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At least 37 records · Page 2

Best-Estimate-Plus-Uncertainty-Informed Deterministic Safety Evaluation

Nuclear power plant (NPP) utilities operate contingent on receiving a favorable safety assessment from their national regulatory and safety authority. Among the many facets of NPP safety addressed is verification of integral design-basis performance - a demonstration of a plant's response to a suite of challenging transient and accident scenarios. Thermal-hydraulic system computer codes like RELAP5, TRAC, CATHARE, and ATHLET are used as the simulation engine as part of a broader evaluation model that accounts for a variety of uncertainties. It is common for these evaluation models to apply either a super-bounding/ deterministic or best-estimate plus uncertainty (BEPU) approach. The trend over the past two decades has been away from the classical deterministic methods towards methods explicitly incorporating parametric uncertainty models. These methods center upon the evaluation of parametric and system response uncertainties, where these uncertainties are derived from the convolution of one or more parametric uncertainty models. Acceptance of BEPU methods has provided the nuclear industry benefits regarding operational flexibility and, in some cases, power output. The advantage of BEPU for new NPPs is less obvious. Generally, these new designs include engineered safety features that practically eliminate fuel damage resulting from design-basis events. To substantiate such claims, applying super-bounding assumptions on uncertainties may be a more expedient demonstration of a plant's safety case than those based on BEPU. In addition, the requirements on design inputs for a deterministic evaluation model are substantially less than that for a BEPU evaluation model. As such, applying a deterministic evaluation model is expected to have the advantage of reducing the duration of the licensing review process. For the current operating fleet of light-water reactors (LWRs), the nuclear safety authorities in most countries have followed the U.S. Nuclear Regulatory Commission's rules for the preparation of safety analysis. These rules are specified in the U.S. Code of Federal Regulations, most notably in, Part 10, Section 50.46, entitled 'acceptance criteria for emergency core cooling systems for light-water nuclear power reactors' and its Appendix K. Notably, Appendix K specifies deterministic requirements for analysis of the loss-of-coolant accident (LOCA), which is generally regarded as the maximum credible accident for LWRs. Projecting 10 CFR 50, Appendix K, to new plants is not obviously applicable as it addresses light water fluid flow and heat transfer phenomena associated with core uncovery. Preventing core uncovery is a requirement for several designs in the class of small modular reactors (SMR). In doing so, the majority of phenomenological uncertainties prescribed in Appendix K are eliminated. Similarly, the impact of other phenomena to effect a change in various safety measures, i.e., figures-of-merit, is expected to be different. The implication is that development of a deterministic evaluation model must be derived with an original technical basis rather than solely rely on Appendix K. While a logical conclusion, the expectation of original bases, regardless of the treatment of uncertainties, is embodied in the U.S. NRC's Regulatory Guide (RG) 1.203, Transient and Accident Analysis. Within the evaluation model development and application process framework of RG 1.203, this paper describes a BEPU-informed deterministic evaluation model for NPPs with large inherent safety margins. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Deterministic LOCC transformation of three-qubit pure states and entanglement transfer

A necessary and sufficient condition of the possibility of a deterministic local operations and classical communication (LOCC) transformation of three-qubit pure states is given. The condition shows that the three-qubit pure states are a partially ordered set parametrized by five well-known entanglement parameters and a novel parameter; the five are the concurrences C{sub AB}, C{sub AC}, C{sub BC}, the tangle {tau}{sub ABC} and the fifth parameter J{sub 5} of Acin et al. (2000) Ref. [19], while the other new one is the entanglement charge Q{sub e}. The order of the partially ordered set is defined by the possibility of a deterministic LOCC transformation from a state to another state. In this sense, the present condition is an extension of Nielsen's work (Nielsen (1999) [14]) to three-qubit pure states. We also clarify the rules of transfer and dissipation of the entanglement which is caused by deterministic LOCC transformations. Moreover, the minimum number of times of measurements to reproduce an arbitrary deterministic LOCC transformation between three-qubit pure states is given. - Highlights: Black-Right-Pointing-Pointer We obtained a necessary and sufficient condition for deterministic LOCC of 3 qubits. Black-Right-Pointing-Pointer We clarified rules of entanglement flow caused by measurements. Black-Right-Pointing-Pointer We found a new parameter which is interpreted as 'Charge of Entanglement'. Black-Right-Pointing-Pointer We gave a set of entanglements which determines whether two states are LU-eq. or not. Black-Right-Pointing-Pointer Our approach to deterministic LOCC of 3 qubits may be applicable to N qubits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A deterministic solution of the first order linear Boltzmann transport equation in the presence of external magnetic fields

