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At least 289 records · Page 16

Certain and possible rules for decision making using rough set theory extended to fuzzy sets

Uncertainty may be caused by the ambiguity in the terms used to describe a specific situation. It may also be caused by skepticism of rules used to describe a course of action or by missing and/or erroneous data. To deal with uncertainty, techniques other than classical logic need to be developed. Although, statistics may be the best tool available for handling likelihood, it is not always adequate for dealing with knowledge acquisition under uncertainty. Inadequacies caused by estimating probabilities in statistical processes can be alleviated through use of the Dempster-Shafer theory of evidence. Fuzzy set theory is another tool used to deal with uncertainty where ambiguous terms are present. Other methods include rough sets, the theory of endorsements and nonmonotonic logic. J. Grzymala-Busse has defined the concept of lower and upper approximation of a (crisp) set and has used that concept to extract rules from a set of examples. We will define the fuzzy analogs of lower and upper approximations and use these to obtain certain and possible rules from a set of examples where the data is fuzzy. Central to these concepts will be the idea of the degree to which a fuzzy set A is contained in another fuzzy set B, and the degree of intersection of a set A with set B. These concepts will also give meaning to the statement; A implies B. The two meanings will be: (1) if x is certainly in A then it is certainly in B, and (2) if x is possibly in A then it is possibly in B. Next, classification will be looked at and it will be shown that if a classification will be looked at and it will be shown that if a classification is well externally definable then it is well internally definable, and if it is poorly externally definable then it is poorly internally definable, thus generalizing a result of Grzymala-Busse. Finally, some ideas of how to define consensus and group options to form clusters of rules will be given.

Dekorvin, Andre↗

Test of Sigmund scaling for low collision energies

A scaling law that describes the most probable vibrorotational excitation in ion-molecule collisions has recently been extended by Sigmund (1981) to cover polyatomic targets. The predictions of this scaling law are examined for collisions of Cl(-) and K(+) with the targets O2, N2, CO, CO2, and CH4 in the energy range 50-200 eV. The experimental results do not all scale according to the theory. The study does demonstrate the usefulness of the scaling variables when examining the most probable vibrorotational excitation in ion-molecule collisions. A collection of isoelectronic scattering results is presented.

Vedder, M.↗

Quest for Cooper Pair Transfer in Heavy-Ion Reactions: The 206 Pb + 118 Sn Case

In this Letter we report on effects of nucleon-nucleon correlations probed in nucleon transfer reactions with heavy ions. We measured with high efficiency and resolution a complete set of observables for neutron transfer channels in the ²⁰⁶Pb + ¹¹⁸Sn system employing a large solid angle magnetic spectrometer, which allowed us to study a wide range of internuclear distances via a detailed excitation function. The coupled channel theory, based on an independent particle transfer mechanism, follows the experimental transfer probabilities for one- and two-neutron pick-up and stripping channels. The experimental two-neutron transfer cross sections indicate that in reactions between pair-vibrational (closed shell) and pair-rotational (open shell) nuclei, correlations manifest via pair-addition and pair-removal modes, which constitute one of the elementary modes of excitations in nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Application of Markov chain theory to ASTP natural environment launch criteria at Kennedy Space Center

To aid the planning of the Apollo Soyuz Test Program (ASTP), certain natural environment statistical relationships are presented, based on Markov theory and empirical counts. The practical results are in terms of conditional probability of favorable and unfavorable launch conditions at Kennedy Space Center (KSC). They are based upon 15 years of recorded weather data which are analyzed under a set of natural environmental launch constraints. Three specific forecasting problems were treated: (1) the length of record of past weather which is useful to a prediction; (2) the effect of persistence in runs of favorable and unfavorable conditions; and (3) the forecasting of future weather in probabilistic terms.

Graves, M. E.↗

On the error probability of general trellis codes with applications to sequential decoding

An upper bound on the average probability of error for maximum-likelihood decoding of the ensemble of random L-branch binary trellis codes of rate R = 1/n with distinction between memory length and tail length is given. It is shown that the bound is independent of the length L of the information sequence if the memory length exceeds the tail length by a specified amount that depends on L. Sequential decoding simulations using the stack algorithm were conducted to test the dependence of the undetected error probability on tail length and memory length, and the results corroborated the theory.

