arXiv subjects

Michael Nestler

Publications and source records attributed to Michael Nestler.

11 recordsLinked to original sources

arXiv2024

The Vienna Architecture Description Language

The Vienna Architecture Description Language (VADL) is a powerful processor description language (PDL) that enables the concise formal specification of processor architectures. By utilizing a single VADL processor specification, the VADL system exhibits the capability to automatically generate a range of artifacts necessary for rapid design space exploration. These include assemblers, compilers, linkers, functional instruction set simulators, cycle-accurate instruction set simulators, synthesizable specifications in a hardware description language, as well as test cases and documentation. One distinctive feature of VADL lies in its separation of the instruction set architecture (ISA) specification and the microarchitecture (MiA) specification. This segregation allows users the flexibility to combine various ISAs with different MiAs, providing a versatile approach to processor design. In contrast to existing PDLs, VADL's MiA specification operates at a higher level of abstraction, enhancing the clarity and simplicity of the design process. Notably, with a single ISA specification, VADL streamlines compiler generation and maintenance by eliminating the need for intricate compiler-specific knowledge. The original VADL implementation has a restricted copyright. Therefore, the open source implementation OpenVADL was started. This article introduces VADL, compares the original VADL implementation with the ongoing OpenVADL implementation, describes the generator techniques in detail and demonstrates the power of the language and the performance of the generators in an empirical evaluation. The evaluation shows the expressiveness and conciseness of VADL and the efficiency of the generated artifacts.

cs.PL↗

arXiv2023

Active smectics on a sphere

The dynamics of active smectic liquid crystals confined on a spherical surface is explored through an active phase field crystal model. Starting from an initially randomly perturbed isotropic phase, several types of topological defects are spontaneously formed, and then annihilate during a coarsening process until a steady state is achieved. The coarsening process is highly complex involving several scaling laws of defect densities as a function of time where different dynamical exponents can be identified. In general the exponent for the final stage towards the steady state is significantly larger than that in the passive and in the planar case, i.e., the coarsening is getting accelerated both by activity and by the topological and geometrical properties of the sphere. A defect type characteristic for this active system is a rotating spiral of evolving smectic layering lines. On a sphere this defect type also determines the steady state. Our results can in principle be confirmed by dense systems of synthetic or biological active particles.

cond-mat.soft↗

arXiv2023

Stability of rotating equilibrium states of fluid deformable surfaces

We consider rotating equilibrium states of fluid deformable surfaces. These states are characterized by a force balance between centrifugal and bending forces, involve surface Killing vector fields and are independent on the surface viscosity. Considering a continuum description based on the incompressible surface Navier Stokes equations with bending forces and conserved enclosed volume we numerically demonstrate that these rotating equilibrium states can be reached, but also that these states are not stable. Any perturbation in shape or rotating flow field leads to dissipation and destroys the rotating equilibrium states. After breaking symmetry the evolution reaches other rotating states with a lower energy for which the symmetry axis and the rotation axis are not aligned. Such flow fields could be characterized by three-dimensional Killing vector fields. However, also these states are not stable. Based on these numerical results we postulate a cascading mechanism of disturbance - force balance reconfiguration - dissipation that contains various rotating equilibrium states as transient configurations but eventually leads to the classical equilibrium shapes of the Helfrich energy.

physics.flu-dyn↗

arXiv2023

Diffusion of tangential tensor fields: numerical issues and influence of geometric properties

We study the diffusion of tangential tensor-valued data on curved surfaces. For this purpose, several finite-element-based numerical methods are collected and used to solve a tangential surface n-tensor heat flow problem. These methods differ with respect to the surface representation used, the geometric information required, and the treatment of the tangentiality condition. We emphasize the importance of geometric properties and their increasing influence as the tensorial degree changes from n=0 to n>=1. A specific example is presented that illustrates how curvature drastically affects the behavior of the solution.

math.NA↗

arXiv2023

A diffuse interface approach for vector-valued PDEs on surfaces

Approximating PDEs on surfaces by the diffuse interface approach allows us to use standard numerical tools to solve these problems. This makes it an attractive numerical approach. We extend this approach to vector-valued surface PDEs and explore their convergence properties. In contrast to the well-studied case of scalar-valued surface PDEs, the optimal order of convergence can only be achieved if certain relations between mesh size and interface width are fulfilled. This difference results from the increased coupling between the surface geometry and the PDE for vector-valued quantities defined on it.

