Arbitrary Curvature Research Articles

Phase-field simulations of fission gas bubbles in high burnup UO2 during steady-state and LOCA transient conditions

To improve the economics of commercial light water reactors, increased understanding of UO2 nuclear fuel with the high burnup structure (HBS) is required in both steady-state and transient conditions. Here, a phase-field model of the fission gas bubble microstructure in nuclear fuel is developed based on the Kim-Kim-Suzuki (KKS) formulation and implemented in Idaho National Laboratory’s Marmot application for phase-field simulation of nuclear materials. The model includes the effects of gas pressure and the surface tension of the bubble-fuel matrix interface for arbitrary interfacial curvature. Simulations of bubble growth in the HBS region during steady-state conditions showed that initially overpressurized bubbles decreased in pressure during growth, but still remained above equilibrium pressure. During a loss-of-coolant accident (LOCA) transient, simulations of bubbles in the HBS region showed that bubble size did not change significantly. The bubble pressure in response to the LOCA transient was calculated for a variety of bubble sizes, initial pressures, and external restraint pressures.

Mixed Graph-FEM phase field modeling of fracture in plates and shells with nonlinearly elastic solids

This paper presents a mixed Graph-FEM (Finite Element Method) approach for the phase field modeling of fracture in plates and shells composed of nonlinearly elastic solids. In this approach, the finite element mesh is deemed equivalent to a typical graph in computer science. The equation for phase field evolution is thus discretized by a graph Laplacian on a curved surface. A corresponding solver is herein developed, considering the matrix sparsity of the discretized system, and constraining irreversible phase field variables (to values greater than zero and less than one). An alternating solution strategy between mechanical equilibrium and the phase field equation is proposed. Our method is then applied to the fracture of plates and shells of arbitrary curvature, exhibiting fast convergence and robustness compared with our previous work, as could be concluded from the several numerical benchmarks we performed. This method opens a new way to efficiently model the fracture of plates and shells, while utilizing conventional shell elements.

Vibroacoustic design optimization of curved composite shells

The need to simultaneously optimize the structural design properties, and attain a satisfactory vibroacoustic performance for composite structures, has been a challenging task for modern structural engineers. This work is aimed at developing a statistical energy analysis (SEA) based numerical scheme for computing the optimal design parameters of each individual layer of layered curved shells having arbitrary complexities and layering. The main novelty of the work focuses on the computation of SEA properties for curved composite shells and derive the sensitivities of the acoustic transmission coefficient, expressed through the computed SEA properties, with respect to the structural design characteristics to be optimized. A wave finite element approach is employed to calculate the wave propagation constants of the curved shell. The calculated wave constants are then applied to compute the vibroacoustic properties for the curved shell using a SEA approach. Sensitivity analyses are conducted on the vibroacoustic properties to estimate their response to changes in the structural properties. Gradient vector is then formulated and hence the Hessian matrix, which is employed to formulate a Newton-like optimisation algorithm for optimizing the properties of the layered composite shell. The developed scheme is applied to a sandwich shell; optimal design parameters of [Formula: see text] and [Formula: see text] are obtained for the facesheet and the core of the shell whose base parameters are [Formula: see text] and [Formula: see text], respectively. This simultaneously optimizes the structure with maximum stiffness and minimum mass and attains a satisfactory dynamic performance for acoustic transmission through the sandwich shell. The principal advantage of the scheme is the ability to accurately model composite panels of arbitrary curvature at a rational computational time.

Vibration analysis of thin-walled functionally graded sandwich beams with non-uniform polygonal cross-sections

In the paper, an analysis of thin-walled functionally graded straight and curved beams for general non-uniform polygonal cross-sections has been introduced for vibration problems. Higher order beam theory that has fully taken into account major deformations, e.g. in-plane distortion, out-of-plane warping, is adopted by means of beam frame modal approach. In addition with the effects of geometric parameters, the study also deals with some consequences resulting from material anisotropy which in turn tackles better in evaluation behaviors of thin-walled beams that enables analytical modeling to have the potential for further extension. Subsequently, the analysis can be applied for general closed cross-section beams with arbitrary curvatures whereas materials properties are assumed to be graded across the wall thickness following a predefined shape function. A numerical verification for the overall analysis and examples have been carried out based on the available results created from benchmark problems and finite element software simulation found in literature. Then, natural frequencies and vibrational mode shapes have been obtained through a robust framework of finite element method. Finally, a parametric study and discussion towards vibration phenomena are fully investigated referring to gradual law, skin-core-skin effects, etc.

