Tangential Layers Research Articles

The value of magnetic resonance ultrashort echo time imaging to evaluate non-calcified cartilage of the knee joint and its damage

ObjectivesTo image knee osteochondral specimens using magnetic resonance (MR) ultrashort echo time imaging with pointwise encoding time reduction with radial acquisition combined fat suppression (PETRA-FS) sequence to determine whether it can reveal non-calcified cartilage, including the deep radial layer, and to assess its effectiveness in cartilage damage diagnosis. Materials and methodsPETRA-FS imaging was performed on 58 osteochondral specimens of the lower femur and upper tibia to observe depth of cartilage damage, combined with histological results to observe signal intensity composition. Sensitivity, specificity, and reliability of PETRA-FS sequence for diagnosing cartilage damage were evaluated using histological results as the gold standard. Diagnostic efficacy was assessed using receiver operating characteristic (ROC) curve. ResultsMR ultrashort echo time imaging PETRA-FS sequence showed non-calcified cartilage, including tangential, transitional, and radial layers, which showed a high signal. PETRA-FS sequence showed 37 cases of cartilage damage and 21 cases of no damage among 58 specimens, kappa value of 0.75. Histological analysis of the 58 osteochondral specimens revealed 38 cases of cartilage injury and 20 cases of undamaged cartilage. Using histological results as the gold standard, PETRA-FS sequence had a sensitivity of 87.00%, specificity of 80.00%, kappa value of 0.81, and an area under the ROC curve (AUC) of 0.83 for cartilage injury diagnosis. ConclusionMR ultrashort echo time imaging PETRA-FS sequence can show non-calcified cartilage, including the deep radial layer (which cannot be shown by conventional MR), by exhibiting a high signal in knee osteo-chondral specimens. Thus, PETRA-FS sequences may have important diagnostic value for cartilage injury diagnosis.

Morphological Study: Ultrastructural Aspects of Articular Cartilage and Subchondral Bone in Patients Affected by Post-Traumatic Shoulder Instability.

Post-traumatic shoulder instability is a frequent condition in active population, representing one of most disabling pathologies, due to altered balance involving joints. No data are so far available on early ultrastructural osteo-chondral damages, associated with the onset of invalidating pathologies, like osteoarthritis-OA. Biopsies of glenoid articular cartilage and sub-chondral bone were taken from 10 adult patients underwent arthroscopic stabilization. Observations were performed under Transmission Electron Microscopy-TEM in tangential, arcuate and radial layers of the articular cartilage and in the sub-chondral bone. In tangential and arcuate layers chondrocytes display normal and very well preserved ultrastructure, probably due to the synovial liquid supply; otherwise, throughout the radial layer (un-calcified and calcified) chondrocytes show various degrees of degeneration; occasionally, in the radial layer evidences of apoptosis/autophagy were also observed. Concerning sub-chondral bone, osteocytes next to the calcified cartilage also show signs of degeneration, while osteocytes farther from the osteo-chondral border display normal ultrastructure, probably due to the bone vascular supply. The ultrastructural features of the osteo-chondral complex are not age-dependent. This study represents the first complete ultrastructural investigation of the articular osteo-chondral complex in shoulder instability, evaluating the state of preservation/viability of both chondrocytes and osteocytes throughout the successive layers of articular cartilage and sub-chondral bone. Preliminary observations here collected represent the morphological basis for further deepening of pathogenesis related to shoulder instability, enhancing the relationship between cell shape and microenvironment; in particular, they could be useful in understanding if the early surgical treatment in shoulder instability could avoid the onset of OA. Anat Rec, 300:1208-1218, 2017. © 2016 Wiley Periodicals, Inc.

