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This work addresses a value problem concerning a system of high-order nonlinear equations with viscoelastic terms acting in both equations and homogeneous Dirichlet conditions. Initially, we demonstrate that the system has a weak local solution by combining fixed point theory and Galerkin's method. Under certain conditions on the variable exponents p (.) , as well as conditions related to the kernel functions η (t) ≤ μ (t) , for all t ≥ 0 , we establish that the solution with positive initial energy exhibits exponential growth. In addition, we study some numerical examples to illustrate our theoretical results and demonstrate the effectiveness of our new approach. [ABSTRACT FROM AUTHOR]

A nonlinear viscoelastic Kirchhoff-type equation with a source, Balakrishnan-Taylor damping, dispersion and delay terms is studied. We prove the blow-up of solutions under suitable hypotheses. [ABSTRACT FROM AUTHOR]

This study focuses on investigating a problem involving a coupled nonlocal singular viscoelastic equation with sources and distributed delay terms. We aim to demonstrate, under appropriate conditions, the exponential growth of solutions with positive initial-energy. [ABSTRACT FROM AUTHOR]

This study develops two new analytical models for constant rate pumping at a partially penetrating well in a double‐porosity confined aquifer, considering skin and formation zones. One model, referred to as the two‐zone model, incorporates a flow equation to depict the flow in the skin around the well. The other model, named the source‐term model, introduces a novel source term at the outer rim of the skin to reflect the effects of both the skin and wellbore storage. The analytical solutions for both models are derived by the Laplace transform and finite Fourier cosine transform. Additionally, a finite element solution for the source‐term model is presented. Results suggest the source‐term model is suitable to most wells when the width of the skin is less than 1 m and the radius of influence exceeds the outer rim of the skin. Temporal drawdown distribution for a negative skin exhibits a triple‐humped shape with two flat stages, while that for a positive skin shows monotonous increase. The source‐term model enables orthogonal 5 × 5 nodes for finite element approximation to discretize a well and its adjacent skin. The finite element solution aligns with early drawdown data measured at an observation well under the effects observed in two field constant rate pumping tests. In conclusion, this study introduces a novel approach to modeling two‐zone flow, which may find practical utility in field applications. Plain Language Summary: Numerical modeling experts always say finely discretizing space as many nodes achieves accurate simulation of groundwater flow in aquifers. However, it takes unnecessary addition to computational cost with applying a large number of orthogonal nodes to discretize the circular rim of a well and the ring‐shaped skin zone around the well. The radius rw of a well is usually 0.1 m. The inner radius of the skin zone equals rw; the other outer radius rs usually falls in 1 m. Our example demonstrates the number of the orthogonal nodes is about 600 if rw = 0.1 m, rs = 1 m, and the well rim is discretized as four nodes, but the prediction of a conventional model is incorrect. This study introduces a new groundwater flow model. The model allows orthogonal 5 × 5 nodes to discretize a well rim and its surrounding skin zone, which is practical at low computational cost. This new model is applied to two field constant‐rate pumping tests in which a well extracts groundwater with a constant volumetric rate. Results suggest the predicted water level by the new model approaches the measured water level in the tests. The model may serve as a useful alternative for groundwater pumping and simulations. Key Points: Two novel analytical models are proposed for flow due to constant rate pumping at a two‐zone double‐porosity confined aquiferOne model named as two‐zone model is built by applying flow equations to both skin and formation zonesA new source term is introduced in the other model, called as source‐term model, to reflect the effects of the skin and wellbore storage [ABSTRACT FROM AUTHOR]

We consider a linear implicit-explicit (IMEX) time discretization of the Cahn-Hilliard equation with a source term, endowed with Dirichlet boundary conditions. For every time step small enough, we build an exponential attractor of the discrete-in-time dynamical system associated to the discretization. We prove that, as the time step tends to 0, this attractor converges for the symmetric Hausdorff distance to an exponential attractor of the continuous-in-time dynamical system associated with the PDE. We also prove that the fractal dimension of the exponential attractor (and consequently, of the global attractor) is bounded by a constant independent of the time step. The results also apply to the classical Cahn-Hilliard equation with Neumann boundary conditions. [ABSTRACT FROM AUTHOR]

