Friday, June 23, 2006


Deterministic Chaos

I am writing a knowledge sharing-attempt on this subject.Articles will be updated time to time
based on what I have studied.It is not reproduction of any book

Welcome to the world of Chaos.Happy learning !

Non-Linear Dynamic Systems

“Simple physical laws such as Newton’s law of motion on simple physical systems such as simple pendulum can turn out an irregular and seemingly random motion that is too complex to predict or compute to any given degree of accuracy in a long run”.

Some examples of chaos are : turbulence of fluid in a flow , convection ,temperature gradient etc.,

Unpredictability of weather and fluctuations of stock markets are underlined by chaos. That’s where very close relation prevails between science and economy.

For instance we had erratic reversals of magnetic poles 14 times in past 4 million years suspected to hide a erratic geo-magnetic dynamo. So, why cant be the same case for earth-quakes ?.

So chaos has its hand on ecology ,epidemiology ,economics, disturbed chemical and biological clocks , circadian rhythms of mosquito.

All physical and chemical reactions are chaotic for some initial conditions and extreme conditions ie., far from equilibrium .

Some of the examples of chaos applications are : Craniological devices such as EEG, ECG etc.,
Chaos says “A chance emerges out of necessity ”

Repeated application (or iteration) of simple recursive rule is the simpe standard tool for creating and analyzing chaos .

After a long iterative run either it can
Put (constant ) or
Repeating on itself (periodic)
Keeps changing without being repeating on itself
The last one signifies chaos.

The Chaos has sensitive dependency to initial conditions .This can be made use to create predicted or expected results.

(Note : Chaotic advectional mixing is effective than Molecular mixing ).

* chapter - 1 *
Why its called deterministic chaos ?
Non-deterministic chaos or Stochastic noise are produced as a result of unreckoned or uncontrollable forces .Eg is Brownian Movement :
Is depicted as movement of a pollen grain inside the water due to the unobserved

......Covered Later :

Logistic map
Circle map
Hamilton chaos
Strange attractor
KAM theorem

bye for now...


Hey this is the reminiscenes of my college Alumni meet

which I shared with my friends..A copy to you


Dear Mani,

The time when I reached erode. it was 5 in the morning..
Early morning signs scattered over here and there..
Beggars who started sleeping long before…when they lost hope of their last night’s food.
Travelers who pretend to sleep holding their shabby bags around their chest…
Paper-walas arranging the morning news papers…And Obviously for carrying those, few future Abdul Kalams too…

I moved around the inches of the most loved spaces of the bus-stand. (I didn’t even miss to ‘piss’ in that appropriate place)
Conductors, who are the ‘drivers’ of the buses advertising themselves…with Sacred ash and Sandal paste in their forehead…
Are distinct creatures, which could not be seen in other spacio…I just thrown a smile over all of them.

Found the first vehicle to IRTT…already stuffed with groceries, vendors and farmers also
former farmers enquiring about the ‘growth-how’ of their coveted reap.
T.M.S was sounding devotionally “Enakkum Idam Undu…
Arul Manakkum En Murugan tiruvadiyil
Enakkum Idam Undu”
Fortunate enough to get a window seat.
On that blossoming morning the city (or town may be) starting revealing itself s l o w l y
. . so....lowly like an young Whore…
The paths frequented by us, the hoardings that captured our eyes and the smell of the town…one bye one passed through the Window. The bus landed before the most coveted lost-paradise.

In the dim morning moon, welcomed by sodium-lamp Spinsters queued beautifully.
The breath of the ‘pulari’ evoked multiple emotions.
Up the hill…and Up the hill…It was as though climbing an emotional Everest.

The A-Block…B-Block..Aur C..The ‘Blessed’ Temple. the Lawn (now dried up)..the flowers of no-name all I passed by.
The Road less passed by,is arrived.It is as black as Night.As mysterious as black holes,,as beautiful as Moon…Saying untold stories of times Foreever.,toThose who are kind enough to keep ear in its heart and feel its Song.
The trees and Bushes sideby,which shared our tears, Joy..( indefinite-Joy : ref : God Of Small Things ).. Anger and Our sorrow,Now detrimented ,it was
Difficult to see that little forest showing it’s soil,which we have never seen.You Know showing soil is a Dishonor for Forests ! .

I felt by that as though Somebody read loud my personal diary…I passed by it soon…

Then Came Our Second Home…Where we discovered ,Lost,and ‘Lived’ a Lot…

Welcome to G-Block ; Boy’s Hostel.

