The spectral representation for stochastic integration operators with respect to the Wiener process is proposed in form of a composition characteristics used mathematical description control systems. This can be defined relative various orthonormal bases. For given deterministic square-integrable kernels, characteristic operator determined as an infinite random matrix. main applications such su...

We propose a geometrically nonlinear extended isogeometric analysis approach for cohesive fracture. A shifting technique is used to enforce compatibility in the direction perpendicular crack path, while blending has been adopted remove effect of discontinuity extension crack. Bézier extraction employed cast formulation finite element datastructure. The use sign function instead Heaviside step r...

With the goal of maximizing thermoelectric (TE) figure merit $ZT$, Mahan and Sofo [Proc. Natl. Acad. Sci. U.S.A. 93, 7436 (1996)] found that optimal transport distribution (TD) is a delta function. Materials, however, have TDs appear to always be finite non-diverging. Motivated by this observation, study focuses on deriving what bounded TD, which determined boxcar function for $ZT$ Heaviside po...

This paper presents a density-based topology optimization approach to design structures under self-weight load. Such loads change their magnitude and/or location as the advances and pose several unique challenges, e.g., non-monotonous behavior of compliance objective, parasitic effects low-stiffness elements, unconstrained nature problems. The modified SIMP material scheme is employed with thre...

We study the behavior of the limit of the spectrum of a non self-adjoint Sturm-Liouville operator with analytic potential as the semiclassical parameter h → 0. We get a good description of the spectrum and limit spectrum near ∞. We also study the action of one special perturbation of the operator (adding a Heaviside function), and prove that the limit spectrum is very unstable. As an illustrati...

This article presents a density-based topology optimization method for designing three-dimensional (3D) compliant mechanisms (CMs) and loadbearing structures with design-dependent pressure loading. Instead of interface-tracking techniques, the Darcy law in conjunction drainage term is employed to obtain field as function design vector. To ensure continuous transition loads evolves, flow coeffic...

An inconsistent boundary condition in eq 2 was corrected. This change does not in any way alter the results or the conclusions of the paper. Page1549, column1, line11. The text reads as follows: “In Laplace space, each transition is modeled with a Heaviside step function, Rp(s) =ΔRp/s, whereΔRp is the instantaneous change in pore resistance, per unit time. We can obtain an expression for the na...

Clifford's geometric algebra has enjoyed phenomenal development over the last 60 years by mathematicians, theoretical physicists, engineers, and computer scientists in robotics, artificial intelligence data analysis, introducing a myriad of different often confusing notations. The Euclidean 3-space, natural generalization both well-known Gibbs-Heaviside vector Hamilton's quaternions, is used he...