This paper presents a new navigation method for mobile robots, based on direct kinematics model and predictive control approach. It is adaptable to all types of robots taking into account their specific constraints. The research of the optimal trajectory is shifted in the continuous parameters space, which enables the exploitation of all of the robot's capabilities. The use of a stochastic algorithm enables the determination of obstacle bypass trajectories, and simulation results show that the navigation in cluttered environment is improved.

I. INTRODUCTION

HIS paper addresses the problem of mobile robots navigation. Indeed, the navigator is key to an autonomous mobile robot since it acts as the link between the robot's motion abilities and its environment. Our contribution is to consider navigation methods based on robot direct kinematics model with a new control approach. These navigation methods are independent of the robot's kinematics constraints; the improvement consists in developing a predictive control to continuously determine an optimal trajectory among a considered class of trajectories.

More generally, research works pertaining to navigation have established three main approaches. A first part of these works does not really make the distinction between the path, the trajectory and the pilot features. This is the case when using neural networks [START_REF] Er | Control of a mobile robot using generalized dynamic fuzzy neural networks[END_REF] [START_REF] Wang | A behavior controller based on spiking neural networks for mobile robots[END_REF] or fuzzy logic [START_REF] Chatterjee | Use of single side reflex for autonomous navigation of mobile robots in unknown environments[END_REF] [START_REF] Xu | A virtual target approach for resolving the limit cycle problem in navigation of a fuzzy behavior-based mobile robot[END_REF], which aim to control the robot's overall behavior in a given environment situation such as the one described in their learning algorithms. These approaches are simple to implement and generate results only in well-defined environments. However, they do not provide long term planning to ensure the convergence toward the final goal, and these methods are subjected to stability issues [13].

The second part of navigation researches treats the issue of following the reference trajectory or the reference path provided by the planning module. Since the majority of robots are non-holonomic, an inverse model does not exist. As a consequence, it is possible that the reference trajectory cannot be systematically followed; some approaches resolve this problem by using transverse functions [START_REF] Fruchard | Méthodologies pour la commande de manipulateurs mobiles non-holonomes[END_REF] [START_REF] Morin | Trajectory tracking for non-holonomic vehicles : overview and case study[END_REF] or flat outputs [START_REF] Fraisse | Stratégie de commande décentralisée d'une flottille de robots mobiles terrestres téléopérés[END_REF]. However, they require the determination of a specific model of the robot, which is non-trivial and nonsystematic. Therefore, they do not allow the development of a generic method that works regardless of the considered robot.

Contact: cyril.novales@bourges.univ-orleans.fr (+33 248 23 84 70) PRISME 63, av. de Lattre de Tassigny F-18020 Bourges cedex, France

The last type of approaches uses the knowledge of the robot direct kinematics, dynamic or geometric model. Among the robot's motion abilities, one can choose the trajectory that will results in the expected behavior [START_REF] Belker | Local Action Planning for Mobile Robot Collision Avoidance[END_REF][12] [START_REF] Morette | Inverse versus Direct Kinematics Model based on Flatness and Escape Lanes to control CyCab Mobile Robot[END_REF]. The advantage of these methods is their adaptability to any kind of robots knowing their direct model; the disadvantage is that they are discrete by nature.

The work, presented here, is directed toward the last type of approach, and concerns the development of a navigator based on the robot's direct kinematics model. Our main contribution is to discard the discrete formalism and to propose a continuous one, which better exploit the kinematic potential of the robot by using a well-tested method of control within regulation processes: the model based control [START_REF] Morette | Contribution à la navigation de robots mobiles : approche par modèle direct et commande prédictive[END_REF] [START_REF] Richalet | Model Predictive Heuristic Control : Applications to Industrial processes[END_REF]. Indeed, the notion of trajectory prediction on a "temporal horizon" in robotics is comparable to the notion of predictive control on a "prediction horizon" when using this control theory [START_REF] Alamir | Stabilization of Nonlinear Systems Using Receding-Horizon Control Schemes : A Parametrized Approach for Fast Systems[END_REF]. Moreover the research of an optimal control system on this horizon is continuous.

In section II, we define our navigator using direct kinematics model (DKM) to generate the robot's trajectories. In section III, we define the cost function used for the proposed model-based navigator, and discuss the optimization tools used to solve the optimization under constraints problem. In section IV, we show some simulations results of our method applied to different mobile robots.

II. FORMULATION OF THE NAVIGATOR USING THE MODEL BASED CONTROL

There are two types of entries provided to the navigator. The first one is a path computed by a path planning module, in the form of a continuous path or a list of waypoints. In this paper, we have considered a path planning module providing successive waypoints. The second entry is a local map of the environment provided by a real time mapping module. We assume that the robots are programmed to map out their local environment.

The navigator has to determine the admissible trajectories for the robot to move safely in a potentially clustered area. It is therefore a trajectory generating module, not a trajectory following controller.

In this first section, we present the generation of trajectories using the direct kinematics model principle.

Direct Model Navigation issue shifted in the continuous domain by a

predictive control approach for mobile robots is generated (Fig. 1).

Fig. 1 : the trajectory generation using DKM

2) Navigation using the trajectory projection principle

The robot is considered to be equipped with exteroceptive sensors and is able to draw a local obstacle map. By projecting the previous computed trajectory on the local obstacle map, the robot is able to determine if the trajectory is safe or not (taking into account the errors on the obstacle position and the slipping of the robot on ] , [ 0 0 p T t t +

).

These trajectories must follow a desired path generated by a path planner: classically a reference path or a set of waypoints. DKM methods must thus follow 3 steps (Fig. 2): -to generate a finite number of trajectories, -to project them in a local map and eliminate the ones colliding with obstacles, -to select the trajectory the nearest to the desired path.

Fig. 2 : the DKM navigation principle

The control function associated to the selected trajectory is sent as an input to the actuators, and applied on a sampling time inferior to the prediction time. The whole process is then repeated periodically with the new updates on the obstacle and robot position, and on the reference path.

All DKM navigation developments are based on this method considering:

-some focus on a specific control function and associated trajectory [START_REF] Bonnafous | Motion generation for a rover on rough terrains[END_REF],

-some focus on the selection criteria [START_REF] Morette | Inverse versus Direct Kinematics Model based on Flatness and Escape Lanes to control CyCab Mobile Robot[END_REF], -some focus on the projection in a neural network map [START_REF] Belker | Local Action Planning for Mobile Robot Collision Avoidance[END_REF].

Their main advantage is the easy adaptation to any mobile robot whose the DKM is known. However, their application is limited to a finite number of trajectories due to the computation time limits for on-line constraints. As a consequence, the robot motion abilities are limited and so is the accuracy with respect to the reference path. That is the reason why we propose a new control approach associated with it.

B. The proposed method 1) DKM navigation in a continuous control functions space

The proposed navigation method is based on the same trajectory projection principle, but extends this principle to a continuous control function space. We propose to use parameterized control function, such as linear functions with a slope p 0 , or parabolic functions defined by two parameters p 1 and p 2 . By making a continuous variation of these parameters, and injecting the corresponding control functions in the robot DKM, it leads to the generation of an infinite number of trajectories. As a consequence, we do not work on a discrete control space and we exploit more thoroughly the robot motion abilities.

Then, we have to determine among this continuous space of trajectories, the one that best fits the navigation problem on ] , [ 0 0 p T t t +

. In order to compare the trajectories, a cost function Z is determined. Finding the set of parameters that minimizes the cost function corresponds to an optimization problem.

