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Bicontinuous Domains and Some Old Problems in Domain Theory

Klaus Keimel
2009 Electronical Notes in Theoretical Computer Science  
In this paper we collect known results, we exhibit substantial examples, we show that these examples are connected with open problems in domain theory, and we indicate directions of research.  ...  Martin and P. Panangaden [12] have made the interesting observation that the causal order in general relativity theory closely relates to domain theoretical notions.  ...  In fact, some old unsolved problems of domain theory might find their solution in this setting, as I will indicate.  ... 
doi:10.1016/j.entcs.2009.11.025 fatcat:kf6tc7f6evh6fnwmtve2igb3ly

Block Copolymers: Past Successes and Future Challenges

Timothy P. Lodge
2003 Macromolecular Chemistry and Physics  
[63, 64] Then, the SCMF in the version developed by Matsen and Schick found G to be preferred among the various bicontinuous cubic phases, and indeed under some conditions to be stable relative to S  ...  Ultimately, re-examination of old SAXS patterns, and measurements on new systems, suggested that in fact the observed phase was G.  ... 
doi:10.1002/macp.200290073 fatcat:55qxl4xkcfcsdcwmezyhcoholu

Directed assembly of copolymer materials on patterned substrates: Balance of simple symmetries in complex structures

Kostas Ch. Daoulas, Marcus Müller, Mark P. Stoykovich, Yioryos J. Papakonstantopoulos, Juan J. de Pablo, Paul F. Nealey, Sang-Min Park, Harun H. Solak
2006 Journal of Polymer Science Part B: Polymer Physics  
The ¢; in the exponential denotes the angle between the straight line connecting the center of the jth nearest neighbor domain to the center of the considered PS-spot and some arbitrary reference axis.  ...  are typically employed in the theory of two- dimensional (2D) melting.'*:!  ... 
doi:10.1002/polb.20904 fatcat:gqleyi4pirapvjqjlkscvcyfii

Bicontinuous extensions of invertible combinatorial functions

Tommaso Toffoli
1981 Mathematical Systems Theory  
Acknowledgments I wish to thank Edward Fredkin for suggestions and encour agement , and Louis N. Howard and Daniel J. Kleitman for useful discussions.  ...  In particular, in all cases domain and range will be products of identical sets and will coincide.  ...  We discuss and solve the problem of constructing a diffeomorphic componentwise extension for an arbitrary invertible combinatorial function.  ... 
doi:10.1007/bf01752388 fatcat:fy3scgdoyvg5dk7yalvobwlrra

Particles at fluid-fluid interfaces: A new Navier-Stokes-Cahn-Hilliard surface- phase-field-crystal model

Sebastian Aland, John Lowengrub, Axel Voigt
2012 Physical Review E  
In this paper we develop an improved Navier-Stokes-Cahn-Hilliard-surface phase-field-crystal model based on the principles of mass conservation and thermodynamic consistency.  ...  A promising approach to simulate these emulsions was presented in Aland et al. [Phys.  ...  J.L. gratefully acknowledges partial support from the National Science Foundation Division of Mathematics and the National Institutes of Health through grant P50GM76516 for a Center of Excellence in Systems  ... 
doi:10.1103/physreve.86.046321 pmid:23214691 pmcid:PMC3833457 fatcat:t6kzpxsdijbnlje3gvsgn6w7ri

Lattice models of amphiphilic assembly

K. A. Dawson
1992 Pure and Applied Chemistry  
The coefficient of the gradient-squared term in the Landau theory is negative and the implications of this for structure, interfacial properties and dynamics are discussed.  ...  We extract an effective Landau theory from the lattice model and under renormalization it is found to represent the microemulsion region of the lattice model quite well.  ...  Financial support in the early days of the research was provided by the Dreyfus and Sloan Foundations.  ... 
doi:10.1351/pac199264111589 fatcat:lsf5jya4zrdbrbk6areg54u3ka

Quasiconformal mappings, with applications to differential equations, function theory and topology

Lipman Bers
1977 Bulletin of the American Mathematical Society  
2 F } I Jordan domain? The theory exposed in §13 gives a qualitative answer: for all X in some simply connected bounded domain A, depending only on j(t).  ...  QUASICONFORMAL MAPPINGS, WITH APPLICATIONS TO DIFFERENTIAL EQUATIONS, FUNCTION THEORY AND TOPOLOGY BY LIPMAN BERS The theory of quasiconformal mappings is nearly 50 years old (see [44] for references  ... 
doi:10.1090/s0002-9904-1977-14390-5 fatcat:ptqqpztdf5e7teq6l3ljay3qxa

Domain Theory and Measurement [chapter]

