A study of the speed and the accuracy of the Boundary Element Method as applied to the computational simulation of biological organs

In this work, first a Fortran code is developed for three dimensional linear elastostatics using constant boundary elements; the code is based on a MATLAB code developed by the author earlier. Next, the code is parallelized using BLACS, MPI, and ScaLAPACK. Later, the parallelized code is used to demonstrate the usefulness of the Boundary Element Method (BEM) as applied to the realtime computational simulation of biological organs, while focusing on the speed and accuracy offered by BEM. A computer cluster is used in this part of the work. The commercial software package ANSYS is used to obtain the `exact' solution against which the solution from BEM is compared; analytical solutions, wherever available, are also used to establish the accuracy of BEM. A pig liver is the biological organ considered. Next, instead of the computer cluster, a Graphics Processing Unit (GPU) is used as the parallel hardware. Results indicate that BEM is an interesting choice for the simulation of biological organs. Although the use of BEM for the simulation of biological organs is not new, the results presented in the present study are not found elsewhere in the literature. Also, a serial MATLAB code, and both serial and parallel versions of a Fortran code, which can solve three dimensional (3D) linear elastostatic problems using constant boundary elements, are provided as supplementary files that can be freely downloaded.

Compact polarization dependent EBG surface with fractal boundary patches

Patches with variants of fractal Minkowski curves as boundaries are used here to design a polarization dependent electromagnetic bandgap surface. Reflection phases of the proposed structure depends upon the polarization state of the incident wave and frequency. The phase difference between the x-polarized and y-polarized components of the reflected wave can be as high as 200 degrees and this is achieved without excessive increase in unit cell dimensions and vias. The performance of the surface is analyzed numerically using CST microwave studio. The potential applications of the surface are in polarization conversion surfaces, polarimetric radar calibration, and RCS reduction.

Codes for solving three dimensional linear elastostatic problems using constant boundary elements while ignoring body forces

Three codes, that can solve three dimensional linear elastostatic problems using constant boundary elements while ignoring body forces, are provided here. The file 'bemconst.m' contains a MATLAB code for solving three dimensional linear elastostatic problems using constant boundary elements while ignoring body forces. The file 'bemconst.f90' is a Fortran translation of the MATLAB code contained in the file 'bemconst.m'. The file 'bemconstp.f90' is a parallelized version of the Fortran code contained in the file 'bemconst.f90'. The file 'inbem96.txt' is the input file for the Fortran codes contained in the files 'bemconst.f90' and 'bemconstp.f90'. Author hereby declares that the present codes are the original works of the author. Further, author hereby declares that any of the present codes, in full or in part, is not a translation or a copy of any of the existing codes written by someone else. Author's institution (Indian Institute of Science) has informed the author in writing that the institution is not interested in claiming any copyright on the present codes. Author is hereby distributing the present codes under the MIT License; full text of the license is included in each of the files that contain the codes.

On the k(1)(-1) scaling in sink-flow turbulent boundary layers

Scaling of the streamwise velocity spectrum phi(11)(k(1)) in the so-called sink-flow turbulent boundary layer is investigated in this work. The present experiments show strong evidence for the k(1)(-1) scaling i.e. phi(11)(k(1)) = Lambda(1)U(tau)(2)k(1)(-1), where k(1)(-1) is the streamwise wavenumber and U-tau is the friction velocity. Interestingly, this k(1)(-1) scaling is observed much farther from the wall and at much lower flow Reynolds number (both differing by almost an order of magnitude) than what the expectations from experiments on a zero-pressure-gradient turbulent boundary layer flow would suggest. Furthermore, the coefficient A(1) in the present sink-flow data is seen to be non-universal, i.e. A(1) varies with height from the wall; the scaling exponent -1 remains universal. Logarithmic variation of the so-called longitudinal structure function, which is the physical-space counterpart of spectral k(1)(-1) scaling, is also seen to be non-universal, consistent with the non-universality of A(1). These observations are to be contrasted with the universal value of A(1) (along with the universal scaling exponent of 1) reported in the literature on zero-pressure-gradient turbulent boundary layers. Theoretical arguments based on dimensional analysis indicate that the presence of a streamwise pressure gradient in sink-flow turbulent boundary layers makes the coefficient A(1) non-universal while leaving the scaling exponent -1 unaffected. This effect of the pressure gradient on the streamwise spectra, as discussed in the present study (experiments as well as theory), is consistent with other recent studies in the literature that are focused on the structural aspects of turbulent boundary layer flows in pressure gradients (Harun etal., J. Flui(d) Mech., vol. 715, 2013, pp. 477-498); the present paper establishes the link between these two. The variability of A(1) accommodated in the present framework serves to clarify the ideas of universality of the k(1)(-1) scaling.

