A virtual pebble game to ensemble average graph rigidity.
González, Luis C; Wang, Hui; Livesay, Dennis R; Jacobs, Donald J
2015-01-01
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. The Virtual Pebble Game (VPG) algorithm is a MFA that retains spatial inhomogeneity in the density of constraints on all length scales. 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 VPG performs about 20% faster than one PG, and it provides a pragmatic alternative to averaging PG rigidity characteristics over an ensemble of constraint topologies. The utility of the VPG falls in between the most
Some remarks on definability of process graphs
Grabmayer, C.A.; Klop, J.W.; Luttik, B.; Baier, C.; Hermanns, H.
2006-01-01
We propose the notions of "density" and "connectivity" of infinite process graphs and investigate them in the context of the wellknown process algebras BPA and BPP. For a process graph G, the density function in a state s maps a natural number n to the number of states of G with distance less or
Graphs for information security control in software defined networks
Grusho, Alexander A.; Abaev, Pavel O.; Shorgin, Sergey Ya.; Timonina, Elena E.
2017-07-01
Information security control in software defined networks (SDN) is connected with execution of the security policy rules regulating information accesses and protection against distribution of the malicious code and harmful influences. The paper offers a representation of a security policy in the form of hierarchical structure which in case of distribution of resources for the solution of tasks defines graphs of admissible interactions in a networks. These graphs define commutation tables of switches via the SDN controller.
Zero Forcing Sets and Controllability of Dynamical Systems Defined on Graphs
Monshizadeh Naini, Nima; Zhang, Shuo; Camlibel, M. Kanat
In this technical note, controllability of systems defined on graphs is discussed. We consider the problem of controllability of the network for a family of matrices carrying the structure of an underlying directed graph. A one-to-one correspondence between the set of leaders rendering the network
Stability analysis of switched linear systems defined by graphs
Athanasopoulos, Nikolaos; Lazar, Mircea
2015-01-01
We present necessary and sufficient conditions for global exponential stability for switched discrete-time linear systems, under arbitrary switching, which is constrained within a set of admissible transitions. The class of systems studied includes the family of systems under arbitrary switching, periodic systems, and systems with minimum and maximum dwell time specifications. To reach the result, we describe the set of rules that define the admissible transitions with a weighted directed gra...
On defining and computing fuzzy kernels on L-valued simple graphs
Bisdorff, R.; Roubens, M.
1996-01-01
In this paper we introduce the concept of fuzzy kernels defined on valued-finite simple graphs in a sense close to fuzzy preference modelling. First we recall the classic concept of kernel associated with a crisp binary relation defined on a finite set. In a second part, we introduce fuzzy binary relations. In a third part, we generalize the crisp kernel concept to such fuzzy binary relations and in a last part, we present an application to fuzzy choice functions on fuzzy outranking relations
Pebble bed pebble motion: Simulation and Application
Cogliati, Joshua J.
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. A new mechanical motion simulator, PEBBLES, efficiently simulates the key elements 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. PEBBLES runs on shared memory architectures and distributed memory architectures. 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 PEBBLES code provides new capabilities for understanding and optimizing PBRs. The PEBBLES code has provided the pebble motion data required to calculate the motion of pebbles during a simulated earthquake. The PEBBLES code provides the ability to
Failure initiation and propagation of Li4SiO4 pebbles in fusion blankets
Zhao Shuo; Gan Yixiang; Kamlah, Marc
2013-01-01
Lithium orthosilicate (Li 4 SiO 4 ) pebbles are considered to be a candidate as solid tritium breeder in the helium cooled pebble bed (HCPB) blanket. These ceramic pebbles might be crushed during thermomechanical loading in the blanket. In this work, the failure initiation and propagation of pebbles in pebble beds is investigated using the discrete element method (DEM). Pebbles are simplified as mono-sized elastic spheres. Every pebble has a contact strength in terms of critical strain energy, which is derived from a validated strength model and crush test data for pebbles from a specific batch of Li 4 SiO 4 pebbles. Pebble beds are compressed uniaxially and triaxially in DEM simulations. When the strain energy absorbed by a pebble exceeds its critical energy it fails. The failure initiation is defined as a given small fraction of pebbles crushed. It is found that the load level for failure initiation can be very low. For example, if failure initiation is defined as soon as 0.02% of the pebbles have been crushed, the pressure required for uniaxial loading is about 2.5 MPa. Therefore, it is essential to study the influence of failure propagation on the macroscopic response of pebble beds. Thus a reduction ratio defined as the size ratio of a pebble before and after its failure is introduced. The macroscopic stress–strain relation is investigated with different reduction ratios. A typical stress plateau is found for a small reduction ratio.
A Preliminary Study on Calculation of Inter-Pebble Dancoff Factor in a Pebble Type Core
Kim, Song Hyun; Kim, Hong Chul; Kim, Soon Young; Noh, Jae Man; Kim, Jong Kyung
2009-01-01
The Dancoff factor is an entering probability of the neutron escaped from specific fuel kernel to another one without the interaction with moderators. Currently, Dancoff factors are mainly evaluated from stochastic methods, hence a research on analytical method is considerably insufficient in this field. In order to analytically evaluate Dancoff factor considering double-heterogeneous effect, inter-pebble and intra-pebble Dancoff factors should be calculated, respectively. Intra-pebble Dancoff factor related with the fuel kernels in one pebble was analyzed in past study. For the evaluation of inter-pebble Dancoff factor, fuel region to region Dancoff factor (FRDF) was defined and the method to calculate the FRDF is developed in this study. The result is compared with the calculation result of the MCNP5 code
Effect of friction on pebble flow pattern in pebble bed reactor
Li, Yu; Gui, Nan; Yang, Xingtuan; Tu, Jiyuan; Jiang, Shengyao
2016-01-01
Highlights: • A 3D DEM study on particle–wall/particle friction in pebble bed reactor is carried out. • Characteristic values are defined to evaluate features of pebble flow pattern quantitatively. • Particle–wall friction is dominant to determine flow pattern in a specific pebble bed. • Friction effect of hopper part on flow field is more critical than that of cylinder part. • Three cases of 1:1 full scale practical pebble beds are simulated for demonstration. - Abstract: Friction affects pebble flow pattern in pebble-bed high temperature gas-cooled reactor (HTGR) significantly. Through a series of three dimensional DEM (discrete element method) simulations it is shown that reducing friction can be beneficial and create a uniform and consistent flow field required by nuclear engineering. Particle–wall friction poses a decisive impact on flow pattern, and particle–particle friction usually plays a secondary role; relation between particle–wall friction and flow pattern transition is also concluded. Moreover, new criteria are created to describe flow patterns quantitatively according to crucial issues in HTGR like stagnant zone, radial uniformity and flow sequence. Last but not least, it is proved that friction control of hopper part is more important than that of cylinder part in practical pebble beds, so reducing friction between pebbles and hopper surface is the engineering priority.
Software Defined Network Monitoring Scheme Using Spectral Graph Theory and Phantom Nodes
2014-09-01
networks is the emergence of software - defined networking ( SDN ) [1]. SDN has existed for the...Chapter III for network monitoring. A. SOFTWARE DEFINED NETWORKS SDNs provide a new and innovative method to simplify network hardware by logically...and R. Giladi, “Performance analysis of software - defined networking ( SDN ),” in Proc. of IEEE 21st International Symposium on Modeling, Analysis
Modeling stationary and moving pebbles in a pebble bed reactor
Zhao, Xiang; Montgomery, Trent; Zhang, Sijun
2015-01-01
Highlights: • The stationary and moving pebbles in a PBR are numerically studied by DEM. • The packing structure of stationary pebbles is simulated by a filling process. • The packing structural properties are obtained and analyzed. • The dynamic behavior of pebbles is predicted and discussed. - Abstract: 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
Modeling stationary and dynamic pebbles in a pebble bed reactor
Zhao, Xiang; Montgomery, Trent; Zhang, Sijun
2011-01-01
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. The packing structural properties are obtained and analyzed. 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. 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. (author)
Pebble-bed pebble motion: Simulation and Applications
Joshua J. Cogliati; Abderrafi M. Ougouag
2011-11-01
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 report presents a method for simulation of motion of the pebbles in a PBR. A new mechanical motion simulator, PEBBLES, efficiently simulates the key elements 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. PEBBLES runs on shared memory architectures and distributed memory architectures. 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 PEBBLES code provides new capabilities for understanding and optimizing PBRs. The PEBBLES code has provided the pebble motion data required to calculate the motion of pebbles during a simulated earthquake. The PEBBLES code provides the ability to
Pebble-bed pebble motion: Simulation and Applications
Cogliati, Joshua J.; Ougouag, Abderrafi M.
2011-01-01
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 report presents a method for simulation of motion of the pebbles in a PBR. A new mechanical motion simulator, PEBBLES, efficiently simulates the key elements 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. PEBBLES runs on shared memory architectures and distributed memory architectures. 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 PEBBLES code provides new capabilities for understanding and optimizing PBRs. The PEBBLES code has provided the pebble motion data required to calculate the motion of pebbles during a simulated earthquake. The PEBBLES code provides the ability to determine
Tuitz, C.
2012-01-01
The spatial clustering of broken pebbles in gravel layers of a Miocene sedimentary succession was investigated. Field observations suggested that the occurrence of broken pebbles could be related with gravel hosted shear deformation bands, which were the result of extensional regional deformation. 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
Lohnert, G.; Mueller-Frank, U.; Heil, J.
1976-01-01
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
1997-01-01
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 0.5 cm across) are visible at the lower center.Mars Pathfinder is the second in NASA's Discovery program of low-cost spacecraft with highly focused science goals. The Jet Propulsion Laboratory, Pasadena, CA, developed and manages the Mars Pathfinder mission for NASA's Office of Space Science, Washington, D.C. JPL is a division of the California Institute of Technology (Caltech).
Joshua J. Cogliati; Abderrafi M. Ougouag
2006-10-01
A comprehensive, high fidelity model for pebble flow has been developed and embodied in the PEBBLES computer code. 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.
2004-01-01
[figure removed for brevity, see original site] Figure 1 In the quest to determine if a pebble was jamming the rock abrasion tool on NASA's Mars Exploration Rover Opportunity, scientists and engineers examined this up-close, approximate true-color image of the tool. The picture was taken by the rover's panoramic camera, using filters centered at 601, 535, and 482 nanometers, at 12:47 local solar time on sol 200 (August 16, 2004). Colored spots have been drawn on this image corresponding to regions where panoramic camera reflectance spectra were acquired (see chart in Figure 1). Those regions are: the grinding wheel heads (yellow); the rock abrasion tool magnets (green); the supposed pebble (red); a sunlit portion of the aluminum rock abrasion tool housing (purple); and a shadowed portion of the rock abrasion tool housing (brown). 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.
Perez Curbelo, J.; Rosales, J.; Garcia, L.; Garcia, C.; Brayner, C.
2013-01-01
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. It consists on randomly located pebbles into the core and TRISO particles into the fuel pebbles. 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. Such models are: Homogeneous Pebble, Five Zone Homogeneous Pebble, Detailed Geometry, and Randomly Detailed Geometry. (Author)
Janssen, P.; Stouffs, R.M.F.; Chaszar, A.T.; Boeykens, S.; Toth, B.
2012-01-01
This paper describes the use of property graphs for mapping data between AEC software tools, which are not linked by common data formats and/or other interoperability measures. The intention of introducing this in practice, education and research is to facilitate the use of diverse, non-integrated
1997-01-01
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.Mars Pathfinder is the second in NASA's Discovery program of low-cost spacecraft with highly focused science goals. The Jet Propulsion Laboratory, Pasadena, CA, developed and manages the Mars Pathfinder mission for NASA's Office of Space Science, Washington, D.C. JPL is a division of the California Institute of Technology (Caltech).
Kim, Song Hyun; Kim, Hong Chul; Kim, Jong Kyung; Noh, Jae Man
2009-01-01
Dancoff factor is an entering probability of the neutron escaped from specific fuel kernel to another one without the interaction with moderators. In order to analytically evaluate Dancoff factor considering double-heterogeneous effect, inter-pebble and intra-pebble Dancoff factors should be calculated, respectively. Intra-pebble Dancoff factor related with the fuel kernels in one pebble was analyzed in the past study. The fuel and moderator pebbles are randomly located in the pebble-type reactor. For the evaluation of inter-pebble Dancoff factor, a repetition of simple pebble structure is commonly assumed to simulate the complex geometry of pebble-type reactor. The evaluation using these structures can be underestimated because of the shadowing effects generated from the repetition of simple pebble structure. Fuel region to region Dancoff factor (FRDF) was defined as an entering probability of the neutron escaped from a specific fuel region to another one without any collision with moderator for a preliminary evaluation of inter-pebble Dancoff factor. To solve the underestimation problem of FRDF from the shadow effect, the specific pebble was assumed and FRDF was evaluated with the approximation method proposed in this study
Operating windows of pebble divertor
Matsuhiro, K.; Isobe, M.; Ohtsuka, Y.; Ueda, Y.; Nishikawa, M.
2001-01-01
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 900K to 1100K. As taking the temperature rise limitation due to pumping effect and the fractural strength due to the induced thermal stress limitation, it was found that the diameter of the pebble is possible to be 1-2 mm in about 20 MW/m 2 for the SiC kernel and 2-3 mm in less than 30 MW/m 2 for the graphite kernel. (author)
Status of the in-pile test of HCPB pebble-bed assemblies in the HFR Petten
Laan, J.G. van der; Fokkens, J.H.; Hofmans, H.E.; Jong, M.; Magielsen, A.J.; Pijlgroms, B.J.; Stijkel, M.P. [NRG, Petten (Netherlands); Conrad, R. [JRC, Inst. for Energy, Petten (Netherlands); Malang, S.; Reimann, J. [FZK, Karlsruhe (Germany); Roux, N. [CEA Saclay (France)
2002-06-01
In the framework of developing the helium cooled pebble-bed (HCPB) blanket an irradiation test of pebble-bed assemblies is prepared at the HFR Petten. The test objective is to concentrate on the effect of neutron irradiation on the thermal-mechanical behaviour of the HCPB breeder pebble-bed at DEMO representative levels of temperature and defined thermal-mechanical loads. The basic test elements are EUROFER-97 cylinders with a horizontal bed of ceramic breeder pebbles sandwiched between two beryllium beds. The pebble beds are separated by EUROFER-97 steel plates. The heat flow is managed such as to have a radial temperature distribution in the ceramic breeder pebble-bed as flat as reasonably possible. The paper reports on the project status, and presents the results of pre-tests, material characteristics, the manufacturing of the pebble-bed assemblies, and the nuclear and thermo-mechanical loading parameters. (orig.)
Seiller, Thomas
2016-01-01
Interaction graphs were introduced as a general, uniform, construction of dynamic models of linear logic, encompassing all Geometry of Interaction (GoI) constructions introduced so far. This series of work was inspired from Girard's hyperfinite GoI, and develops a quantitative approach that should...... be understood as a dynamic version of weighted relational models. Until now, the interaction graphs framework has been shown to deal with exponentials for the constrained system ELL (Elementary Linear Logic) while keeping its quantitative aspect. Adapting older constructions by Girard, one can clearly define...... "full" exponentials, but at the cost of these quantitative features. We show here that allowing interpretations of proofs to use continuous (yet finite in a measure-theoretic sense) sets of states, as opposed to earlier Interaction Graphs constructions were these sets of states were discrete (and finite...
Autoregressive Moving Average Graph Filtering
Isufi, Elvin; Loukas, Andreas; Simonetto, Andrea; Leus, Geert
2016-01-01
One of the cornerstones of the field of signal processing on graphs are graph filters, direct analogues of classical filters, but intended for signals defined on graphs. This work brings forth new insights on the distributed graph filtering problem. We design a family of autoregressive moving average (ARMA) recursions, which (i) are able to approximate any desired graph frequency response, and (ii) give exact solutions for tasks such as graph signal denoising and interpolation. The design phi...
Core homogenization method for pebble bed reactors
Kulik, V.; Sanchez, R.
2005-01-01
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. Performance of the proposed method is tested for the PROTEUS and ASTRA critical reactor facilities. Numerical simulations accomplished with the APOLLO2 transport lattice code show good agreement with the experimental data for the PROTEUS reactor facility and with the TRIPOLI4 Monte Carlo simulations for the ASTRA reactor configuration. 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. (authors)
The Emerging Paradigm of Pebble Accretion
Ormel, C.W.; Pessah, M.; Gressel, O.
2017-01-01
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
PBMR Project - Pebble Fuel Advantages
Slabber, Johan; Matzie, Regis; Casperson, Sten; Kriel, Willem
2006-01-01
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
On the hyperporous non-linear elasticity model for fusion-relevant pebble beds
Di Maio, P.A.; Giammusso, R.; Vella, G.
2010-01-01
Packed pebble beds are particular granular systems composed of a large amount of small particles, arranged in irregular lattices and surrounded by a gas filling interstitial spaces. Due to their heterogeneous structure, pebble beds have non-linear and strongly coupled thermal and mechanical behaviours whose constitutive models seem limited, being not suitable for fusion-relevant design-oriented applications. Within the framework of the modelling activities promoted for the lithiated ceramics and beryllium pebble beds foreseen in the Helium-Cooled Pebble Bed breeding blanket concept of DEMO, at the Department of Nuclear Engineering of the University of Palermo (DIN) a thermo-mechanical constitutive model has been set-up assuming that pebble beds can be considered as continuous, homogeneous and isotropic media. The present paper deals with the DIN non-linear elasticity constitutive model, based on the assumption that during the reversible straining of a pebble bed its effective logarithmic bulk modulus depends on the equivalent pressure according to a modified power law and its effective Poisson modulus remains constant. In these hypotheses the functional dependence of the effective tangential and secant bed deformation moduli on either the equivalent pressure or the volumetric strain have been derived in a closed analytical form. A procedure has been, then, defined to assess the model parameters for a given pebble bed from its oedometric test results and it has been applied to both polydisperse lithium orthosilicate and single size beryllium pebble beds.
Test-element assembly and loading parameters for the in-pile test of HCPB ceramic pebble beds
Laan, J.G. van der E-mail: vanderlaan@nrg-nl.com; Boccaccini, L.V.; Conrad, R.; Fokkens, J.H.; Jong, M.; Magielsen, A.J.; Pijlgroms, B.J.; Reimann, J.; Stijkel, M.P.; Malang, S
2002-11-01
In the framework of developing the helium cooled pebble-bed (HCPB) blanket an irradiation test of pebble-bed assemblies is prepared at the HFR Petten. The test objective is to concentrate on the effect of neutron irradiation on the thermal-mechanical behaviour of the HCPB breeder pebble-bed at DEMO representative levels of temperature and defined thermal-mechanical loads. The paper reports on the project status, and presents the results of pre-tests, material characteristics, the manufacturing of the pebble-bed assemblies, and the nuclear and thermo-mechanical loading parameters.
Vennemann, T.W.; Kesler, S.E.; O' Neil, J.R. (Univ. of Michigan, Ann Arbor (United States))
1992-09-01
Oxygen isotope compositions of pebbles from late Archean to paleo-Proterozoic gold- and/or uranium-bearing oligomictic quartz pebble conglomerates of the Witwatersrand district, South Africa, and Huronian Supergroup, Canada, were determined in an attempt to define the nature of the source terrain. The [delta][sup 18]O values of quartz pebbles within any one sample typically vary by [approximately] 4[per thousand] or more, but occasionally by as much as 8[per thousand], even for adjacent pebbles within the same hand specimen. In addition, adjacent quartz pebbles of widely contrasting [delta][sup 18]O values also preserve distinct isotopic signatures of their fluid inclusions. This overall heterogeneity suggests that the pebbles did not undergo significant oxygen isotope exchange after incorporation in the conglomerates. Therefore, oxygen isotope analyses of such quartz pebbles, in combination with a detailed investigation of their mineral and fluid inclusions, can provide a useful method for characterizing pebble populations and hence dominant sediment source modes. Comparison of values found in this study with [delta][sup 18]O values of quartz from Archean granites, pegmatites, and mesothermal greenstone gold veins, i.e., [delta][sup 18]O values of sources commonly proposed for the conglomerate ores, suggests that uranium is derived from a granitic source, whereas gold has a mesothermal greenstone gold source. Low [delta][sup 18]O values of chert pebbles (9[per thousand] to 11.5[per thousand]) relative to those expected for Archean and Proterozoic marine cherts (commonly [ge] 17[per thousand]) effectively exclude marine cherts, and therefore, auriferous iron formations and exhalatives, as likely sources of gold.
Vennemann, T.W.; Kesler, S.E.; O'Neil, J.R.
1992-01-01
Oxygen isotope compositions of pebbles from late Archean to paleo-Proterozoic gold- and/or uranium-bearing oligomictic quartz pebble conglomerates of the Witwatersrand district, South Africa, and Huronian Supergroup, Canada, were determined in an attempt to define the nature of the source terrain. The δ 18 O values of quartz pebbles within any one sample typically vary by ∼ 4 per-thousand or more, but occasionally by as much as 8 per-thousand, even for adjacent pebbles within the same hand specimen. In addition, adjacent quartz pebbles of widely contrasting δ 18 O values also preserve distinct isotopic signatures of their fluid inclusions. This overall heterogeneity suggests that the pebbles did not undergo significant oxygen isotope exchange after incorporation in the conglomerates. Therefore, oxygen isotope analyses of such quartz pebbles, in combination with a detailed investigation of their mineral and fluid inclusions, can provide a useful method for characterizing pebble populations and hence dominant sediment source modes. Comparison of values found in this study with δ 18 O values of quartz from Archean granites, pegmatites, and mesothermal greenstone gold veins, i.e., δ 18 O values of sources commonly proposed for the conglomerate ores, suggests that uranium is derived from a granitic source, whereas gold has a mesothermal greenstone gold source. Low δ 18 O values of chert pebbles (9 per-thousand to 11.5 per-thousand) relative to those expected for Archean and Proterozoic marine cherts (commonly ≥ 17 per-thousand) effectively exclude marine cherts, and therefore, auriferous iron formations and exhalatives, as likely sources of gold
Simplicial complexes of graphs
Jonsson, Jakob
2008-01-01
A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics, including commutative algebra, geometry, and knot theory. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory. As a byproduct, this volume also provides a loosely defined toolbox for attacking problems in topological combinatorics via discrete Morse theory. In terms of simplicity and power, arguably the most efficient tool is Forman's divide and conquer approach via decision trees; it is successfully applied to a large number of graph and digraph complexes.
Endriss, U.; Grandi, U.
Graph aggregation is the process of computing a single output graph that constitutes a good compromise between several input graphs, each provided by a different source. One needs to perform graph aggregation in a wide variety of situations, e.g., when applying a voting rule (graphs as preference
Pebble Bed Reactor Dust Production Model
Abderrafi M. Ougouag; Joshua J. Cogliati
2008-09-01
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 model developed in this work uses the slip distances and the inter-pebble forces computed by the authors’ PEBBLES. 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.
Pebble Bed Reactor Dust Production Model
Abderrafi M. Ougouag; Joshua J. Cogliati
2008-01-01
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 model developed in this work uses the slip distances and the inter-pebble forces computed by the authors PEBBLES. 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
Automated Design and Optimization of Pebble-bed Reactor Cores
Gougar, Hans D.; Ougouag, Abderrafi M.; Terry, William K.
2010-01-01
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. With PEBBED, the user chooses the type and range of core physics parameters that represent the design space. 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.
Abrasion behavior of graphite pebble in lifting pipe of pebble-bed HTR
Shen, Ke; Su, Jiageng [Institute of Nuclear and New Energy Technology, Advanced Nuclear Energy Technology Cooperation Innovation Center, The Key Laboratory of Advanced Nuclear Engineering and Safety, Ministry of Education, Beijing 10084 (China); Zhou, Hongbo [Institute of Nuclear and New Energy Technology, Advanced Nuclear Energy Technology Cooperation Innovation Center, The Key Laboratory of Advanced Nuclear Engineering and Safety, Ministry of Education, Beijing 10084 (China); Chinergy Co., LTD., Beijing 100193 (China); Peng, Wei; Liu, Bing [Institute of Nuclear and New Energy Technology, Advanced Nuclear Energy Technology Cooperation Innovation Center, The Key Laboratory of Advanced Nuclear Engineering and Safety, Ministry of Education, Beijing 10084 (China); Yu, Suyun, E-mail: suyuan@tsinghua.edu.cn [Center for Combustion Energy, The Key Laboratory for Thermal Science and Power Engineering, Ministry of Educations, Tsinghua University, Beijing 10084 (China)
2015-11-15
Highlights: • Quantitative determination of abrasion rate of graphite pebbles in different lifting velocities. • Abrasion behavior of graphite pebble in helium, air and nitrogen. • In helium, intensive collisions caused by oscillatory motion result in more graphite dust production. - Abstract: 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
Hegeman, J.; Magielsen, A.J.; Peeters, M.; Stijkel, M.P.; Fokkens, J.H.; Laan, J.G. van der
2006-01-01
In the framework of developing the European Helium Cooled Pebble-Bed (HCPB) blanket an irradiation test of pebble-bed assemblies is performed in the HFR Petten. The experiment is focused on the thermo-mechanical behavior of the HCPB type breeder pebble-bed at DEMO representative levels of temperature and defined thermal-mechanical loads. To achieve representative conditions a section of the HCPB is simulated by EUROFER-97 cylinders with a horizontal bed of ceramic breeder pebbles sandwiched between two beryllium beds. Floating Eurofer-97 steel plates separate the pebble-beds. The structural integrity of the ceramic breeder materials is an issue for the design of the Helium Cooled Pebble Bed concept. Therefore the objective of the post irradiation examination is to study deformation of pebbles and the pebble beds and to investigate the microstructure of the ceramic pebbles from the Pebble Bed Assemblies. This paper concentrates on the Post Irradiation Examination (PIE) of the four ceramic pebble beds that have been irradiated in the Pebble Bed Assembly experiment for the HCPB blanket concept. Two assemblies with Li 4 SiO 4 pebble-beds are operated at different maximum temperatures of approximately 600 o C and 800 o C. Post irradiation computational analysis has shown that both have different creep deformation. Two other assemblies have been loaded with a ceramic breeder bed of two types of Li 2 TiO 3 beds having different sintering temperatures and consequently different creep behavior. The irradiation maximum temperature of the Li 2 TiO 3 was 800 o C. To support the first PIE result, the post irradiation thermal analysis will be discussed because thermal gradients have influence on the pebble-bed thermo-mechanical behavior and as a result it may have impact on the structural integrity of the ceramic breeder materials. (author)
Zhang, L.-C.; Patone, M.
2017-01-01
We synthesise the existing theory of graph sampling. We propose a formal definition of sampling in finite graphs, and provide a classification of potential graph parameters. We develop a general approach of Horvitz–Thompson estimation to T-stage snowball sampling, and present various reformulations of some common network sampling methods in the literature in terms of the outlined graph sampling theory.
Postirradiation examination of beryllium pebbles
Gelles, D.S.
1998-01-01
Postirradiation examinations of COBRA-1A beryllium pebbles irradiated in the EBR-II fast reactor at neutron fluences which generated 2700--3700 appm helium have been performed. 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
Kadak, Andrew C. [Massachusetts Institute of Technology, Cambridge (United States)
2007-03-15
The conceptual design of the MIT modular pebble bed reactor is described. This reactor plant is a 250 Mwth, 120 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 900 C providing helium to an intermediate helium to helium heat exchanger (IHX). The outlet of the IHX is input to a three shaft horizontal Brayton Cycle power conversion system. 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 1998 on fuel modeling, silver leakage from coated fuel particles, dynamic simulation, MCNP reactor physics modeling and air ingress analysis.
MIT pebble bed reactor project
Kadak, Andrew C.
2007-01-01
The conceptual design of the MIT modular pebble bed reactor is described. This reactor plant is a 250 Mwth, 120 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 900 C providing helium to an intermediate helium to helium heat exchanger (IHX). The outlet of the IHX is input to a three shaft horizontal Brayton Cycle power conversion system. 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 1998 on fuel modeling, silver leakage from coated fuel particles, dynamic simulation, MCNP reactor physics modeling and air ingress analysis
Contact detection acceleration in pebble flow simulation for pebble bed reactor systems
Li, Y.; Ji, W. [Department of Mechanical, Aerospace, and Nuclear Engineering Rensselaer, Polytechnic Institute, 110 8th street, Troy, NY 12180 (United States)
2013-07-01
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 PBMR400. Since the contact detection accounts for more than 60% of the overall CPU time in the pebble flow simulation, the acceleration of the contact detection can greatly enhance the overall efficiency. 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. (authors)
Contact detection acceleration in pebble flow simulation for pebble bed reactor systems
Li, Y.; Ji, W.
2013-01-01
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 PBMR400. Since the contact detection accounts for more than 60% of the overall CPU time in the pebble flow simulation, the acceleration of the contact detection can greatly enhance the overall efficiency. 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. (authors)
Brouwer, A.E.; Haemers, W.H.; Brouwer, A.E.; Haemers, W.H.
2012-01-01
This chapter presents some simple results on graph spectra.We assume the reader is familiar with elementary linear algebra and graph theory. Throughout, J will denote the all-1 matrix, and 1 is the all-1 vector.
Behavior of beryllium pebbles under irradiation
Dalle-Donne, M.; Scaffidi-Argentina, F. [Forschungszentrum Karlsruhe GmbH Technik und Umwelt (Germany). Inst. fuer Neutronenphysik und Reactortechnik; Baldwin, D.L.; Gelles, D.S.; Greenwood, L.R.; Kawamura, H.; Oliver, B.M.
1998-01-01
Beryllium pebbles are being considered in fusion reactor blanket designs as neutron multiplier. An example is the European `Helium Cooled Pebble Bed Blanket.` Several forms of beryllium pebbles are commercially available but little is known about these forms in response to fast neutron irradiation. Commercially available beryllium pebbles have been irradiated to approximately 1.3 x 10{sup 22} n/cm{sup 2} (E>1 MeV) at 390degC. Pebbles 1-mm in diameter manufactured by Brush Wellman, USA and by Nippon Gaishi Company, Japan, and 3-mm pebbles manufactured by Brush Wellman were included. All were irradiated in the below-core area of the Experimental Breeder Reactor-II in Idaho Falls, USA, in molybdenum alloy capsules containing helium. 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. (author)
PEBBLES Simulation of Static Friction and New Static Friction Benchmark
Cogliati, Joshua J.; Ougouag, Abderrafi M.
2010-01-01
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 paper documents the PEBBLES static friction model. 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.
Port-Hamiltonian Systems on Open Graphs
Schaft, A.J. van der; Maschke, B.M.
2010-01-01
In this talk we discuss how to define in an intrinsic manner port-Hamiltonian dynamics on open graphs. Open graphs are graphs where some of the vertices are boundary vertices (terminals), which allow interconnection with other systems. We show that a directed graph carries two natural Dirac
Effect of bed configuration on pebble flow uniformity and stagnation in the pebble bed reactor
Gui, Nan; Yang, Xingtuan; Tu, Jiyuan; Jiang, Shengyao
2014-01-01
Highlights: • Pebble flow uniformity and stagnation characteristics are very important for HTR-PM. • Arc- and brachistochrone-shaped configuration effects are studied by DEM simulation. • Best bed configurations with uniform flow and no stagnated pebbles are suggested. • Detailed quantified characteristics of bed configuration effects are shown for explanation. - Abstract: Pebble flow uniformity and stagnation characteristics are very important for the design of pebble bed high temperature gas-cooled reactor. Pebble flows inside some specifically designed contraction configurations of pebble bed are studied by discrete element method. The results show the characteristics of stagnation rates, recycling rates, radial distribution of pebble velocity and residence time. It is demonstrated clearly that the bed with a brachistochrone-shaped configuration achieves optimum levels of flow uniformity and recycling rate concentration, and almost no pebbles are stagnated in the bed. Moreover, the optimum choice among the arc-shaped bed configurations is demonstrated too. Detailed information shows the quantified characteristics of bed configuration effects on flow uniformity. In addition, a good design of the pebble bed configuration is suggested
Algorithms for Planar Graphs and Graphs in Metric Spaces
Wulff-Nilsen, Christian
structural properties that can be exploited. For instance, a road network or a wire layout on a microchip is typically (near-)planar and distances in the network are often defined w.r.t. the Euclidean or the rectilinear metric. Specialized algorithms that take advantage of such properties are often orders...... of magnitude faster than the corresponding algorithms for general graphs. The first and main part of this thesis focuses on the development of efficient planar graph algorithms. The most important contributions include a faster single-source shortest path algorithm, a distance oracle with subquadratic...... for geometric graphs and graphs embedded in metric spaces. Roughly speaking, the stretch factor is a real value expressing how well a (geo-)metric graph approximates the underlying complete graph w.r.t. distances. We give improved algorithms for computing the stretch factor of a given graph and for augmenting...
The Cross-Flow Mixing Analysis of Quasi-Static Pebble Flow in Pebble Bed Reactor
Fang Xiang; Liu Zhiyong; Sun Yanfei; Yang Xingtuan; Jiang Shengyao
2014-01-01
In the pebble bed reactor, large number of fuel pebbles’ movement law and moving state can affect the reactor’s design, operation and safety directly. 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. (author)
Khovanov homology of graph-links
Nikonov, Igor M [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
2012-08-31
Graph-links arise as the intersection graphs of turning chord diagrams of links. Speaking informally, graph-links provide a combinatorial description of links up to mutations. Many link invariants can be reformulated in the language of graph-links. Khovanov homology, a well-known and useful knot invariant, is defined for graph-links in this paper (in the case of the ground field of characteristic two). Bibliography: 14 titles.
The effects of temperatures on the pebble flow in a pebble bed high temperature reactor
Sen, R. S.; Cogliati, J. J.; Gougar, H. D.
2012-01-01
The core of a pebble bed high temperature reactor (PBHTR) moves during operation, a feature which leads to better fuel economy (online refueling with no burnable poisons) and lower fuel stress. The pebbles are loaded at the top and trickle to the bottom of the core after which the burnup of each is measured. The pebbles that are not fully burned are recirculated through the core until the target burnup is achieved. The flow pattern of the pebbles through the core is of importance for core simulations because it couples the burnup distribution to the core temperature and power profiles, especially in cores with two or more radial burnup 'zones '. The pebble velocity profile is a strong function of the core geometry and the friction between the pebbles and the surrounding structures (other pebbles or graphite reflector blocks). The friction coefficient for graphite in a helium environment is inversely related to the temperature. The Thorium High Temperature Reactor (THTR) operated in Germany between 1983 and 1989. It featured a two-zone core, an inner core (IC) and outer core (OC), with different fuel mixtures loaded in each zone. The rate at which the IC was refueled relative to the OC in THTR was designed to be 0.56. During its operation, however, this ratio was measured to be 0.76, suggesting the pebbles in the inner core traveled faster than expected. It has been postulated that the positive feedback effect between inner core temperature, burnup, and pebble flow was underestimated in THTR. Because of the power shape, the center of the core in a typical cylindrical PBHTR operates at a higher temperature than the region next to the side reflector. The friction between pebbles in the IC is lower than that in the OC, perhaps causing a higher relative flow rate and lower average burnup, which in turn yield a higher local power density. Furthermore, the pebbles in the center region have higher velocities than the pebbles next to the side reflector due to the
The effects of temperatures on the pebble flow in a pebble bed high temperature reactor
Sen, R. S.; Cogliati, J. J.; Gougar, H. D. [Idaho National Laboratory, P.O. Box 1625, Idaho Falls, ID 83415 (United States)
2012-07-01
The core of a pebble bed high temperature reactor (PBHTR) moves during operation, a feature which leads to better fuel economy (online refueling with no burnable poisons) and lower fuel stress. The pebbles are loaded at the top and trickle to the bottom of the core after which the burnup of each is measured. The pebbles that are not fully burned are recirculated through the core until the target burnup is achieved. The flow pattern of the pebbles through the core is of importance for core simulations because it couples the burnup distribution to the core temperature and power profiles, especially in cores with two or more radial burnup 'zones '. The pebble velocity profile is a strong function of the core geometry and the friction between the pebbles and the surrounding structures (other pebbles or graphite reflector blocks). The friction coefficient for graphite in a helium environment is inversely related to the temperature. The Thorium High Temperature Reactor (THTR) operated in Germany between 1983 and 1989. It featured a two-zone core, an inner core (IC) and outer core (OC), with different fuel mixtures loaded in each zone. The rate at which the IC was refueled relative to the OC in THTR was designed to be 0.56. During its operation, however, this ratio was measured to be 0.76, suggesting the pebbles in the inner core traveled faster than expected. It has been postulated that the positive feedback effect between inner core temperature, burnup, and pebble flow was underestimated in THTR. Because of the power shape, the center of the core in a typical cylindrical PBHTR operates at a higher temperature than the region next to the side reflector. The friction between pebbles in the IC is lower than that in the OC, perhaps causing a higher relative flow rate and lower average burnup, which in turn yield a higher local power density. Furthermore, the pebbles in the center region have higher velocities than the pebbles next to the side reflector due to the
Graph Theory. 1. Fragmentation of Structural Graphs
Lorentz JÄNTSCHI
2002-12-01
Full Text Available The investigation of structural graphs has many fields of applications in engineering, especially in applied sciences like as applied chemistry and physics, computer sciences and automation, electronics and telecommunication. The main subject of the paper is to express fragmentation criteria in graph using a new method of investigation: terminal paths. Using terminal paths are defined most of the fragmentation criteria that are in use in molecular topology, but the fields of applications are more generally than that, as I mentioned before. Graphical examples of fragmentation are given for every fragmentation criteria. Note that all fragmentation is made with a computer program that implements a routine for every criterion.[1] A web routine for tracing all terminal paths in graph can be found at the address: http://vl.academicdirect.ro/molecular_topology/tpaths/ [1] M. V. Diudea, I. Gutman, L. Jäntschi, Molecular Topology, Nova Science, Commack, New York, 2001, 2002.
Experimental and computational investigation of flow of pebbles in a pebble bed nuclear reactor
Khane, Vaibhav B.
The Pebble Bed Reactor (PBR) is a 4th generation nuclear reactor which is conceptually similar to moving bed reactors used in the chemical and petrochemical industries. In a PBR core, nuclear fuel in the form of pebbles moves slowly under the influence of gravity. Due to the dynamic nature of the core, a thorough understanding about slow and dense granular flow of pebbles is required from both a reactor safety and performance evaluation point of view. In this dissertation, a new integrated experimental and computational study of granular flow in a PBR has been performed. Continuous pebble re-circulation experimental set-up, mimicking flow of pebbles in a PBR, is designed and developed. Experimental investigation of the flow of pebbles in a mimicked test reactor was carried out for the first time using non-invasive radioactive particle tracking (RPT) and residence time distribution (RTD) techniques to measure the pebble trajectory, velocity, overall/zonal residence times, flow patterns etc. The tracer trajectory length and overall/zonal residence time is found to increase with change in pebble's initial seeding position from the center towards the wall of the test reactor. Overall and zonal average velocities of pebbles are found to decrease from the center towards the wall. Discrete element method (DEM) based simulations of test reactor geometry were also carried out using commercial code EDEM(TM) and simulation results were validated using the obtained benchmark experimental data. In addition, EDEM(TM) based parametric sensitivity study of interaction properties was carried out which suggests that static friction characteristics play an important role from a packed/pebble beds structural characterization point of view. To make the RPT technique viable for practical applications and to enhance its accuracy, a novel and dynamic technique for RPT calibration was designed and developed. Preliminary feasibility results suggest that it can be implemented as a non
Tailored Random Graph Ensembles
Roberts, E S; Annibale, A; Coolen, A C C
2013-01-01
Tailored graph ensembles are a developing bridge between biological networks and statistical mechanics. The aim is to use this concept to generate a suite of rigorous tools that can be used to quantify and compare the topology of cellular signalling networks, such as protein-protein interaction networks and gene regulation networks. We calculate exact and explicit formulae for the leading orders in the system size of the Shannon entropies of random graph ensembles constrained with degree distribution and degree-degree correlation. We also construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities which converges to a strictly uniform measure and is based on edge swaps that conserve all degrees. The acceptance probabilities can be generalized to define Markov chains that target any alternative desired measure on the space of directed or undirected graphs, in order to generate graphs with more sophisticated topological features.
Vestergaard, Preben Dahl; Hartnell, Bert L.
2006-01-01
There are many results dealing with the problem of decomposing a fixed graph into isomorphic subgraphs. There has also been work on characterizing graphs with the property that one can delete the edges of a number of edge disjoint copies of the subgraph and, regardless of how that is done, the gr...
Thermo-mechanical screening tests to qualify beryllium pebble beds with non-spherical pebbles
Reimann, Joerg, E-mail: joerg.reimann@partner.kit.edu [IKET, Karlsruhe Institute of Technology, Karlsruhe (Germany); Fretz, Benjamin [KBHF GmbH, Eggenstein-Leopoldshafen (Germany); Pupeschi, Simone [IAM, Karlsruhe Institute of Technology, Karlsruhe (Germany)
2015-10-15
Highlights: • In present ceramic breeder blankets, pebble-shaped beryllium is used as a neutron multiplier. • Spherical pebbles are considered as the candidate material, however, non-spherical particles are of economic interest. • Thermo-mechanical pebble bed data do merely exist for non-spherical beryllium grades. • Uniaxial compression tests (UCTs), combined with the Hot Wire Technique (HWT) were used to measure the stress–strain relations and the thermal conductivity. • A small experimental set-up had to be used and a detailed 3D modelling was of prime importance. • Compared to spherical pebble beds, non-spherical pebble beds are generally softer and mainly the thermal conductivity is lower. - Abstract: In present ceramic breeder blankets, pebble-shaped beryllium is used as a neutron multiplier. Fairly spherical pebbles are considered as a candidate material, however, non-spherical particles are of economic interest because production costs are much lower. Yet, thermo-mechanical pebble bed data do merely exist for these beryllium grades, and the blanket relevant potential of these grades cannot be judged. Screening experiments were performed with three different grades of non-spherical beryllium pebbles, produced by different companies, accompanied by experiments with the reference beryllium pebble beds. Uniaxial compression tests (UCTs), combined with the Hot Wire Technique (HWT), were performed to measure both the stress–strain relation and the thermal conductivity, k, at different stress levels. Because of the limited amounts of the non-spherical materials, the experimental set-ups were small and a detailed 3D modelling was of prime importance in order to prove that the used design was appropriate. Compared to the pebble beds consisting of spherical pebbles, non-spherical pebble beds are generally softer (smaller stress for a given strain), and, mainly as a consequence of this, for a given strain value, the thermal conductivity is lower. This
Effects of random pebble distribution on the multiplication factor in HTR pebble bed reactors
Auwerda, G.J., E-mail: g.j.auwerda@tudelft.n [Department of Physics of Nuclear Reactors at the Delft University of Technology, Mekelweg 15, Delft (Netherlands); Kloosterman, J.L.; Lathouwers, D.; Hagen, T.H.J.J. van der [Department of Physics of Nuclear Reactors at the Delft University of Technology, Mekelweg 15, Delft (Netherlands)
2010-08-15
In pebble bed reactors the pebbles have a random distribution within the core. The usual approach in modeling the bed is homogenizing the entire bed. To quantify the errors arising in such a model, this article investigates the effect on k{sub eff} of three phenomena in random pebble distributions: non-uniform packing density, neutron streaming in between the pebbles, and variations in Dancoff factor. For a 100 cm high cylinder with reflective top and bottom boundary conditions 25 pebble beds were generated. Of each bed three core models were made: a homogeneous model, a zones model including density fluctuations, and an exact model with all pebbles modeled individually. The same was done for a model of the PROTEUS facility. k{sub eff} calculations were performed with three codes: Monte Carlo, diffusion, and finite element transport. By comparing k{sub eff} of the homogenized and zones model the effect of including density fluctuations in the pebble bed was found to increase k{sub eff} by 71 pcm for the infinite cylinder and 649 pcm for PROTEUS. The large value for PROTEUS is due to the low packing fraction near the top of the pebble bed, causing a significant lower packing fraction for the bulk of the pebble bed in the homogenized model. The effect of neutron streaming was calculated by comparing the zones model with the exact model, and was found to decrease k{sub eff} by 606 pcm for the infinite cylinder, and by 1240 pcm for PROTEUS. This was compared with the effect of using a streaming correction factor on the diffusion coefficient in the zones model, which resulted in {Delta}{sub streaming} values of 340 and 1085 pcm. From this we conclude neutron streaming is an important effect in pebble bed reactors, and is not accurately described by the correction factor on the diffusion coefficient. Changing the Dancoff factor in the outer part of the pebble bed to compensate for the lower probability of neutrons to enter other fuel pebbles caused no significant changes
Effect of a flow-corrective insert on the flow pattern in a pebble bed reactor
Li, Yu; Gui, Nan; Yang, Xingtuan [Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Tsinghua University, Beijing 100084 (China); Tu, Jiyuan [Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Tsinghua University, Beijing 100084 (China); School of Aerospace, Mechanical & Manufacturing Engineering, RMIT University, Melbourne 3083, VIC (Australia); Jiang, Shengyao, E-mail: shengyaojiang@sina.com [Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Tsinghua University, Beijing 100084 (China)
2016-04-15
Highlights: • Effect of an insert on improving flow uniformity and eliminating stagnant zone is studied. • Three values concerned with the stagnant zone, radial uniformity and flow sequence are used. • Outlet diameter is a critical parameter that determines balancing mechanism of the insert. • Height/location is varied to let the insert work in unbalanced region and avoid adverse effect. - Abstract: A flow-corrective insert is adopted in the pebble-bed high temperature gas-cooled reactor (HTGR) to improve flow performance of the pebble flow for the first time. 3D discrete element method (DEM) modeling is employed to study this slow and dense granular flow. It is verified that locating a properly designed insert in the bed can help transform unsatisfactory flow field to the preferred flow pattern for pebble bed reactors. Three characteristic values on the stagnant zone, radial uniformity and flow sequence of pebble flow are defined to evaluate uniformity of the overall flow field quantitatively. The results demonstrate that the pebble bed equipped with an insert performs better than normal beds from all these three aspects. Moreover, based on numerical experiments, several universal tips for insert design on height, location and outlet diameter are suggested.
Graph Algorithm Animation with Grrr
Rodgers, Peter; Vidal, Natalia
2000-01-01
We discuss geometric positioning, highlighting of visited nodes and user defined highlighting that form the algorithm animation facilities in the Grrr graph rewriting programming language. The main purpose of animation was initially for the debugging and profiling of Grrr code, but recently it has been extended for the purpose of teaching algorithms to undergraduate students. The animation is restricted to graph based algorithms such as graph drawing, list manipulation or more traditional gra...
Graph Sampling for Covariance Estimation
Chepuri, Sundeep Prabhakar
2017-04-25
In this paper the focus is on subsampling as well as reconstructing the second-order statistics of signals residing on nodes of arbitrary undirected graphs. Second-order stationary graph signals may be obtained by graph filtering zero-mean white noise and they admit a well-defined power spectrum whose shape is determined by the frequency response of the graph filter. Estimating the graph power spectrum forms an important component of stationary graph signal processing and related inference tasks such as Wiener prediction or inpainting on graphs. The central result of this paper is that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the second-order statistics of the graph signal from the subsampled observations, and more importantly, without any spectral priors. To this end, both a nonparametric approach as well as parametric approaches including moving average and autoregressive models for the graph power spectrum are considered. The results specialize for undirected circulant graphs in that the graph nodes leading to the best compression rates are given by the so-called minimal sparse rulers. A near-optimal greedy algorithm is developed to design the subsampling scheme for the non-parametric and the moving average models, whereas a particular subsampling scheme that allows linear estimation for the autoregressive model is proposed. Numerical experiments on synthetic as well as real datasets related to climatology and processing handwritten digits are provided to demonstrate the developed theory.
Revision of Drucker-Prager cap creep modelling of pebble beds in fusion blankets
Hofer, D.; Kamlah, M.; Hermsmeyer, S.
2004-01-01
A continuum model commonly used in soil mechanics analysis is compiled by use of a finite element software and has been used to simulate the thermomechanical behaviour of pebble beds. The Drucker-Prager Cap theory accounts for inelastic volume change, cap hardening, nonlinear elasticity and pressure dependent shear failure. The hardening mechanism allows for defining the hydrostatic pressure yield stress as a function of the volumetric inelastic strain. Volumetric creep is considered in order to simulate the pebble bed behaviour at high temperatures. Here, the strain hardening option has been used for the consolidation creep mechanism. The model has been calibrated using the fitting curves of the oedometric test given by Reimann et al. The fitted data has been used to calculate a pebble bed with simplified boundary conditions loaded by non-uniform volumetric heating. This calculation demonstrated that the model is capable of representing creep behaviour under volumetric heating conditions. (author)
Penn State geoPebble system: Design,Implementation, and Initial Results
Urbina, J. V.; Anandakrishnan, S.; Bilen, S. G.; Fleishman, A.; Burkett, P.
2014-12-01
The Penn State geoPebble system is a new network of wirelessly interconnected seismic and GPS sensor nodes with flexible architecture. This network will be used for studies of ice sheets in Antarctica and Greenland, as well as to investigate mountain glaciers. The network will consist of ˜150 geoPebbles that can be deployed in a user-defined spatial geometry. We present our design methodology, which has enabled us to develop these state-of- the art sensors using commercial-off-the-shelf hardware combined with custom-designed hardware and software. Each geoPebble is a self- contained, wirelessly connected sensor for collecting seismic measurements and position information. Key elements of each node encompasses a three-component seismic recorder, which includes an amplifier, filter, and 24- bit analog-to-digital converter that can sample up to 10 kHz. Each unit also includes a microphone channel to record the ground-coupled airwave. The timing for each node is available from GPS measurements and a local precision oscillator that is conditioned by the GPS timing pulses. In addition, we record the carrier-phase measurement of the L1 GPS signal in order to determine location at sub-decimeter accuracy (relative to other geoPebbles within a few kilometers radius). Each geoPebble includes 16 GB of solid-state storage, wireless communications capability to a central supervisory unit, and auxiliary measurements capability (including tilt from accelerometers, absolute orientation from magnetometers and temperature). A novel aspect of the geoPebble is a wireless charging system for the internal battery (using inductive coupling techniques). The geoPebbles include all the sensors (geophones, GPS, microphone), communications (WiFi), and power (battery and charging) internally, so the geoPebble system can operate without any cabling connections (though we do provide an external connector so that different geophones can be used). We report initial field-deployment results and
Pebble Accretion in Turbulent Protoplanetary Disks
Xu, Ziyan; Bai, Xue-Ning; Murray-Clay, Ruth A.
2017-09-01
It has been realized in recent years that the accretion of pebble-sized dust particles onto planetary cores is an important mode of core growth, which enables the formation of giant planets at large distances and assists planet formation in general. The pebble accretion theory is built upon the orbit theory of dust particles in a laminar protoplanetary disk (PPD). For sufficiently large core mass (in the “Hill regime”), essentially all particles of appropriate sizes entering the Hill sphere can be captured. However, the outer regions of PPDs are expected to be weakly turbulent due to the magnetorotational instability (MRI), where turbulent stirring of particle orbits may affect the efficiency of pebble accretion. We conduct shearing-box simulations of pebble accretion with different levels of MRI turbulence (strongly turbulent assuming ideal magnetohydrodynamics, weakly turbulent in the presence of ambipolar diffusion, and laminar) and different core masses to test the efficiency of pebble accretion at a microphysical level. We find that accretion remains efficient for marginally coupled particles (dimensionless stopping time {τ }s˜ 0.1{--}1) even in the presence of strong MRI turbulence. Though more dust particles are brought toward the core by the turbulence, this effect is largely canceled by a reduction in accretion probability. As a result, the overall effect of turbulence on the accretion rate is mainly reflected in the changes in the thickness of the dust layer. On the other hand, we find that the efficiency of pebble accretion for strongly coupled particles (down to {τ }s˜ 0.01) can be modestly reduced by strong turbulence for low-mass cores.
Barra, F.; Gaspard, P.
2001-01-01
We consider the classical evolution of a particle on a graph by using a time-continuous Frobenius-Perron operator that generalizes previous propositions. In this way, the relaxation rates as well as the chaotic properties can be defined for the time-continuous classical dynamics on graphs. These properties are given as the zeros of some periodic-orbit zeta functions. We consider in detail the case of infinite periodic graphs where the particle undergoes a diffusion process. The infinite spatial extension is taken into account by Fourier transforms that decompose the observables and probability densities into sectors corresponding to different values of the wave number. The hydrodynamic modes of diffusion are studied by an eigenvalue problem of a Frobenius-Perron operator corresponding to a given sector. The diffusion coefficient is obtained from the hydrodynamic modes of diffusion and has the Green-Kubo form. Moreover, we study finite but large open graphs that converge to the infinite periodic graph when their size goes to infinity. The lifetime of the particle on the open graph is shown to correspond to the lifetime of a system that undergoes a diffusion process before it escapes
Loads on pebble bed fuel elements
Teuchert, E.; Maly, V.
1974-03-15
A comparison is made of key parameters for multi-recycle pebbles and single-pass once-through (OTTO) pebbles. The parameters analyzed include heat transfer characteristics with burn-up, temperature profiles, power per element as a function of axial position in the core, and burn-up. For the OTTO-scheme, the comparisons addressed the use of the conventional fuel element and the advanced "shell ball" designed to reduce the peak fuel temperature in the center of the fuel element. All studies addressed the uranium-thorium fuel cycle.
