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At least 1,405 records · Page 78

What does Reflection from Cloud Sides tell us about Vertical Distribution of Cloud Droplet Sizes?

Cloud development, the onset of precipitation and the effect of aerosol on clouds depend on the structure of the cloud profiles of droplet size and phase. Aircraft measurements of cloud profiles are limited in their temporal and spatial extent. Satellites were used to observe cloud tops not cloud profiles with vertical profiles of precipitation-sized droplets anticipated from CloudSat. The recently proposed CLAIM-3D satellite mission (cloud aerosol interaction mission in 3-D) suggests to measure profiles of cloud microphysical properties by retrieving them from the solar and infrared radiation reflected or emitted from cloud sides. Inversion of measurements from the cloud sides requires rigorous understanding of the 3-dimentional(3-D) properties of clouds. Here we discuss the reflected sunlight from the cloud sides and top at two wavelengths: one nonabsorbing to solar radiation (0.67 microns) and one with liquid water efficient absorption of solar radiation (2.1 microns). In contrast to the plane-parallel approximation, a conventional approach to all current operational retrievals, 3-D radiative transfer is used for interpreting the observed reflectances. General properties of the radiation reflected from the sides of an isolated cloud are discussed. As a proof of concept, the paper shows a few examples of radiation reflected from cloud fields generated by a simple stochastic cloud model with the prescribed vertically resolved microphysics. To retrieve the information about droplet sizes, we propose to use the probability density function of the droplet size distribution and its first two moments instead of the assumption about fixed values of the droplet effective radius. The retrieval algorithm is based on the Bayesian theorem that combines prior information about cloud structure and microphysics with radiative transfer calculations.

Marshak, A.↗

Parallelized Carbon Oxidation and Surface Recession Model in Direct-Simulation Monte Carlo Code, SPARTA

Ablative thermal protection system (TPS) materials for spacecraft are composites that often consist of a carbon-based reinforcement and a polymeric matrix. During Earth re-entry, they endure high-temperature oxidation and surface recession. Oxidation is an important mechanism for ablation, sometimes leading to the weakening, spallation, or failure of the oxidized fibers at the surface and in the char layer. However, more details are required including accurate material properties of the fiber microstructure, whether the fibers recede homogenously or localized at pits, and the role of pyrolysis outgassing in order to evaluate the role oxidation plays in the degradation and failure mechanisms of these materials. In this work, we demonstrate a parallelizable oxidation-driven ablation model developed for detailed, large-scale simulations in the DSMC code SPARTA. We also develop robust algorithms which handle the conservation of the surface state after an ablation step. Finally, we verify our model for both simple and more complex chemistry as well as microstructures with reaction statistics, oxidation depth calculations, and detailed visualization of oxidation-induced material recession at the microscale.

V Arias↗

A Universal Formula for Extracting the Euler Angles

Recently, the authors completed a study of the Davenport angles, which are a generalization of the Euler angles for which the initial and final Euler axes need not be either mutually parallel or mutually perpendicular or even along the coordinate axes. During the conduct of that study, those authors discovered a relationship which can be used to compute straightforwardly the Euler angles characterizing a proper-orthogonal direction-cosine matrix for an arbitrary Euler-axis set satisfying n(sub 1) x n(sub 2) = 0 and n(sub 3) x n(sub 1) = 0, which is also satisfied by the more usual Euler angles we encounter commonly in the practice of Astronautics. Rather than leave that relationship hidden in an article with very different focus from the present Engineering note, we present it and the universal algorithm derived from it for extracting the Euler angles from the direction-cosine matrix here. We also offer literal "code" for performing the operations, numerical examples, and general considerations about the extraction of Euler angles which are not universally known, particularly, the treatment of statistical error.

Shuster, Malcolm D.↗

3-D CFD in a day - The laser digitizer project

The computation of airflow over complex configurations requires a complete description of the geometry. This can be obtained from CAD data, from blueprints, or from actual models. In any case, the time required is currently estimated at 4 to 6 months. It is proposed to shorten this time by a factor of 10 to 100 through the use of automated software, a fast, highly parallel computer and a three-dimensional laser digitizer. This device can provide (x,y,z) coordinates of surface points at rates exceeding 14,500/sec. Thus, it is possible to digitize an entire model in a few minutes. The accuracy of measurement on a flat white surface is better than 0.005 inches. Higher accuracy is available at higher cost. This work discusses the challenges which remain to be addressed. In particular, the surface point data need to be converted into a surface description, the surface description needs to be made into a surface grid, and the surface grid used to make a volume grid for the flow solver. Algorithms are kept in place or in mind for all of these problems. Integration of the more mature flow solution and visualization algorithms then allows generation of solution graphics directly from a wind tunnel model.

