L.D. Edmonds

L.D. Edmonds
California Institute of Technology | CIT · Jet Propulsion Laboratory

MA

About

110
Publications
42,343
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
1,336
Citations
Research Experience
March 1982 - December 2011
California Institute of Technology
Position
  • Radiation Effects Engineer

Publications

Publications (110)
Technical Report
Full-text available
There appears to be some controversy as to whether the twin paradox as explained by the special theory of relativity implies some inconsistency in the theory. My view is the more conventional view (more conventional but not shared by everyone) that there is no inconsistency. I wrote this paper to explain the understanding that I have. Nothing here...
Technical Report
Full-text available
The Cauchy-Schwarz inequality and triangle inequality are familiar in Euclidean spaces but are more complicated, because they have different forms under different conditions, when distances are defined by a pseudo-metric such as used in relativity. The form of these inequalities depends on whether or not two displacement vectors are "time-ordered"...
Technical Report
Full-text available
When searching the literature for a derivation of Noether’s theorem it is difficult, if not impossible, to find a derivation that is not a very cumbersome manipulation of variations. However, the theorem can also be derived from simple applications of well-known properties of partial derivatives without any mention of variations. Such a derivation...
Technical Report
Full-text available
Many members of the community require additional guidance when using the CREME96 computer code to calculate heavy-ion induced SEU rates. Recommendations are given. This appended version of an earlier report includes a new Section IV discussing multiple bit upsets.
Technical Report
Full-text available
This report derives inequalities relating a solution of one nonlinear Abel Equation to solutions of other nonlinear Abel Equations.
Technical Report
Full-text available
The theory finds a separable function, a product of the form Af(x)g(y), that is the best separable approximation of a given function H(x,y) when best approximation is defined to produce the global minimum of an error measure that has the basic form of an integral of a square error but has some flexibility by allowing the user to specify weight fact...
Technical Report
Full-text available
A variational method is derived for an Abel equation. The variational method is used to construct approximate solutions. Examples and numerical routines are given. Two kinds of error estimates are also given. One is a conservative estimate of function-value error and the other is the right-side error.
Article
This paper reports proton damage in LED and phototransistor of the Micropac 66296 optocoupler. Our results show that the optocoupler current transfer ratio (CTR) data are influenced by the gain of the phototransistor. Analysis of the test data reveals interesting information, such as the dependence of the phototransistor gain on irradiation and pho...
Article
A power MOSFET demonstrated destructive single-event effect (SEE) during ion irradiation in a switching circuit. Further investigation showed that the inductive load causing a spike in the drain-to-source voltage (V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DS</sub> ) that exceeded the manufactur...
Article
This paper reports the results of electron irradiations at various energies of the Samsung 8Gb single-level cell NAND flash memory. The percentage of bit errors from electron exposure are compared to results from 60Co total ionizing dose measurements. Electron irradiation at low energies (below 2 MeV) causes more bit upsets than 60Co gamma exposure...
Technical Report
Full-text available
The derivative of a volume integral that refers to a change in the region of integration is shown to be equal to a surface integral containing a surface velocity. Surface velocity is defined and equations are given for its calculation.
Technical Report
Full-text available
Interpretation of a confidence level in terms of outlier probability is given. The conditions for which passing a pass/fail acceptance test eliminates the need for a parametric acceptance test are identified.
Article
A recent model provides risk estimates for the deprogramming of initially programmed floating gates via prompt charge loss produced by an ionizing radiation environment. The environment can be a mixture of electrons, protons, and heavy ions. The model requires several input parameters. This paper extends the model to include TID effects in the cont...
Technical Report
Full-text available
The case considered is that in which the quality of some manufactured unit, such as an electronic part, is measured by some parameter that will be called the characterization parameter. Another parameter, called a specification limit, determines whether the unit is satisfactory. The unit is unsatisfactory if the characterization parameter exceeds t...
Technical Report
Full-text available
The case considered is that in which the quality of some manufactured unit, such as an electronic part, is measured by some parameter that will be called the characterization parameter. Another parameter, called a specification limit, determines whether the unit is satisfactory. The unit is unsatisfactory if the characterization parameter exceeds t...
