scholarly journals CRITICAL SIZES OF STANDING NUCLEAR BURNING WAVES IN SYSTEMS WITH EXTERNAL CONTROL

2020 ◽  
pp. 16-22
Author(s):  
Yu.Ya. Leleko ◽  
V.V. Gann

The theory of standing waves of nuclear combustion in reactors having a flat, cylindrical or spherical shape of the core is developed. A spherical standing wave occurs when nuclear burning propagates radially from the center of the sphere, and 238UO2 fuel moves to the center and is removed from the system. The stability limits of standing waves of nuclear burning are investigated. It has been established that for standing waves there are minimum (critical) sizes at which they exist. Mathematical modeling of standing waves using the MCNPX code was carried out and critical sizes of standing waves of various symmetries were determined.

2012 ◽  
Vol 23 (5) ◽  
pp. 611-633 ◽  
Author(s):  
JIANQING CHEN ◽  
YONGQING LI ◽  
ZHI-QIANG WANG

This paper is concerned with the stability and instability of standing waves for the quasilinear Schrödinger equation of the form which has been derived in many models from mathematical physics. We find the exact threshold depending upon the interplay of quasilinear and nonlinear terms that separates stability and instability. More precisely, we prove that for α ∈ and odd p ∈ , when $1 < p < 4\alpha -1 +{4\over N}$, the standing wave is stable, and when $4\alpha -1 +{4\over N} \leq p < 2\alpha\cdot 2^\ast -1$ (where $2\alpha\cdot 2^\ast = \frac{4N\alpha}{N-2}$ for N ≥ 3 and 2 α ċ 2* = +∞ for N = 2), the standing wave is strongly unstable. Our results show that the quasilinear term 2 α(△|φ|2α)|φ|2α−2φ makes the standing waves more stable, which is consistent with the physical phenomena.


2004 ◽  
Vol 4 (4) ◽  
Author(s):  
H. Hajaiej ◽  
C.A. Stuart

AbstractWe consider the orbital stability of standing waves of the nonlinear Schrdinger equationby the approach that was laid down by Cazenave and Lions in 1992. Our work covers several situations that do not seem to be included in previous treatments, namely,(i) g(x, s) − g(x, 0) → 0 as |x| → ∞ for all s ≥ 0. This includes linear problems.(ii) g(x, s) is a periodic function of x ∈ ℝ(iii) g(x, s) is asymptotically periodic in the sense that g(x, s) − gFurthermore, we focus attention on the form of the set that is shown to be stable and may be bigger than what is usually known as the orbit of the standing wave.


1994 ◽  
Vol 272 ◽  
pp. 135-156 ◽  
Author(s):  
Peter J. Bryant ◽  
Michael Stiassnie

Multiple forms for standing waves in deep water periodic in both space and time are obtained analytically as solutions of Zakharov's equation and its modification, and investigated computationally as irrotational two-dimensional solutions of the full nonlinear boundary value problem. The different forms are based on weak nonlinear interactions between the fundamental harmonic and the resonating harmonics of 2, 3,…times the frequency and 4, 9,…respectively times the wavenumber. The new forms of standing waves have amplitudes with local maxima at the resonating harmonics, unlike the classical (Stokes) standing wave which is dominated by the fundamental harmonic. The stability of the new standing waves is investigated for small to moderate wave energies by numerical computation of their evolution, starting from the standing wave solution whose only initial disturbance is the numerical error. The instability of the Stokes standing wave to sideband disturbances is demonstrated first, by showing the evolution into cyclic recurrence that occurs when a set of nine equal Stokes standing waves is perturbed by a standing wave of a length equal to the total length of the nine waves. The cyclic recurrence is similar to that observed in the well-known linear instability and sideband modulation of Stokes progressive waves, and is also similar to that resulting from the evolution of the new standing waves in which the first and ninth harmonics are dominant. The new standing waves are only marginally unstable at small to moderate wave energies, with harmonics which remain near their initial amplitudes and phases for typically 100–1000 wave periods before evolving into slowly modulated oscillations or diverging.


