Interpreting Solar Activity: Vorticity and Helicity Patterns Across Various Depths
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On the Origin of Solar Hemispherical Helicity Rules: Simulations of the Rise of Magnetic Flux Concentrations in a Background Field
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Bhishek Manek↗
Kinetic Helicity and Lifetime of Activity Complexes During Solar Cycle 24
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R. Komm↗
On the cross-helicity dependence of the energy spectrum in magnetohydrodynamic turbulence
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J. J. Podesta↗
Counter‐Helical Magnetic Flux Ropes From Magnetic Reconnections in Space Plasmas
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Ying‐Dong Jia↗
Measurement of the rugged invariants of magnetohydrodynamic turbulence in the solar wind
Measurements of the total energy, cross helicity, and magnetic helicity of the solar wind at 1, 2.8, and 5 AU are presented. These quantities are the three rugged invariants of three-dimensional ideal incompressible MHD turbulence theory. The theoretical technique for measuring the magnetic helicity from the matrix of two-point correlations is shown. The length scales characterizing the magnetic helicity are found to be equal to or greater than those which characterize the magnetic energy. The magnetic helicity typically lies at scales larger than the magnetic correlation length, consistent with the expectations of the inverse cascade and selective decay hypotheses of three-dimensional MHD turbulence. At smaller scales, the magnetic helicity oscillates in sign. Measurements of the cross helicity are not fully consistent with the usual interpretation in terms of outward propagating Alfvenic functions. Especially during the interval at 5 AU the cross helicity is found to oscillate in sign indicating fluctuations propagating both outward and inward.
Matthaeus, W. H.↗
AFM Studies of Salt Concentration Effects on the (110) Surface Structure of Tetragonal Lysozyme Crystals
Previous high resolution AFM studies of the (110) surface of tetragonal chicken egg white lysozyme crystals had shown that only one of two possible molecular surfaces is present, those constituting the completed 43 helices. These suggested that the crystal growth process was by the solution-phase assembly of the growth units, which then attach to the surface. However, the best fit for the imaged surfaces, vs. those predicted based upon the bulk crystallographic coordinates, were obtained when the packing about the 43 helices was "tightened up", while maintaining the underlying crystallographic unit cell spacing. This results in a widening of the gap between adjacent helices, and the top- most layer(s) may no longer be in contact. We postulated that the tightened packing about the helices is a result of the high salt concentrations in the bulk solution, used to crystallize the protein, driving hydrophobic interactions. Once the crystal surface is sufficiently buried by subsequent growth layers the ratio of salt to protein molecules decreases and the helices relax to their bulk crystallographic coordinates. The crystal surface helix structure is thus a reflection of the solution structure, and the tightness of the packing about the 43 helices would be a function of the bulk salt concentration. AFM images of the (110) surface of tetragonal lysozyme crystals grown under low (2%) and high (5%) NaCl concentrations reveal differences in the packing about the 43 helices consistent with the above proposal.
Pusey, Marc Lee↗
Structure, Function, Self-Assembly and Origin of Simple Membrane Proteins
Integral membrane proteins perform such essential cellular functions as transport of ions, nutrients and waste products across cell walls, transduction of environmental signals, regulation of cell fusion, recognition of other cells, energy capture and its conversion into high-energy compounds. In fact, 30-40% of genes in modem organisms codes for membrane proteins. Although contemporary membrane proteins or their functional assemblies can be quite complex, their transmembrane fragments are usually remarkably simple. The most common structural motif for these fragments is a bundle of alpha-helices, but occasionally it could be a beta-barrel. In a series of molecular dynamics computer simulations we investigated self-organizing properties of simple membrane proteins based on these structural motifs. Specifically, we studied folding and insertion into membranes of short, nonpolar or amphiphatic peptides. We also investigated glycophorin A, a peptide that forms sequence-specific dimers, and a transmembrane aggregate of four identical alpha-helices that forms an efficient and selective voltage-gated proton channel was investigated. Many peptides are attracted to water-membrane interfaces. Once at the interface, nonpolar peptides spontaneously fold to a-helices. Whenever the sequence permits, peptides that contain both polar and nonpolar amino also adopt helical structures, in which polar and nonpolar amino acid side chains are immersed in water and membrane, respectively. Specific identity of side chains is less important. Helical peptides at the interface could insert into the membrane and adopt a transmembrane conformation. However, insertion of a single helix is unfavorable because polar groups in the peptide become completely dehydrated upon insertion. The unfavorable free energy of insertion can be regained by spontaneous association of peptides in the membrane. The first step in this process is the formation of dimers, although the most common are aggregates of 4-7 helices. The helices could arrange themselves such that they formed pores capable of transporting ions and small molecules across membranes. Stability of transmembrane aggregates of simple proteins is often only marginal and, therefore, it can be regulated by environmental signals or small sequence modifications in the region of interhelical interactions. A key step in the earliest evolution of membrane proteins was the emergence of selectivity for specific substrates. Many channels could become selective if one or only a few properly chosen amino acids are properly placed along the channel, acting as filters or gates. This is a convenient evolutionary solution because it does not require imposing conditions on the whole sequence.