2) Cost function and optimal trajectory

The navigation problem can be translated into an optimization problem, whose cost function Z is structured with 3 parts (eq. ( 1)), Fig. 3:

env robot planif Z Z Z Z + + = (1)
With: -Z planif quantifies the gap between the reference trajectory and the evaluated trajectory of the robot, -Z robot is a penalty considering the constraints inherent to the robot (actuators saturations dynamic constraints...), -Z env is a penalty considering the constraints inherent to the environment (fixed or mobile obstacles).

A set of parameters p i corresponds to a control function on . The set of parameters p i minimizing Z corresponds to the trajectory which is the nearest to the reference trajectory, including all the constraints on the robot and on the environment. The navigation problem at t 0 and on the prediction horizon T p becomes an optimization one under constraints.

Fig. 3 : the cost function Z = Z planif + Z robot + Z env

This problem has to be solved on-line by an optimization algorithm, which can be deterministic (convex problems) or stochastic (non convex problems) as we will see in section III.E.

The trajectory selected by the optimization algorithm is defined on the ] , [ 0

0 p T t t + interval. The control function ] , [ 0 0 p T t t u +
corresponding to the optimal parameters p i is applied during a sampling time T e . The problem is updated every T e , taking into account the changes on the obstacles position, on the planned path and the drift on the robot position. The control loop of this system is inherent to this updating process at the period T e .

III. THE NAVIGATION PROBLEM

A. Class of robot considered

We consider a car-like vehicle whose DKM is classically given by (eq. ( 2), Fig. 4): x and y are the abscissa and ordinate of the robot's control point, θ is its orientation in the basis ) , , 0 ( y x , v its velocity, ξ its steering angle and L its wheelbase.

       = = = L v v y v x ) tan( . ) sin( . ) cos( . ξ θ θ θ & & & (2)
We suppose that the robot circulates on a flat surface, so its movements are confined to a plan parallel to the ground.

We define the robot's state by the vector X:

] , [ 0 0 0 0 ) ( ] , [ p T t t T p s y x T t t X + = + & θ (3)
with T p is the prediction horizon, and s & its curvilinear velocity along the curve. Then, we define a control u vector with m lines containing the articular inputs, which are then applied to the robot:

] , [ 2 1 0 0 0 0 ) ... ( ] , [ p T t t T m p q q q T t t u + = + & & & (4)

B. Z planif : trajectory tracking criteria 1) The reference curve

We assume that the path provided to the robot by the path planner is given in the form of a series of successive waypoints including the speeds and orientations at each point. Since the robot drifts from the planned path, a reference curve has to be computed in order to link the current state of the robot X 0 and the desired state X d corresponding to the next waypoint to be reached. This reference curve has to be defined based on these points' velocities and orientations. Hence, a Bezier curve is used in order to keep the continuity on the robot's positions and velocities, and is defined by four controls parameters, R 1 to R 4 . It passes through the points R1(x1, y1) and R4(x4, y4), and the vectors This Bezier curve is geometric and contains no information concerning the vehicle's kinematics. In order to obtain a reference trajectory, we conduct a parameterization depending on the times shown on this curve (Fig. 5) and developed in 2). that the robot is likely to travel during the prediction horizon T p , the equation of the reference trajectory is given by:

   + - + - + - = + - + - + - = 4 3 3 2 2 2 1 3 4 3 3 2 2 2 1 3 ' ) ' 1 ( ' 3 ) ' 1 ( ' 3 ) ' 1 ( ) ' ( ' ) ' 1 ( ' 3 ) ' 1 ( ' 3 ) ' 1
                =           = ) , (

3) The robot's admissible trajectories

There is an infinite number of control functions u defined on the prediction horizon [t 0 , t 0 +T p ] that fulfills the robot's kinematic constraints. Among these functions, we consider a class of control families, which are parameterized by a finite number of parameters n p . Therefore, each control function will be entirely defined by the set of parameters 1 p to p n p .

To be applied to a car-type mobile robot, the control functions are then defined by two parameters p v1 and p v2 for the velocity control and two parameters p ξ1 and p ξ2 for the steering radius (eq. ( 8)(9), Fig. 6).

] 2 / , [ , ) .( ) ( ) ( ) .( ) ( ) ( 0 0 0 1 0 0 1 0 p v T t t t t t p t t t t p t v t v + ∈    - + = - + = ξ ξ ξ (8) ] , 2 / [ , ) 2 / .( ) 2 / .( ) ( ) ( ) 2 / .( ) 2 / .( ) ( ) ( 0 0 0 2 0 1 0 0 2 0 1 0 p p p p p v p v T t T t t t T t p t T p t t t T t p t T p t v t v + + ∈    - - + - + = - - + - + = ξ ξ ξ ξ (9)

Fig. 6 : The u parameterized control family

The use of this control family into the robot's kinematic model enables the generation of a trajectories family; we then obtain an infinite number of admissible trajectories defined by the set of parameters. A few of these trajectories among this infinite number are represented in Fig. 7. These trajectories show that 2 parameters on the velocity control and 2 parameters on the steering control are sufficient to generate bypass trajectories.

Fig. 7 : wheel prints of a sample of admissible trajectories with (0,0) initial position and a zero initial velocity

Among this infinite number of trajectories, we need to determine the one, which will be the closest to the reference trajectory previously determined with respect to a criterion described in the following section.

4) The cost function

The difference between the planned trajectory of the robot according to the control applied and the references curve is quantified by a cost function, Z planif . It assigns a Z planif (X 0 , t 0 , T p , u) value to each control function u over [t 0 ,t 0 +T p ] and is written in the following general form:

∫ + + + = p T t t p p planif d u X l T t x u T t X Z 0 0 ) ), ( ), ( ( )) ( ( ) , , , ( 0 0 0 τ τ τ τ ψ (10)
The cost function is composed of a function quantifying the stage cost l and a function quantifying the terminal cost ψ, relying on the quadratic distances between the planned trajectory X(t) of the robot and the reference trajectory X ref (t) :

2 0 0 2 0 0 0 )) ( ) ( ( * ) ), ( ), ( (
)) ( ) ( ( * )) ( ( t t X t t X k t t u t X l T t X T t X k T t x ref stage p ref p final p + - + = + - + = + ψ (11)
with k final and k stage of the decoupled weighting matrix.

C. Z robot : Constraints on the robot

Z robot is defined as the penalty function considering the robot's constraints. These constraints are noted as:

{ } r i n i u t t X C ,..., 1 , 0 ) , , , ( 0 0 ∈ ≤ , ( 12
)
where n r is the number of constraints. The constraints are related to kinematic constraints and actuator saturations (the wheels maximum rotation velocity, maximum acceleration and deceleration). The saturations on the set of parameters are given by:

v p v v T T t p T T t C C T p T C C T accel T t v p T decel T t v C C T accel v p T decel v C C p p C C v p p v C C ξ ξ ξ ξ ξ ξ ξ ξ ξ ξ ξ ξ & & & & + + ≤ ≤ - + + ≤ ≤ - + + ≤ ≤ - + + ≤ ≤ - ≤ ≤ ≤ ≤ (13)
These constraints are integrated into the cost function using an hyperbolic functions i B defined by : max

1 i i i C C B - - = (14)
Thus, the Z robot cost function associated with the robot's constraints is given by:

∑ = r n i i robot C B Z ) ( ( 15
)

D. Z env : contraints on the environnent

The second type of constraints is related to the environment. We assume that a mapping of the robot local environment is known, e.g. an on-line refreshed occupancy grid. The idea is to assign a value of 1 or 0 to each square depending on whether or not it is occupied [START_REF] Sun | A traffic cellular automata model based on road network grids and its spatial and temporal resolution's influences on simulation Simulation Modelling Practice and Theory[END_REF]. In order to be able to assimilate the robot's trajectory to a single point trajectory, the obstacles' size is extended to a dimension corresponding to the robot's length.

