Sunday, 12 May 2013

Antimatter and CERN's Large Hadron Collider- You've probably heard of it

If you watch a lot of the popular sitcom, 'The Big Bang Theory' or if you're a big science nerd like me, you've probably heard about these terms, but failed to understand. Let's see if I can be of any help :)

So, lets start with the most popular physics equation, E=mc².It basically says that mass is concentrated energy and mass and energy are interchangeable, kind of like two currencies but with a huge exchange rate. 90 trillion joules of energy is equivalent to 1g of standard mass. If we concentrate huge amounts of energy in a tiny space, new particles will come into existence. If we look closer we see that these particles always come in pairs, like twins. That's because particles( each and every one of them) always have their counterpart an 'antiparticle' and these are always produced in exactly equal amounts (1:1 ratio). This might sound like science fiction, but it's actually true and is the daily life at particle accelerators, CERN LHC  (We'll discuss that soon). 
                                       In the collisions between two protons between CERN's LHC, billions of particles and antiparticles are produced every second. Consider for example the electron. It has a very small mass ( in physics we call it infinitely small)  and a negative charge. It's anti particle, the positron has exactly the same mass but an opposite positive charge. But apart from the opposite charges, both particles are identical and perfectly stable. And the same is true for the heavy cousins, the proton and the anti-proton. Therefore, scientists are convinced that a world made of antimatter would look, feel and smell just like our world. In this anti-world, we might find anti-water, anti-gold, anti-food and maybe anti-you & me! 
                                                                                                                                Now imagine a matter and an antimatter particle are brought together. These two apparently if are in contact, would completely disappear into a big flash of energy, equivalent to an atomic bomb! Because combining matter and antimatter would create so much energy that it can run future spaceships like in Star Wars, cause energy content of antimatter is a billion times more than the conventional fuel. The energy of 1g of antimatter would be enough to put a rocket in our orbit. So why not use antimatter in energy production? Well, antimatter isn't just sitting around. We have to make antimatter before we can combust it. 

And creating antimatter takes a billion times more energy to make antimatter than you get back. So some of us might say that why don't we just dig some antimatter from the space? A few decades ago, many scientists believed that this might be possible. But today, observations have shown that there is no significant amounts of antimatter out there, which is weird cause it was already established that there should be equal amounts of matter and antimatter. Now that is a real mystery. To understand this better, let us go back to the Big Bang.
                                                                                                                                                               The Big Bang suggests that the universe was created in an instant as huge amounts of energy transformed into  mass, and our initial universe contained equal amounts of matter and antimatter. But just a second latter, most  of the matter and all of the antimatter had destroyed one another producing enormous amounts of energy in forms of radiation, that can be still observed today. Now you might say,"Where the hell did all that antimatter  disappear and only matter was left? It seems that we were somehow lucky that there existed a tiny amount of asymmetry between few of the matter and antimatter particles which when collided, matter won and was left.   Hadn't been so, there would no matter at all, and obviously you wouldn't be able to read this right now cause you don't exist. But what causes this asymmetry? This is one of the biggest mysteries of the universe ( Baryogenesis- for which the  the CERN LHC was created.  

                                                  CERN, or the Conseil Européen pour la Recherche Nucléaire  is actually the worlds largest physics laboratory located at Geneva, Switzerland. The 'LHC' stands for the Large Hadron Collider. It basically a particle accelerator, and serves as Mecca to all the physicists around the world. The whole setup is actually of a circle, 27 kilometers in circumference! What it does is pretty neat.
           Hydrogen atoms from a gas cylinder are fed at a precisely controlled rate into the source chamber of the LHC, from where their electrons are stripped off leaving only the protons, or the hydrogen nuclei. These protons are then accelerated using an electric field. This acceleration from the external electric field has caused the protons to attain the speed of a rocket. The packet of protons then slowly reach 1/3rd the speed of light and enters a booster which is another small part-circle(157 m in circumference) of the LHC circle which increases the speed of the photons to 91.6 % of the speed of light and squeezes them closer together , using powerful magnets and electric fields. From there, it enters into another part-circle of the LHC called the proton synchrotron. Let us follow two such protons. Proton is 627m in circumference and they circulate for 1.2 seconds, reaching about 99.9% of the velocity of light. It's here that a point of transition is reached (this is crucial), a point where the energy added to the protons by the electric field cannot increase the velocity of the protons, cause they are already reaching the limiting speed of light(which is maximum). Instead the added energy increases the mass of the protons. In short, the protons can't go faster so they get heavier. At this point, the energy of each proton is measured as 'electronVolts' and is 25 giga eV. The protons now become 25 times heavier then they are at rest. 