Pohorille, Andrew↗
Dipole Alignment in Rotating MHD Turbulence
We present numerical results from long-term CPU and GPU simulations of rotating, homogeneous, magnetohydrodynamic (MHD) turbulence, and discuss their connection to the spherically bounded case. We compare our numerical results with a statistical theory of geodynamo action that has evolved from the absolute equilibrium ensemble theory of ideal MHD turbulence, which is based on the ideal MHD invariants are energy, cross helicity and magnetic helicity. However, for rotating MHD turbulence, the cross helicity is no longer an exact invariant, although rms cross helicity becomes quasistationary during an ideal MHD simulation. This and the anisotropy imposed by rotation suggests an ansatz in which an effective, nonzero value of cross helicity is assigned to axisymmetric modes and zero cross helicity to non-axisymmetric modes. This hybrid statistics predicts a large-scale quasistationary magnetic field due to broken ergodicity , as well as dipole vector alignment with the rotation axis, both of which are observed numerically. We find that only a relatively small value of effective cross helicity leads to the prediction of a dipole moment vector that is closely aligned (less than 10 degrees) with the rotation axis. We also discuss the effect of initial conditions, dissipation and grid size on the numerical simulations and statistical theory.
Shebalin, John V.↗
Determining the Molecular Growth Mechanisms of Tetragonal Lysozyme Crystals
Studies of the growth of tetragonal lysozyme crystals employing atomic force microscopy (AFM) have shown the advantages of this technique in investigating the growth mechanisms of protein crystals [1]. The resolution of these studies was in the micron range, which revealed surface features such as the occurrence of dislocations and 2D nucleation islands, similar to those found in inorganic systems. They clearly showed that the crystals grew by these surface growth mechanisms. However, the studies also revealed some surprising features, such as bimolecular growth step heights and pronounced growth anisotropies on the (110) face, which could not be explained. In previous studies we employed Periodic Bond Chain (PBC) theory to tetragonal lysozyme crystal growth and found that the crystals were constructed by strongly bonded molecular chains forming helices about the 43 axes [2,3]. The helices were connected to each other with weaker bonds. The growth process was shown to proceed by the formation of these 43 helices, resulting in bimolecular growth steps on the (110) face. It was also shown to explain many other observations on tetragonal lysozyme crystal growth. Although PBC analysis is not a new technique [4], it has not been widely used as the mechanisms predicted from it could not be experimentally verified. In this study the growth process of these crystals was investigated, particularly for the (110) face, employing some newly developed high resolution AFM techniques. These techniques allowed individual lysozyme molecules on the crystal faces to be resolved and predictions from PBC analyses to be tested. The analyses had shown that of the two possible packing arrangements on (110) faces, only one would actually occur. Employing the first of the newly developed techniques, these faces were scanned by high resolution AFM. The resulting images were then compared with the theoretically constructed images for the two possible packing arrangements on the (110) face. The theoretical images were constructed by convolution of the crystal surface shape obtained from crystallographic data with the AFM tip shape. The comparison confirmed the prediction that the molecular packing arrangement of these faces corresponded to that for complete 43 helices. The second AFM technique that was developed was used to follow the growth process by measuring the dimensions of individual growth units on the (110) face. Linescans across a growth step, performed near the saturation limit of the crystals, allowed the growth unit dimensions to be measured. These measurements showed that growth on the (110) face proceeded by the formation of new 43 helices from the addition of at least tetramer units in the [110] direction. In the [001] direction growth proceeded by the addition of various aggregate units corresponding to the 4(sub 3) helices.