The family of trajectories generated is projected into this grid. A penalty threshold Z threshold is added in case the robot's trajectories intersect any occupied squares.

   = else Z free if Z threshold env 0 (16)

E. Optimization

The whole navigation issue is now contained in the criterion Z (1), in the continuous parameters space. The optimization algorithm has to find all the parameters p v1 , p v2 , p ξ1 and p ξ2 minimizing this Z criterion.

) ( )) ( ( / / env robot planif p i p Z Z Z Min p u Z Min i i + + = (17)
The optimization algorithms under constraints are classified into two categories: the deterministic and the stochastic algorithms.

The deterministic algorithms generally present the best convergence properties and enable to obtain more precise and quicker solutions; however, they are very sensitive to local minima problems. Moreover, introducing discrete constraints, due to obstacles, has the effect of breaking the cost function convexity and introducing local minima.

Among deterministic algorithms, the widely used Levenberg-Marquardt algorithm was chosen; its convergence step is defined by:

i i i G I H 1 ) ( - + = ∆ λ (18)
with H the Hessien and G the gradient of the cost function for the considered parameters, and λ a setting parameter which increases when the cost function diverges.

The second algorithm category is stochastic algorithms, which are based on probabilistic approaches. They are less accurate and are slower to converge; however, they have the advantage of being less sensitive to local minima problems, which enables them to find obstacle bypass trajectories in cluttered surroundings. The stochastic algorithm considered is a simulated annealing [START_REF] Aarts | Statistical cooling: A general approach to combinatorial optimization problems[END_REF] whose transition rule probability is defined by:

k T Z e P ∆ - - = 1 (19)
With T k respecting the following cooling function:

min 0 max ). 1 ( T T k k T k + - = (20)
Fig. 8 illustrates a situation for which the robot encounters an U-trap shape obstacle, unplanned for by the path planner (Fig. 8 upper left and right figures). In this case, the local minima of the cost function Z(p i ) are generated in the parameters space representation planner (Fig. 8 lower left and right figures). The deterministic algorithm is trapped in this local minimum in the parameters space (Fig. 8 -top left and bottom left) and cannot find the p i parameters corresponding to the global minimum of the Z cost function. The stochastic algorithm manages to find the parameters regardless the initial settings (Fig. 8-top right and bottom right); this algorithm's drawback is that there is no convergence clue.

The convergence of the deterministic algorithm to find the global minimum highly depends on the parameters initialization and on local minima. The simulated annealing algorithm enables to escape from local minima without warranty to reach the global minimum within a finite time.

Fig. 8 : comparison between deterministic and stochastic algorithms in the presence of local minima

The complete bypass trajectory on several iterations of the navigator is shown in Fig. 9.

Therefore, choosing either a stochastic or deterministic algorithm depends on the type of terrain covered (open or cluttered), as well as on whether or not the path planner takes into account any potential obstacles. The simulated annealing stochastic algorithm [START_REF] Aarts | Statistical cooling: A general approach to combinatorial optimization problems[END_REF] was used to proof the robustness of the navigator when faced with an incomplete planning in cluttered surroundings.

A. Application: the CyCab mobile robot

The proposed predictive control navigator was applied to a CyCab vehicle (Fig. 10). The particularity of this vehicle is its double steering radius (front and rear axle) which improves its maneuverability in cluttered places, such as urban areas. 12, shows the case in which the path planner does not take into account any obstacles; this engenders reference trajectories colliding into them. This may occurs for example when dynamic obstacles are present in the environment. Despite this occurrence, the navigator is able to determine the obstacle bypass trajectories, enabling the robot to reach its various waypoints without causing a collision. Indeed, using a simulated annealing algorithm helps us to find solutions avoiding the local minima (induced by the breaking of the convexity of Z due to the presence of obstacles). Besides, using an adapted temporal horizon enables the generation of trajectories, which are long enough to bypass obstacles. We propose the following relationship:

       + = = = = = L k V L V V V y V x C C C C C C ) tan( ) tan( .
3 * ≈ o p ref D T v ( 22
)
where is D 0 the average length of the obstacles' diagonal, chosen in order to determine the appropriate horizon. Fig. 13 shows an even more constraining scenario (with several traps in U). We note that the robot's complete trajectory avoids obstacles and follows the interpolated reference path, validating the overall navigation method in cluttered surroundings.

Fig. 14 presents results on this thirty-second navigation scenario: the distance measures between the robot's trajectory and the nearest obstacle (red line), and the distance between the robot's trajectory and a reference path computed from the waypoints provided by the path planner (blue line). This comparison shows that the navigator presents enough autonomous properties to diverge from the reference path when needed (i.e. due to obstacles presence).

B. Application to a differential wheeled robot

The navigation method was also applied to a differential wheeled robot with the same two scenarii (section IV.A) in order to test the adaptability of the method to different types of kinematics. Fig. 15 and Fig. 16 show these simulation results. The robot moves safely among obstacles, using specific trajectories inherent to its movement abilities. We notice in Fig. 15 and Fig. 16 that the robot makes maneuvers by itself. It is due to the control family used that enables the reverse motions. This behavior can be controlled through the trajectory criteria Z planif . In this article, we have developed a new generation of mobile robot navigators thanks to the predictive control approach, which we have adapted to solve navigation issues. This method is based upon a direct kinematic model, which typically can be adapted to all types of robots taking into account their specific constraints. Furthermore, using the predictive control method, which shifts the optimal trajectory research in the continuous parameters space in lieu of the discrete approach, enables the exploitation of all the robot's kinematics capabilities. In addition, by integrating the parameterized functions we are able to master the robot's behavior throughout its motion. By choosing a stochastic algorithm to solve the optimization problem under constraints we are also able to determine any obstacle bypass trajectories as well as to remedy an inadequate path planning.

This navigator is a pivot between the reactive and deliberative parts of the robot control architecture. From a deliberative point of view, the simulations showed that the robot is capable of anticipating obstacles bypass trajectories on its predictive horizon T p . From a reactive point of view, it takes into account unplanned obstacles during its sampling period near T e . Therefore, these simulations show that the proposed navigator is capable of circulating correctly in cluttered surroundings by avoiding obstacles not accounted for by the path planner. These capabilities facilitate the link between the deliberative part (path planning) and the reactive part of the control architecture. The next phase of this work involves its application to different robots, which will enable us to test proof the compatibility of this method with respect to computing time as well as the perception and environment's model.

Fig. 4 :

 4 Fig. 4 : a considered class of robot

Fig. 5 :

 5 Fig. 5 : the reference curve and reference trajectory

&

  This reference trajectory does not take into account the local environmental constraints and those related to the robot's movements.

Fig. 9 :

 9 Fig. 9 : bypass trajectory performed through simulated annealing algorithm

Fig. 10 :

 10 Fig. 10 : the CyCab robot Fig. 11 shows the scheme of the CyCab robot. In [16], we have developed the CyCab kinematic model:

  the control point of the vehicle, ρ the steering radius and L the wheelbase. When the steering angle on the front axle equals ξ, that of the rear axle equals kξ.