Technical Report
Full-text available
A unit is any object that can be classified as either defective or not defective. A test sample contains m units and an application sample contains n units. This report derives a confidence level, corresponding to an observed count of x defects in the test sample, for the probability of the number of defects in the application sample being less tha...
Technical Report
Full-text available
The diffusion equation describes a variety of physical systems and one of the most frequently cited examples is the heat equation. The rate of heat flow through a boundary surface is an example of a diffusion current that is considered in this report. There are several methods for calculating a diffusion current through a boundary surface. One meth...
Technical Report
Full-text available
The hypergeometric distribution applies to the statistical sampling of a finite population when the sampling is done without replacement. Confidence levels for this distribution are derived in this report, rather than merely asserted, starting from first-principles. These first-principles are the fundamental concepts of probability that are discuss...
Technical Report
Full-text available
Since advancing technology has been producing smaller structures in electronic circuits, the floating gates in modern flash memories are becoming susceptible to prompt charge loss from ionizing radiation environments found in space. A method for estimating the risk of a charge-loss event is given.
Research
Full-text available
Some single-event effect (SEE) tolerant devices use circuitry designed so that a device error is a “dual-node” event. A given cell contains a pair of nodes with the property that a device error requires that each node simultaneously (i.e., from the same particle hit) collect some sufficient amount of charge. When measuring upset cross sections for...
Research
Full-text available
Devices hardened against single-event upset (SEU) via triple-modular redundancy (TMR) require unconventional methods for estimating system error rates in a space environment. We cannot simply integrate a cross section versus linear energy transfer (LET) curve with an environmental LET spectrum because “cross section” has a flux dependence. The stra...
Research
Full-text available
Discussions of confidence levels found in the literature, that are sufficiently rigorous to derive (rather than merely assert) quantitative results, use language and mathematical notation that can be overwhelming to someone that is not an expert in statistics. This report derives the same results using conventional calculus together with elementary...
Technical Report
Full-text available
Total ionizing dose (TID) estimates calculated for space missions, intended to represent the radiation environment that will be encountered by electronic devices used in a mission, usually select either Si or SiO2 as the reference material. Sometimes there is a need to know the amount of dose that the same environment would deposit in a different m...
Research
Full-text available
Discussions of confidence levels found in the literature, that are sufficiently rigorous to derive (rather than merely assert) quantitative results, use language and mathematical notation that can be overwhelming to someone that is not an expert in statistics. This report derives the same results using conventional calculus together with elementary...
Article
The results of recent Single Event Effect (SEE) testing of newly available power MOSFETs are presented.
Article
Transient capture measurements on an irradiated diode show the effect of increasing ion LET and varying strike location on transient current response. Significant modulation of the electrostatic potential in the device depletion region during and after the strike profoundly affects transient characteristics. The peak transient current tends to satu...
Conference Paper
The qualification efforts and results for three 24 bit analog-to-digital converters (ADCs) are presented. These devices demonstrate a noticeable advancement in radiation hardness for the technology with two of the devices exhibiting no Single-Event Latchup.
Article
Pulsed-laser induced charge-collection measurements in a bulk silicon diode are used to investigate charge collection mechanisms during high-level carrier generation conditions. The recently developed Ambipolar Diffusion with a Cutoff (ADC) model for charge collection is used to emphasize the significance of the carrier densities, electric fields,...
Article
Single event rates (SER) can include contributions from low-energy particles such that the linear energy transfer (LET) is not constant. Previous work found that the environmental description that is most relevant to the low-energy contribution to the rate is a “stopping rate per unit volume” even when the physical mechanisms for a single-event eff...
Article
Full-text available
The ADC charge-collection model was derived for silicon diodes containing a single reverse-biased p-n junction. The present paper extends the model to include two junctions, and the goal is to estimate how collected charge is shared between them. The extended model identifies the conditions needed to produce either of three possibilities. One possi...
Article
Full-text available
A recent theoretical analysis considered charge collection from an ionization source in a p-n junction silicon diode under steady-state conditions, i.e., carrier liberation is at a quasi-constant rate, and concluded that the quasi-neutral region partitions into distinct sub-regions. A later empirical investigation (via TCAD simulations) found that...
Article
Full-text available
We present a test methodology for estimating system error rates of Field Programmable Gate Arrays (FPGAs) mitigated with Triple Modular Redundancy (TMR). The test methodology is founded in a mathematical model, which is also presented. Accelerator data from 90 nm Xilinx Military/Aerospace grade FPGA are shown to fit the model. Fault injection (FI)...