BARK ANATOMY OF LATE PERMIAN GLOSSOPTERID TREES FROM ANTARCTICA

The Glossopteridales are an extinct group of seed plants that dominated Gondwanan floras during the Permian. Their remains are found across a wide range of habitats and paleolatitudes, and it is particularly interesting to understand the anatomical characteristics that might have enabled such an extensive distribution. Here, we document for the first time the bark anatomy of high-latitude glossopteridalean trees using peels and thin sections made from a Late Permian trunk from Skaar Ridge, Antarctica. The bark is 3 cm thick. The secondary phloem is composed of sieve cells, axial and ray parenchyma, and fibers arranged in discontinuous unicellular tangential layers. The outer bark is a rhytidome, with numerous alternating layers of periderm and non-conducting secondary phloem showing some proliferation of the axial parenchyma. Successive periderms mostly run parallel to the cambium, with some longitudinal undulation and rare connections between two periderms. A similar anatomy was observed in bark fragments found isolated in the matrix or closely associated with large glossopterid stems or roots. The anatomy of the Skaar Ridge specimens shows that Antarctic Glossopteridales had a relatively thick, probably stringy bark. The retention of a significant amount of insulating dead bark tissue on the trunk likely provided protection of the cambium, conducting secondary phloem, and potential latent buds against biotic and abiotic environmental hazards (fire, frost, scalding, insects, etc.) and may have contributed to the extensive paleolatitudinal distribution of the Glossopteridales during the Permian.

Charcoalified Agathoxylon-type wood with preserved secondary phloem from the lower Permian of the Brazilian Parana Basin

For the first time, secondary phloem tissue of Agathoxylon Hartig (sensu Rößler et al. 2014) is described from Permian charcoalified wood remains. Large (up to 13.4×21.8cm), highly compressed, charred logs and branches were collected from the lower and upper boundaries of a tonstein bed (U/Pb age 291±1.3Ma) interlayered in a Sakmarian coal seam in the Faxinal Coalfield, Rio Grande do Sul, Brazil (Rio Bonito Formation). Small pieces were sampled with a dissecting knife and needles, mounted on standard stubs, gold-coated, and photographed under a scanning electron microscope. The phloem tissue is composed of thin-walled sieve cells, thick-walled fibers, and axial and radial uniseriate parenchyma. The extraordinary preservation shows sieve cells with pores grouped in conspicuous sieve areas occurring on lateral cell walls. Sieve cells are inferred to be arranged in tangential layers alternating with mixed rows of fibers and scarce parenchyma. Conclusions are drawn about preservation conditions involving cyclic environmental dryness and possible affinities with pteridosperms and cordaitaleans.

Asymmetric kinetic equilibria: Generalization of the BAS model for rotating magnetic profile and non-zero electric field

Finding kinetic equilibria for non-collisional/collisionless tangential current layers is a key issue as well for their theoretical modeling as for our understanding of the processes that disturb them, such as tearing or Kelvin Helmholtz instabilities. The famous Harris equilibrium [E. Harris, Il Nuovo Cimento Ser. 10 23, 115–121 (1962)] assumes drifting Maxwellian distributions for ions and electrons, with constant temperatures and flow velocities; these assumptions lead to symmetric layers surrounded by vacuum. This strongly particular kind of layer is not suited for the general case: asymmetric boundaries between two media with different plasmas and different magnetic fields. The standard method for constructing more general kinetic equilibria consists in using Jeans theorem, which says that any function depending only on the Hamiltonian constants of motion is a solution to the steady Vlasov equation [P. J. Channell, Phys. Fluids (1958–1988) 19, 1541 (1976); M. Roth et al., Space Sci. Rev. 76, 251–317 (1996); and F. Mottez, Phys. Plasmas 10, 1541–1545 (2003)]. The inverse implication is however not true: when using the motion invariants as variables instead of the velocity components, the general stationary particle distributions keep on depending explicitly of the position, in addition to the implicit dependence introduced by these invariants. The standard approach therefore strongly restricts the class of solutions to the problem and probably does not select the most physically reasonable. The BAS (Belmont-Aunai-Smets) model [G. Belmont et al., Phys. Plasmas 19, 022108 (2012)] used for the first time the concept of particle accessibility to find new solutions: considering the case of a coplanar-antiparallel magnetic field configuration without electric field, asymmetric solutions could be found while the standard method can only lead to symmetric ones. These solutions were validated in a hybrid simulation [N. Aunai et al., Phys. Plasmas (1994-present) 20, 110702 (2013)], and more recently in a fully kinetic simulation as well [J. Dargent and N. Aunai, Phys. Plasmas (submitted)]. Nevertheless, in most asymmetric layers like the terrestrial magnetopause, one would indeed expect a magnetic field rotation from one direction to another without going through zero [J. Berchem and C. T. Russell, J. Geophys. Res. 87, 8139–8148 (1982)], and a non-zero normal electric field. In this paper, we propose the corresponding generalization: in the model presented, the profiles can be freely imposed for the magnetic field rotation (although restricted to a 180 rotation hitherto) and for the normal electric field. As it was done previously, the equilibrium is tested with a hybrid simulation.

