The Faceted Discrete Growth and Phase Differentiation During the Directional Solidification of 20SiMnMo5 Steel

Science.gov (United States)

Ma, Xiaoping; Li, Dianzhong

2018-07-01

The microstructures, segregation and cooling curve were investigated in the directional solidification of 20SiMnMo5 steel. The typical characteristic of faceted growth is identified. The microstructures within the single cellular and within the single dendritic arm, together with the contradictive segregation distribution against the cooling curve, verify the discrete crystal growth in multi-scales. Not only the single cellular/dendritic arm but also the single martensite zone within the single cellular/dendritic arm is produced by the discrete growth. In the viewpoint of segregation, the basic domain following continuous growth has not been revealed. Along with the multi-scale faceted discrete growth, the phase differentiation happens for both the solid and liquid. The differentiated liquid phases appear and evolve with different sizes, positions, compositions and durations. The physical mechanism for the faceted discrete growth is qualitatively established based on the nucleation of new faceted steps induced by the composition gradient and temperature gradient.

The Faceted Discrete Growth and Phase Differentiation During the Directional Solidification of 20SiMnMo5 Steel

Science.gov (United States)

Ma, Xiaoping; Li, Dianzhong

2018-03-01

The microstructures, segregation and cooling curve were investigated in the directional solidification of 20SiMnMo5 steel. The typical characteristic of faceted growth is identified. The microstructures within the single cellular and within the single dendritic arm, together with the contradictive segregation distribution against the cooling curve, verify the discrete crystal growth in multi-scales. Not only the single cellular/dendritic arm but also the single martensite zone within the single cellular/dendritic arm is produced by the discrete growth. In the viewpoint of segregation, the basic domain following continuous growth has not been revealed. Along with the multi-scale faceted discrete growth, the phase differentiation happens for both the solid and liquid. The differentiated liquid phases appear and evolve with different sizes, positions, compositions and durations. The physical mechanism for the faceted discrete growth is qualitatively established based on the nucleation of new faceted steps induced by the composition gradient and temperature gradient.

Combining Orthogonal Chain-End Deprotections and Thiol-Maleimide Michael Coupling: Engineering Discrete Oligomers by an Iterative Growth Strategy.

Science.gov (United States)

Huang, Zhihao; Zhao, Junfei; Wang, Zimu; Meng, Fanying; Ding, Kunshan; Pan, Xiangqiang; Zhou, Nianchen; Li, Xiaopeng; Zhang, Zhengbiao; Zhu, Xiulin

2017-10-23

Orthogonal maleimide and thiol deprotections were combined with thiol-maleimide coupling to synthesize discrete oligomers/macromolecules on a gram scale with molecular weights up to 27.4 kDa (128mer, 7.9 g) using an iterative exponential growth strategy with a degree of polymerization (DP) of 2 n -1. Using the same chemistry, a "readable" sequence-defined oligomer and a discrete cyclic topology were also created. Furthermore, uniform dendrons were fabricated using sequential growth (DP=2 n -1) or double exponential dendrimer growth approaches (DP=22n -1) with significantly accelerated growth rates. A versatile, efficient, and metal-free method for construction of discrete oligomers with tailored structures and a high growth rate would greatly facilitate research into the structure-property relationships of sophisticated polymeric materials. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

An analytical framework for reliability growth of one-shot systems

International Nuclear Information System (INIS)

Hall, J. Brian; Mosleh, Ali

2008-01-01

In this paper, we introduce a new reliability growth methodology for one-shot systems that is applicable to the case where all corrective actions are implemented at the end of the current test phase. The methodology consists of four model equations for assessing: expected reliability, the expected number of failure modes observed in testing, the expected probability of discovering new failure modes, and the expected portion of system unreliability associated with repeat failure modes. These model equations provide an analytical framework for which reliability practitioners can estimate reliability improvement, address goodness-of-fit concerns, quantify programmatic risk, and assess reliability maturity of one-shot systems. A numerical example is given to illustrate the value and utility of the presented approach. This methodology is useful to program managers and reliability practitioners interested in applying the techniques above in their reliability growth program

Improving the quality of discrete-choice experiments in health: how can we assess validity and reliability?

Science.gov (United States)

Janssen, Ellen M; Marshall, Deborah A; Hauber, A Brett; Bridges, John F P

2017-12-01

The recent endorsement of discrete-choice experiments (DCEs) and other stated-preference methods by regulatory and health technology assessment (HTA) agencies has placed a greater focus on demonstrating the validity and reliability of preference results. Areas covered: We present a practical overview of tests of validity and reliability that have been applied in the health DCE literature and explore other study qualities of DCEs. From the published literature, we identify a variety of methods to assess the validity and reliability of DCEs. We conceptualize these methods to create a conceptual model with four domains: measurement validity, measurement reliability, choice validity, and choice reliability. Each domain consists of three categories that can be assessed using one to four procedures (for a total of 24 tests). We present how these tests have been applied in the literature and direct readers to applications of these tests in the health DCE literature. Based on a stakeholder engagement exercise, we consider the importance of study characteristics beyond traditional concepts of validity and reliability. Expert commentary: We discuss study design considerations to assess the validity and reliability of a DCE, consider limitations to the current application of tests, and discuss future work to consider the quality of DCEs in healthcare.

Possibilities and limitations of applying software reliability growth models to safety-critical software

International Nuclear Information System (INIS)

Kim, Man Cheol; Jang, Seung Cheol; Ha, Jae Joo

2007-01-01

It is generally known that software reliability growth models such as the Jelinski-Moranda model and the Goel-Okumoto's Non-Homogeneous Poisson Process (NHPP) model cannot be applied to safety-critical software due to a lack of software failure data. In this paper, by applying two of the most widely known software reliability growth models to sample software failure data, we demonstrate the possibility of using the software reliability growth models to prove the high reliability of safety-critical software. The high sensitivity of a piece of software's reliability to software failure data, as well as a lack of sufficient software failure data, is also identified as a possible limitation when applying the software reliability growth models to safety-critical software

Procedure for Application of Software Reliability Growth Models to NPP PSA

International Nuclear Information System (INIS)

Son, Han Seong; Kang, Hyun Gook; Chang, Seung Cheol

2009-01-01

As the use of software increases at nuclear power plants (NPPs), the necessity for including software reliability and/or safety into the NPP Probabilistic Safety Assessment (PSA) rises. This work proposes an application procedure of software reliability growth models (RGMs), which are most widely used to quantify software reliability, to NPP PSA. Through the proposed procedure, it can be determined if a software reliability growth model can be applied to the NPP PSA before its real application. The procedure proposed in this work is expected to be very helpful for incorporating software into NPP PSA

Stochastic Differential Equation-Based Flexible Software Reliability Growth Model

Directory of Open Access Journals (Sweden)

P. K. Kapur

2009-01-01

Full Text Available Several software reliability growth models (SRGMs have been developed by software developers in tracking and measuring the growth of reliability. As the size of software system is large and the number of faults detected during the testing phase becomes large, so the change of the number of faults that are detected and removed through each debugging becomes sufficiently small compared with the initial fault content at the beginning of the testing phase. In such a situation, we can model the software fault detection process as a stochastic process with continuous state space. In this paper, we propose a new software reliability growth model based on Itô type of stochastic differential equation. We consider an SDE-based generalized Erlang model with logistic error detection function. The model is estimated and validated on real-life data sets cited in literature to show its flexibility. The proposed model integrated with the concept of stochastic differential equation performs comparatively better than the existing NHPP-based models.

The use of Career Growth Scale in Chinese nurses: Validity and reliability

OpenAIRE

Jingying Liu; Jipeng Yang; Yanhui Liu; Yang Yang; Hongfu Zhang

2015-01-01

Purpose: To test the validity and reliability of a modified Career Growth Scale (CGS) to assess nurse career growth. Method: A cross-sectional design was used to analyze the use of the CGS to survey 600 full-time registered nurses from Grade A hospitals in Tianjin. Results: A modified scale we called Career Growth of Nurse Scale (CGNS) is acceptable, valid, and reliable for the evaluation of nurse career growth in Chinese hospitals. This scale measured three main factors (career goal, c...

A Discrete Heterogeneous-Group Economic Growth Model with Endogenous Leisure Time

Directory of Open Access Journals (Sweden)

Wei-Bin Zhang

2009-01-01

Full Text Available This paper proposes a one-sector multigroup growth model with endogenous labor supply in discrete time. Proposing an alternative approach to behavior of households, we examine the dynamics of wealth and income distribution in a competitive economy with capital accumulation as the main engine of economic growth. We show how human capital levels, preferences, and labor force of heterogeneous households determine the national economic growth, wealth, and income distribution and time allocation of the groups. By simulation we demonstrate, for instance, that in the three-group economy when the rich group's human capital is improved, all the groups will economically benefit, and the leisure times of all the groups are reduced but when any other group's human capital is improved, the group will economically benefit, the other two groups economically lose, and the leisure times of all the groups are increased.

Possibilities and Limitations of Applying Software Reliability Growth Models to Safety- Critical Software

International Nuclear Information System (INIS)

Kim, Man Cheol; Jang, Seung Cheol; Ha, Jae Joo

2006-01-01

As digital systems are gradually introduced to nuclear power plants (NPPs), the need of quantitatively analyzing the reliability of the digital systems is also increasing. Kang and Sung identified (1) software reliability, (2) common-cause failures (CCFs), and (3) fault coverage as the three most critical factors in the reliability analysis of digital systems. For the estimation of the safety-critical software (the software that is used in safety-critical digital systems), the use of Bayesian Belief Networks (BBNs) seems to be most widely used. The use of BBNs in reliability estimation of safety-critical software is basically a process of indirectly assigning a reliability based on various observed information and experts' opinions. When software testing results or software failure histories are available, we can use a process of directly estimating the reliability of the software using various software reliability growth models such as Jelinski- Moranda model and Goel-Okumoto's nonhomogeneous Poisson process (NHPP) model. Even though it is generally known that software reliability growth models cannot be applied to safety-critical software due to small number of expected failure data from the testing of safety-critical software, we try to find possibilities and corresponding limitations of applying software reliability growth models to safety critical software

Stochastic process corrosion growth models for pipeline reliability

International Nuclear Information System (INIS)

Bazán, Felipe Alexander Vargas; Beck, André Teófilo

2013-01-01

Highlights: •Novel non-linear stochastic process corrosion growth model is proposed. •Corrosion rate modeled as random Poisson pulses. •Time to corrosion initiation and inherent time-variability properly represented. •Continuous corrosion growth histories obtained. •Model is shown to precisely fit actual corrosion data at two time points. -- Abstract: Linear random variable corrosion models are extensively employed in reliability analysis of pipelines. However, linear models grossly neglect well-known characteristics of the corrosion process. Herein, a non-linear model is proposed, where corrosion rate is represented as a Poisson square wave process. The resulting model represents inherent time-variability of corrosion growth, produces continuous growth and leads to mean growth at less-than-one power of time. Different corrosion models are adjusted to the same set of actual corrosion data for two inspections. The proposed non-linear random process corrosion growth model leads to the best fit to the data, while better representing problem physics

System reliability of corroding pipelines

International Nuclear Information System (INIS)

Zhou Wenxing

2010-01-01

A methodology is presented in this paper to evaluate the time-dependent system reliability of a pipeline segment that contains multiple active corrosion defects and is subjected to stochastic internal pressure loading. The pipeline segment is modeled as a series system with three distinctive failure modes due to corrosion, namely small leak, large leak and rupture. The internal pressure is characterized as a simple discrete stochastic process that consists of a sequence of independent and identically distributed random variables each acting over a period of one year. The magnitude of a given sequence follows the annual maximum pressure distribution. The methodology is illustrated through a hypothetical example. Furthermore, the impact of the spatial variability of the pressure loading and pipe resistances associated with different defects on the system reliability is investigated. The analysis results suggest that the spatial variability of pipe properties has a negligible impact on the system reliability. On the other hand, the spatial variability of the internal pressure, initial defect sizes and defect growth rates can have a significant impact on the system reliability.

A systematic review of the reliability and validity of discrete choice experiments in valuing non-market environmental goods.

Science.gov (United States)

Rakotonarivo, O Sarobidy; Schaafsma, Marije; Hockley, Neal

2016-12-01

While discrete choice experiments (DCEs) are increasingly used in the field of environmental valuation, they remain controversial because of their hypothetical nature and the contested reliability and validity of their results. We systematically reviewed evidence on the validity and reliability of environmental DCEs from the past thirteen years (Jan 2003-February 2016). 107 articles met our inclusion criteria. These studies provide limited and mixed evidence of the reliability and validity of DCE. Valuation results were susceptible to small changes in survey design in 45% of outcomes reporting reliability measures. DCE results were generally consistent with those of other stated preference techniques (convergent validity), but hypothetical bias was common. Evidence supporting theoretical validity (consistency with assumptions of rational choice theory) was limited. In content validity tests, 2-90% of respondents protested against a feature of the survey, and a considerable proportion found DCEs to be incomprehensible or inconsequential (17-40% and 10-62% respectively). DCE remains useful for non-market valuation, but its results should be used with caution. Given the sparse and inconclusive evidence base, we recommend that tests of reliability and validity are more routinely integrated into DCE studies and suggest how this might be achieved. Copyright © 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.

Powering stochastic reliability models by discrete event simulation

DEFF Research Database (Denmark)

Kozine, Igor; Wang, Xiaoyun

2012-01-01

it difficult to find a solution to the problem. The power of modern computers and recent developments in discrete-event simulation (DES) software enable to diminish some of the drawbacks of stochastic models. In this paper we describe the insights we have gained based on using both Markov and DES models...

A comparative study of the probabilistic fracture mechanics and the stochastic Markovian process approaches for structural reliability assessment

Energy Technology Data Exchange (ETDEWEB)

Stavrakakis, G.; Lucia, A.C.; Solomos, G. (Commission of the European Communities, Ispra (Italy). Joint Research Centre)

1990-01-01

The two computer codes COVASTOL and RELIEF, developed for the modeling of cumulative damage processes in the framework of probabilistic structural reliability, are compared. They are based respectively on the randomisation of a differential crack growth law and on the theory of discrete Markov processes. The codes are applied for fatigue crack growth predictions using two sets of data of crack propagation curves from specimens. The results are critically analyzed and an extensive discussion follows on the merits and limitations of each code. Their transferability for the reliability assessment of real structures is investigated. (author).

Crystallographic fatigue crack growth in a polycrystal: simulations based on FEM and discrete dislocation dynamics

International Nuclear Information System (INIS)

Bertolino, G.; Sauzay, M.; Bertolino, G.; Doquet, V.

2003-01-01

An attempt to model the variability of short cracks development in high-cycle fatigue is made by coupling finite element calculations of the stresses ahead of a microcrack in a polycrystal with simulations of crack growth along slip planes based on discrete dislocations dynamics. The model predicts a large scatter in growth rates related to the roughness of the crack path. It also describes the influence of the mean grain size and the fact that overloads may suppress the endurance limit by allowing arrested cracks to cross the grain boundaries. (authors)

A current value Hamiltonian Approach for Discrete time Optimal Control Problems arising in Economic Growth

OpenAIRE

Naz, Rehana

2018-01-01

Pontrygin-type maximum principle is extended for the present value Hamiltonian systems and current value Hamiltonian systems of nonlinear difference equations for uniform time step $h$. A new method termed as a discrete time current value Hamiltonian method is established for the construction of first integrals for current value Hamiltonian systems of ordinary difference equations arising in Economic growth theory.

Software reliability growth model for safety systems of nuclear reactor

International Nuclear Information System (INIS)

Thirugnana Murthy, D.; Murali, N.; Sridevi, T.; Satya Murty, S.A.V.; Velusamy, K.

2014-01-01

The demand for complex software systems has increased more rapidly than the ability to design, implement, test, and maintain them, and the reliability of software systems has become a major concern for our, modern society.Software failures have impaired several high visibility programs in space, telecommunications, defense and health industries. Besides the costs involved, it setback the projects. The ways of quantifying it and using it for improvement and control of the software development and maintenance process. This paper discusses need for systematic approaches for measuring and assuring software reliability which is a major share of project development resources. It covers the reliability models with the concern on 'Reliability Growth'. It includes data collection on reliability, statistical estimation and prediction, metrics and attributes of product architecture, design, software development, and the operational environment. Besides its use for operational decisions like deployment, it includes guiding software architecture, development, testing and verification and validation. (author)

Preservation properties for the discrete mean residual life ordering

Directory of Open Access Journals (Sweden)

Abdulhakim Al-Babtain

2015-04-01

Full Text Available The purpose of this paper is to prove several preservation properties of stochastic comparisons based on the discrete mean residual life ordering d-MRL under the reliability operations of convolutions, mixtures. Fi…nally we introduce a discrete renewal process application

A study of software reliability growth from the perspective of learning effects

International Nuclear Information System (INIS)

Chiu, K.-C.; Huang, Y.-S.; Lee, T.-Z.

2008-01-01

For the last three decades, reliability growth has been studied to predict software reliability in the testing/debugging phase. Most of the models developed were based on the non-homogeneous Poisson process (NHPP), and S-shaped type or exponential-shaped type of behavior is usually assumed. Unfortunately, such models may be suitable only for particular software failure data, thus narrowing the scope of applications. Therefore, from the perspective of learning effects that can influence the process of software reliability growth, we considered that efficiency in testing/debugging concerned not only the ability of the testing staff but also the learning effect that comes from inspecting the testing/debugging codes. The proposed approach can reasonably describe the S-shaped and exponential-shaped types of behaviors simultaneously, and the results in the experiment show good fit. A comparative analysis to evaluate the effectiveness for the proposed model and other software failure models was also performed. Finally, an optimal software release policy is suggested

Estimating the Parameters of Software Reliability Growth Models Using the Grey Wolf Optimization Algorithm

OpenAIRE

Alaa F. Sheta; Amal Abdel-Raouf

2016-01-01

In this age of technology, building quality software is essential to competing in the business market. One of the major principles required for any quality and business software product for value fulfillment is reliability. Estimating software reliability early during the software development life cycle saves time and money as it prevents spending larger sums fixing a defective software product after deployment. The Software Reliability Growth Model (SRGM) can be used to predict the number of...

INTER-RATER RELIABILITY FOR MOVEMENT PATTERN ANALYSIS (MPA: MEASURING PATTERNING OF BEHAVIORS VERSUS DISCRETE BEHAVIOR COUNTS AS INDICATORS OF DECISION-MAKING STYLE

Directory of Open Access Journals (Sweden)

Brenda L Connors

2014-06-01

Full Text Available The unique yield of collecting observational data on human movement has received increasing attention in a number of domains, including the study of decision-making style. As such, interest has grown in the nuances of core methodological issues, including the best ways of assessing inter-rater reliability. In this paper we focus on one key topic – the distinction between establishing reliability for the patterning of behaviors as opposed to the computation of raw counts – and suggest that reliability for each be compared empirically rather than determined a priori. We illustrate by assessing inter-rater reliability for key outcome measures derived from Movement Pattern Analysis (MPA, an observational methodology that records body movements as indicators of decision-making style with demonstrated predictive validity. While reliability ranged from moderate to good for raw counts of behaviors reflecting each of two Overall Factors generated within MPA (Assertion and Perspective, inter-rater reliability for patterning (proportional indicators of each factor was significantly higher and excellent (ICC = .89. Furthermore, patterning, as compared to raw counts, provided better prediction of observable decision-making process assessed in the laboratory. These analyses support the utility of using an empirical approach to inform the consideration of measuring discrete behavioral counts versus patterning of behaviors when determining inter-rater reliability of observable behavior. They also speak to the substantial reliability that may be achieved via application of theoretically grounded observational systems such as MPA that reveal thinking and action motivations via visible movement patterns.

A mechanism of extreme growth and reliable signaling in sexually selected ornaments and weapons.

Science.gov (United States)

Emlen, Douglas J; Warren, Ian A; Johns, Annika; Dworkin, Ian; Lavine, Laura Corley

2012-08-17

Many male animals wield ornaments or weapons of exaggerated proportions. We propose that increased cellular sensitivity to signaling through the insulin/insulin-like growth factor (IGF) pathway may be responsible for the extreme growth of these structures. We document how rhinoceros beetle horns, a sexually selected weapon, are more sensitive to nutrition and more responsive to perturbation of the insulin/IGF pathway than other body structures. We then illustrate how enhanced sensitivity to insulin/IGF signaling in a growing ornament or weapon would cause heightened condition sensitivity and increased variability in expression among individuals--critical properties of reliable signals of male quality. The possibility that reliable signaling arises as a by-product of the growth mechanism may explain why trait exaggeration has evolved so many different times in the context of sexual selection.

Discrete non-parametric kernel estimation for global sensitivity analysis

International Nuclear Information System (INIS)

Senga Kiessé, Tristan; Ventura, Anne

2016-01-01

This work investigates the discrete kernel approach for evaluating the contribution of the variance of discrete input variables to the variance of model output, via analysis of variance (ANOVA) decomposition. Until recently only the continuous kernel approach has been applied as a metamodeling approach within sensitivity analysis framework, for both discrete and continuous input variables. Now the discrete kernel estimation is known to be suitable for smoothing discrete functions. We present a discrete non-parametric kernel estimator of ANOVA decomposition of a given model. An estimator of sensitivity indices is also presented with its asymtotic convergence rate. Some simulations on a test function analysis and a real case study from agricultural have shown that the discrete kernel approach outperforms the continuous kernel one for evaluating the contribution of moderate or most influential discrete parameters to the model output. - Highlights: • We study a discrete kernel estimation for sensitivity analysis of a model. • A discrete kernel estimator of ANOVA decomposition of the model is presented. • Sensitivity indices are calculated for discrete input parameters. • An estimator of sensitivity indices is also presented with its convergence rate. • An application is realized for improving the reliability of environmental models.

A study of tumour growth based on stoichiometric principles: a continuous model and its discrete analogue.

Science.gov (United States)

Saleem, M; Agrawal, Tanuja; Anees, Afzal

2014-01-01

In this paper, we consider a continuous mathematically tractable model and its discrete analogue for the tumour growth. The model formulation is based on stoichiometric principles considering tumour-immune cell interactions in potassium (K (+))-limited environment. Our both continuous and discrete models illustrate 'cancer immunoediting' as a dynamic process having all three phases namely elimination, equilibrium and escape. The stoichiometric principles introduced into the model allow us to study its dynamics with the variation in the total potassium in the surrounding of the tumour region. It is found that an increase in the total potassium may help the patient fight the disease for a longer period of time. This result seems to be in line with the protective role of the potassium against the risk of pancreatic cancer as has been reported by Bravi et al. [Dietary intake of selected micronutrients and risk of pancreatic cancer: An Italian case-control study, Ann. Oncol. 22 (2011), pp. 202-206].

Sintered tantalum carbide coatings on graphite substrates: Highly reliable protective coatings for bulk and epitaxial growth

Energy Technology Data Exchange (ETDEWEB)

Nakamura, Daisuke; Suzumura, Akitoshi; Shigetoh, Keisuke [Toyota Central R and D Labs., Inc., Nagakute, Aichi 480-1192 (Japan)

2015-02-23

Highly reliable low-cost protective coatings have been sought after for use in crucibles and susceptors for bulk and epitaxial film growth processes involving wide bandgap materials. Here, we propose a production technique for ultra-thick (50–200 μmt) tantalum carbide (TaC) protective coatings on graphite substrates, which consists of TaC slurry application and subsequent sintering processes, i.e., a wet ceramic process. Structural analysis of the sintered TaC layers indicated that they have a dense granular structure containing coarse grain with sizes of 10–50 μm. Furthermore, no cracks or pinholes penetrated through the layers, i.e., the TaC layers are highly reliable protective coatings. The analysis also indicated that no plastic deformation occurred during the production process, and the non-textured crystalline orientation of the TaC layers is the origin of their high reliability and durability. The TaC-coated graphite crucibles were tested in an aluminum nitride (AlN) sublimation growth process, which involves extremely corrosive conditions, and demonstrated their practical reliability and durability in the AlN growth process as a TaC-coated graphite. The application of the TaC-coated graphite materials to crucibles and susceptors for use in bulk AlN single crystal growth, bulk silicon carbide (SiC) single crystal growth, chemical vapor deposition of epitaxial SiC films, and metal-organic vapor phase epitaxy of group-III nitrides will lead to further improvements in crystal quality and reduced processing costs.

Sintered tantalum carbide coatings on graphite substrates: Highly reliable protective coatings for bulk and epitaxial growth

International Nuclear Information System (INIS)

Nakamura, Daisuke; Suzumura, Akitoshi; Shigetoh, Keisuke

2015-01-01

Highly reliable low-cost protective coatings have been sought after for use in crucibles and susceptors for bulk and epitaxial film growth processes involving wide bandgap materials. Here, we propose a production technique for ultra-thick (50–200 μmt) tantalum carbide (TaC) protective coatings on graphite substrates, which consists of TaC slurry application and subsequent sintering processes, i.e., a wet ceramic process. Structural analysis of the sintered TaC layers indicated that they have a dense granular structure containing coarse grain with sizes of 10–50 μm. Furthermore, no cracks or pinholes penetrated through the layers, i.e., the TaC layers are highly reliable protective coatings. The analysis also indicated that no plastic deformation occurred during the production process, and the non-textured crystalline orientation of the TaC layers is the origin of their high reliability and durability. The TaC-coated graphite crucibles were tested in an aluminum nitride (AlN) sublimation growth process, which involves extremely corrosive conditions, and demonstrated their practical reliability and durability in the AlN growth process as a TaC-coated graphite. The application of the TaC-coated graphite materials to crucibles and susceptors for use in bulk AlN single crystal growth, bulk silicon carbide (SiC) single crystal growth, chemical vapor deposition of epitaxial SiC films, and metal-organic vapor phase epitaxy of group-III nitrides will lead to further improvements in crystal quality and reduced processing costs

Comparing the Discrete and Continuous Logistic Models

Science.gov (United States)

Gordon, Sheldon P.

2008-01-01

The solutions of the discrete logistic growth model based on a difference equation and the continuous logistic growth model based on a differential equation are compared and contrasted. The investigation is conducted using a dynamic interactive spreadsheet. (Contains 5 figures.)

Variable elasticity of substituition in a discrete time Solow–Swan growth model with differential saving

International Nuclear Information System (INIS)

Brianzoni, Serena; Mammana, Cristiana; Michetti, Elisabetta

2012-01-01

Highlights: ► One dimensional piecewise smooth map: border collision bifurcations. ► Numerical simulations: complex dynamics. ► Ves production function in the solow–swan growth model and comparison with the ces production function. - Abstract: We study the dynamics shown by the discrete time neoclassical one-sector growth model with differential savings as in Bohm and Kaas while assuming VES production function in the form given by Revankar . It is shown that the model can exhibit unbounded endogenous growth despite the absence of exogenous technical change and the presence of non-reproducible factors if the elasticity of substitution is greater than one. We then consider parameters range related to non-trivial dynamics (i.e. the elasticity of substitution in less than one and shareholders save more than workers) and we focus on local and global bifurcations causing the transition to more and more complex asymptotic dynamics. In particular, as our map is non-differentiable in a subset of the states space, we show that border collision bifurcations occur. Several numerical simulations support the analysis.

OPTIMIZATION OF THE RELIABILITY OF AGRICULTURAL CONSUMERS ELECTRICITY DISTRIBUTING AND SUPPLY SYSTEMS

Directory of Open Access Journals (Sweden)

Lupushor I.

2007-12-01

Full Text Available The problems of the optimization reliability in electrical networks of the different class of voltage have probabilistic nature, they discretely change and depend on the number of factors both definite and indefinite and have importance by selection of electric equipment, graph of development of electrical networks and voltage levels. The definition of the major factors, which have determining significance on their value and speed of their change allow to elaborate methods of their optimization and to elaborate effective methods of their growth limitation in electrical networks with the different class of voltage.

Software reliability growth models with normal failure time distributions

International Nuclear Information System (INIS)

Okamura, Hiroyuki; Dohi, Tadashi; Osaki, Shunji

2013-01-01

This paper proposes software reliability growth models (SRGM) where the software failure time follows a normal distribution. The proposed model is mathematically tractable and has sufficient ability of fitting to the software failure data. In particular, we consider the parameter estimation algorithm for the SRGM with normal distribution. The developed algorithm is based on an EM (expectation-maximization) algorithm and is quite simple for implementation as software application. Numerical experiment is devoted to investigating the fitting ability of the SRGMs with normal distribution through 16 types of failure time data collected in real software projects

Feature Extraction from 3D Point Cloud Data Based on Discrete Curves

Directory of Open Access Journals (Sweden)

Yi An

2013-01-01

Full Text Available Reliable feature extraction from 3D point cloud data is an important problem in many application domains, such as reverse engineering, object recognition, industrial inspection, and autonomous navigation. In this paper, a novel method is proposed for extracting the geometric features from 3D point cloud data based on discrete curves. We extract the discrete curves from 3D point cloud data and research the behaviors of chord lengths, angle variations, and principal curvatures at the geometric features in the discrete curves. Then, the corresponding similarity indicators are defined. Based on the similarity indicators, the geometric features can be extracted from the discrete curves, which are also the geometric features of 3D point cloud data. The threshold values of the similarity indicators are taken from [0,1], which characterize the relative relationship and make the threshold setting easier and more reasonable. The experimental results demonstrate that the proposed method is efficient and reliable.

Stochastic Finite Elements in Reliability-Based Structural Optimization

DEFF Research Database (Denmark)

Sørensen, John Dalsgaard; Engelund, S.

Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect to optimi......Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect...

Reliability and Cost Impacts for Attritable Systems

Science.gov (United States)

2017-03-23

on reliability and cost: a probabilistic model. Electric Power Systems Research, 72(3), 213-224. Kalbfleisch, J.D. & Prentice, R.L. (1980). The...copyright protection in the United States. AFIT-ENV-MS-17-M-172 RELIABILITY AND COST IMPACTS FOR ATTRITABLE SYSTEMS THESIS Presented to... power of discrete time Markov chains, whether homogeneous or non-homogeneous, to model the reliability and dependability of repairable systems should

A Discrete Fracture Network Model with Stress-Driven Nucleation and Growth

Science.gov (United States)

Lavoine, E.; Darcel, C.; Munier, R.; Davy, P.

2017-12-01

The realism of Discrete Fracture Network (DFN) models, beyond the bulk statistical properties, relies on the spatial organization of fractures, which is not issued by purely stochastic DFN models. The realism can be improved by injecting prior information in DFN from a better knowledge of the geological fracturing processes. We first develop a model using simple kinematic rules for mimicking the growth of fractures from nucleation to arrest, in order to evaluate the consequences of the DFN structure on the network connectivity and flow properties. The model generates fracture networks with power-law scaling distributions and a percentage of T-intersections that are consistent with field observations. Nevertheless, a larger complexity relying on the spatial variability of natural fractures positions cannot be explained by the random nucleation process. We propose to introduce a stress-driven nucleation in the timewise process of this kinematic model to study the correlations between nucleation, growth and existing fracture patterns. The method uses the stress field generated by existing fractures and remote stress as an input for a Monte-Carlo sampling of nuclei centers at each time step. Networks so generated are found to have correlations over a large range of scales, with a correlation dimension that varies with time and with the function that relates the nucleation probability to stress. A sensibility analysis of input parameters has been performed in 3D to quantify the influence of fractures and remote stress field orientations.

Growth characteristics of liquid cultures increase the reliability of presumptive identification of Mycobacterium tuberculosis complex.

Science.gov (United States)

Pinhata, Juliana Maira Watanabe; Felippe, Isis Moreira; Gallo, Juliana Failde; Chimara, Erica; Ferrazoli, Lucilaine; de Oliveira, Rosangela Siqueira

2018-04-23

We evaluated the microscopic and macroscopic characteristics of mycobacteria growth indicator tube (MGIT) cultures for the presumptive identification of the Mycobacterium tuberculosis complex (MTBC) and assessed the reliability of this strategy for correctly directing isolates to drug susceptibility testing (DST) or species identification. A total of 1526 isolates of mycobacteria received at the Instituto Adolfo Lutz were prospectively subjected to presumptive identification by the observation of growth characteristics along with cord formation detection via microscopy. The presumptive identification showed a sensitivity, specificity and accuracy of 98.8, 92.5 and 97.9 %, respectively. Macroscopic analysis of MTBC isolates that would have been erroneously classified as non-tuberculous mycobacteria based solely on microscopic morphology enabled us to direct them rapidly to DST, representing a substantial gain to patients. In conclusion, the growth characteristics of mycobacteria in MGIT, when considered along with cord formation, increased the reliability of the presumptive identification, which has a great impact on the laboratory budget and turnaround times.

Discrete gradients in discrete classical mechanics

International Nuclear Information System (INIS)

Renna, L.

1987-01-01

A simple model of discrete classical mechanics is given where, starting from the continuous Hamilton equations, discrete equations of motion are established together with a proper discrete gradient definition. The conservation laws of the total discrete momentum, angular momentum, and energy are demonstrated

Stochastic Finite Elements in Reliability-Based Structural Optimization

DEFF Research Database (Denmark)

Sørensen, John Dalsgaard; Engelund, S.

1995-01-01

Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect to optimi......Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect...... to optimization variables can be performed. A computer implementation is described and an illustrative example is given....

SM50 repeat-polypeptides self-assemble into discrete matrix subunits and promote appositional calcium carbonate crystal growth during sea urchin tooth biomineralization.

Science.gov (United States)

Mao, Yelin; Satchell, Paul G; Luan, Xianghong; Diekwisch, Thomas G H

2016-01-01

The two major proteins involved in vertebrate enamel formation and echinoderm sea urchin tooth biomineralization, amelogenin and SM50, are both characterized by elongated polyproline repeat domains in the center of the macromolecule. To determine the role of polyproline repeat polypeptides in basal deuterostome biomineralization, we have mapped the localization of SM50 as it relates to crystal growth, conducted self-assembly studies of SM50 repeat polypeptides, and examined their effect on calcium carbonate and apatite crystal growth. Electron micrographs of the growth zone of Strongylocentrotus purpuratus sea urchin teeth documented a series of successive events from intravesicular mineral nucleation to mineral deposition at the interface between tooth surface and odontoblast syncytium. Using immunohistochemistry, SM50 was detected within the cytoplasm of cells associated with the developing tooth mineral, at the mineral secreting front, and adjacent to initial mineral deposits, but not in muscles and ligaments. Polypeptides derived from the SM50 polyproline alternating hexa- and hepta-peptide repeat region (SM50P6P7) formed highly discrete, donut-shaped self-assembly patterns. In calcium carbonate crystal growth studies, SM50P6P7 repeat peptides triggered the growth of expansive networks of fused calcium carbonate crystals while in apatite growth studies, SM50P6P7 peptides facilitated the growth of needle-shaped and parallel arranged crystals resembling those found in developing vertebrate enamel. In comparison, SM50P6P7 surpassed the PXX24 polypeptide repeat region derived from the vertebrate enamel protein amelogenin in its ability to promote crystal nucleation and appositional crystal growth. Together, these studies establish the SM50P6P7 polyproline repeat region as a potent regulator in the protein-guided appositional crystal growth that occurs during continuous tooth mineralization and eruption. In addition, our studies highlight the role of species

Cone-beam tomography with discrete data sets

International Nuclear Information System (INIS)

Barrett, H.H.

1994-01-01

Sufficiently conditions for cone-beam data are well known for the case of continuous data collection along a cone-vortex curve with continuous detectors. These continuous conditions are inadequate for real-world data where discrete vertex geometries and discrete detector arrays are used. In this paper we present a theoretical formulation of cone-beam tomography with arbitrary discrete arrays of detectors and vertices. The theory models the imaging system as a linear continuous-to-discrete mapping and represents the continuous object exactly as a Fourier series. The reconstruction problem is posed as the estimation of some subset of the Fourier coefficients. The main goal of the theory is to determine which Fourier coefficients can be reliably determined from the data delivered by a specific discrete design. A fourier component will be well determined by the data if it satisfies two conditions: it makes a strong contribution to the data, and this contribution is relatively independent of the contribution of other Fourier components. To make these considerations precise, we introduce a concept called the cross-talk matrix. A diagonal element of this matrix measures the strength of a Fourier component in the data, while an off-diagonal element quantifies the dependence or aliasing of two different components. (Author)

Discrete mKdV and discrete sine-Gordon flows on discrete space curves

International Nuclear Information System (INIS)

Inoguchi, Jun-ichi; Kajiwara, Kenji; Matsuura, Nozomu; Ohta, Yasuhiro

2014-01-01

In this paper, we consider the discrete deformation of the discrete space curves with constant torsion described by the discrete mKdV or the discrete sine-Gordon equations, and show that it is formulated as the torsion-preserving equidistant deformation on the osculating plane which satisfies the isoperimetric condition. The curve is reconstructed from the deformation data by using the Sym–Tafel formula. The isoperimetric equidistant deformation of the space curves does not preserve the torsion in general. However, it is possible to construct the torsion-preserving deformation by tuning the deformation parameters. Further, it is also possible to make an arbitrary choice of the deformation described by the discrete mKdV equation or by the discrete sine-Gordon equation at each step. We finally show that the discrete deformation of discrete space curves yields the discrete K-surfaces. (paper)

Discrete Curvatures and Discrete Minimal Surfaces

KAUST Repository

Sun, Xiang

2012-06-01

This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads to great interest in studying discrete surfaces. With the rich smooth surface theory in hand, one would hope that this elegant theory can still be applied to the discrete counter part. Such a generalization, however, is not always successful. While discrete surfaces have the advantage of being finite dimensional, thus easier to treat, their geometric properties such as curvatures are not well defined in the classical sense. Furthermore, the powerful calculus tool can hardly be applied. The methods in this thesis, including angular defect formula, cotangent formula, parallel meshes, relative geometry etc. are approaches based on offset meshes or generalized offset meshes. As an important application, we discuss discrete minimal surfaces and discrete Koenigs meshes.

A New Multidisciplinary Design Optimization Method Accounting for Discrete and Continuous Variables under Aleatory and Epistemic Uncertainties

Directory of Open Access Journals (Sweden)

Hong-Zhong Huang

2012-02-01

Full Text Available Various uncertainties are inevitable in complex engineered systems and must be carefully treated in design activities. Reliability-Based Multidisciplinary Design Optimization (RBMDO has been receiving increasing attention in the past decades to facilitate designing fully coupled systems but also achieving a desired reliability considering uncertainty. In this paper, a new formulation of multidisciplinary design optimization, namely RFCDV (random/fuzzy/continuous/discrete variables Multidisciplinary Design Optimization (RFCDV-MDO, is developed within the framework of Sequential Optimization and Reliability Assessment (SORA to deal with multidisciplinary design problems in which both aleatory and epistemic uncertainties are present. In addition, a hybrid discrete-continuous algorithm is put forth to efficiently solve problems where both discrete and continuous design variables exist. The effectiveness and computational efficiency of the proposed method are demonstrated via a mathematical problem and a pressure vessel design problem.

Assessing the Reliability of Curriculum-Based Measurement: An Application of Latent Growth Modeling

Science.gov (United States)

Yeo, Seungsoo; Kim, Dong-Il; Branum-Martin, Lee; Wayman, Miya Miura; Espin, Christine A.

2012-01-01

The purpose of this study was to demonstrate the use of Latent Growth Modeling (LGM) as a method for estimating reliability of Curriculum-Based Measurement (CBM) progress-monitoring data. The LGM approach permits the error associated with each measure to differ at each time point, thus providing an alternative method for examining of the…

Continuous- and Discrete-Time Stimulus Sequences for High Stimulus Rate Paradigm in Evoked Potential Studies

Directory of Open Access Journals (Sweden)

Tao Wang

2013-01-01

Full Text Available To obtain reliable transient auditory evoked potentials (AEPs from EEGs recorded using high stimulus rate (HSR paradigm, it is critical to design the stimulus sequences of appropriate frequency properties. Traditionally, the individual stimulus events in a stimulus sequence occur only at discrete time points dependent on the sampling frequency of the recording system and the duration of stimulus sequence. This dependency likely causes the implementation of suboptimal stimulus sequences, sacrificing the reliability of resulting AEPs. In this paper, we explicate the use of continuous-time stimulus sequence for HSR paradigm, which is independent of the discrete electroencephalogram (EEG recording system. We employ simulation studies to examine the applicability of the continuous-time stimulus sequences and the impacts of sampling frequency on AEPs in traditional studies using discrete-time design. Results from these studies show that the continuous-time sequences can offer better frequency properties and improve the reliability of recovered AEPs. Furthermore, we find that the errors in the recovered AEPs depend critically on the sampling frequencies of experimental systems, and their relationship can be fitted using a reciprocal function. As such, our study contributes to the literature by demonstrating the applicability and advantages of continuous-time stimulus sequences for HSR paradigm and by revealing the relationship between the reliability of AEPs and sampling frequencies of the experimental systems when discrete-time stimulus sequences are used in traditional manner for the HSR paradigm.

Reliability of microprocessor-based relay protection devices: Myths and reality

Directory of Open Access Journals (Sweden)

Gurevich Vladimir

2009-01-01

Full Text Available The article examines four basic theses about the ostensibly extremely high reliability of microprocessor-based relay protection (MP touted by supporters of MP. Through detailed analysis based on many references it is shown that the basis of these theses are widespread myths, and actually MP reliability is lower than the reliability of electromechanical and electronic protective relays on discrete components.

A discrete dislocation–transformation model for austenitic single crystals

International Nuclear Information System (INIS)

Shi, J; Turteltaub, S; Remmers, J J C; Van der Giessen, E

2008-01-01

A discrete model for analyzing the interaction between plastic flow and martensitic phase transformations is developed. The model is intended for simulating the microstructure evolution in a single crystal of austenite that transforms non-homogeneously into martensite. The plastic flow in the untransformed austenite is simulated using a plane-strain discrete dislocation model. The phase transformation is modeled via the nucleation and growth of discrete martensitic regions embedded in the austenitic single crystal. At each instant during loading, the coupled elasto-plasto-transformation problem is solved using the superposition of analytical solutions for the discrete dislocations and discrete transformation regions embedded in an infinite homogeneous medium and the numerical solution of a complementary problem used to enforce the actual boundary conditions and the heterogeneities in the medium. In order to describe the nucleation and growth of martensitic regions, a nucleation criterion and a kinetic law suitable for discrete regions are specified. The constitutive rules used in discrete dislocation simulations are supplemented with additional evolution rules to account for the phase transformation. To illustrate the basic features of the model, simulations of specimens under plane-strain uniaxial extension and contraction are analyzed. The simulations indicate that plastic flow reduces the average stress at which transformation begins, but it also reduces the transformation rate when compared with benchmark simulations without plasticity. Furthermore, due to local stress fluctuations caused by dislocations, martensitic systems can be activated even though transformation would not appear to be favorable based on the average stress. Conversely, the simulations indicate that the plastic hardening behavior is influenced by the reduction in the effective austenitic grain size due to the evolution of transformation. During cyclic simulations, the coupled plasticity

The discrete additive Weibull distribution: A bathtub-shaped hazard for discontinuous failure data

International Nuclear Information System (INIS)

Bebbington, Mark; Lai, Chin-Diew; Wellington, Morgan; Zitikis, Ričardas

2012-01-01

Although failure data are usually treated as being continuous, they may have been collected in a discrete manner, or in fact be discrete in nature. Reliability models with bathtub-shaped hazard rate are fundamental to the concepts of burn-in and maintenance, but how well do they incorporate discrete data? We explore discrete versions of the additive Weibull distribution, which has the twin virtues of mathematical tractability and the ability to produce bathtub-shaped hazard rate functions. We derive conditions on the parameters for the hazard rate function to be increasing, decreasing, or bathtub shaped. While discrete versions may have the same shaped hazard rate for the same parameter values, we find that when fitted to data the fitted hazard rate shapes can vary between versions. Our results are illustrated using several real-life data sets, and the implications of using continuous models for discrete data discussed.

Integer valued autoregressive processes with generalized discrete Mittag-Leffler marginals

Directory of Open Access Journals (Sweden)

Kanichukattu K. Jose

2013-05-01

Full Text Available In this paper we consider a generalization of discrete Mittag-Leffler distributions. We introduce and study the properties of a new distribution called geometric generalized discrete Mittag-Leffler distribution. Autoregressive processes with geometric generalized discrete Mittag-Leffler distributions are developed and studied. The distributions are further extended to develop a more general class of geometric generalized discrete semi-Mittag-Leffler distributions. The processes are extended to higher orders also. An application with respect to an empirical data on customer arrivals in a bank counter is also given. Various areas of potential applications like human resource development, insect growth, epidemic modeling, industrial risk modeling, insurance and actuaries, town planning etc are also discussed.

Software reliability

CERN Document Server

Bendell, A

1986-01-01

Software Reliability reviews some fundamental issues of software reliability as well as the techniques, models, and metrics used to predict the reliability of software. Topics covered include fault avoidance, fault removal, and fault tolerance, along with statistical methods for the objective assessment of predictive accuracy. Development cost models and life-cycle cost models are also discussed. This book is divided into eight sections and begins with a chapter on adaptive modeling used to predict software reliability, followed by a discussion on failure rate in software reliability growth mo

[A reliability growth assessment method and its application in the development of equipment in space cabin].

Science.gov (United States)

Chen, J D; Sun, H L

1999-04-01

Objective. To assess and predict reliability of an equipment dynamically by making full use of various test informations in the development of products. Method. A new reliability growth assessment method based on army material system analysis activity (AMSAA) model was developed. The method is composed of the AMSAA model and test data conversion technology. Result. The assessment and prediction results of a space-borne equipment conform to its expectations. Conclusion. It is suggested that this method should be further researched and popularized.