Purpose: Accurate radiotherapy dose calculation algorithms are essential to any successful radiotherapy program, considering the high level of dose conformity and modulation in many of today’s treatment plans. As technology continues to progress, such as is the case with novel MRI-guided radiotherapy systems, the necessity for dose calculation algorithms to accurately predict delivered dose in increasingly challenging scenarios is vital. To this end, a novel deterministic solution has been developed to the first order linear Boltzmann transport equation which accurately calculates x-ray based radiotherapy doses in the presence of magnetic fields. Methods: The deterministic formalism discussed here with the inclusion of magnetic fields is outlined mathematically using a discrete ordinates angular discretization in an attempt to leverage existing deterministic codes. It is compared against the EGSnrc Monte Carlo code, utilizing the emf-macros addition which calculates the effects of electromagnetic fields. This comparison is performed in an inhomogeneous phantom that was designed to present a challenging calculation for deterministic calculations in 0, 0.6, and 3 T magnetic fields oriented parallel and perpendicular to the radiation beam. The accuracy of the formalism discussed here against Monte Carlo was evaluated with a gamma comparison using a standard 2%/2 mm and a more stringent 1%/1 mm criterion for a standard reference 10 × 10 cm{sup 2} field as well as a smaller 2 × 2 cm{sup 2} field. Results: Greater than 99.8% (94.8%) of all points analyzed passed a 2%/2 mm (1%/1 mm) gamma criterion for all magnetic field strengths and orientations investigated. All dosimetric changes resulting from the inclusion of magnetic fields were accurately calculated using the deterministic formalism. However, despite the algorithm’s high degree of accuracy, it is noticed that this formalism was not unconditionally stable using a discrete ordinate angular discretization. Conclusions: The feasibility of including magnetic field effects in a deterministic solution to the first order linear Boltzmann transport equation is shown. The results show a high degree of accuracy when compared against Monte Carlo calculations in all magnetic field strengths and orientations tested.

60 APPLIED LIFE SCIENCES↗

Soil pH mediates the balance between stochastic and deterministic assembly of bacteria

Little is known about the factors affecting the relative influence of stochastic and deterministic processes that governs the assembly of microbial communities in successional soils. Here, we conducted a meta-analysis of bacterial communities using six different successional soils data sets, scattered across different regions, with different pH conditions in early and late successional soils. We found that soil pH was the best predictor of bacterial community assembly and the relative importance of stochastic and deterministic processes along successional soils. Extreme acidic or alkaline pH conditions lead to assembly of phylogenetically more clustered bacterial communities through deterministic processes, whereas pH conditions close to neutral lead to phylogenetically less clustered bacterial communities with more stochasticity. We suggest that the influence of pH, rather than successional age, is the main driving force in producing trends in phylogenetic assembly of bacteria, and that pH also influences the relative balance of stochastic and deterministic processes along successional soils. Given that pH had a much stronger association with community assembly than did successional age, we evaluated whether the inferred influence of pH was maintained when studying globally-distributed samples collected without regard for successional age. This dataset confirmed the strong influence of pH, suggesting that the influence of soil pH on community assembly processes occurs globally. Extreme pH conditions likely exert more stringent limits on survival and fitness, imposing strong selective pressures through ecological and evolutionary time. Taken together, these findings suggest that the degree to which stochastic vs. deterministic processes shape soil bacterial community assembly is a consequence of soil pH rather than successional age.

Tripathi, Binu M.↗

Deterministic multi-qubit entanglement in a quantum network

High-fidelity deterministic quantum state transfer and multi-qubit entanglement are demonstrated in a quantum network comprising two superconducting quantum nodes one metre apart, with each node including three interconnected qubits. The generation of high-fidelity distributed multi-qubit entanglement is a challenging task for large-scale quantum communication and computational networks. The deterministic entanglement of two remote qubits has recently been demonstrated with both photons and phonons. However, the deterministic generation and transmission of multi-qubit entanglement has not been demonstrated, primarily owing to limited state-transfer fidelities. Here we report a quantum network comprising two superconducting quantum nodes connected by a one-metre-long superconducting coaxial cable, where each node includes three interconnected qubits. By directly connecting the cable to one qubit in each node, we transfer quantum states between the nodes with a process fidelity of 0.911 +/- 0.008. We also prepare a three-qubit Greenberger-Horne-Zeilinger (GHZ) state in one node and deterministically transfer this state to the other node, with a transferred-state fidelity of 0.656 +/- 0.014. We further use this system to deterministically generate a globally distributed two-node, six-qubit GHZ state with a state fidelity of 0.722 +/- 0.021. In this work, the GHZ state fidelities are clearly above the threshold of 1/2 for genuine multipartite entanglement, showing that this architecture can be used to coherently link together multiple superconducting quantum processors, providing a modular approach for building large-scale quantum computers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Preliminary Results of a New Deterministic Iterative Image Reconstruction Algorithm - Paper 117