Article
The ADC model is a charge-collection model mathematically derived for simple p-n junction diodes under steady-state conditions. A transient version of the model is postulated, rather than derived, and tested for correctness by comparisons with TCAD simulation predictions.
Article
Recent heavy ion measurements of the single-event upset (SEU) cross section for 65 nm embedded block random access memory (Block RAM) are presented. Results of initial investigation into the on-chip Error Detection and Correction (EDAC) are also discussed.
Article
Single-event rates in space can include contributions from low-energy particles such that the LET is not constant. A rate calculation algorithm for such a situation is derived.
Article
A unique testing approach based on error-pattern identification with a graphical mapping and color-coding of the full SDRAM memory during single-event characterization is proposed. Results about unique SEFI modes and the role of temperature are discussed.
Article
Full-text available
A previous rigorous mathematical analysis of drift-diffusion equations was used to investigate collected charge in a simple reverse-biased p-n junction diode exposed to an ionization source that liberates carriers (electron-hole pairs) in a quasi-neutral region within the diode. Each of two simple models was found to agree with the more rigorous an...
Article
Full-text available
Optoelectronics such as Si avalanche photodiodes (APDs) used in space are subjected to background cosmic radiation including highly energetic heavy ions. As these swift ions pass through a device, they lose energy by promoting free electron-hole pairs. The resultant ionization track is an extremely dense two-component free carrier plasma with submi...
Article
Full-text available
As part of a "data mining" effort to evaluate the value of ground testing in predicting the performance of microelectronics in space, the responses to single-event upsets of the Clementine 2.1 Gbit solid-state data recorder and two Cassini 2.5 Gbit solid-state recorders were analyzed. As the systems were tested for single-event upset sensitivities...
Article
Full-text available
Spatially-resolved picosecond laser induced transients have been measured in a 0.18 mum CMOS inverter test structure as a function of temperature. Sensitive n -drain and p -drain nodes have been scaled in size to accommodate characteristic differences between ion and laser tracks. Images based on pulse characteristics have been collected from 325 K...
Conference Paper
As part of an on-going "data mining" effort, the response to single event upsets (SEU) of the Clementine 2.1 Gb Solid State Data Recorder (SSDR) was compared to that of the two Cassini 2.5 gigabit (2.1 Gb usable for data) Solid State Recorders (SSRs) to see what lessons could be learned. Both systems were evaluated for their sensitivities to SEUs b...
Article
It was previously thought that stuck bits in the Hyundai 16M times 4 SDRAM were caused by micro-dose. It is argued here that the correct mechanism is micro (i.e., from a single particle hit) displacement damage, which creates a leakage current that drains the storage capacitor.
Article
Protons that produce significant direct ionization in a sensitive volume also slow down, so the LET is not constant in large sensitive volumes. A single-event cross section for energy deposition within the volume that takes this into account is calculated analytically. It is up to the user to select a critical energy and a sensitive volume that giv...
Conference Paper
Full-text available
The range of resulting leakage from single-event gate rupture (SEGR) in power MOSFETs spans several decades, from hundreds of nanoamps to tens of milliamps being qualified as rupture events. The differences in the magnitude of the breaks are correlated to the physical and operational effects of the devices investigated. The maximum leakage current...
Article
A model for estimating proton SEU cross sections from heavy-ion test data has been extended to include 14 MeV neutrons. Accuracy is less consistent for neutrons, but predictions can still be used for upper bounds.
Article
Full-text available
The role of ion track structure on high-injection carrier dynamics in a high-speed GaAs p<sup>+</sup>-n-n<sup>+</sup> sensor is investigated using laser and high-energy heavy ion microbeams. The results are compared to similar data collected on a Si p<sup>+</sup>-n-n<sup>+</sup> device where space charge screening effects (SCSE) result in transient...
Conference Paper
Full-text available
High-injection effects on the impulse response and high-frequency gain of a Si Avalanche Photodiode have been observed for a series of MeV heavy ions species with the same track structure but different injection levels. Focused picosecond laser results have also been collected as a function of laser waist. For the ultra-high injection levels presen...
Technical Report
Full-text available
Many members of the community require additional guidance when using the CREME96 computer code to calculate heavy-ion induced SEU rates. Recommendations are given.
