scholarly journals The Lorenz model for single-mode homogeneously broadened laser: analytical determination of the unpredictable zone

Open Physics ◽  
2014 ◽  
Vol 12 (3) ◽  
Author(s):  
Samia Ayadi ◽  
Olivier Haeberlé
Keyword(s):  
Analytical Solution ◽  
Analytical Procedure ◽  
Dissipative System ◽  
Period Doubling ◽  
Single Mode ◽  
Analytical Determination ◽  
Pumping Rate ◽  
Fifth Order ◽  
Doubling Sequence

AbstractWe have applied harmonic expansion to derive an analytical solution for the Lorenz-Haken equations. This method is used to describe the regular and periodic self-pulsing regime of the single mode homogeneously broadened laser. These periodic solutions emerge when the ratio of the population decay rate ℘ is smaller than 0:11. We have also demonstrated the tendency of the Lorenz-Haken dissipative system to behave periodic for a characteristic pumping rate “2C P”[7], close to the second laser threshold “2C 2th ”(threshold of instability). When the pumping parameter “2C” increases, the laser undergoes a period doubling sequence. This cascade of period doubling leads towards chaos. We study this type of solutions and indicate the zone of the control parameters for which the system undergoes irregular pulsing solutions. We had previously applied this analytical procedure to derive the amplitude of the first, third and fifth order harmonics for the laser-field expansion [7, 17]. In this work, we extend this method in the aim of obtaining the higher harmonics. We show that this iterative method is indeed limited to the fifth order, and that above, the obtained analytical solution diverges from the numerical direct resolution of the equations.

Analytical Determination of Generation-Recombination Rate In Amorphous Silicon

1986 ◽  
Vol 70 ◽  
Author(s):  
Jože Furlan ◽  
Slavko Amon
Keyword(s):  
Analytical Solution ◽  
Amorphous Silicon ◽  
Cross Sections ◽  
Recombination Rate ◽  
Exponential Model ◽  
Localized States ◽  
Analytical Determination ◽  
Capture Cross ◽  
Capture Cross Sections

ABSTRACTA general expression for generation-recombination rate in a-Si based on classical SRH theory including different electron and hole capture cross-sections for donor-like and acceptor-like centers inside the mobility gap is derived. Applying appropriate approximations and two-exponential model for localized states distribution two methods of analytical solution are presented and discussed.

On the Buckley-Leverett Equation With Constant-Pressure Boundary Conditions

SPE Journal ◽  
2016 ◽  
Vol 21 (06) ◽  
pp. 2301-2307 ◽  
Author(s):  
Thormod E. Johansen ◽  
Lesley A. James ◽  
Xiaolong Liu
Keyword(s):  
Analytical Solution ◽  
Flow Rate ◽  
Constant Pressure ◽  
Analytical Determination ◽  
Constant Flow Rate ◽  
Displacement Front ◽  
Constant Rate ◽  
Volumetric Flux

Summary The classical Buckley-Leverett theory applies to 1D linear flow of two immiscible phases under the fundamental assumption that the flow rate (or total volumetric flux) is constant as a function of time. One phase is injected into the medium at a constant rate, thereby displacing the other phase. If the displacing phase is instead injected at constant pressure and the outlet pressure is also constant, the problem is still well-defined; however, the classical Buckley-Leverett theory does not apply. This is because the injected phase and the in-situ phase have different properties such as viscosities. If the boundary pressures are kept constant, the flow rate will, therefore, vary over time. The main result of this paper is to show that the solution of the displacement problem can be obtained from the constant-rate solution through an analytical determination of the flow rate as a function of time, given constant-pressure boundaries. The theory developed in this paper also provides an analytical solution for the location of the displacement front at any given time, the time for frontal breakthrough at the outlet end, and the pressure distribution as a function of time inside the medium. It is demonstrated through computed examples that the constant-flow-rate solution, in general, cannot be used to approximate the corresponding solution for constant-pressure boundaries because the variation in the flow rate is very significant. A standard numerical method has also been applied and compared with the analytical solutions, demonstrating that fine numerical-simulation grids are required for acceptable comparison with the analytical solution.

Problems of Analytical Determination of Journal Bearing Bush Fatigue Strength Estimates

2011 ◽  
Vol 490 ◽  
pp. 247-256 ◽  
Author(s):  
Rafał Gawarkiewicz ◽  
Jan Sikora ◽  
Boguslaw Siwek
Keyword(s):  
Surface Layer ◽  
Fatigue Strength ◽  
Analytical Procedure ◽  
Journal Bearing ◽  
Fatigue Cracks ◽  
Relaxation Method ◽  
Analytical Determination ◽  
University Of Technology ◽  
Bearing Alloy

Problems connected with determination of stress distribution in sliding layer of thin-walled bearing bushes, investigated in bearing fatigue test rigs, have been presented. Using an example of plain bearings tested in the fatigue machine SMOK (built at the Gdańsk University of Technology) problems with obtaining a convergence of iterative procedure for determining the fatigue strength estimators of bearing alloy surface layer are analyzed. Calculations consisting in successive iterations of pressure distribution in oil film and corresponding elastic deformation of the bearing bush and housing were based on finite-element method and utilized ANSYS program. The objective of calculation was the estimation of values of radial, tangential, axial and reduced stresses in surface layer of the bearing bush corresponding to experimentally determined load magnitudes leading to fatigue cracks initiation. The convergence of analytical procedure has been achieved by the use of a relaxation method.

Adipic acid. Determination in workplace air

2017 ◽  
Vol 33 (1(91)) ◽  
pp. 139-149
Author(s):  
Elżbieta DOBRZYŃSKA
Keyword(s):  
Adipic Acid ◽  
Food Industry ◽  
Analytical Procedure ◽  
Analytical Determination ◽  
Array Detector ◽  
Liquid Chromatograph ◽  
Total Uncertainty ◽  
Workplace Air ◽  
Air Sample

Adipic acid is a colorless or white solid. On an industrial scale it is obtained by oxidation of cyclohexanol, cyclohexanone or their mixtures with nitric acid. The compound is utilized in the chemical industry in the production of polyurethanes, polyamides and in the food industry, e.g., as an acidity regulator (E355). Adipic acid is irritating to the eyes. The aim of this study was to develop a method for determining inhalable fraction of adipic acid which enables determination of its concentrations in workplaces air in the range from 1/10 to 2 of MAC values. The developed method is based on the adsorption of adipic acid on a glass fiber filter, a water-extraction and a gas chromatographic analysis of the resulting solution. The tests were performed using a liquid chromatograph (HPLC) 1200 series of Agilent Technologies with diode array detector (DAD). Determinations were performed with application of Allure Organic Acids column (15 cm x 4.6 mm, dp 5 µm). Validation of the method was conducted in accordance with the requirements of the Standard No. EN 482. On the basis of the obtained results, the concentration range was established as 0.036 – 0.72 mg/ml, which corresponds to the concentration range of 0.5 – 10 mg/m3 for 720-L air sample. In the following range the obtained calibration curve was linear as evidenced by the regression coefficient at the level of 0.9999. The overall accuracy of the method was 5.47% and its relative total uncertainty 23.88%. This method enables selective analytical determination of adipic acid in workplace air at the concentration range 0.5 – 10 mg/m3 in the presence of cooccurring compounds, such as cyclohexanone and isopropanol. The method for determining adipic acid is described in the form of analytical procedure in the annex.

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