Hydraulic Fracture Growth in a Layered Formation based on Fracturing Experiments and Discrete Element Modeling

Science.gov (United States)

Yushi, Zou; Xinfang, Ma; Tong, Zhou; Ning, Li; Ming, Chen; Sihai, Li; Yinuo, Zhang; Han, Li

2017-09-01

Hydraulic fracture (HF) height containment tends to occur in layered formations, and it significantly influences the entire HF geometry or the stimulated reservoir volume. This study aims to explore the influence of preexisting bedding planes (BPs) on the HF height growth in layered formations. Laboratory fracturing experiments were performed to confirm the occurrence of HF height containment in natural shale that contains multiple weak and high-permeability BPs under triaxial stresses. Numerical simulations were then conducted to further illustrate the manner in which vertical stress, BP permeability, BP density(or spacing), pump rate, and fluid viscosity control HF height growth using a 3D discrete element method-based fracturing model. In this model, the rock matrix was considered transversely isotropic and multiple BPs can be explicitly represented. Experimental and numerical results show that the vertically growing HF tends to be limited by multi-high-permeability BPs, even under higher vertical stress. When the vertically growing HF intersects with the multi-high-permeability BPs, the injection pressure will be sharply reduced. If a low pumping rate or a low-viscosity fluid is used, the excess fracturing fluid leak-off into the BPs obviously decreases the rate of pressure build up, which will then limit the growth of HF. Otherwise, a higher pumping rate and/or a higher viscosity will reduce the leak-off time and fluid volume, but increase the injection pressure to drive the HF to grow and to penetrate through the BPs.

Hierarchical Discrete Event Supervisory Control of Aircraft Propulsion Systems

Science.gov (United States)

Yasar, Murat; Tolani, Devendra; Ray, Asok; Shah, Neerav; Litt, Jonathan S.

2004-01-01

This paper presents a hierarchical application of Discrete Event Supervisory (DES) control theory for intelligent decision and control of a twin-engine aircraft propulsion system. A dual layer hierarchical DES controller is designed to supervise and coordinate the operation of two engines of the propulsion system. The two engines are individually controlled to achieve enhanced performance and reliability, necessary for fulfilling the mission objectives. Each engine is operated under a continuously varying control system that maintains the specified performance and a local discrete-event supervisor for condition monitoring and life extending control. A global upper level DES controller is designed for load balancing and overall health management of the propulsion system.

Application of discrete function and software control flow to dependability assessment of embedded digital system

International Nuclear Information System (INIS)

Choi, Jong Gyun; Seong, Poong Hyun

2001-01-01

This article describes a combinatorial model for estimating the reliability of the embedded digital system by means of discrete function theory and software control flow. This model includes a coverage model for fault processing mechanisms implemented in digital system. Furthermore, the model considers the interaction between hardware and software. The fault processing mechanisms make it difficult for many types of components in digital system to be treated as binary state, good or bad. The discrete function theory provides a complete analysis of multi-state system as which the digital system can be regarded Through adaptation software control flow to discrete function theory, the HW/SW interaction is considered for estimation of the reliability of digital system. Using this model, we predict the reliability of one board controller in a digital system, Interposing Logic System(ILS), which is installed in YGN nuclear power units 3 and 4. Since the proposed model is general combinatinal model, the simplification of this model becomes a conservative model that treats the system as binary state. Moreover, if information for coverage factor of fault tolerance mechanisms implemented in system through fault injection experiment is obtained, this model can consider detailed interaction of system components

Bayesian methods in reliability

Science.gov (United States)

Sander, P.; Badoux, R.

1991-11-01

The present proceedings from a course on Bayesian methods in reliability encompasses Bayesian statistical methods and their computational implementation, models for analyzing censored data from nonrepairable systems, the traits of repairable systems and growth models, the use of expert judgment, and a review of the problem of forecasting software reliability. Specific issues addressed include the use of Bayesian methods to estimate the leak rate of a gas pipeline, approximate analyses under great prior uncertainty, reliability estimation techniques, and a nonhomogeneous Poisson process. Also addressed are the calibration sets and seed variables of expert judgment systems for risk assessment, experimental illustrations of the use of expert judgment for reliability testing, and analyses of the predictive quality of software-reliability growth models such as the Weibull order statistics.

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2011-01-01

The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...

Baecklund transformations for discrete Painleve equations: Discrete PII-PV

International Nuclear Information System (INIS)

Sakka, A.; Mugan, U.

2006-01-01

Transformation properties of discrete Painleve equations are investigated by using an algorithmic method. This method yields explicit transformations which relates the solutions of discrete Painleve equations, discrete P II -P V , with different values of parameters. The particular solutions which are expressible in terms of the discrete analogue of the classical special functions of discrete Painleve equations can also be obtained from these transformations

Approximate probabilistic cellular automata for the dynamics of single-species populations under discrete logisticlike growth with and without weak Allee effects.

Science.gov (United States)

Mendonça, J Ricardo G; Gevorgyan, Yeva

2017-05-01

We investigate one-dimensional elementary probabilistic cellular automata (PCA) whose dynamics in first-order mean-field approximation yields discrete logisticlike growth models for a single-species unstructured population with nonoverlapping generations. Beginning with a general six-parameter model, we find constraints on the transition probabilities of the PCA that guarantee that the ensuing approximations make sense in terms of population dynamics and classify the valid combinations thereof. Several possible models display a negative cubic term that can be interpreted as a weak Allee factor. We also investigate the conditions under which a one-parameter PCA derived from the more general six-parameter model can generate valid population growth dynamics. Numerical simulations illustrate the behavior of some of the PCA found.

Diagnostic reliability of the cervical vertebral maturation method and standing height in the identification of the mandibular growth spurt.

Science.gov (United States)

Perinetti, Giuseppe; Contardo, Luca; Castaldo, Attilio; McNamara, James A; Franchi, Lorenzo

2016-07-01

To evaluate the capability of both cervical vertebral maturation (CVM) stages 3 and 4 (CS3-4 interval) and the peak in standing height to identify the mandibular growth spurt throughout diagnostic reliability analysis. A previous longitudinal data set derived from 24 untreated growing subjects (15 females and nine males,) detailed elsewhere were reanalyzed. Mandibular growth was defined as annual increments in Condylion (Co)-Gnathion (Gn) (total mandibular length) and Co-Gonion Intersection (Goi) (ramus height) and their arithmetic mean (mean mandibular growth [mMG]). Subsequently, individual annual increments in standing height, Co-Gn, Co-Goi, and mMG were arranged according to annual age intervals, with the first and last intervals defined as 7-8 years and 15-16 years, respectively. An analysis was performed to establish the diagnostic reliability of the CS3-4 interval or the peak in standing height in the identification of the maximum individual increments of each Co-Gn, Co-Goi, and mMG measurement at each annual age interval. CS3-4 and standing height peak show similar but variable accuracy across annual age intervals, registering values between 0.61 (standing height peak, Co-Gn) and 0.95 (standing height peak and CS3-4, mMG). Generally, satisfactory diagnostic reliability was seen when the mandibular growth spurt was identified on the basis of the Co-Goi and mMG increments. Both CVM interval CS3-4 and peak in standing height may be used in routine clinical practice to enhance efficiency of treatments requiring identification of the mandibular growth spurt.

Thermal modelling using discrete vasculature for thermal therapy: a review

Science.gov (United States)

Kok, H.P.; Gellermann, J.; van den Berg, C.A.T.; Stauffer, P.R.; Hand, J.W.; Crezee, J.

2013-01-01

Reliable temperature information during clinical hyperthermia and thermal ablation is essential for adequate treatment control, but conventional temperature measurements do not provide 3D temperature information. Treatment planning is a very useful tool to improve treatment quality and substantial progress has been made over the last decade. Thermal modelling is a very important and challenging aspect of hyperthermia treatment planning. Various thermal models have been developed for this purpose, with varying complexity. Since blood perfusion is such an important factor in thermal redistribution of energy in in vivo tissue, thermal simulations are most accurately performed by modelling discrete vasculature. This review describes the progress in thermal modelling with discrete vasculature for the purpose of hyperthermia treatment planning and thermal ablation. There has been significant progress in thermal modelling with discrete vasculature. Recent developments have made real-time simulations possible, which can provide feedback during treatment for improved therapy. Future clinical application of thermal modelling with discrete vasculature in hyperthermia treatment planning is expected to further improve treatment quality. PMID:23738700

Discrete Curvatures and Discrete Minimal Surfaces

KAUST Repository

Sun, Xiang

2012-01-01

This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads

Discrete radioisotopic relays of a cyclic action

International Nuclear Information System (INIS)

Klempner, K.S.; Vasil'ev, A.G.

1975-01-01

A functional diagram of discrete radioisotopic relay equipment (RRP) with cyclic action was examined. An analysis of its rapid action and reliability under stationary conditions and transition regimes is presented. A structural diagram of radioisotopic relay equipment shows three radiation detectors, a pulse standardizer, an integrator and a power amplifier with a threshold cut-off device. It was established that the basic properties of the RRP - rapid action and reliability - are determined entirely by the counting rate of the average frequency of pulses from the radiation detector, n 0 and n 1 , in the 0 and 1 states (absence of current in the electromagnetic relay winding and activation of the winding of the output relay), capacities N 1 and N 2 of the dual counters, and the frequency of the transition threshold, f, of the generator. Formulas are presented which allow making engineering calculations for determining the optimum RRP parameters. High speed and reliability are shown, which are determined by the production purposes of the relay

Modulational instability and discrete breathers in a nonlinear helicoidal lattice model

Science.gov (United States)

Ding, Jinmin; Wu, Tianle; Chang, Xia; Tang, Bing

2018-06-01

We investigate the problem on the discrete modulation instability of plane waves and discrete breather modes in a nonlinear helicoidal lattice model, which is described by a discrete nonlinear Schrödinger equation with the first-, second-, and third-neighbor coupling. By means of the linear stability analysis, we present an analytical expression of the instability growth rate and identify the regions of modulational instability of plane waves. It is shown that the introduction of the third-neighbor coupling will affect the shape of the areas of modulational instability significantly. Based on the results obtained by the modulational instability analysis, we predict the existence conditions for the stationary breather modes. Otherwise, by making use of the semidiscrete multiple-scale method, we obtain analytical solutions of discrete breather modes and analyze their properties for different types of nonlinearities. Our results show that the discrete breathers obtained are stable for a long time only when the system exhibits the repulsive nonlinearity. In addition, it is found that the existence of the stable bright discrete breather closely relates to the presence of the third-neighbor coupling.

Variability of a "force signature" during windmill softball pitching and relationship between discrete force variables and pitch velocity.

Science.gov (United States)

Nimphius, Sophia; McGuigan, Michael R; Suchomel, Timothy J; Newton, Robert U

2016-06-01

This study assessed reliability of discrete ground reaction force (GRF) variables over multiple pitching trials, investigated the relationships between discrete GRF variables and pitch velocity (PV) and assessed the variability of the "force signature" or continuous force-time curve during the pitching motion of windmill softball pitchers. Intraclass correlation coefficient (ICC) for all discrete variables was high (0.86-0.99) while the coefficient of variance (CV) was low (1.4-5.2%). Two discrete variables were significantly correlated to PV; second vertical peak force (r(5)=0.81, p=0.03) and time between peak forces (r(5)=-0.79; p=0.03). High ICCs and low CVs support the reliability of discrete GRF and PV variables over multiple trials and significant correlations indicate there is a relationship between the ability to produce force and the timing of this force production with PV. The mean of all pitchers' curve-average standard deviation of their continuous force-time curves demonstrated low variability (CV=4.4%) indicating a repeatable and identifiable "force signature" pattern during this motion. As such, the continuous force-time curve in addition to discrete GRF variables should be examined in future research as a potential method to monitor or explain changes in pitching performance. Copyright © 2016 Elsevier B.V. All rights reserved.

Pocket Handbook on Reliability

Science.gov (United States)

1975-09-01

exponencial distributions Weibull distribution, -xtimating reliability, confidence intervals, relia- bility growth, 0. P- curves, Bayesian analysis. 20 A S...introduction for those not familiar with reliability and a good refresher for those who are currently working in the area. LEWIS NERI, CHIEF...includes one or both of the following objectives: a) prediction of the current system reliability, b) projection on the system reliability for someI future

Histogram plots and cutoff energies for nuclear discrete levels

International Nuclear Information System (INIS)

Belgya, T.; Molnar, G.; Fazekas, B.; Oestoer, J.

1997-05-01

Discrete level schemes for 1277 nuclei, from 6 Li through 251 Es, extracted from the Evaluated Nuclear Structure Data File were analyzed. Cutoff energies (U max ), indicating the upper limit of level scheme completeness, were deduced from the inspection of histograms of the cumulative number of levels. Parameters of the constant-temperature level density formula (nuclear temperature T and energy shift U 0 ) were obtained by means of the least square fit of the formula to the known levels below cutoff energy. The results are tabulated for all 1277 nuclei allowing for an easy and reliable application of the constant-temperature level density approach. A complete set of cumulative plots of discrete levels is also provided. (author). 5 figs, 2 tabs

Mimetic discretization methods

CERN Document Server

Castillo, Jose E

2013-01-01

To help solve physical and engineering problems, mimetic or compatible algebraic discretization methods employ discrete constructs to mimic the continuous identities and theorems found in vector calculus. Mimetic Discretization Methods focuses on the recent mimetic discretization method co-developed by the first author. Based on the Castillo-Grone operators, this simple mimetic discretization method is invariably valid for spatial dimensions no greater than three. The book also presents a numerical method for obtaining corresponding discrete operators that mimic the continuum differential and

Modeling of system reliability Petri nets with aging tokens

International Nuclear Information System (INIS)

Volovoi, V.

2004-01-01

The paper addresses the dynamic modeling of degrading and repairable complex systems. Emphasis is placed on the convenience of modeling for the end user, with special attention being paid to the modeling part of a problem, which is considered to be decoupled from the choice of solution algorithms. Depending on the nature of the problem, these solution algorithms can include discrete event simulation or numerical solution of the differential equations that govern underlying stochastic processes. Such modularity allows a focus on the needs of system reliability modeling and tailoring of the modeling formalism accordingly. To this end, several salient features are chosen from the multitude of existing extensions of Petri nets, and a new concept of aging tokens (tokens with memory) is introduced. The resulting framework provides for flexible and transparent graphical modeling with excellent representational power that is particularly suited for system reliability modeling with non-exponentially distributed firing times. The new framework is compared with existing Petri-net approaches and other system reliability modeling techniques such as reliability block diagrams and fault trees. The relative differences are emphasized and illustrated with several examples, including modeling of load sharing, imperfect repair of pooled items, multiphase missions, and damage-tolerant maintenance. Finally, a simple implementation of the framework using discrete event simulation is described

Discrete-space versus continuous-space lesion boundary and area definitions

International Nuclear Information System (INIS)

Sensakovic, William F.; Starkey, Adam; Roberts, Rachael Y.; Armato, Samuel G. III

2008-01-01

Measurement of the size of anatomic regions of interest in medical images is used to diagnose disease, track growth, and evaluate response to therapy. The discrete nature of medical images allows for both continuous and discrete definitions of region boundary. These definitions may, in turn, support several methods of area calculation that give substantially different quantitative values. This study investigated several boundary definitions (e.g., continuous polygon, internal discrete, and external discrete) and area calculation methods (pixel counting and Green's theorem). These methods were applied to three separate databases: A synthetic image database, the Lung Image Database Consortium database of lung nodules and a database of adrenal gland outlines. Average percent differences in area on the order of 20% were found among the different methods applied to the clinical databases. These results support the idea that inconsistent application of region boundary definition and area calculation may substantially impact measurement accuracy

Cost-effective solutions to maintaining smart grid reliability

Science.gov (United States)

Qin, Qiu

As the aging power systems are increasingly working closer to the capacity and thermal limits, maintaining an sufficient reliability has been of great concern to the government agency, utility companies and users. This dissertation focuses on improving the reliability of transmission and distribution systems. Based on the wide area measurements, multiple model algorithms are developed to diagnose transmission line three-phase short to ground faults in the presence of protection misoperations. The multiple model algorithms utilize the electric network dynamics to provide prompt and reliable diagnosis outcomes. Computational complexity of the diagnosis algorithm is reduced by using a two-step heuristic. The multiple model algorithm is incorporated into a hybrid simulation framework, which consist of both continuous state simulation and discrete event simulation, to study the operation of transmission systems. With hybrid simulation, line switching strategy for enhancing the tolerance to protection misoperations is studied based on the concept of security index, which involves the faulted mode probability and stability coverage. Local measurements are used to track the generator state and faulty mode probabilities are calculated in the multiple model algorithms. FACTS devices are considered as controllers for the transmission system. The placement of FACTS devices into power systems is investigated with a criterion of maintaining a prescribed level of control reconfigurability. Control reconfigurability measures the small signal combined controllability and observability of a power system with an additional requirement on fault tolerance. For the distribution systems, a hierarchical framework, including a high level recloser allocation scheme and a low level recloser placement scheme, is presented. The impacts of recloser placement on the reliability indices is analyzed. Evaluation of reliability indices in the placement process is carried out via discrete event

Reliability Engineering

CERN Document Server

Lazzaroni, Massimo

2012-01-01

This book gives a practical guide for designers and users in Information and Communication Technology context. In particular, in the first Section, the definition of the fundamental terms according to the international standards are given. Then, some theoretical concepts and reliability models are presented in Chapters 2 and 3: the aim is to evaluate performance for components and systems and reliability growth. Chapter 4, by introducing the laboratory tests, puts in evidence the reliability concept from the experimental point of view. In ICT context, the failure rate for a given system can be

Intelligent discrete particle swarm optimization for multiprocessor task scheduling problem

Directory of Open Access Journals (Sweden)

S Sarathambekai

2017-03-01

Full Text Available Discrete particle swarm optimization is one of the most recently developed population-based meta-heuristic optimization algorithm in swarm intelligence that can be used in any discrete optimization problems. This article presents a discrete particle swarm optimization algorithm to efficiently schedule the tasks in the heterogeneous multiprocessor systems. All the optimization algorithms share a common algorithmic step, namely population initialization. It plays a significant role because it can affect the convergence speed and also the quality of the final solution. The random initialization is the most commonly used method in majority of the evolutionary algorithms to generate solutions in the initial population. The initial good quality solutions can facilitate the algorithm to locate the optimal solution or else it may prevent the algorithm from finding the optimal solution. Intelligence should be incorporated to generate the initial population in order to avoid the premature convergence. This article presents a discrete particle swarm optimization algorithm, which incorporates opposition-based technique to generate initial population and greedy algorithm to balance the load of the processors. Make span, flow time, and reliability cost are three different measures used to evaluate the efficiency of the proposed discrete particle swarm optimization algorithm for scheduling independent tasks in distributed systems. Computational simulations are done based on a set of benchmark instances to assess the performance of the proposed algorithm.

Continuous versus discrete structures II -- Discrete Hamiltonian systems and Helmholtz conditions

OpenAIRE

Cresson, Jacky; Pierret, Frédéric

2015-01-01

We define discrete Hamiltonian systems in the framework of discrete embeddings. An explicit comparison with previous attempts is given. We then solve the discrete Helmholtz's inverse problem for the discrete calculus of variation in the Hamiltonian setting. Several applications are discussed.

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2011-01-01

; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics...... to new problems. Relations and functions: Define a product set; define and apply equivalence relations; construct and apply functions. Apply these concepts to new problems. Natural numbers and induction: Define the natural numbers; apply the principle of induction to verify a selection of properties...

Digital Discretion

DEFF Research Database (Denmark)

Busch, Peter Andre; Zinner Henriksen, Helle

2018-01-01

discretion is suggested to reduce this footprint by influencing or replacing their discretionary practices using ICT. What is less researched is whether digital discretion can cause changes in public policy outcomes, and under what conditions such changes can occur. Using the concept of public service values......This study reviews 44 peer-reviewed articles on digital discretion published in the period from 1998 to January 2017. Street-level bureaucrats have traditionally had a wide ability to exercise discretion stirring debate since they can add their personal footprint on public policies. Digital......, we suggest that digital discretion can strengthen ethical and democratic values but weaken professional and relational values. Furthermore, we conclude that contextual factors such as considerations made by policy makers on the macro-level and the degree of professionalization of street...

Compatible discrete operator schemes on polyhedral meshes for elliptic and Stokes equations

International Nuclear Information System (INIS)

Bonelle, Jerome

2014-01-01

This thesis presents a new class of spatial discretization schemes on polyhedral meshes, called Compatible Discrete Operator (CDO) schemes and their application to elliptic and Stokes equations In CDO schemes, preserving the structural properties of the continuous equations is the leading principle to design the discrete operators. De Rham maps define the degrees of freedom according to the physical nature of fields to discretize. CDO schemes operate a clear separation between topological relations (balance equations) and constitutive relations (closure laws). Topological relations are related to discrete differential operators, and constitutive relations to discrete Hodge operators. A feature of CDO schemes is the explicit use of a second mesh, called dual mesh, to build the discrete Hodge operator. Two families of CDO schemes are considered: vertex-based schemes where the potential is located at (primal) mesh vertices, and cell-based schemes where the potential is located at dual mesh vertices (dual vertices being in one-to-one correspondence with primal cells). The CDO schemes related to these two families are presented and their convergence is analyzed. A first analysis hinges on an algebraic definition of the discrete Hodge operator and allows one to identify three key properties: symmetry, stability, and P0-consistency. A second analysis hinges on a definition of the discrete Hodge operator using reconstruction operators, and the requirements on these reconstruction operators are identified. In addition, CDO schemes provide a unified vision on a broad class of schemes proposed in the literature (finite element, finite element, mimetic schemes... ). Finally, the reliability and the efficiency of CDO schemes are assessed on various test cases and several polyhedral meshes. (author)

Machine Learning Approach for Software Reliability Growth Modeling with Infinite Testing Effort Function

Directory of Open Access Journals (Sweden)

Subburaj Ramasamy

2017-01-01

Full Text Available Reliability is one of the quantifiable software quality attributes. Software Reliability Growth Models (SRGMs are used to assess the reliability achieved at different times of testing. Traditional time-based SRGMs may not be accurate enough in all situations where test effort varies with time. To overcome this lacuna, test effort was used instead of time in SRGMs. In the past, finite test effort functions were proposed, which may not be realistic as, at infinite testing time, test effort will be infinite. Hence in this paper, we propose an infinite test effort function in conjunction with a classical Nonhomogeneous Poisson Process (NHPP model. We use Artificial Neural Network (ANN for training the proposed model with software failure data. Here it is possible to get a large set of weights for the same model to describe the past failure data equally well. We use machine learning approach to select the appropriate set of weights for the model which will describe both the past and the future data well. We compare the performance of the proposed model with existing model using practical software failure data sets. The proposed log-power TEF based SRGM describes all types of failure data equally well and also improves the accuracy of parameter estimation more than existing TEF and can be used for software release time determination as well.

Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations

KAUST Repository

Mohamed, Mamdouh S.

2017-05-23

A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy otherwise. The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of barycentric Hodge star allows the discretization to admit arbitrary simplicial meshes. The discretization scheme is presented along with various numerical test cases demonstrating its main characteristics.

Computing interval-valued statistical characteristics: What is the stumbling block for reliability applications?

DEFF Research Database (Denmark)

Kozine, Igor; Krymsky, V.G.

2009-01-01

The application of interval-valued statistical models is often hindered by the rapid growth in imprecision that occurs when intervals are propagated through models. Is this deficiency inherent in the models? If so, what is the underlying cause of imprecision in mathematical terms? What kind...... of additional information can be incorporated to make the bounds tighter? The present paper gives an account of the source of this imprecision that prevents interval-valued statistical models from being widely applied. Firstly, the mathematical approach to building interval-valued models (discrete...... and continuous) is delineated. Secondly, a degree of imprecision is demonstrated on some simple reliability models. Thirdly, the root mathematical cause of sizeable imprecision is elucidated and, finally, a method of making the intervals tighter is described. A number of examples are given throughout the paper....

On the influence of spatial discretization in LWR steady state and burnup calculations with HELIOS 1.9

International Nuclear Information System (INIS)

Merk, B.; Weiss, F. P.

2009-01-01

Cell and burnup calculations are fundamental to all deterministic static and transient 3D full core calculations for different operational states of the reactor. The spatial discretization used for the cell and burnup calculations influences significantly the results of full integral transport solutions. The influence of the discretization on k inf is shown for the steady state case and the influence on the neutron spectrum is analyzed. Moreover, the differences in k inf are presented for different spatial discretization strategies in the burnup calculation of Uranium Oxide (UOX) fuel. The resulting different flux distributions cause significant changes in the isotopic densities. The influence of the discretization strategies on the calculation of homogenized few group cross-sections is investigated. This detailed discretization study demonstrates the need for sufficiently fine discretization to produce reliable and accurate results when using integral transport methods. In contrast to the currently used discretization schemes, refined discretization is especially important in the moderator region of the unit cell to reproduce the influence on the thermal neutron spectrum. Additionally, the need for sufficient discretization affects the idea of full core calculations based on integral transport methods since it has to be discussed whether it is worth to do full core calculations with reduced discretization when facing this strong discretization effect. The computer resources required for full core calculations with fine discretization are currently not available. (authors)

Discrete Ramanujan transform for distinguishing the protein coding regions from other regions.

Science.gov (United States)

Hua, Wei; Wang, Jiasong; Zhao, Jian

2014-01-01

Based on the study of Ramanujan sum and Ramanujan coefficient, this paper suggests the concepts of discrete Ramanujan transform and spectrum. Using Voss numerical representation, one maps a symbolic DNA strand as a numerical DNA sequence, and deduces the discrete Ramanujan spectrum of the numerical DNA sequence. It is well known that of discrete Fourier power spectrum of protein coding sequence has an important feature of 3-base periodicity, which is widely used for DNA sequence analysis by the technique of discrete Fourier transform. It is performed by testing the signal-to-noise ratio at frequency N/3 as a criterion for the analysis, where N is the length of the sequence. The results presented in this paper show that the property of 3-base periodicity can be only identified as a prominent spike of the discrete Ramanujan spectrum at period 3 for the protein coding regions. The signal-to-noise ratio for discrete Ramanujan spectrum is defined for numerical measurement. Therefore, the discrete Ramanujan spectrum and the signal-to-noise ratio of a DNA sequence can be used for distinguishing the protein coding regions from the noncoding regions. All the exon and intron sequences in whole chromosomes 1, 2, 3 and 4 of Caenorhabditis elegans have been tested and the histograms and tables from the computational results illustrate the reliability of our method. In addition, we have analyzed theoretically and gotten the conclusion that the algorithm for calculating discrete Ramanujan spectrum owns the lower computational complexity and higher computational accuracy. The computational experiments show that the technique by using discrete Ramanujan spectrum for classifying different DNA sequences is a fast and effective method. Copyright © 2014 Elsevier Ltd. All rights reserved.

Reliability modeling of Clinch River breeder reactor electrical shutdown systems

International Nuclear Information System (INIS)

Schatz, R.A.; Duetsch, K.L.

1974-01-01

The initial simulation of the probabilistic properties of the Clinch River Breeder Reactor Plant (CRBRP) electrical shutdown systems is described. A model of the reliability (and availability) of the systems is presented utilizing Success State and continuous-time, discrete state Markov modeling techniques as significant elements of an overall reliability assessment process capable of demonstrating the achievement of program goals. This model is examined for its sensitivity to safe/unsafe failure rates, sybsystem redundant configurations, test and repair intervals, monitoring by reactor operators; and the control exercised over system reliability by design modifications and the selection of system operating characteristics. (U.S.)

Two routes to the one-dimensional discrete nonpolynomial Schroedinger equation

International Nuclear Information System (INIS)

Gligoric, G.; Hadzievski, Lj.; Maluckov, A.; Salasnich, L.; Malomed, B. A.

2009-01-01

The Bose-Einstein condensate (BEC), confined in a combination of the cigar-shaped trap and axial optical lattice, is studied in the framework of two models described by two versions of the one-dimensional (1D) discrete nonpolynomial Schroedinger equation (NPSE). Both models are derived from the three-dimensional Gross-Pitaevskii equation (3D GPE). To produce 'model 1' (which was derived in recent works), the 3D GPE is first reduced to the 1D continual NPSE, which is subsequently discretized. 'Model 2,' which was not considered before, is derived by first discretizing the 3D GPE, which is followed by the reduction in the dimension. The two models seem very different; in particular, model 1 is represented by a single discrete equation for the 1D wave function, while model 2 includes an additional equation for the transverse width. Nevertheless, numerical analyses show similar behaviors of fundamental unstaggered solitons in both systems, as concerns their existence region and stability limits. Both models admit the collapse of the localized modes, reproducing the fundamental property of the self-attractive BEC confined in tight traps. Thus, we conclude that the fundamental properties of discrete solitons predicted for the strongly trapped self-attracting BEC are reliable, as the two distinct models produce them in a nearly identical form. However, a difference between the models is found too, as strongly pinned (very narrow) discrete solitons, which were previously found in model 1, are not generated by model 2--in fact, in agreement with the continual 1D NPSE, which does not have such solutions either. In that respect, the newly derived model provides for a more accurate approximation for the trapped BEC.

Elementary exact calculations of degree growth and entropy for discrete equations.

Science.gov (United States)

Halburd, R G

2017-05-01

Second-order discrete equations are studied over the field of rational functions [Formula: see text], where z is a variable not appearing in the equation. The exact degree of each iterate as a function of z can be calculated easily using the standard calculations that arise in singularity confinement analysis, even when the singularities are not confined. This produces elementary yet rigorous entropy calculations.

Discrete dislocation plasticity modeling of short cracks in single crystals

NARCIS (Netherlands)

Deshpande, VS; Needleman, A; Van der Giessen, E

2003-01-01

The mode-I crack growth behavior of geometrically similar edge-cracked single crystal specimens of varying size subject to both monotonic and cyclic axial loading is analyzed using discrete dislocation dynamics. Plastic deformation is modeled through the motion of edge dislocations in an elastic

Local and global dynamics of Ramsey model: From continuous to discrete time.

Science.gov (United States)

Guzowska, Malgorzata; Michetti, Elisabetta

2018-05-01

The choice of time as a discrete or continuous variable may radically affect equilibrium stability in an endogenous growth model with durable consumption. In the continuous-time Ramsey model [F. P. Ramsey, Econ. J. 38(152), 543-559 (1928)], the steady state is locally saddle-path stable with monotonic convergence. However, in the discrete-time version, the steady state may be unstable or saddle-path stable with monotonic or oscillatory convergence or periodic solutions [see R.-A. Dana et al., Handbook on Optimal Growth 1 (Springer, 2006) and G. Sorger, Working Paper No. 1505 (2015)]. When this occurs, the discrete-time counterpart of the continuous-time model is not consistent with the initial framework. In order to obtain a discrete-time Ramsey model preserving the main properties of the continuous-time counterpart, we use a general backward and forward discretisation as initially proposed by Bosi and Ragot [Theor. Econ. Lett. 2(1), 10-15 (2012)]. The main result of the study here presented is that, with this hybrid discretisation method, fixed points and local dynamics do not change. For what it concerns global dynamics, i.e., long-run behavior for initial conditions taken on the state space, we mainly perform numerical analysis with the main scope of comparing both qualitative and quantitative evolution of the two systems, also varying some parameters of interest.

Development of scanning micromirror with discrete steering angles

International Nuclear Information System (INIS)

Wang, Z F; Noell, W; Zickar, M; Rooij, N F de; Lim, S P

2006-01-01

This paper describes the development of a new MEMS-based optical mirror, which can perform optical switching (or scanning) function with discrete reflection angles in an outof- plane configuration. The device is fabricated through the Deep Reactive Ion Etching (DRIE) process on silicon-on-insulator (SOI) wafer, followed by wafer dicing and assembly with two metalised glass dies. The MEMS mirror can be tilted under electrostatic force between the opposite electrodes embedded on SOI and glass structures. The most outstanding feature of this MEMS mirror is the discrete and therefore, reliable tilting angles, which generated by its unique mechanical structural design and electrostatic-driven mechanism. In this paper, the concept of the new scanning mirror is presented, followed by the introduction of device design, mechanical simulation, microfabrication process, assembly solution, and some testing results. The potential applications of this new MEMS mirror include optical scanning, optical sensing (or detection), and optical switching

Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations

KAUST Repository

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2017-01-01

A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy

DISCRETE MATHEMATICS/NUMBER THEORY

OpenAIRE

Mrs. Manju Devi*

2017-01-01

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics such as integers, graphs, and statements do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects can often be enumerated by ...

Resonance and web structure in discrete soliton systems: the two-dimensional Toda lattice and its fully discrete and ultra-discrete analogues

International Nuclear Information System (INIS)

Maruno, Ken-ichi; Biondini, Gino

2004-01-01

We present a class of solutions of the two-dimensional Toda lattice equation, its fully discrete analogue and its ultra-discrete limit. These solutions demonstrate the existence of soliton resonance and web-like structure in discrete integrable systems such as differential-difference equations, difference equations and cellular automata (ultra-discrete equations)

Power plant reliability calculation with Markov chain models

International Nuclear Information System (INIS)

Senegacnik, A.; Tuma, M.

1998-01-01

In the paper power plant operation is modelled using continuous time Markov chains with discrete state space. The model is used to compute the power plant reliability and the importance and influence of individual states, as well as the transition probabilities between states. For comparison the model is fitted to data for coal and nuclear power plants recorded over several years. (orig.) [de

Reliability considerations of electronics components for the deep underwater muon and neutrino detection system

International Nuclear Information System (INIS)

Leskovar, B.

1980-02-01

The reliability of some electronics components for the Deep Underwater Muon and Neutrino Detection (DUMAND) System is discussed. An introductory overview of engineering concepts and technique for reliability assessment is given. Component reliability is discussed in the contest of major factors causing failures, particularly with respect to physical and chemical causes, process technology and testing, and screening procedures. Failure rates are presented for discrete devices and for integrated circuits as well as for basic electronics components. Furthermore, the military reliability specifications and standards for semiconductor devices are reviewed

Reliability of length measurements collected by community nurses and health volunteers in rural growth monitoring and promotion services.

Science.gov (United States)

Laar, Matilda E; Marquis, Grace S; Lartey, Anna; Gray-Donald, Katherine

2018-02-17

Length measurements are important in growth, monitoring and promotion (GMP) for the surveillance of a child's weight-for-length and length-for-age. These two indices provide an indication of a child's risk of becoming wasted or stunted, and are more informative about a child's growth than the widely used weight-for-age index (underweight). Although the introduction of length measurements in GMP is recommended by the World Health Organization, concerns about the reliability of length measurements collected in rural outreach settings have been expressed by stakeholders. Our aim was to describe the reliability and challenges associated with community health personnel measuring length for rural outreach GMP activities. Two reliability studies (A and B), using 10 children less than 24 months each, were conducted in the GMP services of a rural district in Ghana. Fifteen nurses and 15 health volunteers (HV) with no prior experience in length measurements were trained. Intra- and inter-observer technical error of measurement (TEM), average bias from expert anthropometrist, and coefficient of reliability (R) of length measurements were assessed and compared across sessions. Observations and interviews were used to understand the ability and experiences of health personnel with measuring length at outreach GMP. Inter-observer TEM was larger than intra-observer TEM for both nurses and HV at both sessions and was unacceptably (compared to error standards) high in both groups at both time points. Average biases from expert's measurements were within acceptable limits, however, both groups tended to underestimate length measurements. The R for lengths collected by nurses (92.3%) was higher at session B compared to that of HV (87.5%). Length measurements taken by nurses and HV, and those taken by an experienced anthropometrist at GMP sessions were of moderate agreement (kappa = 0.53, p reliability of length measurements improved after two refresher trainings for nurses but

Discrete control systems

CERN Document Server

Okuyama, Yoshifumi

2014-01-01

Discrete Control Systems establishes a basis for the analysis and design of discretized/quantized control systemsfor continuous physical systems. Beginning with the necessary mathematical foundations and system-model descriptions, the text moves on to derive a robust stability condition. To keep a practical perspective on the uncertain physical systems considered, most of the methods treated are carried out in the frequency domain. As part of the design procedure, modified Nyquist–Hall and Nichols diagrams are presented and discretized proportional–integral–derivative control schemes are reconsidered. Schemes for model-reference feedback and discrete-type observers are proposed. Although single-loop feedback systems form the core of the text, some consideration is given to multiple loops and nonlinearities. The robust control performance and stability of interval systems (with multiple uncertainties) are outlined. Finally, the monograph describes the relationship between feedback-control and discrete ev...

Software reliability through fault-avoidance and fault-tolerance

Science.gov (United States)

Vouk, Mladen A.; Mcallister, David F.

1992-01-01

Accomplishments in the following research areas are summarized: structure based testing, reliability growth, and design testability with risk evaluation; reliability growth models and software risk management; and evaluation of consensus voting, consensus recovery block, and acceptance voting. Four papers generated during the reporting period are included as appendices.

Passive Fault-tolerant Control of Discrete-time Piecewise Affine Systems against Actuator Faults

DEFF Research Database (Denmark)

Tabatabaeipour, Seyed Mojtaba; Izadi-Zamanabadi, Roozbeh; Bak, Thomas

2012-01-01

In this paper, we propose a new method for passive fault-tolerant control of discrete time piecewise affine systems. Actuator faults are considered. A reliable piecewise linear quadratic regulator (LQR) state feedback is designed such that it can tolerate actuator faults. A sufficient condition f...... is illustrated on a numerical example and a two degree of freedom helicopter....

Discrete Element Modeling

Energy Technology Data Exchange (ETDEWEB)

Morris, J; Johnson, S

2007-12-03

The Distinct Element Method (also frequently referred to as the Discrete Element Method) (DEM) is a Lagrangian numerical technique where the computational domain consists of discrete solid elements which interact via compliant contacts. This can be contrasted with Finite Element Methods where the computational domain is assumed to represent a continuum (although many modern implementations of the FEM can accommodate some Distinct Element capabilities). Often the terms Discrete Element Method and Distinct Element Method are used interchangeably in the literature, although Cundall and Hart (1992) suggested that Discrete Element Methods should be a more inclusive term covering Distinct Element Methods, Displacement Discontinuity Analysis and Modal Methods. In this work, DEM specifically refers to the Distinct Element Method, where the discrete elements interact via compliant contacts, in contrast with Displacement Discontinuity Analysis where the contacts are rigid and all compliance is taken up by the adjacent intact material.

Discrete Address Beacon System (DABS) Software System Reliability Modeling and Prediction.

Science.gov (United States)

1981-06-01

Service ( ATARS ) module because of its interim status. Reliability prediction models for software modules were derived and then verified by matching...System (A’iCR3BS) and thus can be introduced gradually and economically without ma jor olper- ational or procedural change. Since DABS uses monopulse...lineanaly- sis tools or are ured during maintenance or pre-initialization were not modeled because they are not part of the mission software. The ATARS

Reliability analysis of a consecutive r-out-of-n: F system based on neural networks

International Nuclear Information System (INIS)

Habib, Aziz; Alsieidi, Ragab; Youssef, Ghada

2009-01-01

In this paper, we present a generalized Markov reliability and fault-tolerant model, which includes the effects of permanent fault and intermittent fault for reliability evaluations based on neural network techniques. The reliability of a consecutive r-out-of-n: F system was obtained with a three-layer connected neural network represents a discrete time state reliability Markov model of the system. Such that we fed the neural network with the desired reliability of the system under design. Then we extracted the parameters of the system from the neural weights at the convergence of the neural network to the desired reliability. Finally, we obtain simulation results.

Tracking reliability for space cabin-borne equipment in development by Crow model.

Science.gov (United States)

Chen, J D; Jiao, S J; Sun, H L

2001-12-01

Objective. To study and track the reliability growth of manned spaceflight cabin-borne equipment in the course of its development. Method. A new technique of reliability growth estimation and prediction, which is composed of the Crow model and test data conversion (TDC) method was used. Result. The estimation and prediction value of the reliability growth conformed to its expectations. Conclusion. The method could dynamically estimate and predict the reliability of the equipment by making full use of various test information in the course of its development. It offered not only a possibility of tracking the equipment reliability growth, but also the reference for quality control in manned spaceflight cabin-borne equipment design and development process.

Accelerated reliability demonstration under competing failure modes

International Nuclear Information System (INIS)

Luo, Wei; Zhang, Chun-hua; Chen, Xun; Tan, Yuan-yuan

2015-01-01

The conventional reliability demonstration tests are difficult to apply to products with competing failure modes due to the complexity of the lifetime models. This paper develops a testing methodology based on the reliability target allocation for reliability demonstration under competing failure modes at accelerated conditions. The specified reliability at mission time and the risk caused by sampling of the reliability target for products are allocated for each failure mode. The risk caused by degradation measurement fitting of the target for a product involving performance degradation is equally allocated to each degradation failure mode. According to the allocated targets, the accelerated life reliability demonstration test (ALRDT) plans for the failure modes are designed. The accelerated degradation reliability demonstration test plans and the associated ALRDT plans for the degradation failure modes are also designed. Next, the test plan and the decision rules for the products are designed. Additionally, the effects of the discreteness of sample size and accepted number of failures for failure modes on the actual risks caused by sampling for the products are investigated. - Highlights: • Accelerated reliability demonstration under competing failure modes is studied. • The method is based on the reliability target allocation involving the risks. • The test plan for the products is based on the plans for all the failure modes. • Both failure mode and degradation failure modes are considered. • The error of actual risks caused by sampling for the products is small enough

A Discrete Spectral Problem and Related Hierarchy of Discrete Hamiltonian Lattice Equations

International Nuclear Information System (INIS)

Xu Xixiang; Cao Weili

2007-01-01

Staring from a discrete matrix spectral problem, a hierarchy of lattice soliton equations is presented though discrete zero curvature representation. The resulting lattice soliton equations possess non-local Lax pairs. The Hamiltonian structures are established for the resulting hierarchy by the discrete trace identity. Liouville integrability of resulting hierarchy is demonstrated.

Discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes

KAUST Repository

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2016-01-01

A conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a

Asymptotic behavior of discrete holomorphic maps z^c, log(z) and discrete Painleve transcedents

OpenAIRE

Agafonov, S. I.

2005-01-01

It is shown that discrete analogs of z^c and log(z) have the same asymptotic behavior as their smooth counterparts. These discrete maps are described in terms of special solutions of discrete Painleve-II equations, asymptotics of these solutions providing the behaviour of discrete z^c and log(z) at infinity.

Disease Extinction Versus Persistence in Discrete-Time Epidemic Models.

Science.gov (United States)

van den Driessche, P; Yakubu, Abdul-Aziz

2018-04-12

We focus on discrete-time infectious disease models in populations that are governed by constant, geometric, Beverton-Holt or Ricker demographic equations, and give a method for computing the basic reproduction number, [Formula: see text]. When [Formula: see text] and the demographic population dynamics are asymptotically constant or under geometric growth (non-oscillatory), we prove global asymptotic stability of the disease-free equilibrium of the disease models. Under the same demographic assumption, when [Formula: see text], we prove uniform persistence of the disease. We apply our theoretical results to specific discrete-time epidemic models that are formulated for SEIR infections, cholera in humans and anthrax in animals. Our simulations show that a unique endemic equilibrium of each of the three specific disease models is asymptotically stable whenever [Formula: see text].

Discrete port-Hamiltonian systems

NARCIS (Netherlands)

Talasila, V.; Clemente-Gallardo, J.; Schaft, A.J. van der

2006-01-01

Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling

Applied discrete-time queues

CERN Document Server

Alfa, Attahiru S

2016-01-01

This book introduces the theoretical fundamentals for modeling queues in discrete-time, and the basic procedures for developing queuing models in discrete-time. There is a focus on applications in modern telecommunication systems. It presents how most queueing models in discrete-time can be set up as discrete-time Markov chains. Techniques such as matrix-analytic methods (MAM) that can used to analyze the resulting Markov chains are included. This book covers single node systems, tandem system and queueing networks. It shows how queues with time-varying parameters can be analyzed, and illustrates numerical issues associated with computations for the discrete-time queueing systems. Optimal control of queues is also covered. Applied Discrete-Time Queues targets researchers, advanced-level students and analysts in the field of telecommunication networks. It is suitable as a reference book and can also be used as a secondary text book in computer engineering and computer science. Examples and exercises are includ...

Norms for 10,491 Spanish words for five discrete emotions: Happiness, disgust, anger, fear, and sadness.

Science.gov (United States)

Stadthagen-González, Hans; Ferré, Pilar; Pérez-Sánchez, Miguel A; Imbault, Constance; Hinojosa, José Antonio

2017-09-18

The discrete emotion theory proposes that affective experiences can be reduced to a limited set of universal "basic" emotions, most commonly identified as happiness, sadness, anger, fear, and disgust. Here we present norms for 10,491 Spanish words for those five discrete emotions collected from a total of 2,010 native speakers, making it the largest set of norms for discrete emotions in any language to date. When used in conjunction with the norms from Hinojosa, Martínez-García et al. (Behavior Research Methods, 48, 272-284, 2016) and Ferré, Guasch, Martínez-García, Fraga, & Hinojosa (Behavior Research Methods, 49, 1082-1094, 2017), researchers now have access to ratings of discrete emotions for 13,633 Spanish words. Our norms show a high degree of inter-rater reliability and correlate highly with those from Ferré et al. (2017). Our exploration of the relationship between the five discrete emotions and relevant lexical and emotional variables confirmed findings of previous studies conducted with smaller datasets. The availability of such large set of norms will greatly facilitate the study of emotion, language and related fields. The norms are available as supplementary materials to this article.

Time Discretization Techniques

KAUST Repository

Gottlieb, S.; Ketcheson, David I.

