Multi-Phase Equilibrium of Crystalline Solids

A continuum model of crystalline solid equilibrium is presented in which the underlying periodic lattice structure is taken explicitly into account. This model also allows for both point and line defects in the bulk of the lattice and at interfaces, and the kinematics of such defects is discussed in some detail. A Gibbsian variational argument is used to derive the necessary bulk and interfacial conditions for multi-phase equilibrium (crystal-crystal and crystal-melt) where the allowed lattice variations involve the creation and transport of defects in the bulk and at the phase interface. An interfacial energy, assumed to depend on the interfacial dislocation density and the orientation of the interface with respect to the lattices of both phases, is also included in the analysis. Previous equilibrium results based on nonlinear elastic models for incoherent and coherent interfaces are recovered as special cases for when the lattice distortion is constrained to coincide with the macroscopic deformation gradient, thereby excluding bulk dislocations. The formulation is purely spatial and needs no recourse to a fixed reference configuration or an elastic-plastic decomposition of the strain. Such a decomposition can be introduced however through an incremental elastic deformation superposed onto an already dislocated state, but leads to additional equilibrium conditions. The presentation emphasizes the role of {configurational forces} as they provide a natural framework for the description and interpretation of singularities and phase transitions.Comment: 32 pages, to appear in Journal of the Mechanics and Physics of Solid

Strongly coupled quantum criticality with a Fermi surface in two dimensions: fractionalization of spin and charge collective modes

We describe two dimensional models with a metallic Fermi surface which display quantum phase transitions controlled by strongly interacting critical field theories below their upper critical dimension. The primary examples involve transitions with a topological order parameter associated with dislocations in collinear spin density wave ("stripe") correlations: the gapping of the order parameter fluctuations leads to a fractionalization of spin and charge collective modes, and this transition has been proposed as a candidate for the cuprates near optimal doping. The coupling between the order parameter and long-wavelength volume and shape deformations of the Fermi surface is analyzed by the renormalization group, and a runaway flow to a non-perturbative regime is found in most cases. A phenomenological scaling analysis of simple observable properties of possible second order quantum critical points is presented, with results quite similar to those near quantum spin glass transitions and to phenomenological forms proposed by Schroeder et al. (cond-mat/0011002).Comment: 16 pages, 4 figures; (v2) additional clarifying remark

3D scanning of cultural heritage with consumer depth cameras

Three dimensional reconstruction of cultural heritage objects is an expensive and time-consuming process. Recent consumer real-time depth acquisition devices, like Microsoft Kinect, allow very fast and simple acquisition of 3D views. However 3D scanning with such devices is a challenging task due to the limited accuracy and reliability of the acquired data. This paper introduces a 3D reconstruction pipeline suited to use consumer depth cameras as hand-held scanners for cultural heritage objects. Several new contributions have been made to achieve this result. They include an ad-hoc filtering scheme that exploits the model of the error on the acquired data and a novel algorithm for the extraction of salient points exploiting both depth and color data. Then the salient points are used within a modified version of the ICP algorithm that exploits both geometry and color distances to precisely align the views even when geometry information is not sufficient to constrain the registration. The proposed method, although applicable to generic scenes, has been tuned to the acquisition of sculptures and in this connection its performance is rather interesting as the experimental results indicate

Determining Cosserat constants of 2D cellular solids from beam models

We present results of a two-scale model of disordered cellular materials where we describe the microstructure in an idealized manner using a beam network model and then make a transition to a Cosserat-type continuum model describing the same material on the macroscopic scale. In such scale transitions, normally either bottom-up homogenization approaches or top-down reverse modelling strategies are used in order to match the macro-scale Cosserat continuum to the micro-scale beam network. Here we use a different approach that is based on an energetically consistent continuization scheme that uses data from the beam network model in order to determine continuous stress and strain variables in a set of control volumes defined on the scale of the individual microstructure elements (cells) in such a manner that they form a continuous tessellation of the material domain. Stresses and strains are determined independently in all control volumes, and constitutive parameters are obtained from the ensemble of control volume data using a least-square error criterion. We show that this approach yields material parameters that are for regular honeycomb structures in close agreement with analytical results. For strongly disordered cellular structures, the thus parametrized Cosserat continuum produces results that reproduce the behavior of the micro-scale beam models both in view of the observed strain patterns and in view of the macroscopic response, including its size dependence

The origin of the complex character of the ohmic impedance

The local and global Ohmic response for an electrode exhibiting geometry-induced potential and/or current distributions has recently been shown to be represented by a frequency-dependent complex impedance. A physical explanation for this result is provided in terms of the radial contribution to local current density and the decrease in current density along the current lines. Experiments performed with Cu/Al and Mg/Al galvanic couples show that, in regions where a radial current density does not exist, the local Ohmic impedance is independent of position; whereas, in regions where the radial current density cannot be neglected, the local Ohmic impedance is a function of position. Simulations performed on recessed electrodes show that, even in the absence of a radial current, an axial variation of current density gives rise to a complex Ohmic impedance. The complex character of the Ohmic impedance shows that an equivalent circuit, using the usual two-terminal resistor to represent the Ohmic contribution of the electrolyte, provides an inadequate representation of an electrode with geometry-induced current and potential distributions