NERD - Research

Let’s talk Physics…

2017-04-18T00:00:00+05:30

In an attempt to know better about the research work done by professors at IITK, the NERD team decided to talk to them about their fields of research, requesting them to throw some light on the topics they work with. We decided to start with the Physics Department, where we met with Assistant Prof. Arjun Bagchi. Prof. Bagchi specializes in String Theory, Theoretical High Energy Physics and the Holographic Principle. He has been a Fulbright Fellow at Massachusetts Institute of Technology, DST Inspire Faculty at IISER Pune, Lise Meitner Fellow at Vienna University and a Postdoctoral Research Fellow at the University of Edinburgh, UK. He agreed to talk to us about String Theory in Layman terms and discuss various aspects of the theory.

Prof. Bagchi: So, what do you want to know about the string theory?

NERD: We all have heard about the String Theory and have tried to read about it on the internet, but the main problem faced by students is the lack of clarity in the way information is available. We’re hoping that you might be able to explain the theory in simple terms.

Prof. Bagchi: While it’s pretty difficult to understand the complete theory at the Undergraduate level, we can still try and understand this theory from the basics. So, starting from scratch, there exist FOUR FUNDAMENTAL FORCES in nature. These are Electromagnetic Forces, Weak Nuclear Forces (responsible for Beta Decay, etc.), Strong Nuclear Forces (Strongest of all forces, responsible for keeping the nucleus together) and Gravitational Forces.

Now, strange it may seem, although we’ve known gravity ever since the apple fell on Newton’s head, it’s still the least understood of all the forces. So, what is it that we do not know?

The thing is that in order to understand these forces completely, we need to look at them at very small length scales. At small length scales, Quantum Mechanics comes into play. We have a theory known as Quantum Electrodynamics QED) that explains how Quantum Mechanics and Electrodynamics work together. QED is the most successful theory that we know. To give an example, there is a physical quantity in Electrodynamics called the magnetic moment, say of the electron, with a classical value of 2. When Quantum Mechanical effects are taken into account, this value increases to just over 2 (2.00115965218). The experimental value matches with the theoretical prediction to 12 decimal places.

There is a framework called Quantum Field Theory, which is used to explain all the remaining forces except Gravity. It so happens is that this framework fails for Gravitational Forces.

To explain why this happens, let’s go back to Quantum Field Theory. For example, two electrons are thrown at rach other and probabilities for various events are calculated. Since this is Quantum Mechanics we’re talking about, the probability of getting back two electrons might not necessarily be one, we may even get other particles like muons. So, after detailed calculations, it was seen that probabilities for certain events (when considering the number of ways it could happen through Feynman's Diagrams) come out to be infinite. Initially, Quantum Field Theory was considered inconsistent because of these infinities. However, eventually we found a way to make sense out of these infinities. With the mechanisms used to remove these infinities, we came across two types of infinities - removable and unremovable infinities.

In QED, these infinities can be removed and we have made amazing strides here by matching with experiments, as I just mentioned. But, there are some theories where these infinite probabilities are not removable. . These theories are sick theories i.e. those things do not have any physical significance. Gravity turned out to be a sick theory. This means that the language and mechanisms of the quantum field theory doesn't work on gravity. This poses a serious question on the quantum field theory because you cannot dismiss Gravity as a sick theory - it actually exists. So, we need to develop a new theory to give a quantum mechanical picture of gravity. That’s when String Theory comes into picture.

A term which is quite repeatedly coined around is “ The Theory of Everything ” i.e. a theory which seeks to explain all the four fundamental forces completely. String theory promises to be a Theory of Everything.

So, What is String Theory? Ever since we’ve studied Newton’s Laws, we’ve always treated objects to be constituted of point particles. All theories are based on this assumption. What String Theory does is that it rejects the notion of point particles and claims that fundamental particles are composed of extended one-dimensional objects i.e. tiny vibrating strings. These strings are so small that you can’t actually see them, that’s why they look like point particles to us. For e.g. If I take a piece of paper and fold it a lot of times. If your eyes are unable to resolve it, you’ll view it as a point particle. So, it depends upon the equipments used, whether or not you can see the dimensions of an object. To give you an estimate about how small a string is, consider measuring the distance between the Earth and Moon in terms of safety pins. Similar number of strings span a typical atom. In short, these strings are very very short. Now like in classical waves, we have modes of vibration. For e.g.. Fundamental, First Overtone, etc. Similarly in String Theory, each mode of these string forms a new particle.