Iterative reconstruction techniques have become the standard for Single Photon Emission Computed Tomography (SPECT). Advances in computing have allowed these techniques to incorporate more and more detail; however, computation time must be balanced against increased detail. Monte Carlo methods are generally used for modeling the physics of a SPECT study, but can have long computation times. Advances in Monte Carlo-based scatter correction have shown reasonable results, but scatter estimation by measuring narrow energy windows remains more common. An iterative reconstruction technique using a deterministic transport code has been proposed as an alternative. This paper presents preliminary results of the new technique in which the TITAN deterministic code completes the forward projection step in a maximum likelihood expectation maximization (ML-EM) reconstruction of SPECT data. The effectiveness of the deterministic algorithm is examined for a 2-dimensional phantom. This work demonstrates the feasibility of using the TITAN code in an iterative reconstruction algorithm. The appropriate deterministic parameters were chosen by comparing sinograms produced with different mesh sizes, quadrature sets, and anisotropic scattering orders. The TITAN code was then successfully used as the forward projection step in an iterative reconstruction algorithm with a 2-dimensional homogeneous phantom. The impact of deterministic parameters on reconstruction quality is being investigated, along with the incorporation of a smoothing filter. The TITAN source code is being modified to include the ML-EM algorithm and iteration steps. This will significantly improve computation time by eliminating the repeated reading and writing of files for each iteration and allowing some steps to be completed in parallel. Further testing of the new reconstruction algorithm for more realistic phantoms is also underway. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗

SU-E-T-577: Commissioning of a Deterministic Algorithm for External Photon Beams

Purpose: We report commissioning results for a deterministic algorithm for external photon beam treatment planning. A deterministic algorithm solves the radiation transport equations directly using a finite difference method, thus improve the accuracy of dose calculation, particularly under heterogeneous conditions with results similar to that of Monte Carlo (MC) simulation. Methods: Commissioning data for photon energies 6 – 15 MV includes the percentage depth dose (PDD) measured at SSD = 90 cm and output ratio in water (Spc), both normalized to 10 cm depth, for field sizes between 2 and 40 cm and depths between 0 and 40 cm. Off-axis ratio (OAR) for the same set of field sizes was used at 5 depths (dmax, 5, 10, 20, 30 cm). The final model was compared with the commissioning data as well as additional benchmark data. The benchmark data includes dose per MU determined for 17 points for SSD between 80 and 110 cm, depth between 5 and 20 cm, and lateral offset of up to 16.5 cm. Relative comparisons were made in a heterogeneous phantom made of cork and solid water. Results: Compared to the commissioning beam data, the agreement are generally better than 2% with large errors (up to 13%) observed in the buildup regions of the FDD and penumbra regions of the OAR profiles. The overall mean standard deviation is 0.04% when all data are taken into account. Compared to the benchmark data, the agreements are generally better than 2%. Relative comparison in heterogeneous phantom is in general better than 4%. Conclusion: A commercial deterministic algorithm was commissioned for megavoltage photon beams. In a homogeneous medium, the agreement between the algorithm and measurement at the benchmark points is generally better than 2%. The dose accuracy for a deterministic algorithm is better than a convolution algorithm in heterogeneous medium.

07 ISOTOPE AND RADIATION SOURCES↗

Design of Non-Deterministic Quasi-random Nanophotonic Structures Using Fourier Space Representations

Despite their seemingly random appearances in the real space, quasi-random nanophotonic structures exhibit distinct structural correlations and have been widely utilized for effective photon management. However, current design approaches mainly rely on the deterministic representations consisting two-dimensional (2D) discretized patterns in the real space. They fail to capture the inherent non-deterministic characteristic of the quasi-random structures and inevitably result in a large design dimensionality. Here, we report a new design approach that employs the one-dimensional (1D) spectral density function (SDF) as the unique representation of non-deterministic quasi-random structures in the Fourier space with greatly reduced design dimensionality. One 1D SDF representation can be used to generate infinite sets of real space structures in 2D with equally optimized performance, which was further validated experimentally using light-trapping structures in a thin film absorber as a model system. The optimized non-deterministic quasi-random nanostructures improve the broadband absorption by 225% over the unpatterned cell.

