scholarly journals Toward an understanding of the nonlinear nature of atmospheric photochemistry: Origin of the complicated dynamic behaviour of the mesospheric photochemical system

2000 ◽  
Vol 7 (1/2) ◽  
pp. 87-104 ◽  
Author(s):  
I. B. Konovalov ◽  
A. M. Feigin
Keyword(s):  
Atomic Oxygen ◽  
Dynamic Behaviour ◽  
Chemical Processes ◽  
Small Perturbations ◽  
Average Growth ◽  
Photolysis Rates ◽  
Abrupt Changes ◽  
Model Equations ◽  
Dimensional Mapping ◽  
Nonlinear Nature

Abstract. The methods of nonlinear dynamics are used to reveal the origin of complicated dynamic behaviour (CDB) of a dynamic model of the mesospheric photochemical system (PCS) perturbed by diurnal variations in photolysis rates. We found that CDB appearance during the multi-day evolution is unambiguously determined by two peculiarities in the model behaviour during its 24-hours evolution. These peculiarities are the presence of a stage of abrupt changes in reagent concentrations and the "humped" dependence of the end-night atomic hydrogen concentrations on those at the beginning of the night. Using a successive analysis we found that these two peculiarities are, in turn, conditioned by the specific features of the chemical processes involved in the model, namely, by the catalytic cycle whose net rate is independent of the concentration of the destroyed species (here, it is atomic oxygen). We believe that similar peculiarities inherent in other atmospheric PCSs indicate that under appropriate conditions they may also demonstrate CDB. We identified the mechanism of the CDB appearance and described it in two ways. The first one reveals a sequence of the processes causing the exponential (on the average) growth of a perturbation of the solution with time. In particular, we found that the behaviour of small perturbations of an arbitrary solution of model equations is identical to the behaviour of a linear oscillator excited parametrically. The second way shows the mechanism of CDB appearance by means of 1-dimensional mapping, which is, basically, the same as the well-known Feigenbaum mappings.

A chemically informed, control-oriented model of a three-way catalytic converter

2007 ◽  
Vol 221 (9) ◽  
pp. 1169-1182 ◽  
Author(s):  
M I Soumelidis ◽  
R K Stobart ◽  
R A Jackson
Keyword(s):  
Dynamic Behaviour ◽  
Catalytic Converter ◽  
Chemical Processes ◽  
Operating Conditions ◽  
Oxygen Storage ◽  
Water Gas Shift ◽  
Water Gas Shift Reaction ◽  
Proposed Model ◽  
Shift Reaction ◽  
Water Gas

Chemical activity inside a three-way catalytic converter (TWC) is highly complex and usually is not taken into account when developing TWC control-oriented models. Such models still remain to a large extent empirical and do not perform satisfactorily under a wider range of operating conditions. This work demonstrates how a very simple model, based on the basic chemical processes that take place inside the catalytic converter, can successfully capture a large part of the strongly non-linear TWC dynamic behaviour. The proposed model is based on the reactions of ceria oxidation and carbon monoxide oxidation, which appear to dominate the fast dynamics of oxygen storage and release respectively. In addition, the water-gas shift reaction is incorporated into the model, which is responsible for the slower dynamic response of the catalyst under rich operating conditions. With some mild assumptions, a discrete-time version of the model was implemented in MATLAB. The model is sufficiently simple in structure for in-vehicle use and can be used for control and on-board diagnostic purposes.

scholarly journals The chemistry of daytime sprite streamers – a model study

2013 ◽  
Vol 13 (11) ◽  
pp. 29521-29550
Author(s):  
H. Winkler ◽  
J. Notholt
Keyword(s):  
Atomic Oxygen ◽  
Chemical Processes ◽  
Electric Breakdown ◽  
Initial Increase ◽  
Altitude Range ◽  
Ozone Destruction ◽  
Model Study ◽  
Catalytic Ozone Destruction ◽  
Catalytic Ozone ◽  
Breakdown Event