math.NA↗

arXiv2021

Active nematodynamics on curved surfaces -- the influence of geometric forces on motion patterns of topological defects

We derive and numerically solve a surface active nematodynamics model. We validate the numerical approach on a sphere and analyse the influence of hydrodynamics on the oscillatory motion of topological defects. For ellipsoidal surfaces the influence of geometric forces on these motion patterns is addressed by taking into account the effects of intrinsic as well as extrinsic curvature contributions. The numerical experiments demonstrate the stronger coupling with geometric properties if extrinsic curvature contributions are present and provide a possibility to tune flow and defect motion by surface properties.

cond-mat.soft↗

arXiv2020

Defects in active nematics: algorithms for identification and tracking

The growing interest in active nematics and the emerging evidence of the relevance of topological defects in biology asks for reliable data analysis tools to identify, classify and track such defects in simulation and microscopy data. We here provide such tools and demonstrate on two examples, on an active turbulent state in an active nematodynamic model and on emerging nematic order in a multi-phase field model, the possibility to compare statistical data on defect velocities with experimental results. The considered tools, which are physics based and data driven, are compared with each other.

cond-mat.soft↗

arXiv2019

Properties of surface Landau-de Gennes Q-tensor models

Uniaxial nematic liquid crystals whose molecular orientation is subjected to a tangential anchoring on a curved surface offer a non trivial interplay between the geometry and the topology of the surface and the orientational degree of freedom. We consider a general thin film limit of a Landau-de Gennes Q-tensor model which retains the characteristics of the 3D model. From this, previously proposed surface models follow as special cases. We compare fundamental properties, such as alignment of the orientational degrees of freedom with principle curvature lines, order parameter symmetry and phase transition type for these models, and suggest experiments to identify proper model assumptions.

cond-mat.soft↗

arXiv2018

A finite element approach for vector- and tensor-valued surface PDEs

We derive a Cartesian componentwise description of the covariant derivative of tangential tensor fields of any degree on general manifolds. This allows to reformulate any vector- and tensor-valued surface PDE in a form suitable to be solved by established tools for scalar-valued surface PDEs. We consider piecewise linear Lagrange surface finite elements on triangulated surfaces and validate the approach by a vector- and a tensor-valued surface Helmholtz problem on an ellipsoid. We experimentally show optimal (linear) order of convergence for these problems. The full functionality is demonstrated by solving a surface Landau-de Gennes problem on the Stanford bunny. All tools required to apply this approach to other vector- and tensor-valued surface PDEs are provided.

math.NA↗

arXiv2017

Nematic liquid crystals on curved surfaces - a thin film limit

We consider a thin film limit of a Landau-de Gennes Q-tensor model. In the limiting process we observe a continuous transition where the normal and tangential parts of the Q-tensor decouple and various intrinsic and extrinsic contributions emerge. Main properties of the thin film model, like uniaxiality and parameter phase space, are preserved in the limiting process. For the derived surface Landau-de Gennes model, we consider an L2-gradient flow. The resulting tensor-valued surface partial differential equation is numerically solved to demonstrate realizations of the tight coupling of elastic and bulk free energy with geometric properties.

cond-mat.soft↗

arXiv2016

Orientational order on surfaces - the coupling of topology, geometry, and dynamics

We consider the numerical investigation of surface bound orientational order using unit tangential vector fields by means of a gradient-flow equation of a weak surface Frank-Oseen energy. The energy is composed of intrinsic and extrinsic contributions, as well as a penalization term to enforce the unity of the vector field. Four different numerical discretizations, namely a discrete exterior calculus approach, a method based on vector spherical harmonics, a surface finite-element method, and an approach utilizing an implicit surface description, the diffuse interface method, are described and compared with each other for surfaces with Euler characteristic 2. We demonstrate the influence of geometric properties on realizations of the Poincare-Hopf theorem and show examples where the energy is decreased by introducing additional orientational defects.

math.NA↗