Merriam, Marshal↗

A Simple Tool for the Design and Analysis of Multiple-Reflector Antennas in a Multi-Disciplinary Environment

The process of designing and analyzing a multiple-reflector system has traditionally been time-intensive, requiring large amounts of both computational and human time. At many frequencies, a discrete approximation of the radiation integral may be used to model the system. The code which implements this physical optics (PO) algorithm was developed at the Jet Propulsion Laboratory. It analyzes systems of antennas in pairs, and for each pair, the analysis can be computationally time-consuming. Additionally, the antennas must be described using a local coordinate system for each antenna, which makes it difficult to integrate the design into a multi-disciplinary framework in which there is traditionally one global coordinate system, even before considering deforming the antenna as prescribed by external structural and/or thermal factors. Finally, setting up the code to correctly analyze all the antenna pairs in the system can take a fair amount of time, and introduces possible human error. The use of parallel computing to reduce the computational time required for the analysis of a given pair of antennas has been previously discussed. This paper focuses on the other problems mentioned above. It will present a methodology and examples of use of an automated tool that performs the analysis of a complete multiple-reflector system in an integrated multi-disciplinary environment (including CAD modeling, and structural and thermal analysis) at the click of a button. This tool, named MOD Tool (Millimeter-wave Optics Design Tool), has been designed and implemented as a distributed tool, with a client that runs almost identically on Unix, Mac, and Windows platforms, and a server that runs primarily on a Unix workstation and can interact with parallel supercomputers with simple instruction from the user interacting with the client.

Katz, Daniel S.↗

Applicability of the single equivalent point dipole model to represent a spatially distributed bio-electrical source

Although the single equivalent point dipole model has been used to represent well-localised bio-electrical sources, in realistic situations the source is distributed. Consequently, position estimates of point dipoles determined by inverse algorithms suffer from systematic error due to the non-exact applicability of the inverse model. In realistic situations, this systematic error cannot be avoided, a limitation that is independent of the complexity of the torso model used. This study quantitatively investigates the intrinsic limitations in the assignment of a location to the equivalent dipole due to distributed electrical source. To simulate arrhythmic activity in the heart, a model of a wave of depolarisation spreading from a focal source over the surface of a spherical shell is used. The activity is represented by a sequence of concentric belt sources (obtained by slicing the shell with a sequence of parallel plane pairs), with constant dipole moment per unit length (circumferentially) directed parallel to the propagation direction. The distributed source is represented by N dipoles at equal arc lengths along the belt. The sum of the dipole potentials is calculated at predefined electrode locations. The inverse problem involves finding a single equivalent point dipole that best reproduces the electrode potentials due to the distributed source. The inverse problem is implemented by minimising the chi2 per degree of freedom. It is found that the trajectory traced by the equivalent dipole is sensitive to the location of the spherical shell relative to the fixed electrodes. It is shown that this trajectory does not coincide with the sequence of geometrical centres of the consecutive belt sources. For distributed sources within a bounded spherical medium, displaced from the sphere's centre by 40% of the sphere's radius, it is found that the error in the equivalent dipole location varies from 3 to 20% for sources with size between 5 and 50% of the sphere's radius. Finally, a method is devised to obtain the size of the distributed source during the cardiac cycle.