Johannesson, R.↗

Semiempirical hot atom theory. I - Initialization and application

A semiempirical approach to the modeling of the kinetics of reaction systems containing both hot and nonhot atoms is proposed. The approach is based on the probabilistic kinetic theory of hot-atom reactions formulated by Wolfgang (1963), with transmission probabilities estimated for a rectangular potential barrier for hot-atom and nonhot-atom reactions. A computational scheme for determining product concentrations following hot and nonhot reactions in a system containing photolytically produced hot atoms is then applied to the DBr + CH4 and HBr + CD4 hot hydrogen atom systems studied by Martin and Willard (1964), and good agreement is obtained between theoretical and experimental results.

Aronowitz, S.↗

Momentum limiting velocity controls for robotic manipulators

Robotic tasks in space require manipulating massive objects capable of attaining large momentum. The momentum can pose hazardous conditions and introduce destabilizing effects on a space platform. Consequently, a technique for limiting the momentum applied to objects under manipulation subject to arbitrary velocity input commands is proposed. The algorithm does not require mass position or inertia information about the object, and it takes actuator limitations into account in forming the momentum limits. To evaluate the probability that a velocity trajectory will fall within the momentum bounds, reliability theory is employed. This enables autonomously generated trajectories to be validated for compliance with momentum limits.

Mcinroy, John E.↗

Modeling of turbulent supersonic H2-air combustion with an improved joint beta PDF

Attempts at modeling recent experiments of Cheng et al. indicated that discrepancies between theory and experiment can be a result of the form of assumed probability density function (PDF) and/or the turbulence model employed. Improvements in both the form of the assumed PDF and the turbulence model are presented. The results are again used to compare with measurements. Initial comparisons are encouraging.

Baurle, R. A.↗

Nanotube Tunneling as a Consequence of Probable Discrete Trajectories

It has been recently reported that the electrical charge in a semiconductive carbon nanotube is not evenly distributed, but is divided into charge "islands." A clear understanding of tunneling phenomena can be useful to elucidate the mechanism for electrical conduction in nanotubes. This paper represents the first attempt to shed light on the aforementioned phenomenon through viewing tunneling as a natural consequence of "discrete trajectories." The relevance of this analysis is that it may provide further insight into the higher rate of tunneling processes, which makes tunneling devices attractive. In a situation involving particles impinging on a classically impenetrable barrier, the result of quantum mechanics that the probability of detecting transmitted particles falls off exponentially is derived without wave theory. This paper should provide a basis for calculating the charge profile over the length of the tube so that nanoscale devices' conductive properties may be fully exploited.

Robinson, Daryl C.↗

Surface flaw reliability analysis of ceramic components with the SCARE finite element postprocessor program

The SCARE (Structural Ceramics Analysis and Reliability Evaluation) computer program on statistical fast fracture reliability analysis with quadratic elements for volume distributed imperfections is enhanced to include the use of linear finite elements and the capability of designing against concurrent surface flaw induced ceramic component failure. The SCARE code is presently coupled as a postprocessor to the MSC/NASTRAN general purpose, finite element analysis program. The improved version now includes the Weibull and Batdorf statistical failure theories for both surface and volume flaw based reliability analysis. The program uses the two-parameter Weibull fracture strength cumulative failure probability distribution model with the principle of independent action for poly-axial stress states, and Batdorf's shear-sensitive as well as shear-insensitive statistical theories. The shear-sensitive surface crack configurations include the Griffith crack and Griffith notch geometries, using the total critical coplanar strain energy release rate criterion to predict mixed-mode fracture. Weibull material parameters based on both surface and volume flaw induced fracture can also be calculated from modulus of rupture bar tests, using the least squares method with known specimen geometry and grouped fracture data. The statistical fast fracture theories for surface flaw induced failure, along with selected input and output formats and options, are summarized. An example problem to demonstrate various features of the program is included.

