Computer Science

Of all the characteristics of a violin, those that concern its shape are probably the most important ones, as the violin maker has complete control over them. Contemporary violin making, however, is still based more on tradition than understanding, and a definitive scientific study of the specific relations that exist between shape and vibrational properties is yet to come and sorely missed. In this article, using standard statistical learning tools, we show that the modal frequencies of violin tops can, in fact, be predicted from geometric parameters, and that artificial intelligence can be successfully applied to traditional violin making. We also study how modal frequencies vary with the thicknesses of the plate (a process often referred to as {\em plate tuning}) and discuss the complexity of this dependency. Finally, we propose a predictive tool for plate tuning, which takes into account material and geometric parameters.

This paper presents a data-driven method for producing annual continuous dynamic rating of power transformers to serve the long-term planning purpose. Historically, research works on dynamic rating have been focused on real-time/near-future system operations. There has been a lack of research for long-term planning oriented applications. Currently, most utility companies still rely on static rating numbers when planning power transformers for the next few years. In response, this paper proposes a novel and comprehensive method to analyze the past 5-year temperature, loading and load composition data of existing power transformers in a planning region. Based on such data and the forecasted area load composition, a future power transformer loading profile can be constructed by using Gaussian Mixture Model. Then according to IEEE std. C57.91-2011, a power transformer thermal aging model can be established to incorporate future loading and temperature profiles. As a result, annual continuous dynamic rating profiles under different temperature scenarios can be determined. The profiles can reflect the long-term thermal overloading risk in a much more realistic and granular way, which can significantly improve the accuracy of power transformer planning. A real utility application example in Canada has been presented to demonstrate the practicality and usefulness of this method.

The structural response of masonry arches is strongly dominated by the arch geometry, the stone block dimensions and the interaction with backfill material or surrounding walls. Due to their intrinsic discontinuous nature, the nonlinear structural response of these key historical structures can be efficiently modelled in the context of discrete element approaches. Smeared crack finite elements models, based on the assumption of homogenised media and spread plasticity, fail to rigorously predict the actual collapse behaviour of such structures, that are generally governed by rocking and sliding mechanisms along mortar joints between stone blocks. In this paper a new Discrete Macro-Element Method (DMEM) for predicting the nonlinear structural behaviour of masonry arches is proposed. The method is based on a macro-element discretization in which each plane element interacts with the adjacent elements through zero-thickness interfaces and whose internal deformability is related to a single degree of freedom only. Both experimental and numerical validations show the capability of the proposed approach to be applied for the prediction of the non-linear response of masonry arch structures under different loading conditions.

Coherent structures/motions in turbulence inherently give rise to intermittent signals with sharp peaks, heavy-skirt, and skewed distributions of velocity increments, highlighting the non-Gaussian nature of turbulence. That suggests that the spatial nonlocal interactions cannot be ruled out of the turbulence physics. Furthermore, filtering the Navier-Stokes equations in the large eddy simulation of turbulent flows would further enhance the existing nonlocality, emerging in the corresponding subgrid scale fluid motions. That urges the development of new nonlocal closure models, which respect the corresponding non-Gaussian statistics of the subgrid stochastic motions. To this end and starting from the filtered Boltzmann equation, we model the corresponding equilibrium distribution function with a \textit{Lévy}-stable distribution, leading to the proposed fractional-order modeling of subgrid-scale stresses. We approximate the filtered equilibrium distribution function with a power-law term, and derive the corresponding filtered Navier-Stokes equations. Subsequently in our functional modeling, the divergence of subgrid-scale stresses emerges as a single-parameter fractional Laplacian, (−Δ ) α (⋅) , α∈(0,1] , of the filtered velocity field. The only model parameter, i.e., the fractional exponent, appears to be strictly depending on the filter-width and the flow Reynolds number. We furthermore explore the main physical and mathematical properties of the proposed model under a set of mild conditions. Finally, the introduced model undergoes \textit{a priori} evaluations based on the direct numerical simulation database of forced and decaying homogeneous isotropic turbulent flows at relatively high and moderate Reynolds numbers, respectively. Such analysis provides a comparative study of predictability and performance of the proposed fractional model.

This work proposes a novel, general and robust method of determining bond micromoduli for anisotropic linear elastic bond-based peridynamics. The problem of finding a discrete distribution of bond micromoduli that reproduces an anisotropic peridynamic stiffness tensor is cast as a least-squares problem. The proposed numerical method is able to find a distribution of bond micromoduli that is able to exactly reproduce a desired anisotropic stiffness tensor provided conditions of Cauchy's relations are met. Examples of all eight possible elastic material symmetries, from triclinic to isotropic are given and discussed in depth. Parametric studies are conducted to demonstrate that the numerical method is robust enough to handle a variety of horizon sizes, neighborhood shapes, influence functions and lattice rotation effects. Finally, an example problem is presented to demonstrate that the proposed method is physically sound and that the solution agrees with the analytical solution from classical elasticity. The proposed method has great potential for modeling of deformation and fracture in anisotropic materials with bond-based peridynamics.

