The Experts below are selected from a list of 36501 Experts worldwide ranked by ideXlab platform
Volker Springel - One of the best experts on this subject based on the ideXlab platform.
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subsonic turbulence in smoothed particle hydrodynamics and moving mesh simulations
Monthly Notices of the Royal Astronomical Society, 2012Co-Authors: Andreas Bauer, Volker SpringelAbstract:Highly supersonic, compressible turbulence is thought to be of tantamount importance for star formation processes in the interstellar medium. Likewise, cosmic structure formation is expected to give rise to subsonic turbulence in the intergalactic medium, which may substantially modify the thermodynamic structure of gas in virialized dark matter haloes and affect small-scale mixing processes in the gas. Numerical simulations have played a key role in characterizing the properties of astrophysical turbulence, but thus far Systematic Code comparisons have been restricted to the supersonic regime, leaving it unclear whether subsonic turbulence is faithfully represented by the numerical techniques commonly employed in astrophysics. Here we focus on comparing the accuracy of smoothed particle hydrodynamics (SPH) and our new moving-mesh technique AREPO in simulations of driven subsonic turbulence. To make contact with previous results, we also analyse simulations of transsonic and highly supersonic turbulence. We find that the widely employed standard formulation of SPH yields problematic results in the subsonic regime. Instead of building up a Kolmogorov-like turbulent cascade, large-scale eddies are quickly damped close to the driving scale and decay into small-scale velocity noise. Reduced viscosity settings improve the situation, but the shape of the dissipation range differs compared with expectations for a Kolmogorov cascade. In contrast, our moving-mesh technique does yield power-law scaling laws for the power spectra of velocity, vorticity and density, consistent with expectations for fully developed isotropic turbulence. We show that large errors in SPH’s gradient estimate and the associated subsonic velocity noise are ultimately responsible for producing inaccurate results in the subsonic regime. In contrast, SPH’s performance is much better for supersonic turbulence, as here the flow is kinetically dominated and characterized by a network of strong shocks, which can be adequately captured with SPH. When compared to fixed grid Eulerian simulations of turbulence, our moving mesh approach shows qualitatively very similar results, although with somewhat better resolving power at the same number of cells, thanks to reduced advection errors and the automatic adaptivity of the AREPO Code.
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subsonic turbulence in smoothed particle hydrodynamics and moving mesh simulations
arXiv: Cosmology and Nongalactic Astrophysics, 2011Co-Authors: Andreas Bauer, Volker SpringelAbstract:Highly supersonic, compressible turbulence is thought to be of tantamount importance for star formation processes in the interstellar medium. Likewise, cosmic structure formation is expected to give rise to subsonic turbulence in the intergalactic medium, which may substantially modify the thermodynamic structure of gas in virialized dark matter halos and affect small-scale mixing processes in the gas. Numerical simulations have played a key role in characterizing the properties of astrophysical turbulence, but thus far Systematic Code comparisons have been restricted to the supersonic regime, leaving it unclear whether subsonic turbulence is faithfully represented by the numerical techniques commonly employed in astrophysics. Here we focus on comparing the accuracy of smoothed particle hydrodynamics (SPH) and our new moving-mesh technique AREPO in simulations of driven subsonic turbulence. To make contact with previous results, we also analyze simulations of transsonic and highly supersonic turbulence. We find that the widely employed standard formulation of SPH yields problematic results in the subsonic regime. Instead of building up a Kolmogorov-like turbulent cascade, large-scale eddies are quickly damped close to the driving scale and decay into small-scale velocity noise. Reduced viscosity settings improve the situation, but the shape of the dissipation range differs compared with expectations for a Kolmogorov cascade. In contrast, our moving-mesh technique does yield power-law scaling laws for the power spectra of velocity, vorticity and density, consistent with expectations for fully developed isotropic turbulence. We show that large errors in SPH's gradient estimate and the associated subsonic velocity noise are ultimately responsible for producing inaccurate results in the subsonic regime. In contrast, SPH's performance is much better for supersonic turbulence. [Abridged]
Yury Polyanskiy - One of the best experts on this subject based on the ideXlab platform.
