Jean Loi Joseph Perez - Academia.edu (original) (raw)

Papers by Jean Loi Joseph Perez


1990 IJCNN International Joint Conference on Neural Networks, 1990

Original neural network research which results from the intersection of chaos theory and number t... more Original neural network research which results from the intersection of chaos theory and number theory is presented. The chaos theory background stems from the fractal chaos neural network model, and the number theory background stems from particular selective sensitivity emerging from neurons based on Fibonacci's integer number settings. In fact, there is a mutual reinforcement between numerical holographic-like properties related

Geophysical & Astrophysical Fluid Dynamics, 2014

A variety of studies of magnetised plasma turbulence invoke theories for the advection of a passi... more A variety of studies of magnetised plasma turbulence invoke theories for the advection of a passive scalar by turbulent fluctuations. Examples include modelling the electron density fluctuations in the interstellar medium, understanding the chemical composition of galaxy clusters and the intergalactic medium, and testing the prevailing phenomenological theories of magnetohydrodynamic turbulence. While passive scalar turbulence has been extensively studied in the hydrodynamic case, its counterpart in MHD turbulence is significantly less well understood. Herein we conduct a series of high-resolution direct numerical simulations of incompressible, field-guided, MHD turbulence in order to establish the fundamental properties of passive scalar evolution. We study the scalar anisotropy, establish the scaling relation analogous to Yaglom's law, and measure the intermittency of the passive scalar statistics. We also assess to what extent the pseudo Alfvén fluctuations in strong MHD turbulence can be modelled as a passive scalar. The results suggest that the dynamics of a passive scalar in MHD turbulence is considerably more complicated than in the hydrodynamic case.

Physical Review Letters, 2013

The nature of subproton scale fluctuations in the solar wind is an open question, partly because ... more The nature of subproton scale fluctuations in the solar wind is an open question, partly because two similar types of electromagnetic turbulence can occur: kinetic Alfvén turbulence and whistler turbulence. These two possibilities, however, have one key qualitative difference: whistler turbulence, unlike kinetic Alfvén turbulence, has negligible power in density fluctuations. In this Letter, we present new observational data, as well as analytical and numerical results, to investigate this difference. Our results show, for the first time, that the fluctuations well below the proton scale are predominantly kinetic Alfvén turbulence, and, if present at all, the whistler fluctuations make up only a small fraction of the total energy.

Revista Fitotecnia Mexicana, Mar 1, 2010

The inertial-interval energy spectrum of strong magnetohydrodynamic (MHD) turbulence with a unifo... more The inertial-interval energy spectrum of strong magnetohydrodynamic (MHD) turbulence with a uniform background magnetic field was observed numerically to be close to k−3/2k^{-3/2}k−3/2 by a number of independent groups. A dissenting opinion has been voiced by Beresnyak, A. 2011, PRL, 106, 075001-. 2012, MNRAS, 422, 3495-. 2014, ApJ, 784, L20 that the spectral scaling is close to k−5/3k^{-5/3}k−5/3. The conclusions of these papers are however incorrect as they are based on numerical simulations that are drastically unresolved, so that the discrete numerical scheme does not approximate the physical solution at the scales where the measurements are performed. These results have been rebutted in our more detailed papers Perez, J. C., Mason, J., Boldyrev, S., & Cattaneo, F. 2012, PRX, 2, 041005-. 2014, ApJL, 793, L13; here, by popular demand, we present a brief and simple explanation of our major criticism of Beresnyak's work.

The Astrophysical Journal, 2015

The Solar Probe Plus (SPP) spacecraft will explore the near-Sun environment, reaching heliocentri... more The Solar Probe Plus (SPP) spacecraft will explore the near-Sun environment, reaching heliocentric distances less than 10R ⊙. Near Earth, spacecraft measurements of fluctuating velocities and magnetic fields taken in the time domain are translated into information about the spatial structure of the solar wind via Taylor's "frozen turbulence" hypothesis. Near the perihelion of SPP, however, the solar-wind speed is comparable to the Alfvén speed, and Taylor's hypothesis in its usual form does not apply. In this paper, we show that, under certain assumptions, a modified version of Taylor's hypothesis can be recovered in the near-Sun region. We consider only the transverse, non-compressive component of the fluctuations at length scales exceeding the proton gyroradius, and we describe these fluctuations using an approximate theoretical framework developed by Heinemann and Olbert. We show that fluctuations propagating away from the Sun in the plasma frame obey a relation analogous to Taylor's hypothesis when V sc,⊥ ≫ z − and z + ≫ z − , where V sc,⊥ is the component of the spacecraft velocity perpendicular to the mean magnetic field and z + (z −) is the Elsasser variable corresponding to transverse, non-compressive fluctuations propagating away from (towards) the Sun in the plasma frame. Observations and simulations suggest that, in the near-Sun solar wind, the above inequalities are satisfied and z + fluctuations account for most of the fluctuation energy. The modified form of Taylor's hypothesis that we derive may thus make it possible to characterize the spatial structure of the energetically dominant component of the turbulence encountered by SPP.