2016-01-01

The time discretization of hyperbolic partial differential equations is typically the evolution of a system of ordinary differential equations obtained by spatial discretization of the original problem. Methods for this time evolution include

Discrete repulsive oscillator wavefunctions

International Nuclear Information System (INIS)

Munoz, Carlos A; Rueda-Paz, Juvenal; Wolf, Kurt Bernardo

2009-01-01

For the study of infinite discrete systems on phase space, the three-dimensional Lorentz algebra and group, so(2,1) and SO(2,1), provide a discrete model of the repulsive oscillator. Its eigenfunctions are found in the principal irreducible representation series, where the compact generator-that we identify with the position operator-has the infinite discrete spectrum of the integers Z, while the spectrum of energies is a double continuum. The right- and left-moving wavefunctions are given by hypergeometric functions that form a Dirac basis for l 2 (Z). Under contraction, the discrete system limits to the well-known quantum repulsive oscillator. Numerical computations of finite approximations raise further questions on the use of Dirac bases for infinite discrete systems.

Discrete Hamiltonian evolution and quantum gravity

International Nuclear Information System (INIS)

Husain, Viqar; Winkler, Oliver

2004-01-01

We study constrained Hamiltonian systems by utilizing general forms of time discretization. We show that for explicit discretizations, the requirement of preserving the canonical Poisson bracket under discrete evolution imposes strong conditions on both allowable discretizations and Hamiltonians. These conditions permit time discretizations for a limited class of Hamiltonians, which does not include homogeneous cosmological models. We also present two general classes of implicit discretizations which preserve Poisson brackets for any Hamiltonian. Both types of discretizations generically do not preserve first class constraint algebras. Using this observation, we show that time discretization provides a complicated time gauge fixing for quantum gravity models, which may be compared with the alternative procedure of gauge fixing before discretization

Discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes

KAUST Repository

Mohamed, Mamdouh S.

2016-02-11

A conservative discretization of incompressible Navier–Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.

Discrete exterior calculus discretization of incompressible Navier-Stokes equations over surface simplicial meshes

Science.gov (United States)

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2016-05-01

A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.

Explicit solutions to the semi-discrete modified KdV equation and motion of discrete plane curves

International Nuclear Information System (INIS)

Inoguchi, Jun-ichi; Kajiwara, Kenji; Matsuura, Nozomu; Ohta, Yasuhiro

2012-01-01

We construct explicit solutions to continuous motion of discrete plane curves described by a semi-discrete potential modified KdV equation. Explicit formulas in terms of the τ function are presented. Bäcklund transformations of the discrete curves are also discussed. We finally consider the continuous limit of discrete motion of discrete plane curves described by the discrete potential modified KdV equation to motion of smooth plane curves characterized by the potential modified KdV equation. (paper)

Fast Reliability Assessing Method for Distribution Network with Distributed Renewable Energy Generation

Science.gov (United States)

Chen, Fan; Huang, Shaoxiong; Ding, Jinjin; Ding, Jinjin; Gao, Bo; Xie, Yuguang; Wang, Xiaoming

2018-01-01

This paper proposes a fast reliability assessing method for distribution grid with distributed renewable energy generation. First, the Weibull distribution and the Beta distribution are used to describe the probability distribution characteristics of wind speed and solar irradiance respectively, and the models of wind farm, solar park and local load are built for reliability assessment. Then based on power system production cost simulation probability discretization and linearization power flow, a optimal power flow objected with minimum cost of conventional power generation is to be resolved. Thus a reliability assessment for distribution grid is implemented fast and accurately. The Loss Of Load Probability (LOLP) and Expected Energy Not Supplied (EENS) are selected as the reliability index, a simulation for IEEE RBTS BUS6 system in MATLAB indicates that the fast reliability assessing method calculates the reliability index much faster with the accuracy ensured when compared with Monte Carlo method.

An examination of reliability critical items in liquid metal reactors: An analysis by the Centralized Reliability Data Organization (CREDO)

International Nuclear Information System (INIS)

Humphrys, B.L.; Haire, M.J.; Koger, K.H.; Manneschmidt, J.F.; Setoguchi, K.; Nakai, R.; Okubo, Y.

1987-01-01

The Centralized Reliability Data Organization (CREDO) is the largest repository of liquid metal reactor (LMR) component reliability data in the world. It is jointly sponsored by the US Department of Energy (DOE) and the Power Reactor and Nuclear Fuel Development Corporation (PNC) of Japan. The CREDO data base contains information on a population of more than 21,000 components and approximately 1300 event records. A conservative estimation is that the total component operating hours is approaching 3.5 billion hours. Because data gathering for CREDO concentrates on event (failure) information, the work reported here focuses on the reliability information contained in CREDO and the development of reliability critical items lists. That is, components are ranked in prioritized lists from worst to best performers from a reliability standpoint. For the data contained in the CREDO data base, FFTF and JOYO show reliability growth; EBR-II reveals a slight unreliability growth for those components tracked by CREDO. However, tabulations of events which cause reactor shutdowns decrease with time at each site

A discrete exterior approach to structure-preserving discretization of distributed-parameter port-Hamiltonian systems

NARCIS (Netherlands)

Seslija, Marko; Scherpen, Jacquelien M.A.; van der Schaft, Arjan

2011-01-01

This paper addresses the issue of structure-preserving discretization of open distributed-parameter systems with Hamiltonian dynamics. Employing the formalism of discrete exterior calculus, we introduce simplicial Dirac structures as discrete analogues of the Stokes-Dirac structure and demonstrate

Discrete integrable couplings associated with Toda-type lattice and two hierarchies of discrete soliton equations

International Nuclear Information System (INIS)

Zhang Yufeng; Fan Engui; Zhang Yongqing

2006-01-01

With the help of two semi-direct sum Lie algebras, an efficient way to construct discrete integrable couplings is proposed. As its applications, the discrete integrable couplings of the Toda-type lattice equations are obtained. The approach can be devoted to establishing other discrete integrable couplings of the discrete lattice integrable hierarchies of evolution equations

Introduction of hypermatrix and operator notation into a discrete mathematics simulation model of malignant tumour response to therapeutic schemes in vivo. Some operator properties.

Science.gov (United States)

Stamatakos, Georgios S; Dionysiou, Dimitra D

2009-10-21

The tremendous rate of accumulation of experimental and clinical knowledge pertaining to cancer dictates the development of a theoretical framework for the meaningful integration of such knowledge at all levels of biocomplexity. In this context our research group has developed and partly validated a number of spatiotemporal simulation models of in vivo tumour growth and in particular tumour response to several therapeutic schemes. Most of the modeling modules have been based on discrete mathematics and therefore have been formulated in terms of rather complex algorithms (e.g. in pseudocode and actual computer code). However, such lengthy algorithmic descriptions, although sufficient from the mathematical point of view, may render it difficult for an interested reader to readily identify the sequence of the very basic simulation operations that lie at the heart of the entire model. In order to both alleviate this problem and at the same time provide a bridge to symbolic mathematics, we propose the introduction of the notion of hypermatrix in conjunction with that of a discrete operator into the already developed models. Using a radiotherapy response simulation example we demonstrate how the entire model can be considered as the sequential application of a number of discrete operators to a hypermatrix corresponding to the dynamics of the anatomic area of interest. Subsequently, we investigate the operators' commutativity and outline the "summarize and jump" strategy aiming at efficiently and realistically address multilevel biological problems such as cancer. In order to clarify the actual effect of the composite discrete operator we present further simulation results which are in agreement with the outcome of the clinical study RTOG 83-02, thus strengthening the reliability of the model developed.

The continuous 1.5D terrain guarding problem: Discretization, optimal solutions, and PTAS

Directory of Open Access Journals (Sweden)

Stephan Friedrichs

2016-05-01

Full Text Available In the NP-hard continuous 1.5D Terrain Guarding Problem (TGP we are given an $x$-monotone chain of line segments in $R^2$ (the terrain $T$, and ask for the minimum number of guards (located anywhere on $T$ required to guard all of $T$. We construct guard candidate and witness sets $G, W \\subset T$ of polynomial size such that any feasible (optimal guard cover $G^* \\subseteq G$ for $W$ is also feasible (optimal for the continuous TGP. This discretization allows us to: (1 settle NP-completeness for the continuous TGP; (2 provide a Polynomial Time Approximation Scheme (PTAS for the continuous TGP using the PTAS for the discrete TGP by Gibson et al.; (3 formulate the continuous TGP as an Integer Linear Program (IP. Furthermore, we propose several filtering techniques reducing the size of our discretization, allowing us to devise an efficient IP-based algorithm that reliably provides optimal guard placements for terrains with up to $10^6$ vertices within minutes on a standard desktop computer.

Discrete exterior geometry approach to structure-preserving discretization of distributed-parameter port-Hamiltonian systems

NARCIS (Netherlands)

Seslija, Marko; van der Schaft, Arjan; Scherpen, Jacquelien M.A.

This paper addresses the issue of structure-preserving discretization of open distributed-parameter systems with Hamiltonian dynamics. Employing the formalism of discrete exterior calculus, we introduce a simplicial Dirac structure as a discrete analogue of the Stokes-Dirac structure and demonstrate

Growth functions for some uniformly amenable groups

Directory of Open Access Journals (Sweden)

Dronka Janusz

2017-04-01

Full Text Available We present a simple constructive proof of the fact that every abelian discrete group is uniformly amenable. We improve the growth function obtained earlier and find the optimal growth function in a particular case. We also compute a growth function for some non-abelian uniformly amenable group.

Discrete prepotential as an indicator of successful ablation in patients with coronary cusp ventricular arrhythmia.

Science.gov (United States)

Hachiya, Hitoshi; Yamauchi, Yasuteru; Iesaka, Yoshito; Yagishita, Atsuhiko; Sasaki, Takeshi; Higuchi, Koji; Kawabata, Mihoko; Sugiyama, Koji; Tanaka, Yasuaki; Kusa, Shigeki; Nakamura, Hiroaki; Miyazaki, Shinsuke; Taniguchi, Hiroshi; Isobe, Mitsuaki; Hirao, Kenzo

2013-10-01

Although coronary cusp (CC) ventricular arrhythmia (VA) can be treated by catheter ablation, reliable indicators of successful ablation sites have not been fully identified. This study comprised 392 patients undergoing radiofrequency catheter ablation for outflow tract-VA at 3 institutions from January 2007 to August 2012. The successful ablation site was on the left CC or right CC in 35 (8.9%) of the 392 patients. In 9 (26%) of these 35 patients, a discrete prepotential was recognized, 5 of whom had left CC-VAs and 4 of whom had right CC-VAs. Radiofrequency catheter ablation was successful at the site of the prepotential in all 9 of these patients. The duration of the isoelectric line between the end of the discrete prepotential and the onset of the ventricular electrogram was 27±13 ms. The time from onset of the discrete prepotential at the successful ablation site on the CC to the QRS onset (activation time) was 69±20 ms (range, 50-98 ms). Pace mapping was graded as excellent at the successful ablation site in only 1 patient. No discrete prepotential was recorded in any successful right outflow tract-VA ablation case in this study. A discrete prepotential was seen in 9 (26%) of 35 patients with CC-VA. In left and right CC-VA, the site of a discrete prepotential with ≥50 ms activation time may indicate a successful ablation site.

Nonlinear nano-scale localized breather modes in a discrete weak ferromagnetic spin lattice

International Nuclear Information System (INIS)

Kavitha, L.; Parasuraman, E.; Gopi, D.; Prabhu, A.; Vicencio, Rodrigo A.

2016-01-01

We investigate the propagation dynamics of highly localized discrete breather modes in a weak ferromagnetic spin lattice with on-site easy axis anisotropy due to crystal field effect. We derive the discrete nonlinear equation of motion by employing boson mappings and p-representation. We explore the onset of modulational instability both analytically in the framework of linear stability analysis and numerically by means of molecular dynamics (MD) simulations, and a perfect agreement was demonstrated. It is also explored that how the antisymmetric nature of the canted ferromagnetic lattice supports highly localized discrete breather (DBs) modes as shown in the stability/instability windows. The energy exchange between low amplitude discrete breathers favours the growth of higher amplitude DBs, resulting eventually in the formation of few long-lived high amplitude DBs. - Highlights: • The effects of DM and anisotropy interaction on the DB modes are studied. • The antisymmetric nature of the canted ferromagnetic medium supports the DB modes. • Dynamics of ferromagnetic chain is governed by boson mappings and p-representation.

Discrete-Roughness-Element-Enhanced Swept-Wing Natural Laminar Flow at High Reynolds Numbers

Science.gov (United States)

Malik, Mujeeb; Liao, Wei; Li, Fei; Choudhari, Meelan

2015-01-01

Nonlinear parabolized stability equations and secondary-instability analyses are used to provide a computational assessment of the potential use of the discrete-roughness-element technology for extending swept-wing natural laminar flow at chord Reynolds numbers relevant to transport aircraft. Computations performed for the boundary layer on a natural-laminar-flow airfoil with a leading-edge sweep angle of 34.6 deg, freestream Mach number of 0.75, and chord Reynolds numbers of 17 × 10(exp 6), 24 × 10(exp 6), and 30 × 10(exp 6) suggest that discrete roughness elements could delay laminar-turbulent transition by about 20% when transition is caused by stationary crossflow disturbances. Computations show that the introduction of small-wavelength stationary crossflow disturbances (i.e., discrete roughness element) also suppresses the growth of most amplified traveling crossflow disturbances.

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2010-01-01

The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18...

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2010-01-01

The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15...

Two new discrete integrable systems

International Nuclear Information System (INIS)

Chen Xiao-Hong; Zhang Hong-Qing

2013-01-01

In this paper, we focus on the construction of new (1+1)-dimensional discrete integrable systems according to a subalgebra of loop algebra à 1 . By designing two new (1+1)-dimensional discrete spectral problems, two new discrete integrable systems are obtained, namely, a 2-field lattice hierarchy and a 3-field lattice hierarchy. When deriving the two new discrete integrable systems, we find the generalized relativistic Toda lattice hierarchy and the generalized modified Toda lattice hierarchy. Moreover, we also obtain the Hamiltonian structures of the two lattice hierarchies by means of the discrete trace identity

Space-Time Discrete KPZ Equation

Science.gov (United States)

Cannizzaro, G.; Matetski, K.

2018-03-01

We study a general family of space-time discretizations of the KPZ equation and show that they converge to its solution. The approach we follow makes use of basic elements of the theory of regularity structures (Hairer in Invent Math 198(2):269-504, 2014) as well as its discrete counterpart (Hairer and Matetski in Discretizations of rough stochastic PDEs, 2015. arXiv:1511.06937). Since the discretization is in both space and time and we allow non-standard discretization for the product, the methods mentioned above have to be suitably modified in order to accommodate the structure of the models under study.

Discrete density of states

International Nuclear Information System (INIS)

Aydin, Alhun; Sisman, Altug

2016-01-01

By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for bounded and unbounded continua are analytically recovered from discrete ones. Even though substantial fluctuations prevail in discrete DOS, they're almost completely flattened out after summation or integration operation. It's seen that relative errors of analytical expressions of bounded/unbounded continua rapidly decrease for high NOS values (weak confinement or high energy conditions), while the proposed analytical expressions based on Weyl's conjecture always preserve their lower error characteristic. - Highlights: • Discrete density of states considering minimum energy difference is proposed. • Analytical DOS and NOS formulas based on Weyl conjecture are given. • Discrete DOS and NOS functions are examined for various dimensions. • Relative errors of analytical formulas are much better than the conventional ones.

Poisson hierarchy of discrete strings

International Nuclear Information System (INIS)

Ioannidou, Theodora; Niemi, Antti J.

2016-01-01

The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.

Poisson hierarchy of discrete strings

Energy Technology Data Exchange (ETDEWEB)

Ioannidou, Theodora, E-mail: ti3@auth.gr [Faculty of Civil Engineering, School of Engineering, Aristotle University of Thessaloniki, 54249, Thessaloniki (Greece); Niemi, Antti J., E-mail: Antti.Niemi@physics.uu.se [Department of Physics and Astronomy, Uppsala University, P.O. Box 803, S-75108, Uppsala (Sweden); Laboratoire de Mathematiques et Physique Theorique CNRS UMR 6083, Fédération Denis Poisson, Université de Tours, Parc de Grandmont, F37200, Tours (France); Department of Physics, Beijing Institute of Technology, Haidian District, Beijing 100081 (China)

2016-01-28

The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.

Discrete energy formulation of neutron transport theory applied to solving the discrete ordinates equations

International Nuclear Information System (INIS)

Ching, J.; Oblow, E.M.; Goldstein, H.

1976-01-01

An algebraic equivalence between the point-energy and multigroup forms of the Boltzmann transport equation is demonstrated that allows the development of a discrete energy, discrete ordinates method for the solution of radiation transport problems. In the discrete energy method, the group averaging required in the cross-section processing for multigroup calculations is replaced by a faster numerical quadrature scheme capable of generating transfer cross sections describing all the physical processes of interest on a fine point-energy grid. Test calculations in which the discrete energy method is compared with the multigroup method show that, for the same energy grid, the discrete energy method is much faster, although somewhat less accurate, than the multigroup method. However, the accuracy of the discrete energy method increases rapidly as the spacing between energy grid points is decreased, approaching that of multigroup calculations. For problems requiring great detail in the energy spectrum, the discrete energy method is therefore expected to be far more economical than the multigroup technique for equivalent accuracy solutions. This advantage of the point method is demonstrated by application to the study of neutron transport in a thick iron slab

3-D Discrete Analytical Ridgelet Transform

OpenAIRE

Helbert , David; Carré , Philippe; Andrès , Éric

2006-01-01

International audience; In this paper, we propose an implementation of the 3-D Ridgelet transform: the 3-D discrete analytical Ridgelet transform (3-D DART). This transform uses the Fourier strategy for the computation of the associated 3-D discrete Radon transform. The innovative step is the definition of a discrete 3-D transform with the discrete analytical geometry theory by the construction of 3-D discrete analytical lines in the Fourier domain. We propose two types of 3-D discrete lines:...

Discrete fractional calculus

CERN Document Server

Goodrich, Christopher

2015-01-01

This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the...

Chaotic properties between the nonintegrable discrete nonlinear Schroedinger equation and a nonintegrable discrete Heisenberg model

International Nuclear Information System (INIS)

Ding Qing

2007-01-01

We prove that the integrable-nonintegrable discrete nonlinear Schroedinger equation (AL-DNLS) introduced by Cai, Bishop and Gronbech-Jensen (Phys. Rev. Lett. 72 591(1994)) is the discrete gauge equivalent to an integrable-nonintegrable discrete Heisenberg model from the geometric point of view. Then we study whether the transmission and bifurcation properties of the AL-DNLS equation are preserved under the action of discrete gauge transformations. Our results reveal that the transmission property of the AL-DNLS equation is completely preserved and the bifurcation property is conditionally preserved to those of the integrable-nonintegrable discrete Heisenberg model

Using Discrete Choice Experiments to Inform the Benefit-Risk Assessment of Medicines: Are We Ready Yet?

Science.gov (United States)

Vass, Caroline M; Payne, Katherine

2017-09-01

There is emerging interest in the use of discrete choice experiments as a means of quantifying the perceived balance between benefits and risks (quantitative benefit-risk assessment) of new healthcare interventions, such as medicines, under assessment by regulatory agencies. For stated preference data on benefit-risk assessment to be used in regulatory decision making, the methods to generate these data must be valid, reliable and capable of producing meaningful estimates understood by decision makers. Some reporting guidelines exist for discrete choice experiments, and for related methods such as conjoint analysis. However, existing guidelines focus on reporting standards, are general in focus and do not consider the requirements for using discrete choice experiments specifically for quantifying benefit-risk assessments in the context of regulatory decision making. This opinion piece outlines the current state of play in using discrete choice experiments for benefit-risk assessment and proposes key areas needing to be addressed to demonstrate that discrete choice experiments are an appropriate and valid stated preference elicitation method in this context. Methodological research is required to establish: how robust the results of discrete choice experiments are to formats and methods of risk communication; how information in the discrete choice experiment can be presented effectually to respondents; whose preferences should be elicited; the correct underlying utility function and analytical model; the impact of heterogeneity in preferences; and the generalisability of the results. We believe these methodological issues should be addressed, alongside developing a 'reference case', before agencies can safely and confidently use discrete choice experiments for quantitative benefit-risk assessment in the context of regulatory decision making for new medicines and healthcare products.

Discrete density of states

Energy Technology Data Exchange (ETDEWEB)

Aydin, Alhun; Sisman, Altug, E-mail: sismanal@itu.edu.tr

2016-03-22

By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for bounded and unbounded continua are analytically recovered from discrete ones. Even though substantial fluctuations prevail in discrete DOS, they're almost completely flattened out after summation or integration operation. It's seen that relative errors of analytical expressions of bounded/unbounded continua rapidly decrease for high NOS values (weak confinement or high energy conditions), while the proposed analytical expressions based on Weyl's conjecture always preserve their lower error characteristic. - Highlights: • Discrete density of states considering minimum energy difference is proposed. • Analytical DOS and NOS formulas based on Weyl conjecture are given. • Discrete DOS and NOS functions are examined for various dimensions. • Relative errors of analytical formulas are much better than the conventional ones.

Homogenization of discrete media

International Nuclear Information System (INIS)

Pradel, F.; Sab, K.

1998-01-01

Material such as granular media, beam assembly are easily seen as discrete media. They look like geometrical points linked together thanks to energetic expressions. Our purpose is to extend discrete kinematics to the one of an equivalent continuous material. First we explain how we build the localisation tool for periodic materials according to estimated continuum medium type (classical Cauchy, and Cosserat media). Once the bridge built between discrete and continuum media, we exhibit its application over two bidimensional beam assembly structures : the honey comb and a structural reinforced variation. The new behavior is then applied for the simple plan shear problem in a Cosserat continuum and compared with the real discrete solution. By the mean of this example, we establish the agreement of our new model with real structures. The exposed method has a longer range than mechanics and can be applied to every discrete problems like electromagnetism in which relationship between geometrical points can be summed up by an energetic function. (orig.)

Homogenization of discrete media

Energy Technology Data Exchange (ETDEWEB)

Pradel, F.; Sab, K. [CERAM-ENPC, Marne-la-Vallee (France)

1998-11-01

Material such as granular media, beam assembly are easily seen as discrete media. They look like geometrical points linked together thanks to energetic expressions. Our purpose is to extend discrete kinematics to the one of an equivalent continuous material. First we explain how we build the localisation tool for periodic materials according to estimated continuum medium type (classical Cauchy, and Cosserat media). Once the bridge built between discrete and continuum media, we exhibit its application over two bidimensional beam assembly structures : the honey comb and a structural reinforced variation. The new behavior is then applied for the simple plan shear problem in a Cosserat continuum and compared with the real discrete solution. By the mean of this example, we establish the agreement of our new model with real structures. The exposed method has a longer range than mechanics and can be applied to every discrete problems like electromagnetism in which relationship between geometrical points can be summed up by an energetic function. (orig.) 7 refs.

Hybrid discrete dislocation models for fatigue crack growth

NARCIS (Netherlands)

Curtin, W. A.; Deshpande, V. S.; Needleman, A.; Van der Giessen, E.; Wallin, M.

A framework for accurately modeling fatigue crack growth in ductile crystalline solids is necessarily multiscale The creation of new free surface occurs at the atomistic scale, where the material's cohesive strength is controlled by the local chemistry On the other hand, significant dissipation

Discrete differential geometry. Consistency as integrability

OpenAIRE

Bobenko, Alexander I.; Suris, Yuri B.

2005-01-01

A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete geometry studies geometric shapes with finite number of elements (such as polyhedra), the discrete differential geometry aims at the development of discrete equivalents of notions and methods of smooth surface theory. Current interest in this field derives not ...

Advances in discrete differential geometry

CERN Document Server

2016-01-01

This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, ...

Discrete elements method of neutron transport

International Nuclear Information System (INIS)

Mathews, K.A.

1988-01-01

In this paper a new neutron transport method, called discrete elements (L N ) is derived and compared to discrete ordinates methods, theoretically and by numerical experimentation. The discrete elements method is based on discretizing the Boltzmann equation over a set of elements of angle. The discrete elements method is shown to be more cost-effective than discrete ordinates, in terms of accuracy versus execution time and storage, for the cases tested. In a two-dimensional test case, a vacuum duct in a shield, the L N method is more consistently convergent toward a Monte Carlo benchmark solution

Discrete-Feature Model Implementation of SDM-Site Forsmark

Energy Technology Data Exchange (ETDEWEB)

Geier, Joel (Clearwater Hardrock Consulting, Corvallis, OR (United States))

2010-03-15

A discrete-feature model (DFM) was implemented for the Forsmark repository site based on the final site descriptive model from surface based investigations. The discrete-feature conceptual model represents deformation zones, individual fractures, and other water-conducting features around a repository as discrete conductors surrounded by a rock matrix which, in the present study, is treated as impermeable. This approximation is reasonable for sites in crystalline rock which has very low permeability, apart from that which results from macroscopic fracturing. Models are constructed based on the geological and hydrogeological description of the sites and engineering designs. Hydraulic heads and flows through the network of water-conducting features are calculated by the finite-element method, and are used in turn to simulate migration of non-reacting solute by a particle-tracking method, in order to estimate the properties of pathways by which radionuclides could be released to the biosphere. Stochastic simulation is used to evaluate portions of the model that can only be characterized in statistical terms, since many water-conducting features within the model volume cannot be characterized deterministically. Chapter 2 describes the methodology by which discrete features are derived to represent water-conducting features around the hypothetical repository at Forsmark (including both natural features and features that result from the disturbance of excavation), and then assembled to produce a discrete-feature network model for numerical simulation of flow and transport. Chapter 3 describes how site-specific data and repository design are adapted to produce the discrete-feature model. Chapter 4 presents results of the calculations. These include utilization factors for deposition tunnels based on the emplacement criteria that have been set forth by the implementers, flow distributions to the deposition holes, and calculated properties of discharge paths as well as

Discrete-Feature Model Implementation of SDM-Site Forsmark

International Nuclear Information System (INIS)

Geier, Joel

2010-03-01

A discrete-feature model (DFM) was implemented for the Forsmark repository site based on the final site descriptive model from surface based investigations. The discrete-feature conceptual model represents deformation zones, individual fractures, and other water-conducting features around a repository as discrete conductors surrounded by a rock matrix which, in the present study, is treated as impermeable. This approximation is reasonable for sites in crystalline rock which has very low permeability, apart from that which results from macroscopic fracturing. Models are constructed based on the geological and hydrogeological description of the sites and engineering designs. Hydraulic heads and flows through the network of water-conducting features are calculated by the finite-element method, and are used in turn to simulate migration of non-reacting solute by a particle-tracking method, in order to estimate the properties of pathways by which radionuclides could be released to the biosphere. Stochastic simulation is used to evaluate portions of the model that can only be characterized in statistical terms, since many water-conducting features within the model volume cannot be characterized deterministically. Chapter 2 describes the methodology by which discrete features are derived to represent water-conducting features around the hypothetical repository at Forsmark (including both natural features and features that result from the disturbance of excavation), and then assembled to produce a discrete-feature network model for numerical simulation of flow and transport. Chapter 3 describes how site-specific data and repository design are adapted to produce the discrete-feature model. Chapter 4 presents results of the calculations. These include utilization factors for deposition tunnels based on the emplacement criteria that have been set forth by the implementers, flow distributions to the deposition holes, and calculated properties of discharge paths as well as

Discrete Sparse Coding.

Science.gov (United States)

Exarchakis, Georgios; Lücke, Jörg

2017-11-01

Sparse coding algorithms with continuous latent variables have been the subject of a large number of studies. However, discrete latent spaces for sparse coding have been largely ignored. In this work, we study sparse coding with latents described by discrete instead of continuous prior distributions. We consider the general case in which the latents (while being sparse) can take on any value of a finite set of possible values and in which we learn the prior probability of any value from data. This approach can be applied to any data generated by discrete causes, and it can be applied as an approximation of continuous causes. As the prior probabilities are learned, the approach then allows for estimating the prior shape without assuming specific functional forms. To efficiently train the parameters of our probabilistic generative model, we apply a truncated expectation-maximization approach (expectation truncation) that we modify to work with a general discrete prior. We evaluate the performance of the algorithm by applying it to a variety of tasks: (1) we use artificial data to verify that the algorithm can recover the generating parameters from a random initialization, (2) use image patches of natural images and discuss the role of the prior for the extraction of image components, (3) use extracellular recordings of neurons to present a novel method of analysis for spiking neurons that includes an intuitive discretization strategy, and (4) apply the algorithm on the task of encoding audio waveforms of human speech. The diverse set of numerical experiments presented in this letter suggests that discrete sparse coding algorithms can scale efficiently to work with realistic data sets and provide novel statistical quantities to describe the structure of the data.

An Einstein equation for discrete quantum gravity

OpenAIRE

Gudder, Stan

2012-01-01

The basic framework for this article is the causal set approach to discrete quantum gravity (DQG). Let $Q_n$ be the collection of causal sets with cardinality not greater than $n$ and let $K_n$ be the standard Hilbert space of complex-valued functions on $Q_n$. The formalism of DQG presents us with a decoherence matrix $D_n(x,y)$, $x,y\\in Q_n$. There is a growth order in $Q_n$ and a path in $Q_n$ is a maximal chain relative to this order. We denote the set of paths in $Q_n$ by $\\Omega_n$. For...

Wind turbine reliability : a database and analysis approach.

Energy Technology Data Exchange (ETDEWEB)

Linsday, James (ARES Corporation); Briand, Daniel; Hill, Roger Ray; Stinebaugh, Jennifer A.; Benjamin, Allan S. (ARES Corporation)

2008-02-01

The US wind Industry has experienced remarkable growth since the turn of the century. At the same time, the physical size and electrical generation capabilities of wind turbines has also experienced remarkable growth. As the market continues to expand, and as wind generation continues to gain a significant share of the generation portfolio, the reliability of wind turbine technology becomes increasingly important. This report addresses how operations and maintenance costs are related to unreliability - that is the failures experienced by systems and components. Reliability tools are demonstrated, data needed to understand and catalog failure events is described, and practical wind turbine reliability models are illustrated, including preliminary results. This report also presents a continuing process of how to proceed with controlling industry requirements, needs, and expectations related to Reliability, Availability, Maintainability, and Safety. A simply stated goal of this process is to better understand and to improve the operable reliability of wind turbine installations.

A paradigm for discrete physics

International Nuclear Information System (INIS)

Noyes, H.P.; McGoveran, D.; Etter, T.; Manthey, M.J.; Gefwert, C.

1987-01-01

An example is outlined for constructing a discrete physics using as a starting point the insight from quantum physics that events are discrete, indivisible and non-local. Initial postulates are finiteness, discreteness, finite computability, absolute nonuniqueness (i.e., homogeneity in the absence of specific cause) and additivity

Discrete-Event Simulation

Directory of Open Access Journals (Sweden)

Prateek Sharma

2015-04-01

Full Text Available Abstract Simulation can be regarded as the emulation of the behavior of a real-world system over an interval of time. The process of simulation relies upon the generation of the history of a system and then analyzing that history to predict the outcome and improve the working of real systems. Simulations can be of various kinds but the topic of interest here is one of the most important kind of simulation which is Discrete-Event Simulation which models the system as a discrete sequence of events in time. So this paper aims at introducing about Discrete-Event Simulation and analyzing how it is beneficial to the real world systems.

Discrete breathers for a discrete nonlinear Schrödinger ring coupled to a central site.

Science.gov (United States)

Jason, Peter; Johansson, Magnus

2016-01-01

We examine the existence and properties of certain discrete breathers for a discrete nonlinear Schrödinger model where all but one site are placed in a ring and coupled to the additional central site. The discrete breathers we focus on are stationary solutions mainly localized on one or a few of the ring sites and possibly also the central site. By numerical methods, we trace out and study the continuous families the discrete breathers belong to. Our main result is the discovery of a split bifurcation at a critical value of the coupling between neighboring ring sites. Below this critical value, families form closed loops in a certain parameter space, implying that discrete breathers with and without central-site occupation belong to the same family. Above the split bifurcation the families split up into several separate ones, which bifurcate with solutions with constant ring amplitudes. For symmetry reasons, the families have different properties below the split bifurcation for even and odd numbers of sites. It is also determined under which conditions the discrete breathers are linearly stable. The dynamics of some simpler initial conditions that approximate the discrete breathers are also studied and the parameter regimes where the dynamics remain localized close to the initially excited ring site are related to the linear stability of the exact discrete breathers.

Assessing reliability of fatigue indicator parameters for small crack growth via a probabilistic framework

Science.gov (United States)

Rovinelli, Andrea; Guilhem, Yoann; Proudhon, Henry; Lebensohn, Ricardo A.; Ludwig, Wolfgang; Sangid, Michael D.

2017-06-01

Microstructurally small cracks exhibit large variability in their fatigue crack growth rate. It is accepted that the inherent variability in microstructural features is related to the uncertainty in the growth rate. However, due to (i) the lack of cycle-by-cycle experimental data, (ii) the complexity of the short crack growth phenomenon, and (iii) the incomplete physics of constitutive relationships, only empirical damage metrics have been postulated to describe the short crack driving force metric (SCDFM) at the mesoscale level. The identification of the SCDFM of polycrystalline engineering alloys is a critical need, in order to achieve more reliable fatigue life prediction and improve material design. In this work, the first steps in the development of a general probabilistic framework are presented, which uses experimental result as an input, retrieves missing experimental data through crystal plasticity (CP) simulations, and extracts correlations utilizing machine learning and Bayesian networks (BNs). More precisely, experimental results representing cycle-by-cycle data of a short crack growing through a beta-metastable titanium alloy, VST-55531, have been acquired via phase and diffraction contrast tomography. These results serve as an input for FFT-based CP simulations, which provide the micromechanical fields influenced by the presence of the crack, complementing the information available from the experiment. In order to assess the correlation between postulated SCDFM and experimental observations, the data is mined and analyzed utilizing BNs. Results show the ability of the framework to autonomously capture relevant correlations and the equivalence in the prediction capability of different postulated SCDFMs for the high cycle fatigue regime.

Discrete dynamics versus analytic dynamics

DEFF Research Database (Denmark)

Toxværd, Søren

2014-01-01

For discrete classical Molecular dynamics obtained by the “Verlet” algorithm (VA) with the time increment h there exists a shadow Hamiltonian H˜ with energy E˜(h) , for which the discrete particle positions lie on the analytic trajectories for H˜ . Here, we proof that there, independent...... of such an analytic analogy, exists an exact hidden energy invariance E * for VA dynamics. The fact that the discrete VA dynamics has the same invariances as Newtonian dynamics raises the question, which of the formulations that are correct, or alternatively, the most appropriate formulation of classical dynamics....... In this context the relation between the discrete VA dynamics and the (general) discrete dynamics investigated by Lee [Phys. Lett. B122, 217 (1983)] is presented and discussed....

3-D discrete analytical ridgelet transform.

Science.gov (United States)

Helbert, David; Carré, Philippe; Andres, Eric

2006-12-01

In this paper, we propose an implementation of the 3-D Ridgelet transform: the 3-D discrete analytical Ridgelet transform (3-D DART). This transform uses the Fourier strategy for the computation of the associated 3-D discrete Radon transform. The innovative step is the definition of a discrete 3-D transform with the discrete analytical geometry theory by the construction of 3-D discrete analytical lines in the Fourier domain. We propose two types of 3-D discrete lines: 3-D discrete radial lines going through the origin defined from their orthogonal projections and 3-D planes covered with 2-D discrete line segments. These discrete analytical lines have a parameter called arithmetical thickness, allowing us to define a 3-D DART adapted to a specific application. Indeed, the 3-D DART representation is not orthogonal, It is associated with a flexible redundancy factor. The 3-D DART has a very simple forward/inverse algorithm that provides an exact reconstruction without any iterative method. In order to illustrate the potentiality of this new discrete transform, we apply the 3-D DART and its extension to the Local-DART (with smooth windowing) to the denoising of 3-D image and color video. These experimental results show that the simple thresholding of the 3-D DART coefficients is efficient.

Analysis of Discrete Mittag - Leffler Functions

Directory of Open Access Journals (Sweden)

N. Shobanadevi

2015-03-01

Full Text Available Discrete Mittag - Leffler functions play a major role in the development of the theory of discrete fractional calculus. In the present article, we analyze qualitative properties of discrete Mittag - Leffler functions and establish sufficient conditions for convergence, oscillation and summability of the infinite series associated with discrete Mittag - Leffler functions.

Introduction of Hypermatrix and Operator Notation into a Discrete Mathematics Simulation Model of Malignant Tumour Response to Therapeutic Schemes In Vivo. Some Operator Properties

Directory of Open Access Journals (Sweden)

Georgios S. Stamatakos

2009-10-01

Full Text Available The tremendous rate of accumulation of experimental and clinical knowledge pertaining to cancer dictates the development of a theoretical framework for the meaningful integration of such knowledge at all levels of biocomplexity. In this context our research group has developed and partly validated a number of spatiotemporal simulation models of in vivo tumour growth and in particular tumour response to several therapeutic schemes. Most of the modeling modules have been based on discrete mathematics and therefore have been formulated in terms of rather complex algorithms (e.g. in pseudocode and actual computer code. However, such lengthy algorithmic descriptions, although sufficient from the mathematical point of view, may render it difficult for an interested reader to readily identify the sequence of the very basic simulation operations that lie at the heart of the entire model. In order to both alleviate this problem and at the same time provide a bridge to symbolic mathematics, we propose the introduction of the notion of hypermatrix in conjunction with that of a discrete operator into the already developed models. Using a radiotherapy response simulation example we demonstrate how the entire model can be considered as the sequential application of a number of discrete operators to a hypermatrix corresponding to the dynamics of the anatomic area of interest. Subsequently, we investigate the operators’ commutativity and outline the “summarize and jump” strategy aiming at efficiently and realistically address multilevel biological problems such as cancer. In order to clarify the actual effect of the composite discrete operator we present further simulation results which are in agreement with the outcome of the clinical study RTOG 83–02, thus strengthening the reliability of the model developed.

QA support for TFTR reliability improvement program in preparation for DT operation

International Nuclear Information System (INIS)

Parsells, R.F.; Howard, H.P.

1987-01-01

As TFTR approaches experiments in the Q=1 regime, machine reliability becomes a major variable in achieving experimental objectives. This paper describes the methods used to quantify current reliability levels, levels required for D-T operations, proposed methods for reliability growth and improvement, and tracking of reliability performance in that growth. Included in this scope are data collection techniques and short comings, bounding current reliability on the upper end, and requirements for D-T operations. Problem characterization through Pareto diagrams provides insight into recurrent failure modes and the use of Duane plots for charting of reliability changes both cumulative and instantaneous, is explained and demonstrated

Difference Discrete Variational Principles, Euler-Lagrange Cohomology and Symplectic, Multisymplectic Structures I: Difference Discrete Variational Principle

Institute of Scientific and Technical Information of China (English)

GUO Han-Ying,; LI Yu-Qi; WU Ke1; WANG Shi-Kun

2002-01-01

In this first paper of a series, we study the difference discrete variational principle in the framework of multi-parameter differential approach by regarding the forward difference as an entire geometric object in view of noncommutative differential geometry. Regarding the difference as an entire geometric object, the difference discrete version of Legendre transformation can be introduced. By virtue of this variational principle, we can discretely deal with the variation problems in both the Lagrangian and Hamiltonian formalisms to get difference discrete Euler-Lagrange equations and canonical ones for the difference discrete versions of the classical mechanics and classical field theory.

Fracture Failure of Reinforced Concrete Slabs Subjected to Blast Loading Using the Combined Finite-Discrete Element Method

Directory of Open Access Journals (Sweden)

Z. M. Jaini

Full Text Available Abstract Numerical modeling of fracture failure is challenging due to various issues in the constitutive law and the transition of continuum to discrete bodies. Therefore, this study presents the application of the combined finite-discrete element method to investigate the fracture failure of reinforced concrete slabs subjected to blast loading. In numerical modeling, the interaction of non-uniform blast loading on the concrete slab was modeled using the incorporation of the finite element method with a crack rotating approach and the discrete element method to model crack, fracture onset and its post-failures. A time varying pressure-time history based on the mapping method was adopted to define blast loading. The Mohr-Coulomb with Rankine cut-off and von-Mises criteria were applied for concrete and steel reinforcement respectively. The results of scabbing, spalling and fracture show a reliable prediction of damage and fracture.

Discrete mechanics

CERN Document Server

Caltagirone, Jean-Paul

2014-01-01

This book presents the fundamental principles of mechanics to re-establish the equations of Discrete Mechanics. It introduces physics and thermodynamics associated to the physical modeling.  The development and the complementarity of sciences lead to review today the old concepts that were the basis for the development of continuum mechanics. The differential geometry is used to review the conservation laws of mechanics. For instance, this formalism requires a different location of vector and scalar quantities in space. The equations of Discrete Mechanics form a system of equations where the H

Discrete mechanics

International Nuclear Information System (INIS)

Lee, T.D.

1985-01-01

This paper reviews the role of time throughout all phases of mechanics: classical mechanics, non-relativistic quantum mechanics, and relativistic quantum theory. As an example of the relativistic quantum field theory, the case of a massless scalar field interacting with an arbitrary external current is discussed. The comparison between the new discrete theory and the usual continuum formalism is presented. An example is given of a two-dimensional random lattice and its duel. The author notes that there is no evidence that the discrete mechanics is more appropriate than the usual continuum mechanics

Towards early software reliability prediction for computer forensic tools (case study).

Science.gov (United States)

Abu Talib, Manar

2016-01-01

Versatility, flexibility and robustness are essential requirements for software forensic tools. Researchers and practitioners need to put more effort into assessing this type of tool. A Markov model is a robust means for analyzing and anticipating the functioning of an advanced component based system. It is used, for instance, to analyze the reliability of the state machines of real time reactive systems. This research extends the architecture-based software reliability prediction model for computer forensic tools, which is based on Markov chains and COSMIC-FFP. Basically, every part of the computer forensic tool is linked to a discrete time Markov chain. If this can be done, then a probabilistic analysis by Markov chains can be performed to analyze the reliability of the components and of the whole tool. The purposes of the proposed reliability assessment method are to evaluate the tool's reliability in the early phases of its development, to improve the reliability assessment process for large computer forensic tools over time, and to compare alternative tool designs. The reliability analysis can assist designers in choosing the most reliable topology for the components, which can maximize the reliability of the tool and meet the expected reliability level specified by the end-user. The approach of assessing component-based tool reliability in the COSMIC-FFP context is illustrated with the Forensic Toolkit Imager case study.

Synchronization Techniques in Parallel Discrete Event Simulation

OpenAIRE

Lindén, Jonatan

2018-01-01

Discrete event simulation is an important tool for evaluating system models in many fields of science and engineering. To improve the performance of large-scale discrete event simulations, several techniques to parallelize discrete event simulation have been developed. In parallel discrete event simulation, the work of a single discrete event simulation is distributed over multiple processing elements. A key challenge in parallel discrete event simulation is to ensure that causally dependent ...

Discrete gauge symmetries in discrete MSSM-like orientifolds

International Nuclear Information System (INIS)

Ibáñez, L.E.; Schellekens, A.N.; Uranga, A.M.

2012-01-01

Motivated by the necessity of discrete Z N symmetries in the MSSM to insure baryon stability, we study the origin of discrete gauge symmetries from open string sector U(1)'s in orientifolds based on rational conformal field theory. By means of an explicit construction, we find an integral basis for the couplings of axions and U(1) factors for all simple current MIPFs and orientifolds of all 168 Gepner models, a total of 32 990 distinct cases. We discuss how the presence of discrete symmetries surviving as a subgroup of broken U(1)'s can be derived using this basis. We apply this procedure to models with MSSM chiral spectrum, concretely to all known U(3)×U(2)×U(1)×U(1) and U(3)×Sp(2)×U(1)×U(1) configurations with chiral bi-fundamentals, but no chiral tensors, as well as some SU(5) GUT models. We find examples of models with Z 2 (R-parity) and Z 3 symmetries that forbid certain B and/or L violating MSSM couplings. Their presence is however relatively rare, at the level of a few percent of all cases.

Darboux and binary Darboux transformations for discrete integrable systems I. Discrete potential KdV equation

International Nuclear Information System (INIS)

Shi, Ying; Zhang, Da-jun; Nimmo, Jonathan J C

2014-01-01

The Hirota–Miwa equation can be written in ‘nonlinear’ form in two ways: the discrete KP equation and, by using a compatible continuous variable, the discrete potential KP equation. For both systems, we consider the Darboux and binary Darboux transformations, expressed in terms of the continuous variable, and obtain exact solutions in Wronskian and Grammian form. We discuss reductions of both systems to the discrete KdV and discrete potential KdV equation, respectively, and exploit this connection to find the Darboux and binary Darboux transformations and exact solutions of these equations. (paper)

Mathematical Modeling of Contact Problems of Elasticity Theory with Unilateral Discrete Contact

Directory of Open Access Journals (Sweden)

I. V. Stankevich

2015-01-01

Full Text Available Development and operation of modern machinery and latest technology require reliable estimates of the strength characteristics of the critical elements of structures and technological equipment under the impact of high-intensity thermomechanical loading, accompanied, as a rule, by complex contact interaction. Mathematical modeling of stress-strain state of such parts and components in the contact area, based on adequate mathematical models, modern numerical methods and efficient algorithms that implement the direct determination of displacement fields, strains and stresses, is the main tool that allows fast acquisition of data required for the calculations of strength and durability. The paper considers an algorithm for constructing the numerical solution of the contact problem of elasticity theory in relation to the body, which has an obvious one-sided discrete contact interaction with an elastic half-space. The proposed algorithm is specially designed to have a correction of the tangential forces at discrete contact points, allowing us to achieve sufficiently accurate implementation of the adopted law of friction. The algorithm is embedded in a general finite element technology, with which the application code is generated. Numerical study of discrete unilateral contact interaction of an elastic plate and a rigid half-space showed a high efficiency of the developed algorithm and the application code that implements it.

