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Ethan T Vishniac - One of the best experts on this subject based on the ideXlab platform.
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magnetic Stochasticity and diffusion
Physical Review E, 2019Co-Authors: Amir Jafari, Ethan T Vishniac, Vignesh VaikundaramanAbstract:We develop a quantitative relationship between magnetic diffusion and the level of randomness, or Stochasticity, of the diffusing magnetic field in a magnetized medium. A general mathematical formulation of magnetic Stochasticity in turbulence has been developed in previous work in terms of the L_{p} norm S_{p}(t)=1/2∥1-B[over ]_{l}·B[over ]_{L}∥_{p}, pth-order magnetic Stochasticity of the stochastic field B(x,t), based on the coarse-grained fields B_{l} and B_{L} at different scales l≠L. For laminar flows, the Stochasticity level becomes the level of field self-entanglement or spatial complexity. In this paper, we establish a connection between magnetic Stochasticity S_{p}(t) and magnetic diffusion in magnetohydrodynamic (MHD) turbulence and use a homogeneous, incompressible MHD simulation to test this prediction. Our results agree with the well-known fact that magnetic diffusion in turbulent media follows the superlinear Richardson dispersion scheme. This is intimately related to stochastic magnetic reconnection in which superlinear Richardson diffusion broadens the matter outflow width and accelerates the reconnection process.
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magnetic Stochasticity and diffusion
arXiv: High Energy Astrophysical Phenomena, 2019Co-Authors: Amir Jafari, Ethan T Vishniac, Vignesh VaikundaramanAbstract:We develop a quantitative relationship between magnetic diffusion and the level of randomness, or Stochasticity, of the diffusing magnetic field in a magnetized medium. A general mathematical formulation of magnetic Stochasticity in turbulence has been developed in previous work in terms of the ${\cal L}_p$-norm $S_p(t)={1\over 2}|| 1-\hat{\bf B}_l.\hat{\bf B}_L||_p$, $p$th order magnetic Stochasticity of the stochastic field ${\bf B}({\bf x}, t)$, based on the coarse-grained fields, ${\bf B}_l$ and ${\bf B}_L$, at different scales, $l\neq L$. For laminar flows, Stochasticity level becomes the level of field self-entanglement or spatial complexity. In this paper, we establish a connection between magnetic Stochasticity $S_p(t)$ and magnetic diffusion in magnetohydrodynamic (MHD) turbulence and use a homogeneous, incompressible MHD simulation to test this prediction. Our results agree with the well-known fact that magnetic diffusion in turbulent media follows the super-linear Richardson dispersion scheme. This is intimately related to stochastic magnetic reconnection in which super-linear Richardson diffusion broadens the matter outflow width and accelerates the reconnection process.
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topology and Stochasticity of turbulent magnetic fields
Physical Review E, 2019Co-Authors: Amir Jafari, Ethan T VishniacAbstract:We present a mathematical formalism for the topology and Stochasticity of vector fields based on renormalization group methodology. The concept of a scale-split energy density, ψ_{l,L}=B_{l}·B_{L}/2 for vector field B(x,t) renormalized at scales l and L, is introduced in order to quantify the notion of the field topological deformation, topology change, and Stochasticity level. In particular, for magnetic fields, it is shown that the evolution of the field topology is directly related to the field-fluid slippage, which has already been linked to magnetic reconnection in previous work. The magnitude and direction of stochastic magnetic fields, shown to be governed, respectively, by the parallel and vertical components of the renormalized induction equation with respect to the magnetic field, can be studied separately by dividing ψ_{l,L} into two (3+1)-dimensional scalar fields. The velocity field can be approached in a similar way. Magnetic reconnection can then be defined in terms of the extrema of the L_{p} norms of these scalar fields. This formulation in fact clarifies different definitions of magnetic reconnection, which vaguely rely on the magnetic field topology, Stochasticity, and energy conversion. Our results support the well-founded yet partly overlooked picture in which magnetic reconnection in turbulent fluids occurs on a wide range of scales as a result of nonlinearities at large scales (turbulence inertial range) and nonidealities at small scales (dissipative range). Lagrangian particle trajectories, as well as magnetic field lines, are stochastic in turbulent magnetized media in the limit of small resistivity and viscosity. The magnetic field tends to reduce its Stochasticity induced by the turbulent flow by slipping through the fluid, which may accelerate fluid particles. This suggests that reconnection is a relaxation process by which the magnetic field lowers both its topological entanglements induced by turbulence and its energy level.
