Predicted Density Distribution Research Articles

Arbitrary-Scale Point Cloud Upsampling by Voxel-Based Network with Latent Geometric-Consistent Learning

Recently, arbitrary-scale point cloud upsampling mechanism became increasingly popular due to its efficiency and convenience for practical applications. To achieve this, most previous approaches formulate it as a problem of surface approximation and employ point-based networks to learn surface representations. However, learning surfaces from sparse point clouds is more challenging, and thus they often suffer from the low-fidelity geometry approximation. To address it, we propose an arbitrary-scale Point cloud Upsampling framework using Voxel-based Network (PU-VoxelNet). Thanks to the completeness and regularity inherited from the voxel representation, voxel-based networks are capable of providing predefined grid space to approximate 3D surface, and an arbitrary number of points can be reconstructed according to the predicted density distribution within each grid cell. However, we investigate the inaccurate grid sampling caused by imprecise density predictions. To address this issue, a density-guided grid resampling method is developed to generate high-fidelity points while effectively avoiding sampling outliers. Further, to improve the fine-grained details, we present an auxiliary training supervision to enforce the latent geometric consistency among local surface patches. Extensive experiments indicate the proposed approach outperforms the state-of-the-art approaches not only in terms of fixed upsampling rates but also for arbitrary-scale upsampling. The code is available at https://github.com/hikvision-research/3DVision

Dynamics of stochastic-constrained particles

Prior studies have focused on the overall behavior of randomly moving particle swarms. However, the characteristics of the stochastic-constrained particles that form ubiquitously within these swarms remain oblivious. This study demonstrates a generalized diffusion equation for stochastic-constrained particles that considers the velocity and location aggregation effects observed from their parent particle swarm (i.e., a completely random particle swarm). This equation can be approximated as the form of Schrödinger equation in the microcosmic case (low relative density) and describe the dynamics of the total mass distribution in the macrocosmic case (high relative density). The predicted density distribution of the particle swarm in the stable aggregation state is consistent with the total mass distribution of massive, relaxed galaxy clusters (at least in the range of r<r_{textrm{s}}), preventing cuspy problems in the empirical Navarro–Frenk–White profile. This study opens a window to observe the dynamics of stochastic-constrained particles from a third perspective, from which the aggregation effect of particles without gravitation can be saw.

Finite element analysis of bone remodelling with piezoelectric effects using an open-source framework

Bone tissue exhibits piezoelectric properties and thus is capable of transforming mechanical stress into electrical potential. Piezoelectricity has been shown to play a vital role in bone adaptation and remodelling processes. Therefore, to better understand the interplay between mechanical and electrical stimulation during these processes, strain-adaptive bone remodelling models without and with considering the piezoelectric effect were simulated using the Python-based open-source software framework. To discretise numerical attributes, the finite element method (FEM) was used for the spatial variables and an explicit Euler scheme for the temporal derivatives. The predicted bone apparent density distributions were qualitatively and quantitatively evaluated against the radiographic scan of a human proximal femur and the bone apparent density calculated using a bone mineral density (BMD) calibration phantom, respectively. Additionally, the effect of the initial bone density on the resulting predicted density distribution was investigated globally and locally. The simulation results showed that the electrically stimulated bone surface enhanced bone deposition and these are in good agreement with previous findings from the literature. Moreover, mechanical stimuli due to daily physical activities could be supported by therapeutic electrical stimulation to reduce bone loss in case of physical impairment or osteoporosis. The bone remodelling algorithm implemented using an open-source software framework facilitates easy accessibility and reproducibility of finite element analysis made.

The dynamics of collapsing cores and star formation

Low-mass stars are generally understood to form by the gravitational collapse of the dense molecular clouds known as starless cores. Continuum observations have not been able to distinguish among the several different hypotheses that describe the collapse because the predicted density distributions are the almost the same, as they are for all spherical self-gravitating clouds. However, the predicted contraction velocities are different enough that the models can be discriminated by comparing the velocities at large and small radii. This can be done by observing at least two different molecular line transitions that are excited at different densities. For example, the spectral lines of the H2O (110 - 101) and C18O (1-0) have critical densities for collisional de-excitation that differ by 5 orders of magnitude. We compare observations of these lines from the contracting starless core L1544 against the spectra predicted for several different hypothetical models of contraction including the Larson-Penston flow, the inside-out collapse of the singular isothermal sphere, the quasi-equilibrium contraction of an unstable Bonnor-Ebert sphere, and the non-equilibrium collapse of an over-dense Bonnor-Ebert sphere. Only the model of the unstable quasi-equilibrium Bonnor-Ebert sphere is able to produce the observed shapes of both spectral lines. This model allows us to interpret other observations of molecular lines in L1544 to find that the inward velocities seen in observations of CS(2-1) and N2H+ are located within the starless core itself, in particular in the region where the density profile follows an inverse square law. If these conclusions were to hold in the analysis of other starless cores, this would imply that the formation of hydrostatic clouds within the turbulent interstellar medium is not only possible but not exceptional and may be an evolutionary phase in low-mass star formation.

