; Albuquerque, L.C.

1991-01-01

We use bosonization ideas to solve the axial model in the stochastic quantization framework. We obtain the fermion propagator of the theory decoupling directly the Langevin equation, instead of the Fokker-Planck equation. In the Appendix we calculate explicitly the anomalous divergence of the axial-vector current by using a regularization that does not break the Markovian character of the stochastic process

Stochastic model simulation using Kronecker product analysis and Zassenhaus formula approximation.

Science.gov (United States)

Caglar, Mehmet Umut; Pal, Ranadip

2013-01-01

Probabilistic Models are regularly applied in Genetic Regulatory Network modeling to capture the stochastic behavior observed in the generation of biological entities such as mRNA or proteins. Several approaches including Stochastic Master Equations and Probabilistic Boolean Networks have been proposed to model the stochastic behavior in genetic regulatory networks. It is generally accepted that Stochastic Master Equation is a fundamental model that can describe the system being investigated in fine detail, but the application of this model is computationally enormously expensive. On the other hand, Probabilistic Boolean Network captures only the coarse-scale stochastic properties of the system without modeling the detailed interactions. We propose a new approximation of the stochastic master equation model that is able to capture the finer details of the modeled system including bistabilities and oscillatory behavior, and yet has a significantly lower computational complexity. In this new method, we represent the system using tensors and derive an identity to exploit the sparse connectivity of regulatory targets for complexity reduction. The algorithm involves an approximation based on Zassenhaus formula to represent the exponential of a sum of matrices as product of matrices. We derive upper bounds on the expected error of the proposed model distribution as compared to the stochastic master equation model distribution. Simulation results of the application of the model to four different biological benchmark systems illustrate performance comparable to detailed stochastic master equation models but with considerably lower computational complexity. The results also demonstrate the reduced complexity of the new approach as compared to commonly used Stochastic Simulation Algorithm for equivalent accuracy.

Analysis of stochastic effects in Kaldor-type business cycle discrete model

Science.gov (United States)

Bashkirtseva, Irina; Ryashko, Lev; Sysolyatina, Anna

2016-07-01

We study nonlinear stochastic phenomena in the discrete Kaldor model of business cycles. A numerical parametric analysis of stochastically forced attractors (equilibria, closed invariant curves, discrete cycles) of this model is performed using the stochastic sensitivity functions technique. A spatial arrangement of random states in stochastic attractors is modeled by confidence domains. The phenomenon of noise-induced transitions ;chaos-order; is discussed.

Stochastic Spectral Descent for Discrete Graphical Models

International Nuclear Information System (INIS)

Carlson, David; Hsieh, Ya-Ping; Collins, Edo; Carin, Lawrence; Cevher, Volkan

2015-01-01

Interest in deep probabilistic graphical models has in-creased in recent years, due to their state-of-the-art performance on many machine learning applications. Such models are typically trained with the stochastic gradient method, which can take a significant number of iterations to converge. Since the computational cost of gradient estimation is prohibitive even for modestly sized models, training becomes slow and practically usable models are kept small. In this paper we propose a new, largely tuning-free algorithm to address this problem. Our approach derives novel majorization bounds based on the Schatten- norm. Intriguingly, the minimizers of these bounds can be interpreted as gradient methods in a non-Euclidean space. We thus propose using a stochastic gradient method in non-Euclidean space. We both provide simple conditions under which our algorithm is guaranteed to converge, and demonstrate empirically that our algorithm leads to dramatically faster training and improved predictive ability compared to stochastic gradient descent for both directed and undirected graphical models.

On the history of a stochastic ansatz for solving the transport equation

International Nuclear Information System (INIS)

Williams, M.M.R.

2010-01-01

A very useful approximate tool for understanding the role of random material properties on solutions of the transport equation is described and its historical derivation given. The development of this stochastic tool, from its introduction by Randall, to its use in describing current problems involving dichotomic or pseudo-dichotomic Markov processes is discussed.

From complex to simple: interdisciplinary stochastic models

International Nuclear Information System (INIS)

Mazilu, D A; Zamora, G; Mazilu, I

2012-01-01

We present two simple, one-dimensional, stochastic models that lead to a qualitative understanding of very complex systems from biology, nanoscience and social sciences. The first model explains the complicated dynamics of microtubules, stochastic cellular highways. Using the theory of random walks in one dimension, we find analytical expressions for certain physical quantities, such as the time dependence of the length of the microtubules, and diffusion coefficients. The second one is a stochastic adsorption model with applications in surface deposition, epidemics and voter systems. We introduce the ‘empty interval method’ and show sample calculations for the time-dependent particle density. These models can serve as an introduction to the field of non-equilibrium statistical physics, and can also be used as a pedagogical tool to exemplify standard statistical physics concepts, such as random walks or the kinetic approach of the master equation. (paper)

Stochastic fractional differential equations: Modeling, method and analysis

International Nuclear Information System (INIS)

Pedjeu, Jean-C.; Ladde, Gangaram S.

2012-01-01

By introducing a concept of dynamic process operating under multi-time scales in sciences and engineering, a mathematical model described by a system of multi-time scale stochastic differential equations is formulated. The classical Picard–Lindelöf successive approximations scheme is applied to the model validation problem, namely, existence and uniqueness of solution process. Naturally, this leads to the problem of finding closed form solutions of both linear and nonlinear multi-time scale stochastic differential equations of Itô–Doob type. Finally, to illustrate the scope of ideas and presented results, multi-time scale stochastic models for ecological and epidemiological processes in population dynamic are outlined.

Modeling diffusion coefficients in binary mixtures of polar and non-polar compounds

DEFF Research Database (Denmark)

Medvedev, Oleg; Shapiro, Alexander

2005-01-01

The theory of transport coefficients in liquids, developed previously, is tested on a description of the diffusion coefficients in binary polar/non-polar mixtures, by applying advanced thermodynamic models. Comparison to a large set of experimental data shows good performance of the model. Only f...

Diffusion in lattice Lorentz gases with mixtures of point scatterers

International Nuclear Information System (INIS)

Acedo, L.; Santos, A.

1994-01-01

Monte Carlo simulations are carried out to evaluate the diffusion coefficient in some lattice Lorentz gases with mixtures of point scatterers in the limit of a low concentration of scatterers. Two models on a square lattice are considered: (a) right and left stochastic rotators plus pure reflectors and (b) right and left stochastic mirrors plus pure reflectors. The simulation data are compared with the repeated ring approximation (RRA). The agreement is excellent for models in the absence of pure reflectors, suggesting that the RRA gives the correct diffusion coefficient for those cases. As the fraction x B of reflectors increases, the diffusion coefficient decreases and seems to vanish at x B c congruent 0.8 (percolation threshold) with a critical exponent μ congruent 2 (stochastic model) or μ congruent 3 (deterministic rotator model)

A stochastic discrete optimization model for designing container terminal facilities

Science.gov (United States)

Zukhruf, Febri; Frazila, Russ Bona; Burhani, Jzolanda Tsavalista

2017-11-01

As uncertainty essentially affect the total transportation cost, it remains important in the container terminal that incorporates several modes and transshipments process. This paper then presents a stochastic discrete optimization model for designing the container terminal, which involves the decision of facilities improvement action. The container terminal operation model is constructed by accounting the variation of demand and facilities performance. In addition, for illustrating the conflicting issue that practically raises in the terminal operation, the model also takes into account the possible increment delay of facilities due to the increasing number of equipment, especially the container truck. Those variations expectantly reflect the uncertainty issue in the container terminal operation. A Monte Carlo simulation is invoked to propagate the variations by following the observed distribution. The problem is constructed within the framework of the combinatorial optimization problem for investigating the optimal decision of facilities improvement. A new variant of glow-worm swarm optimization (GSO) is thus proposed for solving the optimization, which is rarely explored in the transportation field. The model applicability is tested by considering the actual characteristics of the container terminal.

Discrete element modelling of bedload transport

Science.gov (United States)

Loyer, A.; Frey, P.

2011-12-01

Discrete element modelling (DEM) has been widely used in solid mechanics and in granular physics. In this type of modelling, each individual particle is taken into account and intergranular interactions are modelled with simple laws (e.g. Coulomb friction). Gravity and contact forces permit to solve the dynamical behaviour of the system. DEM is interesting to model configurations and access to parameters not directly available in laboratory experimentation, hence the term "numerical experimentations" sometimes used to describe DEM. DEM was used to model bedload transport experiments performed at the particle scale with spherical glass beads in a steep and narrow flume. Bedload is the larger material that is transported on the bed on stream channels. It has a great geomorphic impact. Physical processes ruling bedload transport and more generally coarse-particle/fluid systems are poorly known, arguably because granular interactions have been somewhat neglected. An existing DEM code (PFC3D) already computing granular interactions was used. We implemented basic hydrodynamic forces to model the fluid interactions (buoyancy, drag, lift). The idea was to use the minimum number of ingredients to match the experimental results. Experiments were performed with one-size and two-size mixtures of coarse spherical glass beads entrained by a shallow turbulent and supercritical water flow down a steep channel with a mobile bed. The particle diameters were 4 and 6mm, the channel width 6.5mm (about the same width as the coarser particles) and the channel inclination was typically 10%. The water flow rate and the particle rate were kept constant at the upstream entrance and adjusted to obtain bedload transport equilibrium. Flows were filmed from the side by a high-speed camera. Using image processing algorithms made it possible to determine the position, velocity and trajectory of both smaller and coarser particles. Modelled and experimental particle velocity and concentration depth

Tsunamis: stochastic models of occurrence and generation mechanisms

Science.gov (United States)

Geist, Eric L.; Oglesby, David D.

2014-01-01

The devastating consequences of the 2004 Indian Ocean and 2011 Japan tsunamis have led to increased research into many different aspects of the tsunami phenomenon. In this entry, we review research related to the observed complexity and uncertainty associated with tsunami generation, propagation, and occurrence described and analyzed using a variety of stochastic methods. In each case, seismogenic tsunamis are primarily considered. Stochastic models are developed from the physical theories that govern tsunami evolution combined with empirical models fitted to seismic and tsunami observations, as well as tsunami catalogs. These stochastic methods are key to providing probabilistic forecasts and hazard assessments for tsunamis. The stochastic methods described here are similar to those described for earthquakes (Vere-Jones 2013) and volcanoes (Bebbington 2013) in this encyclopedia.

ARIMA-Based Time Series Model of Stochastic Wind Power Generation

DEFF Research Database (Denmark)

Chen, Peiyuan; Pedersen, Troels; Bak-Jensen, Birgitte

2010-01-01

This paper proposes a stochastic wind power model based on an autoregressive integrated moving average (ARIMA) process. The model takes into account the nonstationarity and physical limits of stochastic wind power generation. The model is constructed based on wind power measurement of one year from...... the Nysted offshore wind farm in Denmark. The proposed limited-ARIMA (LARIMA) model introduces a limiter and characterizes the stochastic wind power generation by mean level, temporal correlation and driving noise. The model is validated against the measurement in terms of temporal correlation...... and probability distribution. The LARIMA model outperforms a first-order transition matrix based discrete Markov model in terms of temporal correlation, probability distribution and model parameter number. The proposed LARIMA model is further extended to include the monthly variation of the stochastic wind power...

Stochastic Bus Dispatching Model untuk Optimalisasi Jumlah Bus Transjakarta Koridor 3

Directory of Open Access Journals (Sweden)

Zahedi Zahedi

2011-12-01

Full Text Available The increasing number of road user causing traffic jam finds out a way, busway. However, in its implementation, the number of fleet available does not enough to take the passengers. It results in the an amassed of passengers at several bus stops. This leads to passenger dissatisfaction satisfaction which eventually causes Transjakarta users to reuse private cars. Definitely this situation may builds up traffic jams. Stochastic Bus Dispatching Model is used to simulate public transportation that operates regularly. 

Electron heat transport in stochastic magnetic layer

International Nuclear Information System (INIS)

Becoulet, M.; Ghendrih, Ph.; Capes, H.; Grosman, A.

1999-06-01

Progress in the theoretical understanding of the local behaviour of the temperature field in ergodic layer was done in the framework of quasi-linear approach but this quasi-linear theory was not complete since the resonant modes coupling (due to stochasticity) was neglected. The stochastic properties of the magnetic field in the ergodic zone are now taken into account by a non-linear coupling of the temperature modes. The three-dimension heat transfer modelling in the ergodic-divertor configuration is performed by quasi-linear (ERGOT1) and non-linear (ERGOT2) numerical codes. The formalism and theoretical basis of both codes are presented. The most important effect that can be simulated with non-linear code is the averaged temperature profile flattening that occurs in the ergodic zone and the barrier creation that appears near the separatrix during divertor operation. (A.C.)

Modeling stochasticity in biochemical reaction networks

International Nuclear Information System (INIS)

Constantino, P H; Vlysidis, M; Smadbeck, P; Kaznessis, Y N

2016-01-01

Small biomolecular systems are inherently stochastic. Indeed, fluctuations of molecular species are substantial in living organisms and may result in significant variation in cellular phenotypes. The chemical master equation (CME) is the most detailed mathematical model that can describe stochastic behaviors. However, because of its complexity the CME has been solved for only few, very small reaction networks. As a result, the contribution of CME-based approaches to biology has been very limited. In this review we discuss the approach of solving CME by a set of differential equations of probability moments, called moment equations. We present different approaches to produce and to solve these equations, emphasizing the use of factorial moments and the zero information entropy closure scheme. We also provide information on the stability analysis of stochastic systems. Finally, we speculate on the utility of CME-based modeling formalisms, especially in the context of synthetic biology efforts. (topical review)

Two new algorithms to combine kriging with stochastic modelling

Science.gov (United States)

Venema, Victor; Lindau, Ralf; Varnai, Tamas; Simmer, Clemens

2010-05-01

Two main groups of statistical methods used in the Earth sciences are geostatistics and stochastic modelling. Geostatistical methods, such as various kriging algorithms, aim at estimating the mean value for every point as well as possible. In case of sparse measurements, such fields have less variability at small scales and a narrower distribution as the true field. This can lead to biases if a nonlinear process is simulated driven by such a kriged field. Stochastic modelling aims at reproducing the statistical structure of the data in space and time. One of the stochastic modelling methods, the so-called surrogate data approach, replicates the value distribution and power spectrum of a certain data set. While stochastic methods reproduce the statistical properties of the data, the location of the measurement is not considered. This requires the use of so-called constrained stochastic models. Because radiative transfer through clouds is a highly nonlinear process, it is essential to model the distribution (e.g. of optical depth, extinction, liquid water content or liquid water path) accurately. In addition, the correlations within the cloud field are important, especially because of horizontal photon transport. This explains the success of surrogate cloud fields for use in 3D radiative transfer studies. Up to now, however, we could only achieve good results for the radiative properties averaged over the field, but not for a radiation measurement located at a certain position. Therefore we have developed a new algorithm that combines the accuracy of stochastic (surrogate) modelling with the positioning capabilities of kriging. In this way, we can automatically profit from the large geostatistical literature and software. This algorithm is similar to the standard iterative amplitude adjusted Fourier transform (IAAFT) algorithm, but has an additional iterative step in which the surrogate field is nudged towards the kriged field. The nudging strength is gradually

Distributed parallel computing in stochastic modeling of groundwater systems.

Science.gov (United States)

Dong, Yanhui; Li, Guomin; Xu, Haizhen

2013-03-01

Stochastic modeling is a rapidly evolving, popular approach to the study of the uncertainty and heterogeneity of groundwater systems. However, the use of Monte Carlo-type simulations to solve practical groundwater problems often encounters computational bottlenecks that hinder the acquisition of meaningful results. To improve the computational efficiency, a system that combines stochastic model generation with MODFLOW-related programs and distributed parallel processing is investigated. The distributed computing framework, called the Java Parallel Processing Framework, is integrated into the system to allow the batch processing of stochastic models in distributed and parallel systems. As an example, the system is applied to the stochastic delineation of well capture zones in the Pinggu Basin in Beijing. Through the use of 50 processing threads on a cluster with 10 multicore nodes, the execution times of 500 realizations are reduced to 3% compared with those of a serial execution. Through this application, the system demonstrates its potential in solving difficult computational problems in practical stochastic modeling. © 2012, The Author(s). Groundwater © 2012, National Ground Water Association.

A chance-constrained stochastic approach to intermodal container routing problems.

Science.gov (United States)

Zhao, Yi; Liu, Ronghui; Zhang, Xi; Whiteing, Anthony

2018-01-01

We consider a container routing problem with stochastic time variables in a sea-rail intermodal transportation system. The problem is formulated as a binary integer chance-constrained programming model including stochastic travel times and stochastic transfer time, with the objective of minimising the expected total cost. Two chance constraints are proposed to ensure that the container service satisfies ship fulfilment and cargo on-time delivery with pre-specified probabilities. A hybrid heuristic algorithm is employed to solve the binary integer chance-constrained programming model. Two case studies are conducted to demonstrate the feasibility of the proposed model and to analyse the impact of stochastic variables and chance-constraints on the optimal solution and total cost.

Modelling phase equilibria for acid gas mixtures using the CPA equation of state. Part VI. Multicomponent mixtures with glycols relevant to oil and gas and to liquid or supercritical CO_2 transport applications

International Nuclear Information System (INIS)

Tsivintzelis, Ioannis; Kontogeorgis, Georgios M.

2016-01-01

Highlights: • CPA EoS was applied to predict the phase behaviour of multicomponent mixtures containing CO_2, glycols, water and alkanes. • Mixtures relevant to oil and gas, CO_2 capture and liquid or supercritical CO_2 transport applications were investigated. • Results are presented using various modelling approaches/association schemes. • The predicting ability of the model was evaluated against experimental data. • Conclusions for the best modelling approach are drawn. - Abstract: In this work the Cubic Plus Association (CPA) equation of state is applied to multicomponent mixtures containing CO_2 with alkanes, water, and glycols. Various modelling approaches are used i.e. different association schemes for pure CO_2 (assuming that it is a non-associating compound, or that it is a self-associating fluid with two, three or four association sites) and different possibilities for modelling mixtures of CO_2 with other hydrogen bonding fluids (only use of one interaction parameter k_i_j or assuming cross association interactions and obtaining the relevant parameters either via a combining rule or using an experimental value for the cross association energy). Initially, new binary interaction parameters were estimated for (CO_2 + glycol) binary mixtures. Having the binary parameters from the binary systems, the model was applied in a predictive way (i.e. no parameters were adjusted to data on ternary and multicomponent mixtures) to model the phase behaviour of ternary and quaternary systems with CO_2 and glycols. It is concluded that CPA performs satisfactorily for most multicomponent systems considered. Some differences between the various modelling approaches are observed. This work is the last part of a series of studies, which aim to arrive in a single “engineering approach” for applying CPA to acid gas mixtures, without introducing significant changes to the model. An overall assessment, based also on the obtained results of this series (Tsivintzelis

Stochastic lattice model of synaptic membrane protein domains.

Science.gov (United States)

Li, Yiwei; Kahraman, Osman; Haselwandter, Christoph A

2017-05-01

Neurotransmitter receptor molecules, concentrated in synaptic membrane domains along with scaffolds and other kinds of proteins, are crucial for signal transmission across chemical synapses. In common with other membrane protein domains, synaptic domains are characterized by low protein copy numbers and protein crowding, with rapid stochastic turnover of individual molecules. We study here in detail a stochastic lattice model of the receptor-scaffold reaction-diffusion dynamics at synaptic domains that was found previously to capture, at the mean-field level, the self-assembly, stability, and characteristic size of synaptic domains observed in experiments. We show that our stochastic lattice model yields quantitative agreement with mean-field models of nonlinear diffusion in crowded membranes. Through a combination of analytic and numerical solutions of the master equation governing the reaction dynamics at synaptic domains, together with kinetic Monte Carlo simulations, we find substantial discrepancies between mean-field and stochastic models for the reaction dynamics at synaptic domains. Based on the reaction and diffusion properties of synaptic receptors and scaffolds suggested by previous experiments and mean-field calculations, we show that the stochastic reaction-diffusion dynamics of synaptic receptors and scaffolds provide a simple physical mechanism for collective fluctuations in synaptic domains, the molecular turnover observed at synaptic domains, key features of the observed single-molecule trajectories, and spatial heterogeneity in the effective rates at which receptors and scaffolds are recycled at the cell membrane. Our work sheds light on the physical mechanisms and principles linking the collective properties of membrane protein domains to the stochastic dynamics that rule their molecular components.