Science & Technology - Other Topics↗

Balanced stochastic versus deterministic assembly processes benefit diverse yet uneven ecosystem functions in representative agroecosystems

Ecological assembly processes, by influencing community composition, determine ecosystem functions of microbiomes. However, debate remains on how stochastic versus deterministic assembly processes influence ecosystem functions such as carbon and nutrient cycling. Towards a better understanding, we investigated three types of agroecosystems (the upland, paddy, and flooded) that represent a gradient of stochastic versus deterministic assembly processes. Carbon and nutrient cycling multifunctionality, characterized by nine enzymes associated with soil carbon, nitrogen, phosphorous and sulfur cycling, was evaluated and then associated with microbial assembly processes and cooccurrence patterns of vital ecological groups. Our results suggest that strong deterministic processes favour microorganisms with convergent functions (as in the upland agroecosystem), while stochasticity-dominated processes lead to divergent functions (as in the flooded agroecosystem). To benefit agroecosystems services, we speculate that it is critical for a system to maintain balance between its stochastic and deterministic assembly processes (as in the paddy agroecosystem). By doing so, the system can preserve a diverse array of functional traits and also allow for particular traits to flourish. To further confirm this speculation, it is necessary to develop a systematic knowledge beyond merely characterizing general patterns towards the associations among community assembly, composition, and ecosystem functions.

Liu, Wenjing↗

Hole in one: Pathways to deterministic single-acceptor incorporation in Si(100)-2 x 1

We report that stochastic incorporation kinetics can be a limiting factor in the scalability of semiconductor fabrication technologies using atomic-precision techniques. While these technologies have recently been extended from donors to acceptors, the extent to which kinetics will impact single-acceptor incorporation has yet to be assessed. To identify the precursor molecule and dosing conditions that are promising for deterministic incorporation, we develop and apply an atomistic model for the single-acceptor incorporation rates of several recently demonstrated molecules: diborane (B 2 H 6 ), boron trichloride (BCl 3 ), and aluminum trichloride in both monomer (AlCl 3 ) and dimer forms (Al 2 Cl 6 ). While all three precursors can realize single-acceptor incorporation, we predict that diborane is unlikely to realize deterministic incorporation, boron trichloride can realize deterministic incorporation with modest heating (50 °C), and aluminum trichloride can realize deterministic incorporation at room temperature. We conclude that both boron and aluminum trichloride are promising precursors for atomic-precision single-acceptor applications, with the potential to enable the reliable production of large arrays of single-atom quantum devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Invited Review: A review of deterministic effects in cyclic variability of internal combustion engines

Here we review developments in the understanding of cycle to cycle variability in internal combustion engines, with a focus on spark-ignited and premixed combustion conditions. Much of the research on cyclic variability has focused on stochastic aspects, that is, features that can be modeled as inherently random with no short term predictability. In some cases, models of this type appear to work very well at describing experimental observations, but the lack of predictability limits control options. Also, even when the statistical properties of the stochastic variations are known, it can be very difficult to discern their underlying physical causes and thus mitigate them. Some recent studies have demonstrated that under some conditions, cyclic combustion variations can have a relatively high degree of low dimensional deterministic structure, which implies some degree of predictability and potential for real time control. These deterministic effects are typically more pronounced near critical stability limits (e.g. near tipping points associated with ignition or flame propagation) such during highly dilute fueling or near the onset of homogeneous charge compression ignition. We review recent progress in experimental and analytical characterization of cyclic variability where low dimensional, deterministic effects have been observed. We describe some theories about the sources of these dynamical features and discuss prospects for interactive control and improved engine designs. In conclusion, taken as a whole, the research summarized here implies that the deterministic component of cyclic variability will become a pivotal issue (and potential opportunity) as engine manufacturers strive to meet aggressive emissions and fuel economy regulations in the coming decades.

