Chihiro Matsuoka - Academia.edu (original) (raw)

Papers by Chihiro Matsuoka

Bulletin of the American Physical Society, Nov 14, 2013

Submitted for the DPP13 Meeting of The American Physical Society The growth of Richtmyer-Meshkov ... more Submitted for the DPP13 Meeting of The American Physical Society The growth of Richtmyer-Meshkov instability in magnetized plasma TAKAYOSHI SANO, KATSUNOBU NISHIHARA, Osaka University, CHI-HIRO MATSUOKA, Ehime University, TSUYOSHI INOUE, Aoyama Gakuin University-The Richtmyer-Meshkov instability (RMI) is of crucial importance in a variety of applications including astrophysical phenomena and laboratory experiments. The RMI occurs when an incident shock strikes a corrugated contact discontinuity separating two fluids with different densities. Inclusion of a magnetic field brings two important consequences into the RMI, which are the amplification of an ambient field and the suppression of the unstable motions. We demonstrated that the magnetic field can be amplified by the stretching motions at the interface associated with the RMI. We also investigated numerically the critical strength of a magnetic field required for the suppression of the RMI by using a two-dimensional single-mode analysis. For the cases of MHD parallel shocks, the RMI can be stabilized as a result of the extraction of vorticity from the interface. A useful formula describing a critical condition for MHD RMI has been introduced, and which is successfully confirmed by the direct numerical simulations. The critical field strength is found to be largely depending on the Mach number of the incident shock. If the shock is strong enough, even low-β plasmas can be subject to the growth of the RMI.

Journal of Nonlinear Science, Oct 21, 2016

A theoretical model is proposed to describe fully nonlinear dynamics of interfaces in twodimensio... more A theoretical model is proposed to describe fully nonlinear dynamics of interfaces in twodimensional MHD flows based on an idea of non-uniform current-vortex sheet. Application of vortex sheet model to MHD flows has a crucial difficulty because of non-conservative nature of magnetic tension. However it is shown that when a magnetic field is initially parallel to an interface, the concept of vortex sheet can be extended to MHD flows (current-vortex sheet). Two-dimensional MHD flows are then described only by a one-dimensional Lagrange parameter on the sheet. It is also shown that bulk magnetic field and velocity can be calculated from their values on the sheet. The model is tested by MHD Richtmyer-Meshkov instability with sinusoidal vortex sheet strength. Two-dimensional ideal MHD simulations show that the nonlinear dynamics of a shocked interface with density stratification agrees fairly well with that for its corresponding potential flow. Numerical solutions of the model reproduce properly the results of the ideal MHD simulations, such as the roll-up of spike, exponential growth of magnetic field, and its saturation and oscillation. Nonlinear evolution of the interface is found to be determined by the Alfvén and Atwood numbers. Some of their dependence on the sheet dynamics and magnetic field amplification are discussed. It is shown by the model that the magnetic field amplification occurs locally associated with the nonlinear dynamics of the current-vortex sheet. We expect that our model can be applicable to a wide variety of MHD shear flows.

Journal of Magnetism and Magnetic Materials, May 1, 2004

Thermal coagulation technique in which tumors are locally heated up to 60-80 C can be realized by... more Thermal coagulation technique in which tumors are locally heated up to 60-80 C can be realized by application of AC magnetic field from external coils to tumors covered with magnetic particles. We study numerically the temperature distribution in living tissue containing ferrite powder. With this temperature distribution, we calculate the magnitude of damaged region in tissue including a tumor and show a relation between tumor radii and the power of AC magnetic field.

