## The Perspective-Zephyst Editorial

The Perspective-Zephyst is out with its final edition. As in our previous edition, we have focussed mainly on research articles by undergraduates. In fact, in our endeavour to encourage authentic original research, we’ve had to reject a few articles for the first time in our publishing history. Nevertheless, we present a plethora of articles upholding the highest quality standards ranging from Quantum Mechanics and Relativity to Personal Opinions of a graduate student studying in Germany; thus presenting a unique blend of just what you would want to read. We continue to encourage original research reports with due references and experience/opinion articles from students and researchers across the academic spectrum.

## My College made me what I am

Parichay Mazumdar, currently a student at Bonn-Cologne Graduate School of Physics and Astronomy (BCGS), Germany narrates how his alma mater St. Stephen’s College nurtured the Physicist and the amazing personality in him.

Hi, I am a masters student of Physics in the Bonn-Cologne Graduate School of Physics and Astronomy (BCGS), Germany and an ex-student of the Physics department of the St. Stephen’s college, Delhi. I was asked to share how the experience of the life at St. Stephen’s was for me. I am someone who doesn’t know how to wrap memories into beautiful expressions. Still I will try as much as I possibly can in expressing the unforgettable three years of my life. I belong to an unknown small town of Orissa called Bargarh. It all started when I finished my class 12th exams and was battling with the social pressure of joining a medical/ engineering college. I always wanted to do pure sciences. I was looking for reputed institutes in India for a bachelors in physics. And Google told me that St. Stephen’s was the best ranked college in Natural Sciences. I called up my sister in Delhi and asked about it. Her over-enthusiastic reply made me think “I could give it a try!” (I never though such a casual decision would change my life). So I filled up its application online along with a couple of more colleges.

The rest was a fabulous journey. The lack of my vocabulary skills, although I know what snobbish means, might make it sound ordinary, but trust me, it was an extraordinary experience. My classmates were all really smart motivated people trying to make a mark in the world of physics. Suddenly my surroundings changed from a bunch of old people trying to shove me into the engineering fiasco (Yes, you heard me right! That’s what I think it is.) to a group of enthusiastic students and teachers encouraging each other to excel in whatever they found interesting and motivating. There were so many societies in college that I could not decide which ones to join and what to leave. But I had to be careful since I had to make a balance between societies, which would help me build a personality by improving my social skills, and studies which was gonna shape my future. I joined the Music Society, the Social Service League and obviously, the Physics Society. Although music was a greater passion, I always enjoyed doing social work. After a couple of months I was totally integrated into this new community that was young and dynamic and full of positive competition.

Then, there was a whole department of great professors who were nothing short of inspirations for everyone. They always inspired (sometimes scared) students to work hard and enjoy it at the same time. It was in college where I saw for the first time that, the teachers were enjoying what they were teaching and that made learning much more fun. We were encouraged by them and other seniors to apply for summer projects (I had no idea what they were before I stepped onto college!). Thanks to a nice recommendation letter I got to do a very interesting summer project in the National Center for Radio Astrophysics (NCRA-TIFR) Pune. I also worked one winter in the Bose Institute, Kolkata. Interacting with students from other places made me realize that I was indeed very lucky to have such a exceptional bunch of teachers all at one single place while other places hardly even had one or two. While I was busy having a good experience in the world of physics, there were others around me, each with an equally interesting story, if not more, of how they were living their own version of St. Stephen’s. We motivated each other and helped each other to work harder. It might sound like we were just studying and not having fun but the truth is, the amount of fun I had in college is much more than what I had in my whole life. I just don’t wanna explain that because, obviously that’s what college is all about!

I could not stress it enough, but St. Stephen’s changed me from an extremely shy boy from a small town to a really matured and smart person who could take on the world on his own. And its not just me, all my friends have made an equally successful life after college so far. Three students from my class including me got call letters from Cambridge University. Two of them went on and joined Cambridge. Two of my other classmates and I chose BCGS to do our masters degree. Another friend of mine went to Amsterdam via an Erasmus Scholarship. Some joined IISc and IITs after getting enviable ranks in IIT-JAM. Others chose careers totally different from Physics, like fashion or law. A few got hired by MNCs with six digit salaries! St. Stephen’s did a remarkable job in shaping the lives of about a thousand students and it continues doing so every single year. I wish there were at least a hundred more colleges like this in this country of billions so that more people like me could get a good education and a fair shot at life.

## A Compilation of Science News over the last Month

Tuhina Sinha, St. Stephen’s College, Delhi

1st October, 2015

Researchers develop technology to produce low-cost heart valves: Researchers at Colorado State University (CSU) and Ohio State University (OSU) say they have developed a technology to produce low-cost heart valves. The new heart valves, which will be made of flexible plastic, which also contains hyaluronan, will cost half the price of an imported metal valve and not require anti-coagulation therapy. However, clinical trials and approval of the new technology is likely to take another two years. Doctors from all the three institutes announced that they have been working on a project to develop low cost replacement heart valves that are better than the existing metal and tissue-based valves and at the same reduce a patient’s need for medication to prevent formation of blood clots.

