Dr.A.B.Rajib Hazarika's Pattern Recognition on Fusion

8/7/2019 Dr.A.B.Rajib Hazarika's Pattern Recognition on Fusion

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Dr.A.B.Rajib Hazarikas Pattern

recognition on fusion

By Dr.A.B.Rajib Hazarika


2/47Dr.A.B.Rajib Hazarika

Dr.A.B.Rajib Hazarikas Pattern Recognition on Fusion2

Page no.(i)

Dr.A.B.Rajib Hazarika, A.E.S.

MSc, PhD, MIAMP (Germany), FRAS (Lond.), MWASET, MFFS (USA), MIBC (UK), MNPSS

(USA)

Assistant Professor, Res: Anjena Manzil, Kadomtola,

Dept. of Mathematics, Modhupur, P.O. Modhupur,

Diphu Govt. College, Diphu, Dist: Nagaon, Assam, IndiaKarbi Anglong, Assam, India Pin - 782001

Pin- 782462, M- 9435166881 Ph- 03672-256327

************************************************************************

Page no.(ii)

PREFACE ABOUT THE AUTHOR

As available on website: http://wpedia.goo.ne.jp/enwiki/User:Drabrh/Dr.A.B.Rajib_Hazarika

User:Drabrh/Dr.A.B.Rajib Hazarika

From Wikipedia, the free encyclopedia




Dr.A.B.Rajib Hazarika

[[File:Dr.A.B.Rajib Hazarika & his two kids.jpg[1]

|frameless|alt=]]Dr.A.B.Rajib Hazarika with Laquit(son) and Danisha(daughter)

Born

Azad Bin Rajib Hazarika

July 2, 1970 (age 40)

Jammu,Jammu and Kashmir, India

Residence Nagaon,Assam, India

Nationality Indian

Ethnicity AssameseMuslim

Citizenship India

Education PhD,PDF,FRAS

Alma mater

University of Jodhpur

Jai Narayan Vyas University

Institute of Advanced Study in Science & Technology

http://www.iasst.in/]

Kendriya Vidyalaya [1] http://www.akipoonacollege.com/

OccupationAssistant Professor (Lecturer), Diphu Govt. College ,

Diphu,Assam,India

Years active 2004- onwards

EmployerDiphu Government College

Government of Assam ,Assam Education Service

Known for

Lecturer,Assistant Professor,Mathematician,

Academician,Fusion,Astronomy

Home town Nagaon,Assam, India

Salary Rs 40000 per month

Height 6 feet and 2 inches

Weight 100 kg

TitleDoctorate, Dr., FRAS (London), Assam Education Service,

AES
http://commons.wikimedia.org/wiki/File:Dr.A.B.Rajib_Hazarika_&_his_kids.jpghttp://commons.wikimedia.org/wiki/File:Dr.A.B.Rajib_Hazarika_&_his_kids.jpghttp://wpedia.goo.ne.jp/enwiki/Jammuhttp://wpedia.goo.ne.jp/enwiki/Jammuhttp://wpedia.goo.ne.jp/enwiki/Jammu_and_Kashmirhttp://wpedia.goo.ne.jp/enwiki/Jammu_and_Kashmirhttp://wpedia.goo.ne.jp/enwiki/Indiahttp://wpedia.goo.ne.jp/enwiki/Nagaonhttp://wpedia.goo.ne.jp/enwiki/Nagaonhttp://wpedia.goo.ne.jp/enwiki/Assamhttp://wpedia.goo.ne.jp/enwiki/Assamhttp://wpedia.goo.ne.jp/enwiki/Indiahttp://wpedia.goo.ne.jp/enwiki/Indiahttp://wpedia.goo.ne.jp/enwiki/Assamesehttp://wpedia.goo.ne.jp/enwiki/Assamesehttp://wpedia.goo.ne.jp/enwiki/Muslimhttp://wpedia.goo.ne.jp/enwiki/Indiahttp://wpedia.goo.ne.jp/enwiki/PhDhttp://wpedia.goo.ne.jp/enwiki/PhDhttp://wpedia.goo.ne.jp/enwiki/PDFhttp://wpedia.goo.ne.jp/enwiki/PDFhttp://wpedia.goo.ne.jp/enwiki/PDFhttp://wpedia.goo.ne.jp/enwiki/FRAShttp://wpedia.goo.ne.jp/enwiki/FRAShttp://wpedia.goo.ne.jp/enwiki/Alma_materhttp://wpedia.goo.ne.jp/enwiki/University_of_Jodhpurhttp://www.iasst.in/http://wpedia.goo.ne.jp/enwiki/Kendriya_Vidyalayahttp://wpedia.goo.ne.jp/enwiki/Kendriya_Vidyalayahttp://wpedia.goo.ne.jp/enwiki/Kendriya_Vidyalayahttp://wpedia.goo.ne.jp/enwiki/User:Drabrh/Dr.A.B.Rajib_Hazarika#cite_note-0http://wpedia.goo.ne.jp/enwiki/Kendriya_Vidyalayahttp://www.akipoonacollege.com/http://wpedia.goo.ne.jp/enwiki/Diphuhttp://wpedia.goo.ne.jp/enwiki/Diphuhttp://wpedia.goo.ne.jp/enwiki/Assamhttp://wpedia.goo.ne.jp/enwiki/Assamhttp://wpedia.goo.ne.jp/enwiki/Indiahttp://wpedia.goo.ne.jp/enwiki/Diphu_Government_Collegehttp://wpedia.goo.ne.jp/enwiki/Government_of_Assamhttp://wpedia.goo.ne.jp/enwiki/Lecturerhttp://wpedia.goo.ne.jp/enwiki/Lecturerhttp://wpedia.goo.ne.jp/enwiki/Assistant_Professorhttp://wpedia.goo.ne.jp/enwiki/Assistant_Professorhttp://wpedia.goo.ne.jp/enwiki/Assistant_Professorhttp://wpedia.goo.ne.jp/enwiki/Mathematicianhttp://wpedia.goo.ne.jp/enwiki/Academicianhttp://wpedia.goo.ne.jp/enwiki/Academicianhttp://wpedia.goo.ne.jp/enwiki/Fusionhttp://wpedia.goo.ne.jp/enwiki/Fusionhttp://wpedia.goo.ne.jp/enwiki/Fusionhttp://wpedia.goo.ne.jp/enwiki/Astronomyhttp://wpedia.goo.ne.jp/enwiki/Nagaonhttp://wpedia.goo.ne.jp/enwiki/Nagaonhttp://wpedia.goo.ne.jp/enwiki/Assamhttp://wpedia.goo.ne.jp/enwiki/Assamhttp://wpedia.goo.ne.jp/enwiki/Indiahttp://wpedia.goo.ne.jp/enwiki/Doctoratehttp://wpedia.goo.ne.jp/enwiki/Dr.http://commons.wikimedia.org/wiki/File:Dr.A.B.Rajib_Hazarika_&_his_kids.jpghttp://wpedia.goo.ne.jp/enwiki/Jammuhttp://wpedia.goo.ne.jp/enwiki/Jammu_and_Kashmirhttp://wpedia.goo.ne.jp/enwiki/Indiahttp://wpedia.goo.ne.jp/enwiki/Nagaonhttp://wpedia.goo.ne.jp/enwiki/Assamhttp://wpedia.goo.ne.jp/enwiki/Indiahttp://wpedia.goo.ne.jp/enwiki/Indiahttp://wpedia.goo.ne.jp/enwiki/Assamesehttp://wpedia.goo.ne.jp/enwiki/Muslimhttp://wpedia.goo.ne.jp/enwiki/Indiahttp://wpedia.goo.ne.jp/enwiki/PhDhttp://wpedia.goo.ne.jp/enwiki/PDFhttp://wpedia.goo.ne.jp/enwiki/FRAShttp://wpedia.goo.ne.jp/enwiki/Alma_materhttp://wpedia.goo.ne.jp/enwiki/University_of_Jodhpurhttp://www.iasst.in/http://wpedia.goo.ne.jp/enwiki/Kendriya_Vidyalayahttp://wpedia.goo.ne.jp/enwiki/User:Drabrh/Dr.A.B.Rajib_Hazarika#cite_note-0http://www.akipoonacollege.com/http://wpedia.goo.ne.jp/enwiki/Diphuhttp://wpedia.goo.ne.jp/enwiki/Assamhttp://wpedia.goo.ne.jp/enwiki/Indiahttp://wpedia.goo.ne.jp/enwiki/Diphu_Government_Collegehttp://wpedia.goo.ne.jp/enwiki/Government_of_Assamhttp://wpedia.goo.ne.jp/enwiki/Lecturerhttp://wpedia.goo.ne.jp/enwiki/Assistant_Professorhttp://wpedia.goo.ne.jp/enwiki/Mathematicianhttp://wpedia.goo.ne.jp/enwiki/Academicianhttp://wpedia.goo.ne.jp/enwiki/Fusionhttp://wpedia.goo.ne.jp/enwiki/Astronomyhttp://wpedia.goo.ne.jp/enwiki/Nagaonhttp://wpedia.goo.ne.jp/enwiki/Assamhttp://wpedia.goo.ne.jp/enwiki/Indiahttp://wpedia.goo.ne.jp/enwiki/Doctoratehttp://wpedia.goo.ne.jp/enwiki/Dr.