Finite Discrete Gabor Analysis

DEFF Research Database (Denmark)

Søndergaard, Peter Lempel

2007-01-01

frequency bands at certain times. Gabor theory can be formulated for both functions on the real line and for discrete signals of finite length. The two theories are largely the same because many aspects come from the same underlying theory of locally compact Abelian groups. The two types of Gabor systems...... can also be related by sampling and periodization. This thesis extends on this theory by showing new results for window construction. It also provides a discussion of the problems associated to discrete Gabor bases. The sampling and periodization connection is handy because it allows Gabor systems...... on the real line to be well approximated by finite and discrete Gabor frames. This method of approximation is especially attractive because efficient numerical methods exists for doing computations with finite, discrete Gabor systems. This thesis presents new algorithms for the efficient computation of finite...

Adaptive Discrete Hypergraph Matching.

Science.gov (United States)

Yan, Junchi; Li, Changsheng; Li, Yin; Cao, Guitao

2018-02-01

This paper addresses the problem of hypergraph matching using higher-order affinity information. We propose a solver that iteratively updates the solution in the discrete domain by linear assignment approximation. The proposed method is guaranteed to converge to a stationary discrete solution and avoids the annealing procedure and ad-hoc post binarization step that are required in several previous methods. Specifically, we start with a simple iterative discrete gradient assignment solver. This solver can be trapped in an -circle sequence under moderate conditions, where is the order of the graph matching problem. We then devise an adaptive relaxation mechanism to jump out this degenerating case and show that the resulting new path will converge to a fixed solution in the discrete domain. The proposed method is tested on both synthetic and real-world benchmarks. The experimental results corroborate the efficacy of our method.

Principles of discrete time mechanics

CERN Document Server

Jaroszkiewicz, George

2014-01-01

Could time be discrete on some unimaginably small scale? Exploring the idea in depth, this unique introduction to discrete time mechanics systematically builds the theory up from scratch, beginning with the historical, physical and mathematical background to the chronon hypothesis. Covering classical and quantum discrete time mechanics, this book presents all the tools needed to formulate and develop applications of discrete time mechanics in a number of areas, including spreadsheet mechanics, classical and quantum register mechanics, and classical and quantum mechanics and field theories. A consistent emphasis on contextuality and the observer-system relationship is maintained throughout.

Discrete Calculus by Analogy

CERN Document Server

Izadi, F A; Bagirov, G

2009-01-01

With its origins stretching back several centuries, discrete calculus is now an increasingly central methodology for many problems related to discrete systems and algorithms. The topics covered here usually arise in many branches of science and technology, especially in discrete mathematics, numerical analysis, statistics and probability theory as well as in electrical engineering, but our viewpoint here is that these topics belong to a much more general realm of mathematics; namely calculus and differential equations because of the remarkable analogy of the subject to this branch of mathemati

Discrete integrable systems and hodograph transformations arising from motions of discrete plane curves

International Nuclear Information System (INIS)

Feng Baofeng; Maruno, Ken-ichi; Inoguchi, Jun-ichi; Kajiwara, Kenji; Ohta, Yasuhiro

2011-01-01

We consider integrable discretizations of some soliton equations associated with the motions of plane curves: the Wadati-Konno-Ichikawa elastic beam equation, the complex Dym equation and the short pulse equation. They are related to the modified KdV or the sine-Gordon equations by the hodograph transformations. Based on the observation that the hodograph transformations are regarded as the Euler-Lagrange transformations of the curve motions, we construct the discrete analogues of the hodograph transformations, which yield integrable discretizations of those soliton equations. (paper)

Modern approaches to discrete curvature

CERN Document Server

Romon, Pascal

2017-01-01

 This book provides a valuable glimpse into discrete curvature, a rich new field of research which blends discrete mathematics, differential geometry, probability and computer graphics. It includes a vast collection of ideas and tools which will offer something new to all interested readers. Discrete geometry has arisen as much as a theoretical development as in response to unforeseen challenges coming from applications. Discrete and continuous geometries have turned out to be intimately connected. Discrete curvature is the key concept connecting them through many bridges in numerous fields: metric spaces, Riemannian and Euclidean geometries, geometric measure theory, topology, partial differential equations, calculus of variations, gradient flows, asymptotic analysis, probability, harmonic analysis, graph theory, etc. In spite of its crucial importance both in theoretical mathematics and in applications, up to now, almost no books have provided a coherent outlook on this emerging field.

Microstructural modelling of creep crack growth from a blunted crack

NARCIS (Netherlands)

Onck, P.R.; Giessen, E. van der

1998-01-01

The effect of crack tip blunting on the initial stages of creep crack growth is investigated by means of a planar microstructural model in which grains are represented discretely. The actual linking-up process of discrete microcracks with the macroscopic crack is simulated, with full account of the

Affective norms of 875 Spanish words for five discrete emotional categories and two emotional dimensions.

Science.gov (United States)

Hinojosa, J A; Martínez-García, N; Villalba-García, C; Fernández-Folgueiras, U; Sánchez-Carmona, A; Pozo, M A; Montoro, P R

2016-03-01

In the present study, we introduce affective norms for a new set of Spanish words, the Madrid Affective Database for Spanish (MADS), that were scored on two emotional dimensions (valence and arousal) and on five discrete emotional categories (happiness, anger, sadness, fear, and disgust), as well as on concreteness, by 660 Spanish native speakers. Measures of several objective psycholinguistic variables--grammatical class, word frequency, number of letters, and number of syllables--for the words are also included. We observed high split-half reliabilities for every emotional variable and a strong quadratic relationship between valence and arousal. Additional analyses revealed several associations between the affective dimensions and discrete emotions, as well as with some psycholinguistic variables. This new corpus complements and extends prior databases in Spanish and allows for designing new experiments investigating the influence of affective content in language processing under both dimensional and discrete theoretical conceptions of emotion. These norms can be downloaded as supplemental materials for this article from www.dropbox.com/s/o6dpw3irk6utfhy/Hinojosa%20et%20al_Supplementary%20materials.xlsx?dl=0 .

Noether symmetries of discrete mechanico–electrical systems

International Nuclear Information System (INIS)

Fu Jingli; Xie Fengping; Chen Benyong

2008-01-01

This paper focuses on studying Noether symmetries and conservation laws of the discrete mechanico-electrical systems with the nonconservative and the dissipative forces. Based on the invariance of discrete Hamilton action of the systems under the infinitesimal transformation with respect to the generalized coordinates, the generalized electrical quantities and time, it presents the discrete analogue of variational principle, the discrete analogue of Lagrange–Maxwell equations, the discrete analogue of Noether theorems for Lagrange–Maxwell and Lagrange mechanico-electrical systems. Also, the discrete Noether operator identity and the discrete Noether-type conservation laws are obtained for these systems. An actual example is given to illustrate these results. (general)

Asynchronous discrete event schemes for PDEs

Science.gov (United States)

Stone, D.; Geiger, S.; Lord, G. J.

2017-08-01

A new class of asynchronous discrete-event simulation schemes for advection-diffusion-reaction equations is introduced, based on the principle of allowing quanta of mass to pass through faces of a (regular, structured) Cartesian finite volume grid. The timescales of these events are linked to the flux on the face. The resulting schemes are self-adaptive, and local in both time and space. Experiments are performed on realistic physical systems related to porous media flow applications, including a large 3D advection diffusion equation and advection diffusion reaction systems. The results are compared to highly accurate reference solutions where the temporal evolution is computed with exponential integrator schemes using the same finite volume discretisation. This allows a reliable estimation of the solution error. Our results indicate a first order convergence of the error as a control parameter is decreased, and we outline a framework for analysis.

Exact discretization of Schrödinger equation

Energy Technology Data Exchange (ETDEWEB)

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

2016-01-08

There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.

Exact discretization of Schrödinger equation

International Nuclear Information System (INIS)

Tarasov, Vasily E.

2016-01-01

There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.

Discrete Localized States and Localization Dynamics in Discrete Nonlinear Schrödinger Equations

DEFF Research Database (Denmark)

Christiansen, Peter Leth; Gaididei, Yu.B.; Mezentsev, V.K.

1996-01-01

Dynamics of two-dimensional discrete structures is studied in the framework of the generalized two-dimensional discrete nonlinear Schrodinger equation. The nonlinear coupling in the form of the Ablowitz-Ladik nonlinearity is taken into account. Stability properties of the stationary solutions...

Discrete Event Simulation Method as a Tool for Improvement of Manufacturing Systems

Directory of Open Access Journals (Sweden)

Adrian Kampa

2017-02-01

Full Text Available The problem of production flow in manufacturing systems is analyzed. The machines can be operated by workers or by robots, since breakdowns and human factors destabilize the production processes that robots are preferred to perform. The problem is how to determine the real difference in work efficiency between humans and robots. We present an analysis of the production efficiency and reliability of the press shop lines operated by human operators or industrial robots. This is a problem from the field of Operations Research for which the Discrete Event Simulation (DES method has been used. Three models have been developed, including the manufacturing line before and after robotization, taking into account stochastic parameters of availability and reliability of the machines, operators, and robots. We apply the OEE (Overall Equipment Effectiveness indicator to present how the availability, reliability, and quality parameters influence the performance of the workstations, especially in the short run and in the long run. In addition, the stability of the simulation model was analyzed. This approach enables a better representation of real manufacturing processes.

Bifurcation analysis of a delayed mathematical model for tumor growth

International Nuclear Information System (INIS)

Khajanchi, Subhas

2015-01-01

In this study, we present a modified mathematical model of tumor growth by introducing discrete time delay in interaction terms. The model describes the interaction between tumor cells, healthy tissue cells (host cells) and immune effector cells. The goal of this study is to obtain a better compatibility with reality for which we introduced the discrete time delay in the interaction between tumor cells and host cells. We investigate the local stability of the non-negative equilibria and the existence of Hopf-bifurcation by considering the discrete time delay as a bifurcation parameter. We estimate the length of delay to preserve the stability of bifurcating periodic solutions, which gives an idea about the mode of action for controlling oscillations in the tumor growth. Numerical simulations of the model confirm the analytical findings

Observability of discretized partial differential equations

Science.gov (United States)

Cohn, Stephen E.; Dee, Dick P.

1988-01-01

It is shown that complete observability of the discrete model used to assimilate data from a linear partial differential equation (PDE) system is necessary and sufficient for asymptotic stability of the data assimilation process. The observability theory for discrete systems is reviewed and applied to obtain simple observability tests for discretized constant-coefficient PDEs. Examples are used to show how numerical dispersion can result in discrete dynamics with multiple eigenvalues, thereby detracting from observability.

Discrete Mathematics Re "Tooled."

Science.gov (United States)

Grassl, Richard M.; Mingus, Tabitha T. Y.

1999-01-01

Indicates the importance of teaching discrete mathematics. Describes how the use of technology can enhance the teaching and learning of discrete mathematics. Explorations using Excel, Derive, and the TI-92 proved how preservice and inservice teachers experienced a new dimension in problem solving and discovery. (ASK)

Euler-Poincare reduction for discrete field theories

International Nuclear Information System (INIS)

Vankerschaver, Joris

2007-01-01

In this note, we develop a theory of Euler-Poincare reduction for discrete Lagrangian field theories. We introduce the concept of Euler-Poincare equations for discrete field theories, as well as a natural extension of the Moser-Veselov scheme, and show that both are equivalent. The resulting discrete field equations are interpreted in terms of discrete differential geometry. An application to the theory of discrete harmonic mappings is also briefly discussed

Positivity for Convective Semi-discretizations

KAUST Repository

Fekete, Imre

2017-04-19

We propose a technique for investigating stability properties like positivity and forward invariance of an interval for method-of-lines discretizations, and apply the technique to study positivity preservation for a class of TVD semi-discretizations of 1D scalar hyperbolic conservation laws. This technique is a generalization of the approach suggested in Khalsaraei (J Comput Appl Math 235(1): 137–143, 2010). We give more relaxed conditions on the time-step for positivity preservation for slope-limited semi-discretizations integrated in time with explicit Runge–Kutta methods. We show that the step-size restrictions derived are sharp in a certain sense, and that many higher-order explicit Runge–Kutta methods, including the classical 4th-order method and all non-confluent methods with a negative Butcher coefficient, cannot generally maintain positivity for these semi-discretizations under any positive step size. We also apply the proposed technique to centered finite difference discretizations of scalar hyperbolic and parabolic problems.

Integrable discretizations of the short pulse equation

International Nuclear Information System (INIS)

Feng Baofeng; Maruno, Ken-ichi; Ohta, Yasuhiro

2010-01-01

In this paper, we propose integrable semi-discrete and full-discrete analogues of the short pulse (SP) equation. The key construction is the bilinear form and determinant structure of solutions of the SP equation. We also give the determinant formulas of N-soliton solutions of the semi-discrete and full-discrete analogues of the SP equations, from which the multi-loop and multi-breather solutions can be generated. In the continuous limit, the full-discrete SP equation converges to the semi-discrete SP equation, and then to the continuous SP equation. Based on the semi-discrete SP equation, an integrable numerical scheme, i.e. a self-adaptive moving mesh scheme, is proposed and used for the numerical computation of the short pulse equation.

Discrete computational structures

CERN Document Server

Korfhage, Robert R

1974-01-01

Discrete Computational Structures describes discrete mathematical concepts that are important to computing, covering necessary mathematical fundamentals, computer representation of sets, graph theory, storage minimization, and bandwidth. The book also explains conceptual framework (Gorn trees, searching, subroutines) and directed graphs (flowcharts, critical paths, information network). The text discusses algebra particularly as it applies to concentrates on semigroups, groups, lattices, propositional calculus, including a new tabular method of Boolean function minimization. The text emphasize

PV Systems Reliability Final Technical Report.

Energy Technology Data Exchange (ETDEWEB)

Lavrova, Olga [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Flicker, Jack David [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Johnson, Jay [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Armijo, Kenneth Miguel [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Gonzalez, Sigifredo [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Schindelholz, Eric John [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sorensen, Neil R. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Yang, Benjamin Bing-Yeh [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2015-12-01

The continued exponential growth of photovoltaic technologies paves a path to a solar-powered world, but requires continued progress toward low-cost, high-reliability, high-performance photovoltaic (PV) systems. High reliability is an essential element in achieving low-cost solar electricity by reducing operation and maintenance (O&M) costs and extending system lifetime and availability, but these attributes are difficult to verify at the time of installation. Utilities, financiers, homeowners, and planners are demanding this information in order to evaluate their financial risk as a prerequisite to large investments. Reliability research and development (R&D) is needed to build market confidence by improving product reliability and by improving predictions of system availability, O&M cost, and lifetime. This project is focused on understanding, predicting, and improving the reliability of PV systems. The two areas being pursued include PV arc-fault and ground fault issues, and inverter reliability.

An Application of Graph Theory in Markov Chains Reliability Analysis

Directory of Open Access Journals (Sweden)

Pavel Skalny

2014-01-01

Full Text Available The paper presents reliability analysis which was realized for an industrial company. The aim of the paper is to present the usage of discrete time Markov chains and the flow in network approach. Discrete Markov chains a well-known method of stochastic modelling describes the issue. The method is suitable for many systems occurring in practice where we can easily distinguish various amount of states. Markov chains are used to describe transitions between the states of the process. The industrial process is described as a graph network. The maximal flow in the network corresponds to the production. The Ford-Fulkerson algorithm is used to quantify the production for each state. The combination of both methods are utilized to quantify the expected value of the amount of manufactured products for the given time period.

Discrete integrable systems and deformations of associative algebras

International Nuclear Information System (INIS)

Konopelchenko, B G

2009-01-01

Interrelations between discrete deformations of the structure constants for associative algebras and discrete integrable systems are reviewed. Theory of deformations for associative algebras is presented. Closed left ideal generated by the elements representing the multiplication table plays a central role in this theory. Deformations of the structure constants are generated by the deformation driving algebra and governed by the central system of equations. It is demonstrated that many discrete equations such as discrete Boussinesq equation, discrete WDVV equation, discrete Schwarzian KP and BKP equations, discrete Hirota-Miwa equations for KP and BKP hierarchies are particular realizations of the central system. An interaction between the theories of discrete integrable systems and discrete deformations of associative algebras is reciprocal and fruitful. An interpretation of the Menelaus relation (discrete Schwarzian KP equation), discrete Hirota-Miwa equation for KP hierarchy, consistency around the cube as the associativity conditions and the concept of gauge equivalence, for instance, between the Menelaus and KP configurations are particular examples.

Geometry and Hamiltonian mechanics on discrete spaces

International Nuclear Information System (INIS)

Talasila, V; Clemente-Gallardo, J; Schaft, A J van der

2004-01-01

Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a 'smooth' model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to provide a discrete analogue of differential geometry, and to define on these discrete models a formal discrete Hamiltonian structure-in doing so we try to bring together various fundamental concepts from numerical analysis, differential geometry, algebraic geometry, simplicial homology and classical Hamiltonian mechanics. For example, the concept of a twisted derivation is borrowed from algebraic geometry for developing a discrete calculus. The theory is applied to a nonlinear pendulum and we compare the dynamics obtained through a discrete modelling approach with the dynamics obtained via the usual discretization procedures. Also an example of an energy-conserving algorithm on a simple harmonic oscillator is presented, and its effect on the Poisson structure is discussed

Integrable structure in discrete shell membrane theory.

Science.gov (United States)

Schief, W K

2014-05-08

We present natural discrete analogues of two integrable classes of shell membranes. By construction, these discrete shell membranes are in equilibrium with respect to suitably chosen internal stresses and external forces. The integrability of the underlying equilibrium equations is proved by relating the geometry of the discrete shell membranes to discrete O surface theory. We establish connections with generalized barycentric coordinates and nine-point centres and identify a discrete version of the classical Gauss equation of surface theory.

Finite element reliability analysis of fatigue life

International Nuclear Information System (INIS)

Harkness, H.H.; Belytschko, T.; Liu, W.K.

1992-01-01

Fatigue reliability is addressed by the first-order reliability method combined with a finite element method. Two-dimensional finite element models of components with cracks in mode I are considered with crack growth treated by the Paris law. Probability density functions of the variables affecting fatigue are proposed to reflect a setting where nondestructive evaluation is used, and the Rosenblatt transformation is employed to treat non-Gaussian random variables. Comparisons of the first-order reliability results and Monte Carlo simulations suggest that the accuracy of the first-order reliability method is quite good in this setting. Results show that the upper portion of the initial crack length probability density function is crucial to reliability, which suggests that if nondestructive evaluation is used, the probability of detection curve plays a key role in reliability. (orig.)

Discrete port-Hamiltonian systems : mixed interconnections

NARCIS (Netherlands)

Talasila, Viswanath; Clemente-Gallardo, J.; Schaft, A.J. van der

2005-01-01

Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling

Reliability and protection against failure in computer systems

International Nuclear Information System (INIS)

Daniels, B.K.

1979-01-01

Computers are being increasingly integrated into the control and safety systems of large and potentially hazardous industrial processes. This development introduces problems which are particular to computer systems and opens the way to new techniques of solving conventional reliability and availability problems. References to the developing fields of software reliability, human factors and software design are given, and these subjects are related, where possible, to the quantified assessment of reliability. Original material is presented in the areas of reliability growth and computer hardware failure data. The report draws on the experience of the National Centre of Systems Reliability in assessing the capability and reliability of computer systems both within the nuclear industry, and from the work carried out in other industries by the Systems Reliability Service. (author)

Power cycling test of a 650 V discrete GaN-on-Si power device with a laminated packaging embedding technology

DEFF Research Database (Denmark)

Song, Sungyoung; Munk-Nielsen, Stig; Uhrenfeldt, Christian

2017-01-01

A GaN-on-Si power device is a strong candidate to replace power components based on silicon in high-end market for low-voltage applications, thanks to its electrical characteristics. To maximize opportunities of the GaN device in field applications, a package technology plays an important role...... in a discrete GaN power device. A few specialized package technologies having very lower stray inductance and higher thermal conductivity have been proposed for discrete GaN-on-Si power devices. Despite their superior performance, there has been little discussion of their reliability. The paper presents a power...... cycling test of a discrete GaN power device employing a laminated embedded packaging technology subjected to 125 degrees Celsius junction temperature swing. Failure modes are described with collected electrical characteristics and measured temperature data under the test. In conclusion, physical...

Investigation on biokinetics of 134Cs and 241Am radionuclides in three different organisms and a new evaluation by using discrete time model

International Nuclear Information System (INIS)

Guengoer, N.

1999-05-01

In this study, 134 Cs and 241 Am biokinetic experiments have been observed originally for Black Sea condition with using the gastropod Patella coerulea and the macro algae Enteremorpha linza and the common mussel Mytilus galloprovlncialis as bio indicator organisms. The experiments that have at least three originality, have been carried out very carefully and biokinetic parameters have been calculated by using classical model. The results are compared with the proportionally similar experiments in the literature globally. In this thesis, a new model application has proposed for the biokinetic evaluation for loss experiments of organisms. That is discrete time model. Loss experiments can be evaluated proportionally in a quick and easy way by using this model. Then, it can be observed that the calculated decreasing factor (r) by discrete time model, shows the loss process quality. Moreover, the loss experiments can be stopped when the decreasing factor goes to 1. So, the loss experiment can be evaluated rapidly and quickly with the adequate reliability by using discrete time model. Furthermore, the loss process in the organisms becomes slower and biologic half-lives becomes longer, when the decreasing factor (r) goes to 1. On the other hand, the biological depuration rate (k) goes to nearly zero. So, the proposed discrete time model that is applied in this thesis originally for biokinetic, can be evident that it has an adequate reliability for the biokinetic evaluation

Introductory discrete mathematics

CERN Document Server

Balakrishnan, V K

2010-01-01

This concise text offers an introduction to discrete mathematics for undergraduate students in computer science and mathematics. Mathematics educators consider it vital that their students be exposed to a course in discrete methods that introduces them to combinatorial mathematics and to algebraic and logical structures focusing on the interplay between computer science and mathematics. The present volume emphasizes combinatorics, graph theory with applications to some stand network optimization problems, and algorithms to solve these problems.Chapters 0-3 cover fundamental operations involv

Study of the Internal Mechanical response of an asphalt mixture by 3-D Discrete Element Modeling

DEFF Research Database (Denmark)

Feng, Huan; Pettinari, Matteo; Hofko, Bernhard

2015-01-01

and the reliability of which have been validated. The dynamic modulus of asphalt mixtures were predicted by conducting Discrete Element simulation under dynamic strain control loading. In order to reduce the calculation time, a method based on frequency–temperature superposition principle has been implemented......In this paper the viscoelastic behavior of asphalt mixture was investigated by employing a three-dimensional Discrete Element Method (DEM). The cylinder model was filled with cubic array of spheres with a specified radius, and was considered as a whole mixture with uniform contact properties....... The ball density effect on the internal stress distribution of the asphalt mixture model has been studied when using this method. Furthermore, the internal stresses under dynamic loading have been studied. The agreement between the predicted and the laboratory test results of the complex modulus shows...

Laplacians on discrete and quantum geometries

International Nuclear Information System (INIS)

Calcagni, Gianluca; Oriti, Daniele; Thürigen, Johannes

2013-01-01

We extend discrete calculus for arbitrary (p-form) fields on embedded lattices to abstract discrete geometries based on combinatorial complexes. We then provide a general definition of discrete Laplacian using both the primal cellular complex and its combinatorial dual. The precise implementation of geometric volume factors is not unique and, comparing the definition with a circumcentric and a barycentric dual, we argue that the latter is, in general, more appropriate because it induces a Laplacian with more desirable properties. We give the expression of the discrete Laplacian in several different sets of geometric variables, suitable for computations in different quantum gravity formalisms. Furthermore, we investigate the possibility of transforming from position to momentum space for scalar fields, thus setting the stage for the calculation of heat kernel and spectral dimension in discrete quantum geometries. (paper)

Cuspidal discrete series for projective hyperbolic spaces

DEFF Research Database (Denmark)

Andersen, Nils Byrial; Flensted-Jensen, Mogens

2013-01-01

Abstract. We have in [1] proposed a definition of cusp forms on semisimple symmetric spaces G/H, involving the notion of a Radon transform and a related Abel transform. For the real non-Riemannian hyperbolic spaces, we showed that there exists an infinite number of cuspidal discrete series......, and at most finitely many non-cuspidal discrete series, including in particular the spherical discrete series. For the projective spaces, the spherical discrete series are the only non-cuspidal discrete series. Below, we extend these results to the other hyperbolic spaces, and we also study the question...

Discrete-Event Simulation

OpenAIRE

Prateek Sharma

2015-01-01

Abstract Simulation can be regarded as the emulation of the behavior of a real-world system over an interval of time. The process of simulation relies upon the generation of the history of a system and then analyzing that history to predict the outcome and improve the working of real systems. Simulations can be of various kinds but the topic of interest here is one of the most important kind of simulation which is Discrete-Event Simulation which models the system as a discrete sequence of ev...

Positivity for Convective Semi-discretizations

KAUST Repository

Fekete, Imre; Ketcheson, David I.; Loczi, Lajos

2017-01-01

We propose a technique for investigating stability properties like positivity and forward invariance of an interval for method-of-lines discretizations, and apply the technique to study positivity preservation for a class of TVD semi-discretizations

Integrated reliability condition monitoring and maintenance of equipment

CERN Document Server

Osarenren, John

2015-01-01

Consider a Viable and Cost-Effective Platform for the Industries of the Future (IOF) Benefit from improved safety, performance, and product deliveries to your customers. Achieve a higher rate of equipment availability, performance, product quality, and reliability. Integrated Reliability: Condition Monitoring and Maintenance of Equipment incorporates reliable engineering and mathematical modeling to help you move toward sustainable development in reliability condition monitoring and maintenance. This text introduces a cost-effective integrated reliability growth monitor, integrated reliability degradation monitor, technological inheritance coefficient sensors, and a maintenance tool that supplies real-time information for predicting and preventing potential failures of manufacturing processes and equipment. The author highlights five key elements that are essential to any improvement program: improving overall equipment and part effectiveness, quality, and reliability; improving process performance with maint...

Perfect discretization of reparametrization invariant path integrals

International Nuclear Information System (INIS)

Bahr, Benjamin; Dittrich, Bianca; Steinhaus, Sebastian

2011-01-01

To obtain a well-defined path integral one often employs discretizations. In the case of gravity and reparametrization-invariant systems, the latter of which we consider here as a toy example, discretizations generically break diffeomorphism and reparametrization symmetry, respectively. This has severe implications, as these symmetries determine the dynamics of the corresponding system. Indeed we will show that a discretized path integral with reparametrization-invariance is necessarily also discretization independent and therefore uniquely determined by the corresponding continuum quantum mechanical propagator. We use this insight to develop an iterative method for constructing such a discretized path integral, akin to a Wilsonian RG flow. This allows us to address the problem of discretization ambiguities and of an anomaly-free path integral measure for such systems. The latter is needed to obtain a path integral, that can act as a projector onto the physical states, satisfying the quantum constraints. We will comment on implications for discrete quantum gravity models, such as spin foams.

Perfect discretization of reparametrization invariant path integrals

Science.gov (United States)

Bahr, Benjamin; Dittrich, Bianca; Steinhaus, Sebastian

2011-05-01

To obtain a well-defined path integral one often employs discretizations. In the case of gravity and reparametrization-invariant systems, the latter of which we consider here as a toy example, discretizations generically break diffeomorphism and reparametrization symmetry, respectively. This has severe implications, as these symmetries determine the dynamics of the corresponding system. Indeed we will show that a discretized path integral with reparametrization-invariance is necessarily also discretization independent and therefore uniquely determined by the corresponding continuum quantum mechanical propagator. We use this insight to develop an iterative method for constructing such a discretized path integral, akin to a Wilsonian RG flow. This allows us to address the problem of discretization ambiguities and of an anomaly-free path integral measure for such systems. The latter is needed to obtain a path integral, that can act as a projector onto the physical states, satisfying the quantum constraints. We will comment on implications for discrete quantum gravity models, such as spin foams.

A study of discrete nonlinear systems

International Nuclear Information System (INIS)

Dhillon, H.S.

2001-04-01

An investigation of various spatially discrete time-independent nonlinear models was undertaken. These models are generically applicable to many different physical systems including electron-phonon interactions in solids, magnetic multilayers, layered superconductors and classical lattice systems. To characterise the possible magnetic structures created on magnetic multilayers a model has been formulated and studied. The Euler-Lagrange equation for this model is a discrete version of the Sine-Gordon equation. Solutions of this equation are generated by applying the methods of Chaotic Dynamics - treating the space variable associated with the layer number as a discrete time variable. The states found indicate periodic, quasiperiodic and chaotic structures. Analytic solutions to the discrete nonlinear Schroedinger Equation (DNSE) with cubic nonlinearity are presented in the strong coupling limit. Using these as a starting point, a procedure is developed to determine the wave function and the energy eigenvalue for moderate coupling. The energy eigenvalues of the different structures of the wave function are found to be in excellent agreement with the exact strong coupling result. The solutions to the DNSE indicate commensurate and incommensurate spatial structures associated with different localisation patterns of the wave function. The states which arise may be fractal, periodic, quasiperiodic or chaotic. This work is then extended to solve a first order discrete nonlinear equation. The exact solutions for both the first and second order discrete nonlinear equations with cubic nonlinearity suggests that this method of studying discrete nonlinear equations may be applied to solve discrete equations with any order difference and cubic nonlinearity. (author)

Discrete Curvature Theories and Applications

KAUST Repository

Sun, Xiang

2016-08-25

Discrete Di erential Geometry (DDG) concerns discrete counterparts of notions and methods in di erential geometry. This thesis deals with a core subject in DDG, discrete curvature theories on various types of polyhedral surfaces that are practically important for free-form architecture, sunlight-redirecting shading systems, and face recognition. Modeled as polyhedral surfaces, the shapes of free-form structures may have to satisfy di erent geometric or physical constraints. We study a combination of geometry and physics { the discrete surfaces that can stand on their own, as well as having proper shapes for the manufacture. These proper shapes, known as circular and conical meshes, are closely related to discrete principal curvatures. We study curvature theories that make such surfaces possible. Shading systems of freeform building skins are new types of energy-saving structures that can re-direct the sunlight. From these systems, discrete line congruences across polyhedral surfaces can be abstracted. We develop a new curvature theory for polyhedral surfaces equipped with normal congruences { a particular type of congruences de ned by linear interpolation of vertex normals. The main results are a discussion of various de nitions of normality, a detailed study of the geometry of such congruences, and a concept of curvatures and shape operators associated with the faces of a triangle mesh. These curvatures are compatible with both normal congruences and the Steiner formula. In addition to architecture, we consider the role of discrete curvatures in face recognition. We use geometric measure theory to introduce the notion of asymptotic cones associated with a singular subspace of a Riemannian manifold, which is an extension of the classical notion of asymptotic directions. We get a simple expression of these cones for polyhedral surfaces, as well as convergence and approximation theorems. We use the asymptotic cones as facial descriptors and demonstrate the

Application of a discrete-energy, discrete-ordinates technique to the study of neutron transport in iron

International Nuclear Information System (INIS)

Ching, J.T.

1975-01-01

An algebraic equivalence between the point-energy and multigroup forms of the Boltzmann transport equation is demonstrated which allows the development of a discrete-energy, discrete-ordinates method for the solution of radiation transport problems. The method utilizes a modified version of a cross section processing scheme devised for the moments method code BMT and the transport equation solution algorithm from the one-dimensional discrete-ordinates transport code ANISN. The combined system, identified as MOMANS, computes fluxes directly from point cross sections in a single operation. In the cross-section processing, the group averaging required for multigroup calculations is replaced by a fast numerical scheme capable of generating a set of transfer cross sections containing all the physical features of interest, thereby increasing the detail in the calculated results. Test calculations in which the discrete-energy method was compared with the multigroup method have shown that for the same energy grid (number of points = number of groups), the discrete-energy method is faster but somewhat less accurate than the multigroup method. However, the accuracy of the discrete-energy method increases rapidly as the spacing between energy points is decreased, approaching that of multigroup calculations. For problems requiring great detail in the energy spectrum the discrete-energy method has therefore proven to be as accurate as, and more economical than, the multigroup technique. This was demonstrated by the application of the method to the study of the transport of neutrons in an iron sphere. Using the capability of the discrete-energy method for rapidly treating changes in cross-section sets, the propagation of neutrons from a 14 MeV source in a 22 cm radius sphere of iron was analyzed for sensitivity to changes in the microscopic scattering mechanisms

Compatible Spatial Discretizations for Partial Differential Equations

Energy Technology Data Exchange (ETDEWEB)

Arnold, Douglas, N, ed.

2004-11-25

From May 11--15, 2004, the Institute for Mathematics and its Applications held a hot topics workshop on Compatible Spatial Discretizations for Partial Differential Equations. The numerical solution of partial differential equations (PDE) is a fundamental task in science and engineering. The goal of the workshop was to bring together a spectrum of scientists at the forefront of the research in the numerical solution of PDEs to discuss compatible spatial discretizations. We define compatible spatial discretizations as those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. A wide variety of discretization methods applied across a wide range of scientific and engineering applications have been designed to or found to inherit or mimic intrinsic spatial structure and reproduce fundamental properties of the solution of the continuous PDE model at the finite dimensional level. A profusion of such methods and concepts relevant to understanding them have been developed and explored: mixed finite element methods, mimetic finite differences, support operator methods, control volume methods, discrete differential forms, Whitney forms, conservative differencing, discrete Hodge operators, discrete Helmholtz decomposition, finite integration techniques, staggered grid and dual grid methods, etc. This workshop seeks to foster communication among the diverse groups of researchers designing, applying, and studying such methods as well as researchers involved in practical solution of large scale problems that may benefit from advancements in such discretizations; to help elucidate the relations between the different methods and concepts; and to generally advance our understanding in the area of compatible spatial discretization methods for PDE. Particular points of emphasis included: + Identification of intrinsic properties of PDE models that are critical for the fidelity of numerical

Real-Time Exponential Curve Fits Using Discrete Calculus

Science.gov (United States)

Rowe, Geoffrey

2010-01-01

An improved solution for curve fitting data to an exponential equation (y = Ae(exp Bt) + C) has been developed. This improvement is in four areas -- speed, stability, determinant processing time, and the removal of limits. The solution presented avoids iterative techniques and their stability errors by using three mathematical ideas: discrete calculus, a special relationship (be tween exponential curves and the Mean Value Theorem for Derivatives), and a simple linear curve fit algorithm. This method can also be applied to fitting data to the general power law equation y = Ax(exp B) + C and the general geometric growth equation y = Ak(exp Bt) + C.

Product quality, service reliability and management of operations at ...

African Journals Online (AJOL)

High product quality, service reliability, and management of operations are key factors in business growth and sustainability. Analyzing “The Starbucks Experience” is a pedagogical approach to reinforcing the concepts of control and management of quality, service reliability, and efficient operations in action. The objective ...

Perfect discretization of path integrals

International Nuclear Information System (INIS)

Steinhaus, Sebastian

2012-01-01

In order to obtain a well-defined path integral one often employs discretizations. In the case of General Relativity these generically break diffeomorphism symmetry, which has severe consequences since these symmetries determine the dynamics of the corresponding system. In this article we consider the path integral of reparametrization invariant systems as a toy example and present an improvement procedure for the discretized propagator. Fixed points and convergence of the procedure are discussed. Furthermore we show that a reparametrization invariant path integral implies discretization independence and acts as a projector onto physical states.

Perfect discretization of path integrals

Science.gov (United States)

Steinhaus, Sebastian

2012-05-01

In order to obtain a well-defined path integral one often employs discretizations. In the case of General Relativity these generically break diffeomorphism symmetry, which has severe consequences since these symmetries determine the dynamics of the corresponding system. In this article we consider the path integral of reparametrization invariant systems as a toy example and present an improvement procedure for the discretized propagator. Fixed points and convergence of the procedure are discussed. Furthermore we show that a reparametrization invariant path integral implies discretization independence and acts as a projector onto physical states.

Generating Importance Map for Geometry Splitting using Discrete Ordinates Code in Deep Shielding Problem

International Nuclear Information System (INIS)

Kim, Jong Woon; Lee, Young Ouk

2016-01-01

When we use MCNP code for a deep shielding problem, we prefer to use variance reduction technique such as geometry splitting, or weight window, or source biasing to have relative error within reliable confidence interval. To generate importance map for geometry splitting in MCNP calculation, we should know the track entering number and previous importance on each cells since a new importance is calculated based on these information. If a problem is deep shielding problem such that we have zero tracks entering on a cell, we cannot generate new importance map. In this case, discrete ordinates code can provide information to generate importance map easily. In this paper, we use AETIUS code as a discrete ordinates code. Importance map for MCNP is generated based on a zone average flux of AETIUS calculation. The discretization of space, angle, and energy is not necessary for MCNP calculation. This is the big merit of MCNP code compared to the deterministic code. However, deterministic code (i.e., AETIUS) can provide a rough estimate of the flux throughout a problem relatively quickly. This can help MCNP by providing variance reduction parameters. Recently, ADVANTG code is released. This is an automated tool for generating variance reduction parameters for fixed-source continuous-energy Monte Carlo simulations with MCNP5 v1.60

Control of Discrete Event Systems

NARCIS (Netherlands)

Smedinga, Rein

1989-01-01

Systemen met discrete gebeurtenissen spelen in vele gebieden een rol. In dit proefschrift staat de volgorde van gebeurtenissen centraal en worden tijdsaspecten buiten beschouwing gelaten. In dat geval kunnen systemen met discrete gebeurtenissen goed worden gemodelleerd door gebruik te maken van

Connections on discrete fibre bundles

International Nuclear Information System (INIS)

Manton, N.S.; Cambridge Univ.

1987-01-01

A new approach to gauge fields on a discrete space-time is proposed, in which the fundamental object is a discrete version of a principal fibre bundle. If the bundle is twisted, the gauge fields are topologically non-trivial automatically. (orig.)

Rational solutions of the discrete time Toda lattice and the alternate discrete Painleve II equation

International Nuclear Information System (INIS)

Common, Alan K; Hone, Andrew N W

2008-01-01

The Yablonskii-Vorob'ev polynomials y n (t), which are defined by a second-order bilinear differential-difference equation, provide rational solutions of the Toda lattice. They are also polynomial tau-functions for the rational solutions of the second Painleve equation (P II ). Here we define two-variable polynomials Y n (t, h) on a lattice with spacing h, by considering rational solutions of the discrete time Toda lattice as introduced by Suris. These polynomials are shown to have many properties that are analogous to those of the Yablonskii-Vorob'ev polynomials, to which they reduce when h = 0. They also provide rational solutions for a particular discretization of P II , namely the so-called alternate discrete P II , and this connection leads to an expression in terms of the Umemura polynomials for the third Painleve equation (P III ). It is shown that the Baecklund transformation for the alternate discrete Painleve equation is a symplectic map, and the shift in time is also symplectic. Finally we present a Lax pair for the alternate discrete P II , which recovers Jimbo and Miwa's Lax pair for P II in the continuum limit h → 0

Handbook on modelling for discrete optimization

CERN Document Server

Pitsoulis, Leonidas; Williams, H

2006-01-01

The primary objective underlying the Handbook on Modelling for Discrete Optimization is to demonstrate and detail the pervasive nature of Discrete Optimization. While its applications cut across an incredibly wide range of activities, many of the applications are only known to specialists. It is the aim of this handbook to correct this. It has long been recognized that "modelling" is a critically important mathematical activity in designing algorithms for solving these discrete optimization problems. Nevertheless solving the resultant models is also often far from straightforward. In recent years it has become possible to solve many large-scale discrete optimization problems. However, some problems remain a challenge, even though advances in mathematical methods, hardware, and software technology have pushed the frontiers forward. This handbook couples the difficult, critical-thinking aspects of mathematical modeling with the hot area of discrete optimization. It will be done in an academic handbook treatment...

Discrete Gabor transform and discrete Zak transform

NARCIS (Netherlands)

Bastiaans, M.J.; Namazi, N.M.; Matthews, K.

1996-01-01

Gabor's expansion of a discrete-time signal into a set of shifted and modulated versions of an elementary signal or synthesis window is introduced, along with the inverse operation, i.e. the Gabor transform, which uses an analysis window that is related to the synthesis window and with the help of

Discrete Feature Model (DFM) User Documentation

Energy Technology Data Exchange (ETDEWEB)

Geier, Joel (Clearwater Hardrock Consulting, Corvallis, OR (United States))

2008-06-15

This manual describes the Discrete-Feature Model (DFM) software package for modelling groundwater flow and solute transport in networks of discrete features. A discrete-feature conceptual model represents fractures and other water-conducting features around a repository as discrete conductors surrounded by a rock matrix which is usually treated as impermeable. This approximation may be valid for crystalline rocks such as granite or basalt, which have very low permeability if macroscopic fractures are excluded. A discrete feature is any entity that can conduct water and permit solute transport through bedrock, and can be reasonably represented as a piecewise-planar conductor. Examples of such entities may include individual natural fractures (joints or faults), fracture zones, and disturbed-zone features around tunnels (e.g. blasting-induced fractures or stress-concentration induced 'onion skin' fractures around underground openings). In a more abstract sense, the effectively discontinuous nature of pathways through fractured crystalline bedrock may be idealized as discrete, equivalent transmissive features that reproduce large-scale observations, even if the details of connective paths (and unconnected domains) are not precisely known. A discrete-feature model explicitly represents the fundamentally discontinuous and irregularly connected nature of systems of such systems, by constraining flow and transport to occur only within such features and their intersections. Pathways for flow and solute transport in this conceptualization are a consequence not just of the boundary conditions and hydrologic properties (as with continuum models), but also the irregularity of connections between conductive/transmissive features. The DFM software package described here is an extensible code for investigating problems of flow and transport in geological (natural or human-altered) systems that can be characterized effectively in terms of discrete features. With this

Discrete Feature Model (DFM) User Documentation

International Nuclear Information System (INIS)

Geier, Joel

2008-06-01

This manual describes the Discrete-Feature Model (DFM) software package for modelling groundwater flow and solute transport in networks of discrete features. A discrete-feature conceptual model represents fractures and other water-conducting features around a repository as discrete conductors surrounded by a rock matrix which is usually treated as impermeable. This approximation may be valid for crystalline rocks such as granite or basalt, which have very low permeability if macroscopic fractures are excluded. A discrete feature is any entity that can conduct water and permit solute transport through bedrock, and can be reasonably represented as a piecewise-planar conductor. Examples of such entities may include individual natural fractures (joints or faults), fracture zones, and disturbed-zone features around tunnels (e.g. blasting-induced fractures or stress-concentration induced 'onion skin' fractures around underground openings). In a more abstract sense, the effectively discontinuous nature of pathways through fractured crystalline bedrock may be idealized as discrete, equivalent transmissive features that reproduce large-scale observations, even if the details of connective paths (and unconnected domains) are not precisely known. A discrete-feature model explicitly represents the fundamentally discontinuous and irregularly connected nature of systems of such systems, by constraining flow and transport to occur only within such features and their intersections. Pathways for flow and solute transport in this conceptualization are a consequence not just of the boundary conditions and hydrologic properties (as with continuum models), but also the irregularity of connections between conductive/transmissive features. The DFM software package described here is an extensible code for investigating problems of flow and transport in geological (natural or human-altered) systems that can be characterized effectively in terms of discrete features. With this software, the

A Schumpeterian Model of Entrepreneurship, Innovation, and Regional Economic Growth

NARCIS (Netherlands)

Batabyal, A.; Nijkamp, P.

2012-01-01

The authors provide the first theoretical analysis of a one-sector, discrete-time, Schumpeterian model of growth in a regional economy in which consumers are risk neutral, there is no population growth, monopolistic entrepreneurs produce intermediate goods, and a single consumption good is produced

Reliability growth of thin film resistors contact

Directory of Open Access Journals (Sweden)

Lugin A. N.

2010-10-01

Full Text Available Necessity of resistive layer growth under the contact and in the contact zone of resistive element is shown in order to reduce peak values of current flow and power dissipation in the contact of thin film resistor, thereby to increase the resistor stability to parametric and catastrophic failures.

Mode I crack analysis in single crystals with anisotropic discrete dislocation plasticity : I. Formulation and crack growth

NARCIS (Netherlands)

Shishvan, Siamak Soleymani; Van der Giessen, Erik

Analyses of monotonic loading of a plane-strain mode I crack in an fcc single crystal under small-scale yielding are carried out using discrete dislocation plasticity (DDP) incorporating anisotropic elasticity. Two crystallographically symmetric crack orientations are considered where plane-strain

A modified GO-FLOW methodology with common cause failure based on Discrete Time Bayesian Network

International Nuclear Information System (INIS)

Fan, Dongming; Wang, Zili; Liu, Linlin; Ren, Yi

2016-01-01

Highlights: • Identification of particular causes of failure for common cause failure analysis. • Comparison two formalisms (GO-FLOW and Discrete Time Bayesian network) and establish the correlation between them. • Mapping the GO-FLOW model into Bayesian network model. • Calculated GO-FLOW model with common cause failures based on DTBN. - Abstract: The GO-FLOW methodology is a success-oriented system reliability modelling technique for multi-phase missions involving complex time-dependent, multi-state and common cause failure (CCF) features. However, the analysis algorithm cannot easily handle the multiple shared signals and CCFs. In addition, the simulative algorithm is time consuming when vast multi-state components exist in the model, and the multiple time points of phased mission problems increases the difficulty of the analysis method. In this paper, the Discrete Time Bayesian Network (DTBN) and the GO-FLOW methodology are integrated by the unified mapping rules. Based on these rules, the multi operators can be mapped into DTBN followed by, a complete GO-FLOW model with complex characteristics (e.g. phased mission, multi-state, and CCF) can be converted to the isomorphic DTBN and easily analyzed by utilizing the DTBN. With mature algorithms and tools, the multi-phase mission reliability parameter can be efficiently obtained via the proposed approach without considering the shared signals and the various complex logic operation. Meanwhile, CCF can also arise in the computing process.