NASA Discipline Cardiopulmonary↗

Precipitation from Space: Advancing Earth System Science

Of the three primary sources of spatially contiguous precipitation observations (surface networks, ground-based radar, and satellite-based radar/radiometers), only the last is a viable source over ocean and much of the Earth's land. As recently as 15 years ago, users needing quantitative detail of precipitation on anything under a monthly time scale relied upon products derived from geostationary satellite thermal infrared (IR) indices. The Special Sensor Microwave Imager (SSMI) passive microwave (PMW) imagers originated in 1987 and continue today with the SSMI sounder (SSMIS) sensor. The fortunate longevity of the joint National Aeronautics and Space Administration (NASA) and Japan Aerospace Exploration Agency (JAXA) Tropical Rainfall Measuring Mission (TRMM) is providing the environmental science community a nearly unbroken data record (as of April 2012, over 14 years) of tropical and sub-tropical precipitation processes. TRMM was originally conceived in the mid-1980s as a climate mission with relatively modest goals, including monthly averaged precipitation. TRMM data were quickly exploited for model data assimilation and, beginning in 1999 with the availability of near real time data, for tropical cyclone warnings. To overcome the intermittently spaced revisit from these and other low Earth-orbiting satellites, many methods to merge PMW-based precipitation data and geostationary satellite observations have been developed, such as the TRMM Multisatellite Precipitation Product and the Climate Prediction Center (CPC) morphing method (CMORPH. The purpose of this article is not to provide a survey or assessment of these and other satellite-based precipitation datasets, which are well summarized in several recent articles. Rather, the intent is to demonstrate how the availability and continuity of satellite-based precipitation data records is transforming the ways that scientific and societal issues related to precipitation are addressed, in ways that would not be otherwise possible. These developments have taken place in parallel with the growth of an increasingly interconnected scientific environment. Scientists from different disciplines can easily interact with each other via information and materials they encounter online, and collaborate remotely without ever meeting each other in person. Likewise, these precipitation datasets are quickly and easily available via various data portals and are widely used. Within the framework of the NASA/JAXA Global Precipitation Measurement (GPM mission, these applications will become increasingly interconnected. We emphasize that precipitation observations by themselves provide an incomplete picture of the state of the atmosphere. For example, it is unlikely that a richer understanding of the global water cycle will be possible by standalone missions and algorithms, but must also involve some component of data, where model analyses of the physical state are constrained alongside multiple observations (e.g., precipitation, evaporation, radiation). The next section provides examples extracted from the many applications that use various high-resolution precipitation products. The final section summarizes the future system for global precipitation processing.

Kucera, Paul A.↗

The Harmonic Linearized Navier-Stokes Equations for Transition Prediction in Three-Dimensional Flows

The conventional method to predict the onset of laminar-turbulent transition in convectively unstable boundary-layer flows is based on the logarithmic amplification ratio, the so-called N-factor, of the linear instability waves. To calculate the N-factor, the flow variables are decomposed into a laminar basic state solution and the linear disturbances, which are assumed to be harmonic in time. The most commonly used linear stability analysis approaches include the locally parallel linear stability theory (LST) and the nonlocal, weakly nonparallel parabolized stability equations (PSE). However, these methods do not account for strong streamwise gradients that are encountered in several configurations of interest, such as those in the vicinity of roughness elements, steps, gaps, or corners. To compute the linear evolution of disturbances along such strongly nonparallel regions, the harmonic linearized Navier-Stokes equations (HLNSE) need to be solved. The discretization of the HLNSE for spanwise/azimuthally inhomogeneous laminar basic states yields a linear system of complex arithmetic with a leading dimension of the order of 10^(7) to 10^(8) even in relatively simple flows. A combined multithread and multiprocessor algorithm is implemented for the direct solution of such linear systems. Results for a supersonic boundary layer over a three-dimensional roughness patch show good agreement with experimental measurements when the evolution of the instability waves over the roughness patch is included via the HLNSE. Additionally, inflow-resolvent analysis based on the HLNSE for discrete-roughness-induced disturbances in the nose tip of a blunt cone at Mach 6 demonstrates the importance of including the disturbance amplification along the near vicinity of the roughness element and separation region.

Boundary Layer Stability↗

Method of detecting system function by measuring frequency response

Real-time battery impedance spectrum is acquired using a one-time record. Fast Summation Transformation (FST) is a parallel method of acquiring a real-time battery impedance spectrum using a one-time record that enables battery diagnostics. An excitation current to a battery is a sum of equal amplitude sine waves of frequencies that are octave harmonics spread over a range of interest. A sample frequency is also octave and harmonically related to all frequencies in the sum. The time profile of this signal has a duration that is a few periods of the lowest frequency. The voltage response of the battery, average deleted, is the impedance of the battery in the time domain. Since the excitation frequencies are known and octave and harmonically related, a simple algorithm, FST, processes the time record by rectifying relative to the sine and cosine of each frequency. Another algorithm yields real and imaginary components for each frequency.

