Bundle Geometry Research Articles

Synthetic differential geometry of jet bundles

Synthetic differential geometry of jet bundles

On the Geometry of Lagrangian Submanifolds

We prove that a Lagrangian submanifold passes through each point of a symplectic manifold in the direction of arbitrary Lagrangian plane at this point. Generally speaking, such a Lagrangian submanifold is not unique; nevertheless, the set of all such submanifolds in Hermitian extension of a symplectic manifold of dimension greater than 4 for arbitrary initial data contains a totally geodesic submanifold (which we call the s-Lagrangian submanifold) iff this symplectic manifold is a complex space form. We show that each Lagrangian submanifold in a complex space form of holomorphic sectional curvature equal to c is a space of constant curvature c/4. We apply these results to the geometry of principal toroidal bundles.

Towards the design and computational characterization of a membrane protein

The design of a transmembrane four-helix bundle is described. We start with an idealized four-helix bundle geometry, then use statistical information to build a plausible transmembrane bundle. Appropriate residues are chosen using database knowledge on the sequences of membrane helices and loops, then the packing of the bundle core is optimized, and favorable side chain rotamers from rotamer libraries are selected. Next, we use explicit physical knowledge from biomolecular simulation force fields and molecular dynamics simulations to test whether the designed structure is physically possible. These procedures test whether the designed protein will indeed be α-helical, well packed and stable over a time scale of several nanoseconds in a realistic lipid bilayer environment. We then test a modeling approach that does not include sophisticated database knowledge about proteins, but rather relies on applying our knowledge of the physics that governs protein motions. This independent validation of the design is based on simulated annealing and restrained molecular dynamics simulation in vacuo, comparable to procedures used to refine NMR and X-ray structures.

Breakage induced by a grinding ball dropped onto a randomly packed particle bed

Within the Generation-IV (Gen-IV) International Forum, Atomic Energy of Canada Limited (AECL) is leading the effort in developing a conceptual design for the Canadian supercritical water-cooled reactor (SCWR). AECL proposed a new fuel bundle design with two rings of fuel elements placed between the central flow tube and the pressure tube. In the current paper, both the bare-rod and wire-wrapped bundle geometries were tested for the proposed fuel bundle design at 25 MPa using STAR-CCM + CFD code to predict the sheath temperature variation along the axial direction. SST k–ω and Reynolds-stress based turbulence models were compared with each other to assess their capability in predicting wall-to-fluid heat transfer in supercritical flows including the heat transfer deterioration (HTD) phenomenon. Using the turbulence model identified from the sensitivity analysis, the mesh refinement for the bare-rod geometry was performed in accordance with the ASME CFD numerical accuracy guidelines. Following these assessments, the recommended CFD model was then applied to simulate the Canadian SCWR fuel bundle with wire wraps. Predictions for the velocity and temperature variation in bare-rod and wire-wrapped geometries were compared. As a result of this study, it was found that wire wraps reduces the maximum temperature variation significantly for the current SCWR bundle design.

Electrostatic interaction between stereocilia: I. Its role in supporting the structure of the hair bundle

This paper provides theoretical estimates for the forces of electrostatic interaction between adjacent stereocilia in auditory and vestibular hair cells. Estimates are given for parameters within the measured physiological range using constraints appropriate for the known geometry of the hair bundle. Stereocilia are assumed to possess an extended, negatively charged surface coat, the glycocalyx. Different charge distribution profiles within the glycocalyx are analysed. It is shown that charged glycocalices on the apical surface of the hair cells can support spatial separation between adjacent stereocilia in the hair bundles through electrostatic repulsion between stereocilia. The charge density profile within the glycocalyx is a crucial parameter. In fact, attraction instead of repulsion between adjacent stereocilia will be observed if the charge of the glycocalyx is concentrated near the membrane of the stereocilia, thereby making this type of charge distribution unlikely. The forces of electrostatic interaction between stereocilia may influence the mechanical properties of the hair bundle and, being strongly non-linear, contribute to the non-linear phenomena that have been recorded from the periphery of the auditory and vestibular systems.