Interdisciplinary sciences, computational life sciences, 2010

This new bioinformatics research bridges Genomics and Mathematics. We propose a universal "F... more This new bioinformatics research bridges Genomics and Mathematics. We propose a universal "Fractal Genome Code Law": The frequency of each of the 64 codons across the entire human genome is controlled by the codon's position in the Universal Genetic Code table. We analyze the frequency of distribution of the 64 codons (codon usage) within single-stranded DNA sequences. Concatenating 24 Human chromosomes, we show that the entire human genome employs the well known universal genetic code table as a macro structural model. The position of each codon within this table precisely dictates its population. So the Universal Genetic Code Table not only maps codons to amino acids, but serves as a global checksum matrix. Frequencies of the 64 codons in the whole human genome scale are a self-similar fractal expansion of the universal genetic code. The original genetic code kernel governs not only the micro scale but the macro scale as well. Particularly, the 6 folding steps of cod...

Physical Review X, 2012

The energy spectrum of magnetohydrodynamic turbulence attracts interest due to its fundamental im... more The energy spectrum of magnetohydrodynamic turbulence attracts interest due to its fundamental importance and its relevance for interpreting astrophysical data. Here we present measurements of the energy spectra from a series of high-resolution direct numerical simulations of magnetohydrodynamics turbulence with a strong guide field and for increasing Reynolds number. The presented simulations, with numerical resolutions up to 2048 3 mesh points and statistics accumulated over 30 to 150 eddy turnover times, constitute, to the best of our knowledge, the largest statistical sample of steady state magnetohydrodynamics turbulence to date. We study both the balanced case, where the energies associated with Alfvén modes propagating in opposite directions along the guide field, E þ ðk ? Þ and E À ðk ? Þ, are equal, and the imbalanced case where the energies are different. In the balanced case, we find that the energy spectrum converges to a power law with exponent À3=2 as the Reynolds number is increased, which is consistent with phenomenological models that include scale-dependent dynamic alignment. For the imbalanced case, with E þ > E À , the simulations show that E À / k À3=2 ? for all Reynolds numbers considered, while E þ has a slightly steeper spectrum at small Re. As the Reynolds number increases, E þ flattens. Since E AE are pinned at the dissipation scale and anchored at the driving scales, we postulate that at sufficiently high Re the spectra will become parallel in the inertial range and scale as E þ / E À / k À3=2 ?. Questions regarding the universality of the spectrum and the value of the ''Kolmogorov constant'' are discussed.

Submitted for the DPP07 Meeting of The American Physical Society Numerical modeling of anisotropi... more Submitted for the DPP07 Meeting of The American Physical Society Numerical modeling of anisotropic 3D Drift-Alfven turbulence J.C. PEREZ, STANISLAV BOLDYREV, University of Wisconsin-Madison-We present results from extensive numerical simulations of steady state Drift-Alfven turbulence in the presence of a strong guide field. We use a turbulence model based on equations originally derived by Hazeltine as an extension of the Reduced MHD model (RMHD). The model includes three dynamical fields, potential, magnetic flux, density and allows for the existence of a background density gradient that drives large scale electromagnetic drift-wave instabilities. Previous numerical simulations of this type of models have been mostly restricted to 2D or pseudo 2D simulations in the limit of vanishing k , which restrict the turbulence cascade to the field-perpendicular plane. However, recent work in MHD turbulence have shown that the parallel dynamics can play a key role in anisotropic turbulent cascades. In this work we present fully 3D simulations of strong Drift-Alfven turbulence in a rectangular box that reflects the anisotropy of the turbulence imposed by the guide field. Simulations are benchmarked against state-of-the-art simulations of MHD turbulence at large scales and are used to investigate the energy spectrum as the turbulence reaches the ion sound radius, where the Shear Alfven makes the transition to a Kinetic Alfven wave.