Board

member of

Member of Scientific and Technical committee & Editorial

review board of Natuaral and Applied sciences World

Academy of Science ,Engineering & Technologyhttp://www.waset.org/NaturalandAppliedSciences.php?

page=45

ReligionSunni Islam,

Spouse Helmin Begum Hazarika

Children Laquit Ali Hazarika(son), Danisha Begum Hazarika(daughter)

ParentsRosmat Ali Hazarika@Rostam Ali Hazarika@Roufat Ali

Hazarika and Anjena Begum Hazarika

Call-sign Drabrh or Raja

Website

http://www.facebook.com/Drabrajib

http://in.linkedin.com/pub/dr-a-b-rajib-hazarika/25/506/549

http://en.wikipedia.org/wiki/Special:Contributions/Drabrh

http://www.diphugovtcollege.org/

http://www.karbianglong.nic.in/diphugovtcollege.org/teaching.html

Dr.A.B.Rajib Hazarika,PhD,FRAS,AES (born July 02, 1970, in Jammu, Jammu and Kashmir,India) is

Assistant Professor(Lecturer) Diphu Government College ,Diphu in KarbiAnglong district ,Government ofAssam [2] , [3], KarbiAnglong,Assam's largest conglomerate byGovernment of Assam . He is also the

Fellow ofRoyal Astronomical Society [4] ,London ,Member ofInternational Association of Mathematical

Physics, World Academy of Science ,Engineering & Technology ,Focus Fusion Society,Dense Plasma

Focus, Plasma Science Society of India, International Biographical centre, Assam Science Society, Assam

Academy of Mathematics,International Atomic Energy Agency,Nuclear and Plasma Society,Society of

Industrial and Applied Mathematics,German Academy of Mathematics and Mechanics,Fusion Science &

Technology Society,Indian National Science Academy,Indian Science Congress Association,Advisory

Committee of Mathematical Education, Royal Society,International Biographical Centre.

Contents

1 Early life

o 1.1 Early career

1.1.1 Currently working
http://www.waset.org/NaturalandAppliedSciences.php?page=45http://www.waset.org/NaturalandAppliedSciences.php?page=45http://wpedia.goo.ne.jp/enwiki/Sunni_Islamhttp://wpedia.goo.ne.jp/enwiki/Sunni_Islamhttp://www.facebook.com/Drabrajibhttp://in.linkedin.com/pub/dr-a-b-rajib-hazarika/25/506/549http://en.wikipedia.org/wiki/Special:Contributions/Drabrhhttp://www.diphugovtcollege.org/http://www.karbianglong.nic.in/diphugovtcollege.org/teaching.htmlhttp://wpedia.goo.ne.jp/enwiki/PhDhttp://wpedia.goo.ne.jp/enwiki/FRAShttp://wpedia.goo.ne.jp/enwiki/FRAShttp://wpedia.goo.ne.jp/enwiki/FRAShttp://wpedia.goo.ne.jp/enwiki/AEShttp://wpedia.goo.ne.jp/enwiki/Jammuhttp://wpedia.goo.ne.jp/enwiki/Jammu_and_Kashmirhttp://wpedia.goo.ne.jp/enwiki/Jammu_and_Kashmirhttp://wpedia.goo.ne.jp/enwiki/Indiahttp://wpedia.goo.ne.jp/enwiki/Indiahttp://wpedia.goo.ne.jp/enwiki/Diphu_Government_Collegehttp://wpedia.goo.ne.jp/enwiki/Diphuhttp://wpedia.goo.ne.jp/enwiki/Government_of_Assamhttp://wpedia.goo.ne.jp/enwiki/Government_of_Assamhttp://wpedia.goo.ne.jp/enwiki/Government_of_Assamhttp://wpedia.goo.ne.jp/enwiki/Government_of_Assamhttp://www.karbianglong.nic.in/diphugovtcollege/teaching.htmlhttp://wpedia.goo.ne.jp/enwiki/Government_of_Assamhttp://www.diphugovtcollege.org/DGC%20prospectus%2008-09.pdfhttp://www.diphugovtcollege.org/DGC%20prospectus%2008-09.pdfhttp://wpedia.goo.ne.jp/enwiki/Government_of_Assamhttp://wpedia.goo.ne.jp/enwiki/Government_of_Assamhttp://wpedia.goo.ne.jp/enwiki/Royal_Astronomical_Societyhttp://wpedia.goo.ne.jp/enwiki/Royal_Astronomical_Societyhttp://www.ras.org.uk/member?recid==5531http://wpedia.goo.ne.jp/enwiki/Royal_Astronomical_Societyhttp://wpedia.goo.ne.jp/enwiki/Londonhttp://wpedia.goo.ne.jp/enwiki/Londonhttp://wpedia.goo.ne.jp/enwiki/International_Association_of_Mathematical_Physicshttp://wpedia.goo.ne.jp/enwiki/International_Association_of_Mathematical_Physicshttp://wpedia.goo.ne.jp/enwiki/International_Association_of_Mathematical_Physicshttp://wpedia.goo.ne.jp/enwiki/Focus_Fusion_Societyhttp://wpedia.goo.ne.jp/enwiki/Focus_Fusion_Societyhttp://wpedia.goo.ne.jp/enwiki/Focus_Fusion_Societyhttp://wpedia.goo.ne.jp/enwiki/Dense_Plasma_Focushttp://wpedia.goo.ne.jp/enwiki/Dense_Plasma_Focushttp://wpedia.goo.ne.jp/enwiki/Dense_Plasma_Focushttp://wpedia.goo.ne.jp/enwiki/International_Atomic_Energy_Agencyhttp://wpedia.goo.ne.jp/enwiki/International_Atomic_Energy_Agencyhttp://wpedia.goo.ne.jp/enwiki/Indian_National_Science_Academyhttp://wpedia.goo.ne.jp/enwiki/Indian_Science_Congress_Associationhttp://wpedia.goo.ne.jp/enwiki/Indian_Science_Congress_Associationhttp://wpedia.goo.ne.jp/enwiki/International_Biographical_Centrehttp://wpedia.goo.ne.jp/enwiki/User:Drabrh/Dr.A.B.Rajib_Hazarika#Early_lifehttp://wpedia.goo.ne.jp/enwiki/User:Drabrh/Dr.A.B.Rajib_Hazarika#Early_lifehttp://wpedia.goo.ne.jp/enwiki/User:Drabrh/Dr.A.B.Rajib_Hazarika#Early_lifehttp://wpedia.goo.ne.jp/enwiki/User:Drabrh/Dr.A.B.Rajib_Hazarika#Early_careerhttp://wpedia.goo.ne.jp/enwiki/User:Drabrh/Dr.A.B.Rajib_Hazarika#Early_careerhttp://wpedia.goo.ne.jp/enwiki/User:Drabrh/Dr.A.B.Rajib_Hazarika#Early_careerhttp://wpedia.goo.ne.jp/enwiki/User:Drabrh/Dr.A.B.Rajib_Hazarika#Currently_workinghttp://wpedia.goo.ne.jp/enwiki/User:Drabrh/Dr.A.B.Rajib_Hazarika#Currently_workinghttp://wpedia.goo.ne.jp/enwiki/User:Drabrh/Dr.A.B.Rajib_Hazarika#Currently_workinghttp://www.waset.org/NaturalandAppliedSciences.php?page=45http://www.waset.org/NaturalandAppliedSciences.php?page=45http://wpedia.goo.ne.jp/enwiki/Sunni_Islamhttp://www.facebook.com/Drabrajibhttp://in.linkedin.com/pub/dr-a-b-rajib-hazarika/25/506/549http://en.wikipedia.org/wiki/Special:Contributions/Drabrhhttp://www.diphugovtcollege.org/http://www.karbianglong.nic.in/diphugovtcollege.org/teaching.htmlhttp://wpedia.goo.ne.jp/enwiki/PhDhttp://wpedia.goo.ne.jp/enwiki/FRAShttp://wpedia.goo.ne.jp/enwiki/AEShttp://wpedia.goo.ne.jp/enwiki/Jammuhttp://wpedia.goo.ne.jp/enwiki/Jammu_and_Kashmirhttp://wpedia.goo.ne.jp/enwiki/Indiahttp://wpedia.goo.ne.jp/enwiki/Diphu_Government_Collegehttp://wpedia.goo.ne.jp/enwiki/Diphuhttp://wpedia.goo.ne.jp/enwiki/Government_of_Assamhttp://wpedia.goo.ne.jp/enwiki/Government_of_Assamhttp://www.karbianglong.nic.in/diphugovtcollege/teaching.htmlhttp://www.diphugovtcollege.org/DGC%20prospectus%2008-09.pdfhttp://wpedia.goo.ne.jp/enwiki/Government_of_Assamhttp://wpedia.goo.ne.jp/enwiki/Royal_Astronomical_Societyhttp://www.ras.org.uk/member?recid==5531http://wpedia.goo.ne.jp/enwiki/Londonhttp://wpedia.goo.ne.jp/enwiki/International_Association_of_Mathematical_Physicshttp://wpedia.goo.ne.jp/enwiki/International_Association_of_Mathematical_Physicshttp://wpedia.goo.ne.jp/enwiki/Focus_Fusion_Societyhttp://wpedia.goo.ne.jp/enwiki/Dense_Plasma_Focushttp://wpedia.goo.ne.jp/enwiki/Dense_Plasma_Focushttp://wpedia.goo.ne.jp/enwiki/International_Atomic_Energy_Agencyhttp://wpedia.goo.ne.jp/enwiki/Indian_National_Science_Academyhttp://wpedia.goo.ne.jp/enwiki/Indian_Science_Congress_Associationhttp://wpedia.goo.ne.jp/enwiki/International_Biographical_Centrehttp://wpedia.goo.ne.jp/enwiki/User:Drabrh/Dr.A.B.Rajib_Hazarika#Early_lifehttp://wpedia.goo.ne.jp/enwiki/User:Drabrh/Dr.A.B.Rajib_Hazarika#Early_careerhttp://wpedia.goo.ne.jp/enwiki/User:Drabrh/Dr.A.B.Rajib_Hazarika#Currently_working




