The Resource Lectures on Random Interfaces, by Tadahisa Funaki, (electronic resource)

Lectures on Random Interfaces, by Tadahisa Funaki, (electronic resource)

Label
Lectures on Random Interfaces
Title
Lectures on Random Interfaces
Statement of responsibility
by Tadahisa Funaki
Creator
Contributor
Author
Provider
Subject
Language
eng
Summary
Interfaces are created to separate two distinct phases in a situation in which phase coexistence occurs. This book discusses randomly fluctuating interfaces in several different settings and from several points of view: discrete/continuum, microscopic/macroscopic, and static/dynamic theories. The following four topics in particular are dealt with in the book. Assuming that the interface is represented as a height function measured from a fixed-reference discretized hyperplane, the system is governed by the Hamiltonian of gradient of the height functions. This is a kind of effective interface model called ∇φ-interface model. The scaling limits are studied for Gaussian (or non-Gaussian) random fields with a pinning effect under a situation in which the rate functional of the corresponding large deviation principle has non-unique minimizers. Young diagrams determine decreasing interfaces, and their dynamics are introduced. The large-scale behavior of such dynamics is studied from the points of view of the hydrodynamic limit and non-equilibrium fluctuation theory. Vershik curves are derived in that limit. A sharp interface limit for the Allen–Cahn equation, that is, a reaction–diffusion equation with bistable reaction term, leads to a mean curvature flow for the interfaces. Its stochastic perturbation, sometimes called a time-dependent Ginzburg–Landau model, stochastic quantization, or dynamic P(φ)-model, is considered. Brief introductions to Brownian motions, martingales, and stochastic integrals are given in an infinite dimensional setting. The regularity property of solutions of stochastic PDEs (SPDEs) of a parabolic type with additive noises is also discussed. The Kardar–Parisi–Zhang (KPZ) equation , which describes a growing interface with fluctuation, recently has attracted much attention. This is an ill-posed SPDE and requires a renormalization. Especially its invariant measures are studied.
Member of
http://library.link/vocab/creatorName
Funaki, Tadahisa
Image bit depth
0
LC call number
  • QA273.A1-274.9
  • QA274-274.9
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink
Series statement
SpringerBriefs in Probability and Mathematical Statistics,
http://library.link/vocab/subjectName
  • Mathematics
  • Partial differential equations
  • Probabilities
  • Mathematical physics
  • Mathematics
  • Probability Theory and Stochastic Processes
  • Partial Differential Equations
  • Mathematical Physics
Label
Lectures on Random Interfaces, by Tadahisa Funaki, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Dimensions
unknown
Extent
XII, 138 p. 44 illus., 9 illus. in color.
File format
multiple file formats
Form of item
electronic
Isbn
9789811008498
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-981-10-0849-8
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-981-10-0849-8
Label
Lectures on Random Interfaces, by Tadahisa Funaki, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Dimensions
unknown
Extent
XII, 138 p. 44 illus., 9 illus. in color.
File format
multiple file formats
Form of item
electronic
Isbn
9789811008498
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-981-10-0849-8
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-981-10-0849-8

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