On phase transitions and limit theorems for homopolymers

Limit theorems and phase transitions for two models of summation of iid random variables depending on parameters

Doklady Mathematics ◽

10.1134/s1064562413030204 ◽

2013 ◽

Vol 88 (1) ◽

pp. 431-434 ◽

Cited By ~ 3

Author(s):

M. Grabchak ◽

S. A. Molchanov

Keyword(s):

Phase Transitions ◽

Limit Theorems ◽

Random Variables

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Limit theorems and phase transitions for two models of summation of i.i.d. random variables with a parameter

Теория вероятностей и ее применения ◽

10.4213/tvp4568 ◽

2014 ◽

Vol 59 (2) ◽

pp. 340-364 ◽

Cited By ~ 2

Author(s):

M Grabchak ◽

S A Molchanov ◽

S A Molchanov

Keyword(s):

Phase Transitions ◽

Limit Theorems ◽

Random Variables

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Limit Theorems and Phase Transitions for Two Models of Summation of Independent Identically Distributed Random Variables with a Parameter

Theory of Probability and Its Applications ◽

10.1137/s0040585x97t987090 ◽

2015 ◽

Vol 59 (2) ◽

pp. 222-243 ◽

Cited By ~ 3

Author(s):

M. Grabchak ◽

S. A. Molchanov

Keyword(s):

Phase Transitions ◽

Limit Theorems ◽

Random Variables ◽

Independent Identically Distributed

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Electron Microscopy of Graphite Intercalation Compounds

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100055564 ◽

1982 ◽

Vol 40 ◽

pp. 544-545

Author(s):

G. Timp ◽

L. Salamanca-Riba ◽

L.W. Hobbs ◽

G. Dresselhaus ◽

M.S. Dresselhaus

Keyword(s):

Electron Microscopy ◽

Phase Transitions ◽

Domain Wall ◽

Intercalation Compounds ◽

Lattice Plane ◽

Wall Model ◽

Graphite Intercalation Compounds ◽

Fundamental Symmetry ◽

Graphite Intercalation

Electron microscopy can be used to study structures and phase transitions occurring in graphite intercalations compounds. The fundamental symmetry in graphite intercalation compounds is the staging periodicity whereby each intercalate layer is separated by n graphite layers, n denoting the stage index. The currently accepted model for intercalation proposed by Herold and Daumas assumes that the sample contains equal amounts of intercalant between any two graphite layers and staged regions are confined to domains. Specifically, in a stage 2 compound, the Herold-Daumas domain wall model predicts a pleated lattice plane structure.

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Multiple phase transitions investigated by high-speed TEM

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100175880 ◽

1990 ◽

Vol 48 (4) ◽

pp. 550-551

Author(s):

Oleg Bostanjoglo ◽

Peter Thomsen-Schmidt

Keyword(s):

Phase Transitions ◽

High Speed ◽

Short Exposure ◽

Semiconductor Film ◽

Time Resolved ◽

Short Exposure Time ◽

Multiple Phase ◽

Model Substance ◽

History Of ◽

Electron Image

Thin GexTe1-x (x = 0.15-0.8) were studied as a model substance of a composite semiconductor film, in addition being of interest for optical storage material. Two complementary modes of time-resolved TEM were used to trace the phase transitions, induced by an attached Q-switched (50 ns FWHM) and frequency doubled (532 nm) Nd:YAG laser. The laser radiation was focused onto the specimen within the TEM to a 20 μm spot (FWHM). Discrete intermediate states were visualized by short-exposure time doubleframe imaging /1,2/. The full history of a transformation was gained by tracking the electron image intensity with photomultiplier and storage oscilloscopes (space/time resolution 100 nm/3 ns) /3/. In order to avoid radiation damage by the probing electron beam to detector and specimen, the beam is pulsed in this continuous mode of time-resolved TEM,too.Short events ( <2 μs) are followed by illuminating with an extended single electron pulse (fig. 1c)

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