2 Career

3 Research

4 Patent & Innovation

5 Research Guidence

6 Personal life

7 Quotes

8 Awards and recognition

9 References

10 External links

Early life

Dr.A.B.Rajib Hazarika was born into the famous Hazarika family, a prominent family belonging to Dhing's

wealthy Muslim Assamese community ofNagaondistrict. He was born to Anjena Begum Hazarika and

Rusmat Ali Hazarika. He is eldest of two childrens of his parents younger one is a Shamim Ara

Rahman(nee Hazarika)daughter .

Early career

Dr.A.B.Rajib Hazarika completed his PhD degree in Mathematicsfrom J N Vyas University of Jodhpur in

1995 with specialization inPlasma instability, thethesiswas awarded best thesis byAssociation of

Indian Universitiesin 1998 and the Post-Doctoral Fellow Program from Institute of Advanced Study in

Science & Technology[5] inGuwahatiAssamin 1998 asResearch AssociateinPlasma Physics Division

in theory group studying the Sheath phenomenon. As a Part-time Lecturer in Nowgong college, Assam

before joining the present position in Diphu Government College ,Diphu in KarbiAnglong district[6],[7]

He is a member of the wikipedia[8],[9].

He is Fellow of Royal Astronomical Society[10],member of International Association Mathematical

Physics [11], member of World Academy of Science,Engineering & Technology [12], [13],member ofPlasma Science Society of India[14] ,[15] ,member of Focus Fusion Society forum [16],member of Dense

Plasma Focus [17], Member of Assam Science Society[18], Member of Assam Academy of Mathematics

[19]

Currently working

He joined theDiphu Government College [20] in July 2004 asLecturerinMathematics (Gazetted officer)

through Assam Public Service commission[21] in Assam Education Service [22],AES-I. [23] now

redesignated as Assistant Professor.

Career

In May 1993, Dr.A.B.Rajib Hazarika was awarded Junior Research Fellowship, University GrantsCommission,National Eligibility Test and eligibility for Lecturership ,Govt. of India and worked as

JRF(UGC,NET) in Department of Mathematics and Statistics of J N Vyas University in Jodhpur. Later on

in May 1995 got Senior Research Fellowship(UGC,NET) and continued research for completion ofPhDon

27th Dec 1995 .From 1993 onwards taught in Kamala Nehru College for women, Jodhpur and in Faculty of

Science in J N Vyas University in Jodhpur up to the completion ofPhD.In 1998 May joined Plasma
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Physics Division of Institute of Advanced Study in Science & Technology in Guwahati as Research

Associate forPDF in theory group to study the sheath phenomena of National Fusion Programme [24] of

Govt. of India. Then joined Nowgong College as a part-time Lecturer after which in 2004, July joined the

present position of Lecturer in Diphu Government College which is redesignated as Assistant Professor.

Research

During PhD http://www.iopscience.iop.org/1402-4896/51/6/012/pdf/physcr_51_6_012.pdf http://www.iopsciences.iop.org/1402-4896/53/1/011/pdf/1402-4896_53_1_011.pdf

http://www.niscair.res.in/sciencecommunication/abstractingjournals/isa_1jul08.asp

http://en.wiktionary.org/wiki/Wikitionary:Sandbox

http://adsabs.harvard.edu/abs/1996PhyS..53...578

duringPDF the research was based on Astronomy, Astrophysics, Geophysics , for plasma instability with

the title of thesis as Some Problems of instabilities in partially ionized and fully ionized plasmas which

later on in 1998 was assessed as best thesis of the year by Association of Indian Universities in New Delhi.His current interest lies in Astronomy, Astrophysics, Geophysics, Fusion Plasma, and innovation of fusion

devices, design of fusion devices, simulation codes and theoretical mathematical modeling.He is known for

his theoretical research work on Gravitational instability and gravitational collapse M=23/2 Msun as a new

formula for Chandrasekhar limit now known as Bhatia-Hazarika Limit , when the rotating neutron star,

pulsars are formed .When the mass of the star is more than this limit a neutron star shrinks or abberates due

to gravitational collapse up to a point size in space. As it is known that when the star passes limit of the size

of old star more than three times that of mass of sun it passes the Schwarchild radius and there on is a black

hole from where we can receive no more information as its gravitational field is too intense to permitanything , even photons to escape.Research at Diphu Govt. College

http://en.wikipedia.org/wiki/Special:Contributions/Drabrh/File:Drabrhdouble_trios_saiph_star01.pdf

http://en.wikipedia.org/wiki/File:Drabrh_bayer_rti.pdf

http://en.wikipedia.org/wiki/File:Columb_drabrh.pdf

http://en.wikipedia.org/wiki/File:Drabrh_double_trios.pdf

http://en.wikipedia.org/wiki/File:Drabrhiterparabolic2007.pdf

http://en.wikipedia.org/wiki/File:Drabrh_mctc_feedbackloop.pdf

http://en.wikipedia.org/wiki/File:Drabrh_tasso_07.pdf

http://en.wikipedia.org/wiki/File:Abstracts.pdf?page=2

Patent & Innovation

Applied forpatentin US patent and trademarks office has innovated three future fusion devices Double

Tokomak collider (DTC),Magnetic confinement Tokomak collider (MCTC) hub, Duo Triad Tokomak

collider (DTTC) hub .A Hall thruster as diffusion associated neoclassical indigenous system of Hallassembly (DANISHA)is designed applied for international application No.PCT/IB2009/008024 in World

Intellectual Property Organisation [25] .He has innovated a new simulation code Fuzzy Differential

Inclusion Code in 2003 for fusion process.[26], [27]

Research Guidence
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Research guidence is given to two students in Mathematics forMPhildegree

Personal life

Dr.A.B.Rajib Hazarika has a metallic Scarlet red Tata Indigo CS ofTata motorsmake and loves to drivehimself.