Ultrastructural aspects of articular cartilage and sub- chondral bone in patients affected by post-traumatic shoulder instability: preliminary observations

Post traumatic shoulder instability is a frequent condition in young active popula- tion. Notwithstanding a lot of data have been collected on capsular-legament lesions and gleno-humeral defects, no data are available on early ultrastructural ostheo-condral damages that are known to be highly associated with the onset of invalidating pathologies, like osteoarthritis (OA). Thus, the mechanisms of joint instability and the identification of which components in the articular complex are primarily affected in instability are of clinical significance, particularly in the light of deepening knowledge on the onset/development of OA. In the present study, biopsies of the articular cartilage and sub-chondral bone were taken from 10 patients (aged 26-40) underwent surgery in Policlinico of Modena. The withdrawals were immediately fixed and embedded for Transmission Electron Microscopy (TEM). The observations were per- formed in tangential, arcuate, and radial layers of the articular cartilage as well as in sub-chondral bone. TEM observations showed that chondrocytes in the superficial layers (i.e. tangential and arcuate) display normal and very well preserved ultrastruc- ture, probably due to synovial liquid supply; otherwise, chondrocytes in the radial layer (not only in calcified but also in the un-calcified one) show various degrees of degeneration, with cytoplasm partially coerced and variously-sized vacuoles, both signs of suffering; occasionally, in the radial layer, chondrocytes with morphological signs of apoptosis or autophagy were also observed. As far as sub-chondral bone is concerned, osteocytes next the deeper calcified cartilage (within 80-100 micra from the cement line) also show evidences of degeneration, while osteocytes more dis- tant from the osteo-chondral border display normal ultrastructure probably due to the vascular bone supply. In all patients of the study, the ultrastructural features of osteo-chondral complex are not depending on age. The present study represents the first ultrastructural investigation of the articular osteo-chondral complex in shoulder instability, evaluating the state of preservation/viability of both chondrocytes and osteocytes throughout the successive layers of the articular cartilage and sub-chondral bone. These preliminary observations are the basis to understand if the early surgical treatment in shoulder instability could avoid the onset of OA.

Secondary Phloem in Early Carboniferous Seed Plants: Anatomical Diversity and Evolutionary Implications

Premise of research. Secondary phloem produced by a bifacial vascular cambium is the distinctive feature of lignophytes, the group that comprises the seed plants and the progymnosperms. Because secondary phloem is rarely well preserved in the fossil record, our knowledge of the evolution of this tissue remains incomplete.Methodology. We illustrate the secondary phloem anatomy of nine seed plants of Mississippian (Early Carboniferous) age that represent to date the oldest representatives of the group in which this tissue is well preserved. In addition, we review the information available on the secondary phloem anatomy of Devonian progymnosperms and Late Carboniferous–Permian seed plants.Pivotal results. Secondary phloem anatomy was already diversified in the Mississippian seed plants, in terms of cell composition and spatial organization of the different cell types. We propose four models of secondary phloem anatomy and organization in lignophytes of Devonian-Carboniferous age.Conclusions. The diversity of secondary phloem anatomy in Mississippian seed plants parallels what is observed for other parts of their vascular system; it is most likely linked to the Mississippian diversification of seed plant growth architectures and habitats. The accumulated fossil evidence also demonstrates that several characters that have been considered as advanced on the basis of the study of extant gymnosperms (e.g., the presence of fibers in the functional phloem and the arrangement in alternate tangential layers of a same cell type) were actually already present in some early representatives of the lignophytes.

