Scaling Law

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Guomeng Zhao - One of the best experts on this subject based on the ideXlab platform.

  • finite size Scaling Law of the neel temperature in hematite nanostructures
    Journal of Applied Physics, 2014
    Co-Authors: Jun Wang, Guomeng Zhao
    Abstract:

    We report high-temperature magnetic properties of single-crystalline hematite (α-Fe2O3) nanostructures with different shapes. Magnetic measurements under a high vacuum (<9.5 × 10−6 Torr) up to 920 K were used to characterize thermal stability of the nanostructures. The onset temperature of the α-Fe2O3 to Fe3O4 phase transformation and the transformed fraction were found to depend strongly on the shape of the nanostructure. The data demonstrate that the phase transformation mainly occurs at the (001) surfaces. The high thermal stability of the nanoring and nanotube samples allows us to accurately measure their Neel temperatures. The Neel temperatures of the nanoring and nanotube samples were found to decrease with decreasing the mean wall-thickness of the nanoring/nanotube assembly. The data confirm the two-dimensional finite-size Scaling Law for the Neel temperature.

  • curie temperature reduction in sio2 coated ultrafine fe3o4 nanoparticles quantitative agreement with a finite size Scaling Law
    Applied Physics Letters, 2011
    Co-Authors: Jun Wang, Fan Zhao, Guomeng Zhao
    Abstract:

    We report high-temperature magnetic measurements for SiO2-coated ultrafine Fe3O4 nanoparticles. The Curie temperatures of the ultrafine Fe3O4 nanoparticles are significantly reduced and follow a finite-size Scaling Law predicted from Monte Carlo simulations. Our current result provides the first quantitative confirmation of the finite-size Scaling Law for quasi-zero-dimensional magnetic systems.

Mikhail Dzugutov - One of the best experts on this subject based on the ideXlab platform.

  • a universal Scaling Law for atomic diffusion in condensed matter
    Nature, 1996
    Co-Authors: Mikhail Dzugutov
    Abstract:

    THERE is currently no unifying quantitative description of atomic diffusion in condensed matter. Analytic expressions have been obtained for the transport coefficients of an idealized dense fluid of hard spheres1,2, but their generalization to the rich variety of atomic structures in real condensed systems remains a challenge. Here I present evidence from molecular dynamics simulations that a universal relationship exists between the structure and the equilibrium rate of atomic diffusion in liquids and solids. I find that the diffusion coefficient, reduced to a dimensionless form by Scaling by the atomic collision frequency and the atomic diameter, is uniquely defined by the excess entropy, a measure of the number of accessible configurations of the system. A Scaling Law relating these two quantities holds well for simple liquids, and also remains applicable to atomic transport in a quasicrystal and to silver-ion diffusion in the solid-state ionic conductor α-AgI. This makes it possible to estimate diffusion coefficients directly from diffraction measurements of an equilibrium structural characteristic, namely the radial distribution function of the diffusing species.

Jun Wang - One of the best experts on this subject based on the ideXlab platform.

  • finite size Scaling Law of the neel temperature in hematite nanostructures
    Journal of Applied Physics, 2014
    Co-Authors: Jun Wang, Guomeng Zhao
    Abstract:

    We report high-temperature magnetic properties of single-crystalline hematite (α-Fe2O3) nanostructures with different shapes. Magnetic measurements under a high vacuum (<9.5 × 10−6 Torr) up to 920 K were used to characterize thermal stability of the nanostructures. The onset temperature of the α-Fe2O3 to Fe3O4 phase transformation and the transformed fraction were found to depend strongly on the shape of the nanostructure. The data demonstrate that the phase transformation mainly occurs at the (001) surfaces. The high thermal stability of the nanoring and nanotube samples allows us to accurately measure their Neel temperatures. The Neel temperatures of the nanoring and nanotube samples were found to decrease with decreasing the mean wall-thickness of the nanoring/nanotube assembly. The data confirm the two-dimensional finite-size Scaling Law for the Neel temperature.

