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Enlightening Dark Energy

Well I am back after years as I was busy with my research
After a short talk about Dark Matter, this blog will talk about Dark Energy. 
Lets begin,  I hope all of us agree with the law of inertia. The law states that a body preserves its velocity and direction as long as no force  acts on it (In fact a form of Newton’s first law of motion). This means that once a body entered a state of motion (being at rest is a special case of motion with velocity equal to zero) because of an external force an instant acceleration boosts it to a certain velocity. Now this imparted velocity will not change (increase or decrease) until an unless another external force acts on it. While driving a car when we apply accelerator the velocity increases otherwise it remains uniform (ok I know about friction but lets assume an utopic case at the moment). This basic understanding will be instrumental in understanding the concept of Dark Energy.
Now we go back in time, really back, some 13.8 billion years ago (way too long, I know). Time when the so called Big-Bang happened (I am not talking about Lorre and Pardy sitcom).  The Big-Bang is a the most accepted theory rather say model for the origin of universe. The models depicts the origin universe we know as an outcome of a sudden expansion extremely dense state (of what?) . This sudden expansion is called the Big-Bang. The Big-Bang: mostly described as an explosion provided a force that set the mortars of the explosion into motion. These mortars of the explosion later formed galaxies stars and probably everything that we see (matter) and don’t see (dark matter) around. This motion is explained by the phenomenon of red shift in galaxies (many other proofs available). 
Now since the Big-Bang is the only known cause of setting motion in the known universe, this motion should have a uniform velocity. But we have gravity, coming from Newton’s apple. The gravitational energy is an attractive force. If we consider gravity in our case it should pull the above mentioned mortars of Big-Bang towards the centre of the explosion thus causing a deceleration (slow-down). So the galaxies should nevertheless move either with a uniform velocity (if gravitational force is negligible) or slow down their motion. Illustrating again with our car example the initial boost of acceleration (engines power, counterpart of Big-Bang) is impeded by the friction (a counterpart of gravity here)
But the real picture is somewhat different. The motion is neither uniform nor slowing down. This is actually accelerating. This mean the speed at which galaxies are moving away from each other with increasing velocities. Isn’t that intriguing? What is causing this acceleration? There has to be a force to provide this acceleration (the accelerator in car) and for a force there has to be some form of energy. Scientists call this energy the Dark Energy. Dark because we do not know about it. 
With this basic idea of Dark Energy, I close the session. In my next blog I will bring about the computational approach to study this form of Energy; the Dark Energy. It could be the energy of Darth Vader ;) 
cheers,
Fig1DMsim

Unveiling the dark matter: Computational methods

In continuation of previous blog The darkness of the ‘Dark Matter’


Here I discuss some computational physics methods that may sound interesting to you, in terms of dark matter understating and discovery. Though this should involve a lot of alien kind of equations, I try to minimize their use in the current story. 

Cosmologists and physicists are hunting together for the elusive dark matter thought to pervade in the universe. How do you think they look for something that cannot  be seen? How do they model the effect of something they cannot percieve ordinarily? Let us start with a simple illustration. Imagine a heavier body and two lighter one revolving around the former in an elliptical orbit. On applying newtonian mechanics operating therein we can calculate the forces acting at an instant and also the orbital motion. Here we need to update the forces operating, with the changes in distances during their motion.  The calculation is simple as of now, but if we include more bodies, calculations get complicated. To make it appear closer to a galaxy make the centre heavier and the structure an non planar one together with an increase in density on moving towards the centre from the edge.

Such model can be implemented as a computer program and simulated to analyze the motion and evolution of galaxy over time. Ostriker and Pebbles tried such simulation called ‘N-body simulation’ in 1979. They tried to compute all the interacting forces and motion in a model consisting of mass points structured like a galaxy. They astonishingly found that such a system tends to a collapses to a bar shaped dense core in the galaxy model. But in such simulation, if a uniformly distributed mass is added in certain amount, the galactic model tends to show more stability depending on the mass added. This mathematically proves that there is some hidden mass in the galaxy accounting for the shape we observe an also gives an estimate for their mass. However, such simulation have evolved a lot from their ancestors with advent of technology and knowledge. (For those who are interested a possible pseudocode is in figure 1a)


Figure 1a (Left) showing a basic pseudocode for N-body simulation and on right showing the expected velocities (A) and actual velocities (B) at distances from the centre of the galaxy.