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fast magnetic reconnection and spontaneous Stochasticity
The Astrophysical Journal, 2011Co-Authors: Gregory L Eyink, Alex Lazarian, Ethan T VishniacAbstract:Magnetic field lines in astrophysical plasmas are expected to be frozen-in at scales larger than the ion gyroradius. The rapid reconnection of magnetic-flux structures with dimensions vastly larger than the gyroradius requires a breakdown in the standard Alfven flux-freezing law. We attribute this breakdown to ubiquitous MHD plasma turbulence with power-law scaling ranges of velocity and magnetic energy spectra. Lagrangian particle trajectories in such environments become 'spontaneously stochastic', so that infinitely many magnetic field lines are advected to each point and must be averaged to obtain the resultant magnetic field. The relative distance between initial magnetic field lines which arrive at the same final point depends upon the properties of two-particle turbulent dispersion. We develop predictions based on the phenomenological Goldreich and Sridhar theory of strong MHD turbulence and on weak MHD turbulence theory. We recover the predictions of the Lazarian and Vishniac theory for the reconnection rate of large-scale magnetic structures. Lazarian and Vishniac also invoked 'spontaneous Stochasticity', but of the field lines rather than of the Lagrangian trajectories. More recent theories of fast magnetic reconnection appeal to microscopic plasma processes that lead to additional terms in the generalized Ohm's law, such as the collisionless Hall term. We estimatemore » quantitatively the effect of such processes on the inertial-range turbulence dynamics and find them to be negligible in most astrophysical environments. For example, the predictions of the Lazarian and Vishniac theory are unchanged in Hall MHD turbulence with an extended inertial range, whenever the ion skin depth {delta}{sub i} is much smaller than the turbulent integral length or injection-scale L{sub i} .« less
Marie-christine Firpo - One of the best experts on this subject based on the ideXlab platform.
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Impact of the Eulerian chaos of magnetic field lines in magnetic reconnection
Physics of Plasmas, 2016Co-Authors: Marie-christine Firpo, Wahb Ettoumi, A. F. Lifschitz, Alessandro Retinò, R Farengo, H Ferrari, P García-martínezAbstract:Stochasticity is an ingredient that may allow the breaking of the frozen-in law in the reconnec-tion process. It will first be argued that non-ideal effects may be considered as an implicit way to introduce Stochasticity. Yet there also exists an explicit Stochasticity that does not require the invocation of non-ideal effects. This comes from the spatial (or Eulerian) chaos of magnetic field lines that can show up only in a truly three-dimensional description of magnetic reconnection since two-dimensional models impose the integrability of the magnetic field lines. Some implications of this magnetic braiding, such as the increased particle finite-time Lyapunov exponents and increased acceleration of charged particles, are discussed in the frame of tokamak sawteeth that form a laboratory prototype of spontaneous magnetic reconnection. A justification for an increased reconnection rate with chaotic vs integrable magnetic field lines is proposed. Moreover, in 3D, the Eulerian chaos of magnetic field lines may coexist with the Eulerian chaos of velocity field lines, that is more commonly named turbulence.
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Microtearing turbulence: magnetic braiding and disruption limit
Physics of Plasmas, 2015Co-Authors: Marie-christine FirpoAbstract:A realistic reduced model involving a large poloidal spectrum of microtearing modes is used to probe the existence of some Stochasticity of magnetic field lines. Stochasticity is shown to occur even for the low values of the magnetic perturbation δB/B devoted to magnetic turbulence that have been experimentally measured. Because the diffusion coefficient may strongly depend on the radial (or magnetic-flux) coordinate, being very low near some resonant surfaces, and because its evaluation implicitly makes a normal diffusion hypothesis, one turns to another indicator appropriate to diagnose the confinement: the mean residence time of magnetic field lines. Their computation in the microturbulence frame points to the existence of a disruption limit, namely of a critical order of magnitude of δB/B above which Stochasticity is no longer benign yet leads to a macroscopic loss of confinement in some tens to hundred of electron toroidal excursions. Since the level of magnetic turbulence δB/B has been measured to grow with the plasma electron density this would also be a density limit.