K. Martin
2010 Lecture Notes in Physics  
Lecture notes on domain theory and measurement, driven by applications to physics, computer science and information theory, with a hint of provocation.  ...  In domain theory and measurement, it is often possible to take a unified view of the two.  ...  The bridge that connects them is domain theory and measurement.  ... 
doi:10.1007/978-3-642-12821-9_9 fatcat:tof2m7codbaz3l4udkfj7awn7q

Coarsening phenomena [article]

Leticia F. Cugliandolo
2014 arXiv   pre-print
This article gives a short description of pattern formation and coarsening phenomena and focuses on recent experimental and theoretical advances in these fields.  ...  It serves as an introduction to phase ordering kinetics and it will appear in the special issue 'Coarsening dynamics', Comptes Rendus de Physique, edited by F. Corberi and P. Politi.  ...  Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).  ... 
arXiv:1412.0855v1 fatcat:fbwxpxrdafgsdhzbymxkpvgd6m

From Problems to Structures: the Cousin Problems and the Emergence of the Sheaf Concept

Renaud Chorlay
2009 Archive for History of Exact Sciences  
This medium-term narrative provides insight into two more general issues in the history of contemporary mathematics. First, we will focus on the use of problems in theory-making.  ...  This paper concentrates on Henri Cartan's work in the theory of analytic functions of several complex variables and the strikingly different roles it played at two stages of the emergence of sheaf theory  ...  There is no textual indication that Cartan also considered that there was some kind of analogy between changes of base rings in his theory (where they result from changes of domains) and changes of base  ... 
doi:10.1007/s00407-009-0052-3 fatcat:spy2lb52jraltcbq7qftqxcpeq

The "New" Science of "Complex Fluids"

William M. Gelbart, Avinoam Ben-Shaul
1996 The Journal of Physical Chemistry  
In proposing a definition of the field, we discuss first the special role played by phenomenological theory and the limitations of molecular-level description.  ...  In each instance we try to provide a physical basis for the special nature of interactions and long-range ordering transitions in these novel colloidal and thin layer systems.  ...  We are pleased to thank our many students and co-workers for their extremely valuable and  ... 
doi:10.1021/jp9606570 fatcat:wqc4idak7jgibnz6avkbewoucu

Two sides of the coin. Part 1. Lipid and surfactant self-assembly revisited

Barry W. Ninham, Kåre Larsson, Pierandrea Lo Nostro
2017 Colloids and Surfaces B: Biointerfaces  
; and in microemulsions.  ...  Hofmeister, specific ion effects, hydration and van der Waals forces at and between interfaces are factors that determine curvature and microstructure in self assembled aggregates of surfactants and lipids  ...  Acknowledgements We are sincerely thankful to Tommy Nylander, Marcus Larsson, Stephen Hyde and Thomas Zemb.  ... 
doi:10.1016/j.colsurfb.2017.01.022 pmid:28131093 fatcat:j47c2h7ntfgnxfa7sght6emyse

Poincaré's Variational Problem in Potential Theory

Dmitry Khavinson, Mihai Putinar, Harold S. Shapiro
2006 Archive for Rational Mechanics and Analysis  
Prerequisites of potential theory The aim of this section is to assemble some terminology and basic facts of Newtonian potential theory. Let Ω be a bounded domain in R d with boundary Γ.  ...  Section 2 contains some terminology and conventions plus a collection of known facts from the Newtonian potential theory, seen from the modern point of view of distribution theory and Sobolev spaces.  ... 
doi:10.1007/s00205-006-0045-1 fatcat:qr6l37f4ijhwbherrbeyp6xuou

An Examination of Counterexamples in Proofs and Refutations

Samet Bağçe, Can Başkent
2009 Philosophia Scientiæ  
We thus present the mathematical background and basis of Lakatos's philosophy of mathematical methodology in the case of Euler's formula, and thereby develop some intuitions about the function of his notions  ...  In this study, we focus on the mathematical and topological properties which play a role in Lakatos's methodological approach.  ...  Hielcher and David Chabot helped improving the readability of the text.  ... 
doi:10.4000/philosophiascientiae.228 fatcat:37xwr2cgnvbnxg6mnncflpbkdu

The range of convolution operators

Robert Bekes
1984 Pacific Journal of Mathematics  
For non-compact groups we show that when the range and domain are different, such operators rarely have closed range.  ...  Applications of these results are made to representation theory for locally compact groups.  ...  For further discussion of the problem of when μ * L,(G) is closed see I. Glicksberg's paper [4]. 2. An application to representation theory.  ... 
doi:10.2140/pjm.1984.110.257 fatcat:i67pyyyzrnd5rnl3v3pezju7na
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