This is what String Theory tells us.

In String Theory, we use Special Theory of Relativity and Quantum Mechanics together as inputs, and we end up with a class of massless particles with spin 2. Clarifying the above part, we know that the quanta of an Electromagnetic field is a photon, which is a massless particle with spin 1. Similarly, if we try to quantize general relativity, the quanta we find is a massless particle of spin 2. So by considering strings instead of point particles, we end up with a theory of quantum gravity. Do we still get those nasty infinities we talked about earlier? No! The interesting thing is that when we apply String theory on the above process i.e. consider matter to be composed of strings and doing calculations, we get the same result without the infinities. String Theory is a very constrained theory, in the sense that you don’t have enough room to play around. These strings have predefined criteria defining the dimension in which they exist, they can’t exist in any arbitrary dimension. You may have heard about Bosons (particles like the photon) and Fermions(particles like electrons). To have a theory for Bosons, the String theory will be consistent only in 26 dimensions while in the case of Fermions, Superstring Theory is used which is consistent in 10 dimensions. The world we live in has four dimensions, three space dimensions and one time dimension. So how can we deal with something which has nine space dimensions?

For that, let's look at a piece of paper. The paper spans two dimensions if we ignore its width. Now if we roll this sheet to make a cylinder, it still is in two dimensions if we look from the front. Now if we keep rolling the sheet to a point that it looks approximately like a single line when seen from the front, we’ve basically curled up two dimensions into one. Same is proposed in the String Theory is that the other space dimensions are curled up into three. They are there but we can’t see them.

This idea is good but the problem faced by String Theory here is that in ten dimensions, the theory is unique. But there are innumerable consistent ways to get down from ten dimensions to four dimensions. So, in four dimensions there are a wide variety of possibilities, ie… you do not have a single real world. The main problem with this theory is that we do not have a unique path down from multiple dimensions. So a lot of work is yet to be done in this regard. However, if we look at the frameworks trying to link quantum mechanics and gravity, String Theory stands out for being able to give significant results and insights both in Physics and Mathematics. But we’re very far away from any experiments. One should have a reality check; even though this theory has given some exciting ideas, we are very far from claiming that this is the actual theory of nature. But it really is beautiful.

NERD: Sir, you said that dimensions are curled up in string. Is it theoretically possible to extract those dimensions?

Prof. Bagchi: Yeah, theoretically it is possible. Doing some maths will give you the idea about the dimensions but we don’t have any physical experiments to back this. People are actually trying to find more about this in experiments like Large Hadron Collider. But at the moment, if you ask me, experimental verifications are very far away.

NERD: So, what does this theory hold for us? What if we DO find experimental verification for the String Theory? Prof. Bagchi: Then we’ve quantized gravity! We’ll have a framework which helps us deal with all four forces at one go. This is why people are so very excited with it. If this really comes out to be true, we may be able to find out what actually happened at the time of Big Bang, what happens inside the black hole and various such very interesting questions. A lot of things which seem very difficult to deal with may get easier to understand.

NERD: Thank you for your time Sir. It was quite an experience talking to you!

Taming the Ocean at MIT

2016-03-29T00:00:00+05:30

Through this article, I would like to share my research experience and activities of the MSEAS-Multidisciplinary Simulation and Assimilation Systems research group belonging to one of the most prestigious universities, The Massachusetts Institute of Technology. The laws of physics rule our every action and the oceanic ecosystems are no different. Now, as we know that the oceans are bounded by the laws of physics, so can we delve deeper and devise new means to explore, develop and utilize the possibilities?

It was summer 2014 and I received an opportunity to learn from an extremely enthusiastic group of researchers led by Prof. Pierre Lermusiaux at the Department of Mechanical Engineering, Massachusetts Institute of Technology. Oceans are unpredictable, and this is what motivates Prof. Lermusiaux towards all of his research. Conditions at sea have long influenced human activities, from exploration to commerce, fisheries, tourism and even wars. Combining the power of ‘Computational Fluid Mechanics’ with probabilistic modelling, he develops models and assimilation schemes to better predict ocean behavior for a wide range of applications — from planning the most efficient paths for underwater robots, to predicting phytoplankton blooms.

