The Experts below are selected from a list of 11445 Experts worldwide ranked by ideXlab platform
Livio Pizzocchero - One of the best experts on this subject based on the ideXlab platform.
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on power series solutions for the euler equation and the behr necas wu initial datum
Mathematical Modelling and Numerical Analysis, 2013Co-Authors: Carlo Morosi, Mario Pernici, Livio PizzoccheroAbstract:We consider the Euler equation for an incompressible fluid on a three dimensional torus, and the construction of its solution as a power series in time. We point out some general facts on this subject, from Convergence issues for the power series to the role of symmetries of the initial datum. We then turn the attention to a paper by Behr, Necas and Wu, ESAIM: M2AN 35 (2001) 229–238; here, the authors chose a very simple Fourier polynomial as an initial datum for the Euler equation and analyzed the power series in time for the solution, determining the first 35 terms by computer algebra. Their calculations suggested for the series a finite Convergence Radius τ 3 in the H 3 Sobolev space, with 0.32 3 35 (2001) 229–238, using again computer algebra; the order has been increased from 35 to 52, using the symmetries of the initial datum to speed up computations. As for τ 3 , our results agree with the original computations of E. Behr, J. Necas and H. Wu, ESAIM: M2AN 35 (2001) 229–238 (yielding in fact to conjecture that 0.32 3 3 is not at all an indication of a possible blow-up. (b) There is a strong indication that the solution of the Euler equation does not blow up at a time close to τ 3 . In fact, the solution is likely to exist, at least, up to a time θ 3 > 0.47. (c) There is a weak indication, based on Pade analysis, that the solution might blow up at a later time.
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on power series solutions for the euler equation and the behr necas wu initial datum
arXiv: Analysis of PDEs, 2012Co-Authors: Carlo Morosi, Mario Pernici, Livio PizzoccheroAbstract:We consider the Euler equation for an incompressible fluid on a three dimensional torus, and the construction of its solution as a power series in time. We point out some general facts on this subject, from Convergence issues for the power series to the role of symmetries of the initial datum. We then turn the attention to a paper by Behr, Necas and Wu in ESAIM: M2AN 35 (2001) 229-238; here, the authors chose a very simple Fourier polynomial as an initial datum for the Euler equation and analyzed the power series in time for the solution, determining the first 35 terms by computer algebra. Their calculations suggested for the series a finite Convergence Radius \tau_3 in the H^3 Sobolev space, with 0.32 0.47. (c) Pade' analysis gives a rather weak indication that the solution might blow up at a later time.
Sara Tahery - One of the best experts on this subject based on the ideXlab platform.
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complexified quasinormal modes and the pole skipping in a holographic system at finite chemical potential
Journal of High Energy Physics, 2020Co-Authors: Navid Abbasi, Sara TaheryAbstract:We develop a method to study coupled dynamics of gauge-invariant variables, constructed out of metric and gauge field fluctuations on the background of a AdS5 Reissner-Nordstrom black brane. Using this method, we compute the numerical spectrum of quasinormal modes associated with fluctuations of spin 0, 1 and 2, non-perturbatively in μ/T . We also analytically compute the spectrum of hydrodynamic excitations in the small chemical potential limit. Then, by studying the spectral curve at complex momenta in every spin channel, we numerically find points at which hydrodynamic and non-hydrodynamic poles collide. We discuss the relation between such collision points and the Convergence Radius of the hydrodynamic derivative expansion. Specifically in the spin 0 channel, we find that within the range $$ 1.1\underset{\sim }{<}\mu /T\underset{\sim }{<}2 $$ , the Radius of Convergence of the hydrodynamic sound mode is set by the absolute value of the complex momentum corresponding to the point at which the sound pole collides with the hydrodynamic diffusion pole. It shows that in holographic systems at finite chemical potential, the Convergence of the hydrodynamic derivative expansion in the mentioned range is fully controlled by hydrodynamic informa- tion. As the last result, we explicitly show that the relevant information about quantum chaos in our system can be extracted from the pole-skipping points of energy density re- sponse function. We find a threshold value for μ/T , lower than which the pole-skipping points can be computed perturbatively in a derivative expansion.
