Finite Length Effects on Switching Mechanisms in Chains of Magnetic Particles

Periodic systems of magnetic nanoparticles are now of interest as they support GHz spin waves. Their equilibrium configurations, switchable with the external magnetic field, are crucial for such applications. We study infinite and finite chains of particles of two shapes (i) ellipsoidal and (ii) rectangular stripes with long axes perpendicular to the chain axis. A variable magnetic field is applied parallel to the long axes. Micromagnetic simulations are compared with the corresponding discrete spin models (Stoner-Wohlfarth model, S-W). An antiferromagnetic configuration is the ground state for all the systems at vanishing field but a ferromagnetic configuration occurs when the field is strong enough. The switching of the infinite chains to the reversed ferromagnetic configuration proceeds directly for the ellipsoids and by an intermediate configuration, in which the magnetization within the particle is non-uniform, in the case of the stripes. The non-uniform configurations are well represented by tilted states in S-W model. Important differences are found in the finite analogs: the switching of ellipsoids becomes multistage and starts from the innermost particles relatively well reproduced with S-W model, whereas the reversal of the stripes, starts from the outermost particles and has no analog in S-W model. Practical consequences of the findings are discussed.

A modelling framework for finite strain magnetoviscoelasticity

The main objective of this contribution is the theoretical modelling of magnetizable materials that exhibit viscoelastic properties. The current state of the art in the mathematical modelling of non-linear magnetomechanics in deformable media can be easily integrated within the unified framework of continuum thermodynamics, which is crucial in setting the convenient forms for the constitutive laws and evolution equations. Owing to the soft nature of the materials we have in mind, the finite strain range is adopted a priori and, in this first approach, only isotropic materials are considered. We adopt the currently well-accepted multiplicative split of the deformation gradient, which, moreover, gives rise to an intermediate configuration. Herein, the novelty resides in the fact that the magnetic field vectors are transported onto the aforementioned intermediate configuration and, therefore, can be implicitly decomposed. The proposed formulation is based on the magnetic induction as the main independent variable for the magnetic part of the problem. An alternative formulation based on the magnetic field as main independent variable can easily be deduced, but this latter will not be considered in this paper for the sake of clarity. A very simple model example that agrees with the laws of thermodynamics is proposed for the purpose of demonstration to study some phenomena qualitatively.

A Study on the ‘Compatiblity Assumption’ of Contemporary Multiplicative Plasicity Models

Contemporary multiplicative plasticity models are now generally accepted as “proper material models” for modelling plastic behaviour of deformable bodies within the framework of finite-strain elastoplasticity. The models are based on the assumptions that the intermediate configuration of the body is stress-free or locally unstressed, for which no plastic deformation exists that meets the conditions of compatibility. The assumption; however, has never really been questioned nor justified, but was rather taken as an axiom and therefore considered to be generally true. In this study, we take a critical look at the assumption from both, physical and mathematical points of view, in order to investigate whether contemporary multiplicative plasticity models are indeed continuum based and if there are alternatives to them.

An Eulerian formulation of inelasticity: from metal plasticity to growth of biological tissues

The purpose of this paper is to review and contrast the Lagrangian and Eulerian formulations of inelasticity as they apply to metal plasticity and growth of biological tissues. In contrast with the Lagrangian formulation of inelasticity, the Eulerian formulation is unaffected by arbitrary choices of the reference configuration, an intermediate configuration, a total deformation measure and an inelastic deformation measure. Although the Eulerian formulation for growth of biological tissues includes a rate of mass supply and can be used to understand the mechanics of growth, it does not yet model essential mechanobiological processes that control growth. Much research is needed before this theory can help design medical treatments for growth related disease. This article is part of the theme issue ‘Rivlin's legacy in continuum mechanics and applied mathematics’.

Existence for dislocation-free finite plasticity

This note addresses finite plasticity under the constraint that plastic deformations are compatible. In this case, the total elastoplastic deformation of the medium is decomposed as y = ye ○ yp, where the plastic deformation yp is defined on the fixed reference configuration and the elastic deformation ye is a mapping from the varying intermediate configuration yp(Ω). Correspondingly, the energy of the medium features both Lagrangian (plastic, loads) and not Lagrangian contributions (elastic). We present a variational formulation of the static elastoplastic problem in this setting and show that a solution is attained in a suitable class of admissible deformations. Possible extensions of the result, especially in the direction of quasistatic evolutions, are also discussed.

Online, Interactive User Guidance for High-dimensional, Constrained Motion Planning

We consider the problem of planning a collision-free path for a high-dimensional robot. Specifically, we suggest a planning framework where a motion-planning algorithm can obtain guidance from a user. In contrast to existing approaches that try to speed up planning by incorporating experiences or demonstrations ahead of planning, we suggest to seek user guidance only when the planner identifies that it ceases to make significant progress towards the goal. Guidance is provided in the form of an intermediate configuration q^, which is used to bias the planner to go through q^. We demonstrate our approach for the case where the planning algorithm is Multi-Heuristic A* (MHA*) and the robot is a 34-DOF humanoid. We show that our approach allows to compute highly-constrained paths with little domain knowledge. Without our approach, solving such problems requires carefully-crafted domain-dependent heuristics.

HIV-1 Env trimer opens through an asymmetric intermediate in which individual protomers adopt distinct conformations

HIV-1 entry into cells requires binding of the viral envelope glycoprotein (Env) to receptor CD4 and coreceptor. Imaging of individual Env molecules on native virions shows Env trimers to be dynamic, spontaneously transitioning between three distinct well-populated conformational states: a pre-triggered Env (State 1), a default intermediate (State 2) and a three-CD4-bound conformation (State 3), which can be stabilized by binding of CD4 and coreceptor-surrogate antibody 17b. Here, using single-molecule Fluorescence Resonance Energy Transfer (smFRET), we show the default intermediate configuration to be asymmetric, with individual protomers adopting distinct conformations. During entry, this asymmetric intermediate forms when a single CD4 molecule engages the trimer. The trimer can then transition to State 3 by binding additional CD4 molecules and coreceptor.

Intermediate Stage Build of Sheet Metal in Progressive Die Design

Intermediate stage build of Multi-station progressive die is to get intermediate configuration of every station and blank by unfolding product configuration reversely. It needs complicated hand computation and drawing to design intermediate stage with traditional method. In this paper, NX PDW module is used to finish the work. According to the shape of sheet metal, parts are simply classified into three types, and for different type of sheet metal part, different method to unfold the product configuration is discussed. The process of building intermediate stage with PDW is intuitive, timesaving, and also easy to modify.