An elastoplastic theory of dislocations as a physical field theory with torsion

We consider a static theory of dislocations with moment stress in an anisotropic or isotropic elastoplastical material as a T(3)-gauge theory. We obtain Yang-Mills type field equations which express the force and the moment equilibrium. Additionally, we discuss several constitutive laws between the dislocation density and the moment stress. For a straight screw dislocation, we find the stress field which is modified near the dislocation core due to the appearance of moment stress. For the first time, we calculate the localized moment stress, the Nye tensor, the elastoplastic energy and the modified Peach-Koehler force of a screw dislocation in this framework. Moreover, we discuss the straightforward analogy between a screw dislocation and a magnetic vortex. The dislocation theory in solids is also considered as a three-dimensional effective theory of gravity.Comment: 38 pages, 6 figures, RevTe

Existence, uniqueness, and stabilization results for parabolic variational inequalities

In this paper we consider feedback stabilization for parabolic variational inequalities of obstacle type with time and space depending reaction and convection coefficients and show exponential stabilization to nonstationary trajectories. Based on a Moreau--Yosida approximation, a feedback operator is established using a finite (and uniform in the approximation index) number of actuators leading to exponential decay of given rate of the state variable. Several numerical examples are presented addressing smooth and nonsmooth obstacle functions

Measuring rhizosphere hydraulic properties: impact of root mucilage on soil hydraulic conductivity and water retention curve

Roots are hypothesized to alter rhizosphere hydraulic properties by release of mucilage. This mechanism is expected to have strong implications for root water uptake under drought conditions. Direct measurement of rhizosphere hydraulic properties is hindered by the dynamic nature of the components involved; root hydraulics change with ontology; mucilage production, composition and diffusion are not constant; soil water content changes. An experimental approach was developed which enables to simultaneously measure hydraulic conductivity and apparent water retention curve in a radial flow setup, mimicking the flow geometry around roots. The method consists of extracting water at constant suction via a suction cup, which is centrally placed in a soil filled cylinder and recording water outflow and soil matric potential. In the past, the setup was tested for homogeneous distribution of a model substance (calcium-polygalacturonic acid) frequently used to mimic the properties of root mucilage. Now the system has been applied to investigate the impact of plant root mucilage collected from white lupine. As the system allows a local placement of mucilage treated soil around the suction cup to simulate a ‘rhizosphere’ between bulk soil and suction cup, it can be set up with the limited quantity of natural plant root mucilage available from direct collection. Quartz sand has been treated with lupine root mucilage by mixing liquid mucilage with dry sand at a concentration of 2 mg mucilage per gram soil. Treated sand has been placed as a circular layer with 3.75 mm thickness around the suction cup, which has a radius of 1.25 mm. All around this layer, the device has been filled up with untreated sand. The radius of the whole device was 25 mm. To determine soil hydraulic conductivity we inversely fitted the outflow curves and soil matric potential by solving the Richards’ equation in radial coordinates. Water outflow curves show a significant impact of lupine mucilage on water flow rate – it slows water flow from bulk soil to suction cup. Currently modelling is in process to determine soil hydraulic conductivity and water retention curves. Decreasing hydraulic conductivities and increasing water retention due to lupine mucilage treatment are expected

Aharonov-Bohm Effect and Disclinations in an Elastic Medium

In this work we investigate quasiparticles in the background of defects in solids using the geometric theory of defects. We use the parallel transport matrix to study the Aharonov-Bohm effect in this background. For quasiparticles moving in this effective medium we demonstrate an effect similar to the gravitational Aharonov- Bohm effect. We analyze this effect in an elastic medium with one and $N$ defects.Comment: 6 pages, Revtex