The thermoballistic transport model a novel approach to charge carrier transport in semiconductors

CERN Document Server

Lipperheide, Reinhard

2014-01-01

The book presents a comprehensive survey of the thermoballistic approach to charge carrier transport in semiconductors. This semi-classical approach, which the authors have developed over the past decade, bridges the gap between the opposing drift-diffusion and ballistic  models of carrier transport. While incorporating basic features of the latter two models, the physical concept underlying the thermoballistic approach constitutes a novel, unifying scheme. It is based on the introduction of "ballistic configurations" arising from a random partitioning of the length of a semiconducting sample into ballistic transport intervals. Stochastic averaging of the ballistic carrier currents over the ballistic configurations results in a position-dependent thermoballistic current, which is the key element of the thermoballistic concept and forms  the point of departure for the calculation of all relevant transport properties. In the book, the thermoballistic concept and its implementation are developed in great detai...

STOCHASTIC CHARACTERISTICS AND MODELING OF RELATIVE ...

African Journals Online (AJOL)

Test

Results are highly accurate and promising for all models based on Lewis' criteria. ... hydrological cycle. Future increases in ... STOCHASTIC CHARACTERISTICS AND MODELING OF RELATIVE HUMIDITY OF OGUN BASIN, NIGERIA. 71 ...

A probabilistic graphical model based stochastic input model construction

International Nuclear Information System (INIS)

Wan, Jiang; Zabaras, Nicholas

2014-01-01

Model reduction techniques have been widely used in modeling of high-dimensional stochastic input in uncertainty quantification tasks. However, the probabilistic modeling of random variables projected into reduced-order spaces presents a number of computational challenges. Due to the curse of dimensionality, the underlying dependence relationships between these random variables are difficult to capture. In this work, a probabilistic graphical model based approach is employed to learn the dependence by running a number of conditional independence tests using observation data. Thus a probabilistic model of the joint PDF is obtained and the PDF is factorized into a set of conditional distributions based on the dependence structure of the variables. The estimation of the joint PDF from data is then transformed to estimating conditional distributions under reduced dimensions. To improve the computational efficiency, a polynomial chaos expansion is further applied to represent the random field in terms of a set of standard random variables. This technique is combined with both linear and nonlinear model reduction methods. Numerical examples are presented to demonstrate the accuracy and efficiency of the probabilistic graphical model based stochastic input models. - Highlights: • Data-driven stochastic input models without the assumption of independence of the reduced random variables. • The problem is transformed to a Bayesian network structure learning problem. • Examples are given in flows in random media

Deterministic and stochastic CTMC models from Zika disease transmission

Science.gov (United States)

Zevika, Mona; Soewono, Edy

2018-03-01

Zika infection is one of the most important mosquito-borne diseases in the world. Zika virus (ZIKV) is transmitted by many Aedes-type mosquitoes including Aedes aegypti. Pregnant women with the Zika virus are at risk of having a fetus or infant with a congenital defect and suffering from microcephaly. Here, we formulate a Zika disease transmission model using two approaches, a deterministic model and a continuous-time Markov chain stochastic model. The basic reproduction ratio is constructed from a deterministic model. Meanwhile, the CTMC stochastic model yields an estimate of the probability of extinction and outbreaks of Zika disease. Dynamical simulations and analysis of the disease transmission are shown for the deterministic and stochastic models.

Weather Derivatives and Stochastic Modelling of Temperature

Directory of Open Access Journals (Sweden)

Fred Espen Benth

2011-01-01

Full Text Available We propose a continuous-time autoregressive model for the temperature dynamics with volatility being the product of a seasonal function and a stochastic process. We use the Barndorff-Nielsen and Shephard model for the stochastic volatility. The proposed temperature dynamics is flexible enough to model temperature data accurately, and at the same time being analytically tractable. Futures prices for commonly traded contracts at the Chicago Mercantile Exchange on indices like cooling- and heating-degree days and cumulative average temperatures are computed, as well as option prices on them.

Stochastic Modeling Of Wind Turbine Drivetrain Components

DEFF Research Database (Denmark)

Rafsanjani, Hesam Mirzaei; Sørensen, John Dalsgaard

2014-01-01

reliable components are needed for wind turbine. In this paper focus is on reliability of critical components in drivetrain such as bearings and shafts. High failure rates of these components imply a need for more reliable components. To estimate the reliability of these components, stochastic models...... are needed for initial defects and damage accumulation. In this paper, stochastic models are formulated considering some of the failure modes observed in these components. The models are based on theoretical considerations, manufacturing uncertainties, size effects of different scales. It is illustrated how...

Transport appraisal and Monte Carlo simulation by use of the CBA-DK model

DEFF Research Database (Denmark)

Salling, Kim Bang; Leleur, Steen

2011-01-01

calculation, where risk analysis is carried out using Monte Carlo simulation. Special emphasis has been placed on the separation between inherent randomness in the modeling system and lack of knowledge. These two concepts have been defined in terms of variability (ontological uncertainty) and uncertainty......This paper presents the Danish CBA-DK software model for assessment of transport infrastructure projects. The assessment model is based on both a deterministic calculation following the cost-benefit analysis (CBA) methodology in a Danish manual from the Ministry of Transport and on a stochastic...... (epistemic uncertainty). After a short introduction to deterministic calculation resulting in some evaluation criteria a more comprehensive evaluation of the stochastic calculation is made. Especially, the risk analysis part of CBA-DK, with considerations about which probability distributions should be used...

Applied stochastic modelling

CERN Document Server

Morgan, Byron JT; Tanner, Martin Abba; Carlin, Bradley P

2008-01-01

Introduction and Examples Introduction Examples of data sets Basic Model Fitting Introduction Maximum-likelihood estimation for a geometric model Maximum-likelihood for the beta-geometric model Modelling polyspermy Which model? What is a model for? Mechanistic models Function Optimisation Introduction MATLAB: graphs and finite differences Deterministic search methods Stochastic search methods Accuracy and a hybrid approach Basic Likelihood ToolsIntroduction Estimating standard errors and correlations Looking at surfaces: profile log-likelihoods Confidence regions from profiles Hypothesis testing in model selectionScore and Wald tests Classical goodness of fit Model selection biasGeneral Principles Introduction Parameterisation Parameter redundancy Boundary estimates Regression and influence The EM algorithm Alternative methods of model fitting Non-regular problemsSimulation Techniques Introduction Simulating random variables Integral estimation Verification Monte Carlo inference Estimating sampling distributi...

On changes of measure in stochastic volatility models

Directory of Open Access Journals (Sweden)

Bernard Wong

2006-01-01

models. This had led many researchers to “assume the condition away,” even though the condition is not innocuous, and nonsensical results can occur if it is in fact not satisfied. We provide an applicable theorem to check the conditions for a general class of Markovian stochastic volatility models. As an example we will also provide a detailed analysis of the Stein and Stein and Heston stochastic volatility models.

Gompertzian stochastic model with delay effect to cervical cancer growth

International Nuclear Information System (INIS)

Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti; Bahar, Arifah

2015-01-01

In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits

Gompertzian stochastic model with delay effect to cervical cancer growth

Energy Technology Data Exchange (ETDEWEB)

Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti [Faculty of Industrial Sciences and Technology, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300 Gambang, Pahang (Malaysia); Bahar, Arifah [Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor and UTM Centre for Industrial and Applied Mathematics (UTM-CIAM), Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia)

2015-02-03

In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.

A turbulence model in mixtures. First part: Statistical description of mixture

International Nuclear Information System (INIS)

Besnard, D.

1987-03-01

Classical theory of mixtures gives a model for molecular mixtures. This kind of model is based on a small gradient approximation for concentration, temperature, and pression. We present here a mixture model, allowing for large gradients in the flow. We also show that, with a local balance assumption between material diffusion and flow gradients evolution, we obtain a model similar to those mentioned above [fr

Stochastic Modelling, Analysis, and Simulations of the Solar Cycle Dynamic Process

Science.gov (United States)

Turner, Douglas C.; Ladde, Gangaram S.

2018-03-01

Analytical solutions, discretization schemes and simulation results are presented for the time delay deterministic differential equation model of the solar dynamo presented by Wilmot-Smith et al. In addition, this model is extended under stochastic Gaussian white noise parametric fluctuations. The introduction of stochastic fluctuations incorporates variables affecting the dynamo process in the solar interior, estimation error of parameters, and uncertainty of the α-effect mechanism. Simulation results are presented and analyzed to exhibit the effects of stochastic parametric volatility-dependent perturbations. The results generalize and extend the work of Hazra et al. In fact, some of these results exhibit the oscillatory dynamic behavior generated by the stochastic parametric additative perturbations in the absence of time delay. In addition, the simulation results of the modified stochastic models influence the change in behavior of the very recently developed stochastic model of Hazra et al.

Stochastic models of the Social Security trust funds.

Science.gov (United States)

Burdick, Clark; Manchester, Joyce

Each year in March, the Board of Trustees of the Social Security trust funds reports on the current and projected financial condition of the Social Security programs. Those programs, which pay monthly benefits to retired workers and their families, to the survivors of deceased workers, and to disabled workers and their families, are financed through the Old-Age, Survivors, and Disability Insurance (OASDI) Trust Funds. In their 2003 report, the Trustees present, for the first time, results from a stochastic model of the combined OASDI trust funds. Stochastic modeling is an important new tool for Social Security policy analysis and offers the promise of valuable new insights into the financial status of the OASDI trust funds and the effects of policy changes. The results presented in this article demonstrate that several stochastic models deliver broadly consistent results even though they use very different approaches and assumptions. However, they also show that the variation in trust fund outcomes differs as the approach and assumptions are varied. Which approach and assumptions are best suited for Social Security policy analysis remains an open question. Further research is needed before the promise of stochastic modeling is fully realized. For example, neither parameter uncertainty nor variability in ultimate assumption values is recognized explicitly in the analyses. Despite this caveat, stochastic modeling results are already shedding new light on the range and distribution of trust fund outcomes that might occur in the future.

Examining the cost efficiency of Chinese hydroelectric companies using a finite mixture model

International Nuclear Information System (INIS)

Barros, Carlos Pestana; Chen, Zhongfei; Managi, Shunsuke; Antunes, Olinda Sequeira

2013-01-01

This paper evaluates the operational activities of Chinese hydroelectric power companies over the period 2000–2010 using a finite mixture model that controls for unobserved heterogeneity. In so doing, a stochastic frontier latent class model, which allows for the existence of different technologies, is adopted to estimate cost frontiers. This procedure not only enables us to identify different groups among the hydro-power companies analysed, but also permits the analysis of their cost efficiency. The main result is that three groups are identified in the sample, each equipped with different technologies, suggesting that distinct business strategies need to be adapted to the characteristics of China's hydro-power companies. Some managerial implications are developed. - Highlights: ► This paper evaluates the operational activities of Chinese electricity hydric companies. ► This study uses data from 2000 to 2010 using a finite mixture model. ► The model procedure identifies different groups of Chinese hydric companies analysed. ► Three groups are identified in the sample, each equipped with completely different “technologies”. ► This suggests that distinct business strategies need to be adapted to the characteristics of the hydric companies

Biochemical Network Stochastic Simulator (BioNetS: software for stochastic modeling of biochemical networks

Directory of Open Access Journals (Sweden)

Elston Timothy C

2004-03-01

Full Text Available Abstract Background Intrinsic fluctuations due to the stochastic nature of biochemical reactions can have large effects on the response of biochemical networks. This is particularly true for pathways that involve transcriptional regulation, where generally there are two copies of each gene and the number of messenger RNA (mRNA molecules can be small. Therefore, there is a need for computational tools for developing and investigating stochastic models of biochemical networks. Results We have developed the software package Biochemical Network Stochastic Simulator (BioNetS for efficientlyand accurately simulating stochastic models of biochemical networks. BioNetS has a graphical user interface that allows models to be entered in a straightforward manner, and allows the user to specify the type of random variable (discrete or continuous for each chemical species in the network. The discrete variables are simulated using an efficient implementation of the Gillespie algorithm. For the continuous random variables, BioNetS constructs and numerically solvesthe appropriate chemical Langevin equations. The software package has been developed to scale efficiently with network size, thereby allowing large systems to be studied. BioNetS runs as a BioSpice agent and can be downloaded from http://www.biospice.org. BioNetS also can be run as a stand alone package. All the required files are accessible from http://x.amath.unc.edu/BioNetS. Conclusions We have developed BioNetS to be a reliable tool for studying the stochastic dynamics of large biochemical networks. Important features of BioNetS are its ability to handle hybrid models that consist of both continuous and discrete random variables and its ability to model cell growth and division. We have verified the accuracy and efficiency of the numerical methods by considering several test systems.

Electricity Market Stochastic Dynamic Model and Its Mean Stability Analysis

Directory of Open Access Journals (Sweden)

Zhanhui Lu

2014-01-01

Full Text Available Based on the deterministic dynamic model of electricity market proposed by Alvarado, a stochastic electricity market model, considering the random nature of demand sides, is presented in this paper on the assumption that generator cost function and consumer utility function are quadratic functions. The stochastic electricity market model is a generalization of the deterministic dynamic model. Using the theory of stochastic differential equations, stochastic process theory, and eigenvalue techniques, the determining conditions of the mean stability for this electricity market model under small Gauss type random excitation are provided and testified theoretically. That is, if the demand elasticity of suppliers is nonnegative and the demand elasticity of consumers is negative, then the stochastic electricity market model is mean stable. It implies that the stability can be judged directly by initial data without any computation. Taking deterministic electricity market data combined with small Gauss type random excitation as numerical samples to interpret random phenomena from a statistical perspective, the results indicate the conclusions above are correct, valid, and practical.

Aspects if stochastic models for short-term hydropower scheduling and bidding

Energy Technology Data Exchange (ETDEWEB)

Belsnes, Michael Martin [Sintef Energy, Trondheim (Norway); Follestad, Turid [Sintef Energy, Trondheim (Norway); Wolfgang, Ove [Sintef Energy, Trondheim (Norway); Fosso, Olav B. [Dep. of electric power engineering NTNU, Trondheim (Norway)

2012-07-01

This report discusses challenges met when turning from deterministic to stochastic decision support models for short-term hydropower scheduling and bidding. The report describes characteristics of the short-term scheduling and bidding problem, different market and bidding strategies, and how a stochastic optimization model can be formulated. A review of approaches for stochastic short-term modelling and stochastic modelling for the input variables inflow and market prices is given. The report discusses methods for approximating the predictive distribution of uncertain variables by scenario trees. Benefits of using a stochastic over a deterministic model are illustrated by a case study, where increased profit is obtained to a varying degree depending on the reservoir filling and price structure. Finally, an approach for assessing the effect of using a size restricted scenario tree to approximate the predictive distribution for stochastic input variables is described. The report is a summary of the findings of Work package 1 of the research project #Left Double Quotation Mark#Optimal short-term scheduling of wind and hydro resources#Right Double Quotation Mark#. The project aims at developing a prototype for an operational stochastic short-term scheduling model. Based on the investigations summarized in the report, it is concluded that using a deterministic equivalent formulation of the stochastic optimization problem is convenient and sufficient for obtaining a working prototype. (author)

Characterizing economic trends by Bayesian stochastic model specifi cation search

OpenAIRE

Grassi, Stefano; Proietti, Tommaso

2010-01-01

We apply a recently proposed Bayesian model selection technique, known as stochastic model specification search, for characterising the nature of the trend in macroeconomic time series. We illustrate that the methodology can be quite successfully applied to discriminate between stochastic and deterministic trends. In particular, we formulate autoregressive models with stochastic trends components and decide on whether a specific feature of the series, i.e. the underlying level and/or the rate...

Index Option Pricing Models with Stochastic Volatility and Stochastic Interest Rates

NARCIS (Netherlands)

Jiang, G.J.; van der Sluis, P.J.

2000-01-01

This paper specifies a multivariate stochastic volatility (SV) model for the S&P500 index and spot interest rate processes. We first estimate the multivariate SV model via the efficient method of moments (EMM) technique based on observations of underlying state variables, and then investigate the

Plasma transport in mixed magnetic topologies

International Nuclear Information System (INIS)

Hegna, C.C.; Callen, J.D.

1992-12-01

A simple model is introduced to illustrate some features concerning anomalous transport associated with magnetic turbulence. For magnetic topologies that are described as bands of stochasticity separated by regions with good flux surfaces, the transport coefficients deviate significantly from those describing completely stochastic magnetic fields. It is possible to have the electron heat diffusivity exceed a runaway electron diffusion coefficient, despite the existence of widespread magnetic stochasticity. Comparing the ratios of transport coefficients is not an accurate way to determine whether anomalous plasma transport is controlled by electrostatic or electromagnetic fluctuations

Dynamic optimization deterministic and stochastic models

CERN Document Server

Hinderer, Karl; Stieglitz, Michael

2016-01-01

This book explores discrete-time dynamic optimization and provides a detailed introduction to both deterministic and stochastic models. Covering problems with finite and infinite horizon, as well as Markov renewal programs, Bayesian control models and partially observable processes, the book focuses on the precise modelling of applications in a variety of areas, including operations research, computer science, mathematics, statistics, engineering, economics and finance. Dynamic Optimization is a carefully presented textbook which starts with discrete-time deterministic dynamic optimization problems, providing readers with the tools for sequential decision-making, before proceeding to the more complicated stochastic models. The authors present complete and simple proofs and illustrate the main results with numerous examples and exercises (without solutions). With relevant material covered in four appendices, this book is completely self-contained.

Stochastic models for atmospheric dispersion

DEFF Research Database (Denmark)

Ditlevsen, Ove Dalager

2003-01-01

Simple stochastic differential equation models have been applied by several researchers to describe the dispersion of tracer particles in the planetary atmospheric boundary layer and to form the basis for computer simulations of particle paths. To obtain the drift coefficient, empirical vertical...... positions close to the boundaries. Different rules have been suggested in the literature with justifications based on simulation studies. Herein the relevant stochastic differential equation model is formulated in a particular way. The formulation is based on the marginal transformation of the position...... velocity distributions that depend on height above the ground both with respect to standard deviation and skewness are substituted into the stationary Fokker/Planck equation. The particle position distribution is taken to be uniform *the well/mixed condition( and also a given dispersion coefficient...

Hopf bifurcation of the stochastic model on business cycle

International Nuclear Information System (INIS)

Xu, J; Wang, H; Ge, G

2008-01-01

A stochastic model on business cycle was presented in thas paper. Simplifying the model through the quasi Hamiltonian theory, the Ito diffusion process was obtained. According to Oseledec multiplicative ergodic theory and singular boundary theory, the conditions of local and global stability were acquired. Solving the stationary FPK equation and analyzing the stationary probability density, the stochastic Hopf bifurcation was explained. The result indicated that the change of parameter awas the key factor to the appearance of the stochastic Hopf bifurcation

Stochastic models for predicting pitting corrosion damage of HLRW containers

International Nuclear Information System (INIS)

Henshall, G.A.

