Covering classes, strongly flat modules, and completions

We study some closely interrelated notions of Homological Algebra: (1) We define a topology on modules over a not-necessarily commutative ring $R$ that coincides with the $R$-topology defined by Matlis when $R$ is commutative. (2) We consider the class $\mathcal{SF}$ of strongly flat modules when $R$ is a right Ore domain with classical right quotient ring $Q$. Strongly flat modules are flat. The completion of $R$ in its $R$-topology is a strongly flat $R$-module. (3) We consider some results related to the question whether $\mathcal{SF}$ a covering class implies $\mathcal{SF}$ closed under direct limit. This is a particular case of the so-called Enochs' Conjecture (whether covering classes are closed under direct limit). Some of our results concerns right chain domains. For instance, we show that if the class of strongly flat modules over a right chain domain $R$ is covering, then $R$ is right invariant. In this case, flat $R$-modules are strongly flat.Comment: 19 page

Rings whose proper factors are right perfect

We show that practically all the properties of almost perfect rings discovered by Bazzoni and Salce in "Almost perfect domains" (Colloq. Math. 95 (2) (2003), 285-301) for commutative rings hold in the non-commutative setting

Maximal ideals in module categories and applications

We study the existence of maximal ideals in preadditive categories defining an order $\preceq$ between objects, in such a way that if there do not exist maximal objects with respect to $\preceq$, then there is no maximal ideal in the category. In our study, it is sometimes sufficient to restrict our attention to suitable subcategories. We give an example of a category $\mathbf C_F$ of modules over a right noetherian ring $R$ in which there is a unique maximal ideal. The category $\mathbf C_F$ is related to an indecomposable injective module $F$, and the objects of $\mathbf C_F$ are the $R$-modules of finite $F$-rank.Comment: Accepted for publication in Applied Categorical Structure