Quotes

"Fakir(saint) and lakir(line) stops at nothing but at destination"

"Expert criticizes the wrong but demonstrates the right thing"

Intellectuals are measured by their brain not by their age and experience

Two type of persons are happy in life one who knows everything another who doesnt know

anything

Implosion in device to prove every notion wrong for fusion

Meditation gives fakir(saint) long life and fusion devices the long lasting confinement

Awards and recognition

Dr.A.B.Rajib Hazarika got Junior Research Fellowship,Government of India

Senior Research Fellowship,Government of India

Research AssociateshipDST Government of India

Fellow ofRoyal Astronomical Society[28]

Member of Advisory committee of Mathematical Education Royal SocietyLondon

Member of Scientific and Technical committee & editorial review board on Natural and applied sciences of

World Academy of Science ,Engineering &Technology[29]Leading professional of the world-2010 as noted and eminent professional from International Biographical

CentreCambridge

References

1. http://www.kvafsdigaru.org/Poona College of Arts, Science &Commerce

Template:Http://en.wikipedia.org/wiki/Special:contributions/Drabrh

External links

Wikimedia Commons has media related to:Drabrh/Dr.A.B.RajibHazarika

[30]

Dr.A.B.Rajib Hazarika's profile on the Linkedin Website

[31] ]]
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dr ab rajib hazarika aes 19:01, 16 October 2010 (UTC) dr ab rajib hazarika aes

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User:Drabrh/Dr.A.B.Rajib Hazarika English

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User:Drabrh/Dr.A.B.Rajib Hazarika English

User:Drabrh/Dr.A.B.Rajib Hazarika

- goo

CHAPTER-2
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PATTERN RECOGNITION DRABRH-DANISHA ECONOMIC MODEL FOR STOCK MARKET

An economic model for stock market is presented as DRABRH-DANISHA for economic boom. The

present model is for the banking sector in the stock market as it provides with certain parameters which

allows having such boom by using this model. Directly the growth rate and the power factor are presented

as a mathematical formula for better understanding as follows along with the confinement time factor:

Growth-rate

In secs

For power of DRABRH-DANISHA

73

3

=

pipi

heDANISHAl

ccnCmP

hC =Hazarika cost holistic=2.646

First bracket term is volatility component; second bracket term is a constant non-dimensional quantity.

Wpi=wholesale price index

C=cost

w=wholesale valuel= liquidity

Ln=inflation

Vx=volatility

The analysis of the above equation in terms of interpretations provides into the insight of the utility of the

economic model. The growth rate is dependent on inflation as the inflation goes up the growth rate goes

down. Same is the case with the cost as the cost increases the growth rate decreases. Similarly the Hazarika

cost holistic also provides the stability in the growth rate, whereas the volatility, liquidity and wholesale

price index are directly related to the growth rate as these values goes up the growth rate also goes up.

The power of the stock market comes from term Hazarika cost holistic as it varies as the cubic power along

with the earlier presented models in the past. This model provides with the power which is 18.525 times the

earlier models. So that the extra thrust is provided to the stock market leading to the economic boom.

In such process the wholesale price index provides the largest hare to pull down the power of the sharemarket, parameter which plays the crucial role is liquidity because this also leads to the downfall of the

power of stock market. As is known that the power and thrust is necessary for the banking sector the

inverse growth rate provides with the longevity in the banking sector.

1

1

4

2

1

+

== n

pi

h

X gLc

l

lC

V

1=




Cost is another factor which influences the thrust in the stock market as goes ten folds. The growth rate

decreases seven folds whereas the confinement time increases seven folds leading to the economic boom in

the stock market.

CHAPTER-3

FUZZY PATTERN ON QUARKS

It is a pioneering effort to relate the two streams i.e., fuzzy set theory of mathematics and quark theory ofphysics .It is an inter displinary study, which can be used in future pattern recognition for defining and

describing with fuzzy logics. Fuzzy set, fuzzy differential equation and fuzzy differential inclusion (FDI).

A fuzzy set is defined as g: P(X) [ ]1,0 which assign to each crisp subset of X a number in the unitinterval [ ]1,0 .Domain of function g is the power set P(X) is a crisp set X. Now let us define fuzzydifferential equation as follows:

Here x is a phase space , t is time x(t) is a fuzzy valued function defined

on

( ) ( ) CXKXtfdt

dX == 0,,, , where C is a triangular fuzzy number.

Fuzzy differential inclusion (FDI) can be defined as a set of such fuzzy number.

Where ( ) 0,10 xax

For second order derivative we have

where K is a Trapezoidal fuzzy number.

For

Where L, M are Triangular fuzzy numbers.

( ) ( )( ) ( ) 0,, xaxtxtftx ==

( ) ( )( ) ( ) 0,, xaxtxtftx

( ) ( )( ) ( )0,],[ xaxtxtftx

( ) [ ]0,][ Kkkxtx

( ) ][Ltx

( ) ( ) [ ]00,][ xxMtx




Now I shall try to correlate the above fuzzy set theory with the Quark theory by having an analogous

study , for the Pion triplet defined as fuzzy triangular number L for the I(third isospin) with the numbers (-

1,0,1) and pion as ( + ,, 0

0.4 0.6 11.20

.4

-

0

1-

1+

1

Trapezoidal fuzzy no. K

Triangular fuzzy no. L Triangular fuzzy no. M

-

Trian ular fuzz no. x




Quartet Kauons can be defined as trapezoidal fuzzy no. K with I (third isospin no.) as (-1,-1/2, 1, +1/2) and

is denoted by + KKKK ,,,0

0

Eta meson0

can be represented by trapezoidal fuzzy number K. Basic Quantum number of threeQuarks u, d, s ,i.e., up, down and strange is ,-1/2,0 respectively can be again written in the triangular

fuzzy number L for I(third isospin) condition.

- 0

-

- -

-




Whereas the symmetries can be modeled as trapezoidal fuzzy number K (-2/3, -1/3, 0, 1/3) Y (hypercharge)

values.

Similarly, for Q values we have the three Quark model as the trapezoidal fuzzy number (-1/3, 0, 1/3, 2/3)where Q is coordinates.

One can study similarly for the anti- quarks Y and Q values as the Y values of Quark become Q values of

the anti-quark and it we take Q value of quark it becomes Y values of anti- quark.

Baryon can be obtained as trapezoidal fuzzy number K (-1, 0, 1, 2)

Delta can be defined as trapezoidal fuzzy number K for I (third isospin).

Sigma can be represented as triangular fuzzy number L (-1, 0, 1)

If I go further for fuzzy pattern which are useful in plasma modeling leading to he Quark-Gluon

Plasma(QGP) and for studying Quantum chromo dynamics (QCD) which was presented by Hazarika(2003)

in National symposium on plasma science and technology, PLASMA-2003.

-

-

- -




CHAPTER-4

SOLVEV ASSUMPTION PATTERN

A. Solovev a Russian Physicist in 1962 tried to find some similarities in certain theory of the

Jews Torat and the science said in the present days by using certain analogous theory which suffices the

persistent theory in Physics with arts, culture ,tradition, religion, trade and commerce , science and

astronomy in olden days. Earlier a pattern theory was presented by Christian group as Holy Grail in

Islam as Nikah code and so on. Presently such a pattern is known as Solovev assumption. Here I am trying

to put forward such pattern for tokomaks (BETA machine, SST-1, ADITYA Tokomak, SINP Tokomak, or

any other tokomak with circular minor radius). The internal inductance and the poloidal beta as well as the

safety factor on-axis in IR-T1 Tokomak using Solovev assumption in the solution of Grad-Shafranov

equation (GSE) is solved by considering linear source functions and fixed boundary conditions. This

solution has the three quantities (plasma current pI , plasma minor radius pr and 2/ip l+ ) that they are

as input data. The quantities are measured by Rogowski coil, Cosine and Saddle coil and array of discrete

magnetic coils, respectively in IR-T1 Tokomak. This method can be used to evaluate the plasma parameters

for other circular cross section Tokomak. In two typical discharges on IR-T1 Tokomak, we concluded that

the internal inductance at a low value is required to extend the duration of Tokomak plasma discharge.

