The Experts below are selected from a list of 99 Experts worldwide ranked by ideXlab platform
Xavier Lamy - One of the best experts on this subject based on the ideXlab platform.
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Spherical Particle in Nematic Liquid Crystal Under an External Field: The Saturn Ring Regime
Journal of Nonlinear Science, 2018Co-Authors: Stan Alama, Lia Bronsard, Xavier LamyAbstract:We consider a nematic liquid crystal occupying the exterior region in $${\mathbb {R}}^3$$ R 3 outside of a spherical particle, with radial strong anchoRing. Within the context of the Landau-de Gennes theory, we study minimizers subject to an external field, modeled by an additional term which favors nematic alignment parallel to the field. When the external field is high enough, we obtain a scaling law for the energy. The energy scale corresponds to minimizers concentrating their energy in a boundary layer around the particle, with quadrupolar symmetry. This suggests the presence of a Saturn Ring defect around the particle, rather than a dipolar director field typical of a point defect.
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Minimizers of the Landau–de Gennes Energy Around a Spherical Colloid Particle
Archive for Rational Mechanics and Analysis, 2016Co-Authors: Stan Alama, Lia Bronsard, Xavier LamyAbstract:We consider energy minimizing configurations of a nematic liquid crystal around a spherical colloid particle, in the context of the Landau–de Gennes model. The nematic is assumed to occupy the exterior of a ball B _ r 0, and satisfy homeotropic weak anchoRing at the surface of the colloid and approach a uniform uniaxial state as $${|x|\to\infty}$$ | x | → ∞ . We study the minimizers in two different limiting regimes: for balls which are small $${r_0\ll L^{\frac12}}$$ r 0 ≪ L 1 2 compared to the characteristic length scale $${L^{\frac 12}}$$ L 1 2 , and for large balls, $${r_0\gg L^{\frac12}}$$ r 0 ≫ L 1 2 . The relationship between the radius and the anchoRing strength W is also relevant. For small balls we obtain a limiting quadrupolar configuration, with a “Saturn Ring” defect for relatively strong anchoRing, corresponding to an exchange of eigenvalues of the Q -tensor. In the limit of very large balls we obtain an axisymmetric minimizer of the Oseen–Frank energy, and a dipole configuration with exactly one point defect is obtained.
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Analytical description of the Saturn-Ring defect in nematic colloids.
Physical review. E, 2016Co-Authors: Stan Alama, Lia Bronsard, Xavier LamyAbstract:We derive an analytical formula for the Saturn-Ring configuration around a small colloidal particle suspended in nematic liquid crystal. In particular we obtain an explicit expression for the Ring radius and its dependence on the anchoRing energy. We work within Landau-de Gennes theory: Nematic alignment is described by a tensorial order parameter. For nematic colloids this model had previously been used exclusively to perform numerical computations. Our method demonstrates that the tensorial theory can also be used to obtain analytical results, suggesting a different approach to the understanding of nematic colloidal interactions.
Michael Mendillo - One of the best experts on this subject based on the ideXlab platform.
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Saturn Ring rain: Model estimates of water influx into Saturn’s atmosphere
Icarus, 2015Co-Authors: Luke Moore, James O'donoghue, Ingo Müller-wodarg, Marina Galand, Michael MendilloAbstract:Abstract Recently H3+ was detected at Saturn’s low- and mid-latitudes for the first time (O’Donoghue et al. [2013]. Nature 496(7444), 193–195), revealing significant latitudinal structure in H3+ emissions, with local extrema in one hemisphere mirrored at magnetically conjugate latitudes in the opposite hemisphere. The observed minima and maxima were shown to map to regions of increased or decreased density in Saturn’s Rings, implying a direct Ring–atmosphere connection. Here, using the Saturn Thermosphere Ionosphere Model (STIM), we investigate the “Ring rain” explanation of the O’Donoghue et al. (O’Donoghue et al. [2013]. Nature 496(7444), 193–195) observations, wherein charged water group particles from the Rings are guided by magnetic field lines as they “rain” down upon the atmosphere, alteRing local ionospheric chemistry. Based on model reproductions of observed H3+ variations, we derive maximum water influxes of (1.6–16) × 105 H2O molecules cm−2 s−1 across Ring rain latitudes (∼23–49° in the south, and ∼32–54° in the north), with localized regions of enhanced influx near −48°, −38°, 42°, and 53° latitude. We estimate the globally averaged maximum Ring-derived water influx to be (1.6–12) × 105 cm−2 s−1, which represents a maximum total global influx of water from Saturn’s Rings to its atmosphere of (1.0–6.8) × 1026 s−1. The wide range of global water influx estimates stems primarily from uncertainties regarding H3+ temperatures (and consequently column densities). Future Ring rain observations may therefore be able to reduce these uncertainties by determining H3+ temperatures self consistently.
