Décroissance exponentielle du noyau de la chaleur sur la diagonale (II)

Summary We give some conditions for the heat kernel to have an asymptotic expansion in small time such that all coefficients vanish, although the phenomenon seems difficult to understand by large deviations theory. The fact that the leading term is not zero is strongly related to Bismut's condition. These examples are related to the Varadhan estimates of the density of a dynamical system submitted to small random perturbations. To understand that type of asymptotic, one must modify the definition of the distance by adding the Bismut condition (unnoticed, but hidden, in classical cases).     

Beitrag zur katalytischen Selektivit?tsmessung zur Charakterisierung von Oberfl?chen-Azidit?t

Ohne Zusammenfassung     

Conductivity and dielectric relaxation in various polyvinyl alcohol/ammonium salt composites

We studied electrical conductivity and dielectric relaxation in polyvinyl alcohol/ammonium chloride and polyvinyl alcohol/ammonium acetate composite films. Infrared absorbance showed the presence of H-bonding interaction between the salt and the polymer. X-ray diffraction showed the reduction of the grain size of ordered regions in the polymer matrix after adding salt. Thermo gravimetric analysis (TGA) showed water wt% content between 4.2 and 5.8%. Differential Scanning Calorimetry (DSC) showed the decrease of the glass transition due to retained water indicating its plasticizer effect. The ac conductivity studied in the frequency range from 10^?1 Hz to 1 MHz and the temperature range from 10 to 150°C is described by the universal law of Jonsher characterizing the charge transport in disordered materials. With NH₄Cl inclusion, the dc conductivity showed a higher value in the vicinity of 4% but with NH₄CH₃CO₂ the dc conductivity decreases monotonically by increasing the salt amount. By using the dielectric permittivity and dielectric modulus we detected three relaxation processes which we attributed to electrode/sample polarization, alpha relaxation and conductivity relaxation respectively.     

Electrical conductivity studies on carbon black loaded ethylene butylacrylate polymer composites

In this work we studied the electrical properties of carbon black mixed into ethylene butylacrylate copolymer, using impedance spectroscopy, in the frequency range from 100 Hz to 100 kHz and over the temperature range from 150 to 360 K. A series of samples was prepared with several filler contents, below and above the percolation threshold, which was calculated using direct current conductivity measurements. For concentrations below the critical concentration the negative temperature coefficient in resistivity effect is observed, and for concentrations above that threshold the positive temperature coefficient in resistivity effect is present. The dielectric response was analyzed using complex permittivity or modulus formalisms, depending on the concentration of filler in the polymer matrix. Havriliak–Negami model was used to fit the experimental results.     

Universality and extremal aging for dynamics of spin glasses on subexponential time scales

We consider random hopping time (RHT) dynamics of the Sherrington‐Kirkpatrick (SK) model and p‐spin models of spin glasses. For any of these models and for any inverse temperature β > 0 we prove that, on time scales that are subexponential in the dimension, the properly scaled clock process (time‐change process) of the dynamics converges to an extremal process. Moreover, on these time scales, the system exhibits aging‐like behavior, which we call extremal aging. In other words, the dynamics of these models ages as the random energy model (REM) does. Hence, by extension, this confirms Bouchaud's REM‐like trap model as a universal aging mechanism for a wide range of systems that, for the first time, includes the SK model. © 2011 Wiley Periodicals, Inc.