Smooth Geometry Research Articles

Probabilistic prediction of minimum fatigue life behaviour in α + β titanium alloys

AbstractThe objective of this work was to develop and demonstrate a probabilistic life prediction method for the prediction of minimum fatigue lives that are typically used in the design of fracture critical rotating turbine engine components. A Monte Carlo analysis was used to predict the variability in fatigue lives based on the distribution of microstructural features that lead to early crack initiation as well as the variability in small fatigue crack growth rates. Two titanium alloys, both with bimodal microstructures, were tested and analysed in this study. The distribution of critical microstructural features was calibrated based on test results and understanding of microstructure neighbourhood effects. Testing was conducted on both alloys and included both smooth and notched specimens. The predictions are presented and compared with the data for smooth and notch geometries for the various loading conditions. A parametric study was performed to identify the importance of several model inputs and to identify areas for future improvement.

Black holes in presence of cosmological constant: second order in frac{1}{D}

We have extended the results of [1] upto second subleading order in an expansion around large dimension D. Unlike the previous case, there are non-trivial metric corrections at this order. Due to our ‘background-covariant’ formalism, the dependence on Ricci and the Riemann curvature tensor of the background is manifest here. The gravity system is dual to a dynamical membrane coupled with a velocity field. The dual membrane is embedded in some smooth background geometry that also satisfies the Einstein equation in presence of cosmological constant. We explicitly computed the corrections to the equation governing the membrane-dynamics. Our results match with earlier derivations in appropriate limits. We calculated the spectrum of QNM from our membrane equations and matched them against similar results derived from gravity.

Robust multigrid solvers for the biharmonic problem in isogeometric analysis

In this paper, we develop multigrid solvers for the biharmonic problem in the framework of isogeometric analysis (IgA). In this framework, one typically sets up B-splines on the unit square or cube and transforms them to the domain of interest by a global smooth geometry function. With this approach, it is feasible to set up H2-conforming discretizations. We propose two multigrid methods for such a discretization, one based on Gauss–Seidel smoothing and one based on mass smoothing. We prove that both are robust in the grid size, the latter is also robust in the spline degree. Numerical experiments illustrate the convergence theory and indicate the efficiency of the proposed multigrid approaches, particularly of a hybrid approach combining both smoothers.

A Hybridizable Discontinuous Galerkin solver for the Grad–Shafranov equation

In axisymmetric fusion reactors, the equilibrium magnetic configuration can be expressed in terms of the solution to a semi-linear elliptic equation known as the Grad–Shafranov equation, the solution of which determines the poloidal component of the magnetic field. When the geometry of the confinement region is known, the problem becomes an interior Dirichlet boundary value problem. We propose a high order solver based on the Hybridizable Discontinuous Galerkin method. The resulting algorithm (1) provides high order of convergence for the flux function and its gradient, (2) incorporates a novel method for handling piecewise smooth geometries by extension from polygonal meshes, (3) can handle geometries with non-smooth boundaries and x-points, and (4) deals with the semi-linearity through an accelerated two-grid fixed-point iteration. The effectiveness of the algorithm is verified with computations for cases where analytic solutions are known on configurations similar to those of actual devices (ITER with single null and double null divertor, NSTX, ASDEX upgrade, and Field Reversed Configurations).

Entropy solution at concave corners and ridges, and volume boundary layer tangential adaptivity

Two particular aspects of volume boundary layer mesh generation applied to non smooth geometries are considered in this work. First, the treatment of concave ridges and corners is tackled from a generic viewpoint. Entropy satisfying elements are generated where shocks form in the volume. This proves useful to avoid premature halt of the boundary layer, and therefore potential jumps in the normal size. The connection with the Voronoi diagram is commented. Second, boundary layer adaptivity in the tangential plane is considered to honor arbitrary sizing prescription, and avoid size mismatch between the boundary layer and the isotropic sizing.It is shown that a strict semi-structured framework has to be abandoned in general to accommodate changes in the mesh topology. Size transition between boundary layer and fully unstructured anisotropic mesh is automatically taken into account. Both the concavity problem and the tangential adaptivity are presented together, since they require similar mesh operators. Various numerical examples illustrate the method.

The curvature line parametrization from circular nets on a surface

We study local and global approximations of smooth nets of curvature lines and smooth conjugate nets by discrete nets (circular nets and planar quadrilateral nets, respectively) with edges of order ϵ. Both smooth and discrete geometries are described by integrable systems. It is shown that one can obtain an order ϵ2 approximation globally with points of the discrete nets on the smooth surface. A new simple geometric construction of principal directions of smooth surfaces is given.

