Euler diagrams visually represent containment, intersection and exclusion using closed curves. They first appeared several hundred years ago, however, there has been a resurgence in Euler diagram research in the twenty-first century. This was initially driven by their use in visual languages, where they can be used to represent logical expressions diagrammatically. This work lead to the require...

We derive the variational formulation of a gradient damage model by applying energetic rate-independent processes and obtain regularized fracture. The exhibits different behaviour at traction compression has state-dependent dissipation potential which induces path-independent work. will show how such provides natural framework for setting up consistent numerical scheme with underlying structure...

We show that the singular dissipative potential of the phenomenological rate-independent plasticity can be obtained by homogenization of a micro-model with quadratic dissipation. The essential ingredient making this reduction possible is a rugged energy landscape at the micro-scale, generating under external loading a regular cascade of subcritical bifurcations. Such landscape may appear as a r...

We study the asymptotic behavior of L∞ weak-entropy solutions to the compressible Euler equations with damping and vacuum. Previous works on this topic are mainly concerned with the case away from the vacuum and small initial data. In the present paper, we prove that the entropy-weak solution strongly converges to the similarity solution of the porous media equations in L(R) (2 p < ∞) with deca...

We deene an Euler type weak approximation for solutions of nonlinear diiusion processes. We nd the rate of convergence of this scheme in weak form. As in the diiusion case the weak rate of convergence is better than the strong one. The proof uses the integration by parts formula of Malliavin calculus.

This article presents the analysis of the rate of convergence of a stochastic particle method for 1D viscous scalar conservation laws. The convergence rate result is O(∆t+1/ √ N), where N is the number of numerical particles and ∆t is the time step of the first order Euler scheme applied to the dynamic of the interacting particles.

In this short note, a direct proof of L2 convergence of an Euler–Maruyama approximation of a Zakai equation driven by a square integrable martingale is shown. The order of convergence is as known for real-valued stochastic differential equations and for less general driving noises O( √ ∆t) for a time discretization step size ∆t.

A discrete stability theorem for set-valued Euler’s method with state constraints is proven. This theorem is combined with known stability results for differential inclusions with so-called smooth state constraints. As a consequence, order of convergence equal to 1 is proven for set-valued Euler’s method, applied to state-constrained differential inclusions.

Abstract In this paper, we propose a new model to address the problem of negative interest rates that preserves analytical tractability original Cox–Ingersoll–Ross (CIR) without introducing shift market rates, because it is defined as difference two independent CIR processes. The strength our lies within fact very simple and can be calibrated zero yield curve using an formula. We run several nu...