A cluster algorithm for graphs
S. van Dongen
2000-01-01
textabstractA cluster algorithm for graphs called the emph{Markov Cluster algorithm (MCL~algorithm) is introduced. The algorithm provides basically an interface to an algebraic process defined on stochastic matrices, called the MCL~process. The graphs may be both weighted (with nonnegative weight)
Centrosymmetric Graphs And A Lower Bound For Graph Energy Of Fullerenes
Katona Gyula Y.
2014-11-01
Full Text Available The energy of a molecular graph G is defined as the summation of the absolute values of the eigenvalues of adjacency matrix of a graph G. In this paper, an infinite class of fullerene graphs with 10n vertices, n ≥ 2, is considered. By proving centrosymmetricity of the adjacency matrix of these fullerene graphs, a lower bound for its energy is given. Our method is general and can be extended to other class of fullerene graphs.
Geochemical fingerprints and pebbles zircon geochronology
Home; Journals; Journal of Earth System Science; Volume 125; Issue 7. Geochemical fingerprints and pebbles zircon geochronology: Implications for the provenance and tectonic setting of Lower Cretaceous sediments in the Zhucheng Basin (Jiaodong peninsula, North China). Jin-Long Ni Jun-Lai Liu Xiao-Ling Tang ...
"Smart pebble" designs for sediment transport monitoring
Valyrakis, Manousos; Alexakis, Athanasios; Pavlovskis, Edgars
2015-04-01
Sediment transport, due to primarily the action of water, wind and ice, is one of the most significant geomorphic processes responsible for shaping Earth's surface. It involves entrainment of sediment grains in rivers and estuaries due to the violently fluctuating hydrodynamic forces near the bed. Here an instrumented particle, namely a "smart pebble", is developed to investigate the exact flow conditions under which individual grains may be entrained from the surface of a gravel bed. This could lead in developing a better understanding of the processes involved, focusing on the response of the particle during a variety of flow entrainment events. The "smart pebble" is a particle instrumented with MEMS sensors appropriate for capturing the hydrodynamic forces a coarse particle might experience during its entrainment from the river bed. A 3-axial gyroscope and accelerometer registers data to a memory card via a microcontroller, embedded in a 3D-printed waterproof hollow spherical particle. The instrumented board is appropriately fit and centred into the shell of the pebble, so as to achieve a nearly uniform distribution of the mass which could otherwise bias its motion. The "smart pebble" is powered by an independent power to ensure autonomy and sufficiently long periods of operation appropriate for deployment in the field. Post-processing and analysis of the acquired data is currently performed offline, using scientific programming software. The performance of the instrumented particle is validated, conducting a series of calibration experiments under well-controlled laboratory conditions.
Abou-Sena, Ali, E-mail: ali.abou-sena@kit.edu; Arbeiter, Frederik; Boccaccini, Lorenzo V.; Schlindwein, Georg
2014-10-15
Highlights: • The objective is to measure the purge helium pressure drop across various HCPB-relevant pebble beds packed with lithium orthosilicate and glass pebbles. • The purge helium pressure drop significantly increases with decreasing the pebbles diameter from one run to another. • At the same superficial velocity, the pressure drop is directly proportional to the helium inlet pressure. • The Ergun's equation can successfully model the purge helium pressure drop for the HCPB-relevant pebble beds. • The measured values of the purge helium pressure drop for the lithium orthosilicate pebble bed will support the design of the purge gas system for the HCPB breeder units. - Abstract: The lithium orthosilicate pebble beds of the Helium Cooled Pebble Bed (HCPB) blanket are purged by helium to transport the produced tritium to the tritium extraction system. The pressure drop of the purge helium has a direct impact on the required pumping power and is a limiting factor for the purge mass flow. Therefore, the objective of this study is to measure the helium pressure drop across various HCPB-relevant pebble beds packed with lithium orthosilicate and glass pebbles. The pebble bed was formed by packing the pebbles into a stainless steel cylinder (ID = 30 mm and L = 120 mm); then it was integrated into a gas loop that has four variable-speed side-channel compressors to regulate the helium mass flow. The static pressure was measured at two locations (100 mm apart) along the pebble bed and at inlet and outlet of the pebble bed. The results demonstrated that: (i) the pressure drop significantly increases with decreasing the pebbles diameter, (ii) for the same superficial velocity, the pressure drop is directly proportional to the inlet pressure, and (iii) predictions of Ergun's equation agree well with the experimental results. The measured pressure drop for the lithium orthosilicate pebble bed will support the design of the purge gas system for the HCPB.
Well-covered graphs and factors
Randerath, Bert; Vestergaard, Preben D.
2006-01-01
A maximum independent set of vertices in a graph is a set of pairwise nonadjacent vertices of largest cardinality α. Plummer defined a graph to be well-covered, if every independent set is contained in a maximum independent set of G. Every well-covered graph G without isolated vertices has a perf...
"Smart pebble" design for environmental monitoring applications
Valyrakis, Manousos; Pavlovskis, Edgars
2014-05-01
Sediment transport, due to primarily the action of water, wind and ice, is one of the most significant geomorphic processes responsible for shaping Earth's surface. It involves entrainment of sediment grains in rivers and estuaries due to the violently fluctuating hydrodynamic forces near the bed. Here an instrumented particle, namely a "smart pebble", is developed to investigate the exact flow conditions under which individual grains may be entrained from the surface of a gravel bed. This could lead in developing a better understanding of the processes involved, while focusing on the response of the particle during a variety of flow entrainment events. The "smart pebble" is a particle instrumented with MEMS sensors appropriate for capturing the hydrodynamic forces a coarse particle might experience during its entrainment from the river bed. A 3-axial gyroscope and accelerometer registers data to a memory card via a microcontroller, embedded in a 3D-printed waterproof hollow spherical particle. The instrumented board is appropriately fit and centred into the shell of the pebble, so as to achieve a nearly uniform distribution of the mass which could otherwise bias its motion. The "smart pebble" is powered by an independent power to ensure autonomy and sufficiently long periods of operation appropriate for deployment in the field. Post-processing and analysis of the acquired data is currently performed offline, using scientific programming software. The performance of the instrumented particle is validated, conducting a series of calibration experiments under well-controlled laboratory conditions. "Smart pebble" allows for a wider range of environmental sensors (e.g. for environmental/pollutant monitoring) to be incorporated so as to extend the range of its application, enabling accurate environmental monitoring which is required to ensure infrastructure resilience and preservation of ecological health.
X-ray tomography investigations on pebble bed structures
Reimann, J.; Rolli, R.; Pieritz, R.A.; Ferrero, C.; Di Michiel, M.
2007-01-01
Granular materials (pebbles) are used in present ceramic breeder blankets both for the ceramic breeder material and beryllium. The thermal-mechanical behaviour of these pebble beds strongly depends on the arrangement of the pebbles in the bed, their contacts and contact surfaces with other pebbles and with walls. The influence of these quantities is most pronounced for beryllium pebble beds because of the large thermal conductivity ratio of beryllium to helium gas atmosphere. At present, the data base for the pebble bed thermal conductivity (k) and heat transfer coefficient (h) is quite limited for compressed beds and significant discrepancies exist in respect to h. The detailed knowledge of the pebble bed topology is, therefore, essential to better understand the heat transfer mechanisms. In the present work, results from detailed X-ray tomography investigations are reported on pebble topology in i) the pebble bed bulk (which is relevant for k), and ii) the region close to walls with thicknesses of several pebble diameters (relevant for h). At Forschungszentrum Karlsruhe, pebble beds consisting of aluminium spheres with diameters of 2.3 and 5 mm, respectively, (simulating the blanket relevant 1 mm beryllium pebbles), were uniaxially compressed at different pressure levels. High resolution three-dimensional microtomography (MT) experiments were subsequently performed at the European Synchrotron Radiation Facility, Grenoble. Radial and axial void fraction distributions were found to be oscillatory next to the walls and non-oscillatory in the bulk. For non-compressed pebble beds, the bulk void fraction is fairly constant; for compressed beds, a gradient exists along the compression axis. In the bulk, the angular distribution of pebble contacts was found to be fairly constant, indicating that no regular packing structure is induced. In the wall region, the pebble layer touching the wall is composed of zones with hexagonal structures as shown clearly by MT images. This
Spectral zone selection methodology for pebble bed reactors
Mphahlele, Ramatsemela; Ougouag, Abderrafi M.; Ivanov, Kostadin N.; Gougar, Hans D.
2011-01-01
A methodology is developed for determining boundaries of spectral zones for pebble bed reactors. A spectral zone is defined as a region made up of a number of nodes whose characteristics are collectively similar and that are assigned the same few-group diffusion constants. The spectral zones are selected in such a manner that the difference (error) between the reference transport solution and the diffusion code solution takes a minimum value. This is achieved by choosing spectral zones through optimally minimizing this error. The objective function for the optimization algorithm is the total reaction rate error, which is defined as the sum of the leakage, absorption and fission reaction rates errors in each zone. The selection of these spectral zones is such that the core calculation results based on diffusion theory are within an acceptable tolerance as compared to a proper transport reference solution. Through this work, a consistent approach for identifying spectral zones that yield more accurate diffusion results is introduced.
On path hypercompositions in graphs and automata
Massouros Christos G.
2016-01-01
Full Text Available The paths in graphs define hypercompositions in the set of their vertices and therefore it is feasible to associate hypercompositional structures to each graph. Similarly, the strings of letters from their alphabet, define hypercompositions in the automata, which in turn define the associated hypergroups to the automata. The study of the associated hypercompositional structures gives results in both, graphs and automata theory.
Trudeau, Richard J
1994-01-01
Preface1. Pure Mathematics Introduction; Euclidean Geometry as Pure Mathematics; Games; Why Study Pure Mathematics?; What's Coming; Suggested Reading2. Graphs Introduction; Sets; Paradox; Graphs; Graph diagrams; Cautions; Common Graphs; Discovery; Complements and Subgraphs; Isomorphism; Recognizing Isomorphic Graphs; Semantics The Number of Graphs Having a Given nu; Exercises; Suggested Reading3. Planar Graphs Introduction; UG, K subscript 5, and the Jordan Curve Theorem; Are there More Nonplanar Graphs?; Expansions; Kuratowski's Theorem; Determining Whether a Graph is Planar or
Diestel, Reinhard
2017-01-01
This standard textbook of modern graph theory, now in its fifth edition, combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics. It covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each field by one or two deeper results, again with proofs given in full detail. The book can be used as a reliable text for an introductory course, as a graduate text, and for self-study. From the reviews: “This outstanding book cannot be substituted with any other book on the present textbook market. It has every chance of becoming the standard textbook for graph theory.”Acta Scientiarum Mathematiciarum “Deep, clear, wonderful. This is a serious book about the heart of graph theory. It has depth and integrity. ”Persi Diaconis & Ron Graham, SIAM Review “The book has received a very enthusiastic reception, which it amply deserves. A masterly elucidation of modern graph theo...
Effect of a Central Graphite Column on a Pebble Flow in a Pebble Bed Core
In, W. K.; Lee, W. J.; Chang, J. H.
2006-01-01
A pebble bed reactor(PBR) uses coated fuel particles embedded in spherical graphite fuel pebbles. The fuel pebbles flow down through the core during an operation. The pebble bed core is configured as cylindrical or annular depending on the reactor power. It is well known that an annular core can increase a cores' thermal power. The annular inner core zone is typically filled with movable graphite balls or a fixed graphite column. The first problem with this conventional annular core is that it is difficult to maintain a boundary between the central graphite ball zone and the outer fuel zone. The second problem is that it is expensive to replace the central fixed graphite column after several tens of years of reactor operation. In order to resolve these problems, a PBR with a central graphite column in a low core is invented. This paper presents the effect of the central graphite column on a pebble flow by using the computational fluid dynamics(CFD) code, CFX-10
Drucker-Prager-Cap creep modelling of pebble beds in fusion blankets
Hofer, D.; Kamlah, M.
2005-01-01
Modelling of thermal and mechanical behaviour of pebble beds for fusion blankets is an important issue to understand the interaction of solid breeder and beryllium pebble beds with the surrounding structural material. Especially the differing coefficients of thermal expansion of these materials cause high stresses and strains during irradiation induced volumetric heating. To describe this process, the coupled thermomechanical behaviour of both pebble bed materials has to be modelled. Additionally, creep has to be considered contributing to bed deformations and stress relaxation. Motivated by experiments, we use a continuum mechanical approach called Drucker-Prager/Cap theory to model the macroscopic pebble bed behaviour. The model accounts for pressure dependent shear failure, inelastic hardening, and volumetric creep. The elastic part is described by a nonlinear elasticity law. The model has been implemented by user-defined routines in the commercial finite-element code ABAQUS. To check the numerics, the implementation is compared to an analytical solution. Furthermore, the Drucker-Prager/Cap tool is applied to a single ceramic breeder bed subject to creep under volumetric heating
Van Lew, Jon T., E-mail: jtvanlew@fusion.ucla.edu; Ying, Alice; Abdou, Mohamed
2014-10-15
The discrete element method (DEM) is used to study the thermal effects of pebble failure in an ensemble of lithium ceramic spheres. Some pebbles crushing in a large system is unavoidable and this study provides correlations between the extent of pebble failure and the reduction in effective thermal conductivity of the bed. In the model, we homogeneously induced failure and applied nuclear heating until dynamic and thermal steady-state. Conduction between pebbles and from pebbles to the boundary is the only mode of heat transfer presently modeled. The effective thermal conductivity was found to decrease rapidly as a function of the percent of failed pebbles in the bed. It was found that the dominant contributor to the reduction was the drop in inter-particle forces as pebbles fail; implying the extent of failure induced may not occur in real pebble beds. The results are meant to assist designers in the fusion energy community who are planning to use packed beds of ceramic pebbles. The evolution away from experimentally measured thermomechanical properties as pebbles fail is necessary for proper operation of fusion reactors.
Mechanical performance of irradiated beryllium pebbles
Scaffidi-Argentina, F.; Dalle-Donne, M.; Werle, H. [Forschungszentrum Karlsruhe GmbH Technik und Umwelt (Germany). Inst. fuer Neutronenphysik und Reaktortechnik
1998-01-01
For the Helium Cooled Pebble Bed (HCPB) Blanket, which is one of the two reference concepts studied within the European Fusion Technology Programme, the neutron multiplier consists of a mixed bed of about 2 and 0.1-0.2 mm diameter beryllium pebbles. Beryllium has no structural function in the blanket, however microstructural and mechanical properties are important, as they might influence the material behavior under neutron irradiation. The EXOTIC-7 as well as the `Beryllium` experiments carried out in the HFR reactor in Petten are considered as the most detailed and significant tests for investigating it. This paper reviews the present status of beryllium post-irradiation examinations performed at the Forschungszentrum Karlsruhe with samples from these irradiation experiments, emphasizing the effects of irradiation of essential material properties and trying to elucidate the processes controlling the property changes. The microstructure, the porosity distribution, the impurity content, the behavior under compression loads and the compatibility of the beryllium pebbles with lithium orthosilicate (Li{sub 4}SiO{sub 4}) during the in-pile irradiation are presented and critically discussed. Qualitative information on ductility and creep obtained by hardness-type measurements are also supplied. (author)
On some covering graphs of a graph
Shariefuddin Pirzada
2016-10-01
Full Text Available For a graph $G$ with vertex set $V(G=\\{v_1, v_2, \\dots, v_n\\}$, let $S$ be the covering set of $G$ having the maximum degree over all the minimum covering sets of $G$. Let $N_S[v]=\\{u\\in S : uv \\in E(G \\}\\cup \\{v\\}$ be the closed neighbourhood of the vertex $v$ with respect to $S.$ We define a square matrix $A_S(G= (a_{ij},$ by $a_{ij}=1,$ if $\\left |N_S[v_i]\\cap N_S[v_j] \\right| \\geq 1, i\
Xiong, B.; Oude Elberink, S.; Vosselman, G.
2014-07-01
In the task of 3D building model reconstruction from point clouds we face the problem of recovering a roof topology graph in the presence of noise, small roof faces and low point densities. Errors in roof topology graphs will seriously affect the final modelling results. The aim of this research is to automatically correct these errors. We define the graph correction as a graph-to-graph problem, similar to the spelling correction problem (also called the string-to-string problem). The graph correction is more complex than string correction, as the graphs are 2D while strings are only 1D. We design a strategy based on a dictionary of graph edit operations to automatically identify and correct the errors in the input graph. For each type of error the graph edit dictionary stores a representative erroneous subgraph as well as the corrected version. As an erroneous roof topology graph may contain several errors, a heuristic search is applied to find the optimum sequence of graph edits to correct the errors one by one. The graph edit dictionary can be expanded to include entries needed to cope with errors that were previously not encountered. Experiments show that the dictionary with only fifteen entries already properly corrects one quarter of erroneous graphs in about 4500 buildings, and even half of the erroneous graphs in one test area, achieving as high as a 95% acceptance rate of the reconstructed models.
Multiple graph regularized protein domain ranking
Wang, Jim Jing-Yan
2012-11-19
Background: Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods.Results: To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods.Conclusion: The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications. 2012 Wang et al; licensee BioMed Central Ltd.
Multiple graph regularized protein domain ranking
Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin
2012-01-01
Background: Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods.Results: To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods.Conclusion: The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications. 2012 Wang et al; licensee BioMed Central Ltd.
Multiple graph regularized protein domain ranking.
Wang, Jim Jing-Yan; Bensmail, Halima; Gao, Xin
2012-11-19
Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods. To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods. The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications.
Multiple graph regularized protein domain ranking
Wang Jim
2012-11-01
Full Text Available Abstract Background Protein domain ranking is a fundamental task in structural biology. Most protein domain ranking methods rely on the pairwise comparison of protein domains while neglecting the global manifold structure of the protein domain database. Recently, graph regularized ranking that exploits the global structure of the graph defined by the pairwise similarities has been proposed. However, the existing graph regularized ranking methods are very sensitive to the choice of the graph model and parameters, and this remains a difficult problem for most of the protein domain ranking methods. Results To tackle this problem, we have developed the Multiple Graph regularized Ranking algorithm, MultiG-Rank. Instead of using a single graph to regularize the ranking scores, MultiG-Rank approximates the intrinsic manifold of protein domain distribution by combining multiple initial graphs for the regularization. Graph weights are learned with ranking scores jointly and automatically, by alternately minimizing an objective function in an iterative algorithm. Experimental results on a subset of the ASTRAL SCOP protein domain database demonstrate that MultiG-Rank achieves a better ranking performance than single graph regularized ranking methods and pairwise similarity based ranking methods. Conclusion The problem of graph model and parameter selection in graph regularized protein domain ranking can be solved effectively by combining multiple graphs. This aspect of generalization introduces a new frontier in applying multiple graphs to solving protein domain ranking applications.
Ceramic breeder pebble bed packing stability under cyclic loads
Zhang, Chunbo, E-mail: chunbozhang@fusion.ucla.edu [Fusion Science and Technology Center, University of California, Los Angeles, CA 90095-1597 (United States); Ying, Alice; Abdou, Mohamed A. [Fusion Science and Technology Center, University of California, Los Angeles, CA 90095-1597 (United States); Park, Yi-Hyun [National Fusion Research Institute, Daejeon (Korea, Republic of)
2016-11-01
Highlights: • The feasibility of obtaining packing stability for pebble beds is studied. • The responses of pebble bed to cyclic loads have been presented and analyzed in details. • Pebble bed packing saturation and its applications are discussed. • A suggestion is made regarding the improvement of pebbles filling technique. - Abstract: 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. Uniaxial compaction tests have been performed for both KIT’s Li{sub 4}SiO{sub 4} and NFRI’s Li{sub 2}TiO{sub 3} pebble beds at elevated temperatures (up to 750 °C) under cyclic loads (up to 6 MPa). 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. The characterized FEM CAP material models for a Li{sub 4}SiO{sub 4} pebble bed with an edge-on configuration are used to simulate the thermomechanical behavior of pebble bed under ITER pulsed operations. Simulation results have shown the cyclic variation of temperature/stress/strain/gap and also the same saturation trend with experiments under cyclic loads. Therefore, it is feasible for pebble bed to maintain its packing stability during operation when disregarding pebbles’ breakage and irradiation.
Mechanics of a crushable pebble assembly using discrete element method
Annabattula, R.K.; Gan, Y.; Zhao, S.; Kamlah, M.
2012-01-01
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 5000 spherical pebbles is assigned with random critical failure energies with a Weibull distribution in accordance with the experimental observation. Then, the pebble assembly is subjected to uni-axial compression (ε 33 =1.5%) with periodic boundary conditions. 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. Furthermore, a loosely packed pebble assembly shows a higher crush resistance while the critical stress is insensitive to the packing factor (η) of the assembly.
Gould, Ronald
2012-01-01
This introduction to graph theory focuses on well-established topics, covering primary techniques and including both algorithmic and theoretical problems. The algorithms are presented with a minimum of advanced data structures and programming details. This thoroughly corrected 1988 edition provides insights to computer scientists as well as advanced undergraduates and graduate students of topology, algebra, and matrix theory. Fundamental concepts and notation and elementary properties and operations are the first subjects, followed by examinations of paths and searching, trees, and networks. S
Learning heat diffusion graphs
Thanou, Dorina; Dong, Xiaowen; Kressner, Daniel; Frossard, Pascal
2016-01-01
Effective information analysis generally boils down to properly identifying the structure or geometry of the data, which is often represented by a graph. In some applications, this structure may be partly determined by design constraints or pre-determined sensing arrangements, like in road transportation networks for example. In general though, the data structure is not readily available and becomes pretty difficult to define. In particular, the global smoothness assumptions, that most of the...
Chartrand, Gary; Zhang, Ping
2010-01-01
Gary Chartrand has influenced the world of Graph Theory for almost half a century. He has supervised more than a score of Ph.D. dissertations and written several books on the subject. The most widely known of these texts, Graphs and Digraphs, … has much to recommend it, with clear exposition, and numerous challenging examples [that] make it an ideal textbook for the advanced undergraduate or beginning graduate course. The authors have updated their notation to reflect the current practice in this still-growing area of study. By the authors' estimation, the 5th edition is approximately 50% longer than the 4th edition. … the legendary Frank Harary, author of the second graph theory text ever produced, is one of the figures profiled. His book was the standard in the discipline for several decades. Chartrand, Lesniak and Zhang have produced a worthy successor.-John T. Saccoman, MAA Reviews, June 2012 (This book is in the MAA's basic library list.)As with the earlier editions, the current text emphasizes clear...
Graphs with Eulerian unit spheres
Knill, Oliver
2015-01-01
d-spheres in graph theory are inductively defined as graphs for which all unit spheres S(x) are (d-1)-spheres and that the removal of one vertex renders the graph contractible. Eulerian d-spheres are geometric d-spheres which are d+1 colorable. We prove here that G is an Eulerian sphere if and only if the degrees of all the (d-2)-dimensional sub-simplices in G are even. This generalizes a Kempe-Heawood result for d=2 and is work related to the conjecture that all d-spheres have chromatic numb...
Subsampling for graph power spectrum estimation
Chepuri, Sundeep Prabhakar; Leus, Geert
2016-01-01
In this paper we focus on subsampling stationary random signals that reside on the vertices of undirected graphs. Second-order stationary graph signals are obtained by filtering white noise and they admit a well-defined power spectrum. Estimating the graph power spectrum forms a central component of stationary graph signal processing and related inference tasks. We show that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the power spectrum of the graph signal from the subsampled observations, without any spectral priors. In addition, a near-optimal greedy algorithm is developed to design the subsampling scheme.
Subsampling for graph power spectrum estimation
Chepuri, Sundeep Prabhakar
2016-10-06
In this paper we focus on subsampling stationary random signals that reside on the vertices of undirected graphs. Second-order stationary graph signals are obtained by filtering white noise and they admit a well-defined power spectrum. Estimating the graph power spectrum forms a central component of stationary graph signal processing and related inference tasks. We show that by sampling a significantly smaller subset of vertices and using simple least squares, we can reconstruct the power spectrum of the graph signal from the subsampled observations, without any spectral priors. In addition, a near-optimal greedy algorithm is developed to design the subsampling scheme.
PRIVATE GRAPHS – ACCESS RIGHTS ON GRAPHS FOR SEAMLESS NAVIGATION
W. Dorner
2016-06-01
Full Text Available After the success of GNSS (Global Navigational Satellite Systems and navigation services for public streets, indoor seems to be the next big development in navigational services, relying on RTLS – Real Time Locating Services (e.g. WIFI and allowing seamless navigation. In contrast to navigation and routing services on public streets, seamless navigation will cause an additional challenge: how to make routing data accessible to defined users or restrict access rights for defined areas or only to parts of the graph to a defined user group? The paper will present case studies and data from literature, where seamless and especially indoor navigation solutions are presented (hospitals, industrial complexes, building sites, but the problem of restricted access rights was only touched from a real world, but not a technical perspective. The analysis of case studies will show, that the objective of navigation and the different target groups for navigation solutions will demand well defined access rights and require solutions, how to make only parts of a graph to a user or application available to solve a navigational task. The paper will therefore introduce the concept of private graphs, which is defined as a graph for navigational purposes covering the street, road or floor network of an area behind a public street and suggest different approaches how to make graph data for navigational purposes available considering access rights and data protection, privacy and security issues as well.
On characterizing terrain visibility graphs
William Evans
2015-06-01
Full Text Available A terrain is an $x$-monotone polygonal line in the $xy$-plane. Two vertices of a terrain are mutually visible if and only if there is no terrain vertex on or above the open line segment connecting them. A graph whose vertices represent terrain vertices and whose edges represent mutually visible pairs of terrain vertices is called a terrain visibility graph. We would like to find properties that are both necessary and sufficient for a graph to be a terrain visibility graph; that is, we would like to characterize terrain visibility graphs.Abello et al. [Discrete and Computational Geometry, 14(3:331--358, 1995] showed that all terrain visibility graphs are “persistent”. They showed that the visibility information of a terrain point set implies some ordering requirements on the slopes of the lines connecting pairs of points in any realization, and as a step towards showing sufficiency, they proved that for any persistent graph $M$ there is a total order on the slopes of the (pseudo lines in a generalized configuration of points whose visibility graph is $M$.We give a much simpler proof of this result by establishing an orientation to every triple of vertices, reflecting some slope ordering requirements that are consistent with $M$ being the visibility graph, and prove that these requirements form a partial order. We give a faster algorithm to construct a total order on the slopes. Our approach attempts to clarify the implications of the graph theoretic properties on the ordering of the slopes, and may be interpreted as defining properties on an underlying oriented matroid that we show is a restricted type of $3$-signotope.
Disser, Jay; Arthur, Edward; Lambert, Janine
2016-09-01
This report examines a preliminary design for a pebble bed fluoride salt-cooled high temperature reactor (PB-FHR) concept, assessing it from an international safeguards perspective. Safeguards features are defined, in a preliminary fashion, and suggestions are made for addressing further nuclear materials accountancy needs.
A Pebble Bed Reactor cross section methodology
Hudson, Nathanael H.; Ougouag, Abderrafi M.; Rahnema, Farzad; Gougar, Hans
2009-01-01
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. This technique is named the Spectral History Correction (SHC) method. 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.
Surface coating of graphite pebbles for Korean HCCR TBM
Lee, Youngmin [National Fusion Research Institute, Daejeon (Korea, Republic of); Yun, Young-Hoon, E-mail: yunh2@dsu.ac.kr [Dongshin University, Naju (Korea, Republic of); Park, Yi-Hyun; Ahn, Mu-Young; Cho, Seungyon [National Fusion Research Institute, Daejeon (Korea, Republic of)
2014-10-15
Highlights: • A CVR-SiC coating was successfully formed on graphite pebbles for neutron reflector. • Dense and fine-grained surface morphologies of the SiC coatings were observed. • Oxidation resistance of the CVR-SiC-coated graphite pebbles was improved. - Abstract: The new concept of the recently modified Helium-Cooled Ceramic Reflector (HCCR) Test Blanket Module (TBM) is to adopt a graphite reflector in the form of a pebble bed. A protective SiC coating is applied to the graphite pebbles to prohibit their reaction with steam or air as well as dust generation during TBM operation. In this research, the chemical vapor reaction (CVR) method was applied to fabricate SiC-coated graphite pebbles in a silica source. Relatively dense CVR-SiC coating was successfully formed on the graphite pebbles through the reduction of the graphite phase with SiO gas that was simply created from the silica source at 1850 °C (2 h). The microstructural features, XRD patterns, pore-size distribution and oxidation behavior of the SiC-coated graphite pebbles were investigated. To develop the practical process, which will be applied for mass production hereafter, a novel alternative method was applied to form the layer of SiC coating on the graphite pebbles over the silica source.
Fabrication of modified lithium orthosilicate pebbles by addition of titania
Knitter, R., E-mail: regina.knitter@kit.edu [Karlsruhe Institute of Technology (KIT), Institute for Applied Materials (IAM-WPT), Karlsruhe, 76021 (Germany); Kolb, M.H.H.; Kaufmann, U. [Karlsruhe Institute of Technology (KIT), Institute for Applied Materials (IAM-WPT), Karlsruhe, 76021 (Germany); Goraieb, A.A. [Goraieb Versuchstechnik (GVT), Karlsruhe, 76227 (Germany)
2013-11-15
Highlights: ► Lithium orthosilicate pebbles with additions of titania were fabricated by a modified melt-based process. ► The fabricated pebbles exhibit a very fine-grained microstructure with lithium metatitanate as a secondary phase. ► Due to the addition of titanate, the crush load of the pebbles was significantly increased. ► The closed porosity was found to be slightly increased with increasing titanate content. -- Abstract: Lithium orthosilicate pebbles are one of the ceramic tritium breeder materials destined for the European solid breeder test blanket modules of ITER, the large-scale scientific experiment intended to prove the viability of fusion as an energy source, presently under construction in Cadarache, France. While the current reference material is fabricated by melt-spraying with 2.5 wt.% excess of silica, resulting in a two-phase material of lithium orthosilicate and metasilicate, a modified melt-based process was used to fabricate breeder pebbles with additions of titania in order to obtain pebbles with lithium metatitanate as a secondary phase. The fabricated two-phase pebbles exhibit a fine-grained microstructure and increased crush loads. The optimum titanate content has yet to be evaluated, nonetheless the pebbles may have the potential to combine the advantages of both lithium orthosilicate and metatitanate breeder ceramics.
Surface coating of graphite pebbles for Korean HCCR TBM
Lee, Youngmin; Yun, Young-Hoon; Park, Yi-Hyun; Ahn, Mu-Young; Cho, Seungyon
2014-01-01
Highlights: • A CVR-SiC coating was successfully formed on graphite pebbles for neutron reflector. • Dense and fine-grained surface morphologies of the SiC coatings were observed. • Oxidation resistance of the CVR-SiC-coated graphite pebbles was improved. - Abstract: The new concept of the recently modified Helium-Cooled Ceramic Reflector (HCCR) Test Blanket Module (TBM) is to adopt a graphite reflector in the form of a pebble bed. A protective SiC coating is applied to the graphite pebbles to prohibit their reaction with steam or air as well as dust generation during TBM operation. In this research, the chemical vapor reaction (CVR) method was applied to fabricate SiC-coated graphite pebbles in a silica source. Relatively dense CVR-SiC coating was successfully formed on the graphite pebbles through the reduction of the graphite phase with SiO gas that was simply created from the silica source at 1850 °C (2 h). The microstructural features, XRD patterns, pore-size distribution and oxidation behavior of the SiC-coated graphite pebbles were investigated. To develop the practical process, which will be applied for mass production hereafter, a novel alternative method was applied to form the layer of SiC coating on the graphite pebbles over the silica source
Fibonacci number of the tadpole graph
Joe DeMaio
2014-10-01
Full Text Available In 1982, Prodinger and Tichy defined the Fibonacci number of a graph G to be the number of independent sets of the graph G. They did so since the Fibonacci number of the path graph Pn is the Fibonacci number F(n+2 and the Fibonacci number of the cycle graph Cn is the Lucas number Ln. The tadpole graph Tn,k is the graph created by concatenating Cn and Pk with an edge from any vertex of Cn to a pendant of Pk for integers n=3 and k=0. This paper establishes formulae and identities for the Fibonacci number of the tadpole graph via algebraic and combinatorial methods.
How cores grow by pebble accretion. I. Direct core growth
Brouwers, M. G.; Vazan, A.; Ormel, C. W.
2018-03-01
Context. Planet formation by pebble accretion is an alternative to planetesimal-driven core accretion. In this scenario, planets grow by the accretion of cm- to m-sized pebbles instead of km-sized planetesimals. One of the main differences with planetesimal-driven core accretion is the increased thermal ablation experienced by pebbles. This can provide early enrichment to the planet's envelope, which influences its subsequent evolution and changes the process of core growth. Aims: We aim to predict core masses and envelope compositions of planets that form by pebble accretion and compare mass deposition of pebbles to planetesimals. Specifically, we calculate the core mass where pebbles completely evaporate and are absorbed before reaching the core, which signifies the end of direct core growth. Methods: We model the early growth of a protoplanet by calculating the structure of its envelope, taking into account the fate of impacting pebbles or planetesimals. The region where high-Z material can exist in vapor form is determined by the temperature-dependent vapor pressure. We include enrichment effects by locally modifying the mean molecular weight of the envelope. Results: In the pebble case, three phases of core growth can be identified. In the first phase (Mcore mixes outwards, slowing core growth. In the third phase (Mcore > 0.5M⊕), the high-Z inner region expands outwards, absorbing an increasing fraction of the ablated material as vapor. Rainout ends before the core mass reaches 0.6 M⊕, terminating direct core growth. In the case of icy H2O pebbles, this happens before 0.1 M⊕. Conclusions: Our results indicate that pebble accretion can directly form rocky cores up to only 0.6 M⊕, and is unable to form similarly sized icy cores. Subsequent core growth can proceed indirectly when the planet cools, provided it is able to retain its high-Z material.
The Pebble Bed Modular Reactor: An obituary
Thomas, Steve, E-mail: stephen.thomas@gre.ac.u [Public Services International Research Unit (PSIRU), Business School, University of Greenwich, 30 Park Row, London SE10 9LS (United Kingdom)
2011-05-15
The High Temperature Gas-cooled Reactor (HTGR) has exerted a peculiar attraction over nuclear engineers. Despite many unsuccessful attempts over half a century to develop it as a commercial power reactor, there is still a strong belief amongst many nuclear advocates that a highly successful HTGR technology will emerge. The most recent attempt to commercialize an HTGR design, the Pebble Bed Modular Reactor (PBMR), was abandoned in 2010 after 12 years of effort and the expenditure of a large amount of South African public money. This article reviews this latest attempt to commercialize an HTGR design and attempts to identify which issues have led to its failure and what lessons can be learnt from this experience. It concludes that any further attempts to develop HTGRs using Pebble Bed technology should only be undertaken if there is a clear understanding of why earlier attempts have failed and a high level of confidence that earlier problems have been overcome. It argues that the PBMR project has exposed serious weaknesses in accountability mechanisms for the expenditure of South African public money. - Research highlights: {yields} In this study we examine the reasons behind the failure of the South African PBMR programme. {yields} The study reviews the technical issues that have arisen and lessons for future reactor developments. {yields} The study also identifies weaknesses in the accountability mechanisms for public spending.
Chartrand, Gary; Rosen, Kenneth H
2008-01-01
Beginning with the origin of the four color problem in 1852, the field of graph colorings has developed into one of the most popular areas of graph theory. Introducing graph theory with a coloring theme, Chromatic Graph Theory explores connections between major topics in graph theory and graph colorings as well as emerging topics. This self-contained book first presents various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. The remainder of the text deals exclusively with graph colorings. It covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings, and many distance-related vertex coloring...
Efficient Algorithmic Frameworks via Structural Graph Theory
2016-10-28
constant. For example, they measured that, on large samples of the entire network, the Amazon graph has average degree 17.7, the Facebook graph has average...department heads’ opinions of departments, and generally lack transparency and well-defined measures . On the other hand, the National Research Council (the...Efficient and practical resource block allocation for LTE -based D2D network via graph coloring. Wireless Networks 20(4): 611-624 (2014) 50. Hossein
Optimization of MOX fuel cycles in pebble bed HTGR
Wei Jinfeng; Li Fu; Sun Yuliang
2013-01-01
Compared with light water reactor (LWR), the pebble bed high temperature gas-cooled reactor (HTGR) is able to operate in a full mixed oxide (MOX) fuelled core without significant change to core structure design. Based on a reference design of 250 MW pebble bed HTGR, four MOX fuel cycles were designed and evaluated by VSOP program package, including the mixed Pu-U fuel pebbles and mixed loading of separate Pu-pebbles and U-pebbles. Some important physics features were investigated and compared for these four cycles, such as the effective multiplication factor of initial core, the pebble residence time, discharge burnup, and temperature coefficients. Preliminary results show that the overall performance of one case is superior to other equivalent MOX fuel cycles on condition that uranium fuel elements and plutonium fuel elements are separated as the different fuel pebbles and that the uranium fuel elements are irradiated longer in the core than the plutonium fuel elements, and the average discharge burnup of this case is also higher than others. (authors)
Mechanics of binary and polydisperse spherical pebble assembly
Annabattula, R.K.; Gan, Y.; Kamlah, M.
2012-01-01
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. 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.
Mechanics of binary and polydisperse spherical pebble assembly
Annabattula, R.K., E-mail: ratna.annabattula@kit.edu [Institute for Applied Materials (IAM-WBM), Karlsruhe Institute of Technology (KIT), D-76344, Eggenstein-Leopoldshafen (Germany); Gan, Y., E-mail: yixiang.gan@sydney.edu.au [School of Civil Engineering, University of Sydney, 2006 NSW, Sydney (Australia); Kamlah, M., E-mail: marc.kamlah@kit.edu [Institute for Applied Materials (IAM-WBM), Karlsruhe Institute of Technology (KIT), D-76344, Eggenstein-Leopoldshafen (Germany)
2012-08-15
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. 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.
Commuting graphs of matrix algebras
Akbari, S.; Bidkhori, H.; Mohammadian, A.
2006-08-01
The commuting graph of a ring R, denoted by Γ(R), is a graph whose vertices are all non- central elements of R and two distinct vertices x and y are adjacent if and only if xy = yx. The commuting graph of a group G, denoted by Γ(G), is similarly defined. In this paper we investigate some graph theoretic properties of Γ(M n (F)), where F is a field and n ≥ 2. Also we study the commuting graphs of some classical groups such as GL n (F) and SL n (F). We show that Γ(M n (F)) is a connected graph if and only if every field extension of F of degree n contains a proper intermediate field. We prove that apart from finitely many fields, a similar result is true for Γ(GL n (F)) and Γ(SL n (F)). Also we show that for two fields E and F and integers m, n ≥> 2, if Γ(M m (E)) ≅ Γ(M n (F)), then m = n and vertical bar E vertical bar = vertical bar F vertical bar. (author)
The ESKOM pebble bed modular reactor
Gittus, J.H.
1999-01-01
An audit has been made of the design, construction, safety, economics and marketability of the ESKOM pebble bed modular reactor (PBMR). In this paper that audit is briefly summarized. The principal conclusions of the audit are as follows. The design is sound. It is a logical development of the designs proposed for other, modern, high-temperature gas-cooled reactors. More than 80% of the cost of constructing and commissioning a series of PBMRs would be spent in South Africa. The PBMR is much safer than existing nuclear power reactors and for many practical purposes it may be treated as a conventional chemical plant. The PBMR is economically competitive with thermal power stations. There is a substantial global market for the PBMR. (author)
1National Centre for Advanced Research in Discrete Mathematics ... 3Department of Computer Science, Ball State University, Muncie, IN, USA .... The corona of two disjoint graphs G1 and G2 is defined to be the graph G = G1 ◦ G2,.
Advanced Core Design And Fuel Management For Pebble-Bed Reactors
Hans D. Gougar; Abderrafi M. Ougouag; William K. Terry
2004-10-01
A method for designing and optimizing recirculating pebble-bed reactor cores is presented. At the heart of the method is a new reactor physics computer code, PEBBED, which accurately and efficiently computes the neutronic and material properties of the asymptotic (equilibrium) fuel cycle. This core state is shown to be unique for a given core geometry, power level, discharge burnup, and fuel circulation policy. Fuel circulation in the pebble-bed can be described in terms of a few well?defined parameters and expressed as a recirculation matrix. The implementation of a few heat?transfer relations suitable for high-temperature gas-cooled reactors allows for the rapid estimation of thermal properties critical for safe operation. Thus, modeling and design optimization of a given pebble-bed core can be performed quickly and efficiently via the manipulation of a limited number key parameters. Automation of the optimization process is achieved by manipulation of these parameters using a genetic algorithm. The end result is an economical, passively safe, proliferation-resistant nuclear power plant.
Andreas P. Braun
2016-04-01
Full Text Available Box graphs succinctly and comprehensively characterize singular fibers of elliptic fibrations in codimension two and three, as well as flop transitions connecting these, in terms of representation theoretic data. We develop a framework that provides a systematic map between a box graph and a crepant algebraic resolution of the singular elliptic fibration, thus allowing an explicit construction of the fibers from a singular Weierstrass or Tate model. The key tool is what we call a fiber face diagram, which shows the relevant information of a (partial toric triangulation and allows the inclusion of more general algebraic blowups. We shown that each such diagram defines a sequence of weighted algebraic blowups, thus providing a realization of the fiber defined by the box graph in terms of an explicit resolution. We show this correspondence explicitly for the case of SU(5 by providing a map between box graphs and fiber faces, and thereby a sequence of algebraic resolutions of the Tate model, which realizes each of the box graphs.
Graph visualization (Invited talk)
Wijk, van J.J.; Kreveld, van M.J.; Speckmann, B.
2012-01-01
Black and white node link diagrams are the classic method to depict graphs, but these often fall short to give insight in large graphs or when attributes of nodes and edges play an important role. Graph visualization aims obtaining insight in such graphs using interactive graphical representations.
Replica methods for loopy sparse random graphs
Coolen, ACC
2016-01-01
I report on the development of a novel statistical mechanical formalism for the analysis of random graphs with many short loops, and processes on such graphs. The graphs are defined via maximum entropy ensembles, in which both the degrees (via hard constraints) and the adjacency matrix spectrum (via a soft constraint) are prescribed. The sum over graphs can be done analytically, using a replica formalism with complex replica dimensions. All known results for tree-like graphs are recovered in a suitable limit. For loopy graphs, the emerging theory has an appealing and intuitive structure, suggests how message passing algorithms should be adapted, and what is the structure of theories describing spin systems on loopy architectures. However, the formalism is still largely untested, and may require further adjustment and refinement. (paper)
Matrix formulation of pebble circulation in the pebbed code
Gougar, H.D.; Terry, W.K.; Ougouag, A.M.
2002-01-01
The PEBBED technique provides a foundation for equilibrium fuel cycle analysis and optimization in pebble-bed cores in which the fuel elements are continuously flowing and, if desired, recirculating. In addition to the modern analysis techniques used in or being developed for the code, PEBBED incorporates a novel nuclide-mixing algorithm that allows for sophisticated recirculation patterns using a matrix generated from basic core parameters. Derived from a simple partitioning of the pebble flow, the elements of the recirculation matrix are used to compute the spatially averaged density of each nuclide at the entry plane from the nuclide densities of pebbles emerging from the discharge conus. The order of the recirculation matrix is a function of the flexibility and sophistication of the fuel handling mechanism. This formulation for coupling pebble flow and neutronics enables core design and fuel cycle optimization to be performed by the manipulation of a few key core parameters. The formulation is amenable to modern optimization techniques. (author)
Transient heat conduction in a pebble fuel applying fractional model
Gomez A, R.; Espinosa P, G.
2009-10-01
In this paper we presents the equation of thermal diffusion of temporary-fractional order in the one-dimensional space in spherical coordinates, with the objective to analyze the heat transference between the fuel and coolant in a fuel element of a Pebble Bed Modular Reactor. The pebble fuel is the heterogeneous system made by microsphere constitutes by U O, pyrolytic carbon and silicon carbide mixed with graphite. To describe the heat transfer phenomena in the pebble fuel we applied a constitutive law fractional (Non-Fourier) in order to analyze the behaviour transient of the temperature distribution in the pebble fuel with anomalous thermal diffusion effects a numerical model is developed. (Author)
Pragmatic Graph Rewriting Modifications
Rodgers, Peter; Vidal, Natalia
1999-01-01
We present new pragmatic constructs for easing programming in visual graph rewriting programming languages. The first is a modification to the rewriting process for nodes the host graph, where nodes specified as 'Once Only' in the LHS of a rewrite match at most once with a corresponding node in the host graph. This reduces the previously common use of tags to indicate the progress of matching in the graph. The second modification controls the application of LHS graphs, where those specified a...
Thermo-mechanical characterization of ceramic pebbles for breeding blanket
Lo Frano, Rosa, E-mail: rosa.lofrano@ing.unipi.it; Aquaro, Donato; Scaletti, Luca
2016-11-01
Highlights: • Experimental activities to characterize the Li{sub 4}SiO{sub 4}. • Compression tests of pebbles. • Experimental evaluation of thermal conductivity of pebbles bed at different temperatures. • Experimental test with/without compression load. - Abstract: An open issue for fusion power reactor is to design a suitable breeding blanket capable to produce the necessary quantity of the tritium and to transfer the energy of the nuclear fusion reaction to the coolant. The envisaged solution called Helium-Cooled Pebble Bed (HCPB) breeding blanket foresees the use of lithium orthosilicate (Li{sub 4}SiO{sub 4}) or lithium metatitanate (Li{sub 2}TiO{sub 3}) pebble beds. The thermal mechanical properties of the candidate pebble bed materials are presently extensively investigated because they are critical for the feasibility and performances of the numerous conceptual designs which use a solid breeder. This study is aimed at the investigation of mechanical properties of the lithium orthosilicate and at the characterization of the main chemical, physical and thermo-mechanical properties taking into account the production technology. In doing that at the Department of Civil and Industrial Engineering (DICI) of the University of Pisa adequate experiments were carried out. The obtained results may contribute to characterize the material of the pebbles and to optimize the design of the envisaged fusion breeding blankets.
Strategic Port Graph Rewriting: An Interactive Modelling and Analysis Framework
Maribel Fernández
2014-07-01
Full Text Available We present strategic portgraph rewriting as a basis for the implementation of visual modelling and analysis tools. The goal is to facilitate the specification, analysis and simulation of complex systems, using port graphs. A system is represented by an initial graph and a collection of graph rewriting rules, together with a user-defined strategy to control the application of rules. The strategy language includes constructs to deal with graph traversal and management of rewriting positions in the graph. We give a small-step operational semantics for the language, and describe its implementation in the graph transformation and visualisation tool PORGY.
Engineering Object-Oriented Semantics Using Graph Transformations
Kastenberg, H.; Kleppe, A.G.; Rensink, Arend
In this paper we describe the application of the theory of graph transformations to the practise of language design. We have defined the semantics of a small but realistic object-oriented language (called TAAL) by mapping the language constructs to graphs and their operational semantics to graph
Bapat, Ravindra B
2014-01-01
This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reo...
Adaptive Graph Convolutional Neural Networks
Li, Ruoyu; Wang, Sheng; Zhu, Feiyun; Huang, Junzhou
2018-01-01
Graph Convolutional Neural Networks (Graph CNNs) are generalizations of classical CNNs to handle graph data such as molecular data, point could and social networks. Current filters in graph CNNs are built for fixed and shared graph structure. However, for most real data, the graph structures varies in both size and connectivity. The paper proposes a generalized and flexible graph CNN taking data of arbitrary graph structure as input. In that way a task-driven adaptive graph is learned for eac...
b-tree facets for the simple graph partitioning polytope
Sørensen, Michael Malmros
2004-01-01
The simple graph partitioning problem is to partition an edge-weighted graph into mutually disjoint subgraphs, each consisting of no more than b nodes, such that the sum of the weights of all edges in the subgraphs is maximal. In this paper we introduce a large class of facet defining inequalities...... for the simple graph partitioning polytopes P_n(b), b >= 3, associated with the complete graph on n nodes. These inequalities are induced by a graph configuration which is built upon trees of cardinality b. We provide a closed-form theorem that states all necessary and sufficient conditions for the facet...... defining property of the inequalities. Udgivelsesdato: JUN...
Particle flow of ceramic breeder pebble beds in bi-axial compression experiments
Hermsmeyer, S.; Reimann, J.
2002-01-01
Pebble beds of ceramic material are investigated within the framework of developing solid breeder blankets for future fusion power plants. A thermo-mechanical characterisation of such pebble beds is mandatory for understanding the behaviour of pebble beds, and thus the overall blanket, under fusion environment conditions. The mechanical behaviour of pebble beds is typically explored with uni-axial, bi-axial and tri-axial compression experiments. The latter two types of experiment are particularly revealing since they contain explicitly, beyond a compression behaviour of the bed, information on the conditions for pebble flow, i.e. macroscopic relocation, in the pebble bed. (orig.)
C. Dalfo
2015-10-01
Full Text Available We study a family of graphs related to the $n$-cube. The middle cube graph of parameter k is the subgraph of $Q_{2k-1}$ induced by the set of vertices whose binary representation has either $k-1$ or $k$ number of ones. The middle cube graphs can be obtained from the well-known odd graphs by doubling their vertex set. Here we study some of the properties of the middle cube graphs in the light of the theory of distance-regular graphs. In particular, we completely determine their spectra (eigenvalues and their multiplicities, and associated eigenvectors.
Xu, Kexiang; Trinajstić, Nenad
2015-01-01
This is the first book to focus on the topological index, the Harary index, of a graph, including its mathematical properties, chemical applications and some related and attractive open problems. This book is dedicated to Professor Frank Harary (1921—2005), the grandmaster of graph theory and its applications. It has be written by experts in the field of graph theory and its applications. For a connected graph G, as an important distance-based topological index, the Harary index H(G) is defined as the sum of the reciprocals of the distance between any two unordered vertices of the graph G. In this book, the authors report on the newest results on the Harary index of a graph. These results mainly concern external graphs with respect to the Harary index; the relations to other topological indices; its properties and applications to pure graph theory and chemical graph theory; and two significant variants, i.e., additively and multiplicatively weighted Harary indices. In the last chapter, we present a number o...
Neutronic modeling of pebble bed reactors in APOLLO2
Grimod, M.
2010-01-01
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 developed method has been verified using reference Monte Carlo simulations of a simplified PBMR- 400 model. The pebbles in this model are individually positioned and have different randomly assigned burnup values. The APOLLO2 developed method matches the reference core k eff within ± 100 pcm, with relative differences on the production shape factors within ± 4%, and maximum discrepancy of 3% at the hotspot. Moreover, the first criticality experiment of the HTR-10 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 16890, only 77 pebbles less. A method to calculate the equilibrium reactor state was also developed and applied to analyze the simplified PBMR-400 model loaded with different fuel types (UO 2 , Pu, Pu + MA). 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. Thanks to a 'compensation of error
Pebble red modular reactor - South Africa
Fox, M.; Mulder, E.