Analysis of nuclear reactor fuel composition and irradiation characteristics plays a crucial role in reactor design, licensing, safety analysis, and decommissioning. Through in-depth analysis of fuel composition and irradiation processes, it is possible to assess reactor performance, predict fuel lifespan and behavior, and optimize fuel management strategies. To conduct accurate and comprehensive analyses, a robust and reliable database is essential. This database should provide a wide range of key parameters that are vital for fuel analysis, including decay constants, decay branching ratios, decay radiation spectra, decay energies, neutron reaction cross sections, and fission product yields. These parameters are necessary for modeling and simulating the behavior of nuclear materials under different irradiation conditions. In this study, the focus was on developing an advanced methodology for processing refined depletion databases. Several evaluated nuclear databases, including ENDF/B-Ⅷ.0, ENDF/B-Ⅶ.1, JEFF-3.3, and JENDL-5, were utilized as sources of nuclear data. The researchers developed a specialized database generation program called ALG (automatic library generator) to facilitate the creation of a high-quality depletion nuclear database. The resulting database was designed using the HDF5 format, which offers efficient storage and retrieval of large amounts of data. Comparative analyses were conducted to assess the differences in key parameters of critical nuclides among the different evaluated nuclear databases. Three validation cases were conducted, including the pure decay of 237Np, the neutron activation of UO2, and the pulse fission case of 235U. In the first case, which involved the decay of 237Np, excellent results were achieved, with only slight differences observed for short-lived nuclides when compared to the ORIGEN databases. Significant differences were observed in the UO2 activation cases, primarily due to variations in neutron cross sections resulting from different neutron weight spectra. These discrepancies highlight the importance of considering neutron-induced reactions when analyzing activation processes, as the neutron spectrum has a significant impact on the results. For the calculation of the decay γ spectrum in the 235U pulse fission case, three newly processed depletion databases demonstrated excellent agreement with experimental measurements. This alignment between the calculated and experimental data validates the accuracy and reliability of the new processed databases. This evaluation helped identify variations in data, allowing for a better understanding of the uncertainties and limitations associated with different databases. By incorporating the most up-to-date and accurate data into the depletion subroutine DEPTH of the Monte Carlo code RMC, the performance and reliability of the simulation tool were significantly enhanced. The updated database now includes additional information such as decay radiation spectra, energy-dependent fission product yields, and subgroup neutron reaction cross-section parameters. These improvements lay a solid foundation for conducting more refined research on nuclear fuel cycles and supporting advanced reactor design and analysis.

Under irradiation of high-energy particles (neutrons or ions), cascade collisions continue to occur in nuclear materials, producing a large number of vacancy clusters and interstitial clusters. These defect clusters will undergo reactions such as diffusion, aggregation, recombination, and annihilation, forming important microstructures such as voids and dislocation loops. Cluster dynamics (CD) method is one of the important methods for simulating the microstructure evolution of nuclear materials under high-energy particle irradiation. The source term (i.e., the average size distribution of huge number of cascade collision defect clusters) is key input of the CD method. In the classical CD method, the source term is usually obtained by empirical fitting, and the maximum cluster in the source term usually only contains several vacancies or interstitials. According to recent studies on cascade collision simulations based on molecular dynamics (MD) methods, cascade collisions corresponding to high-energy primary knocked atom (PKA) can form clusters with dozens or even hundreds of vacancies or interstitials. So, the initial defect information obtained at the atomic level was not fully utilized in traditional CD simulations. With the development of molecular dynamics, cascade collision defect databases have been greatly enriched. Combined with PKA energy spectrum, it is enough to obtain more reasonable source term. The PKA spectrum is generally a quasi-continuous spectrum, and the number of energy groups is usually tens or hundreds. However, the MD cascade collision defect database usually only contains about ten energy values, which is much smaller than the former. If the MD cascade collision defect database is to be used rationally, a mapping rule from a quasi-continuous spectrum to a finite number of discrete energy values must be determined. In view of this, based on probability theory and the principle of proximity, fully considering the changing characteristics of the PKA spectrum curve, five sampling algorithms were proposed for obtaining discrete values of cascade energy from the quasi-continuous PKA energy spectrum. Based on the probability of discrete values of cascade energy, the defect cluster size distribution in the cascade collision defect database was weighted, grouped, fitted, and a relatively smooth continuous size distribution curve was obtained as the source term of the CD method. In order to test the rationality of the source term algorithms, the CD method was used to simulate the low-dose neutron irradiation of pure tungsten experiment in the HFIR reactor, and compared the defect cluster information. The results are consistent with the experimental data. Since there are differences in the size distribution of defect clusters after irradiation simulation with the five algorithms, after analysis, it is believed that the fifth source term algorithm is the most reasonable. In addition, the shortcomings of the current source term algorithm and CD model used and improvement that can be expected in the future were also summarized.