Fig. 11 :

 11 Fig. 11 : the CyCab model

Fig. 12 -

 12 Fig. 12 -scenario 1: navigation of the CyCab robot in a cluttered environment Fig.12, shows the case in which the path planner does not take into account any obstacles; this engenders reference trajectories colliding into them. This may occurs for example when dynamic obstacles are present in the environment. Despite this occurrence, the navigator is able to determine the obstacle bypass trajectories, enabling the robot to reach its various waypoints without causing a collision. Indeed, using a simulated annealing algorithm helps us to find solutions avoiding the local minima (induced by the breaking of the convexity of Z due to the presence of obstacles). Besides, using an adapted temporal horizon enables the generation of trajectories, which are long enough to bypass obstacles. We propose the following relationship:

Fig. 13 -

 13 Fig. 13 -scenario 2: navigation of the CyCab robot in a cluttered environment with U traps

Fig. 14 :

 14 Fig. 14: comparison between the robot's distance from the initial reference path and from the nearest obstacles in scenario 2

Fig. 15 -

 15 Fig. 15 -scenario 1: navigation of a differential wheeled robot in the same environment

Fig. 16 -

 16 Fig. 16 -scenario 2: navigation of a differential wheeled robot in a cluttered environment with U traps V. CONCLUSION

  Morette N., Novales C., Josserand L., and Vieyres P.

	A. Classical DKM Navigation
		1) Trajectory generation using direct kinematics model
		We consider a prediction horizon T p , and a control
	function u defined on this	, [ 0 0 t t	+	T	p	]	horizon. In order to be
	admissible, this control function has to fulfill the robot
	actuators constraints. By injecting this control function in the
	robot DKM, the corresponding evolutions of the robot in the
	cartesian space	X &			=	(	x	,	y	,	θ	)	T	are determined.
		By integration of these evolutions on T p , the robot's
	motions					relatively				to	its	initial	position
	X	(	t	0	)	=	(	x	(	t	0	),	y	(	t	0	),	θ	(	t	0	))	T	are computed. The whole
	trajectory			, [ 0 0 t t Γ		+	T	p	]	corresponding to the control
	function	u	, [ 0 0 t t	+	T	p	]
	T

& & & &

& & & &


Christine Schwake-Anduschus
email: christine.schwake-anduschus@mri.bund.de

Georg Langenkämper

Guenter Unbehend

Richard Diedrich

Erwin Märtlbauer

Klaus Münzing

R Dietrich

Occurrence of the Fusarium T-2-and HT-2-toxins in oats from cultivar studies in Germany and degradation of the toxins during grain cleaning treatment and food processing*

Keywords: cereal, oats, T-2-/HT-2-toxin, Fusarium, trichothecenes, porridge, bread

    Occurrence of the Fusarium T-2-and HT-2-toxins in oats from cultivar studies in Germany and degradation of the toxins during grain cleaning treatment and food processing

Depending on the Fusarium species, colonisation of the host plant is often accompanied by production of various mycotoxins, including trichothecenes, which are of concern with respect to food and feed safety [START_REF] Kimura | Molecular and genetic studies of fusarium trichothecene biosynthesis: pathways, genes, and evolution[END_REF]). According to their chemical structure, trichothecenes are categorised into four different types, where type A and B trichothecenes often occur in Fusarium infected cereals [START_REF] Foroud | Trichothecenes in cereal grains[END_REF]. The type B trichothecene deoxynivalenol (DON) is regarded the most frequently detected mycotoxin worldwide in cereals and cereal products. Depending on cereal species, production stage and intended use of the foodstuff, the European Union (EU) has set legal limits for DON varying between 200 and 1,750 µg kg -1 (European Commission 2006). The EU has called for more data concerning the occurrence, behaviour and toxicity of T-2-and HT-2-toxins and legal limits for these toxins had been envisaged to be set by July 2008(European Commission 2006). However, these limits have presently not been established.

Toxicity levels of T-2-toxin are approximately 10 times higher than those of DON [START_REF] Ueno | General toxicology[END_REF]. Accordingly, a relatively low temporary Tolerable Daily Intake (tTDI) for the sum of T-2 and HT-2 of 0.06 µg kg -1 body weight has been proposed by the Scientific Committee of Food (European Commission 2001). It has been found that in oats frequency of occurrence and levels of T-2-and HT-2-toxins are considerably higher than e. g. in wheat, rye and soy bean. However, in 2001 the data base was regarded as being too small to assess, if daily uptake of the toxins with food was on average below the tTDI (JECFA 2001). In recent years several authors have studied the occurrence of T-2-and HT-2-toxins in diverse cereals and cereal products, e.g. in conventional and organic bread [START_REF] Schollenberger | Trichothecene toxins in different groups of conventional and organic bread of the German market[END_REF], in diverse grains and feedstuff [START_REF] Schollenberger | Natural occurrence of 16 Fusarium toxins in grains and feedstuffs of plant origin from Germany[END_REF], in conventionally and organically grown oats [START_REF] Gottschalk | Occurrence of type A trichothecenes in conventionally and organically produced oats and oat products[END_REF]Edwards 2009b) and in barley (Edwards 2009a). It was also assessed, whether toxin levels were reduced during processing of oats (e.g. de-hulling) and malting and brewing of barley [START_REF] Edwards | Emerging issues of HT-2 and T-2 toxins in European cereal production[END_REF]. In Germany, there has been performed a relatively large survey of various types of foods for levels of T-2-and HT-2-toxins [START_REF] Curtui | Improvement and validation of analytical methods for type A trichothecenes (T-2 toxin and HT-2 toxin) and occurrence of these mycotoxins in foods from the German market[END_REF]. The outcome of the latter survey was that toxins were found at low concentrations in a large percentage of cereal based products, where highest frequency of occurrence and highest median values for T-2-and HT-2-toxins were obtained in oat based products. The relatively low concentrations of the toxins lead the authors to conclude that for the average consumers health risks would not be expected. On the other hand, it cannot be ruled out that high intake consumers, especially children, are at a health risk due to elevated levels of T-2and HT-2-toxins in oat based products. For this reason the current work examines two aspects concerning levels of T-2 and HT-2 toxins in oats i) influence of different cultivars and different growing areas within Germany and ii) influence of a range of processing steps during the production of oat foodstuffs.

Material and methods

Sample collection, preparation and further treatment

The oat samples from cultivar studies in 2007 were provided from the German Federal Plant Variety Office (BSA) in Hannover, Germany. The four oat cultivars Aragon, Dominik, Ivory and Pergamon were grown on ten different sites, distributed relatively evenly in Germany. On every site, plants were treated analogous to normal agricultural practise with several applications of fungicides. Plant treatments between sites were not uniform and differed due to local conditions such as infection status and weather patterns (2010 personal communication D. Rentel, BSA, unreferenced, see 'Acknowledgements'). At least 2 kg of the harvested raw material was stored at room temperature in the dark until grinding an aliquot of 300 g per sample in a mill with 500 µm sieve pore size (Retsch, Haan, Germany). The ground raw oat samples (n=40) were screened using direct competitive enzyme-linked immunosorbent assays (ELISA) for simultaneous detection of T-2/HT-2-toxins according to [START_REF] Hocke | Entwicklung und Validierung von Enzymimmuntests zum Nachweis von T-2 Toxin und HT-2 Toxin sowie Vorkommen dieser Mykotoxine in Lebensmitteln des Page 12 of 22[END_REF]. Out of these samples, we chose eight samples with levels higher than 100 µg kg -1 T-2/HT-2 for the further experiments.