Gyekenyesi, John P.↗

Surface flaw reliability analysis of ceramic components with the SCARE finite element postprocessor program

The SCARE (Structural Ceramics Analysis and Reliability Evaluation) computer program on statistical fast fracture reliability analysis with quadratic elements for volume distributed imperfections is enhanced to include the use of linear finite elements and the capability of designing against concurrent surface flaw induced ceramic component failure. The SCARE code is presently coupled as a postprocessor to the MSC/NASTRAN general purpose, finite element analysis program. The improved version now includes the Weibull and Batdorf statistical failure theories for both surface and volume flaw based reliability analysis. The program uses the two-parameter Weibull fracture strength cumulative failure probability distribution model with the principle of independent action for poly-axial stress states, and Batdorf's shear-sensitive as well as shear-insensitive statistical theories. The shear-sensitive surface crack configurations include the Griffith crack and Griffith notch geometries, using the total critical coplanar strain energy release rate criterion to predict mixed-mode fracture. Weibull material parameters based on both surface and volume flaw induced fracture can also be calculated from modulus of rupture bar tests, using the least squares method with known specimen geometry and grouped fracture data. The statistical fast fracture theories for surface flaw induced failure, along with selected input and output formats and options, are summarized. An example problem to demonstrate various features of the program is included.

Gyekenyesi, J. P.↗

Inference in infinite-dimensional inverse problems - Discretization and duality

Many techniques for solving inverse problems involve approximating the unknown model, a function, by a finite-dimensional 'discretization' or parametric representation. The uncertainty in the computed solution is sometimes taken to be the uncertainty within the parametrization; this can result in unwarranted confidence. The theory of conjugate duality can overcome the limitations of discretization within the 'strict bounds' formalism, a technique for constructing confidence intervals for functionals of the unknown model incorporating certain types of prior information. The usual computational approach to strict bounds approximates the 'primal' problem in a way that the resulting confidence intervals are at most long enough to have the nominal coverage probability. There is another approach based on 'dual' optimization problems that gives confidence intervals with at least the nominal coverage probability. The pair of intervals derived by the two approaches bracket a correct confidence interval. The theory is illustrated with gravimetric, seismic, geomagnetic, and helioseismic problems and a numerical example in seismology.

Stark, Philip B.↗

The structure and energetics of Cr(CO)6 and Cr(CO)5

The geometric structure of Cr(CO)6 is optimized at the modified coupled pair functional (MCPF), single and double excitation coupled-cluster (CCSD) and CCSD(T) levels of theory (including a perturbational estimate for connected triple excitations), and the force constants for the totally symmetric representation are determined. The geometry of Cr(CO)5 is partially optimized at the MCPF, CCSD, and CCSD(T) levels of theory. Comparison with experimental data shows that the CCSD(T) method gives the best results for the structures and force constants, and that remaining errors are probably due to deficiencies in the one-particle basis sets used for CO. The total binding energies of Cr(CO)6 and Cr(CO)5 are also determined at the MCPF, CCSD, and CCSD(T) levels of theory. The CCSD(T) method gives a much larger total binding energy than either the MCPF or CCSD methods. An analysis of the basis set superposition error (BSSE) at the MCPF level of treatment points out limitations in the one-particle basis used. Calculations using larger basis sets reduce the BSSE, but the total binding energy of Cr(CO)6 is still significantly smaller than the experimental value, although the first CO bond dissociation energy of Cr(CO)6 is well described. An investigation of 3s3p correlation reveals only a small effect. In the largest basis set, the total CO binding energy of Cr(CO)6 is estimated to be 140 kcal/mol at the CCSD(T) level of theory, or about 86 percent of the experimental value. The remaining discrepancy between the experimental and theoretical value is probably due to limitations in the one-particle basis, rather than limitations in the correlation treatment. In particular an additional d function and an f function on each C and O are needed to obtain quantitative results. This is underscored by the fact that even using a very large primitive set (1042 primitive functions contracted to 300 basis functions), the superposition error for the total binding energy of Cr(CO)6 is 22 kcal/mol at the MCPF level of treatment.

