Epi-Two-Dimensional Fluid Flow: A New Topological Paradigm for Dimensionality.

While a variety of fundamental differences are known to separate two-dimensional (2D) and three-dimensional (3D) fluid flows, it is not well understood how they are related. Conventionally, dimensional reduction is justified by an a priori geometrical framework; i.e., 2D flows occur under some geometrical constraint such as shallowness. However, deeper inquiry into 3D flow often finds the presence of local 2D-like structures without such a constraint, where 2D-like behavior may be identified by the integrability of vortex lines or vanishing local helicity. Here we propose a new paradigm of flow structure by introducing an intermediate class, termed epi-two-dimensional flow, and thereby build a topological bridge between 2D and 3D flows. The epi-2D property is local and is preserved in fluid elements obeying ideal (inviscid and barotropic) mechanics; a local epi-2D flow may be regarded as a "particle" carrying a generalized enstrophy as its charge. A finite viscosity may cause "fusion" of two epi-2D particles, generating helicity from their charges giving rise to 3D flow.

Electro-optic Bdot probe measurement of magnetic fluctuations in plasma.

We propose a combined use of a Pockels electro-optic sensor with a pickup loop coil (Bdot probe) for the measurement of magnetic fluctuations in plasmas. In this method, induced fluctuating voltage on the coil loop is converted into an optical signal by a compact electro-optic sensor in the vicinity of the measurement point and is transferred across optical fiber that is unaffected by electric noise or capacitive load issues. Compared with conventional Bdot probes, the electro-optic Bdot probe (1) is electrically isolated and free from noise pickup caused by the metallic transmission line and (2) can be operated at a higher-frequency range because of the smaller capacitance of the operation circuit, both of which are suitable for many plasma experiments. Conversely, the sensitivity of the current electro-optic Bdot probe arrangement is still significantly lower than that of conventional Bdot probes. A preliminary measurement result with the electro-optic Bdot probe showed the detection of a magnetic fluctuation signal around the cyclotron frequency range in the RT-1 magnetospheric plasma experiment.

Twisting space-time: relativistic origin of seed magnetic field and vorticity.

We demonstrate that a purely ideal mechanism, originating in the space-time distortion caused by the demands of special relativity, can break the topological constraint (leading to helicity conservation) that would forbid the emergence of a magnetic field (a generalized vorticity) in an ideal nonrelativistic dynamics. The new mechanism, arising from the interaction between the inhomogeneous flow fields and inhomogeneous entropy, is universal and can provide a finite seed even for mildly relativistic flows.

Magnetospheric vortex formation: self-organized confinement of charged particles.

A magnetospheric configuration gives rise to various peculiar plasma phenomena that pose conundrums to astrophysical studies; at the same time, innovative technologies may draw on the rich physics of magnetospheric plasmas. We have created a "laboratory magnetosphere" with a levitating superconducting ring magnet. Here we show that charged particles (electrons) self-organize a stable vortex, in which particles diffuse inward to steepen the density gradient. The rotating electron cloud is sustained for more than 300 s. Because of its simple geometry and self-organization, this system will have wide applications in confining single- and multispecies charged particles.

Plasma acceleration and cooling by strong laser field due to the action of radiation reaction force.

It is shown that for super intense laser pulses propagating in a hot plasma, the action of the radiation reaction force (appropriately incorporated into the equations of motion) causes strong bulk plasma motion with the kinetic energy raised even to relativistic values; the increase in bulk energy is accompanied by a corresponding cooling (intense cooling) of the plasma. The effects are demonstrated through explicit analytical calculations.

Diffusion with finite-helicity field tensor: A mechanism of generating heterogeneity.