1996-01-01
In 1995 the South African Electricity Utility, ESKOM, was convinced of the economical advantages of high temperature gas-cooled reactors as viable supply side option. Subsequently planning of a techno/economic study for the year 1996 was initiated. Continuation to the construction phase of a prototype plant will depend entirely on the outcome of this study. A reactor plant of pebble bed design coupled with a direct helium cycle is perceived. The electrical output is limited to about 100 MW for reasons of safety, economics and flexibility. Design of the reactor will be based on internationally proven, available technology. An extended research and development program is not anticipated. New licensing rules and regulations will be required. Safety classification of components will be based on the merit of HTGR technology rather than attempting to adhere to traditional LWR rules. A medium term time schedule for the design and construction of a prototype plant, commissioning and performance testing is proposed during the years 2002 and 2003. Pending the performance outcome of this plant and the current power demand, series production of 100 MWe units is foreseen. (author)
A study for fuel reloading strategy in pebble bed core
Kim, Hong Chul
2012-02-01
A fuel reloading analysis system for pebble bed reactor was developed by using a Monte Carlo code. The kinematic model was modified to improve the accuracy of the pebble velocity profile and to develop the model so that the diffusion coefficient is not changed by the geometry of the core. In addition, the point kernel method was employed to solve an equation derived in this study. Then, the analysis system for the pebble bed reactor was developed to accommodate the double heterogeneity, pebble velocity, and pebble refueling features using the MCNPX Monte Carlo code. The batch-tracking method was employed to simulate the movement of the pebbles and an automation system was written in the C programming language to implement it. The proposed analysis system can be utilized to verify new core analysis codes, deep-burn studies, various sensitivity studies, and other analysis tools available for the application of new fuel reloading strategies. It is noted that the proposed algorithm for the optimum fuel reloading pattern differs from other optimization methods using sensitivity analysis. In this algorithm, the reloading strategy, including the loading of fresh fuel and the reloading positions of the fresh and reloaded fuels, is determined by the interrelations of the criticality, the nuclear material inventories in the extracted fuel, and the power density. The devised algorithm was applied to the PBMR and NHDD-PBR200. The results show that the proposed algorithm can apply to satisfy the nuclear characteristics such as the criticality or power density since the pebble bed core has the characteristics that the fuels are reloaded every day
Localization of the hot spots in a pebble bed reactor
Chen, Leisheng; Lee, Wooram; Lee, Jaeyoung
2016-01-01
The pebble bed reactor (PBR) is a candidate reactor type for the very high temperature reactor (VHTR), which is one of the Generation-IV reactor types. The HTGR design concept exhibits excellent safety features due to the low power density and the large amount of graphite present in the core which gives a large thermal inertia in an accident such as loss of coolant. The conclusions are made and may contribute to a better design of a PBR core and a closer inspection of the local hot spots to avoid destruction of pebbles from happening. Thermal field of a PBR core is investigated in this study. Specifically, experiments on measuring the pebbles' surface temperature are performed. It is found that the upper pebble has an overall higher temperature profile than the other pebbles and the stagnation zone under does not increase its surface's temperature. In addition, the temperature profile of the side pebble shows a concave form and it keeps decreasing from the contact point to the vertex in the lower pebble. Lastly, the maximum temperature difference among these points is 5.83 deg. C. These findings above are validated by CFX simulations under two different turbulence models (k-e, SST) and two contact areas (diameter of 6mm and 3.5mm). By contrasting the temperature variation trends of all simulation cases, it is concluded that SST turbulence model with 20% intensity shows a better agreement with the experiment result, nevertheless, slightly deviation is also found in terms of total temperature difference and the peak appears in position 17-19 in experiments
Localization of the hot spots in a pebble bed reactor
Chen, Leisheng; Lee, Wooram; Lee, Jaeyoung [Handong Global University, Pohang (Korea, Republic of)
2016-05-15
The pebble bed reactor (PBR) is a candidate reactor type for the very high temperature reactor (VHTR), which is one of the Generation-IV reactor types. The HTGR design concept exhibits excellent safety features due to the low power density and the large amount of graphite present in the core which gives a large thermal inertia in an accident such as loss of coolant. The conclusions are made and may contribute to a better design of a PBR core and a closer inspection of the local hot spots to avoid destruction of pebbles from happening. Thermal field of a PBR core is investigated in this study. Specifically, experiments on measuring the pebbles' surface temperature are performed. It is found that the upper pebble has an overall higher temperature profile than the other pebbles and the stagnation zone under does not increase its surface's temperature. In addition, the temperature profile of the side pebble shows a concave form and it keeps decreasing from the contact point to the vertex in the lower pebble. Lastly, the maximum temperature difference among these points is 5.83 deg. C. These findings above are validated by CFX simulations under two different turbulence models (k-e, SST) and two contact areas (diameter of 6mm and 3.5mm). By contrasting the temperature variation trends of all simulation cases, it is concluded that SST turbulence model with 20% intensity shows a better agreement with the experiment result, nevertheless, slightly deviation is also found in terms of total temperature difference and the peak appears in position 17-19 in experiments.
Manufacturing Technology of Ceramic Pebbles for Breeding Blanket
Rosa Lo Frano
2018-05-01
Full Text Available An open issue for the fusion power reactor is the choice of breeding blanket material. The possible use of Helium-Cooled Pebble Breeder ceramic material in the form of pebble beds is of great interest worldwide as demonstrated by the numerous studies and research on this subject. Lithium orthosilicate (Li4SiO4 is a promising breeding material investigated in this present study because the neutron capture of Li-6 allows the production of tritium, 6Li (n, t 4He. Furthermore, lithium orthosilicate has the advantages of low activation characteristics, low thermal expansion coefficient, high thermal conductivity, high density and stability. Even if they are far from the industrial standard, a variety of industrial processes have been proposed for making orthosilicate pebbles with diameters of 0.1–1 mm. However, some manufacturing problems have been observed, such as in the chemical stability (agglomeration phenomena. The aim of this study is to provide a new methodology for the production of pebbles based on the drip casting method, which was jointly developed by the DICI-University of Pisa and Industrie Bitossi. Using this new (and alternative manufacturing technology, in the field of fusion reactors, appropriately sized ceramic pebbles could be produced for use as tritium breeders.
Soetevent, A.R.
2010-01-01
This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. I propose an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. One feature of graph models of price competition is that spatial
Graphing Inequalities, Connecting Meaning
Switzer, J. Matt
2014-01-01
Students often have difficulty with graphing inequalities (see Filloy, Rojano, and Rubio 2002; Drijvers 2002), and J. Matt Switzer's students were no exception. Although students can produce graphs for simple inequalities, they often struggle when the format of the inequality is unfamiliar. Even when producing a correct graph of an…
Amine Labriji
2017-07-01
Full Text Available The topic of identifying the similarity of graphs was considered as highly recommended research field in the Web semantic, artificial intelligence, the shape recognition and information research. One of the fundamental problems of graph databases is finding similar graphs to a graph query. Existing approaches dealing with this problem are usually based on the nodes and arcs of the two graphs, regardless of parental semantic links. For instance, a common connection is not identified as being part of the similarity of two graphs in cases like two graphs without common concepts, the measure of similarity based on the union of two graphs, or the one based on the notion of maximum common sub-graph (SCM, or the distance of edition of graphs. This leads to an inadequate situation in the context of information research. To overcome this problem, we suggest a new measure of similarity between graphs, based on the similarity measure of Wu and Palmer. We have shown that this new measure satisfies the properties of a measure of similarities and we applied this new measure on examples. The results show that our measure provides a run time with a gain of time compared to existing approaches. In addition, we compared the relevance of the similarity values obtained, it appears that this new graphs measure is advantageous and offers a contribution to solving the problem mentioned above.
van Dam, Edwin R.; Koolen, Jack H.; Tanaka, Hajime
2016-01-01
This is a survey of distance-regular graphs. We present an introduction to distance-regular graphs for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of distance-regular graphs since the monograph 'BCN'[Brouwer, A.E., Cohen, A.M., Neumaier,
Fuzzy Graph Language Recognizability
Kalampakas , Antonios; Spartalis , Stefanos; Iliadis , Lazaros
2012-01-01
Part 5: Fuzzy Logic; International audience; Fuzzy graph language recognizability is introduced along the lines of the established theory of syntactic graph language recognizability by virtue of the algebraic structure of magmoids. The main closure properties of the corresponding class are investigated and several interesting examples of fuzzy graph languages are examined.
Brouwer, A.E.; Haemers, W.H.
2012-01-01
This book gives an elementary treatment of the basic material about graph spectra, both for ordinary, and Laplace and Seidel spectra. The text progresses systematically, by covering standard topics before presenting some new material on trees, strongly regular graphs, two-graphs, association
Letters initiating Clean Water Act 404(c) review of mining at Pebble deposit
Correspondence between EPA and the Pebble Limited Partnership and the State of Alaska initiating review under section 404(c) of the Clean Water Act of potential adverse environmental effects associated with mining the Pebble deposit in southwest Alaska.
N. Gierse
2015-03-01
The key results of this study are that very high heat fluxes are accessible in the operation space of ferromagnetic pebbles, that ferromagnetic pebbles are compatible with tokamak operation and current divertor designs, that the heat removal capability of ferromagnetic pebbles increases as λq decreases and, finally, that for fusion relevant values of q∥ pebble diameters below 100 μm are required.
Tritium adsorption/release behaviour of advanced EU breeder pebbles
Kolb, Matthias H.H., E-mail: matthias.kolb@kit.edu; Rolli, Rolf; Knitter, Regina
2017-06-15
The tritium loading of current grades of advanced ceramic breeder pebbles with three different lithium orthosilicate (LOS)/lithium metatitanate (LMT) compositions (20–30 mol% LMT in LOS) and pebbles of EU reference material, was performed in a consistent way. The temperature dependent release of the introduced tritium was subsequently investigated by temperature programmed desorption (TPD) experiments to gain insight into the desorption characteristics. The obtained TPD data was decomposed into individual release mechanisms according to well-established desorption kinetics. The analysis showed that the pebble composition of the tested samples does not severely change the release behaviour. Yet, an increased content of lithium metatitanate leads to additional desorption peaks at medium temperatures. The majority of tritium is released by high temperature release mechanisms of chemisorbed tritium, while the release of physisorbed tritium is marginal in comparison. The results allow valuable projections for the tritium release behaviour in a fusion blanket.
Tritium adsorption/release behaviour of advanced EU breeder pebbles
Kolb, Matthias H. H.; Rolli, Rolf; Knitter, Regina
2017-06-01
The tritium loading of current grades of advanced ceramic breeder pebbles with three different lithium orthosilicate (LOS)/lithium metatitanate (LMT) compositions (20-30 mol% LMT in LOS) and pebbles of EU reference material, was performed in a consistent way. The temperature dependent release of the introduced tritium was subsequently investigated by temperature programmed desorption (TPD) experiments to gain insight into the desorption characteristics. The obtained TPD data was decomposed into individual release mechanisms according to well-established desorption kinetics. The analysis showed that the pebble composition of the tested samples does not severely change the release behaviour. Yet, an increased content of lithium metatitanate leads to additional desorption peaks at medium temperatures. The majority of tritium is released by high temperature release mechanisms of chemisorbed tritium, while the release of physisorbed tritium is marginal in comparison. The results allow valuable projections for the tritium release behaviour in a fusion blanket.
Hell, Pavol
2004-01-01
This is a book about graph homomorphisms. Graph theory is now an established discipline but the study of graph homomorphisms has only recently begun to gain wide acceptance and interest. The subject gives a useful perspective in areas such as graph reconstruction, products, fractional and circular colourings, and has applications in complexity theory, artificial intelligence, telecommunication, and, most recently, statistical physics.Based on the authors' lecture notes for graduate courses, this book can be used as a textbook for a second course in graph theory at 4th year or master's level an
On revealing graph cycles via boundary measurements
Belishev, M I; Wada, N
2009-01-01
This paper deals with boundary value inverse problems on a metric graph, the structure of the graph being assumed unknown. The question under consideration is how to detect from the dynamical and/or spectral inverse data whether the graph contains cycles (is not a tree). For any graph Ω, the dynamical as well as spectral boundary inverse data determine the so-called wave diameter d w : H -1 (Ω) → R defined on functionals supported in the graph. The known fact is that if Ω is a tree then d w ≥ 0 holds and, in this case, the inverse data determine Ω up to isometry. A graph Ω is said to be coordinate if the functions {dist Ω (., γ)} γin∂Ω constitute a coordinate system on Ω. For such graphs, we propose a procedure, which reveals the presence/absence of cycles. The hypothesis is that Ω contains cycles if and only if d w takes negative values. We do not justify this hypothesis in the general case but reduce it to a certain special class of graphs (suns)
Introduction to quantum graphs
Berkolaiko, Gregory
2012-01-01
A "quantum graph" is a graph considered as a one-dimensional complex and equipped with a differential operator ("Hamiltonian"). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., "meso-" or "nano-scale") system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on qu...
A Note on the PageRank of Undirected Graphs
Grolmusz, Vince
2012-01-01
The PageRank is a widely used scoring function of networks in general and of the World Wide Web graph in particular. The PageRank is defined for directed graphs, but in some special cases applications for undirected graphs occur. In the literature it is widely noted that the PageRank for undirected graphs are proportional to the degrees of the vertices of the graph. We prove that statement for a particular personalization vector in the definition of the PageRank, and we also show that in gene...
Graphing trillions of triangles.
Burkhardt, Paul
2017-07-01
The increasing size of Big Data is often heralded but how data are transformed and represented is also profoundly important to knowledge discovery, and this is exemplified in Big Graph analytics. Much attention has been placed on the scale of the input graph but the product of a graph algorithm can be many times larger than the input. This is true for many graph problems, such as listing all triangles in a graph. Enabling scalable graph exploration for Big Graphs requires new approaches to algorithms, architectures, and visual analytics. A brief tutorial is given to aid the argument for thoughtful representation of data in the context of graph analysis. Then a new algebraic method to reduce the arithmetic operations in counting and listing triangles in graphs is introduced. Additionally, a scalable triangle listing algorithm in the MapReduce model will be presented followed by a description of the experiments with that algorithm that led to the current largest and fastest triangle listing benchmarks to date. Finally, a method for identifying triangles in new visual graph exploration technologies is proposed.
Gan, Yixiang; Kamlah, Marc
2008-01-01
In this investigation, a thermo-mechanical model of pebble beds is adopted and developed based on experiments by Dr. Reimann at Forschungszentrum Karlsruhe (FZK). The framework of the present material model is composed of a non-linear elastic law, the Drucker-Prager-Cap theory, and a modified creep law. Furthermore, the volumetric inelastic strain dependent thermal conductivity of beryllium pebble beds is taken into account and full thermo-mechanical coupling is considered. Investigation showed that the Drucker-Prager-Cap model implemented in ABAQUS can not fulfill the requirements of both the prediction of large creep strains and the hardening behaviour caused by creep, which are of importance with respect to the application of pebble beds in fusion blankets. Therefore, UMAT (user defined material's mechanical behaviour) and UMATHT (user defined material's thermal behaviour) routines are used to re-implement the present thermo-mechanical model in ABAQUS. An elastic predictor radial return mapping algorithm is used to solve the non-associated plasticity iteratively, and a proper tangent stiffness matrix is obtained for cost-efficiency in the calculation. An explicit creep mechanism is adopted for the prediction of time-dependent behaviour in order to represent large creep strains in high temperature. Finally, the thermo-mechanical interactions are implemented in a UMATHT routine for the coupled analysis. The oedometric compression tests and creep tests of pebble beds at different temperatures are simulated with the help of the present UMAT and UMATHT routines, and the comparison between the simulation and the experiments is made. (authors)
Inferring ontology graph structures using OWL reasoning
Rodriguez-Garcia, Miguel Angel
2018-01-05
Ontologies are representations of a conceptualization of a domain. Traditionally, ontologies in biology were represented as directed acyclic graphs (DAG) which represent the backbone taxonomy and additional relations between classes. These graphs are widely exploited for data analysis in the form of ontology enrichment or computation of semantic similarity. More recently, ontologies are developed in a formal language such as the Web Ontology Language (OWL) and consist of a set of axioms through which classes are defined or constrained. While the taxonomy of an ontology can be inferred directly from the axioms of an ontology as one of the standard OWL reasoning tasks, creating general graph structures from OWL ontologies that exploit the ontologies\\' semantic content remains a challenge.We developed a method to transform ontologies into graphs using an automated reasoner while taking into account all relations between classes. Searching for (existential) patterns in the deductive closure of ontologies, we can identify relations between classes that are implied but not asserted and generate graph structures that encode for a large part of the ontologies\\' semantic content. We demonstrate the advantages of our method by applying it to inference of protein-protein interactions through semantic similarity over the Gene Ontology and demonstrate that performance is increased when graph structures are inferred using deductive inference according to our method. Our software and experiment results are available at http://github.com/bio-ontology-research-group/Onto2Graph .Onto2Graph is a method to generate graph structures from OWL ontologies using automated reasoning. The resulting graphs can be used for improved ontology visualization and ontology-based data analysis.
Inferring ontology graph structures using OWL reasoning.
Rodríguez-García, Miguel Ángel; Hoehndorf, Robert
2018-01-05
Ontologies are representations of a conceptualization of a domain. Traditionally, ontologies in biology were represented as directed acyclic graphs (DAG) which represent the backbone taxonomy and additional relations between classes. These graphs are widely exploited for data analysis in the form of ontology enrichment or computation of semantic similarity. More recently, ontologies are developed in a formal language such as the Web Ontology Language (OWL) and consist of a set of axioms through which classes are defined or constrained. While the taxonomy of an ontology can be inferred directly from the axioms of an ontology as one of the standard OWL reasoning tasks, creating general graph structures from OWL ontologies that exploit the ontologies' semantic content remains a challenge. We developed a method to transform ontologies into graphs using an automated reasoner while taking into account all relations between classes. Searching for (existential) patterns in the deductive closure of ontologies, we can identify relations between classes that are implied but not asserted and generate graph structures that encode for a large part of the ontologies' semantic content. We demonstrate the advantages of our method by applying it to inference of protein-protein interactions through semantic similarity over the Gene Ontology and demonstrate that performance is increased when graph structures are inferred using deductive inference according to our method. Our software and experiment results are available at http://github.com/bio-ontology-research-group/Onto2Graph . Onto2Graph is a method to generate graph structures from OWL ontologies using automated reasoning. The resulting graphs can be used for improved ontology visualization and ontology-based data analysis.
Parametric study for high conversion pebble bed reactor
Teuchert, E.; Ruetten, H. J.
1975-06-15
Tables are presented of fuel cycle costs, conversion ratios and accompanying variations in fuel element designs for a 3,00 MWth high conversion pebble bed reactor with initial high enriched uranium/thorium cycle and subsequent recycling of U-233, Pu-239 and Pu-241.
Uraniferous quartz-pebble conglomerates in South Africa
von Backstroem, J.W.
1981-01-01
The purpose of this paper is to give a short background statement summarizing data on the Dominion Reef Group, the Witwatersrand Supergroup, and the Ventersdorp Contact Reef, with particular reference to the close relationship of gold and uranium with sedimentary features as well as the mineralization, conditions of deposition, and the nature of the quartz-pebble conglomerates
Researchers solve big mysteries of pebble bed reactor
Shams, Afaque; Roelofs, Ferry; Komen, E.M.J. [Nuclear Research and Consultancy Group (NRG), Petten (Netherlands); Baglietto, Emilio [Massachusetts Institute of Technology, Cambridge, MA (United States). Dept. of Nuclear Science and Engineering; Sgro, Titus [CD-adapco, London (United Kingdom). Technical Marketing
2014-03-15
The PBR is one type of High Temperature Reactors, which allows high temperature work while preventing the fuel from melting (bringing huge safety margins to the reactor) and high electricity efficiency. The design is also highly scalable; a plant could be designed to be as large or small as needed, and can even be made mobile, allowing it to be used onboard a ship. In a PBR, small particles of nuclear fuel, embedded in a moderating graphite pebble, are dropped into the reactor as needed. At the bottom, the pebbles can be removed simply by opening a small hatch and letting gravity pull them down. To cool the reactor and create electricity, helium gas is pumped through the reactor to pull heat out which is then run through generators. One of the most difficult problems to deal with has been the possible appearance of local temperature hotspots within the pebble bed heating to the point of melting the graphite moderators surrounding the fuel. Obviously, constructing a reactor and experimenting to investigate this possibility is out of the question. Instead, nuclear engineers have been attempting to simulate a PBR with various CFD codes. The thermo-dynamic analysis to simulate realistic conditions in a pebble bed are described and the results are shown. (orig.)
TEM study of impurity segregations in beryllium pebbles
Klimenkov, M., E-mail: michael.klimenkov@kit.edu [Institute for Applied Materials – Applied Materials Physics, Karlsruhe Institute of Technology, Hermann-von-Helmholz-Platz 1, 76344 Eggenstein-Leopoldshafen (Germany); Chakin, V.; Moeslang, A. [Institute for Applied Materials – Applied Materials Physics, Karlsruhe Institute of Technology, Hermann-von-Helmholz-Platz 1, 76344 Eggenstein-Leopoldshafen (Germany); Rolli, R. [Institute for Applied Materials – Materials and Biomechanics, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen (Germany)
2014-12-15
Beryllium is planned to be used as a neutron multiplier in the Helium-cooled Pebble Bed European concept of a breeding blanket of demonstration power reactor DEMO. In order to evaluate the irradiation performance, individual pebbles and constrained pebble beds were neutron-irradiated at temperatures typical of fusion blankets. Beryllium pebbles 1 mm in diameter produced by the rotating electrode method were subjected to a TEM study before and after irradiation at High Flux Reactor, Petten, Netherlands at 861 K. The grain size varied in a wide range from sub-micron size up to several tens of micrometers, which indicated formation bimodal grain size distribution. Based on the application of combined electron energy loss spectroscopy and energy dispersive X-ray spectroscopy methods, we suggest that impurity precipitates play an important role in controlling the mechanical properties of beryllium. The impurity elements were present in beryllium at a sub-percent concentration form beryllide particles of a complex (Fe/Al/Mn/Cr)B composition. These particles are often ordered along dislocations lines, forming several micron-long chains. It can be suggested that fracture surfaces often extended along these chains in irradiated material.
Transmutation of plutonium in pebble bed type high temperature reactors
Bende, E.E.
1997-01-01
The pebble bed type High Temperature Reactor (HTR) has been studied as a uranium-free burner of reactor grade plutonium. In a parametric study, the plutonium loading per pebble as well as the type and size of the coated particles (CPs) have been varied to determine the plutonium consumption, the final plutonium burnup, the k ∞ and the temperature coefficients as a function of burnup. The plutonium loading per pebble is bounded between 1 and 3 gr Pu per pebble. The upper limit is imposed by the maximal allowable fast fluence for the CPs. A higher plutonium loading requires a longer irradiation time to reach a desired burnup, so that the CPs are exposed to a higher fast fluence. The lower limit is determined by the temperature coefficients, which become less negative with increasing moderator-actinide ratio. A burnup of about 600 MWd/kgHM can be reached. With the HTR's high efficiency of 40%, a plutonium supply of 1520 kg/GW e a is achieved. The discharges of plutonium and minor actinides are then 450 and 110 kg/GW e a, respectively. (author)
Performance Evaluation of a Pebble Bed Solar Crop Dryer ...
Nigerian Journal of Technology ... The solar crop dryer consists of an imbedded pebble bed solar heat storage unit/solar collector ... The crop-drying chamber is made of drying trays of wire gauze while the roof is made of transparent glazing.
Fabrication of Li2TiO3 pebbles by a freeze drying process
Lee, Sang-Jin; Park, Yi-Hyun; Yu, Min-Woo
2013-01-01
Li 2 TiO 3 pebbles were successfully fabricated by using a freeze drying process. The Li 2 TiO 3 slurry was prepared using a commercial powder of particle size 0.5–1.5 μm and the pebble pre-form was prepared by dropping the slurry into liquid nitrogen through a syringe needle. The droplets were rapidly frozen, changing their morphology to spherical pebbles. The frozen pebbles were dried at −10 °C in vacuum. To make crack-free pebbles, some glycerin was employed in the slurry, and long drying time and a low vacuum condition were applied in the freeze drying process. In the process, the solid content in the slurry influenced the spheroidicity of the pebble green body. The dried pebbles were sintered at 1200 °C in an air atmosphere. The sintered pebbles showed almost 40% shrinkage. The sintered pebbles revealed a porous microstructure with a uniform pore distribution and the sintered pebbles were crushed under an average load of 50 N in a compressive strength test. In the present study, a freeze drying process for fabrication of spherical Li 2 TiO 3 pebbles is introduced. The processing parameters, such as solid content in the slurry and the conditions of freeze drying and sintering, are also examined
Chartrand, Gary
1984-01-01
Graph theory is used today in the physical sciences, social sciences, computer science, and other areas. Introductory Graph Theory presents a nontechnical introduction to this exciting field in a clear, lively, and informative style. Author Gary Chartrand covers the important elementary topics of graph theory and its applications. In addition, he presents a large variety of proofs designed to strengthen mathematical techniques and offers challenging opportunities to have fun with mathematics. Ten major topics - profusely illustrated - include: Mathematical Models, Elementary Concepts of Grap
Shixiong Song
2014-01-01
CFD results and empirical correlations’ predictions of pressure drop and local Nusselt numbers. 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.
Adriaan R. Soetevent
2010-01-01
This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. I propose an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. One feature of graph models of price competition is that spatial discontinuities in firm-level demand may occur. I show that the existence result of D'Aspremont et al. (1979) does not extend to simple star graphs. I conjecture that this non-existence result holds...
Pim Heijnen; Adriaan Soetevent
2014-01-01
This paper extends Hotelling's model of price competition with quadratic transportation costs from a line to graphs. We derive an algorithm to calculate firm-level demand for any given graph, conditional on prices and firm locations. These graph models of price competition may lead to spatial discontinuities in firm-level demand. We show that the existence result of D'Aspremont et al. (1979) does not extend to simple star graphs and conjecture that this non-existence result holds more general...
Aleks Kissinger
2014-03-01
Full Text Available String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. Dixon, Duncan and Kissinger introduced string graphs, which are a combinatoric representations of string diagrams, amenable to automated reasoning about diagrammatic theories via graph rewrite systems. In this extended abstract, we show how the power of such rewrite systems can be greatly extended by introducing pattern graphs, which provide a means of expressing infinite families of rewrite rules where certain marked subgraphs, called !-boxes ("bang boxes", on both sides of a rule can be copied any number of times or removed. After reviewing the string graph formalism, we show how string graphs can be extended to pattern graphs and how pattern graphs and pattern rewrite rules can be instantiated to concrete string graphs and rewrite rules. We then provide examples demonstrating the expressive power of pattern graphs and how they can be applied to study interacting algebraic structures that are central to categorical quantum mechanics.
Gelfand, I M; Shnol, E E
1969-01-01
The second in a series of systematic studies by a celebrated mathematician I. M. Gelfand and colleagues, this volume presents students with a well-illustrated sequence of problems and exercises designed to illuminate the properties of functions and graphs. Since readers do not have the benefit of a blackboard on which a teacher constructs a graph, the authors abandoned the customary use of diagrams in which only the final form of the graph appears; instead, the book's margins feature step-by-step diagrams for the complete construction of each graph. The first part of the book employs simple fu
Creating more effective graphs
Robbins, Naomi B
2012-01-01
A succinct and highly readable guide to creating effective graphs The right graph can be a powerful tool for communicating information, improving a presentation, or conveying your point in print. If your professional endeavors call for you to present data graphically, here's a book that can help you do it more effectively. Creating More Effective Graphs gives you the basic knowledge and techniques required to choose and create appropriate graphs for a broad range of applications. Using real-world examples everyone can relate to, the author draws on her years of experience in gr
Lothian, Joshua [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Powers, Sarah S. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Sullivan, Blair D. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Baker, Matthew B. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Schrock, Jonathan [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Poole, Stephen W. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2013-10-01
The benchmarking effort within the Extreme Scale Systems Center at Oak Ridge National Laboratory seeks to provide High Performance Computing benchmarks and test suites of interest to the DoD sponsor. The work described in this report is a part of the effort focusing on graph generation. A previously developed benchmark, SystemBurn, allowed the emulation of different application behavior profiles within a single framework. To complement this effort, similar capabilities are desired for graph-centric problems. This report examines existing synthetic graph generator implementations in preparation for further study on the properties of their generated synthetic graphs.
Mansutti, Alessio; Miculan, Marino; Peressotti, Marco
2017-01-01
We introduce loose graph simulations (LGS), a new notion about labelled graphs which subsumes in an intuitive and natural way subgraph isomorphism (SGI), regular language pattern matching (RLPM) and graph simulation (GS). Being a unification of all these notions, LGS allows us to express directly...... also problems which are “mixed” instances of previous ones, and hence which would not fit easily in any of them. After the definition and some examples, we show that the problem of finding loose graph simulations is NP-complete, we provide formal translation of SGI, RLPM, and GS into LGSs, and we give...
Alberto Apostolico
2009-08-01
Full Text Available The Web Graph is a large-scale graph that does not fit in main memory, so that lossless compression methods have been proposed for it. This paper introduces a compression scheme that combines efficient storage with fast retrieval for the information in a node. The scheme exploits the properties of the Web Graph without assuming an ordering of the URLs, so that it may be applied to more general graphs. Tests on some datasets of use achieve space savings of about 10% over existing methods.
Modelling of thermal and mechanical behaviour of pebble beds
Boccaccini, L.V.; Buehler, L.; Hermsmeyer, S.; Wolf, F.
2001-01-01
FZK (Forshungzentrum Karlsruhe) is developing a Helium Cooled Pebble Bed (HCPB) Blanket Concept for fusion power reactors based on the use of ceramic breeder materials and beryllium multiplier in the form 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. (Y.Tanaka)
Experimental and numerical validation of a two-region-designed pebble bed reactor with dynamic core
Jiang, S.Y.; Yang, X.T.; Tang, Z.W.; Wang, W.J.; Tu, J.Y.; Liu, Z.Y.; Li, J.
2012-01-01
Highlights: ► The experimental installation has been built to investigate the pebble flow. ► The feasibility of two-region pebble bed reactor has been verified. ► The pebble flow is more uniform in a taller vessel than that in a lower vessel. ► Larger base cone angle will decrease the scale of the stagnant zone. - Abstract: The pebble flow is the principal issue for the design of the pebble bed reactor. In order to verify the feasibility of a two-region-designed pebble bed reactor, the experimental installation with a taller vessel has been built, which is proportional to the real pebble bed reactor. With the aid of the experimental installation, the stable establishment and maintenance of the two-region arrangement has been verified, at the same time, the applicability of the DEM program has been also validated. Research results show: (1) The pebble's bouncing on the free surface is an important factor for the mixing of the different colored pebbles. (2) Through the guide plates installed in the top of the pebble packing, the size of the mixing zone can be reduced from 6–7 times to 3–4 times the pebble diameter. (3) The relationship between the width of the central region and the ratio of loading pebbles is approximately linear in the taller vessel. (4) The heighten part of the pebble packing can improve the uniformity of the flowing in the lower. (5) To increase the base cone angle can decrease the scale of the stagnant zone. All of these conclusions are meaningful to the design of the real pebble reactor.
3-biplacement of bipartite graphs
Lech Adamus
2008-01-01
Full Text Available Let \\(G=(L,R;E\\ be a bipartite graph with color classes \\(L\\ and \\(R\\ and edge set \\(E\\. A set of two bijections \\(\\{\\varphi_1 , \\varphi_2\\}\\, \\(\\varphi_1 , \\varphi_2 :L \\cup R \\to L \\cup R\\, is said to be a \\(3\\-biplacement of \\(G\\ if \\(\\varphi_1(L= \\varphi_2(L = L\\ and \\(E \\cap \\varphi_1^*(E=\\emptyset\\, \\(E \\cap \\varphi_2^*(E=\\emptyset\\, \\(\\varphi_1^*(E \\cap \\varphi_2^*(E=\\emptyset\\, where \\(\\varphi_1^*\\, \\(\\varphi_2^*\\ are the maps defined on \\(E\\, induced by \\(\\varphi_1\\, \\(\\varphi_2\\, respectively. We prove that if \\(|L| = p\\, \\(|R| = q\\, \\(3 \\leq p \\leq q\\, then every graph \\(G=(L,R;E\\ of size at most \\(p\\ has a \\(3\\-biplacement.
Topological properties of the limited penetrable horizontal visibility graph family
Wang, Minggang; Vilela, André L. M.; Du, Ruijin; Zhao, Longfeng; Dong, Gaogao; Tian, Lixin; Stanley, H. Eugene
2018-05-01
The limited penetrable horizontal visibility graph algorithm was recently introduced to map time series in complex networks. In this work, we extend this algorithm to create a directed-limited penetrable horizontal visibility graph and an image-limited penetrable horizontal visibility graph. We define two algorithms and provide theoretical results on the topological properties of these graphs associated with different types of real-value series. We perform several numerical simulations to check the accuracy of our theoretical results. Finally, we present an application of the directed-limited penetrable horizontal visibility graph to measure real-value time series irreversibility and an application of the image-limited penetrable horizontal visibility graph that discriminates noise from chaos. We also propose a method to measure the systematic risk using the image-limited penetrable horizontal visibility graph, and the empirical results show the effectiveness of our proposed algorithms.
On the classification of plane graphs representing structurally stable rational Newton flows
Jongen, H.Th.; Jonker, P.; Twilt, F.
1991-01-01
We study certain plane graphs, called Newton graphs, representing a special class of dynamical systems which are closely related to Newton's iteration method for finding zeros of (rational) functions defined on the complex plane. These Newton graphs are defined in terms of nonvanishing angles
Quantum Graphs And Their Resonance Properties
Lipovsky, J.
2016-01-01
In the current review, we study the model of quantum graphs. We focus mainly on the resonance properties of quantum graphs. We define resolvent and scattering resonances and show their equivalence. We present various results on the asymptotics of the number of resolvent resonances in both non-magnetic and magnetic quantum graphs and find bounds on the coefficient by the leading term of the asymptotics. We explain methods how to find the spectral and resonance condition. Most of the notions and theorems are illustrated in examples. We show how to find resonances numerically and, in a simple example, we find trajectories of resonances in the complex plane. We discuss Fermi’s golden rule for quantum graphs and distribution of the mean intensity for the topological resonances. (author)
A graph rewriting programming language for graph drawing
Rodgers, Peter
1998-01-01
This paper describes Grrr, a prototype visual graph drawing tool. Previously there were no visual languages for programming graph drawing algorithms despite the inherently visual nature of the process. The languages which gave a diagrammatic view of graphs were not computationally complete and so could not be used to implement complex graph drawing algorithms. Hence current graph drawing tools are all text based. Recent developments in graph rewriting systems have produced computationally com...
de Mol, M.J.; Rensink, Arend; Hunt, James J.
This paper introduces an approach for adding graph transformation-based functionality to existing JAVA programs. The approach relies on a set of annotations to identify the intended graph structure, as well as on user methods to manipulate that structure, within the user’s own JAVA class
Cohen, A.M.; Beineke, L.W.; Wilson, R.J.; Cameron, P.J.
2004-01-01
In this chapter we investigate the classification of distance-transitive graphs: these are graphs whose automorphism groups are transitive on each of the sets of pairs of vertices at distance i, for i = 0, 1,.... We provide an introduction into the field. By use of the classification of finite
Joyner, W David
2017-01-01
This textbook acts as a pathway to higher mathematics by seeking and illuminating the connections between graph theory and diverse fields of mathematics, such as calculus on manifolds, group theory, algebraic curves, Fourier analysis, cryptography and other areas of combinatorics. An overview of graph theory definitions and polynomial invariants for graphs prepares the reader for the subsequent dive into the applications of graph theory. To pique the reader’s interest in areas of possible exploration, recent results in mathematics appear throughout the book, accompanied with examples of related graphs, how they arise, and what their valuable uses are. The consequences of graph theory covered by the authors are complicated and far-reaching, so topics are always exhibited in a user-friendly manner with copious graphs, exercises, and Sage code for the computation of equations. Samples of the book’s source code can be found at github.com/springer-math/adventures-in-graph-theory. The text is geared towards ad...
Perepelitsa, VA; Sergienko, [No Value; Kochkarov, AM
1999-01-01
Definitions of prefractal and fractal graphs are introduced, and they are used to formulate mathematical models in different fields of knowledge. The topicality of fractal-graph recognition from the point of view, of fundamental improvement in the efficiency of the solution of algorithmic problems
Husfeldt, Thore
2015-01-01
This chapter presents an introduction to graph colouring algorithms. The focus is on vertex-colouring algorithms that work for general classes of graphs with worst-case performance guarantees in a sequential model of computation. The presentation aims to demonstrate the breadth of available...
Packing Degenerate Graphs Greedily
Allen, P.; Böttcher, J.; Hladký, J.; Piguet, Diana
2017-01-01
Roč. 61, August (2017), s. 45-51 ISSN 1571-0653 R&D Projects: GA ČR GJ16-07822Y Institutional support: RVO:67985807 Keywords : tree packing conjecture * graph packing * graph processes Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics
GRAMI: Frequent subgraph and pattern mining in a single large graph
Elseidy, M.; Abdelhamid, Ehab; Skiadopoulos, S.; Kalnis, Panos
2014-01-01
Mining frequent subgraphs is an important operation on graphs; it is defined as finding all subgraphs that appear frequently in a database according to a given frequency threshold. Most existing work assumes a database of many small graphs
Generalized connectivity of graphs
Li, Xueliang
2016-01-01
Noteworthy results, proof techniques, open problems and conjectures in generalized (edge-) connectivity are discussed in this book. Both theoretical and practical analyses for generalized (edge-) connectivity of graphs are provided. Topics covered in this book include: generalized (edge-) connectivity of graph classes, algorithms, computational complexity, sharp bounds, Nordhaus-Gaddum-type results, maximum generalized local connectivity, extremal problems, random graphs, multigraphs, relations with the Steiner tree packing problem and generalizations of connectivity. This book enables graduate students to understand and master a segment of graph theory and combinatorial optimization. Researchers in graph theory, combinatorics, combinatorial optimization, probability, computer science, discrete algorithms, complexity analysis, network design, and the information transferring models will find this book useful in their studies.
Parameterized Verification of Graph Transformation Systems with Whole Neighbourhood Operations
Delzanno, Giorgio; Stückrath, Jan
2014-01-01
We introduce a new class of graph transformation systems in which rewrite rules can be guarded by universally quantified conditions on the neighbourhood of nodes. These conditions are defined via special graph patterns which may be transformed by the rule as well. For the new class for graph rewrite rules, we provide a symbolic procedure working on minimal representations of upward closed sets of configurations. We prove correctness and effectiveness of the procedure by a categorical presenta...
Fey, David L.; Granitto, Matthew; Giles, Stuart A.; Smith, Steven M.; Eppinger, Robert G.; Kelley, Karen D.
2008-01-01
relatively subdued topographic relief with an elevation of around 300 m (1000 ft). This portion of Alaska is part of the subarctic regime mountains division, Yukon intermontane plateaus-tayga-meadow province ecoregion, as defined by Bailey (U.S. Forest Service, 2007). Between June 28th and July 12th, 2007, scientists from the USGS collected soil, water, stream sediment, vegetation, heavy-mineral concentrate, till, and rock samples from the deposit area. This report contains analytical results for soil, water, stream sediment, and vegetation samples. Analyses for the heavy-mineral concentrate, till, and rock samples are still in progress. The sampling was undertaken during relatively dry and stable weather conditions. Only minor scattered rain showers occurred during the sampling period, so surface conditions were largely unaffected by weather. The predominant sample media collected were soils and surface waters. Soil and water (mostly from ponds and springs, some from small creeks) samples were collected along a single 7.8 km-long (4.8 mi) east-west traverse across the Pebble East and Pebble West zones and from more distal background areas around Koktuli and Kaskanak Mountains. Sample sites are shown on figure 2 and plate 1, and locality coordinates are provided in the accompanying Access and Excel files named FieldSite. Water samples were analyzed by USGS laboratories with one subset analyzed by Activation Laboratories (Actlabs), as indicated below. Soils and stream sediments were analyzed for their total content by SGS Minerals Services under a contract with the USGS. Soil samples were also leached by selected partial-extraction leaching procedures and then analyzed by several commercial laboratories, as described below. Vegetation samples were analyzed as indicated below.
Graph theory and the Virasoro master equation
Obers, N.A.J.
1991-01-01
A brief history of affine Lie algebra, the Virasoro algebra and its culmination in the Virasoro master equation is given. By studying ansaetze of the master equation, the author obtains exact solutions and gains insight in the structure of large slices of affine-Virasoro space. He finds an isomorphism between the constructions in the ansatz SO(n) diag , which is a set of unitary, generically irrational affine-Virasoro constructions on SO(n), and the unlabeled graphs of order n. On the one hand, the conformal constructions, are classified by the graphs, while, conversely, a group-theoretic and conformal field-theoretic identification is obtained for every graph of graph theory. He also defines a class of magic Lie group bases in which the Virasoro master equation admits a simple metric ansatz {g metric }, whose structure is visible in the high-level expansion. When a magic basis is real on compact g, the corresponding g metric is a large system of unitary, generically irrational conformal field theories. Examples in this class include the graph-theory ansatz SO(n) diag in the Cartesian basis of SO(n), and the ansatz SU(n) metric in the Pauli-like basis of SU(n). Finally, he defines the 'sine-area graphs' of SU(n), which label the conformal field theories of SU(n) metric , and he notes that, in similar fashion, each magic basis of g defines a generalized graph theory on g which labels the conformal field theories of g metric
Subgraph detection using graph signals
Chepuri, Sundeep Prabhakar
2017-03-06
In this paper we develop statistical detection theory for graph signals. In particular, given two graphs, namely, a background graph that represents an usual activity and an alternative graph that represents some unusual activity, we are interested in answering the following question: To which of the two graphs does the observed graph signal fit the best? To begin with, we assume both the graphs are known, and derive an optimal Neyman-Pearson detector. Next, we derive a suboptimal detector for the case when the alternative graph is not known. The developed theory is illustrated with numerical experiments.
Subgraph detection using graph signals
Chepuri, Sundeep Prabhakar; Leus, Geert
2017-01-01
In this paper we develop statistical detection theory for graph signals. In particular, given two graphs, namely, a background graph that represents an usual activity and an alternative graph that represents some unusual activity, we are interested in answering the following question: To which of the two graphs does the observed graph signal fit the best? To begin with, we assume both the graphs are known, and derive an optimal Neyman-Pearson detector. Next, we derive a suboptimal detector for the case when the alternative graph is not known. The developed theory is illustrated with numerical experiments.
Nonproliferation and safeguard considerations: Pebble Bed reactor fuel cycle evaluation
1978-09-01
Nuclear fuel cycles were evaluated for the Pebble Bed Gas Cooled Reactor under development in the Federal Republic of Germany. The basic fuel cycle specified for the HTR-K and PNP is well qualified and will meet the requirements of these reactors. Twenty alternate fuel cycles are described, including high-conversion cycles, net-breeding cycles, and proliferation-resistant cycles. High-conversion cycles, which have a high probability of being successfully developed, promise a significant improvement in resource utilization. Proliferation-resistant cycles, also with a high probability of successful development, conpare very favorably with those for other types of reactors. Most of the advanced cycles could be adapted to first-generation pebble bed reactors with no significant modifications
Yunia Mayasari, Ratih; Atmojo Kusmayadi, Tri
2018-04-01
Let G be a connected graph with vertex set V(G) and edge set E(G). For every pair of vertices u,v\\in V(G), the interval I[u, v] between u and v to be the collection of all vertices that belong to some shortest u ‑ v path. A vertex s\\in V(G) strongly resolves two vertices u and v if u belongs to a shortest v ‑ s path or v belongs to a shortest u ‑ s path. A vertex set S of G is a strong resolving set of G if every two distinct vertices of G are strongly resolved by some vertex of S. The strong metric basis of G is a strong resolving set with minimal cardinality. The strong metric dimension sdim(G) of a graph G is defined as the cardinality of strong metric basis. In this paper we determine the strong metric dimension of a generalized butterfly graph, starbarbell graph, and {C}mȯ {P}n graph. We obtain the strong metric dimension of generalized butterfly graph is sdim(BFn ) = 2n ‑ 2. The strong metric dimension of starbarbell graph is sdim(S{B}{m1,{m}2,\\ldots,{m}n})={\\sum }i=1n({m}i-1)-1. The strong metric dimension of {C}mȯ {P}n graph are sdim({C}mȯ {P}n)=2m-1 for m > 3 and n = 2, and sdim({C}mȯ {P}n)=2m-2 for m > 3 and n > 2.
Uranium assessment for the Precambrian pebble conglomerates in southeastern Wyoming
Borgman, L.E.; Sever, C.; Quimby, W.F.; Andrew, M.E.; Karlstrom, K.E.; Houston, R.S.
1981-03-01
This volume is a geostatistical resource estimate of uranium and thorium in quartz-pebble conglomerates, and is a companion to Volume 1: The Geology and Uranium Potential to Precambrian Conglomerates in the Medicine Bow Mountains and Sierra Madre of Southeastern Wyoming; and to Volume 2: Drill-Hole Data, Drill-Site Geology, and Geochemical Data from the Study of Precambrian Uraniferous Conglomerates of the Medicine Bow Mountains and the Sierra Madre of Southeastern Wyoming
Bollobas, Bela
2004-01-01
The ever-expanding field of extremal graph theory encompasses a diverse array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume, based on a series of lectures delivered to graduate students at the University of Cambridge, presents a concise yet comprehensive treatment of extremal graph theory.Unlike most graph theory treatises, this text features complete proofs for almost all of its results. Further insights into theory are provided by the numerous exercises of varying degrees of difficulty that accompany each chapter. A
Thermal cycling tests on Li4SiO4 and beryllium pebbles
Dalle Donne, M.; Norajitra, P.; Weisenburger, A.
1995-01-01
The European B.O.T. Demo-relevant solid breeder blanket is based on the use of beds of beryllium and Li 4 SiO 4 pebbles. Particularly dangerous for the pebble integrity are the rapid temperature changes which could occur, for instance, by a sudden blanket power shut-down. A series of thermal cycle tests have been performed for various beds of beryllium and Li 4 SiO 4 pebbles. No breaking was observed in the beryllium pebbles, however the Li 4 SiO 4 pebbles broke by temperature rates of change of about -50 C/sec independently on pebbles size and lithium enrichment. This value is considerably higher than the peak temperature rates of change expected in the blanket. (orig.)
Studies on air ingress for pebble bed reactors
Moore, R.L.; Oh, C.H.; Merrill, B.J.; Petti, D.A.
2002-01-01
A loss-of-coolant accident (LOCA) has been considered a critical event for helium-cooled pebbled bed reactors. Following helium depressurization, it is anticipated that unless countermeasures are taken air will enter the core through the break and then by molecular diffusion and ultimately by natural convection leading to oxidation of the in-core graphite structure and graphite pebbles. Thus, without any mitigating features a LOCA will lead to an air ingress event. The INEEL is studying such an event with two well-respected light water reactor transient response codes: RELAP5/ATHENA and MELCOR. To study the degree of graphite oxidation occurring due to an air ingress event, a MELCOR model of a reference pebble bed design was constructed. A modified version of MELCOR developed at INEEL, which includes graphite oxidation capabilities, and molecular diffusion of air into helium was used for these calculations. Results show that the lower reflector graphite consumes all of the oxygen before reaching the core. The results also show a long time delay between the time that the depressurization phase of the accident is over and the time that natural circulation air through the core occurs. (author)
Benchmark Evaluation of HTR-PROTEUS Pebble Bed Experimental Program
Bess, John D.; Montierth, Leland; Köberl, Oliver
2014-01-01
Benchmark models were developed to evaluate 11 critical core configurations of the HTR-PROTEUS pebble bed experimental program. Various additional reactor physics measurements were performed as part of this program; currently only a total of 37 absorber rod worth measurements have been evaluated as acceptable benchmark experiments for Cores 4, 9, and 10. Dominant uncertainties in the experimental keff for all core configurations come from uncertainties in the 235 U enrichment of the fuel, impurities in the moderator pebbles, and the density and impurity content of the radial reflector. Calculations of k eff with MCNP5 and ENDF/B-VII.0 neutron nuclear data are greater than the benchmark values but within 1% and also within the 3σ uncertainty, except for Core 4, which is the only randomly packed pebble configuration. Repeated calculations of k eff with MCNP6.1 and ENDF/B-VII.1 are lower than the benchmark values and within 1% (~3σ) except for Cores 5 and 9, which calculate lower than the benchmark eigenvalues within 4σ. The primary difference between the two nuclear data libraries is the adjustment of the absorption cross section of graphite. Simulations of the absorber rod worth measurements are within 3σ of the benchmark experiment values. The complete benchmark evaluation details are available in the 2014 edition of the International Handbook of Evaluated Reactor Physics Benchmark Experiments
Geodetic achievement and avoidance games for graphs | Haynes ...
Let G = (V,E) be a nontrivial connected graph. For a subset S ⊆ V, the geodesic closure (S) of S is the set of all vertices on geodesics (shortest paths) between two vertices of S. We study the geodetic achievement and avoidance games defined by Buckley and Harary (Geodetic games for graphs, Quaestiones Math.
Cospectral Graphs and Regular Orthogonal Matrices of Level 2
Abiad Monge, A.; Haemers, W.H.
2012-01-01
Abstract: For a graph Γ with adjacency matrix A, we consider a switching operation that takes Γ into a graph Γ' with adjacency matrix A', defined by A' = QtAQ, where Q is a regular orthogonal matrix of level 2 (that is, QtQ = I, Q1 = 1, 2Q is integral, and Q is not a permutation matrix). If such an
Development of Chinese HTR-PM pebble bed equivalent conductivity test facility
Ren, Cheng; Yang, Xingtuan; Jiang, Shengyao [Tsinghua Univ., Beijing (China). Inst. of Nuclear and New Energy Technology
2016-01-15
The first two 250-MWt high-temperature reactor pebble bed modules (HTR-PM) have been installing at the Shidaowan plant in Shandong Province, China. The values of the effective thermal conductivity of the pebble bed core are essential parameters for the design. For their determination, Tsinghua University in China has proposed a full-scale heat transfer experiment to conduct comprehensive thermal transfer tests in packed pebble bed and to determine the effective thermal conductivity.
A formal definition of data flow graph models
Kavi, Krishna M.; Buckles, Bill P.; Bhat, U. Narayan
1986-01-01
In this paper, a new model for parallel computations and parallel computer systems that is based on data flow principles is presented. Uninterpreted data flow graphs can be used to model computer systems including data driven and parallel processors. A data flow graph is defined to be a bipartite graph with actors and links as the two vertex classes. Actors can be considered similar to transitions in Petri nets, and links similar to places. The nondeterministic nature of uninterpreted data flow graphs necessitates the derivation of liveness conditions.
On some interconnections between combinatorial optimization and extremal graph theory
Cvetković Dragoš M.
2004-01-01
Full Text Available The uniting feature of combinatorial optimization and extremal graph theory is that in both areas one should find extrema of a function defined in most cases on a finite set. While in combinatorial optimization the point is in developing efficient algorithms and heuristics for solving specified types of problems, the extremal graph theory deals with finding bounds for various graph invariants under some constraints and with constructing extremal graphs. We analyze by examples some interconnections and interactions of the two theories and propose some conclusions.
The Atom-Bond Connectivity Index of Catacondensed Polyomino Graphs
Chen, Jinsong; Liu, Jianping; Li, Qiaoliang
2013-01-01
Let G=(V,E) be a graph. The atom-bond connectivity (ABC) index is defined as the sum of weights ((du+dv−2)/dudv)1/2 over all edges uv of G, where du denotes the degree of a vertex u of G. In this paper, we give the atom-bond connectivity index of the zigzag chain polyomino graphs. Meanwhile, we obtain the sharp upper bound on the atom-bond connectivity index of catacondensed polyomino graphs with h squares and determine the corresponding extremal graphs.
Haynes Teresa W.
2014-08-01
Full Text Available A path π = (v1, v2, . . . , vk+1 in a graph G = (V,E is a downhill path if for every i, 1 ≤ i ≤ k, deg(vi ≥ deg(vi+1, where deg(vi denotes the degree of vertex vi ∈ V. The downhill domination number equals the minimum cardinality of a set S ⊆ V having the property that every vertex v ∈ V lies on a downhill path originating from some vertex in S. We investigate downhill domination numbers of graphs and give upper bounds. In particular, we show that the downhill domination number of a graph is at most half its order, and that the downhill domination number of a tree is at most one third its order. We characterize the graphs obtaining each of these bounds
Alspach, BR
1985-01-01
This volume deals with a variety of problems involving cycles in graphs and circuits in digraphs. Leading researchers in this area present here 3 survey papers and 42 papers containing new results. There is also a collection of unsolved problems.
Wilson, Robin J
1985-01-01
Graph Theory has recently emerged as a subject in its own right, as well as being an important mathematical tool in such diverse subjects as operational research, chemistry, sociology and genetics. This book provides a comprehensive introduction to the subject.
Hyperbolicity in median graphs
mic problems in hyperbolic spaces and hyperbolic graphs have been .... that in general the main obstacle is that we do not know the location of ...... [25] Jonckheere E and Lohsoonthorn P, A hyperbolic geometry approach to multipath routing,.
Namhee Kim
Full Text Available Graph representations have been widely used to analyze and design various economic, social, military, political, and biological networks. In systems biology, networks of cells and organs are useful for understanding disease and medical treatments and, in structural biology, structures of molecules can be described, including RNA structures. In our RNA-As-Graphs (RAG framework, we represent RNA structures as tree graphs by translating unpaired regions into vertices and helices into edges. Here we explore the modularity of RNA structures by applying graph partitioning known in graph theory to divide an RNA graph into subgraphs. To our knowledge, this is the first application of graph partitioning to biology, and the results suggest a systematic approach for modular design in general. The graph partitioning algorithms utilize mathematical properties of the Laplacian eigenvector (µ2 corresponding to the second eigenvalues (λ2 associated with the topology matrix defining the graph: λ2 describes the overall topology, and the sum of µ2's components is zero. The three types of algorithms, termed median, sign, and gap cuts, divide a graph by determining nodes of cut by median, zero, and largest gap of µ2's components, respectively. We apply these algorithms to 45 graphs corresponding to all solved RNA structures up through 11 vertices (∼ 220 nucleotides. While we observe that the median cut divides a graph into two similar-sized subgraphs, the sign and gap cuts partition a graph into two topologically-distinct subgraphs. We find that the gap cut produces the best biologically-relevant partitioning for RNA because it divides RNAs at less stable connections while maintaining junctions intact. The iterative gap cuts suggest basic modules and assembly protocols to design large RNA structures. Our graph substructuring thus suggests a systematic approach to explore the modularity of biological networks. In our applications to RNA structures, subgraphs
Nuclear safeguards considerations for pebble bed reactors (PBRs)
Moses, David L.