Cosmological Constant from Condensation of Defect Excitations

A key challenge for many quantum gravity approaches is to construct states that describe smooth geometries on large scales. Here we define a family of (2+1)-dimensional quantum gravity states which arise from curvature excitations concentrated at point like defects and describe homogeneously curved geometries on large scales. These states represent therefore vacua for three-dimensional gravity with different values of the cosmological constant. They can be described by an anomaly-free first class constraint algebra quantized on one and the same Hilbert space for different values of the cosmological constant. A similar construction is possible in four dimensions, in this case the curvature is concentrated along string-like defects and the states are vacua of the Crane-Yetter model. We will sketch applications for quantum cosmology and condensed matter.

Estimation of the solid circulation rate in circulating fluidized bed systems

The results of experiments performed in four different fluidized bed units (two pilot plants and two cold flow models, with a wide range of operating conditions) together with correlations from literature are used to establish methods to estimate the solid circulation rate in a circulating fluidized bed system. The estimation is based on the measured pressure drop in the upper part of the riser as well as particle properties and geometry of the riser exit. Investigations included smooth as well as abrupt riser exit configurations.In case of a smooth riser exit geometry (direct gas solids separation exit), the assumption of a uniformly upflow of solids in the riser is sufficient for the estimation of the solid circulation rate. Further, for an abrupt exit (L-shape exit), two methods were developed. Both methods are based on the assumption that the rate of reflected particles at the top of the riser increases with the so-called exit Froude number. One method is based on a correlation between interstitial gas velocity in the riser, slip velocity, mean particle velocity in the riser, and exit Froude number where it was possible to keep the difference between measured and estimated solid circulation rate in the range of approximately +75% and −40%. Further, this method is not able to consider the local mass flow distribution in the riser. For the other method, the output of a detailed mathematical model, based on information from literature, was used to establish a correlation between, exit Froude number, exit reflecting coefficient and local mass flow to estimate the solid circulation rate. Using this method it was possible to keep the difference between measured and estimated solid circulation rate in the range of ±40%. For both methods, the accuracy of the measurement of the pressure drop in the upper part of the riser is a significant parameter for the prediction of the solid circulation rate.

The Â-genus as a Projective Volume form on the Derived Loop Space

In the present work, we extend our previous work with Gwilliam by realizing $\hat {A}(X)$ as the projective volume form associated to the BV operator in our quantization of a one-dimensional sigma model. We also discuss the associated integration/expectation map. We work in the formalism of L ∞ spaces, objects of which are computationally convenient presentations for derived stacks. Both smooth and complex geometry embed into L ∞ spaces and we specialize our results in both of these cases.

The holographic shape of entanglement and Einstein\u2019s equations

We study shape-deformations of the entanglement entropy and the modular Hamiltonian for an arbitrary subregion and state (with a smooth dual geometry) in a holographic conformal field theory. More precisely, we study a double-deformation comprising of a shape deformation together with a state deformation, where the latter corresponds to a small change in the bulk geometry. Using a purely gravitational identity from the Hollands-Iyer-Wald formalism together with the assumption of equality between bulk and boundary modular flows for the original, undeformed state and subregion, we rewrite a purely CFT expression for this double deformation of the entropy in terms of bulk gravitational variables and show that it precisely agrees with the Ryu-Takayanagi formula including quantum corrections. As a corollary, this gives a novel, CFT derivation of the JLMS formula for arbitrary subregions in the vacuum, without using the replica trick. Finally, we use our results to give an argument that if a general, asymptotically AdS spacetime satisfies the Ryu-Takayanagi formula for arbitrary subregions, then it must necessarily satisfy the non-linear Einstein equation.

The generalized finite difference method for an inverse time-dependent source problem associated with three-dimensional heat equation

This paper presents a meshless numerical scheme for recovering the time-dependent heat source in general three-dimensional (3D) heat conduction problems. The problem considered is ill-posed and the determination of the unknown heat source is achieved here by using the boundary condition, initial condition and the extra measured data from a fixed point placed inside the domain. The extra measured data are used to guarantee the uniqueness of the solution. The generalized finite difference method (GFDM), a recently-developed meshless method, is then adopted to solve the resulting time-dependent boundary-value problem. In our computations, the second-order Crank–Nicolson scheme is employed for the temporal discretization and the proposed GFDM for the spatial discretization. Several benchmark test problems with both smooth and piecewise smooth geometries have been studied to verify the accuracy and efficiency of the proposed method. No need to apply any well-known regularization strategy, the accurate and stable solution could be obtained with a comparatively large level of noise.

