Construction of invariant measures of Lagrangian maps: minimisation and relaxation

If F is an exact symplectic map on the{\it d}-dimensional cylinder , with a generating function h having superlinear growth and uniform bounds on the second derivative, we construct a strictly gradient semiflow on the space of shift-invariant probability measures on the space of configurations . Stationary points of are invariant measures of F, and the rotation vector and all spectral invariants are invariants of . Using and the minimisation technique, we construct minimising measures with an arbitrary rotation vector , and with an additional assumption that F is strongly monotone, we show that the support of every minimising measure is a graph of a Lipschitz function. Using and the relaxation technique, assuming a weak condition on (satisfied e.g. in Hedlund's counter-example, and in the anti-integrable limit) we show existence of double-recurrent orbits of F (and F-ergodic measures) with an arbitrary rotation vector , and action arbitrarily close to the minimal action . Received November 4, 1999; in final form July 29, 2000 / Published online April 12, 2001     

Acid–base features of ex-hydrotalcites Mg-containing and Mg-free mixed oxides

CuNiAl and MgCuNiAl mixed oxides (Cu²⁺/Ni²⁺ = 0.29 and 0.32 mol/mol) were obtained from layered double hydroxide precursors (M²⁺/Al³⁺ = 2 mol/mol) synthesized by pH-controlled co-precipitation. After structural and textural characterization (by X-ray diffraction and N₂ physisorption, respectively), the acid and basic features of the mixed oxides were investigated by adsorption microcalorimetry. NH₃ and CO₂ were used for probing the acid and basic features, respectively. By the use of temperature-programmed technique, the redox features of the oxides were investigated as well. The behaviour of the oxides as catalysts for the conversion of 4-methylpentan-2-ol at 448, 473, and 523 K under atmospheric pressure was studied in a fixed-bed reactor. The dehydration products distribution and the relative extents of the dehydration and dehydrogenation reactions are discussed in terms of the possible occurrence, depending on the lack or presence of Mg in the oxide and the reaction temperature, of either acid–base-governed E1 and E2 mechanisms or Cu-promoted reaction pathways.     

S toP wave form factors in semi-leptonicB decays

We apply HQET to semi-leptonicB andB _s meson decays into the observed charmedp wave states. In order to examine the sensitivity of the results to the choice of a specific model, we perform all calculations using several different meson models, and find that uncertainty introduced by the choice of a particular model is about 30%. Specifically, assuming?? _B=1.50ps andV _cb=0.040, we obtain branching ratios of (0.27±0.08)% and (0.45±0.14)% for $B \to D_1 l\bar \upsilon _1 $ and $B \to D_2^* l\bar \upsilon _1 $ decays, respectively.     

Modeling and simulation of the motion of nanoparticles in cylindrical capillaries allowing particle‐to‐wall interactions

The process of transporting nanoparticles at the blood vessels level stumbles upon various physical and physiological obstacles; therefore, a Mathematical modeling will provide a valuable means through which to understand better this complexity. In this paper, we consider the motion of nanoparticles in capillaries having cylindrical shapes (i.e., tubes of finite size). Under the assumption that these particles have spherical shapes, the motion of these particles reduces to the motion of their centers. Under these conditions, we derive the mathematical model, to describe the motion of these centers, from the equilibrium of the gravitational force, the hemodynamic force and the van der Waals interaction forces. We distinguish between the interaction between the particles and the interaction between each particle and the walls of the tube. Assuming that the minimum distance between the particles is large compared with the maximum radius R of the particles and hence neglecting the interactions between the particles, we derive simpler models for each particle taking into account the particles‐to‐wall interactions. At an error of order O(R) or O(R³)(depending if the particles are 'near' or 'very near' to the walls), we show that the horizontal component of each particle's displacement is solution of a nonlinear integral equation that we can solve via the fixed point theory. The vertical components of the displacement are computable in a straightforward manner as soon as the horizontal components are estimated. Finally, we support this theory with several numerical tests. Copyright © 2016 John Wiley & Sons, Ltd.     

