Relative Local Density Research Articles

Revisiting the original morphology–density relation

In light of recent ndings from the kinematic morphology-density relation, we investigate whether the same trends exist in the original morphology density relation, using the same data as Dressler. In addition to Dressler’s canonical relations, we nd that further renements are possible when considering the average local projected density of galaxies in a cluster. Firstly, the distribution of ellipticals in a cluster depends on the relative local density of galaxies in that cluster: equivalent rises in the elliptical fraction occur at higher local densities for clusters with higher average local densities. This is not true for the late-type fraction, where the variation with local density within a cluster is independent of the average local density of galaxies in that cluster, and is as Dressler originally found. Furthermore, the overall ratio of ellipticals to early-types in a cluster does not depend on the average density of galaxies in that cluster (unlike the ratio of lenticulars to disk systems), and is xed at around 30%. In the paradigm of fast and slow rotators, we show that such an elliptical fraction in the early-type population is consistent with a slow rotator fraction of 15% in the early-type population, using the statistics of the ATLAS 3D survey. We also nd the scatter in the overall ratio of ellipticals to early-types is greatest for clusters with lower average densities, such that clusters with the highest elliptical fractions have the lowest average local densities. Finally, we show that average local projected density correlates well with global projected density, but the latter has diculty in accurately characterising the density of irregular cluster morphologies.

A Contrario 2D Point Alignment Detection.

In spite of many interesting attempts, the problem of automatically finding alignments in a 2D set of points seems to be still open. The difficulty of the problem is illustrated here by very simple examples. We then propose an elaborate solution. We show that a correct alignment detection depends on not less than four interlaced criteria, namely the amount of masking in texture, the relative bilateral local density of the alignment, its internal regularity, and finally a redundancy reduction step. Extending tools of the a contrario detection theory, we show that all of these detection criteria can be naturally embedded in a single probabilistic a contrario model with a single user parameter, the number of false alarms. Our contribution to the a contrario theory is the use of sophisticated conditional events on random point sets, for which expectation we nevertheless find easy bounds. By these bounds the mathematical consistency of our detection model receives a simple proof. Our final algorithm also includes a new formulation of the exclusion principle in Gestalt theory to avoid redundant detections. Aiming at reproducibility, a source code and an online demo open to any data point set are provided. The method is carefully compared to three state-of-the-art algorithms and an application to real data is discussed. Limitations of the final method are also illustrated and explained.

FEM modeling on the compaction of Fe and Al composite powders

The compaction process of Fe and Al composite powders subjected to single action die compaction was numerically modeled by FEM method. The relationship between the overall relative density and compaction pressure of the compacts with various Al contents was firstly identified, and the influences of Al content on the local relative density, stress, and their distributions were studied. Then the compaction pressure effects on the above properties with fixed Al content were discussed. Furthermore, detailed flow behaviors of the composite powders during compaction and the relationship between the compaction pressure and the ejection force/spring back of the compact were analyzed. The results show that: (1) With each compaction pressure, higher relative density can be realized with the increase of Al content and the relative density distribution tends to be uniform; (2) When the Al content is fixed, higher compaction pressure can lead to composite compact with higher relative density, and the equivalent Von Mises stress in the central part of the compact increases gradually; (3) Convective flow occurs at the top and bottom parts of the compact close to the die wall, each indicates a different flow behavior; (4) The larger the compaction pressure for each case, the higher the residual elasticity, and the larger the ejection force needed.

Numerical prediction of disorder effects in solid foams using a probabilistic homogenization scheme

The present study is concerned with a numerical prediction of uncertainties in the macroscopic mechanical properties of microheterogeneous materials with uncertain microstructure. As a model material, solid foams are employed. The stochastic information on the uncertainty is gained in multiple numerical homogenization analyses of small-scale testing volume elements. The local relative density, the cell size distribution, the cell geometry and the spatial orientation of the testing volume elements are assumed to form the set of the relevant stochastic variables. Selected microstructural cases are analyzed for their macroscopic material response. Based on the probability distributions for the stochastic variables defining the microstructures of the testing volume elements, the probability distributions for the mesoscopic material properties are obtained. For the numerical homogenization of the testing volume elements, an enhanced finite element technique is employed, where the components of the macroscopic deformation gradient are introduced as generalized degrees of freedom. Assuming periodic boundary conditions, the global degrees of freedom interact with the conventional displacement degrees of freedom of the discretized microstructure via special boundary coupling elements. The mesoscopic stresses are obtained in a rather efficient manner as the generalized reaction forces for the global degrees of freedom.