Flow over a realistic car model: Wall modeled large eddy simulations assessment and unsteady effects

Numerical simulations are carried out on the flow over a realistic generic car geometry, the DrivAer-fastback car model. Pure large eddy simulations (LES) and wall-modeled large eddy simulations (WMLES) are used and compared to numerical and experimental results to assess the validity of these approaches when solving the flow field around complex automotive geometries. Results show a 70% CPU time reduction when using the wall model. Drag coefficient results show the influence of the wall model on coarser meshes is positive, reducing the difference on those obtained using finer meshes. Pressure profiles exhibit mixed results. The wall model used works well in adverse pressure gradients and smooth geometry changes. Results worsen in sections where the flow detaches and experiences large pressure drops. Flow structures and unsteady effects around the car are also analyzed, obtaining several characteristic frequencies for the different flow structures encountered. It should be noted that the present investigation shows how WMLES helps to reduce the computing cost and response vs pure LES, while providing high-quality unsteady data, although computational cost remains high. Results show potential in the introduction of this tool as a competitive simulation strategy for complex geometries.

Negative branes, supergroups and the signature of spacetime

We study the realization of supergroup gauge theories using negative branes in string theory. We show that negative branes are intimately connected with the possibility of timelike compactification and exotic spacetime signatures previously studied by Hull. Isolated negative branes dynamically generate a change in spacetime signature near their worldvolumes, and are related by string dualities to a smooth M-theory geometry with closed timelike curves. Using negative D3-branes, we show that SU(0|N) supergroup theories are holographically dual to an exotic variant of type IIB string theory on {mathrm{dS}}_{3,2}times {overline{mathrm{S}}}^5 , for which the emergent dimensions are timelike. Using branes, mirror symmetry and Nekrasov’s instanton calculus, all of which agree, we derive the Seiberg-Witten curve for mathcal{N}=2 SU(N |M ) gauge theories. Together with our exploration of holography and string dualities for negative branes, this suggests that supergroup gauge theories may be non-perturbatively well-defined objects, though several puzzles remain.

One thousand and one bubbles

We propose a novel strategy that permits the construction of completely general five-dimensional microstate geometries on a Gibbons-Hawking space. Our scheme is based on two steps. First, we rewrite the bubble equations as a system of linear equations that can be easily solved. Second, we conjecture that the presence or absence of closed timelike curves in the solution can be detected through the evaluation of an algebraic relation. The construction we propose is systematic and covers the whole space of parameters, so it can be applied to find all five-dimensional BPS microstate geometries on a Gibbons-Hawking base. As a first result of this approach, we find that the spectrum of scaling solutions becomes much larger when non-Abelian fields are present. We use our method to describe several smooth horizonless multicenter solutions with the asymptotic charges of three-charge (Abelian and non-Abelian) black holes. In particular, we describe solutions with the centers lying on lines and circles that can be specified with exact precision. We show the power of our method by explicitly constructing a 50-center solution. Moreover, we use it to find the first smooth five-dimensional microstate geometries with arbitrarily small angular momentum.

Asymptotic expansions and effective boundary conditions: a short review for smooth and nonsmooth geometries with thin layers

Problems involving materials with thin layers arise in various application fields. We present here the use of asymptotic expansions for linear elliptic problems to derive and justify so-called ap-proximate or effective boundary conditions. We first recall the known results of the literature, and then discuss the optimality of the error estimates in the smooth case. For non-smooth geometries, the results of [18, 57] are commented and adapted to a model problem, and two improvements of the approximate model are proposed to increase its numerical performance.

Geometry of symplectic log Calabi–Yau pairs

We will survey some aspects of the smooth topology, algebraic geometry, symplectic geometry and contact geometry of anti-canonical pairs in complex dimension two.

Inviscid and RANS Simulation of the NASA-CRM Using the Cartesian Flow Solver UTCart

Inviscid and Reynolds-averaged Navier-Stokes (RANS) simulations of transonic flows around the NASA Common Research Model are conducted using the Cartesian flow solver UTCart. The immersed boundary method is used to represent the smooth geometry surfaces on the Cartesian grids. The wall function is combined with the immersed boundary method to reproduce the turbulent boundary layer on the geometry surface in the RANS simulations. In the inviscid calculations, the qualitative flow feature including the position on the shock-wave on the wing shows agreement with the reference result a body-fitted grid. In the RANS calculations, the trend of pitching moment and drag shows fair agreement with the reference result, while prediction of the flow separation at high angle of attack is still difficult. Compared with the reference result, the differences in the total drag coefficient at a moderate angle of attack on the medium grid (33 million cells) and the fine grid (99 million cells) are 31 drag counts (10%) and 20 drag counts (6.5%), respectively. Furthermore, each of the calculated aerodynamic coefficients shows a consistent trend of grid convergence toward the reference result.

