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Several different methods were used in this work to elucidate these observations. These methods include basic field work, measurements of physical pebble and gravel properties and, the application of different numerical modelling schemes. In particular, the finite element method in 2D and the discrete element method in 2D and 3D were used in order to quantify mechanisms of pebble deformation. The main objective of this work was to identify potential mechanisms that control particle breakage in fluvial gravel, which could explain the clustered spatial distribution of broken pebbles.

The results of 2D finite element stress analysis indicated that the breakage load of differently located and oriented diametrical loading axes on a pebble varies and, that the weakest loading configuration coincides with the smallest principal axis of the pebble. The 3D discrete element method was applied to study the contact load distribution on pebbles in gravel deposits and the influence of different degrees of particle imbrication and orientation. The results showed that an increase of the number of imbricated particles leads to a significant load transfer from the rim to the centre of the oblate sides of the ellipsoidal particles.

The findings of these pebble -scale investigations provided the basis for outcropscale modelling, where simulated gravel layers were subjected to layer-parallel extension. These outcrop-scale models revealed the existence of a particle breakage enhancing mechanism that becomes active during early stages of shear band formation. The interaction of such shear bands with the less deformed host material results in particle stress concentrations and subsequently.

Pebble bed reactors contain large numbers of spherical fuel elements arranged randomly. Determining the motion and location of these fuel elements is required for calculating certain parameters of pebble bed reactor operation. This model uses a three dimensional differential static friction approximation extended from the two dimensional Cundall and Strack model. The derivation of determining the rotational transformation of pebble to pebble static friction force is provided. A new implementation for a differential rotation method for pebble to container static friction force has been created.

Previous published methods are insufficient for pebble bed reactor geometries. A new analytical static friction benchmark is documented that can be used to verify key static friction simulation parameters. This benchmark is based on determining the exact pebble to pebble and pebble to container static friction coefficients required to maintain a stable five sphere pyramid. Pebble bed pebble motion: Pebble bed reactors PBR have moving graphite fuel pebbles. This unique feature provides advantages, but also means that simulation of the reactor requires understanding the typical motion and location of the granular flow of pebbles.

This dissertation presents a method for simulation of motion of the pebbles in a PBR. This model simulates gravitational force and contact forces including kinetic and true static friction. It's used for a variety of tasks including simulation of the effect of earthquakes on a PBR, calculation of packing fractions, Dancoff factors, pebble wear and the pebble force on the walls.

The simulator includes a new differential static friction model for the varied geometries of PBRs. A new static friction benchmark was devised via analytically solving the mechanics equations to determine the minimum pebble-to-pebble friction and pebble -to-surface friction for a five pebble pyramid. This pyramid check as well as a comparison to the Janssen formula was used to test the new static friction equations.

Because larger pebble bed simulations involve hundreds of thousands of pebbles and long periods of time, the PEBBLES code has been parallelized. For the shared memory architecture, the code uses a new O n lock-less parallel collision detection algorithm to determine which pebbles are likely to be in contact. The new collision detection algorithm improves on the traditional non-parallel O n log n collision detection algorithm. These features combine to form a fast parallel pebble motion simulation. The Conditions for Educational Equality.

The contents of this Supplementary Paper are an attempt to refine the meaning of the common concept of equality of opportunity. The following papers are included: Jarrett; "Poverty and Childhood," Jerome S. Webster; "Increasing Educational Opportunity: You have probably already heard about the Panel, but you may have wondered what the Equal Opportunities Programme actually does to ensure fair treatment in the recruitment and career development of men and women, and to allow all to work in an atmosphere of safety, dignity, and mutual respect.

By attending this meeting CERN people will have the chance to learn about the work of the Panel, its recommendations to Management, and the subsequent actions taken by the Organization. Triangle-free graphs whose independence number equals the degree. In a triangle-free graph, the neighbourhood of every vertex is an independent set.

We investigate the class S of triangle-free graphs where the neighbourhoods of vertices are maximum independent sets. A role of valence particles number equal to The importance of the N p N n parametrization was first demonstrated by Casten in connection with the role of the proton-neutron interaction in the growth of deformation away from shell closures, and there have subsequently been many developments in this theme. Social equality in the number of choice options is represented in the ventromedial prefrontal cortex. A distinct aspect of the sense of fairness in humans is that we care not only about equality in material rewards but also about equality in nonmaterial values.

One such value is the opportunity to choose freely among many options, often regarded as a fundamental right to economic freedom. In modern developed societies, equal opportunities in work, living, and lifestyle are enforced by antidiscrimination laws. Despite the widespread endorsement of equal opportunity, no studies have explored how people assign value to it. We used functional magnetic resonance imaging to identify the neural substrates for subjective valuation of equality in choice opportunity. Participants performed a two-person choice task in which the number of choices available was varied across trials independently of choice outcomes.

By using this procedure, we manipulated the degree of equality in choice opportunity between players and dissociated it from the value of reward outcomes and their equality. We found that activation in the ventromedial prefrontal cortex vmPFC tracked the degree to which the number of options between the two players was equal. In contrast, activation in the ventral striatum tracked the number of options available to participants themselves but not the equality between players. Our results demonstrate that the vmPFC, a key brain region previously implicated in the processing of social values, is also involved in valuation of equality in choice opportunity between individuals.

