scholarly journals Magnetic resonance microscopy of samples with translational symmetry with FOVs smaller than sample size

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Igor Serša
Keyword(s):  
Signal To Noise Ratio ◽  
Spin Echo ◽  
Single Point ◽  
Test Sample ◽  
Unit Cell ◽  
Moisture Distribution ◽  
Translational Symmetry ◽  
Image Artifact ◽  
Unit Cells ◽  
Entire Object

AbstractIn MRI, usually the Field of View (FOV) has to cover the entire object. If this condition is not fulfilled, an infolding image artifact is observed, which suppresses visualization. In this study it is shown that for samples with translational symmetry, i.e., those consisting of identical objects in periodic unit cells, the FOV can be reduced to match the unit cell which enables imaging of an average object, of which the signal is originated from all unit cells of the sample, with no punishment by a loss in signal-to-noise ratio (SNR). This theoretical prediction was confirmed by experiments on a test sample with a 7 × 7 mm2 unit cell arranged in a 3 × 3 matrix which was scanned by the spin-echo and by single point imaging methods. Effects of experimental imperfections in size and orientation mismatch between FOV and unit cell were studied as well. Finally, this method was demonstrated on a 3D periodic sample of tablets, which yielded well-resolved images of moisture distribution in an average tablet, while single tablet imaging provided no results. The method can be applied for SNR increase in imaging of any objects with inherently low signals provided they can be arranged in a periodic structure.

Quasicrystals Perspectives and Potential Applications

MRS Bulletin ◽  
1997 ◽  
Vol 22 (11) ◽  
pp. 34-39 ◽  
Author(s):  
Daniel J. Sordelet ◽  
Jean Marie Dubois
Keyword(s):  
Window Glass ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Unit Cell ◽  
Translational Symmetry ◽  
Integer Number ◽  
Unit Cells ◽  
Potential Applications ◽  
Incommensurate Structures ◽  
Three Dimensional Space

For decades scientists have accepted the premise that solid matter can only order in two ways: amorphous (or glassy) like window glass or crystalline with atoms arranged according to translational symmetry. The science of crystallography, now two centuries old, was able to relate in a simple and efficient way all atomic positions within a crystal to a frame of reference in which a single unit cell was defined. Positions within the crystal could all be deduced from the restricted number of positions in the unit cell by translations along vectors formed by a combination of integer numbers of unit vectors of the reference frame. Of course disorder, which is always present in solids, could be understood as some form of disturbance with respect to this rule of construction. Also amorphous solids were naturally referred to as a full breakdown of translational symmetry yet preserving most of the short-range order around atoms. Incommensurate structures, or more simply modulated crystals, could be understood as the overlap of various ordering potentials not necessarily with commensurate periodicities.For so many years, no exception to the canonical rule of crystallography was discovered. Any crystal could be completely described using one unit cell and its set of three basis vectors. In 1848 the French crystallographer Bravais demonstrated that only 14 different ways of arranging atoms exist in three-dimensional space according to translational symmetry. This led to the well-known cubic, hexagonal, tetragonal, and associated structures. Furthermore the dihedral angle between pairs of faces of the unit cell cannot assume just any number since an integer number of unit cells must completely fill space around an edge.

Correlation averaging of two-dimensional crystals: basic strategy and refinements

1986 ◽  
Vol 44 ◽  
pp. 136-139
Author(s):  
W. Baumeister ◽  
R. Rachel ◽  
R. Guckenberger ◽  
R. Hegerl
Keyword(s):  
Low Dose ◽  
Signal To Noise Ratio ◽  
Real Space ◽  
Fourier Domain ◽  
Two Dimensional ◽  
Signal To Noise ◽  
Unit Cells ◽  
Lateral Displacements ◽  
Established Technique ◽  
Crystalline Array

IntroductionCorrelation averaging (CAV) is meanwhile an established technique in image processing of two-dimensional crystals /1,2/. The basic idea is to detect the real positions of unit cells in a crystalline array by means of correlation functions and to average them by real space superposition of the aligned motifs. The signal-to-noise ratio improves in proportion to the number of motifs included in the average. Unlike filtering in the Fourier domain, CAV corrects for lateral displacements of the unit cells; thus it avoids the loss of resolution entailed by these distortions in the conventional approach. Here we report on some variants of the method, aimed at retrieving a maximum of information from images with very low signal-to-noise ratios (low dose microscopy of unstained or lightly stained specimens) while keeping the procedure economical.

