Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “3D Modeling”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,477 records · Page 82
All sourcesNASA NTRSDOE OSTI
NASA NTRS2022

Full-Wave Simulations of Scattering by Corn Fields at L-Band

In this paper, the Numerical Maxwell Model of 3D (NMM3D) full-wave simulation is performed over a corn field using a hybrid method to study the vegetation effect on the microwave. The commercial software of FEKO is used to extract T-matrix of single corn in the first step. Then the calculated T-matrix is combined with Wave Multiple Scattering Theory (W-MST) in the second step to consider the multiple scattering among different plants. The hybrid method is validated with HFSS by solving scattering from 2 corns. A corn field of 25 corn is simulated using the hybrid method and the transmission is calculated and compared with those obtained from the classical radiative transfer model.

Yueh, Simon↗
DOE OSTI2024

Evaluating the mutagenicity of N-nitrosodimethylamine in 2D and 3D HepaRG cell cultures using error-corrected next generation sequencing

Human liver-derived metabolically competent HepaRG cells have been successfully employed in both two-dimensional (2D) and 3D spheroid formats for performing the comet assay and micronucleus (MN) assay. In the present study, we have investigated expanding the genotoxicity endpoints evaluated in HepaRG cells by detecting mutagenesis using two error-corrected next generation sequencing (ecNGS) technologies, Duplex Sequencing (DS) and High-Fidelity (HiFi) Sequencing. Both HepaRG 2D cells and 3D spheroids were exposed for 72 h to N-nitrosodimethylamine (NDMA), followed by an additional incubation for the fixation of induced mutations. NDMA-induced DNA damage, chromosomal damage, and mutagenesis were determined using the comet assay, MN assay, and ecNGS, respectively. The 72-h treatment with NDMA resulted in concentration-dependent increases in cytotoxicity, DNA damage, MN formation, and mutation frequency in both 2D and 3D cultures, with greater responses observed in the 3D spheroids compared to 2D cells. The mutational spectrum analysis showed that NDMA induced predominantly A:T → G:C transitions, along with a lower frequency of G:C → A:T transitions, and exhibited a different trinucleotide signature relative to the negative control. These results demonstrate that the HepaRG 2D cells and 3D spheroid models can be used for mutagenesis assessment using both DS and HiFi Sequencing, with the caveat that severe cytotoxic concentrations should be avoided when conducting DS. With further validation, the HepaRG 2D/3D system may become a powerful human-based metabolically competent platform for genotoxicity testing.

3D spheroids↗
DOE OSTI2014

SU-E-J-128: 3D Surface Reconstruction of a Patient Using Epipolar Geometry

Purpose: To obtain a 3D surface data of a patient in a non-invasive way can substantially reduce the effort for the registration of patient in radiation therapy. To achieve this goal, we introduced the multiple view stereo technique, which is known to be used in a 'photo tourism' on the internet. Methods: 70 Images were taken with a digital single-lens reflex camera from different angles and positions. The camera positions and angles were inferred later in the reconstruction step. A sparse 3D reconstruction model was locating by SIFT features, which is robust for rotation and shift variance, in each image. We then found a set of correspondences between pairs of images by computing the fundamental matrix using the eight-point algorithm with RANSAC. After the pair matching, we optimized the parameter including camera positions to minimize the reprojection error by use of bundle adjustment technique (non-linear optimization). As a final step, we performed dense reconstruction and associate a color with each point using the library of PMVS. Results: Surface data were reconstructed well by visual inspection. The human skin is reconstructed well, althogh the reconstruction was time-consuming for direct use in daily clinical practice. Conclusion: 3D reconstruction using multi view stereo geometry is a promising tool for reducing the effort of patient setup. This work was supported by JSPS KAKENHI(25861128)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2014

Backscattering and absorption coefficients for electrons: Solutions of invariant embedding transport equations using a method of convergence