Morrison, John L.↗

Task scheduling in dataflow computer architectures

Dataflow computers provide a platform for the solution of a large class of computational problems, which includes digital signal processing and image processing. Many typical applications are represented by a set of tasks which can be repetitively executed in parallel as specified by an associated dataflow graph. Research in this area aims to model these architectures, develop scheduling procedures, and predict the transient and steady state performance. Researchers at NASA have created a model and developed associated software tools which are capable of analyzing a dataflow graph and predicting its runtime performance under various resource and timing constraints. These models and tools were extended and used in this work. Experiments using these tools revealed certain properties of such graphs that require further study. Specifically, the transient behavior at the beginning of the execution of a graph can have a significant effect on the steady state performance. Transformation and retiming of the application algorithm and its initial conditions can produce a different transient behavior and consequently different steady state performance. The effect of such transformations on the resource requirements or under resource constraints requires extensive study. Task scheduling to obtain maximum performance (based on user-defined criteria), or to satisfy a set of resource constraints, can also be significantly affected by a transformation of the application algorithm. Since task scheduling is performed by heuristic algorithms, further research is needed to determine if new scheduling heuristics can be developed that can exploit such transformations. This work has provided the initial development for further long-term research efforts. A simulation tool was completed to provide insight into the transient and steady state execution of a dataflow graph. A set of scheduling algorithms was completed which can operate in conjunction with the modeling and performance tools previously developed. Initial studies on the performance of these algorithms were done to examine the effects of application algorithm transformations as measured by such quantities as number of processors, time between outputs, time between input and output, communication time, and memory size.

Katsinis, Constantine↗

Implementation of Adaptive Digital Controllers on Programmable Logic Devices

Much has been made of the capabilities of FPGA's (Field Programmable Gate Arrays) in the hardware implementation of fast digital signal processing (DSP) functions. Such capability also makes and FPGA a suitable platform for the digital implementation of closed loop controllers. There are myriad advantages to utilizing an FPGA for discrete-time control functions which include the capability for reconfiguration when SRAM- based FPGA's are employed, fast parallel implementation of multiple control loops and implementations that can meet space level radiation tolerance in a compact form-factor. Other researchers have presented the notion that a second order digital filter with proportional-integral-derivative (PID) control functionality can be implemented in an FPGA. At Marshall Space Flight Center, the Control Electronics Group has been studying adaptive discrete-time control of motor driven actuator systems using digital signal processor (DSF) devices. Our goal is to create a fully digital, flight ready controller design that utilizes an FPGA for implementation of signal conditioning for control feedback signals, generation of commands to the controlled system, and hardware insertion of adaptive control algorithm approaches. While small form factor, commercial DSP devices are now available with event capture, data conversion, pulse width modulated outputs and communication peripherals, these devices are not currently available in designs and packages which meet space level radiation requirements. Meeting our goals requires alternative compact implementation of such functionality to withstand the harsh environment encountered on spacecraft. Radiation tolerant FPGA's are a feasible option for reaching these goals.

Gwaltney, David A.↗

NASA Tech Briefs, October 2011

Topics covered include: Laser Truss Sensor for Segmented Telescope Phasing; Qualifications of Bonding Process of Temperature Sensors to Deep-Space Missions; Optical Sensors for Monitoring Gamma and Neutron Radiation; Compliant Tactile Sensors; Cytometer on a Chip; Measuring Input Thresholds on an Existing Board; Scanning and Defocusing Properties of Microstrip Reflectarray Antennas; Cable Tester Box; Programmable Oscillator; Fault-Tolerant, Radiation-Hard DSP; Sub-Shot Noise Power Source for Microelectronics; Asynchronous Message Service Reference Implementation; Zero-Copy Objects System; Delay and Disruption Tolerant Networking MACHETE Model; Contact Graph Routing; Parallel Eclipse Project Checkout; Technique for Configuring an Actively Cooled Thermal Shield in a Flight System; Use of Additives to Improve Performance of Methyl Butyrate-Based Lithium-Ion Electrolytes; Li-Ion Cells Employing Electrolytes with Methyl Propionate and Ethyl Butyrate Co-Solvents; Improved Devices for Collecting Sweat for Chemical Analysis; Tissue Photolithography; Method for Impeding Degradation of Porous Silicon Structures; External Cooling Coupled to Reduced Extremity Pressure Device; A Zero-Gravity Cup for Drinking Beverages in Microgravity; Co-Flow Hollow Cathode Technology; Programmable Aperture with MEMS Microshutter Arrays; Polished Panel Optical Receiver for Simultaneous RF/Optical Telemetry with Large DSN Antennas; Adaptive System Modeling for Spacecraft Simulation; Lidar-Based Navigation Algorithm for Safe Lunar Landing; Tracking Object Existence From an Autonomous Patrol Vehicle; Rad-Hard, Miniaturized, Scalable, High-Voltage Switching Module for Power Applications; and Architecture for a 1-GHz Digital RADAR.