Bayesian removal of noise for increased sensitivity in vector pattern recognition lattice imaging of interfaces

1993 ◽  
Vol 51 ◽  
pp. 994-995
Author(s):  
L. Fei ◽  
P. Fraundorf
Keyword(s):  
Pattern Recognition ◽  
Perfect Crystal ◽  
Unit Cell ◽  
Ion Milling ◽  
Beam Radiation ◽  
Major Interest ◽  
Unit Cells ◽  
Mapping Process ◽  
Increased Sensitivity ◽  
Electron Microscopes

Interface structure is of major interest in microscopy. With high resolution transmission electron microscopes (TEMs) and scanning probe microscopes, it is possible to reveal structure of interfaces in unit cells, in some cases with atomic resolution. A. Ourmazd et al. proposed quantifying such observations by using vector pattern recognition to map chemical composition changes across the interface in TEM images with unit cell resolution. The sensitivity of the mapping process, however, is limited by the repeatability of unit cell images of perfect crystal, and hence by the amount of delocalized noise, e.g. due to ion milling or beam radiation damage. Bayesian removal of noise, based on statistical inference, can be used to reduce the amount of non-periodic noise in images after acquisition. The basic principle of Bayesian phase-model background subtraction, according to our previous study, is that the optimum (rms error minimizing strategy) Fourier phases of the noise can be obtained provided the amplitudes of the noise is given, while the noise amplitude can often be estimated from the image itself.

scholarly journals Prediction of Effective Thermal Conductivities of Four-Directional Carbon/Carbon Composites by Unit Cells with Different Sizes

2021 ◽  
Vol 11 (3) ◽  
pp. 1171
Author(s):  
Chang Xu ◽  
Zhihong Sun ◽  
Guowei Shao
Keyword(s):  
Carbon Fiber ◽  
Longitudinal Direction ◽  
Unit Cell ◽  
Carbon Composites ◽  
Temperature Boundary ◽  
The Matrix ◽  
Unit Cells ◽  
Experimental Values ◽  
Different Diameters ◽  
Thermal Conductivities

Two-unit cells developed to predict the effective thermal conductivities of four-directional carbon/carbon composites with the finite element method are proposed in this paper. The smaller-size unit cell is formulated from the larger-size unit cell by two 180° rotational transformations. The temperature boundary conditions corresponding to the two-unit cells are derived, and the validity is verified by the temperature and heat flux distributions at specific positions of the larger-size unit cell and the smaller-size unit cell. The thermal conductivities of the carbon fiber bundles and carbon fiber rods are measured firstly. Then, combined with the properties of the matrix, the effective thermal conductivities of the four-directional carbon/carbon composites are numerically predicted. The results in transverse direction predicted by the larger-size unit cell and the smaller-size unit cell are both higher than experimental values, which are 5.8 to 6.2% and 7.3 to 8.2%, respectively. In longitudinal direction, the calculated thermal conductivities of the larger-size unit cell and the smaller-size unit cell are 6.8% and 6.2% higher than the experimental results, respectively. In addition, carbon fiber rods with different diameters are set to clarify the influence on the effective thermal conductivities of the four-directional carbon/carbon composites.

scholarly journals A Multiband Antenna Stacked with Novel Metamaterial SCSRR and CSSRR for WiMAX/WLAN Applications

Micromachines ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 113
Author(s):  
Rajiv Mohan David ◽  
Mohammad Saadh AW ◽  
Tanweer Ali ◽  
Pradeep Kumar
Keyword(s):  
Split Ring Resonator ◽  
Unit Cell ◽  
Ring Resonators ◽  
Split Ring ◽  
Medium Theory ◽  
High Frequency Structure Simulator ◽  
Dimension Analysis ◽  
Unit Cells ◽  
Coaxial Feed ◽  
Triple Band

This paper presents an innovative method for the design of a triple band meta-mode antenna. This unique design of antenna finds application in a particular frequency band of WLAN and WiMAX. This antenna comprises of a square complimentary split ring resonator (SCSRR), a coaxial feed, and two symmetrical comb shaped split ring resonators (CSSRR). The metamaterial unit cell SCSRR independently gains control in the band range 3.15–3.25 GHz (WiMAX), whereas two symmetrical CSSRR unit cell controls the band in the ranges 3.91–4.01 GHz and 5.79–5.94 GHz (WLAN). This design methodology and the study of the suggested unit cells structure are reviewed in classical waveguide medium theory. The antenna has a miniaturized size of only 0.213λ0 × 0.192λ0 × 0.0271λ0 (20 × 18 × 2.54 mm3, where λ0 is the free space wavelength at 3.2 GHz). The detailed dimension analysis of the proposed antenna and its radiation efficiency are also presented in this paper. All the necessary simulations are carried out in High Frequency Structure Simulator (HFSS) 13.0 tool.