Meeting abstracts of the Physical Society of Japan, Mar 17, 1997

Physics of Fluids, Oct 1, 2020

The interaction of double-layer density stratified interfaces with initial non-uniform velocity s... more The interaction of double-layer density stratified interfaces with initial non-uniform velocity shear is investigated theoretically and numerically, taking the incompressible Richtmyer-Meshkov instability as an example. The linear analysis for providing the initial conditions in numerical calculations is performed, and some numerical examples of vortex double layers are presented using the vortex sheet model. We show that the density stratifications (Atwood numbers), the initial distance between two interfaces, and the distribution of the initial velocity shear determine the evolution of vortex double layers. When the Atwood numbers are large, the deformation of interfaces is small, and the distance between the two interfaces is almost unchanged. On the other hand, when the Atwood numbers are small and the initial distance between two interfaces is sufficiently close (less than or equal to the half of the wavelength of the initial disturbance), the two interfaces get closer to each other and merge at the last computed stage due to the incompressibility. We confirm this theoretically expected fact numerically.

Physics of Plasmas

Vortex dynamics is an important research subject for geophysics, astrophysics, engineering, and p... more Vortex dynamics is an important research subject for geophysics, astrophysics, engineering, and plasma physics. Regarding vortex interactions, only limited problems, such as point vortex interactions, have been studied. Here, the nonlinear interaction of two non-uniform vortex sheets with density stratification is investigated using the vortex sheet model. These non-uniform vortex sheets appear, for example, in the Richtmyer–Meshkov instability that occurs when a shock wave crosses a layer with two corrugated interfaces. When a strong vortex sheet approaches a weaker vortex sheet with opposite-signed vorticity, a locally peaked secondary vorticity is induced on the latter sheet. This emerging secondary vorticity results in a remarkable vorticity amplification on the stronger sheet, and a strong vortex core is formed involving the weak vortex sheet. The amplified vortices with opposite signs on the two vortex sheets form pseudo-vortex pairs, which cause an intense rolling-up of the t...

Meeting Abstracts of the Physical Society of Japan, 2018

Theoretical and applied mechanics Japan, 2006

Physics of Fluids, 2020

The interaction of double-layer density stratified interfaces with initial non-uniform velocity s... more The interaction of double-layer density stratified interfaces with initial non-uniform velocity shear is investigated theoretically and numerically, taking the incompressible Richtmyer–Meshkov instability as an example. The linear analysis for providing the initial conditions in numerical calculations is performed, and some numerical examples of vortex double layers are presented using the vortex sheet model. We show that the density stratifications (Atwood numbers), the initial distance between two interfaces, and the distribution of the initial velocity shear determine the evolution of vortex double layers. When the Atwood numbers are large, the deformation of interfaces is small, and the distance between the two interfaces is almost unchanged. On the other hand, when the Atwood numbers are small and the initial distance between two interfaces is sufficiently close (less than or equal to the half of the wavelength of the initial disturbance), the two interfaces get closer to each ...