1991-10-01

Stochastic models for predicting aqueous pitting corrosion damage of high-level radioactive-waste containers are described. These models could be used to predict the time required for the first pit to penetrate a container and the increase in the number of breaches at later times, both of which would be useful in the repository system performance analysis. Monte Carlo implementations of the stochastic models are described, and predictions of induction time, survival probability and pit depth distributions are presented. These results suggest that the pit nucleation probability decreases with exposure time and that pit growth may be a stochastic process. The advantages and disadvantages of the stochastic approach, methods for modeling the effects of environment, and plans for future work are discussed

Brain-inspired Stochastic Models and Implementations

KAUST Repository

Al-Shedivat, Maruan

2015-05-12

One of the approaches to building artificial intelligence (AI) is to decipher the princi- ples of the brain function and to employ similar mechanisms for solving cognitive tasks, such as visual perception or natural language understanding, using machines. The recent breakthrough, named deep learning, demonstrated that large multi-layer networks of arti- ficial neural-like computing units attain remarkable performance on some of these tasks. Nevertheless, such artificial networks remain to be very loosely inspired by the brain, which rich structures and mechanisms may further suggest new algorithms or even new paradigms of computation. In this thesis, we explore brain-inspired probabilistic mechanisms, such as neural and synaptic stochasticity, in the context of generative models. The two questions we ask here are: (i) what kind of models can describe a neural learning system built of stochastic components? and (ii) how can we implement such systems e ̆ciently? To give specific answers, we consider two well known models and the corresponding neural architectures: the Naive Bayes model implemented with a winner-take-all spiking neural network and the Boltzmann machine implemented in a spiking or non-spiking fashion. We propose and analyze an e ̆cient neuromorphic implementation of the stochastic neu- ral firing mechanism and study the e ̄ects of synaptic unreliability on learning generative energy-based models implemented with neural networks.

Stochastic models to simulate paratuberculosis in dairy herds

DEFF Research Database (Denmark)

Nielsen, Søren Saxmose; Weber, M.F.; Kudahl, Anne Margrethe Braad

2011-01-01

Stochastic simulation models are widely accepted as a means of assessing the impact of changes in daily management and the control of different diseases, such as paratuberculosis, in dairy herds. This paper summarises and discusses the assumptions of four stochastic simulation models and their use...... the models are somewhat different in their underlying principles and do put slightly different values on the different strategies, their overall findings are similar. Therefore, simulation models may be useful in planning paratuberculosis strategies in dairy herds, although as with all models caution...

Numerical computation of the transport matrix in toroidal plasma with a stochastic magnetic field

Science.gov (United States)

Zhu, Siqiang; Chen, Dunqiang; Dai, Zongliang; Wang, Shaojie

2018-04-01

A new numerical method, based on integrating along the full orbit of guiding centers, to compute the transport matrix is realized. The method is successfully applied to compute the phase-space diffusion tensor of passing electrons in a tokamak with a stochastic magnetic field. The new method also computes the Lagrangian correlation function, which can be used to evaluate the Lagrangian correlation time and the turbulence correlation length. For the case of the stochastic magnetic field, we find that the order of magnitude of the parallel correlation length can be estimated by qR0, as expected previously.

Stochastic population oscillations in spatial predator-prey models

International Nuclear Information System (INIS)

Taeuber, Uwe C

2011-01-01

It is well-established that including spatial structure and stochastic noise in models for predator-prey interactions invalidates the classical deterministic Lotka-Volterra picture of neutral population cycles. In contrast, stochastic models yield long-lived, but ultimately decaying erratic population oscillations, which can be understood through a resonant amplification mechanism for density fluctuations. In Monte Carlo simulations of spatial stochastic predator-prey systems, one observes striking complex spatio-temporal structures. These spreading activity fronts induce persistent correlations between predators and prey. In the presence of local particle density restrictions (finite prey carrying capacity), there exists an extinction threshold for the predator population. The accompanying continuous non-equilibrium phase transition is governed by the directed-percolation universality class. We employ field-theoretic methods based on the Doi-Peliti representation of the master equation for stochastic particle interaction models to (i) map the ensuing action in the vicinity of the absorbing state phase transition to Reggeon field theory, and (ii) to quantitatively address fluctuation-induced renormalizations of the population oscillation frequency, damping, and diffusion coefficients in the species coexistence phase.

Linking agent-based models and stochastic models of financial markets.

Science.gov (United States)

Feng, Ling; Li, Baowen; Podobnik, Boris; Preis, Tobias; Stanley, H Eugene

2012-05-29

It is well-known that financial asset returns exhibit fat-tailed distributions and long-term memory. These empirical features are the main objectives of modeling efforts using (i) stochastic processes to quantitatively reproduce these features and (ii) agent-based simulations to understand the underlying microscopic interactions. After reviewing selected empirical and theoretical evidence documenting the behavior of traders, we construct an agent-based model to quantitatively demonstrate that "fat" tails in return distributions arise when traders share similar technical trading strategies and decisions. Extending our behavioral model to a stochastic model, we derive and explain a set of quantitative scaling relations of long-term memory from the empirical behavior of individual market participants. Our analysis provides a behavioral interpretation of the long-term memory of absolute and squared price returns: They are directly linked to the way investors evaluate their investments by applying technical strategies at different investment horizons, and this quantitative relationship is in agreement with empirical findings. Our approach provides a possible behavioral explanation for stochastic models for financial systems in general and provides a method to parameterize such models from market data rather than from statistical fitting.

Modelling of an homogeneous equilibrium mixture model

International Nuclear Information System (INIS)

Bernard-Champmartin, A.; Poujade, O.; Mathiaud, J.; Mathiaud, J.; Ghidaglia, J.M.

2014-01-01

We present here a model for two phase flows which is simpler than the 6-equations models (with two densities, two velocities, two temperatures) but more accurate than the standard mixture models with 4 equations (with two densities, one velocity and one temperature). We are interested in the case when the two-phases have been interacting long enough for the drag force to be small but still not negligible. The so-called Homogeneous Equilibrium Mixture Model (HEM) that we present is dealing with both mixture and relative quantities, allowing in particular to follow both a mixture velocity and a relative velocity. This relative velocity is not tracked by a conservation law but by a closure law (drift relation), whose expression is related to the drag force terms of the two-phase flow. After the derivation of the model, a stability analysis and numerical experiments are presented. (authors)

Stochastic differential equation model to Prendiville processes

International Nuclear Information System (INIS)

Granita; Bahar, Arifah

2015-01-01

The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution

Stochastic differential equation model to Prendiville processes

Energy Technology Data Exchange (ETDEWEB)

Granita, E-mail: granitafc@gmail.com [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); Bahar, Arifah [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); UTM Center for Industrial & Applied Mathematics (UTM-CIAM) (Malaysia)

2015-10-22

The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.

A Two-Stage Maximum Entropy Prior of Location Parameter with a Stochastic Multivariate Interval Constraint and Its Properties

Directory of Open Access Journals (Sweden)

Hea-Jung Kim

2016-05-01

Full Text Available This paper proposes a two-stage maximum entropy prior to elicit uncertainty regarding a multivariate interval constraint of the location parameter of a scale mixture of normal model. Using Shannon’s entropy, this study demonstrates how the prior, obtained by using two stages of a prior hierarchy, appropriately accounts for the information regarding the stochastic constraint and suggests an objective measure of the degree of belief in the stochastic constraint. The study also verifies that the proposed prior plays the role of bridging the gap between the canonical maximum entropy prior of the parameter with no interval constraint and that with a certain multivariate interval constraint. It is shown that the two-stage maximum entropy prior belongs to the family of rectangle screened normal distributions that is conjugate for samples from a normal distribution. Some properties of the prior density, useful for developing a Bayesian inference of the parameter with the stochastic constraint, are provided. We also propose a hierarchical constrained scale mixture of normal model (HCSMN, which uses the prior density to estimate the constrained location parameter of a scale mixture of normal model and demonstrates the scope of its applicability.

Stochastic growth logistic model with aftereffect for batch fermentation process

Energy Technology Data Exchange (ETDEWEB)

Rosli, Norhayati; Ayoubi, Tawfiqullah [Faculty of Industrial Sciences and Technology, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300 Gambang, Pahang (Malaysia); Bahar, Arifah; Rahman, Haliza Abdul [Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia); Salleh, Madihah Md [Department of Biotechnology Industry, Faculty of Biosciences and Bioengineering, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia)

2014-06-19

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

Stochastic growth logistic model with aftereffect for batch fermentation process

Science.gov (United States)

Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md

2014-06-01

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

Stochastic growth logistic model with aftereffect for batch fermentation process

International Nuclear Information System (INIS)

Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md

2014-01-01

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits

Numerical Modelling of Suspended Transport and Deposition of Highway Deposited Sediments

DEFF Research Database (Denmark)

Bentzen, Thomas Ruby; Larsen, Torben; Bach, Christine

Good data for calibration and validation of numerical models are of high importance. In the natural environment data can be hard to archive and the stochastic nature have governing influence on the data archived. Hence for modelling of suspended transport and deposition of particles, originating ...... from the highway surfaces, in highway detention ponds, four experiments are carried out. To simplify the complexity of a real pond and for easy control and measurement the sediment transports where carried out in two rectangular channels....

Long-range correlations in a simple stochastic model of coupled transport

International Nuclear Information System (INIS)

Larralde, Hernan; Sanders, David P

2009-01-01

We study coupled transport in the nonequilibrium stationary state of a model consisting of independent random walkers, moving along a one-dimensional channel, which carry a conserved energy-like quantity, with density and temperature gradients imposed by reservoirs at the ends of the channel. In our model, walkers interact with other walkers at the same site by sharing energy at each time step, but the amount of energy carried does not affect the motion of the walkers. We find that already in this simple model long-range correlations arise in the nonequilibrium stationary state which are similar to those observed in more realistic models of coupled transport. We derive an analytical expression for the source of these correlations, which we use to obtain semi-analytical results for the correlations themselves assuming a local-equilibrium hypothesis. These are in very good agreement with results from direct numerical simulations.

Towards Model Checking Stochastic Process Algebra

NARCIS (Netherlands)

Hermanns, H.; Grieskamp, W.; Santen, T.; Katoen, Joost P.; Stoddart, B.; Meyer-Kayser, J.; Siegle, M.

2000-01-01

Stochastic process algebras have been proven useful because they allow behaviour-oriented performance and reliability modelling. As opposed to traditional performance modelling techniques, the behaviour- oriented style supports composition and abstraction in a natural way. However, analysis of

Methodology for predicting oily mixture properties in the mathematical modeling of molecular distillation

Directory of Open Access Journals (Sweden)

M. F. Gayol

2017-06-01

Full Text Available A methodology for predicting the thermodynamic and transport properties of a multi-component oily mixture, in which the different mixture components are grouped into a small number of pseudo components is shown. This prediction of properties is used in the mathematical modeling of molecular distillation, which consists of a system of differential equations in partial derivatives, according to the principles of the Transport Phenomena and is solved by an implicit finite difference method using a computer code. The mathematical model was validated with experimental data, specifically the molecular distillation of a deodorizer distillate (DD of sunflower oil. The results obtained were satisfactory, with errors less than 10% with respect to the experimental data in a temperature range in which it is possible to apply the proposed method.

Methodology for predicting oily mixture properties in the mathematical modeling of molecular distillation

International Nuclear Information System (INIS)

Gayol, M.F.; Pramparo, M.C.; Miró Erdmann, S.M.

2017-01-01

A methodology for predicting the thermodynamic and transport properties of a multi-component oily mixture, in which the different mixture components are grouped into a small number of pseudo components is shown. This prediction of properties is used in the mathematical modeling of molecular distillation, which consists of a system of differential equations in partial derivatives, according to the principles of the Transport Phenomena and is solved by an implicit finite difference method using a computer code. The mathematical model was validated with experimental data, specifically the molecular distillation of a deodorizer distillate (DD) of sunflower oil. The results obtained were satisfactory, with errors less than 10% with respect to the experimental data in a temperature range in which it is possible to apply the proposed method. [es

Stochastic models for predicting environmental impact in aquatic ecosystems

International Nuclear Information System (INIS)

Stewart-Oaten, A.

1986-01-01

The purpose of stochastic predictions are discussed in relation to the environmental impacts of nuclear power plants on aquatic ecosystems. One purpose is to aid in making rational decisions about whether a power plant should be built, where, and how it should be designed. The other purpose is to check on the models themselves in the light of what eventually happens. The author discusses the role or statistical decision theory in the decision-making problem. Various types of stochastic models and their problems are presented. In addition some suggestions are made for generating usable stochastic models, and checking and improving on them. 12 references

Wave-optics modeling of the optical-transport line for passive optical stochastic cooling

Science.gov (United States)

Andorf, M. B.; Lebedev, V. A.; Piot, P.; Ruan, J.

2018-03-01

Optical stochastic cooling (OSC) is expected to enable fast cooling of dense particle beams. Transition from microwave to optical frequencies enables an achievement of stochastic cooling rates which are orders of magnitude higher than ones achievable with the classical microwave based stochastic cooling systems. A subsystemcritical to the OSC scheme is the focusing optics used to image radiation from the upstream "pickup" undulator to the downstream "kicker" undulator. In this paper, we present simulation results using wave-optics calculation carried out with the SYNCHROTRON RADIATION WORKSHOP (SRW). Our simulations are performed in support to a proof-of-principle experiment planned at the Integrable Optics Test Accelerator (IOTA) at Fermilab. The calculations provide an estimate of the energy kick received by a 100-MeV electron as it propagates in the kicker undulator and interacts with the electromagnetic pulse it radiated at an earlier time while traveling through the pickup undulator.

Introduction to modeling and analysis of stochastic systems

CERN Document Server

Kulkarni, V G

2011-01-01

This is an introductory-level text on stochastic modeling. It is suited for undergraduate students in engineering, operations research, statistics, mathematics, actuarial science, business management, computer science, and public policy. It employs a large number of examples to teach the students to use stochastic models of real-life systems to predict their performance, and use this analysis to design better systems. The book is devoted to the study of important classes of stochastic processes: discrete and continuous time Markov processes, Poisson processes, renewal and regenerative processes, semi-Markov processes, queueing models, and diffusion processes. The book systematically studies the short-term and the long-term behavior, cost/reward models, and first passage times. All the material is illustrated with many examples, and case studies. The book provides a concise review of probability in the appendix. The book emphasizes numerical answers to the problems. A collection of MATLAB programs to accompany...

Relationships of dispersive mass transport and stochastic convective flow through hydrologic systems

International Nuclear Information System (INIS)

Simmons, C.S.

1981-01-01

Uncertainty in water flow velocity appears to be a major factor in determining the magnitude of contaminant dispersion expected in a ground water system. This report discusses some concepts and mathematical methods relating dispersive contaminant transport to stochastic aspects of ground water flow. The theory developed should not be construed as absolutely rigorous mathematics, but is presented with the intention of clarifying the physical concepts

Stochastic Averaging and Stochastic Extremum Seeking

CERN Document Server

Liu, Shu-Jun

2012-01-01

Stochastic Averaging and Stochastic Extremum Seeking develops methods of mathematical analysis inspired by the interest in reverse engineering  and analysis of bacterial  convergence by chemotaxis and to apply similar stochastic optimization techniques in other environments. The first half of the text presents significant advances in stochastic averaging theory, necessitated by the fact that existing theorems are restricted to systems with linear growth, globally exponentially stable average models, vanishing stochastic perturbations, and prevent analysis over infinite time horizon. The second half of the text introduces stochastic extremum seeking algorithms for model-free optimization of systems in real time using stochastic perturbations for estimation of their gradients. Both gradient- and Newton-based algorithms are presented, offering the user the choice between the simplicity of implementation (gradient) and the ability to achieve a known, arbitrary convergence rate (Newton). The design of algorithms...

Complementary programs for stochastic analysis of radionuclide transport

International Nuclear Information System (INIS)

Gomez Hernandez, J.J.

1993-01-01

The present programs will permit to analyze the risks using parametric and non parametric technic. The programs are presented in two groups: 1) variable estimation through indicator krigeaje and variable estimation by Cokrigeaje 2) variable simulation with multi gassiness stochastic model and non gassiness. This report includes new programs for the non parametric geostatistics

Modelling of diesel spray flame under engine-like conditions using an accelerated eulerian stochastic fields method: A convergence study of the number of stochastic fields

DEFF Research Database (Denmark)

Pang, Kar Mun; Jangi, Mehdi; Bai, X.-S.

generated similar results. The principal motivation for ESF compared to Lagrangian particle based PDF is the relative ease of implementation of the former into Eulerian computational fluid dynamics(CFD) codes [5]. Several works have attempted to implement the ESF model for the simulations of diesel spray......The use of transported Probability Density Function(PDF) methods allows a single model to compute the autoignition, premixed mode and diffusion flame of diesel combustion under engine-like conditions [1,2]. The Lagrangian particle based transported PDF models have been validated across a wide range...... combustion under engine-like conditions.The current work aims to further evaluate the performance of the ESF model in this application, with an emphasis on examining the convergence of the number of stochastic fields, nsf. Five test conditions, covering both the conventional diesel combustion and low...

Ion swarm data for electrical discharge modeling in air and flue gas mixtures

International Nuclear Information System (INIS)

Nelson, D.; Benhenni, M.; Eichwald, O.; Yousfi, M.

2003-01-01

The first step of this work is the determination of the elastic and inelastic ion-molecule collision cross sections for the main ions (N 2 + , O 2 + , CO 2 + , H 2 O + and O - ) usually present either in the air or flue gas discharges. The obtained cross section sets, given for ion kinetic energies not exceeding 100 eV, correspond to the interactions of each ion with its parent molecule (symmetric case) or nonparent molecule (asymmetric case). Then by using these different cross section sets, it is possible to obtain the ion swarm data for the different gas mixtures involving N 2 , CO 2 , H 2 O and O 2 molecules whatever their relative proportions. These ion swarm data are obtained from an optimized Monte Carlo method well adapted for the ion transport in gas mixtures. This also allows us to clearly show that the classical linear approximations usually applied for the ion swarm data in mixtures such as Blanc's law are far to be valid. Then, the ion swarm data are given in three cases of gas mixtures: a dry air (80% N 2 , 20% O 2 ), a ternary gas mixture (82% N 2 , 12% CO 2 , 6% O 2 ) and a typical flue gas (76% N 2 , 12% CO 2 , 6% O 2 , 6% H 2 O). From these reliable ion swarm data, electrical discharge modeling for a wire to plane electrode configuration has been carried out in these three mixtures at the atmospheric pressure for different applied voltages. Under the same discharge conditions, large discrepancies in the streamer formation and propagation have been observed in these three mixture cases. They are due to the deviations existing not only between the different effective electron-molecule ionization rates but also between the ion transport properties mainly because of the presence of a highly polar molecule such as H 2 O. This emphasizes the necessity to properly consider the ion transport in the discharge modeling

Predicting Footbridge Response using Stochastic Load Models

DEFF Research Database (Denmark)

Pedersen, Lars; Frier, Christian

2013-01-01

Walking parameters such as step frequency, pedestrian mass, dynamic load factor, etc. are basically stochastic, although it is quite common to adapt deterministic models for these parameters. The present paper considers a stochastic approach to modeling the action of pedestrians, but when doing so...... decisions need to be made in terms of statistical distributions of walking parameters and in terms of the parameters describing the statistical distributions. The paper explores how sensitive computations of bridge response are to some of the decisions to be made in this respect. This is useful...

Threshold Dynamics of a Stochastic Chemostat Model with Two Nutrients and One Microorganism

Directory of Open Access Journals (Sweden)

Jian Zhang

2017-01-01

Full Text Available A new stochastic chemostat model with two substitutable nutrients and one microorganism is proposed and investigated. Firstly, for the corresponding deterministic model, the threshold for extinction and permanence of the microorganism is obtained by analyzing the stability of the equilibria. Then, for the stochastic model, the threshold of the stochastic chemostat for extinction and permanence of the microorganism is explored. Difference of the threshold of the deterministic model and the stochastic model shows that a large stochastic disturbance can affect the persistence of the microorganism and is harmful to the cultivation of the microorganism. To illustrate this phenomenon, we give some computer simulations with different intensity of stochastic noise disturbance.

On modeling of structured multiphase mixtures

International Nuclear Information System (INIS)

Dobran, F.