A comparative study of orthotropic and isotropic bone adaptation in the femur

Functional adaptation of the femur has been studied extensively by embedding remodelling algorithms in finite element models, with bone commonly assumed to have isotropic material properties for computational efficiency. However, isotropy is insufficient in predicting the directionality of bone's observed microstructure. A novel iterative orthotropic 3D adaptation algorithm is proposed and applied to a finite element model of the whole femur. Bone was modelled as an optimised strain-driven adaptive continuum with local orthotropic symmetry. Each element's material orientations were aligned with the local principal stress directions and their corresponding directional Young's moduli updated proportionally to the associated strain stimuli. The converged predicted density distributions for a coronal section of the whole femur were qualitatively and quantitatively compared with the results obtained by the commonly used isotropic approach to bone adaptation and with ex vivo imaging data. The orthotropic assumption was shown to improve the prediction of bone density distribution when compared with the more commonly used isotropic approach, whilst producing lower comparative mass, structurally optimised models. It was also shown that the orthotropic approach can provide additional directional information on the material properties distributions for the whole femur, an advantage over isotropic bone adaptation. Orthotropic bone models can help in improving research areas in biomechanics where local structure and mechanical properties are of key importance, such as fracture prediction and implant assessment. © 2014 The Authors. International Journal for Numerical Methods in Biomedical Engineering published by John Wiley & Sons, Ltd.

Optimal bone density distributions: Numerical analysis of the osteocyte spatial influence in bone remodeling

In this paper a control and optimization procedure for bone remodeling simulations was adopted to study the effect of the osteocyte influence range on the predicted density distribution. In order to reach this goal, the osteocyte network regulating bone remodeling process in a 2-D bone sample was numerically simulated. The assumed proportional-integral-derivative (PID) bone remodeling rule was related to the error signal between the strain energy density and a selected target. Furthermore the control parameters and the target were optimally determined minimizing a suitable cost index: the goal was to minimize the final mass and the energy thus maximizing the stiffness. The continuum model results show that the developed and adapted trabecular structure was consistent with the applied loads and only depended on the external forces, the value of the cost index, the maximum attainable elastic modulus value (hence, the maximum density value) and the value of the energy target. The remodeling phenomenon determined the number and thickness of the trabeculae which are formed from a uniform distribution of mass density in the considered domain; this number and these thicknesses are controlled by the values assigned to the parameters of the model. In particular, the osteocyte decay distance (D) of the influence range affected the trabecular patterns formation, showing an important effect in the adaptive capacity of the optimization numerical model.

Radial tensile strength prediction of relaxing and relaxed compacts by near-infrared chemical imaging

The prediction of radial tensile strength (RTS) of relaxing solid dosage forms by near-infrared hyperspectral chemical imaging was studied. Compacts consisting of starch, lactose, and a mixture of four components were created at different compression forces to develop density models. Predicted density distribution parameters were subsequently used to estimate RTS. Chemical images were collected shortly after compression, repeated every 30 min for 2 h, and a final image was collected after 2 weeks. A two step process, involving first the prediction of compact density at each pixel (using a partial least squares model) and second the relationship between compact density distributions and RTS was implemented. Among the parameters with a significant relationship with RTS, the median of the distribution of density predictions in an image was identified as a robust parameter. Coefficients of determinations for this prediction ranged from 0.96 to 0.99 were obtained with a maximum error in validation of 0.10 MPa for the four-component formulation compacts. The prediction of RTS of fully relaxed compacts from spectral data collected on relaxing compacts was demonstrated. These results demonstrate the potential to use near-infrared chemical imaging in real-time to predict RTS values of fully relaxed compacts.

Finite element simulation of bone remodelling in the human mandible surrounding dental implant

Dental implant is a biocompatible titanium device surgically placed into the jaw bone to support a prosthetic tooth crown in order to replace missing teeth. However, placement of an implant changes the normal mechanical environment of jawbone, which causes the bone density to redistribute and adapt to the new environment by remodelling. This study aims to predict the density distribution in human jawbone surrounding a dental implant. Based on some popular yet distinctive theories for bone remodelling, a new algorithm is proposed that takes into account both the ‘lazy zone’ effect and the self-organizational control process. The proposed algorithm is first verified by a two-dimensional (2D) plate model simulating bone tissue, then, a 2D finite element model of implant and jawbone is studied. The effects of two parameters, viz the reference value of strain energy density (SED) and the ‘lazy zone’ region, on density distribution are also investigated. The proposed algorithm is proven to be effective, and the predicted density distribution patterns correlate well with clinical observations. This study has demonstrated that consideration of the lazy zone is less important than consideration of the stress and strain (quantified as SED) induced within the bone.

