B. E. J. Bodmann

Modeling individual behaviors in crowd simulation

This paper presents a model for studying the impact of individual agent characteristics in emergent groups, based on the evacuation efficiency as a result of local interactions. We used the physically based model of crowd simulation proposed by Helbing et al. (2000) and generalized it in order to deal with different individualities for agent and group behaviors. In addition, we present a framework to visualize the virtual agents and discuss the obtained results. A variety of simulations with different parameter sets shows significant impact on the evacuation scenario.

Analytical Model for Air Pollution in the Atmospheric Boundary Layer

The worldwide concern due to the increasing frequency of ecological disasters on our planet urged the scientific community to take action. One of the possible measures are analytical descriptions of pollution related phenomena, or simulations by effective and operational models with quantitative predictive power. The atmosphere is considered the principal vehicle by which pollutant materials are dispersed in the environment, that are either released from the productive and private sector or eventually in accidental events and thus may result in contamination of plants, animals and humans. Therefore, the evaluation of airborne material transport in the Atmospheric Boundary Layer (ABL) is one of the requirements for maintenance, protection and recovery of the ecological system. In order to analyse the consequences of pollutant discharge, atmospheric dispersion models are of need, which have to be tuned using specific meteorological parameters and conditions for the considered region. Moreover, they shall be subject to the local orography and shall supply with realistic information concerning environmental consequences and further help reduce impact from potential accidents such as fire events and others. Moreover, case studies by model simulations may be used to establish limits for the escape of pollutant material from specific sites into the atmosphere.

On the Fractional Neutron Point Kinetics Equations

This work proposes a fractional derivative model for some anomalous neutron diffusion phenomena in nuclear reactors. The model is solved in terms of the neutron flux density and current. The fractional diffusion model displayed may be applied to large variations neutron cross-section that normally prevent the use of the classic model of the neutron diffusion equation. In this chapter we present a new method and approach for solving the fractional neutron kinetics equations and several precursor groups using the decomposition method.

Non-Linear Radiative-Conductive Heat Transfer in a Heterogeneous Gray Plane-Parallel Participating Medium

Radiative transfer considers problems that involve the physical phenomenon of energy transfer by radiation in media. These phenomena occur in a variety of realms (Ahmad & Deering, 1992; Tsai & Ozisik, 1989; Wilson & Sen, 1986; Yi et al., 1996) including optics (Liu et al., 2006), astrophysics (Pinte et al., 2009), atmospheric science (Thomas & Stamnes, 2002), remote sensing (Shabanov et al., 2007) and engineering applications like heat transport by radiation (Brewster, 1992) for instance or radiative transfer laser applications (Kim & Guo, 2004). Furthermore, applications to other media such as biological tissue, powders, paints among others may be found in the literature (see ref. (Yang & Kruse, 2004) and references therein). Although radiation in its basic form is understood as a photon flux that requires a stochastic approach taking into account local microscopic interactions of a photon ensemble with some target particles like atoms, molecules, or effective micro-particles such as impurities, this scenario may be conveniently modelled by a radiation field, i.e. a radiation intensity, in a continuous medium where a microscopic structure is hidden in effective model parameters, to be specified later. The propagation of radiation through a homogeneous or heterogeneous medium suffers changes by several isotropic or non-isotropic processes like absorption, emission and scattering, respectively, that enter the mathematical approach in form of a non-linear radiative transfer equation. The non-linearity of the equation originates from a local thermal description using the Stefan-Boltzmann law that is related to heat transport by radiation which in turn is related to the radiation intensity and renders the radiative transfer problem a radiative-conductive one (Ozisik, 1973; Pomraning, 2005). Here, local thermal description means, that the domain where a temperature is attributed to, is sufficiently large in order to allow for the definition of a temperature, i.e. a local radiative equilibrium. The principal quantity of interest is the intensity I, that describes the radiation energy flow through an infinitesimal oriented area dΣ = ndΣ with outward normal vector n into the solid angle dΩ = ΩdΩ, where Ω represents the direction of the flow considered, with angle θ of the normal vector and the flow direction n · Ω = cos θ = μ. In the present case we focus on the non-linearity of the radiative-conductive transfer problem and therefore introduce the simplification of an integrated spectral intensity over all wavelengths or equivalently all frequencies that contribute to the radiation flow and further ignore possible effects due to polarization. Also possible effects that need in the formalism properties such as coherence 8

Existence Theory for Radiative Flows

We consider the coupling of radiative heat transfer equations and the energy equation for the temperature Tof a compressible fluid occupying a bounded convex region D with smooth boundary. Using the technique of upper and lower sequences associated with integro-parabolic equations, we establish the existence and uniqueness of a solution T, 0 ≤ Λ− ≤ T(x,t) ≤ Λ+ < ∞ with corresponding radiative intensity I(x,Ω,ν,t) where the total incident radiation satifies ∫S2 I(x,Ω,ν,t)dΩ = Sg B(ν,t)+Sb B(ν,Tb), and where Sb and Sg are positivity preserving linear operator, Tb is the external temperature of the boundary, and B is Plancks function. We also establish certain energy estimates for T.

