Aparajita Bhattacharya, Author at Adamas University

#PhysicsPlus: Particle and Nuclear Physics

Enormous progress in Physics has been seen in the twentieth century. First half of the century is dominated by Einstein Theory of Relativity and development of Quantum Mechanics. In the year 1905 Einstein put forward his Special theory of Relativity and took another 10 years to publish his General theory of relativity to include Gravity which is published in the year 1915. The birth of Quantum theory starts with the Planck’s theory of black body radiation in 1900. Einstein took the Planck’s theory to describe photoelectric effect and predicted the quantum of light (photons) which behaves like particle. Subsequently Niels Bohr, Louis de Broglie, Erwin Schrodinger and Paul M. Dirac, advanced Planck’s theory and developed the theory of quantum mechanics as a mathematical application of the quantum theory with matter and wave equivalence with a probabilistic view in contrast to Classical theory.

The 2^nd half of the twentieth century observed the rise of the Particle Physics. A huge number of particles are identified in high energy accelerators. The systematic study of the properties of these zoo of particles gives us the knowledge of basic interactions and their properties which in turn contribute to the understanding of basic laws of nature. First attempt came from Gell Mann and Zweig in 1964 in Eightfold way scheme where the known Mesons, Baryons and Octet baryons are classified in a geometric pattern according to the quantum numbers and suggested the quark model. The classification can be compared to the classification of elements in Mendeleev’s periodic table with basic difference in quantum numbers and the table is replaced by geometrical patterns like hexagon, triangle etc. These quantum numbers are internal quantum numbers which manifest the underlying symmetry of nature. By the early 1930s, physicists thought they had a complete picture of the constituents of matter with electrons, protons, neutrons, neutrinos and their corresponding antiparticles but in 1936 with the discovery of the muon, a heavier version of the electron comes as big surprise to physics community. Particle collision is fundamental tool for studying elementary particles. The first colliding lepton beam facilities were built in the early 1960s. Subsequently new particle colliders were planned and built, leading to milestone discoveries on November 1974 with observation of the J/Ψ particle, a new unstable state of matter of charm quarks (c-family) simultaneously at SLAC and Brookhaven National Laboratory (BNL) at USA which is termed as ‘November Revolution’. The discovery of the Upsilon (Υ) particle (b-quark family) has been reported at Fermilab in 1977 by the CFS (Columbia-Fermilab-Stony Brook collaboration) E288 experiment. Large particle accelerators of the 1980’s, and the other discoveries established the Standard Model of elementary particles as a well-tested physics theory. As physicists continued to collide the particles at ever higher energies, they discovered more and more particles. A new era of particle physics experiments started with the Large Hadron collider (LHC) at CERN. Discovery of Higgs particle reported in 2012. The experiment is focused to search answers to very fundamental questions like origin of mass, dark matter, Primordial plasma and matter antimatter asymmetry.

Particle Physics/ Nuclear Physics as career:

The career in Particle Physics or High Energy Physics is very exciting. It can be divided into two categories like Theoretical and Experimental. For both the areas the knowledge on quantum field theory (QED), Gauge theory, basics of Particle Collision mechanism are required. The High Energy Physics (HEP) landscape has changed significantly over the past few years. This field involves studying the basic constituent of matter and radiations. The other closely related areas are AstroParticle physics, Early universe, Big Bang nucleosynthesis (study to search for origin of creation of the universe and abundance of different elements we observe in nature), Dark matter, Neutrino Oscillations, CP-violation. Weakly Interacting Massive Particles (WIMPs), Exotic particles, Multiquark states. The area also extended to study the quark Gluon Plasma (QGP), a new state of matter. Particle physicists can find positions in International laboratories working with high energy colliders or at a higher education institute that excels in basic sciences. The United States Department of Energy funds Brookhaven National Laboratory, which employs about 3,000 scientists and hosts 4,000 guest researchers annually from different countries. Particle physicists are able to engage in extensive high-energy research here with their Relativistic Heavy Ion Collider (RHIC), the biggest and most powerful particle accelerator other than the LHC. The RHIC is designed for quark-gluon plasma research. The LHC is housed by the European Organization for Nuclear Research, which employs 2,600 regular staff members, and 7,931 scientists and engineers from different universities and research facilities. Research at CERN mainly focuses on particle physics starting basic structure to super symmetry and physics beyond the Standard Model. Some experimental evidence, including non-zero neutrino masses, baryon asymmetry of the Universe, dark matter and dark energy, indicates the model is still not complete. The situation requires development of theoretical models to explain the specified phenomena, and design of appropriate experimental setups to test these models. India became an associate member of CERN in 2017. A significant contribution has been done by Indian scientists to the construction of LHC, CMS and ALICE experiments with more than 400 scientists from India. The Future Circular Collider Study (FCC) is developing designs for a higher performance particle collider to extend the research of LHC. In India there are many institutes which provide good opportunities in high energy physics research including Astrophysics and Cosmology such as IISc, HRI, TIFR, SINP, VECC, IACS and others. Apart from that there are opportunities in colleges and universities as faculties. Most young high energy physicists appeared eager and optimistic about careers in academia and research however for those who want to work outside of academia may opt for Programming, data analysis, statistical analysis, and oral communication which are among the most applicable skills that were originally developed during High Energy Physics (HEP) training.