These findings may provide valuable insight into the human ability to value equal opportunity, a characteristic long emphasized in politics, economics, and philosophy. Therefore the pebble flow, which is based on the theory of particle streaming, is one of the most important research subjects of the pebble bed reactor engineering. The in-core pebble flow is a very slow particle flow or called quasi-static particle flow , which is very different from the usual particle motion. How to accurately describe the characteristics of in-core pebble flow is a central issue for this subject.

Due to the presence of random flow, the cross-mixing phenomenon will occur inevitably. In the present paper, the mixing phenomenon of pebble flow is generalized on the basis of experiment results. The pebble flow cross-mixing probability serves as the parameter which describes both the regularity and the randomness of pebble flow.

The results are provided in the form of diagrammatic presentation. X-ray tomography investigations on pebble bed structures. With increasing distance from the wall, the regular structure vanishes and the bulk values are approached after the 4th wall layer away from the walls. Concerning the sum of contact surfaces per pebble , it is shown that the component normal to the compression axis normal to the heat flow is approximately independent of the pebble location.

For strongly compressed pebble beds, this implies that by extrapolation of the bulk value of k to the wall a further heat resistance might be neglected. Fusion reactor blanket, pebble beds, granular materials, thermal-mechanical behaviour, thermal conductivity, microtomography, void fraction, co-ordination number , contact surfaces. Modeling stationary and moving pebbles in a pebble bed reactor. This paper presents a numerical study of the stationary and moving pebbles in a pebble bed reactor PBR by means of discrete element method DEM.

The packing structure of stationary pebbles is simulated by a filling process that terminates with the settling of the pebbles into a PBR. The packing structural properties are obtained and analyzed. Subsequently, when the outlet of the PBR is opened during the operation of the PBR, the stationary pebbles start to flow downward and are removed at the bottom of the PBR. The dynamic behavior of pebbles is predicted and discussed. Our results indicate the DEM can offer both macroscopic and microscopic information for PBR design calculations and safety assessment.

Porous structure analysis of large-scale randomly packed pebble bed in high temperature gas-cooled reactor. Nuclear and Radiation Safety Center. A three-dimensional pebble bed corresponding to the randomly packed bed in the heat transfer test facility built for the High Temperature Reactor Pebble bed Modules HTR-PM in Shandong Shidaowan is simulated via discrete element method. Based on the simulation, we make a detailed analysis on the packing structure of the pebble bed from several aspects, such as transverse section image, longitudinal section image, radial and axial porosity distributions, two-dimensional porosity distribution and coordination number distribution.

The calculation results show that radial distribution of porosity is uniform in the center and oscillates near the wall; axial distribution of porosity oscillates near the bottom and linearly varies along height due to effect of gravity; the average coordination number is about seven and equals to the maximum coordination number frequency. The fully established three-dimensional packing structure analysis of the pebble bed in this work is of fundamental significance to understand the flow and heat transfer characteristics throughout the pebble -bed type structure.

Modeling stationary and dynamic pebbles in a pebble bed reactor. This paper presents a numerical study of the stationary and dynamic pebbles in a pebble bed reactor PBR by means of discrete element method DEM. At first, the packing structure of stationary pebbles is simulated by filling process until the settling of pebbles into PBR. Subsequently, when the outlet of PBR is open during the operational maintenance of PBR, the stationary pebbles start to flow downward and are removed at the bottom of PBR.

Directory of Open Access Journals Sweden. Local pebble surface temperature distributions in several default conditions are investigated. Thermal removal capacities of molten salt are confirmed in the case of nominal condition; the pebble surface temperature under the condition of local power distortion shows the tolerance of pebble in extreme neutron dose exposure. The numerical experiments of local pebble insufficient cooling indicate that in the molten salt cooled pebble bed reactor, the pebble surface temperature is not very sensitive to loss of partial coolant.

The methods and results of this paper would be useful for optimum designs and safety analysis of molten salt cooled pebble bed reactors. Pebble -bed pebble motion: This report presents a method for simulation of motion of the pebbles in a PBR. Ceramic breeder pebble bed packing stability under cyclic loads. Considering the optimization of blanket performance, it is desired that the bed morphology and packing state during reactor operation are stable and predictable. Both experimental and numerical work are performed to explore the stability of pebble beds, in particular under pulsed loading conditions.

The obtained data shows the stress-strain loop initially moves towards the larger strain and nearly saturates after a certain number of cyclic loading cycles. Mechanics of a crushable pebble assembly using discrete element method. The influence of crushing of individual pebbles on the overall strength of a pebble assembly is investigated using discrete element method. An assembly comprising of spherical pebbles is assigned with random critical failure energies with a Weibull distribution in accordance with the experimental observation.

The crushable pebble assembly shows a significant difference in stress—strain response in comparison to a non-crushable pebble assembly. The analysis shows that a ideal plasticity like behaviour constant stress with increase in strain is the characteristic of a crushable pebble assembly with sudden damage. The damage accumulation law plays a critical role in determining the critical stress while the critical number of completely failed pebbles at the onset of critical stress is independent of such a damage law.

