Sebastien Harasse
email: harasse@lis.inpg.fr

Laurent Bonnaud
email: bonnaud@lis.inpg.fr

Michel Desvignes
email: desvignes@lis.inpg.fr

MULTIPLE FACES TRACKING USING LOCAL STATISTICS

Our project is to design algorithms to count people in vehicles such as buses from surveillance cameras' video streams. This article presents a method of detection and tracking of multiple faces in a video by using a model of first and second order local moments. The three essential steps of our system are the skin color modeling, the probabilistic shape model and bayesian decision, and the tracking. An iterative processus estimates the position and shape of multiple faces in images, and tracks them. Tracking updates an object history including all spatial and temporal information about this object. Location and size of these tracking object are predicted by constant speed motion analysis and learned trajectories. Results on office and buses video are promising.

Introduction

Estimating the number of people in a noisy environment is a central task in surveillance. A real-time count can be used to enforce the occupancy limit in a building, to manage transport traffic in real time, to actively manage city services and allocate resources for public events. Our project is to add a counting system for moving platforms such as buses, in an existing classical video recorder. Images are captured with a video camera and are analyzed to determine the number of people present. The background scene is therefore not static and vary in a large number of ways : variations in lighting levels, patterns of scene background, movements of objects that might appear or disappear in the scene. The point of view is defined by the location of the camera, in front of the people. This motivates our approach, which is to find people by finding faces.

Previous works

Finding people in images is a difficult task [START_REF] Ioffe | Probabilistic Methods for Finding People[END_REF] due to the high variability in the appearance of people. For human detection and tracking for surveillance, various approaches have been proposed in the past years [START_REF] Yang | Detecting face in images: a survey[END_REF][START_REF] Hjelmas | Face Detection: A Survey[END_REF]. We can dis-tinguish several main classes of approaches to the problem [START_REF] Yang | Detecting face in images: a survey[END_REF].

Background subtraction [START_REF] Haritaoglu | W4: A real-time system for detection and tracking of people and monitoring their activities[END_REF] is often a first step to find objects of interest such as faces. Unfortunately, this approach needs a stationary background as well as interframe motion based approaches [START_REF] Collins | A System for Video Surveillance and Monitoring: VSAM Final Report[END_REF]. Expert systems and structural methods try to represent and recognize face by rules [START_REF] Yang | Human face detection in complex background[END_REF], more often describing spatial relationships between parts of a face. Finding good rules is often an extremely difficult task in an unconstrained environment.

Classical Template matching methods require the learning of several patterns of the whole face [START_REF] Kwon | Face Detection Using Templates[END_REF]. Recent works [START_REF] Nanda | Probabilistic template based pedestrian detection in infrared videos[END_REF][START_REF] Stauffer | Similarity templates for detection and recognition[END_REF] on template matching deal with variation in scale, pose, or shape, in the context of pedestrian detection. In their acquisition conditions, the great variability of human is dramatically reduced.

Feature based approaches extract invariant structural features from one or more images, and then classify extracted objects with statistical classifiers such as Support Vector Machines [START_REF] Xu | Pedestrian Detection and Tracking with Night Vision[END_REF], neural Networks [START_REF] Rowley | Neural Network-Based Face Detection[END_REF], probabilistic approach [START_REF] Schneiderman | Probabilistic Modeling of Local Appearance and Spatial Relationships for Object Recognition[END_REF], or cascade of filters [START_REF] Viola | Robust Real-Time Face Detection[END_REF]. Features are designed to be invariant to some changes in illumination and pose. Several works use Harr wavalets [START_REF] Viola | Robust Real-Time Face Detection[END_REF], DCT [START_REF] Hafed | Face Recognition Using the Discrete Cosine Transform[END_REF] or local descriptors [START_REF] Vogelhuber | Face Detection based on Generic Local Descriptors and Spatial Constraints[END_REF]. However, the largest adopted feature is skin color [START_REF] Yang | Detecting face in images: a survey[END_REF][START_REF] Hjelmas | Face Detection: A Survey[END_REF]. Human skin color forms a relatively tight cluster in color spaces, even when considering darker and brighter skins. Color allows fast processing and is robust to changes in pose and illumination.

The main problem of methods base on skin color is the determination of a probability threshold to be used on each pixel for deciding which pixels correspond to the skin: this is a segmentation step which gives a binary mask for further processing. Our method solves this problem by using a Bayesian approach and reporting the decision to upper stage of processing, combining that real valued information with temporal information. The essential steps of our system are the skin color modeling, the probabilistic shape model and bayesian decision, and the tracking.

System overview

The system overview is illustrated by the data flow (figure 1). The detection can be summarize by steps 1,2,3 un-less tracking is represented by step 4,5,6,. Motion of each object is computed in this step.

5. step 5 predicts the next location of objects from motion.

6. step 6 computes and stores trajectories and also predicts face location in next image using a learning method.

Figure 1. System overview : Data flow chart

In this system, two data levels are defined :

1. Pixel level : skin and face detection are based upon bayesian classifiers and their results are probabilities maps. Such maps are easily combined and merged to enhance or decrease probabilities values. At this level, every results will be given under this format.

2. Object level : after decisions step, objects are obtained, i.e. symbolic representation of face and human. Object tracking is a high level process on these representation and is translated in probabilities map to be merged at the pixel level during the next frame analysis.

Skin Model

A skin color model is needed in order to decide whether a pixel is of skin color or not. Skin chrominance is very specific, as opposed to its luminance, which has a large variability. Numerous works have been done on skin models and several color spaces have been tested [START_REF] Yang | Detecting face in images: a survey[END_REF][START_REF] Hjelmas | Face Detection: A Survey[END_REF]. None of them seems to be really a better choice. In practice, intensity illumination invariant space (Normalized RGB, Lab, Yuv,..) have quite similar performances. Moreover, none of these space is color illumination invariant, which is the major variability in our application (bright sunlight, light in tunnel, sodium light in night, etc). Thus our model is defined in a chrominance color space so that skin pixels are represented in a small portion of the space. The normalizedrgb color space is used here because it is a 2D model, and because with other space color have not out preformed this one on our real data.

Since r + g + b = 1, only two components (r,g) are used for the model. A bidimensionnal gaussian model g skin is obtained to represent skin color in the rg-space. Its parameters are learned from skin pixels from the FERET faces database.

