Real-time Computer Simulation of Three Dimensional Elastostatics using the Finite Point Method

Real-time simulation of deformable solids is essential for some applications such as biological organ simulations for surgical simulators. In this work, deformable solids are approximated to be linear elastic, and an easy and straight forward numerical technique, the Finite Point Method (FPM), is used to model three dimensional linear elastostatics. Graphics Processing Unit (GPU) is used to accelerate computations. Results show that the Finite Point Method, together with GPU, can compute three dimensional linear elastostatic responses of solids at rates suitable for real-time graphics, for solids represented by reasonable number of points.

Experimental evidence for interplay of dynamic heterogeneity and finite-size effect in glassy polymers

Despite two decades of extensive research, direct experimental evidence of a dynamical length scale determining the glass transition of confined polymers has yet to emerge. Using a recently established experimental technique of interface micro-rheology we provide evidence of finite-size effect truncating the growth of a quantity proportional to a dynamical length scale in confined glassy polymers, on cooling towards the glass transition temperature. We show how the interplay of variation of polymer film thickness and this temperature-dependent growing dynamical length scale determines the glass transition temperature, which in our case of 2-3nm thick films, is reduced significantly as compared to their bulk values.

Resource Pricing for Fair and Efficient Link Sharing with a Finite Data Model

The literature on pricing implicitly assumes an "infinite data" model, in which sources can sustain any data rate indefinitely. We assume a more realistic "finite data" model, in which sources occasionally run out of data. Further, we assume that users have contracts with the service provider, specifying the rates at which they can inject traffic into the network. Our objective is to study how prices can be set such that a single link can be shared efficiently and fairly among users in a dynamically changing scenario where a subset of users occasionally has little data to send. We obtain simple necessary and sufficient conditions on prices such that efficient and fair link sharing is possible. We illustrate the ideas using a simple example

An Actor-Critic Algorithm for Finite Horizon Markov Decision Processes

We develop a simulation based algorithm for finite horizon Markov decision processes with finite state and finite action space. Illustrative numerical experiments with the proposed algorithm are shown for problems in flow control of communication networks and capacity switching in semiconductor fabrication.

Spectral Finite Element Formulation for Nanorods via Nonlocal Continuum Mechanics

In this article, the Eringen's nonlocal elasticity theory has been incorporated into classical/local Bernoulli-Euler rod model to capture unique properties of the nanorods under the umbrella of continuum mechanics theory. The spectral finite element (SFE) formulation of nanorods is performed. SFE formulation is carried out and the exact shape functions (frequency dependent) and dynamic stiffness matrix are obtained as function of nonlocal scale parameter. It has been found that the small scale affects the exact shape functions and the elements of the dynamic stiffness matrix. The results presented in this paper can provide useful guidance for the study and design of the next generation of nanodevices that make use of the wave dispersion properties of carbon nanotubes.

Wavelet based spectral finite element modelling and detection of de-lamination in composite beams

In this paper, a model for composite beam with embedded de-lamination is developed using the wavelet based spectral finite element (WSFE) method particularly for damage detection using wave propagation analysis. The simulated responses are used as surrogate experimental results for the inverse problem of detection of damage using wavelet filtering. The WSFE technique is very similar to the fast fourier transform (FFT) based spectral finite element (FSFE) except that it uses compactly supported Daubechies scaling function approximation in time. Unlike FSFE formulation with periodicity assumption, the wavelet-based method allows imposition of initial values and thus is free from wrap around problems. This helps in analysis of finite length undamped structures, where the FSFE method fails to simulate accurate response. First, numerical experiments are performed to study the effect of de-lamination on the wave propagation characteristics. The responses are simulated for different de-lamination configurations for both broad-band and narrow-band excitations. Next, simulated responses are used for damage detection using wavelet analysis.

Spectral Finite Element Modeling of Complex Structures for Applications in Real-time Structural Health Monitoring

In this paper we discuss the recent progresses in spectral finite element modeling of complex structures and its application in real-time structural health monitoring system based on sensor-actuator network and near real-time computation of Damage Force Indicator (DFI) vector. A waveguide network formalism is developed by mapping the original variational problem into the variational problem involving product spaces of 1D waveguides. Numerical convergence is studied using a h()-refinement scheme, where is the wavelength of interest. Computational issues towards successful implementation of this method with SHM system are discussed.

Diffuse optical tomographic imager using a single light source

Near-infrared diffuse optical tomography (DOT) technique has the capability of providing good quantitative reconstruction of tissue absorption and scattering properties with additional inputs such as input and output modulation depths and correction for the photon leakage. We have calculated the two-dimensional (2D) input modulation depth from three-dimensional (3D) diffusion to model the 2D diffusion of photons. The photon leakage when light traverses from phantom to the fiber tip is estimated using a solid angle model. The experiments are carried for single (5 and 6 mm) as well as multiple inhomogeneities (6 and 8 mm) with higher absorption coefficient in a homogeneous phantom. Diffusion equation for photon transport is solved using finite element method and Jacobian is modeled for reconstructing the optical parameters. We study the development and performance of DOT system using modulated single light source and multiple detectors. The dual source methods are reported to have better reconstruction capabilities to resolve and localize single as well as multiple inhomogeneities because of its superior noise rejection capability. However, an experimental setup with dual sources is much more difficult to implement because of adjustment of two out of phase identical light probes symmetrically on either side of the detector during scanning time. Our work shows that with a relatively simpler system with a single source, the results are better in terms of resolution and localization. The experiments are carried out with 5 and 6 mm inhomogeneities separately and 6 and 8 mm inhomogeneities both together with absorption coefficient almost three times as that of the background. The results show that our experimental single source system with additional inputs such as 2D input/output modulation depth and air fiber interface correction is capable of detecting 5 and 6 mm inhomogeneities separately and can identify the size difference of multiple inhomogeneities such as 6 and 8 mm. The localization error is zero. The recovered absorption coefficient is 93% of inhomogeneity that we have embedded in experimental phantom.

Ferroelectric interaction and polarization studies in BaTiO3/SrTiO3 superlattice

Ferroelectric superlattice structures consisting of alternating layers of BaTiO3 and SrTiO3 with variable interlayer thickness were grown on Pt (111)/TiO2/SiO2/Si (100) substrates by pulsed laser deposition. The presence of superlattice reflections in the x-ray diffraction pattern clearly showed the superlattice behavior of the fabricated structures over a range of 6.4–20 nm individual layer thicknesses. Depth profile conducted by secondary ion mass spectrometry analysis showed a periodic concentration of Ba and Sr throughout the film. Polarization hysteresis and the capacitance-voltage characteristics of these films show clear size dependent ferroelectric characteristics. The spontaneous (Ps) and remnant (Pr) polarizations increase gradually with decreasing periodicity, reach a maximum at a finite thickness and then decrease. The competition between the size effect and long-range ferroelectric interaction is suggested as a possible reason for this phenomenon. The temperature dependence of Ps and Pr shows a single ferroelectric phase transition, and the Curie temperature is estimated to be about 316 K. The curve shows that the ferroelectric superlattice tends to form an artificial material, responding as a single structure with an averaged behavior of both the parent systems.