World lines of dust inC-field cosmology

Geodesic and non-geodesic world lines of dust are investigated in Pryce'sC-field cosmology. A Raychaudhuri type equation is derived for the non-geodesic, rotational dust flow.Queen's Mathematical Preprints No. 1970–9.     

Cooling and transport of energetic ions due to the global geodesic acoustic mode

It is shown that (i) the destabilization of global Geodesic Acoustic modes (GAM or E-GAM) by passing energetic ions in tokamaks can be accompanied with a considerable energy transfer from these ions to the mode; (ii) the mode-induced slowing down of the energetic ions leads to a radial shift outwards/inwards of the ions moving in the direction counter to/of the plasma current, in spite of the fact that the canonical angular momentum of the particles is conserved during GAMs. Some practical consequences of these phenomena are discussed.     

Study of Geodesic Acoustic and Alfvén Modes in Toroidal Fusion Devices (Brief Review)

JETP Letters - Geodesic acoustic modes, Alfvén eigenmodes, stationary and oscillating components of the electric field, and their relations to plasma confinement have been studied. Theoretical...     

Geodesic mode instability driven by the electron current in tokamak plasmas

Effect of the parallel electron current on Geodesic Acoustic Modes (GAM) in a tokamak is analyzed by kinetic theory taking into the account the ion Landau damping and diamagnetic drifts. It is shown that the electron current modeled by shifted Maxwell distribution may overcome the phase velocity threshold and ion Landau damping thus resulting in the GAM instability when the parallel electron current velocity is larger than the effective parallel GAM phase velocity Rqω. The instability occurs due to its cross term of the current with the ion diamagnetic drift. Possible applications to tokamak experiments are discussed.     

Generalized space-time paraxial acoustic ray tracing

Paraxial ray tracing has gained popularity in seismology and underwater acoustics for modelling the propagation of sound when the medium is stationary and time independent. In this article differential geometry is used to derive a generalized paraxial ray-tracing procedure valid for any fluid media described by a local sound speed and velocity depending arbitrarily on position and time. Geodesic deviation is used to model acoustic beam deformation, and the sectional curvature along a ray to determine convergence and divergence zones in space. The resulting paraxial equations presented here are the most general that can be derived for the acoustic field and apply to any environment including those with time dependence and fluid motion. Applied to layered media the geodesic deviation equation is solved exactly. Some illustrative examples are included.     

Geodesic acoustic modes and zonal flows in toroidally rotating tokamak plasmas

The effect of equilibrium toroidal rotation on the rotational eigen-modes in large aspect ratio tokamak is studied. The case of equilibrium with uniform plasma density on magnetic surfaces is considered. It is shown that the toroidal rotation results in a frequency up-shift of ordinary Geodesic Acoustic Modes. A new unstable low frequency branch of the continuum modes is found. This mode appears as a consequence of the non-uniform plasma pressure created by the centrifugal force on the magnetic surfaces. This mode represents a linear eigen-mode counterpart of Zonal Flow modes. It is shown that the growth rate of such a mode increases with the increase of the angular velocity of toroidal rotation.     

A dynamical approach to symplectic and spectral invariants for billiards

The Lazutkin parameter for curves which are invariant under the billiard ball map is viewed symplectically in a way which makes it analogous to the sum of the values of a generating function over a closed orbit. This leads to relations among lengths of closed geodesics, lengths of invariant curves for the billiard map, rotation numbers, and the Lazutkin parameter. These relations establish the Birkhoff invariant and the expansion for the lengths of invariant curves in terms of the Lazutkin parameter as symplectic and spectral invariants (for the Dirichlet spectrum) and provide invariants which characterize a family of ellipses among smooth curves with positive curvature. Geodesic flow on a bounded planar region gives rise to several geometric objects among which are closed reflected geodesics and invariant curves-closed curves whose tangents are invariant under reflection at the boundary. On a bounded domain, the map that assigns to each geodesic segment its successor after reflection at the boundary is called the billiard ball map and its dual (in the cotangent bundle for the boundary) is called the boundary map.     

Geodesic deviation equation in f(R,T) gravity

In this paper, we investigate the modified Geodesic Deviation Equation (GDE) in the framework of f(R, T) theory of gravity where R and T are the curvature scalar and the trace of the energy-momentum tensor, respectively, using the FLRW background. In this way, we obtain the GR equivalent (GDE) in f(R, T) metric formalism. We also extend our work to the generalization of the Matting relation and perform the numerical analysis with GDE for null vector.     

Geodesic deviation equation in <Emphasis Type="Italic">f</Emphasis> (<Emphasis Type="Italic">R</Emphasis>) gravity

In this paper we study the Geodesic Deviation Equation (GDE) in metric f (R) gravity. We start giving a brief introduction of the GDE in General Relativity in the case of the standard cosmology. Next we generalize the GDE for metric f (R) gravity using again the FLRW metric. A generalization of the Mattig relation is also obtained. Finally we give and equivalent expression to the Dyer-Roeder equation in General Relativity in the context of f (R) gravity.     