The LHC. Notice the small Proton Synchroton(PS)
The protons are now transferred to the main orbit of the Large Hadron Collider, circumference of 27 kilometers. There are two vacuum pipes in the LHC, containing the proton beams travelling in opposite directions, clockwise and anticlockwise. For half an hour, the PS keeps transferring protons in the LHC. The velocity of the protons is now so high, that it goes round the 27 km circumference, over 11,000 times per second, becoming 7000 times heavier than at rest. The magnetic force needed to bend the protons in the right circular direction of the orbit is so high that the entire LHC is kept colder than the outer space so that the elector magnets present inside the circular tubes become superconducting.
                                                                                                                     Now the protons are made to collide. The collisions emit matter and antimatter particles similar to that of the big bang and the asymmetry is studied. This is the CERN LHC. 

                                                         This took a lot of effort
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Thursday, 9 May 2013

CALCULUS !! Backbone of Higher Mathematics

In day to day life we are often interested in the extent to which a change in one quantity aects a change in another related quantity. This is called a rate of change. For example, if you own a motor car you might be interested in how much a change in the amount of fuel used aects how far you have traveled  This rate of change is called fuel consumption. If your car has high fuel consumption then a large change in the amount of fuel in your tank is accompanied by a small change in the distance you have traveled  Sprinters are interested in how a change in time is related to a change in their position. This rate of change is called velocity. Other rates of change may not have special names like fuel consumption or velocity, but are nonetheless important.
Thus in layman’s language Calculus is the mathematical study of change,[1] in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations.
Origins of Calculus-                                             
The discovery of calculus is often attributed to two men, Isaac Newton and Gottfried Leibniz, who independently developed its foundations. Although they both were instrumental in its creation, they thought of the fundamental concepts in very different ways. While Newton considered variables changing with time, Leibniz thought of the variables x and y as ranging over sequences of infinitely close values. He introduced dx and dy as differences between successive values of these sequences. Leibniz knew that dy/dx gives the tangent but he did not use it as a defining property. On the other hand, Newton used quantities x' and y', which were finite quantities, to compute the tangent. Of course neither Leibniz nor Newton thought in terms of functions, but both always thought in terms of graphs. For Newton the calculus was geometrical while Leibniz took it towards analysis.
The development of Calculus can roughly be described along a timeline which goes through three periods: Anticipation, Development, and Rigorization. In the Anticipation stage techniques were being used by mathematicians that involved infinite processes to find areas under curves or maximize certain quantities. In the Development stage Newton and Leibniz created the foundations of Calculus and brought all of these techniques together under the umbrella of the derivative and integral. However, their methods were not always logically sound, and it took mathematicians a long time during the Rigorization stage to justify them and put Calculus on a sound mathematical foundation.
Applications of Calculus-
You can look at differential calculus as the mathematics of motion and change. Integral calculus covers the accumulation of quantities, such as areas under a curve. The two ideas work inversely together.
 Calculus is deeply integrated in every branch of the physical sciences, such as physics and biology. It is found in computer science, statistics, and engineering; in economics, business, and medicine. Modern developments such as architecture, aviation, and other technologies all make use of what calculus can offer.

Finding the Slope of a Curve
Calculus can give us a generalized method of finding the slope of a curve. The slope of a line is fairly elementary, using some basic algebra it can be found. Although when we are dealing with a curve it is a different story. Calculus allows us to find out how steeply a curve will tilt at any given time. This can be very useful in any area of study.

Calculating the Area of Any Shape
Although we do have standard methods to calculate the area of some shapes, calculus allows us to do much more. Trying to find the area on a shape like this would be very difficult if it wasn't for calculus.