Asteroids are Moon’s main ‘water supply’: Water reserves found on the Moon are the result of asteroids acting as “delivery vehicles” and not of falling ice comets as was previously thought, a new study using computer simulation has found. Scientists have discovered that a large asteroid can deliver more water to the lunar surface than the cumulative fall of comets over a billion year period. Vladimir Svettsov from Institute for Dynamics of Geospheres and Valery Shuvalov from Moscow Institute of Physics and Technology in Russia developed the most probable mechanism of water delivery to the Moon and an approximate “supply” volume, using computerised modeling of the fall of cosmic bodies onto the surface of the Moon.

NZ plans a France-sized marine sanctuary: New Zealand has plans to create a South Pacific marine sanctuary, about the size of France, to protect one of the world’s most pristine ocean environments. Prime Minister John Key said the Kermadec Ocean Sanctuary would cover an area of 620,000 square kilometres (240,000 square miles) about 1,000 kilometres (620 miles) off New Zealand’s northeast coast. Announcing the plans at the United Nations in New York, Key said the Kermadec area was home to thousands of important species, including whales, dolphins, seabirds and endangered turtles. “It contains the world’s longest underwater volcanic arc and the second deepest ocean trench at 10 kilometers deep,” he said.

30th September, 2015

Plastic eating worms could save the world: A tiny worm, which is actually the larva of a beetle, eats Styrofoam and other forms of polystyrene, a Stanford University researcher has found. Microorganisms in the worms’ guts biodegrade the plastic in the process. This first ever finding holds out hope for a world that is being swamped by plastic. These findings, published studies in Environmental Science and Technology, are co-authored by Wei-Min Wu, a senior research engineer in the Department of Civil and Environmental Engineering at Stanford. “Our findings have opened a new door to solve the global plastic pollution problem,” Wu said.

UAE space agency seeks cooperation with ISRO:  A delegation from the UAE Space Agency has undertaken a visit to the Indian Space Research Organisation (ISRO) to discuss possibilities of cooperation between the two space organizations. The delegation was led by Khalifa Al Rumaithi, chairman of the UAE Space Agency, and Mohammed Nasser Al Ahbabi, it’s director-general, according to statement released by official WAM news agency.
This is part of the agency’s efforts to build strategic partnerships and achieve goals of regional and international cooperation within the industry, it said. The UAE delegation learnt about the Indian space sector and the different programmes that ISRO has led within space exploration, it said.

29th September, 2015

Alzheimer’s agony: Fading memory: “I forgot where I kept the car keys.” “I can’t recall my nephew’s name.” “I don’t remember the road that leads to my home.” It’s not uncommon to hear these statements from elderly people in our families. And their statements aren’t taken seriously as forgetfulness is considered normal fallout of old age in our society. Family members don’t realize the serious implication behind such forgetfulness, which can be indicative of something as dangerous as dementia or more precisely Alzheimer’s Disease. Alzheimer’s Disease, one of the commonest forms of dementia (progressive memory loss), is a disease without cure but at the same time, the progress of the disease can be slowed down with early detection and timely treatment. But sadly, people associate memory loss with old age and don’t bother about early screening or cutting down on the risk factors, which is the only way to delay the progression of dementia.

How NASA discovered flowing water on Mars and what it means: Streaks of salty water flow down the mountains and canyons of Mars during summer seasons, raising the odds that life may one day be found on the Red Planet, NASA scientists have announced. An analysis of the dark patches that ebb and flow on the slopes of Mars shows that they contain “hydrated” salt crystals containing molecules of water — the first time scientists have directly detected liquid water on Mars. “The detection of hydrated salts on these slopes means that water plays a vital role in the formation of these streaks,” said Lujendra Ojha, of the Georgia Institute of Technology in Atlanta. Liquid water is considered an essential ingredient for life. However, there is as yet no suggestion that NASA is even close to finding signs of simple microbial life forms on Mars, where the surface is constantly bombarded by life-destroying cosmic radiation, and experiences wide temperature extremes.

Cancer treatment during pregnancy not unsafe: It is among the most delicate and difficult dilemmas in medicine: Should a pregnant woman who has received a cancer diagnosis begin treatment before her child is born? Some hesitant doctors counsel women to deliver preterm or even terminate the pregnancy first. But a new study of more than 100 children who were exposed to cancer treatment during the last two trimesters of their mother’s pregnancy showed they had normal cognitive and cardiac function, researchers said on Monday.”The main message of this study is that termination of pregnancy is not necessarily warrant ed, and that early preterm delivery to be able to do cancer treatment isn’t warranted, either,” said Dr Elyce H Cardonick, a maternal-fetal specialist at Cooper Medica School of Rowan University in Camden, NJ, who was not involved in the new research.

27th September, 2015

Rare supermoon lunar eclipse on Sunday night: A total lunar eclipse will share the stage with a so-called supermoon on Sunday night or early Monday, depending where you are. That combination hasn’t been seen since 1982 and won’t happen again until 2033.When a full or new moon makes its closest approach to Earth, that’s a supermoon. Although, still about 220,000 miles away, this full moon will look bigger and brighter than usual. In fact, it will be the closest full moon of the year, about 30,000 miles closer than the average distance. NASA planetary scientist Noah Petro is hoping the celestial event will ignite more interest in the moon. He is deputy project scientist for the Lunar Reconnaissance Orbiter, or LRO, which has been studying Moon from lunar orbit since 2009.