Physical Review E Statistical Nonlinear and Soft Matter Physics, 2010

The Journal of Physical Chemistry B, 2011

The measurement of the UV-vis absorption spectrum of α-tocopheroxyl (α-Toc(•)) radical was perfor... more The measurement of the UV-vis absorption spectrum of α-tocopheroxyl (α-Toc(•)) radical was performed by reacting aroxyl (ArO(•)) radical with α-tocopherol (α-TocH) in acetonitrile solution including four kinds of alkali and alkaline earth metal salts (MX or MX(2)) (LiClO(4), LiI, NaClO(4), and Mg(ClO(4))(2)), using stopped-flow spectrophotometry. The maximum wavelength (λ(max)) of the absorption spectrum of the α-Toc(•) at 425.0 nm increased with increasing concentration of metal salts (0-0.500 M) in acetonitrile, and it approached constant values, suggesting an [α-Toc(•)-M(+) (or M(2+))] complex formation. The stability constants (K) were determined to be 9.2, 2.8, and 45 M(-1) for LiClO(4), NaClO(4), and Mg(ClO(4))(2), respectively. By reacting ArO(•) with α-TocH in acetonitrile, the absorption of ArO(•) disappeared rapidly, while that of α-Toc(•) appeared and then decreased gradually as a result of the bimolecular self-reaction of α-Toc(•) after passing through the maximum. The second-order rate constants (k(s)) obtained for the reaction of α-TocH with ArO(•) increased linearly with an increasing concentration of metal salts. The results indicate that the hydrogen transfer reaction of α-TocH proceeds via an electron transfer intermediate from α-TocH to ArO(•) radicals followed by proton transfer. Both the coordination of metal cations to the one-electron reduced anions of ArO(•) (ArO:(-)) and the coordination of counteranions to the one-electron oxidized cations of α-TocH (α-TocH(•)(+)) may stabilize the intermediate, resulting in the acceleration of electron transfer. A remarkable effect of metal salts on the rate of bimolecular self-reaction (2k(d)) of the α-Toc(•) radical was also observed. The rate constant (2k(d)) decreased rapidly with increasing concentrations of the metal salts. The 2k(d) value decreased at the same concentration of the metal salts in the following order: no metal salt > NaClO(4) > LiClO(4) > Mg(ClO(4))(2). The complex formation between α-Toc(•) and metal cations may stabilize the energy level of the reactants (α-Toc(•) + α-Toc(•)), resulting in the decrease of the rate constant (2k(d)). The alkali and alkaline earth metal salts having a smaller ionic radius of cation and a larger charge of cation gave larger K and k(s) values and a smaller 2k(d) value.

Physics of Fluids, 2009

Motion of a planar interface in incompressible Richtmyer–Meshkov (RM) and Rayleigh–Taylor (RT) in... more Motion of a planar interface in incompressible Richtmyer–Meshkov (RM) and Rayleigh–Taylor (RT) instabilities with surface tension is investigated numerically by using the boundary integral method. It is shown that when the Atwood number is small, an interface rolls up without regularization of the interfacial velocity. A phenomenon known as “pinching” in the physics of drops is observed in the final stage of calculations at various Atwood numbers and surface tension coefficients, and it is shown that this phenomenon is caused by a vortex dipole induced on the interface. It is also shown that when the surface tension coefficient is large, finite amplitude standing wave solutions exist for the RM instability. This standing wave solution is investigated in detail by nonlinear stability analysis. When gravity is taken into account (RT instability), linearly stable but nonlinearly unstable motion can occur under a critical condition that the frequency of the linear dispersion relation in...

Physics Letters A, 1994

It is shown that there exists a hybrid topological defect of a vortex + half integer vortex + wal... more It is shown that there exists a hybrid topological defect of a vortex + half integer vortex + wall by using a coupled Ginzburg-Landau type equation. The two-dimensional sine-Gordon type equation is introduced to describe a half charge vortex + wall. Double vortex solutions of topological charges 1 and 2 are given. Recently, in liquid crystal, 3He and cosmic theories it has been reported that there exist a half integer charge vortex together with a vortex which has an integer topological charge [ 1 ]. This half charge vortex appears with a phase jump line that corresponds to a wall [2 ], and therefore it may be called a hybrid topological defect of a vortex + half charge vortex + wall. In this Letter we discuss the structure of such a defect by using two coupled complex scalar fields W~ and I412, and consider the following equations as a model [ 3 ],

Journal of the Physical Society of Japan, 2012

Pattern formation in sand dunes due to localized strong winds is investigated taking a downburst ... more Pattern formation in sand dunes due to localized strong winds is investigated taking a downburst as an example. Extending the phenomenological model proposed by Nishimori et al. and taking into account the characteristic of powders, we calculate numerically the temporal evolution of sand patterns without using the hydrodynamic equations. We discuss the relation between the velocity distribution of a downburst and obtained patters qualitatively.

Journal of the Physical Society of Japan, 1989

The propagation of shallow water solitary waves has been investigated in a channel whose depth ch... more The propagation of shallow water solitary waves has been investigated in a channel whose depth changes stepwise. A nonlinear counterpart of Snell's law has been obtained associated with reflection and refraction of waves. The reflection and transmission coefficients of solitons as well as the number of solitons emerged have been estimated with the aid of the inverse scattering method.

