The theta-point and critical point of self-avoiding walks : a phenomenological approach

1992 ◽  
Vol 2 (7) ◽  
pp. 1411-1421 ◽  
Author(s):  
Daniel Lhuillier
Keyword(s):  
Critical Point ◽  
Phenomenological Approach ◽  
Theta Point ◽  
Self Avoiding Walks

The Self-Avoiding-Walk and Percolation Critical Points in High Dimensions

1995 ◽  
Vol 4 (3) ◽  
pp. 197-215 ◽  
Author(s):  
Takashi Hara ◽  
Gordon Slade
Keyword(s):  
Critical Point ◽  
Error Bound ◽  
The Self ◽  
Nearest Neighbour ◽  
High Dimensions ◽  
Lace Expansion ◽  
Connective Constant ◽  
Rigorous Error ◽  
Self Avoiding Walk ◽  
Self Avoiding Walks

We prove the existence of an asymptotic expansion in the inverse dimension, to all orders, for the connective constant for self-avoiding walks on ℤd. For the critical point, defined as the reciprocal of the connective constant, the coefficients of the expansion are computed through orderd−6, with a rigorous error bound of orderd−7Our method for computing terms in the expansion also applies to percolation, and for nearest-neighbour independent Bernoulli bond percolation on ℤdgives the 1/d-expansion for the critical point through orderd−3, with a rigorous error bound of orderd−4The method uses the lace expansion.

Dynamics of roughening and growth of two-dimensional self-avoiding walks

1988 ◽  
Vol 66 (2) ◽  
pp. 187-191 ◽  
Author(s):  
Dietrich Stauffer ◽  
Naeem Jan
Keyword(s):  
Critical Temperature ◽  
Critical Point ◽  
Radius Of Gyration ◽  
Small Ring ◽  
Two Dimensional ◽  
Lattice Fluid ◽  
Length Increase ◽  
The One ◽  
Self Avoiding Walks ◽  
Surface Length

The one-dimensional surface of a two-dimensional lattice fluid is simulated by a method producing self-avoiding walks of varying lengths. Below the critical temperature, the surface width varies as the square root of the surface length in equilibrium, and at the critical point it varies as (time)1/3. Above the critical temperature, the width and the length of the surface increases initially as (time)1/2, whereas finally the "surface" fills the whole lattice. If, instead, we start above the critical point from a small ring, its squared radius of gyration and its length increase initially as (time)2/3. At the critical point, this growth from a small ring gives an average radius proportional to (length)0.75, as for self-avoiding walks.

The Critical Point Drying Method Applied to Scanning Electron Microscopy of L-929 Cells

1970 ◽  
Vol 28 ◽  
pp. 278-279
Author(s):  
Charles TurnbiLL ◽  
Delbert E. Philpott
Keyword(s):  
Electron Microscopy ◽  
Carbon Dioxide ◽  
Surface Tension ◽  
Critical Point ◽  
Freeze Drying ◽  
Attractive Alternative ◽  
Crystal Formation ◽  
Critical Point Drying ◽  
Time Required ◽  
Scanning Electron

The advent of the scanning electron microscope (SCEM) has renewed interest in preparing specimens by avoiding the forces of surface tension. The present method of freeze drying by Boyde and Barger (1969) and Small and Marszalek (1969) does prevent surface tension but ice crystal formation and time required for pumping out the specimen to dryness has discouraged us. We believe an attractive alternative to freeze drying is the critical point method originated by Anderson (1951; for electron microscopy. He avoided surface tension effects during drying by first exchanging the specimen water with alcohol, amy L acetate and then with carbon dioxide. He then selected a specific temperature (36.5°C) and pressure (72 Atm.) at which carbon dioxide would pass from the liquid to the gaseous phase without the effect of surface tension This combination of temperature and, pressure is known as the "critical point" of the Liquid.

SEM Cold Stage Techniques for the Observation of Vegetative and Floral Apices of Oat (Avena sativa L.) Plants

1977 ◽  
Vol 35 ◽  
pp. 590-591
Author(s):  
B. K. Kirchoff ◽  
L.F. Allard ◽  
W.C. Bigelow
Keyword(s):  
Critical Point ◽  
Avena Sativa ◽  
Substantial Improvement ◽  
Fresh Tissue ◽  
Cold Stage ◽  
Critical Point Drying ◽  
Almost All ◽  
Cell Collapse ◽  
Conductive Paint ◽  
Carbon Based

In attempting to use the SEM to investigate the transition from the vegetative to the floral state in oat (Avena sativa L.) it was discovered that the procedures of fixation and critical point drying (CPD), and fresh tissue examination of the specimens gave unsatisfactory results. In most cases, by using these techniques, cells of the tissue were collapsed or otherwise visibly distorted. Figure 1 shows the results of fixation with 4.5% formaldehyde-gluteraldehyde followed by CPD. Almost all cellular detail has been obscured by the resulting shrinkage distortions. The larger cracks seen on the left of the picture may be due to dissection damage, rather than CPD. The results of observation of fresh tissue are seen in Fig. 2. Although there is a substantial improvement over CPD, some cell collapse still occurs.Due to these difficulties, it was decided to experiment with cold stage techniques. The specimens to be observed were dissected out and attached to the sample stub using a carbon based conductive paint in acetone.

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