Sentences with phrase «numerical solutions of»

An analytical model of subtropical mode water is presented, based on ventilated thermocline theory and on numerical solutions of a planetary geostrophic basin model.

Figure 2: The numerical solutions of Lorenz» equations plotted in the same coordinate system.

I'm a scientific programmer, and the relevant work was with numerical solutions of PDEs and in particular the Navier Stokes equations.; and in signal processing.

Dan Hughes blog on numerical solutions of Lorenz equations is a good read.

Using a semi-analytical method to find numerical solutions of the proposed model, they approximated various real - world scenarios.

The numerical solution of the time dependent Schrödinger equation for the investigated atoms in a strong laser field provided excellent agreement of the theory with the experimental data in both regimes.

What is surprising in this method is that the mathematics of shape, in the form of what differential - geometers call the curvature flow, is coupled with techniques that originated in the numerical solution of partial differential equations to deblur and denoise an image.

The principle of the first method lies on the numerical solution of Newton's equations of motion to propagate the system, whereas the second stochastically generates states of a system according to a predetermined statistical mechanical probability distribution.

Just in case you are not aware of it, numerical solution of PDE's and the Navier - Stokes equations is a well developed field where the level of rigor is much higher than in climate science.

The numerical solution of the resulting set of equations is tau = 1.867561.....

Not exact matches

Daniel Ansari is doing his part to remedy that, using both neuroscience tools and behavioral measurements to elucidate the brain basis of numerical and mathematical abilities, to identify the cause of dyscalculia, and to find a solution.

In many cases in numerical optimization, the algorithms fail to converge or take enormous amounts of time to get a feasible solution.»

When the geometry of such a system is specified, the simulator allows the user to vary primary and secondary scattering foil material and thickness and to see results in approximately 100 milliseconds, about 10 million times faster than Monte Carlo simulations, which are simulations and computational algorithms that rely on random sampling to obtain results for extremely complex problems that have only numerical solutions.

He began with fluid dynamics equations, and then used numerical calculations to arrive at approximate solutions for specifics combinations of source flow and spread rates, and crosswind speed.

Researchers measured the rate of digestion of a solution of glucose alone, and assigned it the numerical value of 100.

It is very clear that changes to certain aspects of the mathematical models, numerical solution methods, and application procedures are in fact based on «the match to observations».

Finite precision computer realizations of nonlinear models give unrealistic solutions because of deterministic chaos, a direct consequence of round - off error growth in iterative numerical computations.»

As numerical models can not find solutions of any system of non linear ODEs or PDEs because the system is simply spatially too huge and all the equations are not known anyway, they have no relevance to what I discuss here.

Experience with solution algorithms, data assimilation methods and tools, coupling of components and processes, nonlinear and linear solvers, limiters, and / or other numerical issues common with complex codes within earth system models of varying complexity

It is critical that the actual coding be shown to be exactly what was intended as guided by theoretical analyses of the discrete approximations and numerical solution methods.

Ultimately the numbers calculated by the GCMs are the outcome of numerical solution methods applied to algebraic approximations to the continuous equations on discrete temporal and spatial grids.

«A numerical integration in which the goal is typically to study the behavior of the solution without regard to the initial conditions (to distinguish it from a numerical forecast).

I am only suggesting this point - of - view because David Young's views of numerical stability are likely very valid, but perhaps misdirected when we consider how far we can go with an alternative statistical mechanical solution.

And different models may project different outcomes even under the same assumptions, due to the variety of «equally plausible numerical representations, solutions and approximations for modelling the climate system, given the limitations in computing and observations» [AR5, FAQ 12.1, p. 1036].

Yet tracking down its origin is difficult — it seems to have originated by fitting a log formula to some numerical results from a radiative forcing model, not from the analytical solution of a physical model.

The GCM models themselves use numerical methods and boundary condition assumptions appropriate to solutions of well behaved equations in what in the end is a perturbative expansion method.

Verification of the coding of the equations and Verification of the numerical solution methods are absolutely required before any calculated numbers can be considered to have any relationship to the continuous equations.

As soon as a global climate model readjusts a vertical column to unphysically alter the large scale solution in order to maintain hydrostatic balance (overturning due to unrealistic heating parameterizations necessitate this adjustment), there is no mathematical theory that can justify the nature of the ensuing numerical solution.

There are also broadly similar ways of thinking in, e.g., numerical integration, and in the solution of differential equations on progressively finer grids.)

These are extremely detailed and consequently the numerical solution to the equations require days or weeks of computational time.

This book incorporates the heritage of Russian cloud physics that introduced and developed the kinetic equations for drop and crystal diffusion growth, the fast numerical algorithms for their solutions, and stochastic approach to cloud microphysical processes.

An even better example of a chaotic system still open to numerical solution is the motion of the astroids in the solar system.

The people who utter the D word do not care about what the objects of their ires actually think: because the issue is not one's opinion on the GHG properties of CO2, and not even what the temperature record says, or what the equations may indicate, or how good the numerical solutions we call Models are.

From what I read here there is a great deal of understanding, in depth, of the complexity of both the physical phenomena and processes, the mathematical problems associated with both the continuous and discrete equations, numerical solution methods for the latter, and designing, developing, building, testing, and applying computer software that has all this stuff in it.

article by Heinz and me (reference available on request), once the minimal scale (smallest scale feature of vorticity) is properly resolved by a numerical model, the correct Navier - Stokes dissipation form (second order derivatives) can be used and produces the correct spatial spectrum, i.e. the numerical solutions converge.

If numerical methods can not accurately compute the solution of the basic dynamical system (so called dynamical cores) either because of ill posedness, fast exponential growth, or inadequate resolution to properly resolve the rapid nonlinear cascade of the vertical component of vorticity (requires unphysically large dissipation to overcome), then adding necessarily unphysical parameterizations to overcome these deficiencies can not lead to a correct physical solution as the resolution is reduced.

Each modelling group runs through a variety tests to assess the fidelity of their numerical solutions.

The success of numerical weather prediction at predicting say the 500 hpa height field on the time scale of the lifetime of a baroclinic wave (nominally 4 - 7 days) is a testimony to the credibility of these solutions

In its second application, Verification that the numerical solution methods do in fact lead to solutions of the continuous equations, is also possible.

But the mathematical analysis of the frequencies, the demonstrations of the problems with the continuum systems using convergent numerical solutions on the Exponential thread, and the dynamical core manuscript itself should make the issues very clear.

But, Verification of the coding and numerical solution methods must precede Validation calculations.

I think the correct statement is that when a numerical model can not resolve the small scales of motion in the real solution, one must add some form of damping to prevent those scales from forming in the model.

As I have clearly stated, this problem can be seen without the missing section, but that section will help to clarify the discussion about too large of dissipation impacting the accuracy of the numerical solution and the subsequent need for unphysical forcing to «adjust» the spectrum.

I appreciate your statement «From what I read here there is a great deal of understanding, in depth, of the complexity of both the physical phenomena and processes, the mathematical problems associated with both the continuous and discrete equations, numerical solution methods for the latter, and designing, developing, building, testing, and applying computer software that has all this stuff in it.»

Existence, uniqueness and numerical analysis of solutions of a quasi-linear parabolic problem, S.I.A.M. J. Num.