Structure and representations on the quantum supergroup OSPq(2|2n)

The structure and representations of the quantum supergroup OSPq(2|2n) are studied systematically. The algebra of functions on the quantum supergroup, which specifies the quantum supergroup itself, is taken to be the superalgebra generated by the matrix elements of the vector representation of the quantized universal superalgebra Uq(osp(2|2n)). It is shown that the algebra of functions is dense in the full dual Uq(osp(2|2n))* of Uq(osp(2|2n)) and possesses a Hopf superalgebra structure. The left integral and right integral on the quantum supergroup are discussed. Induced representations are developed using the noncommutative geometry of quantum homogeneous supervector bundles, and a geometric realization of irreducible representations is obtained.

Numerical Method for Simulation of Fluid Flow and Heat Transfer in Geometrically Disturbed Rod Bundles

This paper describes briefly the computational algorithm that includes procedures to obtain finite-difference form of governing convection-diffusion equations, to generate an orthogonal mesh system for complex regions and to solve the finite-difference equation system, and several results of numerical simulation in comparison with experiment. The Reynolds and energy conservation equations for steady-state fully developed turbulent incompressible flows are discretized by the Efficient Finite Difference (EFD) scheme. Here secondary flow components are neglected. In the averaged energy conservation equation, anisotropic turbulent conductivity coefficients are employed based on the axial velocity distribution. An orthogonal mesh generation system has been developed that allows us to model the rod bundle geometry by assembling elementary mesh components generated for every typical sub-domain inside the flow channels. This procedure has been made efficient with a help of object-oriented programming techniques. By solving the derived equations on the boundary-fitted coordinates, good comparisons between calculation and measurement are presented in general for detailed distributions of the local shear stress, axial velocity and wall temperature in a hexagonal rod bundle in the presence of a dislocated rod. Discussion is also made on a discrepancy of the calculated wall shear stress from the experimental data near the narrowest gap position in this “geometrically disturbed” region.

Particle geodesics and spectra in the spacetime tangent bundle

A limiting curvature of worldlines in spacetime serves as a possible basis for the differential geometry of the tangent bundle of spacetime. I first review briefly the resulting differential geometric structure of the spacetime tangent bundle. Next, I examine the relations between bundle geodesies and their projections on the spacetime base manifold. Possible classical particle equations of motion result from geodesic motion in the bundle manifold. Additionally, the Laplace-Beltrami operator is constructed on the bundle manifold. Possible particle spectra are represented by quantum fields that have a null eigenvalue when acted upon by the Laplace-Beltrami operator of the bundle manifold. The fields are shown to be automatically regularized by the limiting curvature of worldlines in spacetime, and particle spectra are shown to be cut off at very high energy.

Auditory sensitivity provided by self-tuned critical oscillations of hair cells.

We introduce the concept of self-tuned criticality as a general mechanism for signal detection in sensory systems. In the case of hearing, we argue that active amplification of faint sounds is provided by a dynamical system that is maintained at the threshold of an oscillatory instability. This concept can account for the exquisite sensitivity of the auditory system and its wide dynamic range as well as its capacity to respond selectively to different frequencies. A specific model of sound detection by the hair cells of the inner ear is discussed. We show that a collection of motor proteins within a hair bundle can generate oscillations at a frequency that depends on the elastic properties of the bundle. Simple variation of bundle geometry gives rise to hair cells with characteristic frequencies that span the range of audibility. Tension-gated transduction channels, which primarily serve to detect the motion of a hair bundle, also tune each cell by admitting ions that regulate the motor protein activity. By controlling the bundle's propensity to oscillate, this feedback automatically maintains the system in the operating regime where it is most sensitive to sinusoidal stimuli. The model explains how hair cells can detect sounds that carry less energy than the background noise.

TOROIDAL DNA: TOPOLOGY, GEOMETRY AND ELECTROSTATICS

Toroidal DNA condensates have received considerable attention as a model of ordered DNA condensation. Geometry and topology of fibre bundles can be efficient tools in order to study these structures. Such methods have given fruitful results when considering toroidal vesicles made of amphiphile films and blue phases structures observed in liquid crystals made of long chiral molecules. We give, in this paper, the geometrical arguments supporting this description. Then, we show how electrostatic interactions could be studied using curved spaces. We show that it is possible to have conditions resulting in attractive interaction between DNA molecules in the presence of positive charges.