1987-01-01

The usual modeling of multiphase mixtures involves a set of conservation and balance equations of mass, momentum, energy and entropy (the basic set) constructed by an averaging procedure or postulated. The averaged models are constructed by averaging, over space or time segments, the local macroscopic field equations of each phase, whereas the postulated models are usually motivated by the single phase multicomponent mixture models. In both situations, the resulting equations yield superimposed continua models and are closed by the constitutive equations which place restrictions on the possible material response during the motion and phase change. In modeling the structured multiphase mixtures, the modeling of intrinsic motion of grains or particles is accomplished by adjoining to the basic set of field equations the additional balance equations, thereby placing restrictions on the motion of phases only within the imposed extrinsic and intrinsic sources. The use of the additional balance equations has been primarily advocated in the postulatory theories of multiphase mixtures and are usually derived through very special assumptions of the material deformation. Nevertheless, the resulting mixture models can predict a wide variety of complex phenomena such as the Mohr-Coulomb yield criterion in granular media, Rayleigh bubble equation, wave dispersion and dilatancy. Fundamental to the construction of structured models of multiphase mixtures are the problems pertaining to the existence and number of additional balance equations to model the structural characteristics of a mixture. Utilizing a volume averaging procedure it is possible not only to derive the basic set of field equation discussed above, but also a very general set of additional balance equations for modeling of structural properties of the mixture

The Asymptotic Behaviour of a Stochastic 3D LANS-α Model

International Nuclear Information System (INIS)

Caraballo, Tomas; Marquez-Duran, Antonio M.; Real, Jose

2006-01-01

The long-time behaviour of a stochastic 3D LANS-α model on a bounded domain is analysed. First, we reformulate the model as an abstract problem. Next, we establish sufficient conditions ensuring the existence of stationary (steady state) solutions of this abstract nonlinear stochastic evolution equation, and study the stability properties of the model. Finally, we analyse the effects produced by stochastic perturbations in the deterministic version of the system (persistence of exponential stability as well as possible stabilisation effects produced by the noise). The general results are applied to our stochastic LANS-α system throughout the paper

Fitting PAC spectra with stochastic models: PolyPacFit

Energy Technology Data Exchange (ETDEWEB)

Zacate, M. O., E-mail: zacatem1@nku.edu [Northern Kentucky University, Department of Physics and Geology (United States); Evenson, W. E. [Utah Valley University, College of Science and Health (United States); Newhouse, R.; Collins, G. S. [Washington State University, Department of Physics and Astronomy (United States)

2010-04-15

PolyPacFit is an advanced fitting program for time-differential perturbed angular correlation (PAC) spectroscopy. It incorporates stochastic models and provides robust options for customization of fits. Notable features of the program include platform independence and support for (1) fits to stochastic models of hyperfine interactions, (2) user-defined constraints among model parameters, (3) fits to multiple spectra simultaneously, and (4) any spin nuclear probe.

Stochastic modelling of two-phase flows including phase change

International Nuclear Information System (INIS)

Hurisse, O.; Minier, J.P.

2011-01-01

Stochastic modelling has already been developed and applied for single-phase flows and incompressible two-phase flows. In this article, we propose an extension of this modelling approach to two-phase flows including phase change (e.g. for steam-water flows). Two aspects are emphasised: a stochastic model accounting for phase transition and a modelling constraint which arises from volume conservation. To illustrate the whole approach, some remarks are eventually proposed for two-fluid models. (authors)

A stochastic model for quantum measurement

International Nuclear Information System (INIS)

Budiyono, Agung

2013-01-01

We develop a statistical model of microscopic stochastic deviation from classical mechanics based on a stochastic process with a transition probability that is assumed to be given by an exponential distribution of infinitesimal stationary action. We apply the statistical model to stochastically modify a classical mechanical model for the measurement of physical quantities reproducing the prediction of quantum mechanics. The system+apparatus always has a definite configuration at all times, as in classical mechanics, fluctuating randomly following a continuous trajectory. On the other hand, the wavefunction and quantum mechanical Hermitian operator corresponding to the physical quantity arise formally as artificial mathematical constructs. During a single measurement, the wavefunction of the whole system+apparatus evolves according to a Schrödinger equation and the configuration of the apparatus acts as the pointer of the measurement so that there is no wavefunction collapse. We will also show that while the outcome of each single measurement event does not reveal the actual value of the physical quantity prior to measurement, its average in an ensemble of identical measurements is equal to the average of the actual value of the physical quantity prior to measurement over the distribution of the configuration of the system. (paper)

Wave-Optics Modeling of the Optical-Transport Line for Passive Optical Stochastic Cooling

Energy Technology Data Exchange (ETDEWEB)

Andorf, M. B. [NICADD, DeKalb; Lebedev, V. A. [Fermilab; Piot, P. [Fermilab; Ruan, J. [Fermilab

2018-03-01

Optical stochastic cooling (OSC) is expected to enable fast cooling of dense particle beams. Transition from microwave to optical frequencies enables an achievement of stochastic cooling rates which are orders of magnitude higher than ones achievable with the classical microwave based stochastic cooling systems. A subsytem critical to the OSC scheme is the focusing optics used to image radiation from the upstream "pickup" undulator to the downstream "kicker" undulator. In this paper, we present simulation results using wave-optics calculation carried out with the {\\sc Synchrotron Radiation Workshop} (SRW). Our simulations are performed in support to a proof-of-principle experiment planned at the Integrable Optics Test Accelerator (IOTA) at Fermilab. The calculations provide an estimate of the energy kick received by a 100-MeV electron as it propagates in the kicker undulator and interacts with the electromagnetic pulse it radiated at an earlier time while traveling through the pickup undulator.

Behavioural Models for Route Choice of Passengers in Multimodal Public Transport Networks

DEFF Research Database (Denmark)

Anderson, Marie Karen

in the estimation of route choice models of public transport users based upon observed choices. Public transport route choice models have not benefitted from the same technological enhancements as car models because of the necessity (i) to collect additional information concerning lines and transfers, and (ii...... modes, public transport modes, lines, transfers, egress modes) is large. This thesis proposes a doubly stochastic approach for generating alternative routes that are relevant to travellers, since the method allows accounting for both perceived costs of the network elements and heterogeneity......The subject of this thesis is behavioural models for route choice of passengers in multimodal public transport networks. While research in sustainable transport has dedicated much attention toward the determinants of choice between car and sustainable travel options, it has devoted less attention...

The critical domain size of stochastic population models.

Science.gov (United States)

Reimer, Jody R; Bonsall, Michael B; Maini, Philip K

2017-02-01

Identifying the critical domain size necessary for a population to persist is an important question in ecology. Both demographic and environmental stochasticity impact a population's ability to persist. Here we explore ways of including this variability. We study populations with distinct dispersal and sedentary stages, which have traditionally been modelled using a deterministic integrodifference equation (IDE) framework. Individual-based models (IBMs) are the most intuitive stochastic analogues to IDEs but yield few analytic insights. We explore two alternate approaches; one is a scaling up to the population level using the Central Limit Theorem, and the other a variation on both Galton-Watson branching processes and branching processes in random environments. These branching process models closely approximate the IBM and yield insight into the factors determining the critical domain size for a given population subject to stochasticity.

Alternative Approaches to Technical Efficiency Estimation in the Stochastic Frontier Model

OpenAIRE

Acquah, H. de-Graft; Onumah, E. E.

2014-01-01

Estimating the stochastic frontier model and calculating technical efficiency of decision making units are of great importance in applied production economic works. This paper estimates technical efficiency from the stochastic frontier model using Jondrow, and Battese and Coelli approaches. In order to compare alternative methods, simulated data with sample sizes of 60 and 200 are generated from stochastic frontier model commonly applied to agricultural firms. Simulated data is employed to co...

Multi-pathway model of nuclide transport in fractured media and its application

International Nuclear Information System (INIS)

Li Xun; Yang Zeping; Li Jinxuan

2010-01-01

In order to know the law of nuclide transport in fracture system, the basic differential equations of nuclide transport in fracture and matrix were obtained based on the dual media theory, and the general analytic solutions of nuclide transport in single fractured media with exponential attenuation source in fracture were deduced by Laplace transform, and one-dimensional multi-pathway model of nuclide transport was proposed based on dual media theory and stochastic distribution of fracture parameters. The transport of Th-229, Cs-135 and Se-79 were simulated with this model, the relative concentration of these nuclides in fracture system were predicted. Further more, it was deduced that aperture and velocity can distinctly influence transport of nuclide by comparing with the results which were simulated by single fracture model. (authors)

Stochastic Modelling of Shiroro River Stream flow Process

OpenAIRE

Musa, J. J

2013-01-01

Economists, social scientists and engineers provide insights into the drivers of anthropogenic climate change and the options for adaptation and mitigation, and yet other scientists, including geographers and biologists, study the impacts of climate change. This project concentrates mainly on the discharge from the Shiroro River. A stochastic approach is presented for modeling a time series by an Autoregressive Moving Average model (ARMA). The development and use of a stochastic stream flow m...

A general mixture model and its application to coastal sandbar migration simulation

Science.gov (United States)

Liang, Lixin; Yu, Xiping

2017-04-01

A mixture model for general description of sediment laden flows is developed and then applied to coastal sandbar migration simulation. Firstly the mixture model is derived based on the Eulerian-Eulerian approach of the complete two-phase flow theory. The basic equations of the model include the mass and momentum conservation equations for the water-sediment mixture and the continuity equation for sediment concentration. The turbulent motion of the mixture is formulated for the fluid and the particles respectively. A modified k-ɛ model is used to describe the fluid turbulence while an algebraic model is adopted for the particles. A general formulation for the relative velocity between the two phases in sediment laden flows, which is derived by manipulating the momentum equations of the enhanced two-phase flow model, is incorporated into the mixture model. A finite difference method based on SMAC scheme is utilized for numerical solutions. The model is validated by suspended sediment motion in steady open channel flows, both in equilibrium and non-equilibrium state, and in oscillatory flows as well. The computed sediment concentrations, horizontal velocity and turbulence kinetic energy of the mixture are all shown to be in good agreement with experimental data. The mixture model is then applied to the study of sediment suspension and sandbar migration in surf zones under a vertical 2D framework. The VOF method for the description of water-air free surface and topography reaction model is coupled. The bed load transport rate and suspended load entrainment rate are all decided by the sea bed shear stress, which is obtained from the boundary layer resolved mixture model. The simulation results indicated that, under small amplitude regular waves, erosion occurred on the sandbar slope against the wave propagation direction, while deposition dominated on the slope towards wave propagation, indicating an onshore migration tendency. The computation results also shows that

Pores-scale hydrodynamics in a progressively bio-clogged three-dimensional porous medium: 3D particle tracking experiments and stochastic transport modelling

Science.gov (United States)

Morales, V. L.; Carrel, M.; Dentz, M.; Derlon, N.; Morgenroth, E.; Holzner, M.

2017-12-01

Biofilms are ubiquitous bacterial communities growing in various porous media including soils, trickling and sand filters and are relevant for applications such as the degradation of pollutants for bioremediation, waste water or drinking water production purposes. By their development, biofilms dynamically change the structure of porous media, increasing the heterogeneity of the pore network and the non-Fickian or anomalous dispersion. In this work, we use an experimental approach to investigate the influence of biofilm growth on pore scale hydrodynamics and transport processes and propose a correlated continuous time random walk model capturing these observations. We perform three-dimensional particle tracking velocimetry at four different time points from 0 to 48 hours of biofilm growth. The biofilm growth notably impacts pore-scale hydrodynamics, as shown by strong increase of the average velocity and in tailing of Lagrangian velocity probability density functions. Additionally, the spatial correlation length of the flow increases substantially. This points at the formation of preferential flow pathways and stagnation zones, which ultimately leads to an increase of anomalous transport in the porous media considered, characterized by non-Fickian scaling of mean-squared displacements and non-Gaussian distributions of the displacement probability density functions. A gamma distribution provides a remarkable approximation of the bulk and the high tail of the Lagrangian pore-scale velocity magnitude, indicating a transition from a parallel pore arrangement towards a more serial one. Finally, a correlated continuous time random walk based on a stochastic relation velocity model accurately reproduces the observations and could be used to predict transport beyond the time scales accessible to the experiment.

TIME-DEPENDENT STOCHASTIC ACCELERATION MODEL FOR FERMI BUBBLES

Energy Technology Data Exchange (ETDEWEB)

Sasaki, Kento; Asano, Katsuaki; Terasawa, Toshio, E-mail: kentos@icrr.u-tokyo.ac.jp, E-mail: asanok@icrr.u-tokyo.ac.jp, E-mail: terasawa@icrr.u-tokyo.ac.jp [Institute for Cosmic Ray Research, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8582 (Japan)

2015-12-01

We study stochastic acceleration models for the Fermi bubbles. Turbulence is excited just behind the shock front via Kelvin–Helmholtz, Rayleigh–Taylor, or Richtmyer–Meshkov instabilities, and plasma particles are continuously accelerated by the interaction with the turbulence. The turbulence gradually decays as it goes away from the shock fronts. Adopting a phenomenological model for the stochastic acceleration, we explicitly solve the temporal evolution of the particle energy distribution in the turbulence. Our results show that the spatial distribution of high-energy particles is different from those for a steady solution. We also show that the contribution of electrons that escaped from the acceleration regions significantly softens the photon spectrum. The photon spectrum and surface brightness profile are reproduced by our models. If the escape efficiency is very high, the radio flux from the escaped low-energy electrons can be comparable to that of the WMAP haze. We also demonstrate hadronic models with the stochastic acceleration, but they are unlikely in the viewpoint of the energy budget.

Stochastic cellular automata model of cell migration, proliferation and differentiation: validation with in vitro cultures of muscle satellite cells.

Science.gov (United States)

Garijo, N; Manzano, R; Osta, R; Perez, M A

2012-12-07

Cell migration and proliferation has been modelled in the literature as a process similar to diffusion. However, using diffusion models to simulate the proliferation and migration of cells tends to create a homogeneous distribution in the cell density that does not correlate to empirical observations. In fact, the mechanism of cell dispersal is not diffusion. Cells disperse by crawling or proliferation, or are transported in a moving fluid. The use of cellular automata, particle models or cell-based models can overcome this limitation. This paper presents a stochastic cellular automata model to simulate the proliferation, migration and differentiation of cells. These processes are considered as completely stochastic as well as discrete. The model developed was applied to predict the behaviour of in vitro cell cultures performed with adult muscle satellite cells. Moreover, non homogeneous distribution of cells has been observed inside the culture well and, using the above mentioned stochastic cellular automata model, we have been able to predict this heterogeneous cell distribution and compute accurate quantitative results. Differentiation was also incorporated into the computational simulation. The results predicted the myotube formation that typically occurs with adult muscle satellite cells. In conclusion, we have shown how a stochastic cellular automata model can be implemented and is capable of reproducing the in vitro behaviour of adult muscle satellite cells. Copyright © 2012 Elsevier Ltd. All rights reserved.

Computer Aided Continuous Time Stochastic Process Modelling

DEFF Research Database (Denmark)

Kristensen, N.R.; Madsen, Henrik; Jørgensen, Sten Bay

2001-01-01

A grey-box approach to process modelling that combines deterministic and stochastic modelling is advocated for identification of models for model-based control of batch and semi-batch processes. A computer-aided tool designed for supporting decision-making within the corresponding modelling cycle...

Review of "Stochastic Modelling for Systems Biology" by Darren Wilkinson

Directory of Open Access Journals (Sweden)

Bullinger Eric

2006-12-01

Full Text Available Abstract "Stochastic Modelling for Systems Biology" by Darren Wilkinson introduces the peculiarities of stochastic modelling in biology. This book is particularly suited to as a textbook or for self-study, and for readers with a theoretical background.

Plasma transport in stochastic magnetic field caused by vacuum resonant magnetic perturbations at diverted tokamak edge

International Nuclear Information System (INIS)

Park, G.; Chang, C. S.; Joseph, I.; Moyer, R. A.

2010-01-01

A kinetic transport simulation for the first 4 ms of the vacuum resonant magnetic perturbations (RMPs) application has been performed for the first time in realistic diverted DIII-D tokamak geometry [J. Luxon, Nucl. Fusion 42, 614 (2002)], with the self-consistent evaluation of the radial electric field and the plasma rotation. It is found that, due to the kinetic effects, the stochastic parallel thermal transport is significantly reduced when compared to the standard analytic model [A. B. Rechester and M. N. Rosenbluth, Phys. Rev. Lett. 40, 38 (1978)] and the nonaxisymmetric perpendicular radial particle transport is significantly enhanced from the axisymmetric level. These trends agree with recent experimental result trends [T. E. Evans, R. A. Moyer, K. H. Burrell et al., Nat. Phys. 2, 419 (2006)]. It is also found, as a side product, that an artificial local reduction of the vacuum RMP fields in the vicinity of the magnetic separatrix can bring the kinetic simulation results to a more detailed agreement with experimental plasma profiles.

Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology.

Science.gov (United States)

Schaff, James C; Gao, Fei; Li, Ye; Novak, Igor L; Slepchenko, Boris M

2016-12-01

Hybrid deterministic-stochastic methods provide an efficient alternative to a fully stochastic treatment of models which include components with disparate levels of stochasticity. However, general-purpose hybrid solvers for spatially resolved simulations of reaction-diffusion systems are not widely available. Here we describe fundamentals of a general-purpose spatial hybrid method. The method generates realizations of a spatially inhomogeneous hybrid system by appropriately integrating capabilities of a deterministic partial differential equation solver with a popular particle-based stochastic simulator, Smoldyn. Rigorous validation of the algorithm is detailed, using a simple model of calcium 'sparks' as a testbed. The solver is then applied to a deterministic-stochastic model of spontaneous emergence of cell polarity. The approach is general enough to be implemented within biologist-friendly software frameworks such as Virtual Cell.

Stochastic Modelling of River Geometry

DEFF Research Database (Denmark)

Sørensen, John Dalsgaard; Schaarup-Jensen, K.

1996-01-01

Numerical hydrodynamic river models are used in a large number of applications to estimate critical events for rivers. These estimates are subject to a number of uncertainties. In this paper, the problem to evaluate these estimates using probabilistic methods is considered. Stochastic models for ...... for river geometries are formulated and a coupling between hydraulic computational methods and numerical reliability methods is presented....

Mass transport thermodynamics in nonisothermal molecular liquid mixtures

Energy Technology Data Exchange (ETDEWEB)

Semenov, Semen N [Institute for Biochemical Physics, Russian Academy of Sciences, Moscow (Russian Federation); Schimpf, M E [Department of Chemistry and Biochemistry, Boise State University, Boise, ID (United States)

2009-10-31

Mass transport in a nonisothermal binary molecular mixture is systematically discussed in terms of nonequilibrium thermodynamics, which for the first time allows a consistent and unambiguous description of the process. The thermodynamic and hydrodynamic approaches are compared, revealing that nonequilibrium thermodynamics and physicochemical hydrodynamics yield essentially the same results for molecular systems. The applicability limits for the proposed version of the thermodynamic approach are determined for large particles. (methodological notes)

Stochastic Volatility and DSGE Models

DEFF Research Database (Denmark)

Andreasen, Martin Møller

This paper argues that a specification of stochastic volatility commonly used to analyze the Great Moderation in DSGE models may not be appropriate, because the level of a process with this specification does not have conditional or unconditional moments. This is unfortunate because agents may...

Stability analysis of multi-group deterministic and stochastic epidemic models with vaccination rate

International Nuclear Information System (INIS)

Wang Zhi-Gang; Gao Rui-Mei; Fan Xiao-Ming; Han Qi-Xing

2014-01-01

We discuss in this paper a deterministic multi-group MSIR epidemic model with a vaccination rate, the basic reproduction number ℛ 0 , a key parameter in epidemiology, is a threshold which determines the persistence or extinction of the disease. By using Lyapunov function techniques, we show if ℛ 0 is greater than 1 and the deterministic model obeys some conditions, then the disease will prevail, the infective persists and the endemic state is asymptotically stable in a feasible region. If ℛ 0 is less than or equal to 1, then the infective disappear so the disease dies out. In addition, stochastic noises around the endemic equilibrium will be added to the deterministic MSIR model in order that the deterministic model is extended to a system of stochastic ordinary differential equations. In the stochastic version, we carry out a detailed analysis on the asymptotic behavior of the stochastic model. In addition, regarding the value of ℛ 0 , when the stochastic system obeys some conditions and ℛ 0 is greater than 1, we deduce the stochastic system is stochastically asymptotically stable. Finally, the deterministic and stochastic model dynamics are illustrated through computer simulations. (general)

Stochastic differential equations used to model conjugation

DEFF Research Database (Denmark)

Philipsen, Kirsten Riber; Christiansen, Lasse Engbo

Stochastic differential equations (SDEs) are used to model horizontal transfer of antibiotic resis- tance by conjugation. The model describes the concentration of donor, recipient, transconjugants and substrate. The strength of the SDE model over the traditional ODE models is that the noise can...

