We develop a Data-Driven framework for the simulation of wave propagation in viscoelastic solids directly from dynamic testing material data, including data Dynamic Mechanical Analysis (DMA), nano-indentation, Shear Testing (DST) and Magnetic Resonance Elastography (MRE), without need regression or modeling. The problem is formulated frequency domain method solution seeks to minimize distance b...

By numerically integrating the three-dimensional Maxwell equations in the time domain with reference to a dispersive quadratically nonlinear material, we study second-harmonic generation in planar photonic crystal microresonators. The proposed scheme allows efficient coupling of the pump radiation to the defect resonant mode. The outcoupled generated second harmonic is maximized by impedance ma...

In [11] the author proved that every quasiconformal harmonic mapping between two Jordan domains with C, 0 < α ≤ 1, boundary is biLipschitz, providing that the domain is convex. In this paper we avoid the restriction of convexity. More precisely we prove: any quasiconformal harmonic mapping between two Jordan domains Ωj , j = 1, 2, with C, j = 1, 2 boundary is bi-Lipschitz.

Variable reactors have been a vital component of power networks for decades, where they used as fault-current limiting devices or reactive compensation. Traditionally, modifying the inductance predominantly mechanically operated variable requires seconds to minutes. In contrast, virtual air gap (VAG) can change within milliseconds, potentially improving system stability. Existing dynamic models...

Certain progress has been made in fault diagnosis under cross-domain scenarios recently. Most researchers have paid almost all their attention to promoting domain adaptation a common space. However, several challenges that will cause negative transfer ignored. In this paper, reweighting method is proposed overcome difficulty from two aspects. First, extracted features differ greatly one another...

An explicit fully discrete finite element method, which satisfies the nonconvex side constraint at every node, is developed for approximating the p-harmonic flow for p ∈ (1,∞). Convergence of the method is established under certain conditions on the domain and mesh. Computational examples are presented to demonstrate finite-time blow-ups and qualitative geometric changes of weak solutions of th...

We describe the relationship between complex-valued harmonic morphisms from Minkowski 4-space and the shear-free ray congruences of mathematical physics. Then we show how a horizontally conformal submersion on a domain of R 3 gives the boundary values at infinity of a complex-valued harmonic morphism on hyperbolic 4-space.

We prove that at a finite singular time for the Harmonic Ricci Flow on a surface of positive genus both the energy density of the map component and the curvature of the domain manifold have to blow up simultaneously. As an immediate consequence, we obtain smooth long-time existence for the Harmonic Ricci Flow with large coupling constant.

We consider harmonic functions with respect to the operator Lu(x) = ∫ [u(x+ h)− u(x)− 1(|h|≤1)h · ∇u(x)]n(x, h) dh. Under suitable conditions on n(x, h) we establish a Harnack inequality for functions that are nonnegative and harmonic in a domain. The operator L is allowed to be anisotropic and of variable order.

We investigate the relationship between the univalence of f and of h in the decomposition f = h+g of a sense-preserving harmonic mapping defined in the unit disk D ⊂ C. Among other results, we determine the holomorphic univalent maps h for which there exists c > 0 such that every harmonic mapping of the form f = h + g with |g| < c|h| is univalent. The notion of a linearly connected domain appea...