There are other computational method which further give the proof in favor of dark matter, but discussing all these will be beyond the scope of this story. Now lets talk about the modeling such dark matter. Modeling gives a better understanding of behavior, nature and interaction of dark matter.  There are few theories about the dark matter viz. cold dark matter, hot dark matter and warm dark matter as mentioned in the previous blog. Taking up the case of cold dark matter the particles move at a slow speed. The slow speed allows the individual galaxies to clump together, whereas in case of hot dark matter the high speed of particles fails to explain the theory of galactic formation. The obvious question that can come to you is why? The reason is very simple. The particles in hot dark matter are ultralight and therefore do not come up with enough gravitational force to explain the formation of galaxies. The cold dark matter on the other hand talks about heavier particles that can explain the the unexplained ones.

To model this, the N-body simulation can be extended with the particle velocity and mass parameters. Thus in our N-body simulations we consider the relative mass of particles that we uniformly add to our galactic system. To simulate a cold dark matter system we add heavier particles and for hot dark matter we add lighter particles. We also consider the velocities of the particles here and run the simulation. The simulation will show how the bodies in the system clump together. This simulation has been tried by many physicist. The model at the University of Illinois, consisted of hot dark matter, cold dark matter and baryons (a mixed model). This model seemed to match the observed distribution, both in terms of temperature and luminosity. But there are numerous possibilities the work still on to model the dark matter.

* I do not mention the bibliographic references here in the blog just to make it shorter, it can be provided if needed. 
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The darkness of the ‘Dark Matter’

Here I talk about a story from my favorite Domain “Physics” (No computation this time but the next blog will relate this story to Computational Physics)


Image Source: http://planetquest.jpl.nasa.gov/news/darkMatterPie_image.html


Although they partially share the names, dark energy and dark matter are otherwise different. The former is a force that makes the universe expand at an increasing speed while, later is a type of matter that outweighs ordinary stars and galaxies 5 to 1 (see Figure above). The dark energy is named so because we hardly know about and the dark matter is dark as it is utterly invisible. We know it’s there because its gravity pulls galaxies and stars around, but it neither emits nor reflects any light. The concept of Dark Energy won the Nobel recently. Well my current story on dark matter is not an advocacy for the nobel committee rather an attempt to tell you something about it. In the next blog I would bring out the how scientific computing is used or can be used for related research. 

For the historical facts regarding previous research and history of discovery I would recommend to look at the wiki page for dark matter as I would like to keep the story close to the scientific analysis. Lets start with a simple question why does matter or better say two bodies separate. If you know about Newton laws of gravity you would come with with the answer that says because the force of attraction acting between two bodies is not enough to hold them together. You are right. So if they expand the force of attraction should get even smaller as the distance has increased. Well done. So we conclude that the masses of the bodies in the universe are somehow important. Great, now I put the same question in a different way.


In terms of orbital motion. Will there be a difference in the orbital velocity of a body orbiting close to the orbital center and the body far from the centre? From what we saw till now the answer should be yes. The body closer to the orbital centre should have a higher speed of revolution as compared to the body far from the orbital centre (Kepler’s 3rd Law). This should happen because the acting force on the orbiting body differs with the distance to the orbital centre. Here is the catch, in the galaxies observed so far, that goes against. The orbital speed at the edge of galaxies is not very different from those at the centre. This made people pause and ponder, looking for a possible explanation. So if our knowledge about physics of motion is correct there should be something around that makes this uniform speed at different distances possible. If there is some distributed matter that compensates for this loss in gravity and makes the orbital speed almost uniform across the galactic radii, it would explain the deviation of our observation from expectation. 