Countdown for launch of ISRO’s Astrosat progressing normally: The 50-hour countdown for the launch of Astrosat has been progressing normally after it began at 8am on Saturday, according to an update on ISRO’s website. A Polar Satellite Launch Vehicle (PSLV-C30) carrying Astrosat, India’s first dedicated multi-wavelength space observatory, and six small satellites will fly from Sriharikota spaceport at 10am on Monday. “Everything is progressing well. No issues,” said K Suryanarayana Sharma, project director, Astrosat. The countdown began following clearance from the Mission Readiness Review (MRR) committee and Launch Authorization Board (LAB).

NASA’s Mars rover ‘smarter’ than Curiosity: NASA’s next nuclear-powered Mars rover, slated to launch in 2020, has started taking shape. The new vehicle will be “smarter” than the previous one on many counts, according to the engineers on the project. For one, the overall system is becoming heavier. The rover’s wheels are getting heavier, with its body becoming a little longer. Engineers said that would change the rover’s mobility system and how it interacts with the ground. “We are really looking at ways to make this largely heritage, built-to-print rover drive faster and do more science on the surface of Mars,” JPL’s mission manager for Mars 2020 and surface-phase lead Jennifer Trosper was quoted as saying.

24th September, 2015

ISRO celebrates one year of Mars Orbiter Mission: Mars Orbiter spacecraft marks one year of its life around the red planet on Thursday. After successfully completing one year of the mission life around Mars, a large data set has been acquired by all five payloads of Mars Orbiter Mission. ISRO to mark the first anniversary of Mars Orbit Insertion released an atlas containing photos taken by the colour camera on board the spacecraft and results obtained by other payload results in a form of scientific atlas.

‘Neglecting arthritis can lead to stress fracture’: Leelaben Raval, 65, from Visnagar had been experiencing severe joint pain, stiffness and weakness in muscles for the past two years. Raval kept neglecting osteoarthritis symptoms and eventually had stress fracture in both her knees. Naranpura resident Rama Patel, 72, also suffered wear and tear of muscles with age. It started with a pain localised to the knee but worsened when she climbed the stairs and stood up from a sitting position. As the disease progressed, the pain made even walking difficult. Both patients recently underwent a customized implant for total knee replacement that could have been avoided had they acted promptly.

21st September, 2015

In this village, girls ‘turn into boys’ at 12: In an isolated village in the Domini can Republic, an estimated one in fifty children are born appearing to be girls but grow male genitalia during puberty. The children are known as Guevedoces, roughly translating as “penis-at-12”, referring to the age where their appearance often starts to change. A BBC documentary called `Countdown to Life: The Extraordinary Making of You’ explores the rare condition as part of a series on development. Johnny, once known as Felicita, told the programme he fought bullies who targeted him when the change started. “They used to say I was a devil, nasty things, bad words and I had no choice but to fight them because they were crossing the line,” he said. “I’d like to get married and have children, a partner who will stand by me through good and bad.”

Dental diseases cost the world $442 billion annually-Report: Improvement in oral health alone can offer the world substantial economic benefit as researchers have estimated that the yearly global economic impact of dental diseases amount to$442 billion. Reporting the economic burden of oral diseases is important to evaluate the societal relevance of preventing and addressing oral diseases. The research by Stefan Listl from Heidelberg University in Germany, and colleagues estimated that the direct treatment costs due to dental diseases worldwide were at \$298 billion yearly, corresponding to an average of 4.6 per cent of global health expenditure.

18th September, 2015

In US, 3-yr-old diagnosed with type-2 diabetes: A three-and-a-half-year-old obese Hispanic girl in the United States has become one of the youngest ever to be diagnosed with type 2 diabetes, a disease linked to poor diet and obesity. The girl had symptoms of excessive urination and thirst. A review of her diet showed poor nutritional habits with uncontrolled counting of calories and fat. The child’s weight was 35 kg (in the top 5% of all children her age). The girl was started on a liquid version of the diabetes drug metformin and her calorie intake was controlled, besides increasing her physical activity. Six months after diagnosis, her blood glucose levels improved.

30,000-yr-old frozen virus still infectious: A 30,000-year-old giant virus discovered deep in the Siberian permafrost is still functional and capable of infecting its host, researchers have found. However, the new virus is not a threat to humans; it infected single-celled amoebas during the Upper Paleolithic, or late Stone Age. Dubbed Mollivirus sibericum, the virus was found in a soil sample about 98 feet below the surface and is member of a new viral family, the fourth such family ever found. M sibericum is wider in diameter than the other giant viruses, at 600 nanometers versus 500. It has a genome of 600,000 base pairs which hold the genetic instructions to create 500 proteins.

Shelters on Mars to be 3D-printed: A French firm has designed a conceptual shelter for future astronauts on Mars that would be 3D-printed on the red planet using local materials. Resembling an igloo from the surface, the shelter, dubbed Sfero, would be partially buried beneath the ground. Access to it would be gained by its one long corridor, which contains an airlock. The interior comprises three floors. The uppermost floor measures just 3 sq m, and food can be grown here, while the next floor measures 29 sq m, comprising a work area and bathroom. The lowermost floor measures 40 sq m and contains sleeping quarters. The occupants would navigate between each floor by a spiral staircase.