The backscattering coefficient is a magnitude whose measurement is fundamental for the characterization of materials with techniques that make use of particle beams and particularly when performing microanalysis. In this work, we report the results of an analytic method to calculate the backscattering and absorption coefficients of electrons in similar conditions to those of electron probe microanalysis. Starting on a five level states ladder model in 3D, we deduced a set of integro-differential coupled equations of the coefficients with a method know as invariant embedding. By means of a procedure proposed by authors, called method of convergence, two types of approximate solutions for the set of equations, namely complete and simple solutions, can be obtained. Although the simple solutions were initially proposed as auxiliary forms to solve higher rank equations, they turned out to be also useful for the estimation of the aforementioned coefficients. In previous reports, we have presented results obtained with the complete solutions. In this paper, we present results obtained with the simple solutions of the coefficients, which exhibit a good degree of fit with the experimental data. Both the model and the calculation method presented here can be generalized to other techniques that make use of different sorts of particle beams.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Hierarchy among the crystal lattice, charge density wave, and superconducting orders in transition metal dichalcogenides

Using high-energy x-ray scattering and large-scale three-dimensional (3D) structure modeling, in this study we investigate the relationship between the crystal lattice, charge density wave (CDW), and superconducting (SC) orders in transition metal dichalcogenides (TMDs). In particular, we systematically substitute Te for Se in Ta-Se-Te solid solutions, determine changes in their crystal lattice, and relate them to changes in the CDW transition temperature, $T_{CDW}$, and SC critical temperature, $T_c$ . We find that strong lattice distortions such as buckling of Ta layers are detrimental to the CDW and SC orders. The presence of a perfect lattice order in two dimensions is a prerequisite to the emergence of CDWs but insufficient to achieve a SC ordered state. For the SC order to emerge, the Ta sublattice should also appear periodic in 3D. Local chemical disorder may promote the SC order, and the perfectness of Ta coordination polyhedra is a factor contributing to its strength. A hierarchical relationship among the crystal lattice, CDW, and SC orders thus appears to exist in TMDs in a sense that different degrees of crystal lattice order-disorder promote and maintain the CDW and SC orders to a different extent, offering an opportunity to control the latter through modifying the former by rational design. Our findings are a step towards a better understanding of the correlation between lattice and electronic degrees of freedom in TMDs. We also demonstrate an efficient experimental approach to study them in fine detail.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2014

Reference Model 2 Scaled Geometry (RM2: River Current Turbine)

Contains the Reference Model 2 (RM2) scaled scale geometry files of the River Current Turbine, developed by the Reference Model Project (RMP). These scaled geometry files are saved as SolidWorks assembly, IGS, and STEP files, and require a CAD program to view. The scaled RM2 device was tested at the Saint Anthony Falls Laboratory (SAFL) at the University of Minnesota flume. The scale of the geometries included in this submission are at a 1:15 scale compared to the full scale geometry. This data was generated upon completion of the project on September 30, 2014. The Reference Model Project (RMP), sponsored by the U.S. Department of Energy (DOE), was a partnered effort to develop open-source MHK point designs as reference models (RMs) to benchmark MHK technology performance and costs, and an open-source methodology for design and analysis of MHK technologies, including models for estimating their capital costs, operational costs, and levelized costs of energy. The point designs also served as open-source test articles for university researchers and commercial technology developers. The RMP project team, led by Sandia National Laboratories (SNL), included a partnership between DOE, three national laboratories, including the National Renewable Energy Laboratory (NREL), Pacific Northwest National Laboratory (PNNL), and Oak Ridge National Laboratory (ORNL), the Applied Research Laboratory of Penn State University, and Re Vision Consulting. Reference Model 2 (RM2) is a variable speed dual-rotor cross-flow river turbine that is deployed at the water?s surface. It was designed for deployment at a reference site modeled after a reach in the Mississippi River near Baton Rouge, Louisiana. The rotors are anchored to a two-pontoon vessel platform. Surface deployment of the turbine minimizes the handling requirements during deployment and recovery and reduces overall costs for all O&M activities, including allowing for easy access to the power conversion chain (PCC). The design (two rotors per platform) also reduces the environmental footprint and associated environmental compliance costs.