scholarly journals Dynamic crushing behavior of closed-cell aluminum foams based on different space-filling unit cells

2021 ◽  
Vol 21 (3) ◽  
Author(s):  
S. Talebi ◽  
R. Hedayati ◽  
M. Sadighi
Keyword(s):  
Surface Area ◽  
Dynamic Behavior ◽  
Energy Absorption ◽  
Peak Stress ◽  
Absorption Capacity ◽  
Unit Cell ◽  
Lattice Structures ◽  
Energy Absorption Capacity ◽  
Closed Cell ◽  
Unit Cells

AbstractClosed-cell metal foams are cellular solids that show unique properties such as high strength to weight ratio, high energy absorption capacity, and low thermal conductivity. Due to being computation and cost effective, modeling the behavior of closed-cell foams using regular unit cells has attracted a lot of attention in this regard. Recent developments in additive manufacturing techniques which have made the production of rationally designed porous structures feasible has also contributed to recent increasing interest in studying the mechanical behavior of regular lattice structures. In this study, five different topologies namely Kelvin, Weaire–Phelan, rhombicuboctahedron, octahedral, and truncated cube are considered for constructing lattice structures. The effects of foam density and impact velocity on the stress–strain curves, first peak stress, and energy absorption capacity are investigated. The results showed that unit cell topology has a very significant effect on the stiffness, first peak stress, failure mode, and energy absorption capacity. Among all the unit cell types, the Kelvin unit cell demonstrated the most similar behavior to experimental test results. The Weaire–Phelan unit cell, while showing promising results in low and medium densities, demonstrated unstable behavior at high impact velocity. The lattice structures with high fractions of vertical walls (truncated cube and rhombicuboctahedron) showed higher stiffness and first peak stress values as compared to lattice structures with high ratio of oblique walls (Weaire–Phelan and Kelvin). However, as for the energy absorption capacity, other factors were important. The lattice structures with high cell wall surface area had higher energy absorption capacities as compared to lattice structures with low surface area. The results of this study are not only beneficial in determining the proper unit cell type in numerical modeling of dynamic behavior of closed-cell foams, but they are also advantageous in studying the dynamic behavior of additively manufactured lattice structures with different topologies.

The Influence of Multiple Inclusions on the Cauchy Stress of a Spherical Particle-Reinforced Composite Under Uniaxial Loading

2014 ◽  
Author(s):  
Ke Niu ◽  
Armin Abedini ◽  
Zengtao Chen
Keyword(s):  
Spherical Particle ◽  
Single Particle ◽  
Volume Fraction ◽  
Unit Cell ◽  
Spherical Particles ◽  
Uniaxial Tensile ◽  
Cauchy Stress ◽  
Particle Volume ◽  
Volume Fractions ◽  
Unit Cells

This paper investigates the influence of multiple inclusions on the Cauchy stress of a spherical particle-reinforced metal matrix composite (MMC) under uniaxial tensile loading condition. The approach of three-dimensional cubic multi-particle unit cell is used to investigate the 15 non-overlapping identical spherical particles which are randomly distributed in the unit cell. The coordinates of the center of each particle are calculated by using the Random Sequential Adsorption algorithm (RSA) to ensure its periodicity. The models with reinforcement volume fractions of 10%, 15%, 20% and 25% are evaluated by using the finite element method. The behaviour of Cauchy stress for each model is analyzed at a far-field strain of 5%. For each reinforcement volume fraction, four models with different particle spatial distributions are evaluated and averaged to achieve a more accurate result. At the same time, single-particle unit cell and analytical model were developed. The stress-strain curves of multi-particle unit cells are compared with single-particle unit cells and the tangent homogenization model coupled with the Mori-Tanaka method. Only little scatters were found between unit cells with the same particle volume fractions. Multi-particle unit cells predict higher response than single particle unit cells. As the volume fraction of reinforcements increases, the Cauchy stress of MMCs increases.

