Osmosis

Diffusion?

Whenever there is a concentration gradient difference of molecules exists, diffusion occurs. Molecules typically move from an area of higher concentration to lower concentration. For example, when you add a spoonful of salt in a test tube, which is separated by a permeable membrane, the salt diffuses across the water.

Solvent – water

Solute – salt

Net result – diffusion

Example in human body: Oxygen diffuses from an area of high concentration (artery) to an area of low concentration (cell).

Osmosis?

Now, in the above example, supposing if the membrane is selectively permeable , i.e., if the membrane allows only the movement of the solvent (water) and not the solute (salt), then osmosis results. Water will diffuse across the semi-permeable membrane from the low-solute concentration (no-salt) to the high solute concentration (salt), until solvent-equilibrium results. This net diffusion of water occurs passively, i.e., they do not require any energy.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

For example, if you sauté any vegetables with salt, the water oozes out because of osmosis!

Example in plant kingdom: roots from trees suck up the water from soil using osmosis.

So, what happen if you place  cell that is covered by a plasma membrane (which is selectively permeable) in hypo or hyper tonic solutions?

1. If you place a cell in a hypertonic solution (less water & more solutes), the cell will shrink in size.

2. If you place a cell in a hypotonic solution (more water & less solutes – example tap water), the cell will drink up the water & swell!

Check these videos to understand the concept better!

http://www.youtube.com/watch?v=K3wG337xmQc

http://www.youtube.com/watch?v=H6N1IiJTmnc&feature=related

 

 

Arithmetic & geometric series

Arithmetic sequence:

If you take a sequence of numbers, the difference between any two numbers will be constant.

Eg: 2, 4, 6, 8, 10, 12, 14…..

Arithmetic series:

Sum of the above mentioned arithmetic sequence of numbers.

Eg: 2+4+6+8+10

Here is a question for u. How will you calculate the sum of the arithmetic series 2+4+6+8+10?

The formula is s = ((a₁+a_n)/2)*n, where a₁ is the first number, a_n is the last number and n is the number of sequence.

S = ((2+10)/2)*5 = 30

Labview – To read a column from two dimensional array

What if you want to read the second column from the two dimensional array given below. Two for loops – one nested inside will read it. 

Click on the following figure to get a clear view!

What about writing it in c??

 Here is the program.

#include <stdio.h>

int main()

{

int a[3][4];  //allocate space for 2-dimensional array

int i, j, p;

for(j=0;j<3;j++)  // to generate the 2-dimensional table – nested loops

{

for(i=1;i<5;i++)

{

a[j][i]=i;

printf(”%d “, a[j][i]);

}

printf(”\n”);

}

printf(”enter column number: “);  

scanf(”%d”,&p);

for(j=0;j<3;j++)

{

for(i=1;i<5;i++)

{

if (i==p)   // to print the rows in that particular column

{a[j][i]=i;

printf(”%d”, a[j][i]);

}

}

printf(”\n”);

}

}

Doubling Time

The quickest way to remember the doubling time if you know the rate of growth (provided it is constant) is to remember this formula:

T₂ = 70/rate

You can ask me how did I get this. Its simple, just take the use of exponential function.  .7 is nothing but the natural log of 2 to base e.

Example: if you have $10,000 in the bank with a constant rate of growth, say 3%. So, when do you think you could get the double amount?

70/3 = 23.3 years. So, in 23 years whatever you’ve invested will double.

Friction

Supposing you are holding a pen statically. The weight of the pen is acting downward which is opposed equally with an opposite upward force by the friction force (F). The perpendicular force that acts across the surface area of the pen will be the normal force (N). At any given time, the friction force will be the product of the normal force and the coefficient of static friction (µ). i.e., F = N * µ.

If the coefficient of friction is high, like in a rough surface, then the normal force required will be less. If the coefficient of friction is very low, like in silky smooth surface, then the normal force will be high to compensate for the slippage.

To put it in other words, the coefficient of friction will be the ratio of the friction force to the normal force. µ = F/N (parallel force/perpendicular force)

Migration of birds….

