Selfavoiding walks on a crystal lattice; a new approach to the mean- square end-to-end length ρn

1972 ◽  
Vol 5 (7) ◽  
pp. L60-L61
Author(s):  
J L Martin
Keyword(s):  
Crystal Lattice ◽  
Mean Square ◽  
New Approach ◽  
The Mean ◽  
End To End

Self‐avoiding walks with span limitations. I. The mean square end‐to‐end distance

1980 ◽  
Vol 72 (4) ◽  
pp. 2702-2707 ◽  
Author(s):  
Ronnie Barr ◽  
Chava Brender ◽  
Melvin Lax
Keyword(s):  
Mean Square ◽  
End Distance ◽  
The Mean ◽  
End To End ◽  
Self Avoiding Walks

scholarly journals The Mean Square Error of Prediction in the Chain Ladder Reserving Method – A Comment

2006 ◽  
Vol 36 (02) ◽  
pp. 543-552 ◽  
Author(s):  
Thomas Mack ◽  
Gerhard Quarg ◽  
Christian Braun
Keyword(s):  
Mean Square Error ◽  
Negative Correlation ◽  
Mean Square ◽  
New Approach ◽  
The Mean ◽  
Chain Ladder ◽  
Original Formula

We discuss some questionable points of the approach taken in the paper by Buchwalder, Bühlmann, Merz and Wüthrich and come to the conclusion that this approach does not yield an improvement of Mack’s original formula. The main reason is that the new approach disregards the negative correlation of the squares of the development factors. The same applies to the formula by Murphy (PCAS 1994).

scholarly journals The Mean Square Error of Prediction in the Chain Ladder Reserving Method – A Comment

2006 ◽  
Vol 36 (2) ◽  
pp. 543-552 ◽  
Author(s):  
Thomas Mack ◽  
Gerhard Quarg ◽  
Christian Braun
Keyword(s):  
Mean Square Error ◽  
Negative Correlation ◽  
Mean Square ◽  
New Approach ◽  
The Mean ◽  
Chain Ladder ◽  
Original Formula

We discuss some questionable points of the approach taken in the paper by Buchwalder, Bühlmann, Merz and Wüthrich and come to the conclusion that this approach does not yield an improvement of Mack’s original formula. The main reason is that the new approach disregards the negative correlation of the squares of the development factors. The same applies to the formula by Murphy (PCAS 1994).

scholarly journals Semiflexible Polymer Enclosed in a 3D Compact Domain

2021 ◽  
Vol 9 ◽  
Author(s):  
Pavel Castro-Villarreal ◽  
J. E. Ramírez
Keyword(s):  
Persistence Length ◽  
Compact Domain ◽  
Mean Square ◽  
Shape Transition ◽  
Conformational States ◽  
Semiflexible Polymer ◽  
End Distance ◽  
The Mean ◽  
End To End ◽  
Polymer Shape

The conformational states of a semiflexible polymer enclosed in a volume V:=ℓ3 are studied as stochastic realizations of paths using the stochastic curvature approach developed in [Rev. E 100, 012503 (2019)], in the regime whenever 3ℓ/ℓp>1, where ℓp is the persistence length. The cases of a semiflexible polymer enclosed in a cube and sphere are considered. In these cases, we explore the Spakowitz–Wang–type polymer shape transition, where the critical persistence length distinguishes between an oscillating and a monotonic phase at the level of the mean-square end-to-end distance. This shape transition provides evidence of a universal signature of the behavior of a semiflexible polymer confined in a compact domain.

MEAN SQUARE SIZE OF POLYELECTROLYTES: ANALOGY WITH THE POLARON PROBLEM

1987 ◽  
Vol 01 (01n02) ◽  
pp. 19-25 ◽  
Author(s):  
D.C. KHANDEKAR ◽  
K.V. BHAGWAT ◽  
F.W. WIEGEL
Keyword(s):  
Electrostatic Interaction ◽  
Path Integrals ◽  
Mean Square ◽  
Polaron Theory ◽  
Polar Crystal ◽  
Formal Analogy ◽  
End Distance ◽  
The Mean ◽  
End To End

We point out that a formal analogy exists between the path integrals for the configuration sum of a polyelectrolyte and for the propagator of a polaron in a polar crystal. Using this analogy and some recent results in polaron theory we evaluate the mean square end-to-end distance <X2> of the polyelectroyte. It is shown that for large polymers the electrostatic interaction does not change the behaviour of <X2> from that of a free polymer.

Dynamic and Static Displacements of Atoms in B2-Phase of TiNi Alloy

2008 ◽  
Vol 59 ◽  
pp. 108-112
Author(s):  
Vyacheslav M. Gundyrev ◽  
Vitaly I. Zel'dovich
Keyword(s):  
Single Crystal ◽  
Crystal Lattice ◽  
Titanium Nickelide ◽  
Tini Alloy ◽  
Mean Square ◽  
Atomic Displacements ◽  
Structure Factors ◽  
The Mean ◽  
B2 Phase ◽  
Integrated Intensities

We measured integrated intensities of 26 reflections of the B2-phase of titanium nickelide single crystal and determined structure factors for these reflections. Based on the structure factors, mean squares of displacements of Ni and Ti atoms with respect to the crystal-lattice sites have been determined. After that we determined the mean squares of atomic displacements <u2>Ni and <u2>Ti in temperature range of existence of the B2-pase, at temperatures Т1=328 K and T2=376 K. We separated the mean squares of atomic displacements <u2>Ni and <u2>Ti into static and dynamic ones. The mean squares of dynamic displacements of Ni and Ti atoms are identical, but the mean square of static displacements is greater by a factor of 4.7 for Ni atoms than for Ti atoms. The Debye temperature calculated from the mean squares of displacements of Ni atoms is 360 K; that calculated for Ti atoms in a similar way is 390 K. The large value of complete atomic displacements in TiNi is due to static rather than dynamic displacements of atoms, mainly due to static displacements of nickel atoms.

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