Calculating Complicated X-intercepts
Without an idea like the Intermediate Value Theorem it would be exceptionally hard to find or even know that a root existed in some functions. Using Newton’s Method you can also calculate an irrational root to any degree of accuracy, something your calculator would not be able to tell you if it wasn't for calculus.

Visualizing Graphs
Using calculus you can practically graph any function or equation you would like. In fact you can find out the maximum and minimum values, where it increases and decreases and much more without even graphing a point, all using calculus.

Finding the Average of a Function
A function can represent many things. One example is the path of an airplane. Using calculus you can calculate its average cruising altitude, velocity and acceleration. Same goes for a car, bus, or anything else that moves along a path. Now what would you do without a speedometer on your car?

Calculating Optimal Values
By using the optimization of functions in just a few steps you can answer very practical and useful questions such as: “You have square piece of cardboard, with sides 1 meter in length. Using that piece of card board, you can make a box, what are the dimensions of a box containing the maximal volume?” These types of problems are a wonderful result of what calculus can do for us.

- Ishan Arora ( Childhood friend ) 

Saturday, 4 May 2013

What up with DNA?

You don't exactly know what DNA is!

So what is DNA, and how does it work?

 DNA, also know as DeoxyRiboNucleic Acid is a molecule. It's a bunch of atoms, stuck together. In the case these bunch of atoms combine to form the shape of a long spiraling ladder . Sort of like this one here. If you've ever studied biology or saw the movie Jurassic Park, you've probably heard , "DNA acts as a blueprint or a recipe for a living thing". But how? How on earth can a mere molecule act as a blueprint for something as beautiful and complex as tree, dog or a dinosaur?  

To answer that question, let's first take a quick look at amino acids. Amino acids are tiny little chemicals inside our bodies which are so important, they are often referred to as the building blocks of life.  

Aspartic Acid (Amino Acid)
Glutamic Acid derivative (Amino Acid)

There's about 20 different kinds of  amino acids, each with there own unique shape. The neat thing about them is that they can be attached to each other ( kinda' like lego's) , to produce an endless variety of larger particles called 'Proteins'. So, amino acids make up proteins. Proteins, along with other chemicals make up living cells. Cells make up tissues.Tissues make up organs. And organs, when they are all put together and functioning, make up living creatures like you and me!

These proteins which make up our bodies, keeping in mind that there are millions of different kinds of them,  they each have to be formed in a perfect shape, in order to function. If they are in the wrong shape, they most likely won't function. That's where DNA comes in.
                                                                                      DNA does a lot of interesting things, some of which we don't fully understand. But one of it's main and well understood functions is to tell amino acids how to line up and form themselves to the perfect protein shape. In theory, if the right proteins are built at the right time and in the right place, everything else from cells to organs and to the creatures will come out just fine.

This here is a simplified model of DNA. It shows us that the steps of a ladder(DNA) are made up of 4 different kinds of chemicals by different colours. If we look at just one half (or one strand) of the model, we can read it's chemical sequence or genetic code from top to bottom, sort of like a book. A single strand of DNA is extremely long. Millions of letters long. It spends most of its coiled up like a noodle of a nucleus of a cell. To help DNA interact with the cytoplasm or the remaining part of the cell other than the nucleus, it converts amino acids (present in the cytoplasm) into proteins. Special chemicals inside the nucleus make 'partial copies' of the DNA code called RNA. These RNA look a lot like DNA but they are shorter and contain only one strand. They are small in shape and this allows them to fit through the tiny pores in the nucleus, from where it goes to the cytoplasm and then into the mouth of another cellular 'organelle' called ribosome. 

Ribosome's are the protein building machines.  They read the RNA code 3 letters at a time, suck amino acids out of their surroundings and stick the newly formed proteins in a chain, according to the RNA code. As the chain grows, it bends and folds and sticks to itself to form a perfectly shaped protein. Every 3 letters of the RNA code tells the ribosome which of the twenty different kinds of should be added next to form a protein.

Once the protein is built, it can then go on to do a number of different things like forming a brand new cell. Then tissue, organ and so on. So the answer to previous question, "What is DNA?". DNA is a molecular blueprint for a living thing. 

This is DNA people.

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