Path planning for robots has been vastly studied in literature, but Prof. Lermusiaux’s research is quite unique. He along with his team of graduate students develops algorithms introducing the uncertainty of the ocean to achieve time and energy optimal path planning for Autonomous Underwater Vehicles (AUVs). The surrounding medium of travel for an AUV is the ocean, a highly dynamic and multi-scaled system with a considerable variability in both time and space. Hence utilizing the dynamic ocean currents to ones benefit, is a great challenge. AUVs in certain cases may choose to ride an ocean current, in order to save energy. However on other hand, there may be forbidden regions due to safety, hazardous conditions, security or naval considerations which the AUV is required to avoid during its course. Making the AUVs intelligent enough to take such decisions, is what the novel algorithms developed by MSEAS do. Such AUVs can be used for seafloor mapping, commercial exploration, military reconnaissance and coastline protection or maybe finding the supposedly drowned Malaysian Airline MH370, who knows!

Next major focus area of MSEAS is Data Assimilation (DA). The ocean physics involves a multitude of phenomena occurring on multiple scales, from molecular dissipation process scales to tsunamis. Oceanic processes cover a wide range of space scales, from about 1 mm to 10,000 km, and of time scales ranging from about 1 s to 100 years and even more (Lermusiaux, 2006). Hence, a reliable modelling scheme becomes an increasing difficult task to accomplish due to practical simplifications, inexact representations or parameterizations and numerical limitations. Or if we try to be totally dependent on ocean data measurements made from ships, aircrafts, underwater vehicles or platforms at sea etc., then the problem demanding consideration is that, such data are limited in time and space. So, there is an inevitable need to combine these various sources of data and different dynamical models, and where finally DA comes to the rescue. Even with all these, the measurements from the oceans have high uncertainties which needs to be taken care of.

My own project dealt with modelling of Nutrients, Phytoplankton and Zooplankton (NPZ) in idealized ocean banks, called Coupled Ocean Biological-Physical Dynamics. There exist mathematical models which can model NPZ systems based on the amount of sunlight available, death rate, regeneration, etc. But these are highly dependent on the values of parameters involved or the complexity of the model. Moreover, the uncertainty of the physics involved (i.e. initial conditions of our simulations or Reynolds number of the flow, etc.) also affects the evolution of NPZ variables over time. To deal with these kinds of problems, we employ stochastically dynamic models. These models can deal with the uncertain initial conditions represented by probability distribution functions, can evolve them over time, and update them based on observations to reduce the uncertainty in the system. For example, we may start with a number of biological models with different parameters, run our simulations, and then use real life observations from the oceans of the NPZ concentrations, to make Bayesian updates and finally tell which model or parameters best describe the real life situation. These kind of studies help us better predict processes like upwelling and hence tell our fisherman where to find fishes.

Learning from this group and contributing to this cause was one of the phenomenal turnovers in my life. Prof. Lermusiaux very actively collaborate with researchers from different institutions all over the globe. And when asked about his take on international internships, he said “Such exchanges are fundamental for the understanding of nations and their people, allowing to make scientific and engineering contributions without borders”. I would also hereby like to thank S. N. Bose Scholars Program 2014, for funding my internship and for all the good memories, I had with this really awesome research group. As I headed back home they are still cultivating ideas for the future, making our lives better and more secured.

For more information, please visit mseas.mit.edu

References

Lermusiaux P. F. J., Uncertainty estimation and prediction for interdisciplinary ocean dynamics, Journal of Computational Physics 217 (2006) 176–199

Transformer

2016-03-29T00:00:00+05:30

When we think of a robot the image that springs to mind is that of a multi limbed machine that performs a variety of tasks with human dexterity and superhuman efficiency. The project Transformer was motivated by this image.

Transformer is a project completed in summer camp ’14 under robotics club IIT Kanpur. The project has been undertaken by four BTech students of Y13. The team members are Ayush Poddar, Harshit Lathi, Anirban Manna and Yugesh Kuma.