It is the winter – The ground is covered with a white carpet of snow. You cannot wander outdoors because of the bone-chilling cold and the freezing water. You sit inside your thermal regulated house, sipping piping hot coffee and lazing around in front of your fireplace. Now tell me, how many of you have wondered about the poor tiny little birds that used to flock your backyards in the spring? Are they still out in the cold or have they gone elsewhere?

Looks like except for a few residential species, most of the birds are vacationing in the warmer south. Can you believe, in North America alone, 5 billion birds annually leave their breeding grounds to go south for winter? So, why do they migrate? It’s for survival – to survive from food scarcity and the harsh winter. Migration is probably the most amazing, inspiring natural phenomenon – Imagine a tiny little bird against the most ferocious elements of nature – it has to overcome the inclement weather, heat exhaustion, fiery wind, and other natural disasters to reach its destination.

Let me show you some of the perilous journeys these birds take. The Arctic terns breed in the arctic summer. They follow the coastline of Africa to reach the Antarctic in November and enjoy the summer there – a total distance of 10,000 miles – they do it twice a year, every year till they perish.

Take the case of barn swallows. Have anyone seen a swallow? It such a teeny-weeny little bird that weighs only a mere 20 g. It nests in the British midlands and go all the way to South Africa, an epic journey of 6000 miles, crossing the formidable Sahara desert that itself stretches around 1000 miles. Of the 5-6 offspring that start the journey, only one will return, a mortality rate of 80%.

Or take the example of bar headed goose. They travel from central Asia to the winter grounds in India – they cross the Himalayas at a height of up to 29,000 feet.

Coming to North America, the tiniest bird that you see in your backyard, the ruby throated humming bird has come from the Yucatan Peninsula crossing the Gulf of Mexico to breed and spend its summer here in the east coast. For that matter, most of the colorful song birds that you see and hear their songs like warblers, thrushes, tanagers, and the birds of prey like hawks, eagles, falcons and ospreys have traveled between 1000 to 8000 miles to breed in the Northern hemisphere. Most of them have wintered in central or south America.

Now that we are in Delaware, can we witness this bird migration first hand? Yes you can. The best place to watch the spring migration of the shore birds is to go to the Delaware Bay in May. Thousands of exhausted shore birds like red knots, sander lings, sandpipers arrive here to feed on the horseshoe crab eggs before continuing their journey to their breeding grounds in the Tundra and Boreal forests of the north.

The best place to watch the fall migration is Cape May. Here you can observe the migratory hawks and millions of songbirds. Here they concentrate in huge flocks to wait for the right weather conditions to cross the Delaware Bay to go south.

Now, next time in spring when you see a colorful bird or hear a heart-rending melodious song, please remember, these tiny little heroes travel thousands of miles every year against all odds just to ‘survive’.

My encounter with elephants….

Before starting my encounter with elephants, let me give you a short introduction about the elephants. Elephants are social animals just like humans. They live in closely knit family groups that are led by the oldest female of the herd. Adult males are rebellious and solitary and associate with the herd only for mating. India holds the largest number of asian elephants – around 25,000, of which southern India is home to around 12,000 elephants. In addition to deforestation, disease and poaching, human-elephant conflict seems to be the most widespread and difficult issue to tackle in elephant conservation. Conflict often occurs when humans move into elephant habitat.

In 2004, when I was working in India, I had a strange request from a scientist friend of mine who works with elephants. He asked me to help him out in ‘elephant census’ in Bannerghatta National Park in southern India about 20 km from Bangalore. So I became a volunteer along with 20 other members for 2 days.

The park spreads around 25, 000 acres. It has hills and valleys with the valley containing moist deciduous forest habitat, while the rest of the park is dominated by dry scrubland and dry deciduous areas. For each of the volunteer 2 forest guards were assigned. I carried a binocular & a camera, while the forest guards carried a small drum, walkie-talkie, the maps, food and water, and two loaded rifles. That was the first time in my life I have actually touched the rifle. I asked naively ‘do u ever use the rifle? for which the foreste guard answered that just one month before a forest guard was trampled by a solitary elephant despite of having a rifle. The gravity of the situation was slowly sinking to me. I got the bottom line message that ‘u don’t take it easy with elephants’.