Approximately 1 kg each of the eight chosen raw oats samples were cleaned using a laboratory scale grain cleaner (Labofix, Schmidt-Seeger, Beilngries, Germany), which separates foreign material from the oat grains. Half of the cleaned oats were de-hulled with an impact de-huller operating with compressed air (Figure 1). Approximately 0.5 kg of each, cleaned and de-hulled oats, were ground separately as described above. The ground samples were stored in glass bottles at room temperature in the dark until analysis and further usage for processing experiments.

For determination of T-2-/HT-2-toxin levels in the eight raw oats samples, the cleaned and de-hulled oat samples as well as in the processed material we employed an LC-MS method.

Preparing "porridge" from oat meal "Porridge" was prepared by adding 20 g whole oat meal, obtained from cleaned oats, to 100 mL tap water. The mixture was stirred thoroughly and the porridge was heated (30 °C to 96 °C in 22 min, 1 min at 96 °C) in a Micro Visco-Amylo-Graph ® MVAG (Brabender, Duisburg, Germany), which ensures good mixing of the sample without sedimentation of particles and steam loss. The preparations were done with a controlled temperature cycle of heating and holding, using fixed shear conditions. This ensures highly reproducible gelatinization and pasting profiles of the oat porridge. After this a freeze-drying procedure of the porridge followed. The porridge preparation from each sample was performed in three replicates, all of which were subsequently analysed for T2-and HT-2-toxins with LC-MS.

Bread manufacturing

In order to obtain bread contaminated with T-2-and HT-2-toxins, wheat flour and whole oat meal (obtained from cleaned oats) with known levels of T-2-and HT-2-toxins was used. The bread recipe contained a mixture of 80% wheat flour and 20% whole oat meal. The wheat flour quality (type 550) was characterised using various ICC-Standard methods. The flour had 14% water content (ICC 110/1), 385 s falling number (ICC 107/1), 11.6% protein content (ICC 105/1), 27.4% gluten content (ICC 137/1), 36 mL sedimentation value (ICC 116/1), 57.8% water absorption (ICC 115/1) and 0.59% ash content (ICC 104/1). Descriptions of the ICC methods are available in the internet at http://www.icc.or.at/methods3.php. The bread dough was mixed using 800 g wheat flour, 200 g whole oat meal, 50 g fresh baker's yeast, 15 g pure peanut oil (partly hydrogenated), 15 g white refined sugar, 20 g table salt and 580 g water. Manufacturing conditions were in principle identical with industrial bread making processes. Details of the conditions are listed in Table 1. For each sample bread manufacturing was replicated three times.

Bread and porridge sample preparation

Bread samples were ripped into small pieces and air dried for two days at room temperature.

Dried bread and freeze-dried porridge samples were ground in a mill (500 µm sieve pore size, Retsch, Haan, Germany). Ground material was stored in glass bottles in the dark. Water content of all materials were analysed with a moisture analyzer (Sartorius AG, Göttingen, Germany).

Chemicals

Methanol (LC-MS grade) was purchased from Roth (Karlsruhe, Germany) and acetonitrile (HPLC grade) was obtained from Baker (Deventer, The Netherlands). Formic acid p.a. was from Merck (Darmstadt, Germany) and the standard solutions of T-2-and HT-2-toxin, both in acetonitrile, were purchased from Biopure (Tulln, Austria).

Analytical methods

Enzyme-linked immunosorbent assay (ELISA)

Briefly, ground oat material (5 g per extraction) was extracted with 70% methanol in water (v/v). After centrifugation the supernatant was cleaned by liquid-liquid extraction with ethyl acetate. Extracts were assayed in quadruplicate for concentration of T-2-and HT-2-toxins using microtitre plates. The limit of quantification for T-2-and HT-2-toxins was 0.5 µg kg -1 and recoveries were greater than 80%. In interlaboratory studies a good reproducibility of the method was obtained: in 11 samples the RSD R values were between 9 % and 31 % and the mean RSD R was 17% [START_REF] Hocke | Entwicklung und Validierung von Enzymimmuntests zum Nachweis von T-2 Toxin und HT-2 Toxin sowie Vorkommen dieser Mykotoxine in Lebensmitteln des Page 12 of 22[END_REF]. Using the described ELISA method and a GC based method for detection of T-2-and HT-2-toxins on identical samples, there was a high correlation in the results (r 2 = 0.96), [START_REF] Majerus | T-2 and HT-2 toxin analysis in cereals and cereal products following IAC cleanup and determination via GC-ECD after derivatization[END_REF].

Liquid Chromatography Mass Spectrometry (LC-MS) -method

Pressurized liquid extraction (PLE) and extract treatment. Ground material (10 g) was mixed with 4 g diatomaceous earth (Varian, Darmstadt, Germany) for keeping the sample porous. This mixture was placed on top of a layer of 2 g activated charcoal (Merck) in a 33 mL stainless steel cell (Dionex, Idstein, Germany). Extraction was done using an Accelerated Solvent Extractor (ASE 300) instrument (Dionex) with 20% water in acetonitrile (v/v) as solvent under the following conditions: preheat 5 min, static 5 min, flush 130%, purge 80 s, cycles 5, pressure 15000 kPa, temperature 85 °C. The extract volume was adjusted to 100 mL with 20% water in acetonitrile (v/v) in a volumetric flask. A 10 mL aliquot of the extract was evaporated to dryness and subsequently redissolved in 0.3 mL methanol and 1.2 mL Milli-Q ® -water (Millipore, Schwalbach, Germany). After filtration through a 0.2 µm disposable syringe filter (Macherey-Nagel, Düren, Germany) extracts were transferred to vials and stored if necessary at minus 20 °C prior to analysis.

Liquid Chromatography-System. Separations were performed using a LC-prominence system (Shimadzu, Duisburg, Germany) equipped with a Luna® phenyl-hexyl-column (150 x 2.0 mm I.D. particle size 5 µm) and a security guard (Phenomenex, Eschborn, Germany) at 40 °C. The flow rate was 0.4 mL per minute and a gradient was mixed using Milli-Q ® -water with 1% (v/v) formic acid as solvent A and methanol as solvent B applying the following gradient programme: start 10% solvent B, 10-40% solvent B (1 min), 40% solvent B (3 min), 40-80% solvent B (6 min), 80% solvent B (4 min), 80-10% solvent B (0.5 min), 10% solvent B (2.5 min).

Mass spectrometry. The linear ion trap triple quadrupole mass spectrometer (4000QTrap, Applied Biosystems, Darmstadt, Germany) with a TurboV ® -Source was operated in ESI(+)multi reaction mode (MRM, Table 2) with the following general settings: Curtain gas 28 psi, CAD gas medium, IS 5500 V, temperature 315 °C, Gas1 50 psi, Gas2 75 psi.

