Plasma acceleration in current sheets formed in helium in two- and three-dimensional magnetic configurations

The processes of heating and acceleration of plasma in current sheets formed in 2D and 3D magnetic configurations with an X-line in helium plasma have been investigated using spectroscopic methods. It is found that, in 2D magnetic configurations, plasma flows with energies of 400?C1000 eV, which are substantially higher than the ion thermal energy, are generated and propagate along the width (the larger transverse dimension) of the sheet. In 3D configurations, the influence of the longitudinal (directed along the X-line) component of the magnetic field on the plasma parameters in the current sheet has been studied. It is shown that plasma acceleration caused by the Amp??re force can be spatially inhomogeneous in the direction perpendicular to the sheet surface, which should lead to sheared plasma flows in the sheet.     

Spectroscopic measurements of the electron and ion temperatures and effective ion charge in current sheets formed in two- and three-dimensional magnetic configurations

The spatial distributions of the electron temperature and density, the effective and average ion charges, and the thermal and directed ion velocities in current sheets formed in two-dimensional magnetic fields and three-dimensional magnetic configurations with an X line were studied using spectroscopic and interference holographic methods. The main attention was paid to studying the time evolution of the intensities of spectral lines of the working-gas (argon) and impurity ions under different conditions. Using these data, the electron temperature was calculated with the help of an original mathematical code based on a collisional-radiative plasma model incorporating the processes of ionization and excitation, as well as MHD plasma flows generated in the stage of the current-sheet formation. It is shown that the electron temperature depends on the longitudinal magnetic field, whereas the ion temperature is independent of it. The effective ion charge of the current-sheet plasma was determined for the first time.     

Study of the structure and dynamics of current sheets in three-dimensional magnetic configurations with an X line by holographic interferometry

Results are presented from studies of the structure and dynamics of current sheets in three-dimensional magnetic configurations with an X line by means of holographic interferometry. It is found that the efficiency of plasma compression into the sheet is reduced as the longitudinal magnetic field B _z , directed along the X line, increases. This effect is attributed to the enhancement of the longitudinal component of the magnetic field within the sheet and to the corresponding increase in the magnetic pressure. It is shown that the formation of a plasma sheet lags behind the beginning of the plasma current pulse, the delay time being close to the characteristic Alfvén time.     

Formation of current sheets in structurally stable and structurally unstable magnetic configurations with two null lines

The nonlinear dynamics of magnetoacoustic and Alfvén MHD perturbations in structurally unstable magnetic configurations with two null lines (X-lines) is studied both analytically and numerically. It is shown that these perturbations cause the electric current to evolve nonlinearly in such a manner that a structurally unstable configuration of the magnetic field transforms into a structurally stable configuration. Such a transformation is forbidden in ideal magnetohydrodynamics but can occur in the process of magnetic field line reconnection. The final magnetic configuration to which the system evolves is shown to contain no separatrices connecting the null lines.     

Engineering functional two- and three-dimensional liver systems in vivo using hepatic tissue sheets

Hepatic tissue engineering using primary hepatocytes has been considered a valuable new therapeutic modality for several classes of liver diseases. Recent progress in the development of clinically feasible liver tissue engineering approaches, however, has been hampered mainly by insufficient cell-to-cell contact of the engrafted hepatocytes. We developed a method to engineer a uniformly continuous sheet of hepatic tissue using isolated primary hepatocytes cultured on temperature-responsive surfaces. Sheets of hepatic tissue transplanted into the subcutaneous space resulted in efficient engraftment to the surrounding cells, with the formation of two-dimensional hepatic tissues that stably persisted for longer than 200 d. The engineered hepatic tissues also showed several characteristics of liver-specific functionality. Additionally, when the hepatic tissue sheets were layered in vivo, three-dimensional miniature liver systems having persistent survivability could be also engineered. This technology for liver tissue engineering is simple, minimally invasive and free of potentially immunogenic biodegradable scaffolds.     

Influence of the initial parameters of the magnetic field and plasma on the spatial structure of the electric current and electron density in current sheets formed in helium

The influence of the initial parameters of the magnetic field and plasma on the spatial structure of the electric current and electron density in current sheets formed in helium plasma in 2D and 3D magnetic configurations with X-type singular lines is studied by the methods of holographic interferometry and magnetic measurements. Significant differences in the structures of plasma and current sheets formed at close parameters of the initial plasma and similar configurations of the initial magnetic fields are revealed.     