12th September, 2015

Found: Galaxy that creates 800 stars/yr: In a rare find, astronomers have discovered a gargantuan galaxy cluster, 9.8 billion light years away , in which the brightest galaxy is rapidly creating about 800 stars every year. The discovery , made with the help of NASA’s Hubble Space telescope, is the first to show that gigantic galaxies at the centre of massive clusters, which are usually made of stellar fossils-old, red or dead stars can grow significantly by feeding off gas stolen from other galaxies. However, the new galaxy, at the heart of a cluster named SpARCS1049+56, seems to be bucking the trend by forming new stars at an incredible rate. “The galaxy is furiously making new stars after merging with a smaller galaxy, which is lending its gas,” said lead author Tracy Webb of McGill University in Canada.

China publishes first report written by ‘robot journalist’: A first business report written by a robot has been published in China this week, stoking fears among local journalists that it could make forays into the country’s state-controlled media, threatening their jobs. The article, was written in Chinese and completed in just one minute by Dreamwriter, a robot journalist designed by Chinese social and gaming giant, Tencent that apparently has few problems covering basic financial news. Tencent released its flawless 916-word article via the company’s instant messaging service. “The piece is very readable. I can’t even tell it wasn’t written by a person,” Li Wei, a reporter was quoted as saying by South China Morning Post.

11th September, 2015

‘Misplaced’ volcanoes on Jupiter’s moon due to magma oceans: Tides flowing in a subsurface ocean of molten rock, or magma, could explain why Jupiter’s moon Io appears to have its volcanoes in the ‘wrong’ place and could also have implications for the search for alien life, a NASA study has found. The research implies that oceans beneath the crusts of tidally stressed moons may be more common and last longer than expected. “This is the first time the amount and distribution of heat produced by fluid tides in a subterranean magma ocean on Io has been studied in detail,” said lead author Robert Tyler of the University of Maryland and NASA’s Goddard Space Flight Centre in US.

REFERENCES

1. The Times of India
2. Hindustan Times
3. BBC

Kevin S. Varghese, St. Stephen’s College, Delhi

## 15 Oct 1931 – 27 July 2015 : SPECTRUM OF VERSATILITY

Pragya Rastogi, St. Stephen’s College, Delhi

Tribute to the persona with unparalleled potential, unalloyed dedication to serve the country and adept to work in science and politics …

Tribute to DR. APJ ABDUL KALAM : THE MISSILE MAN OF INDIA .

## The Makings of a Nobel Prize Experiment

Avleen K. Sahni, St. Stephen’s College, Delhi

Georges Charpak, the last person till date to individually receive a Nobel prize for his revolutionary design in the field of charged particle detectors in particular, the Multi Wire Proportional Counter (or MWPC).

What did he create, and what was the importance of his idea to Science?

Let us consider a typical experiment in nuclear Physics, which aims to understand the structural features of a nucleus, or study different reaction processes involved in heavy ion collisions.

The experiment requires the bombardment of a beam of high energy particles on heavy target nuclei, and the various products of nuclear reactions are detected.

Bombarding the projectile on heavy targets and detecting the various products of the nuclear reactions.

Unlike the chemical reactions we all study about in chemistry, nuclear reactions can have different pathways, depending on the reaction conditions, and each set of reaction products has its own cross section (analogous to the probability of each set of products).

A particular experiment can aim to explore any particular set of these products, and thus we would require detectors that are sensitive to our required products, and transparent to all others.

So now we need to know the reaction product positions, numbers and energies. That is, now we need a charged particle detector.

particle detector or a radiation detector is a device used to detect, track or identify high-energy particle products. Depending on the requirement, detectors may be used to measure other attributes such as energy, charge etc. of the particles.

The De Broglie wavelength of any particle is given by: L = h/v

The incoming particles are accelerated to energies of a few MeV to reduce the De Broglie wavelength to the nuclear dimension (10-15 m). Collision of the energetic projectile with target nuclei could trigger a number of reaction processes like scattering, nucleon exchange, fusion etc. Using appropriate detectors, we can characterise the products.

So the question arises: How is Radiation detected?

Nuclear radiation is detected only through interaction with matter. The fundamental principle of detection is based on the transfer of energy from the incident radiation to the detector which is then converted to a form in which it can be processed electronically. This enables accurate and faster measurement of timing, energy, and position etc. of the incident particles.

Detectors are of different types depending on the radiation being detected. For charged particle detectors, the radiation loses energy through Coulomb interaction in the detector medium resulting in the excitation and ionisation of the detector atoms. While the ionisation produces free charges, the de-excitation of the excited atoms results in the emission of photons.

Thus detectors are of two kinds based on which of the two mechanisms they work on:

1. Ionisation based detectors: Those detecting the free charge carriers
2. Scintillation detectors: Detectors sensing the luminescence photons

For neutral radiation such as gamma rays or neutrons, however, the process should be two-fold: the liberation of an energetic charged particle, and the subsequent detection of this particle.