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graceful degradation over the bec via non linear Codes
International Symposium on Information Theory, 2020Co-Authors: Hajir Roozbehani, Yury PolyanskiyAbstract:We study a problem of constructing Codes that transform a channel with high bit error rate (BER) into one with low BER (at the expense of rate). Our focus is on obtaining Codes with smooth ("graceful") input-output BER curves (as opposed to threshold-like curves typical for long error-correcting Codes).This paper restricts attention to binary erasure channels (BEC) and contains two contributions. First, we introduce the notion of Low Density Majority Codes (LDMCs). These Codes are non-linear sparse-graph Codes, which output majority function evaluated on randomly chosen small subsets of the data bits. This is similar to Low Density Generator Matrix Codes (LDGMs), except that the XOR function is replaced with the majority. We show that even with a few iterations of belief propagation (BP) the attained input-output curves provably improve upon performance of any linear Systematic Code. The effect of nonlinearity bootstraping the initial iterations of BP, suggests that LDMCs should improve performance in various applications where LDGMs have been used traditionally.Second, we establish several two-point converse bounds that lower bound the BER achievable at one erasure probability as a function of BER achieved at another one. The novel nature of our bounds is that they are specific to subclasses of Codes (linear Systematic and non-linear Systematic) and outperform similar bounds implied by the area theorem for the EXIT function.
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low density majority Codes and the problem of graceful degradation
arXiv: Information Theory, 2019Co-Authors: Hajir Roozbehani, Yury PolyanskiyAbstract:We study a problem of constructing Codes that transform a channel with high bit error rate (BER) into one with low BER (at the expense of rate). Our focus is on obtaining Codes with smooth ("graceful'') input-output BER curves (as opposed to threshold-like curves typical for long error-correcting Codes). This paper restricts attention to binary erasure channels (BEC) and contains three contributions. First, we introduce the notion of Low Density Majority Codes (LDMCs). These Codes are non-linear sparse-graph Codes, which output majority function evaluated on randomly chosen small subsets of the data bits. This is similar to Low Density Generator Matrix Codes (LDGMs), except that the XOR function is replaced with the majority. We show that even with a few iterations of belief propagation (BP) the attained input-output curves provably improve upon performance of any linear Systematic Code. The effect of non-linearity bootstraping the initial iterations of BP, suggests that LDMCs should improve performance in various applications, where LDGMs have been used traditionally. Second, we establish several \textit{two-point converse bounds} that lower bound the BER achievable at one erasure probability as a function of BER achieved at another one. The novel nature of our bounds is that they are specific to subclasses of Codes (linear Systematic and non-linear Systematic) and outperform similar bounds implied by the area theorem for the EXIT function.
Hajir Roozbehani - One of the best experts on this subject based on the ideXlab platform.
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graceful degradation over the bec via non linear Codes
International Symposium on Information Theory, 2020Co-Authors: Hajir Roozbehani, Yury PolyanskiyAbstract:We study a problem of constructing Codes that transform a channel with high bit error rate (BER) into one with low BER (at the expense of rate). Our focus is on obtaining Codes with smooth ("graceful") input-output BER curves (as opposed to threshold-like curves typical for long error-correcting Codes).This paper restricts attention to binary erasure channels (BEC) and contains two contributions. First, we introduce the notion of Low Density Majority Codes (LDMCs). These Codes are non-linear sparse-graph Codes, which output majority function evaluated on randomly chosen small subsets of the data bits. This is similar to Low Density Generator Matrix Codes (LDGMs), except that the XOR function is replaced with the majority. We show that even with a few iterations of belief propagation (BP) the attained input-output curves provably improve upon performance of any linear Systematic Code. The effect of nonlinearity bootstraping the initial iterations of BP, suggests that LDMCs should improve performance in various applications where LDGMs have been used traditionally.Second, we establish several two-point converse bounds that lower bound the BER achievable at one erasure probability as a function of BER achieved at another one. The novel nature of our bounds is that they are specific to subclasses of Codes (linear Systematic and non-linear Systematic) and outperform similar bounds implied by the area theorem for the EXIT function.
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low density majority Codes and the problem of graceful degradation
arXiv: Information Theory, 2019Co-Authors: Hajir Roozbehani, Yury PolyanskiyAbstract:We study a problem of constructing Codes that transform a channel with high bit error rate (BER) into one with low BER (at the expense of rate). Our focus is on obtaining Codes with smooth ("graceful'') input-output BER curves (as opposed to threshold-like curves typical for long error-correcting Codes). This paper restricts attention to binary erasure channels (BEC) and contains three contributions. First, we introduce the notion of Low Density Majority Codes (LDMCs). These Codes are non-linear sparse-graph Codes, which output majority function evaluated on randomly chosen small subsets of the data bits. This is similar to Low Density Generator Matrix Codes (LDGMs), except that the XOR function is replaced with the majority. We show that even with a few iterations of belief propagation (BP) the attained input-output curves provably improve upon performance of any linear Systematic Code. The effect of non-linearity bootstraping the initial iterations of BP, suggests that LDMCs should improve performance in various applications, where LDGMs have been used traditionally. Second, we establish several \textit{two-point converse bounds} that lower bound the BER achievable at one erasure probability as a function of BER achieved at another one. The novel nature of our bounds is that they are specific to subclasses of Codes (linear Systematic and non-linear Systematic) and outperform similar bounds implied by the area theorem for the EXIT function.
