A numerical implementation of the transition state theory (TST) is presented which can be used to calculate the attempt frequency $f_{0}$ of arbitrary shaped magnetic nanostructures. The micromagnetic equations are discretized using the finite element method. The climbing image nudged elastic band method is used to calculate the saddle point configuration, which is required for the calculation of $f_{0}$. Excellent agreement of the implemented numerical model and analytical solutions is obtained for single domain particles. The developed method is applied to compare $f_{0}$ for single phase and graded media grains of advanced recording media. $f_{0}$ is predicted to be comparable if the maximum anisotropy is the same in these two media types.
We investigate theoretically and numerically the use of the Least-Squares Finite-element method (LSFEM) to approach data-assimilation problems for the steady-state, incompressible Navier-Stokes equations. Our LSFEM discretization is based on a stress-velocity-pressure (S-V-P) first-order formulation, using discrete counterparts of the Sobolev spaces $H({rm div}) times H^1 times L^2$ respectively. Resolution of the system is via minimization of a least-squares functional representing the magnitude of the residual of the equations. A simple and immediate approach to extend this solver to data-assimilation is to add a data-discrepancy term to the functional. Whereas most data-assimilation techniques require a large number of evaluations of the forward-simulations and are therefore very expensive, the approach proposed in this work uniquely has the same cost as a single forward run. However, the question arises: what is the statistical model implied by this choice? We answer this within the Bayesian framework, establishing the latent background covariance model and the likelihood. Further we demonstrate that - in the linear case - the method is equivalent to application of the Kalman filter, and derive the posterior covariance. We practically demonstrate the capabilities of our method on a backward-facing step case. Our LSFEM formulation (without data) is shown to have good approximation quality, even on relatively coarse meshes - in particular with respect to mass-conservation and reattachment location. Adding limited velocity measurements from experiment, we show that the method is able to correct for discretization error on very coarse meshes, as well as correct for the influence of unknown and uncertain boundary-conditions.
Precise modeling of the magnetization dynamics of nanoparticles with finite size effects at fast varying temperatures is a computationally challenging task. Based on the Landau-Lifshitz-Bloch (LLB) equation we derive a coarse grained model for disordered ferrimagnets, which is both fast and accurate. First, we incorporate stochastic fluctuations to the existing ferrimagnetic LLB equation. Further, we derive a thermodynamic expression for the temperature dependent susceptibilities, which is essential to model finite size effects. Together with the zero field equilibrium magnetization the susceptibilities are used in the stochastic ferrimagnetic LLB to simulate a $5times10$ nm$^2$ ferrimagnetic GdFeCo particle with 70 % FeCo and 30 % Gd under various external applied fields and heat pulses. The obtained trajectories agree well with those of an atomistic model, which solves the stochastic Landau-Lifshitz-Gilbert equation for each atom. Additionally, we derive an expression for the intergrain exchange field which couple the ferromagnetic sublattices of a ferrimagnet. A comparison of the magnetization dynamics obtained from this simpler model with those of the ferrimagnetic LLB equation shows a perfect agreement.
The paper presents a derivation of analytical components of S-matrices for arbitrary planar diffractive structures and metasurfaces in the Fourier domain. Attained general formulas for S-matrix components can be applied within both formulations in the Cartesian and curvilinear metric. A numerical method based on these results can benefit from all previous improvements of the Fourier domain methods. In addition, we provide expressions for S-matrix calculation in case of periodically corrugated layers of 2D materials, which are valid for arbitrary corrugation depth-to-period ratios. As an example the derived equations are used to simulate resonant grating excitation of graphene plasmons and an impact of silica interlayer on corresponding reflection curves.
We investigate the wave effects of gravitational waves (GWs) using numerical simulations with the finite element method (FEM) based on the publicly available code {it deal.ii}. We robustly test our code using a point source monochromatic spherical wave. We examine not only the waveform observed by a local observer but also the global energy conservation of the waves. We find that our numerical results agree very well with the analytical predictions. Based on our code, we study the scattering of GWs by compact objects. Using monochromatic waves as the input source, we find that if the wavelength of GWs is much larger than the Schwarzschild radius of the compact object, the amplitude of the total scattered GWs does not change appreciably due to the strong diffraction effect, for an observer far away from the scatterer. This finding is consistent with the results reported in the literature. However, we also find that, near the scatterer, not only the amplitude of the scattered waves is very large, comparable to that of the incident waves, but also the phase of the GWs changes significantly due to the interference between the scattered and incident waves. As the evolution of the phase of GWs plays a crucial role in the matched filtering technique in extracting GW signals from the noisy background, our findings suggest that wave effects should be taken into account in the data analysis in the future low-frequency GW experiments, if GWs are scattered by nearby compact objects in our local environment.
We present valence electron Compton profiles calculated within the density-functional theory using the all-electron full-potential projector augmented-wave method (PAW). Our results for covalent (Si), metallic (Li, Al) and hydrogen-bonded ((H_2O)_2) systems agree well with experiments and computational results obtained with other band-structure and basis set schemes. The PAW basis set describes the high-momentum Fourier components of the valence wave functions accurately when compared with other basis set schemes and previous all-electron calculations.
G. Fiedler
,J. Fidler
,J. Lee
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(2010)
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"Direct calculation of the attempt frequency of magnetic structures using the finite element method"
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Dieter Suess
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