Sentence examples for instance diffusion from inspiring English sources

However, such a mapping is generally ill-defined; for instance, diffusion measurements are antipodally symmetric (diffusion along x and –x are equal), whereas the distribution of fibre orientations within a voxel is generally not symmetric.

However, it has been found that the constant-order fractional diffusion equations are not capable of characterizing some complex diffusion processes, for instance, diffusion process in aninhomogeneous or heterogeneous medium [7].

For instance, diffusion and thermal expansion coefficients of CNT-reinforced nanocomposites have been studied through micromechanics models without sufficient atomic scale information [6] or molecular dynamics (MD) models with very high computational cost and complexity [7].

Fractional partial differential equations arise in a wide variety of physical situations which are often used to demonstrate the anomalous diffusion behaviors, for instance, diffusion of plasma, transport of fluid in porous media, diffusion at liquid surfaces, Lévy flights in the two-dimensional rotating flow, etc. [3, 4].

For instance, diffusion of small substrates through heme-dependent enzyme molecules requires the transient appearance of channels in the protein structure.

For instance, diffusion from inside the nucleus to the cytoplasm, diffusion from the cytoplasm into the nucleus, or diffusion from the extracellular matrix into a cell all have distinctive boundary conditions that allow for 'driving' molecular directionality.

Larger molecules have slower diffusivities; for instance, the diffusion constant for the protein bovine serum albumin (69 kDa) in an aqueous solution is approximately 1 × 10−11 m2/s [49], while those for small ions and for ethanol in water are around 10−9 m2/s [52].

A new generation of registration algorithms embedding architectural features inferred for instance from diffusion or functional MRI is on the verge to improve the architectural value of spatial normalization.

Deng [15] indicated that, using the nonlocal condition u(0) + h u) = u 0 to describe for instance, the diffusion phenomenon of a small amount of gas in a transparent tube can give better result than using the usual local Cauchy problem u(0) = u 0. Let us observe also that since Deng's papers, the function h is considered.

Deng [15] indicated that using the nonlocal condition u ( 0 ) + h ( u ) = u 0 to describe, for instance, the diffusion phenomenon of a small amount of gas in a transparent tube can give a better result than using the usual local Cauchy problem u ( 0 ) = u 0. Let us observe also that since Deng's papers, the function h is considered h ( u ) = ∑ k = 1 p c k u ( t k ), (1.3).

Deng [17] indicated that, using the nonlocal condition u ( 0 ) + g ( u ) = x 0 to describe for instance, the diffusion phenomenon of a small amount of gas in a transparent tube can give better result than using the usual local Cauchy problem u ( 0 ) = x 0. For example, g ( u ) can be given by g ( u ) = ∑ i = 1 n c i u ( τ i ), (1.3).