This model is applied to an image to obtain a skin map S I where each value is the value of our bidimensionnal gaussian model at the corresponding pixel's color. For an image I, and skin model g skin , the corresponding skin map S I is :

S I (x, y) = g skin (I(x, y))
where (x, y) is a position in the image and I(x, y) is the color of I at this position, in normalized-rgb coordinates.

Shape Model and Bayesian Framework

Statistical Modeling

Our face detector is based on a statistical representation of the problem : a face is a skin region, parametrized by its position, shape and orientation.

Let x be a 5-dimensional random variable modeling the position and shape of a skin object, by its first and second order moments :

x = (µ x , σ x ) with µ x = (µ x1 , µ x2 ), σ x = σ x11 σ x12 σ x12 σ x22
Our face model can be seen as an ellipse centered in µ x with axes defined by covariance matrix σ x . This model has been introduced in [START_REF] Schwerdt | Robust face tracking using color[END_REF] for one single face tracking using color.

And let z be a random variable representing each observed image. That is to say, the realizations for z are the images where faces are to be detected. The face detection problem then involves computing the probablity density p(x/z), from which we can decide where faces are likely to be in the image.

Considering a bayesian framework, the a posteriori probability density p(x/z) is proportional to the product of the observation density p(z/x) by the a priori density p(x) :

p(x/z) ∝ p(z/x).p(x)
For now, x is assumed to be uniformely distributed, which means that any kind of skin colored object could be detected in the image, not restricted to faces only. p(x) is constant. It is always possible to choose another distribution for x if necessary.

Observation density

The observation probability density p(z/x) must now be defined. It represents the probability to observe the image z, knowing that a skin object parametrized by x is present. The number of skin objects in the image is not known, and p(z/x) should allow the estimation of the number of objects and their parameters. Since random variable x is defined as the parameters of only one object, it is 5-dimensional, which is reasonable, but it doesn't allow directly the estimation of many objects. Thus p(z/x) is defined so that there is a local maximum for each x corresponding to a skin object in the image.

The function chosen for the observation probability is the correlation function between the skin map S z of image z and the bidimensional gaussian g x parametrized by x :

p(z/x) ∝ S z (t).g x (t)dt
where t is a bidimensional variable.

p(z/x) has local maxima for each skin object in z, under the hypothesis that objects are well separated from each others. The proof involves approximation of S z with a bidimensional gaussian functions mixture, and studying the behavior of p(z/x) for values of x in the neighbourhood of each skin object.

Skin objects detection

From this point, there are several ways to detect the objects in our image, including the exhaustive search of local maxima in the 5-dimensional function x -→ p(z/x), or sampling algorithms like Condensation [START_REF] Isard | Condensation -conditional density propagation for visual tracking[END_REF]. We propose a method that doesn't require the calculation of p(z/x) for all values.

The random variable x can be seen as two random variables µ x and σ x which represent the first and second order moments of the object respectively. The method proposed here estimates µ x by using a priori information about σ x , then estimates σ x for each detected object, using an iterative process.

First order moment estimation

The detection of the first order moments µ x of objects in the image involves an a priori estimation of σ x . σ m is defined as the average covariance matrix representing a face. With this assumption, the observation density becomes :

p(z/µ x , σ x = σ m ) ∝ S z (t).g µx,σm (t)dt p(z/µ x , σ x = σ m ) ∝ S z (t).g 0,σm (t -µ x )dt
The observation density with fixed σ x = σ m is proportianal to the 2-dimensional convolution product of S z by a gaussian function with covariance matrix σ m , which is an inexpensive computation. Objects' first order moments are detected by finding the local maxima of the function.

Iterative second order moment estimation

Suppose that an object x 0 is present in the image, with first order moment µ x0 . Its second order moment σ x0 must be estimated so that p(z/x 0 ) is a local maxima.

If there is only one skin object in the image, the problem is simply resolved by computing the second order moment of the whole skin map :

σ 2 x0 = (t -µ x0 ) 2 .S z (t)dt
where t is a bidimensional variable.

Since the number of objects in the image is unknown, this method doesn't apply. Our method is to estimate σ x0 by using local moments iteratively. Let W be a 2-dimensional window defined in the same space as S z , with W (t)dt = 1. The second order local moment of S z centered in µ x0 is defined as :

σ 2 Sz,W = (t -µ x0 ) 2 .S z (t)W (t)dt
A sequence of local moments is defined as :

σ 0 = 1 σ 2 n+1 = σ 2 Sz,g(µx 0 ,α.σn) (1)
where g(µ x0 , α.σ n ) is the bidimensional gaussian window of first and second order moments µ x0 and α.σ n respectively, with α > 2.

Practically, the method consists in starting with a window centered in µ x0 with a size smaller than the expected object size, computing the local moments of S z in this window, then using the result multiplied by a constant α as the next window covariance matrix. This sequence converges to the second order moment of the skin object. By using local moments, the computation of σ x0 is not disturbed by the other objects in the image. The detection of multiple skin objects in the image can then be achieved. Figure 2 shows the results obtained with this method.

Tracking

Tracking is based upon a global structure named history, in which all information about existing and past objects and decision are stored. Tracking decision are done as soon as possible, using a prediction verification or observation scheme. When an object is present at any time, some hypothesis about its location in the next frame can be done, because motion is generally smooth. These object level hypotheses are translated at the pixel level and verified on the next frame, by comparing and merging this pixel level hypotheses with the pixel level detection (observation).

Most of the time, in our application, people pass through the left side to the right side of the camera corresponding to the previous prediction. Sometimes, people turn back and the previous prediction is no longer valid. Moreover, some trajectories are more frequent than others. A second prediction is defined to manage these situations, named learned trajectories prediction. From one location, the object location is predicted with different probabilities from all previous stored trajectories in its neighboring. Probability maps are an elegant way to manage these multiple hypothesis, which are easily combined with the motion prediction.

The observation step of skin objects tracking is tightly related to the recursive method used for the second order local moment estimation.

History

The history is a spatio temporal representation of the scene Each detected object is stored, with the following informations:

current position and motion past positions and motions dates of birth and death predicted position photometric values shape : covariance matrix

Prediction step

The bayesian framework is a natural way to manage several methods for a same problem, merging the results in a numeric fusion. As previously mentioned, the prediction scheme is achieved by 2 different methods, given 2 probability maps. The final prediction is a weighted sum of these 2 probabilities.

p 1 (x) = 1 2 i=1 α i . 1 i=0 α i .p i (x) (2)

Motion based prediction

As motion is generally smooth, objects are predicted with a smoothed constant speed by :

x t = x t-1 + 1 N . N i=1 v t-i , p 1 (x) = e -( x T t .σx. xt)
(3) If an object disappears, this prediction step is realized with the stored values unless this virtual object is predicted out of the field of view or when it has disappeared from a long time. Note that only one hypothesis is given by this method.