Nuclear Physics explores nuclear properties in terms of the behavior of its constituents. Rutherford’s large angle scattering experiment in 1911 gives us the idea about nuclear structure and considered it as the discovery of protons. In 1932 neutron were discovered. It is known by then the nucleus consists of protons and neutrons. A number of models for the nuclear structure have been suggested since then to understand the interaction among nucleons which makes the nucleus stable. Till we have challenges in describing atomic nucleus which is a self bound and a complex many body system. Structure of nucleus yet is to be revealed with components of subatomic entities quarks, gluons and their interactions. This is an interface of nuclear and particle physics. A number of theoretical works are going on the areas overlapping with Particle Physics such as exploring the structure of Exotic nucleus (proton and neutron rich nucleus), stellar physics, Big bang Nucleosynthesis, State of matter in Early universe, Quark-gluon Plasma. Hyper-nuclei are strange quark containing nuclei which transform the nuclear matter to up, down and strange quark combinations. These nuclei are experimentally detected and lots of studies are going on hypernuclei now a day. With a new kind of nucleus immense possibilities are there both in theoretical and experimental applications. Nuclear physicists are working with material science in superconductivity for studying cooper pairs and possibility of single cooper pair tunnelling to individual quantum states. This is absolute new research going on. Nuclear Power technology is moving fast. India has set a target of increasing nuclear power generation three times by next 10 years. Clean energy is needed for the hour with environmental crises all over the world. The complete microscopic description of the fission process and the nuclear reactions remains a computationally demanding task. Positron imaging processes where positron-emitting isotopes are used to tag tracer particles both for studying real-time flow in industrial processes and for diagnosis in hospitals. Opportunities of Nuclear Physics in medical science and health care systems are immense. Treatment with positron therapy and with proton, neutron, heavier elements are becoming more and more widespread along with radiation and MRI. Nuclear Physics is the most important candidate for the study of the environment. The use of nuclear equipment are growing for national safety and security purposes. A number of research institutes in India like SINP, RRCAT, DAE, VECC, IIMS recruits nuclear scientists.

Conclusions

The research and application in Nuclear and Particle Physics have entered a new era for the last few years. In all forward move, we need innovation, theory, conception and technique. In Undergraduate and PostGraduate studies in the subject, students develop skill in conceptual and experimental techniques. The opportunities are immense but it should be always remembered that opportunity favours the prepared mind. Apart from that for a student of physics, doing science is a joy which can never be ignored and I quote from a saying of great scientist Henry Poincare ‘Scientist does not study nature because it is useful; he studied it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living’. Key words to success in science.

ENERGY NEXT #NUCLEAR POWER (Electricity)

‘Energy” is a very important word in modern life. It exists in different forms. Most amazing and life changing innovation of humankind is Electricity without which we would be in the dark-age. It has changed everything it touches in our life. We are well aware of the fact that in our daily life we can hardly live without electricity. It has a wide range of complex applications along with our daily commercial needs.

Electricity is a secondary mode of energy and we get it by conversion of primary sources like coal, petrol, crude oil, solar energy, natural gas. While electricity exists in natural forms such as lightning and static electricity, it is usually generated for use on demand by electromechanical generators. These generators may be propelled by the kinetic energy of flowing water and wind, or by the movement of steam produced from water boiled by fuel combustion. The production of electricity and its effect on the environment is one of concern now a days. The electricity generated by natural fossils like petroleum, natural gases produces a number of byproducts that pollute the environment. The gases and chemicals like Carbon dioxide (CO₂), Carbon monoxide (CO),Sulfur dioxide (SO₂), Nitrogen oxides (NOx), Hydrocarbons and Heavy metals like mercury etc. are produced. These byproducts cause health hazards like inflammatory responses in the respiratory system, reducing the ability of the body to carry oxygen in blood, cardiac problems and damage to the central nervous system; fatigue; headaches; nausea and many more.

The structure of the electricity sector has been evolving over the past decade. Increasing global energy demand combined with the need to minimize GreenHouse Gas (GHG) emission require the diversification of energy sources and other technologies with lesser environmental effect. The electricity generation with Solar energy and Nuclear energy are the most promising way to generate clean energy. At present, Nuclear Power appears to be the best choice for many nations. It has a great prospect of supplying sufficient energy with creating less impact to the environment.