Holographic interferometry study of two-fluid properties of the plasma in current sheets formed in heavy noble gases

Two-exposure holographic interferometry was used to study the structure of current sheets formed in three-dimensional magnetic configurations with a singular X line in heavy noble gases (Ar, Kr, and Xe). It is found that, in the presence of a longitudinal magnetic field B _Z directed along the X line, plasma sheets take on an unusual shape: they are titled and asymmetric. Their asymmetry becomes more pronounced as the mass of a plasma ion increases—a manifestation of the two-fluid properties of the plasma. The observed effects can be attributed to additional forces arising due to the interaction of the longitudinal magnetic field B _Z with Hall currents excited in a plane perpendicular to the X line. A qualitative model describing plasma dynamics with allowance for the Hall effect and accounting for most of the experimentally observed effects is proposed.     

Experimental studies of the magnetic structure and plasma dynamics in current sheets (a review)

Based on measurements of magnetic fields in current sheets, spatial distributions of the electric current and electrodynamic forces in successive stages of the sheet evolution are determined. Two new effects manifesting themselves mostly in the late stages of the current sheet evolution have been discovered, namely, expansion of the current flow region at the periphery of the sheet and the appearance of a region with inverse currents, which gradually expands from the periphery toward the center of the sheet. Using spectroscopic methods, generation of superthermal plasma flows accelerated along the sheet width from the center toward the periphery has been revealed and investigated. The measured energies of accelerated plasma ions satisfactorily agree with the Ampère forces determined from magnetic measurements. The excitation of inverse currents additionally confirms the motion of high-speed plasma flows from the center of the current sheet toward its side edges.     

A condition for small bootstrap current in three-dimensional toroidal configurations

It is shown that, if the maximum of the magnetic field strength on a magnetic surface in a threedimensional magnetic confinement configuration with stellarator symmetry constitutes a line that is orthogonal to the field lines and crosses the symmetry line, then the bootstrap current density is smaller compared to that in quasi-axisymmetric (qa) [J. Nührenberg et al., in Proc. of Joint Varenna?Lausanne Int. Workshop on Theory of Fusion Plasmas, Varenna, 1994, p. 3] and quasi-helically (qh) symmetric [J. Nührenberg and R. Zille, Phys. Lett. A 129, 113 (1988)] configurations.     

Kinetic models of current sheets with a sheared magnetic field

Thin current sheets, whose existence in the Earth’s magnetotail is confirmed by numerous spacecraft measurements, are studied analytically and numerically. The thickness of such sheets is on the order of the ion Larmor radius, and the normal component of the magnetic field (B _z ) in the sheet is almost constant, while the tangential (B _x ) and shear (B _y ) components depend on the transverse coordinate z. The current density in the sheet also has two self-consistent components (j _x and j _y , respectively), and the magnetic field lines are deformed and do not lie in a single plane. To study such quasi-one-dimensional current configurations, two kinetic models are used, in particular, a numerical model based on the particle-in-cell method and an analytical model. The calculated results show that two different modes of the self-consistent shear magnetic field B _y and, accordingly, two thin current sheet configurations can exist for the same input parameters. For the mode with an antisymmetric z profile of the B _y component, the magnetic field lines within the sheet are twisted, whereas the profiles of the plasma density, current density component j _y , and magnetic field component B _x differ slightly from those in the case of a shearless magnetic field (B _y = 0). For the symmetric B _y mode, the magnetic field lines lie in a curved surface. In this case, the plasma density in the sheet varies slightly and the current sheet is two times thicker. Analysis of the dependence of the current sheet structure on the flow anisotropy shows that the sheet thickness decreases significantly with decreasing ratio between the thermal and drift plasma velocities, which is caused by the dynamics of quasi-adiabatic ions. It is shown that the results of the analytical and numerical models are in good agreement. The problems of application of these models to describe current sheets at the magnetopause and near magnetic reconnection regions are discussed.     

Thin current sheets in collisionless plasma: Equilibrium structure,plasma instabilities,and particle acceleration

