Smooth Geometry Research Articles

Hybrid modelling of low velocity zones in box culverts to assist upstream fish passage

A culvert is a covered channel designed to pass water through an embankment. The recognition of the adverse ecological impacts of culverts on upstream fish passage is driving the development of new culvert design guidelines, with a focus on small-bodied fish species seeking low velocity zones to minimise energy expenditure. Herein a hybrid modelling technique was applied, combining physical modelling, one-dimensional theoretical calculation and three-dimensional computational fluid dynamics modelling. The results reveal fundamental turbulent processes that may affect small-body-mass fish navigability and provide new insights for the development of standard box culvert design guidelines. Systematic validations were performed to a wide range of initial conditions and smooth barrel geometries. A physical relationship was derived from numerical and experimental data of past and present studies, correlating the dimensionless flow area with a normalised local velocity V/V.

Multilayer Airfoil Ice Accretion Simulations Using a Level-Set Method with B-Spline Representation

This paper presents a partial differential equation approach to model the icing front evolution on airfoils via the level-set equation, offering a high-fidelity alternative to common algebraic approaches. Furthermore, the automation of the multilayer icing process is achieved by using B-spline curves to improve the geometry representation, which is usually limited to linear segments. The B-splines are generated using a curve approximation algorithm based on an error-controlled knot insertion together with a least-square minimization process, allowing an adequate shape representation of the ice irregular features. The evolution of the level-set interface depends on the so-called icing velocity, which is computed locally in the field from the propagated surface ice mass accretion rate solution. Additionally, an explicit swept volume tracking method controls actively the global conservation of the ice volume. A verification phase is performed on analytical cases to highlight the characteristics of the methods and discretization schemes. Multilayer icing results are then presented on two cases and compared with experimental data providing a reasonable global mass error level in each case. Overall, the method shows great potential to model the ice geometry evolution in a globally conservative manner while ensuring a smooth geometry representation that improves multilayer automation.

Design of self-supporting surfaces with isogeometric analysis

Self-supporting surfaces are widely used in contemporary architecture, but their design remains a challenging problem. This paper aims to provide a heuristic strategy for the design of complex self-supporting surfaces. In our method, non-uniform rational B-spline (NURBS) surfaces are used to describe the smooth geometry of the self-supporting surface. The equilibrium state of the surface is derived with membrane shell theory and Airy stresses within the surfaces are used as tunable variables for the proposed heuristic design strategy. The corresponding self-supporting shapes to the given stress states are calculated by the nonlinear isogeometric analysis (IGA) method. Our validation using analytic catenary surfaces shows that the proposed method finds the correct self-supporting shape with a convergence rate one order higher than the degree of the applied NURBS basis function. Tests on boundary conditions show that the boundary’s influence propagates along the main stress directions in the surface. Various self-supporting masonry structures, including models with complex topology, are constructed using the presented method. Compared with existing methods such as thrust network analysis and dynamic relaxation, the proposed method benefits from the advantages of NURBS-based IGA, featuring smooth geometric description, good adaption to complex shapes and increased efficiency of computation.

A framework for biomechanics simulations using four-chamber cardiac models

Computational cardiac models have been extensively used to study different cardiac biomechanics; specifically, finite-element analysis has been one of the tools used to study the internal stresses and strains in the cardiac wall during the cardiac cycle. Cubic-Hermite finite element meshes have been used for simulating cardiac biomechanics due to their convergence characteristics and their ability to capture smooth geometries compactly–fewer elements are needed to build the cardiac geometry–compared to linear tetrahedral meshes. Such meshes have previously been used only with simple ventricular geometries with non-physiological boundary conditions due to challenges associated with creating cubic-Hermite meshes of the complex heart geometry. However, it is critical to accurately capture the different geometric characteristics of the heart and apply physiologically equivalent boundary conditions to replicate the in vivo heart motion. In this work, we created a four-chamber cardiac model utilizing cubic-Hermite elements and simulated a full cardiac cycle by coupling the 3D finite element model with a lumped circulation model. The myocardial fiber-orientations were interpolated within the mesh using the Log-Euclidean method to overcome the singularity associated with interpolation of orthogonal matrices. Physiologically equivalent rigid body constraints were applied to the nodes along the valve plane and the accuracy of the resulting simulations were validated using open source clinical data. We then simulated a complete cardiac cycle of a healthy heart and a heart with acute myocardial infarction. We compared the pumping functionality of the heart for both cases by calculating the ventricular work. We observed a 20% reduction in acute work done by the heart immediately after myocardial infarction. The myocardial wall displacements obtained from the four-chamber model are comparable to actual patient data, without requiring complicated non-physiological boundary conditions usually required in truncated ventricular heart models.