Topological constraints on a dynamical system often manifest themselves as breaking of the Hamiltonian structure; well-known examples are nonholonomic constraints on Lagrangian mechanics. The statistical mechanics under such topological constraints is the subject of this study. Conventional arguments based on phase spaces, Jacobi identity, invariant measure, or the H theorem are no longer applicable since all these notions stem from the symplectic geometry underlying canonical Hamiltonian systems. Remembering that Hamiltonian systems are endowed with field tensors (canonical 2-forms) that have zero helicity, our mission is to extend the scope toward the class of systems governed by finite-helicity field tensors. Here, we introduce a class of field tensors that are characterized by Beltrami vectors. We prove an H theorem for this Beltrami class. The most general class of energy-conserving systems are non-Beltrami, for which we identify the "field charge" that prevents the entropy to maximize, resulting in creation of heterogeneous distributions. The essence of the theory can be delineated by classifying three-dimensional dynamics. We then generalize to arbitrary (finite) dimensions.

Coherence-imaging spectroscopy for 2D distribution of ion temperature and flow velocity in a laboratory magnetosphere.

A coherence-imaging spectroscopy (CIS) technique was developed to investigate plasma confinement in a dipole system that imitates a planetary magnetosphere. Optical interference generated using birefringent crystals enables two-dimensional Doppler spectroscopy to measure ion temperatures and flow velocities in plasmas. CIS covers the entire dynamics of the pole areas as well as of the core and edge areas on a dipole confinement device. The two-dimensional visualization of these quantities in the magnetospheric-plasma device RT-1 was demonstrated using CIS.

Nd:YAG laser Thomson scattering diagnostics for a laboratory magnetosphere.

A new Nd:YAG laser Thomson scattering (TS) system has been developed to explore the mechanism of high-beta plasma formation in the RT-1 device. The TS system is designed to measure electron temperatures (Te) from 10 eV to 50 keV and electron densities (ne) of more than 1.0 × 1017 m-3. To measure at the low-density limit, the receiving optics views the long scattering length (60 mm) using a bright optical system with both a large collection window (260-mm diameter) and large collection lenses (300-mm diameter, a solid angle of ∼68 × 10-3 str). The scattered light of the 1.2-J Nd:YAG laser (repetition frequency: 10 Hz) is detected with a scattering angle of 90° and is transferred via a set of lenses and an optical fiber bundle to a polychromator. After Raman scattering measurement for the optical alignment and an absolute calibration, we successfully measured Te = 72.2 eV and ne = 0.43 × 1016 m-3 for the coil-supported case and Te = 79.2 eV and ne = 1.28 × 1016 m-3 for the coil-levitated case near the inner edge in the magnetospheric plasmas.

Electro-optic probe measurements of electric fields in plasmas.

The direct measurements of high-frequency electric fields in a plasma bring about significant advances in the physics and engineering of various waves. We have developed an electro-optic sensor system based on the Pockels effect. Since the signal is transmitted through an optical fiber, the system has high tolerance for electromagnetic noises. To demonstrate its applicability to plasma experiments, we report the first result of measurement of the ion-cyclotron wave excited in the RT-1 magnetosphere device. This study compares the results of experimental field measurements with simulation results of electric fields in plasmas.

Up-hill diffusion, creation of density gradients: Entropy measure for systems with topological constraints.

It is always some constraint that yields any nontrivial structure from statistical averages. As epitomized by the Boltzmann distribution, the energy conservation is often the principal constraint acting on mechanical systems. Here we investigate a different type: the topological constraint imposed on "space." Such a constraint emerges from the null space of the Poisson operator linking an energy gradient to phase space velocity and appears as an adiabatic invariant altering the preserved phase space volume at the core of statistical mechanics. The correct measure of entropy, built on the distorted invariant measure, behaves consistently with the second law of thermodynamics. The opposite behavior (decreasing entropy and negative entropy production) arises in arbitrary coordinates. An ensemble of rotating rigid bodies is worked out. The theory is then applied to up-hill diffusion in a magnetosphere.

Chaos of energetic positron orbits in a dipole magnetic field and its potential application to a new injection scheme.

