A general relation between the intrinsic convergence properties of SCF Hartree–Fock calculations and the stability conditions of their solutions

1983 ◽  
Vol 79 (7) ◽  
pp. 3421-3423 ◽  
Author(s):  
J. C. Facelli ◽  
R. H. Contreras
Keyword(s):  
General Relation ◽  
Stability Conditions ◽  
Convergence Properties ◽  
Hartree Fock ◽  
The Stability

scholarly journals Causality and stability conditions of a conformal charged fluid

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Farid Taghinavaz
Keyword(s):  
Chemical Potential ◽  
Second Law Of Thermodynamics ◽  
Dense Medium ◽  
Wave Number ◽  
Second Law ◽  
Stability Conditions ◽  
Charged Fluid ◽  
Large Wave ◽  
The Stability ◽  
Large Wave Number

Abstract In this paper, I study the conditions imposed on a normal charged fluid so that the causality and stability criteria hold for this fluid. I adopt the newly developed General Frame (GF) notion in the relativistic hydrodynamics framework which states that hydrodynamic frames have to be fixed after applying the stability and causality conditions. To do this, I take a charged conformal matter in the flat and 3 + 1 dimension to analyze better these conditions. The causality condition is applied by looking to the asymptotic velocity of sound hydro modes at the large wave number limit and stability conditions are imposed by looking to the imaginary parts of hydro modes as well as the Routh-Hurwitz criteria. By fixing some of the transports, the suitable spaces for other ones are derived. I observe that in a dense medium having a finite U(1) charge with chemical potential μ0, negative values for transports appear and the second law of thermodynamics has not ruled out the existence of such values. Sign of scalar transports are not limited by any constraints and just a combination of vector transports is limited by the second law of thermodynamic. Also numerically it is proved that the most favorable region for transports $$ {\tilde{\upgamma}}_{1,2}, $$ γ ˜ 1 , 2 , coefficients of the dissipative terms of the current, is of negative values.

scholarly journals Iterative stability analysis for general polynomial control systems

2021 ◽  
Author(s):  
Bo Xiao ◽  
Hak-Keung Lam ◽  
Zhixiong Zhong
Keyword(s):  
Stability Analysis ◽  
Lyapunov Function ◽  
Control Systems ◽  
Polynomial System ◽  
Stability Conditions ◽  
General Polynomial ◽  
Main Challenge ◽  
Detailed Simulation ◽  
Feasible Solutions ◽  
The Stability

AbstractThe main challenge of the stability analysis for general polynomial control systems is that non-convex terms exist in the stability conditions, which hinders solving the stability conditions numerically. Most approaches in the literature impose constraints on the Lyapunov function candidates or the non-convex related terms to circumvent this problem. Motivated by this difficulty, in this paper, we confront the non-convex problem directly and present an iterative stability analysis to address the long-standing problem in general polynomial control systems. Different from the existing methods, no constraints are imposed on the polynomial Lyapunov function candidates. Therefore, the limitations on the Lyapunov function candidate and non-convex terms are eliminated from the proposed analysis, which makes the proposed method more general than the state-of-the-art. In the proposed approach, the stability for the general polynomial model is analyzed and the original non-convex stability conditions are developed. To solve the non-convex stability conditions through the sum-of-squares programming, the iterative stability analysis is presented. The feasible solutions are verified by the original non-convex stability conditions to guarantee the asymptotic stability of the general polynomial system. The detailed simulation example is provided to verify the effectiveness of the proposed approach. The simulation results show that the proposed approach is more capable to find feasible solutions for the general polynomial control systems when compared with the existing ones.

scholarly journals Mineralogical stabilization of Ternesite in Belite Sulfo-Aluminate Clinker elaborated from limestone, shale and phosphogypsum

2018 ◽  
Vol 149 ◽  
pp. 01073
Author(s):  
K. Ben Addi ◽  
A. Diouri ◽  
N. Khachani ◽  
A. Boukhari
Keyword(s):  
Infrared Spectroscopy ◽  
Phosphoric Acid ◽  
Portland Cement ◽  
Stability Conditions ◽  
X Ray Diffraction ◽  
X Ray ◽  
The Stability

This paper investigates the mineralogical evolution of sulfoaluminate clinker elaborated from moroccan prime materials limestone, shale and phosphogypsum as a byproduct from phosphoric acid factories. The advantage of the production of this type of clinker is related to the low clinkerisation temperature which is known around 1250°C, and to less consumption quantity of limestone thus enabling less CO2 emissions during the decarbonation process compared to that of Portland cement. In this study we determine the stability conditions of belite sulfoaluminate clinker containing belite (C2S) ye’elimite (C4A3$) and ternesite (C5S2$). The hydration compounds of this clinker are also investigated. The monitoring of the synthesized and hydrated phases is performed by X-Ray Diffraction and Infrared spectroscopy. The results show the formation of ternesite at 800°C and the stabilization of clinker containing y’elminite, belite and ternesite at temperatures between 1100 and 1250°C.

scholarly journals Global predictions for astrophysics applications

2020 ◽  
Vol 13 ◽  
pp. 18
Author(s):  
P. Demetriou
Keyword(s):  
Nuclear Reaction ◽  
Cross Sections ◽  
Nuclear Reactions ◽  
Nuclear Astrophysics ◽  
Reaction Network ◽  
Reaction Rates ◽  
Reaction Cross ◽  
Hartree Fock ◽  
Microscopic Models ◽  
The Stability

Nuclear reaction rates play a crucial role in nuclear astrophysics. In the last decades there has been an enormous effort to measure reaction cross sections and extensive experimental databases have been compiled as a result. In spite of these efforts, most nuclear reaction network calculations still have to rely on theoretical predic- tions of experimentally unknown rates. In particular, in astrophysics applications such as the s-, r- and p-process nucleosynthesis involving a large number of nuclei and nuclear reactions (thousands). Moreover, most of the ingredients of the cal- culations of reaction rates have to be extrapolated to energy and/or mass regions that cannot be explored experimentally. For this reason it is important to develop global microscopic or semi-microscopic models of nuclear properties that give an accurate description of existing data and are reliable for predictions far away from the stability line. The need for more microscopic input parameters has led to new devel- opments within the Hartree-Fock-Bogoliubov method, some of which are presented in this paper.