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Saturn Ring rain model estimates of water influx into Saturn s atmosphere
Icarus, 2015Co-Authors: Luke Moore, Marina Galand, James Odonoghue, I C F Mullerwodarg, Michael MendilloAbstract:Abstract Recently H3+ was detected at Saturn’s low- and mid-latitudes for the first time (O’Donoghue et al. [2013]. Nature 496(7444), 193–195), revealing significant latitudinal structure in H3+ emissions, with local extrema in one hemisphere mirrored at magnetically conjugate latitudes in the opposite hemisphere. The observed minima and maxima were shown to map to regions of increased or decreased density in Saturn’s Rings, implying a direct Ring–atmosphere connection. Here, using the Saturn Thermosphere Ionosphere Model (STIM), we investigate the “Ring rain” explanation of the O’Donoghue et al. (O’Donoghue et al. [2013]. Nature 496(7444), 193–195) observations, wherein charged water group particles from the Rings are guided by magnetic field lines as they “rain” down upon the atmosphere, alteRing local ionospheric chemistry. Based on model reproductions of observed H3+ variations, we derive maximum water influxes of (1.6–16) × 105 H2O molecules cm−2 s−1 across Ring rain latitudes (∼23–49° in the south, and ∼32–54° in the north), with localized regions of enhanced influx near −48°, −38°, 42°, and 53° latitude. We estimate the globally averaged maximum Ring-derived water influx to be (1.6–12) × 105 cm−2 s−1, which represents a maximum total global influx of water from Saturn’s Rings to its atmosphere of (1.0–6.8) × 1026 s−1. The wide range of global water influx estimates stems primarily from uncertainties regarding H3+ temperatures (and consequently column densities). Future Ring rain observations may therefore be able to reduce these uncertainties by determining H3+ temperatures self consistently.
Stan Alama - One of the best experts on this subject based on the ideXlab platform.
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Spherical Particle in Nematic Liquid Crystal Under an External Field: The Saturn Ring Regime
Journal of Nonlinear Science, 2018Co-Authors: Stan Alama, Lia Bronsard, Xavier LamyAbstract:We consider a nematic liquid crystal occupying the exterior region in $${\mathbb {R}}^3$$ R 3 outside of a spherical particle, with radial strong anchoRing. Within the context of the Landau-de Gennes theory, we study minimizers subject to an external field, modeled by an additional term which favors nematic alignment parallel to the field. When the external field is high enough, we obtain a scaling law for the energy. The energy scale corresponds to minimizers concentrating their energy in a boundary layer around the particle, with quadrupolar symmetry. This suggests the presence of a Saturn Ring defect around the particle, rather than a dipolar director field typical of a point defect.
