Randomness and its constant uniformity

Random - How do you perceive it? Chaotic? Disorderly? Higgledy-piggledy? For most of us, these are the defining words for "Randomness". When you think about it, sometimes anything random seems to exhibit the most consistent behaviour. I thought of it and have come up with certain examples, the cases in which randomness is not really random!

1) A non-crystalline material

A crystal has the atoms arranged in an orderly manner. Hence, it is anisotropic - that is, it does not exhibit the same characteristics (Physical, optical, etc) in all the directions - irony. But a non crystalline material exhibits properties that uniform regardless of the direction. 

2) Concrete

My prof once asked me why they add small stones to cement and mix it thoroughly. Why? Its because they want the position of stones in the cement to be as random as possible. Again why? They want it to be "Isotropic" so that it does not have any planes or lines of weakness which will be there when the stones are arranged in an orderly way. It can be better explained with a potato and a wooden log. Try cutting a potato in different directions and you'll find it the same effort is required for all the directions. But thats not the case with a wooden log. Its easier to cut the log in the longitudinal direction than the transverse directions because the fibres are lined along the longitudinal direction (An orderly arrangement)

3) Sampling

For quality tests in industries to surveying people, always a "random sample" is taken. Why? It gives a  result that more or less describes the characteristics of the whole group of entities. No survey is accurate only when a particular closely related section of people are answering the questionnaires. 

4) Chemical reactions

Most of the chemical reactions take place when the reactants are "uniformly"  mixed. So, what is this uniform mixture?? Reactant A placed on top, B in the middle and C at the bottom? No, they call it uniform when the mixture is chaotic and random. For that matter, any uniform mixture is one that is random.

Entropy the term that measures the degree of randomness is something so important in this universe. Want to know why? Read this.

Gravitational Red Shift

So...the first thing you'll have to know in order to understand this concept would be Doppler effect and its extension into light waves...

For those who are new to Doppler effect...

Whenever there is a relative motion between the source of sound and the observer, there is a change in the frequency of sound observed by the observer. If the relative motion is such that the source and observer approach each other, there is an increase in frequency, and if the relative motion is such that they recede away from each other, there is a decrease in frequency as observed by the observer.

Consider a similar case with light waves...

If the source moves towards the observer, we have an increase in frequency of light waves which we term as blue shift. If the source moves away from the observer, we have a decrease in frequency which is what we call as red shift. Practically, we don't feel this effect because the speed of the relative motion between the source and the observer is usually negligible compared to the velocity of light waves.

This redshift doesn't necessarily take place because of the Doppler effect.

Consider a photon travelling away from the earth's surface, or, let's say a gravity well. Its path would be similar to that taken up by a projectile which slows down as it gains altitude by transfering its kinetic energy to potential energy. But in the case of a photon, it cannot lose energy by slowing down as they are always considered to travel at 'c' . So we have to comprehend the loss in energy as a lowering in frequency of the photon waves, in other words, reddening of photons. This is termed as gravitational redshifting.

Here too, u have the gravitational blueshifting, which occurs when a photon falls into a gravity well.

If you are one of those techy guys looking for a valid derivation to support this theory, get some book relating to quantum physics.

- Maheshwar

Okay, now that is an interesting article from Mahesh. This article poses some unanswered questions.

1) In doppler effect (Sound) there is an apparent increase in frequency when the observer and source move towards each other. Frequency increase implies increase in energy. Where is this energy coming from?

2) Mahesh says that a photon can't lose or gain its kinetic energy and that is why the energy change happens through alteration of frequency. But a photon is always considered mass-less. Kinetic energy?

3) What is the difference between a normal redshift and a gravitational redshift?

4) If an observer is moving towards a source of light, the relative velocity between the light waves(or photons) and the observer is greater than the velocity of light. It is possible?

Take these questions to the forum or comment here.

-Premkumar

Coanda effect

This post offers a simple description of "The Coanda Effect". My obsession with "effects" continues. It started with the Magnus Effect, then the Domino effect and now the Coanda effect. While the magnus and domino have a strong theory behind them, the Coanda effect is more of a physical phenomenon. I'll briefly write my understanding of this effect.

The Coanda effect is the tendency of a fluid jet to get attracted towards a surface that is close to it. The picture below (Source: Wikipedia) illustrates this phenomenon

The reason for this effect is not all that complicated according to my perception of it. When there is a fluid jet, the nearby fluid gets "entrained" around the jet (Courtesy: wikipedia). This can be best visualized when you blow air into an empty and open polythene bag. The bag gets filled with air immediately. This is because when air is blown into it from the outside, the surrounding air also joins the stream and enters the bag to fill it. This is what I referred to as "entrainment" previously. If a surface is preventing the ambient fluid to get entrained, the jet moves towards the surface and this is the Coanda effect. 

It is to be noted that the this effect is possible only when the jet fluid and the ambient fluid are the same. For the flow to get attracted and stick to the surface, the surface must be smooth and curved. This is why aero foils have a smooth curvature. Even when the angle of attack is increased, the coanda effect directs the fluid to flow along the surface of the foil thus ensuring lift. When the angle of attack is too high, the coanda effect will no longer be able to keep the flow sticking to the surface. The flow will separate and it stalls. (Image courtesy: discoverhover.org)

There was once an aircraft built to use only the coanda effect for producing lift. That effort did not succeed and aircraft never took off the ground. But this effect has been utilised in many modern day aircrafts to augment its aerodynamic abilities.

Domino effect - Its more than just a fall

There is none who hasn't heard of the domino effect. Its the chain reaction triggered by one falling object on the other (dominoes) which in turn fall on the other and so on. Simple isn't it? But when I was surfing the net reading about the energy conversions involved in a domino effect, I was amazed to see how naive I have been in thinking that the effect is nothing but a successive fall of dominoes. Here are some of the interesting aspects of a domino effect that I came across

1) The speed

The speed of the domino effect depends on the distance between the successive dominoes. The farther they are placed apart, the slower is the progression because it takes a longer time for the falling domino to knock down the next one - common sense. 

2) An Infinite arrangement of dominoes

An infinite dominoes set poses some interesting questions. Will the system continuously lose energy continuously through heat and sound and eventually come to a halt? The answer is no. The energy of the system comes from the potential energy of each of the dominoes that was stored while setting them up in a metastable position. An initial trigger to the first domino will convert its potential energy into kinetic energy while falling and a fraction of this kinetic energy will push the next domino to an unstable position thereby making it fall and converting its potential energy into kinetic. Thus the system is self sustained and never comes to a stop. In fact, as the first domino pushes the next at a speed, the second one falls faster than the first. This in turn topples the next one even faster and thus the progression is actually accelerated.

So, if the progression is accelerated, will an infinite dominoes system reach the velocity of light at one point? the answer is no again. Consider this analogy - a ball falling towards the earth's surface from about a height of 1000 km should ideally reach a velocity of 42 km/sec when it reaches the surface. But that does not happen because the atmospheric air dampens its acceleration and makes it reach a "terminal velocity" which will be constant till it touches the ground. Here energy is lost by friction and buoyancy and an equilibrium is reached. In a similar way, in a domino-effect, the energy is lost during the impact through heat and sound. this energy loss is more when the speed of impact is more. Thus the system reaches a point in time when the acceleration and energy loss reach an equilibrium and the progression will be at a constant velocity from then on.

There may be still more to a domino-effect when you consider the size and geometry of the dominoes. May be I'll look for more on this topic and write about it sometime later. From now, when you witness a domino effect, remember, there is more to it than what meets the eye! ;)

References: Wikipedia, www.physicsforums.com