A linear stochastic biharmonic heat equation: hitting probabilities

Consider the linear stochastic biharmonic heat equation on a d–dimen- sional torus ($$d=1,2,3$$ d = 1 , 2 , 3 ), driven by a space-time white noise and with periodic boundary conditions: $$\begin{aligned} \left( \frac{\partial }{\partial t}+(-\varDelta )^2\right) v(t,x)= \sigma \dot{W}(t,x),\ (t,x)\in (0,T]\times {\mathbb {T}}^d, \end{aligned}$$ ∂ ∂ t + ( - Δ ) 2 v ( t , x ) = σ W ˙ ( t , x ) , ( t , x ) ∈ ( 0 , T ] × T d , $$v(0,x)=v_0(x)$$ v ( 0 , x ) = v 0 ( x ) . We find the canonical pseudo-distance corresponding to the random field solution, therefore the precise description of the anisotropies of the process. We see that for $$d=2$$ d = 2 , they include a $$z(\log \tfrac{c}{z})^{1/2}$$ z ( log c z ) 1 / 2 term. Consider D independent copies of the random field solution to (0.1). Applying the criteria proved in Hinojosa-Calleja and Sanz-Solé (Stoch PDE Anal Comp 2021. 10.1007/s40072-021-00190-1), we establish upper and lower bounds for the probabilities that the path process hits bounded Borel sets.This yields results on the polarity of sets and on the Hausdorff dimension of the path process.

J-driven Dynamic Nuclear Polarization for sensitizing high field solution state NMR

Dynamic nuclear polarization (DNP) is widely used to enhance solid state nuclear magnetic resonance (NMR) sensitivity. Its efficiency as a generic signal-enhancing approach for liquid state NMR, however, decays rapidly...

Analytical Iron Loss Evaluation in the Stator Yoke of Slotless Surface-Mounted PM Machines

<div>One of the attractive benefits of slotless machines is low losses at high speeds, which could be emphasized by a careful stator core loss assessment, potentially available already at the pre-design stage. Unfortunately, mainstream iron loss estimation methods are typically implemented in the finite element analysis (FEA) environment with a constant-coefficients dummy model, leading to weak extrapolations with huge errors. In this paper, an analytical method for iron loss prediction in the stator core of slotless PM machines is derived. It is based on the extension of the 2-D field solution over the entire machine geometry. Then, the analytical solution is combined with variable- or constant-coefficient loss models (i.e., VARCO or CCM), which can be efficiently computed by vectorized post-processing. VARCO loss models are shown to be preferred at a general level.Moreover, the paper proposes a lookup-table-based (LUT) solution as an alternative approach. The main contribution lies in the numerical link between the analytical field solution and the iron loss estimate, with the aid of a code implementation of the proposed methodology. First, the models are compared against a sufficiently dense dataset available from laminations manufacturer for validation purposes. Then, all the methods are compared for the slotless machine case. Finally, the models are applied to a real case study and validated experimentally.</div>

Analytical Iron Loss Evaluation in the Stator Yoke of Slotless Surface-Mounted PM Machines

<div>One of the attractive benefits of slotless machines is low losses at high speeds, which could be emphasized by a careful stator core loss assessment, potentially available already at the pre-design stage. Unfortunately, mainstream iron loss estimation methods are typically implemented in the finite element analysis (FEA) environment with a constant-coefficients dummy model, leading to weak extrapolations with huge errors. In this paper, an analytical method for iron loss prediction in the stator core of slotless PM machines is derived. It is based on the extension of the 2-D field solution over the entire machine geometry. Then, the analytical solution is combined with variable- or constant-coefficient loss models (i.e., VARCO or CCM), which can be efficiently computed by vectorized post-processing. VARCO loss models are shown to be preferred at a general level.Moreover, the paper proposes a lookup-table-based (LUT) solution as an alternative approach. The main contribution lies in the numerical link between the analytical field solution and the iron loss estimate, with the aid of a code implementation of the proposed methodology. First, the models are compared against a sufficiently dense dataset available from laminations manufacturer for validation purposes. Then, all the methods are compared for the slotless machine case. Finally, the models are applied to a real case study and validated experimentally.</div>

