An algebraic formulation of exact force-, moment-isotropy in spatial parallel manipulators

In this paper, we present an algebraic method to study and design spatial parallel manipulators that demonstrate isotropy in the force and moment distributions.We use the force and moment transformation matrices separately,and derive conditions for their isotropy individually as well as in combination. The isotropy conditions are derived in closed-form in terms of the invariants of the quadratic forms associated with these matrices. The formulation has been applied to a class of Stewart platform manipulators. We obtain multi-parameter families of isotropic manipulator analytically. In addition to computing the isotropic configurations of an existing manipulator,we demonstrate a procedure for designing the manipulator for isotropy at a given configuration.

Clustering Based Large Margin Classification: A Scalable Approach using SOCP Formulation

This paper presents a novel Second Order Cone Programming (SOCP) formulation for large scale binary classification tasks. Assuming that the class conditional densities are mixture distributions, where each component of the mixture has a spherical covariance, the second order statistics of the components can be estimated efficiently using clustering algorithms like BIRCH. For each cluster, the second order moments are used to derive a second order cone constraint via a Chebyshev-Cantelli inequality. This constraint ensures that any data point in the cluster is classified correctly with a high probability. This leads to a large margin SOCP formulation whose size depends on the number of clusters rather than the number of training data points. Hence, the proposed formulation scales well for large datasets when compared to the state-of-the-art classifiers, Support Vector Machines (SVMs). Experiments on real world and synthetic datasets show that the proposed algorithm outperforms SVM solvers in terms of training time and achieves similar accuracies.

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.

Trapped fermions in a synthetic non-Abelian gauge field

On increasing the coupling strength (lambda) of a non-Abelian gauge field that induces a generalized Rashba spin-orbit interaction, the topology of the Fermi surface of a homogeneous gas of noninteracting fermions of density rho similar to k(F)(3) undergoes a change at a critical value, lambda(T) approximate to k(F) [Phys. Rev. B 84, 014512 ( 2011)]. In this paper we analyze how this phenomenon affects the size and shape of a cloud of spin-1/2 fermions trapped in a harmonic potential such as those used in cold atom experiments. We develop an adiabatic formulation, including the concomitant Pancharatnam-Berry phase effects, for the one-particle states in the presence of a trapping potential and the gauge field, obtaining approximate analytical formulas for the energy levels for some high symmetry gauge field configurations of interest. An analysis based on the local density approximation reveals that, for a given number of particles, the cloud shrinks in a characteristic fashion with increasing.. We explain the physical origins of this effect by a study of the stress tensor of the system. For an isotropic harmonic trap, the local density approximation predicts a spherical cloud even for anisotropic gauge field configurations. We show, via a calculation of the cloud shape using exact eigenstates, that for certain gauge field configurations there is a systematic and observable anisotropy in the cloud shape that increases with increasing gauge coupling lambda. The reasons for this anisotropy are explained using the analytical energy levels obtained via the adiabatic approximation. These results should be useful in the design of cold atom experiments with fermions in non-Abelian gauge fields. An important spin-off of our adiabatic formulation is that it reveals exciting possibilities for the cold-atom realization of interesting condensed matter Hamiltonians by using a non-Abelian gauge field in conjunction with another potential. In particular, we show that the use of a spherical non-Abelian gauge field with a harmonic trapping potential produces a monopole field giving rise to a spherical geometry quantum Hall-like Hamiltonian in the momentum representation.

Algorithmic approach to simulate Hamiltonian dynamics and an NMR simulation of quantum state transfer

We propose an iterative algorithm to simulate the dynamics generated by any n-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator U (unitary) into a product of different time-step unitaries. The algorithm product-decomposes U in a chosen operator basis by identifying a certain symmetry of U that is intimately related to the number of gates in the decomposition. We illustrate the algorithm by first obtaining a polynomial decomposition in the Pauli basis of the n-qubit quantum state transfer unitary by Di Franco et al. [Phys. Rev. Lett. 101, 230502 (2008)] that transports quantum information from one end of a spin chain to the other, and then implement it in nuclear magnetic resonance to demonstrate that the decomposition is experimentally viable. We further experimentally test the resilience of the state transfer to static errors in the coupling parameters of the simulated Hamiltonian. This is done by decomposing and simulating the corresponding imperfect unitaries.

Two-dimensional flow past circular cylinders using finite volume lattice Boltzmann formulation

In this article, an extension to the total variation diminishing finite volume formulation of the lattice Boltzmann equation method on unstructured meshes was presented. The quadratic least squares procedure is used for the estimation of first-order and second-order spatial gradients of the particle distribution functions. The distribution functions were extrapolated quadratically to the virtual upwind node. The time integration was performed using the fourth-order RungeKutta procedure. A grid convergence study was performed in order to demonstrate the order of accuracy of the present scheme. The formulation was validated for the benchmark two-dimensional, laminar, and unsteady flow past a single circular cylinder. These computations were then investigated for the low Mach number simulations. Further validation was performed for flow past two circular cylinders arranged in tandem and side-by-side. Results of these simulations were extensively compared with the previous numerical data. Copyright (C) 2011 John Wiley & Sons, Ltd.