Nuclear Power Generation; Theory:

Nuclear power plants work on splitting of large atoms by nuclear fission process. When large atoms split into one or more smaller atoms, giving off other particles releasing energy, is called nuclear fission. Nuclear fission can happen spontaneously through radioactive decay. It can also be produced in a controlled manner on demand to get energy out of atoms in Nuclear Power plants. The process releases additional neutrons which cause fission in other uranium nuclei and a self-sustaining chain reaction leading to an enormous release of energy. The fission of rare heavy nuclei such as uranium-235 and plutonium-239 are triggered by the capture of one neutron. The nucleus then splits in two highly radioactive fragments, releasing energy and producing new neutrons. Atoms which exist in unstable forms called radioactive isotopes. They decay releasing energy. According to a basic conservation law of physics, the law of conservation of energy, the energy released in a nuclear fission reaction is equal to the total mass of the original atom and minus the total mass of the atoms it splits into which is called binding energy.

Nuclear Fission Process

Nuclear Power Plant:

The purpose of a power plant is to boil water to produce steam to power a generator to produce electricity. Power plants boil water to produce steam that spins the propeller-like blades of a turbine that turns the shaft of a generator. Inside the generator, coils of wire and magnetic fields interact to create electricity. In nuclear power plant steam is produced from the energy released by splitting atoms of uranium. The uranium fuel generates heat through a process of fission.

Nuclear Energy; Energy Next:

To deal with climate change clean energy is a necessity of present day world. Nuclear Power production is supposed to be the main way for production of electricity in future. While nuclear power plants have many similarities to other types of plants that generate electricity, there are some significant differences. It is Clean Energy, Sustainable and produces a huge amount of carbon free power and can produce more energy than other sources. Most of the countries worldwide are going to opt for generation of Nuclear power. According to the Nuclear Energy Institute (NEI), the United States avoided more than 476 million metric tons of carbon dioxide emissions in 2019 which is the equivalent of removing 100 million cars from the road and more than all other clean energy sources combined. The world is marching forward to explore the full potential of nuclear power. This has taken the form of a revolution as countries like Russia, China, France, UK, USA have set successful examples of producing electricity by nuclear reactors. The nuclear capacity growth will be around 25 % in a difference of only 25 years (2015 to 2040). It is not only fulfilling the growing demand but also to ensure a safe environment.

India started her nuclear power program more than sixty years back. The most important source of energy in India in the coming decade will be Nuclear Energy. Tarapur Atomic Power Plant is the first Nuclear power plant in India commissioned in 1968. India has independent indigenous nuclear power program. A significant expansion has been taken which will enable millions of Indians to access electricity. But till date India produces only 3.22% of its total demand as nuclear electricity with install capacity 6780 MWe with 22 operating reactors and 7 nuclear power plants but determined to grow its nuclear power program as a part of a large infrastructure development program. Resource is the main point of concern in nuclear power production. India has small Uranium but large Thorium resources. Three stage nuclear programs have been adopted with the resource of small uranium but large Thorium availability of the country. India is planning to add around ~ 22,000 Mw nuclear power generation capacity over the next decade.

The current consumption rate of fossil fuel will make them extinct by the year 2050 to 2100. Based on these facts, a nuclear power plant is a strategic choice to develop clean energy. India always is in forefront. One of the problems in nuclear power plants is large capital cost and large commissioning time of the construction of the plant but nuclear electricity costs compare well with those of electricity from coal at distances of 800 to 1000 km from the coal fields. Return from nuclear power is also great. To minimize Greenhouse gas emission and global warming, nuclear power plants are one of the possible solutions. Radiation which comes out from the nuclear fuel cycle has less magnitude than natural radiation to ionizing radiation. With the development of science the safety factors related to the nuclear power generation can be well controlled and solved. Nuclear power plants are being integrated to the power production system due to increasing demand for electricity and minimal environmental damage.

References:

[1]. http://www.world-nuclear.org/informationlibrary/current-and-future-generation/plans-for-newreactorsworldwide.aspx.

[2]. Progress in Nuclear energy; Volume 101, Part A, November 2017, Pages 4-18

[3]. Sources and pictures courtesy: Google.

Proton Decay…..A candidate for Finite Age of the Universe?

Birth and end of the universe is a challenging problem for physics. The quest started till the known time. Lots of ideas about the creation of the universe came in the course of time till modern cosmology. Most of the earlier Cosmological models describe the universe as static. After the discovery of Cosmic Background Radiation which is thought to be the relic of Big Bang Cosmology, the Big Bang theory of creation of the universe is accepted although lots of questions are yet to be answered like what causes Big Bang or who is the First Mover. Discovery of Hubble law and redshift indicated the universe is expanding. The ultimate fate of the universe is one of the most important searches of present day cosmology. Modern Cosmology provides more and more evidence for the universe with finite life. The scenario of Proton Decay has something to add to this proposition.