Learned trajectories prediction

As the point of view is fixed, all trajectories are learned to predict the next most probable location of an object. This is done for every position : the underlying idea is that some trajectories are more common than other and well predicted, but rare trajectories must also be predicted with lower probability. For example, in some buses, nearly all the movements are from the left side towards the right side because most of people go into the buses. But sometimes, a person goes out, and cross the field of view from the right side to the left side.

Note that for a given location, it may be possible that no objects have been detected exactly at the same place, due to real previous trajectories or due to poor segmentation accuracy. Then, the learned prediction is computed with all the previously detected neighboring trajectories. From the location x, all the movements given by the previous trajectories are reported on the current frame. Then, the probability is a mixture of gaussian, representing the object shape, weighted by decreasing distance function. All the past movements from location x are noted ( x k , v x,k ). possible locations f rom x :

x i = x t-1 + v x,i : p 2 (x) = 0 i=t-1 e -|| xi-v x,k || 2 .e - || x-x i || σx 2 (4)
With this probability scheme, multiple hypotheses are man-

Figure 3. Prediction with multiple hypotheses

aged (figure 3)until the decision step.

Observation step

The observation step chooses and corrects the predicted position and shape of the object with respect to the observed image. The same iterative algorithm than those of skin object detection is used here. The gaussian function parametrized with the most probable predicted state (position and shape) defines the window in which the first and second order local moments of the object are computed. The initial values are :

µ 0 = 1 card(p(x).p skin ) . Image p(x).p skin σ 0 = 1 card(p(x).p skin ) Image (p(x).p skin -µ 0 ) 2
(5) This step is iterated by using the last computed local moments as the parameters of the gaussian window :

µ n+1 = µ Sz,g(µn,α.σn) , σ 2 n+1 = σ 2 Sz,g(µn,α.σn) (6)
with µ Sz,g(µn,α.σn) the first order local moment of S z in the window g(µ n , α.σ n ), defined by : µ Sz,g(µn,α.σn) = t.S z (t).g(µ n , α.σ n )dt

In this sequence, the σ update step is the same as equation ( 1). This sequence converges to the first and second order moments of each object for the current image.

Occultation

One of the main feature in tracking system is the occultation problem, when people pass behind an obstacle or when people trajectories intersect. In the first case, the observation step will not find any real skin object at the predicted location (µ 0 is equal to zero in equation 5) and the object is just marked as disappeared in the history. This object is still present in the history and will be active in all step where it is necessary, such as prediction.

Figure 4. tracking example

In the second case, illustrated figure 4, the same scheme is followed : one object is marked as disappeared when the trajectories intersect, but is still present and predicted. In these cases, objects are kept in the history unless they are predicted out of the image or when they have disappeared from a long time. Moreover, the learned trajectories prediction with multiple hypotheses management, is able to track 2 persons crossing behind an obstacle.

Results

This tracking method has been tested under real conditions, on video streams from a transport vehicle or from an indoor office.

The office video stream has the following characteristics: 15' duration, spatial resolution 640x480 pixels, frame rate of 30 fps, and illumination conditions fairly controlled. In practice, some background objects have skin color at some moments. During this sequence, 72 persons are present in the temporal scene. Most of them (38) cross the image from left to right, 34 cross from right to left. One turns back. There are 37 intersections of trajectories. Some people have not a constant direction. In this sequence, generally more than 3 persons are visible on the same image. The bus video stream has the following characteristics: 2x3' duration, spatial resolution 702x576 pixels, frame rate of 6 fps, and illumination conditions uncontrolled. In practice, many background objects have skin color at some moments. During this sequence, 30 persons are presents in the temporal scene. 29 cross the image from left to right, 1 crosses from right to left.

Using an appropriate skin model, the detection and tracking of skin objects are efficient. figure 4 shows an example of the tracking of two faces (red and violet ellipses). One arm is also detected in the middle image (white ellipse), because it is a skin object. One part of the wall are sometimes detected as skin, when the sun lights it.

In these sequences, 90 % persons have been detected and tracked. During 2 crossings in the office video, such in figure 4, the tracking has been lost, one object been really suppressed and a new one created. The turn back is well tracked, as illustrated in figure 5.

Figure 5. Sequence with turn back tracking

Another method to validate this tracking system is the trajectories history (figure 6). Most of them are quite regular, with smooth variation. Trajectories in the bottom of the figure are arm trajectories, while faces are localized at the top of the figure. The red trajectory is a real turn back. One error can be seen with the black trajectory, in the middle of the figure : this is a part of the wall, which is skin colored. It is trapped by one person passing near this part and the detection step has included this part in the walking people face. In fact, the tracking is efficient because of good multiple prediction, if the frame rate and the time to life in the history are suitable.

Finally, faces are counted when crossing a predefined line in the images. Counter is incremented when crossing from left to right, decremented when crossing from right to left. The accuracy of the count is 85% compared to the real manual count on the office sequence, 90 % on the transport video. Most false positives were caused by arms being counted, and non-detections face were mainly caused by bad detection of skin pixels.

Conclusion

In this paper, a multiple face tracker has been presented. Based upon the classical skin color detection, it is embedded in a bayesian framework which is an elegant way to manage several algorithms for a same task, like prediction in our tracker. The main feature is then the probability map, data structure shared by the algorithms. A spatio-temporal representation of the scene summarizes the essential information about objects. Reasoning at object level is translated at the image level, by example with the prediction probability map. Although there is no global optimization to find trajectories, multiple hypotheses are managed with an original method of prediction, based on a learning approach. Another interesting feature is the iterative local moments estimation which avoids classical thresholds, used by the skin and face detection algorithm. This approach has been applied to a counting application with promising results on out door videos.

To enhance the performance of the tracker, we are currently working on the fusion of several detection algorithm, including motion analysis and temporal difference, which can be easily integrated in our framework. Trajectories will be improved with a longer temporal and a global spatial analysis and consistency.

Figure 2 .

 2 Figure 2. (a) original image, (b) skin map , (c) five detected objects

Figure 6 .

