We present enhanced physics-based finite element schemes for two families of turbulence models, the NS-ω models and the Stolz-Adams approximate deconvolution models. These schemes are delicate extensions of a method created for the Navier-Stokes equations in Rebholz 2007 , that achieve high physical fidelity by admitting balances of both energy and helicity that match the true physics. The sche...

The spectrum of discrete Schrödinger operator L + V on the d-dimensional lattice is considered, where L denotes the discrete Laplacian and V a delta function with mass at a single point. Eigenvalues of L+V are specified and the absence of singular continuous spectrum is proven. In particular it is shown that an embedded eigenvalue does appear for d ≥ 5 but does not for 1 ≤ d ≤ 4.

The continuing increase in packing density of VLSI circuits requires that the inspection process be completely automated. This paper suggests a new method for automatic inspection of that part of the wire bond where the wire connects to the bond pad on the chip. A popular type of bonding (connected to bond pad) known as “ball bond” is considered here. Although several approaches for ball bond i...

We present an algorithm for approximating the Laplace-Beltrami operator from an arbitrary point cloud obtained from a k-dimensional manifold embedded in the d-dimensional space. We show that this PCD Laplace (Point-Cloud Data Laplace) operator converges to the Laplace-Beltrami operator on the underlying manifold as the point cloud becomes denser. Unlike the previous work, we do not assume that ...

We introduce a Laplace-Beltrami type operator on the Fock space of symmetric functions and show that the Jack symmetric functions are the only family of eigenvectors of the differential operator, thus giving a new characterization of Jack polynomials. This was achieved by explicit computation of its action on generalized homogeneous symmetric functions. Using this new method we give a combinato...

Generalization of the harmonic superposition rule for the case of dependent choice of harmonic functions is given. Dependence of harmonic functions from all (relative and overall) transverse coordinates is considered using the BeltramiLaplace operator. Supersymmetry of IIB 10D supergravity solutions with only non-vanished 5-form field and 11D supergravity solutions is discussed.

We propose Steklov geometry processing, an extrinsic approach to spectral geometry processing and shape analysis. Intrinsic approaches, usually based on the Laplace–Beltrami operator, cannot capture the spatial embedding of a shape up to rigid motion, while many previous extrinsic methods lack theoretical justi cation. Instead, we propose a systematic approach by considering the Steklov eigenva...

The Laplace Beltrami operator, known as an elliptic operator for functions defined on surfaces, appears in some applications in sciences and engineerings. In this paper we consider the Laplace Beltrami operator ∆Γ on surfaces Γ defined as graphs of C2 functions on a flat domain Ω ⊂ Rd−1 (d ≥ 2), ∆Γu = f on Γ, u = 0 on ∂Γ. Based on some properties of differential geometry, we transformed the Lap...

We describe the role of p-harmonic functions in the theory of quasiregular mappings.