Site-Specific Structural Constraints on Protein Sequence Evolutionary Divergence: Local Packing Density versus Solvent Exposure

Protein sequences evolve under selection pressures imposed by functional and biophysical requirements, resulting in site-dependent rates of amino acid substitution. Relative solvent accessibility (RSA) and local packing density (LPD) have emerged as the best candidates to quantify structural constraint. Recent research assumes that RSA is the main determinant of sequence divergence. However, it is not yet clear which is the best predictor of substitution rates. To address this issue, we compared RSA and LPD with site-specific rates of evolution for a diverse data set of enzymes. In contrast with recent studies, we found that LPD measures correlate better than RSA with evolutionary rate. Moreover, the independent contribution of RSA is minor. Taking into account that LPD is related to backbone flexibility, we put forward the possibility that the rate of evolution of a site is determined by the ease with which the backbone deforms to accommodate mutations.

Local Relative Density Modulates Failure and Strength in Vertically Aligned Carbon Nanotubes

Micromechanical experiments, image analysis, and theoretical modeling revealed that local failure events and compressive stresses of vertically aligned carbon nanotubes (VACNTs) were uniquely linked to relative density gradients. Edge detection analysis of systematically obtained scanning electron micrographs was used to quantify a microstructural figure-of-merit related to relative local density along VACNT heights. Sequential bottom-to-top buckling and hardening in stress-strain response were observed in samples with smaller relative density at the bottom. When density gradient was insubstantial or reversed, bottom regions always buckled last, and a flat stress plateau was obtained. These findings were consistent with predictions of a 2D material model based on a viscoplastic solid with plastic non-normality and a hardening-softening-hardening plastic flow relation. The hardening slope in compression generated by the model was directly related to the stiffness gradient along the sample height, and hence to the local relative density. These results demonstrate that a microstructural figure-of-merit, the effective relative density, can be used to quantify and predict the mechanical response.

Improvement in robustness and computational efficiency of material models for finite element analysis of metal powder compaction and experimental validation

In metal powder compaction, density nonuniformity can be a source of flaws. Material models in finite element analysis for the prediction of density distribution still lack robustness and are computationally expensive. In this work, the Drucker–Prager cap (DPC) material model is implemented into the commercial finite element (FE) software ABAQUS/Explicit using the user-subroutine VUMAT. Yield functions in this material model are pressure-dependent and the curvature of the cap yield surface is high. This can cause numerical instability. We implemented a sub-increment technique to address this instability problem in a previous paper (Kashani et al., Trans North Am Manuf Res Inst SME 38:623–631, 2010). The DPC model is also a non-smooth, multi-yield surface material model which has instability problems at the intersection of the yield surfaces; we adopted the corner region in the DPC material models for soils in order to remove instability and the results of which were presented in (Kashani et al., Trans North Am Manuf Res Inst SME 38:623–631, 2010). The computational efficiency of the DPC material model was improved using a novel technique to solve the constitutive equations analytically which was shown in a previous paper by the authors (Kashani et al., Trans North Am Manuf Res Inst SME 38:623–631, 2010). In this paper, experimental tests were conducted where cylindrically shaped parts were compacted from Distaloy AE iron-based powder to 7.0 g/cm3 using 592 MPa of pressure. To measure local density, metallography and image processing were used to find the void area fraction of the surface. The FE results were compared to experimental results and it was shown that the FE analysis predicted local relative density within 3 % of the actual experimental measurements.

Formation of Surface Relief Gratings: Effect of the Density of the Host Material

We use molecular dynamics simulations to investigate the effect of the density of the host material on the isomerization-induced diffusion mechanism that results in surface relief gratings formation. We find that a decrease in density increases the diffusion coefficient in a similar way for driven and spontaneous diffusion. This result suggests that the driving mechanism depends only slightly on the density of the host material. The pressure variations during the isomerization process decrease when the driven diffusion increases due to material softening for smaller densities. These results suggest that the pressure variations are not at the origin of the driven motions. The relative local density variation around the probe is also weakly dependent on the mean density of the host material as long as the material structure is preserved.