Out-of-plane orientation of cellulose elementary fibrils on spruce tracheid wall based on imaging with high-resolution transmission electron microscopy.

A 3D model of the tracheid wall has been proposed based on high-resolution cryo-TEM where, in contrast to the current understanding, the cellulose elementary fibrils protrude from the cell wall plane. The ultrastructure of the tracheid walls of Picea abies was examined through imaging of ultrathin radial, tangential and transverse sections of wood by transmission electron microscopy and with digital image processing. It was found that the elementary fibrils (EFs) of cellulose were rarely deposited in the plane of the concentric cell wall layers, in contrast to the current understanding. In addition to the adopted concept of longitudinal fibril angle, EFs protruded from the cell wall plane in varying angles depending on the layer. Moreover, the out-of-plane fibril angle varied between radial and tangential walls. In the tangential S2 layers, EFs were always out-of-plane whereas planar orientation was typical for the S2 layer in radial walls. The pattern of protruding EFs was evident in almost all axial and transverse images of the S1 layer. Similar out-of-plane orientation was found in the transverse sections of the S3 layer. A new model of the tracheid wall with EF orientation is presented as a summary of this study. The outcome of this study will enhance our understanding of the elementary fibril orientation in the tracheid wall.

The first finding of Mimomys in the Russian Far East

A new species of the Mimomys is described from the Far East Russia (the Medvezhyi Klyk cave, Sikhote-Alin). Layer 7 of the Medvezhyi Klyk cave (1.08–1.18 m) was dated to be 13 790–14 200 BP. Mimomys chandolensis sp. nov. was found in a deeper layer (2.63–2.68 m) and therefore assuming there was no redeposition of the remains and that the accumulation proceeded gradually, the molar specimen we found is 30–50 kyr old. Due to the extent of the preservation we observed in the molar and the structure of the cave, the specimen does not seem likely to have been redeposited. Our hypothesis is that due to the warm and wet climate of the region, the vole, which became extinct more than 600 kyr ago, had been extant there by the Late Pleistocene period. The new species is hypsodont, with a few cement, a lack of enamel isle or prismatic fold; tangential and lamellar layers of enamel ultrastructure are poorly expressed.

First demonstration of an asymmetric kinetic equilibrium for a thin current sheet

The modeling of steady state collisionless asymmetric tangential current layers is a challenging and poorly understood problem. For decades now, this difficulty has been limiting numerical models to approximate equilibria built with locally Maxwellian current layers and theoretical analyses to the very restricted Harris equilibrium. We show how the use of any distribution functions depending only on local macroscopic quantities results in a strong alteration of the current layer internal structure, which converges toward an unpredictable quasi-steady state with emission of ion scale perturbations. This transient can be explained in terms of ion kinetic and electron fluid physics. We demonstrate, for the first time, the validity of an asymmetric kinetic equilibrium model as well as its usability as an initial condition of hybrid kinetic simulations. This offers broad perspectives for the current sheet modeling, for which the early phase of instabilities can be studied within the kinetic formalism.