2012-01-01
Recent reports by the Department of Energy National Laboratories have discussed safeguards considerations for low enriched uranium (LEU)-fueled pebble bed reactors (PBRs) and the need for bulk accountancy of the plutonium in “used fuel.” These reports fail to account for the degree of plutonium dilution in the graphitized-carbon pebbles that is sufficient to meet the International Atomic Energy Agency (IAEA) “provisional” guidelines for termination of safeguards on “measured discards.” The thrust of this finding is not to terminate safeguards but to limit the need for specific accountancy of plutonium in stored used fuel. While the residual uranium in the used fuel is not sufficiently diluted to meet the IAEA provisional guidelines for termination of safeguards, the estimated quantities of the uranium minor isotopes 232 U and 236 U in the used fuel at the target burnup of ∼90 Gigawatt-days per metric ton (GWD/MT) exceed standard specification limits for reprocessed uranium and will require extensive blending with either natural uranium or uranium enrichment tails to dilute the 236 U content to fall within specification. Hence, the PBR used fuel is less desirable for commercial reprocessing and reuse than that from light water reactors. Also the PBR specific activity of a reprocessed uranium isotopic mixture and its A 2 values for effective dose limits if released in a dispersible form during a transportation accident are more limiting than the equivalent values for light-water-reactor used fuel at 55 GWD/MT without accounting for the presence of the principal carry-over fission product (technetium, 99 Tc) and plutonium contamination. Thus, the potentially recoverable uranium from PBR used fuel carries reactivity penalties and radiological penalties likely greater than those for reprocessed uranium from light water reactors. These factors impact the economics of reprocessing, but a more significant consideration is that reprocessing technologies for
Gougar, Hans D.; Reitsma, Frederik; Joubert, Wessel
2009-01-01
Recirculating pebble-bed reactors are distinguished from all other reactor types by the downward movement through and reinsertion of fuel into the core during operation. Core simulators must account for this movement and mixing in order to capture the physics of the equilibrium cycle core. VSOP and PEBBED are two codes used to perform such simulations, but they do so using different methods. In this study, a simplified pebble-bed core with a specified flux profile and cross sections is used as the model for conducting analyses of two types of burnup schemes. The differences between the codes are described and related to the differences observed in the nuclide densities in pebbles discharged from the core. Differences in the methods for computing fission product buildup and average number densities lead to significant differences in the computed core power and eigenvalue. These test models provide a key component of an overall equilibrium cycle benchmark involving neutron transport, cross section generation, and fuel circulation.
Uniform Single Valued Neutrosophic Graphs
S. Broumi
2017-09-01
Full Text Available In this paper, we propose a new concept named the uniform single valued neutrosophic graph. An illustrative example and some properties are examined. Next, we develop an algorithmic approach for computing the complement of the single valued neutrosophic graph. A numerical example is demonstrated for computing the complement of single valued neutrosophic graphs and uniform single valued neutrosophic graph.
Collective Rationality in Graph Aggregation
Endriss, U.; Grandi, U.; Schaub, T.; Friedrich, G.; O'Sullivan, B.
2014-01-01
Suppose a number of agents each provide us with a directed graph over a common set of vertices. Graph aggregation is the problem of computing a single “collective” graph that best represents the information inherent in this profile of individual graphs. We consider this aggregation problem from the
Bollobás, Béla
1998-01-01
The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory such as coloring, matching, extremal theory, and algebraic graph theory, the book presents a detailed ...
Infinite Random Graphs as Statistical Mechanical Models
Durhuus, Bergfinnur Jøgvan; Napolitano, George Maria
2011-01-01
We discuss two examples of infinite random graphs obtained as limits of finite statistical mechanical systems: a model of two-dimensional dis-cretized quantum gravity defined in terms of causal triangulated surfaces, and the Ising model on generic random trees. For the former model we describe a ...
Proxy Graph: Visual Quality Metrics of Big Graph Sampling.
Nguyen, Quan Hoang; Hong, Seok-Hee; Eades, Peter; Meidiana, Amyra
2017-06-01
Data sampling has been extensively studied for large scale graph mining. Many analyses and tasks become more efficient when performed on graph samples of much smaller size. The use of proxy objects is common in software engineering for analysis and interaction with heavy objects or systems. In this paper, we coin the term 'proxy graph' and empirically investigate how well a proxy graph visualization can represent a big graph. Our investigation focuses on proxy graphs obtained by sampling; this is one of the most common proxy approaches. Despite the plethora of data sampling studies, this is the first evaluation of sampling in the context of graph visualization. For an objective evaluation, we propose a new family of quality metrics for visual quality of proxy graphs. Our experiments cover popular sampling techniques. Our experimental results lead to guidelines for using sampling-based proxy graphs in visualization.
The reprocessing of advanced mixed lithium orthosilicate/metatitanate tritium breeder pebbles
Leys, Oliver, E-mail: oliver.leys@kit.edu [Karlsruhe Institute of Technology, Institute for Applied Materials, Eggenstein-Leopoldshafen, 76344 (Germany); Bergfeldt, Thomas; Kolb, Matthias H.H.; Knitter, Regina [Karlsruhe Institute of Technology, Institute for Applied Materials, Eggenstein-Leopoldshafen, 76344 (Germany); Goraieb, Aniceto A. [Karlsruhe Beryllium Handling Facility, Eggenstein-Leopoldshafen, 76344 (Germany)
2016-06-15
Highlights: • The recycling of advanced breeder pebbles without a deterioration of the material properties is possible using a melt-based process. • The only accumulation of impurities upon reprocessing, results from the platinum crucible alloy used for processing. • It is possible to replenish burnt-up lithium by additions of LiOH·H{sub 2}O to the melt during reprocessing. - Abstract: The recycling of tritium breeding materials will be necessary for any future use of nuclear fusion energy due to economical as well as ecological considerations. In the case of the solid breeder blanket concept, the ceramic pebble beds that are intended for the generation of tritium will eventually need to be restored due to depleted lithium levels as well as due to fractured pebbles, which will cause a deterioration of the pebble bed properties. It is proposed that the pebbles, which are fabricated using a melt-based process, are recycled using the same initial process, by replenishing the lithium levels and reforming the pebbles at the same time. To prove this recycling scheme, advanced ceramic pebbles were fabricated and then re-melted multiple times to prove that the reprocessing did not have any negative effect on the pebble properties and secondly, pebbles were produced with a simulated lithium burn-up and subsequently replenished by additions of LiOH to the melt. It was shown that the re-melting and lithium re-enrichment had no effect on the pebble properties, demonstrating that a melt-based process is suitable for recycling used breeder pebbles.
Mechanical behavior of Be–Ti pebbles at blanket relevant temperatures
Kurinskiy, Petr, E-mail: petr.kurinskiy@kit.edu [Karlsruhe Institute of Technology, Institute for Applied Materials—Applied Materials Physics (IAM-AWP), P.O. Box 3640, 76021 Karlsruhe (Germany); Rolli, Rolf [Karlsruhe Institute of Technology, Institute for Applied Materials—Materials Biomechanics (IAM-WBM), P.O. Box 3640, 76021 Karlsruhe (Germany); Kim, Jae-Hwan; Nakamichi, Masaru [Breeding Functional Materials Development Group, Department of Blanket Fusion Institute, Rokkasho Fusion Institute, Sector of Fusion Research and Development, Japan Atomic Energy Agency, 2-166 Oaza-Obuchi-Aza-Omotedate, Rokkasho-mura, Kamikita-gun, Aoori 039-3212 (Japan)
2016-11-01
Highlights: • Mechanical behavior of two kinds of Be–Ti pebbles in the temperature range of 400–800 °C was investigated. • It was experimentally shown that Be-7 at.%Ti pebbles have the enhanced ductile properties compared to Be-7.7 at.%Ti pebbles. • Brittle failure of both kinds of Be–Ti pebbles was observed by testing at 400 °C using the constant loading with 150 N. - Abstract: Mechanical performance of beryllium-based materials is a matter of a great interest from the point of view of their use as neutron multipliers of the tritium breeding blankets. The compression strains which can occur in beryllium pebble beds under blanket working conditions will lead to deformation or even failure of individual pebbles [1,2] (Reimann et al. 2002; Ishitsuka and Kawamura, 1995). Mechanical behavior of Be–Ti pebbles having chemical contents of Be-7.0 at.% Ti and Be-7.7 at.%Ti was investigated in the temperature range of 400–800 °C. Constant loads varying from 10 up to 150 N were applied uniaxially. It was shown that Be–Ti pebbles compared to pure beryllium pebbles possess much lower ductility, although their strength properties exceed corresponding characteristics of pure beryllium. Also, the influence of titanium content on mechanical behavior of Be–Ti pebbles was investigated. Specific features of deformation of pure beryllium and Be–Ti pebbles having different titanium contents at blanket operation temperatures are discussed.
Fabrication of Li_2TiO_3 pebbles by a selective laser sintering process
Zhou, Qilai; Gao, Yue; Liu, Kai; Xue, Lihong; Yan, Youwei
2015-01-01
Highlights: • Selective laser sintering (SLS) is employed to fabricate ceramic pebbles. • Quantities and diameter of the pebbles could be easily controlled by adjusting the model of pebbles. • All the pebbles could be prepared at a time within several minutes. • The Li_2TiO_3 pebbles sintered at 1100 °C show a notable crush load of 43 N. - Abstract: Lithium titanate, Li_2TiO_3, is an important tritium breeding material for deuterium (D)–tritium (T) fusion reactor. In test blanket module (TBM) design of China, Li_2TiO_3 is considered as one candidate material of tritium breeders. In this study, selective laser sintering (SLS) technology was introduced to fabricate Li_2TiO_3 ceramic pebbles. This fabrication process is computer assisted and has a high level of flexibility. Li_2TiO_3 powder with a particle size of 1–3 μm was used as the raw material, whilst epoxy resin E06 was adopted as a binder. Green Li_2TiO_3 pebbles with certain strengths were successfully prepared via SLS. Density of the green pebbles was subsequently increased by cold isostatic pressing (CIP) process. Li_2TiO_3 pebbles with a diameter of about 2 mm were obtained after high temperature sintering. Density of the pebbles reaches 80% of theoretical density (TD) with a comparable crush load of 43 N. This computer assisted approach provides a new efficient route for the production of Li_2TiO_3 ceramic pebbles.
Layered Graph Drawing for Visualizing Evaluation Structures.
Onoue, Yosuke; Kukimoto, Nobuyuki; Sakamoto, Naohisa; Misue, Kazuo; Koyamada, Koji
2017-01-01
An evaluation structure is a hierarchical structure of human cognition extracted from interviews based on the evaluation grid method. An evaluation structure can be defined as a directed acyclic graph (DAG). The authors propose a layer-assignment method that is part of the Sugiyama framework, a popular method for drawing DAGs, to satisfy the requirements for drawing evaluation structures. Their evaluations demonstrate that the layered graph drawing produced by the proposed layer-assignment method is preferred by users and aids in the understanding of evaluation structures.
Grossman, Max [Rice Univ., Houston, TX (United States); Pritchard Jr., Howard Porter [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Budimlic, Zoran [Rice Univ., Houston, TX (United States); Sarkar, Vivek [Rice Univ., Houston, TX (United States)
2016-12-22
Graph500 [14] is an effort to offer a standardized benchmark across large-scale distributed platforms which captures the behavior of common communicationbound graph algorithms. Graph500 differs from other large-scale benchmarking efforts (such as HPL [6] or HPGMG [7]) primarily in the irregularity of its computation and data access patterns. The core computational kernel of Graph500 is a breadth-first search (BFS) implemented on an undirected graph. The output of Graph500 is a spanning tree of the input graph, usually represented by a predecessor mapping for every node in the graph. The Graph500 benchmark defines several pre-defined input sizes for implementers to test against. This report summarizes investigation into implementing the Graph500 benchmark on OpenSHMEM, and focuses on first building a strong and practical understanding of the strengths and limitations of past work before proposing and developing novel extensions.
Yu, Qingbao; Du, Yuhui; Chen, Jiayu; He, Hao; Sui, Jing; Pearlson, Godfrey; Calhoun, Vince D
2017-11-01
A key challenge in building a brain graph using fMRI data is how to define the nodes. Spatial brain components estimated by independent components analysis (ICA) and regions of interest (ROIs) determined by brain atlas are two popular methods to define nodes in brain graphs. It is difficult to evaluate which method is better in real fMRI data. Here we perform a simulation study and evaluate the accuracies of a few graph metrics in graphs with nodes of ICA components, ROIs, or modified ROIs in four simulation scenarios. Graph measures with ICA nodes are more accurate than graphs with ROI nodes in all cases. Graph measures with modified ROI nodes are modulated by artifacts. The correlations of graph metrics across subjects between graphs with ICA nodes and ground truth are higher than the correlations between graphs with ROI nodes and ground truth in scenarios with large overlapped spatial sources. Moreover, moving the location of ROIs would largely decrease the correlations in all scenarios. Evaluating graphs with different nodes is promising in simulated data rather than real data because different scenarios can be simulated and measures of different graphs can be compared with a known ground truth. Since ROIs defined using brain atlas may not correspond well to real functional boundaries, overall findings of this work suggest that it is more appropriate to define nodes using data-driven ICA than ROI approaches in real fMRI data. Copyright © 2017 Elsevier B.V. All rights reserved.
Fundamentals of algebraic graph transformation
Ehrig, Hartmut; Prange, Ulrike; Taentzer, Gabriele
2006-01-01
Graphs are widely used to represent structural information in the form of objects and connections between them. Graph transformation is the rule-based manipulation of graphs, an increasingly important concept in computer science and related fields. This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory. Part I is an introduction to the classical case of graph and typed graph transformation. In Part II basic and advanced results are first shown for an abstract form of replacement systems, so-called adhesive high-level replacement systems based on category theory, and are then instantiated to several forms of graph and Petri net transformation systems. Part III develops typed attributed graph transformation, a technique of key relevance in the modeling of visual languages and in model transformation. Part IV contains a practical case study on model transformation and a presentation of the AGG (attributed graph grammar) tool envir...
The STAPL Parallel Graph Library
Harshvardhan,
2013-01-01
This paper describes the stapl Parallel Graph Library, a high-level framework that abstracts the user from data-distribution and parallelism details and allows them to concentrate on parallel graph algorithm development. It includes a customizable distributed graph container and a collection of commonly used parallel graph algorithms. The library introduces pGraph pViews that separate algorithm design from the container implementation. It supports three graph processing algorithmic paradigms, level-synchronous, asynchronous and coarse-grained, and provides common graph algorithms based on them. Experimental results demonstrate improved scalability in performance and data size over existing graph libraries on more than 16,000 cores and on internet-scale graphs containing over 16 billion vertices and 250 billion edges. © Springer-Verlag Berlin Heidelberg 2013.
Pebble bed blanket design for deuterium burning tandem mirror reactors
Grotz, S.P.; Dhir, V.K.
1983-01-01
The UCLA tandem mirror reactor, SATYR, was developed around the capability of tandem mirrors with thermal barriers to burn deuterium at reasonable efficiency levels. The pebble bed concept has been incorporated into our blanket design for the following reasons: 1) Large area-to-volume ratio for purposes of heat removal; 2) Large volume of structure for high thermal capacity thus increasing the safety margin during off-normal incidents; 3) Relatively inexpensive manufacturing costs because of large acceptable tolerances and lack of exotic materials (i.e., lithium). A simplified stress analysis of the blanket module was performed to optimize and simplify the design. The pre-specified stress intensity limitations used were based upon a 30-year predicted lifetime for each module. Along with stress analysis of the vessel a detailed thermal hydraulic analysis of the pebble bed has been completed. Parameters affecting the pebble bed design are fluidization velocity, pressure drop, heat transfer coefficient, thermally induced stress in the spheres and spatial variation of the power density. Although reasonable gross thermal efficiencies of the 2 designs has been achieved (28% for H 2 O and 39% for He) the high net recirculating power fraction for heating and neutral beams results in relatively low net plant efficiencies (21% and 27%). The results show that a blanket can be designed with good thermal efficiency and a relative-ly simple configuration. However, application of this concept to the high Q deuterium-tritium fuel cycle would have difficulties resulting from the need for continuous removal of the tritium. (orig./HP)
Planet population synthesis driven by pebble accretion in cluster environments
Ndugu, N.; Bitsch, B.; Jurua, E.
2018-02-01
The evolution of protoplanetary discs embedded in stellar clusters depends on the age and the stellar density in which they are embedded. Stellar clusters of young age and high stellar surface density destroy protoplanetary discs by external photoevaporation and stellar encounters. Here, we consider the effect of background heating from newly formed stellar clusters on the structure of protoplanetary discs and how it affects the formation of planets in these discs. Our planet formation model is built on the core accretion scenario, where we take the reduction of the core growth time-scale due to pebble accretion into account. We synthesize planet populations that we compare to observations obtained by radial velocity measurements. The giant planets in our simulations migrate over large distances due to the fast type-II migration regime induced by a high disc viscosity (α = 5.4 × 10-3). Cold Jupiters (rp > 1 au) originate preferably from the outer disc, due to the large-scale planetary migration, while hot Jupiters (rp meaning that more gas giants are formed at larger metallicity. However, our synthetic population of isolated stars host a significant amount of giant planets even at low metallicity, in contradiction to observations where giant planets are preferably found around high metallicity stars, indicating that pebble accretion is very efficient in the standard pebble accretion framework. On the other hand, discs around stars embedded in cluster environments hardly form any giant planets at low metallicity in agreement with observations, where these changes originate from the increased temperature in the outer parts of the disc, which prolongs the core accretion time-scale of the planet. We therefore conclude that the outer disc structure and the planet's formation location determines the giant planet occurrence rate and the formation efficiency of cold and hot Jupiters.
Resistance Distances in Vertex-Face Graphs
Shangguan, Yingmin; Chen, Haiyan
2018-01-01
The computation of two-point resistances in networks is a classical problem in electric circuit theory and graph theory. Let G be a triangulation graph with n vertices embedded on an orientable surface. Define K(G) to be the graph obtained from G by inserting a new vertex vϕ to each face ϕ of G and adding three new edges (u, vϕ), (v, vϕ) and (w, vϕ), where u, v and w are three vertices on the boundary of ϕ. In this paper, using star-triangle transformation and resistance local-sum rules, explicit relations between resistance distances in K(G) and those in G are obtained. These relations enable us to compute resistance distance between any two points of Kk(G) recursively. As explanation examples, some resistances in several networks are computed, including the modified Apollonian network and networks constructed from tetrahedron, octahedron and icosahedron, respectively.
1978-09-01
The Pebble Bed Gas Cooled Reactor, as developed in the Federal Republic of Germany, was reviewed from a United States Safety and Licensing perspective. The primary concepts considered were the steam cycle electric generating pebble bed (HTR-K) and the process heat pebble bed (PNP), although generic consideration of the direct cycle gas turbine pebble bed (HHT) was included. The study examines potential U.S. licensing issues and offers some suggestions as to required development areas
Influence of gas pressure on the effective thermal conductivity of ceramic breeder pebble beds
Dai, Weijing [School of Civil Engineering, The University of Sydney, Sydney (Australia); Pupeschi, Simone [Institute for Applied Materials, Karlsruhe Institute of Technology (KIT) (Germany); Hanaor, Dorian [School of Civil Engineering, The University of Sydney, Sydney (Australia); Institute for Materials Science and Technologies, Technical University of Berlin (Germany); Gan, Yixiang, E-mail: yixiang.gan@sydney.edu.au [School of Civil Engineering, The University of Sydney, Sydney (Australia)
2017-05-15
Highlights: • This study explicitly demonstrates the influence of the gas pressure on the effective thermal conductivity of pebble beds. • The gas pressure influence is shown to correlated to the pebble size. • The effective thermal conductivity is linked to thermal-mechanical properties of pebbles and packing structure. - Abstract: 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.
Influence of gas pressure on the effective thermal conductivity of ceramic breeder pebble beds
Dai, Weijing; Pupeschi, Simone; Hanaor, Dorian; Gan, Yixiang
2017-01-01
Highlights: • This study explicitly demonstrates the influence of the gas pressure on the effective thermal conductivity of pebble beds. • The gas pressure influence is shown to correlated to the pebble size. • The effective thermal conductivity is linked to thermal-mechanical properties of pebbles and packing structure. - Abstract: 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.
The activation analysis of gold in small refractory pebbles
Bibby, D.M.; Chaix, R.P.
1975-08-01
The gold content of a suite of small pebbles, residual to the milling and leach of a gold bearing ore, has been investigated by means of neutron activation analysis (NAA). An NAA technique presenting a sensitivity of 0.02μgm gold, was used as being appropriate to the samples under investigation. An alternative NAA technique developed with the same sample suite showed a sensitivity of the order of 10 -4 to 10 -5 μgm gold. The NAA techniques developed, are appropriate to the determination of gold in small samples of ore not normally amenable to milling and/or dissolution
A 350 MW HTR with an annular pebble bed core
Wang Dazhong; Jiang Zhiqiang; Gao Zuying; Xu Yuanhui
1992-12-01
A conceptual design of HTR-module with an annular pebble bed core was proposed. This design can increase the unit power capacity of HTR-Module from 200 MWt to 350 MWt while it can keep the inherent safety characteristics of modular reactor. The preliminary safety analysis results for 350 MW HTR are given. In order to solve the problem of uneven helium outlet temperature distribution a gas flow mixing structure at bottom of core was designed. The experiment results of a gas mixing simulation test rig show that the mixing function can satisfy the design requirements
Research on application of burnable poison in pebble bed HTR
Wei Chunlin; Zhang Jian; Shan Wenzhi; Jing Xingqing
2013-01-01
Burnable poison in fuel ball was used in pebble bed high-temperature gas-cooled reactor (HTR) to optimize the shape and the peak factor of power distribution in certain conditions. Two options are available and evaluated, that is the homogeneous burnable poison in graphite matrix and burnable poison particles (BPPs) in fuel balls. Due to the absorption cross section of "1"0B, the depletion speed for homogeneous burnable poison is very fast, and difficult to control, on the other side, the depletion speed of BPPs can be optimized respecting to its size, and better shape and peak value of power distribution can be achieved. (authors)
Pebble bed reactor fuel cycle optimization using particle swarm algorithm
Tavron, Barak, E-mail: btavron@bgu.ac.il [Planning, Development and Technology Division, Israel Electric Corporation Ltd., P.O. Box 10, Haifa 31000 (Israel); Shwageraus, Eugene, E-mail: es607@cam.ac.uk [Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ (United Kingdom)
2016-10-15
Highlights: • Particle swarm method has been developed for fuel cycle optimization of PBR reactor. • Results show uranium utilization low sensitivity to fuel and core design parameters. • Multi-zone fuel loading pattern leads to a small improvement in uranium utilization. • Thorium mixes with highly enriched uranium yields the best uranium utilization. - Abstract: Pebble bed reactors (PBR) features, such as robust thermo-mechanical fuel design and on-line continuous fueling, facilitate wide range of fuel cycle alternatives. A range off fuel pebble types, containing different amounts of fertile or fissile fuel material, may be loaded into the reactor core. Several fuel loading zones may be used since radial mixing of the pebbles was shown to be limited. This radial separation suggests the possibility to implement the “seed-blanket” concept for the utilization of fertile fuels such as thorium, and for enhancing reactor fuel utilization. In this study, the particle-swarm meta-heuristic evolutionary optimization method (PSO) has been used to find optimal fuel cycle design which yields the highest natural uranium utilization. The PSO method is known for solving efficiently complex problems with non-linear objective function, continuous or discrete parameters and complex constrains. The VSOP system of codes has been used for PBR fuel utilization calculations and MATLAB script has been used to implement the PSO algorithm. Optimization of PBR natural uranium utilization (NUU) has been carried out for 3000 MWth High Temperature Reactor design (HTR) operating on the Once Trough Then Out (OTTO) fuel management scheme, and for 400 MWth Pebble Bed Modular Reactor (PBMR) operating on the multi-pass (MEDUL) fuel management scheme. Results showed only a modest improvement in the NUU (<5%) over reference designs. Investigation of thorium fuel cases showed that the use of HEU in combination with thorium results in the most favorable reactor performance in terms of
Pebble bed reactor fuel cycle optimization using particle swarm algorithm
Tavron, Barak; Shwageraus, Eugene
2016-01-01
Highlights: • Particle swarm method has been developed for fuel cycle optimization of PBR reactor. • Results show uranium utilization low sensitivity to fuel and core design parameters. • Multi-zone fuel loading pattern leads to a small improvement in uranium utilization. • Thorium mixes with highly enriched uranium yields the best uranium utilization. - Abstract: Pebble bed reactors (PBR) features, such as robust thermo-mechanical fuel design and on-line continuous fueling, facilitate wide range of fuel cycle alternatives. A range off fuel pebble types, containing different amounts of fertile or fissile fuel material, may be loaded into the reactor core. Several fuel loading zones may be used since radial mixing of the pebbles was shown to be limited. This radial separation suggests the possibility to implement the “seed-blanket” concept for the utilization of fertile fuels such as thorium, and for enhancing reactor fuel utilization. In this study, the particle-swarm meta-heuristic evolutionary optimization method (PSO) has been used to find optimal fuel cycle design which yields the highest natural uranium utilization. The PSO method is known for solving efficiently complex problems with non-linear objective function, continuous or discrete parameters and complex constrains. The VSOP system of codes has been used for PBR fuel utilization calculations and MATLAB script has been used to implement the PSO algorithm. Optimization of PBR natural uranium utilization (NUU) has been carried out for 3000 MWth High Temperature Reactor design (HTR) operating on the Once Trough Then Out (OTTO) fuel management scheme, and for 400 MWth Pebble Bed Modular Reactor (PBMR) operating on the multi-pass (MEDUL) fuel management scheme. Results showed only a modest improvement in the NUU (<5%) over reference designs. Investigation of thorium fuel cases showed that the use of HEU in combination with thorium results in the most favorable reactor performance in terms of
White, AT
1985-01-01
The field of topological graph theory has expanded greatly in the ten years since the first edition of this book appeared. The original nine chapters of this classic work have therefore been revised and updated. Six new chapters have been added, dealing with: voltage graphs, non-orientable imbeddings, block designs associated with graph imbeddings, hypergraph imbeddings, map automorphism groups and change ringing.Thirty-two new problems have been added to this new edition, so that there are now 181 in all; 22 of these have been designated as ``difficult'''' and 9 as ``unsolved''''. Three of the four unsolved problems from the first edition have been solved in the ten years between editions; they are now marked as ``difficult''''.
Ribes, Luis
2017-01-01
This book offers a detailed introduction to graph theoretic methods in profinite groups and applications to abstract groups. It is the first to provide a comprehensive treatment of the subject. The author begins by carefully developing relevant notions in topology, profinite groups and homology, including free products of profinite groups, cohomological methods in profinite groups, and fixed points of automorphisms of free pro-p groups. The final part of the book is dedicated to applications of the profinite theory to abstract groups, with sections on finitely generated subgroups of free groups, separability conditions in free and amalgamated products, and algorithms in free groups and finite monoids. Profinite Graphs and Groups will appeal to students and researchers interested in profinite groups, geometric group theory, graphs and connections with the theory of formal languages. A complete reference on the subject, the book includes historical and bibliographical notes as well as a discussion of open quest...
Subdominant pseudoultrametric on graphs
Dovgoshei, A A; Petrov, E A [Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk (Ukraine)
2013-08-31
Let (G,w) be a weighted graph. We find necessary and sufficient conditions under which the weight w:E(G)→R{sup +} can be extended to a pseudoultrametric on V(G), and establish a criterion for the uniqueness of such an extension. We demonstrate that (G,w) is a complete k-partite graph, for k≥2, if and only if for any weight that can be extended to a pseudoultrametric, among all such extensions one can find the least pseudoultrametric consistent with w. We give a structural characterization of graphs for which the subdominant pseudoultrametric is an ultrametric for any strictly positive weight that can be extended to a pseudoultrametric. Bibliography: 14 titles.
Quantitative graph theory mathematical foundations and applications
Dehmer, Matthias
2014-01-01
The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical techniques, this book covers a wide range of quantitative-graph theoretical concepts and methods, including those pertaining to real and random graphs such as:Comparative approaches (graph similarity or distance)Graph measures to characterize graphs quantitat
Cheung, King Sing
2014-01-01
Petri nets are a formal and theoretically rich model for the modelling and analysis of systems. A subclass of Petri nets, augmented marked graphs possess a structure that is especially desirable for the modelling and analysis of systems with concurrent processes and shared resources.This monograph consists of three parts: Part I provides the conceptual background for readers who have no prior knowledge on Petri nets; Part II elaborates the theory of augmented marked graphs; finally, Part III discusses the application to system integration. The book is suitable as a first self-contained volume
Dayal, Amit; Brock, David
2018-01-01
Prashant Chandrasekar, a lead developer for the Social Interactome project, has tasked the team with creating a graph representation of the data collected from the social networks involved in that project. The data is currently stored in a MySQL database. The client requested that the graph database be Cayley, but after a literature review, Neo4j was chosen. The reasons for this shift will be explained in the design section. Secondarily, the team was tasked with coming up with three scena...
Stevanovic, Dragan
2015-01-01
Spectral Radius of Graphs provides a thorough overview of important results on the spectral radius of adjacency matrix of graphs that have appeared in the literature in the preceding ten years, most of them with proofs, and including some previously unpublished results of the author. The primer begins with a brief classical review, in order to provide the reader with a foundation for the subsequent chapters. Topics covered include spectral decomposition, the Perron-Frobenius theorem, the Rayleigh quotient, the Weyl inequalities, and the Interlacing theorem. From this introduction, the
CFD simulation of a coolant flow and a heat transfer in a pebble bed reactor - HTR2008-58334
In, W. K.; Lee, W. J.; Hassan, Y. A.
2008-01-01
This CFD study is to simulate a coolant(gas) flow and heat transfer in a PBR core during a normal operation. This study used a pebble array with direct area contacts among the pebbles which is one of the pebbles arrangements for a detailed simulation of PBR core CFD studies. A CFD model is developed to more adequately represent the pebbles randomly stacked in the PBR core. The CFD predictions showed a large variation of the temperature on the pebble surface as well as in the pebble core. The temperature drop in the outer graphite layer is smaller than that in the pebble-core region. This is because the thermal conductivity of graphite is higher than the fuel (UO, mixture) conductivity in the pebble core. Higher pebble surface temperature is predicted downstream of the pebble contact due to a reverse flow. Multiple vortices are predicted to occur downstream of the spherical pebbles due to a flow separation. The coolant flow structure and fuel temperature in the PBR core appears to largely depend on the in-core distribution of the pebbles. (authors)
John D. Bess; Barbara H. Dolphin; James W. Sterbentz; Luka Snoj; Igor Lengar; Oliver Köberl
2013-03-01
In its deployment as a pebble bed reactor (PBR) critical facility from 1992 to 1996, the PROTEUS facility was designated as HTR-PROTEUS. This experimental program was performed as part of an International Atomic Energy Agency (IAEA) Coordinated Research Project (CRP) on the Validation of Safety Related Physics Calculations for Low Enriched HTGRs. Within this project, critical experiments were conducted for graphite moderated LEU systems to determine core reactivity, flux and power profiles, reaction-rate ratios, the worth of control rods, both in-core and reflector based, the worth of burnable poisons, kinetic parameters, and the effects of moisture ingress on these parameters. Four benchmark experiments were evaluated in this report: Cores 1, 1A, 2, and 3. These core configurations represent the hexagonal close packing (HCP) configurations of the HTR-PROTEUS experiment with a moderator-to-fuel pebble ratio of 1:2. Core 1 represents the only configuration utilizing ZEBRA control rods. Cores 1A, 2, and 3 use withdrawable, hollow, stainless steel control rods. Cores 1 and 1A are similar except for the use of different control rods; Core 1A also has one less layer of pebbles (21 layers instead of 22). Core 2 retains the first 16 layers of pebbles from Cores 1 and 1A and has 16 layers of moderator pebbles stacked above the fueled layers. Core 3 retains the first 17 layers of pebbles but has polyethylene rods inserted between pebbles to simulate water ingress. The additional partial pebble layer (layer 18) for Core 3 was not included as it was used for core operations and not the reported critical configuration. Cores 1, 1A, 2, and 3 were determined to be acceptable benchmark experiments.
John D. Bess; Barbara H. Dolphin; James W. Sterbentz; Luka Snoj; Igor Lengar; Oliver Köberl
2012-03-01
In its deployment as a pebble bed reactor (PBR) critical facility from 1992 to 1996, the PROTEUS facility was designated as HTR-PROTEUS. This experimental program was performed as part of an International Atomic Energy Agency (IAEA) Coordinated Research Project (CRP) on the Validation of Safety Related Physics Calculations for Low Enriched HTGRs. Within this project, critical experiments were conducted for graphite moderated LEU systems to determine core reactivity, flux and power profiles, reaction-rate ratios, the worth of control rods, both in-core and reflector based, the worth of burnable poisons, kinetic parameters, and the effects of moisture ingress on these parameters. Four benchmark experiments were evaluated in this report: Cores 1, 1A, 2, and 3. These core configurations represent the hexagonal close packing (HCP) configurations of the HTR-PROTEUS experiment with a moderator-to-fuel pebble ratio of 1:2. Core 1 represents the only configuration utilizing ZEBRA control rods. Cores 1A, 2, and 3 use withdrawable, hollow, stainless steel control rods. Cores 1 and 1A are similar except for the use of different control rods; Core 1A also has one less layer of pebbles (21 layers instead of 22). Core 2 retains the first 16 layers of pebbles from Cores 1 and 1A and has 16 layers of moderator pebbles stacked above the fueled layers. Core 3 retains the first 17 layers of pebbles but has polyethylene rods inserted between pebbles to simulate water ingress. The additional partial pebble layer (layer 18) for Core 3 was not included as it was used for core operations and not the reported critical configuration. Cores 1, 1A, 2, and 3 were determined to be acceptable benchmark experiments.
Wang, Xiaoliang; Zheng, Jie; Chen, Hongli, E-mail: hlchen1@ustc.edu.cn
2016-05-15
In our precious study, a prediction model, which calculates the effective thermal conductivity k{sub eff} of mono-sized pebble beds, has been developed and validated. Based on this model, here the effects of these influencing factors such as pebble size, thermal radiation, contact area, filling gas, gas flow, gas pressure, etc. on the k{sub eff} of randomly packed fusion pebble beds are studied and analyzed. The pebble beds investigated include Li{sub 4}SiO{sub 4}, Li{sub 2}ZrO{sub 3}, Li{sub 2}TiO{sub 3}, Li{sub 2}O, Be and BeO pebble beds. In the current study, many important and meaningful conclusions are derived and some of them are similar to the existing research results. Particularly, some critters that under which conditions the effect of some influencing factors can be neglected or should be considered are also presented.
Preliminary neutronic study on Pu-based OTTO cycle pebble bed reactor
Setiadipura, Topan; Zuhair [National Nuclear Energy Agency of Indonesia (BATAN), Selatan (Indonesia). Center for Nuclear Reactor Technology and Safety; Irwanto, Dwi [Bandung Institute of Technology (ITB), Bandung (Indonesia). Nuclear Physics and Biophysics Research Group
2017-12-15
The neutron physics characteristic of Pebble Bed Reactor (PBR) allows a better incineration of plutonium (Pu). An optimized design of simple PBR might give a symbiotic solution of providing a safe energy source, effective fuel utilization shown by a higher burnup value, and incineration of Pu stockpiles. This study perform a preliminary neutronic design study of a 200 MWt Once Through Then Out (OTTO) cycle PBR with Pu-based fuel. The safety criteria of the design were represented by the per-fuel-pebble maximum power generation of 4.5 kW/pebble. In this preliminary phase, the parametric survey is limited to the heavy metal (HM) loading per pebble and the average axial speed of the fuel. An optimum high burnup of 419.7 MWd/kg-HM was achieved in this study. This optimum design uses a HM loading of 2.5 g/pebble with average axial fuel velocity 0.5 cm/day.
Iwadachi, T.; Sakamoto, N.; Nishida, K. [NGK Insulators Ltd., Nagoya (Japan); Kawamura, H.
1998-01-01
The particle size distribution of beryllium pebbles produced by the rotating electrode method was investigated. Particle size depends on some physical properties and process parameters, which can practicaly be controlled by varying electrode angular velocities. The average particle sizes produced were expressed by the hyperbolic function with electrode angular velocity. Particles within the range of 0.3 and 2.0 mm in diameter are readily produced by the rotating electrode method while those of 0.2 mm in diameter are also fabricable. Sphericity and surface roughness were good in each size of pebble. Grain sizes of the pebbles are 17 {mu} m in 0.25 mm diameter pebbles and 260 {mu} m in 1.8 mm diameter pebbles. (author)
Mcwilliams, A. J. [Savannah River Site (SRS), Aiken, SC (United States). Savannah River National Lab. (SRNL)
2015-09-08
This report reviews literature on reprocessing high temperature gas-cooled reactor graphite fuel components. A basic review of the various fuel components used in the pebble bed type reactors is provided along with a survey of synthesis methods for the fabrication of the fuel components. Several disposal options are considered for the graphite pebble fuel elements including the storage of intact pebbles, volume reduction by separating the graphite from fuel kernels, and complete processing of the pebbles for waste storage. Existing methods for graphite removal are presented and generally consist of mechanical separation techniques such as crushing and grinding chemical techniques through the use of acid digestion and oxidation. Potential methods for reprocessing the graphite pebbles include improvements to existing methods and novel technologies that have not previously been investigated for nuclear graphite waste applications. The best overall method will be dependent on the desired final waste form and needs to factor in the technical efficiency, political concerns, cost, and implementation.
Application of discrete element method to study mechanical behaviors of ceramic breeder pebble beds
An Zhiyong; Ying, Alice; Abdou, Mohamed
2007-01-01
In this paper, the discrete element method (DEM) approach has been applied to study mechanical behaviors of ceramic breeder pebble beds. Directly simulating the contact state of each individual particle by the physically based interaction laws, the DEM numerical program is capable of predicting the mechanical behaviors of non-standard packing structures. The program can also provide the data to trace the evolution of contact characteristics and forces as deformation proceeds, as well as the particle movement when the pebble bed is subjected to external loadings. Our numerical simulations focus on predicting the mechanical behaviors of ceramic breeder pebble beds, which include typical fusion breeder materials in solid breeder blankets. Current numerical results clearly show that the packing density and the bed geometry can have an impact on the mechanical stiffness of the pebble beds. Statistical data show that the contact forces are highly related to the contact status of the pebbles
Thermal safety analysis for pebble bed blanket fusion-fission hybrid reactor
Wei Renjie
1998-01-01
Pebble bed blanket hybrid reactor may have more advantages than slab element blanket hybrid reactor in nuclear fuel production and nuclear safety. The thermo-hydraulic calculations of the blanket in the Tokamak helium cooling pebble bed blanket fusion-fission hybrid reactor developed in China are carried out using the Code THERMIX and auxiliary code. In the calculations different fuel pebble material and steady state, depressurization and total loss of flow accident conditions are included. The results demonstrate that the conceptual design of the Tokamak helium cooling pebble bed blanket fusion-fission hybrid reactor with dump tank is feasible and safe enough only if the suitable fuel pebble material is selected and the suitable control system and protection system are established. Some recommendations for due conceptual design are also presented
Graph embedding with rich information through heterogeneous graph
Sun, Guolei
2017-01-01
Graph embedding, aiming to learn low-dimensional representations for nodes in graphs, has attracted increasing attention due to its critical application including node classification, link prediction and clustering in social network analysis. Most
Using Graph and Vertex Entropy to Compare Empirical Graphs with Theoretical Graph Models
Tomasz Kajdanowicz
2016-09-01
Full Text Available Over the years, several theoretical graph generation models have been proposed. Among the most prominent are: the Erdős–Renyi random graph model, Watts–Strogatz small world model, Albert–Barabási preferential attachment model, Price citation model, and many more. Often, researchers working with real-world data are interested in understanding the generative phenomena underlying their empirical graphs. They want to know which of the theoretical graph generation models would most probably generate a particular empirical graph. In other words, they expect some similarity assessment between the empirical graph and graphs artificially created from theoretical graph generation models. Usually, in order to assess the similarity of two graphs, centrality measure distributions are compared. For a theoretical graph model this means comparing the empirical graph to a single realization of a theoretical graph model, where the realization is generated from the given model using an arbitrary set of parameters. The similarity between centrality measure distributions can be measured using standard statistical tests, e.g., the Kolmogorov–Smirnov test of distances between cumulative distributions. However, this approach is both error-prone and leads to incorrect conclusions, as we show in our experiments. Therefore, we propose a new method for graph comparison and type classification by comparing the entropies of centrality measure distributions (degree centrality, betweenness centrality, closeness centrality. We demonstrate that our approach can help assign the empirical graph to the most similar theoretical model using a simple unsupervised learning method.
Handbook of graph grammars and computing by graph transformation
Engels, G; Kreowski, H J; Rozenberg, G
1999-01-01
Graph grammars originated in the late 60s, motivated by considerations about pattern recognition and compiler construction. Since then, the list of areas which have interacted with the development of graph grammars has grown quite impressively. Besides the aforementioned areas, it includes software specification and development, VLSI layout schemes, database design, modeling of concurrent systems, massively parallel computer architectures, logic programming, computer animation, developmental biology, music composition, visual languages, and many others.The area of graph grammars and graph tran
Topics in graph theory graphs and their Cartesian product
Imrich, Wilfried; Rall, Douglas F
2008-01-01
From specialists in the field, you will learn about interesting connections and recent developments in the field of graph theory by looking in particular at Cartesian products-arguably the most important of the four standard graph products. Many new results in this area appear for the first time in print in this book. Written in an accessible way, this book can be used for personal study in advanced applications of graph theory or for an advanced graph theory course.
On two energy-like invariants of line graphs and related graph operations
Xiaodan Chen
2016-02-01
Full Text Available Abstract For a simple graph G of order n, let μ 1 ≥ μ 2 ≥ ⋯ ≥ μ n = 0 $\\mu_{1}\\geq\\mu_{2}\\geq\\cdots\\geq\\mu_{n}=0$ be its Laplacian eigenvalues, and let q 1 ≥ q 2 ≥ ⋯ ≥ q n ≥ 0 $q_{1}\\geq q_{2}\\geq\\cdots\\geq q_{n}\\geq0$ be its signless Laplacian eigenvalues. The Laplacian-energy-like invariant and incidence energy of G are defined as, respectively, LEL ( G = ∑ i = 1 n − 1 μ i and IE ( G = ∑ i = 1 n q i . $$\\mathit{LEL}(G=\\sum_{i=1}^{n-1}\\sqrt{ \\mu_{i}} \\quad\\mbox{and}\\quad \\mathit {IE}(G=\\sum_{i=1}^{n} \\sqrt{q_{i}}. $$ In this paper, we present some new upper and lower bounds on LEL and IE of line graph, subdivision graph, para-line graph and total graph of a regular graph, some of which improve previously known results. The main tools we use here are the Cauchy-Schwarz inequality and the Ozeki inequality.
Integrated design approach of the pebble bed modular using models
Venter, P.J.
2005-01-01
The Pebble Bed Modular Reactor (PBMR) is the first pebble bed reactor that will be utilised in a high temperature direct Brayton cycle configuration. This implies that there are a number of unique features in the PBMR that extend from the German experience base. One of the challenges in the design of the PBMR is managing the integrated design process between the designers, the physicists and the analysts. This integrated design process is managed through model-based development work. Three-dimensional CAD models are constructed of the components and parts in the reactor. From the CAD models, CFD models, neutronic models, shielding models, FEM models and other thermodynamic models are derived. These models range from very simple models to extremely detailed and complex models. The models are used in legacy software as well as commercial off-the-shelf software. The different models are also used in code-to-code comparisons to verify the results. This paper will briefly discuss the different models and the interaction between the models, showing the iterative design process that is used in the development of the reactor at PBMR. (author)
Dynamics of a small direct cycle pebble bed HTR
Verkerk, E.C.; Heek, A.I. van
2001-01-01
The Dutch market for combined generation of heat and power identifies a unit size of 40 MW thermal for the conceptual design of a nuclear cogeneration plant. The ACACIA system provides 14 MW(e) electricity combined with 17 t/h of high temperature steam (220 deg. C, 10 bar) with a pebble bed high temperature reactor directly coupled with a helium compressor and a helium turbine. To come to quantitative statements about the ACACIA transient behaviour, a calculational coupling between the high temperature reactor core analysis code package Panthermix (Panther-Thermix/Direkt) and the thermal hydraulic code RELAP5 for the energy conversion system has been made. This paper will present the analysis of safety related transients. The usual incident scenarios Loss of Coolant Incident (LOCI) and Loss of Flow Incident (LOFI) have been analysed. Besides, also a search for the real maximum fuel temperature (inside a fuel pebble anywhere in the core) has been made. It appears that the maximum fuel temperatures are not reached during a LOFI or LOCI with a halted mass flow rate, but for situations with a small mass flow rate, 1-0.5%. As such, a LOFI or LOCI does not represent the worst-case scenario in terms of maximal fuel temperature. (author)
Power Peaking Effect of OTTO Fuel Scheme Pebble Bed Reactor
Setiadipura, T.; Suwoto; Zuhair; Bakhri, S.; Sunaryo, G. R.
2018-02-01
Pebble Bed Reactor (PBR) type of Hight Temperature Gas-cooled Reactor (HTGR) is a very interesting nuclear reactor design to fulfill the growing electricity and heat demand with a superior passive safety features. Effort to introduce the PBR design to the market can be strengthen by simplifying its system with the Once-through-then-out (OTTO) cycle PBR in which the pebble fuel only pass the core once. Important challenge in the OTTO fuel scheme is the power peaking effect which limit the maximum nominal power or burnup of the design. Parametric survey is perform in this study to investigate the contribution of different design parameters to power peaking effect of OTTO cycle PBR. PEBBED code is utilized in this study to perform the equilibrium PBR core analysis for different design parameter and fuel scheme. The parameters include its core diameter, height-per-diameter (H/D), power density, and core nominal power. Results of this study show that diameter and H/D effectsare stronger compare to the power density and nominal core power. Results of this study might become an importance guidance for design optimization of OTTO fuel scheme PBR.
Torques Induced by Scattered Pebble-flow in Protoplanetary Disks
Benítez-Llambay, Pablo; Pessah, Martin E.
2018-03-01
Fast inward migration of planetary cores is a common problem in the current planet formation paradigm. Even though dust is ubiquitous in protoplanetary disks, its dynamical role in the migration history of planetary embryos has not been assessed. In this Letter, we show that the scattered pebble-flow induced by a low-mass planetary embryo leads to an asymmetric dust-density distribution that is able to exert a net torque. By analyzing a large suite of multifluid hydrodynamical simulations addressing the interaction between the disk and a low-mass planet on a fixed circular orbit, and neglecting dust feedback onto the gas, we identify two different regimes, gas- and gravity-dominated, where the scattered pebble-flow results in almost all cases in positive torques. We collect our measurements in a first torque map for dusty disks, which will enable the incorporation of the effect of dust dynamics on migration into population synthesis models. Depending on the dust drift speed, the dust-to-gas mass ratio/distribution, and the embryo mass, the dust-induced torque has the potential to halt inward migration or even induce fast outward migration of planetary cores. We thus anticipate that dust-driven migration could play a dominant role during the formation history of planets. Because dust torques scale with disk metallicity, we propose that dust-driven outward migration may enhance the occurrence of distant giant planets in higher-metallicity systems.
Bisseling, R.H.; Byrka, J.; Cerav-Erbas, S.; Gvozdenovic, N.; Lorenz, M.; Pendavingh, R.A.; Reeves, C.; Röger, M.; Verhoeven, A.; Berg, van den J.B.; Bhulai, S.; Hulshof, J.; Koole, G.; Quant, C.; Williams, J.F.
2006-01-01
Splitting a large software system into smaller and more manageable units has become an important problem for many organizations. The basic structure of a software system is given by a directed graph with vertices representing the programs of the system and arcs representing calls from one program to
Coloring geographical threshold graphs
Bradonjic, Milan [Los Alamos National Laboratory; Percus, Allon [Los Alamos National Laboratory; Muller, Tobias [EINDHOVEN UNIV. OF TECH
2008-01-01
We propose a coloring algorithm for sparse random graphs generated by the geographical threshold graph (GTG) model, a generalization of random geometric graphs (RGG). In a GTG, nodes are distributed in a Euclidean space, and edges are assigned according to a threshold function involving the distance between nodes as well as randomly chosen node weights. The motivation for analyzing this model is that many real networks (e.g., wireless networks, the Internet, etc.) need to be studied by using a 'richer' stochastic model (which in this case includes both a distance between nodes and weights on the nodes). Here, we analyze the GTG coloring algorithm together with the graph's clique number, showing formally that in spite of the differences in structure between GTG and RGG, the asymptotic behavior of the chromatic number is identical: {chi}1n 1n n / 1n n (1 + {omicron}(1)). Finally, we consider the leading corrections to this expression, again using the coloring algorithm and clique number to provide bounds on the chromatic number. We show that the gap between the lower and upper bound is within C 1n n / (1n 1n n){sup 2}, and specify the constant C.
Budhiraja, A.S.; Mukherjee, D.; Wu, R.
2017-01-01
We consider a variation of the supermarket model in which the servers can communicate with their neighbors and where the neighborhood relationships are described in terms of a suitable graph. Tasks with unit-exponential service time distributions arrive at each vertex as independent Poisson
Kucharik, Marcel; Hofacker, Ivo; Stadler, Peter
2014-01-01
of the folding free energy landscape, however, can provide the relevant information. Results We introduce the basin hopping graph (BHG) as a novel coarse-grained model of folding landscapes. Each vertex of the BHG is a local minimum, which represents the corresponding basin in the landscape. Its edges connect...
The STAPL Parallel Graph Library
Harshvardhan,; Fidel, Adam; Amato, Nancy M.; Rauchwerger, Lawrence
2013-01-01
This paper describes the stapl Parallel Graph Library, a high-level framework that abstracts the user from data-distribution and parallelism details and allows them to concentrate on parallel graph algorithm development. It includes a customizable
Winlaw, Manda [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); De Sterck, Hans [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Sanders, Geoffrey [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-10-26
In very simple terms a network can be de ned as a collection of points joined together by lines. Thus, networks can be used to represent connections between entities in a wide variety of elds including engi- neering, science, medicine, and sociology. Many large real-world networks share a surprising number of properties, leading to a strong interest in model development research and techniques for building synthetic networks have been developed, that capture these similarities and replicate real-world graphs. Modeling these real-world networks serves two purposes. First, building models that mimic the patterns and prop- erties of real networks helps to understand the implications of these patterns and helps determine which patterns are important. If we develop a generative process to synthesize real networks we can also examine which growth processes are plausible and which are not. Secondly, high-quality, large-scale network data is often not available, because of economic, legal, technological, or other obstacles [7]. Thus, there are many instances where the systems of interest cannot be represented by a single exemplar network. As one example, consider the eld of cybersecurity, where systems require testing across diverse threat scenarios and validation across diverse network structures. In these cases, where there is no single exemplar network, the systems must instead be modeled as a collection of networks in which the variation among them may be just as important as their common features. By developing processes to build synthetic models, so-called graph generators, we can build synthetic networks that capture both the essential features of a system and realistic variability. Then we can use such synthetic graphs to perform tasks such as simulations, analysis, and decision making. We can also use synthetic graphs to performance test graph analysis algorithms, including clustering algorithms and anomaly detection algorithms.
Groupies in multitype random graphs
Shang, Yilun
2016-01-01
A groupie in a graph is a vertex whose degree is not less than the average degree of its neighbors. Under some mild conditions, we show that the proportion of groupies is very close to 1/2 in multitype random graphs (such as stochastic block models), which include Erd?s-R?nyi random graphs, random bipartite, and multipartite graphs as special examples. Numerical examples are provided to illustrate the theoretical results.
Groupies in multitype random graphs.
Shang, Yilun
2016-01-01
A groupie in a graph is a vertex whose degree is not less than the average degree of its neighbors. Under some mild conditions, we show that the proportion of groupies is very close to 1/2 in multitype random graphs (such as stochastic block models), which include Erdős-Rényi random graphs, random bipartite, and multipartite graphs as special examples. Numerical examples are provided to illustrate the theoretical results.
Temporal Representation in Semantic Graphs
Levandoski, J J; Abdulla, G M
2007-08-07
A wide range of knowledge discovery and analysis applications, ranging from business to biological, make use of semantic graphs when modeling relationships and concepts. Most of the semantic graphs used in these applications are assumed to be static pieces of information, meaning temporal evolution of concepts and relationships are not taken into account. Guided by the need for more advanced semantic graph queries involving temporal concepts, this paper surveys the existing work involving temporal representations in semantic graphs.
Quantum walks on quotient graphs
Krovi, Hari; Brun, Todd A.