1990 IJCNN International Joint Conference on Neural Networks, 1990

Original neural network research which results from the intersection of chaos theory and number t... more Original neural network research which results from the intersection of chaos theory and number theory is presented. The chaos theory background stems from the fractal chaos neural network model, and the number theory background stems from particular selective sensitivity emerging from neurons based on Fibonacci's integer number settings. In fact, there is a mutual reinforcement between numerical holographic-like properties related

Geophysical & Astrophysical Fluid Dynamics, 2014

A variety of studies of magnetised plasma turbulence invoke theories for the advection of a passi... more A variety of studies of magnetised plasma turbulence invoke theories for the advection of a passive scalar by turbulent fluctuations. Examples include modelling the electron density fluctuations in the interstellar medium, understanding the chemical composition of galaxy clusters and the intergalactic medium, and testing the prevailing phenomenological theories of magnetohydrodynamic turbulence. While passive scalar turbulence has been extensively studied in the hydrodynamic case, its counterpart in MHD turbulence is significantly less well understood. Herein we conduct a series of high-resolution direct numerical simulations of incompressible, field-guided, MHD turbulence in order to establish the fundamental properties of passive scalar evolution. We study the scalar anisotropy, establish the scaling relation analogous to Yaglom's law, and measure the intermittency of the passive scalar statistics. We also assess to what extent the pseudo Alfvén fluctuations in strong MHD turbulence can be modelled as a passive scalar. The results suggest that the dynamics of a passive scalar in MHD turbulence is considerably more complicated than in the hydrodynamic case.

Physical Review Letters, 2013

The nature of subproton scale fluctuations in the solar wind is an open question, partly because ... more The nature of subproton scale fluctuations in the solar wind is an open question, partly because two similar types of electromagnetic turbulence can occur: kinetic Alfvén turbulence and whistler turbulence. These two possibilities, however, have one key qualitative difference: whistler turbulence, unlike kinetic Alfvén turbulence, has negligible power in density fluctuations. In this Letter, we present new observational data, as well as analytical and numerical results, to investigate this difference. Our results show, for the first time, that the fluctuations well below the proton scale are predominantly kinetic Alfvén turbulence, and, if present at all, the whistler fluctuations make up only a small fraction of the total energy.

Revista Fitotecnia Mexicana, Mar 1, 2010

The inertial-interval energy spectrum of strong magnetohydrodynamic (MHD) turbulence with a unifo... more The inertial-interval energy spectrum of strong magnetohydrodynamic (MHD) turbulence with a uniform background magnetic field was observed numerically to be close to k−3/2k^{-3/2}k−3/2 by a number of independent groups. A dissenting opinion has been voiced by Beresnyak, A. 2011, PRL, 106, 075001-. 2012, MNRAS, 422, 3495-. 2014, ApJ, 784, L20 that the spectral scaling is close to k−5/3k^{-5/3}k−5/3. The conclusions of these papers are however incorrect as they are based on numerical simulations that are drastically unresolved, so that the discrete numerical scheme does not approximate the physical solution at the scales where the measurements are performed. These results have been rebutted in our more detailed papers Perez, J. C., Mason, J., Boldyrev, S., & Cattaneo, F. 2012, PRX, 2, 041005-. 2014, ApJL, 793, L13; here, by popular demand, we present a brief and simple explanation of our major criticism of Beresnyak's work.

The Astrophysical Journal, 2015

The Solar Probe Plus (SPP) spacecraft will explore the near-Sun environment, reaching heliocentri... more The Solar Probe Plus (SPP) spacecraft will explore the near-Sun environment, reaching heliocentric distances less than 10R ⊙. Near Earth, spacecraft measurements of fluctuating velocities and magnetic fields taken in the time domain are translated into information about the spatial structure of the solar wind via Taylor's "frozen turbulence" hypothesis. Near the perihelion of SPP, however, the solar-wind speed is comparable to the Alfvén speed, and Taylor's hypothesis in its usual form does not apply. In this paper, we show that, under certain assumptions, a modified version of Taylor's hypothesis can be recovered in the near-Sun region. We consider only the transverse, non-compressive component of the fluctuations at length scales exceeding the proton gyroradius, and we describe these fluctuations using an approximate theoretical framework developed by Heinemann and Olbert. We show that fluctuations propagating away from the Sun in the plasma frame obey a relation analogous to Taylor's hypothesis when V sc,⊥ ≫ z − and z + ≫ z − , where V sc,⊥ is the component of the spacecraft velocity perpendicular to the mean magnetic field and z + (z −) is the Elsasser variable corresponding to transverse, non-compressive fluctuations propagating away from (towards) the Sun in the plasma frame. Observations and simulations suggest that, in the near-Sun solar wind, the above inequalities are satisfied and z + fluctuations account for most of the fluctuation energy. The modified form of Taylor's hypothesis that we derive may thus make it possible to characterize the spatial structure of the energetically dominant component of the turbulence encountered by SPP.