Modern methods of railway track safety inspection

Railway and transit tracks are designed and constructed as smooth segments of straight lines and circular curves linked by transitional spirals. Dynamic traffic loads, material wear and environmental cycles gradually produce deviations in the track from the original smooth geometry. Such deviations lead to rough ride in the vehicles and furthermore higher dynamic vehicle-track interaction forces which lead to faster deviation growth. To monitor the geometric condition of the track and to guide maintenance and repair, hand tools were used to take consecutive measurements by track walkers. Modern state-of-the-art technology has since replaced the traditional slow and painful measurement practice. Inspections are now done from a moving vehicle at hundreds of km per hour without contacting the track. All track geometry parameters are measured up four times per meter; data are analysed in real time by onboard software to identify the location and magnitudes of deviations which exceeds the acceptable tolerance. Historical measurements are stored in databases which are used to establish degradation trends and to guide the planning of maintenance. With the help of high-speed imaging technology, automated video inspection systems are installed on some vehicles to detect other faults in the track structure. Four types of such modern inspection tools are introduced in the paper presentation. These are: a single-car comprehensive inspection vehicle; a dedicated inspection train; a highway-railway dual usage truck and an unmanned inspection system. Actual operational systems are used as examples to illustrate the design and capabilities of each of these types of inspection tools.

Modern methods of railway track safety inspection

Railway and transit tracks are designed and constructed as smooth segments of straight lines and circular curves linked by transitional spirals. Dynamic traffic loads, material wear and environmental cycles gradually produce deviations in the track from the original smooth geometry. Such deviations lead to rough ride in the vehicles and furthermore higher dynamic vehicle-track interaction forces which lead to faster deviation growth. To monitor the geometric condition of the track and to guide maintenance and repair, hand tools were used to take consecutive measurements by track walkers. Modern state-of-the-art technology has since replaced the traditional slow and painful measurement practice. Inspections are now done from a moving vehicle at hundreds of km per hour without contacting the track. All track geometry parameters are measured up four times per meter; data are analysed in real time by onboard software to identify the location and magnitudes of deviations which exceeds the acceptable tolerance. Historical measurements are stored in databases which are used to establish degradation trends and to guide the planning of maintenance. With the help of high-speed imaging technology, automated video inspection systems are installed on some vehicles to detect other faults in the track structure. Four types of such modern inspection tools are introduced in the paper presentation. These are: a single-car comprehensive inspection vehicle; a dedicated inspection train; a highway-railway dual usage truck and an unmanned inspection system. Actual operational systems are used as examples to illustrate the design and capabilities of each of these types of inspection tools.

Geometry effect on electrokinetic flow and ionic conductance in pH-regulated nanochannels

Semi-analytical solutions are obtained for the electrical potential, electroosmotic velocity, ionic conductance, and surface physicochemical properties associated with long pH-regulated nanochannels of arbitrary but constant cross-sectional area. The effects of electric double layer overlap, multiple ionic species, and surface association/dissociation reactions are all taken into account, assuming low surface potentials. The method of analysis includes series solutions which the pertinent coefficients are obtained by applying the wall boundary conditions using either of the least-squares or point matching techniques. Although the procedure is general enough to be applied to almost any arbitrary cross section, nine nanogeometries including polygonal, trapezoidal, double-trapezoidal, rectangular, elliptical, semi-elliptical, isosceles triangular, rhombic, and isotropically etched profiles are selected for presentation. For the special case of an elliptic cross section, full analytical solutions are also obtained utilizing the Mathieu functions. We show that the geometrical configuration plays a key role in determination of the ionic conductance, surface charge density, electrical potential and velocity fields, and proton enhancement. In this respect, the net electric charge and convective ionic conductance are higher for channels of larger perimeter to area ratio, whereas the opposite is true for the average surface charge density and mean velocity; the geometry impact on the two latest ones, however, vanishes if the background salt concentration is high enough. Moreover, we demonstrate that considering a constant surface potential equal to the average charge-regulated potential provides sufficiently accurate results for smooth geometries such as an ellipse at medium-high aspect ratios but leads to significant errors for geometries having narrow corners such as a triangle.