정상상태 및 과도상태 해석을 위한 고신뢰도 핵특성 연계 봉단위 열수력 노심 모의 코드 개발

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 에너지시스템공학부, 2021. 2. 주한규.A pin level reactor core thermal-hydraulics (T/H) code capable of massively parallel execution is developed and coupled with a transport direct whole core calculation (DWCC) code and with a pin-by-pin SP3 code for both steady-state and transient neutronics-T/H analyses. The Efficient Simulator of COre Thermal hydraulics (ESCOT) employs the 4-equation drift-flux model for two phase calculations while the numerical solution is obtained by applying the finite volume method and the Semi-Implicit Method for Pressure Linked Equation Consistent (SIMPLEC) algorithm. Important constitutive models to describe key subchannel phenomena, such as turbulent mixing, pressure drops, vapor generation, liquid-vapor interfacial heat transfer and wall heat transfer, are implemented to ensure the validity of subchannel-scale analyses. The ESCOT code solutions are validated through the simulation of various experiments and the comparison between the predicted quantities. The solutions are assessed also by the comparison with the corresponding results of the other subchannel-scale solvers like COBRA-TF, MATRA and/or CUPID. ESCOT has been successfully employed in steady-state transport DWCC analyses by coupling it with the nTRACER code through a wrapping system. The general coupling technique based on the Picard fixed-point iteration (FPI) has low robustness and the application of relaxation factors leaves too much freedom to the user. Thus, the application of the Anderson Acceleration (AA) as an effort to improve the stability of coupled steady-state calculations is analyzed through a series of 3-dimensional problems solved with increasing complexity starting from a single assembly steady-state problem to a full core depletion problem via checker-board (CB) problems. The convergence behavior is examined in terms of true error reduction by comparing the intermediate fission source distributions with the fully converged reference solution obtained by applying a very tight convergence criterion. It turns out that the number of neutronics-T/H iterations is reduced considerably because the oscillatory behaviors of the local solutions noted in the ordinary FPI can be smoothened. Convergence is reached earlier with AA so that the computing times of the coupled calculations can be reduced by about 25% retaining the solution accuracy. In addition, the improvements in both accuracy and details of the time-dependent coupled analyses are shown through the solution of the Main Steam Line Break (MSLB) accident. This scenario involves a considerable reduction of the inlet coolant temperature of one side of the reactor core which results in significant asymmetry in the radial flow characteristics. Because of this asymmetry, the positive reactivity feedback effect introduced by the decrease of the coolant temperature occurs with strong spatial dependence. For sufficient conservatism, a stuck rod in the cold side is assumed during the reactor trip. Thus, employing the pin level solvers increases the fidelity of the calculated results. Despite the increased performances of transport transient solvers, the computing time is still a burden for the calculation of transients lasting longer than 20sec in simulation time. Therefore, ESCOT has been coupled with a pin-by-pin SP3 based code instead of a DWCC code. The analysis of the Nuclear Energy Agency of the Organization for Economic Cooperation and Development MSLB benchmark is performed by solving the Exercise II problem which does not require system modeling since it provides two sets of core flow boundary conditions. It turns out that the better neutronics and T/H nodalization of the core leads to a higher SCRAM worth which implies a lower maximum return-to-power when it is compared with assembly-wise solvers (< 2%). It is noted also that the mixing effect between the hot and cold sides is constrained only to the first assembly row and the size of the mixing region increases with the core axial level. A dominant axial velocity and a CB-like power shape around the separation between the two sides are the primary reasons for the lack of mixing beyond the first assembly row. Moreover, the better T/H nodalization describes more reliably the coolant behavior around the stuck rod. The use of a pin-by-pin solver allows also to capture the high gradient in pin power inside the assemblies close to the stuck rod at the instance of maximum return-to-power, which was not possible with the conventional assembly-wise solvers. The pin-level coupled neutronics-T/H does not increase the computing time noticeably owing to the parallelized execution capability. This study demonstrates the importance of advancing to pin-wise coupled transient analyses in order to fully understand the core power and temperature behaviors in the severe conditions involving highly distorted flow and power distributions.Abstract Contents List of Figures List of Tables Introduction 1 Purpose, Objectives and Scopes of the Research 4 Roadmap of Multiphysics Analyses at SNU Reactor Physics Laboratory 6 Outlines of the Thesis 7 Development of a Pin level Thermal-hydraulics code 9 Four-equation drift-flux model 10 Mixture properties 11 Drift-flux parameters and phasic velocities 12 Balance equations 14 Mixture mass balance 14 Vapor mass balance 14 Mixture momentum balance 14 Mixture energy balance 15 Equations of state 15 Discretization and solution algorithm 16 Description of subchannel-level phenomena 20 Flow regime map 20 Boiling regimes 23 Macro-mesh cell closure laws 25 Micro-mesh cell closure laws 33 Wall temperature calculation 41 Solution of the conduction equation 45 Equations of state for the solid 46 Solution Strategy and Implementation 51 Critical Heat Flux 52 Two phase validation of the ESCOT code 54 RPI Air-water test 55 GE three by three test 58 PSBT Phase I, Exercise Two 62 Parallelization Scheme 67 Analysis of Steady-state Neutronics-Thermal/Hydraulics Coupled Calculations 69 nTRACER/ESCOT coupled system 73 Anderson Acceleration 77 Undamped Anderson Acceleration algorithm 78 Implementation 81 Assessment of the Anderson Acceleration performances 84 Reduced problems 88 Actual core problems 95 Analysis of Transient Neutronics-Thermal/Hydraulics Coupled Calculations 109 Simplified Pthree based neutronics solver 111 Transient neutronics-T/H coupling 113 Analysis of the NEA/OECD MSLB benchmark 115 Description of the scenario 116 Solution of the NEA/OECD MSLB benchmark exercise II 120 Summary and Conclusions 148 Acknowledgements 153 Appendix A Derivation of the Pressure Correction Equation 155 Appendix B Single phase validation 160 Appendix C Decay Heat Model 174 References 177Docto

Cyclically presented modules, projective covers and factorizations

We investigate projective covers of cyclically presented modules, characterizing the rings over which every cyclically presented module has a projective cover as the rings $R$ that are Von Neumann regular modulo their Jacobson radical $J(R)$ and in which idempotents can be lifted modulo $J(R)$. Cyclically presented modules naturally appear in the study of factorizations of elements in non-necessarily commutative integral domains. One of the possible applications is to the modules $M_R$ whose endomorphism ring $E:=(M_R)$ is Von Neumann regular modulo $J(E)$ and in which idempotents lift modulo $J(E)$.Comment: 17 page