A pebble -bed nuclear reactor of large power rating comprises a container having a funnel-shaped bottom forming a pebble run-out having a centrally positioned outlet. A bed of downwardly-flowing substantially spherical nuclear fuel pebbles is positioned in the container and forms a reactive nuclear core maintained by feeding unused pebbles to the bed's top surface while used or burned-out pebbles run out and discharge through the outlet.

A substantially conical body with its apex pointing upwardly and its periphery spaced from the periphery of the container spreads the bottom of the bed outwardly to provide an annular flow down the funnel-shaped bottom forming the runout, to the discharge outlet. This provides a largely constant downward velocity of the spheres throughout the diameter of the bed throughout a substantial portion of the down travel, so that all spheres reach about the same burned-out condition when they leave the core, after a single pass through the core area.

This close-up Sojourner rover image of a small rock shows that weathering has etched-out pebbles to produce sockets. In the image, sunlight is coming from the upper left. Sockets with shadows on top are visible at the lower left and pebbles with bright tops and shadowed bases are seen at the lower center and lower right.

Two pebbles about 0. Internal conversion coefficients for atomic numbers Z less than or equal to Presented here are internal conversion coefficients ICC of gamma rays for 20 values of atomic number , Z, in the range 3 less than or equal to Z less than or equal to 30, including all Z greater than or equal to The tables provide the previously missing data for light elements.

Coefficients are given for 19 values of gamma-ray transition energies up to 6 MeV for the K-electron shell and 18 values up to 2 MeV for three L-subshells. The minimum enegy is 15 keV. The first five electric and magnetic nuclear transition multipolarities are covered. The calculations are relativistic, with screening and finite nuclear size effect taken into account. In this paper, a description of the physical artifacts included in the model is presented and some results from using the computer code for predicting the features of pebble flow and packing in a realistic pebble bed reactor design are shown.

The sensitivity of models to various physical parameters is also discussed. The picture was taken by the rover's panoramic camera, using filters centered at , , and nanometers, at Colored spots have been drawn on this image corresponding to regions where panoramic camera reflectance spectra were acquired see chart in Figure 1.

These spectra demonstrated that the composition of the supposed pebble was clearly different from that of the sunlit and shadowed portions of the rock abrasion tool, while similar to that of the dust-coated rock abrasion tool magnets and grinding heads. This led the team to conclude that the object disabling the rock abrasion tool was indeed a martian pebble.

Voltage equalization of an ultracapacitor module by cell grouping using number partitioning algorithm. Ultracapacitors are low voltage devices and therefore, for practical applications, they need to be used in modules of series-connected cells. Because of the inherent manufacturing tolerance of the capacitance parameter of each cell, and as the maximum voltage value cannot be exceeded, the module requires inter-cell voltage equalization. Previous work shows that a series connection of several sets of paralleled ultracapacitors minimizes the dispersion of equivalent capacitance values, and also the voltage differences between capacitors.

Thus the overall life expectancy is improved. This paper proposes a method to distribute ultracapacitors with a number partitioning-based strategy to reduce the dispersion between equivalent submodule capacitances. Random detailed model for probabilistic neutronic calculation in pebble bed Very High Temperature Reactors. The pebble bed nuclear reactor is one of the main candidates for the next generation of nuclear power plants. In pebble bed type HTRs, the fuel is contained within graphite pebbles in the form of TRISO particles, which form a randomly packed bed inside a graphite-walled cylindrical cavity.

Pebble bed reactors PBR offer the opportunity to meet the sustainability requirements, such as nuclear safety, economic competitiveness, proliferation resistance and a minimal production of radioactive waste. In order to simulate PBRs correctly, the double heterogeneity of the system must be considered. These features are often neglected due to the difficulty to model with MCPN code.

The main reason is that there is a limited number of cells and surfaces to be defined. In this study, a computational tool which allows getting a new geometrical model of fuel pebbles for neutronic calculations with MCNPX code, was developed. The heterogeneity of system is considered, and also the randomly located TRISO particles inside the pebble. Four proposed fuel pebble models were compared regarding their effective multiplication factor and energy liberation profiles.

Mechanics of binary and polydisperse spherical pebble assembly. The micromechanical behavior of an assembly of binary and polydisperse spherical pebbles is studied using discrete element method DEM accounting for microscopic interactions between individual pebbles.

## Black Hole Fed by Cold Intergalactic Deluge

A in-house DEM code has been used to simulate the assemblies consisting of different pebble diameters and the results of the simulations are compared with that of mono-size pebble assemblies. The effect of relative radii and volume fraction of the pebbles on the macroscopic stress—strain response is discussed. Furthermore, the effect of packing factor and coefficient of friction on the overall stress—strain behavior of the system is studied in detail. The shear tangential stiffness between the particles is also another influencing parameter.

For a very small shear stiffness the system shows a strong dependence on the packing factor while a pebble material dependent shear stiffness shows a rather moderate dependence on the packing factor. For a similar packing factor, the mono-size assembly shows a stiff behavior during loading compared to binary assembly. However, the simulations do not show a significant difference between the two behaviors in contrast to the observations made in the experiments.