Towards an updated, enhanced regional gravity field solution for Antarctica

&lt;p&gt;In the frame of the IAG Subcommission 2.4f &amp;#8220;Gravity and Geoid in Antarctica&amp;#8221; (AntGG) a first Antarctic-wide grid of ground-based gravity anomalies was released in 2016 (Scheinert et al. 2016). That data set was provided with a grid space of 10 km and covered about 73% of the Antarctic continent. Since then a considerably amount of new data has been made available, mainly collected by means of airborne gravimetry. Regions which were formerly void of any terrestrial gravity observations and have now been surveyed include especially the polar data gap originating from GOCE satellite gravimetry. Thus, it is timely to come up with an updated and enhanced regional gravity field solution for Antarctica. For this, we aim to improve further aspects in comparison to the AntGG 2016 solution: The grid spacing will be enhanced to 5 km. Instead of providing gravity anomalies only for parts of Antarctica, now the entire continent should be covered. In addition to the gravity anomaly also a regional geoid solution should be provided along with further desirable functionals (e.g. gravity anomaly vs. disturbance, different height levels).&lt;/p&gt;&lt;p&gt;We will discuss the expanded AntGG data base which now includes terrestrial gravity data from Antarctic surveys conducted over the past 40 years. The methodology applied in the analysis is based on the remove-compute-restore technique. Here we utilize the newly developed combined spherical-harmonic gravity field model SATOP1 (Zingerle et al. 2019) which is based on the global satellite-only model GOCO05s and the high-resolution topographic model EARTH2014. We will demonstrate the feasibility to adequately reduce the original gravity data and, thus, to also cross-validate and evaluate the accuracy of the data especially where different data set overlap. For the compute step the recently developed partition-enhanced least-squares collocation (PE-LSC) has been used (Zingerle et al. 2021, in review; cf. the contribution of Zingerle et al. in the same session). This method allows to treat all data available in Antarctica in one single computation step in an efficient and fast way. Thus, it becomes feasible to iterate the computations within short time once any input data or parameters are changed, and to easily predict the desirable functionals also in regions void of terrestrial measurements as well as at any height level (e.g. gravity anomalies at the surface or gravity disturbances at constant height).&lt;/p&gt;&lt;p&gt;We will discuss the results and give an outlook on the data products which shall be finally provided to present the new regional gravity field solution for Antarctica. Furthermore, implications for further applications will be discussed e.g. with respect to geophysical modelling of the Earth&amp;#8217;s interior (cf. the contribution of Schaller et al. in session G4.3).&lt;/p&gt;

Geophysical subsurface modelling based on the updated, enhanced regional gravity field solution in Antarctica

&lt;p&gt;The gravity field reflects mass inhomogeneities (mostly) inside the Earth. Therefore, gravity inversion and geophysical gravity field modelling are important tools to study the Earth's inner structure and tectonic evolution. In Antarctica, it is extremely challenging to carry out geoscientific studies due to its harsh environment and difficult logistics. Additionally, the continent is covered by an up to 5 km thick ice sheet. However, in the framework of IAG Subcommission 2.4f &amp;#8220;Gravity and Geoid in Antarctica&amp;#8221; (AntGG) a large database of airborne, shipborne and ground based gravity data has been compiled. Especially airborne data have been acquired during recent years, among others in the area of the polar gap of satellite gravity data. Now, in a joint project funded by the German Research Foundation (DFG) all existing and new gravity data were processed to infer an enhanced gravity field solution for Antarctica (see contribution by Scheinert et al., session G1.5). Processed data e.g. gravity disturbances on the ground or a constant height and other functionals will be provided on a regular grid with 5 km grid spacing. Subsequently, the new Antarctic gravity field solution can now be used for further geophysical and tectonic studies. We use the newly calculated gravity disturbances to study subglacial topography, sediment thickness and Moho depth and to improve respective existing models in Antarctica. For this, we apply 2D Parker-Oldenburg inversion in combination with results from other gravity based studies and further constraining data (e.g. seismic data and ice penetrating radar). We investigate how the higher resolution (5 km) of the new Antarctic gravity field solution facilitates the study of smaller regions in more detail, specifically parts of Wilkes Land, Dronning Maud Land and the Weddell Sea. Additionally, we will infer accuracy estimates for the resulting boundaries in terms of the used inversion parameters (density contrast, average density and filter wavelengths) and their respective gravity signal. Thus, the challenges of gravity field inversion in Antarctica will be discussed in detail and first results of the subsurface modelling will be presented.&lt;/p&gt;