Decreasing Element Size Research Articles

A Fresnel-inspired approach for steering and focusing of pulsed transmit beams by matrix array transducers

Matrix ultrasound transducers for medical diagnostic purposes are commercially available for a decade. A typical matrix transducer contains 1000 + elements, with a trend towards more and smaller elements. This number renders direct connection of each individual element to an ultrasound machine impractical. Consequently, it is cumbersome to employ traditional focusing and beamforming approaches that are based on transmit and receive signals having an individual time delay for each element. To reduce cable count during receive, one approach is to apply sub-arrays that locally combine the element signals using programmable delay-and-sum hardware, resulting in reduction by a factor 10. In transmit, achieving cable count reduction while keeping focusing and steering capabilities turns problematic once it becomes impossible to locally equip each element with its own high voltage pulser. To overcome this bottleneck for decreasing element size, here we present a Fresnel-inspired hardware and beam forming approach that is based on transmit pulses consisting of several periods of an oscillating waveform. These will be derived from one oscillating high voltage signal by using local switching and timing hardware. To demonstrate the feasibilities of our approach, we will show beam profiles and images for a miniature matrix transducer that we are currently developing.

Subject-specific finite element simulation of the human femur considering inhomogeneous material properties: A straightforward method and convergence study

In numerical finite element (FE) simulations of human bones subject-specific models are necessary to reproduce the physiological conditions, which include the determination of inhomogeneous material properties from computed tomography (CT) scans and their implementation in the numerical model. In the present approach common software packages are directly used for the entire simulation process from segmentation of CT scans, surface reconstruction, mesh generation, calculation of mean element densities to FE simulation. The influence of the mesh discretisation level on the maximum displacement, the total system energy and the principal surface stress distribution of eight human femurs was analysed. Both the maximum displacement and the total system energy showed typical convergence behaviour towards an asymptotic value with decreasing element size. The principal surface stress distribution followed similar qualitative trends at all mesh discretisation levels studied for the same femur. However, the stress distributions did not converge with decreasing element size and still differed significantly between the two smallest element sizes studied of approximately 2mm and 1mm. The magnitude of convergence differed among the individual femurs. Thus, individual convergence studies in terms of local stress or strain distributions are necessary for accurately predicting local stress and strain values in subject-specific FE bone models.

Control of spin configuration in half-metallic La0.7Sr0.3MnO3 nano-structures

We investigate the interplay between the governing magnetic energy terms in patterned La0.7Sr0.3MnO3 (LSMO) elements by direct high-resolution x-ray magnetic microscopy as a function of temperature and geometrical parameters. We show that the magnetic configurations evolve from multidomain to flux-closure states (favored by the shape anisotropy) with decreasing element size, with a thickness-dependent crossover at the micrometer scale. The flux-closure states are stable against thermal excitations up to near the Curie temperature. Our results demonstrate control of the spin state in LSMO elements by judicious choice of the geometry, which is key for spintronics applications requiring high spin-polarizations and robust magnetic states.

Higher order tip enrichment of eXtended Finite Element Method in thermoelasticity

An eXtended Finite Element Method (XFEM) is presented that can accurately predict the stress intensity factors (SIFs) for thermoelastic cracks. The method uses higher order terms of the thermoelastic asymptotic crack tip fields to enrich the approximation space of the temperature and displacement fields in the vicinity of crack tips—away from the crack tip the step function is used. It is shown that improved accuracy is obtained by using the higher order crack tip enrichments and that the benefit of including such terms is greater for thermoelastic problems than for either purely elastic or steady state heat transfer problems. The computation of SIFs directly from the XFEM degrees of freedom and using the interaction integral is studied. Directly computed SIFs are shown to be significantly less accurate than those computed using the interaction integral. Furthermore, the numerical examples suggest that the directly computed SIFs do not converge to the exact SIFs values, but converge roughly to values near the exact result. Numerical simulations of straight cracks show that with the higher order enrichment scheme, the energy norm converges monotonically with increasing number of asymptotic enrichment terms and with decreasing element size. For curved crack there is no further increase in accuracy when more than four asymptotic enrichment terms are used and the numerical simulations indicate that the SIFs obtained directly from the XFEM degrees of freedom are inaccurate, while those obtained using the interaction integral remain accurate for small integration domains. It is recommended in general that at least four higher order terms of the asymptotic solution be used to enrich the temperature and displacement fields near the crack tips and that the J- or interaction integral should always be used to compute the SIFs.