Analysis of strain stress state in roller compaction process

The process of drawing and densification of powdered microcrystalline cellulose by roller press in a steady state operation is analyzed using a 2D modeling with the finite element method and the modified Drucker–Prager Cap model as material behavior. Distributions of process variables in contact surface between powder and roller such as pressure, shear stress and relative speed were predicted and used to analyze the basic mechanisms of the transport and the densification of powder between rolls. The results show clearly the existence of three contiguous zones: a phase where the powder is drawn between rolls by a sliding mechanism, a sticking phase where the powder is transported with the same velocity as the roll and where the densification by deforming the powder bed is achieved under the increase of roll pressure that reaches its peak before the neutral angle. The formed compact is then expulsed out of the gap by a slip mechanism resulting from the change of the sign of the shear stress. The predicted density distribution between the rolls, shows a gradual increase. The density reaches its maximum before the neutral point and shows values in agreement with the density of strips prepared with an instrumented roll press. The effect of varying the material parameters on the maximum pressure and the nip angle is also investigated. Beyond the description of the basic mechanisms of roller compaction, this modeling shows a real potential of the optimization of the roller compaction process.

Radar‐Derived Digital Elevation Models and Field‐Surveyed Variables to Predict Distributions of Juvenile Coho Salmon and Dolly Varden in Remote Streams of Alaska

AbstractWe used field‐surveyed and digital elevation model (DEM) parameters to predict density distributions of juvenile coho salmon Oncorhynchus kisutch and Dolly Varden Salvelinus malma in remote streams on Prince of Wales Island, southeast Alaska, and to identify influences of associated reach‐level habitat characteristics. Fish densities were highest in two reach types (low‐gradient floodplain reaches and moderately contained reaches) characterized by numerous pool habitats, low pool spacing distances, and abundant large woody debris. Regression analyses indicated that channel gradients measured during field surveys (M‐gradients) accounted for significant amounts of the variance in coho salmon and Dolly Varden juvenile densities. The DEMs derived from a 2000 space‐shuttle radar mapping mission were used to estimate channel gradients (DEM‐gradients) and gradient zones: (0–3, &gt;3–6, &gt;6–15, and &gt;15%) in stream networks. A high correlation between DEM‐gradients and M‐gradients (r = 0.92), along with the regressions of M‐gradient and fish density, provided a template for comparing DEM‐gradient and M‐gradient predictions of fish densities within gradient zones of the watersheds. Juvenile coho salmon and Dolly Varden densities (number/100 m2) predicted from the DEM‐gradients and M‐gradients were consistent for a majority of the gradient zones. Our results and expanded analyses should facilitate development of paradigms for assessing fish distributions in remote landscapes.

A new lattice density functional theory for polymer adsorption at solid-liquid interface

We report a new lattice density functional theory for polymer solutions at the solid-liquid interface. The theory accounts for the nearest-neighbor interactions and the long-range correlations due to chain connectivity. A Helmholtz free-energy functional is developed with an exact free-energy functional expression for the ideal chains and a thermodynamic model of lattice polymer solutions for the excess contributions. The local and weighted density approximations are used to calculate the contributions due to the athermal entropy of mixing and the internal energy of mixing, respectively. Mayer function and propagator formalism are adopted to obtain the segment-density distributions for various conformations including adsorbed trains, tails, loops, and free polymers. The predicted density distributions of polymer adsorption are in good agreement with simulation results. The results imply that as a counterbalance between energy and conformational entropy, the weighted density approximation used in the functional can rationally capture the segment-segment correlations.