33 ADVANCED PROPULSION SYSTEMS↗

Relative Roles of Deterministic and Stochastic Processes in Driving the Vertical Distribution of Bacterial Communities in a Permafrost Core from the Qinghai-Tibet Plateau, China

Understanding the processes that influence the structure of biotic communities is one of the major ecological topics, and both stochastic and deterministic processes are expected to be at work simultaneously in most communities. Here, we investigated the vertical distribution patterns of bacterial communities in a 10-m-long soil core taken within permafrost of the Qinghai-Tibet Plateau. To get a better understanding of the forces that govern these patterns, we examined the diversity and structure of bacterial communities, and the change in community composition along the vertical distance (spatial turnover) from both taxonomic and phylogenetic perspectives. Measures of taxonomic and phylogenetic beta diversity revealed that bacterial community composition changed continuously along the soil core, and showed a vertical distance-decay relationship. Multiple stepwise regression analysis suggested that bacterial alpha diversity and phylogenetic structure were strongly correlated with soil conductivity and pH but weakly correlated with depth. There was evidence that deterministic and stochastic processes collectively drived bacterial vertically-structured pattern. Bacterial communities in five soil horizons (two originated from the active layer and three from permafrost) of the permafrost core were phylogenetically random, indicator of stochastic processes. However, we found a stronger effect of deterministic processes related to soil pH, conductivity, and organic carbon content that were structuring the bacterial communities. We therefore conclude that the vertical distribution of bacterial communities was governed primarily by deterministic ecological selection, although stochastic processes were also at work. Furthermore, the strong impact of environmental conditions (for example, soil physicochemical parameters and seasonal freeze-thaw cycles) on these communities underlines the sensitivity of permafrost microorganisms to climate change and potentially subsequent permafrost thaw.

Science & Technology - Other Topics↗

Development of a First-of-a-Kind Deterministic Decision-Making Tool for Supervisory Control System

Decision-making is the process of identifying and choosing alternatives where each alternative offers a different approach or path to move from a given state or condition to a desired state or condition. The generation of consistent decisions requires that a structured, coherent process be defined, immediately leading to a decision-making framework. The overall objective of the generalized framework is for it to be adopted into an autonomous decision-making framework and tailored to specific requirements for various applications. In this context, automation is the use of computing resources to make decisions and implement a structured decision-making process with limited or no human intervention. The overriding goal of automation is to replace or supplement human decision makers with reconfigurable decision- making modules that can perform a given set of tasks reliably. Risk-informed decision making requires a probabilistic assessment of the likelihood of success given the status of the plant/systems and component health, and a deterministic assessment between plant operating parameters and reactor protection parameters to prevent unnecessary trips and challenges to plant safety systems. The implementation of the probabilistic portion of the decision-making engine of the proposed supervisory control system was detailed in previous milestone reports. Once the control options are identified and ranked based on the likelihood of success, the supervisory control system transmits the options to the deterministic portion of the platform. The deterministic multi-attribute decision-making framework uses variable sensor data (e.g., outlet temperature) and calculates where it is within the challenge state, its trajectory, and margin within the controllable domain using utility functions to evaluate current and projected plant state space for different control decisions. Metrics to be evaluated include stability, cost, time to complete (action), power level, etc. The integration of deterministic calculations using multi-physics analyses (i.e., neutronics, thermal, and thermal-hydraulics) and probabilistic safety calculations allows for the examination and quantification of margin recovery strategies. This also provides validation of the control options identified from the probabilistic assessment. Thus, the thermal-hydraulics analyses are used to validate the control options identified from the probabilistic assessment. Future work includes evaluating other possible metrics and computational efficiencies.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Filament-Free Bulk Resistive Memory Enables Deterministic Analogue Switching

Digital computing is nearing its physical limits as computing needs and energy consumption rapidly increase. Analogue-memory-based neuromorphic computing can be orders of magnitude more energy efficient at data-intensive tasks like deep neural networks, but has been limited by the inaccurate and unpredictable switching of analogue resistive memory. Filamentary resistive random access memory (RRAM) suffers from stochastic switching due to the random kinetic motion of discrete defects in the nanometer-sized filament. Here, this stochasticity is overcome by incorporating a solid electrolyte interlayer, in this case, yttria-stabilized zirconia (YSZ), toward eliminating filaments. Filament-free, bulk-RRAM cells instead store analogue states using the bulk point defect concentration, yielding predictable switching because the statistical ensemble behavior of oxygen vacancy defects is deterministic even when individual defects are stochastic. Both experiments and modeling show bulk-RRAM devices using TiO2-X switching layers and YSZ electrolytes yield deterministic and linear analogue switching for efficient inference and training. Bulk-RRAM solves many outstanding issues with memristor unpredictability that have inhibited commercialization, and can, therefore, enable unprecedented new applications for energy-efficient neuromorphic computing. Beyond RRAM, this work shows how harnessing bulk point defects in ionic materials can be used to engineer deterministic nanoelectronic materials and devices.