Abstract In this paper, we investigate a scenario concerning a coupled nonlocal singular viscoelastic equation with sources and distributed delay terms. By establishing suitable conditions, we have proved that a finite-time blow-up occurs in the solution.

Copyright of Atomic Energy Science & Technology is the property of Editorial Board of Atomic Energy Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we investigate a scenario concerning a coupled nonlocal singular viscoelastic equation with sources and distributed delay terms. By establishing suitable conditions, we have proved that a finite-time blow-up occurs in the solution. [ABSTRACT FROM AUTHOR]

In this study, we investigate the inverse problem of the two-dimensional wave equation source term, which arises from the Distributed Acoustic Sensing (DAS) data on the boundary. We construct a new integral operator that maps the interior sources to the DAS-type data at the boundary. Due to the noninjectivity and instability of the integral operator, which violates the well posedness of the inverse problem, a minimization problem on a compact convex subset is formulated, and the existence and uniqueness of the minimizer are obtained. Numerical examples for different cases are illustrated. [ABSTRACT FROM AUTHOR]

Copyright of Atomic Energy Science & Technology is the property of Editorial Board of Atomic Energy Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This work deal with global existence and general decay of solutions of a wave equation with acoustic and fractional boundary conditions coupling by source and delay terms. Under some hypotheses, we study the global existence of the solution and by suitable Lyapunov function the general decay result is proved.

In the current paper, we develop and suggest a modified Rusanov method for simulating twolayer shallow water flows with variable topography. The coupling between two-layers results in a non-conservative product term which involves the partial derivatives of unidentified physical parameters, as a result, the model is conditional hyperbolic. The stages of this scheme are predictor and corrector. A parameter for managing the numerical diffusion is included in the predictor stage, which is accomplished through the use of limiters theory. The balance conservation equation is recovered by the corrector stage. To prove the efficacy of the suggested scheme, we offer a number of numerical tests. The numerical outcomes indicate how accurate and well-balanced the suggested method is for simulating two-layer shallow flows with irregular topography. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Xi'an Jiaotong University is the property of Editorial Office of Journal of Xi'an Jiaotong University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The efficiency of the Adomian decomposition method in the solution of integro-differential equations cannot be overemphasized. However, improvement of the method is needed as its drawbacks have been analyzed and reported in recent literature. This present work develops a new modification of the method and its implementation on linear Fredholm type of integro-differential equations. The approach is based on the modification of the traditional Adomian decomposition method. The idea employs the Taylor series expansion of the source term whose resulting functions were combined in two terms for predicting the solution in each iteration. This approach yields a very high accuracy degree when compared to related methods in literature. The newly proposed method is said to accelerates and converges faster than the standard Adomian Decomposition Method. The procedure proves to be concise, effective and converges faster to the true solution of linear Fredholm Integro-differential problems.

The Adomian decomposition method’s effectiveness has been demonstrated in recent research, the process requires several iterations and can be time-consuming. By breaking down the source term function into series, the current work introduced a new decomposition approach to the Adomian decomposition method. As compared to the conventional Adomian decomposition approach, the newly devised method hastens the convergence of the solution. Numerical experiments were provided to show the superiority qualities.

The accident at the Fukushima Daiichi Nuclear Power Plant in 2011 led to a core meltdown, resulting in the significant release of radioactive materials into the environment, revealing the urgent need for further in-depth development of Level 2 probabilistic safety assessment technology. To help establish an effective source-term migration evaluation method, this study investigates fission product migration behavior across leak pathways. Specifically, an experimental line is developed, and experiments are performed under conditions that simulate the environmental and flow conditions in containment vessel penetrations and failure locations during a severe accident. The experiments are conducted in narrow circular pipes, which represent the leak pathways in the containment vessel and reactor building, to determine the impact of flow rate, particle size, and flow path size on the decontamination factors. Additionally, a turbulent deposition model that accounts for re-entrainment effects has been developed, and the experimentally obtained decontamination factors are compared with the developed model, as well as a conventional model. The predicted decontamination factors from the present model exhibit similar trends and values to the experimental results.