 6 Figure 6. Detected trajectories in office video


Frédérique Battin-Leclerc
email: frederique.battin-leclerc@ensic.inpl-nancy.fr

A A Konnov

J L Jaffrezo

Michel Legrand

Modeling of the formation of short-chain acids in propane flames

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction

It is now recognized that, in addition to sulfuric and nitric acids, monocarboxylic acids (formic and acetic acids, especially) can contribute to the acidity of gas and aqueous phases of the atmosphere in urban, as well as in remote regions. Natural and anthropogenic sources of monocarboxylic acids have been proposed, but the nature of the individual sources and their relative importance are not established yet [1]. While numerous olefin-ozone reactions can produce formic and acetic acids [2], it is of importance to better understand the potential direct emission of monocarboxylic acids from combustion phenomena, from automotive engines especially.

Detailed analyses of gas-phase pollutants emitted from the exhaust of an engine have been published for diesel [3] and gasoline [4] [5] [6] engines. These papers describe the presence of noticeable amounts of monocarboxylic acids. These acids are mainly formic, acetic and propionic acids; the formation of this last one being strongly linked with the presence of aromatic compounds in the fuel. In a gasoline engine, the emission of acids corresponds to 4 to 27% of the total amount of emitted hydrocarbons and is larger by a factor of 1.3 to 10 than that of aldehydes [4].

Despite that, acids are very minor oxidation products in most laboratory experimental gas-phase apparatuses and there are very few studies showing their formation during combustion and no kinetic model explaining their formation and consumption pathways. A single paper by Zervas [7] proposes analyses of the formation of acids in a combustion apparatus which can easily be modeled, a laminar premixed flame of propane at atmospheric pressure, but without providing all the data needed for modelling. By chance, a very detailed study of the temperatures and species profiles in a laminar premixed flame of propane at atmospheric pressure has been recently published by Biet et al. [8]. As the two studies have been performed for some common equivalence ratios, we attempted here to implement a new kinetic mechanism of the formation of acids in a model able to well reproduce the results of Biet et al. [8] and to use this global model to simulate the relative formation of monocarboxylic acids in the flame of Zervas [7].

Kinetic model for the formation of acids in a flame of propane

The mechanism has been written to reproduce the formation and consumption of formic, acetic, propionic and propenic acids under flame conditions; i.e. the lowtemperature reactions of peroxy radicals have not been considered.

This new mechanism was based on the kinetic scheme of the combustion of propane recently proposed to model laminar premixed flame of methane doped with allene or propyne [9]. This C 3 -C 4 reaction base, which was described in details in a previous paper [10], was built from a review of the recent literature and is an extension of our previous C 0 -C 2 reaction base [11]. The C 3 -C 4 reaction base includes reactions involving all the C 3 nooxygenated species and acroleïne, as well as some reactions for selected C 4 and C 5 compounds and the formation of benzene. In this reactions base, pressure-dependent rate constants follow the formalism proposed by Troe [12] and collisional efficiency coefficients have been included.

To extend this model for description of formation and consumption of acids the relevant sub-mechanism was adopted from the kinetic scheme proposed by Konnov [START_REF] Konnov | Proceed. of the 19th International Symposium on Gas Kinetics (GK 2006)[END_REF]. The number of species was increased by 32 and the number of new reactions was about 200. Selected key reactions discussed in the present work are listed in Table 1. Thermodynamic data of the following species: HOCO, HCOO (formyl radical), HCOOH (formic acid), HCCOH, CH2CHOH (vinyl alcohol), CHOCHO, CH 3 CO2H (acetic acid), C 2 H 5 CO (propionaldehyde radical), C2H5CHO (propionaldehyde), CH 2 CHCO (acrolein radical) were taken from the latest database of Burcat [START_REF] Burcat | [END_REF]. HiTempThermo database (2006) [START_REF]HiTempThermo database[END_REF] was used to obtain the data for HCOH (hydroxymethylene), HOCH 3 CHOOH and other species were estimated using the software THERGAS developed in Nancy [17], which is based on the additivity methods proposed by Benson [START_REF] Benson | Thermochemical kinetics[END_REF].

Whenever possible, rate constants have been adopted from the literature and reviews, for instance, of Atkinson et al. [START_REF] Atkinson | [END_REF]; 30 rate constants have been thus found. In many cases, however, rate constants were estimated assuming same reactivity of similar species. For example, the reactivity of CH 2 (OH) 2 , HOCH 2 OO, HOCH 2 OOH and H 2 CCOH were assumed analogous to CH 3 OH, CH 3 O 2 , CH 3 O 2 H and C 2 H 2 OH respectively. Strictly speaking this approach could be more or less valid for true homologues; remote similarity could be misleading due to resonance stabilization of radicals, significant modifications of the bond dissociation energy, etc. On the other hand this is probably the only way for exploratory modelling of the formation of acids, which are usually not included in the contemporary combustion mechanisms.

A few modifications of the sub-mechanism adopted from the Konnov [START_REF] Konnov | Proceed. of the 19th International Symposium on Gas Kinetics (GK 2006)[END_REF] kinetic scheme were made. The rate constant of reaction (10) of addition of OH to formaldehyde is taken as 0.1% that of the H-abstraction, which is in agreement with the value of 4% proposed by Sivakumaran et al. [START_REF] Sivakumaran | [END_REF] as an upper limit for this branching ratio at 298 K. This experimental study of the reaction between OH radicals with formaldehyde by laser photolysis leads the authors to think that the rate constant of the addition is very small as no hydrogen atoms could be observed by resonance fluorescence. The rate constants of the combinations between OH and alcoxy radicals was taken as what proposed by Allara et al. [20] for H-atoms. The reactions of propionic and propenic acids have been deduced from those proposed for acetic acid.

Validation for the modeling of a propane flame

All the simulations have been performed using PREMIX of CHEMKIN II collection [21] with estimated transport coefficients. Comparisons between experimental results [8] and simulations of a laminar premixed propane flame are shown in fig. 1 for = 0.9 and in fig. 2 for = 0.48.