Transient modeling of chemical vapor infiltration of methane using multi-step reaction and deposition models

Based on multi-step reaction and deposition models including the hydrogen inhibition model of pyrocarbon growth, transient 2D simulations of chemical vapor infiltration of methane were carried out by a finite element method (FEM) coupling the mass transfer (by convection and diffusion) and the evolutive surface area model with gas-phase and surface chemical reactions. The continuous infiltration, pyrolysis and deposition of methane and its consecutive C x H y products lead to continuously varying hydrogen concentration inside the carbon felt. The higher diffusibility of hydrogen compared to those of hydrocarbons results in complex distributions of [ H 2 ]/[ C x H y ] ratios inside the carbon felt, significantly affecting the deposition rates of pyrolytic carbon from hydrocarbons. The favorable densification mode (from inside to outside) seems to depend not only on the concentration ratio of [ C 2 H n ]/[ C 6 H m ] but also on the concentration ratio of [H 2]/[ C x H y ]. The effect of various feed compositions of methane and hydrogen on densification of carbon felts was investigated at a temperature of 1368 K. An acceptable agreement was found between the predicted density distribution and experimental data taken from literature.

Liquid–vapor density profiles from equilibrium limit of diffusion equation for interacting particles

Liquid–vapor density profiles are derived from the equilibrium limit of diffusion equation for interacting particles. These profiles are in good agreement with classical hyperbolic tangent relation. For simple Lennard-Jones fluids, predicted density distributions agree with computer simulation data, but have a slightly sharper transition zone. For alkali metals with Lennard-Jones-like potentials, the new equations predict a very good average distribution with quite satisfactory agreement with Monte Carlo simulation results. For liquid metals and water surfaces, accurate interfacial profile predictions also can be achieved by using effective two-body potential data instead of Lennard-Jones parameters.

Formally Exact Truncated Nonuniform Excess Helmholtz Free Energy Density Functional: Test and Application

The functional expansion of the nonuniform excess Helmholtz free energy density functional around the bulk density was truncated at the first order, and then the functional counterpart of the Lagrangian theorem of differential calculus was employed to make the truncation formally exact. The concrete procedure is the following: According to the Lagrangian theorem and the definition of the direct correlation function (DCF), the original expansion coefficient, ,that is, the uniform first-order DCF, was replaced by the nonuniform first-order DCF whose density argument is an appropriate mixture of the density distribution and the bulk density with an adjustable parameter. With reference to the weighted density approximation, the nonuniform first-order DCF was then approximated by its uniform counterpart with a weighted density as its density argument. The weighting function was specified by equating the second-order functional derivative of the present truncated nonuniform excess Helmholtz free energy density functional with respect to the density distribution in the uniform limit to the second-order bulk DCF; the normalization condition of the weighting function specifies the adjustable parameter to be 0.5. The truncated expansion was incorporated into the density functional theory (DFT) formalism to predict the nonuniform hard-sphere fluid density distribution in good agreement with simulation data for three confining geometries: a single hard wall, a spherical cavity, and a bulk hard-sphere particle. The nonuniform Lennard-Jones fluid was investigated by dividing the bulk second-order DCF into a strongly density-depending short-range part and a weakly density-depending long-range part. The latter is treated by functional perturbation expansion truncated at the lowest order whose accuracy depends on how weakly the long-range part depends on the bulk density. The former is treated by the present truncated approximation. The two approximations are put into the density profile equation of the DFT to predict the density distribution for the Lennard-Jones fluid under the influence of two external potentials. The predicted density distribution displays even higher accuracy than that of two previous density functional perturbation theories in the region away from the repulsive wall but is a little inferior to the former approaches in the region near the wall. Also, a functional integral procedure was employed to develop the density functional approximation for the nonuniform first-order DCF to calculate the global thermodynamic properties of the nonuniform fluid.

High-Order Perturbative Density Functional Theory for Nonuniform Fluids with an Attractive Tail near Surfaces

The high-order perturbative density functional theory (DFT) for a nonuniform hard-sphere fluid (S. Zhou and E. Ruckenstein, Phys. Rev. E, 61, 2704, (2000)) was truncated at the third order and reformulated to be adapted for nonuniform non-hard-sphere interaction potential fluids. The only required input parameter (the second-order direct correlation function of a uniform fluid) can be obtained from the Ornstein–Zernike equation numerically or analytically. The constant relating to the bulk fluid parameter and measuring the strength of the third-order term was determined by the sum rule, which specifies the bulk pressure by the hard-wall contact density. The present third-order perturbative DFT predicted density distribution profiles for a Lennard–Jones fluid and an adhesive hard-sphere fluid confined between two hard walls that are in very good agreement with the simulation data. Furthermore, the present third-order perturbative DFT predicted very well the contact density as a function of the gap width for the confined adhesive hard-sphere fluid.

Numerical Analysis of Combustion around a Strut in Supersonic Airflow.