We study the behavior of high-energy positrons emitted from a radioactive source in a magnetospheric dipole field configuration. Because the conservation of the first and second adiabatic invariants is easily destroyed in a strongly inhomogeneous dipole field for high-energy charged particles, the positron orbits are nonintegrable, resulting in chaotic motions. In the geometry of a typical magnetospheric levitated dipole experiment, it is shown that a considerable ratio of positrons from a ^{22}Na source, located at the edge of the confinement region, has chaotic long orbit lengths before annihilation. These particles make multiple toroidal circulations and form a hollow toroidal positron cloud. Experiments with a small ^{22}Na source in the Ring Trap 1 (RT-1) device demonstrated the existence of such long-lived positrons in a dipole field. Such a chaotic behavior of high-energy particles is potentially applicable to the formation of a dense toroidal positron cloud in the strong-field region of the dipole field in future studies.

1H-NMR and rosonance Raman spectra of octaethylporphyrinatoiron(III) perchlorate and its mono imidazole adduct.

The 1H-NMR spectra and the resonance Raman spectra of intermediate spin complex, octaethylporphyrinatoiron (III) perchlorate (OEP-Fe(III)ClO4) and its mono imidazole adduct have been recorded and analyzed. The perchlorate complex was determined to be an intermediate-spin state (S = 3/2) in dichloromethane. The mono imidazole and 2-methylimidazole adducts of OEP-Fe(III)ClO4 were of the high-spin state in dichloromethane, which is a good model for the ferrihemoproteins such as metmyoglobins. The spin state of OEP-Fe(III)ClO4 varies the polarity of solvent from typical high-spin (S = 5/2) to typical low-spin (S = 1/2) state including intermediate-spin state (S = 3/2). The resonance Raman studies of the intermediate-spin complex in various solvents indicate that the complex is a plausible model to reproduce anomalous physico-chemical properties of the ferricytochrome c' at physiological condition.

Influence of steric factors on oxygen binding. I. Studies on 2,4-diisopropyldeuteroheme-myoglobin.

Sperm whale apomyoglobin was recombined with 2,4-diisopropyldeuterohemin to form 2,4-diisopropyldeuteroheme-myoglobin and its various physico-chemical properties were investigated to get an insight into the structural and functional role of the peripheral vinyl groups. 2,4-Diisopropyldeuteroheme-myoglobin showed a four times lower oxygen affinity at 25 degrees C and larger enthalpy and entropy changes of oxygenation than the corresponding values of native myoglobin. 2,4-Diisopropyldeuteroheme-metmyoglobin shows a pKa value of 9.68 which is higher than those of native metmyoglobin and mesoheme-metmyoglobin. The rate of autooxidation of oxy-form was about seven times larger in 2,4-diisopropyldeuteroheme-myoglobin than in native myoglobin. The electron-donating effect of isopropyl groups does not give straightforward explanation for these anomalous properties of 2,4-diisopropyldeuteroheme-myoglobin. It is proposed that site and stereospecific van der Waals' interaction between the polypeptide side chains and the peripheral 2,4-diisopropyl groups may weaken the interaction between the bound oxygen molecule and the distal His, resulting in the decrease in the stability of oxyform.

Studies on reconstituted myoglobins and hemoglobins. II. Role of the heme side chains in the oxygenation of hemoglobin.

To clarify the functional role of the 2- and 4-side chains of heme in hemoglobin we prepared several hemins carrying nonnatural side chains at positions 2 and 4, reconstituted human adult hemoglobins with them, and investigated their optical and oxygen binding properties. The absorption maxima for all these reconstituted hemoglobins, no matter whether they are oxy-, deoxy-, or carbon monoxy-form, shifted toward shorter wavelengths than those for protoheme-hemoglobin. As in the case of myoglobin (Kawabe, K., et al. (1982) J. Biochem. 92, 1703-1712), the absorption spectrum is more significantly affected by resonance effects than by the inductive effects of the peripheral heme substituents. Contrary to the case of myoglobins, the spectral difference between pemptoheme-hemoglobin and isopemptoheme-hemoglobin and that between 2-isopropyl-4-vinyl-deuteroheme-hemoglobin and 2-vinyl-4-isopropyldeuteroheme-hemoglobin were very small. All the reconstituted hemoglobins used in this study showed higher oxygen affinity and reduced cooperativity in oxygen binding than native hemoglobin. We have shown that the 2- and 4-side chains are functionally nonequivalent and that modification of the 4-side chain exerts greater influence on oxygen affinity than modifying the 2-side chain. The magnitude of the Bohr effect and response to 2,3-diphosphoglycerate and inositol hexaphosphate were reduced in the reconstituted hemoglobins. We have proposed a stereochemical mechanism based on constraint of heme movement before ligation against the tight distal side of the heme pocket.