Determination of Optimal Unit-Cell Size of Homogeneous Conformal Unit-Cell Lattice Structure Using Solid Shape Matching

2016 ◽  
Author(s):  
Mahmoud A. Alzahrani ◽  
Seung-Kyum Choi
Keyword(s):  
Cell Size ◽  
Solid Body ◽  
Strain Energy ◽  
Lattice Structure ◽  
Weight Ratio ◽  
Unit Cell ◽  
Optimal Size ◽  
Lattice Structures ◽  
Unit Cell Size ◽  
Unit Cells

With rapid developments and advances in additive manufacturing technology, lattice structures have gained considerable attention. Lattice structures are capable of providing parts with a high strength to weight ratio. Most work done to reduce computational complexity is concerned with determining the optimal size of each strut within the lattice unit-cells but not with the size of the unit-cell itself. The objective of this paper is to develop a method to determine the optimal unit-cell size for homogenous periodic and conformal lattice structures based on the strain energy of a given structure. The method utilizes solid body finite element analysis (FEA) of a solid counter-part with a similar shape as the desired lattice structure. The displacement vector of the lattice structure is then matched to the solid body FEA displacement results to predict the structure’s strain energy. This process significantly reduces the computational costs of determining the optimal size of the unit cell since it eliminates FEA on the actual lattice structure. Furthermore, the method can provide the measurement of relative performances from different types of unit-cells. The developed examples clearly demonstrate how we can determine the optimal size of the unit-cell based on the strain energy. Moreover, the computational cost efficacy is also clearly demonstrated through comparison with the FEA and the proposed method.

Material Behavior of 2D Steel Lattices with Different Unit-Cell Patterns

2021 ◽  
Vol 1046 ◽  
pp. 15-21
Author(s):  
Paiboon Limpitipanich ◽  
Pana Suttakul ◽  
Yuttana Mona ◽  
Thongchai Fongsamootr
Keyword(s):  
Elastic Modulus ◽  
Experimental Studies ◽  
Base Material ◽  
Unit Cell ◽  
Material Behavior ◽  
Closed Form Solutions ◽  
The Past ◽  
Weight Density ◽  
Unit Cells ◽  
Cell Patterns

Over the past years, two-dimensional lattices have attracted the attention of several researchers because they are lightweight compared with their full-solid counterparts, which can be used in various engineering applications. Nevertheless, since lattices are manufactured by reducing the base material, their stiffnesses then become lower. This study presents the weight efficiency of the lattices defined by relations between the elastic modulus and the weight density of the lattices. In this study, the mechanical behavior of 2D lattices is described by the in-plane elastic modulus. Experimental studies on the elastic modulus of the 2D lattices made of steel are performed. Three lattices having different unit cells, including square, body-centered, and triangular unit cells, are considered. The elastic modulus of each lattice is investigated by tensile testing. All specimens of the lattices are made of steel and manufactured by waterjet cutting. The experimental results of the elastic modulus of the lattices with the considered unit-cell patterns are validated with those obtained from finite element simulations. The results obtained in this study are also compared with the closed-form solutions founded in the literature. Moreover, the unit-cell pattern yielding the best elastic modulus for the lattice is discussed through weight efficiency.

scholarly journals Structure of a monoclinic polymorph of human carbonic anhydrase II with a doubledaaxis

2010 ◽  
Vol 66 (5) ◽  
pp. 628-634 ◽  
Author(s):  
Arthur H. Robbins ◽  
John F. Domsic ◽  
Mavis Agbandje-McKenna ◽  
Robert McKenna
Keyword(s):  
Carbonic Anhydrase ◽  
Crystal Packing ◽  
Rotation Axis ◽  
Unit Cell ◽  
Carbonic Anhydrase Ii ◽  
Monoclinic Unit Cell ◽  
Structure Solution ◽  
Unit Cells ◽  
Human Carbonic Anhydrase ◽  
Β Sheet

The crystal structure of human carbonic anhydrase II with a doubledaaxis from that of the usually observed monoclinic unit cell has been determined and refined to 1.4 Å resolution. The diffraction data withh= 2n+ 1 were systematically weaker than those withh= 2n. Consequently, the scaling of the data, structure solution and refinement were challenging. The two molecules comprising the asymmetric unit are related by a noncrystallographic translation of ½ alonga, but one of the molecules has two alternate positions related by a rotation of approximately 2°. This rotation axis is located near the edge of the central β-sheet, causing a maximum distance disparity of 1.7 Å between equivalent atoms on the diametrically opposite side of the molecule. The crystal-packing contacts are similar to two sequential combined unit cells alongaof the previously determined monoclinic unit cell. Abnormally high finalRcrystandRfreevalues (20.2% and 23.7%, respectively) are not unusual for structures containing pseudo-translational symmetry and probably result from poor signal to noise in the weakh-odd data.

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