4.1-Introduction:

In a Tokomak, external magnetic measurements have been applied to determine the important information

on plasma shapes, the safety factor, the sum of the average poloidal beta p and half the plasma internal

inductance 2/il , and for sufficiently elongated plasmas p and il separately Lao et al (1985).There are

methods for extraction of plasma parameters from external magnetic measurements. Swain and Neilson

(1982) presented an efficient method to reconstruct the plasma shapes and line integrals of the boundary

poloidal magnetic field from external magnetic measurements. In their method, the plasma current

distribution is approximated by using a few filament currents. In Luxon and Browns approach (1982), the

plasma current is modeled using distributed sources. The non-linear Grad-Shafranov equation (GSE) is

solved repeatedly to search the best-fit current density profile by considering linear source functions and

circular fixed boundary conditions for circular cross section IR-T1 Tokomak and obtained the poloidal flux

function. This solution has the three quantities (plasma current pI , plasma minor radius pr and 2/ip l+

) that they are as input data in the method. The quantities are measured by Rogowski coil, Cosine and

Saddle coil and array of discrete magnetic coils, respectively. Then according to the definition of the




internal inductance and the poloidal beta and the safety factor, we substituted the poloidal flux function that

obtained by our solution into their definitions. Finally we calculated the time evolution of the

plasma parameters for typical discharges IR-T1 Tokomak and we discussed by them on the subject of

MHD instability.

4.2-Solution of GSE using fixed boundary conditions:

In the reference Zheng et al (1996) is yielded the analytical solution of GSE using linear source function

10A

P=

, 2AF

F =

The function F is a flux function associated with the poloidal current in the system (

( ) 2/0 polIRBF == ), and ( )P is the thermal pressure, 1A and 2A are constant.

This assumption obviously reduces the set of the possible toroidal current density profile shapes to

( )RARAJ /2/1 210 += ; the shape of the current profile is essentially flat. The poloidal magnetic

flux is obtained as in Zheng et al (1992),

224122

4

224

3

2

2128

))ln(()4( ZA

RA

ZRRcZRRcRcc +++= (1)

The equation can be used for Tokomaks that have up-down symmetric or limiter D-shape plasma cross

section. Here, we selected circular contour since IR-T1 (Vacuum camber major radius cmR 450 = ,vacuum chamber minor radius ma c16= , triangularity 0= , and elongation 0= ) has circular crosssection.

We have the six coefficients, it is necessary to have the six equations. We assumed that the plasma

enclosed in a perfectly conducting toroidal boundary with circular cross section where the plasma pressure

vanishes at the boundary ( ( ) 0,)/(),( 01 == boundaryZRAZRp ) Maschik (1996). So using the fixed

boundary conditions, the four equations can be obtained

08)ln()0,(412

4

4

3

2

21 =+++= iiiiii RA

RRcRcRccR (2)

08

)ln()0,( 41244

3

2

21 =+++= oooooo RA

RRcRcRccR (3)

( ) 028

)ln()4(),( 2241224224

3

2

21 =+++= ttttttttttt ZA

RA

ZRRcZRRcRccZR (4)




( ) 02

1)ln(2)2(42),(1 21

4

22

32 =+++= tttttt R

ARcZRcc

dR

ZRd

R

(5)

Here the equatorial innermost and outermost points are iR and oR , and the coordinates of the highest point

is ( tt ZR , ) or equivalently, the plasma major radius 2/)( oim RRR += , the plasma minor radius

2/)( iop RRr = , elongation pt rZ /= , and triangularity 2/)( tm RR = .

The plasma current can be clearly measured by Rogowski coil, so the plasma current can be written

( )

+= dRdZRARAIp /2 210 (6)

We also selected the constraint 2/ip l+ , because the parameter can be experimentally deduced using

four discrete magnetic probes in a circular cross section Tokomak Freidelberg et al (1993) such as IR-T1

Tokomak,

+

=+ dRdZR

ZRAdRdZRZRA

RdRdZI

dll

p

ip

),(5.0),(5.2

)2(

)(2/

212

0

2

. (7)

The sum of the poloidal beta and half the plasma internal inductance, 2/ip l+ and the plasma horizontal

displacement can be measuredFig 1. The magnetic probes position around the chamber.

+

+

=

2

2

2

2

0

2

2

2

0

2

exp11

2ln21

4m

p

m

P

p

m

m

p

p

mp

r

rB

r

rB

I

r

r

r

r

r

R

rH

(8)




( ) ( )

BB

I

R

r

rl

pm

p

ip+++=+

0

0ln12/ (9)

here, pI is the plasma current, pr the plasma minor radius, p the plasma poloidal beta, il plasma

internal inductance,0

R the major radius of the vacuum vessel, expH the plasma measured horizontal

displacement from0

R ,the toroidal and poloidal magnetic field are B = )()0( == BB ,

and B = )2/3()2/( == BB .

If this solution is used for D-shaped Tokomaks, p must be selected as constraint rather than 2/ip l+ ,

because the poloidal beta p can be measured by diamagnetic flux in the D-shaped Tokomaks.

For the determination of plasma minor radius pr , first the plasma horizontal displacement expH is

obtained by multipole moment method,

Fig.2.a) Cosine coil-b) Saddle coil is installed in IR-T1 Tokomak.

The plasma horizontal displacement can be deduced by the expression

( ) ( )0

2

0000

0000 4

)()(

)()( R

rtVtV

dkNI

rtVtV

AknI

rH m

downupp

m

LRp

m

multipole

+

+= (10)

mr Cosine and Saddle radius on the surface of vacuum vessel, 0n turns per length of Cosine coil, A

Cosine coil cross section, N turns of Saddle coil, k and k depend on the circuit characteristics and the

integrator that terminated Cosine and Saddle coils.0

d, depends on Saddle width. The )(0 tV L and )(0 tVR




are voltage signal of left and right Cosine coils. The )(0 tV up and )(0 tV down are voltage signal of up and

down Saddle coils. So that the left side of equation (8) has been found by Cosine and Saddle coilsthe

finding of horizontal displacement by the multipole moment method dont require to knowing the plasma

minor radius- then the plasma minor radius pr can be found by solving nonlinear equation (8) in term of pr

. So this solution has the three parameters (plasma current pI , plasma minor radius pr and 2/ip l+ ) that

are as input data. The parameters are measured by Rogowski coil, Cosine and Saddle coil and array of

discrete magnetic coils, respectively in IR-T1 Tokomak.

4.3-The calculation of the internal inductance and the poloidal beta and the safety factor on-axis:

The six coefficients 214321 ,,,,, AAcccc by solving equations (2-7) can be derived by using Cramers

Rule as can be seen in appendix I. So the poloidal magnetic flux is obtained by substituting the six

coefficients. According to the definition of the internal inductance Atanasui et al (2004)

=RdRdZI

dRdZjdll

p

i 2

0

2

2

)(

(11)

We can acquire the internal inductance with Solovevs assumption

( )dRdZRZRAdRdZRZRARdRdZIdl

lp

i )/),((),()2(

)(

212

0

2

+= (12)

Also the poloidal beta with Solovevs assumption can be gotten as follow Atanasui et al (2004)

( )dRdZRZRARdRdZI

dl

p

p = ),(2)2(

)(

12

0

2

(13)

All the double integrals in the above written relations have to be performed over the total cross-section area

of the plasma column in the IR-T1 Tokomak.

The safety factor at any flux surface can be calculated with the known relation Wesson (2004)

= +=

cons

ZR BBR

dlFq

2222

)((14)

Where RB and ZB are the components of the poloidal magnetic field. The line integral has to be

performed around a flux surface at any cross section. The value of the safety factor on the magnetic axis




axq can be calculated as the continuous limit of the relation (14). For the determination of the magnetic

axis, we can obtain by solving nonlinear equation

02

4))ln(21(2)0,( 21342 =

+++=

axisR

axis RAcRccdRRd (15)

The safety factor on-axis with Solovevs assumption in IR-T1 Tokomak is

=

+

=cons

axis

ax

ZRR

dlRAq

22

2

)()(2

)0,(2

(16)

The line integral in the above relation has to be performed over the circular cross section of the plasma

column in the IR-T1 Tokomak with radius. The is deviation of the magnetic axis from the geometriccenter of the vacuum chamber. So the equation 16 can be written

((

)

( ) )22403223

010004

2

0

3

03020

2

0

2

)2)cos(8()sin(

)cos(5.0)cos())coslog()cos(2())sin)(cos(8

)cos(4()cos(2)cos(/2

)0,(2

AcRc

RARRRcR

RcRcRdRA

qaxis

ax

++++

+++++++

++++

=

(17)

Therefore the poloidal beta and the internal inductance and safety factor can be calculated by above

expressions with knowing the six coefficients.