Gravity from micro-equilibration

We suggest a mechanism for the emergence of classical dynamical spacetime from an underlying quantum gravitational system. This is an example of a more general process, which we name micro-equilibration, and which can be thought of as local thermalization of entanglement. Applied in the context of the AdS/CFT correspondence, we propose that this dynamical process underlies generic evolution towards CFT states whose gravitational dual describes smooth bulk geometries. Hence, contrary to common expectation, such “geometric” CFT states are in fact typical in this sense. Correspondingly, they can be characterized by a specific universal entanglement structure resulting from micro-equilibration of a generic quantum state.

Gravitational instabilities and censorship of large scalar field excursions

Large, localized variations of light scalar fields tend to collapse into black holes, dynamically “censoring” distant points in field space. We show that in some cases, large scalar excursions in asymptotically flat spacetimes can be UV-completed by smooth Kaluza-Klein bubble geometries, appearing to circumvent 4d censorship arguments. However, these spacetimes also exhibit classical instabilities related to the collapse or expansion of a bubble of nothing, providing a different censorship mechanism. We show that the Kerr family of static KK bubbles, which gives rise to an infinite scalar excursion upon dimensional reduction, is classically unstable. We construct a family of initial data in which the static bubbles sit at a local maximum of the energy, and we give a general argument that such a property indeed indicates mechanical instability in gravity. We also discuss the behavior of wound strings near a bubble, a local probe of the large traversal through moduli space.

Holographic Renyi entropy from quantum error correction

We study Renyi entropies Sn in quantum error correcting codes and compare the answer to the cosmic brane prescription for computing {tilde{S}}_nequiv {n}^2{partial}_nleft(frac{n-1}{n}{S}_nright) . We find that general operator algebra codes have a similar, more general prescription. Notably, for the AdS/CFT code to match the specific cosmic brane prescription, the code must have maximal entanglement within eigenspaces of the area operator. This gives us an improved definition of the area operator, and establishes a stronger connection between the Ryu-Takayanagi area term and the edge modes in lattice gauge theory. We also propose a new interpretation of existing holographic tensor networks as area eigenstates instead of smooth geometries. This interpretation would explain why tensor networks have historically had trouble modeling the Renyi entropy spectrum of holographic CFTs, and it suggests a method to construct holographic networks with the correct spectrum.

Thermal design optimization of passive cooling capability in a dry-storage system by adding wall undulations or semi-circular fins

Thermal design investigation of a novel liner inner wall surface geometry alteration of a ventilated concrete cask used for spent nuclear fuel storage is carried out through three-dimensional Computational Fluid Dynamics (CFD) simulations. The present study reveals that the new proposal returns values for the convective heat transfer coefficient that are almost three orders of magnitude higher than the base case. Hence, proving that even making such a rather simple alterations to the smooth walls geometry, i.e. adding undulations or semi-circular fins, can result in a significant convective heat transfer enhancement, therefore, further reducing the risks of structural damages caused by the dry-storage system overheating. Before conducting the design optimization study mentioned above, two validation test cases have been considered in order to examine the Reynolds Averaged Navier-Stokes (RANS) models’ capability to predict the flow under buoyancy driven and low turbulence levels such is the case in the passively cooled dry cask system. The test cases considered in the validation study sections are the experimental measurements of Betts and Bokhari for turbulent natural convection in an enclosed tall cavity and the temperature measurements in concrete-shielded spent fuel storage cask system reported by McKinnon. The models selected for the validation study are namely the k-ω SST model, the v2-f model, the low-Reynolds k-ε model, and the recently formulated elliptic blending k-ε model. It has been found that out of these models, the low-Reynolds k-ε model was found to provide a good combination in returning both; physically realistic and conservative solution. The present validation using well-resolved RANS simulations has shown that a more quantitative and detailed comparison of the predictions is required in order to clearly highlight the discrepancies between the models’ predictions in terms of velocity, turbulent kinetic energy and, in particular, convective heat transfer coefficient profiles. The commonly adopted methodology in limiting the validation process to temperature profiles comparison only, would cover up these differences as the temperature variation is affected by the combined effects of the convective and the radiation heat transfer modes.

Early scrambling and capped BTZ geometries

Geodesic probes in certain horizonless microstate geometries experience extreme tidal forces long before reaching the region where these geometries differ significantl from the extremal BTZ black hole. The purpose of this paper is to show that this behavior is a universal feature of all geometries that have a long BTZ throat that terminates in a cap, regardless of the details of this cap. Hence, incoming probes will scramble into the microstate structure before they encounter the region where the charges of the solution are sourced, and the reason for this premature scrambling is the amplification of tiny geometrical deviations by the relativistic speeds of the probes. To illustrate the phenomenon, we construct a new family of smooth horizonless superstratum microstate geometries, dual to D1-D5 CFT states whose momentum charge is carried by excitations on CFT strands of length k. We also show that, in the large-k limit, these new superstrata resemble a blackened supertube solution everywhere except in the near-supertube region. Thus they resolve the singularity caused by the naive back-reaction of modes with non-linear instabilities near evanescent ergosurfaces.