16 TIDAL AND WAVE POWER↗
DOE OSTI2015

Thermal model development and validation for rapid filling of high pressure hydrogen tanks

This paper describes the development of thermal models for the filling of high pressure hydrogen tanks with experimental validation. Two models are presented; the first uses a one-dimensional, transient, network flow analysis code developed at Sandia National Labs, and the second uses the commercially available CFD analysis tool Fluent. These models were developed to help assess the safety of Type IV high pressure hydrogen tanks during the filling process. The primary concern for these tanks is due to the increased susceptibility to fatigue failure of the liner caused by the fill process. Thus, a thorough understanding of temperature changes of the hydrogen gas and the heat transfer to the tank walls is essential. The effects of initial pressure, filling time, and fill procedure were investigated to quantify the temperature change and verify the accuracy of the models. In this paper we show that the predictions of mass averaged gas temperature for the one and three-dimensional models compare well with the experiment and both can be used to make predictions for final mass delivery. Furthermore, due to buoyancy and other three-dimensional effects, however, the maximum wall temperature cannot be predicted using one-dimensional tools alone which means that a three-dimensional analysis is required for a safety assessment of the system.

42 ENGINEERING↗
DOE OSTI2017

The random-bond Ising model in 2.01 and 3 dimensions

We consider the Ising model between 2 and 4 dimensions perturbed by quenched disorder in the strength of the interaction between nearby spins. In the interval 2 < d < 4 this disorder is a relevant perturbation that drives the system to a new fixed point of the renormalization group. At d = 2 such disorder is marginally irrelevant and can be studied using conformal perturbation theory. Combining conformal perturbation theory with recent results from the conformal bootstrap we compute some scaling exponents in an expansion around d = 2. If one trusts these computations also in d =3, one finds results consistent with experimental data and Monte Carlo simulations. In addition, we perform a direct uncontrolled computation in d= 3 using new results for low-lying operator dimensions and OPE coefficients in the 3d Ising model. We compare these new methods with previous studies. Finally, we comment about the O(2) model in d = 3, where we predict a large logarithmic correction to the infrared scaling of disorder.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Short-Term Effects of Low-LET Radiation on the Endothelial Barrier: Uncoupling of PECAM-1 and the Production of Endothelial Microparticles

A significant target for radiation-induced effects is the microvascular system, which is critical to healthy tissue function and its pathology is linked to disrupted endothelial barrier function. Low-linear energy transfer (LET) ionizing radiation is a source of noncancer pathologies in humans and little is known about the early events that could initiate subsequent diseases. But, it is well known that gamma radiation causes a very early disruption of the endothelial barrier at doses below those required for cytotoxic effects. After irradiation of human umbilical vein endothelial cells (HUVECs) to doses as low as 2 Gy, transendothelial electrical resistance (TEER) is transiently reduced at 3 h, and the platelet-derived endothothelial cell adhesion molecule (PECAM-1 or CD31) is uncoupled from the cells along with the release of endothelial microparticles (EMPs). In this study, we measured TEER reduction as an indicator of barrier function loss, and specifically examined the shedding of EMPs from human endothelial barrier models after a variety of low-LET irradiations, including photons and charged particles. Our findings showed two TEER responses, dependent on radiation type and environmental conditions. The first response was diminishing oscillations of TEER, which occurred during the first 10 h postirradiation. This response occurred after a 5 Gy proton or helium-ion (1 GeV/n) dose in addition to a 5 Gy gamma or X radiation dose. This occurred only in the presence of multiple growth factors and did not show a dose response, nor was it associated with EMP release. The second response was a single acute drop in TEER at 3 h after photon irradiation. Dose response was observed and was associated with the shedding of EMPs in 2D barrier cultures and in 3D vessel models. In this case, helium-ion and proton irradiations did not induce a drop in TEER or shedding of EMPs. The photon radiation effects was observed both in serum-free media and in the presence of multiple growth factors, indicating that it occurs under a range of environmental conditions. Finally, our results show an acute response of the human endothelial barrier that is relevant to photon irradiation. Significantly, it involves the release of EMPs, which have recently attracted attention due to their emerging clinical importance.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2015

