Relaxation intensity in some polyacrylates

Empirical formula suggested by Kita and Koizumi for evaluation of relaxation intensity in a limited range of frequency around the relaxation frequency for the Cole-Cole type distribution has been tested for poly butyl acrylate (PBA), Poly butyl methacrylate (PBMA) and poly isobutyl methacrylate (PiBMA). The relaxation intensity Δε is expressed in terms ofε″ _M , the dielectric loss maxima andW, the frequency separation for half, two thirds or three quarters ofε″ _M , in the form Δε=ε″ _M /[(C ₁/W)+C ₂+C ₃ W], where the numerical constantsC ₁,C ₂,C ₃ are given for the respective type of relaxation.     

Experimental and modelling study of gasoline surrogate mixtures oxidation in jet stirred reactor and shock tube

The oxidation of several mixtures of surrogate for gasoline was studied using a jet stirred reactor and a shock tube. One representative of each classes constituting gasoline was selected: iso-octane, toluene, 1-hexene and ethyl tert-butyl ether (ETBE). The experiments were carried out in the 800-1880 K temperature range, for two different initial pressures (0.2 and 1 MPa), with an initial fuel molar fraction of 0.001. The equivalence ratio varied from 0.5 to 1.5. Each hydrocarbon sub-mechanism was validated using shock tube data. The full mechanism describing the surrogate fuel oxidation is constituted of the sub-mechanisms for each fuel components and by adding interaction reactions between different hydrocarbon fragments. Good agreement between the experimental results and the computations was observed under JSR and shock tube conditions.     

Diffusion-relaxation correlation in simple pore structures

The effects of independent encoding for relaxation and for diffusion using separate time and gradient dimensions are calculated for spins diffusing in plane parallel and spherical pores with relaxing walls. Two-dimensional inverse Laplace transformation is used to obtain computed (D,T(2)) maps for both geometries, in the regime in which the dimensionless diffusion coefficient is less than unity and the dimensionless relaxation parameter of order unity or greater. It is shown that there exist two distinct branches on the (D,T(2)) maps, one with diffusion and relaxation strongly correlated and one in which the diffusion coefficients vary widely independently of relaxation.     

Relaxivities of human liver and spleen ferritin

Ferritin, the iron-storing protein of mammals, is known to darken T₂-weighted magnetic resonance images. This darkening can be used to noninvasively measure an organ's iron content. Significant discrepancies exist between T₂ data obtained with ferritin-containing tissues and with aqueous solutions of horse spleen ferritin (HSF). The NMR properties of stable human ferritin have never been studied in aqueous solutions. Relaxometry results on human liver and spleen ferritin are reported here, showing that the relaxation induced in aqueous solutions by human ferritins is comparable to that induced by HSF. As a consequence, the differences between ferritin-containing human tissues and ferritin solutions cannot be attributed to different NMR properties of human and horse ferritins, but probably to a clustering of the protein in vivo.     

Algebraic description of spin 3/2 dynamics in NMR experiments

The dynamics of spin 3/2 systems is analyzed using the density matrix theory of relaxation. By using the superoperator formalism, an algebraic formulation of the density matrix's evolution is obtained, in which the contributions from free relaxation and RF application are easily factored out. As an intermediate step, an exact form for the propagator of the density matrix for a spin 3/2 system, in the presence of static quadrupolar coupling, inhomogeneous static magnetic field, and relaxation is demonstrated. Using this algebraic formulation, exact expressions for the behavior of the density matrix in the classical one-, two-, and three-pulse experiments are derived. These theoretical formulas are then used to illustrate the bias introduced on the measured relaxation parameters by the presence of large spatial variations in the B0 and B1 fields. The theoretical predictions are easily evaluated through simple matrix algebra and the results agree very well with the experimental observations. This approach could prove useful for the characterization of the spatial variations of the signal intensity in multiple quantum-filtered sodium MRI experiments.     

NMR detection of thermal damage in carbon fiber reinforced epoxy resins

Composite materials of epoxy resins reinforced by carbon fibers are increasingly being used in the construction of aircraft. In these applications, the material may be thermally damaged and weakened by jet blast and accidental fires. The feasibility of using proton NMR relaxation times T1, T1rho, and T2 to detect and quantify the thermal damage is investigated. In conventional spectrometers with homogeneous static magnetic fields, T1rho is readily measured and is found to be well correlated with thermal damage. This suggests that NMR measurements of proton T1rho may be used for non-destructive evaluation of carbon fiber-epoxy composites. Results from T1rho measurements in the inhomogeneous static and RF magnetic fields of an NMR-MOUSE are also discussed.     

Relaxation of an optimal control problem involving a perturbed sweeping process

We establish first, in the setting of infinite dimensional Hilbert space, a result concerning the existence of solutions for perturbed sweeping processes whose perturbations are Lipschitz single-valued maps. Then we use this result to extend to the infinite dimensional setting a relaxation result concerning optimal control problems involving such processes. Dedicated to R. Tyrrell Rockafellar on the occasion of his 70th birthday     

A relaxation algorithm for the minimization of a quasiconcave function on a convex polyhedron

A study was made of the global minimization of a general quasiconcave function on a convex polyhedron. This nonconvex problem arises in economies of scale environments and in alternative formulations of other well-known problems, as in the case of bilinear programming.Although not very important in our final results, a local minimum can be easily obtained. However, a major aspect is the existence of two families of lower bounds on the optimal functional value: one is provided by non-linear programming duality, the other is derived from a lexicographic ordering of basic solutions which allows the use of relaxation concepts. These results were exploited in a finite algorithm for obtaining the global minimum whose initial implementation has had encouraging performance.     

Some relationships between lagrangian and surrogate duality in integer programming

Lagrangian dual approaches have been employed successfully in a number of integer programming situations to provide bounds for branch-and-bound procedures. This paper investigates some relationship between bounds obtained from lagrangian duals and those derived from the lesser known, but theoretically more powerful surrogate duals. A generalization of Geoffrion's integrality property, some complementary slackness relationships between optimal solutions, and some empirical results are presented and used to argue for the relative value of surrogate duals in integer programming. These and other results are then shown to lead naturally to a two-phase algorithm which optimizes first the computationally easier lagrangian dual and then the surrogate dual.