Source record↗

Biomimetic Fly Eye Sensor for Real-Time Target Tracking

The project objective is to design, build, and demonstrate a biomimetic (inspired by biology) smart sensor based on the common house fly eye for real-time target tracking in three dimensions (3-D). The sensor makes use of revolutionary optical sensor design resulting in significantly improved motion detection capabilities when compared with conventional optical sensors. The design is motivated by the parallel nature of the flys vision system and its demonstrated hyperacuity or precision of visual localization beyond the conventional resolution limit. This means that the sensor is able to accurately detect very fast motion and small changes in motion. The analog architecture of the sensor allows for real-time solution at adjustable bandwidths depending on the application. The low cost, exceptionally lightweight, small form factor, low power requirements, and low computation requirements of the sensor make it ideally suited to many aeronautics applications that have limitations on weight, power, and processing time. The sensor is modular and can be easily adapted in scale and manufactured for a wide variety of sensing applications. Advanced target tracking algorithms will be developed to allow the sensor to track a target in 3-D. These algorithms will be implemented in the smart sensors hardware to enable real-time target tracking.

wing position measurement system↗

Measurement of ultrasonic fields in transparent media using a scanning differential interferometer

An experimental system for the detection of three dimensional acoustic fields in optically transparent media using a dual beam differential interferometer is described. In this system, two coherent, parallel, focused laser beams are passed through the specimen and the interference fringe pattern which results when these beams are combined shifts linearly by an amount which is related to the optical pathlength difference between the two beams. It is shown that for small signals, the detector output is directly proportional to the amplitude of the acoustic field integrated along the optical beam path through the specimen. A water tank and motorized optical platform were constructed to allow these dual beams to be scanned through an ultrasonic field generated by a piezoelectric transducer at various distances from the transducer. Scan data for the near, Fresnel, and far zones of a uniform, circular transducer are presented and an algorithm for constructing the radial field profile from this integrated optical data, assuming cylindrical symmetry, is described.

Dockery, G. D.↗

Analysis, Simulation, and Verification of Knowledge-Based, Rule-Based, and Expert Systems

Mathematically sound techniques are used to view a knowledge-based system (KBS) as a set of processes executing in parallel and being enabled in response to specific rules being fired. The set of processes can be manipulated, examined, analyzed, and used in a simulation. The tool that embodies this technology may warn developers of errors in their rules, but may also highlight rules (or sets of rules) in the system that are underspecified (or overspecified) and need to be corrected for the KBS to operate as intended. The rules embodied in a KBS specify the allowed situations, events, and/or results of the system they describe. In that sense, they provide a very abstract specification of a system. The system is implemented through the combination of the system specification together with an appropriate inference engine, independent of the algorithm used in that inference engine. Viewing the rule base as a major component of the specification, and choosing an appropriate specification notation to represent it, reveals how additional power can be derived from an approach to the knowledge-base system that involves analysis, simulation, and verification. This innovative approach requires no special knowledge of the rules, and allows a general approach where standardized analysis, verification, simulation, and model checking techniques can be applied to the KBS.