In the research field on severe accidents in nuclear power plant, a specific scenario correspond to accident with oxidative conditions for which damaged fuel can be highly oxidised with significant releases of ruthenium oxides. Ruthenium chemistry is complex, and the current knowledge has to be deepened to better assess ruthenium source term with potential radioactive releases to the environment as volatile ruthenium tetroxide. In this work, experimental studies are focused on ruthenium behaviour along a stainless-steel thermal gradient tube, with maximum temperature of 1200 °C, simulating the reactor cooling system in oxidizing conditions with mainly steam/air gas mixtures. Results showed that few % of ruthenium oxides (< 10% with SS tube) can reach low temperature, representative of containment temperature, even with low oxygen content in the carrier gas. The ruthenium revaporization process from the Ru deposits along the tube on mid-term was studied. Influence of carrier gas composition (steam %), flow rate and NOx feed are discussed. [ABSTRACT FROM AUTHOR]

In this paper. we consider a system of two coupled wave equations with internal/boundary damping and source terms. The aim of this work is to prove two blow up results in finite time: the first one is concerned with solution with negative initial energy. The second one is concerned with solution with positive initial energy. [ABSTRACT FROM AUTHOR]

In the present work, we consider a nonlinear Klein–Gordon equation with strong damping, distributed delay and source terms. Under suitable conditions, we prove the blow-up result of solutions. Our result is an extension of many other works in this area. [ABSTRACT FROM AUTHOR]

The increasing number of interbasin diversion projects place high demands on fine-grained simulation and control of free-surface and transient mixed flow. Since the numerical oscillation of the transient mixed flow generates more with higher-order finite volume method (FVM), the study is based on a high-precision first-order Harten, Lax, and van Leer (HLL) Riemann solver that considers the source term (HLLS). This study modifies the original HLLS solver and introduces numerical viscosity in the vicinity of filling bores to suppress the numerical oscillations. Furthermore, this study explores the selection of wave velocity calculation methods. A first-order scheme with high accuracy of the free surface and transient flow was developed and verified through various experiments. The results show that the proposed scheme can deal with the bottom slope both in constant free-surface and mixed flow. This is because of the perfect conservation properties of this scheme. Furthermore, the formula shows good performance in transient mixed flow. Therefore, this method can satisfy the requirements for modelling a long-distance complex channel tunnel system. [ABSTRACT FROM AUTHOR]

This study quantitatively evaluated the source term of a linear accelerator according to target thickness for a 6-20 MeV electron beam using MCNP6. The elements of the target were tungsten and copper, and a composite target and single target were simulated by setting different thickness parameters depending on energy. The accumulation of energy generated through interaction with the collided target was evaluated at 0.1-mm intervals, and F6 tally was used. The results indicated that less than 3% reference error was maintained according to the MCNP recommendations. At 6, 8, 10, 15, 18, and 20 MeV, the energy accumulation peaks identified for each target were 0.3 mm in tungsten, 1.3 mm in copper, 1.5 mm in copper, 0.5 mm in tungsten, 0.5 mm in tungsten, and 0.5 mm in tungsten. For 8 and 10 MeV in a single target consisting only of copper, the movement of electrons was confirmed at the end of the target, and the proportion of escaped electrons was 0.00011% and 0.00181%, respectively.

Heterogeneous reactions such as solid–gas reactions are found in various processes that are indispensable to our daily lives, and numerical simulations are becoming more and more widely used to study these processes. In the analysis of processes involving heat transfer, since the conservation equation of energy is solved numerically to obtain temperatures at arbitrary coordinates, the appropriate governing equations should be solved for an accurate understanding of the phenomenon. In this study, the source term of the conservation equation of energy with temperature as a variable is reconsidered for a system with heterogeneous reactions. As a result, it was confirmed that when the source term is inappropriate, temperatures cannot be calculated correctly when chemical species are generated, while temperatures can be calculated correctly when the equation derived in this study is applied. In addition, as an application of the equation derived in this study to solid–gas two-phase flow, a numerical analysis simulating a biomass gasification experiment in a fluidized bed was conducted, and it was confirmed that the equation can represent the experimental result well. The equation derived in this study is expected to ensure the accuracy of analysis of processes related to heat and mass transfer involving heterogeneous reactions.