Use Case Realization Report: UCR-02.08 System Refines Event Location

This architecturally significant use case describes how the System refines event hypothesis location solutions. The System locates events by finding the event location minimizing the difference between signal detection feature measurements and signal detection feature predictions (see 'System Measures Signal Features' UC). The System references both empirical knowledge from past events and geophysical models to form the signal detection feature predictions. The System also computes an uncertainty bound for each event hypothesis location solution describing a region bounding the event hypothesis' hypocenter and origin time at a particular confidence level. The System creates a variety of location solutions for each event hypothesis. These location solutions vary from one another in either the input parameters the System uses or in the location solution components the System restrains to fixed values (e.g. depth) during event location calculations. The System computes location solutions using input parameters configured by the System Maintainer (see ‘Configures Processing Components’ UC). The Analyst has the option to override input parameters originally configured by the System Maintainer (see 'Refines Event Location' UC). This use case is architecturally significant due to the processing and memory resource consumption of 3D earth model calculations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Ising on $\mathbb{S}^2$-- The Affine Conjecture

We review the recent construction \cite{brower2024isingmodelmathbbs2} of the 2d Ising model on a triangulated sphere $\mathbb{S}^2$. Surprisingly, this led to a precise map of the lattice couplings to the target geometry in order to reach the conform field theory (CFT) in the continuum limit. For the integrable 2d Ising CFT, the map was found analytically \cite{Brower_2023}. Here we conjecture how this might be generalized. The discrete geometry is implemented by the piecewise flat triangulation introduced by Regge in 1960 for the Einstein Hilbert action \cite{Regge1961GeneralRW}. Then following our Ising example, we posit the existence of a smooth map of lattice couplings in affine parameters consistent with quantum correlators. A sequence of theoretical investigations and numerical simulations are recommended to test this conjecture. They begin with non-integrable CFT's -- the 2d $\phi^4$ theory on $\mathbb{S}^2$; the 3d Ising model on $\mathbb{S}^3$ and $\mathbb{R} \times \mathbb{S}^2$; QED3 on $\mathbb{R} \times \mathbb{S}^{2} $ as an intermediate step to 4d non-Abelian lattice gauge theory on $\mathbb{R} \times \mathbb{S}^3$.

Brower, Richard C. [Boston U.] (ORCID:000000028185↗
DOE OSTI2014

Reference Model 2 Full Scale Geometry (RM2: River Current Turbine)

Contains the Reference Model 2 (RM2) full scale geometry files of the River Current Turbine, developed by the Reference Model Project (RMP). These full scale geometry files are saved as SolidWorks assembly, IGS, X_T, and STEP files, and require a CAD program to view. This data was generated upon completion of the project on September 30, 2014. The Reference Model Project (RMP), sponsored by the U.S. Department of Energy (DOE), was a partnered effort to develop open-source MHK point designs as reference models (RMs) to benchmark MHK technology performance and costs, and an open-source methodology for design and analysis of MHK technologies, including models for estimating their capital costs, operational costs, and levelized costs of energy. The point designs also served as open-source test articles for university researchers and commercial technology developers. The RMP project team, led by Sandia National Laboratories (SNL), included a partnership between DOE, three national laboratories, including the National Renewable Energy Laboratory (NREL), Pacific Northwest National Laboratory (PNNL), and Oak Ridge National Laboratory (ORNL), the Applied Research Laboratory of Penn State University, and Re Vision Consulting. Reference Model 2 (RM2) is a variable speed dual-rotor cross-flow river turbine that is deployed at the waters surface. It was designed for deployment at a reference site modeled after a reach in the Mississippi River near Baton Rouge, Louisiana. The rotors are anchored to a two-pontoon vessel platform. Surface deployment of the turbine minimizes the handling requirements during deployment and recovery and reduces overall costs for all O&M activities, including allowing for easy access to the power conversion chain (PCC). The design (two rotors per platform) also reduces the environmental footprint and associated environmental compliance costs.

16 TIDAL AND WAVE POWER↗
DOE OSTI2011

THREE-DIMENSIONAL HYDRODYNAMICAL SIMULATIONS OF A PROTON INGESTION EPISODE IN A LOW-METALLICITY ASYMPTOTIC GIANT BRANCH STAR