Analysis of uncertainty effects due to microstructural disorder in cellular or porous materials

Aim of the present study is an analysis of the effect of microstructural uncertainties on the scatter in the macroscopic material properties of highly porous materials consisting of metallic or other constituents. For the numerical analysis of the uncertainty effects, a probabilistic homogenization scheme is proposed. In contrast to direct Monte-Carlo approaches, the thermomechanical response of a limited number of pre-selected cases throughout the range of possible microstructures is analyzed. Their effective properties are determined by means of an energy based homogenization procedure. In a stochastic evaluation, the results of the individual computations are weighted with the probability of the occurrence of the underlying microstructures. As a result, the probability distributions for the effective properties are obtained. The basic uncertain microstructural properties considered in the investigation are the microstructural geometry and orientation, the local relative density and the local pore size distribution. In an application to an experimental data base from other sources, the approach proves to be accurate and numerically efficient compared to direct Monte-Carlo approaches. Parameter studies reveal that uncertainties in the local relative density are the most important factor leading to scatter in the macroscopic material properties of cellular materials.

Interpretation of the I-Regime and transport associated with relevant heavy particle modes

The excitation of a novel kind of heavy particle [B. Coppi et al., Phys. Rev. Lett. 17, 377 (1966); B. Coppi and T. Zhou, MIT(LNS) Report HEP 09/04, 2009, Cambridge, MA [Phys. Lett. A 375, 2916 (2011)]] mode at the edge of the plasma column is considered as the signature of the I-confinement Regime [R. McDermott et al., Bull. Am. Phys. Soc. 53, 112 (2008); R. McDermott et al., Phys. Plasmas 16, 056103 (2009); E. Marmar et al., Bull. Am. Phys. Soc. 54, 97 (2009); D. Whyte et al., Nucl. Fusion 50, 105005 (2010); A. Hubbard et al., Phys. Plasmas 18, 056115 (2011)]. The outward transport of impurities produced by this mode is in fact consistent with the observed expulsion of them from the main body of the plasma column (a high degree of plasma purity is a necessary feature for fusion burning plasmas capable of approaching ignition). Moreover, the theoretically predicted mode phase velocity, in the direction of the electron diamagnetic velocity, has been confirmed by relevant experimental analyses [I. Cziegler, private communication (2010)] of the excited fluctuations (around 200 kHz). The plasma “spontaneous rotation” in the direction of the ion diamagnetic velocity is also consistent, according to the accretion theory [B. Coppi, Nucl. Fusion 42, 1 (2002)] of this phenomenon, with the direction of the mode phase velocity. Another feature of the mode that predicted by the theory is that the I-Regime exhibits a knee of the ion temperature at the edge of the plasma column, but not one of the particle density as the mode excitation factor is the relative main ion temperature gradient exceeding the local relative density gradient. The net plasma current density appearing in the saturation stage of the relevant instability, where the induced particle and energy fluxes are drastically reduced, is associated with the significant amplitudes of the poloidal magnetic field fluctuations [D. Whyte et al., Nucl. Fusion 50, 105005 (2010); A. Hubbard et al., Phys. Plasmas 18, 056115 (2011)] observed to accompany the density fluctuations. The theoretical implications of the significant electron temperature fluctuations [A. White, private communication (2011)] observed are discussed.

A multi-field coupled FEM model for one-step-forming process of spark plasma sintering considering local densification of powder material

A mechanical constitutive model of powder material is introduced to a fully coupled thermal–electric–mechanical finite element model to simulate the one-step-forming spark plasma sintering (SPS) process of metal powders. The effects of displacement field and local density distribution on sintering are considered in this article, which are generally neglected in the existing SPS models. The mechanical, thermal, and electrical parameters of powders are assumed as functions of local relative density and temperature. The simulated varying displacement field remodels the distributions of temperature and electric potential by changing the contact thermoelectric resistances. For the 20, 40, and 60 MPa external pressures, the simulation indicates that the sintering temperature and the temperature gradient within powders are decreased by enhancing the external pressure, and the comprehensive effect of stress promotes the densification of the colder regions. Thus, the interrelationship between the temperature gradient and the intrinsic stress distribution plays an important role in the densification mechanism of SPS powders.

