The average seismic velocity and density jumps across the 410- and 660-kilometer discontinuities in the upper mantle were determined by modeling the observed range dependence in long-period seismic wave arrivals that reflect off of these interfaces. The preliminary reference Earth model (PREM) is within the computed 95 percent confidence ellipse for the 410-km discontinuity but outside the allo...

For Stokes equations with discontinuous viscosity across an arbitrary interface or/and singular forces along the interface, the pressure is known to be discontinuous and the velocity is known to be non-smooth. It has been shown that these discontinuities are coupled together which makes it difficult to obtain accurate numerical solutions. In this paper, a second order accurate numerical method ...

The introduction of non-linear, shock-capturing schemes has improved numerical predictions of hydraulic bores but significant numerical oscillations have been reported in the predictions of pipe-filling bore fronts associated with the transition between open-channel and pressurized flow regimes. These oscillations can compromise the stability of numerical models. A study of these oscillations i...

In this paper, a multi-scale analysis scheme for solidification based on two-scale computational homogenization is discussed. Solidification problems involve evolution of surfaces coupled with flux jump boundary conditions across interfaces. We provide consistent macro-micro transition and averaging rules based on Hill’s macrohomogeneity condition. The overall macro-scale behavior is analyzed w...

In this paper we show that a path-wise solution to the following integral equation Yt = ∫ t 0 f(Yt) dXt Y0 = a ∈ R d exists under the assumption that Xt is a Lévy process of finite p-variation for some p ≥ 1 and that f is an α-Lipschitz function for some α > p. There are two types of solution, determined by the solution’s behaviour at jump times of the process X, one we call geometric the other...

Abstract In this paper, we propose a specific two-layer model consisting of functionally graded (FG) layer and piezoelectric semiconductor (PS) layer. Based on the macroscopic theory PS materials, effects brought about by attached FG piezotronic behaviors homogeneous n-type fibers PN junctions are investigated. The semi-analytical solutions electromechanical fields obtained expanding displaceme...

We solve, theoretically and numerically, the problems of optimal portfolio choice and indifference valuation in a general continuous-time setting. The setting features (i) ambiguity and ambiguity averse preferences, (ii) discontinuities in the asset price processes, with a general and possibly infinite activity jump part next to a continuous diffusion part, and (iii) general and possibly non-co...

We design an adaptive finite element method (AFEM) for mixed boundary value problems associated with the differential operator A − ∇div in H(div,Ω). For A being a variable coefficient matrix with possible jump discontinuities, we provide a complete a posteriori error analysis which applies to both Raviart–Thomas RT and Brezzi– Douglas–Marini BDM elements of any order n in dimensions d = 2, 3. W...

A binding neuron (BN) whith delayed feedback is considered. The neuron is fed externally with a Poisson stream of intensity λ . The neuron’s output spikes are fed into its input with time delay ∆. The resulting output stream of the BN is not Poissonian, and we look for its interspike intervals (ISI) distribution. For BN with threshold 2 an exact mathematical expression as function of λ , ∆ and ...

The signature function of a knot is an integer valued step function defined on the unit circle. The jumps (i.e., the discontinuities) of the signature function can occur only at the roots of the Alexander polynomial on the unit circle. The latter are important in deforming U(1) representations of knot groups to irreducible SU(2) representations. Under the assumption that these roots are simple,...