Quantification was carried out with a matrix matched calibration curve. For this purpose matrix standards were prepared by extracting a blank sample (each for raw oats, cleaned oats bread and porridge respectively) like any other sample until evaporation to dryness (see step PLE). Dried samples were dissolved in 1.2 mL water and 0.3 mL standard T-2-/HT-2 solution in methanol. Calibration-matrix-standards had concentrations between 1 10 -6 and 7 10 -4 g L -1

T-2-and HT-2-toxin in 20% methanol/water (v/v), respectively. Detection limits (Signal to noise ratio ≥3) were between 1 µg kg -1 and 3 µg kg -1 for T-2-toxin and between 3 µg kg -1 and 5 µg kg -1 for HT-2-toxin, depending on the matrix. RFs became more variable. Concentration dependent RFs of T-2-and HT-2-toxins were different in raw oats, bread and porridge samples, respectively. RFs were lowest and little variable for the heated and highly stirred porridge samples, indicating a high, but homogeneous content of interfering organic matrix. The RF values for bread samples were generally factor four higher then in porridge. In bread RF values were very even between 30 and 600 µg kg -1 T2-/HT-2-toxins and increased steadily, when toxin concentrations were lower 30 µg kg -1 . The raw oat samples exhibited highest and slightly more variable RFs. For both, T2-toxin and HT-2-toxin a similar dependency of the RFs from the sample matrix was found.

In order to assess recovery of the toxins in the assay system, spiking experiments were done by adding 1, 2 or 5 µg T-2 and HT-2 to 10 g of a blank sample in three replications. After an incubation time of two hours, the samples were processed as described previously. Recovery data for T-2-toxin were 72% in cleaned oats, 88% in bread and 93% in porridge, respectively.

For the HT-2-toxin we obtained 100% recovery in cleaned oats, 85% in bread and 102% in porridge.

Results and discussion

On ten different agricultural sites, distributed relatively evenly in Germany the four oat cultivars Aragon, Dominik, Ivory and Pergamon had in sum T-2/HT-2 levels ranging from 9 to 623 µg kg -1 , as determined with ELISA (Table 3). Over all cultivars and all growing sites the median was 48 µg kg -1 , the mean was 102 µg kg -1 and the 90 th percentile was 191 µg kg -1 T-2-/HT-2-toxin. In comparison, oats from various regions in the UK showed nearly five times higher values, i. e. for these oats the median and the mean values of the sum of T-2-and HT-2-toxins were 213 µg kg -1 and 570 µg kg -1 , respectively (Edwards 2009b). Our data are more in accordance with results obtained for oats sampled in Germany: e.g. oats from southwest Germany (n=17), collected in the years 2000 and 2001. They had maximum levels of approximately 800 µg kg -1 with a mean of 255 µg kg -1 T-2/HT-2 [START_REF] Schollenberger | Natural occurrence of 16 Fusarium toxins in grains and feedstuffs of plant origin from Germany[END_REF].

Similarly, oats including hulls (n=19) and de-hulled oats (n=21) contained in the mean 118 and 6.9 µg kg -1 T-2/HT-2, respectively [START_REF] Curtui | Improvement and validation of analytical methods for type A trichothecenes (T-2 toxin and HT-2 toxin) and occurrence of these mycotoxins in foods from the German market[END_REF]. Taken together, these findings are in support of the notion that levels of T-2/HT-2 are elevated in the northern European countries and in the UK [START_REF] Langseth | The occurrence of HT-2 toxin and other trichothecenes in Norwegian cereals[END_REF][START_REF] Scudamore | Occurrence and fate of Fusarium mycotoxins during commercial processing of oats in the UK[END_REF][START_REF] Pettersson | T-2 and HT-2 toxins in oats grown in Northern Europe[END_REF] In this study the T-2/HT-2 levels at one agricultural site were approximately six times higher compared to the other sites (Table 3), showing that higher contents of T-2/HT-2 in German oats can occur. This result might be due to local conditions at this agricultural site. Anyway, 80% of all samples in this study here were below 100 µg kg -1 , whereas only 10% showed higher T-2/HT-2-toxin levels with more than 300 µg kg -1 .

Compared to the mean of all cultivars on an individual site, the cultivars Pergamon and Ivory had lower T-2/HT-2 levels for 9 and for 8 out of 10 sites, respectively (Table 3). This result suggests that these cultivars might be less sensitive to infection with Fusarium. By contrast, for the cultivars Aragon and Dominik only 6 (Aragon) or 2 (Dominik) sites had lower values than the mean. The result that Pergamon and Ivory contained decreased levels of T-2/HT-2toxins compared to the average of the cultivars appears promising with respect to the aim of lowering the levels of these toxins in foodstuff. Clearly, more research in this direction is necessary, especially as there are only a limited number of publications addressing the issue of T-2/HT-2 levels in different oat cultivars. In a study on twelve raw oat samples from the UK, Sweden and Finland [START_REF] Scudamore | Occurrence and fate of Fusarium mycotoxins during commercial processing of oats in the UK[END_REF] found in every sample T-2/HT-2-toxins, where concentrations ranged from 143 up to approximately 3500 µg kg -1 . However, they did not match their finding with different cultivars. In another study on oats in the United Kingdom, the variety Gerald cited as the most popular oat variety in the UK had the highest T-2/HT-2 concentration [START_REF] Edwards | Investigation of Fusarium mycotoxins in UK barley and oat production[END_REF]. In summary, the influence of the oat variety on the T-2/HT-2 level appears to be noticeable and should be further investigated.

Eight of the raw oat samples were chosen for various cleaning and food processing procedures. In the course of these experiments all analyses of T-2/HT-2-toxins were carried out using an LC-MS-method, yielding the sum of, and most advantageously, also individual levels of T-2-and HT-2-toxins. In 7 of the 8 raw oat samples HT-2 levels were higher than T-2 levels, where the ratio between HT-2 and T-2 levels ranged between 2.1 and 8.7 (Table 4).

Similar ratios in naturally contaminated oats were found in other surveys also involving oats from Europe [START_REF] Scudamore | Occurrence and fate of Fusarium mycotoxins during commercial processing of oats in the UK[END_REF].

Cleaning the raw oat material using a laboratory grain cleaner led to varying effects on levels of T-2/HT-2-toxins in the grain. Whereas a moderate reduction of toxin levels in the range of 10 to 15% was achieved for highly contaminated samples 5, 6 and 8, no reduction of toxin levels was observed for samples 4 and 7. In contrast, samples 2 and 3 showed a 100% and sample 1 a 69% reduction of toxin concentrations after cleaning. The ratio between both mycotoxins in the cleaned oats was nearly the same as in the raw oats. Overall, there was no consistent effect of cleaning using the "Labofix" grain cleaner on levels of T-2/HT-2-toxins in the eight samples.

A further step in processing of oats is the de-hulling procedure. The glumes (husks) have to be separated from the oat grain before preparing e.g. oat-flakes and other products for direct human consumption. The T-2/HT-2-toxin levels of de-hulled oats are also presented in Table 4. De-hulling of oats led to a T-2/HT-2-reduction of 98% in the mean, where reduction varied between 93.8 and 100%. These are results similar to those in oats from northern Europe [START_REF] Scudamore | Occurrence and fate of Fusarium mycotoxins during commercial processing of oats in the UK[END_REF]) and Canada [START_REF] Clear | The effect of hull removal and pearling on Fusarium species and trichothecenes in hulless barley[END_REF]. The major reduction of T-2/HT-2toxins obtained by de-hulling clarify, why the consumer products from retail markets in Germany had very little T-2-/HT-2 contents although higher concentration in raw oats were found [START_REF] Curtui | Improvement and validation of analytical methods for type A trichothecenes (T-2 toxin and HT-2 toxin) and occurrence of these mycotoxins in foods from the German market[END_REF]). An interesting result from this work here is that after de-hulling, exclusively T-2 toxin was found at low levels in kernels, indicating that HT-2 toxin is more strictly confined to oat hulls (Table 4).