Li, Huayu↗
Computer Modeling of Protocellular Functions: Peptide Insertion in Membranes
Lipid vesicles became the precursors to protocells by acquiring the capabilities needed to survive and reproduce. These include transport of ions, nutrients and waste products across cell walls and capture of energy and its conversion into a chemically usable form. In modem organisms these functions are carried out by membrane-bound proteins (about 30% of the genome codes for this kind of proteins). A number of properties of alpha-helical peptides suggest that their associations are excellent candidates for protobiological precursors of proteins. In particular, some simple a-helical peptides can aggregate spontaneously and form functional channels. This process can be described conceptually by a three-step thermodynamic cycle: 1 - folding of helices at the water-membrane interface, 2 - helix insertion into the lipid bilayer and 3 - specific interactions of these helices that result in functional tertiary structures. Although a crucial step, helix insertion has not been adequately studied because of the insolubility and aggregation of hydrophobic peptides. In this work, we use computer simulation methods (Molecular Dynamics) to characterize the energetics of helix insertion and we discuss its importance in an evolutionary context. Specifically, helices could self-assemble only if their interactions were sufficiently strong to compensate the unfavorable Free Energy of insertion of individual helices into membranes, providing a selection mechanism for protobiological evolution.
Rodriquez-Gomez, D.↗
Statistical Theory of the Ideal MHD Geodynamo
A statistical theory of geodynamo action is developed, using a mathematical model of the geodynamo as a rotating outer core containing an ideal (i.e., no dissipation), incompressible, turbulent, convecting magnetofluid. On the concentric inner and outer spherical bounding surfaces the normal components of the velocity, magnetic field, vorticity and electric current are zero, as is the temperature fluctuation. This allows the use of a set of Galerkin expansion functions that are common to both velocity and magnetic field, as well as vorticity, current and the temperature fluctuation. The resulting dynamical system, based on the Boussinesq form of the magnetohydrodynamic (MHD) equations, represents MHD turbulence in a spherical domain. These basic equations (minus the temperature equation) and boundary conditions have been used previously in numerical simulations of forced, decaying MHD turbulence inside a sphere [1,2]. Here, the ideal case is studied through statistical analysis and leads to a prediction that an ideal coherent structure will be found in the form of a large-scale quasistationary magnetic field that results from broken ergodicity, an effect that has been previously studied both analytically and numerically for homogeneous MHD turbulence [3,4]. The axial dipole component becomes prominent when there is a relatively large magnetic helicity (proportional to the global correlation of magnetic vector potential and magnetic field) and a stationary, nonzero cross helicity (proportional to the global correlation of velocity and magnetic field). The expected angle of the dipole moment vector with respect to the rotation axis is found to decrease to a minimum as the average cross helicity increases for a fixed value of magnetic helicity and then to increase again when average cross helicity approaches its maximum possible value. Only a relatively small value of cross helicity is needed to produce a dipole moment vector that is aligned at approx.10deg with the rotation axis.
Shebalin, J. V.↗
Gravitational scattering of zero-rest-mass plane waves
The Feyman-diagram technique is used to calculate the differential cross sections for the scattering of zero-rest-mass plane waves of spin 0, 1, and 2 by linearized Schwarzschild and Kerr geometries in the long-wavelength weak-field limit. It is found that the polarization of right (or left) circularly polarized electromagnetic waves is unaffected by the scattering process (i.e., helicity is conserved) and that the two helicity (polarization) states of the photon are scattered differently by the Kerr geometry. This coupling between the photon helicity and the angular momentum of the scatterer also leads to a partial polarization of unpolarized incident light. For gravitational waves, on the other hand, there is neither helicity conservation nor helicity-dependent scattering; the angular momentum of the scatterer has no polarizing effect on incident unpolarized gravitational waves.
De Logi, W. K.↗
Calculation of a mirror asymmetric effect in electron scattering from chiral targets
A dynamical calculation is presented of the helicity induced in an initially unpolarized electron beam after elastic scattering from an optically active medium, a process analogous to the circular polarization induced in unpolarized light following Rayleigh scattering from chiral targets. The calculation is based on the bound helical electron model of a chiral molecule, according to which the major contribution to the helicity is provided by the perturbation of the electron bound state by the spin-orbit interaction of the bound electrons moving in the electric field of the molecular core. The net helicity acquired is found to depend directly on a molecular asymmetry factor and the square of the atomic number of the heaviest atom in an asymmetric environment. For the case of carbon, the induced helicity is on the order of 0.00001, which would account for its lack of observation in a recent experiment. Results may have implications for the origin of optical activity in biological molecules by the differential ionization of D and L isomers by beta-decay electrons.