Let’s talk about another unusual phenomenon. When you see an object, light from the object comes to you which produce undistorted image given there in nothing deviating this light between the object and the observer. Now if we place a glass piece (slab, curved or spherical) between the object and observer we get a distorted image of the object. This distortion will depend on the shape of the glass object. This phenomenon has been observed with some of the galactic clusters rendering their distorted image. So we should expect some sort of glass piece between us and those clusters. But there can be other things than glass that produce similar effects, e.g. gravity. With gravity acting as a lens the phenomenon is called “Gravitational Lensing”. The observed images have suggest for a clustered object between the light source and the observers (us). 

This somehow gives us a clue that there is something in the universe that is there in abundance but we cant really see that. This gives rise to the concept of “Dark Matter”. There are some other proposed evidences in favor of their existence, but I prefer not to get into further details, rather we try try to see what really is (or can be) dark matter. Answering this question is somewhat difficult but let me try. 

As of our current knowledge, dark matter:
>> Has gravitational effect
>> Does not interact with light
>> Does not emit light
>> They should be enough in amount to account for our observation
>> They should be retained within galaxy (else they wold escape the galaxies and our observations will be different)

Based on this we take a look at the ordinary matter or known bodies as possible candidates for constituting dark matter. For most of the heavier hidden objects like MACHOs their estimated amount is not enough to be considered absolute for dark matter. The sub-atomic candidate ‘neutrino’ for this has a speed enough to escape galaxies gravitational pull. So dark matter can consist of a completely new kind of matter (or particle) or some known matter (or matter) in unknown state. 

As per our current hypothesis dark matter particles interact with each other only through gravity, moving past each other without collision. Thus there can be numerous dark matter particles around us (even within). A class of hypothetical (rather unknown) particle called WIMPs (Weakly Interacting Massive Particles) is another candidate for constituting the dark matter. But all these are just candidates, yet to be proved and established. Scientist are setting traps to capture and know more about the dark matter but it is yet to be realized. There are theories about cold, warm and hot dark matter based on their speeds (slow, relativistic, fast). But just the theories and at times, competing theories. Currently, the cold dark matter forms the more accepted theory than other candidates and is more agreed upon with our observation. It explains the galactic phenomenon like large structure formation (accumulation of matter) but there are arguments against it as well.

Detecting and understanding physics at this level is complicated. Analyzing data for related experiments is tedious and challenging. In the continuation of this story I will try to bring out the role of computation, algorithms and methods for such studies.


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Steve Jobs; ‘i’ Remembering an innovative genius

It took a genius and an apple to change the way people thought how gravity works back in the 17th century. Again in 21st century a genius and an “Apple” changed the way tech-business works.  The difference is in former case the apple falls and in the later case it kept ascending to new heights with every innovation.
The Beetle fan said “My model for business is The Beatles: They were four guys that kept each other’s negative tendencies in check; they balanced each other. And the total was greater than the sum of the parts. Great things in business are not done by one person, they are done by a team of people”
You will be missed Steve not just by Apple;  the Inc. but by Apple; the community

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Scientific Computing: Let’s get in

Human beings have ever been on a journey to unfold the mysteries of the world, outward and inward. It is an unquenchable thirst and this journey has been ever since the appearance of life on this planet. Inventing fire, wheel, agriculture, weapons in pre-historics and understanding the universe, life and human genome in our recent times; all have been different attempts to fathom the potential of human mystery. With the advent of computer technology and development in the area of mathematics and statistics solving such mystery got easier and faster. Scientific computing deals with the design and analysis of algorithms for numerically or mathematically solving problems in science and engineering. It is an interdisciplinary domain and encompasses applications in science/engineering, applied mathematics, numerical analysis, and computer science (Figure 1). 
 
Figure 1: Scientific Computing as an interdisciplinary domain. 
(Picture Modified from: http://www.siam.org/students/resources/report.php)
 
 
Thus it uses mathematical or statistical methods through a computer to apply them to solve scientific problems, usually by generating mathematical model, numerical analysis or simulations. These computer models and simulations have become an important part of the research repertoire, supplementing or replacing experimentation. 
 
The area has developed a lot in recent years and consists of various applications, few to be listed are: Bioinformatics, Computational Engineering,  Computational Physics, Machine Learning, Pattern recognition and so on. This blog will focus on these aspects of Computational Science which is another name for Scientific Computing by some people.