Hinchey, Mike↗

Active control of fan noise from a turbofan engine

A three channel active control system is applied to an operational turbofan engine in order to reduce tonal noise produced by both the fan and high pressure compressor. The control approach is the feedforward filtered-x least-mean-square algorithm implemented on a digital signal processing board. Reference transducers mounted on the engine case provides blade passing and harmonics frequency information to the controller. Error information is provided by large area microphones placed in the acoustic far field. In order to minimize the error signal, the controller actuates loudspeakers mounted on the inlet to produce destructive interference. The sound pressure level of the fundamental tone of the fan was reduced using the three channel controller by up to 16 dB over a 60 deg angle about the engine axis. A single channel controller could produce reduction over a 30 deg angle. The experimental results show the control to be robust. Simultaneous control of two tones is done with parallel controllers. The fundamental and the first harmonic tones of the fan were controlled simultaneously with reductions of 12 dBA and 5 dBA, respectively, measured on the engine axis. Simultaneous control was also demonstrated for the fan fundamental and the high pressure compressor fundamental tones.

Thomas, Russell H.↗

A General-Purpose Optimization Engine for Multi-Disciplinary Design Applications

A general purpose optimization tool for multidisciplinary applications, which in the literature is known as COMETBOARDS, is being developed at NASA Lewis Research Center. The modular organization of COMETBOARDS includes several analyzers and state-of-the-art optimization algorithms along with their cascading strategy. The code structure allows quick integration of new analyzers and optimizers. The COMETBOARDS code reads input information from a number of data files, formulates a design as a set of multidisciplinary nonlinear programming problems, and then solves the resulting problems. COMETBOARDS can be used to solve a large problem which can be defined through multiple disciplines, each of which can be further broken down into several subproblems. Alternatively, a small portion of a large problem can be optimized in an effort to improve an existing system. Some of the other unique features of COMETBOARDS include design variable formulation, constraint formulation, subproblem coupling strategy, global scaling technique, analysis approximation, use of either sequential or parallel computational modes, and so forth. The special features and unique strengths of COMETBOARDS assist convergence and reduce the amount of CPU time used to solve the difficult optimization problems of aerospace industries. COMETBOARDS has been successfully used to solve a number of problems, including structural design of space station components, design of nozzle components of an air-breathing engine, configuration design of subsonic and supersonic aircraft, mixed flow turbofan engines, wave rotor topped engines, and so forth. This paper introduces the COMETBOARDS design tool and its versatility, which is illustrated by citing examples from structures, aircraft design, and air-breathing propulsion engine design.

Patnaik, Surya N.↗

ISSM: Ice Sheet System Model

In order to have the capability to use satellite data from its own missions to inform future sea-level rise projections, JPL needed a full-fledged ice-sheet/iceshelf flow model, capable of modeling the mass balance of Antarctica and Greenland into the near future. ISSM was developed with such a goal in mind, as a massively parallelized, multi-purpose finite-element framework dedicated to ice-sheet modeling. ISSM features unstructured meshes (Tria in 2D, and Penta in 3D) along with corresponding finite elements for both types of meshes. Each finite element can carry out diagnostic, prognostic, transient, thermal 3D, surface, and bed slope simulations. Anisotropic meshing enables adaptation of meshes to a certain metric, and the 2D Shelfy-Stream, 3D Blatter/Pattyn, and 3D Full-Stokes formulations capture the bulk of the ice-flow physics. These elements can be coupled together, based on the Arlequin method, so that on a large scale model such as Antarctica, each type of finite element is used in the most efficient manner. For each finite element referenced above, ISSM implements an adjoint. This adjoint can be used to carry out model inversions of unknown model parameters, typically ice rheology and basal drag at the ice/bedrock interface, using a metric such as the observed InSAR surface velocity. This data assimilation capability is crucial to allow spinning up of ice flow models using available satellite data. ISSM relies on the PETSc library for its vectors, matrices, and solvers. This allows ISSM to run efficiently on any parallel platform, whether shared or distrib- ISSM: Ice Sheet System Model NASA's Jet Propulsion Laboratory, Pasadena, California uted. It can run on the largest clusters, and is fully scalable. This allows ISSM to tackle models the size of continents. ISSM is embedded into MATLAB and Python, both open scientific platforms. This improves its outreach within the science community. It is entirely written in C/C++, which gives it flexibility in its design, and the power/speed that C/C++ allows. ISSM is svn (subversion) hosted, on a JPL repository, to facilitate its development and maintenance. ISSM can also model propagation of rifts using contact mechanics and mesh splitting, and can interface to the Dakota software. To carry out sensitivity analysis, mesh partitioning algorithms are available, based on the Scotch, Chaco, and Metis partitioners that ensure equal area mesh partitions can be done, which are then usable for sampling and local reliability methods.

Larour, Eric↗