Set Of Grids Research Articles

Fractal analysis of self-mixing speckle signal in velocity sensing

A new method based on fractal theory is proposed to analyze velocity sensing. The waveform of a self-mixing speckle signal is processed as a pattern of a fractal. Fractal boxes are defined as a set of grids used to divide the fractal pattern, and box-counting (BC) is introduced to characterize the statistical property of a speckle signal. A group of simulated speckle signals are analyzed by calculating the BCs corresponding to different velocities of the object. A linear dependence between the BCs of speckle signals and velocities is obtained, the result of which is validated by the analysis of a group of signals obtained from experiments. The performance of the fractal analysis is compared with those of the previous analysis methods. Better linearity and higher measurement sensitivity of the fractal analysis are indicated. The experimental result shows that the fractal method can be used as a valid analysis tool for the self-mixing speckle signal in velocity sensing.

General Methodology to Optimize Damping Functions to Account for Charge Penetration Effects in Electrostatic Calculations Using Multicentered Multipolar Expansions

We developed a methodology to optimize exponential damping functions to account for charge penetration effects when computing molecular electrostatic properties using the multicentered multipolar expansion method (MME). This methodology is based in the optimization of a damping parameter set using a two-step fast local fitting procedure and the ab initio (Hartree-Fock/6-31G** and 6-31G**+) electrostatic potential calculated in a set of concentric grid of points as reference. The principal aspect of the methodology is a first local fitting step which generates a focused initial guess to improve the performance of a simplex method avoiding the use of multiple runs and the choice of initial guesses. Three different strategies for the determination of optimized damping parameters were tested in the following studies: (1) investigation of the error in the calculation of the electrostatic interaction energy for five hydrogen-bonded dimers at standard and nonstandard hydrogen-bonded geometries and at nonequilibrium geometries; (2) calculation of the electrostatic molecular properties (potential and electric field) for eight small molecular systems (methanol, ammonia, water, formamide, dichloromethane, acetone, dimethyl sulfoxide, and acetonitrile) and for the 20 amino acids. Our results show that the methodology performs well not only for small molecules but also for relatively larger molecular systems. The analysis of the distinct parameter sets associated with different optimization strategies show that (i) a specific parameter set is more suitable and more general for electrostatic interaction energy calculations, with an average absolute error of 0.46 kcal/mol at hydrogen-bond geometries; (ii) a second parameter set is more suitable for electrostatic potential and electric field calculations at and outside the van der Waals (vdW) envelope, with an average error decrease >72% at the vdW surface. A more general amino acid damping parameter set was constructed from the original damping parameters derived for the small fragments and for the amino acids. This damping set is more insensitive to protein backbone and residue side-chain conformational changes and can be very useful for future docking and molecular dynamics protein simulations using ab initio based polarizable classical methods.

등가하중을 이용한 원자로 핵연료봉 지지격자 스프링의 비선형 응답 구조 최적설계

The spacer grid set is a part of a nuclear fuel assembly. The set has a spring and the spring supports the fuel rods safely. Although material nonlinearity is involved in the deformation of the spring, nonlinearity has not been considered in design of the spring. Recently a nonlinear response structural optimization method has been developed using equivalent loads. It is called nonlinear response optimization equivalent loads (NROEL). In NROEL, the external loads are transformed to the equivalent loads (EL) for linear static analysis and linear response optimization is carried out based on the EL in a cyclic manner until the convergence criteria are satisfied. EL is the load set which generates the same response field of linear analysis as that of nonlinear analysis. Shape optimization of the spring is carried out based on EL. The objective function is defined by minimizing the maximum stress in the spring while mass is limited and the support force of the spring is larger than a certain value. The results are verified by nonlinear response analysis. ABAQUS is used for nonlinear response analysis and GENESIS is employed for linear response optimization.

Measurements of Current Distribution on a Two-Grid-Ion-Extraction-System Gridlet

Numerical models of ion extraction used in the design of ion thrusters need to be validated by comparison with experimental data; in particular, the magnitudes of ion-impingement currents as functions of screen and discharge voltages should be quantified. This paper provides measurements which may be used to test numerical models of ion extraction using two multiple-hole grids. A grid set, in which an isolated gridlet was embedded in an accelerator grid, was built to measure ion-impingement current distribution. The gridlet was composed of barrel and downstream electrodes, electrically isolated from each other and the rest of the accelerator grid. The obtained measurements of ion-impingement currents on the electrodes can be directly compared with numerical predictions. The barrel-electrode current has been found not to be proportional to the downstream-electrode current, a fact which cannot be shown by measurement of the total accelerator-grid currenL This current was also observed to significantly depend not only on screen voltage but also on discharge voltage, whereas the downstream-electrode current was found to be insensitive to both voltages. The total accelerator-grid current was influenced by both of these.