A nonstiff solution for the stochastic neutron point kinetics equations

Abstract We propose an approach to solve the stochastic neutron point kinetics equations using an adaptation of the diagonalization-decomposition method (DDM). This new approach (Double-DDM) yields a nonstiff solution for the stochastic formulation, allowing the calculation of the neutron and precursor densities at any time of interest without the need of using progressive time steps. We use Double-DDM to compute results for stochastic problems with constant, linear, and sinusoidal reactivities. We show that these results strongly agree with those obtained by other approaches established in the literature. We also compute and analyze the first four statistical moments of the solutions.

ON A CLOSED FORM SOLUTION OF THE POINT KINETICS EQUATIONS WITH REACTIVITY FEEDBACK OF TEMPERATURE

An analytical solution of the point kinetics equations to calculate time-dependent reactivity by the decomposition method has recently appeared in the literature. In this paper, we consider the neutron point kinetics equations together with temperature feedback effects. To this end, point kinetics is perturbed by a temperature equation that depends on the neutron density, obtaining a second-order non-linear ordinary differential equation. This equation is then solved by the decomposition method by expanding the neutron density in a series and expressing the non-linear terms by Adomian polynomials. Upon substituting these expansions into the non-linear ordinary equation, we construct a recursive set of linear problems that can be solved and resulting in an exact analytical representation for the solution. We also report numerical simulations and comparison against literature results.

On an Analytical Model for the Radioactive Contaminant Release in the Atmosphere from Nuclear Power Plants

While the renaissance of nuclear power was motivated by the increasing energy demand and the related climate problem, the recent history of nuclear power, more specifically two disastrous accidents have forced focus on nuclear safety. Although, experience gathered along nuclear reactor developments has sharpened the rules and regulations that lead to the commissioning of latest generation nuclear technology, an issue of crucial concern is the environmental monitoring around nuclear power plants. These measures consider principally the dispersion of radioactive material that either may be released in control actions or in accidents, where in the latter knowledge from simulations guide the planning of emergency actions. In this line the following contribution focuses on the question of radioactive material dispersion after discharge from a nuclear power plant.

An Analytical Solution for the General Perturbed Diffusion Equation by an Integral Transform Technique

In the developments of nuclear energy, new reactor concepts are being proposed and explored, where innovative ideas need to be tested by means of simulations. Although the original neutron calculations start from a transport equation, many approaches reduce the calculation to diffusion equations, since the Boltzmann equation for neutron transport is still considered a challenge (see, for example, [Le05], [Se07], and the references therein). A detailed sequence, starting from a neutron transport equation (Boltzmann equation) until the reduction to a diffusion phenomenon using Fick’s hypothesis, is given, for instance, in [Se07]. Our principal concern here is an effective analytical method for the general perturbed neutron diffusion equation by an integral transform technique. To this end, we present a procedure that allows us to construct an analytical solution of the multi-group neutron diffusion equation in Cartesian geometry using well-established integral transform procedures [He05]. Once the general structure of the solution is determined, we may directly calculate the neutron flux (which is an analytical expression), and the only quantity which is determined numerically at the end of the calculation is criticality. In what follows we present the procedure, considering a generic multi-group calculation for an arbitrary number of energy intervals. Due to the fact that the geometric extension of the reactor core is typically very much larger in one dimension compared to the other two length scales, we may cast the calculation into a two-dimensional (2D) setting.

Recursive solutions for multi-group neutron kinetics diffusion equations in homogeneous three-dimensional rectangular domains with time dependent perturbations

Abstract In the present work we solve in analytical representation the three dimensional neutron kinetic diffusion problem in rectangular Cartesian geometry for homogeneous and bounded domains for any number of energy groups and precursor concentrations. The solution in analytical representation is constructed using a hierarchical procedure, i. e. the original problem is reduced to a problem previously solved by the authors making use of a combination of the spectral method and a recursive decomposition approach. Time dependent absorption cross sections of the thermal energy group are considered with step, ramp and Chebyshev polynomial variations. For these three cases, we present numerical results and discuss convergence properties and compare our results to those available in the literature.