Developing a stochastic traffic volume prediction model for public-private partnership projects

Science.gov (United States)

Phong, Nguyen Thanh; Likhitruangsilp, Veerasak; Onishi, Masamitsu

2017-11-01

Transportation projects require an enormous amount of capital investment resulting from their tremendous size, complexity, and risk. Due to the limitation of public finances, the private sector is invited to participate in transportation project development. The private sector can entirely or partially invest in transportation projects in the form of Public-Private Partnership (PPP) scheme, which has been an attractive option for several developing countries, including Vietnam. There are many factors affecting the success of PPP projects. The accurate prediction of traffic volume is considered one of the key success factors of PPP transportation projects. However, only few research works investigated how to predict traffic volume over a long period of time. Moreover, conventional traffic volume forecasting methods are usually based on deterministic models which predict a single value of traffic volume but do not consider risk and uncertainty. This knowledge gap makes it difficult for concessionaires to estimate PPP transportation project revenues accurately. The objective of this paper is to develop a probabilistic traffic volume prediction model. First, traffic volumes were estimated following the Geometric Brownian Motion (GBM) process. Monte Carlo technique is then applied to simulate different scenarios. The results show that this stochastic approach can systematically analyze variations in the traffic volume and yield more reliable estimates for PPP projects.

Stochastic Differential Equation-Based Flexible Software Reliability Growth Model

Directory of Open Access Journals (Sweden)

P. K. Kapur

2009-01-01

Full Text Available Several software reliability growth models (SRGMs have been developed by software developers in tracking and measuring the growth of reliability. As the size of software system is large and the number of faults detected during the testing phase becomes large, so the change of the number of faults that are detected and removed through each debugging becomes sufficiently small compared with the initial fault content at the beginning of the testing phase. In such a situation, we can model the software fault detection process as a stochastic process with continuous state space. In this paper, we propose a new software reliability growth model based on Itô type of stochastic differential equation. We consider an SDE-based generalized Erlang model with logistic error detection function. The model is estimated and validated on real-life data sets cited in literature to show its flexibility. The proposed model integrated with the concept of stochastic differential equation performs comparatively better than the existing NHPP-based models.

A primer on stochastic epidemic models: Formulation, numerical simulation, and analysis

Directory of Open Access Journals (Sweden)

Linda J.S. Allen

2017-05-01

Full Text Available Some mathematical methods for formulation and numerical simulation of stochastic epidemic models are presented. Specifically, models are formulated for continuous-time Markov chains and stochastic differential equations. Some well-known examples are used for illustration such as an SIR epidemic model and a host-vector malaria model. Analytical methods for approximating the probability of a disease outbreak are also discussed. Keywords: Branching process, Continuous-time Markov chain, Minor outbreak, Stochastic differential equation, 2000 MSC: 60H10, 60J28, 92D30

EMC3-eIRENE simulation of impurity transport in comparison with EUV emission measurements in the stochastic layer of LHD: effects of force balance and transport coefficients

Energy Technology Data Exchange (ETDEWEB)

Dai, S. [National Institute for Fusion Science, Toki (Japan); Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Ministry of Education), School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian (China); Kobayashi, M.; Morita, S.; Oishi, T.; Suzuki, Y. [National Institute for Fusion Science, Toki (Japan); Department of Fusion Science, School of Physical Sciences, SOKENDAI (The Graduate University for Advanced Studies), Toki (Japan); Kawamura, G. [National Institute for Fusion Science, Toki (Japan); Zhang, H.M.; Huang, X.L. [Department of Fusion Science, School of Physical Sciences, SOKENDAI (The Graduate University for Advanced Studies), Toki (Japan); Feng, Y. [Max-Planck-Institut fuer Plasmaphysik, Greifswald (Germany); Wang, D.Z. [Key Laboratory of Materials Modification by Laser, Ion and Electron Beams (Ministry of Education), School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian (China); Collaboration: The LHD experiment group

2016-08-15

The transport properties and line emissions of the intrinsic carbon in the stochastic layer of the Large Helical Device have been investigated with the three-dimensional edge transport code EMC3-EIRENE. The simulations of impurity transport and emissivity have been performed to study the dedicated experiment in which the carbon emission distributions are measured by a space-resolved EUV spectrometer system. A discrepancy of the CIV impurity emission between the measurement and simulation is obtained, which is studied with the variation of the ion thermal force, friction force and the perpendicular diffusivity in the impurity transport model. An enhanced ion thermal force or a reduced friction force in the modelling can increase the CIV impurity emission at the inboard X-point region. Furthermore, the impact of the perpendicular diffusivity Dimp is studied which shows that the CIV impurity emission pattern is very sensitive to Dimp. It is found that the simulation results with the increased Dimp tend to be closer to the experimental observation. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Regional SAR Image Segmentation Based on Fuzzy Clustering with Gamma Mixture Model

Science.gov (United States)

Li, X. L.; Zhao, Q. H.; Li, Y.

2017-09-01

Most of stochastic based fuzzy clustering algorithms are pixel-based, which can not effectively overcome the inherent speckle noise in SAR images. In order to deal with the problem, a regional SAR image segmentation algorithm based on fuzzy clustering with Gamma mixture model is proposed in this paper. First, initialize some generating points randomly on the image, the image domain is divided into many sub-regions using Voronoi tessellation technique. Each sub-region is regarded as a homogeneous area in which the pixels share the same cluster label. Then, assume the probability of the pixel to be a Gamma mixture model with the parameters respecting to the cluster which the pixel belongs to. The negative logarithm of the probability represents the dissimilarity measure between the pixel and the cluster. The regional dissimilarity measure of one sub-region is defined as the sum of the measures of pixels in the region. Furthermore, the Markov Random Field (MRF) model is extended from pixels level to Voronoi sub-regions, and then the regional objective function is established under the framework of fuzzy clustering. The optimal segmentation results can be obtained by the solution of model parameters and generating points. Finally, the effectiveness of the proposed algorithm can be proved by the qualitative and quantitative analysis from the segmentation results of the simulated and real SAR images.

Some Remarks on Stochastic Versions of the Ramsey Growth Model

Czech Academy of Sciences Publication Activity Database

Sladký, Karel

2012-01-01

Roč. 19, č. 29 (2012), s. 139-152 ISSN 1212-074X R&D Projects: GA ČR GAP402/10/1610; GA ČR GAP402/10/0956; GA ČR GAP402/11/0150 Institutional support: RVO:67985556 Keywords : Economic dynamics * Ramsey growth model with disturbance * stochastic dynamic programming * multistage stochastic programs Subject RIV: BB - Applied Statistics, Operational Research http://library.utia.cas.cz/separaty/2013/E/sladky-some remarks on stochastic versions of the ramsey growth model.pdf

Stochastic modeling of consumer preferences for health care institutions.

Science.gov (United States)

Malhotra, N K

1983-01-01

This paper proposes a stochastic procedure for modeling consumer preferences via LOGIT analysis. First, a simple, non-technical exposition of the use of a stochastic approach in health care marketing is presented. Second, a study illustrating the application of the LOGIT model in assessing consumer preferences for hospitals is given. The paper concludes with several implications of the proposed approach.

Estimation of some stochastic models used in reliability engineering

International Nuclear Information System (INIS)

Huovinen, T.

1989-04-01

The work aims to study the estimation of some stochastic models used in reliability engineering. In reliability engineering continuous probability distributions have been used as models for the lifetime of technical components. We consider here the following distributions: exponential, 2-mixture exponential, conditional exponential, Weibull, lognormal and gamma. Maximum likelihood method is used to estimate distributions from observed data which may be either complete or censored. We consider models based on homogeneous Poisson processes such as gamma-poisson and lognormal-poisson models for analysis of failure intensity. We study also a beta-binomial model for analysis of failure probability. The estimators of the parameters for three models are estimated by the matching moments method and in the case of gamma-poisson and beta-binomial models also by maximum likelihood method. A great deal of mathematical or statistical problems that arise in reliability engineering can be solved by utilizing point processes. Here we consider the statistical analysis of non-homogeneous Poisson processes to describe the failing phenomena of a set of components with a Weibull intensity function. We use the method of maximum likelihood to estimate the parameters of the Weibull model. A common cause failure can seriously reduce the reliability of a system. We consider a binomial failure rate (BFR) model as an application of the marked point processes for modelling common cause failure in a system. The parameters of the binomial failure rate model are estimated with the maximum likelihood method

Stochastic ontogenetic growth model

Science.gov (United States)

West, B. J.; West, D.

2012-02-01

An ontogenetic growth model (OGM) for a thermodynamically closed system is generalized to satisfy both the first and second law of thermodynamics. The hypothesized stochastic ontogenetic growth model (SOGM) is shown to entail the interspecies allometry relation by explicitly averaging the basal metabolic rate and the total body mass over the steady-state probability density for the total body mass (TBM). This is the first derivation of the interspecies metabolic allometric relation from a dynamical model and the asymptotic steady-state distribution of the TBM is fit to data and shown to be inverse power law.

Multivariate moment closure techniques for stochastic kinetic models

International Nuclear Information System (INIS)

Lakatos, Eszter; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H.

2015-01-01

Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs

Multivariate moment closure techniques for stochastic kinetic models

Energy Technology Data Exchange (ETDEWEB)

Lakatos, Eszter, E-mail: e.lakatos13@imperial.ac.uk; Ale, Angelique; Kirk, Paul D. W.; Stumpf, Michael P. H., E-mail: m.stumpf@imperial.ac.uk [Department of Life Sciences, Centre for Integrative Systems Biology and Bioinformatics, Imperial College London, London SW7 2AZ (United Kingdom)

2015-09-07

Stochastic effects dominate many chemical and biochemical processes. Their analysis, however, can be computationally prohibitively expensive and a range of approximation schemes have been proposed to lighten the computational burden. These, notably the increasingly popular linear noise approximation and the more general moment expansion methods, perform well for many dynamical regimes, especially linear systems. At higher levels of nonlinearity, it comes to an interplay between the nonlinearities and the stochastic dynamics, which is much harder to capture correctly by such approximations to the true stochastic processes. Moment-closure approaches promise to address this problem by capturing higher-order terms of the temporally evolving probability distribution. Here, we develop a set of multivariate moment-closures that allows us to describe the stochastic dynamics of nonlinear systems. Multivariate closure captures the way that correlations between different molecular species, induced by the reaction dynamics, interact with stochastic effects. We use multivariate Gaussian, gamma, and lognormal closure and illustrate their use in the context of two models that have proved challenging to the previous attempts at approximating stochastic dynamics: oscillations in p53 and Hes1. In addition, we consider a larger system, Erk-mediated mitogen-activated protein kinases signalling, where conventional stochastic simulation approaches incur unacceptably high computational costs.

Compositional Modelling of Stochastic Hybrid Systems

NARCIS (Netherlands)

Strubbe, S.N.

2005-01-01

In this thesis we present a modelling framework for compositional modelling of stochastic hybrid systems. Hybrid systems consist of a combination of continuous and discrete dynamics. The state space of a hybrid system is hybrid in the sense that it consists of a continuous component and a discrete

Stochastic models for turbulent reacting flows

Energy Technology Data Exchange (ETDEWEB)

Kerstein, A. [Sandia National Laboratories, Livermore, CA (United States)

1993-12-01

The goal of this program is to develop and apply stochastic models of various processes occurring within turbulent reacting flows in order to identify the fundamental mechanisms governing these flows, to support experimental studies of these flows, and to further the development of comprehensive turbulent reacting flow models.

Multi-scenario modelling of uncertainty in stochastic chemical systems

International Nuclear Information System (INIS)

Evans, R. David; Ricardez-Sandoval, Luis A.

2014-01-01

Uncertainty analysis has not been well studied at the molecular scale, despite extensive knowledge of uncertainty in macroscale systems. The ability to predict the effect of uncertainty allows for robust control of small scale systems such as nanoreactors, surface reactions, and gene toggle switches. However, it is difficult to model uncertainty in such chemical systems as they are stochastic in nature, and require a large computational cost. To address this issue, a new model of uncertainty propagation in stochastic chemical systems, based on the Chemical Master Equation, is proposed in the present study. The uncertain solution is approximated by a composite state comprised of the averaged effect of samples from the uncertain parameter distributions. This model is then used to study the effect of uncertainty on an isomerization system and a two gene regulation network called a repressilator. The results of this model show that uncertainty in stochastic systems is dependent on both the uncertain distribution, and the system under investigation. -- Highlights: •A method to model uncertainty on stochastic systems was developed. •The method is based on the Chemical Master Equation. •Uncertainty in an isomerization reaction and a gene regulation network was modelled. •Effects were significant and dependent on the uncertain input and reaction system. •The model was computationally more efficient than Kinetic Monte Carlo

Identifiability in stochastic models

CERN Document Server

1992-01-01

The problem of identifiability is basic to all statistical methods and data analysis, occurring in such diverse areas as Reliability Theory, Survival Analysis, and Econometrics, where stochastic modeling is widely used. Mathematics dealing with identifiability per se is closely related to the so-called branch of ""characterization problems"" in Probability Theory. This book brings together relevant material on identifiability as it occurs in these diverse fields.

Model structure selection in convolutive mixtures

DEFF Research Database (Denmark)

Dyrholm, Mads; Makeig, S.; Hansen, Lars Kai

2006-01-01

The CICAAR algorithm (convolutive independent component analysis with an auto-regressive inverse model) allows separation of white (i.i.d) source signals from convolutive mixtures. We introduce a source color model as a simple extension to the CICAAR which allows for a more parsimonious represent......The CICAAR algorithm (convolutive independent component analysis with an auto-regressive inverse model) allows separation of white (i.i.d) source signals from convolutive mixtures. We introduce a source color model as a simple extension to the CICAAR which allows for a more parsimonious...... representation in many practical mixtures. The new filter-CICAAR allows Bayesian model selection and can help answer questions like: ’Are we actually dealing with a convolutive mixture?’. We try to answer this question for EEG data....

Consistency of the MLE under mixture models

OpenAIRE

Chen, Jiahua

2016-01-01

The large-sample properties of likelihood-based statistical inference under mixture models have received much attention from statisticians. Although the consistency of the nonparametric MLE is regarded as a standard conclusion, many researchers ignore the precise conditions required on the mixture model. An incorrect claim of consistency can lead to false conclusions even if the mixture model under investigation seems well behaved. Under a finite normal mixture model, for instance, the consis...

Study on individual stochastic model of GNSS observations for precise kinematic applications

Science.gov (United States)

Próchniewicz, Dominik; Szpunar, Ryszard

2015-04-01

The proper definition of mathematical positioning model, which is defined by functional and stochastic models, is a prerequisite to obtain the optimal estimation of unknown parameters. Especially important in this definition is realistic modelling of stochastic properties of observations, which are more receiver-dependent and time-varying than deterministic relationships. This is particularly true with respect to precise kinematic applications which are characterized by weakening model strength. In this case, incorrect or simplified definition of stochastic model causes that the performance of ambiguity resolution and accuracy of position estimation can be limited. In this study we investigate the methods of describing the measurement noise of GNSS observations and its impact to derive precise kinematic positioning model. In particular stochastic modelling of individual components of the variance-covariance matrix of observation noise performed using observations from a very short baseline and laboratory GNSS signal generator, is analyzed. Experimental test results indicate that the utilizing the individual stochastic model of observations including elevation dependency and cross-correlation instead of assumption that raw measurements are independent with the same variance improves the performance of ambiguity resolution as well as rover positioning accuracy. This shows that the proposed stochastic assessment method could be a important part in complex calibration procedure of GNSS equipment.

Building 235-F Goldsim Fate And Transport Model

Energy Technology Data Exchange (ETDEWEB)

Taylor, G. A.; Phifer, M. A.

2012-09-14

Savannah River National Laboratory (SRNL) personnel, at the request of Area Completion Projects (ACP), evaluated In-Situ Disposal (ISD) alternatives that are under consideration for deactivation and decommissioning (D&D) of Building 235-F and the Building 294-2F Sand Filter. SRNL personnel developed and used a GoldSim fate and transport model, which is consistent with Musall 2012, to evaluate relative to groundwater protection, ISD alternatives that involve either source removal and/or the grouting of portions or all of 235-F. This evaluation was conducted through the development and use of a Building 235-F GoldSim fate and transport model. The model simulates contaminant release from four 235-F process areas and the 294-2F Sand Filter. In addition, it simulates the fate and transport through the vadose zone, the Upper Three Runs (UTR) aquifer, and the Upper Three Runs (UTR) creek. The model is designed as a stochastic model, and as such it can provide both deterministic and stochastic (probabilistic) results. The results show that the median radium activity concentrations exceed the 5 ?Ci/L radium MCL at the edge of the building for all ISD alternatives after 10,000 years, except those with a sufficient amount of inventory removed. A very interesting result was that grouting was shown to basically have minimal effect on the radium activity concentration. During the first 1,000 years grouting may have some small positive benefit relative to radium, however after that it may have a slightly deleterious effect. The Pb-210 results, relative to its 0.06 ?Ci/L PRG, are essentially identical to the radium results, but the Pb-210 results exhibit a lesser degree of exceedance. In summary, some level of inventory removal will be required to ensure that groundwater standards are met.

Building 235-F Goldsim Fate And Transport Model

International Nuclear Information System (INIS)

Taylor, G. A.; Phifer, M. A.

2012-01-01

Savannah River National Laboratory (SRNL) personnel, at the request of Area Completion Projects (ACP), evaluated In-Situ Disposal (ISD) alternatives that are under consideration for deactivation and decommissioning (D and D) of Building 235-F and the Building 294-2F Sand Filter. SRNL personnel developed and used a GoldSim fate and transport model, which is consistent with Musall 2012, to evaluate relative to groundwater protection, ISD alternatives that involve either source removal and/or the grouting of portions or all of 235-F. This evaluation was conducted through the development and use of a Building 235-F GoldSim fate and transport model. The model simulates contaminant release from four 235-F process areas and the 294-2F Sand Filter. In addition, it simulates the fate and transport through the vadose zone, the Upper Three Runs (UTR) aquifer, and the Upper Three Runs (UTR) creek. The model is designed as a stochastic model, and as such it can provide both deterministic and stochastic (probabilistic) results. The results show that the median radium activity concentrations exceed the 5 ρCi/L radium MCL at the edge of the building for all ISD alternatives after 10,000 years, except those with a sufficient amount of inventory removed. A very interesting result was that grouting was shown to basically have minimal effect on the radium activity concentration. During the first 1,000 years grouting may have some small positive benefit relative to radium, however after that it may have a slightly deleterious effect. The Pb-210 results, relative to its 0.06 ρCi/L PRG, are essentially identical to the radium results, but the Pb-210 results exhibit a lesser degree of exceedance. In summary, some level of inventory removal will be required to ensure that groundwater standards are met

Modelling and simulation of an energy transport phenomenon in a solid-fluid mixture

International Nuclear Information System (INIS)

Costa, M.L.M.; Sampaio, R.; Gama, R.M.S. da.

1989-08-01

In the present work a model for a local description of the energy transfer phenomenon in a binary (solid-fluid) saturated mixture is proposed. The heat transfer in a saturated flow (through a porous medium) between two parallel plates is simulated by using the Finite Volumes Method. (author) [pt

Estimation of Stochastic Volatility Models by Nonparametric Filtering

DEFF Research Database (Denmark)

Kanaya, Shin; Kristensen, Dennis

2016-01-01

/estimated volatility process replacing the latent process. Our estimation strategy is applicable to both parametric and nonparametric stochastic volatility models, and can handle both jumps and market microstructure noise. The resulting estimators of the stochastic volatility model will carry additional biases...... and variances due to the first-step estimation, but under regularity conditions we show that these vanish asymptotically and our estimators inherit the asymptotic properties of the infeasible estimators based on observations of the volatility process. A simulation study examines the finite-sample properties...