As it can be seen in fig. 1a and2a, a correct agreement is obtained for the consumption of propane and oxygen and the formation of carbon dioxide for both equivalence ratios. Figure 1b and1c show that the formation of water, hydrogen, carbon monoxide and C 2 compounds are also well reproduced by the model at = 0.9. Similarly good agreement is obtained for = 0.48, as it can be seen in fig. 2b and2c. Figures 1d and2d display the profiles of aldehydes showing that the modelling of formaldehyde and acetaldehyde is also acceptable. These figures present also our prediction for propanaldehyde and acroleïne, which are in agreement with the limit of detection of 100 ppm given by Biet et al. [8].

It is worth noting that the decrease in equivalence ratio does not change markedly the formation of carbon monoxide and aldehydes. That is well explained by Biet et al. [8] by defining an "effective equivalence ratio" based on the proportion of oxygen consumed in the flame and showing that it is always close to 1 when oxygen is in excess.

Figure 1: Modeling of a laminar premixed flame of propane at 1 atm for an equivalence ratio of 0.9. Symbols correspond to experiments [8] and lines to simulations. Symbols correspond to experiments [8] and lines to simulations.

Simulation of the formation of short-chain carboxylic acids

Figure 3 presents the simulated profiles of acids obtained under the same conditions as the flame of Biet et al. [8] using the mechanism which is described above. This figure shows that small amounts of acids are well produced in this flame, the major ones being formic and acetic acids. Amongst C 3 acids, the main one is propenic acid not propanic acid. That is directly related to the bond dissociation energy of C-CO in CH 2 =CH-CO (26.2 kcal/mol) and in CH3-CH2-CO (11.9 kcal/mol). The unsaturated oxygenated radical is less easily decomposed than the saturated one to give carbon monoxide (by a factor 6x10 -3 at 1400 K), its concentration is then larger, which favours its combination with OH radicals.

This figure also shows that the formation of acids in these lean flames does not change much when decreasing the equivalence ratio. That is in agreement with what was noticed above for the formation of aldehydes, but in disagreement with the experimental results of Zervas [7] showing increase of about a factor 2 of the formation of formic and acetic acids when varying the equivalence ratio from 1.17 to 0.77. Figure 4 displays a comparison between the computed proportions (the ratio between the mole fraction of each acid and the sum of their mole fraction) of acids and the experimental one measured by Zervas et al. [7] for an equivalence ratio of 0.9. In Zervas's work, organic acids were collected in deionised water and analysed by two methods: ionic chromatography/conductimetry detection for formic acid and gas chromatography/flame ionisation detection for other acids. No detail was given about calibration. This figure shows that, apart from the disagreement concerning the nature of the C 3 acid, the proportion between C 1 , C 2 and C 3 acid is rather well captured by the model. [7]) and simulated proportions of acids for an equivalence ratio of 0.9 at the maximum of the peak of formic acid.

Analysis of the pathways of formation of acids

Figure 5 presents the main pathways of formation of the four monocarboxylic acids studied. It can be seen that these acids are mainly derived from the aldehyde having the same structure.

• Formic acid is quasi-exclusively obtained from the addition of OH radicals to formaldehyde, followed by the elimination of a hydrogen atom.

C 2 H 5 COOH CH 2 CO+CH 3 C 2 H 5 CO+OH C 2 H 5 CHO+R C 2 H 5 COOH CH 2 CO+CH 3 C 2 H 3 CO+OH C 2 H 3 CHO+R C 2 H 3 COOH C 2 H 3 CO+OH C 2 H 3 CHO+R C 2 H 3 COOH (a) (b) (c) (d)
C 2 H 3 +O

Figure 5 Main pathways of formation of the four monocarboxylic acids studied under the conditions of figure 3a for a distance above the burner corresponding

to the maximum of the peak of formic acid (0.5 cm). The size of the arrows is proportional to the relative flow rates.

Conclusion

A new model for the formation of monocarbocylic acids from C 1 to C 3 has been proposed and tested to reproduce the formation of these compounds in laminar premixed flames of propane. This model has allowed us to correctly reproduce the proportions between C 1 , C 2 and C 3 acids experimentally measured [7], even if the simulations predict the formation of propenic acid while propionic acid has been experimentally reported. Under flame conditions, these acids are mainly derived from the aldehyde having the same structure, by addition of OH radicals for formic acid and by combination of alcoxy and OH radicals for heavier acids. The predicted amounts of acids are up to hundred times lower than that of aldehydes, explaining why the formation of acid is usually not reported in flame experiments. If the emissions of acids from engines are really larger than that of aldehydes, as reported by Zervas et al. [4] at the exhaust of gasoline engines, low temperature reactions, involving peroxy radicals, should be of greater importance for the formation of acids than those proposed here.

Figure 2 :

 2 Figure 2: Modeling of a laminar premixed flame of propane at 1 atm for an equivalence ratio of 0.48.

Figure 3 :

 3 Figure 3: Modeling of the formation of acids in a laminarpremixed flame of propane at 1 atm for an equivalence ratio of (a) 0.9 and (b) 0.48.

Figure 4 :

 4 Figure 4: Comparison between experimental (Zervas[7]) and simulated proportions of acids for an equivalence ratio of 0.9 at the maximum of the peak of formic acid.

