Automatic 3D modeling by combining SBFEM and transfinite element shape functions

The scaled boundary finite element method (SBFEM) has recently been employed as an efficient means to model three-dimensional structures, in particular when the geometry is provided as a voxel-based image. To this end, an octree decomposition of the computational domain is deployed and each cubic cell is treated as an SBFEM subdomain. The surfaces of each subdomain are discretized in the finite element sense. We improve on this idea by combining the semi-analytical concept of the SBFEM with certain transition elements on the subdomains' surfaces. Thus, we avoid the triangulation of surfaces employed in previous works and consequently reduce the number of surface elements and degrees of freedom. In addition, these discretizations allow coupling elements of arbitrary order such that local p-refinement can be achieved straightforwardly

A massively parallel explicit solver for elasto-dynamic problems exploiting octree meshes

Typical areas of application of explicit dynamics are impact, crash test, and most importantly, wave propagation simulations. Due to the numerically highly demanding nature of these problems, efficient automatic mesh generators and transient solvers are required. To this end, a parallel explicit solver exploiting the advantages of balanced octree meshes is introduced. To avoid the hanging nodes problem encountered in standard finite element analysis (FEA), the scaled boundary finite element method (SBFEM) is deployed as a spatial discretization scheme. Consequently, arbitrarily shaped star-convex polyhedral elements are straightforwardly generated. Considering the scaling and transformation of octree cells, the stiffness and mass matrices of a limited number of unique cell patterns are pre-computed. A recently proposed mass lumping technique is extended to 3D yielding a well-conditioned diagonal mass matrix. This enables us to leverage the advantages of explicit time integrator, i.e., it is possible to efficiently compute the nodal displacements without the need for solving a system of linear equations. We implement the proposed scheme together with a central difference method (CDM) in a distributed computing environment. The performance of our parallel explicit solver is evaluated by means of several numerical benchmark examples, including complex geometries and various practical applications. A significant speedup is observed for these examples with up to one billion of degrees of freedom and running on up to 16,384 computing cores

Studies on nematodes of dune sands

Although nematodes abound in soils little has been discovered about their role in the biology of soils. Dune sands were selected for this study since if this "relatively simple" habitat could be understood it would provide a starting point to an understanding of the vastly more complex biology of agricultural soils. It was thought that the nematode fauna in sand dunes would be depauperate, that the environmental conditions might be simple enough to be understandable, if necessary duplicable, and that their variation might explain variation in the nematode fauna. In an attempt to achieve some understanding of the nematode fauna the following points were considered:- 1. Taxonomic characterisation of the nematode fauna to species level. Although de Man (1880, 1884) described several species of nematodes from the coastal dunes of the Netherlands, the nematode fauna of this environment is poorly known. Clark (1960, 1963) and Killick (1964) have described new species from New Zealand dunes. 2. Examination of the population changes of the species in relation to season, depth and other environmental factors. The majority of population studies have concerned economically important species in agricultural soils. 3. Elucidation of trophic relationships. The trophic relationships of many nematodes are unknown or unsubstantiated. Goodey (1963) gives the essence of the knowledge of the bionomics of each genus. 4. General examination of the biology of "free living" nematodes, aided by comparison between conditions in vivo and in vitro. Because of the supposed simplicity of the biota, physics and chemistry of dune sands comparison of results obtained from cultures with those obtained in the field seem more acceptable than if species from a complex agricultural soil were used

Undecidability in number theory

These lecture notes cover classical undecidability results in number theory, Hilbert's 10th problem and recent developments around it, also for rings other than the integers. It also contains a sketch of the authors result that the integers are universally definable in the rationals.Comment: 48 pages. arXiv admin note: text overlap with arXiv:1011.342

Relating different Polynomial-LWE problems

In this paper we focus on Polynomial Learning with Errors (PLWE). This problem is parametrized by a polynomial and we are interested in relating the hardness of the $\text{PLWE}^f$ and $\text{PLWE}^h$ problems for different polynomials $f$ and $h$. More precisely, our main result shows that for a fixed monic polynomial $f$, $\text{PLWE}^{f\circ g}$ is at least as hard as $\text{PLWE}^f$, in both search and decision variants, for any monic polynomial $g$. As a consequence, $\text{PLWE}^{\phi_n}$ is harder than $\text{PLWE}^{f},$ for a minimal polynomial $f$ of an algebraic integer from the cyclotomic field $\mathbb{Q}(\zeta_n)$ with specific properties. Moreover, we prove in decision variant that in the case of power-of-2 polynomials, $\text{PLWE}^{\phi_n}$ is at least as hard as $\text{PLWE}^f,$ for a minimal polynomial $f$ of algebraic integers from the $n$th cyclotomic field with weaker specifications than those from the previous result

A Subfield Lattice Attack on Overstretched NTRU Assumptions:Cryptanalysis of Some FHE and Graded Encoding Schemes

International audienc

On the Hardness of the Computational Ring-LWR Problem and its Applications

In this paper, we propose a new assumption, the Computational Learning With Rounding over rings, which is inspired by the computational Diffie-Hellman problem. Assuming the hardness of ring-LWE, we prove this problem is hard when the secret is small, uniform and invertible. From a theoretical point of view, we give examples of a key exchange scheme and a public key encryption scheme, and prove the worst-case hardness for both schemes with the help of a random oracle. Our result improves both speed, as a result of not requiring Gaussian secret or noise, and size, as a result of rounding. In practice, our result suggests that decisional ring-LWR based schemes, such as Saber, Round2 and Lizard, which are among the most efficient solutions to the NIST post-quantum cryptography competition,stem from a provable secure design. There are no hardness results on the decisional ring-LWR with polynomial modulus prior to this work, to the best of our knowledge

The European press and the question of Norwegian independence in 1814

The French Revolution, with its alternative legitimating principle of popular sovereignty, challenged and undermined the European old regime’s foundation of dynastic-absolutist divine legitimacy. The constitutional fathers of Norway were inspired by the republican revolutions in France and America, and when the country was ceded from Denmark to Sweden according to the Treaty of Kiel in January 1814, they sought to secure Norway’s independence through applying popular sovereignty as a legitimating principle. This qualitative study seeks to contribute to new insights in and understanding of how the dramatic political events of 1814 in Norway were perceived outside Scandinavia by examining historical newspapers from England, France, Prussia, Austria Russia, Saxony, Bavaria and Switzerland. Using discourse analytical tools this study attempts to shed light upon how the question of Norwegian sovereignty were perceived in 1814, whether Norwegian independence was conceptually possible in the eyes of people outside Scandinavia, and what the thinking about the possibility of a new independent state in 1814 looked like. The study establishes that there are to distinctly different discursive representations, or perceptions of reality, when it comes to the question of Norwegian independence in 1814: The Popular Sovereignty Representation and The Dynastic Sovereignty Representation. Furthermore, the study demonstrates that there is a palette of different varieties within these two main representations