Interdisciplinary sciences, computational life sciences, 2010

This new bioinformatics research bridges Genomics and Mathematics. We propose a universal "F... more This new bioinformatics research bridges Genomics and Mathematics. We propose a universal "Fractal Genome Code Law": The frequency of each of the 64 codons across the entire human genome is controlled by the codon's position in the Universal Genetic Code table. We analyze the frequency of distribution of the 64 codons (codon usage) within single-stranded DNA sequences. Concatenating 24 Human chromosomes, we show that the entire human genome employs the well known universal genetic code table as a macro structural model. The position of each codon within this table precisely dictates its population. So the Universal Genetic Code Table not only maps codons to amino acids, but serves as a global checksum matrix. Frequencies of the 64 codons in the whole human genome scale are a self-similar fractal expansion of the universal genetic code. The original genetic code kernel governs not only the micro scale but the macro scale as well. Particularly, the 6 folding steps of cod...

Physical Review X, 2012

The energy spectrum of magnetohydrodynamic turbulence attracts interest due to its fundamental im... more The energy spectrum of magnetohydrodynamic turbulence attracts interest due to its fundamental importance and its relevance for interpreting astrophysical data. Here we present measurements of the energy spectra from a series of high-resolution direct numerical simulations of magnetohydrodynamics turbulence with a strong guide field and for increasing Reynolds number. The presented simulations, with numerical resolutions up to 2048 3 mesh points and statistics accumulated over 30 to 150 eddy turnover times, constitute, to the best of our knowledge, the largest statistical sample of steady state magnetohydrodynamics turbulence to date. We study both the balanced case, where the energies associated with Alfvén modes propagating in opposite directions along the guide field, E þ ðk ? Þ and E À ðk ? Þ, are equal, and the imbalanced case where the energies are different. In the balanced case, we find that the energy spectrum converges to a power law with exponent À3=2 as the Reynolds number is increased, which is consistent with phenomenological models that include scale-dependent dynamic alignment. For the imbalanced case, with E þ > E À , the simulations show that E À / k À3=2 ? for all Reynolds numbers considered, while E þ has a slightly steeper spectrum at small Re. As the Reynolds number increases, E þ flattens. Since E AE are pinned at the dissipation scale and anchored at the driving scales, we postulate that at sufficiently high Re the spectra will become parallel in the inertial range and scale as E þ / E À / k À3=2 ?. Questions regarding the universality of the spectrum and the value of the ''Kolmogorov constant'' are discussed.

Submitted for the DPP07 Meeting of The American Physical Society Numerical modeling of anisotropi... more Submitted for the DPP07 Meeting of The American Physical Society Numerical modeling of anisotropic 3D Drift-Alfven turbulence J.C. PEREZ, STANISLAV BOLDYREV, University of Wisconsin-Madison-We present results from extensive numerical simulations of steady state Drift-Alfven turbulence in the presence of a strong guide field. We use a turbulence model based on equations originally derived by Hazeltine as an extension of the Reduced MHD model (RMHD). The model includes three dynamical fields, potential, magnetic flux, density and allows for the existence of a background density gradient that drives large scale electromagnetic drift-wave instabilities. Previous numerical simulations of this type of models have been mostly restricted to 2D or pseudo 2D simulations in the limit of vanishing k , which restrict the turbulence cascade to the field-perpendicular plane. However, recent work in MHD turbulence have shown that the parallel dynamics can play a key role in anisotropic turbulent cascades. In this work we present fully 3D simulations of strong Drift-Alfven turbulence in a rectangular box that reflects the anisotropy of the turbulence imposed by the guide field. Simulations are benchmarked against state-of-the-art simulations of MHD turbulence at large scales and are used to investigate the energy spectrum as the turbulence reaches the ion sound radius, where the Shear Alfven makes the transition to a Kinetic Alfven wave.