Chaos, Solitons & Fractals, 2012

The topological entropy of the Hénon attractor is estimated using a function that describes the s... more The topological entropy of the Hénon attractor is estimated using a function that describes the stable and unstable manifolds of the Hénon map. This function provides an accurate estimate of the length of curves in the attractor. The estimation method presented here can be applied to cases in which the invariant set is not hyperbolic. From the result of the length calculation, we have estimated the topological entropy h as h $ 0.49703 for the original parameters a = 1.4 and b = 0.3 adopted by Hénon.

Bulletin of the Chemical Society of Japan, 2009

ABSTRACT In order to understand the dynamics of antioxidant actions of vitamin E (α-, β-, γ-, and... more ABSTRACT In order to understand the dynamics of antioxidant actions of vitamin E (α-, β-, γ-, and δ-tocopherols, TocH) in biological systems, kinetic study of the formation and decay reactions of vitamin E radicals (α-, β-, γ-, and γ- tocopheroxyls, Toc •) has been performed in organic solvents, using stopped-flow spectrophotometry. By mixing α-, β-, γ-, and δ-TocH with aryloxyl radical (ArO •) in ethanol, the peaks of the UV-vis absorption due to α-, β-, γ-, and δ-Toe• radical appeared rapidly at ca. 430-340 nm, showed maxima, and then decayed gradually. The second-order rate constants (κ a and 2κ d) for the formation and decay (that is, bimolecular disproportionation) reactions of a-Toe were determined by comparing the observed curves with the simulation ones obtained by the numerical calculation of differential equations related to the above reactions. From the results, the wavelengths of absorption maxima (λ maxi) and molar extinction coefficients (ε) (i = 1-4) of the optical spectra were determined for α-Toc• radical. Notable solvent effects have been observed for the reaction rates (κ f and 2κ d) and absorption spectra (λ maxi and ε i) of α-Toc• radical. The scheme of the formation and decay reactions of α-, β-, γ-, and δ-Toc• radicals has been discussed based on the results obtained.

Bulletin of the American Physical Society, Nov 14, 2013

Submitted for the DPP13 Meeting of The American Physical Society The growth of Richtmyer-Meshkov ... more Submitted for the DPP13 Meeting of The American Physical Society The growth of Richtmyer-Meshkov instability in magnetized plasma TAKAYOSHI SANO, KATSUNOBU NISHIHARA, Osaka University, CHI-HIRO MATSUOKA, Ehime University, TSUYOSHI INOUE, Aoyama Gakuin University-The Richtmyer-Meshkov instability (RMI) is of crucial importance in a variety of applications including astrophysical phenomena and laboratory experiments. The RMI occurs when an incident shock strikes a corrugated contact discontinuity separating two fluids with different densities. Inclusion of a magnetic field brings two important consequences into the RMI, which are the amplification of an ambient field and the suppression of the unstable motions. We demonstrated that the magnetic field can be amplified by the stretching motions at the interface associated with the RMI. We also investigated numerically the critical strength of a magnetic field required for the suppression of the RMI by using a two-dimensional single-mode analysis. For the cases of MHD parallel shocks, the RMI can be stabilized as a result of the extraction of vorticity from the interface. A useful formula describing a critical condition for MHD RMI has been introduced, and which is successfully confirmed by the direct numerical simulations. The critical field strength is found to be largely depending on the Mach number of the incident shock. If the shock is strong enough, even low-β plasmas can be subject to the growth of the RMI.