Monte Carlo simulations and mean-field modeling of electric double layers at weakly and moderately charged spherical macroions.

Monte Carlo simulations are employed to determine the differential capacitance of an electric double layer formed by small size-symmetric anions and cations in the vicinity of weakly to moderately charged macroions. The influence of interfacial curvature is deduced by investigating spherical macroions, ranging from flat to moderately curved. We also calculate the differential capacitance using a previously developed mean-field model where, in addition to electrostatic interactions, the excluded volumes of the ions are taken into account using either the lattice-gas or the Carnahan-Starling equation of state. For both equations of state, we compare the mean-field model for arbitrary curvature with a recently developed second-order curvature expansion. Our Monte Carlo simulations predict an increase in the differential capacitance with growing macroion curvature if the surface charge density is small, whereas for moderately charged macroions the differential capacitance passes through a local minimum. Both mean-field models tend to somewhat overestimate the differential capacitance as compared with Monte Carlo simulations. At the same time, they do reproduce the curvature dependence of the differential capacitance, especially for small surface charge density. Our study suggests that the quality of mean-field modeling does not worsen when weakly or moderately charged macroions exhibit spherical curvature.

Interference patterns produced by an evaporating droplet on a horizontal surface

We study dynamical Newton-ring like fringes created by interfering Fresnel reflections of an evaporating sessile liquid droplet, which acts as a miniature convex lens. We show that conventional thin-film interference theory cannot be applied to explain the physical phenomenon. Because of the large thickness and curvature of the liquid droplet, the geometrical light paths of the reflected beams become very complicated and can no longer be considered approximately collimated. This results in interference fringes of concentric circles with different directional motion depending on the observation plane. The change in the interference pattern as a function of time is demonstrated by both simulation and experiment. This investigation allows us to fully understand the formation of interference patterns of an optical system having arbitrary thickness and curvature. In addition, by analyzing the high-contrast dynamic rings, we demonstrate nanoscale sensitivity to surface height changes of an evaporating water drop.

Universal renormalization procedure for higher curvature gravities in D \u2264 5

We implement a universal method for renormalizing AdS gravity actions applicable to arbitrary higher curvature theories in up to five dimensions. The renormalization procedure considers the extrinsic counterterm for Einstein-AdS gravity given by the Kounterterms scheme, but with a theory-dependent coupling constant that is fixed by the requirement of renormalization for the vacuum solution. This method is shown to work for a generic higher curvature gravity with arbitrary couplings except for a zero measure subset, which includes well-known examples where the asymptotic behavior is modified and the AdS vacua are degenerate, such as Chern-Simons gravity in 5D, Conformal Gravity in 4D and New Massive Gravity in 3D. In order to show the universality of the scheme, we perform a decomposition of the equations of motion into their normal and tangential components with respect to the Poincare coordinate and study the Fefferman-Graham expansion of the metric. We verify the cancellation of divergences of the on-shell action and the well-posedness of the variational principle.

Material characterization of curved shells under finite deformation using the virtual fields method

AbstractAlthough full‐field measurement techniques have been well established, material characterization from these data remains challenging. Often, no closed‐form solution exists between measured quantities and sought material parameters. In this paper, a novel approach to determine the stiffness of thin curved membranes is proposed, based on the virtual fields method (VFM). Utilizing Kirchhoff‐Love shell theory, we show that the displacements can be decomposed into an in‐plane displacement and a rotation of the mid‐surface of the shell. Consequently, the strain tensor at the outer surface of the shell can then be decomposed into a membrane and a bending part. This allows for the VFM to be applied based only on data of the outer surface and on surfaces of arbitrary curvature. The method is first applied to simulated data. It is shown that the elastic modulus can be identified with less than 5% error if the thickness and Poisson ratio are known accurately. A 5% uncertainty in either the Poisson ratio or the thickness changes the identified value by 5%. Then, the method is applied on experimental data acquired on rubber samples having a dome‐like shape. Tensile tests are performed on the same samples, which permits to assess the linearized Young's modulus of this material for moderate strains (0–2.1%). Using regression analysis, a Young's modulus of 1.21 ± 0.08 MPa is found. Next, we performed pressurization tests on eight dome‐like shapes with pressures up to 4 kPa. The average Young's modulus obtained with the novel virtual fields method is 1.20 ± 0.13 MPa. The results are in good agreement with the ones from the tensile test. Future applications could benefit from this method to analyse more complex shapes, for example those found in biological structures like arteries or eardrums.

