Extent of the correlation between the squared radius of gyration and squared end-to-end distance in random flight chains

Mattice, Wayne L.; Sienicki, K.

doi:10.1063/1.456037

Cited by 8 publications

(14 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…First, these quantities were computed using the position information of the distal end of the random walks that are obtained using our method. Then the same statistical quantities were computed using the Mattice method [32]. We also considered the probability of the ring closure.…”

Section: Discussionmentioning

confidence: 99%

“…We compute these quantities using the end points obtained by our method, and we compare them with the results by the method described in [32]. When we compute the quantities, the NRRWs with from 1 to 400 segments are considered.…”

Section: Square Latticementioning

confidence: 99%

“…For convenience, we will refer to as RATIO4, as RATIO6 and as RATIO8. In Figures 2(a),3(a), and 4(a), we respectively compare RATIO4, RATIO6 and RATIO8 obtained using our method (crosses) and by the method described in [32] Another statistical quantity of great importance is that of the ring closure. The approximate probability of the ring closure can be calculated analytically by the method of Jacobson and Stockmayer [21].…”

Section: Square Latticementioning

confidence: 99%

“…Figure 11 shows the distribution of the end points of 10-segment NRRWs on the diamond lattice. Figures 12(a),13(a), and 14(a) show the statistics of the end-to-end distance obtained using our method (crosses) and by the method described in [32] The probability of the ring closure calculated by Jacobson and Stockmayer [21] is for the diamond lattice. In order for a walk on the diamond lattice to terminate in the origin, it has to have even number of segments and the number of segments has to be greater than or equal to six.…”

Section: Diamond Latticementioning

confidence: 99%

See 3 more Smart Citations

Position and Orientation Distributions for Non-Reversal Random Walks using Space-Group Fourier Transforms

2010

View full text Add to dashboard Cite

This paper presents an efficient group-theoretic approach for computing the statistics of non-reversal random walks (NRRW) on lattices. These framed walks evolve on proper crystallographic space groups. In a previous paper we introduced a convolution method for computing the statistics of NRRWs in which the convolution product is defined relative to the space-group operation. Here we use the corresponding concept of the fast Fourier transform for functions on crystallographic space groups together with a non-Abelian version of the convolution theorem. We develop the theory behind this technique and present numerical results for two-dimensional and three-dimensional lattices (square, cubic and diamond). In order to verify our results, the statistics of the end-to-end distance and the probability of ring closure are calculated and compared with results obtained in the literature for the random walks for which closed-form expressions exist.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Square Latticementioning

confidence: 99%

Section: Square Latticementioning

confidence: 99%

Section: Diamond Latticementioning

confidence: 99%

See 2 more Smart Citations

Position and Orientation Distributions for Non-Reversal Random Walks using Space-Group Fourier Transforms

2010

View full text Add to dashboard Cite

show abstract

“…The mean square of the latter 〈R 2 〉 is a very important entity for characterizing the structure of the polymer [20], [4]. Other important physical quantities are related to the distribution of values ofR, denoted here as p N (R) for a chain of length N. A multitude of simulation methods has been developed to obtain information about how p N (R) evolves for polymer chains [10], [11], [12]. These methods have been applied to many models of polymer chains.…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

Position and orientation distributions for locally self-avoiding walks in the presence of obstacles

Skliros¹,

Chirikjian²

2008

Polymer

View full text Add to dashboard Cite

This paper presents a new approach to study the statistics of lattice random walks in the presence of obstacles and local self-avoidance constraints (excluded volume). By excluding sequentially local interactions within a window that slides along the chain, we obtain an upper bound on the number of self-avoiding walks (SAWs) that terminate at each possible position and orientation. Furthermore we develop a technique to include the effects of obstacles. Thus our model is a more realistic approximation of a polymer chain than that of a simple lattice random walk, and it is more computationally tractable than enumeration of obstacle-avoiding SAWs. Our approach is based on the method of the lattice-motion-group convolution. We develop these techniques theoretically and present numerical results for 2-D and 3-D lattices (square, hexagonal, cubic and tetrahedral/ diamond). We present numerical results that show how the connectivity constant μ changes with the length of each self-avoiding window and the total length of the chain. Quantities such as 〈R〉 and others such as the probability of ring closure are calculated and compared with results obtained in the literature for the simple random walk case.

show abstract

Efficient formulation of the large generator matrices required for computation of the higher moments, and mixed moments, of conformation‐dependent properties of chain molecules with independent bonds

Galiatsatos

Mattice

1990

J Comput Chem

Self Cite

View full text Add to dashboard Cite

Dimensionless ratios of various moments of conformation‐dependent physical properties play an important role in the evaluation of the behavior of chain molecules. For example, the correlation coefficient, ρxy, between two conformation‐dependent physical properties, denoted here as x and y, is determined by the three dimensionless ratios 〈x2〉/〈x〉2, 〈y2〉/〈y〉2, and 〈xy〉/〈x〉〈y〉. Angle brackets denote the statistical mechanical average of the enclosed property. In the rotational isomeric state approximation, generator matrices of modest size can often be used for calculation of 〈x〉 and 〈y〉. The dimensions of the matrices grow rapidly upon going to higher moments or to mixed moments, such as 〈xy〉. Formulation of these large matrices, while straight‐forward, has been extremely tedious for chains with independent bonds, arbitrary rotational potentials, and arbitrary bond angles (which need not be fixed). Here we describe an approach that quickly and accurately solves this problem for all cases in which the generator matrices required for 〈x〉 and 〈y〉 are known. The algorithm is validitated by successful use for the computation of ρr2s2 for r2 and s2 for freely jointed chains of various n, a case for which an exact analytical result in closed form is available in the literature. Here r2 and s2 denote the squared end‐to‐end distance and squared radius of gyration for a specified conformation, and n denotes the number of bonds.

show abstract

Extent of the correlation between the squared radius of gyration and squared end-to-end distance in random flight chains

Cited by 8 publications

References 6 publications

Position and Orientation Distributions for Non-Reversal Random Walks using Space-Group Fourier Transforms

Position and Orientation Distributions for Non-Reversal Random Walks using Space-Group Fourier Transforms

Position and orientation distributions for locally self-avoiding walks in the presence of obstacles

Efficient formulation of the large generator matrices required for computation of the higher moments, and mixed moments, of conformation‐dependent properties of chain molecules with independent bonds

Contact Info

Product

Resources

About