TABLE I : SELECTED REACTIONS OF FORMATION AND CONSUMPTION OF C 1 , C 2 AND C 3 ACIDS

 I

	The rate constants are given (k=A T n exp(-E a /RT)) in cc, mol, s, cal units.
	Reactions	A	n	E a	No
	reactions of formic acid
	reactions of HOCO
	CO+OH(+M)=HOCO(+M)	1.20E+07	1.83	-236.0	(1)
	LOW /7.20E+25 -3.85 1550. /
	TROE /0.6 10. 100000./
	HOCO(+M)=H+CO2(+M)	1.74E+12	0.307	32930.0	(2)
	LOW/2.29E+26 -3.02 35070.0/
	HOCO+O2=HO2+CO2	1.26E+12	0.0	0.0	(3)
	CH3CO+OH=CH3+HOCO	3.00E+13	0.0	0.0
	reactions of HCOO
	HCOO+M=H+CO2+M	8.70E+15	0.0	14400.0	(4)
	HCOO+O2=CO2+HO2	1.00E+11	0.0	0.0	(5)
	reactions of HCOOH
	HCOOH+M=CO+H2O+M	2.10E+14	0.0	40400.0	(6)
	HCOOH+M=CO2+H2+M	1.50E+16	0.0	57000.0	(7)
	HCOOH+OH=HOCO+H2O	1.00E+11	0.0	0.0	(8)
	HCOOH+OH=HCOO+H2O	1.00E+11	0.0	0.0	(9)
	HCOOH+HCOO=HOCO+HCOOH	1.00E+11	0.0	0.0
	reactions of HOCH2O
	HCHO+OH=HOCH2O	3.40E+06	1.18	-400.0	(10)
	HOCH2O=HCOOH+H	1.00E+14	0.0	14900.0	(11)
	HOCH2O+O2=HO2+HCOOH	2.10E+10	0.0	0.0	(12)
	reactions of acetic acid
	reactions of CH3CO2H
	CH3CO+OH=CH3CO2H	1.00E+14	0.0	0.0	(13)
	CH3CO2H=CH4+CO2	7.08E+13	0.0	74600.0	(14)
	CH3CO2H=CH2CO+H2O	4.47E+14	0.0	79800.0	(15)
	CH3CO2H+OH=CH3CO2+H2O	2.40E+11	0.0	-400.0	(16)
	reactions of CH3CO2
	CH3CO2+M=CH3+CO2+M	8.70E+15	0.0	14400.0	(17)
	reactions of propanoic acid
	reactions of C2H5CO2H
	C2H5CO+OH=C2H5CO2H	1.00E+14	0.0	0.0	(18)
	C2H5CO2H=C2H6+CO2	7.08E+13	0.0	74600.0	(19)
	C2H5CO2H+OH=C2H5CO2+H2O	2.40E+11	0.0	-400.0	(20)
	reactions of C2H5CO2H
	C2H5CO2+M=C2H5+CO2+M	8.70E+15	0.0	14400.0	(21)

reactions of propenic acid

	Reactions C2H3CO2H
	CH2CHCO+OH=C2H3CO2H	1.00E+14	0.0	0.0	(22)
	C2H3CO2H=C2H4+CO2	7.08E+13	0.0	74600.0	(23)
	C2H3CO2H+OH=C2H3CO2+H2O	2.40E+11	0.0	-400.0	(24)
	reactions of C2H5CO2
	C2H3CO2+M=C2H3+CO2+M	8.70E+15	0.0	14400.0	(25)


H A Gueniche

P A Glaude

R Fournet

F Battin-Leclerc

Formation of aromatics in rich methane flames doped by unsaturated compounds

In order to better understand the importance of the different channels leading to the first aromatic ring, we have investigated, the structure of a laminar rich premixed methane flame doped with several unsaturated hydrocarbons: allene and propyne, as they are precursors of propargyl radicals, which are well known as having an important role in forming benzene, 1,3-butadiene, to put in evidence a possible production of benzene due to reactions of C 4 compounds, and, finally, cyclopentene, which is a source of cyclopentadienyl methylene radicals which are supposed to easily isomerizes to give benzene. A ratio additive / CH 4 of 16 % and an equivalence ratio of 1.79 have been used. These flames have been stabilized on a burner at a pressure of 6.7 kPa using argon as dilutant. A new mechanism for the oxidation of allene, propyne, 1,3-butadiene and cyclopentene has been proposed including the formation and decomposition of benzene and toluene. The main reaction pathways of formation of aromatics have been derived from flow rate analyses and have been compared for the three types of additives.

Introduction

While the formation of PAHs and soot represents an important area of interest for kineticists for two decades, questions still remain even concerning the formation and the oxidation of the first aromatic compounds. In previous studies, the formation of benzene is mostly related to the reactions of C 2 (acetylene), C 3 or C 4 unsaturated species [1][2][3][4][5]. Nevertheless, some papers suggest a link between C 6 and C 5 cyclic species [6,7]. In a recent paper [8], we have investigated the reactions of allene and propyne, as they are precursors of propargyl radicals, which have an important role in forming benzene. In a second part [9], we have analyzed the reaction of 1,3-butadiene in a methane flame and putted in evidence an important production of benzene due to reactions of C 4 compounds under these particular conditions. To finish this work, we have studied the reactions of cyclopentene, which is a source of C 5 radicals [10]. The purpose of the present paper is to compare the results obtained in these three studies for the formation of benzene and toluene and their ways of formation. It is worth noting that the use of methane as the background and, consequently, of a flame rich in methyl radicals favors reactions which can be less important in other combustion systems.

Experimental procedure and main results

The experiments were performed using an apparatus developed in our laboratory to study temperature and stable species profiles in a laminar premixed flat flame at low pressure [8]. This horizontal burner was housed in a water-cooled vacuum chamber evacuated by two primary pumps and maintained at 6.7 kPa by a regulation valve. This chamber was equipped of four quartz windows for an optical access, a microprobe for samples taking and a thermocouple for temperature measurements. The burner could be vertically translated, while the housing and its equipments were kept fixed. Gas flow rates were regulated by RDM 280 Alphagaz and Bronkhorst (El-Flow) mass flow regulators. The C 3 and C 4 reactants and methane were supplied by Alphagaz -L'Air Liquide. Oxygen and argon were supplied by Messer. Liquid cyclopentene (provided by Fluka) flow rate was controlled by using a liquid mass flow controller, mixed to the carrier gas and then evaporated by passing through a single pass heat exchanger, the temperature of which was set above the boiling point of the mixture [10]. Temperature profiles were obtained using a PtRh (6%)-PtRh (30%) type B thermocouple (diameter 100 μm) coated with an inert layer to prevent catalytic effects. Radiative heat losses were corrected using the electric compensation method. The sampling probe was in silica with a hole of about 50 μm diameter. For temperature measurements in the flames perturbed by the probe, the distance between the junction of the thermocouple and the end of the probe was taken to about 100 μm. In the studied flames, the temperature ranged from 600 K close to the burner up to 2150 K. Gas samples were collected in a Pyrex loop and directly obtained by connecting through a heated line the quartz probe to a volume, which was previously evacuated. The pressure drop between the flame and the inlet of the probe ensured reactions to be frozen. (FID). Heavier hydrocarbons from C 3 to C 7 were analysed on a Haysep packed column by FID and nitrogen as gas carrier gas. The identification of these compounds was performed using GC/MS and by comparison of retention times when injecting the product alone in gas phase. Water and small oxygenated compounds, such as acetone, acetaldehyde and formaldehyde, were detected by GC-MS but not quantitatively analysed. Due to problems of stability, a slightly higher dilution (55.6% argon instead of 42.9%) has been used in the flame of cyclopentene compared to the 3 other flames. In the pure methane flame and in all the doped ones, quantified products included carbon monoxide and dioxide, hydrogen, ethane, ethylene, acetylene, propyne (p-C 3 H 4 ), allene (a-C 3 H 4 ), propene (C 3 H 6 ) and propane (C 3 H 8 ). The presence of each of the four additives strongly promotes the formation of acetylene and unsaturated C 3 species. Compared to a methane flame of same equivalence ratio, the maximum of acetylene mole fraction is almost multiplied by a factor 1.6 with the addition of allene, 2 with that of propyne and 1,3-butadiene and 2.5 with that of cyclopentene. Several C 3+ products, which cannot be detected in the pure methane flame, have also been analysed:

• in the case of C 3 additives, butadienes ( • in the case of cyclopentene, butadienes, vinylacetylene, diacetylene, cyclopentadiene (cC 5 H 6 ), 1,3-pentadiene, benzene and toluene [10].