Experimental evaluation of a model for oxygen exchange in a pulsating intravascular artificial lung.

Intravascular oxygenation and carbon dioxide removal remains a potentially attractive means for respiratory support in patients with acute or chronic respiratory failure. Our group has been developing an intravascular hollow fiber artificial lung that uses a pulsating balloon located within the fiber bundle to augment gas transfer. We previously reported on a simple compartmental model for simulating O2 exchange in pulsating intravascular artificial lungs. In this study we evaluate the O2 exchange model with gas exchange and PO2 measurements performed on an idealized intravascular artificial lung (IIVAL) tested in a water perfusion loop. The IIVAL has well-defined bundle geometry and can be operated in balloon pulsation mode, or a steady perfusion mode for determining the mass transfer correlation required by the model. The O2 exchange rates and compartmental O2 tensions measured with balloon pulsation in the IIVAL are within 10% of model predictions for flow and pulsation conditions relevant to intravascular oxygenation. The experiments confirmed that a significant buildup of PO2 occurs within the fiber bundle, which reduces the O2 exchange rate. The agreement between experiments and predictions suggests that the model captures the cardinal processes dictating gas transfer in pulsating intravascular artificial lungs.

Enlarged geometries of gauge bundles

The geometrical picture of gauge theories must be enlarged when a gauge potentialceases to behave like a connection, as it does in electroweak interactions. Whenthe gauge group has dimension four, the vector space isomorphism betweenspacetime and the gauge algebra is realized by a tetrad-like field. The objectmeasuring the deviation from a strict bundle structure has the formal behaviorof a spacetime connection, of which the deformed gauge field strength is thetorsion. A generalized derivative emerges in terms of which the two Bianchiidentities are formally recovered. Effects of gravitational type turn up. Thedynamical equations obtained correspond to a broken gauge model on acurved spacetime.

On differential geometry of tangent and cotangent bundles of Riemannian manifold

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Gauge geometry of financial markets

In this paper we show that financial markets have their own intrinsic underlying geometrical structure: fibre bundle geometry. This structure allows one to formulate a local gauge symmetry of rescaling of asset units in geometrical terms. We take this into account during the course of model construction, thus providing financial economics with physical methodology.

Turbulence Simulation in Tube Bundle Geometries Using the Dynamic Subgrid-Scale Model

The dynamic subgrid-scale (DSGS) closure model is used in a large eddy simulation computer program for incompressible isothermal flows. One of the advantages of the DSGS model is the exclusion of a model coefficient. This model coefficient is evaluated dynamically at each nodal location for a given time step by filtering operations on the grid level and a test filter level. A nonstaggered array tube bundle geometry arrangement is considered in doubly periodic boundary conditions for two-dimensional simulations at high Reynolds number. Results of the DSGS simulation are obtained in the form of power spectral densities and visualization of flow characteristics. The DSGS model simulation results are compared to the Smagorinsky eddy viscosity model simulation and available experimental data. The DSGS model simulation is found to be in good agreement with spectral data available from experiments in similar bundle arrangements. Coherent eddy structures were observed. Body forces acting on the tubes showed satisfactory characteristics. Integral length and timescales are evaluated using correlation functions that describe the turbulence structure. The applicability of large eddy simulation to complex engineering flow situations has been shown using the DSGS model with applications to steam generator bundles for understanding of flow-induced vibration problems revealing the physical phenomena of the flow.

