Biomimetic Design and Fabrication of Interior Architecture of Tissue Scaffolds Using Solid Freeform Fabrication

Modeling, design and fabrication of tissue scaffolds with intricate architecture, porosity and pore size for desired tissue properties presents a challenge in tissue engineering. This paper will present the details of our development in designing and fabrication of the interior architecture of scaffolds using a novel design approach. The Interior Architecture Design (IAD) approach seeks to generate scaffold layered freeform fabrication tool path without forming complicated 3D CAD scaffold models. This involves: applying the principle of layered manufacturing to determine the scaffold individual layered process planes and layered contour; defining the 2D characteristic patterns of the scaffold building blocks (unit cells) to form the Interior Scaffold Pattern; and the generation of process tool path for freeform fabrication of these scaffolds with the specified interior architecture. Feasibility studies applying the IAD algorithm to example models and the generation of fabrication planning instructions will be presented.Mechanical Engineerin

Phase Transitions in Lyotropic Nematic Gels

In this paper, we discuss the equilibrium phases and collapse transitions of a lyotropic nematic gel immersed in an isotropic solvent. A nematic gel consists of a cross-linked polymer network with rod-like molecules embedded in it. Upon decreasing the quality of the solvent, we find that a lyotropic nematic gel undergoes a discontinuous volume change accompanied by an isotropic-nematic transition. We also present phase diagrams that these systems may exhibit. In particular, we show that coexistence of two isotropic phases, of two nematic phases, or of an isotropic and a nematic phase can occur.Comment: 13 pages Revtex, 10 figures, submitted to EPJ

Structural evaluation of concrete expanded polystyrene sandwich panels for slab applications

Sandwich panels are being extensively and increasingly used in building construction because they are light in weight, energy efficient, aesthetically attractive and can be easily handled and erected. This paper presents a structural evaluation of Concrete-Expanded Polystyrene (CEPS) sandwich panels for slab applications using finite element modeling approach. CEPS panels are made of expanded polystyrene foam sandwiched between concrete skins. The use of foam in the middle of sandwich panel reduces the weight of the structure and also acts as insulation against thermal, acoustics and vibration. Applying reinforced concrete skin to both sides of panel takes the advantages of the sandwich concept where the reinforced concrete skins take compressive and tensile loads resulting in higher stiffness and strength and the core transfers shear loads between the faces. This research uses structural software Strand7, which is based on finite element method, to predict the load deformation behaviour of the CEPS sandwich slab panels. Non linear static analysis was used in the numerical investigations. Predicted results were compared with the existing experimental results to validate the numerical approach used

Direct Slicing of STEP Based NURBS Models for Solid Freeform Fabrication

Direct slicing of CAD models to generate process planning instructions for solid freeform fabrication may overcome inherent disadvantages of using STL format in terms of the process accuracy, ease of file management, and incorporation of multiple materials. This paper will present the results of our development of a direct slicing algorithm for layered freeform fabrication. The direct slicing algorithm was based on a neutral, international standard (ISO 10303) STEP-formatted NURBS geometric representation and is intended to be independent of any commercial CAD software. The following aspects of the development effort will be presented: 1) Determination of optimal build direction based upon STEP-based NURBS models; 2) Adaptive subdivision of NURBS data for geometric refinement; and 3) Ray-casting slice generation into sets of raster patterns. Feasibility studies applying the direct slicing algorithm to example models and the generation of fabrication planning instructions involving multi-material structures will also be presented.Mechanical Engineerin

Single polaron properties of the breathing-mode Hamiltonian

We investigate numerically various properties of the one-dimensional (1D) breathing-mode polaron. We use an extension of a variational scheme to compute the energies and wave-functions of the two lowest-energy eigenstates for any momentum, as well as a scheme to compute directly the polaron Greens function. We contrast these results with results for the 1D Holstein polaron. In particular, we find that the crossover from a large to a small polaron is significantly sharper. Unlike for the Holstein model, at moderate and large couplings the breathing-mode polaron dispersion has non-monotonic dependence on the polaron momentum k. Neither of these aspects is revealed by a previous study based on the self-consistent Born approximation

New variables, the gravitational action, and boosted quasilocal stress-energy-momentum

