Efficient Localization of Discontinuities in Complex Computational Simulations

Surrogate models for computational simulations are input-output approximations that allow computationally intensive analyses, such as uncertainty propagation and inference, to be performed efficiently. When a simulation output does not depend smoothly on its inputs, the error and convergence rate of many approximation methods deteriorate substantially. This paper details a method for efficiently localizing discontinuities in the input parameter domain, so that the model output can be approximated as a piecewise smooth function. The approach comprises an initialization phase, which uses polynomial annihilation to assign function values to different regions and thus seed an automated labeling procedure, followed by a refinement phase that adaptively updates a kernel support vector machine representation of the separating surface via active learning. The overall approach avoids structured grids and exploits any available simplicity in the geometry of the separating surface, thus reducing the number of model evaluations required to localize the discontinuity. The method is illustrated on examples of up to eleven dimensions, including algebraic models and ODE/PDE systems, and demonstrates improved scaling and efficiency over other discontinuity localization approaches

Concurrent π\pi-vector fields and energy beta-change

The present paper deals with an \emph{intrinsic} investigation of the notion of a concurrent $\pi$-vector field on the pullback bundle of a Finsler manifold $(M,L)$. The effect of the existence of a concurrent $\pi$-vector field on some important special Finsler spaces is studied. An intrinsic investigation of a particular $\beta$-change, namely the energy $\beta$-change ($\widetilde{L}^{2}(x,y)=L^{2}(x,y)+ B^{2}(x,y) with \ B:=g(\bar{\zeta},\bar{\eta})$;$\bar{\zeta} $being a concurrent$\pi$-vector field), is established. The relation between the two Barthel connections$\Gamma$and$\widetilde{\Gamma}$, corresponding to this change, is found. This relation, together with the fact that the Cartan and the Barthel connections have the same horizontal and vertical projectors, enable us to study the energy$\beta$-change of the fundamental linear connection in Finsler geometry: the Cartan connection, the Berwald connection, the Chern connection and the Hashiguchi connection. Moreover, the change of their curvature tensors is concluded. It should be pointed out that the present work is formulated in a prospective modern coordinate-free form.Comment: 27 pages, LaTex file, Some typographical errors corrected, Some formulas simpifie

A continuous analogue of the tensor-train decomposition

We develop new approximation algorithms and data structures for representing and computing with multivariate functions using the functional tensor-train (FT), a continuous extension of the tensor-train (TT) decomposition. The FT represents functions using a tensor-train ansatz by replacing the three-dimensional TT cores with univariate matrix-valued functions. The main contribution of this paper is a framework to compute the FT that employs adaptive approximations of univariate fibers, and that is not tied to any tensorized discretization. The algorithm can be coupled with any univariate linear or nonlinear approximation procedure. We demonstrate that this approach can generate multivariate function approximations that are several orders of magnitude more accurate, for the same cost, than those based on the conventional approach of compressing the coefficient tensor of a tensor-product basis. Our approach is in the spirit of other continuous computation packages such as Chebfun, and yields an algorithm which requires the computation of "continuous" matrix factorizations such as the LU and QR decompositions of vector-valued functions. To support these developments, we describe continuous versions of an approximate maximum-volume cross approximation algorithm and of a rounding algorithm that re-approximates an FT by one of lower ranks. We demonstrate that our technique improves accuracy and robustness, compared to TT and quantics-TT approaches with fixed parameterizations, of high-dimensional integration, differentiation, and approximation of functions with local features such as discontinuities and other nonlinearities

Shape Memory Alloy Reinforced Concrete Frames Vulnerable to Strong Vertical Excitations

Reinforced concrete (RC) framed buildings dissipate the seismic energy through yielding of the reinforcing bars. This yielding jeopardizes the serviceability of these buildings as it results in residual lateral deformations. Superelastic shape memory alloys (SMAs) can recover inelastic strains by stress removal. This paper extends previous research by the authors that optimized the use of SMA bars in RC frames considering the horizontal seismic excitation by addressing the effect of the vertical seismic excitation. A steel RC six-storey building designed according to current seismic standards is considered as case study. Five different earthquake records with strong vertical components are selected for the nonlinear dynamic analysis. The results were used to evaluate the effect of the vertical excitation on the optimum locations of SMA bars

Generalized β\beta-conformal change and special Finsler spaces

In this paper, we investigate the change of Finslr metrics $$L(x,y) \to\bar{L}(x,y) = f(e^{\sigma(x)}L(x,y),\beta(x,y)),$$ which we refer to as a generalized $\beta$-conformal change. Under this change, we study some special Finsler spaces, namely, quasi C-reducible, semi C-reducible, C-reducible, $C_2$-like, $S_3$-like and $S_4$-like Finsler spaces. We also obtain the transformation of the T-tensor under this change and study some interesting special cases. We then impose a certain condition on the generalized $\beta$-conformal change, which we call the b-condition, and investigate the geometric consequences of such condition. Finally, we give the conditions under which a generalized $\beta$-conformal change is projective and generalize some known results in the literature.Comment: References added, some modifications are performed, LateX file, 24 page

Spectral relationships of the integral equation with logarithmic kernel in some different domains

In this work, the Fredholm integral equation (FIE) with logarithmic kernel is investigated from the contact problem in the plane theory of elasticity. Then, using potential theory method (PTM), the spectral relationships (SRs) of this integral equation are obtained in some different domains of the contact. Many special cases and new SRs are established and discussed from this work

The Results of a Case Study to Evaluate the Application of LIS Implemented by CITL Portsaid Branch in Support of Education andIndustry

The territory of the Suez Canal haswitnessed continuous development activitiesthroughoutthe year 2015, in the heart of those developments resets all activities of logistics. In the light of those developments, the authors of this paper presented in previous work a design of a database and built a logistics information system to support various logistics activities. This paper presents the results of evaluating the application of the implemented LIS system in several places. Some of those places are related to the governmental sector and the other belongs to the private sector. Evaluation methodology based on collecting feedbacks from actual system users. The areas of evaluation are reliability, availability, and serviceability, running cost, time and security. The developed system was tested against manual systems that still exist in abundance and sophisticated LIS such as SAP and Oracle ERP

Flexible body dynamic stability for high performance aircraft

Dynamic equations which include the effects of unsteady aerodynamic forces and a flexible body structure were developed for a free flying high performance fighter aircraft. The linear and angular deformations are assumed to be small in the body reference frame, allowing the equations to be linearized in the deformation variables. Equations for total body dynamics and flexible body dynamics are formulated using the hybrid coordinate method and integrated in a state space format. A detailed finite element model of a generic high performance fighter aircraft is used to generate the mass and stiffness matrices. Unsteady aerodynamics are represented by a rational function approximation of the doublet lattice matrices. The equations simplify for the case of constant angular rate of the body reference frame, allowing the effect of roll rate to be studied by computing the eigenvalues of the system. It is found that the rigid body modes of the aircraft are greatly affected by introducing a constant roll rate, while the effect on the flexible modes is minimal for this configuration