A study of the speed and the accuracy of the Boundary Element Method as applied to the computational simulation of biological organs

In this work, possibility of simulating biological organs in realtime using the Boundary Element Method (BEM) is investigated, with specific reference to the speed and the accuracy offered by BEM. First, a Graphics Processing Unit (GPU) is used to speed up the BEM computations to achieve the realtime performance. Next, instead of the GPU, a computer cluster is used. A pig liver is the biological organ considered. Results indicate that BEM is an interesting choice for the simulation of biological organs. Although the use of BEM for the simulation of biological organs is not new, the results presented in the present study are not found elsewhere in the literature.

On the nature of meandering of the springtime western boundary current in the Bay of Bengal

We present evidence that the springtime western boundary current (WBC) in the Bay of Bengal is a continuous northward-flowing current from about 12 degrees N to 17 degrees N, which then separates from the coast at around 18 degrees N. We first revisit a hydrographic data set collected in 1987 from a potential vorticity perspective, and then analyze absolute dynamic height maps from satellite altimeters during the period 2000-2010. The altimetric maps suggest that the mean configuration of the WBC is that of an intense current with two anticyclonic eddies on the offshore side, which are part of the basin-wide anticyclonic circulation. The WBC consistently separates from the coast at around 18 degrees N in all years between 2000 and 2010. The path of the eastward-flowing mean stream after separation appears to be consistent with isolines of f/H and with Ertel's potential vorticity, based on an analysis of the hydrographic data from 1987.

Long ranged structural modulation in the pre-morphotropic phase boundary cubic-like state of the lead-free piezoelectric Na1/2Bi1/2TiO3-BaTiO3

The nature of the pre-morphotropic phase boundary (MPB) cubic-like state in the lead-free piezoelectric ceramics (1-x)Na1/2Bi1/2TiO3-(x)BaTiO3 at x similar to 0.06 has been examined in detail by electric field and temperature dependent neutron diffraction, x-ray diffraction, dielectric and ferroelectric characterization. The superlattice reflections in the neutron diffraction patterns cannot be explained with the tetragonal P4bm and the rhombohedral (R3c) phase coexistence model. The cubic like state is rather a result of long ranged modulated complex octahedral tilt. This modulated structure exhibits anomalously large dielectric dispersion. The modulated structure transforms to a MPB state on poling. The field-stabilized MPB state is destroyed and the modulated structure is restored on heating the poled specimen above the Vogel-Fulcher freezing temperature. The results show the predominant role of competing octahedral tilts in determining the nature of structural and polar states in Na1/2Bi1/2TiO3-based ferroelectrics. (C) 2013 AIP Publishing LLC.

A Study of Speed of the Boundary Element Method as applied to the Realtime Computational Simulation of Biological Organs

In this work, possibility of simulating biological organs in realtime using the Boundary Element Method (BEM) is investigated. Biological organs are assumed to follow linear elastostatic material behavior, and constant boundary element is the element type used. First, a Graphics Processing Unit (GPU) is used to speed up the BEM computations to achieve the realtime performance. Next, instead of the GPU, a computer cluster is used. Results indicate that BEM is fast enough to provide for realtime graphics if biological organs are assumed to follow linear elastostatic material behavior. Although the present work does not conduct any simulation using nonlinear material models, results from using the linear elastostatic material model imply that it would be difficult to obtain realtime performance if highly nonlinear material models that properly characterize biological organs are used. Although the use of BEM for the simulation of biological organs is not new, the results presented in the present study are not found elsewhere in the literature.

On the absence of shear cracking and grain boundary cavitation in secondary tensile regions of Ti-6Al-4V-0.1B alloy during hot (alpha plus beta)-compression

Deformation instabilities, such as shear cracking and grain boundary cavitation, which are observed in the secondary tensile region of Ti-6Al-4V alloy during compressive deformation in the (+)-phase field, do not form in Ti-6Al-4V-0.1B alloy when processed under the same conditions. This has been attributed to the microstructural modifications, e.g. the absence of grain boundary and adjacent grain boundary retained layers and a lower proportion of 90(o)-misoriented -colonies that occur with boron addition.