Andreas Bauer - One of the best experts on this subject based on the ideXlab platform.
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subsonic turbulence in smoothed particle hydrodynamics and moving mesh simulations
Monthly Notices of the Royal Astronomical Society, 2012Co-Authors: Andreas Bauer, Volker SpringelAbstract:Highly supersonic, compressible turbulence is thought to be of tantamount importance for star formation processes in the interstellar medium. Likewise, cosmic structure formation is expected to give rise to subsonic turbulence in the intergalactic medium, which may substantially modify the thermodynamic structure of gas in virialized dark matter haloes and affect small-scale mixing processes in the gas. Numerical simulations have played a key role in characterizing the properties of astrophysical turbulence, but thus far Systematic Code comparisons have been restricted to the supersonic regime, leaving it unclear whether subsonic turbulence is faithfully represented by the numerical techniques commonly employed in astrophysics. Here we focus on comparing the accuracy of smoothed particle hydrodynamics (SPH) and our new moving-mesh technique AREPO in simulations of driven subsonic turbulence. To make contact with previous results, we also analyse simulations of transsonic and highly supersonic turbulence. We find that the widely employed standard formulation of SPH yields problematic results in the subsonic regime. Instead of building up a Kolmogorov-like turbulent cascade, large-scale eddies are quickly damped close to the driving scale and decay into small-scale velocity noise. Reduced viscosity settings improve the situation, but the shape of the dissipation range differs compared with expectations for a Kolmogorov cascade. In contrast, our moving-mesh technique does yield power-law scaling laws for the power spectra of velocity, vorticity and density, consistent with expectations for fully developed isotropic turbulence. We show that large errors in SPH’s gradient estimate and the associated subsonic velocity noise are ultimately responsible for producing inaccurate results in the subsonic regime. In contrast, SPH’s performance is much better for supersonic turbulence, as here the flow is kinetically dominated and characterized by a network of strong shocks, which can be adequately captured with SPH. When compared to fixed grid Eulerian simulations of turbulence, our moving mesh approach shows qualitatively very similar results, although with somewhat better resolving power at the same number of cells, thanks to reduced advection errors and the automatic adaptivity of the AREPO Code.
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subsonic turbulence in smoothed particle hydrodynamics and moving mesh simulations
arXiv: Cosmology and Nongalactic Astrophysics, 2011Co-Authors: Andreas Bauer, Volker SpringelAbstract:Highly supersonic, compressible turbulence is thought to be of tantamount importance for star formation processes in the interstellar medium. Likewise, cosmic structure formation is expected to give rise to subsonic turbulence in the intergalactic medium, which may substantially modify the thermodynamic structure of gas in virialized dark matter halos and affect small-scale mixing processes in the gas. Numerical simulations have played a key role in characterizing the properties of astrophysical turbulence, but thus far Systematic Code comparisons have been restricted to the supersonic regime, leaving it unclear whether subsonic turbulence is faithfully represented by the numerical techniques commonly employed in astrophysics. Here we focus on comparing the accuracy of smoothed particle hydrodynamics (SPH) and our new moving-mesh technique AREPO in simulations of driven subsonic turbulence. To make contact with previous results, we also analyze simulations of transsonic and highly supersonic turbulence. We find that the widely employed standard formulation of SPH yields problematic results in the subsonic regime. Instead of building up a Kolmogorov-like turbulent cascade, large-scale eddies are quickly damped close to the driving scale and decay into small-scale velocity noise. Reduced viscosity settings improve the situation, but the shape of the dissipation range differs compared with expectations for a Kolmogorov cascade. In contrast, our moving-mesh technique does yield power-law scaling laws for the power spectra of velocity, vorticity and density, consistent with expectations for fully developed isotropic turbulence. We show that large errors in SPH's gradient estimate and the associated subsonic velocity noise are ultimately responsible for producing inaccurate results in the subsonic regime. In contrast, SPH's performance is much better for supersonic turbulence. [Abridged]
K J R Liu - One of the best experts on this subject based on the ideXlab platform.
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Systematic space time trellis Code design for an arbitrary number of transmit antennas
Vehicular Technology Conference, 2001Co-Authors: Zoltan Safar, K J R LiuAbstract:The potential for a capacity increase in multi-antenna wireless communication systems has drawn considerable attention to space-time Codes. In this work, we propose a Systematic Code construction method that jointly considers diversity advantage and coding advantage for an arbitrary number of transmit antennas and any memoryless constellation. Due to the special structure of the channel symbol difference matrix, the Code construction problem is reduced to a combinatorial optimization problem and a computationally efficient suboptimal solution is proposed. The simulations show that our design procedure results in Codes that outperform the ones constructed by previously existing methods. In certain cases, as much as 2-2.5 dB coding gain can be observed.
