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Failure In Internally Pressurized Bent Tubes, Robin Stevenson, Boon-Chai Ng, Peter Polidoro
Failure In Internally Pressurized Bent Tubes, Robin Stevenson, Boon-Chai Ng, Peter Polidoro
Faculty Publications
The analysis and modeling of tube-hydroformed components is more complicated than that employed for sheet-metal panels, due to the lengthier process sequence and variable strain path - from flat-rolled sheet to tube; from straight tube to bent tube; and from bent tube to hydroformed component. These additional process steps make it difficult to determine whether post mortem analyses of tube failure during hydroforming can, and should, be conducted with the same tools and databases as used for simple stampings. To provide a partial answer, the properties of commercially fabricated welded straight tubes were evaluated using a free-expansion internal pressure test …
The Effect Of Gas Pressure On No Conversion Energy Efficiency In Nonthermal Nitrogen Plasma, Morris D. Argyle, Gui-Bing Zhao, S.V.B. Janardhan Garikipati, Xudong Hu, Maciej Radosz
The Effect Of Gas Pressure On No Conversion Energy Efficiency In Nonthermal Nitrogen Plasma, Morris D. Argyle, Gui-Bing Zhao, S.V.B. Janardhan Garikipati, Xudong Hu, Maciej Radosz
Faculty Publications
This work explores the effect of gas pressure on the rate of electron collision reactions and energy consumption for NO conversion in N2 in a pulsed corona discharge reactor. A previous study showed that the rate constant of electron collision reactions, multiplied by the electron concentration, can be expressed as k[e] = βα−0.5P−0.5W0.75exp(−αP/W). The model parameter α remains constant with increasing gas pressure, which verifies the previous assumption that the electron temperature is inversely proportional to gas pressure. However, the model parameter β decreases with increasing gas pressure, which indicates that the rate constant of electron collision reactions decreases with …
Kalman Consensus Strategies And Their Application To Cooperative Control, Randal Beard, Derek Kingston, Wei Ren
Kalman Consensus Strategies And Their Application To Cooperative Control, Randal Beard, Derek Kingston, Wei Ren
Faculty Publications
Sponsorship: AFOSR, NSF. In this paper, we propose discrete-time and continuous-time consensus update schemes motivated by the discrete-time and continuous-time Kalman filters. With certainty information encoded into each agent, the proposed consensus schemes explicitly account for relative confidence in the information that is communicated from each agent in the team. We show mild sufficient conditions under which consensus can be achieved using the proposed schemes in the presence of switching interaction topologies. The Kalman consensus scheme is shown to be input-to-state stable. We show how to exploit this fact in multi-agent cooperative control scenarios.
Coordination Variables And Consensus Building In Multiple Vehicle Systems, Tim Mclain
Coordination Variables And Consensus Building In Multiple Vehicle Systems, Tim Mclain
Faculty Publications
Much of the research focus in the cooperative control community has been on formation control problems. This focus may be due to the fact that the group control problem can be reduced to well-established single-agent control problems by employing a leader-follower type control strategy. For example, single-agent path planning and trajectory generation techniques can be employed for the leader, and conventional trajectory tracking strategies can be employed for the followers. Indeed, formation control problems are much like linear systems theory: we search where the light is the brightest. It can be argued that formation control problems are the simplest type …
Evaluation Of Bus And Truck Automation Operations Concepts, H.-S. Jacob Tsao, Lan Zhang, Lin Lin, Deepa Batni
Evaluation Of Bus And Truck Automation Operations Concepts, H.-S. Jacob Tsao, Lan Zhang, Lin Lin, Deepa Batni
Faculty Publications
Traffic congestion will continue to worsen and likely worsen at a faster rate than ever. People throughput and freight throughput have become critical issues for California and the rest of the nation. PATH has funded with approximately $125K a research project entitled “Evaluation of Bus and Truck Automation Scenarios” jointly proposed by Jan Botha (Principal Investigator) of Department of Civil and Environmental Engineering and Jacob Tsao (Co-PI) of Department of Industrial and Systems Engineering at San Jose State University. This report summarizes the major findings of the research conducted by Professor Tsao and his assistants with approximately $44K out of …
A Review Of Antennas And Propagation For Mimo Wireless Communications, Michael A. Jensen, Jon W. Wallace
A Review Of Antennas And Propagation For Mimo Wireless Communications, Michael A. Jensen, Jon W. Wallace
Faculty Publications
Multiple-input-multiple-output (MIMO) wireless systems use multiple antenna elements at transmit and receive to offer improved capacity over single antenna topologies in multipath channels. In such systems, the antenna properties as well as the multipath channel characteristics play a key role in determining communication performance. This paper reviews recent research findings concerning antennas and propagation in MIMO systems. Issues considered include channel capacity computation, channel measurement and modeling approaches, and the impact of antenna element properties and array configuration on system performance. Throughout the discussion, outstanding research questions in these areas are highlighted.