Simultaneous source localization and boundary mapping for contaminants

This paper addresses the problem of localizing the sources of contaminants spread in the environment, and mapping the boundary of the affected region using an innovative swarm intelligence based technique. Unlike most work in this area the algorithm is capable of localizing multiple sources simultaneously while also mapping the boundary of the contaminant spread. At the same time the algorithm is suitable for implementation using a mobile robotic sensor network. Two types of agents, called the source localization agents (or S-agents) and boundary mapping agents (or B-agents) are used for this purpose. The paper uses the basic glowworm swarm optimization (GSO) algorithm, which has been used only for multiple signal source localization, and modifies it considerably to make it suitable for both these tasks. This requires the definition of new behaviour patterns for the agents based on their terminal performance as well as interactions between them that helps the swarm to split into subgroups easily and identify contaminant sources as well as spread along the boundary to map its full length. Simulations results are given to demonstrate the efficacy of the algorithm.

Shock-boundary layer interaction and transonic flutter

The transonic flutter dip of an aeroelastic system is primarily caused by compressibility of the flowing fluid. Viscous effects are not dominant in the pre-transonic dip region. In fact, an Euler solver can predict this flutter boundary with considerable accuracy. However with an increase in Mach number the shock moves towards the trailing edge causing shock induced separation. This shock-boundary layer interaction changes the flutter boundary in the transonic and post-transonic dip region significantly. We discuss the effect of viscosity in changing the flutter boundary in the post-transonic dip region using a RANS solver coupled to a two-degree of freedom model of the structural dynamics of a wing.

STOKES' SYSTEM IN A DOMAIN WITH OSCILLATING BOUNDARY: HOMOGENIZATION AND ERROR ANALYSIS OF AN INTERIOR OPTIMAL CONTROL PROBLEM

Homogenization and error analysis of an optimal interior control problem in the framework of Stokes' system, on a domain with rapidly oscillating boundary, are the subject matters of this article. We consider a three dimensional domain constituted of a parallelepiped with a large number of rectangular cylinders at the top of it. An interior control is applied in a proper subdomain of the parallelepiped, away from the oscillating volume. We consider two types of functionals, namely a functional involving the L-2-norm of the state variable and another one involving its H-1-norm. The asymptotic analysis of optimality systems for both cases, when the cross sectional area of the rectangular cylinders tends to zero, is done here. Our major contribution is to derive error estimates for the state, the co-state and the associated pressures, in appropriate functional spaces.

MHD arcjet onset boundary of high specific impulse Plasma Thrusters

Magnetoplasmadynamic thrusters are known to enter a strongly unstable regime, calledas onset in the literature, under high specific impulse operation. This paper probes the early signs of onset in relatively moderate specific impulse operation by a single fluid plasma thruster simulation. The procedure involves solving the combined Maxwell’s-Navier-Stokes equation, with an onset criterion of radial current reaching close to zero values near the electrodes. Thruster parameters are varied starting from voltage potential, plasma temperature and cathodic radius. Onset curves are plotted which can provide important engine-specific information in order to understand the onset performance of the plasma thruster.

Closed-form solutions for axially functionally graded Timoshenko beams having uniform cross-section and fixed-fixed boundary condition

In this paper, we study the free vibration of axially functionally graded (AFG) Timoshenko beams, with uniform cross-section and having fixed-fixed boundary condition. For certain polynomial variations of the material mass density, elastic modulus and shear modulus, along the length of the beam, there exists a fundamental closed form solution to the coupled second order governing differential equations with variable coefficients. It is found that there are an infinite number of non-homogeneous Timoshenko beams, with various material mass density, elastic modulus and shear modulus distributions having simple polynomial variations, which share the same fundamental frequency. The derived results can be used as benchmark solutions for testing approximate or numerical methods used for the vibration analysis of non-homogeneous Timoshenko beams. They can also be useful for designing fixed-fixed non-homogeneous Timoshenko beams which may be required to vibrate with a particular frequency. (C) 2013 Elsevier Ltd. All rights reserved.

A Constitutive Equation for Grain Boundary Sliding: An Experimental Approach

Although grain boundary sliding (GBS) has been recognized as an important process during high-temperature deformation in crystalline materials, there is paucity in experimental data for characterizing a constitutive equation for GBS. High-temperature tensile creep experiments were conducted, together with measurements of GBS at different strains, stresses, grain sizes, and temperatures. Experimental data obtained on a Mg AZ31 alloy demonstrate that, for the first time, dynamic recrystallization during creep does not alter the contribution of GBS to creep during high-temperature deformation. The experimentally observed invariance of the sliding contribution with strain was used together with the creep data for developing a constitutive equation for GBS in a manner similar to the standard creep equation. Using this new approach, it is demonstrated that the stress, grain size, and temperature dependence for creep and GBS are identical. This is rationalized by a model based on GBS controlled by dislocations, within grains or near-grain boundaries. (C) The Minerals, Metals & Materials Society and ASM International 2013