36 MATERIALS SCIENCE↗

Deterministic incident-wave elevation prediction in intermediate water depth

Potential performance gains from optimal (non-causal) impedance-matching control of wave energy devices in irregular ocean waves are dependent on deterministic wave elevation prediction techniques that work well in practical applications. Although a number of devices are designed for operation in intermediate water depths, little work has been reported on deterministic wave prediction in such depths. Here, we investigated a deterministic wave-prediction technique based on an approximate propagation model that leads to an analytical formulation, which may be convenient to implement in practice. To improve accuracy, an approach to combine predictions based on multiple up-wave measurement points is evaluated. The overall method is tested using experimental time-series measurements recorded in the U.S. Navy MASK basin in Carderock, MD, USA. For comparison, an alternative prediction approach based on Fourier coefficients is also tested with the same data. Comparison of prediction approaches with direct measurements suggest room for improvement. Possible sources of error including tank reflections are estimated, and potential mitigation approaches are discussed.

16 TIDAL AND WAVE POWER↗

A deterministic method for PWR loading pattern optimization

A new deterministic approach to core loading optimization is presented. Selection of fuel enrichment and burnable poison (BP) arrangement in a pressurized water reactor (PWR) core are optimally determined subject to power peaking factor (PF) constraints. The deterministic approach is based on the method of Lagrange multipliers and the direct adjoining approach for the inequality power PF constraint. The optimality conditions are derived using calculus of variations resulting in the presence of jump conditions and a linear control Hamiltonian. The optimal control problems are addressed by simultaneously minimizing the Hamiltonian using the gradient method and performing Newton's method in different regions of the core to produce viable solutions for the controls. Without active control of the power profile in PWRs during depletion, our methodology is able to satisfy the power PF constraint at all times by proper loading selection at the beginning of cycle (BOC). This is achieved by promoting the proper burnup path forward in time during the calculation of the forward optimality conditions. Here this information is utilized in the adjoint burnup calculation, which acts to propagate the optimal control path back to the BOC during the calculation of the adjoint optimality conditions. The methodology has been developed into a new code DMCO (Deterministic Multi-Control Optimization) which can produce two-dimensional two-group depletion results in approximately seven minutes per optimization iteration on a personal computer. No application of heuristics is required and the code is capable of finding solutions from initial control distributions. A preliminary case study is presented for the Westinghouse AP600 first cycle fuel loading design which achieved an extended fuel cycle while satisfying power PF constraints.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Estimating the epidemic threshold on networks by deterministic connections

For many epidemic networks some connections between nodes are treated as deterministic, while the remainder are random and have different connection probabilities. By applying spectral analysis to several constructed models, we find that one can estimate the epidemic thresholds of these networks by investigating information from only the deterministic connections. Nonetheless, in these models, generic nonuniform stochastic connections and heterogeneous community structure are also considered. The estimation of epidemic thresholds is achieved via inequalities with upper and lower bounds, which are found to be in very good agreement with numerical simulations. Since these deterministic connections are easier to detect than those stochastic connections, this work provides a feasible and effective method to estimate the epidemic thresholds in real epidemic networks.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Stochastic and deterministic methods for the calculation of small-sample reactivity experiments

Several calculations methods for the analysis of small-sample reactivity experiments are presented, as their main advantages and drawbacks. A numerical benchmark has been defined for this study consisting in a regular lattice of UO{sub 2} fuel pins, in which the central one is successively poisoned with isotopes of interest (actinides, absorbers, ...). A first method, based on a forward calculation ('eigenvalues difference method'), is presented, using either a deterministic or a stochastic calculation code. A first perturbative method studied is based on the 'Exact Perturbation Theory' (EPT) implemented in the deterministic code APOLLO2.8, and gives consistent results against forward calculations. A second perturbative method, the 'correlated sampling method', implemented in the stochastic calculation code TRIPOLI4.7 is tested. It should be use carefully as it is generally validated against small atomic density changes, but can be useful for conception studies. An 'hybrid method', based on the EPT formalism, using both Monte Carlo and deterministic results is tested, and shows reliable results. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