Article
It is argued that a silicon p-n junction diode operating at high injection in the forward direction can be analyzed by using the regional approximation together with the classical law of the junction. Erroneous predictions made in the past are attributed to incorrect equations describing the quasineutral regions. Corrected equations (exact analytic...
Article
Full-text available
Devices that respond to radiation on a cell level will produce distributions showing the relative frequency of cell response to radiation damage, i.e., a probability distribution of a cell to be damaged a certain amount. The measured distribution is the convolution of distributions from radiation responses, measurement noise, and manufacturing para...
Article
A comparison of heavy-ion and proton-induced single event effect sensitivities has been made using the Xilinx Virtex-II field programmable gate array (FPGA). Recently fabricated test samples are selected for observations of single event upset and single event functional interrupt. A complex relationship appears to exist between the heavy ion and pr...
Article
Full-text available
This paper discusses the effect of ionizing radiation on two types of deformable MEMS mirrors. Little effect was observed in the technology that was based on electrostatic deflection, consistent with the structural design that does not contain insulators between the two sections. Significant changes in the operating characteristics were observed fo...
Conference Paper
Full-text available
Heavy ion irradiation of high-voltage power MOSFETs with long-range ions (>123μm in silicon) was performed using 14, 19, 22, 24, 28, and 39 MeV-cm<sup>2</sup>/mg ions at normal incidence. Prior to catastrophic failure some DUTs exhibited unusual electrical characteristic: all devices demonstrated high current transients (or current spikes) at volta...
Article
Full-text available
A novel technique for determining the diffusion-charge collection-efficiency function Ω<sub>τ</sub> (x&oarr;), which incorporates mixed-boundary conditions and carrier recombination, is presented and applied to a realistic three-dimensional memory device to obtain the upset cross section a as a function of linear energy transfer (LET) and orientati...
Article
Full-text available
GaAs micro-electromechanical RF relays fabricated by surface micromachining techniques were characterized for their response to total ionizing dose. Microrelays with two different geometries were studied. For one geometry, changes in switch actuation voltage at moderate dose levels were observed. For an alternative geometry, no change in actuation...
Article
Full-text available
Single-event transients are investigated in comparators with switching speed below 80 ns, including one BiCMOS device. Modeling results show that the collapse of internal junctions after an ion strike delays the onset of collector current because of transient currents in the substrate that are not shielded by the buried layer. Transients in high-sp...
Article
Single-event upset tests often change the angle of the ion beam relative to the device to mimic a change in ion linear energy transfer, and the data are then converted via an assumed cosine law. The converted data are intended to represent device susceptibility at normal incidence, but the cosine law sometimes contains considerable error. The stand...
Article
Full-text available
Radiation exposure of certain types of devices tends to stick bits, causing them to not be read out correctly after programming. Evidence of a linear trend in stuck bits in SDRAM memory cells is presented. This trend makes a cross section, as traditionally defined for single-event effects, unambiguous. However, there are considerable part-to-part v...
Article
The diffusion equation has some applications relevant to charge collection from ion tracks in silicon devices. Textbook solutions for the diffusion equation are available only for a few simple boundary geometries and special types of boundary conditions. A broader class of geometries was previously treated via a charge-collection efficiency functio...
Article
Heavy ion irradiations of two types of commercial DRAM's reveal unexpected angular responses. One device's cross section varied by two orders of magnitude with azimuthal angle. Accurate prediction of space rates requires accommodating this effect
Article
Full-text available
A two-step modeling approach is developed for single-event transients in linear circuits that uses the PISCES device simulation program to calculate transient currents in key internal transistor structures. Those currents are then applied at the circuit level using the SPICE circuit analysis program. The results explain the dependence of transients...
Article
Full-text available
Many papers have presented models for estimating proton single event upset (SEU) cross sections from heavy-ion test data, but all rigorous treatments to date are based on the sensitive volume (SV) model for charge collection. Computer simulations have already shown that, excluding devices utilizing physical boundaries for isolation, there is no wel...
Conference Paper
Full-text available
The goal of the NASA HPCC Remote Exploration and Experimentation (REE) Project is to transfer commercial supercomputing technology into space. The project will use state of the art, low-power, non-radiation-hardened, COTS hardware chips and COTS software to the maximum extent possible, and will rely on software-implemented fault tolerance to provid...