Discrete-Time Biomedical Signal Encryption

Directory of Open Access Journals (Sweden)

Victor Grigoraş

2017-12-01

Full Text Available Chaotic modulation is a strong method of improving communication security. Analog and discrete chaotic systems are presented in actual literature. Due to the expansion of digital communication, discrete-time systems become more efficient and closer to actual technology. The present contribution offers an in-depth analysis of the effects chaos encryption produce on 1D and 2D biomedical signals. The performed simulations show that modulating signals are precisely recovered by the synchronizing receiver if discrete systems are digitally implemented and the coefficients precisely correspond. Channel noise is also applied and its effects on biomedical signal demodulation are highlighted.

The origin of discrete particles

CERN Document Server

Bastin, T

2009-01-01

This book is a unique summary of the results of a long research project undertaken by the authors on discreteness in modern physics. In contrast with the usual expectation that discreteness is the result of mathematical tools for insertion into a continuous theory, this more basic treatment builds up the world from the discrimination of discrete entities. This gives an algebraic structure in which certain fixed numbers arise. As such, one agrees with the measured value of the fine-structure constant to one part in 10,000,000 (10 7 ). Sample Chapter(s). Foreword (56 KB). Chapter 1: Introduction

Reliability-Based Topology Optimization Using Stochastic Response Surface Method with Sparse Grid Design

Directory of Open Access Journals (Sweden)

Qinghai Zhao

2015-01-01

Full Text Available A mathematical framework is developed which integrates the reliability concept into topology optimization to solve reliability-based topology optimization (RBTO problems under uncertainty. Two typical methodologies have been presented and implemented, including the performance measure approach (PMA and the sequential optimization and reliability assessment (SORA. To enhance the computational efficiency of reliability analysis, stochastic response surface method (SRSM is applied to approximate the true limit state function with respect to the normalized random variables, combined with the reasonable design of experiments generated by sparse grid design, which was proven to be an effective and special discretization technique. The uncertainties such as material property and external loads are considered on three numerical examples: a cantilever beam, a loaded knee structure, and a heat conduction problem. Monte-Carlo simulations are also performed to verify the accuracy of the failure probabilities computed by the proposed approach. Based on the results, it is demonstrated that application of SRSM with SGD can produce an efficient reliability analysis in RBTO which enables a more reliable design than that obtained by DTO. It is also found that, under identical accuracy, SORA is superior to PMA in view of computational efficiency.

Time-Discrete Higher-Order ALE Formulations: Stability

KAUST Repository

Bonito, Andrea; Kyza, Irene; Nochetto, Ricardo H.

2013-01-01

on the stability of the PDE but may influence that of a discrete scheme. We examine this critical issue for higher-order time stepping without space discretization. We propose time-discrete discontinuous Galerkin (dG) numerical schemes of any order for a time

Fermion systems in discrete space-time

International Nuclear Information System (INIS)

Finster, Felix

2007-01-01

Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure

Fermion systems in discrete space-time

Energy Technology Data Exchange (ETDEWEB)

Finster, Felix [NWF I - Mathematik, Universitaet Regensburg, 93040 Regensburg (Germany)

2007-05-15

Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.

Fermion Systems in Discrete Space-Time

OpenAIRE

Finster, Felix

2006-01-01

Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.

Fermion systems in discrete space-time

Science.gov (United States)

Finster, Felix

2007-05-01

Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.

Discrete ellipsoidal statistical BGK model and Burnett equations

Science.gov (United States)

Zhang, Yu-Dong; Xu, Ai-Guo; Zhang, Guang-Cai; Chen, Zhi-Hua; Wang, Pei

2018-06-01

A new discrete Boltzmann model, the discrete ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) model, is proposed to simulate nonequilibrium compressible flows. Compared with the original discrete BGK model, the discrete ES-BGK has a flexible Prandtl number. For the discrete ES-BGK model in the Burnett level, two kinds of discrete velocity model are introduced and the relations between nonequilibrium quantities and the viscous stress and heat flux in the Burnett level are established. The model is verified via four benchmark tests. In addition, a new idea is introduced to recover the actual distribution function through the macroscopic quantities and their space derivatives. The recovery scheme works not only for discrete Boltzmann simulation but also for hydrodynamic ones, for example, those based on the Navier-Stokes or the Burnett equations.

Designing an Algorithm for Cancerous Tissue Segmentation Using Adaptive K-means Cluttering and Discrete Wavelet Transform.

Science.gov (United States)

Rezaee, Kh; Haddadnia, J

2013-09-01

Breast cancer is currently one of the leading causes of death among women worldwide. The diagnosis and separation of cancerous tumors in mammographic images require accuracy, experience and time, and it has always posed itself as a major challenge to the radiologists and physicians. This paper proposes a new algorithm which draws on discrete wavelet transform and adaptive K-means techniques to transmute the medical images implement the tumor estimation and detect breast cancer tumors in mammograms in early stages. It also allows the rapid processing of the input data. In the first step, after designing a filter, the discrete wavelet transform is applied to the input images and the approximate coefficients of scaling components are constructed. Then, the different parts of image are classified in continuous spectrum. In the next step, by using adaptive K-means algorithm for initializing and smart choice of clusters' number, the appropriate threshold is selected. Finally, the suspicious cancerous mass is separated by implementing the image processing techniques. We Received 120 mammographic images in LJPEG format, which had been scanned in Gray-Scale with 50 microns size, 3% noise and 20% INU from clinical data taken from two medical databases (mini-MIAS and DDSM). The proposed algorithm detected tumors at an acceptable level with an average accuracy of 92.32% and sensitivity of 90.24%. Also, the Kappa coefficient was approximately 0.85, which proved the suitable reliability of the system performance. The exact positioning of the cancerous tumors allows the radiologist to determine the stage of disease progression and suggest an appropriate treatment in accordance with the tumor growth. The low PPV and high NPV of the system is a warranty of the system and both clinical specialists and patients can trust its output.

Memorized discrete systems and time-delay

CERN Document Server

Luo, Albert C J

2017-01-01

This book examines discrete dynamical systems with memory—nonlinear systems that exist extensively in biological organisms and financial and economic organizations, and time-delay systems that can be discretized into the memorized, discrete dynamical systems. It book further discusses stability and bifurcations of time-delay dynamical systems that can be investigated through memorized dynamical systems as well as bifurcations of memorized nonlinear dynamical systems, discretization methods of time-delay systems, and periodic motions to chaos in nonlinear time-delay systems. The book helps readers find analytical solutions of MDS, change traditional perturbation analysis in time-delay systems, detect motion complexity and singularity in MDS; and determine stability, bifurcation, and chaos in any time-delay system.

Discrete Mathematics and Curriculum Reform.

Science.gov (United States)

Kenney, Margaret J.

1996-01-01

Defines discrete mathematics as the mathematics necessary to effect reasoned decision making in finite situations and explains how its use supports the current view of mathematics education. Discrete mathematics can be used by curriculum developers to improve the curriculum for students of all ages and abilities. (SLD)

Exact analysis of discrete data

CERN Document Server

Hirji, Karim F

2005-01-01

Researchers in fields ranging from biology and medicine to the social sciences, law, and economics regularly encounter variables that are discrete or categorical in nature. While there is no dearth of books on the analysis and interpretation of such data, these generally focus on large sample methods. When sample sizes are not large or the data are otherwise sparse, exact methods--methods not based on asymptotic theory--are more accurate and therefore preferable.This book introduces the statistical theory, analysis methods, and computation techniques for exact analysis of discrete data. After reviewing the relevant discrete distributions, the author develops the exact methods from the ground up in a conceptually integrated manner. The topics covered range from univariate discrete data analysis, a single and several 2 x 2 tables, a single and several 2 x K tables, incidence density and inverse sampling designs, unmatched and matched case -control studies, paired binary and trinomial response models, and Markov...

An application of multigrid methods for a discrete elastic model for epitaxial systems

International Nuclear Information System (INIS)

Caflisch, R.E.; Lee, Y.-J.; Shu, S.; Xiao, Y.-X.; Xu, J.

2006-01-01

We apply an efficient and fast algorithm to simulate the atomistic strain model for epitaxial systems, recently introduced by Schindler et al. [Phys. Rev. B 67, 075316 (2003)]. The discrete effects in this lattice statics model are crucial for proper simulation of the influence of strain for thin film epitaxial growth, but the size of the atomistic systems of interest is in general quite large and hence the solution of the discrete elastic equations is a considerable numerical challenge. In this paper, we construct an algebraic multigrid method suitable for efficient solution of the large scale discrete strain model. Using this method, simulations are performed for several representative physical problems, including an infinite periodic step train, a layered nanocrystal, and a system of quantum dots. The results demonstrate the effectiveness and robustness of the method and show that the method attains optimal convergence properties, regardless of the problem size, the geometry and the physical parameters. The effects of substrate depth and of invariance due to traction-free boundary conditions are assessed. For a system of quantum dots, the simulated strain energy density supports the observations that trench formation near the dots provides strain relief

Discrete systems and integrability

CERN Document Server

Hietarinta, J; Nijhoff, F W

2016-01-01

This first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant. While treating the material at an elementary level, the book also highlights many recent developments. Topics include: Darboux and Bäcklund transformations; difference equations and special functions; multidimensional consistency of integrable lattice equations; associated linear problems (Lax pairs); connections with Padé approximants and convergence algorithms; singularities and geometry; Hirota's bilinear formalism for lattices; intriguing properties of discrete Painlevé equations; and the novel theory of Lagrangian multiforms. The book builds the material in an organic way, emphasizing interconnections between the various approaches, while the exposition is mostly done through explicit computations on key examples. Written by respected experts in the field, the numerous exercises and the thoroug...

Microstructure-Evolution and Reliability Assessment Tool for Lead-Free Component Insertion in Army Electronics

Science.gov (United States)

2008-10-01

millions of transistors on a silicon chip in addition to many discrete components such as resistors , inductors and capacitors. All these different... resistors [36]. They have defined an Ag3Sn phase growth parameter, S, and have observed that when subjected to periodic thermal loading, the phase growth...moiré interferometry. The process involves moving the whole interferometer parallel to the specimen grating in small increments, using a piezo

Reliability Constrained Priority Load Shedding for Aerospace Power System Automation

Science.gov (United States)

Momoh, James A.; Zhu, Jizhong; Kaddah, Sahar S.; Dolce, James L. (Technical Monitor)

2000-01-01

The need for improving load shedding on board the space station is one of the goals of aerospace power system automation. To accelerate the optimum load-shedding functions, several constraints must be involved. These constraints include congestion margin determined by weighted probability contingency, component/system reliability index, generation rescheduling. The impact of different faults and indices for computing reliability were defined before optimization. The optimum load schedule is done based on priority, value and location of loads. An optimization strategy capable of handling discrete decision making, such as Everett optimization, is proposed. We extended Everett method to handle expected congestion margin and reliability index as constraints. To make it effective for real time load dispatch process, a rule-based scheme is presented in the optimization method. It assists in selecting which feeder load to be shed, the location of the load, the value, priority of the load and cost benefit analysis of the load profile is included in the scheme. The scheme is tested using a benchmark NASA system consisting of generators, loads and network.

Discrete Painlevé equations: an integrability paradigm

International Nuclear Information System (INIS)

Grammaticos, B; Ramani, A

2014-01-01

In this paper we present a review of results on discrete Painlevé equations. We begin with an introduction which serves as a refresher on the continuous Painlevé equations. Next, in the first, main part of the paper, we introduce the discrete Painlevé equations, the various methods for their derivation, and their properties as well as their classification scheme. Along the way we present a brief summary of the two major discrete integrability detectors and of Quispel–Roberts–Thompson mapping, which plays a primordial role in the derivation of discrete Painlevé equations. The second part of the paper is more technical and focuses on the presentation of new results on what are called asymmetric discrete Painlevé equations. (comment)

From the continuous PV to discrete Painleve equations

International Nuclear Information System (INIS)

Tokihiro, T.; Grammaticos, B.; Ramani, A.

2002-01-01

We study the discrete transformations that are associated with the auto-Baecklund of the (continuous) P V equation. We show that several two-parameter discrete Painleve equations can be obtained as contiguity relations of P V . Among them we find the asymmetric d-P II equation which is a well-known form of discrete P III . The relation between the ternary P I (previously obtained through the discrete dressing approach) and P V is also established. A new discrete Painleve equation is also derived. (author)

Discrete Routh reduction

International Nuclear Information System (INIS)

Jalnapurkar, Sameer M; Leok, Melvin; Marsden, Jerrold E; West, Matthew

2006-01-01

This paper develops the theory of Abelian Routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with Abelian symmetry. The reduction of variational Runge-Kutta discretizations is considered, as well as the extent to which symmetry reduction and discretization commute. These reduced methods allow the direct simulation of dynamical features such as relative equilibria and relative periodic orbits that can be obscured or difficult to identify in the unreduced dynamics. The methods are demonstrated for the dynamics of an Earth orbiting satellite with a non-spherical J 2 correction, as well as the double spherical pendulum. The J 2 problem is interesting because in the unreduced picture, geometric phases inherent in the model and those due to numerical discretization can be hard to distinguish, but this issue does not appear in the reduced algorithm, where one can directly observe interesting dynamical structures in the reduced phase space (the cotangent bundle of shape space), in which the geometric phases have been removed. The main feature of the double spherical pendulum example is that it has a non-trivial magnetic term in its reduced symplectic form. Our method is still efficient as it can directly handle the essential non-canonical nature of the symplectic structure. In contrast, a traditional symplectic method for canonical systems could require repeated coordinate changes if one is evoking Darboux' theorem to transform the symplectic structure into canonical form, thereby incurring additional computational cost. Our method allows one to design reduced symplectic integrators in a natural way, despite the non-canonical nature of the symplectic structure

Foundations of a discrete physics

International Nuclear Information System (INIS)

McGoveran, D.; Noyes, P.

1988-01-01

Starting from the principles of finiteness, discreteness, finite computability and absolute nonuniqueness, we develop the ordering operator calculus, a strictly constructive mathematical system having the empirical properties required by quantum mechanical and special relativistic phenomena. We show how to construct discrete distance functions, and both rectangular and spherical coordinate systems(with a discrete version of ''π''). The richest discrete space constructible without a preferred axis and preserving translational and rotational invariance is shown to be a discrete 3-space with the usual symmetries. We introduce a local ordering parameter with local (proper) time-like properties and universal ordering parameters with global (cosmological) time-like properties. Constructed ''attribute velocities'' connect ensembles with attributes that are invariant as the appropriate time-like parameter increases. For each such attribute, we show how to construct attribute velocities which must satisfy the '' relativistic Doppler shift'' and the ''relativistic velocity composition law,'' as well as the Lorentz transformations. By construction, these velocities have finite maximum and minimum values. In the space of all attributes, the minimum of these maximum velocities will predominate in all multiple attribute computations, and hence can be identified as a fundamental limiting velocity, General commutation relations are constructed which under the physical interpretation are shown to reduce to the usual quantum mechanical commutation relations. 50 refs., 18 figs

Discrete event command and control for networked teams with multiple missions

Science.gov (United States)

Lewis, Frank L.; Hudas, Greg R.; Pang, Chee Khiang; Middleton, Matthew B.; McMurrough, Christopher

2009-05-01

During mission execution in military applications, the TRADOC Pamphlet 525-66 Battle Command and Battle Space Awareness capabilities prescribe expectations that networked teams will perform in a reliable manner under changing mission requirements, varying resource availability and reliability, and resource faults. In this paper, a Command and Control (C2) structure is presented that allows for computer-aided execution of the networked team decision-making process, control of force resources, shared resource dispatching, and adaptability to change based on battlefield conditions. A mathematically justified networked computing environment is provided called the Discrete Event Control (DEC) Framework. DEC has the ability to provide the logical connectivity among all team participants including mission planners, field commanders, war-fighters, and robotic platforms. The proposed data management tools are developed and demonstrated on a simulation study and an implementation on a distributed wireless sensor network. The results show that the tasks of multiple missions are correctly sequenced in real-time, and that shared resources are suitably assigned to competing tasks under dynamically changing conditions without conflicts and bottlenecks.

On the influence of spatial discretization on cross section preparation with HELIOS 1.9

International Nuclear Information System (INIS)

Merk, B.; Koch, R.

2008-01-01

The aim of many reactor calculations is the determination of the neutron flux and the nuclear power distribution. These distributions are in general calculated by solving the space and energy dependent static transport equation. Thus, a reliable computation of the neutron flux distribution within the reactor core would require the solution of the space-, energy- and angle-dependent neutron transport equation for the full nuclear reactor core. It is not yet feasible to solve exactly the neutron transport equation for realistic reactor core geometries in detail in practical use. Thus deterministic reactor calculations are split into the cell and lattice calculation based on static transport and the core simulation based on nodal codes. The cell and lattice calculations are mostly based on multi group transport calculations within two dimensions considering unstructured meshes. The resulting neutron flux is used for the preparation of few group cross sections like they are used in the nodal 3D full core simulation codes. One commercial standard product is the Studsvik Scandpower code system HELIOS 1.9. ''The transport method of HELIOS is called the CCCP method, because it is based on current coupling and collision probabilities (first-flight probabilities).. the system to be calculated consists of space elements that are coupled with each other and with the boundaries by interface currents, while the properties of each space element - its responses to sources and in-currents - are obtained from collision probabilities'' [ 1]. The applied collision probabilities method is based on the flat flux approximation. ''We assume that particles are emitted isotropically and uniformly within each discrete volume. This is known as the flat flux approximation. The flat flux approximation places a restriction on the mesh: if the flux varies rapidly within a region, the mesh should be refined sufficiently to ensure that the flux is well approximated by a piecewise - constant

Theoretical Basics of Teaching Discrete Mathematics

Directory of Open Access Journals (Sweden)

Y. A. Perminov

2012-01-01

Full Text Available  The paper deals with the research findings concerning the process of mastering the theoretical basics of discrete mathematics by the students of vocational pedagogic profile. The methodological analysis is based on the subject and functions of the modern discrete mathematics and its role in mathematical modeling and computing. The modern discrete mathematics (i.e. mathematics of the finite type structures plays the important role in modernization of vocational training. It is especially rele- vant to training students for vocational pedagogic qualifications, as in the future they will be responsible for training the middle and the senior level specialists in engineer- ing and technical spheres. Nowadays in different industries, there arise the problems which require for their solving both continual – based on the classical mathematical methods – and discrete modeling. The teaching course of discrete mathematics for the future vocational teachers should be relevant to the target qualification and aimed at mastering the mathematical modeling, systems of computer mathematics and computer technologies. The author emphasizes the fundamental role of mastering the language of algebraic and serial structures, as well as the logical, algorithmic, combinatory schemes dominating in dis- crete mathematics. The guidelines for selecting the content of the course in discrete mathematics are specified. The theoretical findings of the research can be put into practice whilst developing curricula and working programs for bachelors and masters’ training. 

Discrete symmetries and their stringy origin

International Nuclear Information System (INIS)

Mayorga Pena, Damian Kaloni

2014-05-01

Discrete symmetries have proven to be very useful in controlling the phenomenology of theories beyond the standard model. In this work we explore how these symmetries emerge from string compactifications. Our approach is twofold: On the one hand, we consider the heterotic string on orbifold backgrounds. In this case the discrete symmetries can be derived from the orbifold conformal field theory, and it can be shown that they are in close relation with the orbifold geometry. We devote special attention to R-symmetries, which arise from discrete remnants of the Lorentz group in compact space. Further we discuss the physical implications of these symmetries both in the heterotic mini-landscape and in newly constructed models based on the Z 2 x Z 4 orbifold. In both cases we observe that the discrete symmetries favor particular locations in the orbifold where the particles of standard model should live. On the other hand we consider a class of F-theory models exhibiting an SU(5) gauge group, times additional U(1) symmetries. In this case, the smooth compactification background does not permit us to track the discrete symmetries as transparently as in orbifold models. Hence, we follow a different approach and search for discrete subgroups emerging after the U(1)s are broken. We observe that in this approach it is possible to obtain the standard Z 2 matter parity of the MSSM.

Exterior difference systems and invariance properties of discrete mechanics

International Nuclear Information System (INIS)

Xie Zheng; Xie Duanqiang; Li Hongbo

2008-01-01

Invariance properties describe the fundamental physical laws in discrete mechanics. Can those properties be described in a geometric way? We investigate an exterior difference system called the discrete Euler-Lagrange system, whose solution has one-to-one correspondence with solutions of discrete Euler-Lagrange equations, and use it to define the first integrals. The preservation of the discrete symplectic form along the discrete Hamilton phase flows and the discrete Noether's theorem is also described in the language of difference forms

Reliability importance analysis of Markovian systems at steady state using perturbation analysis

Energy Technology Data Exchange (ETDEWEB)

Phuc Do Van [Institut Charles Delaunay - FRE CNRS 2848, Systems Modeling and Dependability Group, Universite de technologie de Troyes, 12, rue Marie Curie, BP 2060-10010 Troyes cedex (France); Barros, Anne [Institut Charles Delaunay - FRE CNRS 2848, Systems Modeling and Dependability Group, Universite de technologie de Troyes, 12, rue Marie Curie, BP 2060-10010 Troyes cedex (France)], E-mail: anne.barros@utt.fr; Berenguer, Christophe [Institut Charles Delaunay - FRE CNRS 2848, Systems Modeling and Dependability Group, Universite de technologie de Troyes, 12, rue Marie Curie, BP 2060-10010 Troyes cedex (France)

2008-11-15

Sensitivity analysis has been primarily defined for static systems, i.e. systems described by combinatorial reliability models (fault or event trees). Several structural and probabilistic measures have been proposed to assess the components importance. For dynamic systems including inter-component and functional dependencies (cold spare, shared load, shared resources, etc.), and described by Markov models or, more generally, by discrete events dynamic systems models, the problem of sensitivity analysis remains widely open. In this paper, the perturbation method is used to estimate an importance factor, called multi-directional sensitivity measure, in the framework of Markovian systems. Some numerical examples are introduced to show why this method offers a promising tool for steady-state sensitivity analysis of Markov processes in reliability studies.

Reliability importance analysis of Markovian systems at steady state using perturbation analysis

International Nuclear Information System (INIS)

Phuc Do Van; Barros, Anne; Berenguer, Christophe

2008-01-01

Sensitivity analysis has been primarily defined for static systems, i.e. systems described by combinatorial reliability models (fault or event trees). Several structural and probabilistic measures have been proposed to assess the components importance. For dynamic systems including inter-component and functional dependencies (cold spare, shared load, shared resources, etc.), and described by Markov models or, more generally, by discrete events dynamic systems models, the problem of sensitivity analysis remains widely open. In this paper, the perturbation method is used to estimate an importance factor, called multi-directional sensitivity measure, in the framework of Markovian systems. Some numerical examples are introduced to show why this method offers a promising tool for steady-state sensitivity analysis of Markov processes in reliability studies

Reliability of EUCLIDIAN: An autonomous robotic system for image-guided prostate brachytherapy

International Nuclear Information System (INIS)

Podder, Tarun K.; Buzurovic, Ivan; Huang Ke; Showalter, Timothy; Dicker, Adam P.; Yu, Yan

2011-01-01

Purpose: Recently, several robotic systems have been developed to perform accurate and consistent image-guided brachytherapy. Before introducing a new device into clinical operations, it is important to assess the reliability and mean time before failure (MTBF) of the system. In this article, the authors present the preclinical evaluation and analysis of the reliability and MTBF of an autonomous robotic system, which is developed for prostate seed implantation. Methods: The authors have considered three steps that are important in reliability growth analysis. These steps are: Identification and isolation of failures, classification of failures, and trend analysis. For any one-of-a-kind product, the reliability enhancement is accomplished through test-fix-test. The authors have used failure mode and effect analysis for collection and analysis of reliability data by identifying and categorizing the failure modes. Failures were classified according to severity. Failures that occurred during the operation of this robotic system were considered as nonhomogenous Poisson process. The failure occurrence trend was analyzed using Laplace test. For analyzing and predicting reliability growth, commonly used and widely accepted models, Duane's model and the Army Material Systems Analysis Activity, i.e., Crow's model, were applied. The MTBF was used as an important measure for assessing the system's reliability. Results: During preclinical testing, 3196 seeds (in 53 test cases) were deposited autonomously by the robot and 14 critical failures were encountered. The majority of the failures occurred during the first few cases. The distribution of failures followed Duane's postulation as well as Crow's postulation of reliability growth. The Laplace test index was -3.82 (<0), indicating a significant trend in failure data, and the failure intervals lengthened gradually. The continuous increase in the failure occurrence interval suggested a trend toward improved reliability. The MTBF

Reliability of EUCLIDIAN: An autonomous robotic system for image-guided prostate brachytherapy

Energy Technology Data Exchange (ETDEWEB)

Podder, Tarun K.; Buzurovic, Ivan; Huang Ke; Showalter, Timothy; Dicker, Adam P.; Yu, Yan [Department of Radiation Oncology, Kimmel Cancer Center (NCI-designated), Thomas Jefferson University, Philadelphia, Pennsylvania 19107 (United States)

2011-01-15

Purpose: Recently, several robotic systems have been developed to perform accurate and consistent image-guided brachytherapy. Before introducing a new device into clinical operations, it is important to assess the reliability and mean time before failure (MTBF) of the system. In this article, the authors present the preclinical evaluation and analysis of the reliability and MTBF of an autonomous robotic system, which is developed for prostate seed implantation. Methods: The authors have considered three steps that are important in reliability growth analysis. These steps are: Identification and isolation of failures, classification of failures, and trend analysis. For any one-of-a-kind product, the reliability enhancement is accomplished through test-fix-test. The authors have used failure mode and effect analysis for collection and analysis of reliability data by identifying and categorizing the failure modes. Failures were classified according to severity. Failures that occurred during the operation of this robotic system were considered as nonhomogenous Poisson process. The failure occurrence trend was analyzed using Laplace test. For analyzing and predicting reliability growth, commonly used and widely accepted models, Duane's model and the Army Material Systems Analysis Activity, i.e., Crow's model, were applied. The MTBF was used as an important measure for assessing the system's reliability. Results: During preclinical testing, 3196 seeds (in 53 test cases) were deposited autonomously by the robot and 14 critical failures were encountered. The majority of the failures occurred during the first few cases. The distribution of failures followed Duane's postulation as well as Crow's postulation of reliability growth. The Laplace test index was -3.82 (<0), indicating a significant trend in failure data, and the failure intervals lengthened gradually. The continuous increase in the failure occurrence interval suggested a trend toward

Discrete breathers in graphane: Effect of temperature

Energy Technology Data Exchange (ETDEWEB)

Baimova, J. A., E-mail: julia.a.baimova@gmail.com [Russian Academy of Sciences, Institute of Metal Physics, Ural Branch (Russian Federation); Murzaev, R. T.; Lobzenko, I. P.; Dmitriev, S. V. [Russian Academy of Sciences, Institute for Metals Superplasticity Problems (Russian Federation); Zhou, Kun [Nanyang Technological University, School of Mechanical and Aerospace Engineering (Singapore)

2016-05-15

The discrete breathers in graphane in thermodynamic equilibrium in the temperature range 50–600 K are studied by molecular dynamics simulation. A discrete breather is a hydrogen atom vibrating along the normal to a sheet of graphane at a high amplitude. As was found earlier, the lifetime of a discrete breather at zero temperature corresponds to several tens of thousands of vibrations. The effect of temperature on the decay time of discrete breathers and the probability of their detachment from a sheet of graphane are studied in this work. It is shown that closely spaced breathers can exchange energy with each other at zero temperature. The data obtained suggest that thermally activated discrete breathers can be involved in the dehydrogenation of graphane, which is important for hydrogen energetics.

Understanding and predicting metallic whisker growth and its effects on reliability : LDRD final report.

Energy Technology Data Exchange (ETDEWEB)

Michael, Joseph Richard; Grant, Richard P.; Rodriguez, Mark Andrew; Pillars, Jamin; Susan, Donald Francis; McKenzie, Bonnie Beth; Yelton, William Graham

2012-01-01

Tin (Sn) whiskers are conductive Sn filaments that grow from Sn-plated surfaces, such as surface finishes on electronic packages. The phenomenon of Sn whiskering has become a concern in recent years due to requirements for lead (Pb)-free soldering and surface finishes in commercial electronics. Pure Sn finishes are more prone to whisker growth than their Sn-Pb counterparts and high profile failures due to whisker formation (causing short circuits) in space applications have been documented. At Sandia, Sn whiskers are of interest due to increased use of Pb-free commercial off-the-shelf (COTS) parts and possible future requirements for Pb-free solders and surface finishes in high-reliability microelectronics. Lead-free solders and surface finishes are currently being used or considered for several Sandia applications. Despite the long history of Sn whisker research and the recently renewed interest in this topic, a comprehensive understanding of whisker growth remains elusive. This report describes recent research on characterization of Sn whiskers with the aim of understanding the underlying whisker growth mechanism(s). The report is divided into four sections and an Appendix. In Section 1, the Sn plating process is summarized. Specifically, the Sn plating parameters that were successful in producing samples with whiskers will be reviewed. In Section 2, the scanning electron microscopy (SEM) of Sn whiskers and time-lapse SEM studies of whisker growth will be discussed. This discussion includes the characterization of straight as well as kinked whiskers. In Section 3, a detailed discussion is given of SEM/EBSD (electron backscatter diffraction) techniques developed to determine the crystallography of Sn whiskers. In Section 4, these SEM/EBSD methods are employed to determine the crystallography of Sn whiskers, with a statistically significant number of whiskers analyzed. This is the largest study of Sn whisker crystallography ever reported. This section includes a

An integrable semi-discretization of the Boussinesq equation

International Nuclear Information System (INIS)

Zhang, Yingnan; Tian, Lixin

2016-01-01

Highlights: • A new integrable semi-discretization of the Boussinesq equation is present. • A Bäcklund transformation and a Lax pair for the differential-difference system is derived by using Hirota's bilinear method. • The soliton solutions of 'good' Boussinesq equation and numerical algorithms are investigated. - Abstract: In this paper, we present an integrable semi-discretization of the Boussinesq equation. Different from other discrete analogues, we discretize the ‘time’ variable and get an integrable differential-difference system. Under a standard limitation, the differential-difference system converges to the continuous Boussinesq equation such that the discrete system can be used to design numerical algorithms. Using Hirota's bilinear method, we find a Bäcklund transformation and a Lax pair of the differential-difference system. For the case of ‘good’ Boussinesq equation, we investigate the soliton solutions of its discrete analogue and design numerical algorithms. We find an effective way to reduce the phase shift caused by the discretization. The numerical results coincide with our analysis.

Discretization of 3d gravity in different polarizations

Science.gov (United States)

Dupuis, Maïté; Freidel, Laurent; Girelli, Florian

2017-10-01

We study the discretization of three-dimensional gravity with Λ =0 following the loop quantum gravity framework. In the process, we realize that different choices of polarization are possible. This allows us to introduce a new discretization based on the triad as opposed to the connection as in the standard loop quantum gravity framework. We also identify the classical nontrivial symmetries of discrete gravity, namely the Drinfeld double, given in terms of momentum maps. Another choice of polarization is given by the Chern-Simons formulation of gravity. Our framework also provides a new discretization scheme of Chern-Simons, which keeps track of the link between the continuum variables and the discrete ones. We show how the Poisson bracket we recover between the Chern-Simons holonomies allows us to recover the Goldman bracket. There is also a transparent link between the discrete Chern-Simons formulation and the discretization of gravity based on the connection (loop gravity) or triad variables (dual loop gravity).

Discrete fractional solutions of a Legendre equation

Science.gov (United States)

Yılmazer, Resat

2018-01-01

One of the most popular research interests of science and engineering is the fractional calculus theory in recent times. Discrete fractional calculus has also an important position in fractional calculus. In this work, we acquire new discrete fractional solutions of the homogeneous and non homogeneous Legendre differential equation by using discrete fractional nabla operator.

First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media

Science.gov (United States)

Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.

2018-01-01

A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell’s equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell–Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell–Lorentz equations, we trace the development

First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media

International Nuclear Information System (INIS)

Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.

2016-01-01

A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell’s equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell–Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell–Lorentz equations, we trace the development

First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media

Energy Technology Data Exchange (ETDEWEB)

Mishchenko, Michael I., E-mail: michael.i.mishchenko@nasa.gov [NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 (United States); Dlugach, Janna M. [Main Astronomical Observatory of the National Academy of Sciences of Ukraine, 27 Zabolotny Str., 03680, Kyiv (Ukraine); Yurkin, Maxim A. [Voevodsky Institute of Chemical Kinetics and Combustion, SB RAS, Institutskaya str. 3, 630090 Novosibirsk (Russian Federation); Novosibirsk State University, Pirogova 2, 630090 Novosibirsk (Russian Federation); Bi, Lei [Department of Atmospheric Sciences, Texas A& M University, College Station, TX 77843 (United States); Cairns, Brian [NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 (United States); Liu, Li [NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 (United States); Columbia University, 2880 Broadway, New York, NY 10025 (United States); Panetta, R. Lee [Department of Atmospheric Sciences, Texas A& M University, College Station, TX 77843 (United States); Travis, Larry D. [NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 (United States); Yang, Ping [Department of Atmospheric Sciences, Texas A& M University, College Station, TX 77843 (United States); Zakharova, Nadezhda T. [Trinnovim LLC, 2880 Broadway, New York, NY 10025 (United States)

2016-05-16

A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell’s equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell–Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell–Lorentz equations, we trace the development

First-Principles Modeling Of Electromagnetic Scattering By Discrete and Discretely Heterogeneous Random Media

Science.gov (United States)

Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.

2016-01-01

A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell's equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell- Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell-Lorentz equations, we trace the development of

Discrete Mathematics and Its Applications

Science.gov (United States)

Oxley, Alan

2010-01-01

The article gives ideas that lecturers of undergraduate Discrete Mathematics courses can use in order to make the subject more interesting for students and encourage them to undertake further studies in the subject. It is possible to teach Discrete Mathematics with little or no reference to computing. However, students are more likely to be…

Current density and continuity in discretized models

International Nuclear Information System (INIS)

Boykin, Timothy B; Luisier, Mathieu; Klimeck, Gerhard

2010-01-01

Discrete approaches have long been used in numerical modelling of physical systems in both research and teaching. Discrete versions of the Schroedinger equation employing either one or several basis functions per mesh point are often used by senior undergraduates and beginning graduate students in computational physics projects. In studying discrete models, students can encounter conceptual difficulties with the representation of the current and its divergence because different finite-difference expressions, all of which reduce to the current density in the continuous limit, measure different physical quantities. Understanding these different discrete currents is essential and requires a careful analysis of the current operator, the divergence of the current and the continuity equation. Here we develop point forms of the current and its divergence valid for an arbitrary mesh and basis. We show that in discrete models currents exist only along lines joining atomic sites (or mesh points). Using these results, we derive a discrete analogue of the divergence theorem and demonstrate probability conservation in a purely localized-basis approach.

Discrete Calculus as a Bridge between Scales

Science.gov (United States)

Degiuli, Eric; McElwaine, Jim

2012-02-01

Understanding how continuum descriptions of disordered media emerge from the microscopic scale is a fundamental challenge in condensed matter physics. In many systems, it is necessary to coarse-grain balance equations at the microscopic scale to obtain macroscopic equations. We report development of an exact, discrete calculus, which allows identification of discrete microscopic equations with their continuum equivalent [1]. This allows the application of powerful techniques of calculus, such as the Helmholtz decomposition, the Divergence Theorem, and Stokes' Theorem. We illustrate our results with granular materials. In particular, we show how Newton's laws for a single grain reproduce their continuum equivalent in the calculus. This allows introduction of a discrete Airy stress function, exactly as in the continuum. As an application of the formalism, we show how these results give the natural mean-field variation of discrete quantities, in agreement with numerical simulations. The discrete calculus thus acts as a bridge between discrete microscale quantities and continuous macroscale quantities. [4pt] [1] E. DeGiuli & J. McElwaine, PRE 2011. doi: 10.1103/PhysRevE.84.041310

Integrals of Motion for Discrete-Time Optimal Control Problems

OpenAIRE

Torres, Delfim F. M.

2003-01-01

We obtain a discrete time analog of E. Noether's theorem in Optimal Control, asserting that integrals of motion associated to the discrete time Pontryagin Maximum Principle can be computed from the quasi-invariance properties of the discrete time Lagrangian and discrete time control system. As corollaries, results for first-order and higher-order discrete problems of the calculus of variations are obtained.

Effective Hamiltonian for travelling discrete breathers

Science.gov (United States)

MacKay, Robert S.; Sepulchre, Jacques-Alexandre

2002-05-01

Hamiltonian chains of oscillators in general probably do not sustain exact travelling discrete breathers. However solutions which look like moving discrete breathers for some time are not difficult to observe in numerics. In this paper we propose an abstract framework for the description of approximate travelling discrete breathers in Hamiltonian chains of oscillators. The method is based on the construction of an effective Hamiltonian enabling one to describe the dynamics of the translation degree of freedom of moving breathers. Error estimate on the approximate dynamics is also studied. The concept of the Peierls-Nabarro barrier can be made clear in this framework. We illustrate the method with two simple examples, namely the Salerno model which interpolates between the Ablowitz-Ladik lattice and the discrete nonlinear Schrödinger system, and the Fermi-Pasta-Ulam chain.

A Method of Nuclear Software Reliability Estimation

International Nuclear Information System (INIS)

Park, Gee Yong; Eom, Heung Seop; Cheon, Se Woo; Jang, Seung Cheol

2011-01-01

A method on estimating software reliability for nuclear safety software is proposed. This method is based on the software reliability growth model (SRGM) where the behavior of software failure is assumed to follow the non-homogeneous Poisson process. Several modeling schemes are presented in order to estimate and predict more precisely the number of software defects based on a few of software failure data. The Bayesian statistical inference is employed to estimate the model parameters by incorporating the software test cases into the model. It is identified that this method is capable of accurately estimating the remaining number of software defects which are on-demand type directly affecting safety trip functions. The software reliability can be estimated from a model equation and one method of obtaining the software reliability is proposed

Solder joint technology materials, properties, and reliability

CERN Document Server

Tu, King-Ning

2007-01-01

Solder joints are ubiquitous in electronic consumer products. The European Union has a directive to ban the use of Pb-based solders in these products on July 1st, 2006. There is an urgent need for an increase in the research and development of Pb-free solders in electronic manufacturing. For example, spontaneous Sn whisker growth and electromigration induced failure in solder joints are serious issues. These reliability issues are quite complicated due to the combined effect of electrical, mechanical, chemical, and thermal forces on solder joints. To improve solder joint reliability, the science of solder joint behavior under various driving forces must be understood. In this book, the advanced materials reliability issues related to copper-tin reaction and electromigration in solder joints are emphasized and methods to prevent these reliability problems are discussed.

Mittag-Leffler function for discrete fractional modelling

Directory of Open Access Journals (Sweden)

Guo-Cheng Wu

2016-01-01

Full Text Available From the difference equations on discrete time scales, this paper numerically investigates one discrete fractional difference equation in the Caputo delta’s sense which has an explicit solution in form of the discrete Mittag-Leffler function. The exact numerical values of the solutions are given in comparison with the truncated Mittag-Leffler function.

Discrete/PWM Ballast-Resistor Controller

Science.gov (United States)

King, Roger J.

1994-01-01

Circuit offers low switching loss and automatic compensation for failure of ballast resistor. Discrete/PWM ballast-resistor controller improved shunt voltage-regulator circuit designed to supply power from high-resistance source to low-impedance bus. Provides both coarse discrete voltage levels (by switching of ballast resistors) and continuous fine control of voltage via pulse-width modulation.

Discretization of four types of Weyl group orbit functions

International Nuclear Information System (INIS)

Hrivnák, Jiří

2013-01-01

The discrete Fourier calculus of the four families of special functions, called C–, S–, S s – and S l -functions, is summarized. Functions from each of the four families of special functions are discretely orthogonal over a certain finite set of points. The generalizations of discrete cosine and sine transforms of one variable — the discrete S s – and S l -transforms of the group F 4 — are considered in detail required for their exploitation in discrete Fourier spectral methods. The continuous interpolations, induced by the discrete expansions, are presented

Discrete elements method of neutral particle transport

International Nuclear Information System (INIS)

Mathews, K.A.

1983-01-01

A new discrete elements (L/sub N/) transport method is derived and compared to the discrete ordinates S/sub N/ method, theoretically and by numerical experimentation. The discrete elements method is more accurate than discrete ordinates and strongly ameliorates ray effects for the practical problems studied. The discrete elements method is shown to be more cost effective, in terms of execution time with comparable storage to attain the same accuracy, for a one-dimensional test case using linear characteristic spatial quadrature. In a two-dimensional test case, a vacuum duct in a shield, L/sub N/ is more consistently convergent toward a Monte Carlo benchmark solution than S/sub N/, using step characteristic spatial quadrature. An analysis of the interaction of angular and spatial quadrature in xy-geometry indicates the desirability of using linear characteristic spatial quadrature with the L/sub N/ method

Spatially localized, temporally quasiperiodic, discrete nonlinear excitations

International Nuclear Information System (INIS)

Cai, D.; Bishop, A.R.; Gronbech-Jensen, N.

1995-01-01

In contrast to the commonly discussed discrete breather, which is a spatially localized, time-periodic solution, we present an exact solution of a discrete nonlinear Schroedinger breather which is a spatially localized, temporally quasiperiodic nonlinear coherent excitation. This breather is a multiple-soliton solution in the sense of the inverse scattering transform. A discrete breather of multiple frequencies is conceptually important in studies of nonlinear lattice systems. We point out that, for this breather, the incommensurability of its frequencies is a discrete lattice effect and these frequencies become commensurate in the continuum limit. To understand the dynamical properties of the breather, we also discuss its stability and its behavior in the presence of an external potential. Finally, we indicate how to obtain an exact N-soliton breather as a discrete generalization of the continuum multiple-soliton solution

Continuum and discrete approach in modeling biofilm development and structure: a review.

Science.gov (United States)

Mattei, M R; Frunzo, L; D'Acunto, B; Pechaud, Y; Pirozzi, F; Esposito, G

2018-03-01

The scientific community has recognized that almost 99% of the microbial life on earth is represented by biofilms. Considering the impacts of their sessile lifestyle on both natural and human activities, extensive experimental activity has been carried out to understand how biofilms grow and interact with the environment. Many mathematical models have also been developed to simulate and elucidate the main processes characterizing the biofilm growth. Two main mathematical approaches for biomass representation can be distinguished: continuum and discrete. This review is aimed at exploring the main characteristics of each approach. Continuum models can simulate the biofilm processes in a quantitative and deterministic way. However, they require a multidimensional formulation to take into account the biofilm spatial heterogeneity, which makes the models quite complicated, requiring significant computational effort. Discrete models are more recent and can represent the typical multidimensional structural heterogeneity of biofilm reflecting the experimental expectations, but they generate computational results including elements of randomness and introduce stochastic effects into the solutions.

On organizing principles of discrete differential geometry. Geometry of spheres

International Nuclear Information System (INIS)

Bobenko, Alexander I; Suris, Yury B

2007-01-01

Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. This survey contains a discussion of the following two fundamental discretization principles: the transformation group principle (smooth geometric objects and their discretizations are invariant with respect to the same transformation group) and the consistency principle (discretizations of smooth parametrized geometries can be extended to multidimensional consistent nets). The main concrete geometric problem treated here is discretization of curvature-line parametrized surfaces in Lie geometry. Systematic use of the discretization principles leads to a discretization of curvature-line parametrization which unifies circular and conical nets.

Effective lagrangian description on discrete gauge symmetries

International Nuclear Information System (INIS)

Banks, T.

1989-01-01

We exhibit a simple low-energy lagrangian which describes a system with a discrete remnant of a spontaneously broken continuous gauge symmetry. The lagrangian gives a simple description of the effects ascribed to such systems by Krauss and Wilczek: black holes carry discrete hair and interact with cosmic strings, and wormholes cannot lead to violation of discrete gauge symmetries. (orig.)

An integrable semi-discretization of the Boussinesq equation

Energy Technology Data Exchange (ETDEWEB)

Zhang, Yingnan, E-mail: ynzhang@njnu.edu.cn [Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu (China); Tian, Lixin, E-mail: tianlixin@njnu.edu.cn [Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu (China); Nonlinear Scientific Research Center, Jiangsu University, Zhenjiang, Jiangsu (China)

2016-10-23

Highlights: • A new integrable semi-discretization of the Boussinesq equation is present. • A Bäcklund transformation and a Lax pair for the differential-difference system is derived by using Hirota's bilinear method. • The soliton solutions of 'good' Boussinesq equation and numerical algorithms are investigated. - Abstract: In this paper, we present an integrable semi-discretization of the Boussinesq equation. Different from other discrete analogues, we discretize the ‘time’ variable and get an integrable differential-difference system. Under a standard limitation, the differential-difference system converges to the continuous Boussinesq equation such that the discrete system can be used to design numerical algorithms. Using Hirota's bilinear method, we find a Bäcklund transformation and a Lax pair of the differential-difference system. For the case of ‘good’ Boussinesq equation, we investigate the soliton solutions of its discrete analogue and design numerical algorithms. We find an effective way to reduce the phase shift caused by the discretization. The numerical results coincide with our analysis.