Relative local density of states and cloaking in finite clusters of coated cylinders

We describe a method for accurate calculation of the Relative Local Density of States (RLDOS) as a function of frequency and position in finite sets of coated cylinders. The RLDOS is important, since it describes the interaction between sources and their environment, which controls their ability to radiate electromagnetic waves. We give numerical examples of distributions of RLDOS for clusters of cylinders with lossy coatings whose optical properties are in the range typical of metamaterials, and use these to show the tendency of RLDOS to concentrate on the coating boundaries when plasmonic cloaking is occurring.

Green's functions and relative local density of states in two-dimensional lossy structured systems

The local density of states (LDOS) is a function of spatial position and frequency which governs the radiation properties of sources placed within structured optical systems. We show how the enhancement or suppression of the relative LDOS, comparing two-dimensional systems, may be computed from Green's tensors obeying the two-dimensional Helmholtz equation and electromagnetic boundary conditions, both around and within a coated, lossy, non-magnetic cylinder. We illustrate the spatial and spectral variation of this relative LDOS with numerical results for both principal cases of polarization, with either the magnetic or the electric field of the Green's function source along the cylinder axis.

Predicting species distributions based on incomplete survey data: the trade‐off between precision and scale

Systematic species surveys over large areas are mostly not affordable, constraining conservation planners to make best use of incomplete data. Spatially explicit species distribution models (SDM) may be useful to detect and compensate for incomplete information. SDMs can either be based on standardized, systematic sampling in a restricted subarea, or – as a cost‐effective alternative – on data haphazardly collated by “volunteer‐based monitoring schemes” (VMS), area‐wide but inherently biased and of heterogeneous spatial precision. Using data on capercaillie Tetrao urogallus, we evaluated the capacity of SDMs generated from incomplete survey data to localise unknown areas inhabited by the species and to predict relative local observation density. Addressing the trade‐off between data precision, sample size and spatial extent of the sampling area, we compared three different sampling strategies: VMS‐data collected throughout the whole study area (7000 km2) using either 1) exact locations or 2) locations aggregated to grid cells of the size of an average individual home range, and 3) systematic transect counts conducted within a small subarea (23.8 km2). For each strategy, we compared two sample sizes and two modelling methods (ENFA and Maxent), which were evaluated using cross‐validation and independent data. Models based on VMS‐data (strategies 1 and 2) performed equally well in predicting relative observation density and in localizing “unknown” occurrences. They always outperformed strategy 3‐models, irrespective of sample size and modelling method, partly because the VMS‐data provided the more comprehensive clues for setting the discrimination‐threshold for predicting presence or absence. Accounting for potential errors due to extrapolation (e.g. projections outside the environmental domain or potentially biasing variables) reduced, but did not fully compensate for the observed discrepancies. As they cover a broader range of species‐habitat relations, the area‐wide data achieved a better model quality with less a‐priori knowledge. Furthermore, in a highly mobile species like capercaillie a sampling resolution corresponding to an individuals' home range can lead to equally good predictions as the use of exact locations. Consequently, when a trade‐off between the sampling effort and the spatial extent of the sampling area is necessary, less precise data unsystematically collected over a large representative region are preferable to systematically sampled data from a restricted region.

Relative local density of states for homogeneous lossy materials

We derive the appropriate form of the relative local density of states (RLDOS) for the two-dimensional Helmholtz equation in a homogeneous lossy medium, and give the corresponding result for the three-dimensional equation. The RLDOS enables the calculation of the enhancement or suppression of the energy radiated in the form of transverse electromagnetic waves by a localized source in the medium, and so would be useful in studies of either electromagnetic communication from inside a cloaking system or detection of the cloaking system by radiation from thermally excited atoms within it.

Differences In Post-Emergence Growth Of Three Fern Species Could Help Explain Their Varying Local Abundance

Abstract Despite the large number of comparative studies on species with different distribution and abundance, no clear general pattern of attributes explaining species' rarity has yet been found. The relationship between different life-history traits of a species and abundance tend to be conditional and context dependent. We were interested in whether the local relative population density of three fern species in Estonia is related to post-emergence growth of their young sporophytes, i.e., that the locally abundant species, D. carthusiana, has the highest vegetative growth in its first growth periods and the two less abundant species, D. dilatata and D. expansa, have lower. We were also interested in differences between generative traits of young sporophytes of three species, specifically in the number of spores. We grew the species in a garden experiment for two vegetation periods, 2004–2005, until the first sporulation. The relative population density of the three Dryopteris species was related to the ...