Computational design of weingarten surfaces

In this paper we study Weingarten surfaces and explore their potential for fabrication-aware design in freeform architecture. Weingarten surfaces are characterized by a functional relation between their principal curvatures that implicitly defines approximate local congruences on the surface. These symmetries can be exploited to simplify surface paneling of double-curved architectural skins through mold re-use. We present an optimization approach to find a Weingarten surface that is close to a given input design. Leveraging insights from differential geometry, our method aligns curvature isolines of the surface in order to contract the curvature diagram from a 2D region into a 1D curve. The unknown functional curvature relation then emerges as the result of the optimization. We show how a robust and efficient numerical shape approximation method can be implemented using a guided projection approach on a high-order B-spline representation. This algorithm is applied in several design studies to illustrate how Weingarten surfaces define a versatile shape space for fabrication-aware exploration in freeform architecture. Our optimization algorithm provides the first practical tool to compute general Weingarten surfaces with arbitrary curvature relation, thus enabling new investigations into a rich, but as of yet largely unexplored class of surfaces.

Some aspects of the cosmological dynamics in Einstein–Gauss–Bonnet gravity

We study some aspects of dynamical compactification scenario where stabilization of extra dimensions occurs due to the presence of Gauss–Bonnet term and nonzero spatial curvature. In the framework of the model under consideration, there exists two-stages scenario of evolution of a Universe: in the first stage, the space evolves from a totally anisotropic state to the state with three-dimensional (corresponding to our “real” world) expanding and [Formula: see text]-dimensional contracting isotropic subspaces; on the second stage, constant curvature of extra dimensions begins to play role and provide compactification of extra dimensions. It is already known that such a scenario is realizable when constant curvature of extra dimensions is negative. Here we show that a range of coupling constants for which exponential solutions with three-dimensional expanding and [Formula: see text]-dimensional contracting isotropic subspaces are stable is located in a zone where compactification solutions with positively curved extra space are unstable, so that two-stage scenario analogous to the one described above is not realizable. Also we study “nearly-Friedmann” regime for the case of arbitrary constant curvature of extra dimensions and describe new parametrization of the general solution for the model under consideration which provide elegant way of describing areas of existence over parameters space.

Holographic entanglement entropy for perturbative higher-curvature gravities

The holographic entanglement entropy functional for higher-curvature gravities involves a weighted sum whose evaluation, beyond quadratic order, requires a complicated theory-dependent splitting of the Riemann tensor components. Using the splittings of general relativity one can obtain unambiguous formulas perturbatively valid for general higher-curvature gravities. Within this setup, we perform a novel rewriting of the functional which gets rid of the weighted sum. The formula is particularly neat for general cubic and quartic theories, and we use it to explicitly evaluate the corresponding functionals. In the case of Lovelock theories, we find that the anomaly term can be written in terms of the exponential of a differential operator. We also show that order-n densities involving nR Riemann tensors (combined with n−nR Ricci’s) give rise to terms with up to 2nR− 2 extrinsic curvatures. In particular, densities built from arbitrary Ricci curvatures combined with zero or one Riemann tensors have no anomaly term in their functionals. Finally, we apply our results for cubic gravities to the evaluation of universal terms coming from various symmetric regions in general dimensions. In particular, we show that the universal function characteristic of corner regions in d = 3 gets modified in its functional dependence on the opening angle with respect to the Einstein gravity result.

Test of the cosmic distance duality relation for arbitrary spatial curvature

ABSTRACT The cosmic distance duality relation (CDDR), η(z) = (1 + z)2dA(z)/dL(z) = 1, is one of the most fundamental and crucial formulae in cosmology. This relation couples the luminosity and angular diameter distances, two of the most often used measures of structure in the Universe. We here propose a new model-independent method to test this relation, using strong gravitational lensing (SGL) and the high-redshift quasar Hubble diagram reconstructed with a Bézier parametric fit. We carry out this test without pre-assuming a zero spatial curvature, adopting instead the value ΩK = 0.001 ± 0.002 optimized by Planck in order to improve the reliability of our result. We parametrize the CDDR using η(z) = 1 + η0z, 1 + η1z + η2z2, and 1 + η3z/(1 + z), and consider both the SIS and non-SIS lens models for the strong lensing. Our best-fitting results are: $\eta _0=-0.021^{+0.068}_{-0.048}$, $\eta _1=-0.404^{+0.123}_{-0.090}$, $\eta _2=0.106^{+0.028}_{-0.034}$, and $\eta _3=-0.507^{+0.193}_{-0.133}$ for the SIS model, and $\eta _0=-0.109^{+0.044}_{-0.031}$ for the non-SIS model. The measured η(z), based on the Planck parameter ΩK, is essentially consistent with the value (=1) expected if the CDDR were fully respected. For the sake of comparison, we also carry out the test for other values of ΩK, but find that deviations of spatial flatness beyond the Planck optimization are in even greater tension with the CDDR. Future measurements of SGL may improve the statistics and alter this result but, as of now, we conclude that the CDDR favours a flat Universe.

