Stability of Coupled-Core Nuclear Reactors: Selected Exact Results

1967 ◽  
Vol 89 (2) ◽  
pp. 283-286
Author(s):  
S. J. Gage ◽  
F. T. Adler
Keyword(s):  
Time Distribution ◽  
Nuclear Reactors ◽  
Delta Function ◽  
Step Function ◽  
Single Step ◽  
Exact Results ◽  
Stability Criteria ◽  
Function Model ◽  
Analytical Stability ◽  
The One

Exact analytical stability criteria are derived for the coupled-core kinetics equations. Four approximate models for describing the time distribution of the coupling neutrons are considered and a theorem proved by Pontryagin is used to establish the asymptotic stability of the systems. The criterion based on the Single Delta Function Model is compared with the one based on the Single Step Function Model.

The two stream instability in the ‘resonance’ model

1969 ◽  
Vol 3 (4) ◽  
pp. 643-649 ◽  
Author(s):  
E. Infeld ◽  
A. Skorupski
Keyword(s):  
Charged Particles ◽  
Step Function ◽  
Distribution Functions ◽  
Function Model ◽  
Resonance Model ◽  
Step Functions ◽  
The One ◽  
The Masses ◽  
Resonance Function ◽  
Stream Instability

In this note the problem of stability of two hot collisionless streams of charged particles is considered. The masses, charges, densities, and temperatures are arbitrary and the distribution functions are modelled by one ‘resonance’ function for each stream. The problem of stability is resolved by Nyquist diagrams, and, for the case of equal plasma frequencies, also by solving the dispersion relation in ω. A comparison with two Maxwellians on the one hand, and a two step function model on the other, is given. Step functions appear to be too crude for this problem.

Thermodynamic Functions Molecular Polarizability of 2,6-dichloro-4-fluoro Phenol

2015 ◽  
Vol 7 (2) ◽  
pp. 1448-1456
Author(s):  
Dr. Surbhi Malik ◽  
D.P. Singh ◽  
Sarvindra Kumar
Keyword(s):  
Thermodynamic Functions ◽  
Delta Function ◽  
Molecular Polarizability ◽  
Function Model ◽  
Chemical Binding ◽  
One Dimensional ◽  
Laser Raman ◽  
Ft Ir ◽  
The One ◽  
Semi Empirical

The Laser-Raman and FT-IR spectra of 2,6-dichloro-4-fluoro phenol (2,6,4-DCFP) have been recorded. The thermodynamic functions, namely, the enthalpy, the heat capacity, the free energy and entropy of 2,6,4-DCFP have been calculated at a pressure of 1 atmosphere in the temperature range 200-1500 K under rigid rotorharmonic oscillator. The one-dimensional semi-empirical delta-function model of chemical binding has been used to evaluate the average molecular polarizability of 2,6,4-DCFP.

A Short Synthesis of (+)-Brefeldin C via Enantioselective Radical Hydroalkynylation

2019 ◽  
Author(s):  
Lars Gnägi ◽  
Severin Vital Martz ◽  
Daniel Meyer ◽  
Robin Marc Schärer ◽  
Philippe Renaud
Keyword(s):  
Total Synthesis ◽  
Natural Product ◽  
Oxidation State ◽  
Single Step ◽  
Radical Process ◽  
Target Molecule ◽  
Short Synthesis ◽  
The One

<div><div><div><div><p>A very concise total synthesis of (+)-brefeldin C starting from 2-furanylcyclopentene is described. This approach is based on an unprecedented enantioselective radical hydroalkynylation process to introduce the two cyclopentane stereocenters in a single step. The use of a furan substituent allows to achieve a high trans diastereoselectivity during the radical process and it contains the four carbon atoms C1–C4 of the natural product in an oxidation state closely related to the one of the target molecule. The eight-step synthesis require six product purifications and it provides (+)-brefeldin C in 18% overall yield.</p></div></div></div></div>

scholarly journals Synthesis and Polymerization Kinetics of Rigid Tricyanate Ester

Polymers ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 1686
Author(s):  
Andrey Galukhin ◽  
Roman Nosov ◽  
Ilya Nikolaev ◽  
Elena Melnikova ◽  
Daut Islamov ◽  
...  
Keyword(s):  
Kinetic Analysis ◽  
Single Step ◽  
Polymerization Kinetics ◽  
Scanning Calorimetry ◽  
Modulated Differential Scanning Calorimetry ◽  
Diffusion Controlled ◽  
Polymerization Product ◽  
The One ◽  
Kinetics Of