Integrated Optical Waveguides With Liquid Cores, Aaron R. Hawkins, John P. Barber, Dongliang Yin, D. W. Deamer, Holger Schmidt
Integrated Optical Waveguides With Liquid Cores, Aaron R. Hawkins, John P. Barber, Dongliang Yin, D. W. Deamer, Holger Schmidt
Faculty Publications
We report the design, fabrication, and demonstration of single-mode integrated optical waveguides with liquid cores. The principle of the device is based on antiresonant reflecting optical (ARROW) waveguides with hollow cores. We describe design principles for waveguide loss optimization down to 0.1/cm. Using a fabrication process based on conventional silicon microfabrication and sacrificial core layers, waveguides of varying widths and lengths with volumes covering the pico- to nanoliter range were fabricated. We observe confined mode propagation, measure waveguide losses of 2.4/cm, and demonstrate that the waveguides possess tailorable wavelength selectivity. The potential for highly integrated, sensitive devices based on these …
Semi-Autonomous Human-Uav Interfaces For Fixed-Wing Mini-Uavs, Randal Beard, Michael A. Goodrich, Morgan Quigley
Semi-Autonomous Human-Uav Interfaces For Fixed-Wing Mini-Uavs, Randal Beard, Michael A. Goodrich, Morgan Quigley
Faculty Publications
Sponsorship: DARPA, AFOSR. We present several human-robot interfaces that support real-time control of a small semi-autonomous UAV. These interfaces are designed for searching tasks and other missions that typically do not have a precise predetermined flight plan. We present a detailed analysis of a PDA interface and describe how our other interfaces relate to this analysis. We then offer quantative and qualitative performance comparisons of the interfaces, as well as an analysis of their possible real-world applications.
Wind Speed Effect On L-Band Brightness Temperature Inferred From Eurostarrs And Wise 2001 Field Experiments, David G. Long, Jacqueline Etcheto, Emmanuel P. Dinnat, Jacqueline Boutin, Adriano Camps, Stephanie Contardo, J. Wesson, Jordi Font, J. Miller
Wind Speed Effect On L-Band Brightness Temperature Inferred From Eurostarrs And Wise 2001 Field Experiments, David G. Long, Jacqueline Etcheto, Emmanuel P. Dinnat, Jacqueline Boutin, Adriano Camps, Stephanie Contardo, J. Wesson, Jordi Font, J. Miller
Faculty Publications
The results from two field experiments in the Mediterranean Sea are used to study the wind speed dependence of brightness temperature at L-band. During the EuroSTARRS airborne experiment, an L-band radiometer made measurements across a large wind speed gradient, enabling us to study this dependence at high wind speed. We compare our results with a two-scale emissivity model using several representations of the sea state spectrum. While the results are encouraging, unfortunately the accuracy of the measurements does not permit us to distinguish between the so-called twice Durden and Vesecky spectrum and the Elfouhaily spectrum above 7 m X s-1. …
Electromagnetic Bias At Off-Nadir Incidence Angles, David V. Arnold, Floyd W. Millet, Karl F. Warnick
Electromagnetic Bias At Off-Nadir Incidence Angles, David V. Arnold, Floyd W. Millet, Karl F. Warnick
Faculty Publications
Sponsorship: JPL Subcontract 961461. Nadir and off-nadir measurements of electromagnetic (EM) bias measurements are presented and compared with an off-nadir bias model. Measurements of the bias were made during the BYU Off-Nadir Experiment (Y-ONE) in the months of March and April, 2003. Using radar measurements of the surface and backscattered power, the EM bias was computed at angles from nadir to 17º degrees. Simultaneous surface measurements from a laser rangefinder provide accurate measurements of the long wave surface parameters. An off-nadir bias model incorporating the effects of hydrodynamic modulation of short waves and tilt modulation of long waves is developed …
Every Polynomial-Time 1-Degree Collapses If And Only If P=Pspace, Stephen A. Fenner, Stuart A. Kurtz, James S. Royer
Every Polynomial-Time 1-Degree Collapses If And Only If P=Pspace, Stephen A. Fenner, Stuart A. Kurtz, James S. Royer
Faculty Publications
No abstract provided.
