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Random Polymer Models* T) O% N8 d9 p% D7 h: C/ B# x
by Giambattista Giacomin
. N& s/ u1 O3 a& `: ?9 a% r/ YPublisher: Imperial College Press + C% x& t$ M, c" t6 M
Number Of Pages: 260
& h6 a8 N+ ^, `9 c7 JPublication Date: 2007-03-22 4 E6 V) y8 K8 R% Y) \* ~
ISBN-10 / ASIN: 1860947867 7 }# ~5 s/ r0 M D# m. z. K
ISBN-13 / EAN: 9781860947865
8 X+ a& x: y( s1 |/ xBinding: Hardcover
5 [! j6 s! c/ G, R8 ~3 Y7 gProduct Description:
% B, r4 g+ V! L0 E* T; X) A y1 {( F! i* k
This volume introduces readers to the world of disordered systems and to some of the remarkable probabilistic techniques developed in the field. The author explores in depth a class of directed polymer models to which much attention has been devoted in the last 25 years, in particular in the fields of physical and biological sciences. The models treated have been widely used in studying, for example, the phenomena of polymer pinning on a defect line, the behavior of copolymers in proximity to an interface between selective solvents and the DNA denaturation transition. In spite of the apparent heterogeneity of this list, in mathematical terms, a unified vision emerges. One is in fact dealing with the natural statistical mechanics systems built on classical renewal sequences by introducing one-body potentials. This volume is also a self-contained mathematical account of the state of the art for this class of statistical mechanics models.
6 W0 `- ^+ ~; V7 V0 f$ S目录
! k6 j/ c3 ]5 n' M1. Random Polymer Models and their Applications 1# N) h) q2 I$ V" C, X5 J. e8 K+ v. f
1.1 Random Polymers and (De)Localization Phenomena . . . . 1 V( O( Q! H( t, D8 \. ~+ W& s4 `" m
1.2 A First Model: Pinning on a Defect Line . . . . . . . . . . . 6- k, z6 _( S# |( M7 C' N
1.2.1 Pinning a walk on a defect line . . . . . . . . . . . . 6+ |& n: E% ^2 _! E! z6 i
1.2.2 Pinning more general processes on a defect line . . . 13
2 H6 ]( Q7 |/ i( ~& v$ B1.3 Entropic Repulsion and Wetting Phenomena . . . . . . . . 171 E& Y7 n4 e C) ]- u
1.3.1 Walls versus penetrable substrates . . . . . . . . . . 204 z! |& @3 _7 W% ^( j6 U, r W
1.4 The Denaturation Transition: Poland–Scheraga Models . . 21/ H6 a: V3 r, a& u* c
1.5 Force Induced Unzipping . . . . . . . . . . . . . . . . . . . . 26
' F: U, ^8 @1 ^% {1.6 Inhomogeneous Charge Distributions: Copolymers and Pin-) Q9 ?- @; |' h# r; i
ning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29; @4 `5 N. a+ \0 J% n
1.6.1 Periodic pinning models . . . . . . . . . . . . . . . . 30% {0 v2 e; W+ E
1.6.2 Copolymers, periodic copolymers and selective inter-$ o2 I0 }/ j4 g/ Y' [) m
faces . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
7 C* X, c" U7 k3 H+ a1.6.3 Copolymers with adsorption . . . . . . . . . . . . . . 36* O. e3 a- Y( [" Z4 o
1.7 Fully Inhomogeneous Charge Distributions and Disordered+ {7 O9 Q/ X# T0 u
Polymer Models . . . . . . . . . . . . . . . . . . . . . . . . . 37
) M$ [2 {9 N3 g: V' C; \1.7.1 Annealed models . . . . . . . . . . . . . . . . . . . . 41
( L# r X4 e8 |0 u1.8 On the Return Time Viewpoint . . . . . . . . . . . . . . . . 42
3 @! M5 ~& Z; C; K' m- S/ I5 \* L1.9 On Related Classes of Models . . . . . . . . . . . . . . . . . 43, V- X! F" K( L4 a( L$ d( c
1.9.1 More general return times . . . . . . . . . . . . . . . 43/ b1 ]: f- [3 s0 E& e
1.9.2 Rewards and penalties on general structures . . . . . 45; ] _6 V) M4 m: L E
1.10Bibliographic Complements . . . . . . . . . . . . . . . . . . 468 \9 d z$ Q: _6 S
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