Symmetric multiple chessboard complexes and a new theorem of Tverberg type

We prove a new theorem of Tverberg–van Kampen–Flores type, which confirms a conjecture of Blagojevi? et al. about the existence of ‘balanced Tverberg partitions’ (Conjecture 6.6 in [Tverberg plus constraints, Bull. London Math. Soc. 46:953–967 (2014]). The conditions in this theorem are somewhat weaker than in the original conjecture, and we show that the theorem is optimal in the sense that the new (weakened) condition is also necessary. Among the consequences is a positive answer (Theorem 7.2) to the ‘balanced case’ of the question asking whether each admissible r-tuple is Tverberg prescribable (Blagojevi? et al. 2014, Question 6.9).     

Large Eddy Simulation of Flow Control Around a Cube Subjected to Momentum Injection

The concept of Momentum Injection (MI) through Moving Surface Boundary layer Control (MSBC) applied to a cubic structure is numerically studied using Large Eddy Simulation at a Reynolds number of 6.7×10⁴. Two small rotating cylinders are used to add the momentum at the front vertical edges of the cube. Two configurations are studied with the yaw angle of 0° and 30°, respectively, with ratio of the rotation velocity of cylinders and the freestream velocity of 2. The results suggest that MI delays the boundary layer separation and reattachment, and thus reduces the drag. A drag reduction of about 6.2 % is observed in the 0° yaw angle case and about 44.1 % reduction in the 30° yaw angle case. In the case of 0° yaw angle, the main change of the flow field is the disappearance of the separation regions near the rotating cylinders and the wake region is slightly changed due to MI. In the 30° yaw angle case, the flow field is changed a lot. Large flow separations near one rotating cylinder and in the wake is significantly reduced, which results in the large drag reduction. Meanwhile, the yaw moment is increased about 50.5 %.     

Analytic extension and reconstruction of obstacles from few measurements for elliptic second order operators

We deal with an inverse obstacle problem for general second order scalar elliptic operators with real principal part and analytic coefficients near the obstacle. We assume that the boundary of the obstacle is a non-analytic hypersurface. We show that, when we put Dirichlet boundary conditions, one measurement is enough to reconstruct the obstacle. In the Neumann case, we have results only for n = 2, 3 in general. More precisely, we show that one measurement is enough for n = 2 and we need 3 linearly independent inputs for n = 3. However, in the case for the Helmholtz equation, we only need n ? 1 linearly independent inputs, for any n ≥ 2. Here n is the dimension of the space containing the obstacle. These are justified by investigating the analyticity properties of the zero set of a real analytic function. In addition, we give a reconstruction procedure for each case to recover the shape of obstacle. Although we state the results for the scattering problems, similar results are true for the associated boundary value problems.     

Detection of point-like scatterers using one type of scattered elastic waves

In this paper, we are concerned with the detection of point-like obstacles using elastic waves. We show that one type of waves, either the P or the S scattered waves, is enough for localizing the points. We also show how the use of S incident waves gives better resolution than the P waves. These affirmations are demonstrated by several numerical examples using a MUSIC type algorithm.     

An efficient very large eddy simulation model for simulation of turbulent flow

Among the various hybrid methodologies, Speziale's very large eddy simulation (VLES) is one that was proposed very early. It is a unified simulation approach that can change seamlessly from Reynolds Averaged Navier–Stokes (RANS) to direct numerical simulation (DNS) depending on the numerical resolution. The present study proposes a new improved variant of the original VLES model. The advantages are achieved in two ways: (i) RANS simulation can be recovered near the wall which is similar to the detached eddy simulation concept; (ii) a LES subgrid scale model can be reached by the introduction of a third length scale, that is, the integral turbulence length scale. Thus, the new model can provide a proper LES mode between the RANS and DNS limits. This new methodology is implemented in the standard k ? ? model. Applications are conducted for the turbulent channel flow at Reynolds number of Re_τ = 395, periodic hill flow at Re = 10,595, and turbulent flow past a square cylinder at Re = 22,000. In comparison with the available experimental data, DNS or LES, the new VLES model produces better predictions than the original VLES model. Furthermore, it is demonstrated that the new method is quite efficient in resolving the large flow structures and can give satisfactory predictions on a coarse mesh. Copyright © 2012 John Wiley & Sons, Ltd.