Modeling of high-density compaction of granular materials by the Discrete Element Method

Cold compaction of metal powders is now commonly studied at a microscopic scale, to further our understanding of contact mechanics between grains. The Discrete Element Method (DEM) is therefore, a good compromise between calculation time and precision. DEM simulations are in general limited to a relative density of about 0.8, because the existing contact laws do not reproduce all the physical phenomena involved in the densification of granular media. Local contact mechanics can be studied by finite element analyses on meshed distinct elements (MDEM, Meshed Distinct Element Method). However, this method is too time-consuming when in the presence of a large number of grains. In the following work, a new analytical contact law will be formulated with MDEM which will subsequently be used to validate the DEM model. Thus, it will be possible with DEM modeling to reproduce high-density compaction of random packings up to a relative density of about 0.95. By introducing a local relative density parameter in the force–displacement relationship, the incompressibility effects which rule high-density behaviors can be introduced in the modeling of powder compaction.

CLUSTER-DENSE NETWORKS

Small-world networks, exhibiting short nodal distances and high clustering, and scale-free networks, typified by a scale-free, power-law node-degree distribution, have been shown to be widespread both in natural and artificial systems. We propose a new type of network — cluster-dense network — characterized by multiple clusters that are highly intra-connected and sparsely inter-connected. Employing two graph-theoretic measures — local density and relative density — we demonstrate that such networks are prevalent in the world of networks.

MO-E-AUD C-06: Application of 5D Breathing Motion Model for Monitoring Radiation Damage

Purpose: To present a novel method for monitoring radiation damage using the parameters of our 5D lung motion model. Method and Materials: The 5D breathing motion model describes breathing motion as a function of tidal volume ν and airflow f and is parameterized as: , where r is the position of a piece of tissue located at reference position r0. α and β are each functions of r0 and relate tissue motion with tidal volume and airflow. The continuity equation , where ρ is the local density, t is time, and U is the velocity field, is modified to replace tidal volume as the independent variable. At inhalation or exhalation, the f=0 and under these conditions, the continuity equation leads to in the tissue reference frame. This equation provides the relationship between the divergence of α and the relative change in local tissue density. The powerful aspect of this result is that the α parameter is determined using free-breathing scan registrations which inherently include the complex hysteresis interplay, and yet its divergence indicates the local relative density change as a function of tidal volume. The values of α were determined for repeat 5D CT scans for both irradiated and unirradiated lungs. Results: The unirradiated patient had little change in the value of α between two scan sessions. A lung cancer patient had 5D CT scans acquired after 16 Gy and 70 Gy tumor dose. The value of α changed dramatically in the irradiated regions. This result indicates that α is sensitive to radiation dose damage. Conclusion: The divergent of α is shown to be related to the relative local density variation as measured using free-breathing 5DCT. Repeat scans indicate that variations in the α distribution, corresponding to changes in local density variations, may be sensitive to local radiation damage.

An algorithm for point cluster generalization based on the Voronoi diagram

This paper presents an algorithm for point cluster generalization. Four types of information, i.e. statistical, thematic, topological, and metric information are considered, and measures are selected to describe corresponding types of information quantitatively in the algorithm, i.e. the number of points for statistical information, the importance value for thematic information, the Voronoi neighbors for topological information, and the distribution range and relative local density for metric information. Based on these measures, an algorithm for point cluster generalization is developed. Firstly, point clusters are triangulated and a border polygon of the point clusters is obtained. By the border polygon, some pseudo points are added to the original point clusters to form a new point set and a range polygon that encloses all original points is constructed. Secondly, the Voronoi polygons of the new point set are computed in order to obtain the so-called relative local density of each point. Further, the selection probability of each point is computed using its relative local density and importance value, and then mark those will-be-deleted points as ‘deleted’ according to their selection probabilities and Voronoi neighboring relations. Thirdly, if the number of retained points does not satisfy that computed by the Radical Law, physically delete the points marked as ‘deleted’ forming a new point set, and the second step is repeated; else physically deleted pseudo points and the points marked as ‘deleted’, and the generalized point clusters are achieved. Owing to the use of the Voronoi diagram the algorithm is parameter free and fully automatic. As our experiments show, it can be used in the generalization of point features arranged in clusters such as thematic dot maps and control points on cartographic maps.