2007-01-01
A discrete-time quantum walk on a graph Γ is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain initial states the walk will be confined to a subspace of the original Hilbert space. Symmetries of the original graph, given by its automorphism group, can be inherited by the evolution operator. We show that a quantum walk confined to the subspace corresponding to this symmetry group can be seen as a different quantum walk on a smaller quotient graph. We give an explicit construction of the quotient graph for any subgroup H of the automorphism group and illustrate it with examples. The automorphisms of the quotient graph which are inherited from the original graph are the original automorphism group modulo the subgroup H used to construct it. The quotient graph is constructed by removing the symmetries of the subgroup H from the original graph. We then analyze the behavior of hitting times on quotient graphs. Hitting time is the average time it takes a walk to reach a given final vertex from a given initial vertex. It has been shown in earlier work [Phys. Rev. A 74, 042334 (2006)] that the hitting time for certain initial states of a quantum walks can be infinite, in contrast to classical random walks. We give a condition which determines whether the quotient graph has infinite hitting times given that they exist in the original graph. We apply this condition for the examples discussed and determine which quotient graphs have infinite hitting times. All known examples of quantum walks with hitting times which are short compared to classical random walks correspond to systems with quotient graphs much smaller than the original graph; we conjecture that the existence of a small quotient graph with finite hitting times is necessary for a walk to exhibit a quantum speedup
Fabrication and characterization of lithium orthosilicate pebbles using LiOH as a new raw material
Knitter, R.; Reimann, J.; Risthaus, P.; Boccaccini, L.V.; Piazza, G.
2004-01-01
For the European Helium Cooled Pebble Bed (HCPB) blanket slightly overstoichiometric lithium orthosilicate pebbles (Li 4 SiO 4 +SiO 2 ) have been chosen as one optional breeder material. This material is developed in collaboration between Research Centre Karlsruhe (FZK) and the Schott Glas, Mainz. The lithium orthosilicate (OSi) pebbles are fabricated by the melting and spraying method in a semi-industrial scale facility. In the past, the not enriched pebbles were produced from a mixture of Li 4 SiO 4 and SiO 2 powders, but due to the fact that enriched Li 4 SiO 4 is not available on the market, highly enriched carbonate powder was used that finally resulted in nonsatisfying pebble characteristics. Enriched LiOH powder is commercially available, therefore, a new production route was pursued based on the following, simplified reaction: 4 LiOH + SiO 2 → Li 4 SiO 4 + 2 H 2 O. The melting process of LiOH and SiO 2 is less difficult to control than the melting of Li 2 CO 3 in spite of the decomposition of water. The pebbles produced from LiOH and SiO 2 are similar to those produced from Li 4 SiO 4 and SiO 2 . They exhibit a distinctly dendritic structure and show only a small amount of pores and cracks. In addition to the main constituent Li 4 SiO 4 , the high temperature phase Li 6 Si 2 O 7 was detected due to the quenching process and the excess of SiO 2 . This minor constituent, however, decomposes to Li 4 SiO 4 and Li 2 SiO 3 during annealing. In compressive crush load tests of single pebbles a crush load of about 9.5 N was measured for pebbles after drying at 300degC. The chemical analysis revealed a further advantage of the use of LiOH in the melting process. As LiOH is available in high-purity quality, the pebbles contain impurities to a lower degree than pebbles produced from Li 4 SiO 4 or Li 2 CO 3 . In order to obtain characteristic pebble bed data, first Uniaxial Compression Tests (UCTs) were performed at temperatures between ambient and at 850deg
Pressurizing Behavior on Ingress of Coolant into Pebble Bed of Blanket of Fusion DEMO Reactor
Daigo Tsuru; Mikio Enoeda; Masato Akiba
2006-01-01
Solid breeder blankets are being developed as candidate blankets for the Fusion DEMO reactor in Japan. JAEA is performing the development of the water cooled and helium cooled solid breeder blankets. The blanket utilizes ceramic breeder pebbles and multiplier pebbles beds cooled by high pressure water or high pressure helium in the cooling tubes placed in the blanket box structure. In the development of the blanket, it is very important to incorporate the safety technology as well as the performance improvement on tritium production and energy conversion. In the safety design and technology, coolant ingress in the blanket box structure is one of the most important events as the initiators. Especially the thermal hydraulics in the pebble bed in the case of the high pressure coolant ingress is very important to evaluate the pressure propagation and coolant flow behavior. This paper presents the preliminary results of the pressure loss characteristics by the coolant ingress in the pebble bed. Experiments have been performed by using alumina pebble bed (4 litter maximum volume of the pebble bed) and nitrogen gas to simulate the helium coolant ingress into breeder and multiplier pebble beds. Reservoir tank of 10 liter is filled with 1.0 MPa nitrogen. The nitrogen gas is released at the bottom part of the alumina pebble bed whose upper part is open to the atmosphere. The pressure change in the pebble bed is measured to identify the pressure loss. The measured values are compared with the predicted values by Ergun's equation, which is the correlation equation on pressure loss of the flow through porous medium. By the results of the experiments with no constraint on the alumina pebble bed, it was clarified that the measured value agreed in the lower flow rate. However, in the higher flow rate where the pressure loss is high, the measured value is about half of the predicted value. The differences between the measured values and the predicted values will be discussed from
A generalization of total graphs
M Afkhami
2018-04-12
Apr 12, 2018 ... product of any lower triangular matrix with the transpose of any element of U belongs to U. The ... total graph of R, which is denoted by T( (R)), is a simple graph with all elements of R as vertices, and ...... [9] Badawi A, On dot-product graph of a commutative ring, Communications in Algebra 43 (2015). 43–50.
Graph transformation tool contest 2008
Rensink, Arend; van Gorp, Pieter
This special section is the outcome of the graph transformation tool contest organised during the Graph-Based Tools (GraBaTs) 2008 workshop, which took place as a satellite event of the International Conference on Graph Transformation (ICGT) 2008. The contest involved two parts: three “off-line case
On dominator colorings in graphs
colors required for a dominator coloring of G is called the dominator .... Theorem 1.3 shows that the complete graph Kn is the only connected graph of order n ... Conversely, if a graph G satisfies condition (i) or (ii), it is easy to see that χd(G) =.
Xuan, Junyu; Lu, Jie; Zhang, Guangquan; Luo, Xiangfeng
2015-12-01
Graph mining has been a popular research area because of its numerous application scenarios. Many unstructured and structured data can be represented as graphs, such as, documents, chemical molecular structures, and images. However, an issue in relation to current research on graphs is that they cannot adequately discover the topics hidden in graph-structured data which can be beneficial for both the unsupervised learning and supervised learning of the graphs. Although topic models have proved to be very successful in discovering latent topics, the standard topic models cannot be directly applied to graph-structured data due to the "bag-of-word" assumption. In this paper, an innovative graph topic model (GTM) is proposed to address this issue, which uses Bernoulli distributions to model the edges between nodes in a graph. It can, therefore, make the edges in a graph contribute to latent topic discovery and further improve the accuracy of the supervised and unsupervised learning of graphs. The experimental results on two different types of graph datasets show that the proposed GTM outperforms the latent Dirichlet allocation on classification by using the unveiled topics of these two models to represent graphs.
Isotropic covariance functions on graphs and their edges
Anderes, E.; Møller, Jesper; Rasmussen, Jakob Gulddahl
We develop parametric classes of covariance functions on linear networks and their extension to graphs with Euclidean edges, i.e., graphs with edges viewed as line segments or more general sets with a coordinate system allowing us to consider points on the graph which are vertices or points...... on an edge. Our covariance functions are defined on the vertices and edge points of these graphs and are isotropic in the sense that they depend only on the geodesic distance or on a new metric called the resistance metric (which extends the classical resistance metric developed in electrical network theory...... functions in the spatial statistics literature (the power exponential, Matérn, generalized Cauchy, and Dagum classes) are shown to be valid with respect to the resistance metric for any graph with Euclidean edges, whilst they are only valid with respect to the geodesic metric in more special cases....
Xhonneux, Andre, E-mail: a.xhonneux@fz-juelich.de [Forschungszentrum Jülich, 52425 Jülich (Germany); Institute for Reactor Safety and Reactor Technology, RWTH-Aachen, 52064 Aachen (Germany); Kasselmann, Stefan; Rütten, Hans-Jochem [Forschungszentrum Jülich, 52425 Jülich (Germany); Becker, Kai [Institute for Reactor Safety and Reactor Technology, RWTH-Aachen, 52064 Aachen (Germany); Allelein, Hans-Josef [Forschungszentrum Jülich, 52425 Jülich (Germany); Institute for Reactor Safety and Reactor Technology, RWTH-Aachen, 52064 Aachen (Germany)
2014-05-01
The history of gas-cooled high-temperature reactor prototypes in Germany is closely related to Forschungszentrum Jülich and its “Institute of Nuclear Waste Disposal and Reactor Safety (IEK-6)”. A variety of computer codes have been developed, validated and optimized to simulate the different safety and operational aspects of V/HTR. In order to overcome the present limitations of these codes and to exploit the advantages of modern computer clusters, a project has been initiated to integrate these individual programs into a consistent V/HTR code package (VHCP) applying state-of-the-art programming techniques and standards. One important aspect in the simulation of a V/HTR is the modeling of a continuous moving pebble bed or the periodic rearrangement of prismatic block type fuel. Present models are either too coarse to take special issues (e.g. pebble piles) into account or are too detailed and therefore too time consuming to be applicable in the HCP. The new Software for Handling Universal Fuel Elements (SHUFLE) recently being developed is well suited to close this gap. Although at first the code has been designed for pebble bed reactors, it can in principal be applied to all other types of nuclear fuel. The granularity of the mesh grid meets the requirements to consider these special issues while keeping the used computing power within reasonable limits. New features are for example the possibility to consider azimuthally differing flow velocities in the case of a pebble bed reactor or individual void factors to simulate effects to seismic events. The general idea behind this new approach to the simulation of pebble bed reactors is the following: In the preprocessing step, experimental flow lines or flow lines simulated by more detailed codes serve as an input. For each radial mesh column a representative flow line is then determined by interpolation. These representative flow lines are finally mapped to a user defined rectangular grid forming chains of meshes
Xhonneux, Andre; Kasselmann, Stefan; Rütten, Hans-Jochem; Becker, Kai; Allelein, Hans-Josef
2014-01-01
The history of gas-cooled high-temperature reactor prototypes in Germany is closely related to Forschungszentrum Jülich and its “Institute of Nuclear Waste Disposal and Reactor Safety (IEK-6)”. A variety of computer codes have been developed, validated and optimized to simulate the different safety and operational aspects of V/HTR. In order to overcome the present limitations of these codes and to exploit the advantages of modern computer clusters, a project has been initiated to integrate these individual programs into a consistent V/HTR code package (VHCP) applying state-of-the-art programming techniques and standards. One important aspect in the simulation of a V/HTR is the modeling of a continuous moving pebble bed or the periodic rearrangement of prismatic block type fuel. Present models are either too coarse to take special issues (e.g. pebble piles) into account or are too detailed and therefore too time consuming to be applicable in the HCP. The new Software for Handling Universal Fuel Elements (SHUFLE) recently being developed is well suited to close this gap. Although at first the code has been designed for pebble bed reactors, it can in principal be applied to all other types of nuclear fuel. The granularity of the mesh grid meets the requirements to consider these special issues while keeping the used computing power within reasonable limits. New features are for example the possibility to consider azimuthally differing flow velocities in the case of a pebble bed reactor or individual void factors to simulate effects to seismic events. The general idea behind this new approach to the simulation of pebble bed reactors is the following: In the preprocessing step, experimental flow lines or flow lines simulated by more detailed codes serve as an input. For each radial mesh column a representative flow line is then determined by interpolation. These representative flow lines are finally mapped to a user defined rectangular grid forming chains of meshes
Fabrication of Li{sub 2}TiO{sub 3} pebbles by a freeze drying process
Lee, Sang-Jin, E-mail: lee@mokpo.ac.kr [Department of Advanced Materials Science and Engineering, Mokpo National University, Muan 534-729 (Korea, Republic of); Park, Yi-Hyun [National Fusion Research Institute, Daejeon 305-806 (Korea, Republic of); Yu, Min-Woo [Department of Advanced Materials Science and Engineering, Mokpo National University, Muan 534-729 (Korea, Republic of)
2013-11-15
Li{sub 2}TiO{sub 3} pebbles were successfully fabricated by using a freeze drying process. The Li{sub 2}TiO{sub 3} slurry was prepared using a commercial powder of particle size 0.5–1.5 μm and the pebble pre-form was prepared by dropping the slurry into liquid nitrogen through a syringe needle. The droplets were rapidly frozen, changing their morphology to spherical pebbles. The frozen pebbles were dried at −10 °C in vacuum. To make crack-free pebbles, some glycerin was employed in the slurry, and long drying time and a low vacuum condition were applied in the freeze drying process. In the process, the solid content in the slurry influenced the spheroidicity of the pebble green body. The dried pebbles were sintered at 1200 °C in an air atmosphere. The sintered pebbles showed almost 40% shrinkage. The sintered pebbles revealed a porous microstructure with a uniform pore distribution and the sintered pebbles were crushed under an average load of 50 N in a compressive strength test. In the present study, a freeze drying process for fabrication of spherical Li{sub 2}TiO{sub 3} pebbles is introduced. The processing parameters, such as solid content in the slurry and the conditions of freeze drying and sintering, are also examined.
Chakin, V., E-mail: vladimir.chakin@kit.edu [Karlsruhe Institute of Technology, Institute for Applied Materials, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen (Germany); Rolli, R.; Moeslang, A.; Klimenkov, M.; Kolb, M.; Vladimirov, P.; Kurinskiy, P.; Schneider, H.-C. [Karlsruhe Institute of Technology, Institute for Applied Materials, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen (Germany); Til, S. van; Magielsen, A.J. [Nuclear Research and Consultancy Group, Westerduinweg 3, Postbus 25, 1755 ZG Petten (Netherlands); Zmitko, M. [The European Joint Undertaking for ITER and the Development of Fusion Energy, c/Josep Pla, no. 2, Torres Diagonal Litoral, Edificio B3, 08019 Barcelona (Spain)
2013-11-15
The current helium cooled pebble bed (HCPB) tritium breeding blanket concept for fusion reactors includes a bed of 1 mm diameter beryllium pebbles to act as a neutron multiplier. Beryllium pebbles, fabricated by the rotating electrode method, were neutron irradiated in the HFR in Petten within the HIDOBE-01 experiment. This study presents tritium release and retention properties and data on microstructure evolution of beryllium pebbles irradiated at 630, 740, 873, 948 K up to a damage dose of 18 dpa, corresponding to a helium accumulation of about 3000 appm. The measured cumulative released activity from the beryllium pebbles irradiated at 948 K was found to be significantly lower than the calculated value. After irradiation at 873 and 948 K scanning electron microscopy (SEM) and transmission electron microscopy (TEM) analyses revealed large pores or bubbles in the bulk and oxide films with a thickness of up to 8 μm at the surface of the beryllium pebbles. The radiation-enhanced diffusion of tritium and the formation of open porosity networks accelerate the tritium release from the beryllium pebbles during the high-flux neutron irradiation.
Chakin, V., E-mail: vladimir.chakin@kit.edu [Karlsruhe Institute of Technology, Institite for Applied Materials, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen (Germany); Rolli, R.; Moeslang, A. [Karlsruhe Institute of Technology, Institite for Applied Materials, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen (Germany); Zmitko, M. [The European Joint Undertaking for ITER and the Development of Fusion Energy, c/Josep Pla, no. 2, Torres Diagonal Litoral, Edificio B3, 08019 Barcelona (Spain)
2015-04-15
Highlights: • Compression tests of highly neutron irradiated beryllium pebbles have been performed. • Irradiation hardening of beryllium pebbles decreases the steady-state strain-rates. • The steady-state strain-rates of irradiated beryllium pebbles exceed their swelling rates. - Abstract: Results: of mechanical compression tests of irradiated and non-irradiated beryllium pebbles with diameters of 1 and 2 mm are presented. The neutron irradiation was performed in the HFR in Petten, The Netherlands at 686–968 K up to 1890–2950 appm helium production. The irradiation at 686 and 753 K cause irradiation hardening due to the gas bubble formation in beryllium. The irradiation-induced hardening leads to decrease of steady-state strain-rates of irradiated beryllium pebbles compared to non-irradiated ones. In contrary, after irradiation at higher temperatures of 861 and 968 K, the steady-state strain-rates of the pebbles increase because annealing of irradiation defects and softening of the material take place. It was shown that the steady-state strain-rates of irradiated beryllium pebbles always exceed their swelling rates.
Numerical and experimental characterization of ceramic pebble beds under cycling mechanical loading
Pupeschi, S., E-mail: pupeschi.simone@hotmail.it [Institute for Applied Materials, Karlsruhe Institute of Technology (KIT) (Germany); Knitter, R.; Kamlah, M. [Institute for Applied Materials, Karlsruhe Institute of Technology (KIT) (Germany); Gan, Y. [School of Civil Engineering, The University of Sydney, Sydney, NSW, 2006 (Australia)
2016-11-15
Highlights: • The effect of cyclic loading on the mechanical response of pebble beds was assessed. • Numerical simulations were performed with KIT-DEM code. • The numerical simulations were compared with the experimental outcomes. • A good qualitative agreement between experimental and simulation results was found. • The pebble size distribution affects the mechanical response of the assemblies. - Abstract: All solid breeder concepts considered to be tested in ITER (International Thermonuclear Experimental Reactor), make use of lithium-based ceramics in the form of pebble-packed beds as tritium breeder. A thorough understanding of the thermal and mechanical properties of the ceramic pebble beds under fusion relevant conditions is essential for the design of the breeder blanket modules of future fusion reactors. In this study, the effect of cyclic loading on the mechanical behaviour of pebble bed assemblies was investigated using a Discrete Element Method (DEM) code. The numerical simulations were compared with the experimental outcomes. The results of numerical simulations show that the pebble size distribution affects noticeably the stress-strain behaviour of the assemblies. A good qualitative agreement between experimental and simulation results was found in terms of difference between residual strains of consecutive cycles. An increase of the oedometric modulus with the compressive load was observed for all investigated compositions in both experimental and DEM simulations. The numerical results show an increase of the oedometric modulus (E) with progressive compaction of the assemblies due to the cycling loading, while no significant influence of the pebbles size distribution was observed.
Particle flow of ceramic breeder pebble beds in bi-axial compression experiments
Hermsmeyer, S.; Reimann, J.
2002-01-01
Pebble beds of Tritium breeding ceramic material are investigated within the framework of developing solid breeder blankets for future nuclear fusion power plants. For the thermo-mechanical characterisation of such pebble beds, bed compression experiments are the standard tools. New bi-axial compression experiments on 20 and 30 mm high pebble beds show pebble flow effects much more pronounced than in previous 10 mm beds. Owing to the greater bed height, conditions are reached where the bed fails in cross direction and unhindered flow of the pebbles occurs. The paper presents measurements for the orthosilicate and metatitanate breeder materials that are envisaged to be used in a solid breeder blanket. The data are compared with calculations made with a Drucker-Prager soil model within the finite-element code ABAQUS, calibrated with data from other experiments. It is investigated empirically whether internal bed friction angles can be determined from pebble beds of the considered heights, which would simplify, and broaden the data base for, the calibration of the Drucker-Prager pebble bed models
Harary, Frank
2015-01-01
Presented in 1962-63 by experts at University College, London, these lectures offer a variety of perspectives on graph theory. Although the opening chapters form a coherent body of graph theoretic concepts, this volume is not a text on the subject but rather an introduction to the extensive literature of graph theory. The seminar's topics are geared toward advanced undergraduate students of mathematics.Lectures by this volume's editor, Frank Harary, include ""Some Theorems and Concepts of Graph Theory,"" ""Topological Concepts in Graph Theory,"" ""Graphical Reconstruction,"" and other introduc
Spectral fluctuations of quantum graphs
Pluhař, Z.; Weidenmüller, H. A.
2014-01-01
We prove the Bohigas-Giannoni-Schmit conjecture in its most general form for completely connected simple graphs with incommensurate bond lengths. We show that for graphs that are classically mixing (i.e., graphs for which the spectrum of the classical Perron-Frobenius operator possesses a finite gap), the generating functions for all (P,Q) correlation functions for both closed and open graphs coincide (in the limit of infinite graph size) with the corresponding expressions of random-matrix theory, both for orthogonal and for unitary symmetry
Dynamic Representations of Sparse Graphs
Brodal, Gerth Stølting; Fagerberg, Rolf
1999-01-01
We present a linear space data structure for maintaining graphs with bounded arboricity—a large class of sparse graphs containing e.g. planar graphs and graphs of bounded treewidth—under edge insertions, edge deletions, and adjacency queries. The data structure supports adjacency queries in worst...... case O(c) time, and edge insertions and edge deletions in amortized O(1) and O(c+log n) time, respectively, where n is the number of nodes in the graph, and c is the bound on the arboricity....
Domination criticality in product graphs
M.R. Chithra
2015-07-01
Full Text Available A connected dominating set is an important notion and has many applications in routing and management of networks. Graph products have turned out to be a good model of interconnection networks. This motivated us to study the Cartesian product of graphs G with connected domination number, γc(G=2,3 and characterize such graphs. Also, we characterize the k−γ-vertex (edge critical graphs and k−γc-vertex (edge critical graphs for k=2,3 where γ denotes the domination number of G. We also discuss the vertex criticality in grids.
Graph Creation, Visualisation and Transformation
Maribel Fernández
2010-03-01
Full Text Available We describe a tool to create, edit, visualise and compute with interaction nets - a form of graph rewriting systems. The editor, called GraphPaper, allows users to create and edit graphs and their transformation rules using an intuitive user interface. The editor uses the functionalities of the TULIP system, which gives us access to a wealth of visualisation algorithms. Interaction nets are not only a formalism for the specification of graphs, but also a rewrite-based computation model. We discuss graph rewriting strategies and a language to express them in order to perform strategic interaction net rewriting.
Study of Chromatic parameters of Line, Total, Middle graphs and Graph operators of Bipartite graph
Nagarathinam, R.; Parvathi, N.
2018-04-01
Chromatic parameters have been explored on the basis of graph coloring process in which a couple of adjacent nodes receives different colors. But the Grundy and b-coloring executes maximum colors under certain restrictions. In this paper, Chromatic, b-chromatic and Grundy number of some graph operators of bipartite graph has been investigat
Pebble-isolation mass: Scaling law and implications for the formation of super-Earths and gas giants
Bitsch, Bertram; Morbidelli, Alessandro; Johansen, Anders; Lega, Elena; Lambrechts, Michiel; Crida, Aurélien
2018-04-01
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. We use 3D hydrodynamical simulations to measure the pebble isolation mass and derive a simple scaling law that captures the dependence on the local disc structure and the turbulent viscosity parameter α. We find that small pebbles, coupled to the gas, with Stokes number τf gap at pebble isolation mass. 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. Compared to models neglecting the dependence of the pebble isolation mass on the α-viscosity, our models including this effect result in higher core masses for giant planets. These higher core masses are more similar to the core masses of the giant planets in the solar system.
Hendrix, William; Jenkins, John; Padmanabhan, Kanchana; Chakraborty, Arpan
2014-01-01
Practical Graph Mining with R presents a "do-it-yourself" approach to extracting interesting patterns from graph data. It covers many basic and advanced techniques for the identification of anomalous or frequently recurring patterns in a graph, the discovery of groups or clusters of nodes that share common patterns of attributes and relationships, the extraction of patterns that distinguish one category of graphs from another, and the use of those patterns to predict the category of new graphs. Hands-On Application of Graph Data Mining Each chapter in the book focuses on a graph mining task, such as link analysis, cluster analysis, and classification. Through applications using real data sets, the book demonstrates how computational techniques can help solve real-world problems. The applications covered include network intrusion detection, tumor cell diagnostics, face recognition, predictive toxicology, mining metabolic and protein-protein interaction networks, and community detection in social networks. De...
Canonical Labelling of Site Graphs
Nicolas Oury
2013-06-01
Full Text Available We investigate algorithms for canonical labelling of site graphs, i.e. graphs in which edges bind vertices on sites with locally unique names. We first show that the problem of canonical labelling of site graphs reduces to the problem of canonical labelling of graphs with edge colourings. We then present two canonical labelling algorithms based on edge enumeration, and a third based on an extension of Hopcroft's partition refinement algorithm. All run in quadratic worst case time individually. However, one of the edge enumeration algorithms runs in sub-quadratic time for graphs with "many" automorphisms, and the partition refinement algorithm runs in sub-quadratic time for graphs with "few" bisimulation equivalences. This suite of algorithms was chosen based on the expectation that graphs fall in one of those two categories. If that is the case, a combined algorithm runs in sub-quadratic worst case time. Whether this expectation is reasonable remains an interesting open problem.
Tamulevičius, Sigitas; Zariņš, A.; Valtenbergs, O.
2017-01-01
Modified lithium orthosilicate (Li4SiO4) pebbles with additions of titanium dioxide (TiO2) are suggested as an alternative tritium breeding ceramic for the European solid breeder test blanket module. The noble metals – platinum (Pt), gold (Au) and rhodium (Rh), can be introduced into the modified...... Li4SiO4 pebbles during the melt-based process, due to the corrosion of Pt-Rh and Pt-Au alloy crucible components. In this study, the surface microstructure, chemical and phase composition of the modified Li4SiO4 pebbles with different contents of the noble metals was analysed. The influence...
Park, Yi-Hyun, E-mail: yhpark@nfri.re.kr [National Fusion Research Institute, Daejeon (Korea, Republic of); Min, Kyung-Mi; Ahn, Mu-Young; Cho, Seungyon; Lee, Young-Min [National Fusion Research Institute, Daejeon (Korea, Republic of); Park, Sang-Jin; Danish, Rehan; Lim, Chul-Hwan; Jo, Yong-Dae [IVT Co., Ltd., Daegu (Korea, Republic of)
2016-11-01
Highlights: • An automatic dispensing system was developed to improve uniformity and production rate of breeder pebbles. • The production rate of this system for Li{sub 2}TiO{sub 3} pebble was estimated at 50 kg/year. • The optimization of dispensing and sintering conditions for the mass-production of Li{sub 2}TiO{sub 3} pebble was conducted. • Integrity of Li{sub 2}TiO{sub 3} pebble was able to be ensured during mass-production process, especially during batch process. - Abstract: Lithium metatitanate (Li{sub 2}TiO{sub 3}) is being considered as tritium breeding material for solid-type breeding blanket, which are used in pebble-bed form. The total amount of Li{sub 2}TiO{sub 3} pebbles in Helium Cooled Ceramic Reflector (HCCR) Test Blanket Module (TBM) is approximately 80 kg. Furthermore, DEMO reactor requires a great deal of breeder pebbles. Therefore, the development of mass-production system for breeder pebbles is necessary. The slurry droplet wetting method was adopted in the mass-production process for Li{sub 2}TiO{sub 3} pebbles, which had been developed in Korea. In this method, an automatic slurry dispensing system is one of the key apparatuses because the uniformity of pebbles and production rate are able to be improved. The system was successfully manufactured, which was consisted of a dispensing unit for instillation of Li{sub 2}TiO{sub 3} slurry, a glycerin bath for hardening of droplets, and an automatic maintaining unit for constant distance between syringe needle and glycerin surface. The production rate of this system for Li{sub 2}TiO{sub 3} pebble was estimated at 50 kg/year. In this study, it was investigated that the effect of dispensing and sintering conditions on the mass-production of Li{sub 2}TiO{sub 3} pebbles.
Year One Summary of X-energy Pebble Fuel Development at ORNL
Helmreich, Grant W. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Hunn, John D. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); McMurray, Jake W. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Hunt, Rodney D. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Jolly, Brian C. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Trammell, Michael P. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Brown, Daniel R. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Blamer, Brandon J. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Reif, Tyler J. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Kim, Howard T. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
2017-06-01
The Advanced Reactor Concepts X-energy (ARC-Xe) Pebble Fuel Development project at Oak Ridge National Laboratory (ORNL) has successfully completed its first year, having made excellent progress in accomplishing programmatic objectives. The primary focus of research at ORNL in support of X-energy has been the training of X-energy fuel fabrication engineers and the establishment of US pebble fuel production capabilities able to supply the Xe-100 pebble-bed reactor. These efforts have been strongly supported by particle fuel fabrication and characterization expertise present at ORNL from the Advanced Gas Reactor (AGR) Fuel Development and Qualification Program.
An analytical evaluation for spatial-dependent intra-pebble Dancoff factor and escape probability
Kim, Songhyun; Kim, Hong-Chul; Kim, Jong Kyung; Kim, Soon Young; Noh, Jae Man
2009-01-01
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. (author)
Syed, M. Qasim; Lovatt, Ian
2014-01-01
This paper is an addition to the series of papers on the exponential function begun by Albert Bartlett. In particular, we ask how the graph of the exponential function y = e[superscript -t/t] would appear if y were plotted versus ln t rather than the normal practice of plotting ln y versus t. In answering this question, we find a new way to…
Understanding Charts and Graphs.
1987-07-28
Farenheit degrees, which have no Onaturalo zero ); finally, ratio scales have numbers that are ordered so that the magnitudes of differences are important and...system. They have to do with the very nature of how marks serve as meaningful symbols. In the ideal case, a chart or graph will be absolutely unambiguous...and these laws comprise this principle (see Stevens, 1974). Absolute discriminability: A minimal magnitude of a mark is necessary for it to be detected
Applicability of the Directed Graph Methodology
Huszti, Jozsef [Institute of Isotope of the Hungarian Academy of Sciences, Budapest (Hungary); Nemeth, Andras [ESRI Hungary, Budapest (Hungary); Vincze, Arpad [Hungarian Atomic Energy Authority, Budapest (Hungary)
2012-06-15
Possible methods to construct, visualize and analyse the 'map' of the State's nuclear infrastructure based on different directed graph approaches are proposed. The transportation and the flow network models are described in detail. The use of the possible evaluation methodologies and the use of available software tools to construct and maintain the nuclear 'map' using pre-defined standard building blocks (nuclear facilities) are introduced and discussed.
Pebble Bed Reactor: core physics and fuel cycle analysis
Vondy, D.R.; Worley, B.A.
1979-10-01
The Pebble Bed Reactor is a gas-cooled, graphite-moderated high-temperature reactor that is continuously fueled with small spherical fuel elements. The projected performance was studied over a broad range of reactor applicability. Calculations were done for a burner on a throwaway cycle, a converter with recycle, a prebreeder and breeder. The thorium fuel cycle was considered using low, medium (denatured), and highly enriched uranium. The base calculations were carried out for electrical energy generation in a 1200 MW/sub e/ plant. A steady-state, continuous-fueling model was developed and one- and two-dimensional calculations were used to characterize performance. Treating a single point in time effects considerable savings in computer time as opposed to following a long reactor history, permitting evaluation of reactor performance over a broad range of design parameters and operating modes.
Pebble bed reactor with one-zone core
Mueller-Frank, U.; Lohnert, G.
1977-01-01
The claim deals with measures to differentiate the flow rate and to remove spherical fuel elements in the core of a pebble bed reactor. Hence the vertical rate of the fuel elements in the border region is for example twice as much as in the centre. A central funnel-shaped outlet on the floor of the core container over which a conical body is placed with its peak pointing upwards, or also the forming of several outlets can be used to adjust to a certain exit rate for the fuel elements. The main target of the invention is a radially extensively constant coolant outlet temperature at the outlet of the core which determines the effectiveness of the connected heat exchanger and thus contributes to economy. (UA) [de
Uranium deposits in Proterozoic quartz-pebble conglomerates
1987-09-01
This report is the result of an effort to gather together the most important information on uranium deposits in Proterozoic quartz-pebble conglomerates in the United States of America, Canada, Finland, Ghana, South Africa and Australia. The paper discusses the uranium potential (and in some cases also the gold potential in South Africa, Western Australia and Ghana) in terms of ores, sedimentation, mineralization, metamorphism, placers, geologic formations, stratigraphy, petrology, exploration, tectonics and distribution. Geologic history and application of geologic models are also discussed. Glacial outwash and water influx is also mentioned. The uranium deposits in a number of States in the USA are covered. The Witwatersrand placers are discussed in several papers. Refs, figs, tabs
Tightly Coupled Multiphysics Algorithm for Pebble Bed Reactors
Park, HyeongKae; Knoll, Dana; Gaston, Derek; Martineau, Richard
2010-01-01
We have developed a tightly coupled multiphysics simulation tool for the pebble-bed reactor (PBR) concept, a type of Very High-Temperature gas-cooled Reactor (VHTR). The simulation tool, PRONGHORN, takes advantages of the Multiphysics Object-Oriented Simulation Environment library, and is capable of solving multidimensional thermal-fluid and neutronics problems implicitly with a Newton-based approach. Expensive Jacobian matrix formation is alleviated via the Jacobian-free Newton-Krylov method, and physics-based preconditioning is applied to minimize Krylov iterations. Motivation for the work is provided via analysis and numerical experiments on simpler multiphysics reactor models. We then provide detail of the physical models and numerical methods in PRONGHORN. Finally, PRONGHORN's algorithmic capability is demonstrated on a number of PBR test cases.
'Once through' cycles in the pebble bed HTR
Teuchert, E.
1977-12-01
In the pebble bed HTR the 'Once Through' cycles achieve a favorable conservation of uranium resources due to their high burnup and due to the relatively low fissile inventory. A detailed study is given for cycles with highly enriched uranium and thorium, 20% enriched uranium and thorium, and for the low (approximately 8%) enriched cycle. The recommended cycle is based on the known THTR fuel element in the Th/U (93%) cycle. The variant with separate Seed elements and Breed elements presents the best pioneer in view of later recycling and thermal breeding. The minimum proliferation risk is achieved in the Th/U (20%) cycle basing on the fuel element type of the AVR, due to the low amount and high denaturization of the disloaded plutonium. (orig.) [de
Pebble Fuel Handling and Reactivity Control for Salt-Cooled High Temperature Reactors
Peterson, Per [Univ. of California, Berkeley, CA (United States). Dept. of Nuclear Engineering; Greenspan, Ehud [Univ. of California, Berkeley, CA (United States). Dept. of Nuclear Engineering
2015-02-09
This report documents the work completed on the X-PREX facility under NEUP Project 11- 3172. This project seeks to demonstrate the viability of pebble fuel handling and reactivity control for fluoride salt-cooled high-temperature reactors (FHRs). The research results also improve the understanding of pebble motion in helium-cooled reactors, as well as the general, fundamental understanding of low-velocity granular flows. Successful use of pebble fuels in with salt coolants would bring major benefits for high-temperature reactor technology. Pebble fuels enable on-line refueling and operation with low excess reactivity, and thus simpler reactivity control and improved fuel utilization. If fixed fuel designs are used, the power density of salt- cooled reactors is limited to 10 MW/m^{3} to obtain adequate duration between refueling, but pebble fuels allow power densities in the range of 20 to 30 MW/m^{3}. This can be compared to the typical modular helium reactor power density of 5 MW/m3. Pebble fuels also permit radial zoning in annular cores and use of thorium or graphite pebble blankets to reduce neutron fluences to outer radial reflectors and increase total power production. Combined with high power conversion efficiency, compact low-pressure primary and containment systems, and unique safety characteristics including very large thermal margins (>500°C) to fuel damage during transients and accidents, salt-cooled pebble fuel cores offer the potential to meet the major goals of the Advanced Reactor Concepts Development program to provide electricity at lower cost than light water reactors with improved safety and system performance.This report presents the facility description, experimental results, and supporting simulation methods of the new X-Ray Pebble Recirculation Experiment (X-PREX), which is now operational and being used to collect data on the behavior of slow dense granular flows relevant to pebble bed reactor core designs. The X
Pebble Fuel Handling and Reactivity Control for Salt-Cooled High Temperature Reactors
Peterson, Per; Greenspan, Ehud
2015-01-01
This report documents the work completed on the X-PREX facility under NEUP Project 11- 3172. This project seeks to demonstrate the viability of pebble fuel handling and reactivity control for fluoride salt-cooled high-temperature reactors (FHRs). The research results also improve the understanding of pebble motion in helium-cooled reactors, as well as the general, fundamental understanding of low-velocity granular flows. Successful use of pebble fuels in with salt coolants would bring major benefits for high-temperature reactor technology. Pebble fuels enable on-line refueling and operation with low excess reactivity, and thus simpler reactivity control and improved fuel utilization. If fixed fuel designs are used, the power density of salt- cooled reactors is limited to 10 MW/m 3 to obtain adequate duration between refueling, but pebble fuels allow power densities in the range of 20 to 30 MW/m 3 . This can be compared to the typical modular helium reactor power density of 5 MW/m3. Pebble fuels also permit radial zoning in annular cores and use of thorium or graphite pebble blankets to reduce neutron fluences to outer radial reflectors and increase total power production. Combined with high power conversion efficiency, compact low-pressure primary and containment systems, and unique safety characteristics including very large thermal margins (>500°C) to fuel damage during transients and accidents, salt-cooled pebble fuel cores offer the potential to meet the major goals of the Advanced Reactor Concepts Development program to provide electricity at lower cost than light water reactors with improved safety and system performance.This report presents the facility description, experimental results, and supporting simulation methods of the new X-Ray Pebble Recirculation Experiment (X-PREX), which is now operational and being used to collect data on the behavior of slow dense granular flows relevant to pebble bed reactor core designs. The X-PREX facility uses novel
Stability analysis of switched linear systems defined by graphs
Athanasopoulos, N.; Lazar, M.
2014-01-01
We present necessary and sufficient conditions for global exponential stability for switched discrete-time linear systems, under arbitrary switching, which is constrained within a set of admissible transitions. The class of systems studied includes the family of systems under arbitrary switching,
A characterization of horizontal visibility graphs and combinatorics on words
Gutin, Gregory; Mansour, Toufik; Severini, Simone
2011-06-01
A Horizontal Visibility Graph (HVG) is defined in association with an ordered set of non-negative reals. HVGs realize a methodology in the analysis of time series, their degree distribution being a good discriminator between randomness and chaos Luque et al. [B. Luque, L. Lacasa, F. Ballesteros, J. Luque, Horizontal visibility graphs: exact results for random time series, Phys. Rev. E 80 (2009), 046103]. We prove that a graph is an HVG if and only if it is outerplanar and has a Hamilton path. Therefore, an HVG is a noncrossing graph, as defined in algebraic combinatorics Flajolet and Noy [P. Flajolet, M. Noy, Analytic combinatorics of noncrossing configurations, Discrete Math., 204 (1999) 203-229]. Our characterization of HVGs implies a linear time recognition algorithm. Treating ordered sets as words, we characterize subfamilies of HVGs highlighting various connections with combinatorial statistics and introducing the notion of a visible pair. With this technique, we determine asymptotically the average number of edges of HVGs.
Bess, John D. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Montierth, Leland M. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Sterbentz, James W. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Briggs, J. Blair [Idaho National Lab. (INL), Idaho Falls, ID (United States); Gougar, Hans D. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Snoj, Luka [Jozef Stefan Inst. (IJS), Ljubljana (Slovenia); Lengar, Igor [Jozef Stefan Inst. (IJS), Ljubljana (Slovenia); Koberl, Oliver [Paul Scherrer Inst. (PSI), Villigen (Switzerland)
2014-03-01
In its deployment as a pebble bed reactor (PBR) critical facility from 1992 to 1996, the PROTEUS facility was designated as HTR-PROTEUS. This experimental program was performed as part of an International Atomic Energy Agency (IAEA) Coordinated Research Project (CRP) on the Validation of Safety Related Physics Calculations for Low Enriched HTGRs. Within this project, critical experiments were conducted for graphite moderated LEU systems to determine core reactivity, flux and power profiles, reaction-rate ratios, the worth of control rods, both in-core and reflector based, the worth of burnable poisons, kinetic parameters, and the effects of moisture ingress on these parameters. One benchmark experiment was evaluated in this report: Core 4. Core 4 represents the only configuration with random pebble packing in the HTR-PROTEUS series of experiments, and has a moderator-to-fuel pebble ratio of 1:1. Three random configurations were performed. The initial configuration, Core 4.1, was rejected because the method for pebble loading, separate delivery tubes for the moderator and fuel pebbles, may not have been completely random; this core loading was rejected by the experimenters. Cores 4.2 and 4.3 were loaded using a single delivery tube, eliminating the possibility for systematic ordering effects. The second and third cores differed slightly in the quantity of pebbles loaded (40 each of moderator and fuel pebbles), stacked height of the pebbles in the core cavity (0.02 m), withdrawn distance of the stainless steel control rods (20 mm), and withdrawn distance of the autorod (30 mm). The 34 coolant channels in the upper axial reflector and the 33 coolant channels in the lower axial reflector were open. Additionally, the axial graphite fillers used in all other HTR-PROTEUS configurations to create a 12-sided core cavity were not used in the randomly packed cores. Instead, graphite fillers were placed on the cavity floor, creating a funnel-like base, to discourage ordering
John D. Bess; Leland M. Montierth
2013-03-01
In its deployment as a pebble bed reactor (PBR) critical facility from 1992 to 1996, the PROTEUS facility was designated as HTR-PROTEUS. This experimental program was performed as part of an International Atomic Energy Agency (IAEA) Coordinated Research Project (CRP) on the Validation of Safety Related Physics Calculations for Low Enriched HTGRs. Within this project, critical experiments were conducted for graphite moderated LEU systems to determine core reactivity, flux and power profiles, reaction-rate ratios, the worth of control rods, both in-core and reflector based, the worth of burnable poisons, kinetic parameters, and the effects of moisture ingress on these parameters. One benchmark experiment was evaluated in this report: Core 4. Core 4 represents the only configuration with random pebble packing in the HTR-PROTEUS series of experiments, and has a moderator-to-fuel pebble ratio of 1:1. Three random configurations were performed. The initial configuration, Core 4.1, was rejected because the method for pebble loading, separate delivery tubes for the moderator and fuel pebbles, may not have been completely random; this core loading was rejected by the experimenters. Cores 4.2 and 4.3 were loaded using a single delivery tube, eliminating the possibility for systematic ordering effects. The second and third cores differed slightly in the quantity of pebbles loaded (40 each of moderator and fuel pebbles), stacked height of the pebbles in the core cavity (0.02 m), withdrawn distance of the stainless steel control rods (20 mm), and withdrawn distance of the autorod (30 mm). The 34 coolant channels in the upper axial reflector and the 33 coolant channels in the lower axial reflector were open. Additionally, the axial graphite fillers used in all other HTR-PROTEUS configurations to create a 12-sided core cavity were not used in the randomly packed cores. Instead, graphite fillers were placed on the cavity floor, creating a funnel-like base, to discourage ordering
Automatic Generation of Supervisory Control System Software Using Graph Composition
Nakata, Hideo; Sano, Tatsuro; Kojima, Taizo; Seo, Kazuo; Uchida, Tomoyuki; Nakamura, Yasuaki
This paper describes the automatic generation of system descriptions for SCADA (Supervisory Control And Data Acquisition) systems. The proposed method produces various types of data and programs for SCADA systems from equipment definitions using conversion rules. At first, this method makes directed graphs, which represent connections between the equipment, from equipment definitions. System descriptions are generated using the conversion rules, by analyzing these directed graphs, and finding the groups of equipment that involve similar operations. This method can make the conversion rules multi levels by using the composition of graphs, and can reduce the number of rules. The developer can define and manage these rules efficiently.
Building Scalable Knowledge Graphs for Earth Science
Ramachandran, R.; Maskey, M.; Gatlin, P. N.; Zhang, J.; Duan, X.; Bugbee, K.; Christopher, S. A.; Miller, J. J.
2017-12-01
Estimates indicate that the world's information will grow by 800% in the next five years. In any given field, a single researcher or a team of researchers cannot keep up with this rate of knowledge expansion without the help of cognitive systems. Cognitive computing, defined as the use of information technology to augment human cognition, can help tackle large systemic problems. Knowledge graphs, one of the foundational components of cognitive systems, link key entities in a specific domain with other entities via relationships. Researchers could mine these graphs to make probabilistic recommendations and to infer new knowledge. At this point, however, there is a dearth of tools to generate scalable Knowledge graphs using existing corpus of scientific literature for Earth science research. Our project is currently developing an end-to-end automated methodology for incrementally constructing Knowledge graphs for Earth Science. Semantic Entity Recognition (SER) is one of the key steps in this methodology. SER for Earth Science uses external resources (including metadata catalogs and controlled vocabulary) as references to guide entity extraction and recognition (i.e., labeling) from unstructured text, in order to build a large training set to seed the subsequent auto-learning component in our algorithm. Results from several SER experiments will be presented as well as lessons learned.
The partition dimension of cycle books graph
Santoso, Jaya; Darmaji
2018-03-01
Let G be a nontrivial and connected graph with vertex set V(G), edge set E(G) and S ⊆ V(G) with v ∈ V(G), the distance between v and S is d(v,S) = min{d(v,x)|x ∈ S}. For an ordered partition ∏ = {S 1, S 2, S 3,…, Sk } of V(G), the representation of v with respect to ∏ is defined by r(v|∏) = (d(v, S 1), d(v, S 2),…, d(v, Sk )). The partition ∏ is called a resolving partition of G if all representations of vertices are distinct. The partition dimension pd(G) is the smallest integer k such that G has a resolving partition set with k members. In this research, we will determine the partition dimension of Cycle Books {B}{Cr,m}. Cycle books graph {B}{Cr,m} is a graph consisting of m copies cycle Cr with the common path P 2. It is shown that the partition dimension of cycle books graph, pd({B}{C3,m}) is 3 for m = 2, 3, and m for m ≥ 4. pd({B}{C4,m}) is 3 + 2k for m = 3k + 2, 4 + 2(k ‑ 1) for m = 3k + 1, and 3 + 2(k ‑ 1) for m = 3k. pd({B}{C5,m}) is m + 1.
Vertex Degrees and Isomorphic Properties in Complement of an m-Polar Fuzzy Graph
Ch. Ramprasad
2017-01-01
Full Text Available Computational intelligence and computer science rely on graph theory to solve combinatorial problems. Normal product and tensor product of an m-polar fuzzy graph have been introduced in this article. Degrees of vertices in various product graphs, like Cartesian product, composition, tensor product, and normal product, have been computed. Complement and μ-complement of an m-polar fuzzy graph are defined and some properties are studied. An application of an m-polar fuzzy graph is also presented in this article.
Cospectral graphs and regular orthogonal matrices of level 2
Abiad Monge, A.; Haemers, W.H.
2012-01-01
For a graph Γ with adjacency matrix A , we consider a switching operation that takes Γ into a graph Γ′ with adjacency matrix A′ , defined by A′ = Q⊤AQ , where Q is a regular orthogonal matrix of level 2 (that is, Q⊤Q=I , Q1 = 1, 2Q is integral, and Q is not a permutation matrix). If such an
Internally connected graphs and the Kashiwara-Vergne Lie algebra
Felder, Matteo
2018-02-01
It is conjectured that the Kashiwara-Vergne Lie algebra \\widehat{krv}_2 is isomorphic to the direct sum of the Grothendieck-Teichmüller Lie algebra grt_1 and a one-dimensional Lie algebra. In this paper, we use the graph complex of internally connected graphs to define a nested sequence of Lie subalgebras of \\widehat{krv}_2 whose intersection is grt_1 , thus giving a way to interpolate between these two Lie algebras.
Graphs cospectral with a friendship graph or its complement
Alireza Abdollahi
2013-12-01
Full Text Available Let $n$ be any positive integer and let $F_n$ be the friendship (or Dutch windmill graph with $2n+1$ vertices and $3n$ edges. Here we study graphs with the same adjacency spectrum as the $F_n$. Two graphs are called cospectral if the eigenvalues multiset of their adjacency matrices are the same. Let $G$ be a graph cospectral with $F_n$. Here we prove that if $G$ has no cycle of length $4$ or $5$, then $Gcong F_n$. Moreover if $G$ is connected and planar then $Gcong F_n$.All but one of connected components of $G$ are isomorphic to $K_2$.The complement $overline{F_n}$ of the friendship graph is determined by its adjacency eigenvalues, that is, if $overline{F_n}$ is cospectral with a graph $H$, then $Hcong overline{F_n}$.
Decomposing Oriented Graphs into Six Locally Irregular Oriented Graphs
Bensmail, Julien; Renault, Gabriel
2016-01-01
An undirected graph G is locally irregular if every two of its adjacent vertices have distinct degrees. We say that G is decomposable into k locally irregular graphs if there exists a partition E1∪E2∪⋯∪Ek of the edge set E(G) such that each Ei induces a locally irregular graph. It was recently co...
X-Graphs: Language and Algorithms for Heterogeneous Graph Streams
2017-09-01
are widely used by academia and industry. 15. SUBJECT TERMS Data Analytics, Graph Analytics, High-Performance Computing 16. SECURITY CLASSIFICATION...form the core of the DeepDive Knowledge Construction System. 2 INTRODUCTION The goal of the X-Graphs project was to develop computational techniques...memory multicore machine. Ringo is based on Snap.py and SNAP, and uses Python . Ringo now allows the integration of Delite DSL Framework Graph
Analysis of impact of mixing flow on the pebble bed high temperature reactor
Hao Chen; Li Fu; Guo Jiong
2014-01-01
The impact of the mixing flow in the pebble flow on pebble bed high temperature gas cooled reactor (HTR) was analyzed in the paper. New code package MFVSOP which can simulate the mixing flow was developed. The equilibrium core of HTR-PM was selected as reference case, the impact of the mixing flow on the core parameters such as core power peak factor, power distribution was analyzed with different degree of mixing flow, and uncertainty analysis was carried out. Numerical results showed that the mixing flow had little impact on key parameters of pebble bed HTR, and the multiple-pass-operation-mode in pebble bed HTR can reduce the uncertainty arouse from the mixing flow. (authors)
Computational and experimental prediction of dust production in pebble bed reactors, Part II
Hiruta, Mie; Johnson, Gannon [Department of Mechanical Engineering, University of Idaho, 1776 Science Center Drive, Idaho Falls, ID 83401 (United States); Rostamian, Maziar, E-mail: mrostamian@asme.org [Department of Mechanical Engineering, University of Idaho, 1776 Science Center Drive, Idaho Falls, ID 83401 (United States); Potirniche, Gabriel P. [Department of Mechanical Engineering, University of Idaho, 1776 Science Center Drive, Idaho Falls, ID 83401 (United States); Ougouag, Abderrafi M. [Idaho National Laboratory, 2525 N Fremont Avenue, Idaho Falls, ID 83401 (United States); Bertino, Massimo; Franzel, Louis [Department of Physics, Virginia Commonwealth University, Richmond, VA 23284 (United States); Tokuhiro, Akira [Department of Mechanical Engineering, University of Idaho, 1776 Science Center Drive, Idaho Falls, ID 83401 (United States)
2013-10-15
Highlights: • Custom-built high temperature, high pressure tribometer is designed. • Two different wear phenomena at high temperatures are observed. • Experimental wear results for graphite are presented. • The graphite wear dust production in a typical Pebble Bed Reactor is predicted. -- Abstract: This paper is the continuation of Part I, which describes the high temperature and high pressure helium environment wear tests of graphite–graphite in frictional contact. In the present work, it has been attempted to simulate a Pebble Bed Reactor core environment as compared to Part I. The experimental apparatus, which is a custom-designed tribometer, is capable of performing wear tests at PBR relevant higher temperatures and pressures under a helium environment. This environment facilitates prediction of wear mass loss of graphite as dust particulates from the pebble bed. The experimental results of high temperature helium environment are used to anticipate the amount of wear mass produced in a pebble bed nuclear reactor.
Guodong Liu
2013-01-01
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. To understand the mechanism of pebble’s motion in the reactor, we numerically studied the influence of number ratio of fuel and graphite pebbles, funnel angle of the reactor, height of guide ring on the distribution of pebble position, and velocity by means of discrete element method (DEM in a two-dimensional MPBNR. 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.
Pebble fabrication and tritium release properties of an advanced tritium breeder
Hoshino, Tsuyoshi, E-mail: hoshino.tsuyoshi@jaea.go.jp [Breeding Functional Materials Development Group, Department of Blanket Systems Research, Rokkasho Fusion Institute, Sector of Fusion Research and Development, Japan Atomic Energy Agency, 2-166 Obuch, Omotedate, Rokkasho-mura, Kamikita-gun, Aomori 039-3212 (Japan); Edao, Yuki [Tritium Technology Group, Department of Blanket Systems Research, Rokkasho Fusion Institute, Sector of Fusion Research and Development, Japan Atomic Energy Agency, 2-4 Shirakata, Shirane, Tokai-mura, Naka-gun, Ibaraki 319-1195 (Japan); Kawamura, Yoshinori [Blanket Technology Group, Department of Blanket Systems Research, Rokkasho Fusion Institute, Sector of Fusion Research and Development, Japan Atomic Energy Agency, 801-1 Mukoyama, Naka, Ibaraki 311-0193 (Japan); Ochiai, Kentaro [BA Project Coordination Group, Department of Fusion Power Systems Research, Rokkasho Fusion Institute, Sector of Fusion Research and Development, Japan Atomic Energy Agency, 2-166 Obuch, Omotedate, Rokkasho-mura, Kamikita-gun, Aomori 039-3212 (Japan)
2016-11-01
Highlights: • Li{sub 2}TiO{sub 3} with excess Li (Li{sub 2+x}TiO{sub 3+y}) pebble as an advanced tritium breeders was fabricated using emulsion method. • Grain size of Li{sub 2+x}TiO{sub 3+y} pebbles was controlled to be less than 5 μm. • Li{sub 2+x}TiO{sub 3+y} pebbles exhibited good tritium release properties similar to that of Li{sub 2}TiO{sub 3} pebbles. - Abstract: Li{sub 2}TiO{sub 3} with excess Li (Li{sub 2+x}TiO{sub 3+y}) has been developed as an advanced tritium breeder. With respect to the tritium release characteristics of the blanket, the optimum grain size after sintering was less than 5 μm. Therefore, an emulsion method was developed to fabricate pebbles with this target grain size. The predominant factor affecting grain growth was assumed to be the presence of binder in the gel particles; this remaining binder was hypothesized to react with the excess Li, thereby generating Li{sub 2}CO{sub 3}, which promotes grain growth. To inhibit the generation of Li{sub 2}CO{sub 3}, calcined Li{sub 2+x}TiO{sub 3+y} pebbles were sintered under vacuum and subsequently under a 1% H{sub 2}–He atmosphere. The average grain size of the sintered Li{sub 2+x}TiO{sub 3+y} pebbles was less than 5 μm. Furthermore, the tritium release properties of Li{sub 2+x}TiO{sub 3+y} pebbles were evaluated, and deuterium–tritium (DT) neutron irradiation experiments were performed at the Fusion Neutronics Source facility in the Japan Atomic Energy Agency. To remove the tritium produced by neutron irradiation, 1% H{sub 2}–He purge gas was passed through the Li{sub 2+x}TiO{sub 3+y} pebbles. The Li{sub 2+x}TiO{sub 3+y} pebbles exhibited good tritium release properties, similar to those of Li{sub 2}TiO{sub 3} pebbles. In particular, the released amount of tritiated hydrogen gas for easier tritium handling was greater than the released amount of tritiated water.