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Minimizers of the Landau–de Gennes Energy Around a Spherical Colloid Particle
Archive for Rational Mechanics and Analysis, 2016Co-Authors: Stan Alama, Lia Bronsard, Xavier LamyAbstract:We consider energy minimizing configurations of a nematic liquid crystal around a spherical colloid particle, in the context of the Landau–de Gennes model. The nematic is assumed to occupy the exterior of a ball B _ r 0, and satisfy homeotropic weak anchoRing at the surface of the colloid and approach a uniform uniaxial state as $${|x|\to\infty}$$ | x | → ∞ . We study the minimizers in two different limiting regimes: for balls which are small $${r_0\ll L^{\frac12}}$$ r 0 ≪ L 1 2 compared to the characteristic length scale $${L^{\frac 12}}$$ L 1 2 , and for large balls, $${r_0\gg L^{\frac12}}$$ r 0 ≫ L 1 2 . The relationship between the radius and the anchoRing strength W is also relevant. For small balls we obtain a limiting quadrupolar configuration, with a “Saturn Ring” defect for relatively strong anchoRing, corresponding to an exchange of eigenvalues of the Q -tensor. In the limit of very large balls we obtain an axisymmetric minimizer of the Oseen–Frank energy, and a dipole configuration with exactly one point defect is obtained.
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Analytical description of the Saturn-Ring defect in nematic colloids.
Physical review. E, 2016Co-Authors: Stan Alama, Lia Bronsard, Xavier LamyAbstract:We derive an analytical formula for the Saturn-Ring configuration around a small colloidal particle suspended in nematic liquid crystal. In particular we obtain an explicit expression for the Ring radius and its dependence on the anchoRing energy. We work within Landau-de Gennes theory: Nematic alignment is described by a tensorial order parameter. For nematic colloids this model had previously been used exclusively to perform numerical computations. Our method demonstrates that the tensorial theory can also be used to obtain analytical results, suggesting a different approach to the understanding of nematic colloidal interactions.
Luke Moore - One of the best experts on this subject based on the ideXlab platform.
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Saturn Ring rain: Model estimates of water influx into Saturn’s atmosphere
Icarus, 2015Co-Authors: Luke Moore, James O'donoghue, Ingo Müller-wodarg, Marina Galand, Michael MendilloAbstract:Abstract Recently H3+ was detected at Saturn’s low- and mid-latitudes for the first time (O’Donoghue et al. [2013]. Nature 496(7444), 193–195), revealing significant latitudinal structure in H3+ emissions, with local extrema in one hemisphere mirrored at magnetically conjugate latitudes in the opposite hemisphere. The observed minima and maxima were shown to map to regions of increased or decreased density in Saturn’s Rings, implying a direct Ring–atmosphere connection. Here, using the Saturn Thermosphere Ionosphere Model (STIM), we investigate the “Ring rain” explanation of the O’Donoghue et al. (O’Donoghue et al. [2013]. Nature 496(7444), 193–195) observations, wherein charged water group particles from the Rings are guided by magnetic field lines as they “rain” down upon the atmosphere, alteRing local ionospheric chemistry. Based on model reproductions of observed H3+ variations, we derive maximum water influxes of (1.6–16) × 105 H2O molecules cm−2 s−1 across Ring rain latitudes (∼23–49° in the south, and ∼32–54° in the north), with localized regions of enhanced influx near −48°, −38°, 42°, and 53° latitude. We estimate the globally averaged maximum Ring-derived water influx to be (1.6–12) × 105 cm−2 s−1, which represents a maximum total global influx of water from Saturn’s Rings to its atmosphere of (1.0–6.8) × 1026 s−1. The wide range of global water influx estimates stems primarily from uncertainties regarding H3+ temperatures (and consequently column densities). Future Ring rain observations may therefore be able to reduce these uncertainties by determining H3+ temperatures self consistently.