Abstract. The chemical processes in daytime sprite streamers in the altitude range of 30–54 km are investigated by means of a detailed ion-neutral chemistry model (without consideration of transport). The model results indicate that ozone perturbations due to daytime sprites streamers differ considerably from the ones of nighttime events. Due to liberation of atomic oxygen there is an initial increase of ozone. In terms of relative ozone change, this effect decreases with altitude. While for nighttime conditions, reactive nitrogen produced during the electric breakdown is converted into less reactive NO2, in the sunlit atmosphere NOx causes catalytic ozone destruction. As a consequence, there is significant ozone loss in sprite streamers in the daytime atmosphere, in particular at higher altitudes. At an altitude of 54 km, ozone in the streamer column has decreased by about 15% fifteen minutes after the breakdown event.

DYNAMICS OF INTERACTING ALGEBRAIC SOLITONS

1995 ◽  
Vol 09 (17) ◽  
pp. 1985-2081 ◽  
Author(s):  
YOSHIMASA MATSUNO
Keyword(s):  
Water Waves ◽  
Evolution Equations ◽  
Burgers Equation ◽  
Soliton Solutions ◽  
Interaction Process ◽  
Exponential Functions ◽  
Small Perturbations ◽  
Mathematical Properties ◽  
Model Equations ◽  
Overtaking Collision

A survey is made which highlights recent topics on the dynamics of algebraic solitons, which are exact solutions to a certain class of nonlinear integrodifferential evolution equations. The model equations that we consider here are the Benjamin-Ono (BO) and its higher-order equations together with the BO-Burgers equation, a model equation for deep-water waves, the sine-Hilbert (sH) equation and a damped sH equation. While these equations have their origin either in physics or in mathematics, each equation exhibits a novel type of algebraic soliton solution and hence its characteristic is worth studying in its own right. After deriving these equations, we are concerned with each equation separately. We first present explicit N-soliton solutions and then summarize related mathematical properties of the equation. Subsequently, a detailed description is given to the interaction process of two algebraic solitons using the pole expansion of the solution. Particular attention is paid to investigating the effects of small perturbations on the overtaking collision of two BO solitons by employing a direct multisoliton perturbation theory. It is shown that the dynamics of interacting algebraic solitons reveal new aspects which have never been observed in the interaction process of usual solitons expressed in terms of exponential functions.

scholarly journals Adaptive Parameterization for Solving of Thermal/Compositional Nonlinear Flow and Transport With Buoyancy

SPE Journal ◽  
2018 ◽  
Vol 23 (02) ◽  
pp. 522-534 ◽  
Author(s):  
Mark Khait ◽  
Denis Voskov
Keyword(s):  
Practical Interest ◽  
Time Discretization ◽  
Nonlinear Flow ◽  
Approximate Representation ◽  
Flow And Transport ◽  
Operator Form ◽  
State Dependent ◽  
Model Equations ◽  
Simulation Problem ◽  
Nonlinear Nature

Summary The nonlinear nature of flow and transport in porous media requires a linearization of the governing numerical-model equations. We propose a new linearization approach and apply it to complex thermal/compositional problems. The key idea of the approach is the transformation of discretized mass- and energy-conservation equations to an operator form with separate space-dependent and state-dependent components. The state-dependent operators are parameterized using a uniformly distributed mesh in parameter space. Multilinear interpolation is used during simulation for a continuous reconstruction of state-dependent operators that are used in the assembly of the Jacobian and residual of the nonlinear problem. This approach approximates exact physics of a simulation problem, which is similar to an approximate representation of space and time discretization performed in conventional simulation. Maintaining control of the error in approximate physics, we perform an adaptive parameterization to improve the performance and flexibility of the method. In addition, we extend the method to compositional problems with buoyancy. We demonstrate the robustness and convergence of the approach using problems of practical interest.