충격과 마모를 고려한 원자로 핵연료봉 지지격자의 설계

The spacer grid set is a component in the nuclear fuel assembly. The set supports the fuel rods safely. Therefore, the spacer grid set should have sufficient strength for the external impact forces such as earthquake. The fretting wear occurs between the spring of the fuel rod and the spacer grid due to flow-induced vibration. Conceptual design of the spacer grid set is performed based on the Independence Axiom of axiomatic design. Two functional requirements are defined for the impact load and the fretting wear, and corresponding design parameters are selected. The overall flow of design is defined according to the application of axiomatic design. Design for the impact load is carried out by using nonlinear dynamic analysis to determine the length of the dimple. Topology optimization is carried out to determine a new configuration of the spring. The fretting wear is reduced by shape optimization using the homology theory. The deformation of a structure is called homologous if a given geometrical relationship holds before, during, and after the deformation. In the design to reduce the fretting wear, the deformed shape of the spring should be the same as that of the fuel rod. This condition is transformed to a function and considered as a constraint in the shape optimization process. The fretting wear is expected to be reduced due to the homology constraint. The objective function is minimizing the maximum stress to allow a slight plastic deformation. Shape optimization results are confirmed through nonlinear static analysis.

A Composite Grid Method for Moving Conductor Eddy-Current Problem

We present fundamentals and procedures of a composite grid method (CGM) for determining eddy currents in moving conductors. Based on the finite-element method (FEM), CGM uses two separate mesh grids - one coarse and one fine - to calculate in the global region and local region separately. The results of the coarse mesh are interpolated onto the boundary of the fine mesh as its Dirichlet's condition. Then two equations are solved in the fine mesh region in order to obtain the reaction force on the boundary, which is reacted on the coarse mesh to modify its right-hand-side load vector. And the equations in the coarse mesh are re-solved. The iteration continues until the results converge. The advantage of CGM is that it allows two overlapped grids differing greatly in size to be meshed independently. Also, the program is easy to modularize and thus has great flexibility and adaptability. Above all, it ensures good numerical accuracy in each grid set. As an example indicates, CGM is effective in handling 2-D moving conductor eddy-current problems that are tedious to solve by conventional methods such as re-meshing or using a Lagrange multiplier.

Development of Phosphor Screen Having “Gridded Energy Analyzer” for Two-Fluid Nonneutral Plasma Experiments

An ew type of fluorescent screen with a gridded energy analyzer is proposed. This new method clearly has an advantage of clarifying both space distribution of number density and particle energy simultaneously. The fluorescent screen has three potential grids in front of it. Us ing the set of grids, the particle energy is analyzed. The preliminary data show that the potential grids have successfully analyzed the energy o ft he injected electrons. The fluorescent screen seems to emit visible light even af ter the number of electrons is somewhat reduced by the potential grids.

POSTHARVEST LOSSES DUE TO GAPS IN COLD CHAIN IN INDIA-A SOLUTION

About 30% of the fruits and vegetables grown in India (40 million tons amounting to US$ 13 billion) get wasted annually due to gaps in the cold chain such as poor infrastructure, insufficient cold storage capacity, unavailability of cold storages in close proximity to farms, poor transportation infrastructure, etc. This results in instability in prices, farmers not getting remunerative prices, rural impoverishment resulting in farmers' frustrations and suicides. India wastes more fruits and vegetables than it consumes. Enough attention has been paid at the pre-harvest stage for boosting the levels of production by techniques like crop rotation, soil conservation, pest control, fertilizers, irrigation, etc., but, postharvest issues have been addressed inadequately. Despite having achieved national food security, the well-being of over 200 million Indian farmers and farm workers who have been the backbone of Indian agriculture continues to be a matter of grave concern. Operating costs for Indian cold storage units are over $60 per cubic metre per year compared to less than $30 in the West. Energy expenses make up about 28% of the total expenses for Indian cold storages compared to 10% in the West. These factors make setting up cold storages difficult, unviable and uneconomical. About 30-35% of the losses can be reduced by transporting the freshly harvested fruits and vegetables in refrigerated containers thus closing this gap in the cold chain. We would need about 20,000 refrigerated containers of standard TEU size (with about 0.24 million sq. meters using solar PV panels fixed on their rooftops to be totally independent of the power grid or DG sets using fossil fuels, valued at US$ 0.53 billion), to transport the freshly harvested produce, placed strategically at various locations in the farms all across the country. Commercially, the payback period for this mammoth project is quite attractive. Refrigerated containers score substantially over conventional refrigerated trucks in terms of suitability for this application in Indian terrain.