Numerical simulation of combustion around a strut in supersonic airflow at Mach 1.5 was conducted. In previous papers, experimental results on flame-holding characteristics have been shown for the strut divided into two parts, indicating the effectiveness of the flame-holding characteristics of this strut. Stable flame-holding is due to a comparatively long residence time in the subsonic flow region between the two parts of the strut. The present study is analytical evidence of the stable flame-holding of this strut. The Stahl and Warnatz’s detailed chemistry of hydrogen/oxygen reactions and the Baldwin Lomax turbulence algebraic model were employed to simulate the chemical reaction and turbulent flow, respectively. Flame structures such as distributions of chemical species and temperature were obtained. For example, the predicted density distributions explicitly showed an attached shock wave, expansion fans and shear layers, and had good agreement with the shadowgraph of the experiment. The overall equivalence ratio in the space between two strut parts was calculated to evaluate the reaction time in the space between the struts and a particle trace analysis was performed to evaluate the residence time in the space. By obtaining the Damkohler number from two characteristic times, two flame-holding limits, namely the chemical kinetic limit at small interval between two struts and the dynamic limit at large interval, were discussed. The numerical results were qualitatively consistent with the previous experimental results.

Proximal Femoral Density Patterns are Consistent with Bicentric Joint Loads

We developed an alternate method for density-based load estimation and applied it to estimate hip joint load distributions for two femora. Two-dimensional finite element models were constructed from single energy quantitative computed tomography (QCT) data. Load estimation was performed using five loading regions on the femoral head. Within each loading region, individual nodal loads, normal to the local surface, were supplied as input to the load estimation. An optimization procedure independently adjusted individual nodal load magnitudes in each region, and the magnitudes of muscle forces on the greater trochanter, such that the applied tissue stimulus approached the reference stimulus throughout the model. Dominant estimated load resultant directions were generally consistent with published experimental data for loads during gait. The estimated loads also suggested that loads near the extremes of the articulating surface may be important (even required) for development and maintenance of normal bone architecture. Estimated load distributions within nearly all regions predicted bicentric loading patterns, which are consistent with observations of hip joint incongruity. Remodeling simulations with the estimated loads predicted density distributions with features qualitatively similar to the QCT data sets. This study illustrates how applications of density-based bone load estimation can improve understanding of dominant loading patterns in other bones and joints. The prediction of bicentric loading suggests a very fine level of local adaptation to details of joint loading.

The Ring Test for P/M Materials

The application of the ring test to assess die-workpiece interface friction during forging of powder metallurgical materials has been investigated. As for fully dense materials, the change in internal diameter as a function of height reduction was used to quantify friction. To this end, calibration curves were generated by conducting finite element method (FEM) simulations of ring forging with different friction factors. The method was validated by conducting isothermal, hot compression tests on rings of an alpha-two titanium aluminide alloy with starting densities of 75, 85, or 100 percent of full theoretical density. Comparison of the test data to the calibration curves revealed somewhat higher friction factors for the porous materials (as compared to the fully dense material) for both lubricated and unlubricated interface conditions. Furthermore, the accuracy of the FEM simulations of the ring test was confirmed by good agreement between measured and predicted density distributions and load-stroke curves for tests on the porous titanium aluminide material.

Prediction of overall shape of sintered alumina compacts

Abstract The effects of the final aspect ratio on the overall shape of cylindrical sintered compacts, prepared by a uniaxial die pressing technique, are measured and described. An empirical compaction equation, which describes the compaction behaviour of a spray dried AKP-30 alumina powder, is presented. The density distribution along the axis of the compacts was predicted by using an established first-order analysis. From these predicted density distributions, the overall shapes of the sintered compacts were quite accurately predicted by using a set of sintering simulation equations obtained in separate experiments.

Computer simulations of stress-related bone remodeling around noncemented acetabular components

The authors have used computer modeling techniques to examine stress-related bone changes in the acetabular region. Using a previously developed theory for bone development and adaptation, the authors simulated the distribution of bone density in the natural pelvis as well as changes in bone density following total hip arthroplasty. The geometry of the finite element model was based on a two-dimensional slice through the pelvis. Starting from a solid, homogeneous structure, the computer simulations predicted the distribution of bone density throughout the natural pelvis. The predicted bone density distribution in this first simulation agreed well with the actual bone density distribution only when loads representing multiple activities were incorporated. Using the predicted density distribution as a starting point the authors modified the finite element models to study two designs of noncemented, metal-backed acetabular cups. The simulations with fully fixed bone-implant interfaces predicted extensive loss of bone density medial and inferior to the prosthetic components. The simulations with loose interfaces led to more moderate losses of bone density, indicating a load transfer more similar to that which occurs in the natural joint. The differences in simulated bone remodeling between the two component designs were quite minimal. These results indicate that acetabular components with full bony ingrowth may induce significant stress-related bone remodeling due to a nonphysiologic transfer of load.