Proton Decay:

Proton is a fundamental constituent of matter. Since the discovery of radioactivity in 19^th century scientists are compelled to recognize the fact that not only the radioactive element but much of the matter decays eventually. High energy physics reported the decay of many so called elementary particles. Huge numbers of particles which are composed of more fundamental entities like quarks of different flavours disintegrate into lighter particles. Leptons like muon, tau disintegrates to other particles. Free neutron which is a component of the nucleus also decays with half life ~ 10.3min but it is stable when in the nucleus. The neutron is 0.2% more massive than the proton. The lightest composite stable particle is Proton which consists of two up(uu) quarks and one down(d) quark.

Big Bang theory of the universe is successful in explaining two facts, one is 3-K background radiation as remnant of primordial radiation emitted by Big Bang and the second one is current mass ratio of Helium to Hydrogen in terms of nucleosynthesis in first 100second of Big Bang. The major problem is the explanation of ratio of matter (baryon density) to photon density n_B/n_γ and preponderance of matter over antimatter. Proton Decay was first proposed by Andrei Sakharov in 1967. He put forward three points which are called Sakharov conditions to generate baryon asymmetry of the Universe. He argued that if the universe starts from Hot Big Bang, three fundamental considerations must be taken into account. First is the CP asymmetry which must account for (one of the outstanding problems in modern cosmology) the particle antiparticle asymmetry of the universe via CP violating processes. Second is the non-equilibrium dynamics which accounts for the galaxy formation and third is the baryon number violating decay to account for the baryonic matter and anti matter asymmetry of the universe. The universe is globally anti symmetric in matter. He observed that baryonic matter must decay to explain the origin of baryonic matter of the universe.

All decay processes in nature are abide by some basic interactions and corresponding conservation laws. There are four known basic interactions in nature such as Strong, Electromagnetic, Weak and Gravitational interactions. Conservation laws are critical to an understanding of Particle physics. Standard Model (SM) which unifies electromagnetic and weak interactions is supposed to be the gauge theory of Strong Interaction. SM observes baryon number (B) and lepton number (L) symmetry so that B – L are exactly conserved and a proton is stable in the framework of SM. Grand Unification Theory (GUT) unites Strong, Electromagnetic and weak interactions with quarks and leptons and their anti particles. When strong and electro-weak interactions are unified, quarks and leptons appear as members of the same irreducible representation of gauge group. The gauge boson which mediates the interactions transform quark into leptons or anti-quarks and violate baryon number (B). The unification procedure of GUT resulted in the coincidence of the coupling constants of strong, electromagnetic and weak interactions at a certain high energy known as grand unification scale. In GUT quarks could transform into lepton by the exchange of extremely heavy intermediate particles in the energy scale 10¹⁶ GeV. One of the implications of Grand Unified Theory (GUT) is the prediction that proton decay with a half life ~ 10³²years. Protons being composed of three quarks can decay via exchange of extremely massive particles called X and Y bosons with life time that is 20 orders of magnitude longer than the age of the universe. X and Y bosons can mediate the interactions which violate the baryon number B causing proton to decay.

The prominent decay mode of proton (p) is p→ e⁺ + π⁰ i.e. proton ( a baryon) decays into positron (a lepton) and a neutral pion (meson; Fig.1). There are other decay modes of protons but SU(5) predicts two body decay modes of proton to positron and meson will dominate. The new interaction in the framework of GUT predicts Baryon number and Lepton number violating four Fermions interaction via exchange of super heavy particles. The effective coupling constant of such a type of four fermions interaction is very large and makes the proton decay detectable by present generation experiments.

Experimental Searches of Proton Decay:

Baryon numbers violating decay of protons have studied widely both theoretically and experimentally. GUT predicts protons will decay at a very small rate but quite possibly measurable rates determined by the mass M_X of the postulated gauge boson of grand unifying symmetry with M_X ~10¹⁵GeV. A number of experimental efforts were going on till 1980 to detect the proton decay. The average lifetime of protons is very large but according to quantum physics the time of decay is random and if a tiny fraction of protons decay long before the average lifetime, the decay can be detected. The only requirement is a huge number of protons sources which enhances the probability of detection. Water is used as a source of protons. A proton either from Hydrogen or Oxygen decay into positron e⁺ and π⁰ which eventually decays into two photons π⁰ → 2γ (Fig.2). These showers can be observed in detectors and act as a tool for proton decay observation.