The discrepancy can be attributed to i probable difference in packing factors for mono-size and binary assemblies in the experiments, ii arbitrary friction coefficient in the current model and iii the tangential interaction constant shear stiffness implemented in the present model which needs further modification as a function of the load history on the pebbles. Evolution of other micromechanical characteristics such as coordination number , contact force distribution and stored elastic energy of individual pebbles as a function of external load and system parameters is presented which can be used to estimate important macroscopic properties such as overall thermal conductivity and crushing resistance of the pebble beds.

The effect of relative radii and volume fraction of the pebbles on the macroscopic stress-strain response is discussed. Furthermore, the effect of packing factor and coefficient of friction on the overall stress-strain behavior of the system is studied in detail. Pebbles , Cobbles, and Sockets. This Rover image of 'Shark' upper left center , 'Half Dome' upper right , and a small rock right foreground reveal textures and structures not visible in lander camera images.

These rocks are interpreted as conglomerates because their surfaces have rounded protrusions up to several centimeters in size. It is suggested that the protrusions are pebbles and granules. Operating windows of pebble divertor. A marked feature of the pebble divertor is an effect by use of functional multi-layer coated pebble , which consists of a surface plasma facing layer, an intermediate tritium permeation barrier layer, and a kernel for heat removal.

The dimensions, structure and the irradiation conditions of pebbles are the important issues for the development of the pebble divertor. From the view point of resistance of the induced thermal stress, the pebble is taken as small as possible in size. On the other hand, from the view point of the pumping performance, the suitable irradiation temperature range of the surface layer of pebble was estimated from the experiments and the numerical analysis. The pumping process enhanced by dynamic retention is available to extend the higher allowable irradiation temperature range from K to K.

Test of equal effect per fraction and estimation of initial clonogen number in microcolony assays of survival after fractionated irradiation. In the use of multifraction microcolony assays to infer the low-dose response of in situ renewal systems such as intestinal crypts, the assumption of equal effect per dose fraction is required. Moreover, the construction of a cell-survival curve requires knowledge of the initial count of cells capable of repopulating each renewal structure.

We describe a method of designing fractionation protocols which provides a regression estimate of the initial number of clonogens per renewal structure and a test of the hypothesis of equal effect per fraction. The essential factor in the experimental design is the use of common dose fractions use of the same dose per fraction in series with different numbers of fractions. Applications of the method to data for which the assumption of equal effect per fraction holds four-hour fractionation interval murine testis study and does not hold one-hour fractionation interval murine jejunal crypt study are presented.

- Nathaniel und Victoria 1: Unter goldenen Schwingen (German Edition).
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Core homogenization method for pebble bed reactors. This work presents a core homogenization scheme for treating a stochastic pebble bed loading in pebble bed reactors. The reactor core is decomposed into macro-domains that contain several pebble types characterized by different degrees of burnup. A stochastic description is introduced to account for pebble-to-pebble and pebble -to-helium interactions within a macro-domain as well as for interactions between macro-domains. The difference between the proposed method and the traditional volume-averaged homogenization technique is negligible while only one type of fuel pebbles present in the system, but it grows rapidly with the level of pebble heterogeneity.

In this thesis we develop a new iterative homogenization technique for pebble bed reactors, based on a 'macro-stochastic' transport approximation in the collision probability method. A model has been developed to deal with the stochastic distribution of pebbles with different burnup in the core, considering spectral differences in homogenization and depletion calculations.

This is generally not done in the codes presently used for pebble bed analyses, where a pebble with average isotopic composition is considered to perform the cell calculation. Also an iterative core calculation scheme has been set up, where the low-order RZ S N full-core calculation computes the entering currents in the spectrum zones subdividing the core. These currents, together with the core k eff , are then used as surface source in the fine-group heterogeneous calculation of the multi- pebble geometries.

The pebbles in this model are individually positioned and have different randomly assigned burnup values. Moreover, the first criticality experiment of the HTR reactor was used to perform a first validation of the developed model. The computed critical number of pebbles to be loaded in the core is very close to the experimental value of , only 77 pebbles less. The potential of the APOLLO2 method to compute different fluxes for the different pebble types of a multi- pebble geometry was used to evaluate the bias committed by the average composition pebble approximation.

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Thanks to a 'compensation of error. Scaling law and implications for the formation of super-Earths and gas giants. The growth of a planetary core by pebble accretion stops at the so-called pebble isolation mass, when the core generates a pressure bump that traps drifting pebbles outside its orbit. The value of the pebble isolation mass is crucial in determining the final planet mass. If the isolation mass is very low, gas accretion is protracted and the planet remains at a few Earth masses with a mainly solid composition.

For higher values of the pebble isolation mass, the planet might be able to accrete gas from the protoplanetary disc and grow into a gas giant. Previous works have determined a scaling of the pebble isolation mass with cube of the disc aspect ratio. Here, we expand on previous measurements and explore the dependency of the pebble isolation mass on all relevant parameters of the protoplanetary disc. However, as the planetary mass increases, particles must be decreasingly smaller to penetrate the pressure bump. Turbulent diffusion of particles, however, can lead to an increase of the pebble isolation mass by a factor of two, depending on the strength of the background viscosity and on the pebble size.