Journal of Nonlinear Science, Oct 21, 2016

A theoretical model is proposed to describe fully nonlinear dynamics of interfaces in twodimensio... more A theoretical model is proposed to describe fully nonlinear dynamics of interfaces in twodimensional MHD flows based on an idea of non-uniform current-vortex sheet. Application of vortex sheet model to MHD flows has a crucial difficulty because of non-conservative nature of magnetic tension. However it is shown that when a magnetic field is initially parallel to an interface, the concept of vortex sheet can be extended to MHD flows (current-vortex sheet). Two-dimensional MHD flows are then described only by a one-dimensional Lagrange parameter on the sheet. It is also shown that bulk magnetic field and velocity can be calculated from their values on the sheet. The model is tested by MHD Richtmyer-Meshkov instability with sinusoidal vortex sheet strength. Two-dimensional ideal MHD simulations show that the nonlinear dynamics of a shocked interface with density stratification agrees fairly well with that for its corresponding potential flow. Numerical solutions of the model reproduce properly the results of the ideal MHD simulations, such as the roll-up of spike, exponential growth of magnetic field, and its saturation and oscillation. Nonlinear evolution of the interface is found to be determined by the Alfvén and Atwood numbers. Some of their dependence on the sheet dynamics and magnetic field amplification are discussed. It is shown by the model that the magnetic field amplification occurs locally associated with the nonlinear dynamics of the current-vortex sheet. We expect that our model can be applicable to a wide variety of MHD shear flows.

Journal of Magnetism and Magnetic Materials, May 1, 2004

Thermal coagulation technique in which tumors are locally heated up to 60-80 C can be realized by... more Thermal coagulation technique in which tumors are locally heated up to 60-80 C can be realized by application of AC magnetic field from external coils to tumors covered with magnetic particles. We study numerically the temperature distribution in living tissue containing ferrite powder. With this temperature distribution, we calculate the magnitude of damaged region in tissue including a tumor and show a relation between tumor radii and the power of AC magnetic field.

Meeting abstracts of the Physical Society of Japan, Mar 17, 1997

Physics of Fluids, Oct 1, 2020

The interaction of double-layer density stratified interfaces with initial non-uniform velocity s... more The interaction of double-layer density stratified interfaces with initial non-uniform velocity shear is investigated theoretically and numerically, taking the incompressible Richtmyer-Meshkov instability as an example. The linear analysis for providing the initial conditions in numerical calculations is performed, and some numerical examples of vortex double layers are presented using the vortex sheet model. We show that the density stratifications (Atwood numbers), the initial distance between two interfaces, and the distribution of the initial velocity shear determine the evolution of vortex double layers. When the Atwood numbers are large, the deformation of interfaces is small, and the distance between the two interfaces is almost unchanged. On the other hand, when the Atwood numbers are small and the initial distance between two interfaces is sufficiently close (less than or equal to the half of the wavelength of the initial disturbance), the two interfaces get closer to each other and merge at the last computed stage due to the incompressibility. We confirm this theoretically expected fact numerically.

Physics of Plasmas

Vortex dynamics is an important research subject for geophysics, astrophysics, engineering, and p... more Vortex dynamics is an important research subject for geophysics, astrophysics, engineering, and plasma physics. Regarding vortex interactions, only limited problems, such as point vortex interactions, have been studied. Here, the nonlinear interaction of two non-uniform vortex sheets with density stratification is investigated using the vortex sheet model. These non-uniform vortex sheets appear, for example, in the Richtmyer–Meshkov instability that occurs when a shock wave crosses a layer with two corrugated interfaces. When a strong vortex sheet approaches a weaker vortex sheet with opposite-signed vorticity, a locally peaked secondary vorticity is induced on the latter sheet. This emerging secondary vorticity results in a remarkable vorticity amplification on the stronger sheet, and a strong vortex core is formed involving the weak vortex sheet. The amplified vortices with opposite signs on the two vortex sheets form pseudo-vortex pairs, which cause an intense rolling-up of the t...