Hypothesis Grids: Improving Long Baseline Navigation for Autonomous Underwater Vehicles

Navigation continues to fundamentally limit our ability to understand the underwater world. Long baseline navigation uses range measurements to localize a remote vehicle using acoustic time-of-flight estimates. For autonomous surveys requiring high precision navigation, current solutions do not satisfy the performance or robustness requirements. Hypothesis grids represent the survey environment capturing the spatial dependence of acoustic range measurement, providing a framework for improving navigation precision and increasing the robustness with respect to non-Gaussian range observations. Prior association probabilities quantify the measurement quality as a belief that subsequent observations will correspond to the direct-path, a multipath, or an outlier as a function of the estimated location. Such a characterization is directly applicable to Bayesian navigation techniques. The algorithm for creating the representation has three main components: Mixed-density sensor model using Gaussian and uniform probability distributions, measurement classification and multipath model identification using expectation-maximization (EM), and grid-based spatial representation. We illustrate the creation of a set of hypothesis grids, the feasibility of the approach, and the utility of the representation using survey data from the autonomous benthic explorer (ABE)

A charge‐scaling implementation of the variational electrostatic projection method

Two new charge-scaling methods for efficient modeling of the solvated macromolecular environment in hybrid QM/MM calculations of biological reactions are presented. The methods are extensions of the variational electrostatic projection (VEP) method, and allows a subset of atomic charges in the external environment to be adjusted to mimic, in the active dynamical region, the electrostatic potential and field due to the large surrounding macromolecule and solvent. The method has the advantages that it offers improved accuracy, does not require the use of a three-dimensional grid or auxiliary set of fitting points, and requires only minor molecular simulation code modifications. The VEP-cs and VEP-RVM+cs methods are able to attain very high accuracy (relative force errors of 10(-7) or better with appropriate choice of control parameters), and take advantage of a recently introduced set of high-order discretization schemes and Gaussian exponents for boundary element solvation and VEP methods. The methods developed here serve as potentially powerful tools in the arsenal of computational techniques used in multiscale computational modeling problems.

Assessment of numerical uncertainty for the calculations of turbulent flow over a backward‐facing step

AbstractNumerical uncertainty analysis has been performed for the turbulent flow past a backward‐facing step. The analysis is based on calculations on seven non‐rectangular, but structured, grid sets that were provided by the organizers of the 2004 Lisbon Workshop (Proceedings of the Workshop on CFD Uncertainty Analysis, Lisbon, 21–22 October 2004). The calculations were performed by using a commercial code, namely, FLUENT with the Spalart–Allmaras one‐equation turbulence model. The present study constitutes a calculation verification process: a set of partial differential equations are solved on gradually refined grid sets, the selected quantities are extrapolated, and then the overall numerical uncertainty in selected quantities is estimated by various methods. Some new ideas are presented for estimating the coefficient of variation, which is related to standard deviation (or standard error of estimate in case of the least squares method).The major problem that stands out in extrapolation is the cases of non‐monotonic convergence. For such cases some alternative methods are proposed, and the results are compared to assess these methods. Copyright © 2005 John Wiley & Sons, Ltd.

Band structure analysis of crystals with discontinuous metallic wires

The band structure for normal propagation of crystals with finite straight metallic wires is studied for different wire diameters and lengths. The crystal is considered as a set of parallel grids. Dispersion characteristics are obtained by using a transmission line model where the parameters are calculated from the reflection and transmission coefficients of the grids. These coefficients are computed rigorously with a finite difference time domain (FDTD) code. Simulated and experimental results for two structures with the dual behavior, pass-band and stop-band, are presented. This study have potential applications in electrically controlled microwave components.