We finally explore the implications of the new scaling law of the pebble isolation mass on the formation of planetary systems by numerically integrating the growth and migration pathways of planets in evolving protoplanetary discs. These higher core masses are more similar to the core masses of the giant planets in the solar system. The Emerging Paradigm of Pebble Accretion. Pebble accretion is the mechanism in which small particles " pebbles " accrete onto big bodies big planetesimals or planetary embryos in gas-rich environments.

In pebble accretion accretion , accretion occurs by settling and depends only on the mass of the gravitating body gravitating , not its. An overview is presented of all the important issues that influenced the choice of pebble fuel for the High-temperature Gas-cooled Reactor HTGR concept developed by South Africa. Each of these issues is then discussed in detail and compared with other fuel configurations proposed for direct cycle High-temperature Reactor HTR applications.

The comparisons are provided using objective data generated by analyses done for the design of the Pebble Bed Modular Reactor PBMR and data that is available in open literature for the other fuel configurations. Full Text Available Modular pebble -bed nuclear reactor MPBNR technology is promising due to its attractive features such as high fuel performance and inherent safety. Particle motion of fuel and graphite pebbles is highly associated with the performance of pebbled -bed modular nuclear reactor. Velocity distributions at different areas of the reactor as well as mixing characteristics of fuel and graphite pebbles were investigated.

Both fuel and graphite pebbles moved downward, and a uniform motion was formed in the column zone, while pebbles motion in the cone zone was accelerated due to the decrease of the cross sectional flow area. The number ratio of fuel and graphite pebbles and the height of guide ring had a minor influence on the velocity distribution of pebbles , while the variation of funnel angle had an obvious impact on the velocity distribution. Simulated results agreed well with the work in the literature.

Number of sexual partners and sexual assertiveness predict sexual victimization: In previous studies, number of sexual partners and sexual assertiveness were examined as independent risk factors for sexual victimization among college women. Using a sample of college women, this study examined the interaction of number of sexual partners and sexual assertiveness on verbal sexual coercion and rape.

As number of sexual partners increased, instances of verbal sexual coercion increased for women low in relational sexual assertiveness but not for women high in relational sexual assertiveness. A similar relationship was not found for rape. Among women who experienced both verbal sexual coercion and rape, increases in number of partners in the context of low refusal and relational assertiveness were associated with increases in verbal sexual coercion and rape.

Findings suggest sexual assertiveness is related to fewer experiences of sexual coercion. Are numbers , size and brightness equally efficient in orienting visual attention? Evidence from an eye-tracking study. Full Text Available A number of studies have shown strong relations between numbers and oriented spatial codes. For example, perceiving numbers causes spatial shifts of attention depending upon numbers ' magnitude, in a way suggestive of a spatially oriented, mental representation of numbers. Here, we investigated whether this phenomenon extends to non-symbolic numbers , as well as to the processing of the continuous dimensions of size and brightness, exploring whether different quantitative dimensions are equally mapped onto space.

After a numerical symbolic Arabic digits or non-symbolic arrays of dots; Experiment 1 or a non-numerical cue shapes of different size or brightness level; Experiment 2 was presented, participants' saccadic response to a target that could appear either on the left or the right side of the screen was registered using an automated eye-tracker system.

Experiment 1 showed that, both in the case of Arabic digits and dot arrays, right targets were detected faster when preceded by large numbers , and left targets were detected faster when preceded by small numbers. Participants in Experiment 2 were faster at detecting right targets when cued by large-sized shapes and left targets when cued by small-sized shapes, whereas brightness cues did not modulate the detection of peripheral targets.

These findings indicate that looking at a symbolic or a non-symbolic number induces attentional shifts to a peripheral region of space that is congruent with the numbers ' relative position on a mental number line, and that a similar shift in visual attention is induced by looking at shapes of different size. More specifically, results suggest that, while the dimensions of number and size spontaneously map onto an oriented space, the dimension of brightness seems to be independent at a certain level of magnitude elaboration from the dimensions of spatial extent and number , indicating that not all continuous dimensions are equally mapped onto space.

A number of studies have shown strong relations between numbers and oriented spatial codes. A virtual pebble game to ensemble average graph rigidity. The body-bar Pebble Game PG algorithm is commonly used to calculate network rigidity properties in proteins and polymeric materials. To account for fluctuating interactions such as hydrogen bonds, an ensemble of constraint topologies are sampled, and average network properties are obtained by averaging PG characterizations.

At a simpler level of sophistication, Maxwell constraint counting MCC provides a rigorous lower bound for the number of internal degrees of freedom DOF within a body-bar network, and it is commonly employed to test if a molecular structure is globally under-constrained or over-constrained. MCC is a mean field approximation MFA that ignores spatial fluctuations of distance constraints by replacing the actual molecular structure by an effective medium that has distance constraints globally distributed with perfect uniform density.

Network fluctuations due to distance constraints that may be present or absent based on binary random dynamic variables are suppressed by replacing all possible constraint topology realizations with the probabilities that distance constraints are present. The VPG algorithm is isomorphic to the PG algorithm, where integers for counting " pebbles " placed on vertices or edges in the PG map to real numbers representing the probability to find a pebble. In the VPG, edges are assigned pebble capacities, and pebble movements become a continuous flow of probability within the network.