Detection Of Configuration Memory Upsets Causing Persistent Errors In Sram-Based Fpgas, D. Eric Johnson, Keith S. Morgan, Michael J. Wirthlin, Michael P. Caffrey, Paul S. Graham
Detection Of Configuration Memory Upsets Causing Persistent Errors In Sram-Based Fpgas, D. Eric Johnson, Keith S. Morgan, Michael J. Wirthlin, Michael P. Caffrey, Paul S. Graham
Faculty Publications
Sponsorship: Los Alamos National Laboratory. FPGA designers are becoming increasingly aware of fault tolerance issues in modern FPGA designs, especially designs destined for a radiation environment. We classify errors due to upsets within the configuration bitstream into two categories; namely, persistent and non-persistent. Persistent errors generally cannot be tolerated. However, non-persistent errors can be tolerated in certain types of designs as long as they are properly accounted for. We discuss situations in which non-persistent errors are acceptable, and describe a technique for the detection of upsets causing persistent errors within the configuration memor of an SRAM-based FPGA.
Optimal Sampling For Single-Tone Frequency Estimation, Travis E. Oliphant
Optimal Sampling For Single-Tone Frequency Estimation, Travis E. Oliphant
Faculty Publications
Single-tone frequency estimation from irregularly spaced samples is analyzed. The ratio of the Cramr-Rao Bound (CRB) for regularly spaced samples to the bound for irregularly spaced samples is presented and shown to be a globally convex function. It's minima and maxima over the domain of interest are identified which reveals that improvements in the CRB can be obtained using non-equally-spaced samples. For a given sampling density, the best estimates of frequency are obtained when half of the samples are taken at one end of the total available interval and the remaining samples are taken at the other end.
High Efficiency 90 Degree Silica Waveguide Bend Using An Air Hole Photonic Crystal Region, J. Cai, S. Kim, Gregory P. Nordin, J. Jiang
High Efficiency 90 Degree Silica Waveguide Bend Using An Air Hole Photonic Crystal Region, J. Cai, S. Kim, Gregory P. Nordin, J. Jiang
Faculty Publications
We propose the hybrid integration of an air hole photonic crystal (PhC) structure with a high (0.75%) single-mode silica waveguide to achieve an ultracompact high efficiency 90 bend for transverse-magnetic polarized light. Diffraction from the periodic boundary between the PhC and silica waveguide regions is shown to seriously degrade the optical efficiency of the bend. A microgenetic algorithm ( GA) combined with a two-dimensional finite-difference time-domain method is used to modify the PhC and its boundary layer to suppress this diffraction which in turn maximizes bend efficiency. The final optimized structure has a 99.4% bend efficiency at a wavelength of …
3d Analysis Of Hybrid Photonic Crystal/Conventional Waveguide 90° Bend, J. Cai, S. Kim, Gregory P. Nordin, J. Jiang
3d Analysis Of Hybrid Photonic Crystal/Conventional Waveguide 90° Bend, J. Cai, S. Kim, Gregory P. Nordin, J. Jiang
Faculty Publications
We present a three-dimensional (3D) analysis of a hybrid photonic crystal conventional waveguide 90° bend proposed previously [Opt. Express 10, 1334 (2002)] as an ultracompact component for large-scale planar lightwave circuit integration. Both rigorous 3D finite-difference time-domain modeling and a simple perfect mirror model analysis were carried out for different Si post heights in the photonic crystal region. Results show that the bend efficiency increases rapidly with Si post height. For a post height of 6.5 µm, this structure yields a bend efficiency of 97.3% at a wavelength of 1.55 µm for 90° bends in 2 µm X 2 µm …
Cavity Enhancement Of The Magneto-Optic Kerr Effect For Optical Studies Of Magnetic Nanostructures, Aaron R. Hawkins, N. Qureshi, Holger Schmidt
Cavity Enhancement Of The Magneto-Optic Kerr Effect For Optical Studies Of Magnetic Nanostructures, Aaron R. Hawkins, N. Qureshi, Holger Schmidt
Faculty Publications
We present a study of cavity enhancement of the magneto-optic Kerr effect using dielectric multilayers in order to facilitate optical studies of individual single-domain nanomagnets. We develop a transfer matrix theory to analyze Kerr rotation from an arbitrary number of possibly lossy dielectric layers. The combination of one lossless and one thin metallic layer is found to be most favorable for studying individual nanomagnets, providing the best tradeoff between signal enhancement and spatial resolution. Accounting for the microscopic surface structure, we find good agreement between theory and experiment. Using this technique, we demonstrate Kerr enhancements by a factor of more …