EnCurv: Simple Technique of Maintaining Global Membrane Curvature in Molecular Dynamics Simulations.

The EnCurv method for maintaining membrane curvature in molecular dynamics simulations is introduced. The method allows maintaining any desired curvature in a sector of lipid membrane bent in a single plane without adding any unphysical interactions into the system and without restrictions on lateral and transversal lipid diffusion and distribution. The current implementation is limited to the membranes curved in a single plane but generalization to arbitrary curvature and membrane topology is possible. The method is simple, easy to implement, and scales linearly with the system size. EnCurv is agnostic to the force field, simulation parameters, and membrane composition. The proof of principle implementation (https://github.com/yesint/EnCurv) is compatible with the majority of modern simulation packages and shows consistent results on the model systems.

Regularized Lovelock gravity

A four-dimensional regularization of Lovelock–Lanczos gravity up to an arbitrary curvature order is considered. We show that Lovelock–Lanczos terms can provide a non-trivial contribution to the Einstein field equations in four dimensions, for spherically symmetric and Friedmann–Lemaître–Robertson–Walker spacetimes, as well as at first order in perturbation theory around (anti) de Sitter vacua. We will discuss the cosmological and black hole solutions arising from these theories, focusing on the presence of attractors and their stability. Although curvature singularities persist for any finite number of Lovelock terms, it is shown that they disappear in the non-perturbative limit of a theory with a unique vacuum.

A generalized simplified modeling method for electromagnetic coupling effects of uncertainty strapping cable harness

<sec>The cable harness provides a main gateway for electromagnetic interference(EMI) in electromechanical system. The unreasonable electromagnetic compatibility (EMC) design of cable harness will produce EMI to other on-board electronic equipment, bringing great safety risks to the system. Theoretical research and engineering practice indicate that most of the electromechanical systems cannot satisfy EMC standards, which can be attributed to the EMI generated by cables. As for the eletromagnetic(EM) illumination analysis, reliably and efficiently generating a full numerical model of cable harness is becoming more prominent for the EMC designers. Therefore, it is necessary to develop a more effective method to solve the modeling problem of cable harness. </sec><sec>In the practical application, the cable harness has the characteristics of spatial layout, and its characteristics such as “large number of core wires”, “arbitrary curvature of space” and “randomness of wiring” bring challenges to the modeling of EM coupling to cable harness. The numerical simulation of the whole cable harness model requires severe conditions for computational resource and even makes the EM coupling analysis impossible. Thus, considering the uncertainty of wire position, this paper proposes a generalized simplified modeling method for the EM coupling effect of uncertainty strapping cable harness. Firstly, the Gaussian distribution and spline interpolation are used to determine the location of the core conductors in the random bundling. Then, the distribution parameters of the cable harness at different positions are established by using the transposition relationship between the subsegments of the wires. Finally, the effectiveness of the proposed method is verified by numerical examples of the arc-shaped and sine-shaped harness. </sec><sec>In conclusion, this paper proposes a generalized simplification technique to model the EM illumination on cable harness with uncertainty wiring factors. By grouping the conductors together, the required computation time is markedly reduced and the complexity of modeling the completely cable harness is significantly simplified within a good accuracy. The proposed method provides a way of solving the modeling problem caused by “uncertainty strapping” of the complex wiring harnesses in electromechanical systems.</sec>

Steering of quantum signals along coupled paths of arbitrary curvature

Quantum engineering, as a field of research, is currently attracting a huge scientific, funding, and commercial interest. A generic operation behind most of the related device setups is the efficient steering of quantum signals, by channeling or coupling them with specified intensities, to various spatial sections. This work provides several alternative material combinations for a planar guiding configuration, able to squeeze matter waves into tiny apertures while being maximally apt to evanescently couple them. It is also shown that the proposed designs can work under arbitrary curvature by supporting proper resonances, resulting in propagating or standing-wave patterns around them. The signal interaction between straight semiconducting wires and circular rings is demonstrated in layouts that can be used in a variety of components: from beam splitters and quantum memory elements to matter-wave transformers and quantum circuits.