While earlier designs like the Geiger counter, the proportional chamber were being used to determine the number of charged particles detected, the MWPC made it possible to know the position of the charged particle being known.

To understand the working of the MWPC, you need to know the simple formula:

E(r) = CVo/ 2rε∏

A cylinder with a conducting wire along its axis to which a positive voltage, + Vo, relative to the walls is applied. A radial electric field with r: radial distance from axis; C: capacitance per unit length of this configuration; ε is the dielectric constant of the medium inside the cylinder.

Schematic for MWPC

1. An array of closely spaced anode wires between 2 plates of cathodes, enclosed in a chamber.
2. A gas is filled and flows continuously through this chamber.
3. The beam of charged particles enters through a thin entrance window.
4. The incoming charged radiation ionise the gaseous molecules, it loses energy and electron – ion pairs are generated.

Electric field is uniform, except near the wires

The motion of the charges is like a drop: with the electrons drifting faster than heavy positive ions.

1. Electrons formed by ionisation of the gas drift inward towards the plane of anode wires, initially in a nearly uniform field. Near the wire, because of the 1/r dependence, the electric field experienced by the electrons is strong. These electrons acquire sufficient energy to cause secondary collisions, thus creating more electron- ion pairs, leading to an avalanche.
2. A large signal is induced on the anode wire, closest to the electrons striking. The pulse signal on the electrodes of ionization devices is formed by induction due to the movement of the ions and electrons as they drift towards the cathode and anode, rather than by the actual collection of the charges itself.

This signal helps to identify the position of the striking radiation, though information about the energy is mostly lost. Modifications to the basic design can improve timing resolutions or allow for energy measurement. If 2 plates of anode wires are used instead, we can orient them perpendicular to each other to allow for x and y coordinates of position. The resolution in position is proportional to the spacing between the wires. It is fast because avalanche formation near the wire takes place within <1ns.

Thus, the MWPC offers distinct advantages, including very good time resolution and position accuracy, fast response (electrons are used, instead of ions). They can be fabricated with ease in various sizes and geometries based on the experiment with very little cost.

This important invention not only revolutionised data-taking for experiments, ultimately leading to the discovery of the W and Z particles, but found immense applications in the medical physics.

## A Review of Frenkel Poole Emission

The p-n junction for semiconductors has various mathematical models which try to explain the transport phenomena across the junctions for different semiconductor materials and at different temperatures. Here, we review Frenkel Poole Effect and concentrate in the domain of large Electric Fields where the additional increase in conductivity is independent of the Electric Field.

1. INTRODUCTION

In the domain of very large electric fields E for both conductors and insulators, electrical conductivity exponentially tries to catch up till breakdown occurs. The limiting value of such an E is about 106V/cm and a few thousands of volts/cm for an insulator and conductor respectively. Experimentally, it had been noticed that in such fields, illumination of the semi-conductor surface lead to additional increases in conductivity, which could only be explained by their increase in number density, since their mobility wouldn’t increase further. This led Frenkel to publish an article explaining the same in a note to Phy. Rev. Letters, 1938.

2. FRENKEL’S MATHEMATICAL MODEL

In the exorbitantly high electric field domain, the electrons can be considered to be acted upon by a field screened by the the positive ions. Of course the medium still contains some neutral polarizable atoms. Considering the screening due to polarization, the ionization potential reduces by a factor given by the permittivity of the medium,$\epsilon$

FIG. 1: Potential Energy as a function of distance from the positive ion. The dotted line is in the presence of the field while the bold one is in absence of external fields.[1]

In the figure above, we note that on increasing the external field E, following a mechanism similar to Schottky Effect inspired by Richardson’s eponymous equation in 1901, decreases the energy. The height of the potential barrier in the field is thus lowered by:

(1)

Here, r0 is given by:

This thus gives us. Replacing this back in the equation finally gives us:

(2)

Now, the number of free electrons due to thermal ionization is proportional to e(−U0+∆U)/2kT. However, the ionization potential energy had been reduced by a factor,  This thus gives us conductivity differing by:

(3)

This as we see differs from the original Poole’s Law, which was given by

σ = σ0eαE                                                              (4)

Now, the overall conductivity is thus given by:

(5)

Making use of the modified form of Ohm’s Law,

J = σE                                            (6)

we obtain the standard form of Frenkel-Poole Emission Formula as follows:[3]

(7)

where:

1. J is the current density
2. E is the applied Electric Field
3. e is the electronic charge
4. U0 is the voltage barrier in the absence of E that an electron must cross to move from one atom to another in the crystal
5. is the permittivity of the medium
6. kB is the Boltzmann’s constant
7. T is the absolute temperature

3. EXPERIMENTAL VERIFICATION

Frenkel’s mathematical model was found to be in excellent agreement with P. Granofskaja and Joffe’s experiments on pre-breakdown phenomena in electronic semi-conductors performed upto field strengths of about 50,000 volts/cm. [1]

What was unique about the above phenomena was that the effect of the applied field was reduced despite increasing temperature in the given semi-conductor. Electrons can move (slowly) through an insulator by the following method. The electrons are generally trapped in localized states (loosely speaking, they are ”stuck” to a single atom, and not free to move around the crystal). Occasionally, random thermal fluctuations will give that electron enough energy to get out of its localized state, and move to the conduction band. Once there, the electron can move through the crystal, for a brief amount of time, before relaxing into another localized state (in other words, ”sticking” to a different atom).[3]

The Frenkel Poole effect describes how, in a large electric field, the electron doesn’t need as much thermal energy to get into the conduction band (because part of this energy comes from being pulled by the electric field), so it does not need as large a thermal fluctuation and will be able to move more frequently.

