On the Anomalous Increase in the Flux of
Coffee Drinkers in the Coffee House
Ajan M.P.G.* and Yanan H.R. **
* Department of Cofi Science and Engineering, Akaryatha.
** Vetti Institute of Theoretical Studies, Akarmiya.
Following the recent experimental observations reporting the anomalous increase in the flux of coffee drinkers in Indian Coffee House and the other related systems, we have investigated these systems using the Maximum Free Time (MFT) simulation method and method of Interflipping of Drinkons. Both the models predict the anomalous increase in the flux under the conditions of non-availability of 't'. A mechanism for the exchange of information of the non-availability of 't' is also proposed. Also an extension of these results to problems of crowd management in bus-stops, Gymkhana and classrooms are proposed which have very strategic practical applications.
Keywords: flux, coffee, Drinkons, MFT, exchange, t.
It is well known that the time versus flux plots for coffee drinkers invariably reach a peak at nine in the morning and continue to be at the maximum till five in the evening in the coffee house and other related systems. But recent experimental observations indicate that under certain experimental conditions sharp, characteristic lines are superimposed on the original, nearly step function, indicating an anomalous increase in the flux of coffee drinkers . Attempts to explain these results using FTM (Finite Tumbler Method), drink diagrams and other such conventional methods have not been successful [2,3]. Although concepts such as fractional cup and self-similarity in the coffee cup aid in simulating the observed results partly, the main disadvantage with these two methods is that they can also be extended to t in which case also they produce the same kind of results. In this paper we discuss the MFT simulation as well as the method of interflipping of Drinkons which reproduce the observed results to a greater extent, if the assumption of information transfer through Drinkons is made. Also the possible extension of this method to other systems is briefly mentioned.
Maximum Free Time Method (MFT):
Ever since the MFT was shown to be equivalent to the minimisation of work by Joblesass et al. in 1912, the minimisation of work principle is used practically in all numerical calculations. But this problem is a classic example where the MFT is not only successful but also elegant and aesthetically satisfying.
Let us consider the generation of a random number between 0 and 1. If the generated number is greater than 0.5 then a drinker is created. Again a random number is generated and if it is greater than 0.5 then the drinker is said to be a k-drinker (following the German word kaffe). If the generated number is less than 0.5 then the drinker is called a t-drinker. If the first generated random number itself is less than 0.5 then the drinker is straightaway assumed to be a k-drinker. This process is continued till the required result is obtained. If the numbers after the calculation do not yield the required results the above-mentioned values may suitably be changed and the calculation repeated. The iterations for various initial guesses are repeated till the value converges to the experimental one.
The Statistical Mechanics of Drinkons:
Drinkons are the classical particles which also have a half integral spin (1/2). Hence it has two states viz., the k state corresponding to a spin +1/2 and the t state (following the German word Tee and corresponding to the spin value -1/2). The Drinkons obey the Gorbogi-Junc statistics at lower temperatures and at higher temperatures converge to the classical statistics. The distribution function for G-J statistics is
N(k) = 1/(1 + exp E(k)/JT)
where N(k) is the number of Drinkons in the k state with an energy E(k). J is the Junc constant and T is the temperature of the system viz. the room temperature.
Note that as the room temperature is lowered the flux of coffee drinkers increases as is expected. Now under the conditions of non-availability of t, if the information is passed on through Drinkons, the Drinkons in the t state will flip to the k state while those in the k state remain unflipped. This is mathematically achieved by suitable combination of symmetro-asymmetric state functions using Naughter determinant. This will increase the number density of Drinkons in the k state as is required.
Results and Discussion:
Both MFT and Interflipping of Drinkons explain the observed anomaly in the flux of coffee drinkers. The method of interflipping of Drinkons point to the information exchange as the possible mechanism behind the flux increase. Extending these ideas to crowd management in bus-stops, Gymkhana and classrooms the following suggestion is given. The information channel is to be blocked. So if announcements about classes or about the film in the Gymkhana be not made the crowd level will come down enormously. In the case of bus-stops there is an a priori assumption that buses will come. If an information that no buses would ply be made in all bus-stops the flux will be reduced. Theoretically it may even reach zero.
The authors are grateful to a number of colleagues for their useful discussion and critical appreciation. M.P.G.A is grateful to S. Hankara for drawing his attention to this problem. Y. H. R. would like to acknowledge the financial support from Vetti Institute of Theoretical studies.
 Hankara .S., private communication.
 Ajan M.P.G., "On FTM – a Review", Cofi Rev. Z, Vol 120, pp108-25.
 Yanan H.R., "Cofi – a Drink Diagram Approach", Acta Kaffeya, Vol 45, pp1025-32.