Frédéric Thomas - One of the best experts on this subject based on the ideXlab platform.
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Tissue‐disruption‐induced cellular Stochasticity and epigenetic drift: Common origins of aging and cancer?
BioEssays, 2020Co-Authors: Jean‐pascal Capp, Frédéric ThomasAbstract:Age-related and cancer-related epigenomic modifications have been associated with enhanced cell-to-cell gene expression variability that characterizes increased cellular Stochasticity. Since gene expression variability appears to be highly reduced by-and epigenetic and phenotypic stability acquired through-direct or long-range cellular interactions during cell differentiation, we propose a common origin for aging and cancer in the failure to control cellular Stochasticity by cell-cell interactions. Tissue-disruption-induced cellular Stochasticity associated with epigenetic drift would be at the origin of organ dysfunction because of an increase in phenotypic variation among cells, ultimately leading to cell death and organ failure through a loss of coordination in cellular functions, and eventually to cancerization. We propose mechanistic research perspectives to corroborate this hypothesis and explore its evolutionary consequences, highlighting a positive correlation between the median age of mass loss onset (a proxy for the onset of organ aging) and the median age at cancer diagnosis.
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A Similar Speciation Process Relying on Cellular Stochasticity in Microbial and Cancer Cell Populations
iScience, 2020Co-Authors: Jean-pascal Capp, Frédéric ThomasAbstract:Similarities between microbial and cancer cells were noticed in recent years and serve as a basis for an atavism theory of cancer. Cancer cells would rely on the reactivation of an ancestral "genetic program" that would have been repressed in metazoan cells. Here we argue that cancer cells resemble unicellular organisms mainly in their similar way to exploit cellular stochastiity to produce cell specialization and maximize proliferation. Indeed, the relationship between low Stochasticity, specialization, and quiescence found in normal differentiated metazoan cells is lost in cancer. On the contrary, low Stochasticity and specialization are associated with high proliferation among cancer cells, as it is observed for the "specialist" cells in microbial populations that fully exploit nutritional resources to maximize proliferation. Thus, we propose a model where the appearance of cancer phenotypes can be solely due to an adaptation and a speciation process based on initial increase in cellular Stochasticity.
Régis Bataille - One of the best experts on this subject based on the ideXlab platform.
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Multiple Myeloma as a Bone Disease? The Tissue Disruption-Induced Cell Stochasticity (TiDiS) Theory
Cancers, 2020Co-Authors: Jean-pascal Capp, Régis BatailleAbstract:The standard model of multiple myeloma (MM) relies on genetic instability in the normal counterparts of MM cells. MM-induced lytic bone lesions are considered as end organ damages. However, bone is a tissue of significance in MM and bone changes could be at the origin/facilitate the emergence of MM. We propose the tissue disruption-induced cell Stochasticity (TiDiS) theory for MM oncogenesis that integrates disruption of the microenvironment, differentiation, and genetic alterations. It starts with the observation that the bone marrow endosteal niche controls differentiation. As decrease in cellular Stochasticity occurs thanks to cellular interactions in differentiating cells, the initiating role of bone disruption would be in the increase of cellular Stochasticity. Thus, in the context of polyclonal activation of B cells, memory B cells and plasmablasts would compete for localizing in endosteal niches with the risk that some cells cannot fully differentiate if they cannot reside in the niche because of a disrupted microenvironment. Therefore, they would remain in an unstable state with residual proliferation, with the risk that subclones may transform into malignant cells. Finally, diagnostic and therapeutic perspectives are provided.
Amir Jafari - One of the best experts on this subject based on the ideXlab platform.