Studies on reconstituted myoglobins and hemoglobins. I. Role of the heme side chains in the oxygenation of myoglobin.

To clarify the functional role of the 2- and 4-side chains of heme in myoglobin oxygenation, we synthesized several new hemins carrying nonnatural side chains at positions 2 and 4, reconstituted myoglobins with them, and investigated their optical, ionization, and oxygen-binding properties. The absorption maxima for most of the reconstituted myoglobins except those reconstituted with hemins having carbonyl groups, no matter whether they are oxy-, deoxy-, or carbon monoxy-form, shifted by at most 20 nm toward shorter wavelengths than protoheme-myoglobin. The absorption spectrum is more affected by resonance effects than by inductive effects of the peripheral side chains of heme. Differences in optical and oxygenation properties between isomeric myoglobins carrying hemes with different side chains at positions 2 and 4 indicate that the 2- and 4-side chains of heme are functionally nonequivalent, as previously shown by Sono and Asakura [(1975) J. Biol. Chem. 250, 5227-5232] for monoformyl-monovinylheme myoglobins. Modification of the 4-side chain exerts greater influence on the oxygen affinity than that of the 2-side chain. The extrapolation method proposed by Sono and Asakura to correct for the protein factor seems to be applicable only as a special case and does not apply to the isomeric myoglobins studied by us. There was not correlation between pKa of the met-form and the oxygen pressure at half saturation, implying that the electronic effect of the side chains is not decisive for the oxygen affinity of myoglobin. The bulkiness of the 2- and 4-side chains, on the other hand, appear to have a certain relation to the affinity but is not a dominant factor. In addition to these factors, specific stereochemical considerations are required to explain all the oxygenation data for the various reconstituted myoglobins. We have proposed a stereochemical mechanism based on the movement of the heme group upon ligation of native myoglobin.

Crystal structures of modified myoglobins. II. Relation between oxygen affinity properties and structural changes around heme in myoglobins reconstituted with 2,4-diisopropyldeuteroheme, 2-isopropyl-4-vinyldeuteroheme, and 2-vinyl-4-isopropyldeuteroheme.

The crystal structures of sperm whale metmyoglobins reconstituted with three kinds of modified hemes, 2,4-diisopropyldeuteroheme, 2-isopropyl-4-vinyldeuteroheme, and 2-vinyl-4-isopropyldeuteroheme, have been determined and refined at 2.2 A resolution to R = 0.216, 0.219, and 0.195, respectively. All the crystals of these myoglobins are isomorphous with that of native metmyoglobin. The 2-vinyl-4-isopropyldeuteroheme was found to be in a reverse orientation, in which the heme plane is rotated by 180 degrees about an axis through the alpha-gamma-meso carbons, whereas the orientations of the other two hemes were the same as that of protoheme in native myoglobin. In the myoglobins with 2,4-diisopropyldeuteroheme and 2-vinyl-4-isopropyldeuteroheme, both of which have lower oxygen affinities than native myoglobin, the bulky isopropyl side chain pushes Phe 43 0.7 A toward His 64 (the distal histidine) in the former, and the whole E helix at most 1.5 A, including a 0.7 A shift of the His 64 imidazole ring, in the latter. The changes of the structures prevent His 64 from forming a hydrogen bond with the liganded oxygen molecule, so that these two modified myoglobins show low oxygen affinities. On the other hand, there is no such drastic displacement in myoglobin with 2-isopropyl-4-vinyldeuteroheme, which has a slightly higher oxygen affinity than native myoglobin.