In nuclear reactor accident safety studies, the radiological source term is a metric that quantifies the release of radiological material from the reactor to the environment. The present work evaluates heat transfer between high-temperature vapor bubbles and the surrounding coolant and the effect these interactions have on the source term for postulated core disruptive accident scenarios associated with an oxide-fueled, liquid metal–cooled fast reactor class. It is shown that aerosol particle size can influence heat transfer, and it is suggested that the extent of the influence depends on the fineness of the particles in the aerosol. The results are consistent with legacy experiments conducted in the Fuel Aerosol Simulant Test (FAST) facility at Oak Ridge National Laboratory and offer a more comprehensive assessment of vapor condensation by treating the bubble constituents, in the context of radiation heat transfer, as participating media. The model, which couples classical scattering theory to the equation of radiative transfer and the energy equation, provides a means for estimating size-affected radiative cooling times. Solutions are obtained via the P-1 method of spherical harmonics with improved, higher-order boundary conditions. Outcomes include the development of an "extinction-time ratio" criterion for assessing whether ejection of aerosol from the bubble to the cover region is likely. Aerosol release from the coolant pool is evaluated using this criterion with the potential to extend this work to reactor-scale accidents. A baseline evaluation is provided that shows that omission of participatory effects could lead, in a relative sense, to cooling time offsets in excess of 14%. In addition to enhancing previous evaluations of FAST results, these modeling outcomes contribute to knowledge management efforts aimed at developing a more mechanistic assessment of the source term while suggesting potential enhancements to severe accident safety analysis through the use of more comprehensive radiative heat transfer models. [ABSTRACT FROM AUTHOR]

The removal of aerosol particles and vapors in gas bubbles moving through a water pool is known to be an efficient means to reduce source term to the environment during severe accidents, as happened in Fukushima Daiichi. This trapping, called pool scrubbing, entails a complex phenomenology in which hydrodynamics, thermal hydraulics, and aerosol physics strongly affect each other and determine the net transfer of radioactivity coming out from the aqueous pond. More than 20 experimental programs have addressed this issue since the early 1980s, but few of them did it in a systematic and representative way. This paper thoroughly reviews the entire pool scrubbing database until 2016 and assesses the adequacy of the experimental setup, representativeness of boundary conditions, weaknesses in decontamination factor derivation, data uncertainties, and some other aspects to finally synthesize a reduced number of experiments that could be used as an experimental matrix for the validation of pool scrubbing models. More than 500 tests were reviewed and classified as Qualified for Validation, Useful for Understanding, or Not Useful; less than 15% of these experiments are considered in the proposed validation matrix due to different reasons. Major insights and remaining needs are also highlighted. This work was conducted under the framework of the Integration of Pool Scrubbing Research to Enhance Source-Term Calculations, or the IPRESCA project, led by Becker Technologies, in the framework of the Sustainable Nuclear Energy Technology Platform/Nuclear Generation II & III Alliance/Technical Area 2. [ABSTRACT FROM AUTHOR]