Author(s):  
Valery А. Gruzdev ◽  
◽  
Georgy V. Mosolov ◽  
Ekaterina A. Sabayda ◽  
◽  
...  

In order to determine the possibility of using the method of mathematical modeling for making long-term forecasts of channel deformations of trunk line underwater crossing (TLUC) through water obstacles, a methodology for performing and analyzing the results of mathematical modeling of channel deformations in the TLUC zone across the Kuban River is considered. Within the framework of the work, the following tasks were solved: 1) the format and composition of the initial data necessary for mathematical modeling were determined; 2) the procedure for assigning the boundaries of the computational domain of the model was considered, the computational domain was broken down into the computational grid, the zoning of the computational domain was performed by the value of the roughness coefficient; 3) the analysis of the results of modeling the water flow was carried out without taking the bottom deformations into account, as well as modeling the bottom deformations, the specifics of the verification and calibration calculations were determined to build a reliable mathematical model; 4) considered the possibility of using the method of mathematical modeling to check the stability of the bottom in the area of TLUC in the presence of man-made dumping or protective structure. It has been established that modeling the flow hydraulics and structure of currents, making short-term forecasts of local high-altitude reshaping of the bottom, determining the tendencies of erosion and accumulation of sediments upstream and downstream of protective structures are applicable for predicting channel deformations in the zone of the TLUC. In all these cases, it is mandatory to have materials from engineering-hydro-meteorological and engineering-geological surveys in an amount sufficient to compile a reliable mathematical model.


1998 ◽  
Vol 1 (1) ◽  
pp. 23-39
Author(s):  
Carter J. Kerk ◽  
Don B. Chaffin ◽  
W. Monroe Keyserling

The stability constraints of a two-dimensional static human force exertion capability model (2DHFEC) were evaluated with subjects of varying anthropometry and strength capabilities performing manual exertions. The biomechanical model comprehensively estimated human force exertion capability under sagittally symmetric static conditions using constraints from three classes: stability, joint muscle strength, and coefficient of friction. Experimental results showed the concept of stability must be considered with joint muscle strength capability and coefficient of friction in predicting hand force exertion capability. Information was gained concerning foot modeling parameters as they affect whole-body stability. Findings indicated that stability limits should be placed approximately 37 % the ankle joint center to the posterior-most point of the foot and 130 % the distance from the ankle joint center to the maximal medial protuberance (the ball of the foot). 2DHFEC provided improvements over existing models, especially where horizontal push/pull forces create balance concerns.


2004 ◽  
Vol 53 (1) ◽  
Author(s):  
Carsten Hefeker ◽  
Friedrich Heinemann ◽  
Klaus F. Zimmermann

AbstractIn his contribution Carsten Hefeker points out that most of the official arguments concerning the necessity of the Stability and Growth Pact are not convincing. Nevertheless, a mechanism that credibly avoids excessive debts and deficits is needed in most member states. It would be more useful, however, if such rules would focus on overall debt rather than on deficits. In addition, he advocates to create an external control for such fiscal rules, independent from the Commission and ECOFIN. He concludes that the Pact does not need to become more flexible, but more credible.Friedrich Heinemann states that much of the recent reform debate on the Stability Pact is based on a fundamental misconception: The Pact has not been established as a guiding tool for welfare - maximising politicians, but in order to limit detrimental incentives from fiscal short-sightedness. “Stupid” elements like the three-per-cent deficit ceiling have a clear and beneficial strategic function as boundary within the national budgetary process. Furthermore, simple rules are superior to smart ones in increasing the political costs of high deficits in terms of public awareness. The critique on the pact′s missing flexibility is correct mainly regarding its lose logical link to long-run sustainability. Increasing flexibility in a cyclical sense, however, is not a reform priority. Already today the Pact leaves sufficient leeway for responsible politicians. Instead, the reform focus must be on depoliticising the pact in the sense of limiting Council power in the deficit procedure. More flexibility must not come without depoliticising. He recommends that any reform should only be carried into effect with a significant time lag in order to limit the reputation damage which would be the consequence of any quick institutional response to the Pact′s recent crisis.In his paper Klaus F. Zimmermann argues that the Stability and Growth Pact (SGP) has been subject to criticism ever since its inception. He points out that it overlooks business cycle developments within the framework of the consolidation process; it adopts a too short-term view of the stabilisation target which is also hardly under control of policy-makers; and it deals with policy imperfections in a sub-optimal way. Therefore, a reform of the SGP is urgent. The author suggests that the rules must be handled more flexibly. In his opinion, a mediumterm budgetary target and a focus on public expenditures to tackle the pro-cyclical bias is needed. To restore credibility, the task of supervision should be transferred to an independent European institution.