Description of the detailed kinetic model

The mechanism that was proposed to model the oxidation of allene, propyne, 1-3-butadiene and cyclopentene includes an up dated version of the mechanism that was built to model the oxidation of C 3 -C 4 unsaturated hydrocarbons [8,9,11,12], our previous mechanisms of the oxidation of benzene [13] and toluene [14] and a new mechanism for the oxidation of cyclopentene [10]. Thermochemical data were estimated using the software THERGAS developed in our laboratory [15], which is based on the additivity methods proposed by Benson [START_REF] Benson | Thermochemical kinetics[END_REF].

Reaction base for the oxidation of C3-C4 unsaturated hydrocarbons [8,9] This C 3 -C 4 reaction base, which was described in details in previous papers [8,9], was built from a review of the recent literature and is an extension of our previous C 0 -C 2 reaction base [START_REF] Barbé | [END_REF] (6 isomers), as well as some reactions for linear and branched C 5 compounds and the formation of benzene. In this reactions base, pressure-dependent rate constants follow the formalism proposed by Troe [18] and efficiency coefficients have been included.

Mechanisms for the oxidation of benzene and toluene

Our mechanism for the oxidation of benzene contains 135 reactions and includes the reactions of benzene and of cyclohexadienyl, phenyl, phenylperoxy, phenoxy, hydroxyphenoxy, cyclopentadienyl, cyclopentadienoxy and hydroxycyclopentadienyl free radicals, as well as the reactions of ortho-benzoquinone, phenol, cyclopentadiene, cyclopentadienone and vinylketene, which are the primary products yielded [13]. The mechanism for the oxidation of toluene contains 193 reactions and includes the reactions of toluene and of benzyl, tolyl, peroxybenzyl (methylphenyl), alcoxybenzyl and cresoxy free radicals, as well as the reactions of benzaldehyde, benzyl hydroperoxyde, cresol, benzylalcohol, ethylbenzene, styrene and bibenzyl [14].

New mechanism proposed for the oxidation of cyclopentene [10] We have considered the unimolecular reactions of cyclopentene, the additions of H-atoms and OH radicals to the double bonds and the H-abstractions by oxygen molecules and small radicals. Unimolecular reactions include dehydrogenation to give cyclopentadiene, decompositions by breaking of a C-H bond and isomerization to give 1,2-pentadiene. The reactions of cyclopentenyl radicals involved isomerizations, decompositions by breaking of a C-C bond to form linear C 5 radicals including two double bonds or a triple bond, the formation of cyclopentadiene by breaking of a C-H bond or by oxidation with oxygen molecules and terminations steps. Termination steps were written only for the resonance stabilized cyclopentenyl radicals: disproprtionnations with H-atoms and OH radicals gave cyclopentadiene, combinations with HO 2 radicals led to ethylene and CH 2 CHCO and OH radicals, and combinations with CH 3 radicals formed methylcyclopentene. The decomposition by breaking of a C-H bond of cyclopentyl radicals led to the formation of 1-penten-5-yl radicals. The isomerizations (for the radical stabilized isomer) and the decompositions by breaking of a C-C bond of the linear C 5 radicals were also written, while those by breaking of a C-H bond were not considered. The reactions of cyclopentadiene were part of the mechanism for the oxidation of benzene, but reactions for the consumption of methylcyclopentene and methylcyclopentadiene, obtained by recombination of cyclopentadienyl and methyl radicals had to be added. [8,9,10] In order to investigate the relative importance of the different channels, the formation of aromatic compounds was considered through the C 3 , the C 4 and the C 5 pathways:

Ways of formation of aromatic compounds

• For the C 3 pathway, we have used a value of 1.10 12 cm 3 .mol -1 s -1 for the recombination of two propargyl radicals to give phenyl radicals and H-atoms, which is in good agreement with what has been recently proposed by Miller et al. [19] and Rasmussen et al. [20]. We have removed from our previous mechanism the addition of propargyl radicals to allene leading to benzene and H-atoms and the recombination between allene and propargyl radicals to produce phenyl radicals and two H-atoms, which were not considered by Rasmussen et al. [20] and which induced an overprediction of benzene in the case of the flame doped with allene. [7], we have considered the isomerization between both radicals deriving from methylcyclopentadiene (cyclopentadienylmethylene and methylcyclo pentadienyl), and the formation of cyclohexadienyl radicals from cyclopentadienyl methylene radicals. We have not considered the formation of cyclohexadienyl radicals from the resonance stabilized methyl cyclopentadienyl radicals, as proposed by Marinov et al. [4], but their recombination with H-atoms was also added. In order to reproduce the important formation of toluene experimentally observed in the flame doped with cyclopentene, we have considered the formation of benzyl radicals from the addition of acetylene to cyclopendadienyl radicals with a rate constant about 3 times higher than what is usually considered for such an addition [23]. While the decomposition of benzyl radicals to form acetylene and cyclopendadienyl radicals, which was considered in our mechanism for the oxidation of toluene, has been studied by several authors [24][25][26] and has been shown to occur through a several steps mechanism, the reverse addition has never been directly investigated.

