Absolute Time Derivatives

A four dimensional treatment of nonrelativistic space-time gives a natural frame to deal with objective time derivatives. In this framework some well known objective time derivatives of continuum mechanics appear as Lie-derivatives. Their coordinatized forms depends on the tensorial properties of the relevant physical quantities. We calculate the particular forms of objective time derivatives for scalars, vectors, covectors and different second order tensors from the point of view of a rotating observer. The relation of substantial, material and objective time derivatives is treated.Comment: 26 pages, 4 figures (minor revision

Fine strand-like structure in the solar corona from MHD transverse oscillations

Current analytical and numerical modelling suggest the existence of ubiquitous thin current sheets in the corona that could explain the observed heating requirements. On the other hand, new high resolution observations of the corona indicate that its magnetic field may tend to organise itself in fine strand-like structures of few hundred kilometres widths. The link between small structure in models and the observed widths of strand-like structure several orders of magnitude larger is still not clear. A popular theoretical scenario is the nanoflare model, in which each strand is the product of an ensemble of heating events. Here, we suggest an alternative mechanism for strand generation. Through forward modelling of 3D MHD simulations we show that small amplitude transverse MHD waves can lead in a few periods time to strand-like structure in loops in EUV intensity images. Our model is based on previous numerical work showing that transverse MHD oscillations can lead to Kelvin-Helmholtz instabilities that deform the cross-sectional area of loops. While previous work has focused on large amplitude oscillations, here we show that the instability can occur even for low wave amplitudes for long and thin loops, matching those presently observed in the corona. We show that the vortices generated from the instability are velocity sheared regions with enhanced emissivity hosting current sheets. Strands result as a complex combination of the vortices and the line-of-sight angle, last for timescales of a period and can be observed for spatial resolutions of a tenth of loop radius.Comment: Accepted for publication in ApJ

Multiple junction biasing of superconducting tunnel junction detectors

We describe a new biasing scheme for single photon detectors based on superconducting tunnel junctions. It replaces a single detector junction with a circuit of three junctions and achieves biasing of a detector junction at subgap currents without the use of an external magnetic field. The biasing occurs through the nonlinear interaction of the three junctions, which we demonstrate through numerical simulation. This nonlinear state is numerically stable against external fluctuations and is compatible with high fidelity electrical readout of the photon-induced current. The elimination of the external magnetic field potentially increases the capability of these types of photon detectors and eases constraints involved in the fabrication of large detector arrays.Comment: 15 pages, including 3 figure

Innovative all composite multi-pultrusion truss system for stressed arch deployable shelters

Trusses are one of the successful structural forms that have been utilised, at extended scale, since the nineteen century. Fibre composite materials are relatively new to civil engineering applications. The increased interest in using composites in civil applications can be attributed to advantages when compared to other construction materials that offset their associated costs. Using conventional approaches for truss systems in composite materials can undermine their efficiency. This is mainly due to concentration of stresses at connections which usually govern the truss design. The Military Modular Shelter System (M2S2) initiative is a research project that aims to develop a fibre composite re-deployable arched shelter system with rigid PVC or fabric cladding. The main frames are formed from modular fibre composite panels that are connected and stressed into position by prestressing cables. Different geometries can be obtained using this system by changing the number of panels per frame and the packer sizes between panels. This paper presents the development and testing of innovative fibre composite truss modules that were investigated as part of this project. The truss system is based on using multi-pultrusion sections for the chord and vertical members. Truss bracing is provided by a double skin laminated web. This structure offers many advantages including semi-ductile failure that occurred outside the joint area and ease of manufacturing. In spite of being developed for the M2S2 system, the concept is similarly applicable as a general purpose truss system

Stabilization Control of the Differential Mobile Robot Using Lyapunov Function and Extended Kalman Filter

This paper presents the design of a control model to navigate the differential mobile robot to reach the desired destination from an arbitrary initial pose. The designed model is divided into two stages: the state estimation and the stabilization control. In the state estimation, an extended Kalman filter is employed to optimally combine the information from the system dynamics and measurements. Two Lyapunov functions are constructed that allow a hybrid feedback control law to execute the robot movements. The asymptotical stability and robustness of the closed loop system are assured. Simulations and experiments are carried out to validate the effectiveness and applicability of the proposed approach.Comment: arXiv admin note: text overlap with arXiv:1611.07112, arXiv:1611.0711