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magnetic Stochasticity and diffusion
Physical Review E, 2019Co-Authors: Amir Jafari, Ethan T Vishniac, Vignesh VaikundaramanAbstract:We develop a quantitative relationship between magnetic diffusion and the level of randomness, or Stochasticity, of the diffusing magnetic field in a magnetized medium. A general mathematical formulation of magnetic Stochasticity in turbulence has been developed in previous work in terms of the L_{p} norm S_{p}(t)=1/2∥1-B[over ]_{l}·B[over ]_{L}∥_{p}, pth-order magnetic Stochasticity of the stochastic field B(x,t), based on the coarse-grained fields B_{l} and B_{L} at different scales l≠L. For laminar flows, the Stochasticity level becomes the level of field self-entanglement or spatial complexity. In this paper, we establish a connection between magnetic Stochasticity S_{p}(t) and magnetic diffusion in magnetohydrodynamic (MHD) turbulence and use a homogeneous, incompressible MHD simulation to test this prediction. Our results agree with the well-known fact that magnetic diffusion in turbulent media follows the superlinear Richardson dispersion scheme. This is intimately related to stochastic magnetic reconnection in which superlinear Richardson diffusion broadens the matter outflow width and accelerates the reconnection process.
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magnetic Stochasticity and diffusion
arXiv: High Energy Astrophysical Phenomena, 2019Co-Authors: Amir Jafari, Ethan T Vishniac, Vignesh VaikundaramanAbstract:We develop a quantitative relationship between magnetic diffusion and the level of randomness, or Stochasticity, of the diffusing magnetic field in a magnetized medium. A general mathematical formulation of magnetic Stochasticity in turbulence has been developed in previous work in terms of the ${\cal L}_p$-norm $S_p(t)={1\over 2}|| 1-\hat{\bf B}_l.\hat{\bf B}_L||_p$, $p$th order magnetic Stochasticity of the stochastic field ${\bf B}({\bf x}, t)$, based on the coarse-grained fields, ${\bf B}_l$ and ${\bf B}_L$, at different scales, $l\neq L$. For laminar flows, Stochasticity level becomes the level of field self-entanglement or spatial complexity. In this paper, we establish a connection between magnetic Stochasticity $S_p(t)$ and magnetic diffusion in magnetohydrodynamic (MHD) turbulence and use a homogeneous, incompressible MHD simulation to test this prediction. Our results agree with the well-known fact that magnetic diffusion in turbulent media follows the super-linear Richardson dispersion scheme. This is intimately related to stochastic magnetic reconnection in which super-linear Richardson diffusion broadens the matter outflow width and accelerates the reconnection process.
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topology and Stochasticity of turbulent magnetic fields
Physical Review E, 2019Co-Authors: Amir Jafari, Ethan T VishniacAbstract:We present a mathematical formalism for the topology and Stochasticity of vector fields based on renormalization group methodology. The concept of a scale-split energy density, ψ_{l,L}=B_{l}·B_{L}/2 for vector field B(x,t) renormalized at scales l and L, is introduced in order to quantify the notion of the field topological deformation, topology change, and Stochasticity level. In particular, for magnetic fields, it is shown that the evolution of the field topology is directly related to the field-fluid slippage, which has already been linked to magnetic reconnection in previous work. The magnitude and direction of stochastic magnetic fields, shown to be governed, respectively, by the parallel and vertical components of the renormalized induction equation with respect to the magnetic field, can be studied separately by dividing ψ_{l,L} into two (3+1)-dimensional scalar fields. The velocity field can be approached in a similar way. Magnetic reconnection can then be defined in terms of the extrema of the L_{p} norms of these scalar fields. This formulation in fact clarifies different definitions of magnetic reconnection, which vaguely rely on the magnetic field topology, Stochasticity, and energy conversion. Our results support the well-founded yet partly overlooked picture in which magnetic reconnection in turbulent fluids occurs on a wide range of scales as a result of nonlinearities at large scales (turbulence inertial range) and nonidealities at small scales (dissipative range). Lagrangian particle trajectories, as well as magnetic field lines, are stochastic in turbulent magnetized media in the limit of small resistivity and viscosity. The magnetic field tends to reduce its Stochasticity induced by the turbulent flow by slipping through the fluid, which may accelerate fluid particles. This suggests that reconnection is a relaxation process by which the magnetic field lowers both its topological entanglements induced by turbulence and its energy level.
