Hyers–Ulam stability of linear differential operator with constant coefficients

Let P(z) be a polynomial of degree n with complex coefficients and consider the n–th order linear differential operator P(D). We show that the equation P(D)f = 0 has the Hyers–Ulam stability, if and only if the equation P(z) = 0 has no pure imaginary solution. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

CO2 dynamic adsorption/desorption on zeolite 5A studied by 13C magnetic resonance imaging

We present the first 13C magnetic resonance imaging study of CO2 transient adsorption/desorption processes in a zeolite 5A column. CO2 transient concentration profiles were measured with a centric scan spin-echo single point imaging technique. The adsorption wave profiles were determined under flow conditions, with the results analyzed by the Bohart-Adams model. The model adequately accounts for the spatial and the temporal behavior of CO2 in the column. CO2 adsorption rate constants were calculated from the fit. Desorption profiles were acquired by blowing a helium stream through a zeolite 5A column saturated with CO2. An asymmetry between the adsorption and desorption profiles is readily apparent. A linear relationship between the CO2 condensed phase concentration and square root of time was observed.     

Group-velocity-matched cascaded quadratic nonlinearities of femtosecond pulses in periodically poled MgO:LiNbO3

Large nonlinear phase shifts were generated with femtosecond pulses at 1560 nm through cascaded quadratic interactions in periodically poled MgO-doped LiNbO3. The off-diagonal component of the nonlinear coefficient was utilized for simultaneous quasi phase matching and group-velocity matching. The effective nonlinear refractive index was varied from -2.9 x 10(-14) to +3.3 x 10(-14) cm2/W by tuning the phase-mismatch conditions.     

Single component and binary diffusion of n-heptane and toluene in SBA-15 materials

In this work, the diffusion properties of single component n-heptane and toluene as well as their binary mixtures in two SBA-15 samples with different structural characteristics were studied by the standard Zero Length Column (ZLC) technique under three different concentration levels. A theoretical ZLC desorption model considering the Generalized Maxwell-Stefan (GMS) formulation was developed. Using the independently measured single component equilibrium and kinetic parameters, the model was able to reasonably predict experimental binary ZLC desorption curve for countercurrent diffusion of toluene in the presence of n-heptane. However, there was a significant deviation between model prediction results and experimental data for countercurrent desorption of n-heptane in the presence of toluene. The diffusion of n-heptane is reduced by the presence of toluene, regardless of the relative content of micropores in the intrawall pores, while that of toluene is virtually unaffected by the counter-diffusion of n-heptane. The observed phenomena cannot be addressed by the simple model considering the cross term diffusion effect. The structural property of material and the molecular characteristics of probe molecules were used to account for the difference in the behavior between n-heptane and toluene.     

Structure and diffusion characterization of SBA-15 materials

In situ formation of the micro- and mesoporous structures of SBA-15 materials was investigated. It was found that the structure is significantly different from that for cylindrical or hexagonal pores, which suggests that the SBA-15 is more complex than an array of hexagonally ordered channels. Nitrogen adsorption isotherms at 77 K provided evidence that large (primary) mesopores are accompanied by a certain amount of significantly smaller pores with a broad distribution in the micropore/small-mesopore range within the mesoporous walls of main channels. It was found that the microporosity can be controlled by the time of heating as well as the synthesis temperature. The diffusion properties of n-heptane as a probe molecule in four selected SBA-15 samples with different micropore volumes were studied by the standard zero length column technique and related to their structural characteristics. The results have shown that the diffusion process involving n-heptane at a low concentration level takes place inside the walls of main mesoporous channels and depends on the relative content of micropores. In the samples that have a relatively high content of micropores, n-heptane diffusivities are relatively low, their activation energies are high, and the process is similar to diffusion in typical microporous adsorbents, like zeolites. As the micropore content is decreased, diffusion becomes more and more controlled by secondary mesopores of the intrawall pore structure, rendering diffusion faster and activation energies lower.     

Influence of the variance of degree distributions on the evolution of cooperation in complex networks

We study how initial network structure affects the evolution of cooperation in a spatial prisoner’s dilemma game. The network structure is characterized by various statistical properties. Among those properties, we focus on the variance of the degree distribution, and inquire how it affects the evolution of cooperation by three methods of imitation. For every method, it was found that a scale-free network does not always promote the evolution of cooperation, and that there exists an appropriate value of the variance, at which cooperation is optimal.     

Toward observation of single-file diffusion using the tracer zero-length column method

The tracer zero-length column (ZLC) method has been employed to study the diffusion of toluene in one-dimensional ZSM-12 and SAPO-5 zeolites. A significant deviation in the shape of the measured tracer exchange curves from monoexponential behavior was observed for toluene diffusion in both adsorbents in the limit of long-time asymptotes. In contrast, water/ZSM-12 and acetylene/SAPO-5 systems exhibit tracer exchange curves that are close to monoexponential behavior. Monoexponential curves are usually observed for systems obeying normal (Fickian) diffusion. Such diffusion is expected for the latter two systems because the diameters of both sorbates are less than the radii of their corresponding host channels. The differences in the shape of the tracer exchange curves for large and small sorbates can be explained by assuming the occurrence of anomalous, single-file diffusion for large sorbates in narrow, one-dimensional channels.