This paper presents a complete set of quasilocal densities which describe the stress-energy-momentum content of the gravitational field and which are built with Ashtekar variables. The densities are defined on a two-surface $B$ which bounds a generic spacelike hypersurface $\Sigma$ of spacetime. The method used to derive the set of quasilocal densities is a Hamilton-Jacobi analysis of a suitable covariant action principle for the Ashtekar variables. As such, the theory presented here is an Ashtekar-variable reformulation of the metric theory of quasilocal stress-energy-momentum originally due to Brown and York. This work also investigates how the quasilocal densities behave under generalized boosts, i. e. switches of the $\Sigma$ slice spanning $B$. It is shown that under such boosts the densities behave in a manner which is similar to the simple boost law for energy-momentum four-vectors in special relativity. The developed formalism is used to obtain a collection of two-surface or boost invariants. With these invariants, one may ``build" several different mass definitions in general relativity, such as the Hawking expression. Also discussed in detail in this paper is the canonical action principle as applied to bounded spacetime regions with ``sharp corners."Comment: Revtex, 41 Pages, 4 figures added. Final version has been revised and improved quite a bit. To appear in Classical and Quantum Gravit

On the Canonical Reduction of Spherically Symmetric Gravity

In a thorough paper Kuchar has examined the canonical reduction of the most general action functional describing the geometrodynamics of the maximally extended Schwarzschild geometry. This reduction yields the true degrees of freedom for (vacuum) spherically symmetric general relativity. The essential technical ingredient in Kuchar's analysis is a canonical transformation to a certain chart on the gravitational phase space which features the Schwarzschild mass parameter $M_{S}$, expressed in terms of what are essentially Arnowitt-Deser-Misner variables, as a canonical coordinate. In this paper we discuss the geometric interpretation of Kuchar's canonical transformation in terms of the theory of quasilocal energy-momentum in general relativity given by Brown and York. We find Kuchar's transformation to be a ``sphere-dependent boost to the rest frame," where the ``rest frame'' is defined by vanishing quasilocal momentum. Furthermore, our formalism is general enough to cover the case of (vacuum) two-dimensional dilaton gravity. Therefore, besides reviewing Kucha\v{r}'s original work for Schwarzschild black holes from the framework of hyperbolic geometry, we present new results concerning the canonical reduction of Witten-black-hole geometrodynamics.Comment: Revtex, 35 pages, no figure

Entanglement and the nonlinear elastic behavior of forests of coiled carbon nanotubes

Helical or coiled nanostructures have been object of intense experimental and theoretical studies due to their special electronic and mechanical properties. Recently, it was experimentally reported that the dynamical response of foamlike forest of coiled carbon nanotubes under mechanical impact exhibits a nonlinear, non-Hertzian behavior, with no trace of plastic deformation. The physical origin of this unusual behavior is not yet fully understood. In this work, based on analytical models, we show that the entanglement among neighboring coils in the superior part of the forest surface must be taken into account for a full description of the strongly nonlinear behavior of the impact response of a drop-ball onto a forest of coiled carbon nanotubes.Comment: 4 pages, 3 figure

The relation between gas density and velocity power spectra in galaxy clusters: qualitative treatment and cosmological simulations

We address the problem of evaluating the power spectrum of the velocity field of the ICM using only information on the plasma density fluctuations, which can be measured today by Chandra and XMM-Newton observatories. We argue that for relaxed clusters there is a linear relation between the rms density and velocity fluctuations across a range of scales, from the largest ones, where motions are dominated by buoyancy, down to small, turbulent scales: $(\delta\rho_k/\rho)^2 = \eta_1^2 (V_{1,k}/c_s)^2$, where $\delta\rho_k/\rho$ is the spectral amplitude of the density perturbations at wave number $k$, $V_{1,k}^2=V_k^2/3$ is the mean square component of the velocity field, $c_s$ is the sound speed, and $\eta_1$ is a dimensionless constant of order unity. Using cosmological simulations of relaxed galaxy clusters, we calibrate this relation and find $\eta_1\approx 1 \pm 0.3$. We argue that this value is set at large scales by buoyancy physics, while at small scales the density and velocity power spectra are proportional because the former are a passive scalar advected by the latter. This opens an interesting possibility to use gas density power spectra as a proxy for the velocity power spectra in relaxed clusters, across a wide range of scales.Comment: 6 pages, 3 figures, submitted to ApJ Letter

Direct slicing of STEP based NURBS models for layered manufacturing

Abstract Direct slicing of CAD models to generate process planning instructions for solid freeform fabrication may overcome inherent disadvantages of using stereolithography format in terms of the process accuracy, ease of file management, and incorporation of multiple materials. This paper will present the results of our development of a direct slicing algorithm for layered freeform fabrication. The direct slicing algorithm was based on a neutral, international standard (ISO 10303) STEP-formatted non-uniform rational B-spline (NURBS) geometric representation and is intended to be independent of any commercial CAD software. The following aspects of the development effort will be presented: (1) determination of optimal build direction based upon STEP-based NURBS models; (2) adaptive subdivision of NURBS data for geometric refinement; and (3) ray-casting slice generation into sets of raster patterns. The development also provides for multi-material slicing and will provide an effective tool in heterogeneous slicing processes.