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  • Articles  (118)
  • diffusion  (118)
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  • Articles  (118)
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  • Springer  (118)
  • Blackwell Publishing Ltd
  • Elsevier
  • International Union of Crystallography
  • Taylor & Francis
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Stochastic environmental research and risk assessment 11 (1997), S. 397-422 
    ISSN: 1436-3259
    Keywords: Random flow field ; diffusion ; concentration ; fluctuations ; covariance ; variance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The concentration c(x,t) of a nonreactive solute undergoing advection and diffusion in a spatially random divergence-free flow field is analyzed. A leading order formulation for the spatial covariance of the concentration field, $$\overline {c'\left( {x,t} \right)c'\left( {x,t} \right)} $$ , is made. That formulation includes the velocity variability induced macrodispersive flux of the covariance field, and the smoothing effects of diffusion. Previous formulations of the concentration covariance had dropped at least one of these effects. It is shown that both these effects need to be included to obtain a qualitatively correct description of the concentration fluctuations.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Rheologica acta 21 (1982), S. 639-640 
    ISSN: 1435-1528
    Keywords: Non-homogeneous flow ; macromolecule ; diffusion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Adsorption 2 (1996), S. 77-87 
    ISSN: 1572-8757
    Keywords: diffusion ; molecular-dynamics simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract In this paper, we review our recent theoretical and simulation studies of the surface diffusion of n-alkanes, ranging in size from ethane to hexadecane, physically adsorbed on Pt(111). The model system exhibits many features seen experimentally. Through both animation of the molecular trajectories and determination of the minimum-energy path for nearest-neighbor hopping, we find that the shorter molecules (ethane through octane) all have similar diffusion mechanisms, involving coupled translation and rigid rod-like rotation in the surface plane. In addition, the diffusion energy barriers for these molecules increase nearly linearly with chain length in both the static and dynamic calculations. The diffusion of decane and hexadecane does not adhere to the trends for the shorter molecules and a decrease can be observed in the dynamical diffusion energies for these molecules. The diffusion of the longer molecules involves hops, with unique mechanisms, to second and third neighbor sites. Our static analysis has indicated, for decane, that the diffusion-energy barrier for third-neighbor hopping is lower than that for nearest-neighbor hopping and is in agreement with the trend seen in the dynamical diffusion barriers. Even though there is agreement between theoretical and simulated diffusion energy barriers for many of the molecules, the motion observed in the MD simulations does not agree with the assumptions of the hopping model. A model that can incorporate the influence of long flights would provide a more realistic description of the motion.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Adsorption 2 (1996), S. 95-101 
    ISSN: 1572-8757
    Keywords: osmosis ; reverse osmosis ; adsorption ; diffusion ; molecular dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract Computer simulation studies using the method of molecular dynamics have been carried out to investigate osmosis and reverse osmosis in solutions separated by semi-permeable membranes. The method has been used to study the dynamic approach to equilibrium in such systems from their initial nonequilibrium state. In addition density profiles of both the solute and solvent molecules have been investigated, especially near the walls for adsorption effects. Finally the diffusion coefficients and osmotic pressure have also been measured. Our results show both osmosis and reverse osmosis, as well as a smooth transition between the two when either the solution concentration is changed, or the density (pressure) difference between the solvent and solution compartments is varied. We believe this new method can be used to improve our understanding of these two important phenomena at the molecular level.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Adsorption 2 (1996), S. 133-143 
    ISSN: 1572-8757
    Keywords: diffusion ; sorption kinetics ; ZLC
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract The theoretical model and underlying assumptions used in the analysis of ZLC (zero length column) desorption curves are examined in detail. It is shown that the long time analysis generally yields reliable diffusivity values although, if the initial equilibrium condition is not properly established there will be significant error in the apparent equilibrium constant. The short time analysis is much more sensitive to such errors and a modified way of data analysis is suggested to overcome this problem. Varying the initial equilibration time provides an alternative ZLC experiment that can be used to establish the nature of the rate controlling mass transfer resistance. The utility of this approach is illustrated experimentally for the system C3H8-13X zeolite.