Synergetic Control Of Power Converters For Pulse Current Charging Of Advanced Batteries From A Fuel Cell Power Source, Zhenhua Jiang, Roger A. Dougal
Synergetic Control Of Power Converters For Pulse Current Charging Of Advanced Batteries From A Fuel Cell Power Source, Zhenhua Jiang, Roger A. Dougal
Faculty Publications
This paper presents a synergetic controller for pulse current charging of advanced batteries from a fuel cell power source. Pulse current charging protocol that has been shown to have many advantages over the traditional constant current/constant voltage protocol is applied in a fuel cell powered battery-charging station to reduce the total charging time. Strong nonlinearity and dynamics exist in such systems. In this paper, the synergetic control approach is applied to regulate the buck converters that control the pulse charging currents to the many batteries. A practical synergetic controller to coordinate pulse current charging of the battery is synthesized and …
Simultaneous Wind And Rain Retrieval Using Seawinds Data, David G. Long, David W. Draper
Simultaneous Wind And Rain Retrieval Using Seawinds Data, David G. Long, David W. Draper
Faculty Publications
The SeaWinds scatterometers onboard the QuikSCAT and the Advanced Earth Observing Satellite 2 measure ocean winds on a global scale via the relationship between the normalized radar backscattering cross section of the ocean and the vector wind. The current wind retrieval method ignores scattering and attenuation of ocean rain, which alter backscatter measurements and corrupt retrieved winds. Using a simple rain backscatter and attenuation model, two methods of improving wind estimation in the presence of rain are evaluated. First, if no suitable prior knowledge of the rain rate is available, a maximum-likelihood estimation technique is used to simultaneously retrieve the …
New Stereology For The Recovery Of Grain-Boundary Plane Distributions In The Crystal Frame, Brent L. Adams, Ryan J. Larsen
New Stereology For The Recovery Of Grain-Boundary Plane Distributions In The Crystal Frame, Brent L. Adams, Ryan J. Larsen
Faculty Publications
One of the authors (RJL) is grateful to the Office of Naval Research for fellowship support. BLA acknowledges the support of the NSF through the Materials Research Science and Engineering Center, Carnegie Mellon University (Grant No. DMR-0079996). A new experimental method is given for recovering the probability-distribution function Sv(ns/g). The function Sv(na/g) is the grain-boundary area per unit volume as a function of grain-boundary plane orientation (na), given a lattice misorientation (g) between the adjoining grains. The grain-boundary normal (na) is expressed in the crystal frame in which the misorientation g originates. The proposed method recovers the three-dimensional Sv(na/g) function …
Measuring The Five-Parameter Grain-Boundary Distribution From Observations Of Planar Sections, Brent L. Adams, Bassem S. El-Dasher, Gregory S. Rohrer, David M. Saylor
Measuring The Five-Parameter Grain-Boundary Distribution From Observations Of Planar Sections, Brent L. Adams, Bassem S. El-Dasher, Gregory S. Rohrer, David M. Saylor
Faculty Publications
One of the authors (DMS) thanks his colleagues at NIST, Edwin R. Fuller, Jr. and Grady S. White, for their helpful advice and criticisms, as well as Mark D. Vaudin and James A. Warren for their critical review of this manuscript. This work was supported at CMU by the MRSEC program of the National Science Foundation under Award No. DMR-0079996. A sterological method is described for estimating the distribution of grain-boundary types in poly-crystalline materials on the basis of observations from a single planar section. The grain-boundary distribution is expressed in terms of five macroscopically observable parameters that include: three …
Automatic Detection And Validity Of The Sea-Ice Edge: An Application Of Enhanced-Resolution Quikscat/Seawinds Data, David G. Long, Jorg Haarpaintner, Rasmus T. Tonboe, Michael L. Van Woert
Automatic Detection And Validity Of The Sea-Ice Edge: An Application Of Enhanced-Resolution Quikscat/Seawinds Data, David G. Long, Jorg Haarpaintner, Rasmus T. Tonboe, Michael L. Van Woert
Faculty Publications
Sea-ice edge detection is an essential task at the different national ice services to secure navigation in ice-covered seas. Comparison between the Remund and Long ice mask image from enhanced-resolution QuikScat/SeaWinds (QS) products and the analyzed ice edge from high-resolution RADARSAT synthetic aperture radar has shown that the automatically determined QS ice mask underestimates the Arctic ice extent. QS data was statistically analyzed by colocating the data with ice charts around Greenland and with the National Aeronautics and Space Administration Team's Special Sensor Microwave/Imager (SSM/I) ice concentration algorithm over the whole Arctic region. All variables, i.e., the backscatter in vertical …