The further investigations on cooked porridge and bread were done using cleaned raw oats as starting materials for cooking and baking, because these oats had higher toxin levels than the de-hulled oat kernels. Utilisation of de-hulled kernels would very probably have resulted in T-2/HT-2-toxin levels close to the limit of detection (LOD) in the final products, which has to be avoided from the analytical point of view.

The cooking of the ground cleaned raw oats with water was performed in an increasing temperature gradient of 3°C per min from 30°C to 96°C and a holding time of 1 min at 96°C. In the resulting "porridge" the mean T-2/HT-2-toxin levels varied from minus 40 to plus 46% compared to the theoretical value of T-2/HT-2-toxins that would have been expected in the various samples without any T-2/HT-2-toxin alteration (Figure 3). At the present stage of experimentation we would not suggest that a significant difference between cooking treatment and T-2/HT-2-toxin level exists, because standard deviations in the cooked samples were relatively large. Analysis of matrix effects and recovery indicate that the analytical method is not the major cause of the observed variations (see Material and Methods section), leading us to conclude that the variations are due to the porridge production procedure. To our knowledge this is the first time T-2/HT-2-toxin levels were examined comparing raw and cooked oats. Despite the variations, the absolute T-2/HT-2-toxin levels were relatively stable during short time cooking. This is especially relevant for infant and baby food processing, as they are the consumers with a relative high consumption of cooked oats.

Observation of the T-2/HT-2-toxin levels during baking experiments was also carried out using the ground cleaned raw oats. The four highest contaminated oat meals were baked to bread in triplicate each. After baking, the resulting mean T-2/HT-2-concentration in the bread was minus 23% compared to the theoretical value of T-2/HT-2 levels without baking (Table 4). Variations ranged from plus 12 to minus 44%. The significance of the result is that only a moderate reduction of toxins levels can be achieved during the baking process. One explanation is that T-2-/HT-2-toxins are relatively stable at elevated temperatures. As with preparation of porridge, the variations of the toxin levels are probably due to the bread making and baking processes, since parameters of the analytical method had no major influence (see Material and Method section). Both, preparation of porridge and bread making need to be further evaluated with respect to behaviour of T-2-and HT-2 levels under controlled conditions.

Our results illustrate that concentrations of T-2-and HT-2-toxins in oats from Germany can vary considerably, depending on variety and also location. Whereas the efficacy of cleaning was limited, de-hulling had a major reduction effect on T-2-and HT-2-toxin levels in oats. At the present stage of experimentation, results of food processing experiments indicated that cooking of porridge and bread making had little effect on T-2/HT-2-toxin levels. Notes: a value lower than the mean of all cultivars at the same agricultural site. b samples chosen for further experiments involving cleaning and processing procedures.

Introduction

  Fusarium spp. are phytopathogenic fungi infecting a large number of plant species.

  Matrix effects and recovery. To determine the matrix effects the response factors (RF) of the peak areas were calculated as a function of the analyte concentration added with the matrix matched calibration standards. The results for the RFs of T-2 and HT-2 in raw oats, porridge and bread are shown in Figure2. The response factors within a specific matrix were very constant down to a concentration of 30 µg kg -1 . At toxin concentrations lower 30 µg kg -1

  compared to Germany in the more central area of Europe.

Figure 1 .

 1 Figure 1. Schematic diagram of the procedures and the equipments used for preparing oat based whole meal, porridge and bread.

Figure 2 .

 2 Figure 2. Response factors for T-2-and HT-2-toxins obtained from matrix matched calibration standards. Triangles represent T-2-and rhombuses HT-2-toxin in raw oats, bread and porridge.

Figure 3 .

 3 Figure 3. T-2/HT-2 toxins in cooked porridge samples. Porridge was prepared from five different oat samples (n=3). Mean values and standard deviations as well as the theoretical content that would be expected without cooking are presented.

Figure 4 .

 4 Figure 4. T-2/HT-2 toxins in bread. Bread was prepared from four different oat samples (n=3). Mean values and standard deviations as well as the theoretical content that would be expected without baking are presented.

  Table4. Sum and individual levels of T-2-and HT-2-toxin (µg kg -1 ) in raw, cleaned and de-hulled oats and ratio of both toxins in the samples. Data acquired with LC-MS.

Table 1 .

 1 Terms and conditions of bread manufacturing process.

	Process parameter	condition	special equipment
	kneading	1 min slow / 5 min fast	DIOSNA spiralkneader, type SP 8
	dough temperature	26 °C
	dough rest	10 min
	dough per bread	dough weight/2 = ~0.8 kg
	intermediate proofing	15 min
	forming	manuell
	final proofing		MANZ proofer, type G 86 W
	-relative humidity	80%
	-temperature	32 °C
	-proofing time	35 min
	baking conditions		DAUB Backmeister, type BTO
	-steam jet	10 s	21613-S
	-baking temperature	220 °C
	-baking time	40 min

Table 2 .

 2 MRM transitions and conditions.

			Food Additives and Contaminants	Page 16 of 22
	Analyte	Q1 mass [amu]	Q3 mass [amu]	declustering potential [V]	entrance potential [V]	collision energy [V]	cell exit potential [V]
	T-2	467	305	40	10	17	19
		467	245	45	10	17	19
	HT-2	425	263	50	10	12	15
		425	105	50	10	12	15

http://mc.manuscriptcentral.com/tfac Email: fac@tandf.co.uk

Table 3 .

 3 Levels of the sum of T-2/HT-2 (µg kg -1 ) in four oat cultivars from ten agricultural sites that are distributed evenly in Germany and mean levels of T-2/HT-2 (µg kg -1 ) of all four cultivars at one site. Data acquired with ELISA.

	Site number	Aragon	Dominik	Ivory	Pergamon	mean at one site
	1	67	40 a	33 a	36 a	44
	2	100 a,b	120 b	95 a	163	120
	3	28 a	87	9 a	20 a	36
	4	42 a	42 a	129	28 a	94
	5	61	50	34 a	26 a	43
	6	104 b	118 b	39 a	48 a	77
	7	15 a	69	19 a	20 a	31
	8	26 a	54	27 a	31 a	34
	9	623 b	570 b	584 b	322 a,b	525
	10	14 a	20	14 a	10 a	15

  Notes: mean data of 3 replicates, determined with LC-MS. For T-2 the Limit of Quantification (S/N≥6) was 6 and for HT-2 the Limit of Quantification (S/N≥6) was 15. *indicates that values were below the LOQ.

													2
	1	104	23	81	3.5	36	*	36	-	-	*	*	-
	2	171	40	130	3.3	-	*	*	-	-	*	*	-
	3	14	14	*	-	-	*	*	-	-	*	*	-
	4	155	30	125	4.2	156	30	126	4.2	-	*	*	-
	5	670	214	456	2.1	569	150 419	2.8	13	13	*	-
	6	845	87	758	8.7	765	85	680	8.0	-	*	*	-
	7	476	101	375	3.7	486	85	401	4.7	29	29	*	-
	8	584	156	428	2.7	436	96	340	3.5	15	15	*	-

http://mc.manuscriptcentral.com/tfac Email: fac@tandf.co.ukFood Additives and Contaminants

Acknowledgements

The authors thank Dirk Rentel from the Federal Plant Variety Office (Bundessortenamt) for making available the oat samples and for providing information concerning the cultivation conditions of the oat varieties that are contained in internal documents not accessible to scholars. The screening work using the T-2/HT-2 antibodies was financially supported by the BMELV (Project No. 05HS001).


