Bayesian inference for the stochastic identification of elastoplastic material parameters: Introduction, misconceptions and insights

E-print/Working paper (n.d.)

We discuss Bayesian inference (BI) for the probabilistic identification of material parameters. This contribution aims to shed light on the use of BI for the identification of elastoplastic material ... [more ▼]

We discuss Bayesian inference (BI) for the probabilistic identification of material parameters. This contribution aims to shed light on the use of BI for the identification of elastoplastic material parameters. For this purpose a single spring is considered, for which the stress-strain curves are artificially created. Besides offering a didactic introduction to BI, this paper proposes an approach to incorporate statistical errors both in the measured stresses, and in the measured strains. It is assumed that the uncertainty is only due to measurement errors and the material is homogeneous. Furthermore, a number of possible misconceptions on BI are highlighted based on the purely elastic case. [less ▲]

The first-digit law

E-print/Working paper (n.d.)

Four Riddles with Four Brothers

E-print/Working paper (n.d.)

Junior BINGO

E-print/Working paper (n.d.)

A new one point quadrature rule over arbitrary star convex polygon/polyhedron

E-print/Working paper (n.d.)

The Linear Smoothing (LS) scheme \cite{francisa.ortiz-bernardin2017} ameliorates linear and quadratic approximations over convex polytopes by employing a three-point integration scheme. In this work, we ... [more ▼]

The Linear Smoothing (LS) scheme \cite{francisa.ortiz-bernardin2017} ameliorates linear and quadratic approximations over convex polytopes by employing a three-point integration scheme. In this work, we propose a linearly consistent one point integration scheme which possesses the properties of the LS scheme with three integration points but requires one third of the integration computational time. The essence of the proposed technique is to approximate the strain by the smoothed nodal derivatives that are determined by the discrete form of the divergence theorem. This is done by the Taylor's expansion of the weak form which facilitates the evaluation of the smoothed nodal derivatives acting as stabilization terms. The smoothed nodal derivatives are evaluated only at the centroid of each integration cell. These integration cells are the simplex subcells (triangle/tetrahedron in two and three dimensions) obtained by subdividing the polytope. The salient feature of the proposed technique is that it requires only $n$ integrations for an $n-$ sided polytope as opposed to $3n$ in~\cite{francisa.ortiz-bernardin2017} and $13n$ integration points in the conventional approach. The convergence properties, the accuracy, and the efficacy of the LS with one point integration scheme are discussed by solving few benchmark problems in elastostatics. [less ▲]

Verification of the Quillen conjecture in the rank 2 imaginary quadratic case

E-print/Working paper (n.d.)

We confirm a conjecture of Quillen in the case of the mod 2 cohomology of arithmetic groups SL_2(A[1/2]), where A is an imaginary quadratic ring of integers. To make explicit the free module structure on ... [more ▼]

We confirm a conjecture of Quillen in the case of the mod 2 cohomology of arithmetic groups SL_2(A[1/2]), where A is an imaginary quadratic ring of integers. To make explicit the free module structure on the cohomology ring conjectured by Quillen, we compute the mod 2 cohomology of SL_2(Z[sqrt(−2)][1/2]) via the amalgamated decomposition of the latter group. [less ▲]

Modelling challenges & simulation results comparison study for inactive elements activation approach in numerical simulation of Selective Laser Melting Additive Manufacturing process

E-print/Working paper (n.d.)

Weakening the tight coupling between geometry and simulation in isogeometric analysis: from sub- and super- geometric analysis to Geometry Independent Field approximaTion (GIFT)

E-print/Working paper (n.d.)

This paper presents an approach to generalize the concept of isogeometric analysis (IGA) by allowing different spaces for parameterization of the computational domain and for approximation of the solution ... [more ▼]

This paper presents an approach to generalize the concept of isogeometric analysis (IGA) by allowing different spaces for parameterization of the computational domain and for approximation of the solution field. The method inherits the main advantage of isogeometric analysis, i.e. preserves the original, exact CAD geometry (for example, given by NURBS), but allows pairing it with an approximation space which is more suitable/flexible for analysis, for example, T-splines, LR-splines, (truncated) hierarchical B-splines, and PHT-splines. This generalization offers the advantage of adaptive local refinement without the need to re-parameterize the domain, and therefore without weakening the link with the CAD model. We demonstrate the use of the method with different choices of the geometry and field splines, and show that, despite the failure of the standard patch test, the optimum convergence rate is achieved for non-nested spaces. [less ▲]

Deniable Public-Key Authenticated Quantum Key Exchange

E-print/Working paper (n.d.)

In this work, we explore the notion of deniability in public-key authenticated quantum key exchange (QKE), which allows two parties to establish a shared secret key without leaving any evidence that would ... [more ▼]

In this work, we explore the notion of deniability in public-key authenticated quantum key exchange (QKE), which allows two parties to establish a shared secret key without leaving any evidence that would bind a session to either party. The deniability property is expressed in terms of being able to simulate the transcripts of a protocol. The ability to deny a message or an action has applications ranging from secure messaging to secure e-voting and whistle-blowing. While quite well-established in classical cryptography, it remains largely unexplored in the quantum setting. Here, we first present a natural extension of classical definitions in the simulation paradigm to the setting of quantum computation and formalize the requirements for a deniable QKE scheme. We then prove that the BB84 variant of QKE, when authenticated using a strong designated verifier signature scheme, satisfies deniability and, finally, propose a concrete instantiation. [less ▲]