scholarly journals The chemistry of daytime sprite streamers – a model study

2014 ◽  
Vol 14 (7) ◽  
pp. 3545-3556 ◽  
Author(s):  
H. Winkler ◽  
J. Notholt
Keyword(s):  
Electric Fields ◽  
Ozone Depletion ◽  
Atomic Oxygen ◽  
Chemical Processes ◽  
Short Term ◽  
Night Time ◽  
Model Study ◽  
Nitrogen Radicals ◽  
Catalytic Ozone Destruction ◽  
Catalytic Ozone

Abstract. The chemical processes in daytime sprite streamers in the altitude range of 30–54 km are investigated by means of a detailed ion–neutral chemistry model (without consideration of transport). The focus lies on nitrogen, hydrogen and oxygen species, and in particular on ozone perturbations. Initial effects of the breakdown electric fields at the tip of sprite streamers include a short-term loss of ozone due to ion–chemical reactions, a production of nitrogen radicals, and a liberation of atomic oxygen. The latter leads to a formation of ozone. In terms of relative ozone change, this effect decreases with altitude. The model results indicate that the subsequent ozone perturbations due to daytime sprites streamers differ considerably from the ones of night-time events. For night-time conditions, reactive nitrogen produced at the streamer heads is rapidly converted into significantly less reactive NO2, and there is basically no ozone depletion. The situation is different for daytime conditions where NOx causes catalytic ozone destruction. As a consequence, there is significant ozone loss in sprite streamers in the daytime atmosphere, in particular at higher altitudes. At an altitude of 54 km, ozone in the streamer column has decreased by about 15% fifteen minutes after the sprite event.

scholarly journals Centrifugal spinning of viscoelastic nanofibres

2022 ◽  
Vol 934 ◽  
Author(s):  
S. Noroozi ◽  
W. Arne ◽  
R.G. Larson ◽  
S.M. Taghavi
Keyword(s):  
Energy Equation ◽  
Dynamic Behaviour ◽  
Viscosity Ratio ◽  
Polymer Melt ◽  
String Model ◽  
Flow Parameters ◽  
Centrifugal Spinning ◽  
Spinning Process ◽  
Model Equations ◽  
Viscoelastic Constitutive Model

The centrifugal spinning method is a recently invented technique to extrude polymer melts/solutions into ultra-fine nanofibres. Here, we present a superior integrated string-based mathematical model, to quantify the nanofibre fabrication performance in the centrifugal spinning process. Our model enables us to analyse the critical flow parameters covering an extensive range, by incorporating the angular momentum equations, the Giesekus viscoelastic constitutive model, the air-to-fibre drag effects and the energy equation into the string model equations. Using the model, we can analyse the dynamic behaviour of polymer melt/solution jets through the dimensionless flow parameters, namely, the Rossby ( $Rb$ ), Reynolds ( $Re$ ), Weissenberg ( $Wi$ ), Weber ( $We$ ), Froude ( $Fr$ ), air Péclet ( $Pe^*$ ) and air Reynolds ( $Re^*$ ) numbers as well as the viscosity ratio ( $\delta _s$ ), corresponding to rotational, inertial, viscous, viscoelastic, surface tension, gravitational, air thermal diffusivity, aerodynamic and viscosity ratio effects. We find that the nonlinear rheology remarkably affects the fibre trajectory, radius and normal stresses. Increasing $Wi$ leads to a thicker fibre, whereas increasing $\delta _s$ shows an opposite trend. In addition, by increasing $Wi$ , the fibre curvature is enhanced, causing the fibre to spiral closer to the rotation centre.

scholarly journals Impact of large solar zenith angles on lower stratospheric dynamical and chemical processes in a coupled chemistry-climate model