Venkatesa Iyengar

Vasanta Ram

Instabilities and transition in three-dimensional flows with rotation ON THE RELATION BETWEEN THE EQUATIONS FOR LARGE-EDDY SIMULATION OF TURBULENT FLOW AND FOR WEAKLY NONLINEAR EVOLUTION OF DISTURBANCES FOR FLOWS IN TRANSITION

Summary

The work submitted herewith is based on the author's attempt to unveil the relationship between the equations for large-eddy simulation of turbulent flow (LES) and those for weakly nonlinear evolution of disturbances on the route to transition according to the nonlinear stability theory of Stewartson and Stuart [START_REF] Stewartson | A nonlinear instability theory for a wave system in plane Poiseuille flow[END_REF]. Two flow examples in which three-dimensionality and rotation exercise significant effects on transition have been chosen for the purpose of illustrating the nature of this relationship. These are:

• The swirling flow between concentric circular cylinders with a rotating inner cylinder and an imposed axial pressure gradient, and

• The plane channel flow on a rotating system undergoing transition under the influence of the Coriolis force.

The relationship brought out by the study may be summarised in words as follows:

The amplitude evolution equation may be interpreted as one governing the slow modulation of the amplitude of a wave packet of disturbances under the influence of Reynolds-stress like terms. The profiles of the Reynolds-stress like terms in the wall-normal direction are given by those of the products of the fluctuating velocity components on the surface of neutral stability according to the classical linear stability theory.

Basic ideas of the two approaches

• Large-eddy simulation The basic idea in large-eddy simulation is a division of the turbulent motion in the flow into one with widely differing scales, viz. large eddies, and small-scale motion or the rest.

Averaging of the equations of motion is performed only over scales of the latter, a procedure that filters out details of the small-scale motion leaving equations for the filtered quantities in which, however a sub-grid scale stress tensor appears, see eg. [START_REF] Lesieur | Turbulence in Fluids[END_REF], [START_REF] Meneveau | Scale-Invariance and Turbulence Models for Large-Eddy Simulation[END_REF]. There arises a necessity for a closure hypothesis.

• Nonlinear stability Theory The nonlinear stability theory of Stewartson and Stuart [START_REF] Stewartson | A nonlinear instability theory for a wave system in plane Poiseuille flow[END_REF] seeks the bifurcating solution of the complete equations of motion when the flow parameter assumes values just beyond transition. The formalism of their method can be understood in terms of multiple scales, see eg. [START_REF] Huerre | Hydrodynamic Instabilities of Open Flows[END_REF]. At values of the flow parameters just beyond transition, the classical linearized equations of motion for small-amplitude disturbances yield exponentially growing disturbances, however with a growth rate that remains small when the departure of the flow parameters from those on the surface of neutral stability is small. The slow growth rate for amplification of disturbances from linear theory may be associated with further scales of time and length entering the problem and suited to account for the effects from the nonlinearities (Reynolds stres like terms) that were ignored in the linear theory. The solution of the nonlinear problem is sought in a form closely related to the wave-form of disturbances according to linear stability theory, but with an amplitude that gets modulated by the nonlinearities in the problem.

The approach results in a nonlinear matrix equation that describes the amplitude evolution in terms of the newly introduced scales.

3 Outline of the work

• Step 1: Solution of the classical linearized problem for small-amplitude disturbances 1. Starting from the set of nonlinear equations of motion for the disturbance, solutions of the equations for infinitesimally small disturbances in the flow in question are obtained by a suitable numerical method, see eg. [START_REF] Schmid | Stability and Transition in Shear Flows[END_REF]. The classical eigenvalue problem thus posed has nontrivial solutions only when a certain dispersion relation of the problem is fulfilled which we write in conventional notation symbolically as follows:

EUROMECH Colloquium 525, 21-23 June 2011, Écully, France Instabilities and transition in three-dimensional flows with rotation -For the swirling annular flow with rotation of the inner cylinder and small gap width this is ω = ω(λ x , n ϕ ; T a, S i ), where T a is the Taylornumber and S i is a swirl parameter. -For the plane channel flow on a rotating system this is ω = ω(λ x , λ z ; Re, Ro), where Re and Ro are the Reynoldsnumber and the Rotation number respectively. The dispersion relations for infinitesimally small disturbances yield the surface of neutral stability which is a surface in the space of the flow parameters, i.e. (T a, S i ) or (Re, Ro) as the case may be, on which the imaginary part of the frequency, denoted ω i , is zero. 2. From the solution of the classical eigenvalue problem, the solution for the propagation of a disturbance for arbitrary initial conditions is obtained as a Fourier-superposition of wave-modes for which the velocity disturbance u may be written in the form u = a(y) exp[iΘ]+ c.c.. Here, y is the co-ordinate normal to the walls, and the column vector u and the phase Θ are as follows:

-In the swirling annular flow: u = (u r , u ϕ , u x ) T ; Θ(x, ϕ, t) = (λ x x + n ϕ ϕωt).

-In the plane channel flow: u = (u y , u z , u x ) T ; Θ(x, z, t) = (λ x x + λ z zωt); Here the wave-number pair (λ x , n ϕ ), or (λ x , λ z ) or as the case may be, are real but the frequency ω is permitted to be complex. Values on the entire real axis are permissible for λ x , λ z whereas n ϕ may assume only real integer values. 3. For initial conditions that generate waves that remain close to the surface of neutral stabilty, the classical linear theory leads to the result that the form of the wave-packet for long times and at large distances from the source assumes a form similar to that of a single mode. The components of this (column) vector, written as a diagonal matrix U may be written in a coordinate system travelling with the wave-packet as we introduce an amplitude parameter, ǫ A , that is small and defined for the two flows as a linear combination of the departures of the flow parameters from their values on the surface of neutral stability. The amplitude parameter ǫ A is defined through:

U N = A N (y) exp[iΘ N ] exp[ω N i t] + c.
for the swirling annular flow: for B for the flow problems in question. Their relationship to LES will be discussed at EC525.

ǫ A = ω N i = d T a |T a -T a N | + d Si |S i -S iN |,

• Step 2 :

 2 c.. Here the subscript N denotes values on the surface of neutral stability and i the imaginary part. It is seen that a wave-packet has a growth rate given by ω N i , which depends upon the departure of the flow parameters from those on the surface of neutral stability, (T a N , S iN ) or (Re N , Ro N ). Extension of the solution to the classical linearized problem to weakly nonlinear evolution of disturbances according to the method of Stewartson and Stuart 1. The method of Stewartson and Stuart examines solutions for flow parameters in the neighbourhood of the surface of neutral stability when ω N i is small but > 0. Following Stewartson and Stuart, [1],

  and for the plane channel flow:ǫ A = ω N i = d Re |Re -Re N | + d Ro |Ro -Ro N |. 2.A solution for the nonlinear problem is sought in the form U ≃ BA N exp[iΘ N ] + c.c where the diagonal matrix B is a function of the set of newly introduced scales. The elements of the diagonal matrix U -these are (B r , B ϕ , B x ), or (B y , B z , B x ) as the case may be -may be regarded as the components of the filtered velocity disturbance. 3. A solvability condition yields the amplitude evolution equations (nonlinear matrix equations)