The review is devoted to plasma structures with an extremely small transverse size, namely, thin current sheets that have been discovered and investigated by spacecraft observations in the Earth’s magnetotail in the last few decades. The formation of current sheets is attributed to complicated dynamic processes occurring in a collisionless space plasma during geomagnetic perturbations and near the magnetic reconnection regions. The models that describe thin current structures in the Earth’s magnetotail are reviewed. They are based on the assumption of the quasi-adiabatic ion dynamics in a relatively weak magnetic field of the magnetotail neutral sheet, where the ions can become unmagnetized. It is shown that the ion distribution can be represented as a function of the integrals of particle motion—the total energy and quasi-adiabatic invariant. Various modifications of the initial equilibrium are considered that are obtained with allowance for the currents of magnetized electrons, the contribution of oxygen ions, the asymmetry of plasma sources, and the effects related to the non-Maxwellian particle distributions. The theoretical results are compared with the observational data from the Cluster spacecraft mission. Various plasma instabilities developing in thin current sheets are investigated. The evolution of the tearing mode is analyzed, and the parameter range in which the mode can grow are determined. The paradox of complete stabilization of the tearing mode in current sheets with a nonzero normal magnetic field component is thereby resolved based on the quasi-adiabatic model. It is shown that, over a wide range of current sheet parameters and the propagation directions of large-scale unstable waves, various modified drift instabilities—kink and sausage modes—can develop in the system. Based on the concept of a turbulent electromagnetic field excited as a result of the development and saturation of unstable waves, a mechanism for charged particle acceleration in turbulent current sheets is proposed and the energy spectra of the accelerated particles are obtained.     

Magnetic structure of current sheets in magnetic fields with a singular X line

Direct measurements of magnetic fields in a plasma show that current sheets can form in magnetic configurations with an X line in the presence of a longitudinal magnetic field. It is found that, in a plane perpendicular to the X line and to the direction of the main current, the current sheet has two very different dimensions. The tangential and normal components of the magnetic field and current density in the sheet are determined. The influence of the initial conditions (such as the strength of the longitudinal magnetic field, the gradient of the transverse field, and the plasma ion mass) on the current sheet parameters is investigated.     

Vinculin regulates directionality and cell polarity in two- and three-dimensional matrix and three-dimensional microtrack migration

During metastasis, cells can use proteolytic activity to form tube-like “microtracks” within the extracellular matrix (ECM). Using these microtracks, cells can migrate unimpeded through the stroma. To investigate the molecular mechanisms of microtrack migration, we developed an in vitro three-dimensional (3D) micromolded collagen platform. When in microtracks, cells tend to migrate unidirectionally. Because focal adhesions are the primary mechanism by which cells interact with the ECM, we examined the roles of several focal adhesion molecules in driving unidirectional motion. Vinculin knockdown results in the repeated reversal of migration direction compared with control cells. Tracking the position of the Golgi centroid relative to the position of the nucleus centroid reveals that vinculin knockdown disrupts cell polarity in microtracks. Vinculin also directs migration on two-dimensional (2D) substrates and in 3D uniform collagen matrices, as indicated by reduced speed, shorter net displacement, and decreased directionality in vinculin-deficient cells. In addition, vinculin is necessary for focal adhesion kinase (FAK) activation in three dimensions, as vinculin knockdown results in reduced FAK activation in both 3D uniform collagen matrices and microtracks but not on 2D substrates, and, accordingly, FAK inhibition halts cell migration in 3D microtracks. Together these data indicate that vinculin plays a key role in polarization during migration.     

MHD stability of a finite-pressure plasma in axisymmetric configurations of the poloidal magnetic field

A set of linear integrodifferential equations is presented for the plasma displacement components that minimize the Kruskal-Oberman functional of the potential energy of an MHD perturbation. Marginal stability results when the smallest eigenvalue of this set of equations is zero.     

Three-dimensional rotational plasma flows near solid surfaces in an axial magnetic field

A rotational flow of a conducting viscous medium near an extended dielectric disk in a uniform axial magnetic field is analyzed in the magnetohydrodynamic (MHD) approach. An analytical solution to the system of nonlinear differential MHD equations of motion in the boundary layer for the general case of different rotation velocities of the disk and medium is obtained using a modified Slezkin–Targ method. A particular case of a medium rotating near a stationary disk imitating the end surface of a laboratory device is considered. The characteristics of a hydrodynamic flow near the disk surface are calculated within the model of a finite-thickness boundary layer. The influence of the magnetic field on the intensity of the secondary flow is studied. Calculations are performed for a weakly ionized dense plasma flow without allowance for the Hall effect and plasma compressibility. An MHD flow in a rotating cylinder bounded from above by a retarding cap is considered. The results obtained can be used to estimate the influence of the end surfaces on the main azimuthal flow, as well as the intensities of circulating flows in various devices with rotating plasmas, in particular, in plasma centrifuges and laboratory devices designed to study instabilities of rotating plasmas.     

