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Sample records for avrami equation inadequacy

  1. Modification of the Kolmogorov-Johnson-Mehl-Avrami rate equation for non-isothermal experiments and its analytical solution

    OpenAIRE

    Farjas, Jordi; Roura, Pere

    2008-01-01

    Avrami's model describes the kinetics of phase transformation under the assumption of spatially random nucleation. In this paper we provide a quasi-exact analytical solution of Avrami's model when the transformation takes place under continuous heating. This solution has been obtained with different activation energies for both nucleation and growth rates. The relation obtained is also a solution of the so-called Kolmogorov-Johnson-Mehl-Avrami transformation rate equation. The corresponding n...

  2. Ingroup Rejection among Women: The Role of Personal Inadequacy

    Science.gov (United States)

    Cowan, Gloria; Ullman, Jodie B.

    2006-01-01

    We examined predictors and outcomes of women's hostility toward other women. Based on a projection model, we hypothesized and tested the theory via structural equation modeling that women's sense of personal inadequacy, the tendency to stereotype, and general anger would predict hostility toward women, and hostility toward women would predict…

  3. Phase transformation kinetics of Voronoi cells in space tessellation governed by the Kolmogorov–Johnson–Mehl–Avrami model

    Energy Technology Data Exchange (ETDEWEB)

    Tomellini, Massimo, E-mail: tomellini@uniroma2.it

    2017-03-26

    On the basis of the Kolmogorov–Johnson–Mehl–Avrami (KJMA) method for space tessellation the kinetics of Voronoi cell filling, by central grain growth, has been studied as a function of the cell size. This is done by solving an integral equation for which a class of solutions is obtained in closed form, where the cell-size probability density is the Gamma distribution function. The computation gives the time evolution of the mean grain size, as a function of cell volume, which is further employed for describing the grain-size probability density function. The present approach is applied to determine, analytically, the exact grain-size distribution function in 1D and the size distributions in 2D and 3D through approximation. - Highlights: • The kinetics of cell filling is determined for Poisson–Voronoi tessellation in dD. • The kinetics is obtained in closed form by solving an integral equation. • Connection between the evolution of the mean grain and the size distribution is studied. • The exact grain-size distribution function is determined, analytically, in 1D.

  4. Microstructure development in Kolmogorov, Johnson-Mehl, and Avrami nucleation and growth kinetics

    Science.gov (United States)

    Pineda, Eloi; Crespo, Daniel

    1999-08-01

    A statistical model with the ability to evaluate the microstructure developed in nucleation and growth kinetics is built in the framework of the Kolmogorov, Johnson-Mehl, and Avrami theory. A populational approach is used to compute the observed grain-size distribution. The impingement process which delays grain growth is analyzed, and the effective growth rate of each population is estimated considering the previous grain history. The proposed model is integrated for a wide range of nucleation and growth protocols, including constant nucleation, pre-existing nuclei, and intermittent nucleation with interface or diffusion-controlled grain growth. The results are compared with Monte Carlo simulations, giving quantitative agreement even in cases where previous models fail.

  5. A revisited Johnson-Mehl-Avrami-Kolmogorov model and the evolution of grain-size distributions in steel

    OpenAIRE

    Hömberg, D.; Patacchini, F. S.; Sakamoto, K.; Zimmer, J.

    2016-01-01

    The classical Johnson-Mehl-Avrami-Kolmogorov approach for nucleation and growth models of diffusive phase transitions is revisited and applied to model the growth of ferrite in multiphase steels. For the prediction of mechanical properties of such steels, a deeper knowledge of the grain structure is essential. To this end, a Fokker-Planck evolution law for the volume distribution of ferrite grains is developed and shown to exhibit a log-normally distributed solution. Numerical parameter studi...

  6. Folate inadequacy in the diet of pregnant women

    Directory of Open Access Journals (Sweden)

    Lívia de Castro Crivellenti

    2014-06-01

    Full Text Available OBJECTIVE: To estimate food and dietary folate inadequacies in the diets of adult pregnant women. METHODS: A prospective study was conducted with 103 healthy pregnant adult users of the Public Health Care System of Ribeirão Preto, São Paulo, Brazil. The present study included the 82 women with complete food intake data during pregnancy, which were collected by three 24-hour dietary recalls. Food folate (folate naturally present in foods and dietary folate (food folate plus folate from fortified wheat flour and cornmeal inadequacies were determined, using the Estimated Average Requirement as cutoff. RESULTS: The diets of 100% and 94% of the pregnant women were inadequate in food folate and dietary folate, respectively. However, fortified foods increased the medium availability of the nutrient by 87%. CONCLUSION: The large number of pregnant women consuming low-folate diets was alarming. Nationwide population studies are needed to confirm the hypothesized high prevalence of low-folate diets among pregnant women.