Barnes, Leslie A.↗

Constraining (n,γ) cross sections via surrogate measurements with hyperion

Indirect measurement techniques, such as the surrogate method, are necessary to constrain cross sections and reaction rates that are inaccessible for direct measurement. The surrogate method uses an alternate reaction channel to populate a nucleus of interest, and combines resulting experimental data with theory to constrain the desired (n,γ) cross section. Individual γ-decay probabilities are experimentally extracted using γ-ray spectroscopy. This project utilizes surrogate analysis of 64,70 Zn(p,d) and 64,70 Zn(p,t) reactions measured with the Hyperion array at Texas A&M University's Cyclotron Facility to probe the relevant neutron capture reactions 61,62,67,68 Zn(n,γ). As an example, preliminary γ-decay probabilities are presented for 69 Zn.

Neutron capture↗

Supersaturation, Nucleation, and Phase Separation of Mesoscopic Systems

Supersaturation, nucleation, and phase separation are ubiquitous phenomena of great interest in both science and industry. However, a unified, quantitative understanding of these phenomena has yet to be achieved for mesoscopic systems. Here, we present a set of general equations that determine the monomer saturation degree, the size distribution, and the free energy of mesoscopic systems, as well as their phase-transition conditions. These equations reveal that, under supersaturation, the largest cluster size (LCS) is an important state variable; the supersaturation degree decreases with the LCS, approaching unity in the macroscopic limit. We identify the critical supersaturation, at which the nuclei undergo the phase transition to form large crystals. Below this critical supersaturation, the nucleus size distribution is either a unimodal function or a monotonically decreasing function of size, depending on the system and temperature. We also predict the most probable nucleus size and the direction of spontaneous changes of the LCS. Our theory provides a unified, quantitative explanation of the nucleus-size-distribution across six different systems, including nanoparticles and biological condensates. This work serves as a general theoretical framework useful for understanding and designing nucleation and phase transitions of mesoscopic systems.

Kang, Jingyu↗

Understanding and Controlling the Formation of Nonradiative Defects in Blue Organic Triplet Emitters

Phosphorescent organic light-emitting devices (PHOLEDs) suffer from destructive molecular processes due to triplet-polaron and triplet-triplet annihilation. These processes are energetically driven and hence are particularly active in decreasing the lifetime of blue PHOLEDs. It has recently been shown that increasing triplet radiative rates via the Purcell effect effectively extends the device operational lifetime by reducing the triplet radiative lifetime, thus decreasing their density and the probability of triplet-annihilation reactions. We provide an analytical framework using Marcus theory to explain the observed, approximately exponential relationship between exciton energy and device lifetime. From transient drift-diffusion dynamics, we show that the Purcell effect reduces the exciton density in the steady state and increases the photoluminescent yield, thereby reducing defect generation rates and extending the device lifetime. We control the radiative rate of excitons in microcavities, thereby connecting the exciton energy and decay rates with the observed device lifetime. The device lifetime is shown to follow a power-law dependence on the Purcell factor ( PF m ) with m = 1.5 to 2.5, dependent on the TTA-to-TPA ratio and photoluminescence quantum yield. From our analysis, a fivefold increase in PF has the potential to extend the blue PHOLED lifetime by up to 2 orders of magnitude, making the blue PHOLED lifetime comparable to that of state-of-the-art green PHOLEDs. Published by the American Physical Society 2024

Zhao, Haonan (ORCID:0000000190584422)↗

Uniform Mechanical Loading Can Test for Nonuniform Loading Durability

In this work, we present a method to evaluate the equivalency between any module mechanical loading conditions. The method is developed to address the specific failure mode of glass fracture and is based on Weibull analysis and weakest link theory. It considers the varying stress profile across the module to calculate the probability of glass fracture, which is used as the metric of equivalency. An idealized nonuniform loading scheme is employed to demonstrate the method and introduce the concept of the equivalent uniform load factor: a factor applied to the maximum pressure of the nonuniform load to obtain the equivalent uniform load value. It is demonstrated that this factor is less than unity for all nonuniform load cases considered, including snow and various characters of wind loading. These significant results suggest that uniform loading may be reliably, and practically, employed to evaluate photovoltaic module glass for nonuniform loading durability.

14 SOLAR ENERGY↗