This study analyses an approach to consistently recover the second-order convergence of the lattice Boltzmann method (LBM), which is frequently degraded by an improper discretisation of the required source terms. The current work focuses on advection-diffusion models, in which the source terms are dependent on the intensity of transported fields. Such terms can be observed in reaction-type equations used in heat and mass transfer problems or multiphase flows. The investigated scheme is applicable to a wide range of formulations within the LBM framework. All considered source terms are interpreted as contributions to the zeroth-moment of the distribution function. These account for sources in a scalar field, such as density, concentration, temperature or a phase field. Further application of this work can be found in the method of manufactured solutions or in the immersed boundary method. This paper is dedicated to three aspects regarding proper inclusion of the source term in LBM schemes. Firstly, it identifies the differences observed between the ways in which source terms are included in the LBM schemes present in the literature. The algebraic manipulations are explicitly presented in this paper to clarify the observed differences, and to identify their origin. Secondly, it analyses in full detail, the implicit relation between the value of the transported macroscopic field, and the sum of the LBM densities. This relation is valid for any source term discretization scheme. It is a crucial ingredient for preserving the second-order convergence in the case of complex source terms. Moreover, three equivalent forms of the second-order accurate collision operator are presented. Finally, closed form solutions of this implicit relation are shown for a variety of common models, including general linear and second order terms; population growth models, such as the Logistic or Gompertz model and the Allen-Cahn equation. The second-order convergence of the proposed LBM schemes is verified on both linear and non-linear source terms. The pitfalls of the commonly used acoustic and diffusive scalings are identified and discussed. Furthermore, for a simplified case, the competing errors are shown visually with isolines of error in the space of spatial and temporal resolutions. [ABSTRACT FROM AUTHOR]

Extensive studies have been carried out on the behavior of core degradation and fission products of common pressurized water reactors (PWRs). However, few of them have investigated the relationship between thermal hydraulic and fission product behavior in advanced passive PWRs. Due to the impact of thermal hydraulic behaviors in different accident sequences on the release and transportation of fission products, an integrated severe accident analysis (ISAA) code with highly coupled thermal hydraulic and source term calculations is required to simultaneously analyze thermal hydraulic and source term behavior. For advanced passive PWRs, important safety systems that may affect the behavior of the core and fission products should be considered. It is therefore necessary to simulate the thermal hydraulic and fission product behavior of advanced passive PWRs. In this study, the ISAA code is adopted to simulate the occurrence of a hypothetical double ended cold leg LBLOCA of HPR1000 in three scenarios of equipment failure. The results show that the high-temperature fuel rods and cladding materials exhibit delayed failure at the lower position of the active core, whereas earlier failure at higher position during the reflooding. Active and passive equipment affects fuel temperature, the oxidation conditions of the fuel, the interaction of fission products and structural materials, and the state of the fuel, thereby affecting the release of fission products in the fuel. HPR1000 only relies on passive equipment to relieve the core degradation in severe accidents, realize the in-vessel retention of melt, and eliminate the ex-vessel release possibility of fission product. It is hoped that the results can provide references for HPR1000 to formulate the severe accident management guidelines (SAMG).

The accurate simulation of the self-sustaining equilibrium atmospheric boundary layer is essential in computational wind engineering. In order to solve the problem of poor self-sustaining equilibrium atmospheric boundary layer, the method of adding source terms to the transport equation of the turbulence model was adopted to make the inlet profiles of average wind and turbulence wind consistent with the turbulence model. The consistency of the average wind profiles, turbulent characteristics of the three models at several different positions with and without considering the source terms were investigated respectively according to the corresponding CFD numerical example. Take the TTU low-rise building as an example, the proposed method of numerical simulations of the wind load on the structure surface. The results show that by adding source terms to the transport equations of the SST k-ω turbulence model can better achieve the self-sustaining of the atmospheric boundary layer. The velocity profiles and turbulence characteristics profiles of TTU low-rise building at the entrance and exit have high consistency when adding the source terms. The numerical simulation results of the wind pressure coefficient on the surface of the structure are in good agreement with the wind tunnel tests and field measurement results. It is shown that the method can effectively improve the accuracy simulation of the self-sustaining equilibrium of atmospheric boundary layer. The study conclusion proposes a new idea or research method for modeling the equilibrium atmosphere boundary layer and also provides further CFD simulations in structural wind engineering with theoretical and actual values.

This paper introduces a new point depletion-based source term calculation code named BESNA (Bateman Equation Solver for Nuclear Applications), which is aimed to estimate nuclide inventories and source terms from spent nuclear fuels. The BESNA code employs a new modified CE/CM (Constant Extrapolation – Constant Midpoint) predictor-corrector scheme in depletion calculations for improving computational efficiency. In this modified CE/CM scheme, the decay components leading to the large norm of the depletion matrix are excluded in the corrector, and hence the corrector calculation involves only the reaction components, which can be efficiently solved with the Talyor Expansion Method (TEM). The numerical test shows that the new scheme substantially reduces computing time without loss of accuracy in comparison with the conventional scheme using CRAM (Chebyshev Rational Approximation Method), especially when the substep calculations are applied. The depletion calculation and source term estimation capability of BESNA are verified and validated through several problems, where results from BESNA are compared with those calculated by other codes as well as measured data. The analysis results show the computational efficiency of the new modified scheme and the reliability of BESNA in both isotopic predictions and source term estimations.