A Simulation-Based Dynamic Stochastic Route Choice Model for Evacuation

Directory of Open Access Journals (Sweden)

Xing Zhao

2012-01-01

Full Text Available This paper establishes a dynamic stochastic route choice model for evacuation to simulate the propagation process of traffic flow and estimate the stochastic route choice under evacuation situations. The model contains a lane-group-based cell transmission model (CTM which sets different traffic capacities for links with different turning movements to flow out in an evacuation situation, an actual impedance model which is to obtain the impedance of each route in time units at each time interval and a stochastic route choice model according to the probit-based stochastic user equilibrium. In this model, vehicles loading at each origin at each time interval are assumed to choose an evacuation route under determinate road network, signal design, and OD demand. As a case study, the proposed model is validated on the network nearby Nanjing Olympic Center after the opening ceremony of the 10th National Games of the People's Republic of China. The traffic volumes and clearing time at five exit points of the evacuation zone are calculated by the model to compare with survey data. The results show that this model can appropriately simulate the dynamic route choice and evolution process of the traffic flow on the network in an evacuation situation.

On the small-time behavior of stochastic logistic models

Directory of Open Access Journals (Sweden)

Dung Tien Nguyen

2017-09-01

Full Text Available In this paper we investigate the small-time behaviors of the solution to  a stochastic logistic model. The obtained results allow us to estimate the number of individuals in the population and can be used to study stochastic prey-predator systems.

Transport benchmarks for one-dimensional binary Markovian mixtures revisited

International Nuclear Information System (INIS)

Malvagi, F.

2013-01-01

The classic benchmarks for transport through a binary Markovian mixture are revisited to look at the probability distribution function of the chosen 'results': reflection, transmission and scalar flux. We argue that the knowledge of the ensemble averaged results is not sufficient for reliable predictions: a measure of the dispersion must also be obtained. An algorithm to estimate this dispersion is tested. (author)

A BGK model for reactive mixtures of polyatomic gases with continuous internal energy

Science.gov (United States)

Bisi, M.; Monaco, R.; Soares, A. J.

2018-03-01

In this paper we derive a BGK relaxation model for a mixture of polyatomic gases with a continuous structure of internal energies. The emphasis of the paper is on the case of a quaternary mixture undergoing a reversible chemical reaction of bimolecular type. For such a mixture we prove an H -theorem and characterize the equilibrium solutions with the related mass action law of chemical kinetics. Further, a Chapman-Enskog asymptotic analysis is performed in view of computing the first-order non-equilibrium corrections to the distribution functions and investigating the transport properties of the reactive mixture. The chemical reaction rate is explicitly derived at the first order and the balance equations for the constituent number densities are derived at the Euler level.

Modelling an Ammonium Transporter with SCLS

Directory of Open Access Journals (Sweden)

Angelo Troina

2009-10-01

Full Text Available The Stochastic Calculus of Looping Sequences (SCLS is a recently proposed modelling language for the representation and simulation of biological systems behaviour. It has been designed with the aim of combining the simplicity of notation of rewrite systems with the advantage of compositionality. It also allows a rather simple and accurate description of biological membranes and their interactions with the environment.In this work we apply SCLS to model a newly discovered ammonium transporter. This transporter is believed to play a fundamental role for plant mineral acquisition, which takes place in the arbuscular mycorrhiza, the most wide-spread plant-fungus symbiosis on earth. Due to its potential application in agriculture this kind of symbiosis is one of the main focuses of the BioBITs project. In our experiments the passage of NH3 / NH4+ from the fungus to the plant has been dissected in known and hypothetical mechanisms; with the model so far we have been able to simulate the behaviour of the system under different conditions. Our simulations confirmed some of the latest experimental results about the LjAMT2;2 transporter. The initial simulation results of the modelling of the symbiosis process are promising and indicate new directions for biological investigations.

Spatial stochastic regression modelling of urban land use

International Nuclear Information System (INIS)

Arshad, S H M; Jaafar, J; Abiden, M Z Z; Latif, Z A; Rasam, A R A

2014-01-01

Urbanization is very closely linked to industrialization, commercialization or overall economic growth and development. This results in innumerable benefits of the quantity and quality of the urban environment and lifestyle but on the other hand contributes to unbounded development, urban sprawl, overcrowding and decreasing standard of living. Regulation and observation of urban development activities is crucial. The understanding of urban systems that promotes urban growth are also essential for the purpose of policy making, formulating development strategies as well as development plan preparation. This study aims to compare two different stochastic regression modeling techniques for spatial structure models of urban growth in the same specific study area. Both techniques will utilize the same datasets and their results will be analyzed. The work starts by producing an urban growth model by using stochastic regression modeling techniques namely the Ordinary Least Square (OLS) and Geographically Weighted Regression (GWR). The two techniques are compared to and it is found that, GWR seems to be a more significant stochastic regression model compared to OLS, it gives a smaller AICc (Akaike's Information Corrected Criterion) value and its output is more spatially explainable

Stochastic optimal charging of electric-drive vehicles with renewable energy

International Nuclear Information System (INIS)

Pantoš, Miloš

2011-01-01

The paper presents the stochastic optimization algorithm that may eventually be used by electric energy suppliers to coordinate charging of electric-drive vehicles (EDVs) in order to maximize the use of renewable energy in transportation. Due to the stochastic nature of transportation patterns, the Monte Carlo simulation is applied to model uncertainties presented by numerous scenarios. To reduce the problem complexity, the simulated driving patterns are not individually considered in the optimization but clustered into fleets using the GAMS/SCENRED tool. Uncertainties of production of renewable energy sources (RESs) are presented by statistical central moments that are further considered in Hong’s 2-point + 1 estimation method in order to define estimate points considered in the optimization. Case studies illustrate the application of the proposed optimization in achieving maximal exploitation of RESs in transportation by EDVs. -- Highlights: ► Optimization model for EDV charging applying linear programming. ► Formation of EDV fleets based on the driving patterns assessment applying the GAMS/SCENRED. ► Consideration of uncertainties of RES production and energy prices in the market. ► Stochastic optimization. ► Application of Hong’s 2-point + 1 estimation method.

Probabilistic mixture-based image modelling

Czech Academy of Sciences Publication Activity Database

Haindl, Michal; Havlíček, Vojtěch; Grim, Jiří

2011-01-01

Roč. 47, č. 3 (2011), s. 482-500 ISSN 0023-5954 R&D Projects: GA MŠk 1M0572; GA ČR GA102/08/0593 Grant - others:CESNET(CZ) 387/2010; GA MŠk(CZ) 2C06019; GA ČR(CZ) GA103/11/0335 Institutional research plan: CEZ:AV0Z10750506 Keywords : BTF texture modelling * discrete distribution mixtures * Bernoulli mixture * Gaussian mixture * multi-spectral texture modelling Subject RIV: BD - Theory of Information Impact factor: 0.454, year: 2011 http://library.utia.cas.cz/separaty/2011/RO/haindl-0360244.pdf

Poisson Mixture Regression Models for Heart Disease Prediction.

Science.gov (United States)

Mufudza, Chipo; Erol, Hamza

2016-01-01

Early heart disease control can be achieved by high disease prediction and diagnosis efficiency. This paper focuses on the use of model based clustering techniques to predict and diagnose heart disease via Poisson mixture regression models. Analysis and application of Poisson mixture regression models is here addressed under two different classes: standard and concomitant variable mixture regression models. Results show that a two-component concomitant variable Poisson mixture regression model predicts heart disease better than both the standard Poisson mixture regression model and the ordinary general linear Poisson regression model due to its low Bayesian Information Criteria value. Furthermore, a Zero Inflated Poisson Mixture Regression model turned out to be the best model for heart prediction over all models as it both clusters individuals into high or low risk category and predicts rate to heart disease componentwise given clusters available. It is deduced that heart disease prediction can be effectively done by identifying the major risks componentwise using Poisson mixture regression model.

Poisson Mixture Regression Models for Heart Disease Prediction

Science.gov (United States)

Erol, Hamza

2016-01-01

Early heart disease control can be achieved by high disease prediction and diagnosis efficiency. This paper focuses on the use of model based clustering techniques to predict and diagnose heart disease via Poisson mixture regression models. Analysis and application of Poisson mixture regression models is here addressed under two different classes: standard and concomitant variable mixture regression models. Results show that a two-component concomitant variable Poisson mixture regression model predicts heart disease better than both the standard Poisson mixture regression model and the ordinary general linear Poisson regression model due to its low Bayesian Information Criteria value. Furthermore, a Zero Inflated Poisson Mixture Regression model turned out to be the best model for heart prediction over all models as it both clusters individuals into high or low risk category and predicts rate to heart disease componentwise given clusters available. It is deduced that heart disease prediction can be effectively done by identifying the major risks componentwise using Poisson mixture regression model. PMID:27999611

Stochastic Geometric Models with Non-stationary Spatial Correlations in Lagrangian Fluid Flows

Science.gov (United States)

Gay-Balmaz, François; Holm, Darryl D.

2018-01-01

Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration's "Global Drifter Program", this paper develops data-driven stochastic models of geophysical fluid dynamics (GFD) with non-stationary spatial correlations representing the dynamical behaviour of oceanic currents. Three models are considered. Model 1 from Holm (Proc R Soc A 471:20140963, 2015) is reviewed, in which the spatial correlations are time independent. Two new models, called Model 2 and Model 3, introduce two different symmetry breaking mechanisms by which the spatial correlations may be advected by the flow. These models are derived using reduction by symmetry of stochastic variational principles, leading to stochastic Hamiltonian systems, whose momentum maps, conservation laws and Lie-Poisson bracket structures are used in developing the new stochastic Hamiltonian models of GFD.

Stochastic Geometric Models with Non-stationary Spatial Correlations in Lagrangian Fluid Flows

Science.gov (United States)

Gay-Balmaz, François; Holm, Darryl D.

2018-06-01

Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration's "Global Drifter Program", this paper develops data-driven stochastic models of geophysical fluid dynamics (GFD) with non-stationary spatial correlations representing the dynamical behaviour of oceanic currents. Three models are considered. Model 1 from Holm (Proc R Soc A 471:20140963, 2015) is reviewed, in which the spatial correlations are time independent. Two new models, called Model 2 and Model 3, introduce two different symmetry breaking mechanisms by which the spatial correlations may be advected by the flow. These models are derived using reduction by symmetry of stochastic variational principles, leading to stochastic Hamiltonian systems, whose momentum maps, conservation laws and Lie-Poisson bracket structures are used in developing the new stochastic Hamiltonian models of GFD.

Markov Chain Models for the Stochastic Modeling of Pitting Corrosion

Directory of Open Access Journals (Sweden)

A. Valor

2013-01-01

Full Text Available The stochastic nature of pitting corrosion of metallic structures has been widely recognized. It is assumed that this kind of deterioration retains no memory of the past, so only the current state of the damage influences its future development. This characteristic allows pitting corrosion to be categorized as a Markov process. In this paper, two different models of pitting corrosion, developed using Markov chains, are presented. Firstly, a continuous-time, nonhomogeneous linear growth (pure birth Markov process is used to model external pitting corrosion in underground pipelines. A closed-form solution of the system of Kolmogorov's forward equations is used to describe the transition probability function in a discrete pit depth space. The transition probability function is identified by correlating the stochastic pit depth mean with the empirical deterministic mean. In the second model, the distribution of maximum pit depths in a pitting experiment is successfully modeled after the combination of two stochastic processes: pit initiation and pit growth. Pit generation is modeled as a nonhomogeneous Poisson process, in which induction time is simulated as the realization of a Weibull process. Pit growth is simulated using a nonhomogeneous Markov process. An analytical solution of Kolmogorov's system of equations is also found for the transition probabilities from the first Markov state. Extreme value statistics is employed to find the distribution of maximum pit depths.

A stochastic model for the financial market with discontinuous prices

Directory of Open Access Journals (Sweden)

Leda D. Minkova

1996-01-01

Full Text Available This paper models some situations occurring in the financial market. The asset prices evolve according to a stochastic integral equation driven by a Gaussian martingale. A portfolio process is constrained in such a way that the wealth process covers some obligation. A solution to a linear stochastic integral equation is obtained in a class of cadlag stochastic processes.

Stochastic higher spin six vertex model and Macdonald measures

Science.gov (United States)

Borodin, Alexei

2018-02-01

We prove an identity that relates the q-Laplace transform of the height function of a (higher spin inhomogeneous) stochastic six vertex model in a quadrant on one side and a multiplicative functional of a Macdonald measure on the other. The identity is used to prove the GUE Tracy-Widom asymptotics for two instances of the stochastic six vertex model via asymptotic analysis of the corresponding Schur measures.

Urban Freight Management with Stochastic Time-Dependent Travel Times and Application to Large-Scale Transportation Networks

Directory of Open Access Journals (Sweden)

Shichao Sun

2015-01-01

Full Text Available This paper addressed the vehicle routing problem (VRP in large-scale urban transportation networks with stochastic time-dependent (STD travel times. The subproblem which is how to find the optimal path connecting any pair of customer nodes in a STD network was solved through a robust approach without requiring the probability distributions of link travel times. Based on that, the proposed STD-VRP model can be converted into solving a normal time-dependent VRP (TD-VRP, and algorithms for such TD-VRPs can also be introduced to obtain the solution. Numerical experiments were conducted to address STD-VRPTW of practical sizes on a real world urban network, demonstrated here on the road network of Shenzhen, China. The stochastic time-dependent link travel times of the network were calibrated by historical floating car data. A route construction algorithm was applied to solve the STD problem in 4 delivery scenarios efficiently. The computational results showed that the proposed STD-VRPTW model can improve the level of customer service by satisfying the time-window constraint under any circumstances. The improvement can be very significant especially for large-scale network delivery tasks with no more increase in cost and environmental impacts.

Improved ensemble-mean forecast skills of ENSO events by a zero-mean stochastic model-error model of an intermediate coupled model

Science.gov (United States)

Zheng, F.; Zhu, J.

2015-12-01

To perform an ensemble-based ENSO probabilistic forecast, the crucial issue is to design a reliable ensemble prediction strategy that should include the major uncertainties of a forecast system. In this study, we developed a new general ensemble perturbation technique to improve the ensemble-mean predictive skill of forecasting ENSO using an intermediate coupled model (ICM). The model uncertainties are first estimated and analyzed from EnKF analysis results through assimilating observed SST. Then, based on the pre-analyzed properties of the model errors, a zero-mean stochastic model-error model is developed to mainly represent the model uncertainties induced by some important physical processes missed in the coupled model (i.e., stochastic atmospheric forcing/MJO, extra-tropical cooling and warming, Indian Ocean Dipole mode, etc.). Each member of an ensemble forecast is perturbed by the stochastic model-error model at each step during the 12-month forecast process, and the stochastical perturbations are added into the modeled physical fields to mimic the presence of these high-frequency stochastic noises and model biases and their effect on the predictability of the coupled system. The impacts of stochastic model-error perturbations on ENSO deterministic predictions are examined by performing two sets of 21-yr retrospective forecast experiments. The two forecast schemes are differentiated by whether they considered the model stochastic perturbations, with both initialized by the ensemble-mean analysis states from EnKF. The comparison results suggest that the stochastic model-error perturbations have significant and positive impacts on improving the ensemble-mean prediction skills during the entire 12-month forecast process. Because the nonlinear feature of the coupled model can induce the nonlinear growth of the added stochastic model errors with model integration, especially through the nonlinear heating mechanism with the vertical advection term of the model, the

Stochastic hyperfine interactions modeling library

Science.gov (United States)

Zacate, Matthew O.; Evenson, William E.

2011-04-01

The stochastic hyperfine interactions modeling library (SHIML) provides a set of routines to assist in the development and application of stochastic models of hyperfine interactions. The library provides routines written in the C programming language that (1) read a text description of a model for fluctuating hyperfine fields, (2) set up the Blume matrix, upon which the evolution operator of the system depends, and (3) find the eigenvalues and eigenvectors of the Blume matrix so that theoretical spectra of experimental techniques that measure hyperfine interactions can be calculated. The optimized vector and matrix operations of the BLAS and LAPACK libraries are utilized; however, there was a need to develop supplementary code to find an orthonormal set of (left and right) eigenvectors of complex, non-Hermitian matrices. In addition, example code is provided to illustrate the use of SHIML to generate perturbed angular correlation spectra for the special case of polycrystalline samples when anisotropy terms of higher order than A can be neglected. Program summaryProgram title: SHIML Catalogue identifier: AEIF_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIF_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU GPL 3 No. of lines in distributed program, including test data, etc.: 8224 No. of bytes in distributed program, including test data, etc.: 312 348 Distribution format: tar.gz Programming language: C Computer: Any Operating system: LINUX, OS X RAM: Varies Classification: 7.4 External routines: TAPP [1], BLAS [2], a C-interface to BLAS [3], and LAPACK [4] Nature of problem: In condensed matter systems, hyperfine methods such as nuclear magnetic resonance (NMR), Mössbauer effect (ME), muon spin rotation (μSR), and perturbed angular correlation spectroscopy (PAC) measure electronic and magnetic structure within Angstroms of nuclear probes through the hyperfine interaction. When

Scalable inference for stochastic block models

KAUST Repository

Peng, Chengbin; Zhang, Zhihua; Wong, Ka-Chun; Zhang, Xiangliang; Keyes, David E.

2017-01-01

Community detection in graphs is widely used in social and biological networks, and the stochastic block model is a powerful probabilistic tool for describing graphs with community structures. However, in the era of "big data," traditional inference

Stochastic modelling of fusion-product transport and thermalization with nuclear elastic scattering

International Nuclear Information System (INIS)

Deveaux, J.C.

1983-01-01

Monte Carlo methods are developed to model fusion-product (fp) transport and thermalization with both Rutherford scattering and nuclear elastic scattering (NES) in high-temperature (T/sub i/, T/sub e-/ > 50 keV), advanced-fuel (e.g. Cat-D, D- 3 He) plasmas. A discrete-event model is used to superimpose NES collisions on a Rutherford scattering model that contains the Spitzer coefficients of drag, velocity diffusion (VD), and pith-angle scattering (PAS). The effects of NES on fp transport and thermalization are investigated for advanced-fuel, Field-Reversed Mirror (FRM) plasmas that have a significant Hamiltonian-canonical angular momentum (H-Ptheta) space loss cone which scales with the characteristic size (S identical with R/sub HV//3p/sub i/) and applied vacuum magnetic field (B 0 )

Mixture of Regression Models with Single-Index

OpenAIRE

Xiang, Sijia; Yao, Weixin

2016-01-01

In this article, we propose a class of semiparametric mixture regression models with single-index. We argue that many recently proposed semiparametric/nonparametric mixture regression models can be considered special cases of the proposed model. However, unlike existing semiparametric mixture regression models, the new pro- posed model can easily incorporate multivariate predictors into the nonparametric components. Backfitting estimates and the corresponding algorithms have been proposed for...