  7. Inadequacy representation of flamelet-based RANS model for turbulent non-premixed flame

    Science.gov (United States)

    Lee, Myoungkyu; Oliver, Todd; Moser, Robert

    2017-11-01

    Stochastic representations for model inadequacy in RANS-based models of non-premixed jet flames are developed and explored. Flamelet-based RANS models are attractive for engineering applications relative to higher-fidelity methods because of their low computational costs. However, the various assumptions inherent in such models introduce errors that can significantly affect the accuracy of computed quantities of interest. In this work, we develop an approach to represent the model inadequacy of the flamelet-based RANS model. In particular, we pose a physics-based, stochastic PDE for the triple correlation of the mixture fraction. This additional uncertain state variable is then used to construct perturbations of the PDF for the instantaneous mixture fraction, which is used to obtain an uncertain perturbation of the flame temperature. A hydrogen-air non-premixed jet flame is used to demonstrate the representation of the inadequacy of the flamelet-based RANS model. This work was supported by DARPA-EQUiPS(Enabling Quantification of Uncertainty in Physical Systems) program.

  8. Cell-size distribution and scaling in a one-dimensional Kolmogorov-Johnson-Mehl-Avrami lattice model with continuous nucleation

    Science.gov (United States)

    Néda, Zoltán; Járai-Szabó, Ferenc; Boda, Szilárd

    2017-10-01

    The Kolmogorov-Johnson-Mehl-Avrami (KJMA) growth model is considered on a one-dimensional (1D) lattice. Cells can grow with constant speed and continuously nucleate on the empty sites. We offer an alternative mean-field-like approach for describing theoretically the dynamics and derive an analytical cell-size distribution function. Our method reproduces the same scaling laws as the KJMA theory and has the advantage that it leads to a simple closed form for the cell-size distribution function. It is shown that a Weibull distribution is appropriate for describing the final cell-size distribution. The results are discussed in comparison with Monte Carlo simulation data.

  9. Daytime Sleepiness and Sleep Inadequacy as Risk Factors for Dementia

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    Angeliki Tsapanou

    2015-07-01

    Full Text Available Background/Aims: To examine the association between self-reported sleep problems and incidence of dementia in community-dwelling elderly people. Methods: 1,041 nondemented participants over 65 years old were examined longitudinally. Sleep problems were estimated using the RAND Medical Outcomes Study Sleep Scale examining sleep disturbance, snoring, sleep short of breath or with a headache, sleep adequacy, and sleep somnolence. Cox regression analysis was used to examine the association between sleep problems and risk for incident dementia. Age, gender, education, ethnicity, APOE-ε4, stroke, heart disease, hypertension, diabetes, and depression were included as covariates. Results: Over 3 years of follow-up, 966 (92.8% participants remained nondemented, while 78 (7.2% developed dementia. In unadjusted models, sleep inadequacy (‘Get the amount of sleep you need' at the initial visit was associated with increased risk of incident dementia (HR = 1.20; 95% CI 1.02-1.42; p = 0.027. Adjusting for all the covariates, increased risk of incident dementia was still associated with sleep inadequacy (HR = 1.20; 95% CI 1.01-1.42; p = 0.040, as well as with increased daytime sleepiness (‘Have trouble staying awake during the day' (HR = 1.24; 95% CI 1.00-1.54; p = 0.047. Conclusion: Our results suggest that sleep inadequacy and increased daytime sleepiness are risk factors for dementia in older adults, independent of demographic and clinical factors.