2003 ◽  
Vol 3 (6) ◽  
pp. 1981-1990 ◽  
Author(s):  
D. Lamago ◽  
M. Dameris ◽  
C. Schnadt ◽  
V. Eyring ◽  
C. Brühl
Keyword(s):  
Atmospheric Chemistry ◽  
Lower Stratosphere ◽  
Climate Model ◽  
Chemical Processes ◽  
Sensitivity Experiment ◽  
Mean Values ◽  
Ozone Destruction ◽  
Photolysis Rates ◽  
The Impact ◽  
Ozone Column

Abstract. Actinic fluxes at large solar zenith angles (SZAs) are important for atmospheric chemistry, especially under twilight conditions in polar winter and spring. The results of a sensitivity experiment employing the fully coupled 3D chemistry-climate model ECHAM4.L39(DLR)/CHEM have been analysed to quantify the impact of SZAs larger than 87.5º on dynamical and chemical processes in the lower stratosphere, in particular their influence on the ozone layer. Although the actinic fluxes at SZAs larger than 87.5º are small, ozone concentrations are significantly affected because daytime photolytic ozone destruction is switched on earlier, especially at the end of polar night the conversion of Cl2 and Cl2O2 into ClO in the lower stratosphere. Comparing climatological mean ozone column values of a simulation considering SZAs up to 93º with those of the sensitivity run with SZAs confined to 87.5º total ozone is reduced by about 20% in the polar Southern Hemisphere, i.e., the ozone hole is "deeper'' if twilight conditions are considered in the model because there is about 4 weeks more time for ozone destruction. This causes an additional cooling of the polar lower stratosphere (50 hPa) up to -4 K with obvious consequences for chemical processes. In the Northern Hemisphere the impact of large SZAs cannot be determined on the basis of climatological mean values due to the pronounced dynamic variability of the stratosphere in winter and spring. This study clearly shows the necessity of considering large SZAs for the calculation of photolysis rates in atmospheric models.

Transonic aerofoils admitting anomalous behaviour of lift coefficient

2014 ◽  
Vol 118 (1202) ◽  
pp. 425-433 ◽  
Author(s):  
A. Kuzmin ◽  
A. Ryabinin
Keyword(s):  
Free Stream ◽  
Stokes Equations ◽  
Numerical Study ◽  
Lift Coefficient ◽  
Flow Simulation ◽  
Navier Stokes ◽  
Small Perturbations ◽  
Navier Stokes Equations ◽  
Adverse Conditions ◽  
Abrupt Changes

Abstract Transonic flow past a Boeing 737 Outboard aerofoil and Whitcomb one with a defected aileron is studied. The flow simulation is based on the system of Reynolds-averaged Navier-Stokes equations. The numerical study demonstrates the existence of free-stream conditions in which small perturbations produce abrupt changes of the lift coefficient. Also the simulation reveals adverse conditions in which aileron deflections have no influence on the lift.

A New Aeroelastic Oscillator, Theory and Experiments

1995 ◽  
Author(s):  
A. H. P. van der Burgh ◽  
T. I. Haaker ◽  
B.-W. van Oudheusden
Keyword(s):  
Wind Tunnel ◽  
Model Equation ◽  
Dynamic Behaviour ◽  
Cross Flow ◽  
Low Frequency ◽  
Aerodynamic Coefficients ◽  
New Type ◽  
Model Equations ◽  
Oscillator Theory ◽  
Theory And Experiments

Abstract This paper reviews recent work on the development of a new type of an aeroelastic oscillator with one degree of freedom in a uniform windfield. The typical characteristics of the oscillator are the low frequency (less than 1 Hz) allowing application of a quasi-steady modeling and a combined translational and rotational motion in cross-flow. The oscillator is developed for the study of galloping oscillations in a wind tunnel. The model equation is validated by comparing its solutions with the experimental results. In the quasi-steady modeling for the dynamic behaviour use is made of the numerical values of aerodynamic coefficients obtained from wind tunnel measurements on the oscillator in a static position. Particularly the dependence of limit amplitudes on the flow velocity, obtained from the analysis of the model equations are compared with the ones obtained from experiments.

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