Physics-Based Band Gap Model for Relaxed and Strained 100] Silicon Nanowires

In this paper, we propose a physics-based simplified analytical model of the energy band gap and electron effective mass in a relaxed and strained rectangular 100] silicon nanowires (SiNWs). Our proposed formulation is based on the effective mass approximation for the nondegenerate two-band model and 4 x 4 Luttinger Hamiltonian for energy dispersion relation of conduction band electrons and the valence band heavy and light holes, respectively. Using this, we demonstrate the effect of the uniaxial strain applied along 100]-direction and a biaxial strain, which is assumed to be decomposed from a hydrostatic deformation along 001] followed by a uniaxial one along the 100]-direction, respectively, on both the band gap and the transport and subband electron effective masses in SiNW. Our analytical model is in good agreement with the extracted data using the extended-Huckel-method-based numerical simulations over a wide range of device dimensions and applied strain.

Nonlocal continuum mechanics formulation for axial, flexural, shear and contraction coupled wave propagation in single walled carbon nanotubes

This paper presents the effect of nonlocal scaling parameter on the coupled i.e., axial, flexural, shear and contraction, wave propagation in single-walled carbon nanotubes (SWCNTs). The axial and transverse motion of SWCNT is modeled based on first order shear deformation theory (FSDT) and thickness contraction. The governing equations are derived based on nonlocal constitutive relations and the wave dispersion analysis is also carried out. The studies shows that the nonlocal scale parameter introduces certain band gap region in all wave modes where no wave propagation occurs. This is manifested in the wavenumber plots as the region where the wavenumber tends to infinite or wave speed tends to zero. The frequency at which this phenomenon occurs is called the escape frequency. Explicit expressions are derived for cut-off and escape frequencies of all waves in SWCNT. It is also shown that the cut-off frequencies of shear and contraction mode are independent of the nonlocal scale parameter. The results provided in this article are new and are useful guidance for the study and design of the next generation of nanodevices that make use of the coupled wave propagation properties of single-walled carbon nanotubes.

Continuum theory of edge states of topological insulators: variational principle and boundary conditions

We develop a continuum theory to model low energy excitations of a generic four-band time reversal invariant electronic system with boundaries. We propose a variational energy functional for the wavefunctions which allows us to derive natural boundary conditions valid for such systems. Our formulation is particularly suited for developing a continuum theory of the protected edge/surface excitations of topological insulators both in two and three dimensions. By a detailed comparison of our analytical formulation with tight binding calculations of ribbons of topological insulators modelled by the Bernevig-Hughes-Zhang (BHZ) Hamiltonian, we show that the continuum theory with a natural boundary condition provides an appropriate description of the low energy physics.

Formulation development and evaluation of lamivudine controlled release tablets using cross-linked sago starch

Objectives: Modified starches based polymeric substances find utmost applicability in pharmaceutical formulation development. Cross-linked starches showed very promising results in drug delivery application. The present investigation concerns with the development of controlled release tablets of lamivudine using cross-linked sago starch. Methods: The cross-linked derivative was synthesized with phosphorous oxychloride and native sago starch in basic pH medium. The cross-linked sago starch was tested for acute toxicity and drug-excipient compatibility study. The formulated tablets were evaluated for various physical characteristics, in vitro dissolution release study and in vivo pharmacokinetic study in rabbit model. Results: In vitro release study showed that the optimized formulation exhibited highest correlation (R) in case of zero order kinetic model and the release mechanism followed a combination of diffusion and erosion process. There was a significant difference in the pharmacokinetic parameters (T-max, C-max, AUC, V-d, T-1/2, and MDT) of the optimized formulation as compared to the marketed conventional tablet Lamivir (R). Conclusion: The cross-linked starch showed promising results in terms of controlling the release behavior of the active drug from the matrix. The hydrophilic matrix synthesized by cross-linking could be used with a variety of active pharmaceutical ingredients for making their controlled/sustained release formulations.