  10. Vitamin D inadequacy in Belgian postmenopausal osteoporotic women

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    Collette Julien

    2007-04-01

    Full Text Available Abstract Background Inadequate serum vitamin D [25(OHD] concentrations are associated with secondary hyperparathyroidism, increased bone turnover and bone loss, which increase fracture risk. The objective of this study is to assess the prevalence of inadequate serum 25(OHD concentrations in postmenopausal Belgian women. Opinions with regard to the definition of vitamin D deficiency and adequate vitamin D status vary widely and there are no clear international agreements on what constitute adequate concentrations of vitamin D. Methods Assessment of 25-hydroxyvitamin D [25(OHD] and parathyroid hormone was performed in 1195 Belgian postmenopausal women aged over 50 years. Main analysis has been performed in the whole study population and according to the previous use of vitamin D and calcium supplements. Four cut-offs of 25(OHD inadequacy were fixed : Results Mean (SD age of the patients was 76.9 (7.5 years, body mass index was 25.7 (4.5 kg/m2. Concentrations of 25(OHD were 52.5 (21.4 nmol/L. In the whole study population, the prevalence of 25(OHD inadequacy was 91.3 %, 87.5 %, 43.1 % and 15.9% when considering cut-offs of 80, 75, 50 and 30 nmol/L, respectively. Women who used vitamin D supplements, alone or combined with calcium supplements, had higher concentrations of 25(OHD than non-users. Significant inverse correlations were found between age/serum PTH and serum 25(OHD (r = -0.23/r = -0.31 and also between age/serum PTH and femoral neck BMD (r = -0.29/r = -0.15. There is a significant positive relation between age and PTH (r = 0.16, serum 25(OHD and femoral neck BMD (r = 0.07. (P Vitamin D concentrations varied with the season of sampling but did not reach statistical significance (P = 0.09. Conclusion This study points out a high prevalence of vitamin D inadequacy in Belgian postmenopausal osteoporotic women, even among subjects receiving vitamin D supplements.

  11. Anemia in postmenopausal women: dietary inadequacy or non-dietary factors

    Science.gov (United States)

    Postmenopausal women are disproportionately affected by anemia, and the prevalence in females > 65 years of age in the United States is approximately 10%. The manifestation of anemia in older populations is associated with dietary inadequacy, blood loss, genetics, alterations in bioavailability, ren...

  12. Evidence of dietary calcium and vitamin D inadequacies in a population of dental patients.

    Science.gov (United States)

    Pehowich, Daniel J; Pehowich, Enid D

    2016-12-01

    To determine the dietary calcium and vitamin D intake of a cohort of dental patients identified as being at risk of inadequacy based on a 24-hour food recall. A retrospective chart analysis was carried out on 5-day food record and nutrient analyses of 670 dental patients aged 18 to 82 years obtained over a 10-year period. All patients had scored poorly on a 24-hour food recall survey during their initial examination. The overall mean and median calcium and vitamin D intakes of the patients were significantly lower than the current estimated needs for the general population. Although calcium intake did not change over the 10-year period, vitamin D consumption decreased. The greatest dietary intake inadequacies for both calcium and vitamin D were seen in both male and female patients over age 50 years. A 24-Hour Food Recall Questionnaire may be an effective means for the oral health professional to screen patients for calcium and vitamin D and other nutrient inadequacies. Screening for potential dietary inadequacies of calcium and vitamin D may identify patients potentially at risk for poor bone health. Our results indicate that the dental health professional can obtain evidence necessary to change patient dietary behavior and thus contribute to successful treatment outcomes. Copyright © 2016 Elsevier Inc. All rights reserved.

  13. Vitamin D inadequacy is widespread in Tunisian active boys and is ...

    African Journals Online (AJOL)

    Vitamin D inadequacy is widespread in Tunisian active boys and is related to diet but not to adiposity or insulin resistance. Ikram Bezrati, Mohamed Kacem Ben Fradj, Nejmeddine Ouerghi, Moncef Feki, Anis Chaouachi, Naziha Kaabachi ...

  14. GENERAL EQUATIONS OF CARBONIZATION OF EUCALYPTUS SPP KINETIC MECHANISMS

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    Túlio Jardim Raad

    2006-06-01

    Full Text Available In the present work, a set of general equations related to kinetic mechanism of wood compound carbonization: hemicelluloses, cellulose and lignin was obtained by Avrami-Eroffev and Arrhenius equations and Thermogravimetry of Eucalyptus cloeziana, Eucalyptus camaldulensis, Corymbia citriodora, Eucalyptus urophylla and Eucalyptus grandis samples, TG-Isothermal and TG-Dynamic. The different thermal stabilities and decomposition temperature bands of those species compounds were applied as strategy to obtain the kinetic parameters: activation energy, exponential factor and reaction order. The kinetic model developed was validated by thermogravimetric curves from carbonization of others biomass such as coconut. The kinetic parameters found were - Hemicelluloses: E=98,6 kJmol, A=3,5x106s-1 n=1,0; - Cellulose: E=182,2 kJmol, A=1,2x1013s-1 n=1,5; - Lignin: E=46,6 kJmol, A=2,01s-1 n=0,41. The set of equations can be implemented in a mathematical model of wood carbonization simulation (with heat and mass transfer equations with the aim of optimizing the control and charcoal process used to produce pig iron.