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  • 6
    ISSN: 1572-8757
    Keywords: diffusion ; kinetic measurements ; NaX zeolite ; water
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract The thermal frequency response and pulsed field gradient NMR methods are applied in a comparative study of water diffusion in zeolite NaX under non-equilibrium and equilibrium conditions. The obtained results are found to be in satisfactory agreement with each other, indicating that by applying the thermal frequency response method, complications due to uncontrolled water adsorption at the chamber walls inherent in conventional frequency response measurements may be circumvented.
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Adsorption 2 (1996), S. 265-277 
    ISSN: 1572-8757
    Keywords: frequency response ; diffusion cell ; kinetics ; diffusion ; heat effects
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract This paper deals with frequency response (FR) analysis of a closed diffusion cell system with two resonators, that is both the LHS and RHS volumes are modulated. The analysis is made for a homogeneous particle described by a single effective diffusivity as well as a biporous pellet described by macropore and micropore diffusions. It is shown that if the perturbation of the volume of the reservoir #2 is lagged behind that of the reservoir #1 by 3π/2, the pressure response in reservoir #1 is significantly enhanced with larger amplitude as well as phase angle. When the perturbations of the two reservoirs are out of phase, the heat effect is reduced and can become insignificant when the two perturbations are completely out of phase (ψ = π). Under such a condition, the pressure difference between the two reservoirs could be doubled. In the case of biporous pellets, it is shown that the FR behaviours obtained for micropore diffusion control and macropore diffusion control are well distinguished. In the former case, the FR system reduces to a traditional batch adsorber one while in the latter case, the FR behaviour is the same as for a two resonator system with homogeneous particles. This difference can be used for the discrimination of micropore and macropore diffusion processes.
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Celestial mechanics and dynamical astronomy 73 (1999), S. 65-76 
    ISSN: 1572-9478
    Keywords: resonance ; chaotic motion ; diffusion ; secondary resonances
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present a 3-D symplectic mapping model that is valid at the 2:1 mean motion resonance in the asteroid motion, in the Sun-Jupiter-asteroid model. This model is used to study the dynamics inside this resonance and several features of the system have been made clear. The introduction of the third dimension, through the inclination of the asteroid orbit, plays an important role in the evolution of the asteroid and the appearance of chaotic motion. Also, the existence of the secondary resonances is clearly shown and their role in the appearance of chaotic motion and the slow diffusion of the elements of the orbit is demonstrated.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Journal of theoretical probability 8 (1995), S. 77-96 
    ISSN: 1572-9230
    Keywords: Random walk ; diffusion ; spectral density ; graphs ; fractal dimensions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper continues the study of exponentsd(x), d ω (x), d R (x) andd μ (x) for graphG; and the nearest neighbor random walk {X n } n∈N onG, if the starting pointX 0=x is fixed. These exponents are responsible for the geometric, resistance, diffusion and spectral properties of the graph. The main concern of this paper is the relation of these exponents to the spectral density of the transition matrix. A series of new exponentse, e ω ,e R ,e μ are introduced by allowingx to vary along the vertices. The results suggest that the geometric and resistance properties of the graph are responsible for the diffusion speed on the graph.
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Celestial mechanics and dynamical astronomy 64 (1996), S. 21-31 
    ISSN: 1572-9478
    Keywords: KAM tori ; diffusion ; symplectic maps ; standard map
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Using mappings as model problem we study the structure around the last invariant KAM torus for different values of the perturbing parameter. We used the standard map for the analysis of the hierarchical structure existing around invariant KAM tori applying two complementary methods: the Laskar's frequency map analysis and the sup-map analysis. We recover and extend the theoretical prediction recently given by Morbidelli and Giorgilli about the existence of a neighborhood almost completely full of slave tori around a chief torus. We then make tests about the diffusion in order to measure the barrier to diffusion which still remains after the break-up of the last KAM torus.
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