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A Rechnitzer - One of the best experts on this subject based on the ideXlab platform.

  • minimal knotted polygons in Cubic Lattices
    2011
    Co-Authors: E Janse J Van Rensburg, A Rechnitzer
    Abstract:

    In this paper we examine numerically the properties of minimal length knotted lattice polygons in the simple Cubic, face-centered Cubic, and body-centered Cubic Lattices by sieving minimal length polygons from a data stream of a Monte Carlo algorithm, implemented as described in Aragao de Carvalho and Caracciolo (1983 Phys. Rev. B 27 1635), Aragao de Carvalho et al (1983 Nucl. Phys. B 215 209) and Berg and Foester (1981 Phys. Lett. B 106 323). The entropy, mean writhe, and mean curvature of minimal length polygons are computed (in some cases exactly). While the minimal length and mean curvature are found to be lattice dependent, the mean writhe is found to be only weakly dependent on the lattice type. Comparison of our results to numerical results for the writhe obtained elsewhere (see Janse van Rensburg et al 1999 Contributed to Ideal Knots (Series on Knots and Everything vol 19) ed Stasiak, Katritch and Kauffman (Singapore: World Scientific), Portillo et al 2011 J. Phys. A: Math. Theor. 44 275004) shows that the mean writhe is also insensitive to the length of a knotted polygon. Thus, while these results for the mean writhe and mean absolute writhe at minimal length are not universal, our results demonstrate that these values are quite close the those of long polygons regardless of the underlying lattice and length.

  • minimal knotted polygons in Cubic Lattices
    2011
    Co-Authors: E Janse J Van Rensburg, A Rechnitzer
    Abstract:

    An implementation of BFACF-style algorithms on knotted polygons in the simple Cubic, face centered Cubic and body centered Cubic lattice is used to estimate the statistics and writhe of minimal length knotted polygons in each of the Lattices. Data are collected and analysed on minimal length knotted polygons, their entropy, and their lattice curvature and writhe.

  • bfacf style algorithms for polygons in the body centered and face centered Cubic Lattices
    2011
    Co-Authors: E Janse J Van Rensburg, A Rechnitzer
    Abstract:

    In this paper, the elementary moves of the BFACF-algorithm (Aragao de Carvalho and Caracciolo 1983 Phys. Rev. B 27 1635–45, Aragao de Carvalho and Caracciolo 1983 Nucl. Phys. B 215 209–48, Berg and Foester 1981 Phys. Lett. B 106 323–6) for lattice polygons are generalized to elementary moves of BFACF-style algorithms for lattice polygons in the body-centered (BCC) and face-centered (FCC) Cubic Lattices. We prove that the ergodicity classes of these new elementary moves coincide with the knot types of unrooted polygons in the BCC and FCC Lattices and so expand a similar result for the Cubic lattice (see Janse van Rensburg and Whittington (1991 J. Phys. A: Math. Gen. 24 5553–67)). Implementations of these algorithms for knotted polygons using the GAS algorithm produce estimates of the minimal length of knotted polygons in the BCC and FCC Lattices.

  • bfacf style algorithms for polygons in the body centered and face centered Cubic Lattices
    2010
    Co-Authors: E Janse J Van Rensburg, A Rechnitzer
    Abstract:

    In this paper the elementary moves of the BFACF-algorithm for lattice polygons are generalised to elementary moves of BFACF-style algorithms for lattice polygons in the body-centred (BCC) and face-centred (FCC) Cubic Lattices. We prove that the ergodicity classes of these new elementary moves coincide with the knot types of unrooted polygons in the BCC and FCC Lattices and so expand a similar result for the Cubic lattice. Implementations of these algorithms for knotted polygons using the GAS algorithm produce estimates of the minimal length of knotted polygons in the BCC and FCC Lattices.

Damian J J Farnell - One of the best experts on this subject based on the ideXlab platform.

Wolfhard Janke - One of the best experts on this subject based on the ideXlab platform.

  • percolation thresholds and fractal dimensions for square and Cubic Lattices with long range correlated defects
    2017
    Co-Authors: Johannes Zierenberg, Niklas Fricke, Martin Marenz, F P Spitzner, V Blavatska, Wolfhard Janke
    Abstract:

    We study long-range power-law correlated disorder on square and Cubic Lattices. In particular, we present high-precision results for the percolation thresholds and the fractal dimension of the largest clusters as a function of the correlation strength. The correlations are generated using a discrete version of the Fourier filtering method. We consider two different metrics to set the length scales over which the correlations decay, showing that the percolation thresholds are highly sensitive to such system details. By contrast, we verify that the fractal dimension d_{f} is a universal quantity and unaffected by the choice of metric. We also show that for weak correlations, its value coincides with that for the uncorrelated system. In two dimensions we observe a clear increase of the fractal dimension with increasing correlation strength, approaching d_{f}→2. The onset of this change does not seem to be determined by the extended Harris criterion.

  • percolation thresholds and fractal dimensions for square and Cubic Lattices with long range correlated defects
    2017
    Co-Authors: Johannes Zierenberg, Niklas Fricke, Martin Marenz, F P Spitzner, V Blavatska, Wolfhard Janke
    Abstract:

    We study long-range power-law correlated disorder on square and Cubic Lattices. In particular, we present high-precision results for the percolation thresholds and the fractal dimension of the largest clusters as a function of the correlation strength. The correlations are generated using a discrete version of the Fourier filtering method. We consider two different metrics to set the length scales over which the correlations decay, showing that the percolation thresholds are highly sensitive to such system details. By contrast, we verify that the fractal dimension ${d}_{\mathrm{f}}$ is a universal quantity and unaffected by the choice of metric. We also show that for weak correlations, its value coincides with that for the uncorrelated system. In two dimensions we observe a clear increase of the fractal dimension with increasing correlation strength, approaching ${d}_{\mathrm{f}}\ensuremath{\rightarrow}2$. The onset of this change does not seem to be determined by the extended Harris criterion.