-
Saturn Ring rain model estimates of water influx into Saturn s atmosphere
Icarus, 2015Co-Authors: Luke Moore, Marina Galand, James Odonoghue, I C F Mullerwodarg, Michael MendilloAbstract:Abstract Recently H3+ was detected at Saturn’s low- and mid-latitudes for the first time (O’Donoghue et al. [2013]. Nature 496(7444), 193–195), revealing significant latitudinal structure in H3+ emissions, with local extrema in one hemisphere mirrored at magnetically conjugate latitudes in the opposite hemisphere. The observed minima and maxima were shown to map to regions of increased or decreased density in Saturn’s Rings, implying a direct Ring–atmosphere connection. Here, using the Saturn Thermosphere Ionosphere Model (STIM), we investigate the “Ring rain” explanation of the O’Donoghue et al. (O’Donoghue et al. [2013]. Nature 496(7444), 193–195) observations, wherein charged water group particles from the Rings are guided by magnetic field lines as they “rain” down upon the atmosphere, alteRing local ionospheric chemistry. Based on model reproductions of observed H3+ variations, we derive maximum water influxes of (1.6–16) × 105 H2O molecules cm−2 s−1 across Ring rain latitudes (∼23–49° in the south, and ∼32–54° in the north), with localized regions of enhanced influx near −48°, −38°, 42°, and 53° latitude. We estimate the globally averaged maximum Ring-derived water influx to be (1.6–12) × 105 cm−2 s−1, which represents a maximum total global influx of water from Saturn’s Rings to its atmosphere of (1.0–6.8) × 1026 s−1. The wide range of global water influx estimates stems primarily from uncertainties regarding H3+ temperatures (and consequently column densities). Future Ring rain observations may therefore be able to reduce these uncertainties by determining H3+ temperatures self consistently.
Lia Bronsard - One of the best experts on this subject based on the ideXlab platform.
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Spherical Particle in Nematic Liquid Crystal Under an External Field: The Saturn Ring Regime
Journal of Nonlinear Science, 2018Co-Authors: Stan Alama, Lia Bronsard, Xavier LamyAbstract:We consider a nematic liquid crystal occupying the exterior region in $${\mathbb {R}}^3$$ R 3 outside of a spherical particle, with radial strong anchoRing. Within the context of the Landau-de Gennes theory, we study minimizers subject to an external field, modeled by an additional term which favors nematic alignment parallel to the field. When the external field is high enough, we obtain a scaling law for the energy. The energy scale corresponds to minimizers concentrating their energy in a boundary layer around the particle, with quadrupolar symmetry. This suggests the presence of a Saturn Ring defect around the particle, rather than a dipolar director field typical of a point defect.
-
Minimizers of the Landau–de Gennes Energy Around a Spherical Colloid Particle
Archive for Rational Mechanics and Analysis, 2016Co-Authors: Stan Alama, Lia Bronsard, Xavier LamyAbstract:We consider energy minimizing configurations of a nematic liquid crystal around a spherical colloid particle, in the context of the Landau–de Gennes model. The nematic is assumed to occupy the exterior of a ball B _ r 0, and satisfy homeotropic weak anchoRing at the surface of the colloid and approach a uniform uniaxial state as $${|x|\to\infty}$$ | x | → ∞ . We study the minimizers in two different limiting regimes: for balls which are small $${r_0\ll L^{\frac12}}$$ r 0 ≪ L 1 2 compared to the characteristic length scale $${L^{\frac 12}}$$ L 1 2 , and for large balls, $${r_0\gg L^{\frac12}}$$ r 0 ≫ L 1 2 . The relationship between the radius and the anchoRing strength W is also relevant. For small balls we obtain a limiting quadrupolar configuration, with a “Saturn Ring” defect for relatively strong anchoRing, corresponding to an exchange of eigenvalues of the Q -tensor. In the limit of very large balls we obtain an axisymmetric minimizer of the Oseen–Frank energy, and a dipole configuration with exactly one point defect is obtained.
-
Analytical description of the Saturn-Ring defect in nematic colloids.
Physical review. E, 2016Co-Authors: Stan Alama, Lia Bronsard, Xavier LamyAbstract:We derive an analytical formula for the Saturn-Ring configuration around a small colloidal particle suspended in nematic liquid crystal. In particular we obtain an explicit expression for the Ring radius and its dependence on the anchoRing energy. We work within Landau-de Gennes theory: Nematic alignment is described by a tensorial order parameter. For nematic colloids this model had previously been used exclusively to perform numerical computations. Our method demonstrates that the tensorial theory can also be used to obtain analytical results, suggesting a different approach to the understanding of nematic colloidal interactions.