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complexified quasinormal modes and the pole skipping in a holographic system at finite chemical potential
arXiv: High Energy Physics - Theory, 2020Co-Authors: Navid Abbasi, Sara TaheryAbstract:We develop a method to study coupled dynamics of gauge-invariant variables, constructed out of metric and gauge field fluctuations on the background of a AdS$_5$ Reissner-Nordstrom black brane. Using this method, we compute the numerical spectrum of quasinormal modes associated with fluctuations of spin 0, 1 and 2, non-perturbatively in $\mu/T$. We also analytically compute the spectrum of hydrodynamic excitations in the small chemical potential limit. Then, by studying the spectral curve at complex momenta in every spin channel, we numerically find points at which hydrodynamic and non-hydrodynamic poles collide. We discuss the relation between such collision points and the Convergence Radius of the hydrodynamic derivative expansion. Specifically in the spin 0 channel, we find that within the range $1.1\lesssim \mu/T\lesssim 2$, the Radius of Convergence of the hydrodynamic sound mode is set by the absolute value of the complex momentum corresponding to the point at which the sound pole collides with the hydrodynamic diffusion pole. It shows that in holographic systems at finite chemical potential, the Convergence of the hydrodynamic derivative expansion in the mentioned range is fully controlled by hydrodynamic information. As the last result, we explicitly show that the relevant information about quantum chaos in our system can be extracted from the pole-skipping points of energy density response function. We find a threshold value for $\mu/T$, lower than which the pole-skipping points can be computed perturbatively in a derivative expansion.
Carlo Morosi - One of the best experts on this subject based on the ideXlab platform.
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on power series solutions for the euler equation and the behr necas wu initial datum
Mathematical Modelling and Numerical Analysis, 2013Co-Authors: Carlo Morosi, Mario Pernici, Livio PizzoccheroAbstract:We consider the Euler equation for an incompressible fluid on a three dimensional torus, and the construction of its solution as a power series in time. We point out some general facts on this subject, from Convergence issues for the power series to the role of symmetries of the initial datum. We then turn the attention to a paper by Behr, Necas and Wu, ESAIM: M2AN 35 (2001) 229–238; here, the authors chose a very simple Fourier polynomial as an initial datum for the Euler equation and analyzed the power series in time for the solution, determining the first 35 terms by computer algebra. Their calculations suggested for the series a finite Convergence Radius τ 3 in the H 3 Sobolev space, with 0.32 3 35 (2001) 229–238, using again computer algebra; the order has been increased from 35 to 52, using the symmetries of the initial datum to speed up computations. As for τ 3 , our results agree with the original computations of E. Behr, J. Necas and H. Wu, ESAIM: M2AN 35 (2001) 229–238 (yielding in fact to conjecture that 0.32 3 3 is not at all an indication of a possible blow-up. (b) There is a strong indication that the solution of the Euler equation does not blow up at a time close to τ 3 . In fact, the solution is likely to exist, at least, up to a time θ 3 > 0.47. (c) There is a weak indication, based on Pade analysis, that the solution might blow up at a later time.
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on power series solutions for the euler equation and the behr necas wu initial datum
arXiv: Analysis of PDEs, 2012Co-Authors: Carlo Morosi, Mario Pernici, Livio PizzoccheroAbstract:We consider the Euler equation for an incompressible fluid on a three dimensional torus, and the construction of its solution as a power series in time. We point out some general facts on this subject, from Convergence issues for the power series to the role of symmetries of the initial datum. We then turn the attention to a paper by Behr, Necas and Wu in ESAIM: M2AN 35 (2001) 229-238; here, the authors chose a very simple Fourier polynomial as an initial datum for the Euler equation and analyzed the power series in time for the solution, determining the first 35 terms by computer algebra. Their calculations suggested for the series a finite Convergence Radius \tau_3 in the H^3 Sobolev space, with 0.32 0.47. (c) Pade' analysis gives a rather weak indication that the solution might blow up at a later time.
Navid Abbasi - One of the best experts on this subject based on the ideXlab platform.
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complexified quasinormal modes and the pole skipping in a holographic system at finite chemical potential
Journal of High Energy Physics, 2020Co-Authors: Navid Abbasi, Sara TaheryAbstract:We develop a method to study coupled dynamics of gauge-invariant variables, constructed out of metric and gauge field fluctuations on the background of a AdS5 Reissner-Nordstrom black brane. Using this method, we compute the numerical spectrum of quasinormal modes associated with fluctuations of spin 0, 1 and 2, non-perturbatively in μ/T . We also analytically compute the spectrum of hydrodynamic excitations in the small chemical potential limit. Then, by studying the spectral curve at complex momenta in every spin channel, we numerically find points at which hydrodynamic and non-hydrodynamic poles collide. We discuss the relation between such collision points and the Convergence Radius of the hydrodynamic derivative expansion. Specifically in the spin 0 channel, we find that within the range $$ 1.1\underset{\sim }{<}\mu /T\underset{\sim }{<}2 $$ , the Radius of Convergence of the hydrodynamic sound mode is set by the absolute value of the complex momentum corresponding to the point at which the sound pole collides with the hydrodynamic diffusion pole. It shows that in holographic systems at finite chemical potential, the Convergence of the hydrodynamic derivative expansion in the mentioned range is fully controlled by hydrodynamic informa- tion. As the last result, we explicitly show that the relevant information about quantum chaos in our system can be extracted from the pole-skipping points of energy density re- sponse function. We find a threshold value for μ/T , lower than which the pole-skipping points can be computed perturbatively in a derivative expansion.
