The potential for future applications in CFD is large as computing capabilities are expected to continue to increase and more complex physical systems can be modeled realistically. The practice of CFD is more Engineering (art) than a rigorous mathematical science as many combinations of physical and...
and (b) derived features were developed and tested. We predicted that deep learning methods ingesting raw MRI imagery would ultimately have more representational power and would demonstrate better results. However, due to the complexity of the raw MRI imagery, the deep learning models we...
which require the solution of a free-boundary problem. Within this problem, the governing equations of fluid flow are coupled with a domain deformation approach. This work reviews five of those approaches: interface tracking using a boundary-conforming mesh and, in the interface...
These systems exhibit complex behaviors due to the interplay between bulk fluid coupling and surface effects, necessitating advanced modeling and simulation techniques [1]. The ability to accurately predict and control interfacial phenomena is of paramount importance in industrial processes such as oil ...
(Let us note that, when considered in the fluid cells of different periodicities, the dynamical systems described by the same system of Equations (1) are distinct, and thus the emergence of chaos in double- and quadruple-period elongated cells does not imply that the attractor for triple-...
On the other hand, it can be stated that the potential difference in performance of the studied systems will be related to the differences of the magnetic field distribution and may be evaluated by, and compared using, the experiment. Moreover, empirical comparison of the studied system’s ...
4.2. Solving Master Equation with the Aid of Wavelet Expansion Now we restrict our considerations to systems of master Equations (16) and (17) with symmetric transition probabilities, pi(x|y) = pi(y|x), depending only on the minimal ball containing the points x and y. Here: pip x|y ...
Therefore, the simplifying mathematical assumptions made in continuum mechanics are not satisfied by this model and should not be enforced especially in studies of living systems. New experimental protocols and devices will be needed in order to successfully use the proposed model in practice. 2.2. ...
Third, we divide Equation (7c) by the mass density and multiply it by the time step ∆t and bring it also to the unit of power. The choice of the unit, herein the unit of power, is arbitrary. Often the formulation is employed in a dimensionless form generating the well-known ...