  15. Macronutrient intake and inadequacies of community-dwelling older adults, a systematic review

    NARCIS (Netherlands)

    Borg, ter S.J.; Verlaan, S.; Mijnarends, D.; Schols, J.M.G.A.; Groot, de C.P.G.M.; Luiking, Y.C.

    2015-01-01

    Background: Anorexia of ageing may predispose older adults to under-nutrition and protein energy malnutrition. Studies, however, report a large variation in nutrient inadequacies among community-dwelling older adults. Summary: This systematic review provides a comprehensive overview of the energy

  16. Study of Non-Isothermal Crystallization Kinetics of Biodegradable Poly(ethylene adipate/SiO2 Nanocomposites

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    M. R. Memarzadeh

    2013-09-01

    Full Text Available Poly(ethylene adipte and poly(ethylene adipate/silica nanocomposite (PEAd/SiO2 containing 3 wt. % SiO2  were prepared by an in situ method. The examinations on the non-isothermal crystallization kinetic behavior have been conducted by means of differential scanning calorimeter (DSC. The Avrami, Ozawa, and combined Avrami and Ozawa equations were applied to describe the crystallization kinetics and to determine the crystallization parameters of the prepared PEAd/SiO2 nanocomposites. It is found that the inclusion of the silica nanoparticles can accelerate the nucleation rate due to heterogeneous nucleation effect of silica on the polymer matrix. According to the obtained results, the combined Avrami and Ozawa equation shown that the better model for examination of this system.

  17. Dietary diversity scores: an indicator of micronutrient inadequacy instead of obesity for Chinese children.

    Science.gov (United States)

    Zhao, Wenzhi; Yu, Kai; Tan, Shengjie; Zheng, Yingdong; Zhao, Ai; Wang, Peiyu; Zhang, Yumei

    2017-05-12

    Micronutrient malnutrition affects the well-being of both adults and children. Dietary diversity score (DDS) is a useful evaluation index with a relatively well-developed guideline by FAO. It's meaningful to assess and predict inadequate micronutrient intakes using DDS in Chinese children, after ruling out the risk of obesity coming with more dietary diversity. Data for evaluation were extracted from the Nutrition Study of Preschool Children and School Children, which is a cross-sectional study covering 8 cities of China, including 1694 children in kindergartens and primary schools. This study applied DDS to Chinese children to test the validity for micronutrient inadequacy, and then explored the relationship between dietary diversity and obesity. It reveals that dietary diversity varied with age and place of residence; the older ones and the ones living in rural areas tend to have poorer dietary diversity. Another discovery is that DDS is positively correlated with indicators of micronutrient adequacy, with a score of 6-8 indicating the lowest risk of micronutrient inadequacy in different groups of children. In our study population, dietary diversity is not related with obesity. Dietary diversity score is a valid indicator to evaluate micronutrient inadequacy in Chinese children, though there is still room for improvement of the method. Besides, the relationship between increase of dietary diversity and risk of obesity should be treated circumspectly.

  18. [The inadequacy of official classification of work accidents in Brazil].

    Science.gov (United States)

    Cordeiro, Ricardo

    2018-02-19

    Traditionally, work accidents in Brazil have been categorized in government documents and legal and academic texts as typical work accidents and commuting accidents. Given the increase in urban violence and the increasingly precarious work conditions in recent decades, this article addresses the conceptual inadequacy of this classification and its implications for the underestimation of work accidents in the country. An alternative classification is presented as an example and a contribution to the discussion on the improvement of statistics on work-related injuries in Brazil.

  19. Assessment of intake inadequacy and food sources of zinc of people in China

    NARCIS (Netherlands)

    Ma Guansheng,; Li Yanping,; Kok, F.J.; Xiaoguang, Y.