We yielded a method for the calculation of the internal inductance and the poloidal beta and the safety

factor on the magnetic axis in the circular cross section Tokomaks. According to the aforementioned

definitions of the internal inductance and the poloidal beta and the safety factor on-axis, the calculated




evolution in term of time is illustrated for different discharges on the IR-T1 Tokomak in the figure 3, 4.

Figure3-thecalculated evolution in term of time the internal inductance and the poloidal beta and the safety

factor on-axis for a discharge with a flat current region on the IR-T1 Tokomak. (Courtesy: A Ahmed Radi

and Ghoranevesis).

These discharges have obtained from different initial pressures of hydrogen gas. In the two figures can be

clearly observed that the calculated internal inductance and the calculated poloidal beta and the calculated

safety factor on-axis depend on kind of discharge or plasma current. The figure 3 shows a discharge that the

plasma current has a 15ms zone of flat-top current. The calculated safety factor on-axis, the calculated




internal inductance and the calculated poloidal beta have the value of about 1, .5 and .5 respectively, except

the begging zone.

Figure4-the calculated evolution in term of time the internal inductance and the poloidal beta and the safety

factor on-axis for a discharge with current disruption on the IR-T1 Tokomak (Courtesy: A Ahmed Radi and

Ghoranevesis).

The figure 4 shows a discharge that the plasma current has hard disruption in the 14ms and the calculated

safety factor on-axis approach to zero in the region of 7-14ms. The calculated internal inductance and the

calculated poloidal beta approach to 0.57 and 1.5 respectively, in the ending of discharge. We know that the

safety factor on-axis is limited by saw tooth oscillations and the actual limiting value is about 7.0axq

as given by Staceys book in the figure 3 the calculated safety factor on-axis has a value between 6.0 to

2.1 in the discharge time 2-32ms, so the saw tooth constrain hold in this discharge, but in the figure 4 the

calculated safety factor on-axis has a value between 1.5 to 0 in the discharge time 2-7ms and the zero value




in the discharge time 7-14ms. Maybe the zero value of safety factor on-axis has caused the disruption of

plasma current. This saw tooth constraint limits the allowable values of internal inductance. With

comparison the discharges in the figures 3, 4 can be understood that the internal inductance at a low value

is required to extend the duration of Tokomak plasma discharge.

References:

Lao (1985)- L.L. Lao, et al, Nuclear Fusion, .25, (1985)1611

Swain and Neilson (1982)-Swain, D.W., Neilson, G.H., Nuclear fusion 22 (1982)1015

Luxon and Brown (1982)- Luxon, J.L., Brown, B.B., Nuclear fusion 22(1982)813.

Zheng et al (1996)- S. B. Zheng, A. J. Wootton, and E. R. Solano, Phys. Plasmas 3, 1176 (1996)

Maschik (1996)-E. K. MASCHK, Plasma Physics, Vol. 15, pp. 535 541(1996)Freidelberg et al (1993)- J P Freidberg, et al, Plasma. Phys. Control. Fusion 35 (1993) 1641-1648.

Atanasui et al (2004)-C. V. Atanasiu, et al Physics of Plasma Volume 11, number 7 July 2004

Mukhovatov and Shefranov(1971) Mukhovatov, V. S. And Shafranov, V.D., Nucl, fusion 11 (1971)605

Hiromasa and Suzuki(1982) Hiromasa, Ninomiya and Norio Suzuki, Japanese Journal of Applied physics,

Vol.21, No. 9 ,September, 1982 pp. 1323-1327

Lopez-Callejas (2001) - R. Lopez-Callejas. et.al .Fusion Engineering and Design 54 (2001(

2129

Chen (1997)-Lei Chen, et al, Fusion Engineering and Design 34-35 (1997)721724

Wesson (2004)- Wesson J 2004 Tokomaks (CLARENDON PRESS OXFORD)

Stacey (2004)- Weston M. Stacey, Fusion plasma physics, WILEY-VCH




CHAPTER-5

A FEW IDEAS FROM KNOT PHYSICS PATTERN

In knot physics we use a topological approach to describe particles. To do this a 4-dimensional space-time

manifold in a Minkowski 6-space is considered. From this simple assumption, we can derive many physical

results.

Something easier to imagine:

Let's begin with a simple example. Suppose we have a space-time manifold that has 1 dimension of spaceand 1 dimension of time. We would embed that manifold in 4 dimensions. A constant time slice of the

space-time manifold looks like an infinitely long piece of string embedded in 3 dimensions. By taking

consecutive constant time slices, we can watch the string move around. We require that the string cannot

pass through itself. This means that a knot in the string cannot be removed. If there are multiple knots in the

string then they can move around and interact with each other. In this description, the string is like space

and the knots are like particles. This space-time manifold with 1 space dimension and 1 time dimension has

its own physics. Can a similar type of physics also apply to a space-time with more dimensions?

This is a constant time slice of a space-time manifold with 1 dimension of space and 1 dimension of time.This constant time slice is knotted.

More like our universe:

Suppose we have a space-time manifold with n dimensions of space and 1 dimension of time. Is it still

possible to have knots on the space-time manifold? We can consider the constant time slices. Each constanttime slice is a n-dimensional manifold. From topology, we know that an n-dimensional manifold can have

knots if and only if it is embedded in an n+2-dimensional space. We assume that the space-time manifold

has 3 dimensions of space and 1 dimension of time. Therefore, knots in the space-time manifold require

that the manifold is embedded in a space with 3+2+1=6 dimensions.

Distinguishing time and space:

We now have a 4-dimensional manifold embedded in a 6-dimensional space. What distinguishes a "time"direction from a "space" direction? The manifold is embedded in a 6-dimensional space and we assume that

the 6-space is Minkowski. The metric on the Minkowski 6-space is diag (1,-1,-1,-1,-1,-1). The metric on

the space-time manifold comes from the metric on the Minkowski 6-space. This gives the space-time

manifold a metric which is Lorentzian almost everywhere. The directions on the space-time manifold that

have positive metric signature are time like.




How can this make physics?

We know that we need a space-time manifold to explain physics. Relativity describes the manifold as

Lorentzian and gravity results when the metric is not constant. The space-time manifold we describe here is

embedded in a 6-space and it does not need to be flat. When it is not flat, it has curvature. We show in the

papers that the equations of its curvature match the equations of general relativity.

But what else can we explain using just the manifold? If particles are knots on the manifold then the

properties of those knots should generate the properties of particles. Particle topology affects the manifold

geometry. We show in the papers that the affect on manifold geometry explains the observed fields.

Therefore we have an explanation of particles and fields that only assumes the space-time manifold.

Has anyone else tried this?

There is one result that discouraged further research into knots as an explanation of particles: a Lorentzian

manifold cannot change topology. If we take constant time slices of a manifold that is everywhere

Lorentzian, then those slices must always have the same topology. If the manifold cannot change topology

then there can be no knots and therefore no particles in this description. People typically assume that the

space-time manifold is everywhere Lorentzian.

So... that's the end of the story, right?

In knot physics the space-time manifold is embedded in a Minkowski 6-space. An embedded manifold is

Lorentzian if it is moving at less than light speed. If it is moving at light speed then the metric is

degenerate. The manifold must have finite energy. By relativity, if the manifold is moving then the energy

density is proportional to . But is infinite at light speed. That means that the manifold must be Lorentzian

everywhere except a set of measure zero. The metric is degenerate on the measure zero set. A degeneratemetric means the manifold can be kinked. This allows topology change.

An example :

Let's try this with an example in lower dimensions with a cylinder

to describe a space-time manifold we use a n-manifold embedded in a Minkowski space. In this example

our space-time is a 3-manifold with boundary. This picture is a space like slice of the space-time. It is a 2-

manifold with boundary; specifically, it is a cylinder.