Development of a safeguards system for the THTR pebble bed reactor
Engelhardt, H.
1978-08-01
This report provides a survey of the technical possibilities of safeguarding the THTR-300 pebble bed reactor in accordance with the NPT. Description of the reactor system, the operational mode, and the operator's material control system are presented in Sections 2, 3 and 4. A suggested safeguards approach which is based on an item counting of pebble elements with containment and surveillance as a supplementary measure is described in the Sections 5 and 6
Preliminary Neutronic Design of High Burnup OTTO Cycle Pebble Bed Reactor
Setiadipura, T; Irwanto, D; Zuhair, Zuhair
2015-01-01
The pebble bed type High Temperature Gas-cooled Reactor (HTGR) is among the interesting nuclear reactor designs in terms of safety and flexibility for co-generation applications. In addition, the strong inherent safety characteristics of the pebble bed reactor (PBR) which is based on natural mechanisms improve the simplicity of the PBR design, in particular for the Once-Through-Then-Out (OTTO) cycle PBR design. One of the important challenges of the OTTO cycle PBR design, and nuclear reactor ...
Zuhair; Suwoto; Setiadipura, T.; Bakhri, S.; Sunaryo, G. R.
2018-02-01
As a part of the solution searching for possibility to control the plutonium, a current effort is focused on mechanisms to maximize consumption of plutonium. Plutonium core solution is a unique case in the high temperature reactor which is intended to reduce the accumulation of plutonium. However, the safety performance of the plutonium core which tends to produce a positive temperature coefficient of reactivity should be examined. The pebble bed inherent safety features which are characterized by a negative temperature coefficient of reactivity must be maintained under any circumstances. The purpose of this study is to investigate the characteristic of temperature coefficient of reactivity for plutonium core of pebble bed reactor. A series of calculations with plutonium loading varied from 0.5 g to 1.5 g per fuel pebble were performed by the MCNPX code and ENDF/B-VII library. The calculation results show that the k eff curve of 0.5 g Pu/pebble declines sharply with the increase in fuel burnup while the greater Pu loading per pebble yields k eff curve declines slighter. The fuel with high Pu content per pebble may reach long burnup cycle. From the temperature coefficient point of view, it is concluded that the reactor containing 0.5 g-1.25 g Pu/pebble at high burnup has less favorable safety features if it is operated at high temperature. The use of fuel with Pu content of 1.5 g/pebble at high burnup should be considered carefully from core safety aspect because it could affect transient behavior into a fatal accident situation.
Endomorphisms of graph algebras
Conti, Roberto; Hong, Jeong Hee; Szymanski, Wojciech
2012-01-01
We initiate a systematic investigation of endomorphisms of graph C*-algebras C*(E), extending several known results on endomorphisms of the Cuntz algebras O_n. Most but not all of this study is focused on endomorphisms which permute the vertex projections and globally preserve the diagonal MASA D...... that the restriction to the diagonal MASA of an automorphism which globally preserves both D_E and the core AF-subalgebra eventually commutes with the corresponding one-sided shift. Secondly, we exhibit several properties of proper endomorphisms, investigate invertibility of localized endomorphisms both on C...
Yap, Hian-Poh
1996-01-01
This book provides an up-to-date and rapid introduction to an important and currently active topic in graph theory. The author leads the reader to the forefront of research in this area. Complete and easily readable proofs of all the main theorems, together with numerous examples, exercises and open problems are given. The book is suitable for use as a textbook or as seminar material for advanced undergraduate and graduate students. The references are comprehensive and so it will also be useful for researchers as a handbook.
Steamworlds: Atmospheric Structure and Critical Mass of Planets Accreting Icy Pebbles
Chambers, John
2017-01-01
In the core accretion model, gas-giant planets first form a solid core, which then accretes gas from a protoplanetary disk when the core exceeds a critical mass. Here, we model the atmosphere of a core that grows by accreting ice-rich pebbles. The ice fraction of pebbles evaporates in warm regions of the atmosphere, saturating it with water vapor. Excess water precipitates to lower altitudes. Beneath an outer radiative region, the atmosphere is convective, following a moist adiabat in saturated regions due to water condensation and precipitation. Atmospheric mass, density, and temperature increase with core mass. For nominal model parameters, planets with core masses (ice + rock) between 0.08 and 0.16 Earth masses have surface temperatures between 273 and 647 K and form an ocean. In more massive planets, water exists as a supercritical convecting fluid mixed with gas from the disk. Typically, the core mass reaches a maximum (the critical mass) as a function of the total mass when the core is 2–5 Earth masses. The critical mass depends in a complicated way on pebble size, mass flux, and dust opacity due to the occasional appearance of multiple core-mass maxima. The core mass for an atmosphere of 50% hydrogen and helium may be a more robust indicator of the onset of gas accretion. This mass is typically 1–3 Earth masses for pebbles that are 50% ice by mass, increasing with opacity and pebble flux and decreasing with pebble ice/rock ratio.
Steamworlds: Atmospheric Structure and Critical Mass of Planets Accreting Icy Pebbles
Chambers, John, E-mail: jchambers@carnegiescience.edu [Carnegie Institution for Science Department of Terrestrial Magnetism, 5241 Broad Branch Road, NW, Washington, DC 20015 (United States)
2017-11-01
In the core accretion model, gas-giant planets first form a solid core, which then accretes gas from a protoplanetary disk when the core exceeds a critical mass. Here, we model the atmosphere of a core that grows by accreting ice-rich pebbles. The ice fraction of pebbles evaporates in warm regions of the atmosphere, saturating it with water vapor. Excess water precipitates to lower altitudes. Beneath an outer radiative region, the atmosphere is convective, following a moist adiabat in saturated regions due to water condensation and precipitation. Atmospheric mass, density, and temperature increase with core mass. For nominal model parameters, planets with core masses (ice + rock) between 0.08 and 0.16 Earth masses have surface temperatures between 273 and 647 K and form an ocean. In more massive planets, water exists as a supercritical convecting fluid mixed with gas from the disk. Typically, the core mass reaches a maximum (the critical mass) as a function of the total mass when the core is 2–5 Earth masses. The critical mass depends in a complicated way on pebble size, mass flux, and dust opacity due to the occasional appearance of multiple core-mass maxima. The core mass for an atmosphere of 50% hydrogen and helium may be a more robust indicator of the onset of gas accretion. This mass is typically 1–3 Earth masses for pebbles that are 50% ice by mass, increasing with opacity and pebble flux and decreasing with pebble ice/rock ratio.
Experimental measurement of effective thermal conductivity of packed lithium-titanate pebble bed
Mandal, D.; Sathiyamoorthy, D.; Vinjamur, M.
2012-01-01
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.
CFD study on the supercritical carbon dioxide cooled pebble bed reactor
Yu, Dali, E-mail: ydlmitd@outlook.com; Peng, Minjun; Wang, Zhongyi
2015-01-15
Highlights: • An innovation concept of supercritical carbon dioxide cooled pebble bed reactor is proposed. • Body-centered cuboid (BCCa) arrangement is adopted for the pebbles. • S-CO{sub 2} would be a good candidate coolant for using in pebble bed reactor. - Abstract: The thermal hydraulic study of using supercritical carbon dioxide (S-CO{sub 2}), a superior fluid state brayton cycle medium, in pebble bed type nuclear reactor is assessed through computational fluid dynamics (CFD) methodology. Preliminary concept design of this S-CO{sub 2} cooled pebble bed reactor (PBR) is implemented by the well-known KTA heat transfer correlation and Ergun pressure drop equation. Eddy viscosity transport turbulence model is adopted and verified by KTA calculated results. Distributions of the temperature, velocity, pressure and Nusselt (Nu) number of the coolant near the surface of the middle spherical fuel element are obtained and analyzed. The conclusion of the assessment is that S-CO{sub 2} would be a good candidate coolant for using in pebble bed reactor due primarily to its good heat transfer characteristic and large mass density, which could lead to achieve lower pressure drop and higher power density.
Arc plasma assisted rotating electrode process for preparation of metal pebbles
Mohanty, T.; Tripathi, B.M.; Mahata, T.; Sinha, P.K.
2014-01-01
Spherical beryllium pebbles of size ranging from 0.2-2 mm are required as neutron multiplying material in solid Test Blanket Module (TBM) of International Thermonuclear Experimental Reactor (ITER). Rotating electrode process (REP) has been identified as a suitable technique for preparation of beryllium pebbles. In REP, arc plasma generated between non-consumable electrode (cathode) and rotating metal electrode (anode) plays a major role for continuous consumption of metal electrode and preparation of spherical metal pebbles. This paper focuses on description of the process, selection of sub-systems for development of REP experimental set up and optimization of arc parameters, such as, cathode geometry, arc current, arc voltage, arc gap and carrier gas flow rate for preparation of required size spherical metal pebbles. Other parameters which affect the pebbles sizes are rotational speed, metal electrode diameter and physical properties of the metal. As beryllium is toxic in nature its surrogate metals such as stainless steel (SS) and Titanium (Ti) were selected to evaluate the performance of the REP equipment. Several experiments were carried out using SS and Ti electrode and process parameters have been optimized for preparation of pebbles of different sizes. (author)
Cyclic loading tests on ceramic breeder pebble bed by discrete element modeling
Zhang, Hao [School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230027 (China); Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang 621900 (China); Guo, Haibing; Shi, Tao [Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang 621900 (China); Ye, Minyou [School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230027 (China); Huang, Hongwen, E-mail: hhw@caep.cn [Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang 621900 (China); Li, Zhenghong, E-mail: inpcnyb@sina.com [Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang 621900 (China); University of Science and Technology of China, Hefei 230027 (China)
2017-05-15
Highlights: • Methods of cyclic loading tests on the pebble beds were developed in DEM. • Size distribution and sphericity of the pebbles were considered for the specimen. • Mechanical responses of the pebble beds under cyclic loading tests were assessed. - Abstract: Complex mechanics and packing instability can be induced by loading operation on ceramic breeder pebble bed for its discrete nature. A numerical approach using discrete element method (DEM) is applied to study the mechanical performance of the ceramic breeder pebble bed under quasi-static and cyclic loads. A preloaded specimen can be made with servo-control mechanism, the quasi-static and dynamic stress-strain performances are studied during the tests. It is found that the normalized normal contact forces under quasi-static loads have the similar distributions, and increase with increasing loads. Furthermore, the relatively low volumetric strain can be absorbed by pebble bed after several loading and unloading cycles, but the peak normal contact force can be extremely high during the first cycle. Cyclic loading with target pressure is recommended for densely packing, irreversible volume reduction gradually increase with cycles, and the normal contact forces decrease with cycles.
Cyclic loading tests on ceramic breeder pebble bed by discrete element modeling
Zhang, Hao; Guo, Haibing; Shi, Tao; Ye, Minyou; Huang, Hongwen; Li, Zhenghong
2017-01-01
Highlights: • Methods of cyclic loading tests on the pebble beds were developed in DEM. • Size distribution and sphericity of the pebbles were considered for the specimen. • Mechanical responses of the pebble beds under cyclic loading tests were assessed. - Abstract: Complex mechanics and packing instability can be induced by loading operation on ceramic breeder pebble bed for its discrete nature. A numerical approach using discrete element method (DEM) is applied to study the mechanical performance of the ceramic breeder pebble bed under quasi-static and cyclic loads. A preloaded specimen can be made with servo-control mechanism, the quasi-static and dynamic stress-strain performances are studied during the tests. It is found that the normalized normal contact forces under quasi-static loads have the similar distributions, and increase with increasing loads. Furthermore, the relatively low volumetric strain can be absorbed by pebble bed after several loading and unloading cycles, but the peak normal contact force can be extremely high during the first cycle. Cyclic loading with target pressure is recommended for densely packing, irreversible volume reduction gradually increase with cycles, and the normal contact forces decrease with cycles.
Jeong, Sangyun; Yang, Da-Som; Hong, Young Gi; Mitchell, Sarah P; Brown, Matthew P; Kolodkin, Alex L
2017-09-26
The transmembrane semaphorin Sema-1a acts as both a ligand and a receptor to regulate axon-axon repulsion during neural development. Pebble (Pbl), a Rho guanine nucleotide exchange factor, mediates Sema-1a reverse signaling through association with the N-terminal region of the Sema-1a intracellular domain (ICD), resulting in cytoskeletal reorganization. Here, we uncover two additional Sema-1a interacting proteins, varicose (Vari) and cheerio (Cher), each with neuronal functions required for motor axon pathfinding. Vari is a member of the membrane-associated guanylate kinase (MAGUK) family of proteins, members of which can serve as scaffolds to organize signaling complexes. Cher is related to actin filament cross-linking proteins that regulate actin cytoskeleton dynamics. The PDZ domain binding motif found in the most C-terminal region of the Sema-1a ICD is necessary for interaction with Vari, but not Cher, indicative of distinct binding modalities. Pbl/Sema-1a-mediated repulsive guidance is potentiated by both vari and cher Genetic analyses further suggest that scaffolding functions of Vari and Cher play an important role in Pbl-mediated Sema-1a reverse signaling. These results define intracellular components critical for signal transduction from the Sema-1a receptor to the cytoskeleton and provide insight into mechanisms underlying semaphorin-induced localized changes in cytoskeletal organization.
Global scaling analysis for the pebble bed advanced high temperature reactor
Blandford, E.D.; Peterson, P.F.
2009-01-01
Scaled Integral Effects Test (IET) facilities play a critical role in the design certification process of innovative reactor designs. Best-estimate system analysis codes, which minimize deliberate conservatism, require confirmatory data during the validation process to ensure an acceptable level of accuracy as defined by the regulator. The modular Pebble Bed Advanced High Temperature Reactor (PB-AHTR), with a nominal power output of 900 MWth, is the most recent UC Berkeley design for a liquid fluoride salt cooled, solid fuel reactor. The PB-AHTR takes advantage of technologies developed for gas-cooled high temperature thermal and fast reactors, sodium fast reactors, and molten salt reactors. In this paper, non-dimensional scaling groups and similarity criteria are presented at the global system level for a loss of forced circulation transient, where single-phase natural circulation is the primary mechanism for decay heat removal following a primary pump trip. Due to very large margin to fuel damage temperatures, the peak metal temperature of primary-loop components was identified as the key safety parameter of interest. Fractional Scaling Analysis (FSA) methods were used to quantify the intensity of each transfer process during the transient and subsequently rank them by their relative importance while identifying key sources of distortion between the prototype and model. The results show that the development of a scaling hierarchy at the global system level informs the bottom-up scaling analysis. (author)
The forwarding indices of graphs - a survey
Jun-Ming Xu
2013-01-01
Full Text Available A routing \\(R\\ of a connected graph \\(G\\ of order \\(n\\ is a collection of \\(n(n-1\\ simple paths connecting every ordered pair of vertices of \\(G\\. The vertex-forwarding index \\(\\xi(G,R\\ of \\(G\\ with respect to a routing \\(R\\ is defined as the maximum number of paths in \\(R\\ passing through any vertex of \\(G\\. The vertex-forwarding index \\(\\xi(G\\ of \\(G\\ is defined as the minimum \\(\\xi(G,R\\ over all routings \\(R\\ of \\(G\\. Similarly, the edge-forwarding index \\(\\pi(G,R\\ of \\(G\\ with respect to a routing \\(R\\ is the maximum number of paths in \\(R\\ passing through any edge of \\(G\\. The edge-forwarding index \\(\\pi(G\\ of \\(G\\ is the minimum \\(\\pi(G,R\\ over all routings \\(R\\ of \\(G\\. The vertex-forwarding index or the edge-forwarding index corresponds to the maximum load of the graph. Therefore, it is important to find routings minimizing these indices and thus has received much research attention for over twenty years. This paper surveys some known results on these forwarding indices, further research problems and several conjectures, also states some difficulty and relations to other topics in graph theory.
Optimization Problems on Threshold Graphs
Elena Nechita
2010-06-01
Full Text Available During the last three decades, different types of decompositions have been processed in the field of graph theory. Among these we mention: decompositions based on the additivity of some characteristics of the graph, decompositions where the adjacency law between the subsets of the partition is known, decompositions where the subgraph induced by every subset of the partition must have predeterminate properties, as well as combinations of such decompositions. In this paper we characterize threshold graphs using the weakly decomposition, determine: density and stability number, Wiener index and Wiener polynomial for threshold graphs.
Eulerian Graphs and Related Topics
Fleischner, Herbert
1990-01-01
The two volumes comprising Part 1 of this work embrace the theme of Eulerian trails and covering walks. They should appeal both to researchers and students, as they contain enough material for an undergraduate or graduate graph theory course which emphasizes Eulerian graphs, and thus can be read by any mathematician not yet familiar with graph theory. But they are also of interest to researchers in graph theory because they contain many recent results, some of which are only partial solutions to more general problems. A number of conjectures have been included as well. Various problems (such a
BootGraph: probabilistic fiber tractography using bootstrap algorithms and graph theory.
Vorburger, Robert S; Reischauer, Carolin; Boesiger, Peter
2013-02-01
Bootstrap methods have recently been introduced to diffusion-weighted magnetic resonance imaging to estimate the measurement uncertainty of ensuing diffusion parameters directly from the acquired data without the necessity to assume a noise model. These methods have been previously combined with deterministic streamline tractography algorithms to allow for the assessment of connection probabilities in the human brain. Thereby, the local noise induced disturbance in the diffusion data is accumulated additively due to the incremental progression of streamline tractography algorithms. Graph based approaches have been proposed to overcome this drawback of streamline techniques. For this reason, the bootstrap method is in the present work incorporated into a graph setup to derive a new probabilistic fiber tractography method, called BootGraph. The acquired data set is thereby converted into a weighted, undirected graph by defining a vertex in each voxel and edges between adjacent vertices. By means of the cone of uncertainty, which is derived using the wild bootstrap, a weight is thereafter assigned to each edge. Two path finding algorithms are subsequently applied to derive connection probabilities. While the first algorithm is based on the shortest path approach, the second algorithm takes all existing paths between two vertices into consideration. Tracking results are compared to an established algorithm based on the bootstrap method in combination with streamline fiber tractography and to another graph based algorithm. The BootGraph shows a very good performance in crossing situations with respect to false negatives and permits incorporating additional constraints, such as a curvature threshold. By inheriting the advantages of the bootstrap method and graph theory, the BootGraph method provides a computationally efficient and flexible probabilistic tractography setup to compute connection probability maps and virtual fiber pathways without the drawbacks of
Maunz, Peter Lukas Wilhelm [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sterk, Jonathan David [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Lobser, Daniel [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Parekh, Ojas D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ryan-Anderson, Ciaran [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2016-01-01
In recent years, advanced network analytics have become increasingly important to na- tional security with applications ranging from cyber security to detection and disruption of ter- rorist networks. While classical computing solutions have received considerable investment, the development of quantum algorithms to address problems, such as data mining of attributed relational graphs, is a largely unexplored space. Recent theoretical work has shown that quan- tum algorithms for graph analysis can be more efficient than their classical counterparts. Here, we have implemented a trapped-ion-based two-qubit quantum information proces- sor to address these goals. Building on Sandia's microfabricated silicon surface ion traps, we have designed, realized and characterized a quantum information processor using the hyperfine qubits encoded in two 171 Yb + ions. We have implemented single qubit gates using resonant microwave radiation and have employed Gate set tomography (GST) to characterize the quan- tum process. For the first time, we were able to prove that the quantum process surpasses the fault tolerance thresholds of some quantum codes by demonstrating a diamond norm distance of less than 1 . 9 x 10 [?] 4 . We used Raman transitions in order to manipulate the trapped ions' motion and realize two-qubit gates. We characterized the implemented motion sensitive and insensitive single qubit processes and achieved a maximal process infidelity of 6 . 5 x 10 [?] 5 . We implemented the two-qubit gate proposed by Molmer and Sorensen and achieved a fidelity of more than 97 . 7%.
Total edge irregularity strength of (n,t)-kite graph
Winarsih, Tri; Indriati, Diari
2018-04-01
Let G(V, E) be a simple, connected, and undirected graph with vertex set V and edge set E. A total k-labeling is a map that carries vertices and edges of a graph G into a set of positive integer labels {1, 2, …, k}. An edge irregular total k-labeling λ :V(G)\\cup E(G)\\to \\{1,2,\\ldots,k\\} of a graph G is a labeling of vertices and edges of G in such a way that for any different edges e and f, weights wt(e) and wt(f) are distinct. The weight wt(e) of an edge e = xy is the sum of the labels of vertices x and y and the label of the edge e. The total edge irregularity strength of G, tes(G), is defined as the minimum k for which a graph G has an edge irregular total k-labeling. An (n, t)-kite graph consist of a cycle of length n with a t-edge path (the tail) attached to one vertex of a cycle. In this paper, we investigate the total edge irregularity strength of the (n, t)-kite graph, with n > 3 and t > 1. We obtain the total edge irregularity strength of the (n, t)-kite graph is tes((n, t)-kite) = \\lceil \\frac{n+t+2}{3}\\rceil .
GSMNet: A Hierarchical Graph Model for Moving Objects in Networks
Hengcai Zhang
2017-03-01
Full Text Available Existing data models for moving objects in networks are often limited by flexibly controlling the granularity of representing networks and the cost of location updates and do not encompass semantic information, such as traffic states, traffic restrictions and social relationships. In this paper, we aim to fill the gap of traditional network-constrained models and propose a hierarchical graph model called the Geo-Social-Moving model for moving objects in Networks (GSMNet that adopts four graph structures, RouteGraph, SegmentGraph, ObjectGraph and MoveGraph, to represent the underlying networks, trajectories and semantic information in an integrated manner. The bulk of user-defined data types and corresponding operators is proposed to handle moving objects and answer a new class of queries supporting three kinds of conditions: spatial, temporal and semantic information. Then, we develop a prototype system with the native graph database system Neo4Jto implement the proposed GSMNet model. In the experiment, we conduct the performance evaluation using simulated trajectories generated from the BerlinMOD (Berlin Moving Objects Database benchmark and compare with the mature MOD system Secondo. The results of 17 benchmark queries demonstrate that our proposed GSMNet model has strong potential to reduce time-consuming table join operations an d shows remarkable advantages with regard to representing semantic information and controlling the cost of location updates.
Plutonium burning in a pebble-bed type high temperature nuclear reactor
Bende, E.E
2000-01-24
This thesis deals with the pebble-bed High Temperature Reactor that is fuelled with pure reactor-grade plutonium. It is stressed that neither burnable poisons nor fertile materials like 238U and 212Th are present in the calculational models throughout this thesis. Chapter 2 discusses the general properties of the pebble-bed HTR: the passive safety features of this reactor; different fuel scenarios according to which the pebble-bed HTR can be operated; properties of the pebbles and the coated particles (CPs), including a concise overview of the mechanisms that can lead to coated particle failure. Special attention is paid to the effect of Pu as fuel inside these CPs thereby aiming to indicate which mechanisms are of concern when such CPs are considered as fuel in future reactors. In the last part of this chapter constraints are listed that were imposed to the models considered in the framework of this thesis. Chapter 3 presents the results of unit-cell calculations performed with three code systems. The main objective of this chapter is to compare the calculational results of one particular code system, which is a candidate for the generation of cross sections for a full-core calculation, to those of the other two code systems. Also some reactor physics interpretations of the calculational results are presented. The unit-cell calculations embrace the computation of a number of reactor physics parameters for pebbles with a varying plutonium mass per pebble and with different types of coated particles. For one pebble configuration, these parameters have been calculated for various fuel temperatures and over-all (uniform) temperatures. For that particular pebble configuration, also the results of a two burnup calculations were compared. Chapter 4 reports the results of a parameter study in which the number of coated particles per pebble as well as the type and size of the CPs have been varied. The effect of different pebble configurations on several reactor physics
Analysis and enumeration algorithms for biological graphs
Marino, Andrea
2015-01-01
In this work we plan to revise the main techniques for enumeration algorithms and to show four examples of enumeration algorithms that can be applied to efficiently deal with some biological problems modelled by using biological networks: enumerating central and peripheral nodes of a network, enumerating stories, enumerating paths or cycles, and enumerating bubbles. Notice that the corresponding computational problems we define are of more general interest and our results hold in the case of arbitrary graphs. Enumerating all the most and less central vertices in a network according to their eccentricity is an example of an enumeration problem whose solutions are polynomial and can be listed in polynomial time, very often in linear or almost linear time in practice. Enumerating stories, i.e. all maximal directed acyclic subgraphs of a graph G whose sources and targets belong to a predefined subset of the vertices, is on the other hand an example of an enumeration problem with an exponential number of solutions...
Random broadcast on random geometric graphs
Bradonjic, Milan [Los Alamos National Laboratory; Elsasser, Robert [UNIV OF PADERBORN; Friedrich, Tobias [ICSI/BERKELEY; Sauerwald, Tomas [ICSI/BERKELEY
2009-01-01
In this work, we consider the random broadcast time on random geometric graphs (RGGs). The classic random broadcast model, also known as push algorithm, is defined as: starting with one informed node, in each succeeding round every informed node chooses one of its neighbors uniformly at random and informs it. We consider the random broadcast time on RGGs, when with high probability: (i) RGG is connected, (ii) when there exists the giant component in RGG. We show that the random broadcast time is bounded by {Omicron}({radical} n + diam(component)), where diam(component) is a diameter of the entire graph, or the giant component, for the regimes (i), or (ii), respectively. In other words, for both regimes, we derive the broadcast time to be {Theta}(diam(G)), which is asymptotically optimal.
Asymptote Misconception on Graphing Functions: Does Graphing Software Resolve It?
Mehmet Fatih Öçal
2017-01-01
Full Text Available Graphing function is an important issue in mathematics education due to its use in various areas of mathematics and its potential roles for students to enhance learning mathematics. The use of some graphing software assists students’ learning during graphing functions. However, the display of graphs of functions that students sketched by hand may be relatively different when compared to the correct forms sketched using graphing software. The possible misleading effects of this situation brought a discussion of a misconception (asymptote misconception on graphing functions. The purpose of this study is two- fold. First of all, this study investigated whether using graphing software (GeoGebra in this case helps students to determine and resolve this misconception in calculus classrooms. Second, the reasons for this misconception are sought. The multiple case study was utilized in this study. University students in two calculus classrooms who received instructions with (35 students or without GeoGebra assisted instructions (32 students were compared according to whether they fell into this misconception on graphing basic functions (1/x, lnx, ex. In addition, students were interviewed to reveal the reasons behind this misconception. Data were analyzed by means of descriptive and content analysis methods. The findings indicated that those who received GeoGebra assisted instruction were better in resolving it. In addition, the reasons behind this misconception were found to be teacher-based, exam-based and some other factors.
Risk-informed design of a pebble bed gas reactor
Ritterbusch, Stanley; Dimitrijevic, Vesna; Simic Zdenko; Savkina Marina
2003-01-01
One of the major challenges to the successful deployment of new nuclear plants in the United States is the regulatory process, which is largely based on water-reactor design technology and operating experience. While ongoing and expected efforts to license new LWR designs are based primarily on current regulations, guidance, and past experience, the pre-application review of the gas-cooled Pebble Bed Modular Reactor (PBMR) has shown that efforts are being made to provide additional 'risk-informed' improvements to the licensing process. These improvements are aimed at resolving new design and regulatory issues using a plant-wide integrated evaluation method - state-of-the-art Probabilistic Risk Assessment - which addresses all significant design features and operating modes. The integrated PRA evaluation is supported by the usual deterministic design analyses, engineering judgments, and margins added to address uncertainties (i.e., defense-in-depth). The work performed for this paper was completed as part of the United States Department of Energy's Nuclear Energy Research Initiative. The purpose of this particular project was to develop the methods for a new 'highly risk-informed' design and regulatory process. In this work. PRA techniques were applied in order to provide an integrated and systematic analysis of the plant design, to quantify uncertainties and explicitly account for defense-in-depth features. This work concentrates on the application of the risk-informed principles to a new plant design such as the PBMR. The implementation example completed for this project included specification of the design configuration, use of the PRA to evaluate the design, and iterations to identify design changes that improve the overall level of safety and system reliability. This paper summarizes the new 'highly risk-informed' design process, the design of the PBMR, and the results obtained. These results, consistent with the known inherent safety features of a pebble
Laplacian eigenvectors of graphs Perron-Frobenius and Faber-Krahn type theorems
Biyikoğu, Türker; Stadler, Peter F
2007-01-01
Eigenvectors of graph Laplacians have not, to date, been the subject of expository articles and thus they may seem a surprising topic for a book. The authors propose two motivations for this new LNM volume: (1) There are fascinating subtle differences between the properties of solutions of Schrödinger equations on manifolds on the one hand, and their discrete analogs on graphs. (2) "Geometric" properties of (cost) functions defined on the vertex sets of graphs are of practical interest for heuristic optimization algorithms. The observation that the cost functions of quite a few of the well-studied combinatorial optimization problems are eigenvectors of associated graph Laplacians has prompted the investigation of such eigenvectors. The volume investigates the structure of eigenvectors and looks at the number of their sign graphs ("nodal domains"), Perron components, graphs with extremal properties with respect to eigenvectors. The Rayleigh quotient and rearrangement of graphs form the main methodology.
ON BIPOLAR SINGLE VALUED NEUTROSOPHIC GRAPHS
Said Broumi; Mohamed Talea; Assia Bakali; Florentin Smarandache
2016-01-01
In this article, we combine the concept of bipolar neutrosophic set and graph theory. We introduce the notions of bipolar single valued neutrosophic graphs, strong bipolar single valued neutrosophic graphs, complete bipolar single valued neutrosophic graphs, regular bipolar single valued neutrosophic graphs and investigate some of their related properties.
Graph Theory. 2. Vertex Descriptors and Graph Coloring
Lorentz JÄNTSCHI
2002-12-01
Full Text Available This original work presents the construction of a set of ten sequence matrices and their applications for ordering vertices in graphs. For every sequence matrix three ordering criteria are applied: lexicographic ordering, based on strings of numbers, corresponding to every vertex, extracted as rows from sequence matrices; ordering by the sum of path lengths from a given vertex; and ordering by the sum of paths, starting from a given vertex. We also examine a graph that has different orderings for the above criteria. We then proceed to demonstrate that every criterion induced its own partition of graph vertex. We propose the following theoretical result: both LAVS and LVDS criteria generate identical partitioning of vertices in any graph. Finally, a coloring of graph vertices according to introduced ordering criteria was proposed.
On an edge partition and root graphs of some classes of line graphs
K Pravas
2017-04-01
Full Text Available The Gallai and the anti-Gallai graphs of a graph $G$ are complementary pairs of spanning subgraphs of the line graph of $G$. In this paper we find some structural relations between these graph classes by finding a partition of the edge set of the line graph of a graph $G$ into the edge sets of the Gallai and anti-Gallai graphs of $G$. Based on this, an optimal algorithm to find the root graph of a line graph is obtained. Moreover, root graphs of diameter-maximal, distance-hereditary, Ptolemaic and chordal graphs are also discussed.
Multiple Illuminant Colour Estimation via Statistical Inference on Factor Graphs.
Mutimbu, Lawrence; Robles-Kelly, Antonio
2016-08-31
This paper presents a method to recover a spatially varying illuminant colour estimate from scenes lit by multiple light sources. Starting with the image formation process, we formulate the illuminant recovery problem in a statistically datadriven setting. To do this, we use a factor graph defined across the scale space of the input image. In the graph, we utilise a set of illuminant prototypes computed using a data driven approach. As a result, our method delivers a pixelwise illuminant colour estimate being devoid of libraries or user input. The use of a factor graph also allows for the illuminant estimates to be recovered making use of a maximum a posteriori (MAP) inference process. Moreover, we compute the probability marginals by performing a Delaunay triangulation on our factor graph. We illustrate the utility of our method for pixelwise illuminant colour recovery on widely available datasets and compare against a number of alternatives. We also show sample colour correction results on real-world images.
Some relations between rank, chromatic number and energy of graphs
Akbari, S.; Ghorbani, E.; Zare, S.
2006-08-01
The energy of a graph G is defined as the sum of the absolute values of all eigenvalues of G and denoted by E(G). Let G be a graph and rank(G) be the rank of the adjacency matrix of G. In this paper we characterize all the graphs with E(G) = rank(G). Among other results we show that apart from a few families of graphs, E(G) ≥ 2max(χ(G), n - χ(G--bar)), where G-bar and χ(G) are the complement and the chromatic number of G, respectively. Moreover some new lower bounds for E(G) in terms of rank(G) are given. (author)
On the Additively Weighted Harary Index of Some Composite Graphs
Behrooz Khosravi
2017-03-01
Full Text Available The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. The additively weighted Harary index H A ( G is a modification of the Harary index in which the contributions of vertex pairs are weighted by the sum of their degrees. This new invariant was introduced in (Alizadeh, Iranmanesh and Došlić. Additively weighted Harary index of some composite graphs, Discrete Math, 2013 and they posed the following question: What is the behavior of H A ( G when G is a composite graph resulting for example by: splice, link, corona and rooted product? We investigate the additively weighted Harary index for these standard graph products. Then we obtain lower and upper bounds for some of them.
The planar cubic Cayley graphs
Georgakopoulos, Agelos
2018-01-01
The author obtains a complete description of the planar cubic Cayley graphs, providing an explicit presentation and embedding for each of them. This turns out to be a rich class, comprising several infinite families. He obtains counterexamples to conjectures of Mohar, Bonnington and Watkins. The author's analysis makes the involved graphs accessible to computation, corroborating a conjecture of Droms.
Groupies in random bipartite graphs
Yilun Shang
2010-01-01
A vertex $v$ of a graph $G$ is called a groupie if its degree is notless than the average of the degrees of its neighbors. In thispaper we study the influence of bipartition $(B_1,B_2)$ on groupiesin random bipartite graphs $G(B_1,B_2,p)$ with both fixed $p$ and$p$ tending to zero.
Nested Dynamic Condition Response Graphs
Hildebrandt, Thomas; Mukkamala, Raghava Rao; Slaats, Tijs
2012-01-01
We present an extension of the recently introduced declarative process model Dynamic Condition Response Graphs ( DCR Graphs) to allow nested subgraphs and a new milestone relation between events. The extension was developed during a case study carried out jointly with our industrial partner...
Bell inequalities for graph states
Toth, G.; Hyllus, P.; Briegel, H.J.; Guehne, O.
2005-01-01
Full text: In the last years graph states have attracted an increasing interest in the field of quantum information theory. Graph states form a family of multi-qubit states which comprises many popular states such as the GHZ states and the cluster states. They also play an important role in applications. For instance, measurement based quantum computation uses graph states as resources. From a theoretical point of view, it is remarkable that graph states allow for a simple description in terms of stabilizing operators. In this contribution, we investigate the non-local properties of graph states. We derive a family of Bell inequalities which require three measurement settings for each party and are maximally violated by graph states. In turn, any graph state violates at least one of the inequalities. We show that for certain types of graph states the violation of these inequalities increases exponentially with the number of qubits. We also discuss connections to other entanglement properties such as the positively of the partial transpose or the geometric measure of entanglement. (author)
Graph Sampling for Covariance Estimation
Chepuri, Sundeep Prabhakar; Leus, Geert
2017-01-01
specialize for undirected circulant graphs in that the graph nodes leading to the best compression rates are given by the so-called minimal sparse rulers. A near-optimal greedy algorithm is developed to design the subsampling scheme for the non
Network reconstruction via graph blending
Estrada, Rolando
2016-05-01
Graphs estimated from empirical data are often noisy and incomplete due to the difficulty of faithfully observing all the components (nodes and edges) of the true graph. This problem is particularly acute for large networks where the number of components may far exceed available surveillance capabilities. Errors in the observed graph can render subsequent analyses invalid, so it is vital to develop robust methods that can minimize these observational errors. Errors in the observed graph may include missing and spurious components, as well fused (multiple nodes are merged into one) and split (a single node is misinterpreted as many) nodes. Traditional graph reconstruction methods are only able to identify missing or spurious components (primarily edges, and to a lesser degree nodes), so we developed a novel graph blending framework that allows us to cast the full estimation problem as a simple edge addition/deletion problem. Armed with this framework, we systematically investigate the viability of various topological graph features, such as the degree distribution or the clustering coefficients, and existing graph reconstruction methods for tackling the full estimation problem. Our experimental results suggest that incorporating any topological feature as a source of information actually hinders reconstruction accuracy. We provide a theoretical analysis of this phenomenon and suggest several avenues for improving this estimation problem.
Advanced modularity design for the MIT pebble bed reactor
Kadak, Andrew C. [Department of Nuclear Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, 24-202 Cambridge, MA 02139-4307 (United States)]. E-mail: kadak@mit.edu; Berte, Marc V. [Department of Nuclear Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, 24-202 Cambridge, MA 02139-4307 (United States)]. E-mail: mvberte@yahoo.com
2006-03-15
The future of all reactors will depend on whether they can be economically built and operated. One of the major impediments to new nuclear construction is the capital cost due in large part to the length of construction time and complexity of the plant. Pebble bed reactors offer the opportunity to reduce the complexity of the plant because the number of safety systems required is significantly reduced due to the inherent safety of the technology. However, because of its small size, the capital cost per kilowatt is likely to be large if traditional construction approaches are followed. This strongly suggests the need for innovative construction concepts to reduce the construction time and cost. MIT has proposed a modularity approach in which the plant is pre-built in space-frame type modules which are built in factories. These space frames would contain all the equipment contained in a given volume. Once equipment in the space frame is installed, the space frame would then be shipped to the site and assembled 'lego-style.' Studies presently underway have demonstrated the feasibility of the concept. Thermal stress analysis has been performed and an integrated design with the space frames has been developed. It is expected that this modularity approach will significantly shorten construction time and expense. This paper proposes a concept for further development, not a final design for the entire plant.
Advanced modularity design for the MIT pebble bed reactor
Kadak, Andrew C.; Berte, Marc V.
2006-01-01
The future of all reactors will depend on whether they can be economically built and operated. One of the major impediments to new nuclear construction is the capital cost due in large part to the length of construction time and complexity of the plant. Pebble bed reactors offer the opportunity to reduce the complexity of the plant because the number of safety systems required is significantly reduced due to the inherent safety of the technology. However, because of its small size, the capital cost per kilowatt is likely to be large if traditional construction approaches are followed. This strongly suggests the need for innovative construction concepts to reduce the construction time and cost. MIT has proposed a modularity approach in which the plant is pre-built in space-frame type modules which are built in factories. These space frames would contain all the equipment contained in a given volume. Once equipment in the space frame is installed, the space frame would then be shipped to the site and assembled 'lego-style.' Studies presently underway have demonstrated the feasibility of the concept. Thermal stress analysis has been performed and an integrated design with the space frames has been developed. It is expected that this modularity approach will significantly shorten construction time and expense. This paper proposes a concept for further development, not a final design for the entire plant
Effective thermal conductivity of advanced ceramic breeder pebble beds
Pupeschi, S., E-mail: simone.pupeschi@kit.edu; Knitter, R.; Kamlah, M.
2017-03-15
As the knowledge of the effective thermal conductivity of ceramic breeder pebble beds under fusion relevant conditions is essential for the development of solid breeder blanket concepts, the EU advanced and reference lithium orthosilicate material were investigated with a newly developed experimental setup based on the transient hot wire method. The effective thermal conductivity was investigated in the temperature range RT–700 °C. Experiments were performed in helium and air atmospheres in the pressure range 0.12–0.4 MPa (abs.) under a compressive load up to 6 MPa. Results show a negligible influence of the chemical composition of the solid material on the bed’s effective thermal conductivity. A severe reduction of the effective thermal conductivity was observed in air. In both atmospheres an increase of the effective thermal conductivity with the temperature was detected, while the influence of the compressive load was found to be small. A clear dependence of the effective thermal conductivity on the pressure of the filling gas was observed in helium in contrast to air, where the pressure dependence was drastically reduced.
Cisneros, Anselmo Tomas, Jr.
The Fluoride salt cooled High temperature Reactor (FHR) is a class of advanced nuclear reactors that combine the robust coated particle fuel form from high temperature gas cooled reactors, direct reactor auxillary cooling system (DRACS) passive decay removal of liquid metal fast reactors, and the transparent, high volumetric heat capacitance liquid fluoride salt working fluids---flibe (33%7Li2F-67%BeF)---from molten salt reactors. This combination of fuel and coolant enables FHRs to operate in a high-temperature low-pressure design space that has beneficial safety and economic implications. In 2012, UC Berkeley was charged with developing a pre-conceptual design of a commercial prototype FHR---the Pebble Bed- Fluoride Salt Cooled High Temperature Reactor (PB-FHR)---as part of the Nuclear Energy University Programs' (NEUP) integrated research project. The Mark 1 design of the PB-FHR (Mk1 PB-FHR) is 236 MWt flibe cooled pebble bed nuclear heat source that drives an open-air Brayton combine-cycle power conversion system. The PB-FHR's pebble bed consists of a 19.8% enriched uranium fuel core surrounded by an inert graphite pebble reflector that shields the outer solid graphite reflector, core barrel and reactor vessel. The fuel reaches an average burnup of 178000 MWt-d/MT. The Mk1 PB-FHR exhibits strong negative temperature reactivity feedback from the fuel, graphite moderator and the flibe coolant but a small positive temperature reactivity feedback of the inner reflector and from the outer graphite pebble reflector. A novel neutronics and depletion methodology---the multiple burnup state methodology was developed for an accurate and efficient search for the equilibrium composition of an arbitrary continuously refueled pebble bed reactor core. The Burnup Equilibrium Analysis Utility (BEAU) computer program was developed to implement this methodology. BEAU was successfully benchmarked against published results generated with existing equilibrium depletion codes VSOP
Shams, A.; Roelofs, F.; Komen, E.M.J.; Baglietto, E.
2013-01-01
Highlights: ► Quasi direct numerical simulations (q-DNS) of a pebble bed configuration has been performed. ► This q-DNS database may serve as a reference for the validation of different turbulence modeling approaches. ► A wide range of qualitative and quantitative data throughout the computational domain has been generated. ► Results for mean, RMS and covariance of velocity field are extensively reported in this paper. -- Abstract: High temperature reactors (HTR) are being considered for deployment around the world because of their excellent safety features. The fuel is embedded in a graphite moderator and can sustain very high temperatures. However, the appearance of hot spots in the pebble bed cores of HTR's may affect the integrity of the pebbles. A good prediction of the flow and heat transport in such a pebble bed core is a challenge for available turbulence models and such models need to be validated. In the present article, quasi direct numerical simulations (q-DNS) of a pebble bed configuration are reported, which may serve as a reference for the validation of different turbulence modeling approaches. Such approaches can be used in order to perform calculations for a randomly arranged pebble bed. Simulations are performed at a Reynolds number of 3088, based on pebble diameter, with a porosity level of 0.42. Detailed flow analyses have shown complex physics flow behavior and make this case challenging for turbulence model validation. Hence, a wide range of qualitative and quantitative data for velocity and temperature field have been extracted for this benchmark. In the present article (part I), results related to the flow field (mean, RMS and covariance of velocity) are documented and discussed in detail. Moreover, the discussion regarding the temperature field will be published in a separate article
Preliminary neutronic design of high burnup OTTO cycle pebble bed reactor
Setiadipura, T.; Zuhair; Irwanto, D.
2015-01-01
The pebble bed type High Temperature Gas-cooled Reactor (HTGR) is among the interesting nuclear reactor designs in terms of safety and flexibility for co-generation applications. In addition, the strong inherent safety characteristics of the pebble bed reactor (PBR) which is based on natural mechanisms improve the simplicity of the PBR design, in particular for the Once-Through-Then-Out (OTTO) cycle PBR design. One of the important challenges of the OTTO cycle PBR design, and nuclear reactor design in general, is improving the nuclear fuel utilization which is shown by attaining a higher burnup value. This study performed a preliminary neutronic design study of a 200 MWt OTTO cycle PBR with high burnup while fulfilling the safety criteria of the PBR design.The safety criteria of the design was represented by the per-fuel-pebble maximum power generation of 4.5 kW/pebble. The maximum burnup value was also limited by the tested maximum burnup value which maintained the integrity of the pebble fuel. Parametric surveys were performed to obtain the optimized parameters used in this study, which are the fuel enrichment, per-pebble heavy metal (HM) loading, and the average axial speed of the fuel. An optimum design with burnup value of 131.1 MWd/Kg-HM was achieved in this study which is much higher compare to the burnup of the reference design HTR-MODUL and a previously proposed OTTO-cycle PBR design. This optimum design uses 17% U-235 enrichment with 4 g HM-loading per fuel pebble. (author)
Preliminary Neutronic Design of High Burnup OTTO Cycle Pebble Bed Reactor
T. Setiadipura
2015-04-01
Full Text Available The pebble bed type High Temperature Gas-cooled Reactor (HTGR is among the interesting nuclear reactor designs in terms of safety and flexibility for co-generation applications. In addition, the strong inherent safety characteristics of the pebble bed reactor (PBR which is based on natural mechanisms improve the simplicity of the PBR design, in particular for the Once-Through-Then-Out (OTTO cycle PBR design. One of the important challenges of the OTTO cycle PBR design, and nuclear reactor design in general, is improving the nuclear fuel utilization which is shown by attaining a higher burnup value. This study performed a preliminary neutronic design study of a 200 MWt OTTO cycle PBR with high burnup while fulfilling the safety criteria of the PBR design.The safety criteria of the design was represented by the per-fuel-pebble maximum power generation of 4.5 kW/pebble. The maximum burnup value was also limited by the tested maximum burnup value which maintained the integrity of the pebble fuel. Parametric surveys were performed to obtain the optimized parameters used in this study, which are the fuel enrichment, per-pebble heavy metal (HM loading, and the average axial speed of the fuel. An optimum design with burnup value of 131.1 MWd/Kg-HM was achieved in this study which is much higher compare to the burnup of the reference design HTR-MODUL and a previously proposed OTTO-cycle PBR design. This optimum design uses 17% U-235 enrichment with 4 g HM-loading per fuel pebble
Planar graphs theory and algorithms
Nishizeki, T
1988-01-01
Collected in this volume are most of the important theorems and algorithms currently known for planar graphs, together with constructive proofs for the theorems. Many of the algorithms are written in Pidgin PASCAL, and are the best-known ones; the complexities are linear or 0(nlogn). The first two chapters provide the foundations of graph theoretic notions and algorithmic techniques. The remaining chapters discuss the topics of planarity testing, embedding, drawing, vertex- or edge-coloring, maximum independence set, subgraph listing, planar separator theorem, Hamiltonian cycles, and single- or multicommodity flows. Suitable for a course on algorithms, graph theory, or planar graphs, the volume will also be useful for computer scientists and graph theorists at the research level. An extensive reference section is included.
Quantum chaos on discrete graphs
Smilansky, Uzy
2007-01-01
Adapting a method developed for the study of quantum chaos on quantum (metric) graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76), spectral ζ functions and trace formulae for discrete Laplacians on graphs are derived. This is achieved by expressing the spectral secular equation in terms of the periodic orbits of the graph and obtaining functions which belong to the class of ζ functions proposed originally by Ihara (1966 J. Mat. Soc. Japan 18 219) and expanded by subsequent authors (Stark and Terras 1996 Adv. Math. 121 124, Kotani and Sunada 2000 J. Math. Sci. Univ. Tokyo 7 7). Finally, a model of 'classical dynamics' on the discrete graph is proposed. It is analogous to the corresponding classical dynamics derived for quantum graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76). (fast track communication)
RJSplot: Interactive Graphs with R.
Barrios, David; Prieto, Carlos
2018-03-01
Data visualization techniques provide new methods for the generation of interactive graphs. These graphs allow a better exploration and interpretation of data but their creation requires advanced knowledge of graphical libraries. Recent packages have enabled the integration of interactive graphs in R. However, R provides limited graphical packages that allow the generation of interactive graphs for computational biology applications. The present project has joined the analytical power of R with the interactive graphical features of JavaScript in a new R package (RJSplot). It enables the easy generation of interactive graphs in R, provides new visualization capabilities, and contributes to the advance of computational biology analytical methods. At present, 16 interactive graphics are available in RJSplot, such as the genome viewer, Manhattan plots, 3D plots, heatmaps, dendrograms, networks, and so on. The RJSplot package is freely available online at http://rjsplot.net. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Liu, Hongbing, E-mail: liuhb07@mails.tsinghua.edu.cn [Department of Mechanical Engineering, Tsinghua University, Beijing 100084 (China); Key Laboratory for Advanced Materials Processing Technology, Ministry of Education P. R. China, Beijing 100084 (China); Du, Dong, E-mail: dudong@tsinghua.edu.cn [Department of Mechanical Engineering, Tsinghua University, Beijing 100084 (China); Key Laboratory for Advanced Materials Processing Technology, Ministry of Education P. R. China, Beijing 100084 (China); Huang, An; Chang, Baohua; Han, Zandong [Department of Mechanical Engineering, Tsinghua University, Beijing 100084 (China); Key Laboratory for Advanced Materials Processing Technology, Ministry of Education P. R. China, Beijing 100084 (China); He, Ayada [Shanghai Electric Power Generation Group Shanghai Generator Works, Shanghai 200240 (China)
2016-08-15
Highlights: • A detection system for locations of pebbles transported in pipes is introduced. • The detection system is based on vibration signal processing, which is original. • The characteristics of the vibration signals of the pipe are analyzed. • The experiment shows that the detection results are accurate. • The research provides an important basis for the design of the reactor. - Abstract: Pebble-bed high temperature gas-cooled reactors have many advantages such as inherent safety, high efficiency, etc., and have been considered as a candidate for Generation IV nuclear reactors. During the operation of the reactor, there are thousands of fuel pebbles transported in the pipes outside the core by gravity and helium flow. The pattern of the pipes which consist of straight and arc sections is very complex. When a fuel pebble is transported, it will constantly collide with the pipes, especially in the arc sections. The collisions will lead to the vibration of the pipes. This paper aims to provide a detection system for the location of fuel pebbles transported in pipes in a pebble-bed reactor based on vibration signal processing. Before the reactor is running, the system acquires the vibration signals of several key sections by sensors. Then the frequency characteristics of the signals are obtained by joint time–frequency analysis. When the reactor is running, the system detects the signals and processes them based on their frequency characteristics in real time. According to the results of the processing, the system can correctly judge whether the fuel pebble has passed through the section and records the time of the passing. The experiment validates the accuracy and reliability of the detection results. In this way, the operational condition of the reactor can be monitored so that the normal running of the reactor can be ensured. Additionally, the detection data are of great significance to the evaluation and optimization of the reactor performance
Liu, Hongbing; Du, Dong; Huang, An; Chang, Baohua; Han, Zandong; He, Ayada
2016-01-01
Highlights: • A detection system for locations of pebbles transported in pipes is introduced. • The detection system is based on vibration signal processing, which is original. • The characteristics of the vibration signals of the pipe are analyzed. • The experiment shows that the detection results are accurate. • The research provides an important basis for the design of the reactor. - Abstract: Pebble-bed high temperature gas-cooled reactors have many advantages such as inherent safety, high efficiency, etc., and have been considered as a candidate for Generation IV nuclear reactors. During the operation of the reactor, there are thousands of fuel pebbles transported in the pipes outside the core by gravity and helium flow. The pattern of the pipes which consist of straight and arc sections is very complex. When a fuel pebble is transported, it will constantly collide with the pipes, especially in the arc sections. The collisions will lead to the vibration of the pipes. This paper aims to provide a detection system for the location of fuel pebbles transported in pipes in a pebble-bed reactor based on vibration signal processing. Before the reactor is running, the system acquires the vibration signals of several key sections by sensors. Then the frequency characteristics of the signals are obtained by joint time–frequency analysis. When the reactor is running, the system detects the signals and processes them based on their frequency characteristics in real time. According to the results of the processing, the system can correctly judge whether the fuel pebble has passed through the section and records the time of the passing. The experiment validates the accuracy and reliability of the detection results. In this way, the operational condition of the reactor can be monitored so that the normal running of the reactor can be ensured. Additionally, the detection data are of great significance to the evaluation and optimization of the reactor performance
On θ-commutators and the corresponding non-commuting graphs
Shalchi S.
