scholarly journals Assessment of the unified analytical solution of the steady-state atmospheric diffusion equation for stable conditions

2014 ◽  
Vol 470 (2167) ◽  
pp. 20140021 ◽  
Author(s):  
L. C. G. Pimentel ◽  
J. S. Pérez Guerrero ◽  
A. G. Ulke ◽  
F. P. Duda ◽  
P. F. L. Heilbron Filho
Keyword(s):  
Steady State ◽  
Wind Speed ◽  
Analytical Solution ◽  
Eigenvalue Problem ◽  
Atmospheric Diffusion ◽  
Stable Conditions ◽  
Prairie Grass ◽  
The Stability ◽  
Good Agreement ◽  
Diffusion Problems

In this work, the performance of a unified formal analytical solution for the simulation of atmospheric diffusion problems under stable conditions is evaluated. The eigenquantities required by the formal analytical solution are obtained by solving numerically the associated eigenvalue problem based on a newly developed algorithm capable of being used in high orders and without missing eigenvalues. The performance of the formal analytical solution is evaluated by comparing the converged predicted results against the observed values in the stable runs of the Prairie Grass experiment as well as the simulated results available in the literature. It was found that the developed algorithm was efficient and that the convergence rate depends on the stability condition and the considered parametrizations for wind speed and turbulence. The comparisons among predicted and observed concentrations showed a good agreement and indicate that the considered dispersion formulations are appropriate to simulate dispersion under slightly to moderate atmospheric stable conditions.

ANALYTICAL SOLUTION FOR THE STEADY-STATE CHRONOAMPEROMETRIC CURRENT FOR AN EC′ REACTION AT SPHEROIDAL ULTRAMICROELECTRODES

2006 ◽  
Vol 05 (01) ◽  
pp. 11-24 ◽  
Author(s):  
L. RAJENDRAN
Keyword(s):  
Steady State ◽  
Analytical Solution ◽  
Reaction Rates ◽  
Diffusion Limited ◽  
Limited Current ◽  
State Diffusion ◽  
Simulation Results ◽  
Disc Electrodes ◽  
Steady State Diffusion ◽  
Good Agreement

The steady-state chronoamperometric current for an EC′ reactions at spheroidal ultramicroelectrodes is derived from the non-steady-state diffusion limited current. The polynomial expressions pertaining to two extreme limits of reaction rates are combined for all reaction rates. Starting with the result for spheroidal electrode, equations are obtained for the steady-state currents at disc, oblate, hemisphere and prolate electrodes. Tabular compilation of dimensionless current for disc electrodes are reported. A good agreement with previously available simulation results is noticed.

scholarly journals A unified analytical solution of the steady-state atmospheric diffusion equation

2012 ◽  
Vol 55 ◽  
pp. 201-212 ◽  
Author(s):  
J.S. Pérez Guerrero ◽  
L.C.G. Pimentel ◽  
J.F. Oliveira-Júnior ◽  
P.F.L. Heilbron Filho ◽  
A.G. Ulke
Keyword(s):  
Steady State ◽  
Analytical Solution ◽  
Diffusion Equation ◽  
Atmospheric Diffusion

scholarly journals The Relationship between Air Stability and Visibility over Baghdad City

2021 ◽  
Vol 32 (2) ◽  
pp. 82
Author(s):  
Ahmed F. Hassoon ◽  
Mohammed M. Ahmed ◽  
Nadia M. Abd
Keyword(s):  
Wind Speed ◽  
Solar Radiation ◽  
Atmospheric Stability ◽  
Weather Conditions ◽  
Neutral Condition ◽  
Stability Class ◽  
Stable Conditions ◽  
Class B ◽  
Using Data ◽  
The Stability

In this study, Pasquill atmospheric stability determined at daytime for January and July 2010 fixed for Baghdad city. The classification of stability was made using data of wind speed and solar radiation. These classes were compared with atmospheric stability recorded hourly in Baghdad airport station. The results show that stability class, B and C make up the highest percentages, while class A is non-existent during winter "this" can be attributed to prevailing parameter weather and their frequencies such as temperature, wind speed, and solar radiation. The stability classes were estimated to be medium to moderate. In summer, B and A-B stability classes were more predominant than others. Visibility in January month is very high and concentrated at 8500-11500 meters and has a rate of 75%, while the bad visibility range at this month is about 7.6%. In July month the rate of clear weather conditions of visibility is about 65.8%. Atmospheric elements (temperature, relative humidity wind speed, solar radiation) are compared with visibility at specified stability class to show it’s affected on visibility. If more stable conditions existed this refers to the better extent of visibility, this means unstable conditions reduce atmospheric visibility with help of atmospheric elements. Overall, the most affected class on the visibility is neutral condition and near-neutral condition, but you may determine the location if there is near to the location of emission pollutant or aerosols, consequently, the case is different.

