Related papers: Geometrically Explicit Cosserat-Rod Modeling with …
The equations for strands of rigid charge configurations interacting nonlocally are formulated on the special Euclidean group, SE(3), which naturally generates helical conformations. Helical stationary shapes are found by minimizing the…
We propose a finite element method for simulating one-dimensional solid models moving and experiencing large deformations while immersed in generalized Newtonian fluids. The method is oriented towards applications involving microscopic…
We propose a general method for deriving one-dimensional models for nonlinear structures. It captures the contribution to the strain energy arising not only from the macroscopic elastic strain as in classical structural models, but also…
In this paper we linearise the recently introduced geometrically nonlinear constrained Cosserat-shell model. In the framework of the linear constrained Cosserat-shell model, we provide a comparison of our linear models with the classical…
This paper considers a combination of actuation tendons and measurement strings to achieve accurate shape sensing and direct kinematics of continuum robots. Assuming general string routing, a methodical Lie group formulation for the shape…
This paper proposes an explicit computational method for solving a three-dimensional system of nonlinear elastodynamic sine-Gordon equations subject to appropriate initial and boundary conditions. The time derivative is approximated by…
Geometric optimization problems are at the core of many applications in geometry processing. The choice of a representation fitting an optimization problem can considerably simplify solving the problem. We consider the Nonlinear…
We present new methods and results for constructing optimal Kobon triangle arrangements. First, we introduce a compact table notation for describing arrangements of pseudolines, enabling the representation and analysis of complex cases,…
We rigorously derive an effective bending model for elastoplastic rods starting from three-dimensional finite plasticity. For the derivation we lean on a framework of evolutionary $\Gamma$-convergence for rate-independent systems. The main…
Real physical systems with reflective and rotational symmetries such as viruses, fullerenes and quasicrystals have recently been modeled successfully in terms of three-dimensional (affine) Coxeter groups. Motivated by this progress, we…
In the perspective of homogenization theory, strain-gradient elasticity is a strategy to describe the overall behaviour of materials with coarse mesostructure. In this approach, the effect of the mesostructure is described by the use of…
Tendon-driven robotic catheters are capable of precise execution of minimally invasive cardiac procedures including ablations and imaging. These procedures require accurate mathematical models of not only the catheter and tendons but also…
For nonlinear Cosserat elasticity, we consider multiscale methods in this paper. In particular, we explore the generalized multiscale finite element method (GMsFEM) to solve an isotropic Cosserat problem with strain-limiting property…
The irreducible representations of the Lie algebra ${\frak su}$(3) describe rotational bands in the context of the nuclear shell and interacting boson models. The density matrices associated with ${\frak su}$(3) provide an alternative…
The paper presents a two-dimensional geometrically nonlinear formulation of a beam element that can accommodate arbitrarily large rotations of cross sections. The formulation is based on the integrated form of equilibrium equations, which…
This paper is devoted to studying the global and finite convergence of the semi-smooth Newton method for solving a piecewise linear system that arises in cone-constrained quadratic programming problems and absolute value equations. We first…
The identification of repeating patterns in discrete grids is rudimentary within symbolic reasoning, algorithm synthesis and structural optimization across diverse computational domains. Although statistical approaches targeting noisy data…
For the study of highly nonlinear, conservative dynamic systems, finding special periodic solutions which can be seen as generalization of the well-known normal modes of linear systems is very attractive. However, the study of…
Classical mathematical techniques such as discrete integration, gradient descent optimization, and state estimation (exemplified by the Runge-Kutta method, Gauss-Newton minimization, and extended Kalman filter or EKF, respectively), rely on…
We use a numerical algorithm on the Lie group of rotation matrices to obtain rotated constellations for Rayleigh fading channels. Our approach minimizes the union bound for the pairwise error probability to produce rotations optimized for a…