2017-12-01
Full Text Available The θ-commutators of elements of a group with respect to an automorphism are introduced and their properties are investigated. Also, corresponding to θ-commutators, we define the θ-non-commuting graphs of groups and study their correlations with other notions. Furthermore, we study independent sets in θ-non-commuting graphs, which enable us to evaluate the chromatic number of such graphs.
Forbidden minors for the class of graphs G with $\\xi (G) \\leq 2$
Hogben, L.; Holst, van der H.
2007-01-01
For a given simple graph G, is defined to be the set of real symmetric matrices A whose (i,j)th entry is nonzero whenever i¿j and ij is an edge in G. In [F. Barioli, S. Fallat, L. Hogben, A variant on the graph parameters of Colin de Verdière: Implications to the minimum rank of graphs, Electron. J.
Graph embedding with rich information through heterogeneous graph
Sun, Guolei
2017-11-12
Graph embedding, aiming to learn low-dimensional representations for nodes in graphs, has attracted increasing attention due to its critical application including node classification, link prediction and clustering in social network analysis. Most existing algorithms for graph embedding only rely on the topology information and fail to use the copious information in nodes as well as edges. As a result, their performance for many tasks may not be satisfactory. In this thesis, we proposed a novel and general framework for graph embedding with rich text information (GERI) through constructing a heterogeneous network, in which we integrate node and edge content information with graph topology. Specially, we designed a novel biased random walk to explore the constructed heterogeneous network with the notion of flexible neighborhood. Our sampling strategy can compromise between BFS and DFS local search on heterogeneous graph. To further improve our algorithm, we proposed semi-supervised GERI (SGERI), which learns graph embedding in an discriminative manner through heterogeneous network with label information. The efficacy of our method is demonstrated by extensive comparison experiments with 9 baselines over multi-label and multi-class classification on various datasets including Citeseer, Cora, DBLP and Wiki. It shows that GERI improves the Micro-F1 and Macro-F1 of node classification up to 10%, and SGERI improves GERI by 5% in Wiki.
South African safety assessment framework for the pebble bed modular reactor - HTR2008-58192
Joubert, J.; Kohtz, N.; Coe, I.
2008-01-01
It is planned to construct a first of a kind Pebble Bed Modular Reactor (PBMR) in South Africa. A need has been recognized to accompany the licensing process for the PBMR with independent safety assessments to ensure that the safety case submitted by the applicant complies with the licensing requirements of the NNR. At the HTR 2006 Conference, the framework and major challenges on safety assessment that the South African National Nuclear Regulator (NNR) faces in developing and applying appropriate strategies and tools were presented. This paper discusses the current status of the various NNR assessment activities and describes how this will be considered in the NNR Final Report on the PBMR Safety Case. The traditional safety assessment process has been adapted to take into account the developmental nature of the project. By performing safety assessments, the designer and applicant must ensure that the design as proposed for construction and as-built meets the safety requirements defined by the regulatory framework. The regulator performs independent safety assessments, including independent analyses in areas deemed safety significant and potentially safety significant. The developmental nature of the project also led to the identification of a series of regulatory assessment activities preceding the formal assessment of the safety case. Besides an assessment of the resolution of Key Licensing Issues which have been defined in an early stage of the project and are discussed in /l/, these activities comprise the participation in an SAR Early Intervention Process, the execution of a regulatory HAZOP and the development of a regulatory assessment specification for the formal assessment of the safety case. This paper briefly describes these activities and their current status. During the last two years, significant progress was made with the development or adjustment of tools for the independent analysis by the regulator of the steady state core design, of the transient
CORECLUSTER: A Degeneracy Based Graph Clustering Framework
Giatsidis , Christos; Malliaros , Fragkiskos; Thilikos , Dimitrios M. ,; Vazirgiannis , Michalis
2014-01-01
International audience; Graph clustering or community detection constitutes an important task forinvestigating the internal structure of graphs, with a plethora of applications in several domains. Traditional tools for graph clustering, such asspectral methods, typically suffer from high time and space complexity. In thisarticle, we present \\textsc{CoreCluster}, an efficient graph clusteringframework based on the concept of graph degeneracy, that can be used along withany known graph clusteri...
Conceptual design of a passively safe thorium breeder Pebble Bed Reactor
Wols, F.J.; Kloosterman, J.L.; Lathouwers, D.; Hagen, T.H.J.J. van der
2015-01-01
Highlights: • This work proposes three possible designs for a thorium Pebble Bed Reactor. • A high-conversion PBR (CR > 0.96), passively safe and within practical constraints. • A thorium breeder PBR (220 cm core) in practical regime, but not passively safe. • A passively safe breeder, requiring higher fuel reprocessing and recycling rates. - Abstract: More sustainable nuclear power generation might be achieved by combining the passive safety and high temperature applications of the Pebble Bed Reactor (PBR) design with the resource availability and favourable waste characteristics of the thorium fuel cycle. It has already been known that breeding can be achieved with the thorium fuel cycle inside a Pebble Bed Reactor if reprocessing is performed. This is also demonstrated in this work for a cylindrical core with a central driver zone, with 3 g heavy metal pebbles for enhanced fission, surrounded by a breeder zone containing 30 g thorium pebbles, for enhanced conversion. The main question of the present work is whether it is also possible to combine passive safety and breeding, within a practical operating regime, inside a thorium Pebble Bed Reactor. Therefore, the influence of several fuel design, core design and operational parameters upon the conversion ratio and passive safety is evaluated. A Depressurized Loss of Forced Cooling (DLOFC) is considered the worst safety scenario that can occur within a PBR. So, the response to a DLOFC with and without scram is evaluated for several breeder PBR designs using a coupled DALTON/THERMIX code scheme. With scram it is purely a heat transfer problem (THERMIX) demonstrating the decay heat removal capability of the design. In case control rods cannot be inserted, the temperature feedback of the core should also be able to counterbalance the reactivity insertion by the decaying xenon without fuel temperatures exceeding 1600 °C. Results show that high conversion ratios (CR > 0.96) and passive safety can be combined in
Meng Xianke; Sun Zhongning; Xu Guangzhan
2012-01-01
Graphical abstract: The core of the water-cooled pebble bed reactor is the porous channels which stacked with spherical fuel elements. The gaps between the adjacent fuel elements are complex because they are stochastic and often shift. We adopt electromagnetic induction heating method to overall heat the pebble bed. By comparing and analyzing the experimental data, we get the rule of power distribution and the rule of heat transfer coefficient with particle diameter, heat flux density, inlet temperature and working fluid's Re number. Highlights: ► We adopt electromagnetic induction heating method to overall heat the pebble bed to be the internal heat source. ► The ball diameter is smaller, the effect of the heat transfer is better. ► With Re number increasing, heat transfer coefficient is also increasing and eventually tends to stabilize. ► The changing of heat power makes little effect on the heat transfer coefficient of pebble bed channels. - Abstract: The reactor core of a water-cooled pebble bed reactor includes porous channels that are formed by spherical fuel elements. This structure has notably improved heat transfer. Due to the variability and randomness of the interstices in pebble bed channels, heat transfer is complex, and there are few studies regarding this topic. To study the heat transfer characters of pebble bed channels with internal heat sources, oxidized stainless steel spheres with diameters of 3 and 8 mm and carbon steel spheres with 8 mm diameters are used in a stacked pebble bed. Distilled water is used as a refrigerant for the experiments, and the electromagnetic induction heating method is used to heat the pebble bed. By comparing and analyzing the experimental results, we obtain the governing rules for the power distribution and the heat transfer coefficient with respect to particle diameter, heat flux density, inlet temperature and working fluid Re number. From fitting of the experimental data, we obtain the dimensionless average
Improvement of burnup analysis for pebble bed reactors with an accumulative fuel loading scheme
Simanullang, Irwan Liapto; Obara, Toru
2015-01-01
Given the limitations of natural uranium resources, innovative nuclear power plant concepts that increase the efficiency of nuclear fuel utilization are needed. The Pebble Bed Reactor (PBR) shows some potential to achieve high efficiency in natural uranium utilization. To simplify the PBR concept, PBR with an accumulation fuel loading scheme was introduced and the Fuel Handling System (FHS) removed. In this concept, the pebble balls are added little by little into the reactor core until the pebble balls reach the top of the reactor core, and all pebble balls are discharged from the core at the end of the operation period. A code based on the MVP/MVP-BURN method has been developed to perform an analysis of a PBR with the accumulative fuel loading scheme. The optimum fuel composition was found using the code for high burnup performance. Previous efforts provided several motivations to improve the burnup performance: First, some errors in the input code were corrected. This correction, and an overall simplification of the input code, was implemented for easier analysis of a PBR with the accumulative fuel loading scheme. Second, the optimum fuel design had been obtained in the infinite geometry. To improve the optimum fuel composition, a parametric survey was obtained by varying the amount of Heavy Metal (HM) uranium per pebble and the degree of uranium enrichment. Moreover, an entire analysis of the parametric survey was obtained in the finite geometry. The results show that improvements in the fuel composition can lead to more accurate analysis with the code. (author)
Irwanto, Dwi; Setiadipura, Topan; Pramutadi, Asril
2017-07-01
There are two type of High Temperature Gas Reactor (HTGR), prismatic and pebble bed. Pebble Bed type has unique configuration because the fuels are randomly distributed inside the reactor core. In term of safety features, Pebble Bed Reactor (PBR) is one of the most promising reactor type in avoiding severe nuclear accidents. In order to analyze heat transfer and safety of this reactor type, a computer code is now under development. As a first step, calculation method proposed by Stroh [1] is adopted. An approach has been made to treat randomly distributed pebble balls contains fissile material inside the reactor core as a porous medium. Helium gas act as coolant on the reactor system are carrying heat flowing in the area between the pebble balls. Several parameters and constants are taken into account in the new developed code. Progress of the development of the code especially comparison of several thermal conductivity constants for a certain PBR-case are reported in the present study.
THE ROLE OF PEBBLE FRAGMENTATION IN PLANETESIMAL FORMATION. II. NUMERICAL SIMULATIONS
Jansson, Karl Wahlberg; Johansen, Anders [Lund Observatory, Department of Astronomy and Theoretical Physics, Lund University, Box 43, SE-221 00 Lund (Sweden); Syed, Mohtashim Bukhari; Blum, Jürgen [Technische Universität Braunschweig, Institut für Geophysik und extraterrestrische Physik, Mendelssohnstraße 3, D-38106 Braunschweig (Germany)
2017-01-20
Some scenarios for planetesimal formation go through a phase of collapse of gravitationally bound clouds of millimeter- to centimeter-size pebbles. Such clouds can form, for example, through the streaming instability in protoplanetary disks. We model the collapse process with a statistical model to obtain the internal structure of planetesimals with solid radii between 10 and 1000 km. During the collapse, pebbles collide, and depending on their relative speeds, collisions have different outcomes. A mixture of particle sizes inside a planetesimal leads to better packing capabilities and higher densities. In this paper we apply results from new laboratory experiments of dust aggregate collisions (presented in a companion paper) to model collision outcomes. We find that the internal structure of a planetesimal is strongly dependent on both its mass and the applied fragmentation model. Low-mass planetesimals have no/few fragmenting pebble collisions in the collapse phase and end up as porous pebble piles. The number of fragmenting collisions increases with increasing cloud mass, resulting in wider particle size distributions and higher density. The collapse is nevertheless “cold” in the sense that collision speeds are damped by the high collision frequency. This ensures that a significant fraction of large pebbles survive the collapse in all but the most massive clouds. Our results are in broad agreement with the observed increase in density of Kuiper Belt objects with increasing size, as exemplified by the recent characterization of the highly porous comet 67P/Churyumov–Gerasimenko.
A prediction model for the effective thermal conductivity of mono-sized pebble beds
Wang, Xiaoliang; Zheng, Jie; Chen, Hongli, E-mail: hlchen1@ustc.edu.cn
2016-02-15
Highlights: • One new method to couple the contact area with bed strain is developed. • The constant coefficient to correlate the effect of gas flow is determined. • This model is valid for various cases, and its advantages are showed obviously. - Abstract: A model is presented here to predict the effective thermal conductivity of porous medium packed with mono-sized spherical pebbles, and it is valid when pebbles’ size is far less than the characteristic length of porous medium just like the fusion pebble beds. In this model, the influences of parameters such as properties of pebble and gas materials, bed porosity, pebble size, gas flow, contact area, thermal radiation, contact resistance, etc. are all taken into account, and one method to couple the contact areas with bed strains is also developed and implemented preliminarily. Compared with available theoretical models, CFD numerical simulations and experimental data, this model is verified to be successful to forecast the bed effective thermal conductivity in various cases and its advantages are also showed obviously. Especially, the convection in pebble beds is focused on and a constant coefficient C to correlate the effect of gas flow is determined for the fully developed region of beds by numerical simulation, which is close to some experimental data.
The importance of the AVR pebble-bed reactor for the future of nuclear power
Pohl, P.
2006-01-01
The AVR pebble-bed high temperature gas-cooled reactor (HTGR) at Juelich (Germany)) operated from 1967 to 1988 and was certainly the most important HTGR project of the past. The reactor was the mass test bed for all development steps of HTGR pebble fuel. Some early fuel charges failed under high temperature conditions and contaminated the reactor. An accurate pebble measurement (Cs 137) allowed to clean the core from unwanted pebbles after 1981. The coolant activity went down and remained very low for the remaining reactor operation. A melt-wire experiment in 1986 revealed max. coolant temperatures of >1280 deg. C and fuel temperatures of >1350 deg. C, explained by under-estimated bypasses. The fuel still in the core achieved high burn-ups and showed under the extreme temperature conditions excellent fission product retention. Thus, the AVR operation qualified the HTGR fuel, and an average discharge burn-up of 112% fifa revealed an excellent fuel economy of the pebble-bed reactor. Furthermore, the AVR operation offers many meaningful data for code-to-experiment comparisons. (authors)
Features and validation of discrete element method for simulating pebble flow in reactor core
Xu Yong; Li Yanjie
2005-01-01
The core of a High-Temperature Gas-cooled Reactor (HTGR) is composed of big number of fuel pebbles, their kinetic behaviors are of great importance in estimating the path and residence time of individual pebble, the evolution of the mixing zone for the assessment of the efficiency of a reactor. Numerical method is highlighted in modern reactor design. In view of granular flow, the Discrete Element Model based on contact mechanics of spheres was briefly described. Two typical examples were presented to show the capability of the DEM method. The former is piling with glass/steel spheres, which provides validated evidences that the simulated angles of repose are in good coincidence with the experimental results. The later is particle discharge in a flat- bottomed silo, which shows the effects of material modulus and demonstrates several features. The two examples show the DEM method enables to predict the behaviors, such as the evolution of pebble profiles, streamlines etc., and provides sufficient information for pebble flow analysis and core design. In order to predict the cyclic pebble flow in a HTGR core precisely and efficiently, both model and code improvement are needed, together with rational specification of physical properties with proper measuring techniques. Strategic and methodological considerations were also discussed. (authors)
Numerical Simulation of a Coolant Flow and Heat Transfer in a Pebble Bed Reactor
In, Wang-Kee; Kim, Min-Hwan; Lee, Won-Jae
2008-01-01
Pebble Bed Reactor(PBR) is one of the very high temperature gas cooled reactors(VHTR) which have been reviewed in the Generation IV International Forum as potential sources for future energy needs, particularly for a hydrogen production. The pebble bed modular reactor(PBMR) exhibits inherent safety features due to the low power density and the large amount of graphite present in the core. PBR uses coated fuel particles(TRISO) embedded in spherical graphite fuel pebbles. The fuel pebbles flow down through the PBR core during a reactor operation and the coolant flows around randomly distributed spheres. For the reliable operation and the safety of the PBR, it is important to understand the coolant flow structure and the fuel pebble temperature in the PBR core. There have been few experimental and numerical studies to investigate the fluid and heat transfer phenomena in the PBR core. The objective of this paper is to predict the fluid and heat transfer in the PBR core. The computational fluid dynamics (CFD) code, STAR-CCM+(V2.08) is used to perform the CFD analysis using the design data for the PBMR400
Stability and convergence analysis of the quasi-dynamics method for the initial pebble packing
Li, Y.; Ji, W.
2012-01-01
The simulation for the pebble flow recirculation within Pebble Bed Reactors (PBRs) requires an efficient algorithm to generate an initial overlap-free pebble configuration within the reactor core. In the previous work, a dynamics-based approach, the Quasi-Dynamics Method (QDM), has been proposed to generate densely distributed pebbles in PBRs with cylindrical and annular core geometries. However, the stability and the efficiency of the QDM were not fully addressed. In this work, the algorithm is reformulated with two control parameters and the impact of these parameters on the algorithm performance is investigated. Firstly, the theoretical analysis for a 1-D packing system is conducted and the range of the parameter in which the algorithm is convergent is estimated. Then, this estimation is verified numerically for a 3-D packing system. Finally, the algorithm is applied to modeling the PBR fuel loading configuration and the convergence performance at different packing fractions is presented. Results show that the QDM is efficient in packing pebbles within the realistic range of the packing fraction in PBRs, and it is capable in handling cylindrical geometry with packing fractions up to 63.5%. (authors)
A comparative study on the effective thermal conductivity of a single size beryllium pebble bed
Abou-Sena, A.; Ying, A.; Abdou, M.
2004-01-01
Solid breeder blankets generally use beryllium-helium pebble beds to ensure sufficient tritium breeding. The data of the effective thermal conductivity, k eff , of beryllium pebble beds is important to the design of fusion blankets. It serves as a database for benchmarking the models of pebble beds. The objective of this paper is to review and compare the available data (obtained by several studies) of the effective thermal conductivity of beryllium pebble beds in order to address the current status of these data. Two comparisons are presented: one for the data of k eff versus bed mean temperature and the second one for the data of k eff versus external applied pressures. The data (k eff versus bed temperature) reported by Enoeda et al., Dalle Donne et al., and UCLA, have a similar particle size and packing fraction. Despite their similarity, the standard deviation values of their data are around 32%. Also, the data of the effective thermal conductivity as a function of mechanical pressure have standard deviation values of ∼50%. From the presented comparisons, significant discrepancies among the available data of k eff of the beryllium pebble beds were observed. These discrepancies may be attributed to the apparent differences among available studies, such as experiment technique, packing fraction, particle characteristics, bed dimensions, and temperature range and gradient across the bed. (author)
Hierarchy of modular graph identities
D’Hoker, Eric; Kaidi, Justin
2016-01-01
The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus. In earlier work, surprising identities between two-loop graphs at all weights, and between higher-loop graphs of weights four and five were constructed. In the present paper, these results are generalized in two complementary directions. First, all identities at weight six and all dihedral identities at weight seven are obtained and proven. Whenever the Laurent polynomial at the cusp is available, the form of these identities confirms the pattern by which the vanishing of the Laurent polynomial governs the full modular identity. Second, the family of modular graph functions is extended to include all graphs with derivative couplings and worldsheet fermions. These extended families of modular graph functions are shown to obey a hierarchy of inhomogeneous Laplace eigenvalue equations. The eigenvalues are calculated analytically for the simplest infinite sub-families and obtained by Maple for successively more complicated sub-families. The spectrum is shown to consist solely of eigenvalues s(s−1) for positive integers s bounded by the weight, with multiplicities which exhibit rich representation-theoretic patterns.
Semantic graphs and associative memories
Pomi, Andrés; Mizraji, Eduardo
2004-12-01
Graphs have been increasingly utilized in the characterization of complex networks from diverse origins, including different kinds of semantic networks. Human memories are associative and are known to support complex semantic nets; these nets are represented by graphs. However, it is not known how the brain can sustain these semantic graphs. The vision of cognitive brain activities, shown by modern functional imaging techniques, assigns renewed value to classical distributed associative memory models. Here we show that these neural network models, also known as correlation matrix memories, naturally support a graph representation of the stored semantic structure. We demonstrate that the adjacency matrix of this graph of associations is just the memory coded with the standard basis of the concept vector space, and that the spectrum of the graph is a code invariant of the memory. As long as the assumptions of the model remain valid this result provides a practical method to predict and modify the evolution of the cognitive dynamics. Also, it could provide us with a way to comprehend how individual brains that map the external reality, almost surely with different particular vector representations, are nevertheless able to communicate and share a common knowledge of the world. We finish presenting adaptive association graphs, an extension of the model that makes use of the tensor product, which provides a solution to the known problem of branching in semantic nets.
Hierarchy of modular graph identities
D’Hoker, Eric; Kaidi, Justin [Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy,University of California,Los Angeles, CA 90095 (United States)
2016-11-09
The low energy expansion of Type II superstring amplitudes at genus one is organized in terms of modular graph functions associated with Feynman graphs of a conformal scalar field on the torus. In earlier work, surprising identities between two-loop graphs at all weights, and between higher-loop graphs of weights four and five were constructed. In the present paper, these results are generalized in two complementary directions. First, all identities at weight six and all dihedral identities at weight seven are obtained and proven. Whenever the Laurent polynomial at the cusp is available, the form of these identities confirms the pattern by which the vanishing of the Laurent polynomial governs the full modular identity. Second, the family of modular graph functions is extended to include all graphs with derivative couplings and worldsheet fermions. These extended families of modular graph functions are shown to obey a hierarchy of inhomogeneous Laplace eigenvalue equations. The eigenvalues are calculated analytically for the simplest infinite sub-families and obtained by Maple for successively more complicated sub-families. The spectrum is shown to consist solely of eigenvalues s(s−1) for positive integers s bounded by the weight, with multiplicities which exhibit rich representation-theoretic patterns.
Munk-Madsen, Andreas
2005-01-01
"Project" is a key concept in IS management. The word is frequently used in textbooks and standards. Yet we seldom find a precise definition of the concept. This paper discusses how to define the concept of a project. The proposed definition covers both heavily formalized projects and informally...... organized, agile projects. Based on the proposed definition popular existing definitions are discussed....
Smith, Suzanne M; Nedorost, Susan T
2010-01-01
The term "dermatitis" can be defined narrowly or broadly, clinically or histologically. A common and costly condition, dermatitis is underresourced compared to other chronic skin conditions. The lack of a collectively understood definition of dermatitis and its subcategories could be the primary barrier. To investigate how dermatologists define the term "dermatitis" and determine if a consensus on the definition of this term and other related terms exists. A seven-question survey of dermatologists nationwide was conducted. Of respondents (n = 122), half consider dermatitis to be any inflammation of the skin. Nearly half (47.5%) use the term interchangeably with "eczema." Virtually all (> 96%) endorse the subcategory "atopic" under the terms "dermatitis" and "eczema," but the subcategories "contact," "drug hypersensitivity," and "occupational" are more highly endorsed under the term "dermatitis" than under the term "eczema." Over half (55.7%) personally consider "dermatitis" to have a broad meaning, and even more (62.3%) believe that dermatologists as a whole define the term broadly. There is a lack of consensus among experts in defining dermatitis, eczema, and their related subcategories.
Shannon limit of the channel. Among the earliest discovered codes that approach the. Shannon limit were the low density parity check (LDPC) codes. The term low density arises from the property of the parity check matrix defining the code. We will now define this matrix and the role that it plays in decoding. 2. Linear Codes.
Graph based techniques for tag cloud generation
Leginus, Martin; Dolog, Peter; Lage, Ricardo Gomes
2013-01-01
Tag cloud is one of the navigation aids for exploring documents. Tag cloud also link documents through the user defined terms. We explore various graph based techniques to improve the tag cloud generation. Moreover, we introduce relevance measures based on underlying data such as ratings...... or citation counts for improved measurement of relevance of tag clouds. We show, that on the given data sets, our approach outperforms the state of the art baseline methods with respect to such relevance by 41 % on Movielens dataset and by 11 % on Bibsonomy data set....
Nuclear Safeguards Considerations For The Pebble Bed Modular Reactor (PBMR)
Phillip Casey Durst; David Beddingfield; Brian Boyer; Robert Bean; Michael Collins; Michael Ehinger; David Hanks; David L. Moses; Lee Refalo
2009-10-01
High temperature reactors (HTRs) have been considered since the 1940s, and have been constructed and demonstrated in the United Kingdom (Dragon), United States (Peach Bottom and Fort Saint Vrain), Japan (HTTR), Germany (AVR and THTR-300), and have been the subject of conceptual studies in Russia (VGM). The attraction to these reactors is that they can use a variety of reactor fuels, including abundant thorium, which upon reprocessing of the spent fuel can produce fissile U-233. Hence, they could extend the stocks of available uranium, provided the fuel is reprocessed. Another attractive attribute is that HTRs typically operate at a much higher temperature than conventional light water reactors (LWRs), because of the use of pyrolytic carbon and silicon carbide coated (TRISO) fuel particles embedded in ceramic graphite. Rather than simply discharge most of the unused heat from the working fluid in the power plant to the environment, engineers have been designing reactors for 40 years to recover this heat and make it available for district heating or chemical conversion plants. Demonstrating high-temperature nuclear energy conversion was the purpose behind Fort Saint Vrain in the United States, THTR-300 in Germany, HTTR in Japan, and HTR-10 and HTR-PM, being built in China. This resulted in nuclear reactors at least 30% or more thermodynamically efficient than conventional LWRs, especially if the waste heat can be effectively utilized in chemical processing plants. A modern variant of high temperature reactors is the Pebble Bed Modular Reactor (PBMR). Originally developed in the United States and Germany, it is now being redesigned and marketed by the Republic of South Africa and China. The team examined historical high temperature and high temperature gas reactors (HTR and HTGR) and reviewed safeguards considerations for this reactor. The following is a preliminary report on this topic prepared under the ASA-100 Advanced Safeguards Project in support of the NNSA Next
XML Graphs in Program Analysis
Møller, Anders; Schwartzbach, Michael I.
2011-01-01
of XML graphs against different XML schema languages, and provide a software package that enables others to make use of these ideas. We also survey the use of XML graphs for program analysis with four very different languages: XACT (XML in Java), Java Servlets (Web application programming), XSugar......XML graphs have shown to be a simple and effective formalism for representing sets of XML documents in program analysis. It has evolved through a six year period with variants tailored for a range of applications. We present a unified definition, outline the key properties including validation...
Rabern, Landon
2007-01-01
We improve upper bounds on the chromatic number proven independently in \\cite{reedNote} and \\cite{ingo}. Our main lemma gives a sufficient condition for two paths in graph to be completely joined. Using this, we prove that if a graph has an optimal coloring with more than $\\frac{\\omega}{2}$ singleton color classes, then it satisfies $\\chi \\leq \\frac{\\omega + \\Delta + 1}{2}$. It follows that a graph satisfying $n - \\Delta < \\alpha + \\frac{\\omega - 1}{2}$ must also satisfy $\\chi \\leq \\frac{\\ome...
Mining the inner structure of the Web graph
Donato, Debora; Leonardi, Stefano; Millozzi, Stefano; Tsaparas, Panayiotis
2008-01-01
Despite being the sum of decentralized and uncoordinated efforts by heterogeneous groups and individuals, the World Wide Web exhibits a well-defined structure, characterized by several interesting properties. This structure was clearly revealed by Broder et al (2000 Graph structure in the web Comput. Netw. 33 309) who presented the evocative bow-tie picture of the Web. Although, the bow-tie structure is a relatively clear abstraction of the macroscopic picture of the Web, it is quite uninformative with respect to the finer details of the Web graph. In this paper, we mine the inner structure of the Web graph. We present a series of measurements on the Web, which offer a better understanding of the individual components of the bow-tie. In the process, we develop algorithmic techniques for performing these measurements. We discover that the scale-free properties permeate all the components of the bow-tie which exhibit the same macroscopic properties as the Web graph itself. However, close inspection reveals that their inner structure is quite distinct. We show that the Web graph does not exhibit self similarity within its components, and we propose a possible alternative picture for the Web graph, as it emerges from our experiments
Szabó, György; Fáth, Gábor
2007-07-01
Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first four sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fifth section surveys the topological complications implied by non-mean-field-type social network structures in general. The next three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.
Tree-type values for cycle-free directed graph games
Khmelnitskaya, Anna Borisovna; Talman, Dolf
2010-01-01
For arbitrary cycle-free directed graph games tree-type values are introduced axiomatically and their explicit formula representation is provided. These values may be considered as natural extensions of the tree and sink values as has been defined correspondingly for rooted and sink forest graph
On the Equivalence between some Local and Global Chinese Postman and Traveling Salesman Graphs
Granot, D.; Hamers, H.J.M.
2000-01-01
A connected graph G=(V,E), a vertex in V and a non-negative weight function defined on Ecan be used to induce Chinese postman and traveling salesman (cooperative) games. A graph G=(V,E) is said to be locally (respectively, globally) Chinese postman balanced (respectively, totally balanced,
Sum of All-Pairs Shortest Path Distances in a Planar Graph in Subquadratic Time
Wulff-Nilsen, Christian
2008-01-01
We consider the problem of computing the Wiener index of a graph, defined as the sum of distances between all pairs of its vertices. It is an open problem whether the Wiener index of a planar graph can be found in subquadratic time. We solve this problem by presenting an algorithm with O(n^2*log...
Study of the fracture behavior of mortar and concretes with crushed rock or pebble aggregates
Sebastião Ribeiro
2011-03-01
Full Text Available The objective of this work was to compare the fracture energy of mortar and concretes produced with crushed rock and pebble aggregates using zero, 10, 20, 30 and 40% of aggregates mixed with standard mortar and applying the wedge splitting method to achieve stable crack propagation. The samples were cast in a special mold and cured for 28 days, after which they were subjected to crack propagation tests by the wedge splitting method to determine the fracture energies of the mortar and concrete. The concretes showed higher fracture energy than the mortar, and the concretes containing crushed rock showed higher resistance to crack propagation than all the compositions containing pebbles. The fracture energy varied from 38 to 55 J.m-2. A comparison of the number of aggregates that separated from the two concrete matrices with the highest fracture energies indicated that the concrete containing pebbles crumbled more easily and was therefore less resistant to crack propagation.
Progress on pebble bed experimental activity for the HE-FUS3 mock-ups
Dell'Orco, G.; Sansone, L.; Simoncini, M.; Zito, D.
2002-01-01
The EU Long Term for DEMO Programme foresees the qualification of the reference design of the helium cooled pebble bed (HCPB) - test blanket module (TBM) to be tested in ITER Reactor. In this frame, FZK and ENEA have launched many experimental activities for the evaluation of the interactions between the Tritium breeder and neutron multiplier pebble beds and the steel containment walls. Main aim of these activities is the measuring the pebble bed effective thermal conductivity, the wall heat transfer coefficient as well as their dependency from the mechanical constraints. The paper presents the progress of the testing activity and results of the tests on two mock-up, called Tazza and Helichetta, carried out on the HE-FUS3 facility at ENEA Brasimone. (orig.)
Numerical characterization of thermo-mechanical performance of breeder pebble beds
An, Zhiyong; Ying, Alice; Abdou, Mohamed
2008-01-01
A numerical approach using the discrete element method (DEM) has been applied to study the thermo-mechanical properties of ceramic breeder pebble beds. This numerical scheme is able to predict the inelastic behavior observed in a loading and unloading operation. In addition, it demonstrates that the average value of contact force increases linearly with overall pressure, but at a much faster rate, about 3.4 times the overall pressure increase rate. In this paper, the thermal creep properties of two different ceramic breeder pebble materials, Li 4 SiO 4 and Li 2 O, are also examined by the current numerical code. The difference found in the properties of candidate materials is reflected numerically in the overall strain in the pebble bed when the stress magnitude becomes smaller. (author)
Consideration of emergency source terms for pebble-bed high temperature gas-cooled reactor
Tao, Liu; Jun, Zhao; Jiejuan, Tong; Jianzhu, Cao
2009-01-01
Being the last barrier in the nuclear power plant defense-in-depth strategy, emergency planning (EP) is an integrated project. One of the key elements in this process is emergency source terms selection. Emergency Source terms for light water reactor (LWR) nuclear power plant (NPP) have been introduced in many technical documents, and advanced NPP emergency planning is attracting attention recently. Commercial practices of advanced NPP are undergoing in the world, pebble-bed high-temperature gas-cooled reactor (HTGR) power plant is under construction in China which is considered as a representative of advanced NPP. The paper tries to find some pieces of suggestion from our investigation. The discussion of advanced NPP EP will be summarized first, and then the characteristics of pebble-bed HTGR relating to EP will be described. Finally, PSA insights on emergency source terms selection and current pebble-bed HTGR emergency source terms suggestions are proposed
Thermal-hydraulic analysis techniques for axisymmetric pebble bed nuclear reactor cores
Stroh, K.R.
1979-03-01
The pebble bed reactor's cylindrical core volume contains a random bed of small, spherical fuel-moderator elements. These graphite spheres, containing a central region of dispersed coated-particle fissile and fertile material, are cooled by high pressure helium flowing through the connected interstitial voids. A mathematical model and numerical solution technique have been developed which allow calculation of macroscopic values of thermal-hydraulic variables in an axisymmetric pebble bed nuclear reactor core. The computer program PEBBLE is based on a mathematical model which treats the bed macroscopically as a generating, conducting porous medium. The steady-state model uses a nonlinear Forchheimer-type relation between the coolant pressure gradient and mass flux, with newly derived coefficients for the linear and quadratic resistance terms. The remaining equations in the model make use of mass continuity, and thermal energy balances for the solid and fluid phases
Numerical characterization of thermo-mechanical performance of breeder pebble beds
An, Zhiyong; Ying, Alice; Abdou, Mohamed
2007-01-01
A numerical approach using the discrete element method (DEM) has been applied to study the thermo-mechanical properties of ceramic breeder pebble beds. This numerical scheme is able to predict the inelastic behavior observed in a loading and unloading operation. In addition, it demonstrates that the average value of contact force increases linearly with overall pressure, but at a much faster rate, about 3.4 times the overall pressure increase rate. In this paper, the thermal creep properties of two different ceramic breeder pebble materials, Li 4 SiO 4 and Li 2 O, are also examined by the current numerical code. The difference found in the properties of candidate materials is reflected numerically in the overall strain in the pebble bed when the stress magnitude becomes smaller
Verification of two-temperature method for heat transfer process within a pebble fuel
Yu Dali; Peng Minjun
2014-01-01
A typical pebble fuel that used in high temperature reactor (HTR), mainly consists of a graphite matrix with numerous dispersed tristructural-isotropic (TRISO) fuel particles and a surrounding thin non-fueled graphite shell. These high heterogeneities lead to difficulty in explicit thermal calculation of a pebble fuel. We proposed a two-temperature method (TTM) to calculate the temperature distribution within a pebble fuel. The method is not only convenient to perform but also gives more realistic results since particles and graphite matrix are considered separately while the traditional ways are considering the fuel zone as average heat generation source. The method is validated both by Computational Fluid Dynamics (CFD) method and Wiener bounds. Results show that TTM has a stable performance and high accuracy. (author)
DEM-CFD simulation of purge gas flow in a solid breeder pebble bed
Zhang, Hao [School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230027 (China); Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang 621900 (China); Li, Zhenghong [Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang 621900 (China); University of Science and Technology of China, Hefei 230027 (China); Guo, Haibing [Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang 621900 (China); Ye, Minyou [School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230027 (China); Huang, Hongwen, E-mail: inpclane@sina.com [Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang 621900 (China)
2016-12-15
Solid tritium breeding blanket applying pebble bed concept is promising for fusion reactors. Tritium bred in the pebble bed is purged out by inert gas. The flow characteristics of the purge gas are important for the tritium transport from the solid breeder materials. In this study, a randomly packed pebble bed was generated by Discrete Element Method (DEM) and verified by radial porosity distribution. The flow parameters of the purge gas in channels were solved by Computational Fluid Dynamics (CFD) method. The results show that the normalized velocity magnitudes have the same damped oscillating patterns with radial porosity distribution. Besides, the bypass flow near the wall cannot be ignored in this model, and it has a slight increase with inlet velocity. Furthermore, higher purging efficiency becomes with higher inlet velocity and especially higher in near wall region.
Measurement of flow field in the pebble bed type high temperature gas-cooled reactor
Lee, Sa Ya; Lee, Jae Young
2008-01-01
In this study, flow field measurement of the Pebble Bed Reactor(PBR) for the High Temperature Gascooled Reactor(HTGR) was performed. Large number of pebbles in the core of PBR provides complicated flow channel. Due to the complicated geometries, numerical analysis has been intensively made rather than experimental observation. However, the justification of computational simulation by the experimental study is crucial to develop solid analysis of design method. In the present study, a wind tunnel installed with pebbles stacked was constructed and equipped with the Particle Image Velocimetry(PIV). We designed the system scaled up to realize the room temperature condition according to the similarity. The PIV observation gave us stagnation points, low speed region so that the suspected high temperature region can be identified. With the further supplementary experimental works, the present system may produce valuable data to justify the Computational Fluid Dynamics(CFD) simulation method
Computational and experimental prediction of dust production in pebble bed reactors, Part II
Mie Hiruta; Gannon Johnson; Maziar Rostamian; Gabriel P. Potirniche; Abderrafi M. Ougouag; Massimo Bertino; Louis Franzel; Akira Tokuhiro
2013-10-01
This paper is the continuation of Part I, which describes the high temperature and high pressure helium environment wear tests of graphite–graphite in frictional contact. In the present work, it has been attempted to simulate a Pebble Bed Reactor core environment as compared to Part I. The experimental apparatus, which is a custom-designed tribometer, is capable of performing wear tests at PBR relevant higher temperatures and pressures under a helium environment. This environment facilitates prediction of wear mass loss of graphite as dust particulates from the pebble bed. The experimental results of high temperature helium environment are used to anticipate the amount of wear mass produced in a pebble bed nuclear reactor.
Xiao, Chengjian; Gao, Xiaoling; Kobayashi, Makoto; Kawasaki, Kiyotaka; Uchimura, Hiromichi; Toda, Kensuke; Kang, Chunmei; Chen, Xiaojun; Wang, Heyi; Peng, Shuming; Wang, Xiaolin; Oya, Yasuhisa; Okuno, Kenji
2013-01-01
Tritium release kinetics in lithium orthosilicate (Li 4 SiO 4 ) ceramic pebbles irradiated with low thermal-neutron fluence was studied by out-of-pile annealing experiments. It was found that the tritium produced in Li 4 SiO 4 pebbles was mainly released as tritiated water vapor (HTO). The apparent desorption activation energy of tritium on the pebble surface was consistent with the diffusion activation energy of tritium in the crystal grains, indicating that tritium release was mainly controlled by diffusion process. The diffusion coefficients of tritium in the crystal grains at temperatures ranging from 450 K to 600 K were obtained by isothermal annealing tests, and the Arrhenius relation was determined to be D = 1 × 10 −7.0 exp (−40.3 × 10 3 /RT) cm 2 s −1
Xiao, Chengjian; Gao, Xiaoling [Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Box 919-214, Mian Yang 621900 (China); Kobayashi, Makoto; Kawasaki, Kiyotaka; Uchimura, Hiromichi; Toda, Kensuke [China Academy of Engineering Physics, Box 919-1, Mian Yang 621900 (China); Kang, Chunmei; Chen, Xiaojun; Wang, Heyi; Peng, Shuming [Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Box 919-214, Mian Yang 621900 (China); Wang, Xiaolin, E-mail: xlwang@caep.ac.cn [China Academy of Engineering Physics, Box 919-1, Mian Yang 621900 (China); Oya, Yasuhisa; Okuno, Kenji [Radiochemistry Research Laboratory, Faculty of Science, Shizuoka University, 836 Ohya, Shizuoka 422-8529 (Japan)
2013-07-15
Tritium release kinetics in lithium orthosilicate (Li{sub 4}SiO{sub 4}) ceramic pebbles irradiated with low thermal-neutron fluence was studied by out-of-pile annealing experiments. It was found that the tritium produced in Li{sub 4}SiO{sub 4} pebbles was mainly released as tritiated water vapor (HTO). The apparent desorption activation energy of tritium on the pebble surface was consistent with the diffusion activation energy of tritium in the crystal grains, indicating that tritium release was mainly controlled by diffusion process. The diffusion coefficients of tritium in the crystal grains at temperatures ranging from 450 K to 600 K were obtained by isothermal annealing tests, and the Arrhenius relation was determined to be D = 1 × 10{sup −7.0} exp (−40.3 × 10{sup 3}/RT) cm{sup 2} s{sup −1}.
Electrical behaviour of ceramic breeder blankets in pebble form after γ-radiation
E. Carella
2015-07-01
Full Text Available Lithium orthosilicate (Li4SiO4 ceramics in from of pebble bed is the European candidate for ITER testing HCPB (Helium Cooled Pebble Bed breeding modules. The breeder function and the shielding role of this material, represent the areas upon which attention is focused. Electrical measurements are proposed for monitoring the modification created by ionizing radiation and at the same time provide information on lithium movement in this ceramic structure. The electrical tests are performed on pebbles fabricated by Spray-dryer method before and after gamma-irradiation through a 60Co source to a fluence of 4.8 Gy/s till a total dose of 5 ∗ 105 Gy. The introduction of thermal annealing treatments during the electrical impedance spectroscopy (EIS measurements points out the recombination effect of the temperature on the γ-induced defects.
Kurinskiy, P., E-mail: petr.kurinskiy@kit.edu [Karlsruhe Institute of Technology, Institute for Applied Materials – Applied Materials Physics (IAM-AWP), P.O. Box 3640, Karlsruhe 76021 (Germany); Vladimirov, P.; Moeslang, A. [Karlsruhe Institute of Technology, Institute for Applied Materials – Applied Materials Physics (IAM-AWP), P.O. Box 3640, Karlsruhe 76021 (Germany); Rolli, R. [Karlsruhe Institute of Technology, Institute for Applied Materials – Materials and Biomechanics (IAM-WBM), P.O. Box 3640, Karlsruhe 76021 (Germany); Zmitko, M. [The European Joint Undertaking for ITER and the Development of Fusion Energy, c/Josep Pla, no. 2, Torres Diagonal Litoral, Edificio B3, Barcelona 08019 (Spain)
2014-10-15
Highlights: • Tritium release properties and characteristics of microstructure of beryllium pebbles having different sizes of grains were studied. • Fine-grained beryllium pebbles showed the best ability to release tritium compared to pebbles from another charges. • Be pebbles with the grain sizes exceeding 100 μm contain a great number of small pores and inclusions presumably referring to the history of material fabrication. • The sizes of grains are one of a key characteristic of microstructure which influences the parameters of tritium release. - Abstract: 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. Up to now, the design of helium-cooled breeding blanket in ITER project foresees the use of 1 mm beryllium pebbles fabricated by NGK Insulators Ltd., Japan. 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.
Gongyi Yu
2017-01-01
Full Text Available A nonuniform distribution of tristructural isotropic (TRISO particles within a high-temperature gas-cooled reactor (HTGR pebble may lead to excessive thermal gradients and nonuniform thermal expansion during operation. If the particles are closely clustered, local hotspots may form, leading to excessive stresses on particle layers and an increased probability of particle failure. Although X-ray digital radiography (DR is currently used to evaluate the TRISO distributions in pebbles, X-ray DR projection images are two-dimensional in nature, which would potentially miss some details for 3D evaluation. This paper proposes a method of 3D visualization and evaluation of the TRISO distribution in HTGR pebbles using cone-beam computed tomography (CBCT: first, a pebble is scanned on our high-resolution CBCT, and 2D cross-sectional images are reconstructed; secondly, all cross-sectional images are restructured to form the 3D model of the pebble; then, volume rendering is applied to segment and display the TRISO particles in 3D for visualization and distribution evaluation. For method validation, several pebbles were scanned and the 3D distributions of the TRISO particles within the pebbles were produced. Experiment results show that the proposed method provides more 3D than DR, which will facilitate pebble fabrication research and production quality control.
Properly colored connectivity of graphs
Li, Xueliang; Qin, Zhongmei
2018-01-01
A comprehensive survey of proper connection of graphs is discussed in this book with real world applications in computer science and network security. Beginning with a brief introduction, comprising relevant definitions and preliminary results, this book moves on to consider a variety of properties of graphs that imply bounds on the proper connection number. Detailed proofs of significant advancements toward open problems and conjectures are presented with complete references. Researchers and graduate students with an interest in graph connectivity and colorings will find this book useful as it builds upon fundamental definitions towards modern innovations, strategies, and techniques. The detailed presentation lends to use as an introduction to proper connection of graphs for new and advanced researchers, a solid book for a graduate level topics course, or as a reference for those interested in expanding and further developing research in the area.
Graph anomalies in cyber communications
Vander Wiel, Scott A [Los Alamos National Laboratory; Storlie, Curtis B [Los Alamos National Laboratory; Sandine, Gary [Los Alamos National Laboratory; Hagberg, Aric A [Los Alamos National Laboratory; Fisk, Michael [Los Alamos National Laboratory
2011-01-11
Enterprises monitor cyber traffic for viruses, intruders and stolen information. Detection methods look for known signatures of malicious traffic or search for anomalies with respect to a nominal reference model. Traditional anomaly detection focuses on aggregate traffic at central nodes or on user-level monitoring. More recently, however, traffic is being viewed more holistically as a dynamic communication graph. Attention to the graph nature of the traffic has expanded the types of anomalies that are being sought. We give an overview of several cyber data streams collected at Los Alamos National Laboratory and discuss current work in modeling the graph dynamics of traffic over the network. We consider global properties and local properties within the communication graph. A method for monitoring relative entropy on multiple correlated properties is discussed in detail.
Open Graphs and Computational Reasoning
Lucas Dixon
2010-06-01
Full Text Available We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of half-edges (edges which are drawn with an unconnected end and enjoy rich compositional principles by connecting graphs along these half-edges. In particular, this allows equations and rewrite rules to be specified between graphs. Particular computational models can then be encoded as an axiomatic set of such rules. Further rules can be derived graphically and rewriting can be used to simulate the dynamics of a computational system, e.g. evaluating a program on an input. Examples of models which can be formalised in this way include traditional electronic circuits as well as recent categorical accounts of quantum information.
Woeginger, G.J.
1998-01-01
In this short note we argue that the toughness of split graphs can be computed in polynomial time. This solves an open problem from a recent paper by Kratsch et al. (Discrete Math. 150 (1996) 231–245).
Generating random networks and graphs
Coolen, Ton; Roberts, Ekaterina
2017-01-01
This book supports researchers who need to generate random networks, or who are interested in the theoretical study of random graphs. The coverage includes exponential random graphs (where the targeted probability of each network appearing in the ensemble is specified), growth algorithms (i.e. preferential attachment and the stub-joining configuration model), special constructions (e.g. geometric graphs and Watts Strogatz models) and graphs on structured spaces (e.g. multiplex networks). The presentation aims to be a complete starting point, including details of both theory and implementation, as well as discussions of the main strengths and weaknesses of each approach. It includes extensive references for readers wishing to go further. The material is carefully structured to be accessible to researchers from all disciplines while also containing rigorous mathematical analysis (largely based on the techniques of statistical mechanics) to support those wishing to further develop or implement the theory of rand...
Challenges in forming the solar system's giant planet cores via pebble accretion
Kretke, K. A.; Levison, H. F.
2014-01-01
Though ∼10 M ⊕ mass rocky/icy cores are commonly held as a prerequisite for the formation of gas giants, theoretical models still struggle to explain how these embryos can form within the lifetimes of gaseous circumstellar disks. In recent years, aerodynamic-aided accretion of 'pebbles', objects ranging from centimeters to meters in size, has been suggested as a potential solution to this long-standing problem. While pebble accretion has been demonstrated to be extremely effective in local simulations that look at the detailed behavior of these pebbles in the vicinity of a single planetary embryo, to date there have been no global simulations demonstrating the effectiveness of pebble accretion in a more complicated, multi-planet environment. Therefore, we have incorporated the aerodynamic-aided accretion physics into LIPAD, a Lagrangian code that can follow the collisional/accretional/dynamical evolution of a protoplanetary system, to investigate how pebble accretion manifests itself in the larger planet formation picture. We find that under generic circumstances, pebble accretion naturally leads to an 'oligarchic' type of growth in which a large number of planetesimals grow to similar-sized planets. In particular, our simulations tend to form hundreds of Mars- and Earth-mass objects between 4 and 10 AU. While merging of some oligarchs may grow massive enough to form giant planet cores, leftover oligarchs lead to planetary systems that cannot be consistent with our own solar system. We investigate various ideas presented in the literature (including evaporation fronts and planet traps) and find that none easily overcome this tendency toward oligarchic growth.
Experimental study of flow field characteristics on bed configurations in the pebble bed reactor
Jia, Xinlong; Gui, Nan; Yang, Xingtuan; Tu, Jiyuan; Jia, Haijun; Jiang, Shengyao
2017-01-01
Highlights: • PTV study of flow fields of pebble bed reactor with different configurations are carried out. • Some criteria are proposed to quantify vertical velocity field and flow uniformity. • The effect of different pebble bed configurations is also compared by the proposed criteria. • The displacement thickness is used analogically to analyze flow field characteristics. • The effect of mass flow variation in the stagnated region of the funnel flow is measured. - Abstract: The flow field characteristics are of fundamental importance in the design work of the pebble bed high temperature gas cooled reactor (HTGR). The different effects of bed configurations on the flow characteristics of pebble bed are studied through the PTV (Particle Tracking Velocimetry) experiment. Some criteria, e.g. flow uniformity (σ) and mass flow level (α), are proposed to estimate vertical velocity field and compare the bed configurations. The distribution of the Δθ (angle difference between the individual particle velocity and the velocity vector sum of all particles) is also used to estimate the resultant motion consistency level. Moreover, for each bed configuration, the thickness of displacement is analyzed to measure the effect of the funnel flow zone based on the boundary layer theory. Detailed information shows the quantified characteristics of bed configuration effects on flow uniformity and other characteristics; and the sequence of levels of each estimation criterion is obtained for all bed configurations. In addition, a good design of the pebble bed configuration is suggested and these estimation criteria can be also applied and adopted in testing other geometry designs of pebble bed.
Graph theory and its applications
Gross, Jonathan L
2006-01-01
Gross and Yellen take a comprehensive approach to graph theory that integrates careful exposition of classical developments with emerging methods, models, and practical needs. Their unparalleled treatment provides a text ideal for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology.
Interim report on core physics and fuel cycle analysis of the pebble bed reactor power plant concept
Vondy, D.R.
1977-12-01
Calculations were made to predict the performance of a pebble bed reactor operated in a mode to produce fissile fuel (high conversion or breeding). Both a one pebble design and a design involving large primary feed pebbles and small fertile pebbles were considered. A relatively short residence time of the primary pebbles loaded with 233 U fuel was found to be necessary to achieve a high breeding ratio, but this leads to relatively high fuel costs. A high fissile inventory is associated with a low C/Th ratio and a high thorium loading, causing the doubling time to be long, even though the breeding ratio is high, and the fuel cost of electrical product to be high. Production of 233 U fuel from 235 U feed was studied and performances of the converter and breeder reactor concepts were examined varying the key parameters
Research and application of packing density for pebble bed in HTR
Yu Fujiang; Xie Fei; Sun Ximing
2015-01-01
The pebble bed high temperature gas-cooled reactor is one of the major types of reactors developed by Chinese nuclear technology. The statistical analysis for packing density in the pebble bed is an important issue of physical-thermal calculation and safety analysis. Aimed to this problem, a new kind of method was set up to solve this problem. Compared with the traditional lattice-fill method and the experiment, its efficiency and accuracy were verified, while helping to find out the best length of unit in the traditional lattice-fill method. This method was used to analyze the boundary effects observed by experiments. (authors)
Optimization of a radially cooled pebble bed reactor - HTR2008-58117
Boer, B.; Kloosterman, J. L.; Lathouwers, D.; Van Der Hagen, T. H. J. J.; Van Dam, H.
2008-01-01
By altering the coolant flow direction in a pebble bed reactor from axial to radial, the pressure drop can be reduced tremendously. In this case the coolant flows from the outer reflector through the pebble bed and finally to flow paths in the inner reflector. As a consequence, the fuel temperatures are elevated due to the reduced heat transfer of the coolant. However, the power profile and pebble size in a radially cooled pebble bed reactor can be optimized to achieve lower fuel temperatures than current axially cooled designs, while the low pressure drop can be maintained. The radial power profile in the core can be altered by adopting multi-pass fuel management using several radial fuel zones in the core. The optimal power profile yielding a flat temperature profile is derived analytically and is approximated by radial fuel zoning. In this case, the pebbles pass through the outer region of the core first and each consecutive pass is located in a fuel zone closer to the inner reflector. Thereby, the resulting radial distribution of the fissile material in the core is influenced and the temperature profile is close to optimal. The fuel temperature in the pebbles can be further reduced by reducing the standard pebble diameter from 6 cm to a value as low as I cm. An analytical investigation is used to demonstrate the effects on the fuel temperature and pressure drop for both radial and axial cooling. Finally, two-dimensional numerical calculations were performed, using codes for neutronics, thermal-hydraulics and fuel depletion analysis, in order to validate the results for the optimized design that were obtained from the analytical investigations. It was found that for a radially cooled design with an optimized power profile and reduced pebble diameter (below 3.5 cm) both a reduction in the pressure drop (Δp = -2.6 bar), which increases the reactor efficiency with several percent, and a reduction in the maximum fuel temperature (ΔT = -50 deg. C) can be achieved
Renewable side reflector structure for a pebble bed high temperature reactor
Martin, Roger.