2010 ◽  
Vol 645 ◽  
pp. 411-434 ◽  
Author(s):  
PETER GUBA ◽  
M. GRAE WORSTER

We study nonlinear, two-dimensional convection in a mushy layer during solidification of a binary mixture. We consider a particular limit in which the onset of oscillatory convection just precedes the onset of steady overturning convection, at a prescribed aspect ratio of convection patterns. This asymptotic limit allows us to determine nonlinear solutions analytically. The results provide a complete description of the stability of and transitions between steady and oscillatory convection as functions of the Rayleigh number and the compositional ratio. Of particular focus are the effects of the basic-state asymmetries and non-uniformity in the permeability of the mushy layer, which give rise to abrupt (hysteretic) transitions in the system. We find that the transition between travelling and standing waves, as well as that between standing waves and steady convection, can be hysteretic. The relevance of our theoretical predictions to recent experiments on directionally solidifying mushy layers is also discussed.


2010 ◽  
Vol 24 (15n16) ◽  
pp. 3124-3130 ◽  
Author(s):  
HUI CONG LIU ◽  
XIU QING XU ◽  
WEI PING LI ◽  
YAN HONG GUO ◽  
LI-QUN ZHU

The shell material of microcapsules has an important effect on the electrolytic co-deposition behavior, the release of core material and the surface performance of composite coating. This paper discussed the tensile property and the stability of three shell materials including polyvinyl alcohol (PVA), gelatin and methyl cellulose (MC). It is found that these three shell materials have good mechanical strength and flexibility which are favorable to electrolytic co-deposition and stability of microcapsules in composite coating and that MC has well permeability and porosity which has a positive effect on the release of the core material in composite coating. Moreover, the study of the thermal properties and water vapor permeability of the three shell materials showed that their permeability improved with increase of temperature and humidity. In addition, the composite copper coating containing microcapsules with PVA, gelatin or MC as shell material was prepared respectively.


Biochemistry ◽  
1996 ◽  
Vol 35 (6) ◽  
pp. 2037-2046 ◽  
Author(s):  
Vassiliki Karantza ◽  
Ernesto Freire ◽  
Evangelos N. Moudrianakis

2007 ◽  
Vol 342-343 ◽  
pp. 505-508
Author(s):  
Sung Won Kim ◽  
Yun Sik Nam ◽  
Yeon Jin Min ◽  
Jong Ho Kim ◽  
Kwang Meyong Kim ◽  
...  

Stability and disintegration of natural polyelectrolyte complex microspheres for protein drugs delivery have been extensively investigated because of their great influence on the drug release patterns. In this study, we tested stability of microspheres with alginate (Alg) core layered by either chitosan (Chi) or glycol chitosan (GChi) by examining release profiles of fluorophorelabeled bovine serum albumin (BSA) and lysozyme (Lys) from the microspheres. While GChi shell was disintegrated quickly, Chi-shell microspheres showed good stability in PBS. Disintegration of the coated layer induced the core material instable. The results indicated that while the charges of the shell material provided additional diffusion barrier against the protein release, the key factor to hold the proteins inside the microspheres was the integrity of the outer coating layer.


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