  • curie temperature reduction in sio2 coated ultrafine fe3o4 nanoparticles quantitative agreement with a finite size Scaling Law
    Applied Physics Letters, 2011
    Co-Authors: Jun Wang, Fan Zhao, Guomeng Zhao
    Abstract:

    We report high-temperature magnetic measurements for SiO2-coated ultrafine Fe3O4 nanoparticles. The Curie temperatures of the ultrafine Fe3O4 nanoparticles are significantly reduced and follow a finite-size Scaling Law predicted from Monte Carlo simulations. Our current result provides the first quantitative confirmation of the finite-size Scaling Law for quasi-zero-dimensional magnetic systems.

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

  • on the Scaling Law of jkr contact model for coarse grained cohesive particles
    Chemical Engineering Science, 2020
    Co-Authors: Xizhong Chen, James A Elliott
    Abstract:

    Abstract The computational cost of using discrete element method (DEM) simulations for particulate processes with fine and cohesive particles is enormously large. To overcome this limitation, various coarse-grain DEM models have been developed which use a smaller number of larger sized particles. Although the computational cost is significantly reduced, the accuracy of the simulations depends on the underlying Scaling Law. We propose a Scaling of the Johnson-Kendall-Roberts (JKR) contact model for adhesive viscoelastic particles. A Scaling Law using a single Bond number or Cohesion number criterion is insufficient to keep the motion of the coarse-grained particles the same as the original particles. The Scaling Law in this work is developed based on mass, momentum and energy conservation, which achieves good consistency between the kinematic characteristics of the coarse-grained and original particles. The simulated effective coefficients of restitution were compared for a range of particle-wall impact velocities and validated against experimental data.

Rudiger Urbanke - One of the best experts on this subject based on the ideXlab platform.

  • a Scaling Law to predict the finite length performance of spatially coupled ldpc codes
    IEEE Transactions on Information Theory, 2015
    Co-Authors: Pablo M Olmos, Rudiger Urbanke
    Abstract:

    Spatially-coupled low-density parity-check (SC-LDPC) codes are known to have excellent asymptotic properties. Much less is known regarding their finite-length performance. We propose a Scaling Law to predict the error probability of finite-length spatially coupled code ensembles when transmission takes place over the binary erasure channel. We discuss how the parameters of the Scaling Law are connected to fundamental quantities appearing in the asymptotic analysis of these ensembles and we verify that the predictions of the Scaling Law fit well to the data derived from simulations over a wide range of parameters. The ultimate goal of this line of research is to develop analytic tools for the design of SC-LDPC codes under practical constraints.

  • a Scaling Law to predict the finite length performance of spatially coupled ldpc codes
    arXiv: Information Theory, 2014
    Co-Authors: Pablo M Olmos, Rudiger Urbanke
    Abstract:

    Spatially-coupled LDPC codes are known to have excellent asymptotic properties. Much less is known regarding their finite-length performance. We propose a Scaling Law to predict the error probability of finite-length spatially-coupled ensembles when transmission takes place over the binary erasure channel. We discuss how the parameters of the Scaling Law are connected to fundamental quantities appearing in the asymptotic analysis of these ensembles and we verify that the predictions of the Scaling Law fit well to the data derived from simulations over a wide range of parameters. The ultimate goal of this line of research is to develop analytic tools for the design of spatially-coupled LDPC codes under practical constraints.

  • an empirical Scaling Law for polar codes
    International Symposium on Information Theory, 2010
    Co-Authors: Satish Babu Korada, Andrea Montanari, Emre Telatar, Rudiger Urbanke
    Abstract:

    Using Scaling Laws, we obtain estimates of the block error probability of polar codes under successive cancellation decoding. For the binary erasure channel we present an upper and a lower bound for the Scaling parameter. Numerically these two bounds match. We also present a Scaling Law for general binary discrete memoryless channels.