Meeting Abstracts of the Physical Society of Japan, 2018

Theoretical and applied mechanics Japan, 2006

Physics of Fluids, 2020

The interaction of double-layer density stratified interfaces with initial non-uniform velocity s... more The interaction of double-layer density stratified interfaces with initial non-uniform velocity shear is investigated theoretically and numerically, taking the incompressible Richtmyer–Meshkov instability as an example. The linear analysis for providing the initial conditions in numerical calculations is performed, and some numerical examples of vortex double layers are presented using the vortex sheet model. We show that the density stratifications (Atwood numbers), the initial distance between two interfaces, and the distribution of the initial velocity shear determine the evolution of vortex double layers. When the Atwood numbers are large, the deformation of interfaces is small, and the distance between the two interfaces is almost unchanged. On the other hand, when the Atwood numbers are small and the initial distance between two interfaces is sufficiently close (less than or equal to the half of the wavelength of the initial disturbance), the two interfaces get closer to each ...

Physical Review E Statistical Nonlinear and Soft Matter Physics, 2010

The Journal of Physical Chemistry B, 2011

The measurement of the UV-vis absorption spectrum of α-tocopheroxyl (α-Toc(•)) radical was perfor... more The measurement of the UV-vis absorption spectrum of α-tocopheroxyl (α-Toc(•)) radical was performed by reacting aroxyl (ArO(•)) radical with α-tocopherol (α-TocH) in acetonitrile solution including four kinds of alkali and alkaline earth metal salts (MX or MX(2)) (LiClO(4), LiI, NaClO(4), and Mg(ClO(4))(2)), using stopped-flow spectrophotometry. The maximum wavelength (λ(max)) of the absorption spectrum of the α-Toc(•) at 425.0 nm increased with increasing concentration of metal salts (0-0.500 M) in acetonitrile, and it approached constant values, suggesting an [α-Toc(•)-M(+) (or M(2+))] complex formation. The stability constants (K) were determined to be 9.2, 2.8, and 45 M(-1) for LiClO(4), NaClO(4), and Mg(ClO(4))(2), respectively. By reacting ArO(•) with α-TocH in acetonitrile, the absorption of ArO(•) disappeared rapidly, while that of α-Toc(•) appeared and then decreased gradually as a result of the bimolecular self-reaction of α-Toc(•) after passing through the maximum. The second-order rate constants (k(s)) obtained for the reaction of α-TocH with ArO(•) increased linearly with an increasing concentration of metal salts. The results indicate that the hydrogen transfer reaction of α-TocH proceeds via an electron transfer intermediate from α-TocH to ArO(•) radicals followed by proton transfer. Both the coordination of metal cations to the one-electron reduced anions of ArO(•) (ArO:(-)) and the coordination of counteranions to the one-electron oxidized cations of α-TocH (α-TocH(•)(+)) may stabilize the intermediate, resulting in the acceleration of electron transfer. A remarkable effect of metal salts on the rate of bimolecular self-reaction (2k(d)) of the α-Toc(•) radical was also observed. The rate constant (2k(d)) decreased rapidly with increasing concentrations of the metal salts. The 2k(d) value decreased at the same concentration of the metal salts in the following order: no metal salt > NaClO(4) > LiClO(4) > Mg(ClO(4))(2). The complex formation between α-Toc(•) and metal cations may stabilize the energy level of the reactants (α-Toc(•) + α-Toc(•)), resulting in the decrease of the rate constant (2k(d)). The alkali and alkaline earth metal salts having a smaller ionic radius of cation and a larger charge of cation gave larger K and k(s) values and a smaller 2k(d) value.

Physics of Fluids, 2009

Motion of a planar interface in incompressible Richtmyer–Meshkov (RM) and Rayleigh–Taylor (RT) in... more Motion of a planar interface in incompressible Richtmyer–Meshkov (RM) and Rayleigh–Taylor (RT) instabilities with surface tension is investigated numerically by using the boundary integral method. It is shown that when the Atwood number is small, an interface rolls up without regularization of the interfacial velocity. A phenomenon known as “pinching” in the physics of drops is observed in the final stage of calculations at various Atwood numbers and surface tension coefficients, and it is shown that this phenomenon is caused by a vortex dipole induced on the interface. It is also shown that when the surface tension coefficient is large, finite amplitude standing wave solutions exist for the RM instability. This standing wave solution is investigated in detail by nonlinear stability analysis. When gravity is taken into account (RT instability), linearly stable but nonlinearly unstable motion can occur under a critical condition that the frequency of the linear dispersion relation in...