We use the three-dimensional (3D) stellar structure code DJEHUTY to model the ingestion of protons into the intershell convection zone of a 1 M{sub Sun} asymptotic giant branch star of metallicity Z = 10{sup -4}. We have run two simulations: a low-resolution one of around 300,000 zones and a high-resolution one consisting of 2,000,000 zones. Both simulations have been evolved for about 4 hr of stellar time. We observe the existence of fast, downward flowing plumes that are able to transport hydrogen into close proximity to the helium-burning shell before burning takes place. The intershell in the 3D model is richer in protons than the 1D model by several orders of magnitude and so we obtain substantially higher hydrogen-burning luminosities-over 10{sup 8} L{sub Sun} in the high-resolution simulation-than are found in the 1D model. Convective velocities in these simulations are over ten times greater than the predictions of mixing length theory, though the 3D simulations have greater energy generation due to the enhanced hydrogen burning. We find no evidence of the convective zone splitting into two, though this could be as a result of insufficient spatial resolution or because the models have not been evolved for long enough. We suggest that the 1D mixing length theory and particularly the use of a diffusion algorithm for mixing do not give an accurate picture of these events. An advective mixing scheme may give a better representation of the transport processes seen in the 3D models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Quantum critical behavior in three-dimensional one-band Hubbard model at half-filling

A one-band Hubbard model with hopping parameter t and Coulomb repulsion U is considered at half-filling. By means of the Schwinger bosons and slave fermions representation of the electron operators and integrating out the spin–singlet Fermi fields an effective Heisenberg model with antiferromagnetic exchange constant is obtained for vectors which identifies the local orientation of the spin of the itinerant electrons. The amplitude of the spin vectors is an effective spin of the itinerant electrons accounting for the fact that some sites, in the ground state, are doubly occupied or empty. Accounting adequately for the magnon–magnon interaction the Néel temperature is calculated. When the ratio t/U is small enough (t/U ≤0.09) the effective model describes a system of localized electrons. Increasing the ratio increases the density of doubly occupied states which in turn decreases the effective spin and Néel temperature. The phase diagram in the plane of temperature (T{sub N})/U and parameter t/U is presented. The quantum critical point (T{sub N}=0) is reached at t/U =0.9. The magnons in the paramagnetic phase are studied and the contribution of the magnons’ fluctuations to the heat capacity is calculated. At the Néel temperature the heat capacity has a peak which is suppressed when the system approaches a quantum critical point. It is important to stress that, at half-filling, the ground state, determined by fermions, is antiferromagnetic. The magnon fluctuations drive the system to quantum criticality and when the effective spin is critically small these fluctuations suppress the magnetic order. -- Highlights: •Technique of calculation is introduced which permits us to study the magnons’ fluctuations. •Quantum critical point is obtained in the one-band 3D Hubbard model at half-filling. •The present analytical results supplement the numerical ones (see Fig. 7)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

TH-C-12A-11: Target Correlation of a 3D Surface Surrogate for Left Breast Irradiation Using the Respiratory-Gated Deep-Inspiration Breath-Hold Technique

Purpose: To evaluate the use of 3D optical surface imaging as a new surrogate for respiratory motion gated deep-inspiration breath-hold (DIBH) technique for left breast cancer patients. Methods: Patients with left-sided breast cancer after lumpectomy or mastectomy were selected as candidates for DIBH technique for their external beam radiation therapy. Treatment plans were created on both free breathing (FB) and DIBH CTs to determine whether DIBH was beneficial in reducing heart doses. The Real-time Position Management (RPM) system was used to acquire patient's breathing trace during DIBH CT acquisition and treatment delivery. The reference 3D surface models from FB and DIBH CTs were generated and transferred to the “AlignRT” system for patient positioning and real-time treatment monitoring. MV Cine images were acquired for each beam as quality assurance for intra-fractional position verification. The chest wall excursions measured on these images were used to define the actual target position during treatment, and to investigate the accuracy and reproducibility of RPM and AlignRT. Results: Reduction in heart dose can be achieved for left-sided breast patients using DIBH. Results showed that RPM has poor correlation with target position, as determined by the MV Cine imaging. This indicates that RPM may not be an adequate surrogate in defining the breath-hold level when used alone. Alternatively, the AlignRT surface imaging demonstrated a better correlation with the actual CW excursion during DIBH. Both the vertical and magnitude real-time deltas (RTDs) reported by AlignRT can be used as the gating parameter, with a recommend threshold of ±3 mm and 5 mm, respectively. Conclusion: 3D optical surface imaging serves as a superior target surrogate for the left breast treatment when compared to RPM. Working together with the realtime MV Cine imaging, they ensure accurate patient setup and dose delivery, while minimizing the imaging dose to patients.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2012

