The no-slip boundary condition at a solid-liquid interface is at the center of our understanding of fluid mechanics. However, this condition is an assumption that cannot be derived from first principles and could, in theory, be violated. In this chapter, we present a review of recent experimental, numerical and theoretical investigations on the subject. The physical picture that emerges is that...

This paper explores the implications of the incompressibility of complex systems for the analysis and modelling of such systems. In particular, a provisional epistemology will be developed that attempts to remain faithful to the limitations derived from this aspect of complexity science. We will argue that such an investigation of complex systems highlights the relevance of paradigmatic plurali...

BACKGROUND Research has shown that accurate and timely communication between multidisciplinary clinicians involved in the care of complex and chronic health conditions is often challenging. The domain knowledge for these conditions is heterogeneous, with poorly categorized, unstructured, and inconsistent clinical vocabulary. The potential of boundary object as a technique to bridge communicatio...

We study the chromatic polynomials for m × n square-lattice strips, of width 9 ≤ m ≤ 13 (with periodic boundary conditions) and arbitrary length n (with free boundary conditions). We have used a transfer matrix approach that allowed us also to extract the limiting curves when n → ∞. In this limit we have also obtained the isolated limiting points for these square-lattice strips and checked some...

For implementation of the free surface boundary condition, a new subroutine has been introduced to an existing steady 3-D body fitted code. This code was previously written for steady flow simulation in closed ducts. The algorithm used in this subroutine reduces the instability problem according to the free surface wave generation. For code validation, it was applied to two different open cha...

We prove global stability results of DiPerna-Lions renormalized solutions to the initial boundary value problem for kinetic equations. The (possibly nonlinear) boundary conditions are completely or partially diffuse, which include the so-called Maxwell boundary condition, and we prove that it is realized (it is not relaxed!). The techniques are illustrated with the Fokker-Planck-Boltzmann equat...

Boundary states for D-branes at orbifold fixed points are constructed in close analogy with Cardy’s derivation of consistent boundary states in RCFT. Comments are made on the interpretation of the various coefficients in the explicit expressions, and the relation between fractional branes and wrapped branes is investigated for C/Γ orbifolds. The boundary states are generalised to theories with ...

The Sicily Channel Regional Model forecasting system: initial boundary conditions sensitivity and case study evaluation S. Gaberšek, R. Sorgente, S. Natale, A. Ribotti, A. Olita, M. Astraldi, and M. Borghini IMC – International Marine Centre Loc. Sa Mardini, 09170 Oristano, Italy University of Ljubljana, Department of Mathematics and Physics, Jadranska 19, Ljubljana, 1000, Slovenia ISMAR CNR se...

2 History of the no-slip condition 2 2.1 The previous centuries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 Traditional situations where slip occurs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.4 Newtonian liquids: no-sl...

It was recently shown that spacetime singularities in numerical relativity could be avoided by excising a region inside the apparent horizon in numerical evolutions. In this paper we report on the details of the implementation of this scheme. The scheme is based on using (1) a horizon locking coordinate which locks the coordinate system to the geometry, and (2) a finite differencing scheme whic...