The added elemental degrees of freedom approximate the displacement jumps associated with the discontinuity and are defined independently from element to element, thus allowing their static condensation at the element level without affecting the global mechanical problem in terms of the number and topology...
These terms tell us that dynamic range due to internal distortion is a function of the input signal level at the input mixer. Let’s see how this works, using as our definition of dynamic range, the difference in dB between the fundamental tone and the internally generated distortion. The a...
This object, member, or enumeration is deprecated and is not intended to be used in your code.Methods Expand table AutoFormat() Automatically formats a range. Calculate() Calculates a mathematical expression within a range. CheckGrammar() Begins a spelling and grammar check for the specified ...
The large r expansion of the pair-correlation function g(r) is calculated by first-order perturbation theory in the dense metallic electron liquid regime of jellium. The non-oscillatory terms in g(r) - 1 at large r are completely changed from the Hartree-Fock (HF) case, the leading term...
Fig. 2: Pangu-Weather produces higher accuracy than the operational IFS and FourCastNet in deterministic forecasts on the ERA5 data. Ten variables were compared in terms of latitude-weighted RMSE (lower is better) and ACC (higher is better), where the first five variables were reported in Fo...
we find the Stuart–Landau equation in the subcritical range of a Hopf bifurcation to be appropriate since it is the canonical form to describe a system in the vicinity of a limit cycle, responding to perturbation with oscillations with decaying amplitude from basic mathematical principles, with th...
The mathematical model is formulated in terms of the Stokes steam function, ¨, and the governing equations of fluid motion are solved using finite-difference techniques. The injection flow of the exhaust hood is modelled as a turbulent radial jet and the entrained flow is assumed to be an ...
We consider the entanglement entropy of the ground state \(\left|0\right\rangle\) in terms of the spectral gap Δ just above the ground-state energy. We assume that the ground state is not degenerate. We now discuss our main theorem. We define the interaction between two concatenated sub...
The main contribution of this paper is to show the suitability of the four-layer model in terms of source localization in a complex (range-dependent) environment. The sound-speed profile is assumed to be vertically irregular and horizontally slowly varying and the bottom is nonflat. In the ...
The mathematical representation for linear viscoelastic materials also provides a means to easily test whether one is in the linear range of a given material. To sufficiently ensure material linearity, two common techniques are used: the first method is to perform short-term creep tests on the mat...