Erez Gilad

Vegetation patterns along a rainfall gradient

A continuum model for vegetation patterns in water limited systems is presented. The model involves two variables, the vegetation biomass density and the soil water density, and takes into account positive feedback relations between the two. The model predicts transitions from bare-soil at low precipitation to homogeneous vegetation at high precipitation through intermediate states of spot, stripe and gap patterns. It also predicts the appearance of ring-like shapes as transient forms toward asymptotic stripes. All these patterns have been identified in observations made on two types of perennial grasses in the Northern Negev. Another prediction of the model is the existence of wide precipitation ranges where different stable states coexist, e.g. a bare soil state and a spot pattern, a spot pattern and a stripe pattern, and so on. This result suggests the interpretation of desertification followed by recovery as an hysteresis loop and sheds light on the irreversibility of desertification. 2003 Elsevier Ltd. All rights reserved.

Endemic disease, awareness, and local behavioural response

The spread of a contagious disease is often accompanied by a rise in awareness of those in the social vicinity of infected individuals, and a subsequent change in behaviour. Such reactions can manifest themselves in lower susceptibility as people try to prevent themselves from catching the disease, but also in lower infectivity because of self-imposed quarantine or better hygiene, shorter durations of infectiousness or longer immunity. We here focus on the scenario of an endemic disease of which members of the population can be either aware or unaware, and consider a broad set of possible reactions. We quantify the impact on the endemicity of a disease in a well-mixed population under the variation of different disease parameters as a consequence of growing awareness in the population. Applying a pair-closure scheme allows us to analyse the effect of local correlations if aware individuals tend to occur near infected cases, and to link this to the amount of overlap between the networks underlying the spread of awareness and disease, respectively. Lastly, we study the consequences on the dynamics when the pathogen and awareness spread at different velocities.

Localized structures in dryland vegetation: Forms and functions

Vegetation patches in drylands are localized structures of biomass and water. We study these structures using a mathematical modeling approach that captures biomass-water feedbacks. Biomass-water structures are found to differ in their spatial forms and ecological functions, depending on species type, soil conditions, precipitation range, and other environmental factors. Asymptotic spot structures can destabilize to form ring structures, expanding in the radial direction, or crescent structures, migrating uphill. Stable spot structures can differ in their soil-water distributions, forming water-enriched patches or water-deprived patches. The various biomass-water structures are expected to function differently in the context of a plant community, forming landscapes of varying species diversity.

A fast algorithm for convolution integrals with space and time variant kernels

Mathematical models in many fields of the physical sciences involve nonlocal terms which are formally similar to convolution integrals. We show that it is possible to approximate a particular class of such integrals, which by themselves are not convolutions, as a linear combination of convolution integrals, allowing for their efficient numerical computation as an O ( N log N ) process.

12 – Model Studies of Ecosystem Engineering in Plant Communities

This chapter presents a synthetic review of the various studies emphasizing aspects of ecosystem engineering. The chapter discusses the spatially explicit dynamic model for plant communities in drylands and explains how it captures the various biomass-water feedbacks. It also describes the model to a single life-form, studying conditions under which it functions as an ecosystem engineer by concentrating the water resource. Considering next the version of the model for two life-forms, the chapter also presents the study the response of herbaceous life-forms to the engineering of woody life forms at different levels of patch organization. It concludes with a few remarks on the significance of detailed modeling of biomass-water feedbacks for studying ecosystem engineering, and with a note on future directions.

Experimental estimation of the delayed neutron fraction βeff of the MAESTRO core in the MINERVE zero power reactor

A method for determining the effective delayed neutron fraction βeff using in-pile reactivity oscillations and Fourier analysis is presented. This method is based on measurements of the reactors power response to small periodic in-pile reactivity perturbations and utilizes Fourier analysis for reconstruction of the reactor zero power transfer function. This approach enables the estimation of βeff using multi-parameter nonlinear weighted least-squares fit. The method extends previous works by accounting for higher harmonics excitation in the frequency domain by the trapezoidal reactivity signal, both in the reactivity perturbation and in the reactor power response. We show that by using this new approach it is possible to obtain the reactor transfer function in a wide range of frequencies, using only a single oscillation frequency. This method is applied to a set of measurements of the MAESTRO core configuration in the MINERVE zero power reactor (ZPR) located at the Cadarache Research Center. The derived value of βeff, using this method, is 711 ± 17 pcm.