Coupled nonlinear mechanics for the electromechanical response of multi-stable piezoelectric shallow shells with piezoelectric films

This paper considers the nonlinear electromechanical response of shallow piezoelectric laminated shells of arbitrary double curvature, undergoing to snap through buckling and eventually to elastic instability, under mechanical pressure loads. The computational framework is based on coupled nonlinear mechanics encompassing the electromechanical coupling field and geometric nonlinearity due to large displacements and rotations. The first shear deformation theory is combined with a linear layerwise theory for describing the elastic and electric state variables through the laminate thickness, respectively. The governing equations are expressed with respect to an orthogonal curvilinear coordinate system. Building upon the nonlinear multifield mechanics an eight-node shell finite element is developed to discretize the generalized coupled nonlinear equations, which are subsequently linearized and iteratively solved, using the Cylindrical Arc-Length method in combination with the Newton-Raphson iterative technique. Numerical results demonstrate the capability of the present model to predict the complex electromechanical response of shallow cylindrical shells that transit between two stable equilibrium states. The electromechanical (generated electric charge-energy) conversion is highly complex (depending on both nonlinear piezoelectric and stiffness matrices) and predicted along the stable and unstable paths of bi-stability. At the same time the feasibility to relate the sensory electric potential with the snap through buckling of smart shells is also quantified. The influence of shell thickness, curvature and laminate configuration on the electromechanical conversion, is finally investigated.

Curved p-version C1 finite elements for the finite deformation analysis of isotropic and composite laminated thin shells in irregular shape

In this work, we generalize our recently developed p-version curved C1 plate elements to the finite deformation analysis of general isotropic and laminated thin shells with arbitrary curvature and shape. The kinematic formulations are based on the geometrically-exact nonlinear thin shell model where the Kirchhoff-Love hypothesis is strictly implemented during the deformation. Since high accurate curved coarse meshes are required in the implementation of p-version finite element method, the quasi regional mapping technique is employed and modified to obtain the high-order meshes with fitted boundaries. Through this method, shells with irregular shapes can be easily modeled. To avoid dealing the difficult problem of constructing fully C1 conforming displacement fields on shell surface, the C1 conformity of present elements is implemented on the selected Gauss-Lobatto nodes, which had been found to be able to produce very fast convergence. Nodal variables including second-order directional derivatives on surfaces are derived and used for element assembly. In this manner, direct construction of displacement fields on shell mid-surface defined by the quasi regional mapping is allowed. Several benchmark problems of large deformation analysis of isotropic and laminated thin shells are presented to illustrate the accuracy as well as robustness of the present method.

Nonlinear vibration and dynamic instability analyses of laminated doubly curved panels in thermal environments

Nonlinear dynamic analysis for a shear deformable anisotropic laminated doubly curved panel of rectangular planform resting on elastic foundations is presented. A new panel model of arbitrary curvature and arbitrary fiber stacking sequences but constant thickness is developed and established. The governing equations are based on an extended higher order shear deformation shell theory with von Kármán-type of kinematic nonlinearity and including the anisotropic couplings. The nonlinear deformations and initial deflections of the panel are both taken into account. A two-step perturbation technique combining with the Galerkin method is employed to determine the linear and nonlinear vibration frequencies and forced responses. Nonlinear forced harmonic vibration in a Duffing oscillator for anisotropic laminated doubly curved panel is also investigated and discussed together with the effects of damping and excitation by using multiscale and Melnikov methods. The numerical results are validated for various lamination schemes through a comparison with solutions for free vibration frequencies of saddle (hyperbolic), flat plate, cylindrical and spherical shells available in the literature or obtained by the commercial finite element software. The numerical illustrations concern nonlinear vibration and dynamic response of moderately thick, anisotropic laminated doubly curved panels under different values of panel geometric parameters and mechanical excitation.

On the continuum limit of Benincasa–Dowker–Glaser causal set action

We study the continuum limit of the Benincasa–Dowker–Glaser causal set action on a causally convex compact region. In particular, we compute the action of a causal set randomly sprinkled on a small causal diamond in the presence of arbitrary curvature in various spacetime dimensions. In the continuum limit, we show that the action admits a finite limit. More importantly, the limit is composed by an Einstein–Hilbert bulk term as predicted by the Benincasa–Dowker–Glaser action, and a boundary term exactly proportional to the codimension-two joint volume. Our calculation provides strong evidence in support of the conjecture that the Benincasa–Dowker–Glaser action naturally includes codimension-two boundary terms when evaluated on causally convex regions.