    2007-01-01

    Objectives: To assess the intake inadequacy and food sources of zinc of people in China. Design and subjects: Diets of 68 962 subjects aged 2-101 years (urban 21103, rural 47859) in the 2002 China National Nutrition and Health Survey were analysed. Dietary intake was assessed using 24-hour recall

  20. 78 FR 889 - Finding of Substantial Inadequacy of Implementation Plan; Call for California State...

    Science.gov (United States)

    2013-01-07

    ... Resources Defense Council; and Physicians for Social Responsibility--Los Angeles, (``environmental and... ENVIRONMENTAL PROTECTION AGENCY 40 CFR Part 52 [EPA-R09-OAR-2012-0721; FRL-9767-3] Finding of Substantial Inadequacy of Implementation Plan; Call for California State Implementation Plan Revision; South...

  1. Inadequacy of vitamins and minerals among high-school pupils in Ouarzazate, Morocco.

    Science.gov (United States)

    Anzid, Karim; Baali, Abdellatif; Vimard, Patrice; Levy-Desroches, Susan; Cherkaoui, Mohamed; López, Pilar Montero

    2014-08-01

    To assess micronutrient intakes and the prevalence of inadequacy in a sample of high-school pupils in Ouarzazate, Morocco. Food records were compiled over three non-consecutive days by pre-trained pupils. Micronutrient intakes were estimated using the DIAL software, adapted to include foods commonly eaten in Morocco. The prevalence of inadequacy was estimated by the proportion of individuals with intakes below the Estimated Average Requirement (EAR) for vitamins B12, A and K, thiamin, riboflavin, niacin, pyridoxine, folate, ascorbic acid, iodine, Ca, Mg and P; below the Adequate Intake (AI) level for pantothenic acid, biotin, Na and K; and using the probability approach for Fe. Data were adjusted for intra-individual variation with exclusion of under-reporters. Ouarzazate, a semi-urban region situated on the southern slopes of the High Atlas with little industrial development but an important tourism sector. A self-selected sample of 312 pupils aged 15-19 years from the five public high schools. After exclusion of under-reporters, 293 remained for analysis. The highest proportions of below-EAR/AI intakes were seen for pantothenic acid (girls 85·1 %, boys 78·0 %), biotin (boys 83·1 %, girls 79·4 %), thiamin (boys 66·9 %), folate (girls 93·1 %, boys 74·6 %), iodine (boys 94·9 %, girls 88·0 %) and Ca (girls 83·4 %, boys 74·6 %). Na intake was generally in excess whereas K intake was below the AI level. In general, girls had better-quality diets than boys, who appeared to consume more 'empty calories'. Our findings suggest that in this population of Moroccan adolescents, nutritional intervention and educational strategies are needed to promote healthy eating habits and correct micronutrient inadequacies. To provide reliable and precise estimates of nutrient intakes, an update of Moroccan food composition databases is urgently needed. We recommend that national authorities address these issues.

  2. F-centers in alkaline-earth fluorides. Inadequacy of the muffin-tin approximation

    International Nuclear Information System (INIS)

    Oliveira, L.E.; Oliveira, P.M.; Maffeo, B.

    1977-01-01

    The SCF-MSXα (Self Consisting F-centers-Multiple Scattering Xα) method has been applied in the study of the electronic structure of F centers in CaF 2 , SrF 2 and BaF 2 . The predicted optical transition energies are in disagreement with the experimental data. An explanation for the discrepancy is provided showing the inadequacy of the spherical averaging of the potential within the muffin-tin approximation [pt

  3. Vitamin D inadequacy is widespread in Tunisian active boys and is related to diet but not to adiposity or insulin resistance

    Directory of Open Access Journals (Sweden)