A direct Chebyshev collocation method for the numerical solutions of three-dimensional Helmholtz-type equations

In this study, a new framework for the numerical solutions of inhomogeneous Helmholtz-type equations on three-dimensional (3D) arbitrary domains is presented. A Chebyshev collocation scheme (CCS) is introduced for the efficient and accurate approximation of particular solution for the given 3D boundary value problem. We collocate the numerical scheme at the Gauss–Lobatto nodes to ensure the pseudo-spectral convergence of the Chebyshev interpolation. After the particular solution is evaluated, the introduced CCS is coupled with a two-stage and one-stage numerical schemes to evaluate the final solutions of the given problem. In the two-stage approach, the given inhomogeneous problem is converted to a homogeneous equation and then the boundary-type methods, such as the method of fundamental solutions (MFS), can be used to evaluate the resulting homogeneous solutions. In the one-stage scheme, by imposing the boundary conditions directly to the CCS procedure, the final solutions of the given inhomogeneous problem can be obtained straightforward without the need of using the MFS or other boundary methods to find the homogeneous solution. Two benchmark numerical examples in both smooth and piecewise smooth 3D geometries are presented to demonstrate the applicability and efficiency of the proposed method.

Comparison of advanced discretization techniques for image-based modelling of heterogeneous porous rocks

This contribution presents an assessment of computational techniques enabling automated simulations of complex porous rocks microstructures based on 3D imaging techniques. A subset of a CT-scanned sandstone sample is used to compare the results obtained by two advanced discretization frameworks. Raw scan results are processed by a level-set-based segmentation technique to produce smooth geometries prone to finite element discretizations. A recently developed technique is outlined for conforming mesh generation for complex porous geometries described implicitly by functions. This allows generating high-quality tetrahedral meshes with selective refinement. Next to this, a technique that uses a kinematic enrichment by incompatible modes to represent the heterogeneous geometry is explained. Both techniques use the same implicit geometry as main input for the simulations. Mechanical simulations are conducted on a subset of a scanned sample of a sandstone under triaxial loading conditions for isotropic compressive loading and for loading conditions involving a stress deviator. The results are compared and discussed based on local stress distributions and on a Mohr–Coulomb criterion with tensile cut-off. The results show that both discretization strategies yield complementary tools and allow envisioning automated simulations based on raw CT scan data for porous rocks exhibiting complex pore space morphologies.

Supercharging superstrata

We construct a new class of smooth horizonless microstate geometries of the supersymmetric D1-D5-P black hole in type IIB supergravity. We first work in the AdS3 × S3 decoupling limit and use the fermionic symmetries of the theory to generate new momentum carrying perturbations in the bulk that have an explicit CFT dual description. We then use the supergravity equations to calculate the backreaction of these perturbations and find the full non-linear solutions both in the asymptotically AdS and asymptotically flat case. These new geometries have a simpler structure than the previously known superstrata solutions.

Deep Vascular Phenotyping in Patients With Renal Multifocal Fibromuscular Dysplasia.

Arterial fibromuscular dysplasia is a nonatherosclerotic, noninflammatory vascular disease, whose pathophysiology is still unknown. We performed deep image-based vascular phenotyping of nonaffected arteries to look for systemic vascular alterations in fibromuscular dysplasia. This single center cross-sectional study included 50 patients with multifocal renal fibromuscular dysplasia, 50 hypertensive patients, and 50 healthy controls, matched for age, sex, and ethnicity; hypertensive patients were matched also for blood pressure. Brachial artery endothelium-dependent and endothelium-independent dilation were studied by echotracking. Aortic stiffness was assessed by carotid-to-femoral pulse wave velocity. We quantified the presence of supernumerary acoustic interfaces within the common carotid wall by the triple signal (TS) score. We plotted the Young incremental elastic modulus/stress curves for common carotid artery, derived from echotracking and tonometry. Patients with fibromuscular dysplasia had impaired endothelium-independent dilation (adjusted P=0.002), smaller brachial artery diameter but comparable endothelium-dependent dilation and aortic stiffness. The prevalence of TS score >6 was 56%, 40%, 24% in patients with fibromuscular dysplasia, hypertensives, and controls, respectively ( P=0.005). Fibromuscular dysplasia remained significantly associated with TS in the multiple regression model ( P=0.022). Impaired endothelium-dependent dilation was present only in patients with fibromuscular dysplasia, TS score >6 ( P=0.047). Incremental elastic modulus was higher for a given wall stress (80 kPa) in the presence of a TS score >6, especially in fibromuscular dysplasia. In conclusion, nonclinically affected large- and medium-sized arteries in patients with multifocal renal fibromuscular dysplasia exhibit a cluster of diffuse alterations in smooth muscle cell function, arterial geometry, wall characteristics, and mechanical properties. Clinical Trial Registration URL: http://www.clinicaltrials.gov . Unique identifier: NCT01935752.