Bark Anatomy of an Early Carboniferous Tree from Australia

Our knowledge of the evolution of secondary phloem and periderm anatomy in early lignophytes (progymnosperms and seed plants) is limited by the scarcity of well-preserved fossil bark. Here, I describe the bark of a Mississippian (Early Carboniferous) tree from Australia based on macro- and microscopic observation of two permineralized specimens. The bark tissues are up to 1.5 cm in thickness. The secondary phloem is organized in repeated, multicellular tangential layers of fibers and of thin-walled cells that correspond to axial parenchyma and sieve cells. Fibers are abundant even in the youngest, presumably functional, secondary phloem. Older phloem shows a proliferation of axial parenchyma that further separates the fiber layers. Successive periderm layers originate deep within the phloem and lead to the formation of a rhytidome-type bark, one of the oldest documented in the fossil record. These fossils add to our knowledge of the bark anatomy of Early Carboniferous trees, previously based on a few specimens from slightly younger strata of Western Europe. The complexity of the secondary phloem tissue in Devonian-Carboniferous lignophytes and possible anatomical differences related to growth habit are discussed.

Neocortical neurogenesis is not really “neo”: A new evolutionary model derived from a comparative study of chick pallial development

The neocortex facilitates mammalian adaptive radiation by conferring highly sophisticated cognitive and motor abilities. A unique feature of the mammalian neocortex is its laminar structure in which similar neuronal subtypes are arranged in tangential layers and construct columnar circuits via interlaminar connections. The neocortical layer structure is completely conserved among all mammalian species, including monotremes and marsupials. However, this structure is missing in non-mammalian sister groups, such as birds and reptiles. The evolutionary origins of neocortical layers and cytoarchitectural borders have been the subject of debate over the past century. Using the chicken embryos as a model of evolutionary developmental biology (evo-devo model), we recently provided evidence suggesting that the evolutionary origin of layer-specific neuron subtypes predates the emergence of laminar structures. Based on this finding, we review the evolutionary conservation and divergence of neocortical development between mammals and non-mammals and discuss how the layered cytoarchitecture of the mammalian neocortex originated during evolution.

Kinetic equilibrium for an asymmetric tangential layer

Finding kinetic (Vlasov) equilibria for tangential current layers is a long standing problem, especially in the context of reconnection studies, when the magnetic field reverses. Its solution is of pivotal interest for both theoretical and technical reasons when such layers must be used for initializing kinetic simulations. The famous Harris equilibrium is known to be limited to symmetric layers surrounded by vacuum, with constant ion and electron flow velocities, and with current variation purely dependent on density variation. It is clearly not suited for the “magnetopause-like” layers, which separate two plasmas of different densities and temperatures, and for which the localization of the current density j=nδv is due to the localization of the electron-to-ion velocity difference δv and not of the density n. We present here a practical method for constructing a Vlasov stationary solution in the asymmetric case, extending the standard theoretical methods based on the particle motion invariants. We show that, in the case investigated of a coplanar reversal of the magnetic field without electrostatic field, the distribution function must necessarily be a multi-valued function of the invariants to get asymmetric profiles for the plasma parameters together with a symmetric current profile. We show also how the concept of “accessibility” makes these multi-valued functions possible, due to the particle excursion inside the layer being limited by the Larmor radius. In the presented method, the current profile across the layer is chosen as an input, while the ion density and temperature profiles in between the two asymptotic imposed values are a result of the calculation. It is shown that, assuming the distribution is continuous along the layer normal, these profiles have always a more complex profile than the profile of the current density and extends on a larger thickness. The different components of the pressure tensor are also outputs of the calculation and some conclusions concerning the symmetries of this tensor are pointed out.