The inverse problem for simultaneously identifying the space-dependent source term and the initial value in a time-fractional diffusion equation is studied in this paper. The simultaneous inversion is formulated into a system of two operator equations based on the Fourier method to the time-fractional diffusion equation. Under some suitable assumptions, the conditional stability of simultaneous inversion solutions is established, and the exponential Tikhonov regularization method is proposed to obtain the good approximations of simultaneous inversion solutions. Then the convergence estimations of inversion solutions are presented for a priori and a posteriori selections of regularization parameters. Finally, numerical experiments are conducted to illustrate effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The existence and non-existence of stationary solutions of multicomponent coagulation equations with a constant flux of mass towards large sizes is investigated. The flux may be induced by a source of small clusters or by a flux boundary condition at the origin of the composition space, and the coagulation kernel can be very general, merely satisfying certain power law asymptotic bounds in terms of the total number of monomers in a cluster. Our set-up, including an appropriate definition of multicomponent flux, allows a sharp classification of the existence of stationary solutions. In particular, this analysis extends previous results for one-component systems to a larger class of kernels. [ABSTRACT FROM AUTHOR]

This article establishes an asymptotic behavior for the elasticity systems with nonlinear source and dissipative terms in a three-dimensional thin domain, which generalizes some previous works. We consider the limit when the thickness tends to zero, and we prove that the limit solution u∗{u}^{\ast } is a solution of a two-dimensional boundary value problem with lower Tresca’s free-boundary conditions. Moreover, we obtain the weak Reynolds-type equation.

Molten salt reactors (MSRs) are innovative advanced nuclear reactors that utilize nuclear fuel by dissolving it in a high-temperature liquid salt. This unique feature differentiates MSRs from other types of reactors and allows for enhanced safety and economic performance. The liquid fuel also entails several multiphysics effects that can complicate reactor design and operation. One primary effect termed here as depletion-driven thermochemistry is a driving force in altering the multiphysics behavior of the reactor. Essentially, depletion-driven thermochemistry is the effect that fuel depletion has on changing the chemical redox potential of the fuel salt over time. As the fuel is consumed, the redox potential shifts toward a more oxidizing state. Without active control, the changing chemistry due to depletion increases corrosion thereby limiting reactor component lifetimes. Additionally, the changing redox potential of the fuel salt alters the vapor pressures of chemical species dissolved in the fuel salt. Changing vapor pressures of species in the fuel salt is an important parameter to understand when off-gassing volatile species during normal reactor operation, and for source term characterization during accident scenario transients. The present work represents a fundamental step toward modeling and coupling the driving physics (i.e., neutronics and chemistry) involved in altering the redox potential in an MSR. Here, the neutronic code Griffin models the depletion of the fuel-salt system, while the chemical equilibrium code Thermochimica calculates the thermochemical state of the isotopic inventory, using the Molten Salt Thermodynamic Database - Thermochemical (MSTDB-TC). These two codes are tightly coupled to predict the impact of fuel depletion in altering the chemistry in MSR systems. Redox potential control methods are discussed and can be modeled using this multiphysics approach. The vapor pressures of chemical species that could be extracted to an off-gas system, as determined by the reactor’s thermochemical state, are examined. The neutronics-chemistry coupling developed in this work is expected to have potential application for analyzing corrosion, source term evolution, and material safeguards in MSR systems. Lastly, suggestions for areas of further improvements of the models to expand these capabilities by incorporating other coupled physics effects is provided.