ATTRACTABILITY AND LOCATION OF EQUILIBRIUM POINT OF CELLULAR NEURAL NETWORKS WITH TIME-VARYING DELAYS

2004 ◽  
Vol 14 (05) ◽  
pp. 337-345 ◽  
Author(s):  
ZHIGANG ZENG ◽  
DE-SHUANG HUANG ◽  
ZENGFU WANG
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Global Exponential Stability ◽  
Cellular Neural Networks ◽  
Stability Conditions ◽  
Time Varying ◽  
The Stability ◽  
Theoretical Results

This paper presents new theoretical results on global exponential stability of cellular neural networks with time-varying delays. The stability conditions depend on external inputs, connection weights and delays of cellular neural networks. Using these results, global exponential stability of cellular neural networks can be derived, and the estimate for location of equilibrium point can also be obtained. Finally, the simulating results demonstrate the validity and feasibility of our proposed approach.

Scanning system for high-energy electron diffractometry

1999 ◽  
Vol 32 (6) ◽  
pp. 1033-1038 ◽  
Author(s):  
A. S. Avilov ◽  
A. K. Kuligin ◽  
U. Pietsch ◽  
J. C. H. Spence ◽  
V. G. Tsirelson ◽  
...  
Keyword(s):  
High Energy ◽  
Scanning System ◽  
Registration System ◽  
Hartree Fock ◽  
Intensity Measurements ◽  
Structure Factors ◽  
Additional Control ◽  
Thin Polycrystalline ◽  
The Stability ◽  
Electron Diffractometry

A new electron diffractometer with a diffraction-pattern scanning system in front of a fixed counter has been developed. Significant improvement was achieved in the measured diffraction intensities by using fast electronics and additional control of the stability of the electron beam. The measurement of and accounting for the gear-frequency characteristic of the registration system was performed, and the signal accumulation mode for intensity measurements together with advanced statistical data processing were employed. Good agreement between the experimental and Hartree–Fock structure factors for LiF, NaF and MgO was achieved (to avoid strong extinction effects, rather thin polycrystalline films were used as samples).

scholarly journals Stability of the Regular Hayward Thin-Shell Wormholes

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
M. Sharif ◽  
Saadia Mumtaz
Keyword(s):  
Black Hole ◽  
Thin Shell ◽  
Energy Conditions ◽  
Stability Conditions ◽  
Energy Tensor ◽  
Stress Energy Tensor ◽  
Cosmic Expansion ◽  
Stress Energy ◽  
Thin Shell Wormholes ◽  
The Stability

The aim of this paper is to construct regular Hayward thin-shell wormholes and analyze their stability. We adopt Israel formalism to calculate surface stresses of the shell and check the null and weak energy conditions for the constructed wormholes. It is found that the stress-energy tensor components violate the null and weak energy conditions leading to the presence of exotic matter at the throat. We analyze the attractive and repulsive characteristics of wormholes corresponding toar>0andar<0, respectively. We also explore stability conditions for the existence of traversable thin-shell wormholes with arbitrarily small amount of fluid describing cosmic expansion. We find that the space-time has nonphysical regions which give rise to event horizon for0<a0<2.8and the wormhole becomes nontraversable producing a black hole. The nonphysical region in the wormhole configuration decreases gradually and vanishes for the Hayward parameterl=0.9. It is concluded that the Hayward and Van der Waals quintessence parameters increase the stability of thin-shell wormholes.

Chaos in the Rulkov Neuron Model Based on Marotto’s Theorem

2021 ◽  
Vol 31 (15) ◽  
Author(s):  
Penghe Ge ◽  
Hongjun Cao
Keyword(s):  
Neuron Model ◽  
Initial Conditions ◽  
Stability Conditions ◽  
Two Dimensional ◽  
Bifurcation Diagrams ◽  
Fast Subsystem ◽  
One Dimensional ◽  
Sensitive Dependence ◽  
The Stability ◽  
Slow Subsystem

The existence of chaos in the Rulkov neuron model is proved based on Marotto’s theorem. Firstly, the stability conditions of the model are briefly renewed through analyzing the eigenvalues of the model, which are very important preconditions for the existence of a snap-back repeller. Secondly, the Rulkov neuron model is decomposed to a one-dimensional fast subsystem and a one-dimensional slow subsystem by the fast–slow dynamics technique, in which the fast subsystem has sensitive dependence on the initial conditions and its snap-back repeller and chaos can be verified by numerical methods, such as waveforms, Lyapunov exponents, and bifurcation diagrams. Thirdly, for the two-dimensional Rulkov neuron model, it is proved that there exists a snap-back repeller under two iterations by illustrating the existence of an intersection of three surfaces, which pave a new way to identify the existence of a snap-back repeller.

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