Statistical characterization of meso-scale uniaxial compressive strength in brittle materials with randomly occurring flaws

Increasingly fine spatial resolution in numerical models of brittle materials promises to improve prediction and characterization of dynamic failure in these materials. However, as the resolution of these numerical models begins to approach the material micro-scale, the associated discretization requires a definitive connection to the microstructure. In many cases a numerical model (e.g., a finite element mesh) that explicitly resolves each flaw within the material is not feasible for macro-scale analyses. As an alternative, each element can be treated as a meso-scale continuum with constitutive properties that reflect the characteristics of the underlying microstructure. Small scale elements will exhibit random variations in the constitutive properties as a result of the random variations in the number and types of flaws and the flaw sizes contained within each element. The present paper proposes a technique for assigning probability distributions to these element properties, which can be thought of as the meso-scale constitutive properties. In particular, the strain-rate dependent compressive uniaxial strength of a ceramic is modeled using a two-dimensional analytical model developed by Paliwal and Ramesh (2008). The effect on the probability distribution of meso-scale (or element-level) strength from flaw density, flaw size distribution, flaw clustering, and strain rate are studied. Higher strain rates, more flaw clustering, and decreasing element size all contribute to greater scatter in uniaxial compressive strength. Variations in flaw size increase the scatter in the strength more for low strain rate loadings and less clustered microstructures. The results provide interesting comparisons to the classical assumption of a two-parameter Weibull-distributed strength, showing that a three-parameter Weibull distribution and even a lognormal distribution fit better with the simulated strength data.

Multi-scale homogenization of moving interface problems with flux jumps: application to solidification

In this paper, a multi-scale analysis scheme for solidification based on two-scale computational homogenization is discussed. Solidification problems involve evolution of surfaces coupled with flux jump boundary conditions across interfaces. We provide consistent macro-micro transition and averaging rules based on Hill’s macro- homogeneity condition. The overall macro-scale behavior is analyzed with solidification at the micro-scale modeled using an enthalpy formulation. The method is versatile in the sense that two different models can be employed at the macro- and micro-scales. The micro-scale model can incorporate all the physics associated with solidification including moving interfaces and flux discontinuities, while the macro-scale model needs to only model thermal conduction using continuous (homogenized) fields. The convergence behavior of the tightly coupled macro-micro finite element scheme with respect to decreasing element size is analyzed by comparing with a known analytical solution of the Stefan problem.

Ion-beam induced magnetic nanopatterning of interlayer exchange coupled Fe/Cr/Fe trilayers

We demonstrate that antiferromagnetically coupled Fe/Cr/Fe trilayers can be magnetically patterned on the micrometer and sub-micrometer scale by irradiation with keV Ga + ions, which induces a local transition to ferromagnetic coupling due to direct contact between the two Fe layers via ferromagnetic pinholes. The irradiated areas act as ferromagnetic elements which are embedded into a surrounding, antiferromagnetically coupled trilayer. We also demonstrate that the magnetic properties of the elements fabricated by this method are size dependent, including a transition from multi-domain to single-domain configurations with decreasing element size, and we determine an effective intrinsic limit to the lateral resolution of this patterning technique.

CPP-GMR enhancement in spin valves using a thin Ru layer

Current perpendicular to plane giant magnetoresistance (CPP-GMR) of single spin valves with two kinds free layers has been investigated. One is a single ferromagnetic layer (Conventional structure) and the other is a ferromagnetic layer with thin Ru cap layer (Ru cap structure). Both structure had increasing resistance and resistance changes with decreasing element size. The CPP-GMR ratio for a Ru cap structure was enhanced from 0.70 to 4.3% at room temperature. We think the MR enhancement is caused by the spin dependent scattering due to strong reflection of majority spins at the Co 90Fe 10/Ru interface.