Actuation of the Kagome Double-Layer Grid. Part 2: Effect of imperfections on the measured and predicted actuation stiffness

The actuation stiffness of a set of steel Kagome Double-Layer Grid (KDLG) structures with brazed joints is measured experimentally and compared with predictions by the finite element method. The predicted actuation stiffnesses for the perfect KDLGs much exceed the measured values, and it is argued that the low values of observed actuation stiffness are due to the presence of geometric imperfections introduced during manufacture. In order to assess the significance of geometric defects upon actuation stiffness, finite element calculations are performed on structures with a stochastic dispersion in nodal position from the perfectly periodic arrangement, and on structures with wavy bars. It is found that bar waviness has the dominant effect upon the actuation stiffness. The predicted actuation stiffness for the imperfect structures are in satisfactory agreement with the measured values assuming the same level of imperfection between theory and experiment.

Improved detector response characterization method in ISOCS and LabSOCS

The In-Situ Object Calibration Software (ISOCS) and the Laboratory Sourceless Calibration Software (LabSOCS) developed and patented by Canberra Industries have found widespread use in the gamma spectrometry community. Using the ISOCS methodology, one can determine the full energy peak efficiencies of a Germanium detector in the 45 keV - 7 MeV energy range, for practically any source matrix and geometry. The underlying mathematical techniques used in ISOCS (and LabSOCS) have undergone significant improvements and enhancements since their first release in 1996. One of these improvements is a spatial response characterization technique that is capable of handling the large variations in efficiency that occurs within a small region. The technique has been in use in ISOCS and LabSOCS releases since 1999, and has significantly improved the overall quality of the close-in and off-axis response characterization for HPGe detectors, especially for Canberra's Broad Energy Germanium (BEGe) detectors. In this method, the detector response is characterized by creating a set of fine spatial efficiency grids at 15 energies in the 45 keV - 7 MeV range. The spatial grids are created in (r,θ) space about the detector, with the radius r varying from 0 to 500 meters, and the angle θ varying from 0 to π. The reference efficiencies for creating the spatial grids are determined from MCNP calculations using a validated detector model. Once the efficiency grids are created, the detector response can be determined at any arbitrary point within a sphere of 500-meter radius, and at any arbitrary energy within the specified range. Results are presented highlighting the improved performance achieved using the gridding methodology.

RF Plasma source for a Heavy Ion Fusion injector

We are developing high-current ion sources for Heavy Ion Fusion (HIF) applications. Our proposed RF plasma source starts with an array of high current density mini-beamlets (of a few milliampere each at ∼100 mA/cm 2) that are kept separated from each other within a set of acceleration grids. After they have gained sufficient kinetic energy (>1.2 MeV), the mini-beamlets are allowed to merge together to form a high current beam (about 0.5 A) with low emittance. Simulations have been done to maximize the beam brightness within the physical constraints of the source. We have performed a series of experiments on an RF plasma source. A 80-kV 20-μs source has produced up to 5 mA of Ar + in a single beamlet and we measured the emittance of a beamlet, its energy spread, and the fraction of ions in higher charge states. We have also tested a 50-kV 61-hole multi-beamlet array. Two upcoming experiments are being prepared: the first experiment will test full-gradient extraction and transport of 61 beamlets through the first four electrodes, and the second experiment will converge 119 beamlets into an ESQ channel at one-quarter scaled voltage of a 1.6 MV HIF injector.

Resistance to earth of earthing grids buried in multi-layer soil

Expressions for the resistance to earth of earthing grids buried in uniform, two- and three-layer soils are proposed based upon the examination of a large set of grids and soil structures using the finite-element approach. Simple empirical correction factors are introduced to modify the earth resistance formulae for uniform soil to account for the multi-layer soil structure. A comparative analysis of available expressions for uniform and two-layer soils is performed in order to check their applicability in various cases.

