Existence of stationary turbulent flows with variable positive vortex intensity

We prove the existence of stationary turbulent flows with arbitrary positive vortex circulation on non-simply connected domains. Our construction yields solutions for all real values of the inverse temperature with the exception of a quantized set, for which blow-up phenomena may occur. Our results complete the analysis initiated in Ricciardi and Zecca (2016).     

The equation of state of the hard-disc fluid revisited

Some points about the search for analytical expressions for the equation of state of the hard-disc fluid are discussed in the light of the most recent advances in the field. New and accurate equations of state for this fluid are proposed.     

An Algorithm for Computing the Singularity of the Generic Germ of a Pencil of Plane Curves

Abstract

We give an algorithm that describes the singularity of all but finitely-many germs in a pencil generated by two arbitrary germs of plane curve.     

A Singular Limit Problem for Conservation Laws Related to the Camassa–Holm Shallow Water Equation

We consider a shallow water equation of the Camassa–Holm type, which contains nonlinear dispersive effects as well as fourth order dissipative effects. We prove that as the diffusion and dispersion parameters tend to zero, with a condition on the relative balance between these two parameters, smooth solutions of the shallow water equation converge to discontinuous weak solutions of a scalar conservation law. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the L ^p setting.     

Correlations between quantum and stochastic systems with a dephasing coupling

Correlations between single qubit and classical environment are studied by means of the stochastic Liouville equation, where a dephasing coupling between them is assumed. When the dephasing of the qubit is characterized by the two-state-jump Markov process, the properties of the total, classical and quantum correlations are examined.     

Optimal error estimates of a decoupled scheme based on two-grid finite element for mixed Stokes–Darcy model

Although the numerical results suggest the optimal convergence order of the two-grid finite element decoupled scheme for mixed Stokes–Darcy model with Beavers–Joseph–Saffman interface condition in literatures, the numerical analysis only gets the optimal error order for porous media flow and a non-optimal error order that is half order lower than the optimal one in fluid flow. The purpose of this paper is to fill in the gap between the numerical results and the theoretical analysis.     

A transmission problem on a polygonal partition: regularity and shape differentiability

We consider a transmission problem on a polygonal partition for the two-dimensional conductivity equation. For suitable classes of partitions we establish the exact behaviour of the gradient of solutions in a neighbourhood of the vertexes of the partition. This allows to prove shape differentiability of solutions and to establish an explicit formula for the shape derivative.