scholarly journals Thermodynamic Stability Conditions as an Eigenvalues Fundamental Problem

2021 ◽  
Author(s):  
Francisco Nogueira Lima
Keyword(s):  
Thermodynamic Stability ◽  
Quadratic Forms ◽  
Mechanical Stability ◽  
Fundamental Problem ◽  
Physical Stability ◽  
Analytical Techniques ◽  
Stability Conditions ◽  
Mathematical Techniques ◽  
The Stability ◽  
Physical Laws

Quadratic forms diagonalization methods can be used in addressing the stability of physical systems. Thermodynamic stability conditions appears as an eigenvalues fundamental problem, in particular when postulational approaches is taken. The second-order derivatives or appropriate relations between such derivatives of the energy, entropy or any considered thermodynamic potential, as Helmholtz, enthalpy and Gibbs, have interesting mathematical features that directly imply in the physical stability, obtained by use and as consequence of analytical techniques. Formal aspects on the thermal and mechanical stability become simple consequences, but no less formal, of the superposition of rigorously established physical laws, and appropriate applications of mathematical techniques.

scholarly journals Longitudinal Tension and Mechanical Stability of a Pressurized Straw Tube

Instruments ◽  
2018 ◽  
Vol 2 (4) ◽  
pp. 27
Author(s):  
Levan Glonti ◽  
Temur Enik ◽  
Vladimir Kekelidze ◽  
Alexander Kolesnikov ◽  
Dmitry Madigozhin ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Charged Particle ◽  
Measurement Technique ◽  
Mechanical Stability ◽  
Stability Conditions ◽  
Particle Detectors ◽  
Straw Tube ◽  
Special Measurement ◽  
The Stability ◽  
Tube Study

For the development of charged particle detectors based on straw tubes operating in vacuum, a special measurement technique is required for the evaluation of their mechanical properties. A summary of the known equations that govern straw behavior under internal pressure is provided, and a new experimental method of a strained pressurized straw tube study is presented in this paper. The Poisson’s ratio of the straw wall, which defines the stability conditions of a built-in tube, was measured for the NA62 spectrometer straw, and its minimum pre-tension was estimated.

STABILITY OF NUMERICAL DISCRETIZATIONS IN MODELLING VIBRATIONAL CHARACTERISTICS OF PIEZOELECTRIC CYLINDRICAL SHELLS

2002 ◽  
Vol 02 (02) ◽  
pp. 241-264
Author(s):  
R. V. N. MELNIK ◽  
K. N. MELNIK
Keyword(s):  
Conventional Treatment ◽  
Numerical Approximation ◽  
Piezoelectric Materials ◽  
Analytical Techniques ◽  
Stability Conditions ◽  
Cylindrical Shape ◽  
Vibrational Characteristics ◽  
Electromechanical Energy ◽  
The Stability ◽  
Piezoelectric Structures

Many problems in applications of piezoelectric materials are essentially time-dependent, and a conventional treatment of such problems with analytical or semi-analytical techniques based on the analysis of harmonic oscillations become inadequate in those cases where a complete dynamic picture of electromechanical energy transfer is required. For such situations we have developed an efficient explicit numerical methodology allowing us to compute dynamic electromechanical characteristics of piezoelectric structures and devices under various loading conditions. In this paper we demonstrate that the stability conditions for our numerical approximation can be obtained from a discrete conservation law, and can be cast in a form similar to that of the classical CFL condition. However, in our case the velocities of wave propagations, participating in the formulation of the stability conditions, are clearly dependent on the pattern of electromectromechanical coupling. Our discussion in this paper, including computational examples, is centred around finite piezoelectric shells of cylindrical shape.

scholarly journals Thermodynamic stability of a Schwarzschild thin-shell wormhole

2019 ◽  
Vol 28 (11) ◽  
pp. 1950142
Author(s):  
S. Danial Forghani ◽  
S. Habib Mazharimousavi ◽  
M. Halilsoy
Keyword(s):  
Heat Capacity ◽  
Thermodynamic Stability ◽  
Thin Shell ◽  
Classical Method ◽  
Regular Function ◽  
Entropy Function ◽  
Stability Conditions ◽  
Intrinsic Stability ◽  
Thin Shell Wormholes ◽  
The Stability