    Ikram Bezrati

    2016-04-01

    Full Text Available Background: Vitamin D inadequacy is widespread in children and adolescents worldwide. The present study was undertaken to assess the vitamin D status in active children living in a sunny climate and to identify the main determinants of the serum concentration of 25-hydroxyvitamin D (25-OHD. Methods: This cross-sectional study included 225 children aged 7–15 years practicing sports in a football academy. Anthropometric measures were performed to calculate body mass index (BMI, fat mass, and maturity status. A nutritional enquiry was performed including 3-day food records and food frequency questionnaire. Plasma 25-OHD and insulin were assessed by immunoenzymatic methods ensuring categorization of vitamin D status and calculation of insulin sensitivity/resistance indexes. A logistic regression model was applied to identify predictors for vitamin D inadequacy. Results: Vitamin D deficiency (25-OHD<12 µg/L was observed in 40.9% of children and insufficiency (12<25-OHD<20 µg/L was observed in 44% of children. In a multivariate analysis, vitamin D deficiency and insufficiency were associated with a lower dietary intake of vitamin D, proteins, milk, red meat, fish, and eggs. However, no significant relationship was observed with maturation status, adiposity, or insulin resistance. Conclusions: Tunisian children and adolescents are exposed to a high risk of vitamin D inadequacy despite living in a sunny climate. Circulating 25-OHD concentrations are related to the intake of vitamin D food sources but not to maturation status or body composition. Ensuring sufficient and safe sun exposure and adequate vitamin D intake may prevent vitamin D inadequacy in children from sunny environments.

  4. Is cancer a pure growth curve or does it follow a kinetics of dynamical structural transformation?

    Science.gov (United States)

    González, Maraelys Morales; Joa, Javier Antonio González; Cabrales, Luis Enrique Bergues; Pupo, Ana Elisa Bergues; Schneider, Baruch; Kondakci, Suleyman; Ciria, Héctor Manuel Camué; Reyes, Juan Bory; Jarque, Manuel Verdecia; Mateus, Miguel Angel O'Farril; González, Tamara Rubio; Brooks, Soraida Candida Acosta; Cáceres, José Luis Hernández; González, Gustavo Victoriano Sierra

    2017-03-07

    Unperturbed tumor growth kinetics is one of the more studied cancer topics; however, it is poorly understood. Mathematical modeling is a useful tool to elucidate new mechanisms involved in tumor growth kinetics, which can be relevant to understand cancer genesis and select the most suitable treatment. The classical Kolmogorov-Johnson-Mehl-Avrami as well as the modified Kolmogorov-Johnson-Mehl-Avrami models to describe unperturbed fibrosarcoma Sa-37 tumor growth are used and compared with the Gompertz modified and Logistic models. Viable tumor cells (1×10 5 ) are inoculated to 28 BALB/c male mice. Modified Gompertz, Logistic, Kolmogorov-Johnson-Mehl-Avrami classical and modified Kolmogorov-Johnson-Mehl-Avrami models fit well to the experimental data and agree with one another. A jump in the time behaviors of the instantaneous slopes of classical and modified Kolmogorov-Johnson-Mehl-Avrami models and high values of these instantaneous slopes at very early stages of tumor growth kinetics are observed. The modified Kolmogorov-Johnson-Mehl-Avrami equation can be used to describe unperturbed fibrosarcoma Sa-37 tumor growth. It reveals that diffusion-controlled nucleation/growth and impingement mechanisms are involved in tumor growth kinetics. On the other hand, tumor development kinetics reveals dynamical structural transformations rather than a pure growth curve. Tumor fractal property prevails during entire TGK.

  5. Smoking and dietary inadequacy among Inuvialuit women of child bearing age in the Northwest Territories, Canada

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    Kolahdooz Fariba

    2013-02-01

    Full Text Available Abstract Objective The prevalence of smoking in Aboriginal Canadians is higher than non-Aboriginal Canadians, a behavior that also tends to alter dietary patterns. Compared with the general Canadian population, maternal smoking rates are almost twice as high. The aim of this study was to compare dietary adequacy of Inuvialuit women of childbearing age comparing smokers versus non-smokers. Research methods & procedures A cross-sectional study, where participants completed a culturally specific quantitative food frequency questionnaire. Non-parametric analysis was used to compare mean nutrient intake, dietary inadequacy and differences in nutrient density among smokers and non-smokers. Multiple logistic regression analyses were performed for key nutrients inadequacy and smoking status. Data was collected from three communities in the Beaufort Delta region of the Northwest Territories, Canada from randomly selected Inuvialuit women of childbearing age (19-44 years. Results Of 92 participants, 75% reported being smokers. There were no significant differences in age, BMI, marital status, education, number of people in household working and/or number of self employed, and physical activity between smokers and non-smokers. Non-parametric analysis showed no differences in nutrient intake between smokers and non-smokers. Logistic regression however revealed there was a positive association between smoking and inadequacies of vitamin C (OR = 2.91, 95% CI, 1.17-5.25, iron (OR = 3.16, 95% CI, 1.27-5.90, and zinc (OR = 2.78, 95% CI, 1.12-4.94. A high percentage of women (>60%, regardless of smoking status, did not meet the dietary recommendations for fiber, vitamin D, E and potassium. Conclusions This study provides evidence of inadequate dietary intake among Inuvialuit of childbearing age regardless of smoking behavior.

