We extend our approach for the exact solution of the Riemann problem in relativistic hydrodynamics to the case in which the fluid velocity has components tangential to the initial discontinuity. As in one-dimensional flows, we here show that the wave-pattern produced in a multidimensional relativistic Riemann problem can be predicted entirely by examining the initial conditions. Our method is l...

In Newtonian and relativistic hydrodynamics the Riemann problem determines the evolution of a fluid which is initially characterized by two states having different rest-mass density, pressure, and velocity. When the fluid is allowed to relax, one of three possible wave patterns is produced, corresponding to the propagation in opposite directions of two nonlinear hydrodynamical waves. New effect...

The motion of vortex sheets with surface tension has been analyzed in the setting of irrotational flows by Ambrose [1] and Ambrose & Masmoudi [2] in 2D, and by Ambrose & Masmoudi [3] in 3D. With irrotationality, the nonlinear Euler equations reduce to Poisson’s equation for the pressure function in the bulk, and the motion of the vortex sheet is decoupled from that of the fluid, thus allowing b...

Many hydrodynamic instability patterns can be put into correspondence with a subset of characteristic surfaces of tangential discontinuities. These topological limits sets to systems of hyperbolic PDE's are locally unstable, but a certain subset associated with minimal surfaces are globally stabilized, persistent and non-dissipative. Sections of these surfaces are the spiral scrolls so often ob...

Numerical methods such as boundary element and finite element methods are widely used for the stress analysis in solid mechanics. This study presents boundary element method based on the displacement discontinuity formulation to solve general problems of interaction between hydraulic fracturing and discontinuities. The crack tip element and a higher order boundary displacement collocation techn...

In this talk, I document the existence of degenerate discontinuity-induced bifurcation scenarios in the lowcontact-velocity dynamics during tapping-mode atomic-force microscopy. Specifically, numerical analysis of a model of the microscope dynamics shows branch point and isola bifurcations associated with the emergence of two families of saddle-node bifurcation points along a branch of low-ampl...

numerical methods such as boundary element and finite element methods are widely used for the stress analysis in solid mechanics. this study presents boundary element method based on the displacement discontinuity formulation to solve general problems of interaction between hydraulic fracturing and discontinuities. the crack tip element and a higher order boundary displacement collocation techn...

The transition from the ordered commensurate phase to the incommensurate gaussian phase of the antiferroelectric asymmetric six-vertex model is investigated by keeping the temperature constant below the roughening point and varying the external fields (h, v). In the (h, v) plane, the phase boundary is approached along straight lines δv = kδh, where (δh, δv) measures the displacement from the ph...