1977-01-01
The description is given of a renewable side reflector structure for a pebble bed high temperature reactor of the kind comprising a cylindrical graphite vessel constituting the neutron reflector, this vessel being filled with graphite pebbles containing the nuclear fuel and enclosed in a concrete protective containment. The internal peripheral area of the vessel is constituted by a line of adjacent graphite rods mounted so that they can rotate about their longitudinal axis and manoeuvrable from outside the concrete containment by means of a shaft passing into it [fr
Pebble pile-up and planetesimal formation at the snow line
Drazkowska, J.
2017-09-01
The planetesimal formation stage represents a major gap in our understanding of planet formation process. Because of this, the late-stage planet accretion models typically make arbitrary assumptions about planetesimals and pebbles distribution, while the state-of-the-art dust evolution models predict no or little planetesimal formation. With this contribution, I present a step toward bridging the gap between the early and late stages of planet formation by models that connect dust coagulation and planetesimal formation. With the aid of evaporation, outward diffusion, and re-condensation of water vapor, pile-up of large pebbles is formed outside of the snow line that facilitates planetesimal formation by streaming instability.
Acceleration of coupled granular flow and fluid flow simulations in pebble bed energy systems
Li, Yanheng; Ji, Wei
2013-01-01
Highlights: ► Fast simulation of coupled pebble flow and coolant flow in PBR systems is studied. ► Dimension reduction based on axisymmetric geometry shows significant speedup. ► Relaxation of coupling frequency is investigated and an optimal range is determined. ► A total of 80% efficiency increase is achieved by the two fast strategies. ► Fast strategies can be applied to simulating other general fluidized bed systems. -- Abstract: Fast and accurate approaches to simulating the coupled particle flow and fluid flow are of importance to the analysis of large particle-fluid systems. This is especially needed when one tries to simulate pebble flow and coolant flow in Pebble Bed Reactor (PBR) energy systems on a routine basis. As one of the Generation IV designs, the PBR design is a promising nuclear energy system with high fuel performance and inherent safety. A typical PBR core can be modeled as a particle-fluid system with strong interactions among pebbles, coolants and reactor walls. In previous works, the coupled Discrete Element Method (DEM)-Computational Fluid Dynamics (CFD) approach has been investigated and applied to modeling PBR systems. However, the DEM-CFD approach is computationally expensive due to large amounts of pebbles in PBR systems. This greatly restricts the PBR analysis for the real time prediction and inclusion of more physics. In this work, based on the symmetry of the PBR geometry and the slow motion characteristics of the pebble flow, two acceleration strategies are proposed. First, a simplified 3D-DEM/2D-CFD approach is proposed to speed up the DEM-CFD simulation without loss of accuracy. Pebble flow is simulated by a full 3D DEM, while the coolant flow field is calculated with a 2D CFD simulation by averaging variables along the annular direction in the cylindrical and annular geometries. Second, based on the slow motion of pebble flow, the impact of the coupling frequency on the computation accuracy and efficiency is
Acceleration of coupled granular flow and fluid flow simulations in pebble bed energy systems
Li, Yanheng, E-mail: liy19@rpi.edu [Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY (United States); Ji, Wei, E-mail: jiw2@rpi.edu [Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY (United States)
2013-05-15
Highlights: ► Fast simulation of coupled pebble flow and coolant flow in PBR systems is studied. ► Dimension reduction based on axisymmetric geometry shows significant speedup. ► Relaxation of coupling frequency is investigated and an optimal range is determined. ► A total of 80% efficiency increase is achieved by the two fast strategies. ► Fast strategies can be applied to simulating other general fluidized bed systems. -- Abstract: Fast and accurate approaches to simulating the coupled particle flow and fluid flow are of importance to the analysis of large particle-fluid systems. This is especially needed when one tries to simulate pebble flow and coolant flow in Pebble Bed Reactor (PBR) energy systems on a routine basis. As one of the Generation IV designs, the PBR design is a promising nuclear energy system with high fuel performance and inherent safety. A typical PBR core can be modeled as a particle-fluid system with strong interactions among pebbles, coolants and reactor walls. In previous works, the coupled Discrete Element Method (DEM)-Computational Fluid Dynamics (CFD) approach has been investigated and applied to modeling PBR systems. However, the DEM-CFD approach is computationally expensive due to large amounts of pebbles in PBR systems. This greatly restricts the PBR analysis for the real time prediction and inclusion of more physics. In this work, based on the symmetry of the PBR geometry and the slow motion characteristics of the pebble flow, two acceleration strategies are proposed. First, a simplified 3D-DEM/2D-CFD approach is proposed to speed up the DEM-CFD simulation without loss of accuracy. Pebble flow is simulated by a full 3D DEM, while the coolant flow field is calculated with a 2D CFD simulation by averaging variables along the annular direction in the cylindrical and annular geometries. Second, based on the slow motion of pebble flow, the impact of the coupling frequency on the computation accuracy and efficiency is
Absorber rod for nuclear reactors in a pebble bed of spherical operating elements
Reinstein, D.; Gnutzmann, H.
1978-01-01
The claim refers to the constructional configuration of an absorber rod, whose and penetrating into the pebble bed has an opening to reduce the fracture rate, so that the operating elements can escape into a channel within the absorber rod. To suit this to the direction of movement of the elements a part of the end of the rod is flexibly connected to the hollow absorber rod via a joint. In this way the mechanical load of the element particles is reduced and simultaneously one achieves that much lower force is required to insert the absorber rod into the pebble bed. (UA) [de
Hunt, Brian R; Ott, Edward
2015-09-01
In this paper, we propose, discuss, and illustrate a computationally feasible definition of chaos which can be applied very generally to situations that are commonly encountered, including attractors, repellers, and non-periodically forced systems. This definition is based on an entropy-like quantity, which we call "expansion entropy," and we define chaos as occurring when this quantity is positive. We relate and compare expansion entropy to the well-known concept of topological entropy to which it is equivalent under appropriate conditions. We also present example illustrations, discuss computational implementations, and point out issues arising from attempts at giving definitions of chaos that are not entropy-based.
A faithful functor among algebras and graphs
Falcón Ganfornina, Óscar Jesús; Falcón Ganfornina, Raúl Manuel; Núñez Valdés, Juan; Pacheco Martínez, Ana María; Villar Liñán, María Trinidad; Vigo Aguiar, Jesús (Coordinador)
2016-01-01
The problem of identifying a functor between the categories of algebras and graphs is currently open. Based on a known algorithm that identifies isomorphisms of Latin squares with isomorphism of vertex-colored graphs, we describe here a pair of graphs that enable us to find a faithful functor between finite-dimensional algebras over finite fields and these graphs.
Graphs with branchwidth at most three
Bodlaender, H.L.; Thilikos, D.M.
1997-01-01
In this paper we investigate both the structure of graphs with branchwidth at most three, as well as algorithms to recognise such graphs. We show that a graph has branchwidth at most three, if and only if it has treewidth at most three and does not contain the three-dimensional binary cube graph
A Modal-Logic Based Graph Abstraction
Bauer, J.; Boneva, I.B.; Kurban, M.E.; Rensink, Arend; Ehrig, H; Heckel, R.; Rozenberg, G.; Taentzer, G.
2008-01-01
Infinite or very large state spaces often prohibit the successful verification of graph transformation systems. Abstract graph transformation is an approach that tackles this problem by abstracting graphs to abstract graphs of bounded size and by lifting application of productions to abstract
Graphs whose complement and square are isomorphic
Pedersen, Anders Sune
2014-01-01
We study square-complementary graphs, that is, graphs whose complement and square are isomorphic. We prove several necessary conditions for a graph to be square-complementary, describe ways of building new square-complementary graphs from existing ones, construct infinite families of square-compl...
Acyclicity in edge-colored graphs
Gutin, Gregory; Jones, Mark; Sheng, Bin
2017-01-01
A walk W in edge-colored graphs is called properly colored (PC) if every pair of consecutive edges in W is of different color. We introduce and study five types of PC acyclicity in edge-colored graphs such that graphs of PC acyclicity of type i is a proper superset of graphs of acyclicity of type...
Building Scalable Knowledge Graphs for Earth Science
Ramachandran, Rahul; Maskey, Manil; Gatlin, Patrick; Zhang, Jia; Duan, Xiaoyi; Miller, J. J.; Bugbee, Kaylin; Christopher, Sundar; Freitag, Brian
2017-01-01
Knowledge Graphs link key entities in a specific domain with other entities via relationships. From these relationships, researchers can query knowledge graphs for probabilistic recommendations to infer new knowledge. Scientific papers are an untapped resource which knowledge graphs could leverage to accelerate research discovery. Goal: Develop an end-to-end (semi) automated methodology for constructing Knowledge Graphs for Earth Science.
Constructing Dense Graphs with Unique Hamiltonian Cycles
Lynch, Mark A. M.
2012-01-01
It is not difficult to construct dense graphs containing Hamiltonian cycles, but it is difficult to generate dense graphs that are guaranteed to contain a unique Hamiltonian cycle. This article presents an algorithm for generating arbitrarily large simple graphs containing "unique" Hamiltonian cycles. These graphs can be turned into dense graphs…
Skew-adjacency matrices of graphs
Cavers, M.; Cioaba, S.M.; Fallat, S.; Gregory, D.A.; Haemers, W.H.; Kirkland, S.J.; McDonald, J.J.; Tsatsomeros, M.
2012-01-01
The spectra of the skew-adjacency matrices of a graph are considered as a possible way to distinguish adjacency cospectral graphs. This leads to the following topics: graphs whose skew-adjacency matrices are all cospectral; relations between the matchings polynomial of a graph and the characteristic
Chromatic polynomials of random graphs
Van Bussel, Frank; Fliegner, Denny; Timme, Marc; Ehrlich, Christoph; Stolzenberg, Sebastian
2010-01-01
Chromatic polynomials and related graph invariants are central objects in both graph theory and statistical physics. Computational difficulties, however, have so far restricted studies of such polynomials to graphs that were either very small, very sparse or highly structured. Recent algorithmic advances (Timme et al 2009 New J. Phys. 11 023001) now make it possible to compute chromatic polynomials for moderately sized graphs of arbitrary structure and number of edges. Here we present chromatic polynomials of ensembles of random graphs with up to 30 vertices, over the entire range of edge density. We specifically focus on the locations of the zeros of the polynomial in the complex plane. The results indicate that the chromatic zeros of random graphs have a very consistent layout. In particular, the crossing point, the point at which the chromatic zeros with non-zero imaginary part approach the real axis, scales linearly with the average degree over most of the density range. While the scaling laws obtained are purely empirical, if they continue to hold in general there are significant implications: the crossing points of chromatic zeros in the thermodynamic limit separate systems with zero ground state entropy from systems with positive ground state entropy, the latter an exception to the third law of thermodynamics.
A note on intrinsic conditional autoregressive models for disconnected graphs
Freni-Sterrantino, Anna; Ventrucci, Massimo; Rue, Haavard
2018-01-01
In this note we discuss (Gaussian) intrinsic conditional autoregressive (CAR) models for disconnected graphs, with the aim of providing practical guidelines for how these models should be defined, scaled and implemented. We show how these suggestions can be implemented in two examples, on disease mapping.
Bi-induced sub graphs and stability number
Zverovich I.E.
2004-01-01
Full Text Available We define a 2-parametric hierarchy CLAP (m, n of bi-hereditary classes of graphs, and show that a maximum stable set can be found in polynomial time within each class CLAP (m, n. The classes can be recognized in polynomial time.
A Graph Based Framework to Model Virus Integration Sites
Raffaele Fronza
2016-01-01
Here, we addressed the challenge to: 1 define the notion of CIS on graph models, 2 demonstrate that the structure of CIS enters in the category of scale-free networks and 3 show that our network approach analyzes CIS dynamically in an integrated systems biology framework using the Retroviral Transposon Tagged Cancer Gene Database (RTCGD as a testing dataset.
A note on intrinsic conditional autoregressive models for disconnected graphs
Freni-Sterrantino, Anna
2018-05-23
In this note we discuss (Gaussian) intrinsic conditional autoregressive (CAR) models for disconnected graphs, with the aim of providing practical guidelines for how these models should be defined, scaled and implemented. We show how these suggestions can be implemented in two examples, on disease mapping.
Bond graph to digraph conversion: A sensor placement optimization ...
In this paper, we consider the optimal sensors placement problem for ... is due to the fact that the construction is generally done from the state equations, ... The Bond Graph (BG) tool defined in Paynter (1961) formal- ... Sensor placement and structural problem formulation .... Thus the obtained four matrices are as follows:.
Critical Behavior of the Annealed Ising Model on Random Regular Graphs
Can, Van Hao
2017-11-01
In Giardinà et al. (ALEA Lat Am J Probab Math Stat 13(1):121-161, 2016), the authors have defined an annealed Ising model on random graphs and proved limit theorems for the magnetization of this model on some random graphs including random 2-regular graphs. Then in Can (Annealed limit theorems for the Ising model on random regular graphs, arXiv:1701.08639, 2017), we generalized their results to the class of all random regular graphs. In this paper, we study the critical behavior of this model. In particular, we determine the critical exponents and prove a non standard limit theorem stating that the magnetization scaled by n^{3/4} converges to a specific random variable, with n the number of vertices of random regular graphs.
Graph Quasicontinuous Functions and Densely Continuous Forms
Lubica Hola
2017-07-01
Full Text Available Let $X, Y$ be topological spaces. A function $f: X \\to Y$ is said to be graph quasicontinuous if there is a quasicontinuous function $g: X \\to Y$ with the graph of $g$ contained in the closure of the graph of $f$. There is a close relation between the notions of graph quasicontinuous functions and minimal usco maps as well as the notions of graph quasicontinuous functions and densely continuous forms. Every function with values in a compact Hausdorff space is graph quasicontinuous; more generally every locally compact function is graph quasicontinuous.
Englander, Elizabeth; Donnerstein, Edward; Kowalski, Robin; Lin, Carolyn A; Parti, Katalin
2017-11-01
Is cyberbullying essentially the same as bullying, or is it a qualitatively different activity? The lack of a consensual, nuanced definition has limited the field's ability to examine these issues. Evidence suggests that being a perpetrator of one is related to being a perpetrator of the other; furthermore, strong relationships can also be noted between being a victim of either type of attack. It also seems that both types of social cruelty have a psychological impact, although the effects of being cyberbullied may be worse than those of being bullied in a traditional sense (evidence here is by no means definitive). A complicating factor is that the 3 characteristics that define bullying (intent, repetition, and power imbalance) do not always translate well into digital behaviors. Qualities specific to digital environments often render cyberbullying and bullying different in circumstances, motivations, and outcomes. To make significant progress in addressing cyberbullying, certain key research questions need to be addressed. These are as follows: How can we define, distinguish between, and understand the nature of cyberbullying and other forms of digital conflict and cruelty, including online harassment and sexual harassment? Once we have a functional taxonomy of the different types of digital cruelty, what are the short- and long-term effects of exposure to or participation in these social behaviors? What are the idiosyncratic characteristics of digital communication that users can be taught? Finally, how can we apply this information to develop and evaluate effective prevention programs? Copyright © 2017 by the American Academy of Pediatrics.
Interactive Graph Layout of a Million Nodes
Peng Mi; Maoyuan Sun; Moeti Masiane; Yong Cao; Chris North
2016-01-01
Sensemaking of large graphs, specifically those with millions of nodes, is a crucial task in many fields. Automatic graph layout algorithms, augmented with real-time human-in-the-loop interaction, can potentially support sensemaking of large graphs. However, designing interactive algorithms to achieve this is challenging. In this paper, we tackle the scalability problem of interactive layout of large graphs, and contribute a new GPU-based force-directed layout algorithm that exploits graph to...
The graph representation approach to topological field theory in 2 + 1 dimensions
Martin, S.P.
1991-02-01
An alternative definition of topological quantum field theory in 2+1 dimensions is discussed. The fundamental objects in this approach are not gauge fields as in the usual approach, but non-local observables associated with graphs. The classical theory of graphs is defined by postulating a simple diagrammatic rule for computing the Poisson bracket of any two graphs. The theory is quantized by exhibiting a quantum deformation of the classical Poisson bracket algebra, which is realized as a commutator algebra on a Hilbert space of states. The wavefunctions in this ''graph representation'' approach are functionals on an appropriate set of graphs. This is in contrast to the usual ''connection representation'' approach in which the theory is defined in terms of a gauge field and the wavefunctions are functionals on the space of flat spatial connections modulo gauge transformations
A Study on the Amount of Random Graph Groupies
Lu, Daodi
2013-01-01
In 1980, Ajtai, Komlos and Szemer{\\'e}di defined "groupie": Let $G=(V,E)$ be a simple graph, $|V|=n$, $|E|=e$. For a vertex $v\\in V$, let $r(v)$ denote the sum of the degrees of the vertices adjacent to $v$. We say $v\\in V$ is a {\\it groupie}, if $\\frac{r(v)}{\\deg(v)}\\geq\\frac{e}{n}.$ In this paper, we prove that in random graph $B(n,p)$, $0
The Eccentric-distance Sum of Some Graphs
P, Padmapriya; Mathad, Veena
2017-01-01
Let $G = (V,E)$ be a simple connected graph. Theeccentric-distance sum of $G$ is defined as$\\xi^{ds}(G) =\\ds\\sum_{\\{u,v\\}\\subseteq V(G)} [e(u)+e(v)] d(u,v)$, where $e(u)$ %\\dsis the eccentricity of the vertex $u$ in $G$ and $d(u,v)$ is thedistance between $u$ and $v$. In this paper, we establish formulaeto calculate the eccentric-distance sum for some graphs, namelywheel, star, broom, lollipop, double star, friendship, multi-stargraph and the join of $P_{n-2}$ and $P_2$.
The eccentric-distance sum of some graphs
Padmapriya P
2017-04-01
Full Text Available Let $G = (V,E$ be a simple connected graph. Theeccentric-distance sum of $G$ is defined as$\\xi^{ds}(G =\\ds\\sum_{\\{u,v\\}\\subseteq V(G} [e(u+e(v] d(u,v$, where $e(u$ %\\dsis the eccentricity of the vertex $u$ in $G$ and $d(u,v$ is thedistance between $u$ and $v$. In this paper, we establish formulaeto calculate the eccentric-distance sum for some graphs, namelywheel, star, broom, lollipop, double star, friendship, multi-stargraph and the join of $P_{n-2}$ and $P_2$.
The b-chromatic number of power graphs
Brice Effantin
2003-06-01
Full Text Available The b-chromatic number of a graph G is defined as the maximum number k of colors that can be used to color the vertices of G, such that we obtain a proper coloring and each color i, with 1 ≤ i≤ k, has at least one representant x i adjacent to a vertex of every color j, 1 ≤ j ≠ i ≤ k. In this paper, we discuss the b-chromatic number of some power graphs. We give the exact value of the b-chromatic number of power paths and power complete binary trees, and we bound the b-chromatic number of power cycles.
Internally connected graphs and the Kashiwara-Vergne Lie algebra
Felder, Matteo
2016-01-01
It is conjectured that the Kashiwara-Vergne Lie algebra $\\widehat{\\mathfrak{krv}}_2$ is isomorphic to the direct sum of the Grothendieck-Teichm\\"uller Lie algebra $\\mathfrak{grt}_1$ and a one-dimensional Lie algebra. In this paper, we use the graph complex of internally connected graphs to define a nested sequence of Lie subalgebras of $\\widehat{\\mathfrak{krv}}_2$ whose intersection is $\\mathfrak{grt}_1$, thus giving a way to interpolate between these two Lie algebras.
Eigenfunction statistics on quantum graphs
Gnutzmann, S.; Keating, J.P.; Piotet, F.
2010-01-01
We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for which such a model was proposed by Berry in 1977. The autocorrelation functions we calculate for an individual quantum graph exhibit a universal component, which completely determines a Gaussian Random Wave Model, and a system-dependent deviation. This deviation depends on the graph only through its underlying classical dynamics. Classical criteria for quantum universality to be met asymptotically in the large graph limit (i.e. for the non-universal deviation to vanish) are then extracted. We use an exact field theoretic expression in terms of a variant of a supersymmetric σ model. A saddle-point analysis of this expression leads to the estimates. In particular, intensity correlations are used to discuss the possible equidistribution of the energy eigenfunctions in the large graph limit. When equidistribution is asymptotically realized, our theory predicts a rate of convergence that is a significant refinement of previous estimates. The universal and system-dependent components of intensity correlation functions are recovered by means of an exact trace formula which we analyse in the diagonal approximation, drawing in this way a parallel between the field theory and semiclassics. Our results provide the first instance where an asymptotic Gaussian Random Wave Model has been established microscopically for eigenfunctions in a system with no disorder.
Degree-based graph construction
Kim, Hyunju; Toroczkai, Zoltan; Erdos, Peter L; Miklos, Istvan; Szekely, Laszlo A
2009-01-01
Degree-based graph construction is a ubiquitous problem in network modelling (Newman et al 2006 The Structure and Dynamics of Networks (Princeton Studies in Complexity) (Princeton, NJ: Princeton University Press), Boccaletti et al 2006 Phys. Rep. 424 175), ranging from social sciences to chemical compounds and biochemical reaction networks in the cell. This problem includes existence, enumeration, exhaustive construction and sampling questions with aspects that are still open today. Here we give necessary and sufficient conditions for a sequence of nonnegative integers to be realized as a simple graph's degree sequence, such that a given (but otherwise arbitrary) set of connections from an arbitrarily given node is avoided. We then use this result to present a swap-free algorithm that builds all simple graphs realizing a given degree sequence. In a wider context, we show that our result provides a greedy construction method to build all the f-factor subgraphs (Tutte 1952 Can. J. Math. 4 314) embedded within K n setmn S k , where K n is the complete graph and S k is a star graph centred on one of the nodes. (fast track communication)
Hierarchical organisation of causal graphs
Dziopa, P.
1993-01-01
This paper deals with the design of a supervision system using a hierarchy of models formed by graphs, in which the variables are the nodes and the causal relations between the variables of the arcs. To obtain a representation of the variables evolutions which contains only the relevant features of their real evolutions, the causal relations are completed with qualitative transfer functions (QTFs) which produce roughly the behaviour of the classical transfer functions. Major improvements have been made in the building of the hierarchical organization. First, the basic variables of the uppermost level and the causal relations between them are chosen. The next graph is built by adding intermediary variables to the upper graph. When the undermost graph has been built, the transfer functions parameters corresponding to its causal relations are identified. The second task consists in the upwelling of the information from the undermost graph to the uppermost one. A fusion procedure of the causal relations has been designed to compute the QFTs relevant for each level. This procedure aims to reduce the number of parameters needed to represent an evolution at a high level of abstraction. These techniques have been applied to the hierarchical modelling of nuclear process. (authors). 8 refs., 12 figs
Recent progress in the modelling of helium and tritium behaviour in irradiated beryllium pebbles
Rabaglino, E.; Ronchi, C.; Cardella, A.
2003-01-01
One of the key issues of the European Helium Cooled Pebble Bed blanket is the behaviour under irradiation of beryllium pebbles, which have the function of neutron multiplier. An intense production of helium occurs in-pile, as well as a non negligible generation of tritium. Helium bubbles induce swelling and a high tritium inventory is a safety issue. Extensive studies for a better understanding, characterisation and modelling of the behaviour of helium and tritium in irradiated beryllium pebbles are being carried out, with the final aim to enable a reliable prediction of gas release and swelling in the full range of operating and accidental conditions of a Fusion Power Reactor. The general strategy consists in integrating studies on macroscopic phenomena (gas release) with the characterisation of corresponding microscopic diffusion phenomena (bubble kinetics) and the assessment of some fundamental diffusion parameter for the models (gas atomic diffusion coefficients). The present work gives a summary of the latest achievements in this context. By an inverse analysis of experimental out-of-pile gas release from weakly irradiated pebbles, coupled to the study of the characteristics of bubble population, it has been possible to assess the thermal diffusion coefficients of helium and tritium in and to improve and validate the classical model of gas precipitation into bubbles inside the grain. The improvement of the description of gas atomic diffusion and precipitation is the first step to enable a more reliable prediction of gas release
Optimized core design and fuel management of a pebble-bed type nuclear reactor
Boer, B.
2009-01-01
The core design of a pebble-bed type Very High Temperature Reactor (VHTR) is optimized, aiming for an increase of the coolant outlet temperature to 1000 C, while retaining its inherent safety features. The VHTR has been selected by the international Generation IV research initiative as one of the
A solid target for SINQ based on a Pb-shot Pebble-bed
Atchison, F.; Heidenreich, G.
1991-01-01
Preliminary results from scoping calculations examining the possibilities of implementing a Pebble-bed of Pb-shot as a target for SINQ are presented. The primary design objects are set out and estimates of heating and activation given. Cooling circuit parameters are discussed and estimates for operating conditions presented. A short discussion of problems associated with a realisation is included. (author)
Aines, Roger D
2015-03-31
A method for separating CO.sub.2 from gas mixtures uses a slurried media impregnated with buffer compounds and coating the solid media with a catalyst or enzyme that promotes the transformation of CO.sub.2 to carbonic acid. Buffer sorbent pebbles with a catalyst or enzyme coating are provided for rapid separation of CO.sub.2 from gas mixtures.
Optimized Core Design and Fuel Management of a Pebble-Bed Type Nuclear Reactor
Boer, Brian
2007-01-01
The Very High Temperature Reactor (VHTR) has been selected by the international Generation IV research initiative as one of the six most promising nuclear reactor concepts that are expected to enter service in the second half of the 21st century. The VHTR is characterized by a high plant efficiency and a high fuel discharge burnup level. More specifically, the (pebble-bed type) High Temperature Reactor (HTR) is known for its inherently safe characteristics, coming from a negative temperature reactivity feedback, a low power density and a large thermal inertia of the core. The core of a pebble-bed reactor consists of graphite spheres (pebbles) that form a randomly packed porous bed, which is cooled by high pressure helium. The pebbles contain thousands of fuel particles, which are coated with several pyrocarbon and silicon carbon layers that are designed to contain the fission products that are formed during operation of the reactor. The inherent safety concept has been demonstrated in small pebble-bed reactors in practice, but an increase in the reactor size and power is required for cost-effective power production. An increase of the power density in order to increase the helium coolant outlet temperature is attractive with regard to the efficiency and possible process heat applications. However, this increase leads in general to higher fuel temperatures, which could lead to a consequent increase of the fuel coating failure probability. This thesis deals with the pebble-bed type VHTR that aims at an increased coolant outlet temperature of 1000 degrees C and beyond. For the simulation of the neutronic and thermal-hydraulic behavior of the reactor the DALTON-THERMIX coupled code system has been developed and has been validated against experiments performed in the AVR and HTR-10 reactors. An analysis of the 400 MWth Pebble Bed Modular Reactor (PBMR) design shows that the inherent safety concept that has been demonstrated in practice in the smaller AVR and HTR-10
Aines, Roger D.
2013-03-12
A method for separating CO.sub.2 from gas mixtures uses a slurried media impregnated with buffer compounds and coating the solid media with a catalyst or enzyme that promotes the transformation of CO.sub.2 to carbonic acid. Buffer sorbent pebbles with a catalyst or enzyme coating are provided for rapid separation of CO.sub.2 from gas mixtures.
Kusnick, Judi
2002-01-01
Analyzes narrative essays--stories of rock formation--written by pre-service elementary school teachers. Reports startling misconceptions among preservice teachers on pebbles that grow, human involvement in rock formation, and sedimentary rocks forming as puddles as dry up, even though these students had completed a college level course on Earth…
Discussion on Design Transients of Pebble-bed High Temperature Gas-cooled Reactor
Wang Yan; Li Fu; Zheng Yanhua
2014-01-01
In order to assure high quality for the components and their supports in the reactor coolant system, etc., some thermal-hydraulic transient conditions will be selected and researched for equipment design evaluation to satisfy the requirements ASME code, which are based on the conservative estimates of the magnitude and frequency of the temperature and pressure transients resulting from various operating conditions in the plant. In the mature design on pressurized water reactor, five conditions are considered. For the developing advanced pebble-bed high temperature gas-cooled reactor(HTGR), its design and operation has much difference with other reactors, so the transients of the pebble-bed high temperature gas-cooled reactor have distinctive characteristics. In this paper, the possible design transients of the pebble-bed HTGR will be discussed, and the frequency of design transients for equipment fatigue analysis and stress analysis due to cyclic stresses is also studied. The results will provide support for the design and construct of the pebble-bed HTGR. (author)
Integer Flows and Circuit Covers of Graphs and Signed Graphs
Cheng, Jian
The work in Chapter 2 is motivated by Tutte and Jaeger's pioneering work on converting modulo flows into integer-valued flows for ordinary graphs. For a signed graphs (G, sigma), we first prove that for each k ∈ {2, 3}, if (G, sigma) is (k - 1)-edge-connected and contains an even number of negative edges when k = 2, then every modulo k-flow of (G, sigma) can be converted into an integer-valued ( k + 1)-ow with a larger or the same support. We also prove that if (G, sigma) is odd-(2p+1)-edge-connected, then (G, sigma) admits a modulo circular (2 + 1/ p)-flows if and only if it admits an integer-valued circular (2 + 1/p)-flows, which improves all previous result by Xu and Zhang (DM2005), Schubert and Steffen (EJC2015), and Zhu (JCTB2015). Shortest circuit cover conjecture is one of the major open problems in graph theory. It states that every bridgeless graph G contains a set of circuits F such that each edge is contained in at least one member of F and the length of F is at most 7/5∥E(G)∥. This concept was recently generalized to signed graphs by Macajova et al. (JGT2015). In Chapter 3, we improve their upper bound from 11∥E( G)∥ to 14/3 ∥E(G)∥, and if G is 2-edgeconnected and has even negativeness, then it can be further reduced to 11/3 ∥E(G)∥. Tutte's 3-flow conjecture has been studied by many graph theorists in the last several decades. As a new approach to this conjecture, DeVos and Thomassen considered the vectors as ow values and found that there is a close relation between vector S1-flows and integer 3-NZFs. Motivated by their observation, in Chapter 4, we prove that if a graph G admits a vector S1-flow with rank at most two, then G admits an integer 3-NZF. The concept of even factors is highly related to the famous Four Color Theorem. We conclude this dissertation in Chapter 5 with an improvement of a recent result by Chen and Fan (JCTB2016) on the upperbound of even factors. We show that if a graph G contains an even factor, then it
Modular Software-Defined Radio
Rhiemeier Arnd-Ragnar
2005-01-01
Full Text Available In view of the technical and commercial boundary conditions for software-defined radio (SDR, it is suggestive to reconsider the concept anew from an unconventional point of view. The organizational principles of signal processing (rather than the signal processing algorithms themselves are the main focus of this work on modular software-defined radio. Modularity and flexibility are just two key characteristics of the SDR environment which extend smoothly into the modeling of hardware and software. In particular, the proposed model of signal processing software includes irregular, connected, directed, acyclic graphs with random node weights and random edges. Several approaches for mapping such software to a given hardware are discussed. Taking into account previous findings as well as new results from system simulations presented here, the paper finally concludes with the utility of pipelining as a general design guideline for modular software-defined radio.
Computational Investigation of On-Line Interrogation of Pebble Bed Reactor Fuel
Hawari, A. I.; Chen, Jianwei
2005-10-01
Pebble bed reactors are characterized by multipass fuel systems in which spherical fuel pebbles are circulated through the core until they reach a proposed burnup limit (80000-100000 MWD/MTU). For such reactors, the fuel is assayed on-line to ensure that the burnup limit is not breached. We considered assaying the fuel using an HPGe detector to perform passive gamma-ray spectrometry of fission products. Since neither fresh nor irradiated fuel is readily available, computer simulations were utilized to identify the radionuclides that can be used as burnup indicators, and to visualize the gamma-ray spectra at various levels of burnup. Specifically, we used the ORIGEN-MONTEBURNS-MCNP code system. This allowed the establishment of the burnup dependent one-group gas reactor cross-sections for the radionuclides of interest. Subsequently, ORIGEN was used to simulate in-core pebble depletion to establish the irradiated pebble isotopics. Finally, the codes MCNP and SYNTH were used to simulate the response of the HPGe gamma-ray spectrometer. The results show that absolute and relative indicators can be used on-line to determine unambiguously the enrichment and burnup on a pebble-by-pebble basis. The activity of Cs-137 or the activity ratio of Co-60/Cs-134 can be combined with the activity ratio of Np-239/I-132 to yield the enrichment and burnup information. To use the relative indicators, a relative efficiency calibration of the gamma-ray spectrometer can be performed using the La-140 gamma lines that are emitted by the irradiated pebble. I-132, Cs-134, Cs-137, La-140, and Np-239 are produced upon the irradiation of the fuel. Co-60 is produced by doping the fuel with a small amount (/spl sim/100 ppm) of Co-59. Using this approach, the uncertainty in burnup determination due to factors such as power history variation, detector efficiency calibration, and counting statistics is expected to remain in the range of /spl plusmn/5% to /spl plusmn/10%.
Computational prediction of dust production in graphite moderated pebble bed reactors
Rostamian, Maziar
The scope of the work reported here, which is the computational study of graphite wear behavior, supports the Nuclear Engineering University Programs project "Experimental Study and Computational Simulations of Key Pebble Bed Thermomechanics Issues for Design and Safety" funded by the US Department of Energy. In this work, modeling and simulating the contact mechanics, as anticipated in a PBR configuration, is carried out for the purpose of assessing the amount of dust generated during a full power operation year of a PBR. A methodology that encompasses finite element analysis (FEA) and micromechanics of wear is developed to address the issue of dust production and its quantification. Particularly, the phenomenon of wear and change of its rate with sliding length is the main focus of this dissertation. This work studies the wear properties of graphite by simulating pebble motion and interactions of a specific type of nuclear grade graphite, IG-11. This study consists of two perspectives: macroscale stress analysis and microscale analysis of wear mechanisms. The first is a set of FEA simulations considering pebble-pebble frictional contact. In these simulations, the mass of generated graphite particulates due to frictional contact is calculated by incorporating FEA results into Archard's equation, which is a linear correlation between wear mass and wear length. However, the experimental data by Johnson, University of Idaho, revealed that the wear rate of graphite decreases with sliding length. This is because the surfaces of the graphite pebbles become smoother over time, which results in a gradual decrease in wear rate. In order to address the change in wear rate, a more detailed analysis of wear mechanisms at room temperature is presented. In this microscale study, the wear behavior of graphite at the asperity level is studied by simulating the contact between asperities of facing surfaces. By introducing the effect of asperity removal on wear rate, a nonlinear
Measurement of thermal expansion for a Li2TiO3 pebble bed
Hisashi Tanigawa; Mikio Enoeda; Masato Akiba
2006-01-01
In the current design of the blanket with ceramic breeders, pebbles of breeding materials are packed into a container and used as a pebble bed. Thermal and mechanical conditions externally loaded on the bed affect thermal and mechanical properties of the bed. It is necessary to analyze thermo-mechanical properties of the bed under controlled thermal and mechanical conditions. In the present paper, thermal expansion of a Li 2 TiO 3 pebble bed was investigated. Our apparatus consists of a tensile test-apparatus and a measurement chamber. Pebbles of Li 2 TiO 3 with 2 mm diameter were used. They were packed into a container made of alumina. At first, thermal expansion of the apparatus was calibrated because the measured deformation included thermal expansions of the load rods and the container. Instead of the pebble bed, a column made of copper was installed and thermal expansion of the system was measured for the calibration. Taking into account the estimated thermal expansion of the column, thermal expansion of the rods and the container could be analyzed. Based on the correction, thermal expansion of the pebble bed was measured under compression of 0.1 MPa. Temperature of the bed was regulated from room temperature to 973 K. From the measured expansion of the bed, average thermal expansion coefficient was estimated. For the beds with different packing factors ranging from 65.5 to 68.5 %, thermal expansion coefficients were 1.4 ± 0. 10-5 K -1 . In the first measurement of the beds without pre-loading, expansion coefficients were larger for the cooling process than heating. When the beds were successively heated and cooled, the difference decreased. This means that relocation of the pebbles arises in the first heat treatment and progress of compaction is larger in the cooling process than heating. After a few heat treatments, packing states of the beds reach stable and expansion coefficients for both heat and cooling processes are close. In the case of the beds that
An industrial robot singular trajectories planning based on graphs and neural networks
Łęgowski, Adrian; Niezabitowski, Michał
2016-06-01
Singular trajectories are rarely used because of issues during realization. A method of planning trajectories for given set of points in task space with use of graphs and neural networks is presented. In every desired point the inverse kinematics problem is solved in order to derive all possible solutions. A graph of solutions is made. The shortest path is determined to define required nodes in joint space. Neural networks are used to define the path between these nodes.
GraphAlignment: Bayesian pairwise alignment of biological networks
Kolář Michal
2012-11-01
Full Text Available Abstract Background With increased experimental availability and accuracy of bio-molecular networks, tools for their comparative and evolutionary analysis are needed. A key component for such studies is the alignment of networks. Results We introduce the Bioconductor package GraphAlignment for pairwise alignment of bio-molecular networks. The alignment incorporates information both from network vertices and network edges and is based on an explicit evolutionary model, allowing inference of all scoring parameters directly from empirical data. We compare the performance of our algorithm to an alternative algorithm, Græmlin 2.0. On simulated data, GraphAlignment outperforms Græmlin 2.0 in several benchmarks except for computational complexity. When there is little or no noise in the data, GraphAlignment is slower than Græmlin 2.0. It is faster than Græmlin 2.0 when processing noisy data containing spurious vertex associations. Its typical case complexity grows approximately as O(N2.6. On empirical bacterial protein-protein interaction networks (PIN and gene co-expression networks, GraphAlignment outperforms Græmlin 2.0 with respect to coverage and specificity, albeit by a small margin. On large eukaryotic PIN, Græmlin 2.0 outperforms GraphAlignment. Conclusions The GraphAlignment algorithm is robust to spurious vertex associations, correctly resolves paralogs, and shows very good performance in identification of homologous vertices defined by high vertex and/or interaction similarity. The simplicity and generality of GraphAlignment edge scoring makes the algorithm an appropriate choice for global alignment of networks.
Fabrication of Li{sub 4}SiO{sub 4} pebbles by a sol-gel technique
Wu Xiangwei [Shanghai Institute of Ceramics, Chinese Academy of Sciences, 1295 Dingxi Road, Shanghai 200050 (China); Wen Zhaoyin [Shanghai Institute of Ceramics, Chinese Academy of Sciences, 1295 Dingxi Road, Shanghai 200050 (China)], E-mail: zywen@mail.sic.ac.cn; Xu Xiaogang; Liu Yu [Shanghai Institute of Ceramics, Chinese Academy of Sciences, 1295 Dingxi Road, Shanghai 200050 (China)
2010-04-15
Li{sub 4}SiO{sub 4} pebbles are considered as candidate ceramic breeder materials in many blanket designs. In this work, Li{sub 4}SiO{sub 4} pebbles with adequate sphericity were fabricated by a water-based sol-gel process using LiOH and SiO{sub 2} (aerosil) as the raw materials, which has not been reported for fabrication of Li{sub 4}SiO{sub 4} pebbles previously. Thermal analysis, phase analysis and morphological observations were carried out systematically. The effects of LiOH/C{sub 6}H{sub 8}O{sub 7} molar ratios and sintering temperature on the microstructure and density of the pebbles were discussed. Experimental results showed that when the LiOH/C{sub 6}H{sub 8}O{sub 7} molar ratio was 3, the microstructure of the Li{sub 4}SiO{sub 4} pebbles was the most favorable. While sintered at 900 deg. C for 4 h, Li{sub 4}SiO{sub 4} pebbles with about 1.2 mm in diameter were obtained and the density of the pebbles achieved about 74%.
DeMange, P.; Marian, J.; Caro, M.; Caro, A.
2009-01-01
Concept designs for the laser inertial fusion/fission energy (LIFE) engine include a neutron multiplication blanket containing Be pebbles flowing in a molten salt coolant. These pebbles must be designed to withstand the extreme irradiation and temperature conditions in the blanket to enable a reliable and cost-effective operation of LIFE. In this work, we develop design criteria for spherical Be pebbles on the basis of their thermo-mechanical behaviour under continued neutron exposure. We consider the effects of high fluence and fast fluxes on the elastic, thermal and mechanical properties of nuclear-grade Be. Our results suggest a maximum pebble diameter of 30 mm to avoid tensile failure, coated with an anti-corrosive, high-strength metallic shell to avoid failure by pebble contact. Moreover, we find that the operation temperature must always be kept above 450 deg. C to enable creep to relax the stresses induced by swelling. Under these circumstances, we estimate the pebble lifetime to be at least 16 months if uncoated, and up to six years when coated. We identify the sources of uncertainty on the properties used and discuss the advantages of new intermetallic beryllides and their use in LIFE's neutron multiplier. To establish Be-pebble lifetimes with improved confidence, reliable experiments to measure irradiation creep must be performed.
Essential spectra of difference operators on Zn-periodic graphs
Rabinovich, Vladimir S; Roch, Steffen
2007-01-01
Let (X, ρ) be a discrete metric space. We suppose that the group Z n acts freely on X and that the number of orbits of X with respect to this action is finite. Then we call X a Z n -periodic discrete metric space. We examine the Fredholm property and essential spectra of band-dominated operators on l p (X) when 1 n and their limit operators. In the case where X is the set of vertices of a combinatorial graph, the graph structure defines a Schroedinger operator on l p (X) in a natural way. We illustrate our approach by determining the essential spectra of Schroedinger operators with slowly oscillating potential both on zig-zag and on hexagonal graphs, the latter being related to nano-structures
Optimum Criteria for Developing Defined Structures
Ion IVAN
2008-01-01
Full Text Available Basic aspects concerning distributed applications are presented: definition, particularities and importance. For distributed applications linear, arborescent, graph structures are defined with different versions and aggregation methods. Distributed applications have associated structures which through their characteristics influence the costs of the stages in the development cycle and the exploitation costs transferred to each user. The complexity of the defined structures is analyzed. The minimum and maximum criteria are enumerated for optimizing distributed application structures.
Liu, Shichang; Li, Zeguang; Wang, Kan; Cheng, Quan; She, Ding
2018-01-01
Highlights: •A new random geometry was developed in RMC for mixed and polytype particle/pebble. •This capability was applied to the full core calculations of HTR-10 benchmark. •Reactivity, temperature coefficient and control rod worth of HTR-10 were compared. •This method can explicitly model different packing fraction of different pebbles. •Monte Carlo code with this method can simulate polytype particle/pebble type reactor. -- Abstract: With the increasing demands of high fidelity neutronics analysis and the development of computer technology, Monte Carlo method is becoming more and more attractive in accurate simulation of pebble bed High Temperature gas-cooled Reactor (HTR), owing to its advantages of the flexible geometry modeling and the use of continuous-energy nuclear cross sections. For the double-heterogeneous geometry of pebble bed, traditional Monte Carlo codes can treat it by explicit geometry description. However, packing methods such as Random Sequential Addition (RSA) can only produce a sphere packing up to 38% volume packing fraction, while Discrete Element Method (DEM) is troublesome and also time consuming. Moreover, traditional Monte Carlo codes are difficult and inconvenient to simulate the mixed and polytype particles or pebbles. A new random geometry method was developed in Monte Carlo code RMC to simulate the particle transport in polytype particle/pebble in double heterogeneous geometry systems. This method was verified by some test cases, and applied to the full core calculations of HTR-10 benchmark. The reactivity, temperature coefficient and control rod worth of HTR-10 were compared for full core and initial core in helium and air atmosphere respectively, and the results agree well with the benchmark results and experimental results. This work would provide an efficient tool for the innovative design of pebble bed, prism HTRs and molten salt reactors with polytype particles or pebbles using Monte Carlo method.
Chen, Lei [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, Anhui 230031 (China); University of Science and Technology of China, Hefei, Anhui 230027 (China); Chen, Youhua [University of Science and Technology of China, Hefei, Anhui 230027 (China); Huang, Kai [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, Anhui 230031 (China); Liu, Songlin, E-mail: slliu@ipp.ac.cn [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, Anhui 230031 (China); University of Science and Technology of China, Hefei, Anhui 230027 (China)
2016-05-15
Highlights: • A CFD-DEM coupled numerical model is built based on the prototypical blanket pebble bed. • The numerical model can be applied to simulate heat transfer of a pebble bed and estimate effective thermal conductivity. • The numerical model agrees well with the theoretical SZB model. • Effective thermal conductivity of pebble beds for WCCB is estimated by the current model. - Abstract: The mono-sized beryllium pebble bed and the multi-sized Li{sub 2}TiO{sub 3}/Be{sub 12}Ti mixed pebble bed are the main schemes for the Water-cooled ceramic breeder blanket (WCCB) of China Fusion Engineering Test Reactor (CFETR). And the effective thermal conductivity (k{sub eff}) of the pebble beds is important to characterize the thermal performance of WCCB. In this study, a one-way coupled CFD-DEM method was employed to simulate heat transfer and estimate k{sub eff}. The geometric topology of a prototypical blanket pebble bed was produced by the discrete element method (DEM). Based on the geometric topology, the temperature distribution and the k{sub eff} were obtained by the computational fluid dynamics (CFD) analysis. The current numerical model presented a good performance to calculate k{sub eff} of the beryllium pebble bed, and according to the modeling of the Li{sub 2}TiO{sub 3}/Be{sub 12}Ti mixed pebble bed, k{sub eff} was estimated with values ranged between 2.0 and 4.0 W/(m∙K).
Graph modeling systems and methods
Neergaard, Mike
2015-10-13
An apparatus and a method for vulnerability and reliability modeling are provided. The method generally includes constructing a graph model of a physical network using a computer, the graph model including a plurality of terminating vertices to represent nodes in the physical network, a plurality of edges to represent transmission paths in the physical network, and a non-terminating vertex to represent a non-nodal vulnerability along a transmission path in the physical network. The method additionally includes evaluating the vulnerability and reliability of the physical network using the constructed graph model, wherein the vulnerability and reliability evaluation includes a determination of whether each terminating and non-terminating vertex represents a critical point of failure. The method can be utilized to evaluate wide variety of networks, including power grid infrastructures, communication network topologies, and fluid distribution systems.
Feder, Tomá s; Motwani, Rajeev
2009-01-01
Results on graph turnpike problem without distinctness, including its NP-completeness, and an O(m+n log n) algorithm, is presented. The usual turnpike problem has all pairwise distances given, but does not specify which pair of vertices w e corresponds to. There are two other problems that can be viewed as special cases of the graph turnpike problem, including the bandwidth problem and the low-distortion graph embedding problem. The aim for the turnpike problem in the NP-complete is to orient the edges with weights w i in either direction so that when the whole cycle is transversed in the real line, it returns to a chosen starting point for the cycle. An instance of the turnpike problem with or without distinctness is uniquely mappable if there exists at most one solution up to translation and choice of orientation.
Feder, Tomás
2009-06-01
Results on graph turnpike problem without distinctness, including its NP-completeness, and an O(m+n log n) algorithm, is presented. The usual turnpike problem has all pairwise distances given, but does not specify which pair of vertices w e corresponds to. There are two other problems that can be viewed as special cases of the graph turnpike problem, including the bandwidth problem and the low-distortion graph embedding problem. The aim for the turnpike problem in the NP-complete is to orient the edges with weights w i in either direction so that when the whole cycle is transversed in the real line, it returns to a chosen starting point for the cycle. An instance of the turnpike problem with or without distinctness is uniquely mappable if there exists at most one solution up to translation and choice of orientation.
Negation switching invariant signed graphs
Deepa Sinha
2014-04-01
Full Text Available A signed graph (or, $sigraph$ in short is a graph G in which each edge x carries a value $\\sigma(x \\in \\{-, +\\}$ called its sign. Given a sigraph S, the negation $\\eta(S$ of the sigraph S is a sigraph obtained from S by reversing the sign of every edge of S. Two sigraphs $S_{1}$ and $S_{2}$ on the same underlying graph are switching equivalent if it is possible to assign signs `+' (`plus' or `-' (`minus' to vertices of $S_{1}$ such that by reversing the sign of each of its edges that has received opposite signs at its ends, one obtains $S_{2}$. In this paper, we characterize sigraphs which are negation switching invariant and also see for what sigraphs, S and $\\eta (S$ are signed isomorphic.
Rosmanis, Ansis
2011-01-01
I introduce a continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First, I analyze the quantum snake walk on the line, and I show that, even though most states stay localized throughout the evolution, there are specific states that most likely move on the line as wave packets with momentum inversely proportional to the length of the snake. Next, I discuss how an algorithm based on the quantum snake walk might potentially be able to solve an extended version of the glued trees problem, which asks to find a path connecting both roots of the glued trees graph. To the best of my knowledge, no efficient quantum algorithm solving this problem is known yet.
A study on Monte Carlo analysis of Pebble-type VHTR core for hydrogen production
Kim, Hong Chul
2005-02-01
In order to pursue exact the core analysis for VHTR core which will be developed in future, a study on Monte Carol method was carried out. In Korea, pebble and prism type core are under investigation for VHTR core analysis. In this study, pebble-type core was investigated because it was known that it should not only maintain the nuclear fuel integrity but also have the advantage in economical efficiency and safety. The pebble-bed cores of HTR-PROTEUS critical facility in Swiss were selected for the benchmark model. After the detailed MCNP modeling of the whole facility, calculations of nuclear characteristics were performed. The two core configurations, Core 4.3 and Core 5 (reference state no. 3), among the 10 configurations of the HTR-PROTEUS cores were chosen to be analyzed in order to treat different fuel loading pattern and modeled. The former is a random packing core and the latter deterministic packing core. Based on the experimental data and the benchmark result of other research groups for the two different cores, some nuclear characteristics were calculated. Firstly, keff was calculated for these cores. The effect for TRIO homogeneity model was investigated. Control rod and shutdown rod worths also were calculated and the sensitivity analysis on cross-section library and reflector thickness was pursued. Lastly, neutron flux profiles were investigated in reflector regions. It is noted that Monte Carlo analysis of pebble-type VHTR core was firstly carried out in Korea. Also, this study should not only provide the basic data for pebble-type VHTR core analysis for hydrogen production but also be utilized as the verified data to validate a computer code for VHTR core analysis which will be developed in future
Quasi-direct numerical simulation of a pebble bed configuration, Part-II: Temperature field analysis
Shams, A.; Roelofs, F.; Komen, E.M.J.; Baglietto, E.
2013-01-01
Highlights: ► Quasi direct numerical simulations (q-DNSs) of a pebble bed configuration have been performed. ► This q-DNS database may serve as a reference for the validation of different turbulence modeling approaches. ► A wide range of qualitative and quantitative data throughout the computational domain has been generated. ► Results for mean, RMS of temperature and respective turbulent heat fluxes are extensively reported in this paper. -- Abstract: Good prediction of the flow and heat transfer phenomena in the pebble bed core of a high temperature reactor (HTR) is a challenge for available turbulence models, which still require to be validated. While experimental data are generally desirable in this validation process, due to the complex geometric configuration and measurement difficulties, a very limited amount of data is currently available. On the other hand, direct numerical simulation (DNS) is considered an accurate simulation technique, which may serve as an alternative for validating turbulence models. In the framework of the present study, quasi-direct numerical simulation (q-DNS) of a single face cubic centered pebble bed is performed, which will serve as a reference for the validation of different turbulence modeling approaches in order to perform calculations for a randomly arranged pebble bed. These simulations were performed at a Reynolds number of 3088, based on pebble diameter, with a porosity level of 0.42. Results related to flow field (mean, RMS and covariance of velocity) have been presented in Part-I, whereas, in the present article, we focus our attention to the analysis of the temperature field. A wide range of qualitative and quantitative data for the thermal field (mean, RMS and turbulent heat flux) has been generated
Neutron Fluence And DPA Rate Analysis In Pebble-Bed HTR Reactor Vessel Using MCNP
Hamzah, Amir; Suwoto; Rohanda, Anis; Adrial, Hery; Bakhri, Syaiful; Sunaryo, Geni Rina
2018-02-01
In the Pebble-bed HTR reactor, the distance between the core and the reactor vessel is very close and the media inside are carbon and He gas. Neutron moderation capability of graphite material is theoretically lower than that of water-moderated reactors. Thus, it is estimated much more the fast neutrons will reach the reactor vessel. The fast neutron collisions with the atoms in the reactor vessel will result in radiation damage and could be reducing the vessel life. The purpose of this study was to obtain the magnitude of neutron fluence in the Pebble-bed HTR reactor vessel. Neutron fluence calculations in the pebble-bed HTR reactor vessel were performed using the MCNP computer program. By determining the tally position, it can be calculated flux, spectrum and neutron fluence in the position of Pebble-bed HTR reactor vessel. The calculations results of total neutron flux and fast neutron flux in the reactor vessel of 1.82x108 n/cm2/s and 1.79x108 n/cm2/s respectively. The fast neutron fluence in the reactor vessel is 3.4x1017 n/cm2 for 60 years reactor operation. Radiation damage in stainless steel material caused by high-energy neutrons (> 1.0 MeV) will occur when it has reached the neutron flux level of 1.0x1024 n/cm2. The neutron fluence results show that there is no radiation damage in the Pebble-bed HTR reactor vessel, so it is predicted that it will be safe to operate at least for 60 years.