4. APPLICATIONS AND SUMMARY

It remains the question about the transport mechanism which is responsible for transport in the case of overoxidized or underoxidized junctions. Several candidates have been checked. In a certain range of voltages and temperatures, Poole-Frenkel emission thermally stimulated emission of carriers from donor like trap sites seems to be the most probable.[2] Its voltage and temperature dependence is described by:

I ∝ √V exp(2a V/kT eU0/kT) (8)

where

FIG. 2: A plot of ln(I/V ) versus 1/T results in a straight line for the Poole-Frenkel effect, which is found here above 200 K, with an applied voltage of 30 mV.[2]

lines if Poole-Frenkel conduction is indeed the main conduction mechanism. These straight lines have been found for temperatures above 200 K at 30 mV bias voltage Fig. 2. According to the derivation by Frenkel, the dielectric constant enters the formula as the ability of the material surrounding a trap site to screen its positive charge.[2]

Frenkel states a radius of influence of the trap on the order of 30 angstroms. For our thin barriers, however, metallic material of the electrodes is met within this radius. This gives rise to a much more effective screening due to the high mobility of metal electrons, which in turn explains the much higher dielectric constant. Recently, these concepts have been used of in the fabrication of epitaxial layers on the semi-conductors especially benzotriazole and benzothiadiazole based organic devices.[4]

References

• [1] Frenkel, ”On the Pre-Breakdown Phenomena in Elec-tronic Semi-Conductors”, 1938.
• [2] Rottlander, M. Hehn, A. Schul ”Determining the Interfacial Barrier Height and its Relation to Magnetoresistance”, 2002.
• [4] E. Yildiz, ”Leakage current by Frenkel Poole emission on benzotriazole and benzothiadiazole based organic devices”, 2014.

## Elementary Connections between Gravitation and Quantum Mechanics (non-relativistic limit)

Rishabh Jha,
Department of Physics,
Indian Institute of Technology Kanpur
(Dated: December 15, 2014)

Abstract:
1: Consistency relation between general relativity and quantum mechanics (both non-relativistic limit)
2: Direct conflict between principle of equivalence and lineraity principle in quantum mechanics
3: Time required for linearity postulate to fail in quantum mechanics due to the effect of principle of equivalence
4: Consistency relation between Newtonian gravity and non-relativistic quantum mechanics by modifying the
expression for Newtonian potential

1. CONSISTENCY RELATION BETWEEN GENERAL RELATIVITY AND QUANTUM MECHANICS (BOTH NON-RELATIVISTIC LIMIT)

Consider 2 situations

• a quantum measurement being done where gravitational potential energy is included, then the Schrödinger’s equation becomes:

• for the same experiment done in a freely falling lift, the Schrödinger’s equation becomes:

Notations: (−x , t) for (1) and (−x, t’) for (2).

Since we are using Schrödinger’s equation, so we are in the non-relativistic realm. Then the coordinated of (1) and (2) are related as:

Now we invoke the fundamental principle of general relativity: the Principle of Equivalence. Since Physics should not change, hence | ᴪ1|2 = | ᴪ2|2

Let the ansatz for Φ be:

Also using (3) and (4), we get:

we get:

But ᴪ1 satisfies (1) as well. Hence, comparing the coefficient of x on RHS of (1) and (8), we get:

All the other extra terms in (8) should cancel, leading to the following results:

and

Plugging (9), (10) and (11) in (5), we get the required consistency relation between general relativity and quantum mechanics (both non-relativistic cases):

II. CONSEQUENCES OF THIS RESULT
We can clearly see that there is a non − linearity in t present which occurs for gravitational fields only because while deriving the consistency relation (12), we made use of principle of equivalence which holds for gravitational fields only. Of course, the acceleration due to gravity g can be replaced by any other acceleration ’a’ and the above result will continue to hold. This non-linearity in t has crucial outcomes:

1. From quantum field theory, we know that this non linearity and acceleration will lead to a different vacuum observed by a person who is not accelerating. These 2 vacua corresponds to different vector spaces and from the fundamental postulate of QFT, we cannot superimpose 2 different vector spaces and hence, linearity postulate fails.
2. My postulate for the critical time after which nonlinear terms should dominate is:

where E is the energy difference between the 2 superimposed states. After this time, linear  combination of states fail and   s time passes on,  the postulate to exist in both the states prior to  measurement becomes more and more unstable. One of the plausible argument behind this postulate is that in the energy-time uncertainty relation E ∗ t ≥ ~ 2 , t is not the standard deviation of a collection of time measurements, but the time required by the system to change state  substantially and E being the energy difference between those 2 states. A similar situation is here,  where changing the states will cause failure of linearity principle and the time associated with this transition should be of the order as shown in (13) after which non- linear terms in time will  dominate.

