Statistical Mechanics of pressurized two-dimensional polymer rings (Record no. 48822)

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fixed length control field 02900nam a2200253Ia 4500
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fixed length control field 160627s2009||||xx |||||||||||||| ||und||
080 ## - UNIVERSAL DECIMAL CLASSIFICATION NUMBER
Universal Decimal Classification number HBNI Th 18
100 ## - MAIN ENTRY--AUTHOR NAME
Personal name Mitra, Mithun Kumar
Relator term author
245 ## - TITLE STATEMENT
Title Statistical Mechanics of pressurized two-dimensional polymer rings
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Year of publication 2009
300 ## - PHYSICAL DESCRIPTION
Number of Pages 121p.
502 ## - DISSERTATION NOTE
Dissertation note 2009
502 ## - DISSERTATION NOTE
Degree Type Ph.D
502 ## - DISSERTATION NOTE
Name of granting institution HBNI
520 3# - SUMMARY, ETC.
Summary, etc This thesis studies the statistical mechanics of pressurized ring polymers. These can be thought of as a simple low-dimensional models for the understanding of vesicle shapes and phase transitions, a classic problem first studied several decades ago in the context of the shapes of red blood cells. The model for the two-dimensional vesicle presents many difficulties for analytic studies, arising principally from the self-avoidance constraint. A related class of models in which the polymer ring is allowed to intersect itself, and the pressure term is conjugate to an algebraic or signed area. The effects of semi-flexibility in the inextensible self-intersecting ring problem is investigated. The flexible chain problem is characterised by a continuous phase transition at a critical value of an appropriately scaled pressure, separating collapsed and inflated regimes of the ring. It is shown that this transition survives for non-zero values of the bending rigidity and an analytic form is obtained for the phase boundary separating the collapsed and inflated phases in the scaled pressure-bending rigidity plane.An analogy with the quantum mechanical problem of an electron moving in a magnetic field applied transverse to the plane of motion, is used to reproduce exact results for the flexible chain. Then incorporated with semi-flexibility in both the continuum and lattice models through scaling arguments, obtains very good agreement with numerics. The numerical data was obtained through the exact enumeration method, which explicitly counts the total number of allowed polygons, and hence the partition function. Also several mean-field approaches to this model are performed. The different mean-field approximations, motivated by physical arguments, model the behaviour of the system in different regimes of parameter space are discussed. The usefulness of these results for more realistic systems lies in the fact that self-intersections are irrelevant in the large pressure limit. The results obtained at large pressures should therefore apply both qualitatively and qualitatively to the more realistic case of a pressurised self-avoiding polymer.
650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical Term Physics
653 10 - INDEX TERM--UNCONTROLLED
Uncontrolled term HBNI TH 18
653 10 - INDEX TERM--UNCONTROLLED
Uncontrolled term Statistical Mechanics
720 1# - ADDED ENTRY--UNCONTROLLED NAME
Thesis Advisor Menon, Gautam I.
Relator term Thesis advisor [ths]
720 1# - ADDED ENTRY--UNCONTROLLED NAME
Thesis Advisor Rajesh, R.
Relator term Thesis advisor [ths]
856 ## - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier http://www.imsc.res.in/xmlui/handle/123456789/178
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Koha item type THESIS & DISSERTATION
Holdings
Withdrawn status Lost status Damaged status Not for loan Current library Full call number Accession Number Uniform Resource Identifier Koha item type
        IMSc Library HBNI Th 18 63453 http://www.imsc.res.in/xmlui/handle/123456789/178 THESIS & DISSERTATION
The Institute of Mathematical Sciences, Chennai, India

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