Mutual Coupling In Mimo Wireless Systems: A Rigorous Network Theory Analysis, Michael A. Jensen, Jon W. Wallace
Mutual Coupling In Mimo Wireless Systems: A Rigorous Network Theory Analysis, Michael A. Jensen, Jon W. Wallace
Faculty Publications
A new framework for the analysis of multiple-input multiple-output (MIMO) wireless systems is introduced to account for mutual coupling effects in the antenna arrays. The multiport interactions at transmit and receive are characterized by representing the channel using a scattering parameter matrix. A new power constraint that limits the average radiated power is also introduced. The capacity of the MIMO system with mutual coupling is defined as the maximum mutual information of the transmit and receive vectors over all possible transmit signaling and receive loading. Full-wave electromagnetic antenna simulations combined with a simple path-based channel model are used to demonstrate …
Description And Assessment Of A Business Plan Competition And New Venture Fair At San José State University, Malu Roldan, Asbjorn Osland, Michael Solt, Burton Dean
Description And Assessment Of A Business Plan Competition And New Venture Fair At San José State University, Malu Roldan, Asbjorn Osland, Michael Solt, Burton Dean
Faculty Publications
After the first business plan competition, in May 2003, San José State University (SJSU) faculty and community entrepreneurs serving on the university’s Silicon Valley Center for Entrepreneurship (SVCE) concluded that the process should be spread over an academic year. Hence, the New Venture Fair (NVF) was born, which was held Dec. 16, 2003. The feedback from all sources has been very positive regarding the NVF. A significant NVF exhibit was the Hewlett Packard Mobile Computing Grant (HPMCG). All teams completed projects that were impressive to most observers from the university and greater community but additional lessons were learned that will …
Use Of Collaborative Learning Exercises To Increase Student Motivation And Learning In An Introduction To Materials Engineering Course, Stacy Gleixner, Hilary Lackritz
Use Of Collaborative Learning Exercises To Increase Student Motivation And Learning In An Introduction To Materials Engineering Course, Stacy Gleixner, Hilary Lackritz
Faculty Publications
A collection of collaborative, in-class exercises have been designed for use in a freshmen/sophomore level Introduction to Materials Science and Engineering class. The activities are team based problems that include open ended design problems, calculation questions, and thought problems on unanswered research questions. The activities have been designed with the goal of having one or two a week embedded in a more traditional lecture setting. The exercises relate to the topics covered in most standard Introduction to Materials classes (crystal structure, mechanical properties, polymers, phase diagrams…). Each activity is designed specifically to engage the students in the lecture and excite …
Autostereoscopic 3d Display Based On Micromirror Array, Gregory P. Nordin, C. H. Ahn, H. J. Cho, S. T. Kowel, J. H. Kulick, J. Yan
Autostereoscopic 3d Display Based On Micromirror Array, Gregory P. Nordin, C. H. Ahn, H. J. Cho, S. T. Kowel, J. H. Kulick, J. Yan
Faculty Publications
A novel approach for three-dimensional (3-D) display systems implemented with a micromirror array was proposed, designed, realized, and tested. The major advantages of this approach include the following: 1 micromirrors are reflective and hence achromatic (panchromatic), 2 a wide variety of displays can be used as image sources, and 3 time multiplexing can be introduced on top of space multiplexing to optimize the viewing zone arrangements. A two-view (left and right) 3-D autostereoscopic display system was first constructed. Left- and right-eye views in the forms of both still and motion 3-D scenes were displayed, and viewers were able to fuse …
Response To Comments On “Passivity-Based Control Of Saturated Induction Motors”, Levent U. Gökdere, Marwan A. Simaan, Charles W. Brice
Response To Comments On “Passivity-Based Control Of Saturated Induction Motors”, Levent U. Gökdere, Marwan A. Simaan, Charles W. Brice
Faculty Publications
Contrary to the claims made in the comments to our paper, the passivity-based controller developed for induction motors has already been tested on the same demanding trajectories used for the input–output linearization controller. The experimental results show that the passivitybased controller provides closer tracking of the same mechanical trajectory, when compared with the input–output linearization controller.