A 2+1 non-isospectral discrete integrable system and its discrete integrable coupling system

International Nuclear Information System (INIS)

Yu Fajun; Zhang Hongqing

2006-01-01

In this Letter by considering a (2+1)-dimensional discrete non-isospectral linear problem, a new (2+1)-dimensional integrable lattice hierarchy is constructed. It shows that generalization of the Blaszak-Marciniak lattice hierarchy can be obtained as a reduction. Then an extended algebraic system X-bar of X is presented, from which the integrable coupling system of the (2+1)-dimensional discrete non-isospectral Blaszak-Marciniak lattice equations are obtained

Hairs of discrete symmetries and gravity

Energy Technology Data Exchange (ETDEWEB)

Choi, Kang Sin [Scranton Honors Program, Ewha Womans University, Seodaemun-Gu, Seoul 03760 (Korea, Republic of); Center for Fields, Gravity and Strings, CTPU, Institute for Basic Sciences, Yuseong-Gu, Daejeon 34047 (Korea, Republic of); Kim, Jihn E., E-mail: jihnekim@gmail.com [Department of Physics, Kyung Hee University, 26 Gyungheedaero, Dongdaemun-Gu, Seoul 02447 (Korea, Republic of); Center for Axion and Precision Physics Research (IBS), 291 Daehakro, Yuseong-Gu, Daejeon 34141 (Korea, Republic of); Kyae, Bumseok [Department of Physics, Pusan National University, 2 Busandaehakro-63-Gil, Geumjeong-Gu, Busan 46241 (Korea, Republic of); Nam, Soonkeon [Department of Physics, Kyung Hee University, 26 Gyungheedaero, Dongdaemun-Gu, Seoul 02447 (Korea, Republic of)

2017-06-10

Gauge symmetries are known to be respected by gravity because gauge charges carry flux lines, but global charges do not carry flux lines and are not conserved by gravitational interaction. For discrete symmetries, they are spontaneously broken in the Universe, forming domain walls. Since the realization of discrete symmetries in the Universe must involve the vacuum expectation values of Higgs fields, a string-like configuration (hair) at the intersection of domain walls in the Higgs vacua can be realized. Therefore, we argue that discrete charges are also respected by gravity.

Hairs of discrete symmetries and gravity

Directory of Open Access Journals (Sweden)

Kang Sin Choi

2017-06-01

Full Text Available Gauge symmetries are known to be respected by gravity because gauge charges carry flux lines, but global charges do not carry flux lines and are not conserved by gravitational interaction. For discrete symmetries, they are spontaneously broken in the Universe, forming domain walls. Since the realization of discrete symmetries in the Universe must involve the vacuum expectation values of Higgs fields, a string-like configuration (hair at the intersection of domain walls in the Higgs vacua can be realized. Therefore, we argue that discrete charges are also respected by gravity.

Solving discretely-constrained MPEC problems with applications in electric power markets

International Nuclear Information System (INIS)

Gabriel, Steven A.; Leuthold, Florian U.

2010-01-01

Many of the European energy markets are characterized by dominant players that own a large share of their respective countries' generation capacities. In addition to that, there is a significant lack of cross-border transmission capacity. Combining both facts justifies the assumption that these dominant players are able to influence the market outcome of an internal European energy market due to strategic behavior. In this paper, we present a mathematical formulation in order to solve a Stackelberg game for a network-constrained energy market using integer programming. The strategic player is the Stackelberg leader and the independent system operator (including the decisions of the competitive fringe firms) acts as follower. We assume that there is one strategic player which results in a mathematical program with equilibrium constraints (MPEC). This MPEC is reformulated as mixed-integer linear program (MILP) by using disjunctive constraints and linearization. The MILP formulation gives the opportunity to solve the problems reliably and paves the way to add discrete constraints to the original MPEC formulation which can be used in order to solve discretely-constrained mathematical programs with equilibrium constraints (DC-MPECs). We report computational results for a small illustrative network as well as a stylized Western European grid with realistic data. (author)

Solving discretely-constrained MPEC problems with applications in electric power markets

Energy Technology Data Exchange (ETDEWEB)

Gabriel, Steven A. [1143 Glenn L. Martin Hall, Department of Civil and Environmental Engineering, University of Maryland, College Park, MD 20742-3021 (United States); Leuthold, Florian U. [Chair of Energy Economics and Public Sector Management, Dresden University of Technology, 01069 Dresden (Germany)

2010-01-15

Many of the European energy markets are characterized by dominant players that own a large share of their respective countries' generation capacities. In addition to that, there is a significant lack of cross-border transmission capacity. Combining both facts justifies the assumption that these dominant players are able to influence the market outcome of an internal European energy market due to strategic behavior. In this paper, we present a mathematical formulation in order to solve a Stackelberg game for a network-constrained energy market using integer programming. The strategic player is the Stackelberg leader and the independent system operator (including the decisions of the competitive fringe firms) acts as follower. We assume that there is one strategic player which results in a mathematical program with equilibrium constraints (MPEC). This MPEC is reformulated as mixed-integer linear program (MILP) by using disjunctive constraints and linearization. The MILP formulation gives the opportunity to solve the problems reliably and paves the way to add discrete constraints to the original MPEC formulation which can be used in order to solve discretely-constrained mathematical programs with equilibrium constraints (DC-MPECs). We report computational results for a small illustrative network as well as a stylized Western European grid with realistic data. (author)

Numerical modeling of the dynamic behavior of structures under impact with a discrete elements / finite elements coupling

International Nuclear Information System (INIS)

Rousseau, J.

2009-07-01

That study focuses on concrete structures submitted to impact loading and is aimed at predicting local damage in the vicinity of an impact zone as well as the global response of the structure. The Discrete Element Method (DEM) seems particularly well suited in this context for modeling fractures. An identification process of DEM material parameters from macroscopic data (Young's modulus, compressive and tensile strength, fracture energy, etc.) will first be presented for the purpose of enhancing reproducibility and reliability of the simulation results with DE samples of various sizes. Then, a particular interaction, between concrete and steel elements, was developed for the simulation of reinforced concrete. The discrete elements method was validated on quasi-static and dynamic tests carried out on small samples of concrete and reinforced concrete. Finally, discrete elements were used to simulate impacts on reinforced concrete slabs in order to confront the results with experimental tests. The modeling of a large structure by means of DEM may lead to prohibitive computation times. A refined discretization becomes required in the vicinity of the impact, while the structure may be modeled using a coarse FE mesh further from the impact area, where the material behaves elastically. A coupled discrete-finite element approach is thus proposed: the impact zone is modeled by means of DE and elastic FE are used on the rest of the structure. An existing method for 3D finite elements was extended to shells. This new method was then validated on many quasi-static and dynamic tests. The proposed approach is then applied to an impact on a concrete structure in order to validate the coupled method and compare computation times. (author)

Integrable lattices and their sublattices: From the discrete Moutard (discrete Cauchy-Riemann) 4-point equation to the self-adjoint 5-point scheme

International Nuclear Information System (INIS)

Doliwa, A.; Grinevich, P.; Nieszporski, M.; Santini, P. M.

2007-01-01

We present the sublattice approach, a procedure to generate, from a given integrable lattice, a sublattice which inherits its integrability features. We consider, as illustrative example of this approach, the discrete Moutard 4-point equation and its sublattice, the self-adjoint 5-point scheme on the star of the square lattice, which are relevant in the theory of the integrable discrete geometries and in the theory of discrete holomorphic and harmonic functions (in this last context, the discrete Moutard equation is called discrete Cauchy-Riemann equation). Therefore an integrable, at one energy, discretization of elliptic two-dimensional operators is considered. We use the sublattice point of view to derive, from the Darboux transformations and superposition formulas of the discrete Moutard equation, the Darboux transformations and superposition formulas of the self-adjoint 5-point scheme. We also construct, from algebro-geometric solutions of the discrete Moutard equation, algebro-geometric solutions of the self-adjoint 5-point scheme. In particular, we show that the corresponding restrictions on the finite-gap data are of the same type as those for the fixed energy problem for the two-dimensional Schroedinger operator. We finally use these solutions to construct explicit examples of discrete holomorphic and harmonic functions, as well as examples of quadrilateral surfaces in R 3

A practical discrete-adjoint method for high-fidelity compressible turbulence simulations

International Nuclear Information System (INIS)

Vishnampet, Ramanathan; Bodony, Daniel J.; Freund, Jonathan B.

2015-01-01

its accuracy is limited by computing precision, and we demonstrate it on the aeroacoustic control of a mixing layer with a challengingly broad range of turbulence scales. For comparison, the error from a corresponding discretization of the continuous-adjoint equations is quantified to potentially explain its limited success in past efforts to control jet noise. The differences are illuminating: the continuous-adjoint is shown to suffer from exponential error growth in (reverse) time even for the best-resolved largest turbulence scales. Implications for jet noise reduction and turbulence control in general are discussed

Discrete tomography in neutron radiography

International Nuclear Information System (INIS)

Kuba, Attila; Rodek, Lajos; Kiss, Zoltan; Rusko, Laszlo; Nagy, Antal; Balasko, Marton

2005-01-01

Discrete tomography (DT) is an imaging technique for reconstructing discrete images from their projections using the knowledge that the object to be reconstructed contains only a few homogeneous materials characterized by known discrete absorption values. One of the main reasons for applying DT is that we will hopefully require relatively few projections. Using discreteness and some a priori information (such as an approximate shape of the object) we can apply two DT methods in neutron imaging by reducing the problem to an optimization task. The first method is a special one because it is only suitable if the object is composed of cylinders and sphere shapes. The second method is a general one in the sense that it can be used for reconstructing objects of any shape. Software was developed and physical experiments performed in order to investigate the effects of several reconstruction parameters: the number of projections, noise levels, and complexity of the object to be reconstructed. We give a summary of the experimental results and make a comparison of the results obtained using a classical reconstruction technique (FBP). The programs we developed are available in our DT reconstruction program package DIRECT

How Triage Nurses Use Discretion: a Literature Review

Directory of Open Access Journals (Sweden)

Lars Emil Fagernes Johannessen

2016-02-01

Full Text Available Discretion is quintessential for professional work. This review aims to understand how nurses use discretion when they perform urgency assessments in emergency departments with formalised triage systems—systems that are intended to reduce nurses’ use of discretion. Because little research has dealt explicitly with this topic, this review addresses the discretionary aspects of triage by reinterpreting qualitative studies of how triage nurses perform urgency assessments. The review shows (a how inexhaustive guidelines and a hectic work environment are factors that necessitate nurses’ use of discretion and (b how nurses reason within this discretionary space by relying on their experience and intuition, judging patients according to criteria such as appropriateness and believability, and creating urgency ratings together with their patients. The review also offers a synthesis of the findings’ discretionary aspects and suggests a new interactionist dimension of discretion.Keywords: Triage, discretion, emergency department, meta-ethnography, review, decision-making

Application of an efficient Bayesian discretization method to biomedical data

Directory of Open Access Journals (Sweden)

Gopalakrishnan Vanathi

2011-07-01

Full Text Available Abstract Background Several data mining methods require data that are discrete, and other methods often perform better with discrete data. We introduce an efficient Bayesian discretization (EBD method for optimal discretization of variables that runs efficiently on high-dimensional biomedical datasets. The EBD method consists of two components, namely, a Bayesian score to evaluate discretizations and a dynamic programming search procedure to efficiently search the space of possible discretizations. We compared the performance of EBD to Fayyad and Irani's (FI discretization method, which is commonly used for discretization. Results On 24 biomedical datasets obtained from high-throughput transcriptomic and proteomic studies, the classification performances of the C4.5 classifier and the naïve Bayes classifier were statistically significantly better when the predictor variables were discretized using EBD over FI. EBD was statistically significantly more stable to the variability of the datasets than FI. However, EBD was less robust, though not statistically significantly so, than FI and produced slightly more complex discretizations than FI. Conclusions On a range of biomedical datasets, a Bayesian discretization method (EBD yielded better classification performance and stability but was less robust than the widely used FI discretization method. The EBD discretization method is easy to implement, permits the incorporation of prior knowledge and belief, and is sufficiently fast for application to high-dimensional data.

Reliability of cervical vertebral maturation staging.

Science.gov (United States)

Rainey, Billie-Jean; Burnside, Girvan; Harrison, Jayne E

2016-07-01

Growth and its prediction are important for the success of many orthodontic treatments. The aim of this study was to determine the reliability of the cervical vertebral maturation (CVM) method for the assessment of mandibular growth. A group of 20 orthodontic clinicians, inexperienced in CVM staging, was trained to use the improved version of the CVM method for the assessment of mandibular growth with a teaching program. They independently assessed 72 consecutive lateral cephalograms, taken at Liverpool University Dental Hospital, on 2 occasions. The cephalograms were presented in 2 different random orders and interspersed with 11 additional images for standardization. The intraobserver and interobserver agreement values were evaluated using the weighted kappa statistic. The intraobserver and interobserver agreement values were substantial (weighted kappa, 0.6-0.8). The overall intraobserver agreement was 0.70 (SE, 0.01), with average agreement of 89%. The interobserver agreement values were 0.68 (SE, 0.03) for phase 1 and 0.66 (SE, 0.03) for phase 2, with average interobserver agreement of 88%. The intraobserver and interobserver agreement values of classifying the vertebral stages with the CVM method were substantial. These findings demonstrate that this method of CVM classification is reproducible and reliable. Copyright © 2016 American Association of Orthodontists. Published by Elsevier Inc. All rights reserved.

Discrete Riccati equation solutions: Distributed algorithms

Directory of Open Access Journals (Sweden)

D. G. Lainiotis

1996-01-01

Full Text Available In this paper new distributed algorithms for the solution of the discrete Riccati equation are introduced. The algorithms are used to provide robust and computational efficient solutions to the discrete Riccati equation. The proposed distributed algorithms are theoretically interesting and computationally attractive.

Discrete Fourier analysis of multigrid algorithms

NARCIS (Netherlands)

van der Vegt, Jacobus J.W.; Rhebergen, Sander

2011-01-01

The main topic of this report is a detailed discussion of the discrete Fourier multilevel analysis of multigrid algorithms. First, a brief overview of multigrid methods is given for discretizations of both linear and nonlinear partial differential equations. Special attention is given to the

Time Discretization Techniques

KAUST Repository

Gottlieb, S.

2016-10-12

The time discretization of hyperbolic partial differential equations is typically the evolution of a system of ordinary differential equations obtained by spatial discretization of the original problem. Methods for this time evolution include multistep, multistage, or multiderivative methods, as well as a combination of these approaches. The time step constraint is mainly a result of the absolute stability requirement, as well as additional conditions that mimic physical properties of the solution, such as positivity or total variation stability. These conditions may be required for stability when the solution develops shocks or sharp gradients. This chapter contains a review of some of the methods historically used for the evolution of hyperbolic PDEs, as well as cutting edge methods that are now commonly used.

Ensemble simulations with discrete classical dynamics

DEFF Research Database (Denmark)

Toxværd, Søren

2013-01-01

For discrete classical Molecular dynamics (MD) obtained by the "Verlet" algorithm (VA) with the time increment $h$ there exist a shadow Hamiltonian $\\tilde{H}$ with energy $\\tilde{E}(h)$, for which the discrete particle positions lie on the analytic trajectories for $\\tilde{H}$. $\\tilde......{E}(h)$ is employed to determine the relation with the corresponding energy, $E$ for the analytic dynamics with $h=0$ and the zero-order estimate $E_0(h)$ of the energy for discrete dynamics, appearing in the literature for MD with VA. We derive a corresponding time reversible VA algorithm for canonical dynamics...

Discrete symmetries and de Sitter spacetime

Energy Technology Data Exchange (ETDEWEB)

Cotăescu, Ion I., E-mail: gpascu@physics.uvt.ro; Pascu, Gabriel, E-mail: gpascu@physics.uvt.ro [West University of Timişoara, V. Pârvan Ave. 4, RO-300223 Timişoara (Romania)

2014-11-24

Aspects of the ambiguity in defining quantum modes on de Sitter spacetime using a commuting system composed only of differential operators are discussed. Discrete symmetries and their actions on the wavefunction in commonly used coordinate charts are reviewed. It is argued that the system of commuting operators can be supplemented by requiring the invariance of the wavefunction to combined discrete symmetries- a criterion which selects a single state out of the α-vacuum family. Two such members of this family are singled out by particular combined discrete symmetries- states between which exists a well-known thermality relation.

Discrete convolution-operators and radioactive disintegration. [Numerical solution

Energy Technology Data Exchange (ETDEWEB)

Kalla, S L; VALENTINUZZI, M E [UNIVERSIDAD NACIONAL DE TUCUMAN (ARGENTINA). FACULTAD DE CIENCIAS EXACTAS Y TECNOLOGIA

1975-08-01

The basic concepts of discrete convolution and discrete convolution-operators are briefly described. Then, using the discrete convolution - operators, the differential equations associated with the process of radioactive disintegration are numerically solved. The importance of the method is emphasized to solve numerically, differential and integral equations.

Periodic, quasiperiodic and chaotic discrete breathers in a parametrical driven two-dimensional discrete diatomic Klein–Gordon lattice

International Nuclear Information System (INIS)

Quan, Xu; Qiang, Tian

2009-01-01

We study a two-dimensional (2D) diatomic lattice of anharmonic oscillators with only quartic nearest-neighbor interactions, in which discrete breathers (DBs) can be explicitly constructed by an exact separation of their time and space dependence. DBs can stably exist in the 2D discrete diatomic Klein–Gordon lattice with hard and soft on-site potentials. When a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system, we can obtain the stable quasiperiodic discrete breathers (QDBs) and chaotic discrete breathers (CDBs) by changing the amplitude of the driver. But the DBs and QDBs with symmetric and anti-symmetric profiles that are centered at a heavy atom are more stable than at a light atom, because the frequencies of the DBs and QDBs centered at a heavy atom are lower than those centered at a light atom

Discrete-Time Nonlinear Control of VSC-HVDC System

Directory of Open Access Journals (Sweden)

TianTian Qian

2015-01-01

Full Text Available Because VSC-HVDC is a kind of strong nonlinear, coupling, and multi-input multioutput (MIMO system, its control problem is always attracting much attention from scholars. And a lot of papers have done research on its control strategy in the continuous-time domain. But the control system is implemented through the computer discrete sampling in practical engineering. It is necessary to study the mathematical model and control algorithm in the discrete-time domain. The discrete mathematical model based on output feedback linearization and discrete sliding mode control algorithm is proposed in this paper. And to ensure the effectiveness of the control system in the quasi sliding mode state, the fast output sampling method is used in the output feedback. The results from simulation experiment in MATLAB/SIMULINK prove that the proposed discrete control algorithm can make the VSC-HVDC system have good static, dynamic, and robust characteristics in discrete-time domain.

Discrete modeling considerations in multiphase fluid dynamics

International Nuclear Information System (INIS)

Ransom, V.H.; Ramshaw, J.D.

1988-01-01

The modeling of multiphase flows play a fundamental role in light water reactor safety. The main ingredients in our discrete modeling Weltanschauung are the following considerations: (1) Any physical model must be cast into discrete form for a digital computer. (2) The usual approach of formulating models in differential form and then discretizing them is potentially hazardous. It may be preferable to formulate the model in discrete terms from the outset. (3) Computer time and storage constraints limit the resolution that can be employed in practical calculations. These limits effectively define the physical phenomena, length scales, and time scales which cannot be directly represented in the calculation and therefore must be modeled. This information should be injected into the model formulation process at an early stage. (4) Practical resolution limits are generally so coarse that traditional convergence and truncation-error analyses become irrelevant. (5) A discrete model constitutes a reduced description of a physical system, from which fine-scale details are eliminated. This elimination creates a statistical closure problem. Methods from statistical physics may therefore be useful in the formulation of discrete models. In the present paper we elaborate on these themes and illustrate them with simple examples. 48 refs

Field Programmable Gate Array Reliability Analysis Guidelines for Launch Vehicle Reliability Block Diagrams

Science.gov (United States)

Al Hassan, Mohammad; Britton, Paul; Hatfield, Glen Spencer; Novack, Steven D.

2017-01-01

Field Programmable Gate Arrays (FPGAs) integrated circuits (IC) are one of the key electronic components in today's sophisticated launch and space vehicle complex avionic systems, largely due to their superb reprogrammable and reconfigurable capabilities combined with relatively low non-recurring engineering costs (NRE) and short design cycle. Consequently, FPGAs are prevalent ICs in communication protocols and control signal commands. This paper will identify reliability concerns and high level guidelines to estimate FPGA total failure rates in a launch vehicle application. The paper will discuss hardware, hardware description language, and radiation induced failures. The hardware contribution of the approach accounts for physical failures of the IC. The hardware description language portion will discuss the high level FPGA programming languages and software/code reliability growth. The radiation portion will discuss FPGA susceptibility to space environment radiation.

Forest Growth and Yield Models Viewed From a Different Perspective

Science.gov (United States)

Jeffery C. Goelz

2002-01-01

Typically, when different forms of growth and yield models are considered, they are grouped into convenient discrete classes. As a heuristic device, I chose to use a contrasting perspective, that all growth and yield models are diameter distribution models that merely differ in regard to which diameter distribution is employed and how the distribution is projected to...

Launch and Assembly Reliability Analysis for Human Space Exploration Missions

Science.gov (United States)

Cates, Grant; Gelito, Justin; Stromgren, Chel; Cirillo, William; Goodliff, Kandyce

2012-01-01

NASA's future human space exploration strategy includes single and multi-launch missions to various destinations including cis-lunar space, near Earth objects such as asteroids, and ultimately Mars. Each campaign is being defined by Design Reference Missions (DRMs). Many of these missions are complex, requiring multiple launches and assembly of vehicles in orbit. Certain missions also have constrained departure windows to the destination. These factors raise concerns regarding the reliability of launching and assembling all required elements in time to support planned departure. This paper describes an integrated methodology for analyzing launch and assembly reliability in any single DRM or set of DRMs starting with flight hardware manufacturing and ending with final departure to the destination. A discrete event simulation is built for each DRM that includes the pertinent risk factors including, but not limited to: manufacturing completion; ground transportation; ground processing; launch countdown; ascent; rendezvous and docking, assembly, and orbital operations leading up to trans-destination-injection. Each reliability factor can be selectively activated or deactivated so that the most critical risk factors can be identified. This enables NASA to prioritize mitigation actions so as to improve mission success.

A discrete control model of PLANT

Science.gov (United States)

Mitchell, C. M.

1985-01-01

A model of the PLANT system using the discrete control modeling techniques developed by Miller is described. Discrete control models attempt to represent in a mathematical form how a human operator might decompose a complex system into simpler parts and how the control actions and system configuration are coordinated so that acceptable overall system performance is achieved. Basic questions include knowledge representation, information flow, and decision making in complex systems. The structure of the model is a general hierarchical/heterarchical scheme which structurally accounts for coordination and dynamic focus of attention. Mathematically, the discrete control model is defined in terms of a network of finite state systems. Specifically, the discrete control model accounts for how specific control actions are selected from information about the controlled system, the environment, and the context of the situation. The objective is to provide a plausible and empirically testable accounting and, if possible, explanation of control behavior.

Identification of parameters of discrete-continuous models

International Nuclear Information System (INIS)

Cekus, Dawid; Warys, Pawel

2015-01-01

In the paper, the parameters of a discrete-continuous model have been identified on the basis of experimental investigations and formulation of optimization problem. The discrete-continuous model represents a cantilever stepped Timoshenko beam. The mathematical model has been formulated and solved according to the Lagrange multiplier formalism. Optimization has been based on the genetic algorithm. The presented proceeding’s stages make the identification of any parameters of discrete-continuous systems possible

Identification of parameters of discrete-continuous models

Energy Technology Data Exchange (ETDEWEB)

Cekus, Dawid, E-mail: cekus@imipkm.pcz.pl; Warys, Pawel, E-mail: warys@imipkm.pcz.pl [Institute of Mechanics and Machine Design Foundations, Czestochowa University of Technology, Dabrowskiego 73, 42-201 Czestochowa (Poland)

2015-03-10

In the paper, the parameters of a discrete-continuous model have been identified on the basis of experimental investigations and formulation of optimization problem. The discrete-continuous model represents a cantilever stepped Timoshenko beam. The mathematical model has been formulated and solved according to the Lagrange multiplier formalism. Optimization has been based on the genetic algorithm. The presented proceeding’s stages make the identification of any parameters of discrete-continuous systems possible.

Discrete Mathematics in the Schools. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Volume 36.

Science.gov (United States)

Rosenstein, Joseph G., Ed.; Franzblau, Deborah S., Ed.; Roberts, Fred S., Ed.

This book is a collection of articles by experienced educators and explains why and how discrete mathematics should be taught in K-12 classrooms. It includes evidence for "why" and practical guidance for "how" and also discusses how discrete mathematics can be used as a vehicle for achieving the broader goals of the major…

Symmetries in discrete-time mechanics

International Nuclear Information System (INIS)

Khorrami, M.

1996-01-01

Based on a general formulation for discrete-time quantum mechanics, introduced by M. Khorrami (Annals Phys. 224 (1995), 101), symmetries in discrete-time quantum mechanics are investigated. It is shown that any classical continuous symmetry leads to a conserved quantity in classical mechanics, as well as quantum mechanics. The transformed wave function, however, has the correct evolution if and only if the symmetry is nonanomalous. Copyright copyright 1996 Academic Press, Inc

Finite-dimensional reductions of the discrete Toda chain

International Nuclear Information System (INIS)

Kazakova, T G

2004-01-01

The problem of construction of integrable boundary conditions for the discrete Toda chain is considered. The restricted chains for properly chosen closure conditions are reduced to the well-known discrete Painleve equations dP III , dP V , dP VI . Lax representations for these discrete Painleve equations are found

Convergence of posteriors for discretized log Gaussian Cox processes

DEFF Research Database (Denmark)

Waagepetersen, Rasmus Plenge

2004-01-01

In Markov chain Monte Carlo posterior computation for log Gaussian Cox processes (LGCPs) a discretization of the continuously indexed Gaussian field is required. It is demonstrated that approximate posterior expectations computed from discretized LGCPs converge to the exact posterior expectations...... when the cell sizes of the discretization tends to zero. The effect of discretization is studied in a data example....

Numerical Simulation of Antennae by Discrete Exterior Calculus

International Nuclear Information System (INIS)

Xie Zheng; Ye Zheng; Ma Yujie

2009-01-01

Numerical simulation of antennae is a topic in computational electromagnetism, which is concerned with the numerical study of Maxwell equations. By discrete exterior calculus and the lattice gauge theory with coefficient R, we obtain the Bianchi identity on prism lattice. By defining an inner product of discrete differential forms, we derive the source equation and continuity equation. Those equations compose the discrete Maxwell equations in vacuum case on discrete manifold, which are implemented on Java development platform to simulate the Gaussian pulse radiation on antennaes. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

Characterizing reliability in a product/process design-assurance program

Energy Technology Data Exchange (ETDEWEB)

Kerscher, W.J. III [Delphi Energy and Engine Management Systems, Flint, MI (United States); Booker, J.M.; Bement, T.R.; Meyer, M.A. [Los Alamos National Lab., NM (United States)

1997-10-01

Over the years many advancing techniques in the area of reliability engineering have surfaced in the military sphere of influence, and one of these techniques is Reliability Growth Testing (RGT). Private industry has reviewed RGT as part of the solution to their reliability concerns, but many practical considerations have slowed its implementation. It`s objective is to demonstrate the reliability requirement of a new product with a specified confidence. This paper speaks directly to that objective but discusses a somewhat different approach to achieving it. Rather than conducting testing as a continuum and developing statistical confidence bands around the results, this Bayesian updating approach starts with a reliability estimate characterized by large uncertainty and then proceeds to reduce the uncertainty by folding in fresh information in a Bayesian framework.

Estimating reliability of degraded system based on the probability density evolution with multi-parameter

Directory of Open Access Journals (Sweden)

Jiang Ge

2017-01-01

Full Text Available System degradation was usually caused by multiple-parameter degradation. The assessment result of system reliability by universal generating function was low accurate when compared with the Monte Carlo simulation. And the probability density function of the system output performance cannot be got. So the reliability assessment method based on the probability density evolution with multi-parameter was presented for complexly degraded system. Firstly, the system output function was founded according to the transitive relation between component parameters and the system output performance. Then, the probability density evolution equation based on the probability conservation principle and the system output function was established. Furthermore, probability distribution characteristics of the system output performance was obtained by solving differential equation. Finally, the reliability of the degraded system was estimated. This method did not need to discrete the performance parameters and can establish continuous probability density function of the system output performance with high calculation efficiency and low cost. Numerical example shows that this method is applicable to evaluate the reliability of multi-parameter degraded system.

A Variational Approach to Perturbed Discrete Anisotropic Equations

Directory of Open Access Journals (Sweden)

Amjad Salari

2016-01-01

Full Text Available We continue the study of discrete anisotropic equations and we will provide new multiplicity results of the solutions for a discrete anisotropic equation. We investigate the existence of infinitely many solutions for a perturbed discrete anisotropic boundary value problem. The approach is based on variational methods and critical point theory.

Variance Swap Replication: Discrete or Continuous?

Directory of Open Access Journals (Sweden)

Fabien Le Floc’h

2018-02-01

Full Text Available The popular replication formula to price variance swaps assumes continuity of traded option strikes. In practice, however, there is only a discrete set of option strikes traded on the market. We present here different discrete replication strategies and explain why the continuous replication price is more relevant.

NASA Applications and Lessons Learned in Reliability Engineering

Science.gov (United States)

Safie, Fayssal M.; Fuller, Raymond P.

2011-01-01

Since the Shuttle Challenger accident in 1986, communities across NASA have been developing and extensively using quantitative reliability and risk assessment methods in their decision making process. This paper discusses several reliability engineering applications that NASA has used over the year to support the design, development, and operation of critical space flight hardware. Specifically, the paper discusses several reliability engineering applications used by NASA in areas such as risk management, inspection policies, components upgrades, reliability growth, integrated failure analysis, and physics based probabilistic engineering analysis. In each of these areas, the paper provides a brief discussion of a case study to demonstrate the value added and the criticality of reliability engineering in supporting NASA project and program decisions to fly safely. Examples of these case studies discussed are reliability based life limit extension of Shuttle Space Main Engine (SSME) hardware, Reliability based inspection policies for Auxiliary Power Unit (APU) turbine disc, probabilistic structural engineering analysis for reliability prediction of the SSME alternate turbo-pump development, impact of ET foam reliability on the Space Shuttle System risk, and reliability based Space Shuttle upgrade for safety. Special attention is given in this paper to the physics based probabilistic engineering analysis applications and their critical role in evaluating the reliability of NASA development hardware including their potential use in a research and technology development environment.

Perfect discretization of path integrals

OpenAIRE

Steinhaus, Sebastian

2011-01-01

In order to obtain a well-defined path integral one often employs discretizations. In the case of General Relativity these generically break diffeomorphism symmetry, which has severe consequences since these symmetries determine the dynamics of the corresponding system. In this article we consider the path integral of reparametrization invariant systems as a toy example and present an improvement procedure for the discretized propagator. Fixed points and convergence of the procedure are discu...

A reliability-based approach of fastest routes planning in dynamic traffic network under emergency management situation

Directory of Open Access Journals (Sweden)

Ye Sun

2011-12-01

Full Text Available In order to establish an available emergency management system, it is important to conduct effective evacuation with reliable and real time optimal route plans. This paper aims at creating a route finding strategy by considering the time dependent factors as well as uncertainties that may be encountered during the emergency management system. To combine dynamic features with the level of reliability in the process of fastest route planning, the speed distribution of typical intercity roads is studied in depth, and the strategy of modifying real time speed to a more reliable value based on speed distribution is proposed. Two algorithms of route planning have been developed to find three optimal routes with the shortest travel time and the reliability of 0.9. In order to validate the new strategy, experimental implementation of the route planning method is conducted based on road speed information acquired by field study. The results show that the proposed strategy might provide more reliable routes in dynamic traffic networks by conservatively treating roads with large speed discretion or with relative extreme real speed value.

Lax Pairs for Discrete Integrable Equations via Darboux Transformations

International Nuclear Information System (INIS)

Cao Ce-Wen; Zhang Guang-Yao

2012-01-01

A method is developed to construct discrete Lax pairs using Darboux transformations. More kinds of Lax pairs are found for some newly appeared discrete integrable equations, including the H1, the special H3 and the Q1 models in the Adler—Bobenko—Suris list and the closely related discrete and semi-discrete pKdV, pMKdV, SG and Liouville equations. (general)

Graph-cut based discrete-valued image reconstruction.

Science.gov (United States)

Tuysuzoglu, Ahmet; Karl, W Clem; Stojanovic, Ivana; Castañòn, David; Ünlü, M Selim

2015-05-01

Efficient graph-cut methods have been used with great success for labeling and denoising problems occurring in computer vision. Unfortunately, the presence of linear image mappings has prevented the use of these techniques in most discrete-amplitude image reconstruction problems. In this paper, we develop a graph-cut based framework for the direct solution of discrete amplitude linear image reconstruction problems cast as regularized energy function minimizations. We first analyze the structure of discrete linear inverse problem cost functions to show that the obstacle to the application of graph-cut methods to their solution is the variable mixing caused by the presence of the linear sensing operator. We then propose to use a surrogate energy functional that overcomes the challenges imposed by the sensing operator yet can be utilized efficiently in existing graph-cut frameworks. We use this surrogate energy functional to devise a monotonic iterative algorithm for the solution of discrete valued inverse problems. We first provide experiments using local convolutional operators and show the robustness of the proposed technique to noise and stability to changes in regularization parameter. Then we focus on nonlocal, tomographic examples where we consider limited-angle data problems. We compare our technique with state-of-the-art discrete and continuous image reconstruction techniques. Experiments show that the proposed method outperforms state-of-the-art techniques in challenging scenarios involving discrete valued unknowns.

The reliability of routine anthropometric data collected by health workers: a cross-sectional study.

Science.gov (United States)

Johnson, William; Cameron, Noël; Dickson, Peter; Emsley, Stuart; Raynor, Pauline; Seymour, Claire; Wright, John

2009-03-01

Reliable data on child growth is a prerequisite for monitoring and improving child health. Despite the extensive resources invested in recording anthropometry, there has been little research into the reliability of these data. If these measurements are unreliable growth may be misreported, and health problems may go undetected. To assess the reliability of routine infant growth data, following anthropometric training of health workers responsible for collecting these data, in Bradford, UK. To determine whether being observed by an external administrator influenced reliability. A test-retest design was used. All health workers (n=192) responsible for growth monitoring in Bradford were included in the study, of which 36.5% (n=70) had complete data. Following training in basic anthropometry all health workers were asked to complete a test-retest study, using infants aged 0-2 years. Health workers took two recordings of weight, length, head circumference, and abdominal circumferences on five infants. A peer health worker recorded a third set of measurements on each infant. Twenty-two individuals were selected to be observed by an external administrator during data collection. Technical error of measurements (TEMs) were produced to assess intra-observer and inter-observer reliability. Differences between groups were tested to determine whether external observation influences reliability. None of the TEMs were excessively large, and coefficients of reliability ranged from 0.96 to 1.00. All intra-observer and inter-observer TEMs for the observed group were larger than those for the non-observed group. For example, the observed group's intra-observer TEMs for weight, length, abdominal circumference, and head circumference (46.18 g, 0.60 cm, 0.65 cm, 0.47 cm) were larger than the non-observed group's TEMS (9.14 g, 0.35 cm, 0.34 cm, 0.19 cm). TEMs for weight, abdominal circumference, and head circumference were significantly larger for the observed group, compared to the non

Discrete Chebyshev nets and a universal permutability theorem

International Nuclear Information System (INIS)

Schief, W K

2007-01-01

The Pohlmeyer-Lund-Regge system which was set down independently in the contexts of Lagrangian field theories and the relativistic motion of a string and which played a key role in the development of a geometric interpretation of soliton theory is known to appear in a variety of important guises such as the vectorial Lund-Regge equation, the O(4) nonlinear σ-model and the SU(2) chiral model. Here, it is demonstrated that these avatars may be discretized in such a manner that both integrability and equivalence are preserved. The corresponding discretization procedure is geometric and algebraic in nature and based on discrete Chebyshev nets and generalized discrete Lelieuvre formulae. In connection with the derivation of associated Baecklund transformations, it is shown that a generalized discrete Lund-Regge equation may be interpreted as a universal permutability theorem for integrable equations which admit commuting matrix Darboux transformations acting on su(2) linear representations. Three-dimensional coordinate systems and lattices of 'Lund-Regge' type related to particular continuous and discrete Zakharov-Manakov systems are obtained as a by-product of this analysis

Reliability Analysis of Load-Sharing K-out-of-N System Considering Component Degradation

Directory of Open Access Journals (Sweden)

Chunbo Yang

2015-01-01

Full Text Available The K-out-of-N configuration is a typical form of redundancy techniques to improve system reliability, where at least K-out-of-N components must work for successful operation of system. When the components are degraded, more components are needed to meet the system requirement, which means that the value of K has to increase. The current reliability analysis methods overestimate the reliability, because using constant K ignores the degradation effect. In a load-sharing system with degrading components, the workload shared on each surviving component will increase after a random component failure, resulting in higher failure rate and increased performance degradation rate. This paper proposes a method combining a tampered failure rate model with a performance degradation model to analyze the reliability of load-sharing K-out-of-N system with degrading components. The proposed method considers the value of K as a variable which is derived by the performance degradation model. Also, the load-sharing effect is evaluated by the tampered failure rate model. Monte-Carlo simulation procedure is used to estimate the discrete probability distribution of K. The case of a solar panel is studied in this paper, and the result shows that the reliability considering component degradation is less than that ignoring component degradation.

Discrete Morse functions for graph configuration spaces

International Nuclear Information System (INIS)

Sawicki, A

2012-01-01

We present an alternative application of discrete Morse theory for two-particle graph configuration spaces. In contrast to previous constructions, which are based on discrete Morse vector fields, our approach is through Morse functions, which have a nice physical interpretation as two-body potentials constructed from one-body potentials. We also give a brief introduction to discrete Morse theory. Our motivation comes from the problem of quantum statistics for particles on networks, for which generalized versions of anyon statistics can appear. (paper)

Velocity locking and pulsed invasions of fragmented habitats with seasonal growth

Science.gov (United States)

Korolev, Kirill; Wang, Ching-Hao

From crystal growth to epidemics, spatial spreading is a common mechanism of change in nature. Typically, spreading results from two processes: growth and dispersal in ecology or chemical reactions and diffusion in physics. These two processes combine to produce a reaction-diffusion wave, an invasion front advancing at a constant velocity. We show that the properties of these waves are remarkably different depending whether space and time are continuous, as they are for a chemical reaction, or discrete, as they are for a pest invading a patchy habitat in seasonal climates. For discrete space and time, we report a new type of expansions with velocities that can lock into specific values and become insensitive to changes in dispersal and growth, i.e. the dependence of the velocity on model parameters exhibits plateaus or pauses. As a result, the evolution and response to perturbations in locked expansions can be markedly different compared to the expectations based on continuous models. The phenomenon of velocity locking requires cooperative growth and does not occur when per capita growth rate decline monotonically with population density. We obtain both numerical and analytical results describing highly non-analytic properties of locked expansions.

Manifestly gauge invariant discretizations of the Schrödinger equation

International Nuclear Information System (INIS)

Halvorsen, Tore Gunnar; Kvaal, Simen

2012-01-01

Grid-based discretizations of the time dependent Schrödinger equation coupled to an external magnetic field are converted to manifest gauge invariant discretizations. This is done using generalizations of ideas used in classical lattice gauge theory, and the process defined is applicable to a large class of discretized differential operators. In particular, popular discretizations such as pseudospectral discretizations using the fast Fourier transform can be transformed to gauge invariant schemes. Also generic gauge invariant versions of generic time integration methods are considered, enabling completely gauge invariant calculations of the time dependent Schrödinger equation. Numerical examples illuminating the differences between a gauge invariant discretization and conventional discretization procedures are also presented. -- Highlights: ► We investigate the Schrödinger equation coupled to an external magnetic field. ► Any grid-based discretization is made trivially gauge invariant. ► An extension of classical lattice gauge theory.

Mathematical aspects of the discrete space-time hypothesis

International Nuclear Information System (INIS)

Sardanashvili, G.A.

1979-01-01

A hypothesis of a microcosm space discreteness is considered from the theoretical-mathematical point of view. The type of topological spaces, which formalizes representations on the discrete space-time, is determined. It is explained, how these spaces arise in physical models. The physical task, in which the discrete space could arise as a version of its solution, is considered. It is shown that the discrete structure of space can arise with a certain interaction type in the system, for example, with its considerable self-shielding, which can take place, in particular, in the particles or in the cosmological and astrophysical singularities

Discrete wavelet transform-based denoising technique for advanced state-of-charge estimator of a lithium-ion battery in electric vehicles

International Nuclear Information System (INIS)

Lee, Seongjun; Kim, Jonghoon

2015-01-01

Sophisticated data of the experimental DCV (discharging/charging voltage) of a lithium-ion battery is required for high-accuracy SOC (state-of-charge) estimation algorithms based on the state-space ECM (electrical circuit model) in BMSs (battery management systems). However, when sensing noisy DCV signals, erroneous SOC estimation (which results in low BMS performance) is inevitable. Therefore, this manuscript describes the design and implementation of a DWT (discrete wavelet transform)-based denoising technique for DCV signals. The steps for denoising a noisy DCV measurement in the proposed approach are as follows. First, using MRA (multi-resolution analysis), the noise-riding DCV signal is decomposed into different frequency sub-bands (low- and high-frequency components, A n and D n ). Specifically, signal processing of the high frequency component D n that focuses on a short-time interval is necessary to reduce noise in the DCV measurement. Second, a hard-thresholding-based denoising rule is applied to adjust the wavelet coefficients of the DWT to achieve a clear separation between the signal and the noise. Third, the desired de-noised DCV signal is reconstructed by taking the IDWT (inverse discrete wavelet transform) of the filtered detailed coefficients. Finally, this signal is sent to the ECM-based SOC estimation algorithm using an EKF (extended Kalman filter). Experimental results indicate the robustness of the proposed approach for reliable SOC estimation. - Highlights: • Sophisticated data of the experimental DCV is required for high-accuracy SOC. • DWT (discrete wavelet transform)-based denoising technique is newly investigated. • Three steps for denoising a noisy DCV measurement in this work are implemented. • Experimental results indicate the robustness of the proposed work for reliable SOC

Discrete-Time Systems

Indian Academy of Sciences (India)

We also describe discrete-time systems in terms of difference ... A more modern alternative, especially for larger systems, is to convert ... In other words, ..... picture?) State-variable equations are also called state-space equations because the ...

The weak-scale hierarchy and discrete symmetries

International Nuclear Information System (INIS)

Haba, Naoyuki; Matsuoka, Takeo; Hattori, Chuichiro; Matsuda, Masahisa; Mochinaga, Daizo.

1996-01-01

In the underlying Planck scale theory, we introduce a certain type of discrete symmetry, which potentially brings the stability of the weak-scale hierarchy under control. Under the discrete symmetry the μ-problem and the tadpole problem can be solved simultaneously without relying on some fine-tuning of parameters. Instead, it is required that doublet Higgs and color-triplet Higgs fields reside in different irreducible representations of the gauge symmetry group at the Planck scale and that they have distinct charges of the discrete symmetry group. (author)

Limit sets for the discrete spectrum of complex Jacobi matrices

International Nuclear Information System (INIS)

Golinskii, L B; Egorova, I E

2005-01-01

The discrete spectrum of complex Jacobi matrices that are compact perturbations of the discrete Laplacian is studied. The precise stabilization rate (in the sense of order) of the matrix elements ensuring the finiteness of the discrete spectrum is found. An example of a Jacobi matrix with discrete spectrum having a unique limit point is constructed. These results are discrete analogues of Pavlov's well-known results on Schroedinger operators with complex potential on a half-axis.

Network Science Research Laboratory (NSRL) Discrete Event Toolkit

Science.gov (United States)

2016-01-01

ARL-TR-7579 ● JAN 2016 US Army Research Laboratory Network Science Research Laboratory (NSRL) Discrete Event Toolkit by...Laboratory (NSRL) Discrete Event Toolkit by Theron Trout and Andrew J Toth Computational and Information Sciences Directorate, ARL...Research Laboratory (NSRL) Discrete Event Toolkit 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Theron Trout

Lax pairs for ultra-discrete Painleve cellular automata

International Nuclear Information System (INIS)

Joshi, N; Nijhoff, F W; Ormerod, C

2004-01-01

Ultra-discrete versions of the discrete Painleve equations are well known. However, evidence for their integrability has so far been restricted. In this letter, we show that their Lax pairs can be constructed and, furthermore, that compatibility conditions of the result yield the ultra-discrete Painleve equation. For conciseness, we restrict our attention to a new d-P III . (letter to the editor)

Constitutive equations for discrete electromagnetic problems over polyhedral grids

International Nuclear Information System (INIS)

Codecasa, Lorenzo; Trevisan, Francesco

2007-01-01

In this paper a novel approach is proposed for constructing discrete counterparts of constitutive equations over polyhedral grids which ensure both consistency and stability of the algebraic equations discretizing an electromagnetic field problem. The idea is to construct discrete constitutive equations preserving the thermodynamic relations for constitutive equations. In this way, consistency and stability of the discrete equations are ensured. At the base, a purely geometric condition between the primal and the dual grids has to be satisfied for a given primal polyhedral grid, by properly choosing the dual grid. Numerical experiments demonstrate that the proposed discrete constitutive equations lead to accurate approximations of the electromagnetic field

Painleve test and discrete Boltzmann equations

International Nuclear Information System (INIS)

Euler, N.; Steeb, W.H.