Real miniheaven

For the class of axisymmetric gravitational fields originally treated by Bondi, the existence of a two-dimensional family of asymptotically shear-free slices (good slices) of null infinity is exhibited. They form a real two-dimensional submanifold (miniheaven) of the four-dimensional complex manifold of good slices (heaven) constructed by Newman. The real good slices can be described as surfaces of revolution of geodesic curves. Geodesic deviation due to the Bondi news function gives rise to the geometrical properties of miniheaven. These properties are examined for the special case of axisymmetric Robinson-Trautman solutions. The Robinson-Trautman family of shear-free null hypersurfaces corresponds to a geodesic in miniheaven possessing an infinite number of angular momentum and supermomentum constants of the motion. The global properties of the Robinson-Trautman miniheaven are examined in the linear approximation in which a remarkably simple expression for the curvature of miniheaven is found. The asymptotic properties of miniheaven turn out to be identical to those of the original Robinson-Trautman space-time.Research supported by grant No. MPS74-18020 from the National Science Foundation. The work constitutes part of a doctoral dissertation submitted by R. Dubisch to the University of Pittsburgh.     

Some Information Geometric Aspects of Cyber Security by Face Recognition

Secure user access to devices and datasets is widely enabled by fingerprint or face recognition. Organization of the necessarily large secure digital object datasets, with objects having content that may consist of images, text, video or audio, involves efficient classification and feature retrieval processing. This usually will require multidimensional methods applicable to data that is represented through a family of probability distributions. Then information geometry is an appropriate context in which to provide for such analytic work, whether with maximum likelihood fitted distributions or empirical frequency distributions. The important provision is of a natural geometric measure structure on families of probability distributions by representing them as Riemannian manifolds. Then the distributions are points lying in this geometrical manifold, different features can be identified and dissimilarities computed, so that neighbourhoods of objects nearby a given example object can be constructed. This can reveal clustering and projections onto smaller eigen-subspaces which can make comparisons easier to interpret. Geodesic distances can be used as a natural dissimilarity metric applied over data described by probability distributions. Exploring this property, we propose a new face recognition method which scores dissimilarities between face images by multiplying geodesic distance approximations between 3-variate RGB Gaussians representative of colour face images, and also obtaining joint probabilities. The experimental results show that this new method is more successful in recognition rates than published comparative state-of-the-art methods.     

The existence of homogeneous geodesics in homogeneous pseudo-Riemannian and affine manifolds

It is well known that, in any homogeneous Riemannian manifold, there is at least one homogeneous geodesic through each point. For the pseudo-Riemannian case, even if we assume reductivity, this existence problem is still open. The standard way to deal with homogeneous geodesics in the pseudo-Riemannian case is to use the so-called “Geodesic Lemma”, which is a formula involving the inner product. We shall use a different approach: namely, we imbed the class of all homogeneous pseudo-Riemannian manifolds into the broader class of all homogeneous affine manifolds (possibly with torsion) and we apply a new, purely affine method to the existence problem. In dimension 2, it was solved positively in a previous article by three authors. Our main result says that any homogeneous affine manifold admits at least one homogeneous geodesic through each point. As an immediate corollary, we prove the same result for the subclass of all homogeneous pseudo-Riemannian manifolds.     

An alternative to wave mechanics on curved spaces

Geodesic motion in infinite spaces of constant negative curvature provides for the first time an example where a basically quantum mechanical quantity, a ground-state energy, is derived from Newtonian mechanics in a rigorous, nonsemiclassical way. The ground state energy emerges as the Hausdorff dimension of a quasi-self-similar curve at infinity of three-dimensional hyperbolic spaceH ³ in which our manifolds are embedded and where their universal covers are realized. This curve is just the locus of the limit set () of the Kleinian group of covering transformations, which determines the bounded trajectories in the manifold; all of them lie in the quotientC(), C() being the hyperbolic convex hull of (). The three-dimensional hyperbolic manifolds we construct can be visualized as thickened surfaces, topological productsI×S, I a finite open interval, the fibersS compact Riemann surfaces. We give a short derivation of the Patterson formula connecting the ground-state energy with the Hausdorff dimension of , and give various examples for the calculation of from the tessellations of the boundary ofH ³, induced by the universal coverings of the manifolds.     

Resonances in electron scattering by molecules

The main features of resonance scattering of electrons by molecules are described and resonances are determined on the basis of the theory of collisions in a two-body system, as well as resonances emerging as a result of collisions in a few-body system. Regularities in the emergence of such resonances and their characteristics are analyzed. The results of calculations of these resonant processes occurring during collisions of electrons with diatomic molecules, made on the basis of the quantum theory of scattering in a few-body system, are presented. The results of calculating the cross sections of resonant processes of electron collisions with molecules are compared with the available experimental data and with the results of calculations based on other approximations.     

The influence of contacts on the VA-characteristics of thin-layfr systems with amorphous semiconductors

In the paper the VA-characteristics of a sandwich-type thin-layer system with amorphous semiconductor are discussed, where ohmic and non-ohmic contacts are considered. The VA-characteristics are derived which, in the case of ohmic contacts, lead to a linear dependence of the current on voltage and, in the case of non-ohmic contacts (where barriers are supposed), to a nonlinear dependence, so that VA-characteristics with negative resistance are possible as well. These VA-characteristics are compared with the experimental ones, measured on thin-layer metalamorphous Si-metal and metal-amorphous CdTe-metal structures.     