The search for proton decay has been done in Kolar Gold Field (KGF) Mine in South India 2300 meters below the surface of the earth.140 tonnes of iron which can provide 60,000 billion, billion protons, at least six of which are expected to decay annually. The interference due to cosmic ray background radiation has been minimized. The analysis of data puts the limit on the lifetime of protons as ~ 7 x 10³⁰years whereas the Mont Blanc NUSEX detector experiment puts the limit on proton lifetime τ_p ~10³⁰ years. A large water Cherenkov detector was constructed in a deep mine at Park City, Utah. The detector is sensitive to different decay modes of protons. The detector is protected from background cosmic ray radiation of muon and neutrino by natural walls of mines and using active shields. The Water Cherenkov Detector predicts that the bound proton decay to a lifetime ~ 7 x 10³³years. The IMB experiment was done at Morton Salt Mine at Cleveland, Ohio. Observation was made of 1570 meter of water equivalent to 8000 metric ton water Cherenkov detector. They put the limit on τ_p ~ 1.9 x10³¹.

Most recently the experiment on proton decay has been done by Super Kamiokande, Japan which started observation from 1996. It is a large water Cherenkov detector which is the most sensitive detector in the world used to examine proton decay with huge source with 7.5×10³³ protons or 50,000 tons water Cherenkov detector. The proton decays via most favoured channel in p→ e⁺ + π⁰ in several GUTs model. The neutral pion subsequently decays into two photons as π⁰ → 2γ. So three Cherenkov rings can be observed in the detector (Fig 2.). All the particles can be detected by the Cherenkov detector. The detector has made observations for more than 12 years and put the lower limit on the lifetime of protons as >1.6 10³⁴years. Till now there is no concrete evidence of proton decay from any experimental group.

Proton Decay and age of the universe:

Proton decay has immense cosmological implications. Protons which are the basic building blocks of all matter decay into lighter particles and supposed to be unstable. It may have a very long lifetime but still it is finite and cannot exist for ever. So the matter around us which is composed of protons must have been produced no more than a finite time and it cannot be infinite in time. It has been suggested that true eternal life depends on whether or not protons can decay and there may be inexorable decay of matter all over the universe. In billions of years from now the 10 billion galaxies that constitute the known universe may no longer exist. Proton decay has not been detected experimentally till now probably because of the fact that the event is extremely rare. Super Kamiokande observed no event in the limit of 10³³ years. At present time there is neither convincing evidence for believing protons and bound nucleons in nucleus undergo decay nor any good reason for believing that they live forever. No fundamental laws of nature prevent protons from decay. It is based on compelling theory. Science is a way of thinking. Failure of any experiment leads the new way. Thomas Alva Edison once said, ’I have not failed. I’ve just found 10,000 ways that won’t work.’ New experiments are being designed. Hyper Kamiokande experiment for detecting proton decay is on line. This experiment aimed to explain GUT and to reveal the evolution of the universe through proton decay and CP violation. Hyper-Kamiokande has sensitivity up to more than one order longer than the current lower lifetime of protons. We are hopeful that Hyper-Kamiokande will discover proton decays and will elucidate the root of materials and mysteries in the genesis of the universe beyond the Standard Model. A Baryon non-conserving process with a small asymmetry in the early universe may make the universe evolve from a symmetric state of matter to an asymmetric state of matter. Symmetry and asymmetry together make our beautiful universe. Universe is full of magical thing beyond our imagination. There are lots of questions to answer and the quest will continue. In the end let us quote from Heisenberg “Not only is the universe stranger than we think, it is stranger than we ‘can’ think”!!

Courtesy : Pictures from Google.

Euclidean to Fractal……Geometry of Nature…

Most of the physical systems of nature are not regular geometric shapes of standard geometry derived from Euclid. Most of the shapes we deal with Euclidean or classical geometry are smooth shapes like circles, triangle, rectangular volume, spheres, arc, cylinder, lines, planes etc and are classified to have integer dimensions 1, 2 or 3. A line is one dimensional because we need only one number to uniquely define any point on it. This number may be the distance from any point. This also includes curve, boundary etc. In surface we need two numbers to specify any point on it and for volume it is three numbers. Concept of dimension is basically described by two ways. The number of co-ordinates we need to describe the system or number of dynamical variables needed to specify the system. But the fact is that the natural objects we see around us are strikingly different. Randomness is natural ingredients of most Natural phenomena. A different geometry is needed to describe them. Concept of dimensions seems to be different in such systems. ‘Clouds are not sphere, mountains are not cone, coast lines are not circles, bark is not smooth nor does the lightening travel in straight line’. How dimension can be defined to describe such systems? B. Mandelbrot gave a deeper thought into it.

How long is Coast of Norway?