Improvement in Bone Properties by Using Risedronate Adsorbed Hydroxyapatite Novel Nanoparticle Based Formulation in a Rat Model of Osteoporosis

A superior drug formulation capable of achieving efficient osteogenesis is in imperative demand for the treatment of osteoporosis. In the present study we investigated the potential of using novel risedronate-hydroxyapatite (HA) nanoparticle based formulation in an animal model of established osteoporosis. Nanoparticles of HA loaded with risedronate (NHLR) of various sizes (80-130 nm) were generated for bone targeted drug delivery. Three months after ovariectomy, 36 ovariectomized (OVX) rats were divided into 6 equal groups and treated with various doses of NHLR (500,350 and 250 mu g/kg intravenous single dose) and sodium risedronate (500 mu g/kg, intravenous single dose). Untreated OVX and sham OVX served as controls. One month after drug administration, the left tibia and femur were tested for bone mechanical properties and histology, respectively. In the right femur, bone density was measured by method based on Archimedes principle and bone porosity analyses were performed using X-ray imaging. NHLR (250 mu g/kg) showed a significant increase in bone density and reduced bone porosity when compared with OVX control. Moreover, NHLR (250 mu g/kg) significantly increased bone mechanical properties and bone quality when compared with OVX control. The results strongly suggest that the NHLR, which is a novel nanoparticle based formulation, has a therapeutic advantage over risedronate sodium monotherapy for the treatment of osteoporosis in a rat model of postmenopausal osteoporosis.

A risk-estimation-based formulation for speech enhancement and its relation to Wiener filtering

The goal of speech enhancement algorithms is to provide an estimate of clean speech starting from noisy observations. The often-employed cost function is the mean square error (MSE). However, the MSE can never be computed in practice. Therefore, it becomes necessary to find practical alternatives to the MSE. In image denoising problems, the cost function (also referred to as risk) is often replaced by an unbiased estimator. Motivated by this approach, we reformulate the problem of speech enhancement from the perspective of risk minimization. Some recent contributions in risk estimation have employed Stein's unbiased risk estimator (SURE) together with a parametric denoising function, which is a linear expansion of threshold/bases (LET). We show that the first-order case of SURE-LET results in a Wiener-filter type solution if the denoising function is made frequency-dependent. We also provide enhancement results obtained with both techniques and characterize the improvement by means of local as well as global SNR calculations.

Chapman-Enskog analysis for finite-volume formulation of lattice Boltzmann equation

The classical Chapman-Enskog expansion is performed for the recently proposed finite-volume formulation of lattice Boltzmann equation (LBE) method D.V. Patil, K.N. Lakshmisha, Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh, J. Comput. Phys. 228 (2009) 5262-5279]. First, a modified partial differential equation is derived from a numerical approximation of the discrete Boltzmann equation. Then, the multi-scale, small parameter expansion is followed to recover the continuity and the Navier-Stokes (NS) equations with additional error terms. The expression for apparent value of the kinematic viscosity is derived for finite-volume formulation under certain assumptions. The attenuation of a shear wave, Taylor-Green vortex flow and driven channel flow are studied to analyze the apparent viscosity relation.

Formulation of a mathematical approach to regional frequency analysis

Estimation of design quantiles of hydrometeorological variables at critical locations in river basins is necessary for hydrological applications. To arrive at reliable estimates for locations (sites) where no or limited records are available, various regional frequency analysis (RFA) procedures have been developed over the past five decades. The most widely used procedure is based on index-flood approach and L-moments. It assumes that values of scale and shape parameters of frequency distribution are identical across all the sites in a homogeneous region. In real-world scenario, this assumption may not be valid even if a region is statistically homogeneous. To address this issue, a novel mathematical approach is proposed. It involves (i) identification of an appropriate frequency distribution to fit the random variable being analyzed for homogeneous region, (ii) use of a proposed transformation mechanism to map observations of the variable from original space to a dimensionless space where the form of distribution does not change, and variation in values of its parameters is minimal across sites, (iii) construction of a growth curve in the dimensionless space, and (iv) mapping the curve to the original space for the target site by applying inverse transformation to arrive at required quantile(s) for the site. Effectiveness of the proposed approach (PA) in predicting quantiles for ungauged sites is demonstrated through Monte Carlo simulation experiments considering five frequency distributions that are widely used in RFA, and by case study on watersheds in conterminous United States. Results indicate that the PA outperforms methods based on index-flood approach.

Automatic finite element formulation and assembly of hyperelastic higher order structural models

The formulation of higher order structural models and their discretization using the finite element method is difficult owing to their complexity, especially in the presence of non-linearities. In this work a new algorithm for automating the formulation and assembly of hyperelastic higher-order structural finite elements is developed. A hierarchic series of kinematic models is proposed for modeling structures with special geometries and the algorithm is formulated to automate the study of this class of higher order structural models. The algorithm developed in this work sidesteps the need for an explicit derivation of the governing equations for the individual kinematic modes. Using a novel procedure involving a nodal degree-of-freedom based automatic assembly algorithm, automatic differentiation and higher dimensional quadrature, the relevant finite element matrices are directly computed from the variational statement of elasticity and the higher order kinematic model. Another significant feature of the proposed algorithm is that natural boundary conditions are implicitly handled for arbitrary higher order kinematic models. The validity algorithm is illustrated with examples involving linear elasticity and hyperelasticity. (C) 2013 Elsevier Inc. All rights reserved.