A generalization of Brillouin's theorem and the stability conditions in the quantum-mechanical variation principle in the case of general trial wave functions

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.

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Iterative stability analysis for general polynomial control systems

Nonlinear Dynamics ◽

10.1007/s11071-021-06768-7 ◽

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.

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Numerical Analysis on the Stability Conditions of an Electrohydrodynamic Jet

10.1115/1.0004437v ◽

2021 ◽

Author(s):

S\xedlvio C\xe2ndido ◽

Jose Pascoa

Keyword(s):

Numerical Analysis ◽

Stability Conditions ◽

The Stability

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Variation principle in calculating the flow of a two-phase mixture in the pipes of the cooling systems in high-rise buildings

E3S Web of Conferences ◽

10.1051/e3sconf/20183302063 ◽

2018 ◽

Vol 33 ◽

pp. 02063 ◽

Cited By ~ 1

Author(s):

Andrey Aksenov ◽

Anna Malysheva

Keyword(s):

Channel Cross Section ◽

Variation Principle ◽

Two Phase ◽

Liquid Phases ◽

Rate Of Increase ◽

Annular Layer ◽

Gas Liquid Flow ◽

The Stability ◽

Air Conditioning Systems ◽

Physical Laws

The analytical solution of one of the urgent problems of modern hydromechanics and heat engineering about the distribution of gas and liquid phases along the channel cross-section, the thickness of the annular layer and their connection with the mass content of the gas phase in the gas-liquid flow is given in the paper.The analytical method is based on the fundamental laws of theoretical mechanics and thermophysics on the minimum of energy dissipation and the minimum rate of increase in the system entropy, which determine the stability of stationary states and processes. Obtained dependencies disclose the physical laws of the motion of two-phase media and can be used in hydraulic calculations during the design and operation of refrigeration and air conditioning systems.

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INTEGRAL TRANSFORM TECHNIQUE FOR MESON WAVE FUNCTIONS

Modern Physics Letters A ◽

10.1142/s0217732396001612 ◽

1996 ◽

Vol 11 (20) ◽

pp. 1611-1626 ◽

Cited By ~ 15

Author(s):

A.P. BAKULEV ◽

S.V. MIKHAILOV

Keyword(s):

Wave Function ◽

Sum Rules ◽

Integral Transform ◽

Wave Functions ◽

Sum Rule ◽

New Approach ◽

Exactly Solvable ◽

The Stability ◽

The Masses ◽

Integral Transform Technique

In a recent paper1 we have proposed a new approach for extracting the wave function of the π-meson φπ(x) and the masses and wave functions of its first resonances from the new QCD sum rules for nondiagonal correlators obtained in Ref. 2. Here, we test our approach using an exactly solvable toy model as illustration. We demonstrate the validity of the method and suggest a pure algebraic procedure for extracting the masses and wave functions relating to the case under investigation. We also explore the stability of the procedure under perturbations of the theoretical part of the sum rule. In application to the pion case, this results not only in the mass and wave function of the first resonance (π′), but also in the estimation of π″-mass.

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

MATEC Web of Conferences ◽

10.1051/matecconf/201814901073 ◽

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.

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An analysis on Quantum mechanical Stability of Regular Polygons on a Point Base Using Heisenberg Uncertainty Principle

International Journal for Research in Applied Science and Engineering Technology ◽

10.22214/ijraset.2021.38321 ◽

2021 ◽

Vol 9 (10) ◽

pp. 74-79

Author(s):

Anurag Chapagain

Keyword(s):

Quantum Mechanics ◽

Uncertainty Principle ◽

Stability Problem ◽

Classical Mechanics ◽

Quantum Mechanical ◽

Heisenberg Uncertainty Principle ◽

Heisenberg Uncertainty ◽

Degree Of Stability ◽

The Stability ◽

Heisenberg's Uncertainty Principle

Abstract: It is a well-known fact in physics that classical mechanics describes the macro-world, and quantum mechanics describes the atomic and sub-atomic world. However, principles of quantum mechanics, such as Heisenberg’s Uncertainty Principle, can create visible real-life effects. One of the most commonly known of those effects is the stability problem, whereby a one-dimensional point base object in a gravity environment cannot remain stable beyond a time frame. This paper expands the stability question from 1- dimensional rod to 2-dimensional highly symmetrical structures, such as an even-sided polygon. Using principles of classical mechanics, and Heisenberg’s uncertainty principle, a stability equation is derived. The stability problem is discussed both quantitatively as well as qualitatively. Using the graphical analysis of the result, the relation between stability time and the number of sides of polygon is determined. In an environment with gravity forces only existing, it is determined that stability increases with the number of sides of a polygon. Using the equation to find results for circles, it was found that a circle has the highest degree of stability. These results and the numerical calculation can be utilized for architectural purposes and high-precision experiments. The result is also helpful for minimizing the perception that quantum mechanical effects have no visible effects other than in the atomic, and subatomic world. Keywords: Quantum mechanics, Heisenberg Uncertainty principle, degree of stability, polygon, the highest degree of stability

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l-state Solutions of the Relativistic and Non-Relativistic Wave Equations for Modified Hylleraas-Hulthen Potential Using the Nikiforov-Uvarov Quantum Formalism

Oriental Journal of Physical Sciences ◽

10.13005/ojps03.01.02 ◽

2018 ◽

Vol 3 (1) ◽

pp. 03-09 ◽

Cited By ~ 1

Author(s):

Hitler Louis ◽

Ita B. Iserom ◽

Ozioma U. Akakuru ◽

Nelson A. Nzeata-Ibe ◽

Alexander I. Ikeuba ◽

...

Keyword(s):

Wave Equations ◽

Approximation Scheme ◽

Jacobi Polynomials ◽

Energy Eigenvalue ◽

Relativistic Wave Equations ◽

Wave Functions ◽

Quantum Mechanical ◽

Relativistic Wave ◽

Type Approximation ◽

Klein Gordon

An exact analytical and approximate solution of the relativistic and non-relativistic wave equations for central potentials has attracted enormous interest in recent years. By using the basic Nikiforov-Uvarov quantum mechanical concepts and formalism, the energy eigenvalue equations and the corresponding wave functions of the Klein–Gordon and Schrodinger equations with the interaction of Modified Hylleraas-Hulthen Potentials (MHHP) were obtained using the conventional Pekeris-type approximation scheme to the orbital centrifugal term. The corresponding unnormalized eigen functions are evaluated in terms of Jacobi polynomials.

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

International Journal of Neural Systems ◽

10.1142/s0129065704002054 ◽

2004 ◽

Vol 14 (05) ◽

pp. 337-345 ◽

Cited By ~ 7

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.

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