Magnetic switching in 100 nm patterned pseudo spin valves

Progress in developing operative high-density magnetoresistive random access memory (MRAM) devices relies critically on tailoring the magnetic switching occurring in arrays of small patterned pseudo spin valve (PSV) elements. Co/Cu/NiFe PSV films, produced by sputtering in the presence of a magnetic field, have an in-plane anisotropy and switching fields of typically 10 Oe for the soft NiFe and 40 Oe for the hard Co. These films were patterned into arrays of elliptical and circular elements with dimensions of 80 nm to 10 /spl mu/m. The layered structure in these large-area arrays of compositionally modulated PSV elements is preserved through the patterning processes. Hysteresis measurements of the dot arrays show that the switching field of the hard layer increases significantly with decreasing element size, reaching 600 Oe for the smallest elements. Additionally, in patterned elements the soft layer switches prior to field reversal due to magnetostatic coupling between the layers, leading to antiparallel alignment at remanence.

Giant magnetroresistance properties of specular spin valve films in a current perpendicular to plane structure

Conventional and specular spin valve films in a current perpendicular to plane (CPP) structure have been investigated. The specular spin valve film with bottom type structure had two oxidized layers: one in the pinned layer, which was oxidized during an in situ deposition process, and the other in the free layer, which was a naturally oxidized Cu/Ta cap. Both films had increasing resistance, R, and resistance change, ΔR, with decreasing element size. The conventional spin valve film showed a resistance times area product, RA, of 144 mΩ μm2 and a resistance change area product, ΔRA, of 0.7 mΩ μm2 while the specular spin valve film showed RA of 1120 mΩ μm2 and ΔRA of 23 mΩ μm2. The ΔRA of the specular spin valve film was about 33 times larger than that of the conventional spin valve film. The calculated magnetoresistance (MR) ratios, MRSV, of each spin valve film were 1.9% and 2.3%, respectively. We think oxidized layers in the spin valve film caused the specular electron scattering and this lengthened the path of the conduction electrons, enhancing the interfacial and bulk spin dependent scattering. We estimated the output voltage change of the 0.01 μm2 element, the size required for 150 Gb/in.2 recording density, of the specular spin valve film in CPP mode to be 5.3 mV. It was almost six times larger than that of the conventional spin valve film at constant power consumption. Specular spin valve film are advantageous for the CPP structure element for future giant MR sensors.

NUMERICAL ERRORS OF THE GALERKIN FINITE-ELEMENT METHOD FOR NATURAL CONVECTION OF A FLUID LAYER OR A FLUID-SATURATED POROUS LAYER

This paper describes the effects of element size and formula used for the calculation of temperature gradients on the local and average Nusselt numbers of natural convection for the widely used Galerlan finite-element method. Two cases of laminar two-dimensional natural convection are examined, namely, a fluid layer and a porous layer. The numerical error in the Nusselt numbers decreases with decreasing element size. The maximum error occurs at the position of a maximum of the local Nusselt number. In addition to the effect of element size, the Nusselt numbers are shown to vary with the formula used for calculating temperature gradients. The Nusselt numbers extrapolated to zero element size for different formulas are found, in both cases, to be virtually identical and also to agree well with the experimental data and the results computed by finite-difference methods

Heterochromatic brightness matching with checkerboard patterns.

Heterochromatic brightness matches with checkerboard patterns made up of a white reference and a chromatic test element for various element sizes from 3' to 2 degrees 30' square and with a 5 degrees bipartite field were carried out with a color cathode-ray tube. The brightness-to-luminance (B/L) ratios of six chromatic stimuli were obtained, and the brightness additivity for the mixture of red and green was tested. When the reference and test elements were juxtaposed without a gap, the B/L ratio of the test chromatic stimulus decreased with decreasing element size. Brightness additivity failed for an element size of 30' and a 5 degrees bipartite field. Brightness additivity held for a small element size of 3'. When the reference and test elements were separated by a gap 3' in width, the B/L ratios were generally greater than unity regardless of element size. Under these conditions, the brightness additivity also failed for the smallest, that is, the 3' element size.