The thermodynamic stability of a thin-shell wormhole in a Schwarzschild bulk is considered. From the first law, entropy function is found which satisfies the local intrinsic stability conditions. Heat capacity emerges as a well-defined regular function justifying the stability of a Schwarzschild thin-shell wormhole. Our method applies only to static thin-shell wormholes and in this sense it may be considered as supplementary to the classical method of stability. The scope of applications of the method is not limited by the Schwarzschild wormhole.

scholarly journals Analyzing Stability Conditions and Ore Dilution in Open Stope Mining

Minerals ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 1404
Author(s):  
Andreas Delentas ◽  
Andreas Benardos ◽  
Pavlos Nomikos
Keyword(s):  
Production Process ◽  
Underground Mining ◽  
Fundamental Problem ◽  
Numerical Models ◽  
Simulation Models ◽  
Stability Conditions ◽  
Mining Operations ◽  
Design Characteristics ◽  
The Stability ◽  
Stability Graph

Ore dilution is a fundamental problem for the production process in underground mining operations. Especially in open stoping methods of underground mining, the continuous estimation, monitoring and treatment of instability issues is considered necessary in order to maintain the consistency of the production process. This paper aims to combine empirical nomograms of stability estimation and numerical approaches and thus link the extensive experiences of the empirical design and the quantitative data derived by numerical analyses. To facilitate this, a large number of different geomechanical conditions were modeled and analyzed in the pursuit of obtaining valid and applicable relationships between the empirical stability graphs’ approaches and the numerical simulation models. The parametric analysis was made to express the stability conditions and the dilution with specific design characteristics, using prevalent stability-graph approaches while the numerical models were tested using the RS2 software package. The obtained results include direct and easy-to-use mathematical expressions that can be applied during the initial design of the stoping process, especially for the case of sidewalls (hanging walls and foot walls). Furthermore, through the research, an initial proposal is made for a dilution-based stability graph that could be utilized for the early identification of dilution.

An analysis of the transport properties and mechanical stability of rapidly solidified Al-Sb alloy

2015 ◽  
Vol 10 (2) ◽  
pp. 2663-2681
Author(s):  
Rizk El- Sayed ◽  
Mustafa Kamal ◽  
Abu-Bakr El-Bediwi ◽  
Qutaiba Rasheed Solaiman
Keyword(s):  
Mechanical Properties ◽  
Thermal Conductivity ◽  
Melt Spinning ◽  
Elastic Moduli ◽  
Mechanical Stability ◽  
Microstructural Analysis ◽  
Alloy System ◽  
Antimony Content ◽  
The Stability ◽  
Rapidly Solidified

The structure of a series of AlSb alloys prepared by melt spinning have been studied in the as melt–spun ribbons  as a function of antimony content .The stability  of these structures has  been  related to that of the transport and mechanical properties of the alloy ribbons. Microstructural analysis was performed and it was found that only Al and AlSb phases formed for different composition.  The electrical, thermal and the stability of the mechanical properties are related indirectly through the influence of the antimony content. The results are interpreted in terms of the phase change occurring to alloy system. Electrical resistivity, thermal conductivity, elastic moduli and the values of microhardness are found to be more sensitive than the internal friction to the phase changes. 

Thermodynamic Stability of Hexagonal and Rhombohedral Bn at Cvd Conditions from Van der Waals Corrected First Principles Calculations

2019 ◽  
Author(s):  
Henrik Pedersen ◽  
Björn Alling ◽  
Hans Högberg ◽  
Annop Ektarawong
Keyword(s):  
Thin Films ◽  
Thermodynamic Stability ◽  
First Principles ◽  
Thermal Equilibrium ◽  
Density Functional ◽  
Van Der Waals ◽  
Chemical Vapor ◽  
First Principles Calculations ◽  
Functional Theory ◽  
The Stability