Article
Full-text available
Abstract--The goal of the NASA HPCC Remote Exploration and Experimentation (REE) Project is to transfer commercial supercomputing technology into space. The project will use state of the art, low-power, nonradiation-hardened, commercial Off-The-Shelf (COTS) hardware chips and COTS software to the maximum extent possible, and will rely on Software-I...
Article
Full-text available
Single event gate rupture (SEGR) was studied using three types of power MOSFET devices with ions having incident linear energy transfers (LETs) in silicon from 26 to 82 MeV/spl middot/cm/sup 2//mg. Results are: (1) consistent with Wrobel's oxide breakdown for V/sub DS/=0 volts (for both normal incidence and angle); and (2) when V/sub GS/=0 volts, e...
Article
Full-text available
Transient upsets from protons in high-speed optocouplers were investigated over a range of incident angles and energies. At energies below 50 MeV, very large increases in cross section occurred at angles above 60/spl deg/, consistent with the increase in cross section that is expected when direct proton ionization begins to contribute to the cross...
Article
Full-text available
A modified form of Ohm's law, describing electric currents through ion tracks, is presented as a tool for future theoretical modeling efforts related to charge collection from ion tracks in silicon devices. The equation is rigorously derived from the drift/diffusion equations and accounts for all currents (electron and hole, drift, and diffusion)....
Article
Full-text available
Single-event upset is investigated for optocouplers using heavy ions. The threshold LET for optocouplers with internal high-gain amplifiers is very low, causing output transients to occur even when the optocouplers are irradiated with short-range alpha particles. Although previous work with high-energy protons showed that transients were caused by...
Article
Full-text available
Particle irradiation on the mechanical sensor of the ADXL50 microelectromechanical accelerometer shifts the output voltage. An earlier conclusion, that a dielectric below the sensor becomes charged, is extended by quantifying the effect of this charge on device output. It is shown that an electrostatic force is consistent with the observation that...
Article
Full-text available
Breakdown of thin gate oxides from heavy ions is investigated using capacitor test structures. Soft breakdown was observed for 45 Å oxides, but not for 75 Å oxides. Lower critical fields were observed when experiments were done with high fluences during each successive step. This implies that oxide defects play an important role in breakdown from h...
Article
Full-text available
Charge collected by diffusion from ion tracks in a semiconductor substrate may be influenced by the substrate diffusion length, which is related to recombination losses. A nonuniform spatial distribution of recombination centers results in a nonuniform diffusion length function. A theoretical analysis shows that, excluding some extreme cases, charg...
Article
Full-text available
Proton latchup was investigated for several CMOS integrated circuits, including a modern microprocessor. The proton latchup cross sections of these devices differed by more than two orders of magnitude. A modeling approach that takes differences in charge collection processes for long- and short-range particles into account was effective in compari...
Article
Charge collection from ion tracks in epi diodes is investigated. As previously noted by others, the collected charge can exceed the charge liberated in the epi layer. Fundamental concepts are discussed and illustrated by computer simulation results. It is found that the n <sup>+</sup>-p-p<sup>+</sup> diode displays a funneling regime and a diffusio...
Article
A simple theoretical prediction of single-event upset (SEU) cross section versus linear energy transfer (LET) is derived from a diffusion analysis, and the result is compared to some real device curves. It was found that at least some real device curves show two regimes. One regime (high-LET) is characterized by a very good fit to the theoretical p...
Article
Full-text available
Results of an experiment providing initial validation of the use of charge-collection spectroscopy to measure the over-layer and epitaxial thickness and substrate diffusion length are given for several CMOS SRAM test devices
Article
Full-text available
The diffusion equation has some applications relevant to charge collection from ion tracks in silicon devices. This problem has been treated in the past for cases in which the entire upper surface can be represented as a sink for minority carriers. The present paper treats the case in which there are a number of disconnected upper junctions separat...
Article
Full-text available
A theoretical analysis solves for the steady-state photocurrents produced by a given photo-generation rate function with negligible recombination in simple silicon diodes, consisting of a uniformly doped quasi-neutral region (called 'substrate' below) adjacent to a p-n junction depletion region (DR). Special attention is given to conditions that pr...