Vegetation state change and consequent carbon dynamics in savanna woodlands of Australia in response to grazing, drought and fire: a scenario approach using 113 years of synthetic annual fire and grassland growth

A spatially explicit state and transition model for assessing the interactive effects of grazing, fire and climate on carbon dynamics in Australian savannas is described. The model runs on a yearly time step. It is based on a sequential treatment of events within each year, involving, in order, growth of biomass, consumption of biomass by livestock and burning of the remaining fuel (growth minus consumption). The major drivers are 113 years of annual rainfall data, annual modelled rangeland growth, synthetic fire incidence and timing data, and data describing stocking rates in dry sheep equivalents. Baseline carbon stocks are derived from pre-settlement estimates from the VAST steady-state carbon model. State and transition models for nine vegetation zones define vegetation condition and consequent carbon stock. Change is mediated by key indices of driver variables such as grazing, growth and fire, a series of parameters and default thresholds, and a set of rules. The model is run for three 113-year spin-up cycles to establish a set of initial condition grids that represent a plausible synthetic current state. Sensitivity analyses on selected parameters and index thresholds showed that fire and growth thresholds were most important for woodland zones, and utilisation rates and degradation and recovery periods were most important for grassland zones. The model was used to examine a series of scenarios involving changes to grazing pressure and suppression of fire for different climate sequences. Changes to a few parameters enabled simulation of low and high levels of encroachment of woody weeds, and hence carbon accumulation, in the Astrebla (Mitchell) grasslands; and effective capture of the climate-induced variation in grassland condition, and hence potential for soil carbon loss, within Heteropogon spp.-dominated grasslands in northern Queensland. The scenario results suggest that this simple state and transition model with an annual time step provides a potentially useful and flexible scenario model framework for exploration of vegetation and consequent carbon dynamics of the Australian tropical savanna region.

Free-Surface Boundary Condition in Finite-Difference Elastic Wave Modeling

We design a new frequency-domain, finite-difference approach, based on a displacement formulation, which correctly describes the stress-free conditions at a free surface. In the conventional, displacement-based finite-difference method, we assign both displacements and material properties such as density and Lame constants to nodal points (a node-based grid set), whereas in our new finite-difference method, displacements are still defined at nodal points but material properties within cells (a cell-based grid set). In our new finite-difference technique using the cell-based grid set, stress-free conditions at the free surface are described by the changes in the material properties without any additional stress-free boundary condition. By conducting accuracy tests, we confirmed that the new second-order finite differences formulated in the cell-based grid set generate numerical solutions compatible with analytic solutions within the range of errors determined by dispersion analysis; the new, cell-based, weighted-averaging finite-difference method also yields better solutions than the old, node-based, weighted-averaging finite-difference method. The cell-based finite-difference method does not violate the reciprocity.

Mean cutting force prediction in ball-end milling using force map method

In this paper, a new method is proposed to predict mean cutting force in ball-end milling of sculptured surfaces. The cutter contact area, which is obtained from Z-map of the hemispherical part of the cutter, is expressed as a set of grids on the cutter plane orthogonal to the cutter axis. Before calculation of cutting force, cutting force density in each grid is calculated using empirical cutting parameters. The calculated force density corresponding to the grid position on the cutter plane is defined as a force map. The mean cutting force in an arbitrary cutter contact area is easily calculated by summing up the cutting force densities of the engaged grids in the force map. The proposed method was verified through the slotting and slanted surface machining by varying the surface inclination angle. From the experimental results, it was shown that mean cutting force can be calculated accurately and fast.

A quantization algorithm for solving multidimensional discrete-time optimal stopping problems

A new grid method for computing the Snell envelope of a function of an $\mathbb{R}^d$-valued simulatable Markov chain $(X_k)_{0\lambda \leq k\lambda \leq n}$ is proposed. (This is a typical nonlinear problem that cannot be solved by the standard Monte Carlo method.) Every $X_k$ is replaced by a `quantized approximation' $\widehat{X}_k$ taking its values in a grid $\Gamma_k$ of size $N_k$. The $n$ grids and their trans\-ition probability matrices form a discrete tree on which a pseudo-Snell envelope is devised by mimicking the regular dynamic programming formula. Using the quantization theory of random vectors, we show the existence of a set of optimal grids, given the total number $N$ of elementary $\mathbb{R}^d$-valued quantizers. A recursive stochastic gradient algorithm, based on simulations of $(X_k)_{0\lambda \leq k \lambda \leq n}$, yields these optimal grids and their transition probability matrices. Some a priori error estimates based on the $L^p$-quantization errors $\|X_k-\widehat X_k\|_{_p}$ are established. These results are applied to the computation of the Snell envelope of a diffusion approximated by its (Gaussian) Euler scheme. We apply these result to provide a discretization scheme for reflected backward stochastic differential equations. Finally, a numerical experiment is carried out on a two-dimensional American option pricing problem.