Comparisons between the VPG and average PG results over a test set of proteins and disordered lattices demonstrate the VPG quantitatively estimates the ensemble average PG results well. The utility of the VPG falls in between the most. Influence of gas pressure on the effective thermal conductivity of ceramic breeder pebble beds. Lithium ceramics have been considered as tritium breeder materials in many proposed designs of fusion breeding blankets. Heat generated in breeder pebble beds due to nuclear breeding reaction must be removed by means of actively cooled plates while generated tritiums is recovered by purge gas slowly flowing through beds.

Therefore, the effective thermal conductivity of pebble beds that is one of the governing parameters determining heat transport phenomenon needs to be addressed with respect to mechanical status of beds and purge gas pressure. In this study, a numerical framework combining finite element simulation and a semi-empirical correlation of gas gap conduction is proposed to predict the effective thermal conductivity. The purge gas pressure is found to vary the effective thermal conductivity, in particular with the presence of various sized gaps in pebble beds.

Random packing of pebble beds is taken into account by an approximated correlation considering the packing factor and coordination number of pebble beds. The model prediction is compared with experimental observation from different sources showing a quantitative agreement with the measurement. A Pebble Bed Reactor cross section methodology. A method is presented for the evaluation of microscopic cross sections for the Pebble Bed Reactor PBR neutron diffusion computational models during convergence to an equilibrium asymptotic fuel cycle.

This method considers the isotopics within a core spectral zone and the leakages from such a zone as they arise during reactor operation. The randomness of the spatial distribution of fuel grains within the fuel pebbles and that of the fuel and moderator pebbles within the core, the double heterogeneity of the fuel, and the indeterminate burnup of the spectral zones all pose a unique challenge for the computation of the local microscopic cross sections. As prior knowledge of the equilibrium composition and leakage is not available, it is necessary to repeatedly re-compute the group constants with updated zone information.

A method is presented to account for local spectral zone composition and leakage effects without resorting to frequent spectrum code calls. Fine group data are pre-computed for a range of isotopic states. Microscopic cross sections and zone nuclide number densities are used to construct fine group macroscopic cross sections, which, together with fission spectra, flux modulation factors, and zone buckling, are used in the solution of the slowing down balance to generate a new or updated spectrum. The microscopic cross-sections are then re-collapsed with the new spectrum for the local spectral zone.

It is found that this method accurately recalculates local broad group microscopic cross sections. Significant improvement in the core eigenvalue, flux, and power peaking factor is observed when the local cross sections are corrected for the effects of the spectral zone composition and leakage in two-dimensional PBR test problems. The operation of pebble bed reactors, including fuel circulation, can generate graphite dust, which in turn could be a concern for internal components; and to the near field in the remote event of a break in the coolant circuits.

The design of the reactor system must, therefore, take the dust into account and the operation must include contingencies for dust removal and for mitigation of potential releases. Such planning requires a proper assessment of the dust inventory. This paper presents a predictive model of dust generation in an operating pebble bed with recirculating fuel.

In this preliminary work the production model is based on the use of the assumption of proportionality between the dust production and the normal force and distance traveled. The code, based on the discrete element method, simulates the relevant static and kinetic friction interactions between the pebbles as well as the recirculation of the pebbles through the reactor vessel. The interaction between pebbles and walls of the reactor vat is treated using the same approach. The amount of dust produced is proportional to the wear coefficient for adhesive wear taken from literature and to the slip volume, the product of the contact area and the slip distance.

The paper will compare the predicted volume with the measured production rates. The simulation tallies the dust production based on the location of creation. Two peak production zones from intra pebble forces are predicted within the bed. The first zone is located near the pebble inlet chute due to the speed of the dropping pebbles. The second peak zone occurs lower in the reactor with increased pebble contact force due to the weight of supported pebbles.

This paper presents the first use of a Discrete Element Method simulation of pebble bed dust production. This result was conjectured by Bernevig and Haldane, who proposed that these Jack polynomials are model wavefunctions for fractional quantum Hall states. Special cases of these Jack polynomials include the wavefunctions of Laughlin and Read-Rezayi. In fact, along these lines we prove several vanishing theorems known as clustering properties for Jack polynomials in the mathematical physics literature, special cases of which had previously been conjectured by Bernevig and Haldane. Abrasion behavior of graphite pebble in lifting pipe of pebble -bed HTR.

A pebble -bed high-temperature gas-cooled reactor pebble -bed HTR uses a helium coolant, graphite core structure, and spherical fuel elements. The pebble -bed design enables on-line refueling, avoiding refueling shutdowns. During circulation process, the pebbles are lifted pneumatically via a stainless steel lifting pipe and reinserted into the reactor. Inevitably, the movement of the fuel elements as they recirculate in the reactor produces graphite dust.

Mechanical wear is the primary source of graphite dust production. Specifically, the sources are mechanisms of pebble— pebble contact, pebble—wall structural graphite contact, and fuel handling pebble—metal abrasion. The key contribution to graphite dust production is from the fuel handling system, particularly from the lifting pipe.