Volterra Distortions, Spinning Strings, and Cosmic Defects

Cosmic strings, as topological spacetime defects, show striking resemblance to defects in solid continua: distortions, which can be classified into disclinations and dislocations, are line-like defects characterized by a delta function-valued curvature and torsion distribution giving rise to rotational and translational holonomy. We exploit this analogy and investigate how distortions can be adapted in a systematic manner from solid state systems to Einstein-Cartan gravity. As distortions are efficiently described within the framework of a SO(3) {\rlap{\supset}\times}} T(3) gauge theory of solid continua with line defects, we are led in a straightforward way to a Poincar\'e gauge approach to gravity which is a natural framework for introducing the notion of distorted spacetimes. Constructing all ten possible distorted spacetimes, we recover, inter alia, the well-known exterior spacetime of a spin-polarized cosmic string as a special case of such a geometry. In a second step, we search for matter distributions which, in Einstein-Cartan gravity, act as sources of distorted spacetimes. The resulting solutions, appropriately matched to the distorted vacua, are cylindrically symmetric and are interpreted as spin-polarized cosmic strings and cosmic dislocations.Comment: 24 pages, LaTeX, 9 eps figures; remarks on energy conditions added, discussion extended, version to be published in Class. Quantum Gra

Probing non-Riemannian spacetime geometry

The equations of motion for matter in non-Riemannian spacetimes are derived via a multipole method. It is found that only test bodies with microstructure couple to the non-Riemannian spacetime geometry. Consequently it is impossible to detect spacetime torsion with the satellite experiment Gravity Probe B, contrary to some recent claims in the literature.Comment: 8 pages, 1 figure, matches published version including the erratum in Phys. Lett. A 373 (2009) 160

Heavy Meson Decays into Light Resonances

We analyse the Lorentz structures of weak decay matrix elements bewteen meson states of arbitrary spin. Simplifications arise in the transition amplitudes for a heavy meson decaying into a light one via a Bethe-Salpeter approach which incorporates heavy quark symmetry. Phenomenological consequences on several semileptonic, nonleptonic and FCNC induced decays of heavy flavoured mesons are derived and discussed.Comment: 20 RevTex pages, Preprint # UTAS-PHYS-94-0

A planar multipole ion trap

We report on the realisation of a chip-based multipole ion trap manufactured using micro-electromechanical systems (MEMS) technology. It provides ion confinement in an almost field-free volume between two planes of radiofrequency electrodes, deposited on glass substrates, which allows for optical access to the trap. An analytical model of the effective trapping potential is presented and compared with numerical calculations. Stable trapping of argon ions is achieved and a lifetime of 16s is measured. Electrostatic charging of the chip surfaces is studied and found to agree with a numerical estimate

The gauge theory of dislocations: a uniformly moving screw dislocation

In this paper we present the equations of motion of a moving screw dislocation in the framework of the translation gauge theory of dislocations. In the gauge field theoretical formulation, a dislocation is a massive gauge field. We calculate the gauge field theoretical solutions of a uniformly moving screw dislocation. We give the subsonic and supersonic solutions. Thus, supersonic dislocations are not forbidden from the field theoretical point of view. We show that the elastic divergences at the dislocation core are removed. We also discuss the Mach cones produced by supersonic screw dislocations.Comment: 16 pages, 5 figure

Disclinations, dislocations and continuous defects: a reappraisal

Disclinations, first observed in mesomorphic phases, are relevant to a number of ill-ordered condensed matter media, with continuous symmetries or frustrated order. They also appear in polycrystals at the edges of grain boundaries. They are of limited interest in solid single crystals, where, owing to their large elastic stresses, they mostly appear in close pairs of opposite signs. The relaxation mechanisms associated with a disclination in its creation, motion, change of shape, involve an interplay with continuous or quantized dislocations and/or continuous disclinations. These are attached to the disclinations or are akin to Nye's dislocation densities, well suited here. The notion of 'extended Volterra process' takes these relaxation processes into account and covers different situations where this interplay takes place. These concepts are illustrated by applications in amorphous solids, mesomorphic phases and frustrated media in their curved habit space. The powerful topological theory of line defects only considers defects stable against relaxation processes compatible with the structure considered. It can be seen as a simplified case of the approach considered here, well suited for media of high plasticity or/and complex structures. Topological stability cannot guarantee energetic stability and sometimes cannot distinguish finer details of structure of defects.Comment: 72 pages, 36 figure