NOTE: From these 2 points, we can conclude that the fundamental assumption of quantum mechanics (linear combination of states) and general relativity (principle of equivalence) are in sharp contrast.
3. We may suspect to have Unruh effect into play but the Unruh temperature

where,

Since we are in non-relativistic limit, c → ∞.

So, this is another type of vacuum observed from lift and is definitely not thermal in nature.

4. Hence, the time evolution operator U (which is unitary) should be a linear approximation of a more general non-linear theory of quantum  mechanics which is yet to be discovered and the correction factor to the present state of quantum
mechanics to achieve its final form should come from the theory of gravitation, i.e., general theory of relativity as this new type of vacuum and nonlinear effects in time are observed for gravitational fields, as we saw above.

A. Consistency relation between Newtonian gravity and non-relativistic quantum mechanics
5. (1) can be further extended as follows: To make the case more general, let us add some general potential function U (−→x ,t) apart from the gravitational potential function V:

Now consider a volume element dV  ′ which is at a displacement of r ′ from origin. Then consider a  point of interest P which is at a displacement of r from the origin. We define the displacement vector  from the volume element to the point of interest as  R such that

Probability density to find a particle = | ᴪ1|2 ⇒ Probability to find that particle in the volume dV ′ = | ᴪ1|2*dV ′

where,

• integration is done over the entire specified domain,
• 1 = 1(−→r , t)
• t is the time instant at which potential V needs to be calculated.
In differential form:

NOTE:
• (18) & (19) are 2 different forms of the required consistency relation between Newtonian gravity and non-relativistic quantum mechanics  by modifying the expression of Newtonian gravitational potential.
• We can observe from (16), (18) and (19) that adding a constant phase factor to 1 (phase shifts) do not change the Physics and these equations are invariant under constant phase shifts.

## The 2015 Wolfram Science Summer School in Massachusetts

–Leah Chrestien
April 22, 2015 was perhaps the most eventful day of my life because that was the day I received an invitation letter from the senior director of the Wolfram Science Summer School, congratulating me on being accepted as a part of the Wolfram Research Community.
Being a rising senior at my University, I saw this as a wonderful opportunity to delve deep into the world of fundamental research where one comes across great minds from all disciplines, shares a common platform of developing new ideas and turns them into reality.
The Wolfram Science Summer School was first started in the year 2003 under the initiative of Dr. Stephen Wolfram, founder and CEO of the multi-millionaire dollar company Wolfram Research and the chief developer of the Wolfram Language, Mathematica and has grown ever since- producing outstanding research scholars and working alongside some of the world’s most notable companies mainly, Apple Inc.
The summer school was held amidst the lush green campus of Bentley University situated in Waltham, about 20 minutes from Boston in the state of Massachusetts. The truly cosmopolitan nature of the summer school was manifested by the fact that there were students from different fields of study and at different levels in their academic career. The three weeks of the summer school saw rigorous Mathematica training where each student was allotted  a project and an instructor to work under.
My interaction with Dr. Stephen Wolfram , author of A New Kind of Science has proved to be perhaps the most eventful incident of my life. I was at that point in my academic life where everything seemed to be redundant and I was unappreciative of my strengths. He has infused in me the hope that was once lost. He made me feel special and 10 years from now , I will have a lot to be grateful for.
The city of Boston and Cambridge on the banks of river Charles continues to spin its charms to travellers and storytellers alike. The fourth of July or the day of American Independence saw a large gathering of people and spectacular display of fireworks.
The last week of the summer school proved to be busy for all of us as we were on the verge of wrapping up our projects – making reports, presentations and project notebooks. Under Dr. Matthew  Szudzik who is a professor of Mathematics at Carnegie Mellon University, I had managed to put up a paper on Constraint tiling.
Constraint tiling has been one of the greatest challenges of mathematics, resulting in the what we know today as the famous Penrose tiles, which have successfully solved the age-long problem of five-fold symmetry using the Golden Ratio, a universal constant that is well known since the time of ancient Greeks.
In this  summer school, I was given the task of studying two-colour periodic tilings of a hexagonal lattice that satisfy up to three nearest-neighbour constraints and their rotations.  After running computer simulations for over 28,000 such constraints, one of the many interesting patterns that emerged, proved to bear witness to the laws of periodicity.
The 2015 Wolfram Science Summer School conducted at Bentley University in Waltham, MA has proved to be an eye-opener for students like me who dream big and hope to make a contribution to the scientific community in their own small way.

## Protein Imported Kinetics in Isolated Mitochondria

Bhavyata Patel

INTRODUCTION:

About 10% to 15% of the nuclear genes of eukaryotic organisms encode mitochondrial proteins. These proteins are synthesized in the cytosol and recognised by the receptors on the surface of mitochondria. Translocases in the outer and inner membrane of mitochondria mediate the import and intramitochondrial sorting of these proteins. The import is regulated by the coorpoeration of the two main mitochondrial preprotein translocases, the Translocase of Outer Membrane (TOM) complex in the outer membrane and the TIM (Translocase of Inner Membrane) 23 complex in the inner membrane. These complexes interact  with each other to transfer the pre-proteins across both membranes. Pre-proteins fold inside the matrix to form mature functional proteins.