Growth And Transport Properties Of Complementary Germanium Nanowire Field Effect Transistors, Andrew B. Greytak, Lincoln J. Lauhon, Mark S. Gudiksen, Charles M. Lieber
Growth And Transport Properties Of Complementary Germanium Nanowire Field Effect Transistors, Andrew B. Greytak, Lincoln J. Lauhon, Mark S. Gudiksen, Charles M. Lieber
Faculty Publications
n- and p-type Ge nanowires were synthesized by a multistep process in which axial elongation, via vapor–liquid–solid (VLS) growth, and doping were accomplished in separate chemical vapor deposition steps. Intrinsic, single-crystal, Ge nanowires prepared by Au nanocluster-mediated VLS growth were surface-doped in situ using diborane or phosphine, and then radial growth of an epitaxial Ge shell was used to cap the dopant layer. Field-effect transistors prepared from these Ge nanowires exhibited on currents and transconductances up to 850 µA/µm and 4.9 µA/V, respectively, with device yields of >85%.
Control Strategies For Active Power Sharing In A Fuel-Cell-Powered Battery-Charging Station, Zhenhua Jiang, Roger A. Dougal
Control Strategies For Active Power Sharing In A Fuel-Cell-Powered Battery-Charging Station, Zhenhua Jiang, Roger A. Dougal
Faculty Publications
This paper presents an effective system design for a fuel-cell-powered battery-charging station and three control strategies for active power sharing among the batteries. This battery-charging station allows multiple batteries to be simultaneously charged. Three control strategies were investigated to coordinate the active power distribution among the battery-charging branches. The baseline control strategy Was equal rate charging. Two advanced control strategies, proportional rate charging and pulse current charging, were compared to the baseline strategy. These control strategies were realized in MaTLaB/Simulink, and the current and voltage regulations were implemented using the classical proportional-integral control approach. The system simulation was conducted in …
Noble Metal Nanostructures Synthesized Inside Mesoporous Nanotemplate Pores, J. Arbiol, E. Rossinyol, A. Cabot, F. Peiro, A. Cornet, J. R. Morante, Fanglin Chen, Meilin Liu
Noble Metal Nanostructures Synthesized Inside Mesoporous Nanotemplate Pores, J. Arbiol, E. Rossinyol, A. Cabot, F. Peiro, A. Cornet, J. R. Morante, Fanglin Chen, Meilin Liu
Faculty Publications
Noble metal impregnation has resulted in the inclusion of metal nanostructures within the SBA-15 mesoporous silica hexagonal pores (from nanoclusters to nanowires). A bright-field transmission electron microscopy three-dimensional reconstruction is proposed to analyze the localization of nanostructures within the pores of mesoporous nanotemplates. The method allows corroboration whether the nanostructures are synthesized inside the pores or they are synthesized alternatively on the nanotemplate aggregates exterior surface.
Gradient-Based Non-Linear Microstructure Design, Brent L. Adams, M. Lyon
Gradient-Based Non-Linear Microstructure Design, Brent L. Adams, M. Lyon
Faculty Publications
The support of this research by the Army Research Office is gratefully acknowledged. M. Lyon is supported by a National Science Foundation Graduate Research Fellowship. Fourier analysis is implemented on the orientation distribution of a polycrystalline microstructure. The linearity and convexity of the Fourier space, with respect to orientation, allows one to consider all possible distributions by considering all linear combinations of single-grain orientations. The limits of the Fourier space are therefore defined by the solutions to a set of linear programming problems. A unique approach to the linear programming, similar to the Krylov subspace methods for obtaining solutions to …