1989-01-01

The Painleve test for various discrete Boltzmann equations is performed. The connection with integrability is discussed. Furthermore the Lie symmetry vector fields are derived and group-theoretical reduction of the discrete Boltzmann equations to ordinary differentiable equations is performed. Lie Backlund transformations are gained by performing the Painleve analysis for the ordinary differential equations. 16 refs

Analysis of information security reliability: A tutorial

International Nuclear Information System (INIS)

Kondakci, Suleyman

2015-01-01

This article presents a concise reliability analysis of network security abstracted from stochastic modeling, reliability, and queuing theories. Network security analysis is composed of threats, their impacts, and recovery of the failed systems. A unique framework with a collection of the key reliability models is presented here to guide the determination of the system reliability based on the strength of malicious acts and performance of the recovery processes. A unique model, called Attack-obstacle model, is also proposed here for analyzing systems with immunity growth features. Most computer science curricula do not contain courses in reliability modeling applicable to different areas of computer engineering. Hence, the topic of reliability analysis is often too diffuse to most computer engineers and researchers dealing with network security. This work is thus aimed at shedding some light on this issue, which can be useful in identifying models, their assumptions and practical parameters for estimating the reliability of threatened systems and for assessing the performance of recovery facilities. It can also be useful for the classification of processes and states regarding the reliability of information systems. Systems with stochastic behaviors undergoing queue operations and random state transitions can also benefit from the approaches presented here. - Highlights: • A concise survey and tutorial in model-based reliability analysis applicable to information security. • A framework of key modeling approaches for assessing reliability of networked systems. • The framework facilitates quantitative risk assessment tasks guided by stochastic modeling and queuing theory. • Evaluation of approaches and models for modeling threats, failures, impacts, and recovery analysis of information systems

Recent developments in discrete ordinates electron transport

International Nuclear Information System (INIS)

Morel, J.E.; Lorence, L.J. Jr.

1986-01-01

The discrete ordinates method is a deterministic method for numerically solving the Boltzmann equation. It was originally developed for neutron transport calculations, but is routinely used for photon and coupled neutron-photon transport calculations as well. The computational state of the art for coupled electron-photon transport (CEPT) calculations is not as developed as that for neutron transport calculations. The only production codes currently available for CEPT calculations are condensed-history Monte Carlo codes such as the ETRAN and ITS codes. A deterministic capability for production calculations is clearly needed. In response to this need, we have begun the development of a production discrete ordinates code for CEPT calculations. The purpose of this paper is to describe the basic approach we are taking, discuss the current status of the project, and present some new computational results. Although further characterization of the coupled electron-photon discrete ordinates method remains to be done, the results to date indicate that the discrete ordinates method can be just as accurate and from 10 to 100 times faster than the Monte Carlo method for a wide variety of problems. We stress that these results are obtained with standard discrete ordinates codes such as ONETRAN. It is clear that even greater efficiency can be obtained by developing a new generation of production discrete ordinates codes specifically designed to solve the Boltzmann-Fokker-Planck equation. However, the prospects for such development in the near future appear to be remote

Discrete quantum gravity

International Nuclear Information System (INIS)

Williams, Ruth M

2006-01-01

A review is given of a number of approaches to discrete quantum gravity, with a restriction to those likely to be relevant in four dimensions. This paper is dedicated to Rafael Sorkin on the occasion of his sixtieth birthday

Integrable discretizations of the (2+1)-dimensional sinh-Gordon equation

International Nuclear Information System (INIS)

Hu, Xing-Biao; Yu, Guo-Fu

2007-01-01

In this paper, we propose two semi-discrete equations and one fully discrete equation and study them by Hirota's bilinear method. These equations have continuum limits into a system which admits the (2+1)-dimensional generalization of the sinh-Gordon equation. As a result, two integrable semi-discrete versions and one fully discrete version for the sinh-Gordon equation are found. Baecklund transformations, nonlinear superposition formulae, determinant solution and Lax pairs for these discrete versions are presented

Overcoming some limitations of imprecise reliability models

DEFF Research Database (Denmark)

Kozine, Igor; Krymsky, Victor

2011-01-01

The application of imprecise reliability models is often hindered by the rapid growth in imprecision that occurs when many components constitute a system and by the fact that time to failure is bounded from above. The latter results in the necessity to explicitly introduce an upper bound on time ...

Integrable discretization s of derivative nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Tsuchida, Takayuki

2002-01-01

We propose integrable discretizations of derivative nonlinear Schroedinger (DNLS) equations such as the Kaup-Newell equation, the Chen-Lee-Liu equation and the Gerdjikov-Ivanov equation by constructing Lax pairs. The discrete DNLS systems admit the reduction of complex conjugation between two dependent variables and possess bi-Hamiltonian structure. Through transformations of variables and reductions, we obtain novel integrable discretizations of the nonlinear Schroedinger (NLS), modified KdV (mKdV), mixed NLS, matrix NLS, matrix KdV, matrix mKdV, coupled NLS, coupled Hirota, coupled Sasa-Satsuma and Burgers equations. We also discuss integrable discretizations of the sine-Gordon equation, the massive Thirring model and their generalizations. (author)

Continuous Measurements and Quantitative Constraints: Challenge Problems for Discrete Modeling Techniques

Science.gov (United States)

Goodrich, Charles H.; Kurien, James; Clancy, Daniel (Technical Monitor)

2001-01-01

We present some diagnosis and control problems that are difficult to solve with discrete or purely qualitative techniques. We analyze the nature of the problems, classify them and explain why they are frequently encountered in systems with closed loop control. This paper illustrates the problem with several examples drawn from industrial and aerospace applications and presents detailed information on one important application: In-Situ Resource Utilization (ISRU) on Mars. The model for an ISRU plant is analyzed showing where qualitative techniques are inadequate to identify certain failure modes and to maintain control of the system in degraded environments. We show why the solution to the problem will result in significantly more robust and reliable control systems. Finally, we illustrate requirements for a solution to the problem by means of examples.

Multivariable biorthogonal continuous--discrete Wilson and Racah polynomials

International Nuclear Information System (INIS)

Tratnik, M.V.

1990-01-01

Several families of multivariable, biorthogonal, partly continuous and partly discrete, Wilson polynomials are presented. These yield limit cases that are purely continuous in some of the variables and purely discrete in the others, or purely discrete in all the variables. The latter are referred to as the multivariable biorthogonal Racah polynomials. Interesting further limit cases include the multivariable biorthogonal Hahn and dual Hahn polynomials

Degree distribution in discrete case

International Nuclear Information System (INIS)

Wang, Li-Na; Chen, Bin; Yan, Zai-Zai

2011-01-01

Vertex degree of many network models and real-life networks is limited to non-negative integer. By means of measure and integral, the relation of the degree distribution and the cumulative degree distribution in discrete case is analyzed. The degree distribution, obtained by the differential of its cumulative, is only suitable for continuous case or discrete case with constant degree change. When degree change is not a constant but proportional to degree itself, power-law degree distribution and its cumulative have the same exponent and the mean value is finite for power-law exponent greater than 1. -- Highlights: → Degree change is the crux for using the cumulative degree distribution method. → It suits for discrete case with constant degree change. → If degree change is proportional to degree, power-law degree distribution and its cumulative have the same exponent. → In addition, the mean value is finite for power-law exponent greater than 1.

Direct Discrete Method for Neutronic Calculations

International Nuclear Information System (INIS)

Vosoughi, Naser; Akbar Salehi, Ali; Shahriari, Majid

2002-01-01

The objective of this paper is to introduce a new direct method for neutronic calculations. This method which is named Direct Discrete Method, is simpler than the neutron Transport equation and also more compatible with physical meaning of problems. This method is based on physic of problem and with meshing of the desired geometry, writing the balance equation for each mesh intervals and with notice to the conjunction between these mesh intervals, produce the final discrete equations series without production of neutron transport differential equation and mandatory passing from differential equation bridge. We have produced neutron discrete equations for a cylindrical shape with two boundary conditions in one group energy. The correction of the results from this method are tested with MCNP-4B code execution. (authors)

On the discrete Gabor transform and the discrete Zak transform

NARCIS (Netherlands)

Bastiaans, M.J.; Geilen, M.C.W.

1996-01-01

Gabor's expansion of a discrete-time signal into a set of shifted and modulated versions of an elementary signal (or synthesis window) and the inverse operation -- the Gabor transform -- with which Gabor's expansion coefficients can be determined, are introduced. It is shown how, in the case of a

Robust DEA under discrete uncertain data: a case study of Iranian electricity distribution companies

Science.gov (United States)

Hafezalkotob, Ashkan; Haji-Sami, Elham; Omrani, Hashem

2015-06-01

Crisp input and output data are fundamentally indispensable in traditional data envelopment analysis (DEA). However, the real-world problems often deal with imprecise or ambiguous data. In this paper, we propose a novel robust data envelopment model (RDEA) to investigate the efficiencies of decision-making units (DMU) when there are discrete uncertain input and output data. The method is based upon the discrete robust optimization approaches proposed by Mulvey et al. (1995) that utilizes probable scenarios to capture the effect of ambiguous data in the case study. Our primary concern in this research is evaluating electricity distribution companies under uncertainty about input/output data. To illustrate the ability of proposed model, a numerical example of 38 Iranian electricity distribution companies is investigated. There are a large amount ambiguous data about these companies. Some electricity distribution companies may not report clear and real statistics to the government. Thus, it is needed to utilize a prominent approach to deal with this uncertainty. The results reveal that the RDEA model is suitable and reliable for target setting based on decision makers (DM's) preferences when there are uncertain input/output data.

Discrete Choice and Rational Inattention

DEFF Research Database (Denmark)

Fosgerau, Mogens; Melo, Emerson; de Palma, André

2017-01-01

This paper establishes a general equivalence between discrete choice and rational inattention models. Matejka and McKay (2015, AER) showed that when information costs are modelled using the Shannon entropy, the result- ing choice probabilities in the rational inattention model take the multinomial...... logit form. We show that when information costs are modelled using a class of generalized entropies, then the choice probabilities in any rational inattention model are observationally equivalent to some additive random utility discrete choice model and vice versa. This equivalence arises from convex...

Process algebra with timing : real time and discrete time

NARCIS (Netherlands)

Baeten, J.C.M.; Middelburg, C.A.; Bergstra, J.A.; Ponse, A.J.; Smolka, S.A.

2001-01-01

We present real time and discrete time versions of ACP with absolute timing and relative timing. The starting-point is a new real time version with absolute timing, called ACPsat, featuring urgent actions and a delay operator. The discrete time versions are conservative extensions of the discrete

Process algebra with timing: Real time and discrete time

NARCIS (Netherlands)

Baeten, J.C.M.; Middelburg, C.A.

1999-01-01

We present real time and discrete time versions of ACP with absolute timing and relative timing. The startingpoint is a new real time version with absolute timing, called ACPsat , featuring urgent actions and a delay operator. The discrete time versions are conservative extensions of the discrete

A hierarchy of Liouville integrable discrete Hamiltonian equations

Energy Technology Data Exchange (ETDEWEB)

Xu Xixiang [College of Science, Shandong University of Science and Technology, Qingdao 266510 (China)], E-mail: xixiang_xu@yahoo.com.cn

2008-05-12

Based on a discrete four-by-four matrix spectral problem, a hierarchy of Lax integrable lattice equations with two potentials is derived. Two Hamiltonian forms are constructed for each lattice equation in the resulting hierarchy by means of the discrete variational identity. A strong symmetry operator of the resulting hierarchy is given. Finally, it is shown that the resulting lattice equations are all Liouville integrable discrete Hamiltonian systems.

Variational discretization of the nonequilibrium thermodynamics of simple systems

Science.gov (United States)

Gay-Balmaz, François; Yoshimura, Hiroaki

2018-04-01

In this paper, we develop variational integrators for the nonequilibrium thermodynamics of simple closed systems. These integrators are obtained by a discretization of the Lagrangian variational formulation of nonequilibrium thermodynamics developed in (Gay-Balmaz and Yoshimura 2017a J. Geom. Phys. part I 111 169–93 Gay-Balmaz and Yoshimura 2017b J. Geom. Phys. part II 111 194–212) and thus extend the variational integrators of Lagrangian mechanics, to include irreversible processes. In the continuous setting, we derive the structure preserving property of the flow of such systems. This property is an extension of the symplectic property of the flow of the Euler–Lagrange equations. In the discrete setting, we show that the discrete flow solution of our numerical scheme verifies a discrete version of this property. We also present the regularity conditions which ensure the existence of the discrete flow. We finally illustrate our discrete variational schemes with the implementation of an example of a simple and closed system.

Discrete breathers in Bose–Einstein condensates

International Nuclear Information System (INIS)

Franzosi, Roberto; Politi, Antonio; Livi, Roberto; Oppo, Gian-Luca

2011-01-01

Discrete breathers, originally introduced in the context of biopolymers and coupled nonlinear oscillators, are also localized modes of excitation of Bose–Einstein condensates (BEC) in periodic potentials such as those generated by counter-propagating laser beams in an optical lattice. Static and dynamical properties of breather states are analysed in the discrete nonlinear Schrödinger equation that is derived in the limit of deep potential wells, tight-binding and the superfluid regime of the condensate. Static and mobile breathers can be formed by progressive re-shaping of initial Gaussian wave-packets or by transporting atomic density towards dissipative boundaries of the lattice. Static breathers generated via boundary dissipations are determined via a transfer-matrix approach and discussed in the two analytic limits of highly localized and very broad profiles. Mobile breathers that move across the lattice are well approximated by modified analytical expressions derived from integrable models with two independent parameters: the core-phase gradient and the peak amplitude. Finally, possible experimental realizations of discrete breathers in BEC in optical lattices are discussed in the presence of residual harmonic trapping and in interferometry configurations suitable to investigate discrete breathers' interactions. (invited article)

Hopf Bifurcation Analysis for a Stochastic Discrete-Time Hyperchaotic System

Directory of Open Access Journals (Sweden)

Jie Ran

2015-01-01

Full Text Available The dynamics of a discrete-time hyperchaotic system and the amplitude control of Hopf bifurcation for a stochastic discrete-time hyperchaotic system are investigated in this paper. Numerical simulations are presented to exhibit the complex dynamical behaviors in the discrete-time hyperchaotic system. Furthermore, the stochastic discrete-time hyperchaotic system with random parameters is transformed into its equivalent deterministic system with the orthogonal polynomial theory of discrete random function. In addition, the dynamical features of the discrete-time hyperchaotic system with random disturbances are obtained through its equivalent deterministic system. By using the Hopf bifurcation conditions of the deterministic discrete-time system, the specific conditions for the existence of Hopf bifurcation in the equivalent deterministic system are derived. And the amplitude control with random intensity is discussed in detail. Finally, the feasibility of the control method is demonstrated by numerical simulations.

Discretization-induced delays and their role in the dynamics

International Nuclear Information System (INIS)

Ramani, A; Grammaticos, B; Satsuma, J; Willox, R

2008-01-01

We show that a discretization of a continuous system may entail 'hidden' delays and thus introduce instabilities. In this case, while the continuous system has an attractive fixed point, the instabilities present in the equivalent discrete one may lead to the appearance of a limit cycle. We explain that it is possible, thanks to the proper staggering of the discrete variables, to eliminate the hidden delay. However, in general, other instabilities may appear in the discrete system which can even lead to chaotic behaviour

Discrete mathematics in the high school curriculum

NARCIS (Netherlands)

Anderson, I.; Asch, van A.G.; van Lint, J.H.

2004-01-01

In this paper we present some topics from the field of discrete mathematics which might be suitable for the high school curriculum. These topics yield both easy to understand challenging problems and important applications of discrete mathematics. We choose elements from number theory and various

Manipulating Rayleigh-Taylor Growth Using Adjoints

Science.gov (United States)

Kord, Ali; Capecelatro, Jesse

2017-11-01

It has been observed that initial interfacial perturbations affect the growth of Rayleigh-Taylor (RT) instabilities. However, it remains to be seen to what extent the perturbations alter the RT growth rate. Direct numerical simulations (DNS) provide a powerful means for studying the effects of initial conditions (IC) on the growth rate. However, a brute-force approach for identifying optimal initial perturbations is not practical via DNS. In addition, identifying sensitivity of the RT growth to the large number of parameters used in defining the IC is computationally expensive. A discrete adjoint is formulated to measure sensitivities of multi-mode RT growth to ICs in a high-order finite difference framework. The sensitivity is used as a search direction for adjusting the initial perturbations to both maximize and suppress the RT growth rate during its non-linear regime. The modes that contribute the greatest sensitivity are identified, and optimized perturbation energy spectrum are reported. PhD Student, Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI.

Hybrid discrete-time neural networks.

Science.gov (United States)

Cao, Hongjun; Ibarz, Borja

2010-11-13

Hybrid dynamical systems combine evolution equations with state transitions. When the evolution equations are discrete-time (also called map-based), the result is a hybrid discrete-time system. A class of biological neural network models that has recently received some attention falls within this category: map-based neuron models connected by means of fast threshold modulation (FTM). FTM is a connection scheme that aims to mimic the switching dynamics of a neuron subject to synaptic inputs. The dynamic equations of the neuron adopt different forms according to the state (either firing or not firing) and type (excitatory or inhibitory) of their presynaptic neighbours. Therefore, the mathematical model of one such network is a combination of discrete-time evolution equations with transitions between states, constituting a hybrid discrete-time (map-based) neural network. In this paper, we review previous work within the context of these models, exemplifying useful techniques to analyse them. Typical map-based neuron models are low-dimensional and amenable to phase-plane analysis. In bursting models, fast-slow decomposition can be used to reduce dimensionality further, so that the dynamics of a pair of connected neurons can be easily understood. We also discuss a model that includes electrical synapses in addition to chemical synapses with FTM. Furthermore, we describe how master stability functions can predict the stability of synchronized states in these networks. The main results are extended to larger map-based neural networks.

Stochastic Kuramoto oscillators with discrete phase states

Science.gov (United States)

Jörg, David J.

2017-09-01

We present a generalization of the Kuramoto phase oscillator model in which phases advance in discrete phase increments through Poisson processes, rendering both intrinsic oscillations and coupling inherently stochastic. We study the effects of phase discretization on the synchronization and precision properties of the coupled system both analytically and numerically. Remarkably, many key observables such as the steady-state synchrony and the quality of oscillations show distinct extrema while converging to the classical Kuramoto model in the limit of a continuous phase. The phase-discretized model provides a general framework for coupled oscillations in a Markov chain setting.

Stochastic Kuramoto oscillators with discrete phase states.

Science.gov (United States)

Jörg, David J

2017-09-01

We present a generalization of the Kuramoto phase oscillator model in which phases advance in discrete phase increments through Poisson processes, rendering both intrinsic oscillations and coupling inherently stochastic. We study the effects of phase discretization on the synchronization and precision properties of the coupled system both analytically and numerically. Remarkably, many key observables such as the steady-state synchrony and the quality of oscillations show distinct extrema while converging to the classical Kuramoto model in the limit of a continuous phase. The phase-discretized model provides a general framework for coupled oscillations in a Markov chain setting.

On discrete models of space-time

International Nuclear Information System (INIS)

Horzela, A.; Kempczynski, J.; Kapuscik, E.; Georgia Univ., Athens, GA; Uzes, Ch.

1992-02-01

Analyzing the Einstein radiolocation method we come to the conclusion that results of any measurement of space-time coordinates should be expressed in terms of rational numbers. We show that this property is Lorentz invariant and may be used in the construction of discrete models of space-time different from the models of the lattice type constructed in the process of discretization of continuous models. (author)

Test–Retest Reliability of Self-Reported Sexual Behavior History in Urbanized Nigerian Women

Directory of Open Access Journals (Sweden)

Eileen O. Dareng

2017-07-01

Full Text Available BackgroundStudies assessing risk of sexual behavior and disease are often plagued by questions about the reliability of self-reported sexual behavior. In this study, we evaluated the reliability of self-reported sexual history among urbanized women in a prospective study of cervical HPV infections in Nigeria.MethodsWe examined test–retest reliability of sexual practices using questionnaires administered at study entry and at follow-up visits. We used the root mean squared approach to calculate within-person coefficient of variation (CVw and calculated the intra-class correlation coefficient (ICC using two way, mixed effects models for continuous variables and (κ^ statistics for discrete variables. To evaluate the potential predictors of reliability, we used linear regression and log binomial regression models for the continuous and categorical variables, respectively.ResultsWe found that self-reported sexual history was generally reliable, with overall ICC ranging from 0.7 to 0.9; however, the reliability varied by nature of sexual behavior evaluated. Frequency reports of non-vaginal sex (agreement = 63.9%, 95% CI: 47.5–77.6% were more reliable than those of vaginal sex (agreement = 59.1%, 95% CI: 55.2–62.8%. Reports of time-invariant behaviors were also more reliable than frequency reports. The CVw for age at sexual debut was 10.7 (95% CI: 10.6–10.7 compared with the CVw for lifetime number of vaginal sex partners, which was 35.2 (95% CI: 35.1–35.3. The test–retest interval was an important predictor of reliability of responses, with longer intervals resulting in increased inconsistency (average change in unreliability for each 1 month increase = 0.04, 95% CI = 0.07–0.38, p = 0.005.ConclusionOur findings suggest that overall, the self-reported sexual history among urbanized Nigeran women is reliable.

Finite Element Reliability Analysis of Chloride Ingress into Reinforced Concrete Structures

DEFF Research Database (Denmark)

Frier, Christian; Sørensen, John Dalsgaard

2007-01-01

For many reinforced concrete structures corrosion of the reinforcement is an important problem since it can result in maintenance and repair actions. Further, a reduction of the load-bearing capacity can occur. In the present paper the Finite Element Reliability Method (FERM) is employed for obta......For many reinforced concrete structures corrosion of the reinforcement is an important problem since it can result in maintenance and repair actions. Further, a reduction of the load-bearing capacity can occur. In the present paper the Finite Element Reliability Method (FERM) is employed...... concentration and reinforcement cover depth are modelled by stochastic fields, which are discretized using the Expansion Optimum Linear Estimation (EOLE) approach. The response gradients needed for FORM analysis are derived analytically using the Direct Differentiation Method (DDM). As an example, a bridge pier...... in a marine environment is considered and the results are given in terms of distributions of time for initiation of corrosion....

Reflectionless discrete Schr\\"odinger operators are spectrally atypical

OpenAIRE

VandenBoom, Tom

2017-01-01

We prove that, if an isospectral torus contains a discrete Schr\\"odinger operator with nonconstant potential, the shift dynamics on that torus cannot be minimal. Consequently, we specify a generic sense in which finite unions of nondegenerate closed intervals having capacity one are not the spectrum of any reflectionless discrete Schr\\"odinger operator. We also show that the only reflectionless discrete Schr\\"odinger operators having zero, one, or two spectral gaps are periodic.

A Baecklund transformation between two integrable discrete hungry systems

International Nuclear Information System (INIS)

Fukuda, Akiko; Yamamoto, Yusaku; Iwasaki, Masashi; Ishiwata, Emiko; Nakamura, Yoshimasa

2011-01-01

The discrete hungry Toda (dhToda) equation and the discrete hungry Lotka-Volterra (dhLV) system are known as integrable discrete hungry systems. In this Letter, through finding the LR transformations associated with the dhToda equation and the dhLV system, we present a Baecklund transformation between these integrable systems.

A Baecklund transformation between two integrable discrete hungry systems

Energy Technology Data Exchange (ETDEWEB)

Fukuda, Akiko, E-mail: j1409704@ed.kagu.tus.ac.j [Department of Mathematical Information Science, Graduate School of Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); Yamamoto, Yusaku [Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501 (Japan); Iwasaki, Masashi [Department of Informatics and Environmental Science, Kyoto Prefectural University, 1-5, Nakaragi-cho, Shimogamo, Sakyo-ku, Kyoto 606-8522 (Japan); Ishiwata, Emiko [Department of Mathematical Information Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); Nakamura, Yoshimasa [Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501 (Japan)

2011-01-17

The discrete hungry Toda (dhToda) equation and the discrete hungry Lotka-Volterra (dhLV) system are known as integrable discrete hungry systems. In this Letter, through finding the LR transformations associated with the dhToda equation and the dhLV system, we present a Baecklund transformation between these integrable systems.

An introduction to non-Abelian discrete symmetries for particle physicists

CERN Document Server

Ishimori, Hajime; Ohki, Hiroshi; Okada, Hiroshi; Shimizu, Yusuke; Tanimoto, Morimitsu

2012-01-01

These lecture notes provide a tutorial review of non-Abelian discrete groups and show some applications to issues in physics where discrete symmetries constitute an important principle for model building in particle physics. While Abelian discrete symmetries are often imposed in order to control couplings for particle physics - in particular model building beyond the standard model - non-Abelian discrete symmetries have been applied to understand the three-generation flavor structure in particular. Indeed, non-Abelian discrete symmetries are considered to be the most attractive choice for the flavor sector: model builders have tried to derive experimental values of quark and lepton masses, and mixing angles by assuming non-Abelian discrete flavor symmetries of quarks and leptons, yet, lepton mixing has already been intensively discussed in this context, as well. The possible origins of the non-Abelian discrete symmetry for flavors is another topic of interest, as they can arise from an underlying theory -...

Partition-based discrete-time quantum walks

Science.gov (United States)

Konno, Norio; Portugal, Renato; Sato, Iwao; Segawa, Etsuo

2018-04-01

We introduce a family of discrete-time quantum walks, called two-partition model, based on two equivalence-class partitions of the computational basis, which establish the notion of local dynamics. This family encompasses most versions of unitary discrete-time quantum walks driven by two local operators studied in literature, such as the coined model, Szegedy's model, and the 2-tessellable staggered model. We also analyze the connection of those models with the two-step coined model, which is driven by the square of the evolution operator of the standard discrete-time coined walk. We prove formally that the two-step coined model, an extension of Szegedy model for multigraphs, and the two-tessellable staggered model are unitarily equivalent. Then, selecting one specific model among those families is a matter of taste not generality.

Stabilizing the discrete vortex of topological charge S=2

International Nuclear Information System (INIS)

Kevrekidis, P.G.; Frantzeskakis, D.J.

2005-01-01

We study the instability of the discrete vortex with topological charge S=2 in a prototypical lattice model and observe its mediation through the central lattice site. Motivated by this finding, we analyze the model with the central site being inert. We identify analytically and observe numerically the existence of a range of linearly stable discrete vortices with S=2 in the latter model. The range of stability is comparable to that of the recently observed experimentally S=1 discrete vortex, suggesting the potential for observation of such higher charge discrete vortices

Group-theoretical aspects of the discrete sine-Gordon equation

International Nuclear Information System (INIS)

Orfanidis, S.J.

1980-01-01

The group-theoretical interpretation of the sine-Gordon equation in terms of connection forms on fiber bundles is extended to the discrete case. Solutions of the discrete sine-Gordon equation induce surfaces on a lattice in the SU(2) group space. The inverse scattering representation, expressing the parallel transport of fibers, is implemented by means of finite rotations. Discrete Baecklund transformations are realized as gauge transformations. The three-dimensional inverse scattering representation is used to derive a discrete nonlinear sigma model, and the corresponding Baecklund transformation and Pohlmeyer's R transformation are constructed

Solitonlike solutions of the generalized discrete nonlinear Schrödinger equation

DEFF Research Database (Denmark)

Rasmussen, Kim; Henning, D.; Gabriel, H.

1996-01-01

We investigate the solution properties oi. a generalized discrete nonlinear Schrodinger equation describing a nonlinear lattice chain. The generalized equation interpolates between the integrable discrete Ablowitz-Ladik equation and the nonintegrable discrete Schrodinger equation. Special interes...... nonlinear Schrodinger equation. In this way eve are able to construct coherent solitonlike structures of profile determined by the map parameters.......We investigate the solution properties oi. a generalized discrete nonlinear Schrodinger equation describing a nonlinear lattice chain. The generalized equation interpolates between the integrable discrete Ablowitz-Ladik equation and the nonintegrable discrete Schrodinger equation. Special interest...

Local discrete symmetries from superstring derived models

International Nuclear Information System (INIS)

Faraggi, A.E.

1996-10-01

Discrete and global symmetries play an essential role in many extensions of the Standard Model, for example, to preserve the proton lifetime, to prevent flavor changing neutral currents, etc. An important question is how can such symmetries survive in a theory of quantum gravity, like superstring theory. In a specific string model the author illustrates how local discrete symmetries may arise in string models and play an important role in preventing fast proton decay and flavor changing neutral currents. The local discrete symmetry arises due to the breaking of the non-Abelian gauge symmetries by Wilson lines in the superstring models and forbids, for example dimension five operators which mediate rapid proton decay, to all orders of nonrenormalizable terms. In the context of models of unification of the gauge and gravitational interactions, it is precisely this type of local discrete symmetries that must be found in order to insure that a given model is not in conflict with experimental observations

Discrete dispersion models and their Tweedie asymptotics

DEFF Research Database (Denmark)

Jørgensen, Bent; Kokonendji, Célestin C.

2016-01-01

The paper introduce a class of two-parameter discrete dispersion models, obtained by combining convolution with a factorial tilting operation, similar to exponential dispersion models which combine convolution and exponential tilting. The equidispersed Poisson model has a special place in this ap......The paper introduce a class of two-parameter discrete dispersion models, obtained by combining convolution with a factorial tilting operation, similar to exponential dispersion models which combine convolution and exponential tilting. The equidispersed Poisson model has a special place...... in this approach, whereas several overdispersed discrete distributions, such as the Neyman Type A, Pólya-Aeppli, negative binomial and Poisson-inverse Gaussian, turn out to be Poisson-Tweedie factorial dispersion models with power dispersion functions, analogous to ordinary Tweedie exponential dispersion models...... with power variance functions. Using the factorial cumulant generating function as tool, we introduce a dilation operation as a discrete analogue of scaling, generalizing binomial thinning. The Poisson-Tweedie factorial dispersion models are closed under dilation, which in turn leads to a Poisson...

Use cases of discrete event simulation. Appliance and research

Energy Technology Data Exchange (ETDEWEB)

Bangsow, Steffen (ed.)

2012-11-01

Use Cases of Discrete Event Simulation. Includes case studies from various important industries such as automotive, aerospace, robotics, production industry. Written by leading experts in the field. Over the last decades Discrete Event Simulation has conquered many different application areas. This trend is, on the one hand, driven by an ever wider use of this technology in different fields of science and on the other hand by an incredibly creative use of available software programs through dedicated experts. This book contains articles from scientists and experts from 10 countries. They illuminate the width of application of this technology and the quality of problems solved using Discrete Event Simulation. Practical applications of simulation dominate in the present book. The book is aimed to researchers and students who deal in their work with Discrete Event Simulation and which want to inform them about current applications. By focusing on discrete event simulation, this book can also serve as an inspiration source for practitioners for solving specific problems during their work. Decision makers who deal with the question of the introduction of discrete event simulation for planning support and optimization this book provides a contribution to the orientation, what specific problems could be solved with the help of Discrete Event Simulation within the organization.

Discrete bacteria foraging optimization algorithm for graph based problems - a transition from continuous to discrete

Science.gov (United States)

Sur, Chiranjib; Shukla, Anupam

2018-03-01

Bacteria Foraging Optimisation Algorithm is a collective behaviour-based meta-heuristics searching depending on the social influence of the bacteria co-agents in the search space of the problem. The algorithm faces tremendous hindrance in terms of its application for discrete problems and graph-based problems due to biased mathematical modelling and dynamic structure of the algorithm. This had been the key factor to revive and introduce the discrete form called Discrete Bacteria Foraging Optimisation (DBFO) Algorithm for discrete problems which exceeds the number of continuous domain problems represented by mathematical and numerical equations in real life. In this work, we have mainly simulated a graph-based road multi-objective optimisation problem and have discussed the prospect of its utilisation in other similar optimisation problems and graph-based problems. The various solution representations that can be handled by this DBFO has also been discussed. The implications and dynamics of the various parameters used in the DBFO are illustrated from the point view of the problems and has been a combination of both exploration and exploitation. The result of DBFO has been compared with Ant Colony Optimisation and Intelligent Water Drops Algorithms. Important features of DBFO are that the bacteria agents do not depend on the local heuristic information but estimates new exploration schemes depending upon the previous experience and covered path analysis. This makes the algorithm better in combination generation for graph-based problems and combination generation for NP hard problems.

Discrete Pathophysiology is Uncommon in Patients with Nonspecific Arm Pain.

Science.gov (United States)

Kortlever, Joost T P; Janssen, Stein J; Molleman, Jeroen; Hageman, Michiel G J S; Ring, David

2016-06-01

Nonspecific symptoms are common in all areas of medicine. Patients and caregivers can be frustrated when an illness cannot be reduced to a discrete pathophysiological process that corresponds with the symptoms. We therefore asked the following questions: 1) Which demographic factors and psychological comorbidities are associated with change from an initial diagnosis of nonspecific arm pain to eventual identification of discrete pathophysiology that corresponds with symptoms? 2) What is the percentage of patients eventually diagnosed with discrete pathophysiology, what are those pathologies, and do they account for the symptoms? We evaluated 634 patients with an isolated diagnosis of nonspecific upper extremity pain to see if discrete pathophysiology was diagnosed on subsequent visits to the same hand surgeon, a different hand surgeon, or any physician within our health system for the same pain. There were too few patients with discrete pathophysiology at follow-up to address the primary study question. Definite discrete pathophysiology that corresponded with the symptoms was identified in subsequent evaluations by the index surgeon in one patient (0.16% of all patients) and cured with surgery (nodular fasciitis). Subsequent doctors identified possible discrete pathophysiology in one patient and speculative pathophysiology in four patients and the index surgeon identified possible discrete pathophysiology in four patients, but the five discrete diagnoses accounted for only a fraction of the symptoms. Nonspecific diagnoses are not harmful. Prospective randomized research is merited to determine if nonspecific, descriptive diagnoses are better for patients than specific diagnoses that imply pathophysiology in the absence of discrete verifiable pathophysiology.

Implementing the Standards. Teaching Discrete Mathematics in Grades 7-12.

Science.gov (United States)

Hart, Eric W.; And Others

1990-01-01

Discrete mathematics are defined briefly. A course in discrete mathematics for high school students and teaching discrete mathematics in grades 7 and 8 including finite differences, recursion, and graph theory are discussed. (CW)

Endogenous population growth may imply chaos.

Science.gov (United States)

Prskawetz, A; Feichtinger, G

1995-01-01

The authors consider a discrete-time neoclassical growth model with an endogenous rate of population growth. The resulting one-dimensional map for the capital intensity has a tilted z-shape. Using the theory of nonlinear dynamical systems, they obtain numerical results on the qualitative behavior of time paths for changing parameter values. Besides stable and periodic solutions, erratic time paths may result. In particular, myopic and far-sighted economies--assumed to be characterized by low and high savings rate respectively--are characterized by stable per capita capital stocks, while solutions with chaotic windows exist between these two extremes.

Discretized representations of harmonic variables by bilateral Jacobi operators

Directory of Open Access Journals (Sweden)

Andreas Ruffing

2000-01-01

Full Text Available Starting from a discrete Heisenberg algebra we solve several representation problems for a discretized quantum oscillator in a weighted sequence space. The Schrödinger operator for a discrete harmonic oscillator is derived. The representation problem for a q-oscillator algebra is studied in detail. The main result of the article is the fact that the energy representation for the discretized momentum operator can be interpreted as follows: It allows to calculate quantum properties of a large number of non-interacting harmonic oscillators at the same time. The results can be directly related to current research on squeezed laser states in quantum optics. They reveal and confirm the observation that discrete versions of continuum Schrodinger operators allow more structural freedom than their continuum analogs do.

Discrete stochastic charging of aggregate grains

Science.gov (United States)

Matthews, Lorin S.; Shotorban, Babak; Hyde, Truell W.

2018-05-01

Dust particles immersed in a plasma environment become charged through the collection of electrons and ions at random times, causing the dust charge to fluctuate about an equilibrium value. Small grains (with radii less than 1 μm) or grains in a tenuous plasma environment are sensitive to single additions of electrons or ions. Here we present a numerical model that allows examination of discrete stochastic charge fluctuations on the surface of aggregate grains and determines the effect of these fluctuations on the dynamics of grain aggregation. We show that the mean and standard deviation of charge on aggregate grains follow the same trends as those predicted for spheres having an equivalent radius, though aggregates exhibit larger variations from the predicted values. In some plasma environments, these charge fluctuations occur on timescales which are relevant for dynamics of aggregate growth. Coupled dynamics and charging models show that charge fluctuations tend to produce aggregates which are much more linear or filamentary than aggregates formed in an environment where the charge is stationary.

Current Density and Continuity in Discretized Models

Science.gov (United States)

Boykin, Timothy B.; Luisier, Mathieu; Klimeck, Gerhard

2010-01-01

Discrete approaches have long been used in numerical modelling of physical systems in both research and teaching. Discrete versions of the Schrodinger equation employing either one or several basis functions per mesh point are often used by senior undergraduates and beginning graduate students in computational physics projects. In studying…

Discretization vs. Rounding Error in Euler's Method

Science.gov (United States)

Borges, Carlos F.

2011-01-01

Euler's method for solving initial value problems is an excellent vehicle for observing the relationship between discretization error and rounding error in numerical computation. Reductions in stepsize, in order to decrease discretization error, necessarily increase the number of steps and so introduce additional rounding error. The problem is…

On the Importance of Both Dimensional and Discrete Models of Emotion.

Science.gov (United States)

Harmon-Jones, Eddie; Harmon-Jones, Cindy; Summerell, Elizabeth

2017-09-29

We review research on the structure and functions of emotions that has benefitted from a serious consideration of both discrete and dimensional perspectives on emotion. To illustrate this point, we review research that demonstrates: (1) how affective valence within discrete emotions differs as a function of individuals and situations, and how these differences relate to various functions; (2) that anger (and other emotional states) should be considered as a discrete emotion but there are dimensions around and within anger; (3) that similarities exist between approach-related positive and negative discrete emotions and they have unique motivational functions; (4) that discrete emotions and broad dimensions of emotions both have unique functions; and (5) evidence that a "new" discrete emotion with discrete functions exists within a broader emotion family. We hope that this consideration of both discrete and dimensional perspectives on emotion will assist in understanding the functions of emotions.

On the Importance of Both Dimensional and Discrete Models of Emotion

Science.gov (United States)

Harmon-Jones, Eddie

2017-01-01

We review research on the structure and functions of emotions that has benefitted from a serious consideration of both discrete and dimensional perspectives on emotion. To illustrate this point, we review research that demonstrates: (1) how affective valence within discrete emotions differs as a function of individuals and situations, and how these differences relate to various functions; (2) that anger (and other emotional states) should be considered as a discrete emotion but there are dimensions around and within anger; (3) that similarities exist between approach-related positive and negative discrete emotions and they have unique motivational functions; (4) that discrete emotions and broad dimensions of emotions both have unique functions; and (5) evidence that a “new” discrete emotion with discrete functions exists within a broader emotion family. We hope that this consideration of both discrete and dimensional perspectives on emotion will assist in understanding the functions of emotions. PMID:28961185

Based on Weibull Information Fusion Analysis Semiconductors Quality the Key Technology of Manufacturing Execution Systems Reliability

Science.gov (United States)

Huang, Zhi-Hui; Tang, Ying-Chun; Dai, Kai

2016-05-01

Semiconductor materials and Product qualified rate are directly related to the manufacturing costs and survival of the enterprise. Application a dynamic reliability growth analysis method studies manufacturing execution system reliability growth to improve product quality. Refer to classical Duane model assumptions and tracking growth forecasts the TGP programming model, through the failure data, established the Weibull distribution model. Combining with the median rank of average rank method, through linear regression and least squares estimation method, match respectively weibull information fusion reliability growth curve. This assumption model overcome Duane model a weakness which is MTBF point estimation accuracy is not high, through the analysis of the failure data show that the method is an instance of the test and evaluation modeling process are basically identical. Median rank in the statistics is used to determine the method of random variable distribution function, which is a good way to solve the problem of complex systems such as the limited sample size. Therefore this method has great engineering application value.

Discretization-dependent model for weakly connected excitable media

Science.gov (United States)

Arroyo, Pedro André; Alonso, Sergio; Weber dos Santos, Rodrigo

2018-03-01

Pattern formation has been widely observed in extended chemical and biological processes. Although the biochemical systems are highly heterogeneous, homogenized continuum approaches formed by partial differential equations have been employed frequently. Such approaches are usually justified by the difference of scales between the heterogeneities and the characteristic spatial size of the patterns. Under different conditions, for example, under weak coupling, discrete models are more adequate. However, discrete models may be less manageable, for instance, in terms of numerical implementation and mesh generation, than the associated continuum models. Here we study a model to approach discreteness which permits the computer implementation on general unstructured meshes. The model is cast as a partial differential equation but with a parameter that depends not only on heterogeneities sizes, as in the case of quasicontinuum models, but also on the discretization mesh. Therefore, we refer to it as a discretization-dependent model. We validate the approach in a generic excitable media that simulates three different phenomena: the propagation of action membrane potential in cardiac tissue, in myelinated axons of neurons, and concentration waves in chemical microemulsions.

Discrete Variational Approach for Modeling Laser-Plasma Interactions

Science.gov (United States)

Reyes, J. Paxon; Shadwick, B. A.

2014-10-01

The traditional approach for fluid models of laser-plasma interactions begins by approximating fields and derivatives on a grid in space and time, leading to difference equations that are manipulated to create a time-advance algorithm. In contrast, by introducing the spatial discretization at the level of the action, the resulting Euler-Lagrange equations have particular differencing approximations that will exactly satisfy discrete versions of the relevant conservation laws. For example, applying a spatial discretization in the Lagrangian density leads to continuous-time, discrete-space equations and exact energy conservation regardless of the spatial grid resolution. We compare the results of two discrete variational methods using the variational principles from Chen and Sudan and Brizard. Since the fluid system conserves energy and momentum, the relative errors in these conserved quantities are well-motivated physically as figures of merit for a particular method. This work was supported by the U. S. Department of Energy under Contract No. DE-SC0008382 and by the National Science Foundation under Contract No. PHY-1104683.

Discrete Tomography and Imaging of Polycrystalline Structures

DEFF Research Database (Denmark)

Alpers, Andreas

High resolution transmission electron microscopy is commonly considered as the standard application for discrete tomography. While this has yet to be technically realized, new applications with a similar flavor have emerged in materials science. In our group at Ris� DTU (Denmark's National...... Laboratory for Sustainable Energy), for instance, we study polycrystalline materials via synchrotron X-ray diffraction. Several reconstruction problems arise, most of them exhibit inherently discrete aspects. In this talk I want to give a concise mathematical introduction to some of these reconstruction...... problems. Special focus is on their relationship to classical discrete tomography. Several open mathematical questions will be mentioned along the way....

Product reliability and thin-film photovoltaics

Science.gov (United States)

Gaston, Ryan; Feist, Rebekah; Yeung, Simon; Hus, Mike; Bernius, Mark; Langlois, Marc; Bury, Scott; Granata, Jennifer; Quintana, Michael; Carlson, Carl; Sarakakis, Georgios; Ogden, Douglas; Mettas, Adamantios

2009-08-01

Despite significant growth in photovoltaics (PV) over the last few years, only approximately 1.07 billion kWhr of electricity is estimated to have been generated from PV in the US during 2008, or 0.27% of total electrical generation. PV market penetration is set for a paradigm shift, as fluctuating hydrocarbon prices and an acknowledgement of the environmental impacts associated with their use, combined with breakthrough new PV technologies, such as thin-film and BIPV, are driving the cost of energy generated with PV to parity or cost advantage versus more traditional forms of energy generation. In addition to reaching cost parity with grid supplied power, a key to the long-term success of PV as a viable energy alternative is the reliability of systems in the field. New technologies may or may not have the same failure modes as previous technologies. Reliability testing and product lifetime issues continue to be one of the key bottlenecks in the rapid commercialization of PV technologies today. In this paper, we highlight the critical need for moving away from relying on traditional qualification and safety tests as a measure of reliability and focus instead on designing for reliability and its integration into the product development process. A drive towards quantitative predictive accelerated testing is emphasized and an industrial collaboration model addressing reliability challenges is proposed.

Cuspidal discrete series for semisimple symmetric spaces

DEFF Research Database (Denmark)

Andersen, Nils Byrial; Flensted-Jensen, Mogens; Schlichtkrull, Henrik

2012-01-01

We propose a notion of cusp forms on semisimple symmetric spaces. We then study the real hyperbolic spaces in detail, and show that there exists both cuspidal and non-cuspidal discrete series. In particular, we show that all the spherical discrete series are non-cuspidal. (C) 2012 Elsevier Inc. All...

Geometry and Hamiltonian mechanics on discrete spaces

NARCIS (Netherlands)

Talasila, V.; Clemente Gallardo, J.J.; Clemente-Gallardo, J.; van der Schaft, Arjan

2004-01-01

Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a 'smooth' model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to

Characterizing a discrete-to-discrete X-ray transform for iterative image reconstruction with limited angular-range scanning in CT

DEFF Research Database (Denmark)

Sidky, Emil; Jørgensen, Jakob Heide; Pan, Xiaochuan

2012-01-01

Iterative image reconstruction in computed tomography often employs a discrete-to-discrete (DD) linear data model, and many of the aspects of the image recovery relate directly to the properties of this linear model. While much is known about the properties of the continuous X-ray, the correspond...

An innovative discrete multilevel sampler design

International Nuclear Information System (INIS)

Marvin, B.K.; De Clercq, P.J.; Taylor, B.B.; Mauro, D.M.