Stochastic Parametrisations and Regime Behaviour of Atmospheric Models

Science.gov (United States)

Arnold, Hannah; Moroz, Irene; Palmer, Tim

2013-04-01

The presence of regimes is a characteristic of non-linear, chaotic systems (Lorenz, 2006). In the atmosphere, regimes emerge as familiar circulation patterns such as the El-Nino Southern Oscillation (ENSO), the North Atlantic Oscillation (NAO) and Scandinavian Blocking events. In recent years there has been much interest in the problem of identifying and studying atmospheric regimes (Solomon et al, 2007). In particular, how do these regimes respond to an external forcing such as anthropogenic greenhouse gas emissions? The importance of regimes in observed trends over the past 50-100 years indicates that in order to predict anthropogenic climate change, our climate models must be able to represent accurately natural circulation regimes, their statistics and variability. It is well established that representing model uncertainty as well as initial condition uncertainty is important for reliable weather forecasts (Palmer, 2001). In particular, stochastic parametrisation schemes have been shown to improve the skill of weather forecast models (e.g. Berner et al., 2009; Frenkel et al., 2012; Palmer et al., 2009). It is possible that including stochastic physics as a representation of model uncertainty could also be beneficial in climate modelling, enabling the simulator to explore larger regions of the climate attractor including other flow regimes. An alternative representation of model uncertainty is a perturbed parameter scheme, whereby physical parameters in subgrid parametrisation schemes are perturbed about their optimal value. Perturbing parameters gives a greater control over the ensemble than multi-model or multiparametrisation ensembles, and has been used as a representation of model uncertainty in climate prediction (Stainforth et al., 2005; Rougier et al., 2009). We investigate the effect of including representations of model uncertainty on the regime behaviour of a simulator. A simple chaotic model of the atmosphere, the Lorenz '96 system, is used to study

Model tracking dual stochastic controller design under irregular internal noises

International Nuclear Information System (INIS)

Lee, Jong Bok; Heo, Hoon; Cho, Yun Hyun; Ji, Tae Young

2006-01-01

Although many methods about the control of irregular external noise have been introduced and implemented, it is still necessary to design a controller that will be more effective and efficient methods to exclude for various noises. Accumulation of errors due to model tracking, internal noises (thermal noise, shot noise and l/f noise) that come from elements such as resistor, diode and transistor etc. in the circuit system and numerical errors due to digital process often destabilize the system and reduce the system performance. New stochastic controller is adopted to remove those noises using conventional controller simultaneously. Design method of a model tracking dual controller is proposed to improve the stability of system while removing external and internal noises. In the study, design process of the model tracking dual stochastic controller is introduced that improves system performance and guarantees robustness under irregular internal noises which can be created internally. The model tracking dual stochastic controller utilizing F-P-K stochastic control technique developed earlier is implemented to reveal its performance via simulation

Model for cadmium transport and distribution in CHO cells

Energy Technology Data Exchange (ETDEWEB)

Hayden, T.L.; Turner, J.E.; Williams, M.W.; Cook, J.S.; Hsie, A.W.

1982-01-01

A compartmental model is developed to study the transport and distribution of cadmium in Chinese hamster ovary (CHO) cells. Of central importance to the model is the role played by sequestering components which bind free Cd/sup 2 +/ ions. The most important of these is a low-molecular-weight protein, metallothionein, which is produced by the cells in response to an increase in the cellular concentration of Cd/sup 2 +/. Monte Carlo techniques are used to generate a stochastic model based on existing experimental data describing the intracellular transport of cadmium between different compartments. This approach provides an alternative to the usual numerical solution of differential-delay equations that arise in deterministic models. Our model suggests subcellular structures which may be responsible for the accumulation of cadmium and, hence, could account for cadmium detoxification. 4 figures, 1 table.

Network interdiction and stochastic integer programming

CERN Document Server

2003-01-01

On March 15, 2002 we held a workshop on network interdiction and the more general problem of stochastic mixed integer programming at the University of California, Davis. Jesús De Loera and I co-chaired the event, which included presentations of on-going research and discussion. At the workshop, we decided to produce a volume of timely work on the topics. This volume is the result. Each chapter represents state-of-the-art research and all of them were refereed by leading investigators in the respective fields. Problems - sociated with protecting and attacking computer, transportation, and social networks gain importance as the world becomes more dep- dent on interconnected systems. Optimization models that address the stochastic nature of these problems are an important part of the research agenda. This work relies on recent efforts to provide methods for - dressing stochastic mixed integer programs. The book is organized with interdiction papers first and the stochastic programming papers in the second part....

Simulation of nuclear plant operation into a stochastic energy production model

International Nuclear Information System (INIS)

Pacheco, R.L.

1983-04-01

A simulation model of nuclear plant operation is developed to fit into a stochastic energy production model. In order to improve the stochastic model used, and also reduce its computational time burdened by the aggregation of the model of nuclear plant operation, a study of tail truncation of the unsupplied demand distribution function has been performed. (E.G.) [pt

A complementarity model for solving stochastic natural gas market equilibria

International Nuclear Information System (INIS)

Jifang Zhuang; Gabriel, S.A.

2008-01-01

This paper presents a stochastic equilibrium model for deregulated natural gas markets. Each market participant (pipeline operators, producers, etc.) solves a stochastic optimization problem whose optimality conditions, when combined with market-clearing conditions give rise to a certain mixed complementarity problem (MiCP). The stochastic aspects are depicted by a recourse problem for each player in which the first-stage decisions relate to long-term contracts and the second-stage decisions relate to spot market activities for three seasons. Besides showing that such a market model is an instance of a MiCP, we provide theoretical results concerning long-term and spot market prices and solve the resulting MiCP for a small yet representative market. We also note an interesting observation for the value of the stochastic solution for non-optimization problems. (author)

A complementarity model for solving stochastic natural gas market equilibria

International Nuclear Information System (INIS)

Zhuang Jifang; Gabriel, Steven A.

2008-01-01

This paper presents a stochastic equilibrium model for deregulated natural gas markets. Each market participant (pipeline operators, producers, etc.) solves a stochastic optimization problem whose optimality conditions, when combined with market-clearing conditions give rise to a certain mixed complementarity problem (MiCP). The stochastic aspects are depicted by a recourse problem for each player in which the first-stage decisions relate to long-term contracts and the second-stage decisions relate to spot market activities for three seasons. Besides showing that such a market model is an instance of a MiCP, we provide theoretical results concerning long-term and spot market prices and solve the resulting MiCP for a small yet representative market. We also note an interesting observation for the value of the stochastic solution for non-optimization problems

Deterministic and stochastic models for middle east respiratory syndrome (MERS)

Science.gov (United States)

Suryani, Dessy Rizki; Zevika, Mona; Nuraini, Nuning

2018-03-01

World Health Organization (WHO) data stated that since September 2012, there were 1,733 cases of Middle East Respiratory Syndrome (MERS) with 628 death cases that occurred in 27 countries. MERS was first identified in Saudi Arabia in 2012 and the largest cases of MERS outside Saudi Arabia occurred in South Korea in 2015. MERS is a disease that attacks the respiratory system caused by infection of MERS-CoV. MERS-CoV transmission occurs directly through direct contact between infected individual with non-infected individual or indirectly through contaminated object by the free virus. Suspected, MERS can spread quickly because of the free virus in environment. Mathematical modeling is used to illustrate the transmission of MERS disease using deterministic model and stochastic model. Deterministic model is used to investigate the temporal dynamic from the system to analyze the steady state condition. Stochastic model approach using Continuous Time Markov Chain (CTMC) is used to predict the future states by using random variables. From the models that were built, the threshold value for deterministic models and stochastic models obtained in the same form and the probability of disease extinction can be computed by stochastic model. Simulations for both models using several of different parameters are shown, and the probability of disease extinction will be compared with several initial conditions.

Topological interlocking provides stiffness to stochastically micro-cracked materials beyond the transport percolation limit

Science.gov (United States)

Pal, Anirban; Picu, Catalin; Lupulescu, Marian V.

We study the mechanical behavior of two-dimensional, stochastically microcracked continua in the range of crack densities close to, and above the transport percolation threshold. We show that these materials retain stiffness up to crack densities much larger than the transport percolation threshold, due to topological interlocking of sample sub-domains. Even with a linear constitutive law for the continuum, the mechanical behavior becomes non-linear in the range of crack densities bounded by the transport and stiffness percolation thresholds. The effect is due to the fractal nature of the fragmentation process and is not linked to the roughness of individual cracks. We associate this behavior to that of itacolumite, a sandstone that exhibits unusual flexibility.

A computer model of the biosphere, to estimate stochastic and non-stochastic effects of radionuclides on humans

International Nuclear Information System (INIS)

Laurens, J.M.

1985-01-01

A computer code was written to model food chains in order to estimate the internal and external doses, for stochastic and non-stochastic effects, on humans (adults and infants). Results are given for 67 radionuclides, for unit concentration in water (1 Bq/L) and in atmosphere (1 Bq/m 3 )

A coupled stochastic rainfall-evapotranspiration model for hydrological impact analysis

Science.gov (United States)

Pham, Minh Tu; Vernieuwe, Hilde; De Baets, Bernard; Verhoest, Niko E. C.

2018-02-01

A hydrological impact analysis concerns the study of the consequences of certain scenarios on one or more variables or fluxes in the hydrological cycle. In such an exercise, discharge is often considered, as floods originating from extremely high discharges often cause damage. Investigating the impact of extreme discharges generally requires long time series of precipitation and evapotranspiration to be used to force a rainfall-runoff model. However, such kinds of data may not be available and one should resort to stochastically generated time series, even though the impact of using such data on the overall discharge, and especially on the extreme discharge events, is not well studied. In this paper, stochastically generated rainfall and corresponding evapotranspiration time series, generated by means of vine copulas, are used to force a simple conceptual hydrological model. The results obtained are comparable to the modelled discharge using observed forcing data. Yet, uncertainties in the modelled discharge increase with an increasing number of stochastically generated time series used. Notwithstanding this finding, it can be concluded that using a coupled stochastic rainfall-evapotranspiration model has great potential for hydrological impact analysis.

Stochastic Modeling and Analysis of Power System with Renewable Generation

DEFF Research Database (Denmark)

Chen, Peiyuan

Unlike traditional fossil-fuel based power generation, renewable generation such as wind power relies on uncontrollable prime sources such as wind speed. Wind speed varies stochastically, which to a large extent determines the stochastic behavior of power generation from wind farms...... that such a stochastic model can be used to simulate the effect of load management on the load duration curve. As CHP units are turned on and off by regulating power, CHP generation has discrete output and thus can be modeled by a transition matrix based discrete Markov chain. As the CHP generation has a strong diurnal...

Extinction in neutrally stable stochastic Lotka-Volterra models

Science.gov (United States)

Dobrinevski, Alexander; Frey, Erwin

2012-05-01

Populations of competing biological species exhibit a fascinating interplay between the nonlinear dynamics of evolutionary selection forces and random fluctuations arising from the stochastic nature of the interactions. The processes leading to extinction of species, whose understanding is a key component in the study of evolution and biodiversity, are influenced by both of these factors. Here, we investigate a class of stochastic population dynamics models based on generalized Lotka-Volterra systems. In the case of neutral stability of the underlying deterministic model, the impact of intrinsic noise on the survival of species is dramatic: It destroys coexistence of interacting species on a time scale proportional to the population size. We introduce a new method based on stochastic averaging which allows one to understand this extinction process quantitatively by reduction to a lower-dimensional effective dynamics. This is performed analytically for two highly symmetrical models and can be generalized numerically to more complex situations. The extinction probability distributions and other quantities of interest we obtain show excellent agreement with simulations.

Markov Stochastic Technique to Determine Galactic Cosmic Ray ...

Indian Academy of Sciences (India)

A new numerical model of particle propagation in the Galaxy has been developed, which allows the study of cosmic-ray production and propagation in 2D. The model has been used to solve cosmic ray diffusive transport equation with a complete network of nuclear interactions using the time backward Markov stochastic ...

Applications of stochastic models and geostatistical analyses to study sources and spatial patterns of soil heavy metals in a metalliferous industrial district of China.

Science.gov (United States)

Zhong, Buqing; Liang, Tao; Wang, Lingqing; Li, Kexin

2014-08-15

An extensive soil survey was conducted to study pollution sources and delineate contamination of heavy metals in one of the metalliferous industrial bases, in the karst areas of southwest China. A total of 597 topsoil samples were collected and the concentrations of five heavy metals, namely Cd, As (metalloid), Pb, Hg and Cr were analyzed. Stochastic models including a conditional inference tree (CIT) and a finite mixture distribution model (FMDM) were applied to identify the sources and partition the contribution from natural and anthropogenic sources for heavy metal in topsoils of the study area. Regression trees for Cd, As, Pb and Hg were proved to depend mostly on indicators of anthropogenic activities such as industrial type and distance from urban area, while the regression tree for Cr was found to be mainly influenced by the geogenic characteristics. The FMDM analysis showed that the geometric means of modeled background values for Cd, As, Pb, Hg and Cr were close to their background values previously reported in the study area, while the contamination of Cd and Hg were widespread in the study area, imposing potentially detrimental effects on organisms through the food chain. Finally, the probabilities of single and multiple heavy metals exceeding the threshold values derived from the FMDM were estimated using indicator kriging (IK) and multivariate indicator kriging (MVIK). The high probabilities exceeding the thresholds of heavy metals were associated with metalliferous production and atmospheric deposition of heavy metals transported from the urban and industrial areas. Geostatistics coupled with stochastic models provide an effective way to delineate multiple heavy metal pollution to facilitate improved environmental management. Copyright © 2014 Elsevier B.V. All rights reserved.

Model predictive control classical, robust and stochastic

CERN Document Server

Kouvaritakis, Basil

2016-01-01

For the first time, a textbook that brings together classical predictive control with treatment of up-to-date robust and stochastic techniques. Model Predictive Control describes the development of tractable algorithms for uncertain, stochastic, constrained systems. The starting point is classical predictive control and the appropriate formulation of performance objectives and constraints to provide guarantees of closed-loop stability and performance. Moving on to robust predictive control, the text explains how similar guarantees may be obtained for cases in which the model describing the system dynamics is subject to additive disturbances and parametric uncertainties. Open- and closed-loop optimization are considered and the state of the art in computationally tractable methods based on uncertainty tubes presented for systems with additive model uncertainty. Finally, the tube framework is also applied to model predictive control problems involving hard or probabilistic constraints for the cases of multiplic...

Mixture Modeling: Applications in Educational Psychology

Science.gov (United States)

Harring, Jeffrey R.; Hodis, Flaviu A.

2016-01-01

Model-based clustering methods, commonly referred to as finite mixture modeling, have been applied to a wide variety of cross-sectional and longitudinal data to account for heterogeneity in population characteristics. In this article, we elucidate 2 such approaches: growth mixture modeling and latent profile analysis. Both techniques are…

A low-bias simulation scheme for the SABR stochastic volatility model

NARCIS (Netherlands)

B. Chen (Bin); C.W. Oosterlee (Cornelis); J.A.M. van der Weide

2012-01-01

htmlabstractThe Stochastic Alpha Beta Rho Stochastic Volatility (SABR-SV) model is widely used in the financial industry for the pricing of fixed income instruments. In this paper we develop an lowbias simulation scheme for the SABR-SV model, which deals efficiently with (undesired)

Stochastic mixed-mode oscillations in a three-species predator-prey model

Science.gov (United States)

Sadhu, Susmita; Kuehn, Christian

2018-03-01

The effect of demographic stochasticity, in the form of Gaussian white noise, in a predator-prey model with one fast and two slow variables is studied. We derive the stochastic differential equations (SDEs) from a discrete model. For suitable parameter values, the deterministic drift part of the model admits a folded node singularity and exhibits a singular Hopf bifurcation. We focus on the parameter regime near the Hopf bifurcation, where small amplitude oscillations exist as stable dynamics in the absence of noise. In this regime, the stochastic model admits noise-driven mixed-mode oscillations (MMOs), which capture the intermediate dynamics between two cycles of population outbreaks. We perform numerical simulations to calculate the distribution of the random number of small oscillations between successive spikes for varying noise intensities and distance to the Hopf bifurcation. We also study the effect of noise on a suitable Poincaré map. Finally, we prove that the stochastic model can be transformed into a normal form near the folded node, which can be linked to recent results on the interplay between deterministic and stochastic small amplitude oscillations. The normal form can also be used to study the parameter influence on the noise level near folded singularities.

Stochastic resonance in models of neuronal ensembles

International Nuclear Information System (INIS)

Chialvo, D.R.; Longtin, A.; Mueller-Gerkin, J.

1997-01-01

Two recently suggested mechanisms for the neuronal encoding of sensory information involving the effect of stochastic resonance with aperiodic time-varying inputs are considered. It is shown, using theoretical arguments and numerical simulations, that the nonmonotonic behavior with increasing noise of the correlation measures used for the so-called aperiodic stochastic resonance (ASR) scenario does not rely on the cooperative effect typical of stochastic resonance in bistable and excitable systems. Rather, ASR with slowly varying signals is more properly interpreted as linearization by noise. Consequently, the broadening of the open-quotes resonance curveclose quotes in the multineuron stochastic resonance without tuning scenario can also be explained by this linearization. Computation of the input-output correlation as a function of both signal frequency and noise for the model system further reveals conditions where noise-induced firing with aperiodic inputs will benefit from stochastic resonance rather than linearization by noise. Thus, our study clarifies the tuning requirements for the optimal transduction of subthreshold aperiodic signals. It also shows that a single deterministic neuron can perform as well as a network when biased into a suprathreshold regime. Finally, we show that the inclusion of a refractory period in the spike-detection scheme produces a better correlation between instantaneous firing rate and input signal. copyright 1997 The American Physical Society

A Rigorous Temperature-Dependent Stochastic Modelling and Testing for MEMS-Based Inertial Sensor Errors

Directory of Open Access Journals (Sweden)

Spiros Pagiatakis

2009-10-01

Full Text Available In this paper, we examine the effect of changing the temperature points on MEMS-based inertial sensor random error. We collect static data under different temperature points using a MEMS-based inertial sensor mounted inside a thermal chamber. Rigorous stochastic models, namely Autoregressive-based Gauss-Markov (AR-based GM models are developed to describe the random error behaviour. The proposed AR-based GM model is initially applied to short stationary inertial data to develop the stochastic model parameters (correlation times. It is shown that the stochastic model parameters of a MEMS-based inertial unit, namely the ADIS16364, are temperature dependent. In addition, field kinematic test data collected at about 17 °C are used to test the performance of the stochastic models at different temperature points in the filtering stage using Unscented Kalman Filter (UKF. It is shown that the stochastic model developed at 20 °C provides a more accurate inertial navigation solution than the ones obtained from the stochastic models developed at −40 °C, −20 °C, 0 °C, +40 °C, and +60 °C. The temperature dependence of the stochastic model is significant and should be considered at all times to obtain optimal navigation solution for MEMS-based INS/GPS integration.

A Rigorous Temperature-Dependent Stochastic Modelling and Testing for MEMS-Based Inertial Sensor Errors.

Science.gov (United States)

El-Diasty, Mohammed; Pagiatakis, Spiros

2009-01-01

In this paper, we examine the effect of changing the temperature points on MEMS-based inertial sensor random error. We collect static data under different temperature points using a MEMS-based inertial sensor mounted inside a thermal chamber. Rigorous stochastic models, namely Autoregressive-based Gauss-Markov (AR-based GM) models are developed to describe the random error behaviour. The proposed AR-based GM model is initially applied to short stationary inertial data to develop the stochastic model parameters (correlation times). It is shown that the stochastic model parameters of a MEMS-based inertial unit, namely the ADIS16364, are temperature dependent. In addition, field kinematic test data collected at about 17 °C are used to test the performance of the stochastic models at different temperature points in the filtering stage using Unscented Kalman Filter (UKF). It is shown that the stochastic model developed at 20 °C provides a more accurate inertial navigation solution than the ones obtained from the stochastic models developed at -40 °C, -20 °C, 0 °C, +40 °C, and +60 °C. The temperature dependence of the stochastic model is significant and should be considered at all times to obtain optimal navigation solution for MEMS-based INS/GPS integration.

Stochastic volatility and multi-dimensional modeling in the European energy market

Energy Technology Data Exchange (ETDEWEB)

Vos, Linda

2012-07-01

In energy prices there is evidence for stochastic volatility. Stochastic volatility has effect on the price of path-dependent options and therefore has to be modeled properly. We introduced a multi-dimensional non-Gaussian stochastic volatility model with leverage which can be used in energy pricing. It captures special features of energy prices like price spikes, mean-reversion, stochastic volatility and inverse leverage. Moreover it allows modeling dependencies between different commodities.The derived forward price dynamics based on this multi-variate spot price model, provides a very flexible structure. It includes cotango, backwardation and hump shape forward curves.Alternatively energy prices could be modeled by a 2-factor model consisting of a non-Gaussian stable CARMA process and a non-stationary trend models by a Levy process. Also this model is able to capture special features like price spikes, mean reversion and the low frequency dynamics in the market. An robust L1-filter is introduced to filter out the states of the CARMA process. When applying to German electricity EEX exchange data an overall negative risk-premium is found. However close to delivery a positive risk-premium is observed.(Author)

Stochastic Load Models and Footbridge Response

DEFF Research Database (Denmark)

Pedersen, Lars; Frier, Christian

2015-01-01

Pedestrians may cause vibrations in footbridges and these vibrations may potentially be annoying. This calls for predictions of footbridge vibration levels and the paper considers a stochastic approach to modeling the action of pedestrians assuming walking parameters such as step frequency, pedes...