Thin films of boron nitride (BN), particularly the sp<sup>2</sup>-hybridized polytypes hexagonal BN (h-BN) and rhombohedral BN (r-BN) are interesting for several electronic applications given band gaps in the UV. They are typically deposited close to thermal equilibrium by chemical vapor deposition (CVD) at temperatures and pressures in the regions 1400-1800 K and 1000-10000 Pa, respectively. In this letter, we use van der Waals corrected density functional theory and thermodynamic stability calculations to determine the stability of r-BN and compare it to that of h-BN as well as to cubic BN and wurtzitic BN. We find that r-BN is the stable sp<sup>2</sup>-hybridized phase at CVD conditions, while h-BN is metastable. Thus, our calculations suggest that thin films of h-BN must be deposited far from thermal equilibrium.

scholarly journals Influence of Whey Protein Micro-Gel Particles and Whey Protein Micro-Gel Particles-Xanthan Gum Complexes on the Stability of O/W Emulsions

Polymers ◽  
2021 ◽  
Vol 13 (14) ◽  
pp. 2301
Author(s):  
Man Zhang ◽  
Bin Liang ◽  
Hongjun He ◽  
Changjian Ji ◽  
Tingting Cui ◽  
...  
Keyword(s):  
Oxidative Stability ◽  
Whey Protein ◽  
High Speed ◽  
Xanthan Gum ◽  
Physical Stability ◽  
Theoretical Support ◽  
Gel Particles ◽  
Oil In Water ◽  
The Stability ◽  
The Impact

Appropriate pretreatment of proteins and addition of xanthan gum (XG) has the potential to improve the stability of oil-in-water (O/W) emulsions. However, the factors that regulate the enhancement and the mechanism are still not clear, which restricts the realization of improving the emulsion stability by directional design of its structure. Therefore, the effects of whey protein micro-gel particles (WPMPs) and WPMPs-XG complexes on the stability of O/W emulsion were investigated in this article to provide theoretical support. WPMPs with different structures were prepared by pretreatment (controlled high-speed shear treatment of heat-set WPC gels) at pH 3.5–8.5. The impact of initial WPC structure and XG addition on Turbiscan Indexes, mean droplet size and the peroxide values of O/W emulsions was investigated. The results indicate that WPMPs and XG can respectively inhibit droplet coalescence and gravitational separation to improve the physical stability of WPC-stabilized O/W emulsions. The pretreatment significantly enhanced the oxidative stability of WPC-stabilized O/W emulsions. The addition of XG did not necessarily enhance the oxidative stability of O/W emulsions. Whether the oxidative stability of the O/W emulsion with XG is increased or decreased depends on the interface structure of the protein-XG complex. This study has significant implications for the development of novel structures containing lipid phases that are susceptible to oxidation.

scholarly journals 3D sub-nanometer analysis of glucose in an aqueous solution by cryo-atom probe tomography

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
T. M. Schwarz ◽  
C. A. Dietrich ◽  
J. Ott ◽  
E. M. Weikum ◽  
R. Lawitzki ◽  
...  
Keyword(s):  
Atom Probe Tomography ◽  
Density Functional ◽  
Chemical Characterization ◽  
Analytical Techniques ◽  
Atom Probe ◽  
Characterization Methods ◽  
Signal Deconvolution ◽  
The Stability ◽  
Frozen Solutions ◽  
3D Volume

AbstractAtom Probe Tomography (APT) is currently a well-established technique to analyse the composition of solid materials including metals, semiconductors and ceramics with up to near-atomic resolution. Using an aqueous glucose solution, we now extended the technique to frozen solutions. While the mass signals of the common glucose fragments CxHy and CxOyHz overlap with (H2O)nH from water, we achieved stoichiometrically correct values via signal deconvolution. Density functional theory (DFT) calculations were performed to investigate the stability of the detected pyranose fragments. This paper demonstrates APT’s capabilities to achieve sub-nanometre resolution in tracing whole glucose molecules in a frozen solution by using cryogenic workflows. We use a solution of defined concentration to investigate the chemical resolution capabilities as a step toward the measurement of biological molecules. Due to the evaporation of nearly intact glucose molecules, their position within the measured 3D volume of the solution can be determined with sub-nanometre resolution. Our analyses take analytical techniques to a new level, since chemical characterization methods for cryogenically-frozen solutions or biological materials are limited.

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.

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