KNITTED CARBON FIBER REINFORCED THERMOPLASTICS

The paper provides an overview over a 4 years research work embedded in the framework of a BRITEEURAM Project. In this study, PEEK and PA12 as matrix systems intermingled with the carbon fiber yarns, either continuous or staple spun yarns, were investigated. Structure-properties relations of knitted fabric reinforced composites were elucidated varying systematically, fiber content, number of knit layers, yarn and matrix properties. The 3-dimensional fiber orientation in the composite was assessed by reconstruction of the bundle geometry from stacked cross sections. Static tensile and bending properties were determined at various angles between wale and course direction indicating a strong correlation between these properties and the respective knit orientation. Fatigue tests revealed a considerable influence of the yarn properties indicating a higher fatigue resistance for staple yarns than for continuous yarns. Fracture mechanical as well as impact failure studies supported the importance of the fiber bundle for the understanding of the properties of the composite and they proved the insensitivity of these materials against delamination and notch effects.

Integral manifolds of contact distributions

The existence of an integral manifold of the contact distribution (a Legendre submanifold) that passes through an arbitrary point in a contact manifold , in an arbitrary totally real -dimensional direction is established. A Legendre submanifold with these initial data is not unique in general, but in the case of a -contact manifold of dimension greater than 5 the set of these submanifolds is shown to contain a totally geodesic submanifold (which is called a Blair submanifold in the paper) if and only if this -contact manifold is a Sasakian space form. Each Blair submanifold of a Sasakian space form of -holomorphic sectional curvature is a space of constant curvature . Applications of these results to the geometry of principal toroidal bundles are found.

Bundle-Flowline Thermal Analysis

Summary The bundle flowline involves packaging multiple flowlines, control, and injection lines within a single carrier pipe. A bundle is claimed to provide an effective means of insulating flowlines by use of low-cost materials; however, no rigorous heat transfer analysis of bundled flowline systems has been offered by the literature or the vendors. For this reason, the thermal performance of bundle- insulated flowlines has been studied with a general-purpose, finite- element, partial-differential equation solver. Steady-state and transient cooldown performance were analyzed for six different bundle configurations. Overall heat transfer coefficients for individual flowlines within a bundle have been determined in addition to cooldown performance for different insulation levels and pipe sizes. These results have been compared with results obtained for the simple bundle geometry of a pipe-in-pipe system, and found comparable. To expedite the calculation of overall heat transfer coefficients for bundle flowlines, simplified heat transfer calculations were developed as an approximation to the finite-element solutions. These approximations are on the average within 5% of the finite- element solution.

Spinors and field interactions in higher order anisotropic spaces

We formulate the theory of field interactions with higher order anisotropy. The concepts of higher order anisotropic space and locally anisotropic space (in brief, ha-space and la-space) are introduced as general ones for various types of higher order extensions of Lagrange and Finsler geometry and higher dimension (Kaluza-Klein type) spaces. The spinors on ha-spaces are defined in the framework of the geometry of Clifford bundles provided with compatible nonlinear and distinguished connections and metric structures (d-connection and d-metric). The spinor differential geometry of ha-spaces is constructed. There are discussed some related issues connected with the physical aspects of higher order anisotropic interactions for gravitational, gauge, spinor, Dirac spinor and Proca fields. Motion equations in higher order generalizations of Finsler spaces, of the mentioned type of fields, are defined by using bundles of linear and affine frames locally adapted to the nonlinear connection structure.

Assessment of a tube-based bundle CHF prediction method using a subchannel code

At the conceptual design stage for advanced water-cooled reactors (AWCRs), a general critical heat flux (CHF) prediction method with a wide applicable range and reasonable accuracy is essential to the thermal-hydraulic design and safety analysis. A basic idea for general CHF prediction is to utilize the tube-based CHF models covering wide applicable ranges with the help of supplementary terms for bundle effects. In this study, feasibility assessments have been performed with the bundle CHF data relevant to pressurized water reactors. A subchannel analysis is adopted in order to be able to consider the geometrical variations properly even in untested fuel bundle geometries. As a result, a CHF look-up table method (i.e., the use of a round tube CHF table with appropriate bundle effect factors) turns out to be a promising way to fulfill the needs in many aspects among some selected correlations and theoretical models. Though improvements of the supplementary factors, especially for the cold wall and the bundle heated length effects, are desirable to make better predictions, the tube-based bundle CHF prediction method clearly shows a potential as a general CHF predictor.