And so we set off for the elephant census.

The temperature was hovering around in the 90s. We were basically targeting water bodies and ponds where the elephant loves to hang out because of the heat. We were very particular in not going too near them to precipitate an anxiety attack from them. They are highly territorial. Anytime we came across a thick bamboo bush, the guards bellowed loudly at times beating even the drum when they were not quite sure what was lurking behind the bushes. Besides elephants, the Bannerghatta national park is also home to a wide variety of wild animals and reptiles like poisonous snake and scorpions.

We counted atleast five herds for the first day. We photographed the dung, and the footprint of the elephants. It was a productive and tiring day. One of the guards spotted a small honeycomb on our way back and he made a bold attempt to grab it from the few bees that were hovering around it. We plucked few broad leaves and used them as our container while the forest guard poked the honeycomb with a twig to extract the honey. Needless to say, that was the best fresh honey that I’ve ever tasted in my life!!

The next day we were not that lucky to spot a single herd. It was almost late afternoon, when we approached a valley. One of the range guards climbed a tree and spotted a herd at the bottom of the valley, wallowing in a flowing stream. Since we were not sure about the number of elephants in the herd we thought we could approach them a little closer. It was a difficult climb downhill with thorny bushes and no paths. We had to be careful about the reptiles too. After climbing down almost half of the distance one of the rangers told us to pause suddenly. He stood straight straining to catch some sound. There was an eerie silence. All I could hear was the gentle rustling of the trees and the shrubs and my own heavy breathing. Then I realized something was wrong. The ranger guard who was in front of me saw some 5-6 elephants that were coming towards us with their trunks lifted high and were trying to sniff our scents.

Thatz when I saw some 30 feet away a glimpse of a brown mass. I felt rooted to that place just like the tree… and that split second the guard grabbed my hand and started to run down hill on the other direction coz the wind will be in the opposite direction if we run downhill. I don’t know where we had that super human strength. We were bolting like winds and I couldn’t cope up with the speed of the guards where I stumbled and fell twice. That guy never left his grip he just dragged me till we reached the bottom of the valley. It was the mother of all runs. After reaching the valley the forest guard pulled out his rifle and fired a shot in the air. A deafening boom. My knees were shivering and my whole body was covered with dust, bruises and scratches.

By then the guards explained to me that probably that chase was a mock charge because calves were there in the herd. If the elephant were to chase us really they would have got us within no time.

Till this day this incident remains one of the most memorable events in my life….

check this site

Radiocarbon and radiometric dating.

Radio Carbon Dating – Example for Exponential Decay

As cosmic radiation bombards earth’s atmosphere, nitrogen gets split into Carbon 14, an unstable isotope (C14 is called ‘radiocarbon’ because it is radioactive). Now because of lightening and other natural phenomenon, carbon 14 gets into the atmosphere that is taken up readily by the plants through photosynthesis. Now when we eat the plants, it gets deposited in our system. As long as we ingest carbon 14 till we die, the ratio of carbon 14 to carbon 12 remains stable in our body too, just like in the atmosphere. But the minute we die, whatever carbon 14 left in our system starts decaying. The half-life of carbon 14 is 5730 years. I.e., after 5730 years, the carbon 14 would have decayed half the amount when compared to the stable atmospheric ratio of carbon 14 to 12.

OK ….here is a simple problem to solve. In your backyard, when you are digging for your gardening work, you are coming across a mummified body . You are curious and determined that the ‘mummy’ belongs to B.C period. How will you find out the age of that ‘mummy’?

You can use the help of carbon dating to find out the ratio of carbon 14 to carbon 12 that is currently present in the mummified body. Let us presume it was 1.2 х 10 ^–12 grams. Then compare it with the atmospheric ratio of carbon 14 to carbon 12, that is 1.3 х 10 ^–12 grams.

Use the exponential decay formula. Check out the previous blog of exponential function.

A = C e ^kt

Where C is the initial amount, k is the rate of growth, t is the time, and A is the amount after time t.

We know half-life of carbon 14 is 5730 years. We need to find the rate of decay.