A new rigid tricyanate ester consisting of seven conjugated aromatic units is synthesized, and its structure is confirmed by X-ray analysis. This ester undergoes thermally stimulated polymerization in a liquid state. Conventional and temperature-modulated differential scanning calorimetry techniques are employed to study the polymerization kinetics. A transition of polymerization from a kinetic- to a diffusion-controlled regime is detected. Kinetic analysis is performed by combining isoconversional and model-based computations. It demonstrates that polymerization in the kinetically controlled regime of the present monomer can be described as a quasi-single-step, auto-catalytic, process. The diffusion contribution is parameterized by the Fournier model. Kinetic analysis is complemented by characterization of thermal properties of the corresponding polymerization product by means of thermogravimetric and thermomechanical analyses. Overall, the obtained experimental results are consistent with our hypothesis about the relation between the rigidity and functionality of the cyanate ester monomer, on the one hand, and its reactivity and glass transition temperature of the corresponding polymer, on the other hand.

scholarly journals The BAW and SAW coupling analysis of patterned piezoelectric films as inter-digital transducers on diamond substrates using delta-function model

AIP Advances ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 085006
Author(s):  
B. W. Xie ◽  
F. Z. Ding ◽  
H. J. Shang ◽  
D. X. Huang ◽  
T. G. Li ◽  
...  
Keyword(s):  
Delta Function ◽  
Function Model ◽  
Coupling Analysis ◽  
Piezoelectric Films ◽  
Digital Transducers

Enhancement of bi-objective function model to master straight-line facilities sequences using frequency from-to chart

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
SHROUQ GAMAL ◽  
Mohamed K. El-Nemr ◽  
Ahmed M. El-Kassas
Keyword(s):  
Objective Function ◽  
Independent Solution ◽  
Transportation Cost ◽  
Exact Results ◽  
Function Model ◽  
Content Type ◽  
Large Size ◽  
Straight Line ◽  
Time Problem ◽  
Comparative Results

Purpose The purpose of this study is to understand the functional power of frequency from-to chart (FFTC) as an independent solution-key for generation optimal (exact) facilities sequences with an equal distance of straight-line flow patterns. The paper will propose a bi-objective function model based on the Torque Method then will turn it into a computer-based technique with a permutative manner using the full enumeration method. This model aims to figure out if there is a difference between the moment minimization and backtracking treatment. Furthermore, the proposed technique will measure the performance of related works from literature to numerically highlight their limitations. Design/methodology/approach The literature of related works provided two-principles assumed mastering material flow sequences. The researchers gathered and analyzed the three methods – used FFTC as an independent technique – mentioned in the literature then measured their performance with the proposed technique. The proposed technique is based on the computation of torque value using an enhancement of bi-objective function model then application a permutative approach with full enumeration methodology. The bi-objective function model used once to mimic the grand moment value of FFTC and again to study the reflection of minimizing the congestion of backtracking movements on the minimization of total transportation cost. Findings Based on the analysis of literature and comparative results of its three case studies using the proposed technique, it is found that: there are optimum facilities sequences with rich opportunities of exact pathway selection. Reduction methodology is an inefficient way to generate exact results. There is a gap between combining the minimization of the grand moment and the treatment of the backtracking problem. Research limitations/implications This study is one of the first contributions that discusses the assumption of integration between optimization moment value and its relation to treatment backtracking problem. Also, the illness of reduction methodology to reach optimal solutions. The further direction of this research will highlight the conjecture of searching the exact results for small size problems, analyzing the given data and its logical dimensions, developing logical rules for solving and verifying large size problems based on the exact results (The conjecture of P = NP). Originality/value This paper provides a detailed numerical analysis of the most common problems generally faced facility layout problems through understanding the lack of integration between moment minimization and backtracking minimization. Also, the inefficiency of reliance on reduction methodology either in scores of frequencies between facilities with weak relation or the number of permutations. Based on those findings, further study will search the logical philosophy exactly optimizing FFTC manually or without having to deal with a permutative approach for large size problems – which considered non-deterministic polynomial-time problem.

scholarly journals Improved bounds for the availability and unavailability in a fixed time interval for systems of maintained, interdependent components

1980 ◽  
Vol 12 (01) ◽  
pp. 200-221 ◽  
Author(s):  
B. Natvig
Keyword(s):  
Lower Bound ◽  
System Reliability ◽  
Nuclear Reactors ◽  
Random Variables ◽  
Fixed Time ◽  
Time Interval ◽  
Coherent System ◽  
Exact Results ◽  
Fixed Time Interval ◽  
Special Case

In this paper we arrive at a series of bounds for the availability and unavailability in the time interval I = [t A , t B ] ⊂ [0, ∞), for a coherent system of maintained, interdependent components. These generalize the minimal cut lower bound for the availability in [0, t] given in Esary and Proschan (1970) and also most bounds for the reliability at time t given in Bodin (1970) and Barlow and Proschan (1975). In the latter special case also some new improved bounds are given. The bounds arrived at are of great interest when trying to predict the performance process of the system. In particular, Lewis et al. (1978) have revealed the great need for adequate tools to treat the dependence between the random variables of interest when considering the safety of nuclear reactors. Satyanarayana and Prabhakar (1978) give a rapid algorithm for computing exact system reliability at time t. This can also be used in cases where some simpler assumptions on the dependence between the components are made. It seems, however, impossible to extend their approach to obtain exact results for the cases treated in the present paper.

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