A Multi-Methods Approach to HRA and Human Performance Modeling: A Field Assessment

The Advanced Test Reactor (ATR) is a research reactor at the Idaho National Laboratory is primarily designed and used to test materials to be used in other, larger-scale and prototype reactors. The reactor offers various specialized systems and allows certain experiments to be run at their own temperature and pressure. The ATR Canal temporarily stores completed experiments and used fuel. It also has facilities to conduct underwater operations such as experiment examination or removal. In reviewing the ATR safety basis, a number of concerns were identified involving the ATR canal. A brief study identified ergonomic issues involving the manual handling of fuel elements in the canal that may increase the probability of human error and possible unwanted acute physical outcomes to the operator. In response to this concern, that refined the previous HRA scoping analysis by determining the probability of the inadvertent exposure of a fuel element to the air during fuel movement and inspection was conducted. The HRA analysis employed the SPAR-H method and was supplemented by information gained from a detailed analysis of the fuel inspection and transfer tasks. This latter analysis included ergonomics, work cycles, task duration, and workload imposed by tool and workplace characteristics, personal protective clothing, and operational practices that have the potential to increase physical and mental workload. Part of this analysis consisted of NASA-TLX analyses, combined with operational sequence analysis, computational human performance analysis (CHPA), and 3D graphical modeling to determine task failures and precursors to such failures that have safety implications. Experience in applying multiple analysis techniques in support of HRA methods is discussed.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRSDate not supplied

Towards Surrogate Modeling of Subgrid Turbulent Transport for 3D Radiative Hydrodynamic Simulations of the Quiet Sun

In this work, we investigate the use of deep learn-ing techniques as surrogate models, to enhance the estimationof effects of subgrid turbulent transport for 3D radiatuve hy-drodynamic simulations of the quiet Sun. We develop two dis-tinct 3D Convolutional Neural Networks (3DCNNs) to capturespatio-temporal dependencies in 3D velocity fields, leveragingdifferent activation functions and architectural designs. Thesemodels integrate both averaged velocity vector components andscalar features such as plasma density to enhance predictionaccuracy. Additionally, a Multilayer Perceptron (MLP) modelis employed to approximate complex nonlinear relationships,offering a comparison in performance between convolutionaland fully connected architectures. Logarithmic transformationis applied to the targets to handle heavily skewed data, im-proving model performance. All models are compared againsta physics-based Gradient Model. Results show that the 3DCNNmodels excel at approximating Reynolds stress tensors, makingthem a candidate for assisting in producing reduced resolutionsimulations, and thereby reducing computational overheadwhile maintaining higher accuracy than the baseline. Thesefindings demonstrate the potential of deep learning, particu-larly CNNs, to advance scalable and accurate simulations ofsolar dynamics, offering a promising alternative to traditionalturbulence models.

Heliophysics↗
DOE OSTI2013

Finite size effects in L1{sub o}-FePt nanoparticles

Finite size effects on the temperature dependence of the uniaxial magnetic anisotropy, longitudinal and transverse susceptibilities and specific heat are examined for L1{sub o}-ordered FePt nanoparticles using an atomistic model based on an effective classical spin Hamiltonian. At low temperatures below criticality, we study the intrinsic uniaxial magnetic anisotropy energy (MAE) K{sub 1} and its scaling with magnetization K{sub 1}(T)∼M{sub s}(T){sup δ} and using Langevin dynamics simulations we show that the dependence of the exponent δ on the size L and aspect ratio of the grain arises from decomposition of the MAE into bulk and surface dependent terms. Monte Carlo simulations in the critical regime near the Curie temperature T{sub c}, show that the temperature variation of the specific heat and longitudinal susceptibility is given by finite size scaling relations c=L{sup α/ν}c{sup ~}(L{sup 1/ν}ϵ) and χ=L{sup γ/ν}χ{sup ~}(L{sup 1/ν}ϵ), respectively, where ϵ=(T−T{sub c})/T{sub c} is the reduced temperature, and the susceptibility scaling function χ{sup ~} can be approximated by a Lorentzian. Our estimates of the critical exponents α,γ, and ν appear to be in agreement with the universality class of the 3D Ising model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