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31.
Gunter Moeller 《Journal of Polymer Science.Polymer Physics》2009,47(16):1573-1587
We used atomic force microscopy (AFM) nanoindentation to measure mechanical properties of polymers. Although AFM is generally acknowledged as a high‐resolution imaging tool, accurate quantification of AFM nanoindentation results is challenging. Two main challenges are determination of the projected area for objects as small as AFM tips and use of appropriate analysis methods for viscoelastic materials. We report significant accuracy improvements for modulus measurements when large end‐radius tips with appropriate cantilever stiffnesses are used for indentation. Using this approach, the instantaneous elastic modulus of four polymers we studied was measured within 30 to 40% of Dynamic Mechanical Analysis (DMA) results. The probes can, despite their size and very high stiffnesses, be used for imaging of very small domains in heterogeneous materials. For viscoelastic materials, we developed an AFM creep test to determine the instantaneous elastic modulus. The AFM method allows application of a nearly perfect stepload that facilitates data analysis based on hereditary integrals. Results for three polymers suggest that the observed creep in the materials has a strong plastic flow component even at small loads. In this respect, the spherical indenter tips behave like “sharp” indenters used in indentation studies with instrumented indenters. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1573–1587, 2009 相似文献
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Fernando Pigeard de Almeida Prado Gunter M. Schütz 《Journal of statistical physics》2011,142(5):984-999
We consider a kinetic Ising model which represents a generic agent-based model for various types of socio-economic systems.
We study the case of a finite (and not necessarily large) number of agents N as well as the asymptotic case when the number of agents tends to infinity. The main ingredient are individual decision thresholds
which are either fixed over time (corresponding to quenched disorder in the Ising model, leading to nonlinear deterministic
dynamics which are generically non-ergodic) or which may change randomly over time (corresponding to annealed disorder, leading
to ergodic dynamics). We address the question how increasing the strength of annealed disorder relative to quenched disorder
drives the system from non-ergodic behavior to ergodicity. Mathematically rigorous analysis provides an explicit and detailed
picture for arbitrary realizations of the quenched initial thresholds, revealing an intriguing “jumpy” transition from non-ergodicity
with many absorbing sets to ergodicity. For large N we find a critical strength of annealed randomness, above which the system becomes asymptotically ergodic. Our theoretical
results suggests how to drive a system from an undesired socio-economic equilibrium (e.g. high level of corruption) to a desirable
one (low level of corruption). 相似文献
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Christophe Gallesco Serguei Popov Gunter M. Schütz 《Journal of statistical physics》2013,150(2):285-298
We consider a continuous time random walk X in a random environment on ?+ such that its potential can be approximated by the function V:?+→? given by $V(x)=\sigma W(x) -\frac {b}{1-\alpha}x^{1-\alpha}$ where σW a Brownian motion with diffusion coefficient σ>0 and parameters b, α are such that b>0 and 0<α<1/2. We show that P-a.s. (where P is the averaged law) $\lim_{t\to\infty} \frac{X_{t}}{(C^{*}(\ln\ln t)^{-1}\ln t)^{\frac{1}{\alpha}}}=1$ with $C^{*}=\frac{2\alpha b}{\sigma^{2}(1-2\alpha)}$ . In fact, we prove that by showing that there is a trap located around $(C^{*}(\ln\ln t)^{-1}\ln t)^{\frac{1}{\alpha}}$ (with corrections of smaller order) where the particle typically stays up to time t. This is in sharp contrast to what happens in the “pure” Sinai’s regime, where the location of this trap is random on the scale ln2 t. 相似文献
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Gunter Dufner 《Periodica Mathematica Hungarica》1995,30(1):37-60
Ohne Zusammenfassung
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We introduce root systems for those imprimitive complex reflection groups which are generated by involutory reflections, and study the associated length functions. These have many properties in common with the usual length functions for finite Weyl groups. 相似文献
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