Motivated by the enlightenment that diminishing jump at cell boundary can effectively reduce numerical dissipation near critical region, and a novel constrained interpolation profile conservative semi-Lagrangian method is proposed based on newly designed variation algorithm. First, scheme with piecewise tangent of hyperbola for interface capturing as one candidate to represent jump-like discont...

When two liquid droplets approach at negligible velocity in air, their coalescence spontaneously occurs by jump-to-contact instability and a connecting bridge joining the facing interfaces nanoscale is created. We report experimental investigations of expansion this initial means high-speed imaging. By considering water, polydimethylsiloxane, or paraffin few hundred micrometers, we investigate ...

The location and nature of the percolation transition in random networks is a subject of intense interest. Recently, a series of graph evolution processes have been introduced that lead to discontinuous percolation transitions where the addition of a single edge causes the size of the largest component to exhibit a significant macroscopic jump in the thermodynamic limit. These processes can hav...

We present a new method for estimating the edges in a piecewise smooth function from blurred and noisy Fourier data. The proposed method is constructed by combining the so called concentration factor edge detection method, which uses a finite number of Fourier coefficients to approximate the jump function of a piecewise smooth function, with compressed sensing ideas. Due to the global nature of...

This paper presents mathematical derivation of enrichment functions in the extended finite element method (XFEM) for numerical modelling of strong and weak discontinuities. The proposed approach consists in combining the level set method with characteristic functions as well as domain decomposition and reproduction technique. We start with the simple case of a triangular linear element cut by o...

We extend a model of positive feedback and contagion in large mean-field systems, by introducing common source noise driven Brownian motion. Although the driving dynamics are continuous, effect can lead to ‘blow-up’ phenomena whereby solutions develop jump-discontinuities. Our main results twofold concern conditional McKean–Vlasov formulation model. First foremost, we show that there global thi...

The Earth is characterised by variability on many scales, and the significance of these scales depends on the particular problem under consideration. Natural spatial discontinuities, such as faults and lithological boundaries, separate regions within which the physical properties, processes or geological evolution may be similar. Similarly, time series may show very rapid changes (effectively d...

In the present paper we generalize Eckhoff’s method, i.e., the method for approximating the locations of discontinuities and the associated jumps of a piecewise smooth function by means of its Fourier-Chebyshev coefficients. A new method enables us to approximate the locations of discontinuities and the associated jumps of a discontinuous function, which belongs to a restricted class of the pie...

S U M M A R Y The reversible jump algorithm is a statistical method for Bayesian inference with a variable number of unknowns. Here, we apply this method to the seismic tomography problem. The approach lets us consider the issue of model parametrization (i.e. the way of discretizing the velocity field) as part of the inversion process. The model is parametrized using Voronoi cells with mobile g...

Fluid flow in pipes with discontinuous cross section or kinks is described through balance laws a non conservative product the source. At jump discontinuities pipes’ geometry, physics of problem suggests how to single out solution. On this basis, we present definition solution for general BV geometry and prove an existence result, consistent limiting procedure from piecewise constant geometries...