Inversion of the matrix continued fraction

1979 ◽  
Vol 24 (4) ◽  
pp. 666-667
Author(s):  
A. Kumar ◽  
V. Singh
Keyword(s):  
Continued Fraction ◽  
The Matrix ◽  
Matrix Continued Fraction

scholarly journals Fluctuating noise drives Brownian transport

2012 ◽  
Vol 9 (77) ◽  
pp. 3554-3563 ◽  
Author(s):  
Yoshihiko Hasegawa ◽  
Masanori Arita
Keyword(s):  
Noise Intensity ◽  
Continued Fraction ◽  
Molecular Mechanisms ◽  
Time Correlation ◽  
Optimal Time ◽  
Extrinsic Noise ◽  
Maximum Current ◽  
The Matrix ◽  
Matrix Continued Fraction ◽  
Fraction Method

The transport properties of Brownian ratchet were studied in the presence of stochastic intensity noise in both overdamped and underdamped regimes. In the overdamped case, an analytical solution using the matrix-continued fraction method revealed the existence of a maximum current when the noise intensity fluctuates on intermediate timescale regions. Similar effects were observed for the underdamped case by Monte Carlo simulations. The optimal time-correlation for Brownian transport coincided with the experimentally observed time-correlation of the extrinsic noise in Escherichia coli gene expression and implied the importance of environmental noise for molecular mechanisms.

LATTICE DYNAMICS OF AN F-TYPE ICOSAHEDRAL QUASICRYSTAL

1993 ◽  
Vol 07 (06n07) ◽  
pp. 1487-1504 ◽  
Author(s):  
G. KASNER ◽  
H. BÖTTGER
Keyword(s):  
Lattice Dynamics ◽  
Continued Fraction ◽  
Pair Interaction ◽  
Icosahedral Quasicrystal ◽  
Cluster Approach ◽  
Vibrational States ◽  
Lennard Jones ◽  
Cluster Calculations ◽  
Face Centered ◽  
Matrix Continued Fraction

By using a matrix-continued fraction approach we calculate the density of vibrational states (DOS) of a tiling model based on the 6D face centered lattice. Parameters of the Lennard-Jones pair interaction are obtained from relaxation calculations. With a ternary decoration the tiling was found to be stable. The DOS was approximated by weighting the local DOS (LDOS) of the allowed vertex configurations by their relative frequencies in the infinite tiling. These frequencies were obtained by using extended deflation rules. Results of this approach are compared to exact finite cluster calculations and an embedded cluster approach. We find the DOS to consist of a single band (in our resolution) and a rich structure at higher frequencies.

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