Xiangkun Kong - One of the best experts on this subject based on the ideXlab platform.

  • investigation on the dispersion of three dimensional non magnetized plasma photonic crystals with faced centered Cubic Lattices
    2013
    Co-Authors: Haifeng Zhang, Shaobin Liu, Xiangkun Kong
    Abstract:

    Abstract Dispersion properties of two types of three-dimensional (3D) nomagnetized plasma photonic crystals (PPCs) with face-centered-Cubic Lattices have been investigated by a modified plane wave expansion (PWE) method. The first type (type-1) is a 3D PPCs which dielectric spheres are arranged in the plasma background periodically with face-centered-Cubic Lattices, while the second one (type-2) is a complementary structure composed of plasma spheres in the dielectric background. It is found that a flatbands region and two stop gaps appear in Γ–X and Γ–L directions, respectively. The results show that the upper edges of flatbands regions for both types of PPCs cannot be tuned except for plasma frequency. The stop gaps in Γ–X and Γ–L directions for both types of PPCs can be modulated by the filling factor, relative dielectric constant and plasma frequency, respectively. However, the plasma collision frequency has no effect on the locations of stop gaps in Γ–X and Γ–L directions, and also cannot control the upper edges of flatbands regions for both types of PPCs. The results may provide theoretical foundations to design the new tunable photonic crystals devices in microwave communications.

E Janse J Van Rensburg - One of the best experts on this subject based on the ideXlab platform.

  • minimal knotted polygons in Cubic Lattices
    2011
    Co-Authors: E Janse J Van Rensburg, A Rechnitzer
    Abstract:

    In this paper we examine numerically the properties of minimal length knotted lattice polygons in the simple Cubic, face-centered Cubic, and body-centered Cubic Lattices by sieving minimal length polygons from a data stream of a Monte Carlo algorithm, implemented as described in Aragao de Carvalho and Caracciolo (1983 Phys. Rev. B 27 1635), Aragao de Carvalho et al (1983 Nucl. Phys. B 215 209) and Berg and Foester (1981 Phys. Lett. B 106 323). The entropy, mean writhe, and mean curvature of minimal length polygons are computed (in some cases exactly). While the minimal length and mean curvature are found to be lattice dependent, the mean writhe is found to be only weakly dependent on the lattice type. Comparison of our results to numerical results for the writhe obtained elsewhere (see Janse van Rensburg et al 1999 Contributed to Ideal Knots (Series on Knots and Everything vol 19) ed Stasiak, Katritch and Kauffman (Singapore: World Scientific), Portillo et al 2011 J. Phys. A: Math. Theor. 44 275004) shows that the mean writhe is also insensitive to the length of a knotted polygon. Thus, while these results for the mean writhe and mean absolute writhe at minimal length are not universal, our results demonstrate that these values are quite close the those of long polygons regardless of the underlying lattice and length.

  • minimal knotted polygons in Cubic Lattices
    2011
    Co-Authors: E Janse J Van Rensburg, A Rechnitzer
    Abstract:

    An implementation of BFACF-style algorithms on knotted polygons in the simple Cubic, face centered Cubic and body centered Cubic lattice is used to estimate the statistics and writhe of minimal length knotted polygons in each of the Lattices. Data are collected and analysed on minimal length knotted polygons, their entropy, and their lattice curvature and writhe.

  • bfacf style algorithms for polygons in the body centered and face centered Cubic Lattices
    2011
    Co-Authors: E Janse J Van Rensburg, A Rechnitzer
    Abstract:

    In this paper, the elementary moves of the BFACF-algorithm (Aragao de Carvalho and Caracciolo 1983 Phys. Rev. B 27 1635–45, Aragao de Carvalho and Caracciolo 1983 Nucl. Phys. B 215 209–48, Berg and Foester 1981 Phys. Lett. B 106 323–6) for lattice polygons are generalized to elementary moves of BFACF-style algorithms for lattice polygons in the body-centered (BCC) and face-centered (FCC) Cubic Lattices. We prove that the ergodicity classes of these new elementary moves coincide with the knot types of unrooted polygons in the BCC and FCC Lattices and so expand a similar result for the Cubic lattice (see Janse van Rensburg and Whittington (1991 J. Phys. A: Math. Gen. 24 5553–67)). Implementations of these algorithms for knotted polygons using the GAS algorithm produce estimates of the minimal length of knotted polygons in the BCC and FCC Lattices.

  • bfacf style algorithms for polygons in the body centered and face centered Cubic Lattices
    2010
    Co-Authors: E Janse J Van Rensburg, A Rechnitzer
    Abstract:

    In this paper the elementary moves of the BFACF-algorithm for lattice polygons are generalised to elementary moves of BFACF-style algorithms for lattice polygons in the body-centred (BCC) and face-centred (FCC) Cubic Lattices. We prove that the ergodicity classes of these new elementary moves coincide with the knot types of unrooted polygons in the BCC and FCC Lattices and so expand a similar result for the Cubic lattice. Implementations of these algorithms for knotted polygons using the GAS algorithm produce estimates of the minimal length of knotted polygons in the BCC and FCC Lattices.