Article
Report presents theoretical calculations of contribution of Auger recombination to depletion of charge carriers from ionization track left by passage of energetic heavy ion through silicon-based electronic device.
Article
Upper bounds on rates of single-event upsets (SEU's) in digital integrated circuits and other electronic devices exposed to anisotropic fluxes of energetic ionizing particles computed by use of improved method. Derived from simplified, worst-case mathematical models of charge-collecting volumes and physical phenomena in electronic devices.
Article
Two reports describe preliminary theoretical and experimental studies based on method described in "Laser Scanner Tests For Single-Event Upsets" (NPO-18216). Laser-scan and heavy-ion data found correlated within factor of two. Method of testing for single-event upsets intended to overcome disadvantages of, complement, and/or substitute for more-exp...
Article
A picosec pulsed dye laser beam was at selected wavelengths successfully used to simulate heavy-ion single-event effects (SEEs) in negative channel NMOS DRAMs. A DRAM was used to develop the test technique because bit-mapping capability and previous heavy-ion upset data were available. The present analysis is the first to establish such a correlati...
Article
Full-text available
The theoretical analysis presented indicates that Auger recombination can reduce charge collection from very dense ion tracks in silicon devices. It is of marginal importance for tracks produced by 270-MeV krypton, and therefore it is of major importance for ions exhibiting a significantly larger loss. The analysis shows that recombination loss is...
Article
A method for constructing upper bound estimates for device single event upset (SEU) rates is presented. A directional Heinrich flux, as a function of direction, must be known. A computer code, included, converts the directional Heinrich flux into an 'effective flux'. The effective flux provides a simple way to estimate upper bound SEU rates for dev...
Article
Charge-carrier diffusion from an ion track in a silicon substrate at least a few hundred microns thick is analyzed. The substrate upper surface is treated as reflective except for a small section, intended to represent a reverse-biased junction, which is treated as a sink. Total charge collected by the sink is calculated by assuming transport to be...
Article
Funneling is qualitatively discussed in detail, and a quantitative analysis is given for the total (time-integrated) collected charge. It is shown that, for an n<sup>+</sup>/p junction, the total collected charge Q <sub>T</sub> is given by Q T=(1+μ<sub>n</sub>/μ<sub>p</sub>) Q <sub>D</sub>+2 Q <sub>diff</sub>, where Q <sub>D</sub> is the charge ini...
Article
Multiple-bit errors caused by single-ion tracks in a 256-kb DRAM fabricated by a bulk process were observed for different ion species and stopping power values. The results demonstrate the utility of this device for the evaluation of ion-beam uniformity and ion-beam-induced charge collection in IC devices. The data indicate that single-ion-induced...
Article
Full-text available
This analysis applies to a quasi-neutral region of uniformly doped semiconductor material. The objective is to solve for the current density in terms of the carrier density and the electric potential boundary values. It is shown that the combined effects of drift and diffusion can be calculated by assuming the current density to obey Ohm's law, but...
Article
Theory of single-event upsets (SEU) (changes in logic state caused by energetic charged subatomic particles) in complementary metal oxide/semiconductor (CMOS) logic devices extended to provide upper-bound estimates of rates of SEU when limited experimental information available and configuration and dimensions of SEU-sensitive regions of devices un...
Article
The spread of charge induced by an ion track in an integrated circuit and its subsequent collection at sensitive nodal junctions can cause multiple-bit errors. The authors have experimentally and analytically investigated this phenomenon using a 256-kb dynamic random-access memory (DRAM). The effects of different charge-transport mechanisms are ill...
Article
Theoretical study takes new look at current-vs.-voltage behavior of silicon controlled rectifiers (SCR's), four-layer complementary metal oxide/semiconductor (CMOS) devices, and similar devices susceptible to latchup. For purposes of analysis, "latchup" denotes transition of such device from lower-current-conducting steady state to distinct higher-...
Article
Full-text available
It is suggested that the chord length distribution method could be useful for predicting double-bit upset rates in certain circumstances. A chord length distribution function for simultaneous path lengths in two parallelepipeds, applicable to a unidirectional flux, is derived. A proof of the system is outlined for the case under consideration

Questions

Questions (16)

Projects

Projects (6)
Project
After retiring as an engineer, I have started to study modern theoretical physics for fun. Papers in this project help me to understand these studies.