Physics Letters A, 1994

It is shown that there exists a hybrid topological defect of a vortex + half integer vortex + wal... more It is shown that there exists a hybrid topological defect of a vortex + half integer vortex + wall by using a coupled Ginzburg-Landau type equation. The two-dimensional sine-Gordon type equation is introduced to describe a half charge vortex + wall. Double vortex solutions of topological charges 1 and 2 are given. Recently, in liquid crystal, 3He and cosmic theories it has been reported that there exist a half integer charge vortex together with a vortex which has an integer topological charge [ 1 ]. This half charge vortex appears with a phase jump line that corresponds to a wall [2 ], and therefore it may be called a hybrid topological defect of a vortex + half charge vortex + wall. In this Letter we discuss the structure of such a defect by using two coupled complex scalar fields W~ and I412, and consider the following equations as a model [ 3 ],

Journal of the Physical Society of Japan, 2012

Pattern formation in sand dunes due to localized strong winds is investigated taking a downburst ... more Pattern formation in sand dunes due to localized strong winds is investigated taking a downburst as an example. Extending the phenomenological model proposed by Nishimori et al. and taking into account the characteristic of powders, we calculate numerically the temporal evolution of sand patterns without using the hydrodynamic equations. We discuss the relation between the velocity distribution of a downburst and obtained patters qualitatively.

Journal of the Physical Society of Japan, 1989

The propagation of shallow water solitary waves has been investigated in a channel whose depth ch... more The propagation of shallow water solitary waves has been investigated in a channel whose depth changes stepwise. A nonlinear counterpart of Snell's law has been obtained associated with reflection and refraction of waves. The reflection and transmission coefficients of solitons as well as the number of solitons emerged have been estimated with the aid of the inverse scattering method.

Chaos, Solitons & Fractals, 2012

The topological entropy of the Hénon attractor is estimated using a function that describes the s... more The topological entropy of the Hénon attractor is estimated using a function that describes the stable and unstable manifolds of the Hénon map. This function provides an accurate estimate of the length of curves in the attractor. The estimation method presented here can be applied to cases in which the invariant set is not hyperbolic. From the result of the length calculation, we have estimated the topological entropy h as h $ 0.49703 for the original parameters a = 1.4 and b = 0.3 adopted by Hénon.

Bulletin of the Chemical Society of Japan, 2009

ABSTRACT In order to understand the dynamics of antioxidant actions of vitamin E (α-, β-, γ-, and... more ABSTRACT In order to understand the dynamics of antioxidant actions of vitamin E (α-, β-, γ-, and δ-tocopherols, TocH) in biological systems, kinetic study of the formation and decay reactions of vitamin E radicals (α-, β-, γ-, and γ- tocopheroxyls, Toc •) has been performed in organic solvents, using stopped-flow spectrophotometry. By mixing α-, β-, γ-, and δ-TocH with aryloxyl radical (ArO •) in ethanol, the peaks of the UV-vis absorption due to α-, β-, γ-, and δ-Toe• radical appeared rapidly at ca. 430-340 nm, showed maxima, and then decayed gradually. The second-order rate constants (κ a and 2κ d) for the formation and decay (that is, bimolecular disproportionation) reactions of a-Toe were determined by comparing the observed curves with the simulation ones obtained by the numerical calculation of differential equations related to the above reactions. From the results, the wavelengths of absorption maxima (λ maxi) and molar extinction coefficients (ε) (i = 1-4) of the optical spectra were determined for α-Toc• radical. Notable solvent effects have been observed for the reaction rates (κ f and 2κ d) and absorption spectra (λ maxi and ε i) of α-Toc• radical. The scheme of the formation and decay reactions of α-, β-, γ-, and δ-Toc• radicals has been discussed based on the results obtained.