More specifically, motion is first estimated at the coarsest resolution level. As coarse resolution input images are obtained by low-pass filtering and subsampling, noise is largely smoothed out and large-range interactions can be efficiently taken into account. Hence, a robust estimation is obtained, which captures the large trends in motion.

Traditional multi-grid method is a way of efficiently solving a large
system of algebraic equations, which may arise from the discretization
of some partial differential equations. For this reason, the
effective operators used at each level can all be regarded as an
approximation to the original operator at that level. In recent
years, Brandt has proposed to extend the multi-grid method to cases
when the effective problems solved at different levels correspond to
very different kinds of models (Brandt, 2002). For example, the
models used at the finest level might be molecular dynamics or Monte
Carlo models whereas the effective models used at the coarse levels
correspond to some continuum models. Brandt noted that there is no
need to have closed form macroscopic models at the coarse scale since
coupling to the models used at the fine scale grids automatically
provides effective models at the coarse scale.

h European Symposium on Computer Aided Process Engineering

This model determines the mechanical behavior of the material during laser melting. With the emergence of commercial software purporting to predict the distortion of components manufactured using laser powder bed fusion (LPBF) processes, it is necessary to have a public library of parts for modeling tool validation. This was the impetus for the formation of the Engage research conglomerate under America Makes, which is a National Center for Defense Manufacturing and Machining (NCDMM) project [1]. Through the America Makes project, production side research groups manufactured a number of geometries which were then used for validation of LPBF processes by additive manufacturing simulation software companies. This work describes one of the most difficult to model Inconel® 625 geometries from production at the General Electric Global Research Center (GEGRC) and simulated using Netfabb Simulation by Autodesk Inc.

Numerical results of mean gradient MI measured performance for a number of multisensor sequences are provided in Table 18.2. In almost all cases the objectively adaptive approach improves the performance compared to the non-adaptive case. This demonstrates the advantage of introducing the adaptation of fusion parameters to deal with changing input conditions and how it adds robustness to the fusion process. If the forward adaptive framework, based on QAB/F, is also applied to feature selection the performance improves further, e.g. A Digital Model of the BTEC Pilot Scale Bioreactor producing Green Fluorescent Protein (GFP) has been developed and implemented in Matlab Simulink. Furthermore, by analyzing the GFP production details, it was concluded to develop a multi-scale approach to increase the digital model’s fidelity.

Nanoindentation/scratching at finite temperatures: Insights from atomistic-based modeling

The advent of parallel computing also contributed to the development of multiscale modeling. Since more degrees of freedom could be resolved by parallel computing environments, more accurate and precise algorithmic formulations could be admitted. This thought also drove the political leaders to encourage the simulation-based design concepts. The periodicity of the weave pattern is usually used to reduce the RVE of the textile composite to a periodic unit cell. Obviously, a unit cell of a textile composite is an idealisation similar to the assumption of a regular fibre arrangement in a UD composite, whereas real samples exhibit some variations from this pattern.

The data extracted from the plant and the loop show that the wear rate is a function of the mean time between two consecutives steps (Lemaire and Le Calvar, 2001; Ford, 1992). Simulators are also useful to ascertain component characteristics (frequency, contact force level, kinematic’s etc.) when they result from vibrations induced by the water flow. These kinds of simulator are very sophisticated and difficult to use in regard to their dimensions and conditioning duration.

The development of multiscale models for predicting the mechanical response of GNP reinforced composite plate

When the system varies on a macroscopic scale, these
conserved densities also vary, and their dynamics is described by a
set of hydrodynamic equations (Spohn, 1991). In this case, locally,
the microscopic state of the system is close to some local equilibrium
states parametrized by the local values of the conserved densities. Partly for
this reason, the same approach has been followed in modeling complex
fluids, such as polymeric fluids. In order to model the complex rheological properties of polymer fluids,
one is forced to make more complicated constitutive assumptions with
more and more parameters. For polymer fluids we are often interested in
understanding how the conformation of the polymer interacts with the
flow. This kind of information is missing in the kind of empirical
approach described above.

Tests performed on tribometers in PWR conditions like Aurore (AREVA NP) that will be described in Section 15.4. The environment is simulated using autoclaves for the temperature and pressure parameters and experiments are performed in aqueous solution containing the same chemical compounds as the primary coolant. The contact kinematics are simulated taking into account results on dedicated loops (the MAGALY mock-up for instance). The main results were the reproduction of the same wear scars than those observed in nuclear power plants. The major difference concerns the wear rate which was four times lower in the loop test even if the number of steps was respected, but performed in a smallest duration between two contacts (1 s in the loop compared with 100 s minimum in power plants).

Multiscale analysis

In the equation-free approach, particularly patch
dynamics or the gap-tooth scheme, the starting point is the microscale
model. Various tricks are then used to entice the microscale
simulations on small domains to behave like a full simulation on the
whole domain. The other extreme is to work https://wizardsdev.com/en/news/multiscale-analysis/ with a microscale model, such as the first principle of quantum mechanics. As was declared by Dirac back in 1929 (Dirac, 1929), the right physical principle for most of what we are interested in is already provided by the principles of quantum mechanics, there is no need to look further.

• However, experimental determination of mechanical behaviour of dry yarns requires additional studies and can be a challenging problem.
• An artificial yarn path and constant yarn cross-section can lead to inadequate representation of the actual geometry.
• For simple fluids, this will result in the same
  Navier-Stokes equation we derived earlier, now with a formula for
  \(\mu\) in terms of the output from the microscopic model.
• Concurrent coupling allows
  one to evaluate these forces at the locations where they are needed.
• Then this temperature history is used to compute the mechanical response to the thermal loading, i.e. thermal, elastic, and plastic stresses and strains.

Post-process residual stresses can be determined using hole cutting methods [33,35–38], X-ray diffraction [6,13,39,40], or neutron diffraction [29,41]. Residual stresses, while excellent tools for the validation of mechanical models, are difficult to implement as hole drilling methods are limited to certain geometries, and diffraction techniques are often prohibitively expensive to complete. Furthermore many components are stress relieved post-build, limiting the industrial interest in residual stresses. Measurements of deformation however are simple and inexpensive to implement, while providing vital data to the experimentalist about the quality of the build and to the modeler about the quality of the simulation. Optical techniques can be used to compare post-process distortion, such as the photograph–model comparisons in Michaleris and DeBiccari [10], and Alimardani et al. [26]. Direct post-process measurements of deflection can also be effective, however the most comprehensive methods of post-process distortion measurement are 3D scanning techniques, as implemented by Hojny [42].

These two effects would require a tremendous amount of time, processing power, and data storage to complete. When one uses matched asymptotic expansions, the solution is constructed in different regions that are then patched together to form a composite expansion. The method of multiple scales differs from this approach in that it essentially starts with a generalized version of a composite expansion. In doing this, one introduces coordinates for each region (or layer), and these new variables are considered to be independent of one another. A consequence of this is that what may start out as an ordinary differential equation is transformed into a partial differential equation.

The same filtering and subsampling operations are then applied again on the resulting image, in a recursive way. The multi-scale approach rests upon the principle that physical phenomena can be lumped together in time, space, or both time and space. Several proposals have been made regarding general methodologies for
designing multiscale algorithms. This is a general strategy of
decomposing functions or more generally signals into components at
different scales.