  6. An Analysis on the Constitutive Models for Forging of Ti6Al4V Alloy Considering the Softening Behavior

    Science.gov (United States)

    Souza, Paul M.; Beladi, Hossein; Singh, Rajkumar P.; Hodgson, Peter D.; Rolfe, Bernard

    2018-05-01

    This paper developed high-temperature deformation constitutive models for a Ti6Al4V alloy using an empirical-based Arrhenius equation and an enhanced version of the authors' physical-based EM + Avrami equations. The initial microstructure was a partially equiaxed α + β grain structure. A wide range of experimental data was obtained from hot compression of the Ti6Al4 V alloy at deformation temperatures ranging from 720 to 970 °C, and at strain rates varying from 0.01 to 10 s-1. The friction- and adiabatic-corrected flow curves were used to identify the parameter values of the constitutive models. Both models provided good overall accuracy of the flow stress. The generalized modified Arrhenius model was better at predicting the flow stress at lower strain rates. However, the model was inaccurate in predicting the peak strain. In contrast, the enhanced physical-based EM + Avrami model revealed very good accuracy at intermediate and high strain rates, but it was also better at predicting the peak strain. Blind sample tests revealed that the EM + Avrami maintained good predictions on new (unseen) data. Thus, the enhanced EM + Avrami model may be preferred over the Arrhenius model to predict the flow behavior of Ti6Al4V alloy during industrial forgings, when the initial microstructure is partially equiaxed.

  7. Some fundamental considerations of the equation of radiative transfer

    International Nuclear Information System (INIS)

    Kuriyan, J.G.; Sudarshan, E.C.G.

    1978-10-01

    The radiation transfer of the vector electromagnetic field was first formulated by Chandrasekhar while deriving the polarization characteristics of a sunlit sky. There are two subtle problems underlying this treatment. The first concerns the crucial identification of a Stokes parameter with the specific intensity of radiation. While both depend on position in 3-D space, the latter has, intrinsic to it, an additional angular dependence defining the flow of the radiation field. How can this inadequacy be remedied without damaging the results obtained heretofore from Chandrasekhar's formalism. The second problem arises from the fact that the radiative transfer equation describes the transport of an incoherent radiation field through space. This, however, seems to contradict the results of the Van Cittert-Zernike-Wolf theorem which implies that an incoherent field develops coherence as it passes through free space implying, of course, that the radiative transfer equation must involve not incoherent but partially coherent fields. The vector transfer equation of the direct beam (Beer's law) is derived from first principles. The analysis of this equation provides a satisfactory resolution of these two problems. The result also shows that the Beer's law will have to be modified to a matrix law to accommodate systems that are not spherically symmetric. 13 references

  8. Treatment of velopharyngeal inadequacy in a patient with submucous cleft palate and myasthenia gravis.

    Science.gov (United States)

    Rikihisa, Naoaki; Udagawa, Akikazu; Yoshimoto, Shinya; Ichinose, Masaharu; Kimura, Tomoe; Shimizu, Sara

    2009-09-01

    To describe the clinical course and management of a patient with submucous cleft palate who developed myasthenia gravis (MG) as an adult and suffered recurrent hypernasality. Few reports have described MG patients undergoing pharyngeal flap surgery for velopharyngeal incompetence, and these have described only slight speech improvement in such patients. Case report. The patient underwent primary pushback palatoplasty and superiorly based pharyngeal flap surgery for submucous cleft and short palate at age 7. Hypernasality showed major improvement after initial surgery. At age 19, the patient developed MG that triggered the recurrence of velopharyngeal incompetence. After MG was treated, revision pushback palatoplasty was performed for velopharyngeal incompetence when the patient was 24 years old. Preoperatively and postoperatively, the patient was evaluated by the same speech-language-hearing therapists, each with at least 5 years of clinical experience in cleft palate speech. After the second pushback palatoplasty, hypernasality and audible nasal air emission during speech decreased to mild. Primary pushback palatoplasty and pharyngeal flap surgery were performed for the submucous cleft palate. Revision pushback palatoplasty improved velopharyngeal inadequacy induced by MG. Decreased perceived nasality positively influenced the patient's quality of life. Combined pushback palatoplasty and pharyngeal flap surgery is thus an option in surgical treatment for velopharyngeal inadequacy to close the cleft and the velopharyngeal orifice in cases of cleft palate and MG.