Now rotate the cylinder in the direction of the red arrow. Every point is in motion and the blue line segment

is moving at light speed.

It can describe the manifold as "moving". It can also describe the manifold as having a shape in space and

time. The descriptions are equivalent.

This induces a relativistic length contraction along the blue line segment. The metric is degenerate at the

point where the cylinder meets the blue line.

For any speed less than light speed, the manifold is Lorentzian: we can make a change of reference frame

that puts the manifold velocity equal to zero. At light speed, there is no such frame change. At that speed

the metric is degenerate.

We can twist around that point of degeneracy. This produces a twist in the cylinder.

At the metric degeneracy the manifold tapers to a point and it can rotate freely around that point.




If we stop moving the manifold it returns to being Lorentzian. The metric degeneracy disappears. However,

the twist in the cylinder remains. It is now a Mobius strip.

The Mobius strip has different topology than the cylinder. This topology change is a convenient example

because it is easy to visualize. However, the Mobius strip is a manifold with boundary, unlike the space-time manifold. Performing an analogous change on a 2-manifold without boundary makes a P2 (a projective

plane). If the manifold has a field (like space-time) then the P2 must be produced in pairs, like particle/anti-

particle pairs.

What happened? Relativity uses a Minkowski metric. If the manifold is always moving at less than lightspeed then no topology change is possible because the Minkowksi metric makes the manifold everywhere

Lorentzian. However, that same metric allows a topology change if we allow some part of the manifold tomove at light speed.

We can use this same technique to allow topology change on the space-time manifold. For a cylinder, the

topology change can make a Mobius strip. The degenerate metric allows the manifold to "kink". Then wecan twist around that kink. For space-time, a degenerate metric also produces a kink. When we twist around

that kink, the topology change can produce a pair of twists. Each twist is a topology called S 1P2. A S1P2

is fermions in knot physics. In the papers we show how S1P2 can produce fractional spin statistics, charge,

and spin angular momentum. The correspondence between S1P2 and the fermions is precise. There are

three generations with particles corresponding to charged leptons, neutrinos, and quarks.

For hadrons we link multiple copies of S1P2. This is similar to the way that circles can be linked, but in

higher dimensions. Each S1P2 is a quark and the linked quarks are hadrons. Linked S 1P2 cannot be

separated, in the same way that quarks cannot be removed from their hadrons.

Linked circles embedded in 3 dimensions cannot be separated. Similarly, linked P2 in 4 dimensions cannot

be separated. Let L be a link of multiple P2. Then S1L is a link of multiple S1P2 in 5 dimensions. EachS1P2 is a quark and the quarks cannot be separated. This corresponds to quark confinement. At close

distances the links exert no force on each other. This corresponds to asymptotic freedom. Extending this

idea produces a field equation that is quite similar to QCD.

This is only a brief introduction. The papers cover this material in greater detail as well as many other

aspects of the theory. In particular, the papers demonstrate the fields and forces, quantum field theory, and

a variety of other topics.

If you find this interesting, feel free to contact me and send this on to anyone else. (Contact info is available

in the papers.)

Knot Theory

There is of course an enormous body of work on knot invariants, the 3-manifold topology of knotcomplements, connections between knot theory and statistical mechanics, etc. I am instead interested here

primarily in geometric questions arising from knot embeddings.

Atlas of oriented knots and links , Corinne Cerf extends previous lists of all small knots and links,

to allow each component of the link to be marked by an orientation.
http://www.ics.uci.edu/~eppstein/junkyard/topo.htmlhttp://www.ics.uci.edu/~eppstein/junkyard/topo.htmlhttp://www.ics.uci.edu/~eppstein/junkyard/topo.htmlhttp://www.ics.uci.edu/~eppstein/junkyard/topo.htmlhttp://at.yorku.ca/t/a/i/c/31.htmhttp://at.yorku.ca/t/a/i/c/31.htmhttp://at.yorku.ca/t/a/i/c/31.htmhttp://www.ics.uci.edu/~eppstein/junkyard/topo.htmlhttp://www.ics.uci.edu/~eppstein/junkyard/topo.htmlhttp://at.yorku.ca/t/a/i/c/31.htm




Borromean rings don't exist . Geoff Mess relates a proof that the Borromean ring configuration (in

which three loops are tangled together but no pair is linked) can not be formed out of circles. Dan

Asimov discusses some related higher dimensional questions. Matthew Cook conjectures the

converse.

Are Borromean links so rare? S. Javan relates the history of the links and describes variousgeneralizations with more than three rings. For more history and symbolism of the Borromean

rings, seePeter Cromwell's web site.

Borromean paper clips .

A Brunnian link . Cutting any one of five links allows the remaining four to be disconnected from

each other, so this is in some sense a generalization of the Borromean rings. However since each

pair of links crosses four times, it can't be drawn with circles.

Colinear points on knots .Greg Kuperbergshows that a non-trivial knot or link in R3 necessarily

has four colinear points.

Curvature of knots . Steve Fenner proves the Fary-Milnor theorem that any smooth, simple, closedcurve in 3-space must have total curvature at least 4 pi.

Cut-the-knot logo . With a proof of the origami-folklore that this folded-flat overhand knot forms a

regular pentagon.

Detecting the unknot in polynomial time , C. Delman and K. Wolcott, Eastern Illinois U.

Figure eight knot / horoball diagram . Research of A. Edmonds into the symmetries of knots,relating them to something that looks like a packing of spheres. The MSRI Computing Group uses

another horoball diagram as their logo.

Geometric Arts . Knots, fractals, tesselations, and op art. Formerly Quincy Kim's World of

Geometry.

Geometry and the Imagination in Minneapolis . Notes from a workshop led by Conway, Doyle,

Gilman, and Thurston. Includes several sections on polyhedra, knots, and symmetry groups.

Hyperbolic Knot . From Eric Weisstein's treasure trove of mathematics.

Aaron Kellner Linear Sculpture . Art in the form of geometric tangles of metal and wood rods. Knot art . Keith and Fran Griffin.

Knot pictures . Energy-minimized smooth and polygonal knots, from the ming knot evolver, Y.

Wu, U. Iowa.

KnotPlot . Pictures of knots and links, from Robert Scharein at UBC.

Knots on the Web , P. Suber. Includes sections on knot tying and knot art as well as knot theory.

Mathematical imagery by Jos Leys . Knots, Escher tilings, spirals, fractals, circle inversions,

hyperbolic tilings, Penrose tilings, and more.

Louis Bel's povray galleries: les polyhdres rguliers, knots, andmore knots.

Maille Weaves . Different repetitive patterns formed by linked circles along a plane in space, asused for making chain mail. Along with some linear patterns for jewelry chains.

Mathematics in John Robinson's symbolic sculptures . Borromean rings, torus knots, fiber bundles,

and unorientable geometries.

Meru Foundation appears to be another sacred geometry site, with animated gifs of torus knots

and other geometric visualizations and articles.

Modularity in art. Slavik Jablan explores connections between art, tiling, knotwork, and other