Comparison of the formation of benzene and toluene in the four flames

All the simulations have been performed using PREMIX of CHEMKIN II [START_REF] Kee | Sandia Laboratories Report[END_REF] with estimated transport coefficients and the same kinetic mechanism. Comparisons between experimental results and simulations are displays for benzene in fig. 1 and for toluene in fig. 2. The experimental results show important changes in the formation of aromatic compounds depending on the additives. The flame showing the largest formation of benzene is that doped with cyclopentene. The maximum of the peak of benzene is three times smaller in the flame doped with 1,3-butadiene, ten times in the flame doped by allene and fifteen times in that doped by propyne. The flame doped with 1,3-butadiene exhibits the lowest production of toluene. The maximum of the peak of toluene is two times higher in the flame doped with C 3 compounds and almost hundred times larger in that doped with cyclopentene. The production of aromatic compounds occur the closest to the burner in the flames doped by C 3 compounds and the furthest in the flame seeded by cyclopentene. Simulations reproduce correctly the formation of benzene and toluene except in the case of the flame doped with cyclopentene for which the production of toluene is undersestimated by a factor 3.

Discussion

Figure 3 presents a flow rate analysis for the production and consumption of aromatic compounds for the flames doped by allene (a similar picture is obtained for propyne), A particular interest of the flames doped by 1,3-butadiene and cyclopentene is that the production of benzene is mainly due to other reactions than the C 3 pathway as it is usually the case in the flames of the literature [20]. Differences are also encountered for the ways of formation of toluene:

• in the allene flame, toluene is mainly produced from the recombination of methyl and phenyl radicals, • in the 1,3-butadiene and cyclopentene flames, the most important way to give toluene is the addition of resonance stabilized cyclopentadienyl radicals to acetylene. In the C 3 flames, benzene and toluene are primary products deriving directly from propargyl and phenyl radicals. That explains why their formation occurs early in the flame. In these flames, the production of benzene is relatively weak because the self recombination of propargyl radicals, at the low pressure studied here, leads mainly to phenyl radicals, which react rapidly with oxygen molecules. It is worth noting that our simulation using a value of the rate constant for the self-combination of propargyl radicals close to that now admitted in the literature leads to a good agreement for the formation of benzene. The rate constant of the recombination of methyl and phenyl radicals, which is not well known [14] is a sensitive parameters to predict the formation of toluene. Many similarities exist between allene and propyne flames in both reactivity and products formation. Nevertheless, the pool of small radicals is slightly larger in the propyne flame, which leads to a faster consumption of propargyl radicals and a lower formation of benzene than in the flame seeded by allene [8].

• + H•, + OH• + CH 3 + O 2 /-• O• • + H• + H•, + OH • • -H +• O•/-H• + O 2 + H• + CO HC CH + • CH=CH 2 + CO + H• 2 (HC C-CH 2 • • HC= C=CH 2 ) 2 (HC C-CH 2 • • HC= C=CH 2 ) • + H•/ -CH 3 • + H•, + OH • + H• + HC CH -H H• + +• O• + H•, + OH • /-CO C H 3 CH 2 • + H•, + OH • +• O• /-HCO • CH3 • + H•, + OH • + H•/ -C 2 H 5 • + CH 3 -CH 3 H 2 C=CH -CH=CH 2 + H 2 C=CH • + H• -H 2 OH O O O O CH O
Figure 3: Flow rate analysis for the formation and consumption of benzene and toluene for a position in the flame corresponding to the peak of benzene profile. The size of the arrows is proportional to the relative flow rates. Red arrows are related to the flame doped with allene (T= 1236 K) , green arrows to that doped with 1,3-butadiene (T= 1483 K) and black arrows to that seeded with cyclopentene (T= 1354 K, the lower temperature compared to the case of 1,3-butadiene is due to a higher dilution).

Cyclopendadienyl radicals are rapidly obtained from the decomposition of phenoxy radicals, which are produced by the reaction of phenyl radicals with oxygen molecules. Due to their resonance stabilization, they are present with an important concentration in every system containing phenyl radicals and benzene. The formation of toluene by addition of cyclopentadienyl radicals to acetylene could then be of importance in many combustion systems rich in acetylene.

When the concentration of toluene is high enough, a non negligible formation of benzene occurs also through the ipso-addition of H-atoms with elimination of methyl radicals. The concentrations of benzene and toluene are thus closely linked. Figure 3 shows that the addition of allene, 1,3-butadiene and cyclopentene leads also to the formation of benzoquinone, phenol, cyclopentadienone and benzaldehyde, which have not been analysed experimentally here.

Conclusion

This paper compares the formation of benzene and toluene in a rich ( =1.8) methane flame seeded with allene, propyne, 1,3-butadiene and cyclopentene, respectively, and shows that the amount of aromatic compounds formed are very different depending on the additive. This effect is due to differences in the pathways of formation of these aromatic species depending on the dopant. For the flames doped with C 4 and C 5 compounds, the self-combination of propargyl is not the preponderant channel of formation of benzene.

Figure 1 :

 1 Figure 1: Experimental and simulated profiles of benzene in a methane flame doped with (a) allene and propyne, (b) 1,3-butadiene and (c) cyclopentene. Symbols correspond to experiments, lines to simulations.

Figure 2 :

 2 Figure 2: Experimental and simulated profiles of toluene in a methane flame doped with (a) allene and propyne, (b) 1,3-butadiene and (c) cyclopentene. Symbols correspond to experiments, lines to simulations.

  . The C 3 -C 4 reaction base includes reactions involving C 3 H 2 , C 3 H 3 , C 3 H 4 (allene and propyne), C 3 H 5 , C 3 H 6 , C 4 H 2 , C 4 H 3 , C 4 H 4 , C 4 H 5 , C 4 H 6 (1,3-butadiene, 1,2-butadiene, methyl-cyclopropene, 1-butyne and 2-butyne), C 4 H 7

  1,3-butadiene and cyclopentene. This figure shows well that the ways of formation of benzene are very different depending on the additive:

	• in the allene flame, benzene is produced by
	combination of H-atoms with phenyl radicals, which
	are obtained by self-combination of propargyl
	radicals,
	• in the 1,3-butadiene flame, benzene is rapidly
	formed from the addition/cyclization of vinyl radicals
	to produce cyclohexadiene, which reacts either by
	dehydrogenation or by methatheses with H-atoms
	and OH radicals, followed by the decomposition of
	the obtained cyclic C 6 H 7 radicals,
	• in the cyclopentene flame, the major source of
	benzene is the isomerization of cyclopentadienyl
	methylene radicals, which are obtained either directly
	by H-abstractions by H-atoms or OH radicals from
	methylcyclopentadiene or by isomerisation from the
	resonance stabilized methyl cyclopentadienyl
	radicals, which are also obtained by H-abstractions
	by	H-atoms	or	OH	radicals	from
	methylcyclopentadiene.