Study Group Problems |
| 1) An adaptive traffic light system( M. Zihni Serdar, Erisim Electronics) |
Figure An adaptive light control system |
An adaptive traffic light system on a cross road is to be developed with the control being the data obtained through fixed cameras attached to the light system. The control itself is to be adaptive as there is no need for collecting data during the time when there is no traffic at all. Thus the problem is to collect data adaptively and control the light system accordingly. The idea, of course, is not to have people wait for unnecessary amount of time along the way, while there is no traffic across roads. Though looks rather reasonable, a very good adaptive strategy and an accompanying algorithm needs to be developed. The study group is asked for such an algorithm. The problem requires collaborative work of mathematicians, computer scientists and electrical engineers. |
|
| 2) S. Hacısalihoglu(TTSO, Medical decontemination system) |
An effective Medical Decontamination System is to be designed. The system is thought be in cylindrical shape as shown in the Figure. On the surface of the cylinder are light emitting tubes through which medical waste is exposed to a certain type of physical light, aimed to convert medical waste into a regular one. The waste proceeds forward through annular region as it rotates to get maximum exposure. The exposure depends on many parameters: axial and rotational speed, the number, location and size of tubes. An effective system is to provide maximal volume of exposure by the time waste leaves off the system. Given a typical range of parameters, the study group is asked to develop a formulation to estimate the others that will lead to effective design and operation.
|
Figure: A medical decontaminant |
| |
3) TİSAŞ(Targets problem)
|
 |
TİSAŞ is a handgun manufacturer located in Trabzon that aims to meet demands of people of Blacksea and abroad with a variety of models such as Kanuni, named after Kanuni Sultan Suleyman or better known Suleyman the Magnificant who was born in Trabzon, and Zigana, named after high mountains nearby Trabzon. The company would like to optimize its production reinvestigating the models at hand:a statistical and a modelling approach seems to be needed for their request initially.
a) A laboratory test, aimed to check the compliance of the model with demand, indicates that consecutive fires of about 10 centers around a circular region with a radius of 10cm. The fact that the fires, though performed at the same conditions, do not target at the same point is called focusing uncertanity of the handgun. Furthermore, it is observed, by myself also, that bullet velocity measured 10 metters from gun varies up to about 7m/s( around 340m/s) among the firing set of 10. There are about ten different models and each model seems to display a different magnitude of uncertanity and velocity deviation from the expected average. The company, being willing to produce more data at request, asks to see if the focusing uncertanity and variation in bullet velocities can some how be corelated. And with some help from other disciplines, the fact behind such uncertainities..? Experiment apparatus or manufacturing process. If latter, which manufacturing unit contributes more?
b) The other problem posed by the firm is wheather a reasonable model can be formulated to help analyse the effect of barrel geometry(or polygonal shape in particular) on the speed of bullet
|
|
|
| 4) Trabzonspor(Spinning soccer ball trajectory)
As can be remembered from the recent World Cup, uncertainities in the trajectory of a soccer ball at high speeds have led to some criticism on the ball manufacturers. The existing ball trajectory models assume that as the ball spins, a layer of air, say a boundary layer, follows the motion of the ball, thus spins with it. This, in turn, induces a velocity difference on the sides normal to ball's trajectory. The velocity difference then leads to pressure difference due to Bernoulli's principle. If  represents the axis of spin and  is the linear velocity, the resulting Magnus force would be in the direction of  .
Figure. A soccer ball trajectory and the induced velocity difference
Yet, the resulting trajectory models do not seem to account for rapid changes in the trajectories. The study group is then asked to analyse the asumptions of the existing models and modify them if necessary to come up with a satisfactory model. |
| |
5) A plumber problem
Laminar versus helical flow characteristics in pipe containing fluid and particles
The plumber, while forming pipe lines, pay attention to avoiding lines being nearly vertical. Because, based on their observation, the nearly vertical lines lead to helical flow. In such a flow, the discontinuous nature of kitchen pipe flows leads to accumulation of flow residues around the pipes each time after a short flow period. In the long term, accumulation of chemicals with food particles obscure the flow. On the other hand, the pipelines away from vertical positions lead to laminar flow. This type of pipelines do not sem to give rise to any problems, and thus prefered.
Howeever, there are situations where a nearyl veritical pipeline is unavoidable. In this case, the plumbers would like to know laminar versus helical flow boundaries as a function of typical fluid pressure, pipe radius and angle with horizontal, etc. This will allow them to be in the safe zone while setting up their pipelines.
|
|
|
| NEWS |
|
|
| ACCOMMODATION and TRANSPORTATION |
|
| PREVIOUS INDUSTRIAL MATHEMATICS WORKSHOPS |
|
|
| TURKISH INDUSTRIAL MATHEMATICS GROUP |
|
|
|
|
|