mathematical topics.
http://www.ics.uci.edu/~eppstein/junkyard/borromeo.htmlhttp://www.ics.uci.edu/~eppstein/junkyard/borromeo.htmlhttp://paradise.caltech.edu/~cook/Workshop/Math/Borromean/Borrring.htmlhttp://paradise.caltech.edu/~cook/Workshop/Math/Borromean/Borrring.htmlhttp://paradise.caltech.edu/~cook/Workshop/Math/Borromean/Borrring.htmlhttp://paradise.caltech.edu/~cook/Workshop/Math/Borromean/Borrring.htmlhttp://members.tripod.com/vismath5/bor/index.htmlhttp://members.tripod.com/vismath5/bor/index.htmlhttp://www.liv.ac.uk/~spmr02/rings/index.htmlhttp://www.liv.ac.uk/~spmr02/rings/index.htmlhttp://www.liv.ac.uk/~spmr02/rings/index.htmlhttp://members.aol.com/mensanator/borromean_paper_clips.htmhttp://members.aol.com/mensanator/borromean_paper_clips.htmhttp://www.lsus.edu/sc/math/rmabry/venn/5colors.gifhttp://www.lsus.edu/sc/math/rmabry/venn/5colors.gifhttp://www.ics.uci.edu/~eppstein/junkyard/knot-colinear.htmlhttp://www.ics.uci.edu/~eppstein/junkyard/knot-colinear.htmlhttp://www.ics.uci.edu/~eppstein/junkyard/knot-colinear.htmlhttp://www.math.ucdavis.edu/~greg/http://www.math.ucdavis.edu/~greg/http://www.math.ucdavis.edu/~greg/http://www.ics.uci.edu/~eppstein/junkyard/knot-curvature.htmlhttp://www.ics.uci.edu/~eppstein/junkyard/knot-curvature.htmlhttp://www.ics.uci.edu/~eppstein/junkyard/knot-curvature.htmlhttp://en.wikipedia.org/wiki/Fary-Milnor_theoremhttp://www.cut-the-knot.com/logo.htmlhttp://www.cut-the-knot.com/logo.htmlhttp://www.cut-the-knot.com/logo.htmlhttp://www.math.uiowa.edu/~wu/conf/delman.htmlhttp://www.math.uiowa.edu/~wu/conf/delman.htmlhttp://www.math.uiowa.edu/~wu/conf/delman.htmlhttp://www.indiana.edu/~rcapub/v17n2/10c.htmlhttp://www.indiana.edu/~rcapub/v17n2/10c.htmlhttp://www.msri.org/local/computing/logo/http://geometricarts.googlepages.com/http://geometricarts.googlepages.com/http://web.archive.org/web/20030416234110/http:/geometricarts.freeyellow.com/Main.htmhttp://web.archive.org/web/20030416234110/http:/geometricarts.freeyellow.com/Main.htmhttp://math.dartmouth.edu/~doyle/docs/gi/gi/gi.htmlhttp://math.dartmouth.edu/~doyle/docs/gi/gi/gi.htmlhttp://mathworld.wolfram.com/HyperbolicKnot.htmlhttp://mathworld.wolfram.com/HyperbolicKnot.htmlhttp://mathworld.wolfram.com/HyperbolicKnot.htmlhttp://www.aaronkellner.com/http://www.aaronkellner.com/http://web.archive.org/web/20010226184203/http:/galifrey.triode.net.au/Maths/Knots/knots.htmlhttp://web.archive.org/web/20010226184203/http:/galifrey.triode.net.au/Maths/Knots/knots.htmlhttp://web.archive.org/web/19990218170103/http:/www.math.uiowa.edu/~wu/examples.htmlhttp://web.archive.org/web/19990218170103/http:/www.math.uiowa.edu/~wu/examples.htmlhttp://web.archive.org/web/19990218170103/http:/www.math.uiowa.edu/~wu/examples.htmlhttp://www.math.uiowa.edu/~wu/min/ming.htmlhttp://www.math.uiowa.edu/~wu/min/ming.htmlhttp://www.cs.ubc.ca/nest/imager/contributions/scharein/KnotPlot.htmlhttp://www.cs.ubc.ca/nest/imager/contributions/scharein/KnotPlot.htmlhttp://www.earlham.edu/suber/knotlink.htmhttp://www.earlham.edu/suber/knotlink.htmhttp://www.earlham.edu/suber/knotlink.htmhttp://www.josleys.com/http://www.josleys.com/http://www.josleys.com/http://louisbel.free.fr/scenes/scene02.shtmlhttp://louisbel.free.fr/galerie/gal10.shtmlhttp://louisbel.free.fr/galerie/gal10.shtmlhttp://louisbel.free.fr/galerie/gal11.shtmlhttp://louisbel.free.fr/galerie/gal11.shtmlhttp://www.doomlegends.com/maille/weaves.htmlhttp://www.doomlegends.com/maille/weaves.htmlhttp://www.doomlegends.com/maille/weaves.htmlhttp://web.archive.org/web/20010221183755/http:/www.cpm.sees.bangor.ac.uk/sculmath/intromath.htmhttp://web.archive.org/web/20010221183755/http:/www.cpm.sees.bangor.ac.uk/sculmath/intromath.htmhttp://www.meru.org/http://www.meru.org/http://www.mi.sanu.ac.yu/~jablans/osn.htmhttp://www.ics.uci.edu/~eppstein/junkyard/borromeo.htmlhttp://paradise.caltech.edu/~cook/Workshop/Math/Borromean/Borrring.htmlhttp://paradise.caltech.edu/~cook/Workshop/Math/Borromean/Borrring.htmlhttp://members.tripod.com/vismath5/bor/index.htmlhttp://www.liv.ac.uk/~spmr02/rings/index.htmlhttp://members.aol.com/mensanator/borromean_paper_clips.htmhttp://www.lsus.edu/sc/math/rmabry/venn/5colors.gifhttp://www.ics.uci.edu/~eppstein/junkyard/knot-colinear.htmlhttp://www.math.ucdavis.edu/~greg/http://www.ics.uci.edu/~eppstein/junkyard/knot-curvature.htmlhttp://en.wikipedia.org/wiki/Fary-Milnor_theoremhttp://www.cut-the-knot.com/logo.htmlhttp://www.math.uiowa.edu/~wu/conf/delman.htmlhttp://www.indiana.edu/~rcapub/v17n2/10c.htmlhttp://www.msri.org/local/computing/logo/http://geometricarts.googlepages.com/http://web.archive.org/web/20030416234110/http:/geometricarts.freeyellow.com/Main.htmhttp://web.archive.org/web/20030416234110/http:/geometricarts.freeyellow.com/Main.htmhttp://math.dartmouth.edu/~doyle/docs/gi/gi/gi.htmlhttp://mathworld.wolfram.com/HyperbolicKnot.htmlhttp://www.aaronkellner.com/http://web.archive.org/web/20010226184203/http:/galifrey.triode.net.au/Maths/Knots/knots.htmlhttp://web.archive.org/web/19990218170103/http:/www.math.uiowa.edu/~wu/examples.htmlhttp://www.math.uiowa.edu/~wu/min/ming.htmlhttp://www.cs.ubc.ca/nest/imager/contributions/scharein/KnotPlot.htmlhttp://www.earlham.edu/suber/knotlink.htmhttp://www.josleys.com/http://louisbel.free.fr/scenes/scene02.shtmlhttp://louisbel.free.fr/galerie/gal10.shtmlhttp://louisbel.free.fr/galerie/gal11.shtmlhttp://www.doomlegends.com/maille/weaves.htmlhttp://web.archive.org/web/20010221183755/http:/www.cpm.sees.bangor.ac.uk/sculmath/intromath.htmhttp://www.meru.org/http://www.mi.sanu.ac.yu/~jablans/osn.htm




Mutations and knots . Connections between knot theory and dissection of hyperbolic polyhedra.

Orthogonal discrete knots . Hew Wolff asks questions about the minimum total length, or the

minimum volume of a rectangular box, needed to form different knots as three-dimensional

polygons using only integer-length axis-parallel edges.

Penrose mandala and five-way Borromean rings. The Pretzel Page . Eric Sedgwick uses animated movies of twisting pretzel knots to visualize a

theorem about Heegard splittings (ways of dividing a complex topological space into two simple

pieces).

Programming for 3d modeling , T. Longtin. Tensegrity structures, twisted torus space frames,

Moebius band gear assemblies, jigsaw puzzle polyhedra, Hilbert fractal helices, herds of turtles,

and more.

In search of the ideal knot . Piotr Pieranski applies an iterative shrinking heuristic to find the

minimum length unit-diameter rope that can be used to tie a given knot.

SnapPea , powerful software for computing geometric properties of knot complements and other 3-manifolds.

Soap films on knots . Ken Brakke, Susquehanna.

Space Cubes plastic geometric modeling puzzle based on a rectangular Borromean link.

Square Knots . This article by Brian Hayes for American Scientist examines how likely it is that arandom lattice polygon is knotted.

String figure mathematics, or trivial knot theory .

Morwen Thistlethwait , sphere packing, computational topology, symmetric knots, and giant ray-

traced floating letters.

Trefoil knot stairs . Java animation of an Escher-like infinite stair construction, intended as a

Montreal metro station sculpture, by Guillaume LaBelle.

Triangulating 3-dimensional polygons . This is always possible (with exponentially many Steiner

points) if the polygon is unknotted, but NP-complete if no Steiner points are allowed. The proof

uses gadgets in which quadrilaterals arestacked like Pringlesto form wires. UMass Gang libraryof knots, surfaces, surface deformation movies, and minimal surface meshing software.

Just for a be

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