Prawin is waiting in G-17.

CONTINUED… (written after 3 months)

…my bench phase started and thought it’s the right time for me to recollect the lost memoirs…
Stepping into the G-Block …heart as heavy as sodden cloth and mind as fragile as bird’s wing.
It is an outlandish sand-clock. When mind frees, the heart fills.

Still I can find bees squall around drops of leftover tea patches. I remember sometime when we shared tea in a single cup and nearby storm of bees share a drop of tea “we smiled at our indifferences with those creatures”.

Hopefully I didn’t met many of the people in that morning .I slipped to the ground floor –right wing .First Room
Vimal’s .I a hurry that I might miss him before I leave …the letters I wrote on his door with crayons “Vimal, Raja Bye! don’t Forget me!! ”.I felt the ferocity of the words by running my fingers over it. The music of the words and the unspoken were tantalizing .Before any one could see me I slipped into the dark hand of the verandah and the closed doors. I was not courage enough to face the ‘treasure room’ .Turned aside unnoticed I knocked at room no : 5 to look at our old friend . Surprised by one another’s presence. Through our conversations past lived once again.

Absolutely uninterested by what’s going to happen at the ‘stage’ we were interested in the real-dramas. Not every one of us was present, but through one another’s words every one was present. An argumentative smell went thru the air of IRTT. A phenomenal exchange took place. Smiles, Hugs, Pats, tears, good news, gossips and many more.

There we could see many more people like us older in age but as young as us in their relational-attire. What I have learned from the scenes going on there was “relational emotions are less influencing than emotional relations” in ones life-being.

Next the most awaited ceremony for many of them, great grand dinner (I mention it as dinner hoping that would be their last meal of that day !).But our thought lingered around our II and III yr mess. We didn’t try to make out a move…but I couldn’t restrict from doing so. When we passed through each and every closed doors of the hostels an open-world of thoughts followed it. Hostel rooms are not non-livings .They are burdened by the memoirs of the past. We could feel ourselves walking on our own footsteps impressed there some time back.

Passed through the ground floor verandah, the sight of the open doors of the mess. The one which fed us. One which taught us to share. Involuntarily our foot carried us into that strange world, where our evenings prospered. The tasteless food even, we ate it ceaselessly we had one another on the other side. Then we started to realize, taste to the food is added not only by the what we have in it (ingredients) but also by with whom we have.

It was deserted. The people might have left to the ‘great grand dinner’ as we did when we were at their time. Some serving women and cleaning ladies were seen scattered. Few of them was able to identify our identity and inquired “hey sons! How do you do .Got married? Coming from madras? ”. when we attempt to explain “ma ! you misundersto..” they took over “yes yes I know , you are from that sebestian batch know …I know well .Nice boys. Always creating problems. Would come and ask for food at any time . Have u seen seba… please say him the old lady enquired him. Ramesh , that salem boy …his name… hmm every thing I remember ” . we were to say nothing always some ramesh and suresh are in the memories of these ladies. We just nodded heads taking the responsibilities of those rameshs and Sureshs. She pleaded “Take some food. today is brinjal sambhar and carrot curry .Tomato Rasam is good today.” Hesitantly she said “all big men won’t take food again in mess”. On this we were taken aback and explained “no ma ! We are always your children. Just we had food. Some butter milk would be okay”. We had mouthfuls of buttermilk which once kept our afternoon classes sleepy. She gave our leave saying “God bless you, take care of your parents well when they are old”. Great amount of seclusion unexpressed poignancy hidden in those words. We tried to offer a hundred rupees note for her to spend. She refused to get it “What I am going to do with so much money. Just give some thing for betel leaves its enough. All I need is you all be like this always”. On hearing the ‘master’s’ voice she took our leave and left our hearts burdened for ever.

Next our legs wandered around the unlimited roads of the campus and the cricket ground which was our study rooms during our exams days. Still some body is seen under the trees with books undisturbed by our presence very exactly as we did and whispering to others once we left “Will we too come like this One day ? ”.

The college has seen many changes. Every year , changes are irresistible. Irrespective of changes, it is same for every one who visits it. Not only people, even the trees are familiar. The missing one and the new ones are known to us. Topographic picture of that landscape is measured in our hearts.

Sun started sliding down the mountains when we started leaving the pleasure-Island, touching the trees , plucking the leaves and smelling the flowers , giving adieu to them, giving promises to each other… we left the campus arch without knowing answer for one question …When we will meet next ? …

The Sky is Dark Now …
Half moon…
No clouds…