Evaluation of cooperativity for phase transitions in two- and three-dimensional systems

Use of the so-called "cooperative unit" (readily obtainable from the midpoint slope of phase transition curves) is discussed for the determination of cluster sizes and cooperative interaction energies. This quantity has been commonly employed in a rather empirical way since its correct interpretation is known only for some special cases (linear systems, all-or-none transitions). It is shown in the framework of a lattice model (Ising model) that the cooperative unit may be interpreted in terms of correlation functions and that it defines an average cluster corresponding to the patch size as obtained from scattering experiments. Relations between the cooperative unit and a cooperativity parameter are given for various lattices. Different types of transition curves are discussed using a simple analytical formalism, the quasichemical approximation. Some important nonideality effects are investigated which may lead to a "smearing-out" of first-order transitions.     

Asymmetric configurations of a thin current sheet with a constant normal magnetic field component

A possible mechanism for the formation of a quasi-equilibrium asymmetric current sheet in the magnetospheric tail due to the asymmetry of peripheral plasma sources is analyzed using a self-consistent particle- in-cell model of a thin collisionless current sheet with a constant normal magnetic field component. For the case in which the current sheet is produced by only one source, quasi-equilibrium sheet configurations with maximum possible asymmetry are obtained for different input parameters of the model. In such configurations, the equilibrium force balance is satisfied with high accuracy and the shape of the current density profile remains nearly symmetric, but the current sheet itself is slightly shifted from the source as compared to the symmetric case. The configurations obtained using numerical simulations are compared with those calculated using the previous analytical model of a thin current sheet. It is found that the results provided by these models agree well both qualitatively and quantitatively.     

Classification of small molecules by two- and three-dimensional decomposition kernels

MOTIVATION: Several kernel-based methods have been recently introduced for the classification of small molecules. Most available kernels on molecules are based on 2D representations obtained from chemical structures, but far less work has focused so far on the definition of effective kernels that can also exploit 3D information. RESULTS: We introduce new ideas for building kernels on small molecules that can effectively use and combine 2D and 3D information. We tested these kernels in conjunction with support vector machines for binary classification on the 60 NCI cancer screening datasets as well as on the NCI HIV data set. Our results show that 3D information leveraged by these kernels can consistently improve prediction accuracy in all datasets. AVAILABILITY: An implementation of the small molecule classifier is available from http://www.dsi.unifi.it/neural/src/3DDK.     

Expansion and differentiation of human primary osteoblasts in two- and three-dimensional culture

Abstract

Despite the regenerative capability of bone, treatment of large defects often requires bone grafts. The challenge for bone grafting is to establish rapid and sufficient vascularization. Three-dimensional (3D) multicellular spheroids consisting of the relevant cell types can be used as “mini tissues” to study the complexity of angiogenesis. We investigated two-dimensional (2D) expansion, differentiation and characterization of primary osteoblasts as steps toward the establishment of 3D multicellular spheroids. Supplementation of cell culture medium with vitamin D₃ induces the osteocalcin expression of osteoblasts. An increased osteocalcin concentration of 10.8 ± 0.58 ng/ml could be measured after 19 days in supplemented medium. Vitamin D₃ has no influence on the expression of alkaline phosphatase or the deposition of calcium. Expression of these additional osteogenic markers requires addition of a cocktail of osteogenic factors that, conversely, have no influence on the expression of osteocalcin. Supplementation of the cell culture medium with both vitamin D₃ and a cocktail of osteogenic factors is recommended to produce an osteoblast phenotype that secretes osteocalcin, expresses alkaline phosphatase and deposits calcium. In such a supplemented medium, a mean osteocalcin concentration of 11.63 ± 4.85 ng/ml was secreted by the osteoblasts. Distinguishing osteoblasts and fibroblasts remains a challenge. Neither differentiated nor undifferentiated osteoblasts can be distinguished from fibroblasts by the expression of CD90, ED-A-fibronectin or α-smooth muscle actin; however, these cell types exhibit clear differences in their growth characteristics. Osteoblasts can be arranged as 3D spheroids by coating the bottom of the cell culture device with agarose. The cellular composition of 3D multicellular spheroids can be evaluated quantitatively using vital fluorescence labeling techniques. Spheroids are a promising tool for studying angiogenic and osteogenic phenomena in vivo and in vitro.     

Islands and ergodicity of the plasma current in toroidal magnetic confinement systems

Magnetic and current structures arising due to resonant perturbations of an equilibrium current-carrying magnetic configuration are analyzed using the Hamiltonian formalism. Special attention is paid to axisymmetric tokamak and pinch configurations. It is shown that, due to the very different dependences of the magnetic and current rotational transforms on the plasma pressure, the resonances (islands) of the magnetic field may not coincide with those of the current. The perturbed force-free equilibrium of a cylindrical pinch in which the field and current islands overlap is analyzed. The long-lived ribbon structures observed in the JET tokamak are explained as a manifestation of a force-free magneto-current island.