Protein import and therefore, its kinetics can be studied if we know the concentration of precursor proteins and if we can quantitate the amount of mature proteins inside the mitochondrial matrix. We can use this concept to study how protein import is affected and to what extent in different conditions, mutations and in critical concentrations of the essential components of the protein import machinery to study the importance of each.

MATERIALS AND METHODS:

Principle: Protein import is regulated by an electro-chemical gradient and the availability of ATP. If this “electro-chemical gradient” is broken, we can separate the mature proteins from mitochondria through SDS PAGE and quantitate them. The technique comprises of facilitating import by addition of ATP, NADPH, import buffer etc. and then addition of valinomycin at regular intervals which breaks the gradient to stop the import.

Requirements:

• HEK 293 T Mitochondria
• ATP———————————————————–10.5μl
• Precursor Protein Cytb2(47)-DHFR———————–35μl
• Water———————————————————-124μl
• Mitochondria————————————————-55μl
• Import buffer: 100mM HEPES/KOH (pH 7.2)

6% fatty acid free BSA

1M sorbitol

1mM KCl

20 mM Magnesium Acetate

4 mM KH2PO4

2 mM Manganese Chloride

• Valinomycin———————————————-0.1mM in ethanol
• PMSF——————————————————0.2M in ethanol
• Porteinase K———————————————-10mg/ml in water
• SH Buffer: 0.6M Sorbitol

20mM HEPES/KOH

Protocol:

RESULTS AND DISCUSSION:

The in vitro protein import assay carried out in HEK 293 T cells shows that gradual import of precursor protein [Cytb2(47)-DHFR] has taken place.

Time (minutes)

Cytb2DHFR

Fig.:  Plot of percent import at different time intervals.

CONCLUSION:

It is clearly demonstrated from the blot obtained above that import of proteins has taken place. The graph obtained after quantizing the proteins depicts the kinetics of protein import. Thus it can be concluded that the protein import assay has worked on HEK 293 T cell line and can be used as an experiment to study how protein import can be affected by altering the normal cellular conditions and also to understand how different cellular components like proteins play a role in its import.

REFERENCES:

1. Walter Neupert and Johannes M. Herrmann. Transloction of Mitochondria. Annu.Rev. Biochem. 2007. 76:723–49
2. Life Sciences Fundamentals and Practice; Part 1. Third Edition

## An Introduction to Perturbation Method

–Abhinav Joshi

In physics, we come across problems which are very difficult, sometimes impossible to solve. These problems come in form of equations whose exact solution is very difficult to find. By exact solution we mean an expression once substituted in an equation solves it exactly.

Take the following equation for example,

Here is a function of which we need to find and is an arbitrary function of. This equation is exactly solvable only for a very few choices of. This is the famously celebrated ‘Schrodinger Equation’. Solutions of this equation help us to understand the nature and different choices of represent different systems. Unfortunately this is a very hard problem and coming up with an exact solution is mostly impossible.

On the other side, an easy problem is the one which can be solved exactly. For example, the solution to this problem can be found by integrating and it is . There are different ways to go about the solution of the hard problems. Here are two of the most common and useful. One is using a computer, you could write a program which solves the equation and shows you the result. In this process we tend to lose the insights and the details of the problem but still it is a very popular one because some problems are just too difficult. Another beautiful method which keeps the insights and details intact is Perturbation Method. In this method, we smartly break the problem into a lot of easy problems and solving these easy problems gives us the exact solution we need. But, there is a catch. There are infinitely many easy problems and we can solve only finite of them in finite time. Therefore we never get an exact answer but an approximate answer. Now, we can take as much time as we want and get better and better approximation.

In Perturbation method, we introduce a variable in the problem. This variable can be considered as a control knob in the problem. For example, consider the following problem Here, we have a hard problem. To use Perturbation method we insert a variable, let’s call it α. We can do it in many ways, one is the following. We decided to have α as a coefficient of . By changing the value of α we change the solution. If α is 0, the equation becomes trivial with solution . If α is 1, we get the hard problem. In the process of finding solution for α=1, we assume the solution to be a power series in α, substitute it in the equation and expand. Matching the powers, we get a large set of easy problems which can be solved to get a series approximating as a function of α. Substituting α back as 1, we solve the equation. The series usually have different behaviours, some converge fast others converge slowly but the most interesting are the one which don’t converge at all. In physics from time to time these series are diverging and if you go on a quest of adding them up term by term you will end up with infinities.

There is elaborate mathematics explaining how to make sense of these divergences. The method of perturbation is very useful in physics for solving problems. It has elaborate use in both Quantum Mechanics and Quantum Field Theory (QFT). In QFT, this subject forms basis of Perturbative QFT.

Following are some links which can be looked up for more detail and further understanding.

https://www.youtube.com/watch?v=LYNOGk3ZjFM (Series of informative lectures on Perturbation Theory by Carl Bender)

https://plus.maths.org/content/infinity-or-just-112 (Very informative article on summing diverging)

http://www.cims.nyu.edu/~eve2/reg_pert.pdf (Introduction to Perturbation Theory and solution of a problem like ).