During pneumatic lift, graphite pebbles undergo multiple collisions with the stainless steel lifting pipe, thereby causing abrasion of the graphite pebbles and producing graphite dust. The present work explored the abrasion behavior of graphite pebble in the lifting pipe by measuring the abrasion rate at different lifting velocities. The abrasion rate of the graphite pebble in helium was found much higher than those in air and nitrogen. This gas environment effect could be explained by either tribology behavior or dynamic behavior.

Friction testing excluded the possibility of tribology reason. The dynamic behavior of the graphite pebble was captured by analysis of the audio waveforms during pneumatic lift. The analysis results revealed unique dynamic behavior of the graphite pebble in helium. Oscillation and consequently intensive collisions occur during pneumatic lift, causing. An analytical evaluation for spatial-dependent intra- pebble Dancoff factor and escape probability.

The analytical evaluation of spatial-dependent intra- pebble Dancoff factors and their escape probabilities is pursued by the model developed in this study. Intra- pebble Dancoff factors and their escape probabilities are calculated as a function of fuel kernel radius, number of fuel kernels, and fuel region radius.

The method in this study can be easily utilized to analyze the tendency of spatial-dependent intra- pebble Dancoff factor and spatial-dependent fuel region escape probability for the various geometries because it is faster than the MCNP method as well as good accuracy. We present a conceptual design approach for high-temperature gas-cooled reactors using recirculating pebble -bed cores. The design approach employs PEBBED, a reactor physics code specifically designed to solve for and analyze the asymptotic burnup state of pebble -bed reactors, in conjunction with a genetic algorithm to obtain a core that maximizes a fitness value that is a function of user-specified parameters.

The uniqueness of the asymptotic core state and the small number of independent parameters that define it suggest that core geometry and fuel cycle can be efficiently optimized toward a specified objective. PEBBED exploits a novel representation of the distribution of pebbles that enables efficient coupling of the burnup and neutron diffusion solvers. With this method, even complex pebble recirculation schemes can be expressed in terms of a few parameters that are amenable to modern optimization techniques.

A set of traits, each with acceptable and preferred values expressed by a simple fitness function, is used to evaluate the candidate reactor cores. The stochastic search algorithm automatically drives the generation of core parameters toward the optimal core as defined by the user. The optimized design can then be modeled and analyzed in greater detail using higher resolution and more computationally demanding tools to confirm the desired characteristics. For this study, the design of pebble -bed high temperature reactor concepts subjected to demanding physical constraints demonstrated the efficacy of the PEBBED algorithm.

Modelling of thermal and mechanical behaviour of pebble beds. The design of such a blanket requires models and computer codes describing the thermal-mechanical behavior of pebble beds to evaluate the temperatures, stresses, deformations and mechanical interactions between pebble beds and the structure with required accuracy and reliability.

The objective to describe the beginning of life condition for the HCPB blanket seems near to be reached. Mechanical models that describe the thermo-mechanical behavior of granular materials used in form of pebble beds are implemented in a commercial structure code. These models have been calibrated using the results of a large series of dedicated experiments. The modeling work is practically concluded for ceramic breeder; it will be carried on in the next year for beryllium to obtain the required correlations for creep and the thermal conductivity.

The difficulties for application in large components such as the HCPB blanket are the limitations of the present commercial codes to manage such a set of constitutive equations under complex load conditions and large mesh number. The further objective is to model the thermal cycles during operation; the present correlations have to be adapted for the release phase. A complete description of the blanket behavior during irradiation is at the present out of our capability; this objective requires an extensive R and D program that at the present is only at the beginning.

Exact integer concepts are fundamental to a wide array of human activities, but their origins are obscure. Some have proposed that children are endowed with a system of natural number concepts, whereas others have argued that children construct these concepts by mastering verbal counting or other numeric symbols. Children aged months, who possessed no symbols for exact numbers beyond 4, were given one-to-one correspondence cues to help them track a set of puppets, and their enumeration of the set was assessed by a non-verbal manual search task.

Children used one-to-one correspondence relations to reconstruct exact quantities in sets of 5 or 6 objects, as long as the elements forming the sets remained the same individuals. In contrast, they failed to track exact quantities when one element was added, removed, or substituted for another. These results suggest an alternative to both nativist and symbol-based constructivist theories of the development of natural number concepts: Before learning symbols for exact numbers , children have a partial understanding of the properties of exact numbers.

Postirradiation examination of beryllium pebbles. Measurements included density change, optical microscopy, scanning electron microscopy, and transmission electron microscopy. The major change in microstructure is development of unusually shaped helium bubbles forming as highly non-equiaxed thin platelet-like cavities on the basal plane.

Measurement of the swelling due to cavity formation was in good agreement with density change measurements. MIT pebble bed reactor project. The conceptual design of the MIT modular pebble bed reactor is described. This reactor plant is a Mwth, Mwe indirect cycle plant that is designed to be deployed in the near term using demonstrated helium system components.

The primary system is a conventional pebble bed reactor with a dynamic central column with an outlet temperature of C providing helium to an intermediate helium to helium heat exchanger IHX. The design constraint used in sizing the plant is based on a factory modularity principle which allows the plant to be assembled 'Lego' style instead of constructed piece by piece.