On steady rotational cyclonic flows: The viscous bidirectional vortex

This study is focused on the tangential boundary layers of a bidirectional vortex, specifically those forming at the core and the sidewall of a swirl-driven cyclonic chamber. Our analysis is based on the regularized, tangential momentum equation which is rescaled in a manner to capture the forced vortex near the chamber axis and the no slip requirement at the sidewall. After identifying the coordinate transformations needed to resolve the rapid changes in the regions of nonuniformity, two inner expansions are constructed. These expansions are then matched with the outer, free vortex solution that is sandwiched between the core and the hard wall. By combining inner and outer expansions, uniformly valid approximations are subsequently obtained for the swirl velocity, vorticity, and pressure. These are shown to be strongly influenced by a dimensionless grouping that we refer to as the vortex Reynolds number, V. This keystone parameter appears as a ratio of the mean flow Reynolds number and the product of the swirl number and the chamber aspect ratio. Based on V, several fundamental features of the bidirectional vortex are quantified. Among them are the thicknesses of the viscous core and sidewall boundary layers; these decrease with V1/2 and V, respectively. The converse may be said of the peak velocity which increases with V1/2. In the same vein, the angular speed of the rigid-body rotation of the forced vortex is found to be linearly proportional to V. Our laminar swirl velocity is reminiscent of Sullivan’s two-cell vortex except for its additional dependence on the aspect ratio of the chamber. For the purpose of verification, theoretical predictions are compared to particle image velocimetry measurements and Navier–Stokes simulations at high vortex Reynolds numbers. By properly accounting for the turbulent eddy viscosity in the analytical model, local agreement is obtained with both laboratory measurements and computer simulations.

Numerical modelling of rotating tangential layers (jets) in shells under strong uniform magnetic field

AbstractA numerical study of tangential layers in steady‐state magnetohydrodynamic rotating flows is presented using CFD to solve the inductionless governing equations. The analysis considers two basic flow configurations. In the first, a fluid is enclosed in a cylinder with electrically perfect conducting walls and the flow is driven by a small rotating, conducting disk. In the second, a flow is considered in a spherical shell with an inner rotating sphere. The fluid in both cases is subjected to an external axial uniform magnetic field. The results show that these flows exhibit two different types of flow cores separated from each other by a tangential layer parallel to the axis of rotation. The inner core follows a solid‐body rotation while the outer is quasistagnant. A counter‐rotating jet is developed in the tangential layer between the cores. The characteristics of the tangential layer and the properties of the meridional motion are determined for a wide range of Hartmann numbers. Distributions of angular velocity of circumferential flow and electric potential are obtained and the results are compared with those of analytic methods. Copyright © 2009 John Wiley & Sons, Ltd.

Anatomical features that facilitate radial flow across growth rings and from xylem to cambium in Cryptomeria japonica

Although the lateral movement of water and gas in tree stems is an important issue for understanding tree physiology, as well as for the development of wood preservation technologies, little is known about the vascular pathways for radial flow. The aim of the current study was to understand the occurrence and the structure of anatomical features of sugi (Cryptomeria japonica) wood including the tracheid networks, and area fractions of intertracheary pits, tangential walls of ray cells and radial intercellular spaces that may be related to the radial permeability (conductivity) of the xylem. Wood structure was investigated by light microscopy and scanning electron microscopy of traditional wood anatomical preparations and by a new method of exposed tangential faces of growth-ring boundaries. Radial wall pitting and radial grain in earlywood and tangential wall pitting in latewood provide a direct connection between subsequent tangential layers of tracheids. Bordered pit pairs occur frequently between earlywood and latewood tracheids on both sides of a growth-ring boundary. In the tangential face of the xylem at the interface with the cambium, the area fraction of intertracheary pit membranes is similar to that of rays (2.8 % and 2.9 %, respectively). The intercellular spaces of rays are continuous across growth-ring boundaries. In the samples, the mean cross-sectional area of individual radial intercellular spaces was 1.2 microm(2) and their total volume was 0.06 % of that of the xylem and 2.07 % of the volume of rays. A tracheid network can provide lateral apoplastic transport of substances in the secondary xylem of sugi. The intertracheid pits in growth-ring boundaries can be considered an important pathway, distinct from that of the rays, for transport of water across growth rings and from xylem to cambium.