On cross-currency models with stochastic volatility and correlated interest rates

NARCIS (Netherlands)

Grzelak, L.A.; Oosterlee, C.W.

2010-01-01

We construct multi-currency models with stochastic volatility and correlated stochastic interest rates with a full matrix of correlations. We first deal with a foreign exchange (FX) model of Heston-type, in which the domestic and foreign interest rates are generated by the short-rate process of

On the Realistic Stochastic Model of GPS Observables: Implementation and Performance

Science.gov (United States)

Zangeneh-Nejad, F.; Amiri-Simkooei, A. R.; Sharifi, M. A.; Asgari, J.

2015-12-01

High-precision GPS positioning requires a realistic stochastic model of observables. A realistic GPS stochastic model of observables should take into account different variances for different observation types, correlations among different observables, the satellite elevation dependence of observables precision, and the temporal correlation of observables. Least-squares variance component estimation (LS-VCE) is applied to GPS observables using the geometry-based observation model (GBOM). To model the satellite elevation dependent of GPS observables precision, an exponential model depending on the elevation angles of the satellites are also employed. Temporal correlation of the GPS observables is modelled by using a first-order autoregressive noise model. An important step in the high-precision GPS positioning is double difference integer ambiguity resolution (IAR). The fraction or percentage of success among a number of integer ambiguity fixing is called the success rate. A realistic estimation of the GNSS observables covariance matrix plays an important role in the IAR. We consider the ambiguity resolution success rate for two cases, namely a nominal and a realistic stochastic model of the GPS observables using two GPS data sets collected by the Trimble R8 receiver. The results confirm that applying a more realistic stochastic model can significantly improve the IAR success rate on individual frequencies, either on L1 or on L2. An improvement of 20% was achieved to the empirical success rate results. The results also indicate that introducing the realistic stochastic model leads to a larger standard deviation for the baseline components by a factor of about 2.6 on the data sets considered.

Inexact Multistage Stochastic Chance Constrained Programming Model for Water Resources Management under Uncertainties

Directory of Open Access Journals (Sweden)

Hong Zhang

2017-01-01

Full Text Available In order to formulate water allocation schemes under uncertainties in the water resources management systems, an inexact multistage stochastic chance constrained programming (IMSCCP model is proposed. The model integrates stochastic chance constrained programming, multistage stochastic programming, and inexact stochastic programming within a general optimization framework to handle the uncertainties occurring in both constraints and objective. These uncertainties are expressed as probability distributions, interval with multiply distributed stochastic boundaries, dynamic features of the long-term water allocation plans, and so on. Compared with the existing inexact multistage stochastic programming, the IMSCCP can be used to assess more system risks and handle more complicated uncertainties in water resources management systems. The IMSCCP model is applied to a hypothetical case study of water resources management. In order to construct an approximate solution for the model, a hybrid algorithm, which incorporates stochastic simulation, back propagation neural network, and genetic algorithm, is proposed. The results show that the optimal value represents the maximal net system benefit achieved with a given confidence level under chance constraints, and the solutions provide optimal water allocation schemes to multiple users over a multiperiod planning horizon.

The Role of Stochastic Models in Interpreting the Origins of Biological Chirality

Directory of Open Access Journals (Sweden)

Gábor Lente

2010-04-01

Full Text Available This review summarizes recent stochastic modeling efforts in the theoretical research aimed at interpreting the origins of biological chirality. Stochastic kinetic models, especially those based on the continuous time discrete state approach, have great potential in modeling absolute asymmetric reactions, experimental examples of which have been reported in the past decade. An overview of the relevant mathematical background is given and several examples are presented to show how the significant numerical problems characteristic of the use of stochastic models can be overcome by non-trivial, but elementary algebra. In these stochastic models, a particulate view of matter is used rather than the concentration-based view of traditional chemical kinetics using continuous functions to describe the properties system. This has the advantage of giving adequate description of single-molecule events, which were probably important in the origin of biological chirality. The presented models can interpret and predict the random distribution of enantiomeric excess among repetitive experiments, which is the most striking feature of absolute asymmetric reactions. It is argued that the use of the stochastic kinetic approach should be much more widespread in the relevant literature.

Moment Closure for the Stochastic Logistic Model

National Research Council Canada - National Science Library

Singh, Abhyudai; Hespanha, Joao P

2006-01-01

..., which we refer to as the moment closure function. In this paper, a systematic procedure for constructing moment closure functions of arbitrary order is presented for the stochastic logistic model...

Stochastic persistence and stationary distribution in an SIS epidemic model with media coverage

Science.gov (United States)

Guo, Wenjuan; Cai, Yongli; Zhang, Qimin; Wang, Weiming

2018-02-01

This paper aims to study an SIS epidemic model with media coverage from a general deterministic model to a stochastic differential equation with environment fluctuation. Mathematically, we use the Markov semigroup theory to prove that the basic reproduction number R0s can be used to control the dynamics of stochastic system. Epidemiologically, we show that environment fluctuation can inhibit the occurrence of the disease, namely, in the case of disease persistence for the deterministic model, the disease still dies out with probability one for the stochastic model. So to a great extent the stochastic perturbation under media coverage affects the outbreak of the disease.

Persistence and extinction for a stochastic logistic model with infinite delay

Directory of Open Access Journals (Sweden)

Chun Lu

2013-11-01

Full Text Available This article, studies a stochastic logistic model with infinite delay. Using a phase space, we establish sufficient conditions for the extinction, nonpersistence in the mean, weak persistence, and stochastic permanence. A threshold between weak persistence and extinction is obtained. Our results state that different types of environmental noises have different effects on the persistence and extinction, and that the delay has no impact on the persistence and extinction for the stochastic model in the autonomous case. Numerical simulations illustrate the theoretical results.

Stochastic modeling for reliability shocks, burn-in and heterogeneous populations

CERN Document Server

Finkelstein, Maxim

2013-01-01

Focusing on shocks modeling, burn-in and heterogeneous populations, Stochastic Modeling for Reliability naturally combines these three topics in the unified stochastic framework and presents numerous practical examples that illustrate recent theoretical findings of the authors.  The populations of manufactured items in industry are usually heterogeneous. However, the conventional reliability analysis is performed under the implicit assumption of homogeneity, which can result in distortion of the corresponding reliability indices and various misconceptions. Stochastic Modeling for Reliability fills this gap and presents the basics and further developments of reliability theory for heterogeneous populations. Specifically, the authors consider burn-in as a method of elimination of ‘weak’ items from heterogeneous populations. The real life objects are operating in a changing environment. One of the ways to model an impact of this environment is via the external shocks occurring in accordance with some stocha...

Some recent developments in stochastic volatility modelling

DEFF Research Database (Denmark)

Barndorff-Nielsen, Ole Eiler; Nicolato, Elisa; Shephard, N.

2002-01-01

This paper reviews and puts in context some of our recent work on stochastic volatility (SV) modelling for financial economics. Here our main focus is on: (i) the relationship between subordination and SV, (ii) OU based volatility models, (iii) exact option pricing, (iv) realized power variation...

A stochastic inventory policy with limited transportation capacity

NARCIS (Netherlands)

Dabia, S.; Kiesmüller, G.P.; Dellaert, N.P.

2007-01-01

In this paper we consider a stochastic single-item inventory problem. A retailer keeps a single product on stock to satisfy customers stochastic demand. The retailer is replenished periodically from a supplier with ample stock. For the delivery of the product, trucks with finite capacity are

Scalable inference for stochastic block models

KAUST Repository

Peng, Chengbin

2017-12-08

Community detection in graphs is widely used in social and biological networks, and the stochastic block model is a powerful probabilistic tool for describing graphs with community structures. However, in the era of "big data," traditional inference algorithms for such a model are increasingly limited due to their high time complexity and poor scalability. In this paper, we propose a multi-stage maximum likelihood approach to recover the latent parameters of the stochastic block model, in time linear with respect to the number of edges. We also propose a parallel algorithm based on message passing. Our algorithm can overlap communication and computation, providing speedup without compromising accuracy as the number of processors grows. For example, to process a real-world graph with about 1.3 million nodes and 10 million edges, our algorithm requires about 6 seconds on 64 cores of a contemporary commodity Linux cluster. Experiments demonstrate that the algorithm can produce high quality results on both benchmark and real-world graphs. An example of finding more meaningful communities is illustrated consequently in comparison with a popular modularity maximization algorithm.

A stochastic analysis for a phytoplankton-zooplankton model

International Nuclear Information System (INIS)

Ge, G; Wang, H-L; Xu, J

2008-01-01

A simple phytoplankton-zooplankton nonlinear dynamical model was proposed to study the coexistence of all the species and a Hopf bifurcation was observed. In order to study the effect of environmental robustness on this system, we have stochastically perturbed the system with respect to white noise around its positive interior equilibrium. We have observed that the system remains stochastically stable around the positive equilibrium for same parametric values in the deterministic situation

ARMA modeling of stochastic processes in nuclear reactor with significant detection noise

International Nuclear Information System (INIS)

Zavaljevski, N.

1992-01-01

The theoretical basis of ARMA modelling of stochastic processes in nuclear reactor was presented in a previous paper, neglecting observational noise. The identification of real reactor data indicated that in some experiments the detection noise is significant. Thus a more rigorous theoretical modelling of stochastic processes in nuclear reactor is performed. Starting from the fundamental stochastic differential equations of the Langevin type for the interaction of the detector with neutron field, a new theoretical ARMA model is developed. preliminary identification results confirm the theoretical expectations. (author)

INFERENCE AND SENSITIVITY IN STOCHASTIC WIND POWER FORECAST MODELS.

KAUST Repository

Elkantassi, Soumaya

2017-10-03

Reliable forecasting of wind power generation is crucial to optimal control of costs in generation of electricity with respect to the electricity demand. Here, we propose and analyze stochastic wind power forecast models described by parametrized stochastic differential equations, which introduce appropriate fluctuations in numerical forecast outputs. We use an approximate maximum likelihood method to infer the model parameters taking into account the time correlated sets of data. Furthermore, we study the validity and sensitivity of the parameters for each model. We applied our models to Uruguayan wind power production as determined by historical data and corresponding numerical forecasts for the period of March 1 to May 31, 2016.

INFERENCE AND SENSITIVITY IN STOCHASTIC WIND POWER FORECAST MODELS.

KAUST Repository

Elkantassi, Soumaya; Kalligiannaki, Evangelia; Tempone, Raul

2017-01-01

Reliable forecasting of wind power generation is crucial to optimal control of costs in generation of electricity with respect to the electricity demand. Here, we propose and analyze stochastic wind power forecast models described by parametrized stochastic differential equations, which introduce appropriate fluctuations in numerical forecast outputs. We use an approximate maximum likelihood method to infer the model parameters taking into account the time correlated sets of data. Furthermore, we study the validity and sensitivity of the parameters for each model. We applied our models to Uruguayan wind power production as determined by historical data and corresponding numerical forecasts for the period of March 1 to May 31, 2016.

Guaranteed Bounds on Information-Theoretic Measures of Univariate Mixtures Using Piecewise Log-Sum-Exp Inequalities

KAUST Repository

Nielsen, Frank

2016-12-09

Information-theoreticmeasures, such as the entropy, the cross-entropy and the Kullback-Leibler divergence between two mixture models, are core primitives in many signal processing tasks. Since the Kullback-Leibler divergence of mixtures provably does not admit a closed-form formula, it is in practice either estimated using costly Monte Carlo stochastic integration, approximated or bounded using various techniques. We present a fast and generic method that builds algorithmically closed-form lower and upper bounds on the entropy, the cross-entropy, the Kullback-Leibler and the α-divergences of mixtures. We illustrate the versatile method by reporting our experiments for approximating the Kullback-Leibler and the α-divergences between univariate exponential mixtures, Gaussian mixtures, Rayleigh mixtures and Gamma mixtures.

Parameter discovery in stochastic biological models using simulated annealing and statistical model checking.

Science.gov (United States)

Hussain, Faraz; Jha, Sumit K; Jha, Susmit; Langmead, Christopher J

2014-01-01

Stochastic models are increasingly used to study the behaviour of biochemical systems. While the structure of such models is often readily available from first principles, unknown quantitative features of the model are incorporated into the model as parameters. Algorithmic discovery of parameter values from experimentally observed facts remains a challenge for the computational systems biology community. We present a new parameter discovery algorithm that uses simulated annealing, sequential hypothesis testing, and statistical model checking to learn the parameters in a stochastic model. We apply our technique to a model of glucose and insulin metabolism used for in-silico validation of artificial pancreata and demonstrate its effectiveness by developing parallel CUDA-based implementation for parameter synthesis in this model.

Modeling VOC transport in simulated waste drums

International Nuclear Information System (INIS)

Liekhus, K.J.; Gresham, G.L.; Peterson, E.S.; Rae, C.; Hotz, N.J.; Connolly, M.J.

1993-06-01

A volatile organic compound (VOC) transport model has been developed to describe unsteady-state VOC permeation and diffusion within a waste drum. Model equations account for three primary mechanisms for VOC transport from a void volume within the drum. These mechanisms are VOC permeation across a polymer boundary, VOC diffusion across an opening in a volume boundary, and VOC solubilization in a polymer boundary. A series of lab-scale experiments was performed in which the VOC concentration was measured in simulated waste drums under different conditions. A lab-scale simulated waste drum consisted of a sized-down 55-gal metal drum containing a modified rigid polyethylene drum liner. Four polyethylene bags were sealed inside a large polyethylene bag, supported by a wire cage, and placed inside the drum liner. The small bags were filled with VOC-air gas mixture and the VOC concentration was measured throughout the drum over a period of time. Test variables included the type of VOC-air gas mixtures introduced into the small bags, the small bag closure type, and the presence or absence of a variable external heat source. Model results were calculated for those trials where the VOC permeability had been measured. Permeabilities for five VOCs [methylene chloride, 1,1,2-trichloro-1,2,2-trifluoroethane (Freon-113), 1,1,1-trichloroethane, carbon tetrachloride, and trichloroethylene] were measured across a polyethylene bag. Comparison of model and experimental results of VOC concentration as a function of time indicate that model accurately accounts for significant VOC transport mechanisms in a lab-scale waste drum

Stochastic modelling in design of mechanical properties of nanometals

International Nuclear Information System (INIS)

Tengen, T.B.; Wejrzanowski, T.; Iwankiewicz, R.; Kurzydlowski, K.J.

2010-01-01

Polycrystalline nanometals are being fabricated through different processing routes and conditions. The consequence is that nanometals having the same mean grain size may have different grain size dispersion and, hence, may have different material properties. This has often led to conflicting reports from both theoretical and experimental findings about the evolutions of the mechanical properties of nanomaterials. The present paper employs stochastic model to study the impact of microstructure evolution during grain growth on the mechanical properties of polycrystalline nanometals. The stochastic model for grain growth and the stochastic model for changes in mechanical properties of nanomaterials are proposed. The model for the mechanical properties developed is tested on aluminium samples.Many salient features of the mechanical properties of the aluminium samples are revealed. The results show that the different mechanisms of grain growth impart different nature of response to the material mechanical properties. The conventional, homologous and anomalous temperature dependences of the yield stress have also been revealed to be due to different nature of interactions of the microstructures during evolution.

Bayesian inference for hybrid discrete-continuous stochastic kinetic models

International Nuclear Information System (INIS)

Sherlock, Chris; Golightly, Andrew; Gillespie, Colin S

2014-01-01

We consider the problem of efficiently performing simulation and inference for stochastic kinetic models. Whilst it is possible to work directly with the resulting Markov jump process (MJP), computational cost can be prohibitive for networks of realistic size and complexity. In this paper, we consider an inference scheme based on a novel hybrid simulator that classifies reactions as either ‘fast’ or ‘slow’ with fast reactions evolving as a continuous Markov process whilst the remaining slow reaction occurrences are modelled through a MJP with time-dependent hazards. A linear noise approximation (LNA) of fast reaction dynamics is employed and slow reaction events are captured by exploiting the ability to solve the stochastic differential equation driving the LNA. This simulation procedure is used as a proposal mechanism inside a particle MCMC scheme, thus allowing Bayesian inference for the model parameters. We apply the scheme to a simple application and compare the output with an existing hybrid approach and also a scheme for performing inference for the underlying discrete stochastic model. (paper)

Stochastic processes in cell biology

CERN Document Server

Bressloff, Paul C

2014-01-01

This book develops the theory of continuous and discrete stochastic processes within the context of cell biology.  A wide range of biological topics are covered including normal and anomalous diffusion in complex cellular environments, stochastic ion channels and excitable systems, stochastic calcium signaling, molecular motors, intracellular transport, signal transduction, bacterial chemotaxis, robustness in gene networks, genetic switches and oscillators, cell polarization, polymerization, cellular length control, and branching processes. The book also provides a pedagogical introduction to the theory of stochastic process – Fokker Planck equations, stochastic differential equations, master equations and jump Markov processes, diffusion approximations and the system size expansion, first passage time problems, stochastic hybrid systems, reaction-diffusion equations, exclusion processes, WKB methods, martingales and branching processes, stochastic calculus, and numerical methods.   This text is primarily...

Fitting Social Network Models Using Varying Truncation Stochastic Approximation MCMC Algorithm

KAUST Repository

Jin, Ick Hoon

2013-10-01

The exponential random graph model (ERGM) plays a major role in social network analysis. However, parameter estimation for the ERGM is a hard problem due to the intractability of its normalizing constant and the model degeneracy. The existing algorithms, such as Monte Carlo maximum likelihood estimation (MCMLE) and stochastic approximation, often fail for this problem in the presence of model degeneracy. In this article, we introduce the varying truncation stochastic approximation Markov chain Monte Carlo (SAMCMC) algorithm to tackle this problem. The varying truncation mechanism enables the algorithm to choose an appropriate starting point and an appropriate gain factor sequence, and thus to produce a reasonable parameter estimate for the ERGM even in the presence of model degeneracy. The numerical results indicate that the varying truncation SAMCMC algorithm can significantly outperform the MCMLE and stochastic approximation algorithms: for degenerate ERGMs, MCMLE and stochastic approximation often fail to produce any reasonable parameter estimates, while SAMCMC can do; for nondegenerate ERGMs, SAMCMC can work as well as or better than MCMLE and stochastic approximation. The data and source codes used for this article are available online as supplementary materials. © 2013 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.

Stochastic Model of Vesicular Sorting in Cellular Organelles

Science.gov (United States)

Vagne, Quentin; Sens, Pierre

2018-02-01

The proper sorting of membrane components by regulated exchange between cellular organelles is crucial to intracellular organization. This process relies on the budding and fusion of transport vesicles, and should be strongly influenced by stochastic fluctuations, considering the relatively small size of many organelles. We identify the perfect sorting of two membrane components initially mixed in a single compartment as a first passage process, and we show that the mean sorting time exhibits two distinct regimes as a function of the ratio of vesicle fusion to budding rates. Low ratio values lead to fast sorting but result in a broad size distribution of sorted compartments dominated by small entities. High ratio values result in two well-defined sorted compartments but sorting is exponentially slow. Our results suggest an optimal balance between vesicle budding and fusion for the rapid and efficient sorting of membrane components and highlight the importance of stochastic effects for the steady-state organization of intracellular compartments.

Stochastic model of radioiodine transport

International Nuclear Information System (INIS)

Schwarz, G.; Hoffman, F.O.

1980-01-01

A research project has been underway at the Oak Ridge National Laboratory with the objective to evaluate dose assessment models and to determine the uncertainty associated with the model predictions. This has resulted in the application of methods to propagate uncertainties through models. Some techniques and results related to this problem are discussed

Modeling field scale unsaturated flow and transport processes

International Nuclear Information System (INIS)