This principle employs space frames which contain the power conversion system that permits the Lego-like modules to be shipped by truck or train to sites. This paper also describes the research that has been conducted at MIT since on fuel modeling, silver leakage from coated fuel particles, dynamic simulation, MCNP reactor physics modeling and air ingress analysis.

A number of design and development methods, including participatory design and agile software development, are premised on an underlying assumption of equality amongst relevant stakeholders such as designers, developers, product owners, and end users. Equality , however, is not a straightforwardly Contact detection acceleration in pebble flow simulation for pebble bed reactor systems.

Pebble flow simulation plays an important role in the steady state and transient analysis of thermal-hydraulics and neutronics for Pebble Bed Reactors PBR. The Discrete Element Method DEM and the modified Molecular Dynamics MD method are widely used to simulate the pebble motion to obtain the distribution of pebble concentration, velocity, and maximum contact stress. Although DEM and MD present high accuracy in the pebble flow simulation, they are quite computationally expensive due to the large quantity of pebbles to be simulated in a typical PBR and the ubiquitous contacts and collisions between neighboring pebbles that need to be detected frequently in the simulation, which greatly restricted their applicability for large scale PBR designs such as PBMR In the present work, based on the design features of PBRs, two contact detection algorithms, the basic cell search algorithm and the bounding box search algorithm are investigated and applied to pebble contact detection.

The influence from the PBR system size, core geometry and the searching cell size on the contact detection efficiency is presented. Our results suggest that for present PBR applications, the bounding box algorithm is less sensitive to the aforementioned effects and has superior performance in pebble contact detection compared with basic cell search algorithm. Experimental measurement of effective thermal conductivity of packed lithium-titanate pebble bed. Lithium titanate is a promising solid breeder material for the fusion reactor blanket. Packed lithium titanate pebble bed is considered for the blanket.

The thermal energy; that will be produced in the bed during breeding and the radiated heat from the reactor core absorbed must be removed. So, the experimental thermal property data are important for the blanket design. In past, a significant amount of works were conducted to determine the effective thermal conductivity of packed solid breeder pebble bed, in helium atmosphere, but no flow of gas was considered.

With increase in gas flow rate, effective thermal conductivity of pebble bed increases. Particle size and void fraction also affect the thermal properties of the bed significantly. An experimental facility with external heat source was designed and installed. Experiments were carried out with lithium-titanate pebbles of different sizes at variable gas flow rates and at different bed wall temperature.

It was observed that effective thermal conductivity of pebble bed is a function of particle Reynolds number and temperature. From the experimental data two correlations have been developed to estimate the effective thermal conductivity of packed lithium-titanate pebble bed for different particle Reynolds number and at different temperatures. The experimental details and results are discussed in this paper. Behavior of beryllium pebbles under irradiation. Beryllium pebbles are being considered in fusion reactor blanket designs as neutron multiplier.

Commercially available beryllium pebbles have been irradiated to approximately 1. Post-irradiation results are presented on density change measurements, tritium release by assay, stepped-temperature anneal, and thermal ramp desorption tests, and helium release by assay and stepped-temperature anneal measurements, for Be pebbles from two manufacturing methods, and with two specimen diameters.

The experimental results on density change and tritium and helium release are compared with the predictions of the code ANFIBE. Characteristics of microstructure and tritium release properties of different kinds of beryllium pebbles for application in tritium breeding modules. Box , Karlsruhe Germany ; Vladimirov, P. Box , Karlsruhe Germany ; Rolli, R. Box , Karlsruhe Germany ; Zmitko, M.

## pebbling number equals: Topics by irideryjawex.tk

Beryllium pebbles with diameters of 1 mm are considered to be perspective material for the use as neutron multiplier in tritium breeding modules of fusion reactors. It is notable that beryllium pebbles from Russian Federation and USA are also available and the possibility of their large-scale fabrication is under study. Presented work is dedicated to a study of characteristics of microstructure and parameters of tritium release of beryllium pebbles produced by Bochvar Institute, Russian Federation, and Materion Corporation, USA. By continuing to use this website, you are giving consent to our use of cookies.

For more information on how ESO uses data and how you can disable cookies, please view our privacy policy. The results will appear in the journal Nature on 9 June The new ALMA observation is the first direct evidence that cold dense clouds can coalesce out of hot intergalactic gas and plunge into the heart of a galaxy to feed its central supermassive black hole.

The new ALMA observations show that, when the intergalactic weather conditions are right, black holes can also gorge on a clumpy, chaotic downpour of giant clouds of very cold molecular gas. Tremblay and his team used ALMA to peer into an unusually bright cluster of about 50 galaxies, collectively known as Abell At its core is a massive elliptical galaxy, descriptively named the Abell Brightest Cluster Galaxy.

Near the centre of this galaxy the researchers discovered just this scenario: Each cloud contains as much material as a million Suns and is tens of light-years across. While ALMA was only able to detect three clouds of cold gas near the black hole, the astronomers speculate that there may be thousands like them in the vicinity, setting up the black hole for a continuing downpour that could fuel its activity for a long time.