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complexified quasinormal modes and the pole skipping in a holographic system at finite chemical potential
arXiv: High Energy Physics - Theory, 2020Co-Authors: Navid Abbasi, Sara TaheryAbstract:We develop a method to study coupled dynamics of gauge-invariant variables, constructed out of metric and gauge field fluctuations on the background of a AdS$_5$ Reissner-Nordstrom black brane. Using this method, we compute the numerical spectrum of quasinormal modes associated with fluctuations of spin 0, 1 and 2, non-perturbatively in $\mu/T$. We also analytically compute the spectrum of hydrodynamic excitations in the small chemical potential limit. Then, by studying the spectral curve at complex momenta in every spin channel, we numerically find points at which hydrodynamic and non-hydrodynamic poles collide. We discuss the relation between such collision points and the Convergence Radius of the hydrodynamic derivative expansion. Specifically in the spin 0 channel, we find that within the range $1.1\lesssim \mu/T\lesssim 2$, the Radius of Convergence of the hydrodynamic sound mode is set by the absolute value of the complex momentum corresponding to the point at which the sound pole collides with the hydrodynamic diffusion pole. It shows that in holographic systems at finite chemical potential, the Convergence of the hydrodynamic derivative expansion in the mentioned range is fully controlled by hydrodynamic information. As the last result, we explicitly show that the relevant information about quantum chaos in our system can be extracted from the pole-skipping points of energy density response function. We find a threshold value for $\mu/T$, lower than which the pole-skipping points can be computed perturbatively in a derivative expansion.
Mario Pernici - One of the best experts on this subject based on the ideXlab platform.
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on power series solutions for the euler equation and the behr necas wu initial datum
Mathematical Modelling and Numerical Analysis, 2013Co-Authors: Carlo Morosi, Mario Pernici, Livio PizzoccheroAbstract:We consider the Euler equation for an incompressible fluid on a three dimensional torus, and the construction of its solution as a power series in time. We point out some general facts on this subject, from Convergence issues for the power series to the role of symmetries of the initial datum. We then turn the attention to a paper by Behr, Necas and Wu, ESAIM: M2AN 35 (2001) 229–238; here, the authors chose a very simple Fourier polynomial as an initial datum for the Euler equation and analyzed the power series in time for the solution, determining the first 35 terms by computer algebra. Their calculations suggested for the series a finite Convergence Radius τ 3 in the H 3 Sobolev space, with 0.32 3 35 (2001) 229–238, using again computer algebra; the order has been increased from 35 to 52, using the symmetries of the initial datum to speed up computations. As for τ 3 , our results agree with the original computations of E. Behr, J. Necas and H. Wu, ESAIM: M2AN 35 (2001) 229–238 (yielding in fact to conjecture that 0.32 3 3 is not at all an indication of a possible blow-up. (b) There is a strong indication that the solution of the Euler equation does not blow up at a time close to τ 3 . In fact, the solution is likely to exist, at least, up to a time θ 3 > 0.47. (c) There is a weak indication, based on Pade analysis, that the solution might blow up at a later time.
-
on power series solutions for the euler equation and the behr necas wu initial datum
arXiv: Analysis of PDEs, 2012Co-Authors: Carlo Morosi, Mario Pernici, Livio PizzoccheroAbstract:We consider the Euler equation for an incompressible fluid on a three dimensional torus, and the construction of its solution as a power series in time. We point out some general facts on this subject, from Convergence issues for the power series to the role of symmetries of the initial datum. We then turn the attention to a paper by Behr, Necas and Wu in ESAIM: M2AN 35 (2001) 229-238; here, the authors chose a very simple Fourier polynomial as an initial datum for the Euler equation and analyzed the power series in time for the solution, determining the first 35 terms by computer algebra. Their calculations suggested for the series a finite Convergence Radius \tau_3 in the H^3 Sobolev space, with 0.32 0.47. (c) Pade' analysis gives a rather weak indication that the solution might blow up at a later time.