In this paper we present a fully-coupled, two-scale homogenization method for dynamic loading in the spirit of FE 2 methods. The framework considers the balance of linear momentum including inertia at the microscale to capture possible dynamic effects arising from micro heterogeneities. A finite-strain formulation is adapted to account for geometrical nonlinearities enabling the study of e.g. plasticity or fiber pullout, which may be associated with large deformations. A consistent kinematic scale link is established as displacement constraint on the whole representative volume element. The consistent macroscopic material tangent moduli are derived including micro inertia in closed form. These can easily be calculated with a loop over all microscopic finite elements, only applying existing assembly and solving procedures. Thus, making it suitable for standard finite element program architectures. Numerical examples of a layered periodic material are presented and compared to direct numerical simulations to demonstrate the capability of the proposed framework.

Two of the most significant challenges in uncertainty propagation pertain to the high computational cost for the simulation of complex physical models and the high dimension of the random inputs. In applications of practical interest both of these problems are encountered and standard methods for uncertainty quantification either fail or are not feasible. To overcome the current limitations, we propose a probabilistic multi-fidelity framework that can exploit lower-fidelity model versions of the original problem in a small data regime. The approach circumvents the curse of dimensionality by learning dependencies between the outputs of high-fidelity models and lower-fidelity models instead of explicitly accounting for the high-dimensional inputs. We complement the information provided by a low-fidelity model with a low-dimensional set of informative features of the stochastic input, which are discovered by employing a combination of supervised and unsupervised dimensionality reduction techniques. The goal of our analysis is an efficient and accurate estimation of the full probabilistic response for a high-fidelity model. Despite the incomplete and noisy information that low-fidelity predictors provide, we demonstrate that accurate and certifiable estimates for the quantities of interest can be obtained in the small data regime, i.e., with significantly fewer high-fidelity model runs than state-of-the-art methods for uncertainty propagation. We illustrate our approach by applying it to challenging numerical examples such as Navier-Stokes flow simulations and monolithic fluid-structure interaction problems.

Molecular photo-switches as, e.g., azobenzene molecules allow, when embedded into a polymeric matrix, for photo-active polymer compounds responding mechanically when exposed to light of certain wavelength. Photo-mechanics, i.e. light-matter interaction in photo-active polymers holds great promise for, e.g., remote and contact-free activation of photo-driven actuators. In a series of earlier contributions, Oates et al. developed a successful continuum formulation for the coupled electric, electronic and mechanical problem capturing azobenzene polymer compounds, thereby mainly focussing on geometrically linearized kinematics. Building on that formulation, we here explore the variational setting of a geometrically exact continuum framework based on Dirichlet's and Hamilton's principle as well as, noteworthy, Hamilton's equations. Thereby, when treating the dissipative case, we resort to incremental versions of the various variational problems via suited incorporation of a dissipation potential. In particular, the Hamiltonian setting of geometrically exact photo-mechanics is up to now largely under-explored even for the energetic case, arguably since the corresponding Lagrangian is degenerate in Dirac's sense. Moreover, in general, the Hamiltonian setting of dissipative dynamical systems is a matter of ongoing debate per se. In this contribution, by advocating a novel incremental version of the Hamiltonian setting exemplified for the dissipative case of photo-mechanics, we aim to also unify the variational approach to dissipative dynamical systems. Taken together, the variational setting of a geometrically exact continuum framework of photo-mechanics paves the way for forthcoming theoretical and numerical analyses.

A higher-order fictitious domain method (FDM) for Reissner-Mindlin shells is proposed which uses a three-dimensional background mesh for the discretization. The midsurface of the shell is immersed into the higher-order background mesh and the geometry is implied by level-set functions. The mechanical model is based on the Tangential Differential Calculus (TDC) which extends the classical models based on curvilinear coordinates to implicit geometries. The shell model is described by PDEs on manifolds and the resulting FDM may typically be called Trace FEM. The three standard key aspects of FDMs have to be addressed in the Trace FEM as well to allow for a higher-order accurate method: (i) numerical integration in the cut background elements, (ii) stabilization of awkward cut situations and elimination of linear dependencies, and (iii) enforcement of boundary conditions using Nitsche's method. The numerical results confirm that higher-order accurate results are enabled by the proposed method provided that the solutions are sufficiently smooth.

Lithium-ion batteries (LIBs) of high energy density and light-weight design, have found wide applications in electronic devices and systems. Degradation mechanisms that caused by lithiation is a main challenging problem for LIBs with high capacity electrodes like silicon (Si), which eventually can reduce the lifetime of batteries. In this paper, a hybrid phase field model (PFM) is proposed to study the fracture behavior of LIB electrodes. The model considers the coupling effects between lithium (Li) -ion diffusion process, stress evolution and crack propagation. Also, the dependency of Elastic properties on the concentration magnitude of Li-ion is considered. A numerical implementation based on a MATLAB finite element (FE) code is elaborated. Then, the proposed hybrid PF approach is applied to a Nanowire (NW) Si electrode particle. It is shown that the hybrid model shows less tendency to crack growth than the isotropic model.