Solving the Navier-Stokes equations involves three computations to update the velocity at each time step: advection, diffusion, and force application. The result is a new velocity field, w, with nonzero divergence. But the continuity equation requires that we end each time step with a d...
Developing the next generation of low-emission, high-efficiency combustion devices rely on precise information on the distribution of gas species and gas temperature within the process. This, in turn, requires measurement methods that offer high spatial resolution while requiring minimal optical access....
why is the denoising diffusion model designed in terms of the forward process, the forward process posteriors, and backward process. And what is the relationship among these processes? By the way, in this article I call the forward process posteriors “the reverse of the forward process” ...
The first three gradients explained ~37% of the variance in the functional connectivity matrices. Source data are provided as a Source Data file. Full size image The cortical gradient analysis was used to map the functional brain connectome in a nonlinear diffusion space12. The method decomposes ...
u(t,x) is the expected value of the discounted future price calculated as X(T) exp(−∫Ttr(t) dt) under the condition X(t) = x. μ(t,X) and σ(t,X) are drift and diffusion of the stochastic process X(t). Get syms mu(t, X) sigma(t, X) r(t, X) u(t, X...
Understanding coal permeability as impacted by thermal damage is crucial to the detection of coal and gas hazards in deep coal mining. In this study, tri-axial compression experiments were performed to examine the damage and the permeability evolution process of methane-containing coal under different...
(Fig.5). Moreover, with the development of the preparation process of one put reaction, precipitation, sol–gel multi-step swelling, and polymerization in the presence of surface-active agents were used to obtain spherical particles with the desired size [40,41]. Nowadays, the assortments of...
The prediction of transient granular material flow is of fundamental industrial importance. The potential of using numerical methods in system design for i
The resulting cortical hypoperfusion and heterogeneous flow distribution in peritubular capillaries35, create large functional oxygen diffusion distances that are most effectively overcome if physical oxygen partial pressures are high36. Moreover, in our present experiments, we could not disclose any ...
the mild particle detachment could favor the balanced electrical and ionic conductivity of the particle. We point out that, beyond the diffusion kinetics, the particle detachment could have a negative impact from the mechanical perspective. Although it is beyond the scope of the present work, we ...