Voltammetric interpretation of the potential at an ion-selective electrode, based on current-scan polarograms observed at the aqueous/organic solution interface.

The potential-generating process at ion-selective electrodes (ISE) of liquid-membrane types has been interpreted by comparing the ISE potential with the current-scan polarogram which indicates the transfer of a particular ion i(z+) at the aqueous/organic solution (w/o) interface. The potential at zero current, DeltaV(l = 0), in the composite polarogram observed with i(z+) in both w and o, corresponds to the ISE potential. A stable potential giving Nernstian response to the concentration of i(z+) in w is obtained at the ISE only when the w/o interface is depolarized byi(z+). The detection limits are controlled by the final rise and final descent of the residual current in the polarogram. The interference of a second ion,j(z+), in the ISE measurement of i(z+), and the role of an ionophore in the membrane of the ISE can be explained by considering the shift of DeltaV(l = 0) in the composite polarogram ofi(z+) in the presence of j(z+) in w or the ionophore in o. Equations which express the ISE potential, the interference at the ISE, and the effect of an ionophore on the ISE potential have been derived, connected with the polarographic equations for ion-transfer at the w/o interface.

Spectrophotometric measurement of uranium(VI)-tributylphosphate complex in supercritical carbon dioxide.

UV-visible absorption spectra of uranium(VI)-tributylphosphate (U(VI)-TBP) complex dissolved in supercritical CO(2) at 40-60 degrees C and 100-250 kg cm(-2) were recorded. Wavelengths and molar extinction coefficients for the absorption peaks of U(VI)-TBP were determined and confirmed to be in good agreement with those of UO(2)(NO(3))(2)(TBP)(2) complex dissolved in organic solvents such as n-hexane. The absorbance at a given wavelength was proportional to the concentration of U(VI) species in supercritical CO(2), indicating a feasibility of in-situ determination of U(VI) concentration in CO(2) phase. A lower detection limit of U(VI)-TBP complex was estimated to be ca. 1x10(-3)M. The molar extinction coefficient of U(VI)-TBP in supercritical CO(2) decreased slightly with an increase of the density of CO(2) medium, suggesting that the solute-solvent interaction of U(VI)-TBP complex with CO(2) was affected by the density. On the basis of the spectra obtained, phase behavior and solubility of UO(2)(NO(3))(2)(TBP)(2)+H(NO(3))(TBP)+TBP in supercritical CO(2) were elucidated.

Resonant production of secondary electrons generating a discrete energy structure in a magnetized electron beam system.

In a system of magnetized electron beams, multiplication of electrons can occur if the incident and return beams (the latter one is produced by secondary electrons emitted at the end of the incident beam) satisfy a resonance condition on the gyration phase. The beams propagate between two boundaries; one is an electron gun and the other is a Faraday cup detector. The resonance condition demands discrete energies (eigenvalues) of the Hamiltonian that generates a propagator of the beam. This model has been compared with Varma's formulation of discrete energies [R. K. Varma and A. M. Punithavelu, Mod. Phys. Lett. A 8, 167 (1993)].

Asymptotic analysis and renormalized perturbation theory of the non-Hermitian dynamics of an inviscid vortex.

An analysis of the non-Hermitian fluid systems described by the Rayleigh equation in an unbounded domain has been carried out in the regime of large wave numbers. The evolution of a special class of localized vorticities is also discussed. Asymptotic and perturbative approaches lead to the same final result. In the limit considered, the system is stable. The perturbation analysis reveals interesting pathologies of the non-Hermitian systems. Under specific conditions, the expansion is found to show secular growth. A discussion about the mechanism of insurgence of such singular behavior is presented. It is also shown that the divergent expansion is renormalizable by means of the renormalization group method-the renormalized results are in complete conformity with the asymptotic solutions.