Dead time corrections on the Feynman-Y curve using the backward extrapolation method

ABSTRACT Dead time losses in neutron detection, caused by both the detector and the electronics dead time, is a highly nonlinear effect, known to create high biasing in physical experiments as the power grows over a certain threshold. Analytic modeling of the dead time losses is a highly complicated task due to the different nature of the dead time in the different components of the monitoring system (paralyzing vs. non-paralyzing), and the stochastic nature of the fission chains. The most basic analytic models for a paralyzing dead time correction assume a non-correlated source, resulting in an exponential model for the dead time correction. While this model is often used and very useful for correcting the average count rate in low count rates, it is totally impractical in noise experiments and the so-called Feynman-α experiments. In the present study, a new technique is introduced for dead time corrections, based on backward extrapolation of the losses, created by imposing increasing artificial dead time on the data, back to zero. The method is implemented on neutron noise measurements carried out in the MINERVE reactor, demonstrating high accuracy in restoring the corrected values of the Feynman-Y variance-to-mean-ratio.

Novel genetic algorithms for in-core fuel management

Novel genetic algorithms (GAs) are developed by using state-of-the-art selection and crossover operators, e.g., rank selection or tournament selection instead of the traditional roulette (fitness proportionate (FP)) selection operator and novel crossover and mutation operators by considering the chromosomes as permutations (which is a specific feature of the loading pattern (LP) problem). The algorithm is applied to a representative model of a modern pressurized water reactor (PWR) core and implemented using a single objective fitness function (FF), i.e., keff. The results obtained for some reference cases using this setup are excellent. They are obtained using a tournament selection operator with a linear ranking (LR) selection probability method and a new geometric crossover operator that allows for geometrical, rather than random, swaps of gene segments between the chromosomes and control over the sizes of the swapped segments. Finally, the effect of boundary conditions (BCs) on the symmetry of the obtained best solutions is studied and the validity of the “symmetric loading patterns” assumption is tested. [DOI: 10.1115/1.4035883]

Development and Verification of the Dynamic System Code THERMO-T for Research Reactor Accident Analysis

Abstract The application of best-estimate codes [coupled neutron kinetics (NK)/thermal hydraulics (TH)] for safety analyses of research reactors (RRs) has gained considerable momentum during the past decade. Application of these codes is largely facilitated by the high level of technological maturity and expertise that these codes allow as a safety technology in nuclear power plants, and it is largely driven by International Atomic Energy Agency activities. The present study belongs in this framework and presents the development and application of the coupled NK and TH code THERMO-T to the analysis of protected reactivity insertion accidents and loss-of-flow accidents in a typical RR with standard Materials Testing Reactor plate-type fuel elements. The coupling is realized by considering the neutronic reactivity feedbacks of the fuel and coolant temperatures and a heat generation model for the reactor power. The neutron flux in the reactor core is solved by applying point reactor kinetic equations and employing radial and axial power distributions calculated from a three-dimensional full-core model by the continuous-energy Monte Carlo reactor physics code Serpent. The evolution of temporal and spatial distributions of the fuel, cladding, and coolant temperatures is calculated for all fuel channels by using a finite volume time implicit numerical scheme for solving a three-conservation equation model. In this study, additional features, such as critical heat flux ratio prediction and decay heat model, are implemented for both highly enriched uranium and low-enriched uranium cores, and a comprehensive comparison of THERMO-T results is performed against other codes.

A Dynamical System Approach to Aridity and Desertification

A large-scale view of arid regions often shows that the vegetation grows in patterns. These are related to the amount of precipitation as well as to the topography. A model is presented that reproduces the wide range of patterns observed in water-limited regions, from bare soil at very low precipitation to uniform cover at high precipitation, through intermediate states of spot-, stripe-and hole-patterns. The model predicts the coexistence of more than one stable state in a given range