1995-01-01

An innovative, small-diameter PVC discrete multilevel sampler (DMLS) was designed for the Electric Power Research Institute (EPRI) to provide low-cost, discrete groundwater samples from shallow aquifers. When combined with appropriately-sized direct push soil sampling technologies, high resolution aquifer characterization can be achieved during initial site assessment or remediation monitoring activities. The sampler is constructed from 1-inch diameter PVC well materials, containing polyethylene tubing threaded through PVC disks. Self-expanding annular and internal bentonite seals were developed which isolate discrete sampling zones. The DMLS design allows customization of sampling and isolation zone lengths to suit site-specific goals. Installation of the DMLS is achieved using a temporary, expendable-tipped casting driven by direct push methods. This technique minimizes mobilization costs, site and soil column disturbances, and allows rapid installation in areas of limited overhead clearance. Successful pilot installations of the DMLS prototype have been made at a former manufactured gas plant (MGP) site and a diesel fuel spill site. Analysis of groundwater samples from these sites, using relative compound distributions and contaminant concentration profiling, confirmed that representative discrete samples were collected. This design provides both economical and versatile groundwater monitoring during all phases of site assessment and remediation

Discrete structures in F-theory compactifications

Energy Technology Data Exchange (ETDEWEB)

Till, Oskar

2016-05-04

In this thesis we study global properties of F-theory compactifications on elliptically and genus-one fibered Calabi-Yau varieties. This is motivated by phenomenological considerations as well as by the need for a deeper understanding of the set of consistent F-theory vacua. The global geometric features arise from discrete and arithmetic structures in the torus fiber and can be studied in detail for fibrations over generic bases. In the case of elliptic fibrations we study the role of the torsion subgroup of the Mordell-Weil group of sections in four dimensional compactifications. We show how the existence of a torsional section restricts the admissible matter representations in the theory. This is shown to be equivalent to inducing a non-trivial fundamental group of the gauge group. Compactifying F-theory on genus-one fibrations with multisections gives rise to discrete selection rules. In field theory the discrete symmetry is a broken U(1) symmetry. In the geometry the higgsing corresponds to a conifold transition. We explain in detail the origin of the discrete symmetry from two different M-theory phases and put the result into the context of torsion homology. Finally we systematically construct consistent gauge fluxes on genus-one fibrations and show that these induce an anomaly free chiral spectrum.

Geometric phases in discrete dynamical systems

Energy Technology Data Exchange (ETDEWEB)

Cartwright, Julyan H.E., E-mail: julyan.cartwright@csic.es [Instituto Andaluz de Ciencias de la Tierra, CSIC–Universidad de Granada, E-18100 Armilla, Granada (Spain); Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada (Spain); Piro, Nicolas, E-mail: nicolas.piro@epfl.ch [École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne (Switzerland); Piro, Oreste, E-mail: piro@imedea.uib-csic.es [Departamento de Física, Universitat de les Illes Balears, E-07122 Palma de Mallorca (Spain); Tuval, Idan, E-mail: ituval@imedea.uib-csic.es [Mediterranean Institute for Advanced Studies, CSIC–Universitat de les Illes Balears, E-07190 Mallorca (Spain)

2016-10-14

In order to study the behaviour of discrete dynamical systems under adiabatic cyclic variations of their parameters, we consider discrete versions of adiabatically-rotated rotators. Parallelling the studies in continuous systems, we generalize the concept of geometric phase to discrete dynamics and investigate its presence in these rotators. For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number of the system. For the discrete version of the rotated rotator considered by Berry, the rotated standard map, we further explore this connection as well as the role of the geometric phase at the onset of chaos. Further into the chaotic regime, we show that the geometric phase is also related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent. - Highlights: • We extend the concept of geometric phase to maps. • For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number. • For the rotated standard map, we explore the role of the geometric phase at the onset of chaos. • We show that the geometric phase is related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent.

Mapping of uncertainty relations between continuous and discrete time.

Science.gov (United States)

Chiuchiù, Davide; Pigolotti, Simone

2018-03-01

Lower bounds on fluctuations of thermodynamic currents depend on the nature of time, discrete or continuous. To understand the physical reason, we compare current fluctuations in discrete-time Markov chains and continuous-time master equations. We prove that current fluctuations in the master equations are always more likely, due to random timings of transitions. This comparison leads to a mapping of the moments of a current between discrete and continuous time. We exploit this mapping to obtain uncertainty bounds. Our results reduce the quests for uncertainty bounds in discrete and continuous time to a single problem.

Discrete stochastic analogs of Erlang epidemic models.

Science.gov (United States)

Getz, Wayne M; Dougherty, Eric R

2018-12-01

Erlang differential equation models of epidemic processes provide more realistic disease-class transition dynamics from susceptible (S) to exposed (E) to infectious (I) and removed (R) categories than the ubiquitous SEIR model. The latter is itself is at one end of the spectrum of Erlang SE[Formula: see text]I[Formula: see text]R models with [Formula: see text] concatenated E compartments and [Formula: see text] concatenated I compartments. Discrete-time models, however, are computationally much simpler to simulate and fit to epidemic outbreak data than continuous-time differential equations, and are also much more readily extended to include demographic and other types of stochasticity. Here we formulate discrete-time deterministic analogs of the Erlang models, and their stochastic extension, based on a time-to-go distributional principle. Depending on which distributions are used (e.g. discretized Erlang, Gamma, Beta, or Uniform distributions), we demonstrate that our formulation represents both a discretization of Erlang epidemic models and generalizations thereof. We consider the challenges of fitting SE[Formula: see text]I[Formula: see text]R models and our discrete-time analog to data (the recent outbreak of Ebola in Liberia). We demonstrate that the latter performs much better than the former; although confining fits to strict SEIR formulations reduces the numerical challenges, but sacrifices best-fit likelihood scores by at least 7%.

Integrable semi-discretizations of the reduced Ostrovsky equation

International Nuclear Information System (INIS)

Feng, Bao-Feng; Maruno, Ken-ichi; Ohta, Yasuhiro

2015-01-01

Based on our previous work on the reduced Ostrovsky equation (J. Phys. A: Math. Theor. 45 355203), we construct its integrable semi-discretizations. Since the reduced Ostrovsky equation admits two alternative representations, one being its original form, the other the differentiated form (the short wave limit of the Degasperis–Procesi equation) two semi-discrete analogues of the reduced Ostrovsky equation are constructed possessing the same N-loop soliton solution. The relationship between these two versions of semi-discretizations is also clarified. (paper)

An algebra of discrete event processes

Science.gov (United States)

Heymann, Michael; Meyer, George

1991-01-01

This report deals with an algebraic framework for modeling and control of discrete event processes. The report consists of two parts. The first part is introductory, and consists of a tutorial survey of the theory of concurrency in the spirit of Hoare's CSP, and an examination of the suitability of such an algebraic framework for dealing with various aspects of discrete event control. To this end a new concurrency operator is introduced and it is shown how the resulting framework can be applied. It is further shown that a suitable theory that deals with the new concurrency operator must be developed. In the second part of the report the formal algebra of discrete event control is developed. At the present time the second part of the report is still an incomplete and occasionally tentative working paper.

The discretized Schroedinger equation and simple models for semiconductor quantum wells

International Nuclear Information System (INIS)

Boykin, Timothy B; Klimeck, Gerhard

2004-01-01

The discretized Schroedinger equation is one of the most commonly employed methods for solving one-dimensional quantum mechanics problems on the computer, yet many of its characteristics remain poorly understood. The differences with the continuous Schroedinger equation are generally viewed as shortcomings of the discrete model and are typically described in purely mathematical terms. This is unfortunate since the discretized equation is more productively viewed from the perspective of solid-state physics, which naturally links the discrete model to realistic semiconductor quantum wells and nanoelectronic devices. While the relationship between the discrete model and a one-dimensional tight-binding model has been known for some time, the fact that the discrete Schroedinger equation admits analytic solutions for quantum wells has gone unnoted. Here we present a solution to this new analytically solvable problem. We show that the differences between the discrete and continuous models are due to their fundamentally different bandstructures, and present evidence for our belief that the discrete model is the more physically reasonable one

On the Importance of Both Dimensional and Discrete Models of Emotion

Directory of Open Access Journals (Sweden)

Eddie Harmon-Jones

2017-09-01

Full Text Available We review research on the structure and functions of emotions that has benefitted from a serious consideration of both discrete and dimensional perspectives on emotion. To illustrate this point, we review research that demonstrates: (1 how affective valence within discrete emotions differs as a function of individuals and situations, and how these differences relate to various functions; (2 that anger (and other emotional states should be considered as a discrete emotion but there are dimensions around and within anger; (3 that similarities exist between approach-related positive and negative discrete emotions and they have unique motivational functions; (4 that discrete emotions and broad dimensions of emotions both have unique functions; and (5 evidence that a “new” discrete emotion with discrete functions exists within a broader emotion family. We hope that this consideration of both discrete and dimensional perspectives on emotion will assist in understanding the functions of emotions.

Comparison of discrete Hodge star operators for surfaces

KAUST Repository

Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi

2016-01-01

We investigate the performance of various discrete Hodge star operators for discrete exterior calculus (DEC) using circumcentric and barycentric dual meshes. The performance is evaluated through the DEC solution of Darcy and incompressible Navier

Friction stress effects on mode I crack growth predictions

NARCIS (Netherlands)

Chen, Q.; Deshpande, V.S.; Giessen, E. van der; Needleman, A.

2003-01-01

The effect of a lattice friction stress on the monotonic growth of a plane strain mode I crack under small-scale yielding conditions is analyzed using discrete dislocation plasticity. When the friction stress is increased from zero to half the dislocation nucleation stress, the crack tip stress

Properties of wavelet discretization of Black-Scholes equation

Science.gov (United States)

Finěk, Václav

2017-07-01

Using wavelet methods, the continuous problem is transformed into a well-conditioned discrete problem. And once a non-symmetric problem is given, squaring yields a symmetric positive definite formulation. However squaring usually makes the condition number of discrete problems substantially worse. This note is concerned with a wavelet based numerical solution of the Black-Scholes equation for pricing European options. We show here that in wavelet coordinates a symmetric part of the discretized equation dominates over an unsymmetric part in the standard economic environment with low interest rates. It provides some justification for using a fractional step method with implicit treatment of the symmetric part of the weak form of the Black-Scholes operator and with explicit treatment of its unsymmetric part. Then a well-conditioned discrete problem is obtained.

Discrete symmetries and solar neutrino mixing

Energy Technology Data Exchange (ETDEWEB)

Kapetanakis, D.; Mayr, P.; Nilles, H.P. (Physik Dept., Technische Univ. Muenchen, Garching (Germany) Max-Planck-Inst. fuer Physik, Werner-Heisenberg-Inst., Muenchen (Germany))

1992-05-21

We study the question of resonant solar neutrino mixing in the framework of the supersymmetric extension of the standard model. Discrete symmetries that are consistent with solar neutrino mixing and proton stability are classified. In the minimal model they are shown to lead to two distinct patterns of allowed dimension-four operators. Imposing anomaly freedom, only three different discrete Z{sub N}-symmetries (with N=2, 3, 6) are found to be phenomenologically acceptable. (orig.).

Discrete symmetries and solar neutrino mixing

International Nuclear Information System (INIS)

Kapetanakis, D.; Mayr, P.; Nilles, H.P.

1992-01-01

We study the question of resonant solar neutrino mixing in the framework of the supersymmetric extension of the standard model. Discrete symmetries that are consistent with solar neutrino mixing and proton stability are classified. In the minimal model they are shown to lead to two distinct patterns of allowed dimension-four operators. Imposing anomaly freedom, only three different discrete Z N -symmetries (with N=2, 3, 6) are found to be phenomenologically acceptable. (orig.)

Discrete approximations to vector spin models

Energy Technology Data Exchange (ETDEWEB)

Van Enter, Aernout C D [University of Groningen, Johann Bernoulli Institute of Mathematics and Computing Science, Postbus 407, 9700 AK Groningen (Netherlands); Kuelske, Christof [Ruhr-Universitaet Bochum, Fakultaet fuer Mathematik, D44801 Bochum (Germany); Opoku, Alex A, E-mail: A.C.D.v.Enter@math.rug.nl, E-mail: Christof.Kuelske@ruhr-uni-bochum.de, E-mail: opoku@math.leidenuniv.nl [Mathematisch Instituut, Universiteit Leiden, Postbus 9512, 2300 RA, Leiden (Netherlands)

2011-11-25

We strengthen a result from Kuelske and Opoku (2008 Electron. J. Probab. 13 1307-44) on the existence of effective interactions for discretized continuous-spin models. We also point out that such an interaction cannot exist at very low temperatures. Moreover, we compare two ways of discretizing continuous-spin models, and show that except for very low temperatures, they behave similarly in two dimensions. We also discuss some possibilities in higher dimensions. (paper)

Discrete approximations to vector spin models

International Nuclear Information System (INIS)

Van Enter, Aernout C D; Külske, Christof; Opoku, Alex A

2011-01-01

We strengthen a result from Külske and Opoku (2008 Electron. J. Probab. 13 1307–44) on the existence of effective interactions for discretized continuous-spin models. We also point out that such an interaction cannot exist at very low temperatures. Moreover, we compare two ways of discretizing continuous-spin models, and show that except for very low temperatures, they behave similarly in two dimensions. We also discuss some possibilities in higher dimensions. (paper)

Geometry and Hamiltonian mechanics on discrete spaces

NARCIS (Netherlands)

Talasila, V.; Clemente-Gallardo, J.; Schaft, A.J. van der

2004-01-01

Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a ‘smooth’ model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to

On localization in the discrete nonlinear Schrödinger equation

DEFF Research Database (Denmark)

Bang, O.; Juul Rasmussen, J.; Christiansen, P.L.

1993-01-01

For some values of the grid resolution, depending on the nonlinearity, the discrete nonlinear Schrodinger equation with arbitrary power nonlinearity can be approximated by the corresponding continuum version of the equation. When the discretization becomes too coarse, the discrete equation exhibits...

Monte Carlo simulation of continuous-space crystal growth

International Nuclear Information System (INIS)

Dodson, B.W.; Taylor, P.A.

1986-01-01

We describe a method, based on Monte Carlo techniques, of simulating the atomic growth of crystals without the discrete lattice space assumed by conventional Monte Carlo growth simulations. Since no lattice space is assumed, problems involving epitaxial growth, heteroepitaxy, phonon-driven mechanisms, surface reconstruction, and many other phenomena incompatible with the lattice-space approximation can be studied. Also, use of the Monte Carlo method circumvents to some extent the extreme limitations on simulated timescale inherent in crystal-growth techniques which might be proposed using molecular dynamics. The implementation of the new method is illustrated by studying the growth of strained-layer superlattice (SLS) interfaces in two-dimensional Lennard-Jones atomic systems. Despite the extreme simplicity of such systems, the qualitative features of SLS growth seen here are similar to those observed experimentally in real semiconductor systems

Diakoptical reliability analysis of transistorized systems

International Nuclear Information System (INIS)

Kontoleon, J.M.; Lynn, J.W.; Green, A.E.

1975-01-01

Limitations both on high-speed core availability and computation time required for assessing the reliability of large-sized and complex electronic systems, such as used for the protection of nuclear reactors, are very serious restrictions which continuously confront the reliability analyst. Diakoptic methods simplify the solution of the electrical-network problem by subdividing a given network into a number of independent subnetworks and then interconnecting the solutions of these smaller parts by a systematic process involving transformations based on connection-matrix elements associated with the interconnecting links. However, the interconnection process is very complicated and it may be used only if the original system has been cut in such a manner that a relation can be established between the constraints appearing at both sides of the cut. Also, in dealing with transistorized systems, one of the difficulties encountered is that of modelling adequately their performance under various operating conditions, since their parameters are strongly affected by the imposed voltage and current levels. In this paper a new interconnection approach is presented which may be of use in the reliability analysis of large-sized transistorized systems. This is based on the partial optimization of the subdivisions of the torn network as well as on the optimization of the torn paths. The solution of the subdivisions is based on the principles of algebraic topology, with an algebraic structure relating the physical variables in a topological structure which defines the interconnection of the discrete elements. Transistors, and other nonlinear devices, are modelled using their actual characteristics, under normal and abnormal operating conditions. Use of so-called k factors is made to facilitate accounting for use of electrical stresses. The approach is demonstrated by way of an example. (author)

On some properties of the discrete Lyapunov exponent

International Nuclear Information System (INIS)

Amigo, Jose M.; Kocarev, Ljupco; Szczepanski, Janusz

2008-01-01

One of the possible by-products of discrete chaos is the application of its tools, in particular of the discrete Lyapunov exponent, to cryptography. In this Letter we explore this question in a very general setting

Discrete-time inverse optimal control for nonlinear systems

CERN Document Server

Sanchez, Edgar N

2013-01-01

Discrete-Time Inverse Optimal Control for Nonlinear Systems proposes a novel inverse optimal control scheme for stabilization and trajectory tracking of discrete-time nonlinear systems. This avoids the need to solve the associated Hamilton-Jacobi-Bellman equation and minimizes a cost functional, resulting in a more efficient controller. Design More Efficient Controllers for Stabilization and Trajectory Tracking of Discrete-Time Nonlinear Systems The book presents two approaches for controller synthesis: the first based on passivity theory and the second on a control Lyapunov function (CLF). Th

Multilevel Fast Multipole Method for Higher Order Discretizations

DEFF Research Database (Denmark)

Borries, Oscar Peter; Meincke, Peter; Jorgensen, Erik

2014-01-01

The multi-level fast multipole method (MLFMM) for a higher order (HO) discretization is demonstrated on high-frequency (HF) problems, illustrating for the first time how an efficient MLFMM for HO can be achieved even for very large groups. Applying several novel ideas, beneficial to both lower...... order and higher order discretizations, results from a low-memory, high-speed MLFMM implementation of a HO hierarchical discretization are shown. These results challenge the general view that the benefits of HO and HF-MLFMM cannot be combined....

Discrete quantum geometries and their effective dimension

International Nuclear Information System (INIS)

Thuerigen, Johannes

2015-01-01

In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing issue is then how the smooth geometries of general relativity, expressed in terms of suitable geometric observables, arise from such discrete quantum geometries in some semiclassical and continuum limit. In this thesis I tackle the question of suitable observables focusing on the effective dimension of discrete quantum geometries. For this purpose I give a purely combinatorial description of the discrete structures which these geometries have support on. As a side topic, this allows to present an extension of group field theory to cover the combinatorially larger kinematical state space of loop quantum gravity. Moreover, I introduce a discrete calculus for fields on such fundamentally discrete geometries with a particular focus on the Laplacian. This permits to define the effective-dimension observables for quantum geometries. Analysing various classes of quantum geometries, I find as a general result that the spectral dimension is more sensitive to the underlying combinatorial structure than to the details of the additional geometric data thereon. Semiclassical states in loop quantum gravity approximate the classical geometries they are peaking on rather well and there are no indications for stronger quantum effects. On the other hand, in the context of a more general model of states which are superposition over a large number of complexes, based on analytic solutions, there is a flow of the spectral dimension from the topological dimension d on low energy scales to a real number between 0 and d on high energy scales. In the particular case of 1 these results allow to understand the quantum geometry as effectively fractal.

New non-structured discretizations for fluid flows with reinforced incompressibility

International Nuclear Information System (INIS)

Heib, S.

2003-01-01

This work deals with the discretization of Stokes and Navier-Stokes equations modeling the flow of incompressible fluids on 2-D or 3-D non-structured meshes. Triangles and tetrahedrons are used for 2-D and 3-D meshes, respectively. The developments and calculations are performed with the code Priceles (fast CEA-EdF industrial platform for large Eddy simulation). This code allows to perform simulations both on structured and non-structured meshes. A finite-volume resolution method is used: a finite difference volume (FDV) method is used for the structured meshes and a finite element volume (FEV) method is used for the non-structured meshes. The finite element used in the beginning of this work has several defects. Starting from this situation, the discretization is improved by adding modifications to this element and the new elements introduced are analyzed theoretically. In parallel to these analyses, the new discretizations are implemented in order to test them numerically and to confirm the theoretical analyses. The first chapter presents the physical and mathematical modeling used in this work. The second chapter treats of the discretization of Stokes equations and presents the FEV resolution method. Chapter 3 presents a first attempt of improvement of this finite element and leads to the proposal of a new element which is presented in details. The problem encountered with the new discretization leads to a modification presented in chapter 4. This new discretization gives all the expected convergence results and sometimes shows super-convergence properties. Chapter 5 deals with the study and discretization of the Navier-Stokes equations. The study of the filtered Navier-Stokes equations, used for large Eddy simulations, requires to give a particular attention to the discretization of the diffusive terms. Then, the convective terms are considered. The effects of the convective terms in the initial discretization and in the improved method are compared. The use of

Discrete choice experiments of pharmacy services: a systematic review.

Science.gov (United States)

Vass, Caroline; Gray, Ewan; Payne, Katherine

2016-06-01

Background Two previous systematic reviews have summarised the application of discrete choice experiments to value preferences for pharmacy services. These reviews identified a total of twelve studies and described how discrete choice experiments have been used to value pharmacy services but did not describe or discuss the application of methods used in the design or analysis. Aims (1) To update the most recent systematic review and critically appraise current discrete choice experiments of pharmacy services in line with published reporting criteria and; (2) To provide an overview of key methodological developments in the design and analysis of discrete choice experiments. Methods The review used a comprehensive strategy to identify eligible studies (published between 1990 and 2015) by searching electronic databases for key terms related to discrete choice and best-worst scaling (BWS) experiments. All healthcare choice experiments were then hand-searched for key terms relating to pharmacy. Data were extracted using a published checklist. Results A total of 17 discrete choice experiments eliciting preferences for pharmacy services were identified for inclusion in the review. No BWS studies were identified. The studies elicited preferences from a variety of populations (pharmacists, patients, students) for a range of pharmacy services. Most studies were from a United Kingdom setting, although examples from Europe, Australia and North America were also identified. Discrete choice experiments for pharmacy services tended to include more attributes than non-pharmacy choice experiments. Few studies reported the use of qualitative research methods in the design and interpretation of the experiments (n = 9) or use of new methods of analysis to identify and quantify preference and scale heterogeneity (n = 4). No studies reported the use of Bayesian methods in their experimental design. Conclusion Incorporating more sophisticated methods in the design of pharmacy

Reliability engineering

International Nuclear Information System (INIS)

Lee, Chi Woo; Kim, Sun Jin; Lee, Seung Woo; Jeong, Sang Yeong

1993-08-01

This book start what is reliability? such as origin of reliability problems, definition of reliability and reliability and use of reliability. It also deals with probability and calculation of reliability, reliability function and failure rate, probability distribution of reliability, assumption of MTBF, process of probability distribution, down time, maintainability and availability, break down maintenance and preventive maintenance design of reliability, design of reliability for prediction and statistics, reliability test, reliability data and design and management of reliability.

Discrimination between discrete and continuum scattering from the sub-seafloor.

Science.gov (United States)

Holland, Charles W; Steininger, Gavin; Dosso, Stan E

2015-08-01

There is growing evidence that seabed scattering is often dominated by heterogeneities within the sediment volume as opposed to seafloor roughness. From a theoretical viewpoint, sediment volume heterogeneities can be described either by a fluctuation continuum or by discrete particles. In at-sea experiments, heterogeneity characteristics generally are not known a priori. Thus, an uninformed model selection is generally made, i.e., the researcher must arbitrarily select either a discrete or continuum model. It is shown here that it is possible to (acoustically) discriminate between continuum and discrete heterogeneities in some instances. For example, when the spectral exponent γ3>4, the volume scattering cannot be described by discrete particles. Conversely, when γ3≤2, the heterogeneities likely arise from discrete particles. Furthermore, in the range 2discrete vs continuum heterogeneities via acoustic remote sensing may lead to improved observations and concomitant increased understanding of the marine benthic environment.

Discrete-time optimal control and games on large intervals

CERN Document Server

Zaslavski, Alexander J

2017-01-01

Devoted to the structure of approximate solutions of discrete-time optimal control problems and approximate solutions of dynamic discrete-time two-player zero-sum games, this book presents results on properties of approximate solutions in an interval that is independent lengthwise, for all sufficiently large intervals. Results concerning the so-called turnpike property of optimal control problems and zero-sum games in the regions close to the endpoints of the time intervals are the main focus of this book. The description of the structure of approximate solutions on sufficiently large intervals and its stability will interest graduate students and mathematicians in optimal control and game theory, engineering, and economics. This book begins with a brief overview and moves on to analyze the structure of approximate solutions of autonomous nonconcave discrete-time optimal control Lagrange problems.Next the structures of approximate solutions of autonomous discrete-time optimal control problems that are discret...

A Discrete Monetary Economic Growth Model with the MIU Approach

Directory of Open Access Journals (Sweden)

Wei-Bin Zhang

2008-01-01

Full Text Available This paper proposes an alternative approach to economic growth with money. The production side is the same as the Solow model, the Ramsey model, and the Tobin model. But we deal with behavior of consumers differently from the traditional approaches. The model is influenced by the money-in-the-utility (MIU approach in monetary economics. It provides a mechanism of endogenous saving which the Solow model lacks and avoids the assumption of adding up utility over a period of time upon which the Ramsey approach is based.

A systematic review of the reliability and validity of discrete choice experiments in valuing non-market environmental goods

DEFF Research Database (Denmark)

Rokotonarivo, Sarobidy; Schaafsma, Marije; Hockley, Neal

2016-01-01

reliability measures. DCE results were generally consistent with those of other stated preference techniques (convergent validity), but hypothetical bias was common. Evidence supporting theoretical validity (consistency with assumptions of rational choice theory) was limited. In content validity tests, 2...

Discrete Bose-Einstein spectra

International Nuclear Information System (INIS)

Vlad, Valentin I.; Ionescu-Pallas, Nicholas

2001-03-01

The Bose-Einstein energy spectrum of a quantum gas, confined in a rigid cubic box, is shown to become discrete and strongly dependent on the box geometry (size L), temperature, T and atomic mass number, A at , in the region of small γ=A at TV 1/3 . This behavior is the consequence of the random state degeneracy in the box. Furthermore, we demonstrate that the total energy does not obey the conventional law any longer, but a new law, which depends on γ and on the quantum gas fugacity. This energy law imposes a faster decrease to zero than it is classically expected, for γ→0. The lighter the gas atoms, the higher the temperatures or the box size, for the same effects in the discrete Bose-Einstein regime. (author)

Nonlinear integrodifferential equations as discrete systems

Science.gov (United States)

Tamizhmani, K. M.; Satsuma, J.; Grammaticos, B.; Ramani, A.

1999-06-01

We analyse a class of integrodifferential equations of the `intermediate long wave' (ILW) type. We show that these equations can be formally interpreted as discrete, differential-difference systems. This allows us to link equations of this type with previous results of ours involving differential-delay equations and, on the basis of this, propose new integrable equations of ILW type. Finally, we extend this approach to pure difference equations and propose ILW forms for the discrete lattice KdV equation.

Distinct timing mechanisms produce discrete and continuous movements.

Directory of Open Access Journals (Sweden)

Raoul Huys

2008-04-01

Full Text Available The differentiation of discrete and continuous movement is one of the pillars of motor behavior classification. Discrete movements have a definite beginning and end, whereas continuous movements do not have such discriminable end points. In the past decade there has been vigorous debate whether this classification implies different control processes. This debate up until the present has been empirically based. Here, we present an unambiguous non-empirical classification based on theorems in dynamical system theory that sets discrete and continuous movements apart. Through computational simulations of representative modes of each class and topological analysis of the flow in state space, we show that distinct control mechanisms underwrite discrete and fast rhythmic movements. In particular, we demonstrate that discrete movements require a time keeper while fast rhythmic movements do not. We validate our computational findings experimentally using a behavioral paradigm in which human participants performed finger flexion-extension movements at various movement paces and under different instructions. Our results demonstrate that the human motor system employs different timing control mechanisms (presumably via differential recruitment of neural subsystems to accomplish varying behavioral functions such as speed constraints.

String constraints on discrete symmetries in MSSM type II quivers

Energy Technology Data Exchange (ETDEWEB)

Anastasopoulos, Pascal [Technische Univ. Wien (Austria). Inst. fur Theor. Phys.; Cvetic, Mirjam [Univ. of Pennsylvania, Philadelphia PA (United States). Dept. of Physics and Astronomy; Univ. of Maribor (Slovenia). Center for Applied Mathematics and Theoretical Physics; Richter, Robert [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Vaudrevange, Patrick K.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2012-11-15

We study the presence of discrete gauge symmetries in D-brane semirealistic compactifications. After establishing the constraints on the transformation behaviour of the chiral matter for the presence of a discrete gauge symmetry we perform a systematic search for discrete gauge symmetries within semi-realistic D-brane realizations, based on four D-brane stacks, of the MSSM and the MSSM with three right-handed neutrinos. The systematic search reveals that Proton hexality, a discrete symmetry which ensures the absence of R-parity violating terms as well as the absence of dangerous dimension 5 proton decay operators, is only rarely realized. Moreover, none of the semi-realistic local D-brane configurations exhibit any family dependent discrete gauge symmetry.

Modeling discrete time-to-event data

CERN Document Server

Tutz, Gerhard

2016-01-01

This book focuses on statistical methods for the analysis of discrete failure times. Failure time analysis is one of the most important fields in statistical research, with applications affecting a wide range of disciplines, in particular, demography, econometrics, epidemiology and clinical research. Although there are a large variety of statistical methods for failure time analysis, many techniques are designed for failure times that are measured on a continuous scale. In empirical studies, however, failure times are often discrete, either because they have been measured in intervals (e.g., quarterly or yearly) or because they have been rounded or grouped. The book covers well-established methods like life-table analysis and discrete hazard regression models, but also introduces state-of-the art techniques for model evaluation, nonparametric estimation and variable selection. Throughout, the methods are illustrated by real life applications, and relationships to survival analysis in continuous time are expla...

An exact and consistent adjoint method for high-fidelity discretization of the compressible flow equations

Science.gov (United States)

Subramanian, Ramanathan Vishnampet Ganapathi

, with finite-difference spatial operators for the adjoint system. Its computational cost only modestly exceeds that of the flow equations. We confirm that its accuracy is limited only by computing precision, and we demonstrate it on the aeroacoustic control of a mixing layer with a challengingly broad range of turbulence scales. For comparison, the error from a corresponding discretization of the continuous-adjoint equations is quantified to potentially explain its limited success in past efforts to control jet noise. The differences are illuminating: the continuous-adjoint is shown to suffer from exponential error growth in (reverse) time even for the best-resolved largest turbulence scales. Though the gradient from our fully discrete adjoint is formally exact, it does include sensitivity to numerical solutions that are only an artifact of the discretization. These are typically saw-tooth type features, such as seen in under-resolved numerical simulations. Since these have no physical analog, for physical analysis or design of realistic actuators, such solutions are in a sense spurious. This has been addressed without sacrificing accuracy by redesigning the basic discretization to be dual-consistent, for which the discrete-adjoint is consistent with the adjoint of the continuous system, and thus, free from spurious numerical sensitivity modes. We extend our exact discrete-adjoint to a spatially dual-consistent discretization of the compressible flow equations and demonstrate its practical application for aeroacoustic control of a Mach 1.3 turbulent jet. The formulation admits a broad class of finite-difference schemes that satisfy a summation by-parts rule, and extends to multi-block curvilinear grids for efficient handling of complex geometries. The formulation is developed for several boundary conditions commonly used in simulation of free-shear and wall-bounded flows. In addition, the proposed discretization leads to superconvergent approximations of functionals

Image Retrieval Algorithm Based on Discrete Fractional Transforms

Science.gov (United States)

Jindal, Neeru; Singh, Kulbir

2013-06-01

The discrete fractional transforms is a signal processing tool which suggests computational algorithms and solutions to various sophisticated applications. In this paper, a new technique to retrieve the encrypted and scrambled image based on discrete fractional transforms has been proposed. Two-dimensional image was encrypted using discrete fractional transforms with three fractional orders and two random phase masks placed in the two intermediate planes. The significant feature of discrete fractional transforms benefits from its extra degree of freedom that is provided by its fractional orders. Security strength was enhanced (1024!)4 times by scrambling the encrypted image. In decryption process, image retrieval is sensitive for both correct fractional order keys and scrambling algorithm. The proposed approach make the brute force attack infeasible. Mean square error and relative error are the recital parameters to verify validity of proposed method.

Design for a Crane Metallic Structure Based on Imperialist Competitive Algorithm and Inverse Reliability Strategy

Science.gov (United States)

Fan, Xiao-Ning; Zhi, Bo

2017-07-01

Uncertainties in parameters such as materials, loading, and geometry are inevitable in designing metallic structures for cranes. When considering these uncertainty factors, reliability-based design optimization (RBDO) offers a more reasonable design approach. However, existing RBDO methods for crane metallic structures are prone to low convergence speed and high computational cost. A unilevel RBDO method, combining a discrete imperialist competitive algorithm with an inverse reliability strategy based on the performance measure approach, is developed. Application of the imperialist competitive algorithm at the optimization level significantly improves the convergence speed of this RBDO method. At the reliability analysis level, the inverse reliability strategy is used to determine the feasibility of each probabilistic constraint at each design point by calculating its α-percentile performance, thereby avoiding convergence failure, calculation error, and disproportionate computational effort encountered using conventional moment and simulation methods. Application of the RBDO method to an actual crane structure shows that the developed RBDO realizes a design with the best tradeoff between economy and safety together with about one-third of the convergence speed and the computational cost of the existing method. This paper provides a scientific and effective design approach for the design of metallic structures of cranes.

An extended discrete gradient formula for oscillatory Hamiltonian systems

International Nuclear Information System (INIS)

Liu Kai; Shi Wei; Wu Xinyuan

2013-01-01

In this paper, incorporating the idea of the discrete gradient method into the extended Runge–Kutta–Nyström integrator, we derive and analyze an extended discrete gradient formula for the oscillatory Hamiltonian system with the Hamiltonian H(p,q)= 1/2 p T p+ 1/2 q T Mq+U(q), where q:R→R d represents generalized positions, p:R→R d represents generalized momenta and M is an element of R dxd is a symmetric and positive semi-definite matrix. The solution of this system is a nonlinear oscillator. Basically, many nonlinear oscillatory mechanical systems with a partitioned Hamiltonian function lend themselves to this approach. The extended discrete gradient formula presented in this paper exactly preserves the energy H(p, q). We derive some properties of the new formula. The convergence is analyzed for the implicit schemes based on the discrete gradient formula, and it turns out that the convergence of the implicit schemes based on the extended discrete gradient formula is independent of ‖M‖, which is a significant property for the oscillatory Hamiltonian system. Thus, it transpires that a larger step size can be chosen for the new energy-preserving schemes than that for the traditional discrete gradient methods when applied to the oscillatory Hamiltonian system. Illustrative examples show the competence and efficiency of the new schemes in comparison with the traditional discrete gradient methods in the scientific literature. (paper)

Galerkin v. discrete-optimal projection in nonlinear model reduction

Energy Technology Data Exchange (ETDEWEB)

Carlberg, Kevin Thomas [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Barone, Matthew Franklin [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Antil, Harbir [George Mason Univ., Fairfax, VA (United States)

2015-04-01

Discrete-optimal model-reduction techniques such as the Gauss{Newton with Approximated Tensors (GNAT) method have shown promise, as they have generated stable, accurate solutions for large-scale turbulent, compressible ow problems where standard Galerkin techniques have failed. However, there has been limited comparative analysis of the two approaches. This is due in part to difficulties arising from the fact that Galerkin techniques perform projection at the time-continuous level, while discrete-optimal techniques do so at the time-discrete level. This work provides a detailed theoretical and experimental comparison of the two techniques for two common classes of time integrators: linear multistep schemes and Runge{Kutta schemes. We present a number of new ndings, including conditions under which the discrete-optimal ROM has a time-continuous representation, conditions under which the two techniques are equivalent, and time-discrete error bounds for the two approaches. Perhaps most surprisingly, we demonstrate both theoretically and experimentally that decreasing the time step does not necessarily decrease the error for the discrete-optimal ROM; instead, the time step should be `matched' to the spectral content of the reduced basis. In numerical experiments carried out on a turbulent compressible- ow problem with over one million unknowns, we show that increasing the time step to an intermediate value decreases both the error and the simulation time of the discrete-optimal reduced-order model by an order of magnitude.

Discrete inverse scattering theory and the continuum limit

International Nuclear Information System (INIS)

Berryman, J.G.; Greene, R.R.

1978-01-01

The class of satisfactory difference approximations for the Schroedinger equation in discrete inverse scattering theory is shown smaller than previously supposed. A fast algorithm (analogous to the Levinson algorithm for Toeplitz matrices) is found for solving the discrete inverse problem. (Auth.)

Supporting scalable Bayesian networks using configurable discretizer actuators

CSIR Research Space (South Africa)

Osunmakinde, I

2009-04-01

Full Text Available The authors propose a generalized model with configurable discretizer actuators as a solution to the problem of the discretization of massive numerical datasets. Their solution is based on a concurrent distribution of the actuators and uses dynamic...

Demonstrating the Safety and Reliability of a New System or Spacecraft: Incorporating Analyses and Reviews of the Design and Processing in Determining the Number of Tests to be Conducted

Science.gov (United States)

Vesely, William E.; Colon, Alfredo E.

2010-01-01

Design Safety/Reliability is associated with the probability of no failure-causing faults existing in a design. Confidence in the non-existence of failure-causing faults is increased by performing tests with no failure. Reliability-Growth testing requirements are based on initial assurance and fault detection probability. Using binomial tables generally gives too many required tests compared to reliability-growth requirements. Reliability-Growth testing requirements are based on reliability principles and factors and should be used.

Beta oscillations define discrete perceptual cycles in the somatosensory domain.

Science.gov (United States)

Baumgarten, Thomas J; Schnitzler, Alfons; Lange, Joachim

2015-09-29

Whether seeing a movie, listening to a song, or feeling a breeze on the skin, we coherently experience these stimuli as continuous, seamless percepts. However, there are rare perceptual phenomena that argue against continuous perception but, instead, suggest discrete processing of sensory input. Empirical evidence supporting such a discrete mechanism, however, remains scarce and comes entirely from the visual domain. Here, we demonstrate compelling evidence for discrete perceptual sampling in the somatosensory domain. Using magnetoencephalography (MEG) and a tactile temporal discrimination task in humans, we find that oscillatory alpha- and low beta-band (8-20 Hz) cycles in primary somatosensory cortex represent neurophysiological correlates of discrete perceptual cycles. Our results agree with several theoretical concepts of discrete perceptual sampling and empirical evidence of perceptual cycles in the visual domain. Critically, these results show that discrete perceptual cycles are not domain-specific, and thus restricted to the visual domain, but extend to the somatosensory domain.

Switching dynamics in reaction networks induced by molecular discreteness

International Nuclear Information System (INIS)

Togashi, Yuichi; Kaneko, Kunihiko

2007-01-01

To study the fluctuations and dynamics in chemical reaction processes, stochastic differential equations based on the rate equation involving chemical concentrations are often adopted. When the number of molecules is very small, however, the discreteness in the number of molecules cannot be neglected since the number of molecules must be an integer. This discreteness can be important in biochemical reactions, where the total number of molecules is not significantly larger than the number of chemical species. To elucidate the effects of such discreteness, we study autocatalytic reaction systems comprising several chemical species through stochastic particle simulations. The generation of novel states is observed; it is caused by the extinction of some molecular species due to the discreteness in their number. We demonstrate that the reaction dynamics are switched by a single molecule, which leads to the reconstruction of the acting network structure. We also show the strong dependence of the chemical concentrations on the system size, which is caused by transitions to discreteness-induced novel states

Use Cases of Discrete Event Simulation Appliance and Research

CERN Document Server

2012-01-01

Over the last decades Discrete Event Simulation has conquered many different application areas. This trend is, on the one hand, driven by an ever wider use of this technology in different fields of science and on the other hand by an incredibly creative use of available software programs through dedicated experts. This book contains articles from scientists and experts from 10 countries. They illuminate the width of application of this technology and the quality of problems solved using Discrete Event Simulation. Practical applications of simulation dominate in the present book.   The book is aimed to researchers and students who deal in their work with Discrete Event Simulation and which want to inform them about current applications. By focusing on discrete event simulation, this book can also serve as an inspiration source for practitioners for solving specific problems during their work. Decision makers who deal with the question of the introduction of discrete event simulation for planning support and o...

Semiclassical expanding discrete space-times

International Nuclear Information System (INIS)

Cobb, W.K.; Smalley, L.L.

1981-01-01

Given the close ties between general relativity and geometry one might reasonably expect that quantum effects associated with gravitation might also be tied to the geometry of space-time, namely, to some sort of discreteness in space-time itself. In particular it is supposed that space-time consists of a discrete lattice of points rather than the usual continuum. Since astronomical evidence seems to suggest that the universe is expanding, the lattice must also expand. Some of the implications of such a model are that the proton should presently be stable, and the universe should be closed although the mechanism for closure is quantum mechanical. (author)

IDENTIFYING FRACTURE ORIGIN IN CERAMICS BY COMBINATION OF NONDESTRUCTIVE TESTING AND DISCRETE ELEMENT ANALYSIS

International Nuclear Information System (INIS)

Senapati, Rajeev; Zhang Jianmei

2010-01-01

Advanced ceramic materials have been extensively applied in aerospace, automobile and other industries. However, the reliability of the advanced ceramics is a major concern because of the brittle nature of the materials. In this paper, combination of nondestructive testing and numerical modeling Discrete Element Method is proposed to identify the fracture origin in ceramics. The nondestructive testing--laser scattering technology is first performed on the ceramic components to reveal the machining-induced damage such as cracks and the material-inherent flaws such as voids, then followed by the four point bending test. Discrete Element software package PFC 2D is used to simulate the four point bending test and try to identify where the fractures start. The numerical representation of the ceramic materials is done by generating a densely packed particle system using the specimen genesis procedure and then applying the suitable microparameters to the particle system. Simulation of four point bending test is performed on materials having no defects, materials having manufacturing-induced defects like cracks, and materials having material-inherent flaws like voids. The initiation and propagation of defects is modeled and the mean contact force on the loading ball is also plotted. The simulation prediction results are well in accordance with the nondestructive testing results.

A Low Complexity Discrete Radiosity Method

OpenAIRE

Chatelier , Pierre Yves; Malgouyres , Rémy

2006-01-01

International audience; Rather than using Monte Carlo sampling techniques or patch projections to compute radiosity, it is possible to use a discretization of a scene into voxels and perform some discrete geometry calculus to quickly compute visibility information. In such a framework , the radiosity method may be as precise as a patch-based radiosity using hemicube computation for form-factors, but it lowers the overall theoretical complexity to an O(N log N) + O(N), where the O(N) is largel...

Detecting long-term growth trends using tree rings: a critical evaluation of methods.

Science.gov (United States)

Peters, Richard L; Groenendijk, Peter; Vlam, Mart; Zuidema, Pieter A

2015-05-01

Tree-ring analysis is often used to assess long-term trends in tree growth. A variety of growth-trend detection methods (GDMs) exist to disentangle age/size trends in growth from long-term growth changes. However, these detrending methods strongly differ in approach, with possible implications for their output. Here, we critically evaluate the consistency, sensitivity, reliability and accuracy of four most widely used GDMs: conservative detrending (CD) applies mathematical functions to correct for decreasing ring widths with age; basal area correction (BAC) transforms diameter into basal area growth; regional curve standardization (RCS) detrends individual tree-ring series using average age/size trends; and size class isolation (SCI) calculates growth trends within separate size classes. First, we evaluated whether these GDMs produce consistent results applied to an empirical tree-ring data set of Melia azedarach, a tropical tree species from Thailand. Three GDMs yielded similar results - a growth decline over time - but the widely used CD method did not detect any change. Second, we assessed the sensitivity (probability of correct growth-trend detection), reliability (100% minus probability of detecting false trends) and accuracy (whether the strength of imposed trends is correctly detected) of these GDMs, by applying them to simulated growth trajectories with different imposed trends: no trend, strong trends (-6% and +6% change per decade) and weak trends (-2%, +2%). All methods except CD, showed high sensitivity, reliability and accuracy to detect strong imposed trends. However, these were considerably lower in the weak or no-trend scenarios. BAC showed good sensitivity and accuracy, but low reliability, indicating uncertainty of trend detection using this method. Our study reveals that the choice of GDM influences results of growth-trend studies. We recommend applying multiple methods when analysing trends and encourage performing sensitivity and reliability

Generalized Reduction Formula for Discrete Wigner Functions of Multiqubit Systems

Science.gov (United States)

Srinivasan, K.; Raghavan, G.

2018-03-01

Density matrices and Discrete Wigner Functions are equally valid representations of multiqubit quantum states. For density matrices, the partial trace operation is used to obtain the quantum state of subsystems, but an analogous prescription is not available for discrete Wigner Functions. Further, the discrete Wigner function corresponding to a density matrix is not unique but depends on the choice of the quantum net used for its reconstruction. In the present work, we derive a reduction formula for discrete Wigner functions of a general multiqubit state which works for arbitrary quantum nets. These results would be useful for the analysis and classification of entangled states and the study of decoherence purely in a discrete phase space setting and also in applications to quantum computing.

Modelling and real-time simulation of continuous-discrete systems in mechatronics

Energy Technology Data Exchange (ETDEWEB)

Lindow, H. [Rostocker, Magdeburg (Germany)

1996-12-31

This work presents a methodology for simulation and modelling of systems with continuous - discrete dynamics. It derives hybrid discrete event models from Lagrange`s equations of motion. This method combines continuous mechanical, electrical and thermodynamical submodels on one hand with discrete event models an the other hand into a hybrid discrete event model. This straight forward software development avoids numeric overhead.

The boundary value problem for discrete analytic functions

KAUST Repository

Skopenkov, Mikhail

2013-01-01

This paper is on further development of discrete complex analysis introduced by R.Isaacs, J.Ferrand, R.Duffin, and C.Mercat. We consider a graph lying in the complex plane and having quadrilateral faces. A function on the vertices is called discrete

Discrete symmetries and coset space dimensional reduction

International Nuclear Information System (INIS)

Kapetanakis, D.; Zoupanos, G.

1989-01-01

We consider the discrete symmetries of all the six-dimensional coset spaces and we apply them in gauge theories defined in ten dimensions which are dimensionally reduced over these homogeneous spaces. Particular emphasis is given in the consequences of the discrete symmetries on the particle content as well as on the symmetry breaking a la Hosotani of the resulting four-dimensional theory. (orig.)