Dependence on substrate topography of growth of nanosized dendritic structures in an electron-beam-induced deposition process

Nanometer-sized W-dendrites are fabricated on Al₂O₃ substrates with an electron-beam-induced deposition process. Dependence of growth of nanodendrite on surface topography is investigated with transmission electron microscopy. It is confirmed that the nanodendrite grows on convex surfaces but not around a hole on a substrate. These are attributed to different distribution of charges on surfaces with different topographies during electron beam irradiation when charges are produced on the surface due to emission of second electrons. The charges accumulate on convex surface and do not distribute around a hole. Therefore, the nanodendrite grows on the former and not on the latter.     

Molecular dynamic simulation of lubricant spreading： effect from the substrate and endbead

Molecular dynamic simulations based on a coarse-grained, bead-spring model are adopted to investigate the spreading of both nonfunctional and functional perfluoropolyether (PFPE) on solid substrates. For nonfunctional PFPE, the spreading generally exhibits a smooth profile with a precursor film. The spreading profiles on different substrates are compared, which indicate that the bead-substrate interaction has a significant effect on the spreading behaviour, especially on the formation of the precursor film. For functional PFPE, the spreading generally exhibits a complicated terraced profile. The spreading profiles with different endbeads are compared, which indicate that the endbead-substrate interaction and the endbead--endbead interaction, especially the latter, have a significant effect on the spreading behaviour.     

Chemical mechanical planarization of Ge_2Sb_2Te_5 using IC1010 and Politex reg pads in acidic slurry

In the paper, chemical mechanical planarization(CMP) of Ge2Sb2Te5(GST) is investigated using IC1010 and Politex reg pads in acidic slurry. For the CMP with blank wafer, it is found that the removal rate(RR) of GST increases with the increase of pressure for both pads, but the RR of GST polished using IC1010 is far more than that of Politex reg. To check the surface defects, GST film is observed with an optical microscope(OM) and scanning electron microscope(SEM). For the CMP with Politex reg, many spots are observed on the surface of the blank wafer with OM, but no obvious spots are observed with SEM. With regard to the patterned wafer, a few stains are observed on the GST cell, but many residues are found on other area with OM. However, from SEM results, a few residues are observed on the GST cell, more dielectric loss is revealed about the trench structure. For the CMP with IC1010, the surface of the polished blank wafer suffers serious scratches found with both OM and SEM, which may result from a low hardness of GST, compared with those of IC1010 and abrasives. With regard to the patterned wafer, it can achieve a clean surface and almost no scratches are observed with OM, which may result from the high-hardness SiO2 film on the surface, not from the soft GST film across the whole wafer. From the SEM results, a clean interface and no residues are observed on the GST surface, and less dielectric loss is revealed. Compared with Politex reg, the patterned wafer can achieve a good performance after CMP using IC1010.     

Complete description of the interactions of a quadrupolar nucleus with a radiofrequency field. Implications for data fitting

We present a theory, with experimental tests, that treats exactly the effect of radiofrequency (RF) fields on quadrupolar nuclei, yet retains the symbolic expressions as much as possible. This provides a mathematical model of these interactions that can be easily connected to state-of-the-art optimization methods, so that chemically-important parameters can be extracted from fits to experimental data. Nuclei with spins >1/2 typically experience a Zeeman interaction with the (possibly anisotropic) local static field, a quadrupole interaction and are manipulated with RF fields. Since RF fields are limited by hardware, they seldom dominate the other interactions of these nuclei and so the spectra show unusual dependence on the pulse width used. The theory is tested with ²³Na NMR nutation spectra of a single crystal of sodium nitrate, in which the RF is comparable with the quadrupole coupling and is not necessarily on resonance with any of the transitions. Both the intensity and phase of all three transitions are followed as a function of flip angle. This provides a more rigorous trial than a powder sample where many of the details are averaged out. The formalism is based on a symbolic approach which encompasses all the published results, yet is easily implemented numerically, since no explicit spin operators or their commutators are needed. The classic perturbation results are also easily derived. There are no restrictions or assumptions on the spin of the nucleus or the relative sizes of the interactions, so the results are completely general, going beyond the standard first-order treatments in the literature.     

Capture of DNA in microfluidic channel using magnetic beads: Increasing capture efficiency with integrated microfluidic mixer

We have studied the hybridization of target DNA in solution with probe DNA on magnetic beads immobilized on the channel sidewalls in a magnetic bead separator. The hybridization is carried out under a liquid flow and is diffusion limited. Two systems are compared: one with a straight microfluidic channel and one with an integrated staggered herringbone mixer. Fluorescence microscopy studies show that the hybridization is much more efficient in the system with the integrated mixer. The results, which are discussed in terms of a simple model, are relevant for any diffusion-limited reaction taking place on the surface in a microfluidic system.