Depth-to-basement for the East European Craton and Teisseyre-Tornquist Zone in Poland based on potential field data

Results of a depth-to-basement study are presented for the East European Craton and the Teisseyre-Tornquist Zone (TTZ) in Poland. The terrestrial gravity data are inverted for the top of the Paleoproterozoic basement and, independently, for the top of the Ediacaran using seismic horizons from the PolandSPAN™ seismic survey and well tops as input depth measurements. The depth to the Ediacaran modelling was additionally extended to cover the Łysogóry Block and northern Małopolska Block. The results are visualised as isobath maps for the top of the Paleoproterozoic basement and top of the Ediacaran and an isopach map for the Ediacaran, supplemented with qualitative structural interpretation based on gravity and magnetic data. The results of modelling show a smooth crystalline basement slope within the TTZ with the top of the Paleoproterozoic basement uniformly descending south-westwards by 10–14 km. The thickness of the Ediacaran in SE Poland increases in the same direction to more than 10 km within the TTZ. Such a crustal architecture, in combination with the earlier documented Moho elevation of 4–6 km, reveals significant thinning of the Paleoproterozoic crust within the TTZ to form a crustal necking zone due to the Ediacaran rifting. A smooth geometry of the top of basement along with the lack of basement-rooted faults suggests a ductile mode of crustal thinning during rifting of Rodinia. Moreover, the development of the NW–SE-oriented rift, a precursor of the Tornquist Ocean, was associated with rifting in a NE–SW direction parallel to the Orsha-Volyn Rift.

Kähler-Dirac fermions on Euclidean dynamical triangulations

We study K\"ahler-Dirac fermions on Euclidean dynamical triangulations. This fermion formulation furnishes a natural extension of staggered fermions to random geometries without requring vielbeins and spin connections. We work in the quenched approximation where the geometry is allowed to fluctuate but there is no back-reaction from the matter on the geometry. By examining the eigenvalue spectrum and the masses of scalar mesons we find evidence for a four fold degeneracy in the fermion spectrum in the large volume, continuum limit. It is natural to associate this degeneracy with the well known equivalence in continuum flat space between the K\"ahler-Dirac fermion and four copies of a Dirac fermion. Lattice effects then lift this degeneracy in a manner similar to staggered fermions on regular lattices. The evidence that these discretization effects vanish in the continuum limit suggests both that lattice continuum K\"ahler-Dirac fermions are recovered at that point, and that this limit truly corresponds to smooth continuum geometries. One additional advantage of the K\"ahler-Dirac action is that it respects an exact $U(1)$ symmetry on any random triangulation. This $U(1)$ symmetry is related to continuum chiral symmetry. By examining fermion bilinear condensates we find strong evidence that this $U(1)$ symmetry is not spontaneously broken in the model at order the Planck scale. This is a necessary requirement if models based on dynamical triangulations are to provide a valid ultraviolet complete formulation of quantum gravity.

SiPM-based PET detector module for a 4π span scanner

Abstract Detectors in Positron Emission Tomography (PET) scanners are usually arranged in rings with the specimen lying along the axial direction. This distribution, however, does not maximize the geometrical sensitivity unless the axial extent becomes much longer than the axial Field of View (FOV), a very costly solution. The optimal geometry for a PET scanner is a sphere with the specimen located at the center. The state of the art of scintillator crystals and detectors for γ -rays does not facilitate smooth spherical geometry design. In this work we propose a PET scanner of 4 π steradian coverage for preclinical imaging as a proof of concept. As a first approximation to the ideal spherical topology, the scanner is shaped as an icosahedron. Furthermore we also present the new custom-tailored hexagonal Silicon Photomultiplier (SiPM) and a monolithic laser-engraved LYSO scintillator crystal that tiles the twenty scanner faces. Preliminary results of the scanner performance based on simulations point to enhanced sensitivity. Initial results on the characterization of the hexagonal photodetector by collection of pulses from a 22Na point source show similar performance as conventional square pixels with the benefit of the increased sensitivity and resolution.

An integrable geometrical foundation of gravity

In a talk at the conference Geometrical Foundations of Gravity at Tartu[Formula: see text] 2017, it was suggested that the affine spacetime connection could be associated with purely fictitious forces. This leads to gravitation in a flat and smooth geometry. Fermions are found to nevertheless couple with the metrical connection and a phase gauge field. The theory is reviewed in this proceeding in a Palatini, and in a metric-affine gauge formulation.

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.