Triple crossings of a string of magnetic islands at duskside magnetopause encountered by AMPTE/IRM satellite on 8 August 1985

[1] There have been a number of reports on the existence of pearl-like magnetic island structures at the magnetopause current layer based on the analyses of single spacecraft data and two-dimensional reconstruction method of solving the Grad-Shafranov equation as a spatial initial value problem. This paper presents an unusual event of multiple magnetopause crossings encountered by AMPTE/IRM satellite at the duskside equatorial plane on 8 August, 1985. In a total of 11 magnetopause crossings spanning for nearly 2 hours, crossing 3, 4, and 9 display similar features of a string of magnetic islands imbedded within the overall tangential discontinuity-like current layers. In these crossings, the deHoffmann-Teller velocities form approximately 90° from the magnetopause normal that the in-and-out magnetopause motion becomes subsiding for the satellite to pick up the pearl-like plasmoids with island width of about 6–12 ion inertial length. In particular, crossing 3 and 9 are 1 hour apart but have almost the same magnetopause normal and deHoffmann-Teller velocity as well as similar invariant axis. A region of cold plasma adjacent to the magnetopause within the magnetosphere, the low-latitude boundary layer, is seen in all three crossings.

Erratum: “Exact nonlinear analytic Vlasov–Maxwell tangential equilibria with arbitrary density and temperature profiles” [Phys. Plasmas 10, 2501 (2003)

The tangential layers are characterized by a bulk plasma velocity and a magnetic field that are perpendicular to the gradient direction. They have been extensively described in the frame of the Magneto-Hydro-Dynamic (MHD) theory. But the MHD theory does not look inside the transition region if the transition has a size of a few ion gyroradii. A series of kinetic tangential equilibria, valid for a collisionless plasma is presented. These equilibria are exact analytical solutions of the Maxwell-Vlasov equations. The particle distribution functions are sums of an infinite number of elementary functions parametrized by a vector potential. Examples of equilibria relevant to space plasmas are shown. A model for the deep and sharp density depletions observed in the auroral zone of the Earth is proposed. Tangential equilibria are also relevant for the study of planetary environments and of remote astrophysical plasmas.

Exact nonlinear analytic Vlasov–Maxwell tangential equilibria with arbitrary density and temperature profiles

The tangential layers are characterized by a bulk plasma velocity and a magnetic field that are perpendicular to the gradient direction. They have been extensively described in the frame of the magnetohydrodynamic (MHD) theory. But the MHD theory does not look inside the transition region if the transition has a size of a few ion gyroradii. A series of kinetic tangential equilibria, valid for a collisionless plasma is presented. These equilibria are exact analytical solutions of the Maxwell–Vlasov equations. The particle distribution functions are sums of an infinite number of elementary functions parametrized by a vector potential. Examples of equilibria relevant to space plasmas are shown. A model for the deep and sharp density depletions observed in the auroral zone of the Earth is proposed. Tangential equilibria are also relevant for the study of planetary environments and of remote astrophysical plasmas.

Quasi-Laue neutron-diffraction study of the water arrangement in crystals of triclinic hen egg-white lysozyme.

Triclinic crystals of lysozyme, hydrogen-deuterium exchanged in deuterated solvent, have been studied using neutron quasi-Laue techniques and a newly developed cylinder image-plate detector. The wavelength range employed was from 2.7 to 3.5 A, which gave 9426 significant reflections [F >/= 2sigma(F)] to a resolution limit of 1. 7 A. The deuteration states of the H atoms in the protein molecule were identified, followed by an extensive analysis of the water structure surrounding the protein. The final R factor was 20.4% (Rfree = 22.1%). In total, the 244 observed water molecules form approximately one layer of water around the protein with far fewer water molecules located further away. Water molecules covering the apolar patches make tangential layers at 4-5 A from the surface or form C-H...O contacts, and several water-molecule sites can be identified in the apolar cavities. Many of the water molecules are apparently orientationally disordered, and only 115 out of the 244 water molecules sit in mean single orientations. Comparison of these results with quasi-elastic neutron scattering observations of the water dynamics leads to a picture of the water molecules forming an extended constantly fluctuating network covering the protein surface.