The Stability of Steady-State Depth Distributions of Marine Phytoplankton

1974 ◽  
Vol 108 (963) ◽  
pp. 679-687 ◽  
Author(s):  
W. O. Criminale, ◽  
D. F. Winter
Keyword(s):  
Steady State ◽  
Marine Phytoplankton ◽  
The Stability ◽  
Depth Distributions

scholarly journals Semi-Analytical Solution to Assess CO2 Leakage in the Subsurface through Abandoned Wells

Energies ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2452
Author(s):  
Tian Qiao ◽  
Hussein Hoteit ◽  
Marwan Fahs
Keyword(s):  
Analytical Solution ◽  
Storage Site ◽  
Co2 Leakage ◽  
Transient Pressure ◽  
Flow Paths ◽  
Abandoned Wells ◽  
Diffusivity Equation ◽  
Carbon Dioxide Co2 ◽  
Good Agreement

Geological carbon storage is an effective method capable of reducing carbon dioxide (CO2) emissions at significant scales. Subsurface reservoirs with sealing caprocks can provide long-term containment for the injected fluid. Nevertheless, CO2 leakage is a major concern. The presence of abandoned wells penetrating the reservoir caprock may cause leakage flow-paths for CO2 to the overburden. Assessment of time-varying leaky wells is a need. In this paper, we propose a new semi-analytical approach based on pressure-transient analysis to model the behavior of CO2 leakage and corresponding pressure distribution within the storage site and the overburden. Current methods assume instantaneous leakage of CO2 occurring with injection, which is not realistic. In this work, we employ the superposition in time and space to solve the diffusivity equation in 2D radial flow to approximate the transient pressure in the reservoirs. Fluid and rock compressibilities are taken into consideration, which allow calculating the breakthrough time and the leakage rate of CO2 to the overburden accurately. We use numerical simulations to verify the proposed time-dependent semi-analytical solution. The results show good agreement in both pressure and leakage rates. Sensitivity analysis is then conducted to assess different CO2 leakage scenarios to the overburden. The developed semi-analytical solution provides a new simple and practical approach to assess the potential of CO2 leakage outside the storage site. This approach is an alternative to numerical methods when detailed simulations are not feasible. Furthermore, the proposed solution can also be used to verify numerical codes, which often exhibit numerical artifacts.

scholarly journals Steady-state $$\dot{V}{\text{O}}_{2}$$ above MLSS: evidence that critical speed better represents maximal metabolic steady state in well-trained runners

2021 ◽  
Author(s):  
Rebekah J. Nixon ◽  
Sascha H. Kranen ◽  
Anni Vanhatalo ◽  
Andrew M. Jones
Keyword(s):  
Steady State ◽  
Critical Speed ◽  
Lactate Concentration ◽  
Practical Interest ◽  
Blood Lactate Concentration ◽  
Distance Runners ◽  
Severe Intensity ◽  
The Stability ◽  
Trained Runners ◽  
Over Time

AbstractThe metabolic boundary separating the heavy-intensity and severe-intensity exercise domains is of scientific and practical interest but there is controversy concerning whether the maximal lactate steady state (MLSS) or critical power (synonymous with critical speed, CS) better represents this boundary. We measured the running speeds at MLSS and CS and investigated their ability to discriminate speeds at which $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 was stable over time from speeds at which a steady-state $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 could not be established. Ten well-trained male distance runners completed 9–12 constant-speed treadmill tests, including 3–5 runs of up to 30-min duration for the assessment of MLSS and at least 4 runs performed to the limit of tolerance for assessment of CS. The running speeds at CS and MLSS were significantly different (16.4 ± 1.3 vs. 15.2 ± 0.9 km/h, respectively; P < 0.001). Blood lactate concentration was higher and increased with time at a speed 0.5 km/h higher than MLSS compared to MLSS (P < 0.01); however, pulmonary $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 did not change significantly between 10 and 30 min at either MLSS or MLSS + 0.5 km/h. In contrast, $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 increased significantly over time and reached $$\dot{V}{\text{O}}_{2\,\,\max }$$ V ˙ O 2 max at end-exercise at a speed ~ 0.4 km/h above CS (P < 0.05) but remained stable at a speed ~ 0.5 km/h below CS. The stability of $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 at a speed exceeding MLSS suggests that MLSS underestimates the maximal metabolic steady state. These results indicate that CS more closely represents the maximal metabolic steady state when the latter is appropriately defined according to the ability to stabilise pulmonary $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 .

Stability and Natural Characteristics of a Supported Beam

2011 ◽  
Vol 338 ◽  
pp. 467-472 ◽  
Author(s):  
Ji Duo Jin ◽  
Xiao Dong Yang ◽  
Yu Fei Zhang
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Axial Force ◽  
Critical Values ◽  
Rotational Spring ◽  
Analytical Expression ◽  
The Stability ◽  
Spring Constants ◽  
Critical Axial Force ◽  
Natural Characteristics

The stability, natural characteristics and critical axial force of a supported beam are analyzed. The both ends of the beam are held by the pinned supports with rotational spring constraints. The eigenvalue problem of the beam with these boundary conditions is investigated firstly, and then, the stability of the beam is analyzed using the derived eigenfuntions. According to the analytical expression obtained, the effect of the spring constants on the critical values of the axial force is discussed.

OPTIMAL VELOCITY MODEL WITH RELATIVE VELOCITY

2006 ◽  
Vol 17 (01) ◽  
pp. 65-73 ◽  
Author(s):  
SHIRO SAWADA
Keyword(s):  
Nonlinear Analysis ◽  
Relative Velocity ◽  
Velocity Model ◽  
Fundamental Diagram ◽  
Optimal Velocity ◽  
Traffic Jam ◽  
Optimal Velocity Model ◽  
Linear And Nonlinear ◽  
The Stability ◽  
Good Agreement

The optimal velocity model which depends not only on the headway but also on the relative velocity is analyzed in detail. We investigate the effect of considering the relative velocity based on the linear and nonlinear analysis of the model. The linear stability analysis shows that the improvement in the stability of the traffic flow is obtained by taking into account the relative velocity. From the nonlinear analysis, the relative velocity dependence of the propagating kink solution for traffic jam is obtained. The relation between the headway and the velocity and the fundamental diagram are examined by numerical simulation. We find that the results by the linear and nonlinear analysis of the model are in good agreement with the numerical results.

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