0.5 = e ^5730k

5730k = ln (0.5)

k =ln (0.5)/5730

Now substituting in our exponential decay formula, we have,

1.2 х 10 ^–12 = 1.3 х 10 ^–12 e ^{ln (0.5)/5730 t}

1.2 х 10 ^–12/1.3 х 10 ^–12 = e ^{ln (0.5)/5730 t}

ln (1.2 х 10 ^–12/1.3 х 10 ^–12) = ln (0.5)/5730 t

5730 ln (1.2/1.3) / ln 0.5 = t

t = 661. 69 years. So, this mummified body does not belong to B.C period. Nevertheless, it is an interesting 600 years old ‘mummy’.

Here, is a question for you. How long do u think that this radio-carbon dating be used to calculate the age? We know that every 5570 years, the radio-carbon in any given material is halved. So, if we keep computing, by the end of 60,000 years almost all the radio-carbon would have disappeared. So , radio-carbon dating would not be used to date anything that is beyond 60,000 years old!

Argon-argon dating (which has a half-life of  1250 million years) and other isotopes  are used to find the age of the rocks that are millions of years old and from that the age of the dinosaurs are calculated. This process is called as radiometric dating.

Constant Error, Variable Error, Absolute Error and Root Mean Square Error – Labview

Imagine a target where archer A and archer B are trying their luck for a good shot. The following figure is the outcome. Now let us try to figure out who has done the best. Again it depends on what you want to see. The common error measurements are as follows:

 

 

 

 

 

 

 

 

 

 

Constant Error:

 

Constant error measures the deviation from the target. The formula for it is: Σ (xi-T)/N, where T is the target and N is the number of shots. It comes with a positive or negative sign which points out the direction of the error. Absolute constant error will give the absolute value of CE alone without mentioning the direction.

 

Variable Error :

 

Variable error measures the consistency of the shots. It calculates the standard deviation of the total shots. Its formula is sq.root (Σ (xi-M)^2/N, where M is the average shot.

 

Absolute Error:

Absolute error is the overall deviation without considering the direction. In constant error there is a danger of cancellations of error because of direction. However, the error due to bidirection gets eliminated in absolute error. Its formula is Σ absolute ((xi-T)/N).

 

 

 

 

 

 

 

 

So here is a question for you? Among A and B, who is the better archer? Are you bothered about the deviationper se or concerned more about the consistency? I would say bet on archer B than A because he has lesser variablity.

Root Mean Square Error:

 

This measures both the deviation and the consistency of the shots. Its formula is sq.root (Σ (xi-T)2/N).

 

 

 

 

Coefficient of Variation:

It is nothing but standard deviation divided by mean. It gives a clear picture about the deviation. If there are lots of tremors, then the standard deviation increases and so the coefficient of variation.

Check:
Constant Error, Variable Error, Absolute Error & Root Mean Square Error

Ref:

Richard A. Schmidt, Timothy D Lee, (1999. Motor Control and Learning (Third Edition). Human Kinetics.

Click on the image to get a close-up view!

The explanations about all the errors are here. Click the link below.
Measurements of Error

Calculating Earth’s Circumference: Eratosthenus (276-195 B.C)

Eratosthenus was the first person to calculate the earth’s circumference with fair accuracy. It took us another 2500 years to confirm his calculation!

His calculation is very simple and logical. He was intrigued that at Syene, a southern city of Egypt the sun was directly overhead at noon time (which means there were no shadows) on June 21 (summer solstice). At the same time, there was a considerable amount of shadow in Alexandria, a city 800 km from Syene. If earth were to be parallel this cannot be the case. At both places there won’t be a shadow from any pillar or building.

But in reality, in Syene there is not a shadow, but in Alexandria there is a shadow. He thought logically about this problem. He could  conclude that  only if the two places are not parallel that can happen, which means that earth is not flat but is curved or rounded!!!

He applied simple geometry and found the angle of shadow from the pillar to be 7⁰. He extended the angle to the center of the earth which corresponded to 800 kms, the distance between Syene and Alexandria. He then easily calculated the circumference of the earth to be 41, 000 kms which is very true with less than 1% of error!

Imagine he did this feat 2500 years back and it took almost 2000 years for the mankind to re-discover his calculation!