Rich, A.↗
The effect of swirl recovery vanes on the cruise noise of an advanced propeller
The SR-7A propeller was acoustically tested with and without downstream swirl recovery vanes to determine if any extra noise was caused by the interaction of the propeller wakes and vortices with these vanes. No additional noise was observed at the cruise condition over the angular range tested. The presence of the swirl recovery vanes did unload the propeller and some small peak noise reductions were observed from lower propeller loading noise. The propeller was also tested alone to investigate the behavior of the peak propeller noise with helical tip Mach number. As observed before on other propellers, the peak noise first rose with helical tip Mach number and then leveled off or decreased at higher helical tip Mach numbers. Detailed pressure-time histories indicate that a portion of the primary pressure pulse is progressively cancelled by a secondary pulse as the helical tip Mach number is increased. This cancellation appears to be responsible for the peak noise behavior at high helical tip Mach numbers.
Dittmar, James H.↗
The effect of swirl recovery vanes on the cruise noise of an advanced propeller
The SR-7A propeller was acoustically tested with and without downstream swirl recovery vanes to determine if any extra noise was caused by the interaction of the propeller wakes and vortices with these vanes. No additional noise was observed at the cruise condition over the angular range tested. The presence of the swirl recovery vanes did unload the propeller and some small peak noise reductions were observed from lower propeller loading noise. The propeller was also tested alone to investigate the behavior of the peak propeller noise with helical tip Mach number. As observed before on other propellers, the peak noise first rose with helical tip Mach number and then leveled off or decreased at higher helical tip Mach numbers. Detailed pressure-time histories indicate that a portion of the primary pressure pulse is progressively cancelled by a secondary pulse as the helical tip Mach number is increased. This cancellation appears to be responsible for the peak noise behavior at high helical tip Mach numbers.
Dittmar, James H.↗
Electrorepulsive actuator
The invention is a linear actuator that operates under the principle that like charges repel and opposite charges attract. The linear actuator consists of first and second pairs of spaced opposed conductors where one member of each pair of conductors is attached to a fixed member, and where the other member of each pair of conductors is attached to a movable member such as an elongated rod. The two pairs of spaced conductors may be provided in the form of two spacedly interwound helical vanes where the conductors are located on the opposite sides of the two helical vanes. One helical vane extends inwardly from a housing and the other helical vane extends outwardly from an elongated rod. The elongated rod may be caused to move linearly with respect to the housing by applying appropriate charges of like or opposite polarity to the electrical conductors on the helical vanes.
Collins, Earl R., Jr.↗
Nonlinear evolution of the coronal magnetic field under reconnective relaxation
Recently, Vekstein et al. (Vekstein, Priest, & Steele 1993) have developed a model for coronal heating in which the corona responds to photospheric footpoint motions by small-scale reconnection events that bring about a relaxed state while conserving magnetic helicity but not field-line connectivity. Vekstein et al. consider a partially open field configuration in which magnetic helicity is ejected to infinity on open field lines but retained in the closed-field region. Under this scheme, they describe the evolution of an initially potential field, in response to helicity injection, in the linear regime. The present work uses numerical calculations to extend the model of Vekstein et al. into the fully nonlinear regime. The results show a rise and bulging of the field lines of the closed-field region with increasing magnetic helicity, to a point where further solutions are impossible. We interpret these solution-sequence endpoints as indicating a possible loss of equilibrium, in the sense that a relaxed equilibrium state may no longer be available to the corona when sufficient helicity has been injected. The rise and bulging behavior is reminiscent of what is observed in a helmet streamer just before the start of a coronal mass ejection (CME), and so our model suggests that a catastrophic loss of magnetic equilibrium might be the initiation mechanism for CMEs. We also find that some choices of boundary conditions can result in qualitative changes in the magnetic topology, with the appearance of magnetic islands. Whether or not this behavior occurs depends on the relative strengths of the fields in the closed- and open-field regions; in particular, island formation is most likely when the open field (which is potential) is strong and thus acts to confine the force-free closed field. Finally, we show that the energy released through reconnective relaxation can be a substantial fraction of the magnetic energy injected into the corona through footpoint motions and may be sufficient for heating the corona above active regions.
Wolfson, R.↗