This is the most interesting question asked about the length of the coast of Norway. If we go for a straight cut answer it will be it depends how closely you look at it or how long your measuring stick is.

Fig-1 –Coast of Norway

Fig-2- Measured length in log-log plot

In Fig-1 the deep fjords in western coast of Norway is shown clearly. If one takes the map and measure with a ruler one can get certain value but if one opt for walking along the coast and measure the steps, one will arrive at a very different and larger value of the perimeter. While passing one could walk a divider with steps ‘δ’ km each along the coast line on the map and count the number of steps. If N (δ) number of steps are needed to move from one end to other in the map, the estimated length will be L (δ) = N(δ).δ. Every time we increase the resolution δ, we will observe increase in the measure of length of the coastline. Fig-2 shows the measured length L (δ) as function of size δ of the δ x δ square to cover the coastline on the map and shows that the coastline does not have any fixed value of length as we reduce the yardstick length δ. It is interesting to observe the curve fitted well with the expression L (δ ) = A. δ^1-D with D ~1.52. For ordinary curve the ‘A’ should be equal to total length i.e. for sufficiently small δ exponent D equals to1 but here it is 1.52.The coast line curve is a Fractal with fractal Dimension 1.52. Fractal dimensions are usually non-integers.

Fractal Dimension: Koch Curve:

Once we leave the secure ground of conventional geometry a whole zoo of fractal dimension appears! The fractals are defined in several ways. It is found that objects, curves, function and sets are fractal when their form is extremely irregular and/or fragmented at all scales. Fractals are characterized by the fact that they show structures at all scales as shown in Fig-4. Such fragmentation at all scale indicates a scale dependence of various properties of fractals.

Fig-3successive approximation Koch curve D_T=1, D_F= ln4/ln3

Fig-4 -Zoom of fractal curve.

Fig-3 describes a typical Koch curve. The line-1 is called initiator. We then remove middle third of initiator replacing it by two lines each of length (1/3) as the remaining lines in each sides (2^nd line in Fig-3). This is called the Generator which generates the new form. We repeat the process for level-2 and level-3. The length of the curve increases with each iterations. It has infinite length! The fractal dimension is found here to be D_F=1.2628 (ln4/ln3) and length may be expressed as L(δ) = δ ^1-D = δ^D^T^-D^Fwhere D_Fis fractal dimension and D_T is topological dimension which is integer. One of the basic characteristics of fractal is geometry is its dependence on resolution.

Definition of Fractals:

An irregular geometric object with an infinite nesting of structure at all scales are defined as fractals. B. Mandelbrot, the father of fractal dimension has defined the fractals in several ways. He defined the fractal a set for which Housdorff- Besicovitch dimensions strictly exceeds the topological dimension. Another definition offered by him is as Fractal is a shape made of parts similar to the whole in some way which is termed as self similarity. An object is self-similar if it is congruent to a uniformly scaled piece of itself. Fractals are characterized by non differentiability and non integer dimensions. They are defined as sets of topological dimension D_Tand Fractal dimension D_F such that D_F> D_T. Sometimes fractals are characterised by their scale divergence. This means that they are metric spaces for which a finite measure can be defined but whose standard measure which correspond their topological dimension like length of the curve, area of the surface etc. tends to infinite as resolution tends to zero. This includes power law divergences.

Similarly Fractal surfaces are characterized by surface fractal dimension greater than 2. Menger sponge is a 3d fractal but its fractal dimension is less than 3. Several kinds of fractals are defined. This includes usual fractal (power law divergence), underfractal (logarithmic divergence) and superfractal which shows exponential divergence. Usually fractal dimensions are non-integer but there are several kinds of fractals which has integer fractal dimension such as Brownian motion which has fractal dimension 2. However there are disagreement concerning the exact definition of fractal among mathematicians and it is suggested to use fractals without a pedantic definition.

Fractals-applications:

Fractals have wide range of application in almost every domain of science, engineering and bio sciences. There are lots of natural phenomena that can be defined and predicted using fractals. Some of these shapes include clouds, vegetables, colour patterns, lightning, and snowflakes. Fractal can define images that are not otherwise can be defined by Euclidean