The main objective of this project was to make a robot which performs multitasking like overcoming a passage, climbing stairs, ascending sloped surfaces and also challenging rough surfaces. It is a kind of all – terrain robot meant to detect surfaces and switching its mode to accustom to that particular type of terrain.

The robot is four limbed, each leg is an assembly of four servo motors connected through brackets. It is fixed to the chassis on one end and has a wheel mounted on a dc motor on the other end.

A servomotor is a rotary actuator that allows for precise control of angular position, velocity and acceleration. It consists of a suitable motor coupled to a sensor for position feedback. Its angle can be set as desired and can be controlled through a microcontroller.

Arduino mega has been encorporated as the 3.3.microcontroller in this project.

Arduino is an open-source electronics prototyping platform based on flexible, easy-to-use hardware and software. The software consists of a standard programming language compiler and the boot loader that runs on the board.The microcontroller on the board is programmed using the Arduino programming language

A 7.4 V, 3300 mAh Li-Po battery is used to power the robot, voltage regulators were used to supply a constant voltage of 6v to the servo motors (the voltage required for their proper functioning) against the 7.4v provided by the battery.The voltage regulator used here is 7806,which comes under a family of 78XX type of voltage regulators.

The four motors attached to the last servo of each legs are driven by motor drivers. Its main function is to amplify the current given by arduino to the rated current of the motors.The current which can be drawn out from the arduino is very small (order of milli – amps) hence there exists a need to amplify the currents upto the order of 1 amps for the motors to work properly. Motor driver is comprised of ICs. They also protect the circuit against short – circuiting and overheating.

All the above mentioned circuit elements are mounted on a GPB () which is to the chassis.the chassis is made of wooden ply coated with glass fiber.

The robot is programmed using the Arduino software and then controlled by a serial monitor (putty is used in this project) and the serial communication is done through a Bluetooth module which is a part of the circuit.

Before starting the assembly of the components a design is made with the help of auto-desk inventor and the circuit diagram is planned

WORKING

Command is given from laptop through a serial monitor to the robot there are commands to control individual components (servos,motors) as well as to perform a group of tasks such as reducing the level of the robot,crawling as a whole without controlling individual components.

When encountering a passage a command is given which performs specific movements and reduces its height.Next command drives all the motors forward hence crossing the passage.

When a slope is encountered the robot again reduces its height and moves forward towards the slope and ascends it. Ascending slopes upto an angle of 45degree has been achieved (the slope angle may vary depending on motor`s torque and rpm).When it reaches the topmost part of the slope it rises a little to cross the edged part.

When it reaches the stairs the front two legs are raised and laid support against the stair wall.now the motors of front legs are driven and a thrust is provided by rear legs by raising it the two actions are performed simultaneously. The front motors are driven till the rear legs come near stair walls then the bot is rested upon the upper stair the rear legs are then brought upwards and folded inwards thus achieving a perfect stair climb.

While encountering a rough surface the robot lowers itself by initial mechanisms a command is now given which transforms it into crawling mode in this mode the bot is in its lowermost position and the wheels face upwards.The legs are now moved forward in an inclined fashion and grips the ground. The thrust to move forward is provided by the legs which forces against the ground, leaping the bot forward.

The robot is currently operational in a semi-autonomous state future plans include the installation of sensors so as to detect the type of terrain and obstacles encountered and seeking out efficient ways to perform the tasks in completely autonomous state.

This project has won the best implementation award in research convocation’14.

With the consent of DRDO (Defence Research & Development Organisation) and further modifications from there side might increase its chance of being inducted into defence forces. It might be used to explore unknown territories and might also be useful in rescue operations.

REFERENCES:

https://www.youtube.com/watch?v=6tD3dsDzbeg

VIDEO LINKS:

INVENTOR DESIGN( .iam FILE) :

https://www.dropbox.com/s/3v580r68kpem9sa/fINAL%20dESIGN.iam?dl=0

This project has also made its appearance in a national newspaper.

http://timesofindia.indiatimes.com/city/kanpur/IITians-develop-robot-capable-of-climbing-stairs/articleshow/40435670.cms