Taking inventories in reactor cores is critical for understanding their radioactive source terms and establishing the relationship between the activity concentration in the primary loop and the status of the reactor core's fuel. However, there is a niche in which a simple but accurate relationship between reactor conditions and nuclide inventories can reliably predict the fission gas nuclide activities of the reactor core in the primary loop. In this study, a simple and efficient model called "Inventories of a Point Reactor for Fission Gas Nuclides" (IPRFGN) was proposed to calculate and interpret such inventories, in which a 10 MW high-temperature gas-cooled experimental reactor (HTR-10) was used as the test case. The present study findings were consistent with those of a general point–depletion burnup code such as the KORIGEN code. Here, the relative error was <1%. Based on the application of the IPRFGN model in HTR-10, the results indicate that the proposed IPRFGN model has provided the relationship between the inventories of fission gas nuclides in the core and the reactor conditions in all types of nuclear fission reactors. In the future, the IPRFGN model will be used for calculating fission gas nuclide inventories in various reactors. [ABSTRACT FROM AUTHOR]

The Xisha islands is a unique area where offshore structures can be utilized as exploration bases in the remote sea. Forecasting of sea state parameters is critical for the design and operation of offshore structures. The goal of this work is to establish an effective operational model to simulate wind waves in the Xisha Islands based on the third-generation wave model WAVEWATCH-III. During the process, two significant difficulties are highlighted and addressed: grid modeling optimization and physical source terms assessment. Typhoon-induced waves using different grid modeling techniques and physical parameterizations were modeled and evaluated using buoy measurements near islands and reefs. It was found that the unstructured triangular grid had a better performance than the other grid options in complex terrain environments like the Xisha Islands. The ST2 source-term package can provide efficient and accurate results in significant wave heights than the other source-term packages in the South China Sea. [ABSTRACT FROM AUTHOR]

The EU-DEMO must demonstrate the possibility of generating electricity through nuclear fusion reactions. Moreover, it must denote the necessary technologies to control a powerful plasma with adequate availability and to meet the safety requirements for plant licensing. However, the extensive radioactive materials inventory, the complexity of the plant, and the presence of massive energy sources require a rigorous safety approach to fully realize fusion power's environmental advantages. The Tokamak building barrier design must address two main issues: radioactive mass transport hazards and energy-related or pressure/vacuum hazards. Safety studies are performed in the frame of the EUROfusion Safety And Environment (SAE) work package to support design improvement and evaluate the thermal-hydraulic behavior of confinement building environments during accident conditions in addition to source term mobilization. This paper focuses on developing a thermal-hydraulic model of the EU-DEMO Tokamak building. A preliminary model of the heat ventilation and air conditioning system and vent detritiation system is developed. A loss-of-coolant accident is studied by investigating the Tokamak building pressurization, source term mobilization, and release. Different nodalizations were compared, highlighting their effects on source term estimation. Results suggest that the building design should be improved to maintain the pressure below safety limits; some mitigative systems are preliminarily investigated for this purpose. [ABSTRACT FROM AUTHOR]

Simulated free surface transients in periodic urban layouts have been reported to be self-similar in the space-time domain when averaged on the scale of the building period. Such self-similarity is incompatible with the head loss model formulae used in most porosity-based shallow water models. Verifying it experimentally is thus of salient importance. New dam-break flow laboratory experiments are reported, where two different configurations of idealized periodic buildings layouts are explored. A space-time analysis of the experimental water level fields validates the self-similar character of the flow. Simulating the experiment using the two-dimensional shallow water model also yields self-similar period-averaged flow solutions. Then, the Single Porosity (SP), Integral Porosity (IP) and Dual Integral Porosity (DIP) models are applied. Although all three models behave in a similar fashion when the storage and connectivity porosities are close to each other, the DIP model is the one that upscales best the refined 2D solution. [ABSTRACT FROM AUTHOR]

Uranium aerosols are released from uranium-containing materials in high-temperature environments caused by nuclear accidents or other processes. Research on the generation characteristics of uranium aerosols under such conditions is an important part of nuclear-safety analysis. In this experiment, the similarity between metal cerium aerosols and uranium material aerosols was evaluated from the aspects of particle size distribution and source term. Combined with the experiment data, the effect of air flow rate and sampling time is discussed. The calculation result of the air release fraction (ARF) is 6.07 × 10−3–4.8 × 10−2, and the respirable fraction (RF) is 0.810–0.978, respectively, showing that the size distribution of particles and ARF of the cerium aerosol are different from the results of the uranium aerosols in the literature, while the RF is similar to the results obtained by using the uranium–niobium alloy in the literature. [ABSTRACT FROM AUTHOR]