geometry. Trees, rivers, coastlines, mountains, clouds, lightning, snowflakes and hurricanes, earthquake are all displaying or obeying fractal rules. A fractal description of many things is a story about how they grow. The fractal patterns are used by artists for a long time. The image created by a fractal is complex yet striking. Fractals are used to capture the complex organic structure and to analyze various biological processes or phenomena such as the growth pattern of bacteria. In lungs and blood vessels fractal structure can be observed with larger passages branching into smaller passages which branch again into yet smaller ones. It is widely used in image processing. Fractals are related to chaos as they are complex systems that have definite properties. Many disordered media are fractal structures. A number of works are done on deterministic fractal lattices by investigating random walk on them. It has been used to study the scattering of electromagnetic wave or scalar wave by random variation of refractive index. One of the interesting areas is the study of physics underlying irreversible growth phenomena that generates fractal structures or Kinetic Critical phenomena. New research has discovered that fractals can be put to good use in photonics by creating transparent ultrathin metallic electrodes with superior optoelectronic properties. Our world is fractal world. Its uses ranges from the branching of tracheal tubes, leaves, trees, vegetables, veins in hand, water swirling and twisting out of a tap, a puffy cumulus cloud, turbulent flow, tiny oxygen molecule or the DNA molecule and finally film and stoke market too!! There are many surprises in generating fractals and investigating their properties. It proves to be a useful tool despite all its intricacies.

A new approach to microphysics started with Fractals. The particle distribution in High Energy collision often show self similarity and power law behaviour which in turn can be related to the fractal structure of hadrons. Many works focuses on the path of the quantum particles and fundamental physics. The internal fractal structure of the path of quantum particle may be attributed to the non-differentiable space –time. In that respect laws nature can be replaced by scale relativity. This generalizes Einstein’s principle of (motion) relativity to scale transformation. Fractal is deeply related to in-homogeneity. Fractal approach has been made to study large scale distribution of galaxies which is a new approach for understanding galaxy clustering. Universe is suggested to have fractal structure at all scales. Fractals seem to prevail in nature starting from macro to micro scale. In the end if we ask why fractals? Possible answer could be structural manifestation of the fundamental non differentiability of Nature which leads to the fact that Laws of Nature are non-differentiable!!

References:

Feder : Fractals, Plenum Press, (1989)
B. Mandelbrot: Fractal Geometry of Nature, W.H Freeman and Co (1982).
Nottale: Scale Relativity and Fractal Space Time. Imperial College Press (2011)

Pictures; Courtesy Google picture.

Atoms to Quarks…A Quest for Ultimate Structure of Matter

Human mind always thrived to venture the uncharted territories of unknown. Tiny constituents of matter, energy and their relation with cosmology are ventured by enthusiast of Particle Physics. Investigations are carried out to probe deeper into the structure of matter in order to seek at every stage the constituents of previously so called ‘Fundamental Entity’. In our search of ultimate structure of matter, it was only known that the atom is basic constituents of matter and it is electrically neutral as a whole.

Atom Model:

The quest for fundamental particle inspirited by J.J. Thomson to look inside the atom with the discovery of electron in 1897 and an era of fundamental particles began. Thomson conception of atom- first suggested in1903. He imagined that atom consists of positive sphere of electrification within which were the negative electrons where all positively and negatively charges are uniformly distributed within a sphere of radius ~10^-10m making the atom electrically neutral.

This Plum Pudding model of Thomson is challenged by Rutherford by his pioneering experiment of large angle scattering of Alpha particles (α) by thin gold foil in 1911. Rutherford showed such conception of atom model could not possibly account for the number of alpha particles scattered through large angles in Geiger and Marsden’s experiment. Alpha particle (₂He⁴) is a positively charged particle and the particle suffers an intense repulsive electrostatic force and found to scatter almost at an angle more than 150⁰. The core of atom is alleged to consist of a minute positively charged nucleus which provides the intense electric field. Under the action of central inverse square law of force of repulsion, the path of α particle will be a hyperbola with nucleus as external focus.

A plot of the scattering angle vs number of scattered particle shows that the positively charged particles (protons) are concentrated at a core called nucleus. Thus suggesting the fact that ‘the atom has structure’! He also showed that the effect of the electrons outside the nucleus is negligible for deflection of α particle more than 1⁰. Rutherford succeeded in estimating the size of the nucleus subsequently. He also discovered proton in 1919.

Long before the ninetinth century it was known from experimental observation that the elements emit line spectra and there are similarities in appearance of the spectra of different alkai metals. Some genuine explanation on these series spectra were extended by Balmer, Rydberg and others but there was little idea of the nature of mechanism in the atoms responsible for emission of spectral lines of characteristic fequencies. In 1900 Planck explained the law of blackbody radiation postulating that radiation of energy is not emitted or absorbed in cotinuous manner but in the form of discrete ‘Quanta’ of energy of magnitude ‘hν’ where h is Planck’s constant.

