Stationary turbulent closure via the Hopf functional equation

Exact closed-form solutions are exhibited for the Hopf equation for stationary incompressible 3D Navier-Stokes flow, for the cases of homogeneous forced flow (including a solution with depleted nonlinearity) and inhomogeneous flow with arbitrary boundary conditions. This provides an exact method for computing two- and higher-point moments, given the mean flow.     

Spectral decomposition of an elementary 3-fermion 2-body operator

The eigenvalues and eigenfunctions of an elementary 3-fermion 2-body operator 3P²_g∧I¹A³∑_{1≤i≤j≤3}P²_g(i, j)A³ acting on a 3-particle antisymmetric finite-dimensional Hilbert space have been found. Here P_g² denotes the projection operator onto a 2-particle antisymmetric function g², while A³ denotes the 3-particle antisymmetrizing operator.     

A laser Doppler anemometry technique for Reynolds stresses measurement

A technique is described for the measurement of all components of mean velocity and Reynolds stresses, in a complex turbulent flow where achieving coincidence data acquisition is difficult. The method is based on data recorded using four orientations of the laser probe. It is shown that the measurement errors are not the same for all the components of the Reynolds tensor, but they are sufficiently small to give a good accuracy. An application to a turbomachinery flow is given to illustrate the method.     

On-line cysteine modification for protein analysis: new probes for electrochemical tagging nanospray mass spectrometry

A series of electrogenerated selective electrophiles based on substituted benzoquinones has been characterized as tags for l-cysteine and cysteine residues in proteins. The electrophiles are generated electrochemically from the corresponding hydroquinones. It is shown from mass spectrometry analysis that the electrogenerated benzoquinone can tag the biomolecules. The rate constants pertaining to the addition of l-cysteine onto the electrogenerated benzoquinones have been determined using electrochemical techniques. The substitution patterns have been unraveled leading to the assessment of site-specific rate constants. It is shown that the rate constants are primarily dependent on the electronic nature of the substituents as expressed by the Hammett substitution constant. The apparent tagging yields observed for l-cysteine in nanospray mass spectrometry experiments do not correspond to the yields expected from the electrochemical study, as the ionisation efficiencies are highly dependent on the tag. Finally, the on-line tagging has been tested using β-lactoglobulin A and myoglobin. Based on these results, it is concluded that the tagging reaction is selective towards cysteine when it takes place in the nanospray interface. The results show that the methodology presented can be used for a rapid characterization and identification of reactive sites in biomolecules.     

Quantitative Comparison of REAPDOR and TRAPDOR Experiments by Numerical Simulations and Determination of H–Al Distances in Zeolites

Quantitative H–Al distances in acid sites of two zeolites with MFI and IFR framework topology were obtained by numerical simulation of ¹H{²⁷Al} rotational echo adiabatic passage double resonance (REAPDOR) experiments. A ²⁷Al offset-dependent data set yields for each resolved ¹H NMR line a corresponding nuclear electric quadrupole coupling constant of the neighboring ²⁷Al site. This information is used for analyzing a second data set for on-resonance irradiation, where the dipolar evolution time (number of rotor cycles) was varied, to yield the ¹H–²⁷Al dipolar coupling constant. Numerical simulations indicate that the REAPDOR method does not depend significantly on the polar angles, defining the orientation of the electric field gradient tensor of ²⁷Al with respect to the Al–H dipolar vector. In contrast, the transfer of populations in double resonance sequence is sensitive to these angles, and it can be thus used to measure them.     

Differential effects of synchronous and asynchronous multifinger coactivation on human tactile performance

Background  

Repeated execution of a tactile task enhances task performance. In the present study we sought to improve tactile performance with unattended activation-based learning processes (i.e., focused stimulation of dermal receptors evoking neural coactivation (CA)). Previous studies show that the application of CA to a single finger reduced the stationary two-point discrimination threshold and significantly increased tactile acuity. These changes were accompanied by an expansion of the cortical finger representation in primary somatosensory cortex (SI). Here we investigated the effect of different types of multifinger CA on the tactile performance of each finger of the right hand.     

Discrete duality finite volume schemes for Leray−Lions−type elliptic problems on general 2D meshes

Discrete duality finite volume schemes on general meshes, introduced by Hermeline and Domelevo and Omnès for the Laplace equation, are proposed for nonlinear diffusion problems in 2D with nonhomogeneous Dirichlet boundary condition. This approach allows the discretization of non linear fluxes in such a way that the discrete operator inherits the key properties of the continuous one. Furthermore, it is well adapted to very general meshes including the case of nonconformal locally refined meshes. We show that the approximate solution exists and is unique, which is not obvious since the scheme is nonlinear. We prove that, for general W^?1,p′(Ω) source term and W^1‐(1/p),p(?Ω) boundary data, the approximate solution and its discrete gradient converge strongly towards the exact solution and its gradient, respectively, in appropriate Lebesgue spaces. Finally, error estimates are given in the case where the solution is assumed to be in W^2,p(Ω). Numerical examples are given, including those on locally refined meshes. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Barycentric systems and stretchability

Using a general resolution of barycentric systems we give a generalization of Tutte's theorem on convex drawing of planar graphs. We deduce a characterization of the edge coverings into pairwise non-crossing paths which are stretchable: such a system is stretchable if and only if each subsystem of at least two paths has at least three free vertices (vertices of the outer face of the induced subgraph which are internal to none of the paths of the subsystem). We also deduce that a contact system of pseudo-segments is stretchable if and only if it is extendible.