The first concept of quatum behaviour of nature. This discrete quanta is now known as photon named by G.N Lewis later on. Bhor has used all these concept to explain the spectrum of hydrogen. His postulates are based on discrete nature of atomic spectra in particular certain spectral lines of Hydrogen spectra in visible range (Balmer Series). In 1913 Bohr put forward his model for atoms with his postulates where the negatively charged electrons are suggested to be moving around the nucleus in some quantized stationary orbits. If an electron made a quantum jump from a statinary orbit, it will radiate frequency ν of energy hν. He is the key figure for driving the subsequent theoretical development of Quantum Mechanics. His explanation for line spectra may be considered as the first triumph of Quantum Dynamics too. With Bohr postulates we come across a picture of an atoms with nucleus at the centre and electrons moving around in quantized orbit.

The complete picture of an atom was yet to be obtained. The Helium nucleus is found to be more massive than the prediction. Scientists were sure about the fact that something is missing with the discrepencies between mass number and atomic numbers. In the year 1932 James Chadwick discovered a particle named neutron from the Cavendish Laboratoty. His discovery comes from the apparant incompatibility of the energy momentum conservation of bombarment of Beryllium by alpha particle.The discovery of neutron completely reshaped the lanscape in the field of Nuclear and Particle Physics.

Deep Inelastic Scattering Experiments (DIS) and Quark Model:

In our quest for atomic structure we come across three elementary particles. Electron which is a Lepton (small mass), proton and neutron. Elementary particles are the particles to which no internal structure can be assigned. But much more surprises were waiting for physicists as more experimental results on scattering at much higher energy started to arrive.

In high energy accelerators, electrons are accelerated at very high energy and allowed to scatter from a stationary proton. Proton gets disrupted due to high energies and produce various new particles. In such an inelastic scattering, the scattering cross section is found to drop abruptly while over all cross section of events producing the other particles remains almost constant. This type of scattering guides us to the recent depiction of proton. This experimental result suggests that proton possess three point of deflection and it has structure!

In order to search for the sub structure of hadrons (baryons like proton and also mesons) Gell Mann and Zweig put forward their Eightfold way in 1961 and Quark hypothesis. They have suggested that all baryons and mesons are composed of a much fundamental ‘entity’ of fractional electric charge which they named Quarks. Baryons are supposed to be three quarks

system whereas meson is quark anti-quark system. They first proposed the existence of fractionally charged particles. Initially three types of quark flavour are suggested (up, down, Strange). Proton consists of three quarks namely two up(u) quarks, a down quark (d) whereas neutron consists of two down quarks and a up quark. Subsequently more three type quarks are suggested making the number of quark flavour six in total to account for the structure of zoo of subatomic particles discovered later on. Six types of leptons are known. Probably the Quark-Lepton symmetry of nature will restrict the number of quarks upto six although QCD, theory of strong interaction predicts more types of quarks theoretically. So the Fundamental particles includes quarks, leptons and mediators who are the bosons mediating the basic interactions.

Quantum Chromo Dynamics (QCD) which is dynamics of strong interaction is characterised by Asymptotic Freedom and Confinement. Each quark can come into three colours-Red, Green and Blue in order to honour Pauli Exclusion Principle. Permanent confinement of quarks inside hadrons prevents us to observe a free quark- a consequence of the fact that all physical observable of states of nature are colour neutral.

Study of the structure of proton revealed that it is not a fundamental particle. So in our quest to ultimate structure of matter, we ended up with electrons and quarks (the constituent of proton and neutrons) which are elementary particles constituting an atom. The modern picture of atom can be seen in the picture above… electrons moving around and nucleus consists of quarks. This wonderful journey of Particle physics in search of the structure of atom from electrons to quark extends almost 75 years! First imagination of atom model came from Thomson and gradually we move forward with subsequent steps. In science each and every step is great either right or wrong as Newton said ‘If I have seen further than others, it is by standing upon the shoulders of giants’!!

The story does not end here. We have a long way to go. Proton is not as simple as consisting of three valence quarks only. Last picture shows its probable structure. It has a sea of virtual clouds consisting quark-anti quark pairs. As we probe smaller and smaller distances i.e. at higher energies, the structure seems to be more and more complicated. Till we know little about proton size, shape, mass, magnetic moment and spin. The size and shape of proton is yet to be determined which is very important as we know geometry depicts the interaction. Some theoretical investigations suggest that it can have fractal structure!!.The discovery by EMC collaboration indicates that constituent quarks appear to contribute very little to the proton spin which is termed as Proton spin crisis. Recent experiments suggest proton can have strange quark virtual sea in addition to up and down quarks and contribution from gluons, the mediator of quark-quark interaction. Deep inside proton may discover a new state of matter. In fact Proton may contain a universe inside!

Science is always an adventure, scientists love mysteries. This never ending journey is no less wonderful than that of journey of ‘Alice in Wonderland’. In the end let us remember famous quote by Rutherford himself ‘All of Physics is either impossible or trivial. It is impossible until you understand it, and then it becomes trivial’!!!

Till let journey continue….

Courtesy : Pictures from Google.