  9. Development of a screening tool for detecting undernutrition and dietary inadequacy among rural elderly in Malaysia: simple indices to identify individuals at high risk.

    Science.gov (United States)

    Shahar, S; Dixon, R A; Earland, J

    1999-11-01

    Undernutrition and the consumption of poor diets are prevalent among elderly people in developing countries. Recognising the importance of the early identification of individuals at high nutritional risk, this study aimed to develop a simple tool for screening. A cross-sectional study was conducted on 11 randomly selected villages among the 62 in Mersing District, Malaysia. Undernutrition was assessed using body mass index, plasma albumin and haemoglobin on 285 subjects. Dietary inadequacy (a count of nutrients falling below two-thirds of the Recommended Dietary Allowances) was examined for 337 subjects. Logistic regression analysis was performed to identify significant predictors of undernutrition and dietary inadequacy from social and health factors, and to derive appropriate indices based on these predictions. The multivariate predictors of undernutrition were 'no joint disease', 'smoker', 'no hypertension', 'depended on others for economic resource', 'respiratory disease', 'perceived weight loss' and 'chewing difficulty', with a joint sensitivity of 56% and specificity of 84%. The equivalent predictors of dietary inadequacy were 'unable to take public transport', 'loss of appetite', 'chewing difficulty', 'no regular fruit intake' and 'regularly taking less than three meals per day', with a joint sensitivity of 77% and specificity of 47%. These predictions, with minor modification to simplify operational use, led to the production of a simple screening tool. The tool can be used by public health professionals or community workers or leaders as a simple and rapid instrument to screen individual at high risk of undernutrition and/or dietary inadequacy.

  10. A new constitutive equation for strain hardening and softening of fcc metals during severe plastic deformation

    International Nuclear Information System (INIS)

    Wei, W.; Wei, K.X.; Fan, G.J.

    2008-01-01

    The stress-strain relationship for strain hardening and softening of high-purity aluminum and copper, which were deformed by equal channel angular pressing (ECAP) at ambient temperature, was analyzed by combining the Estrin and Mecking (EM) model and an Avrami-type equation with experimental data during severe plastic deformation. The initial strain hardening can be described by the EM model, while the flow stress arrives at the peak stress after it was saturated. However, strain softening similar to plastic deformation at high temperatures is observed after the peak stress. Moreover, the peak strain at the maximum flow stress is ∼4 for copper and ∼2 for aluminum. A new constitutive equation was developed to describe strain softening at high strain levels, which was supported well by tensile, compression and microhardness tests at room temperature and low strain rate. It was observed that dynamic recovery and recrystallization occurs in copper, and recrystallized grains and their growth in aluminum. The results indicate that dynamic recovery and recrystallization was the dominant softening mechanism, which was confirmed by scanning electron microscopy-electron channeling contrast observations and the abnormal relationship between the imposed strain during ECAP and subsequent recrystallization temperature after ECAP

  11. Reconstructive Surgery for Severe Penile Inadequacy: Phalloplasty with a Free Radial Forearm Flap or a Pedicled Anterolateral Thigh Flap

    Directory of Open Access Journals (Sweden)

    N. Lumen

    2008-01-01

    Full Text Available Objectives. Severe penile inadequacy in adolescents is rare. Phallic reconstruction to treat this devastating condition is a major challenge to the reconstructive surgeon. Phallic reconstruction using the free radial forearm flap (RFF or the pedicled anterolateral thigh flap (ALTF has been routinely used in female-to-male transsexuals. Recently we started to use these techniques in the treatment of severe penile inadequacy. Methods. Eleven males (age 15 to 42 years were treated with a phallic reconstruction. The RFF is our method of choice; the ALTF is an alternative when a free flap is contraindicated or less desired by the patient. The RFF was used in 7 patients, the ALTF in 4 patients. Mean followup was 25 months (range: 4–49 months. Aesthetic and functional results were evaluated. Results. There were no complications related to the flap. Aesthetic results were judged as “good” in 9 patients and “moderate” in 2 patients. Sensitivity in the RFF was superior compared to the ALTF. Four patients developed urinary complications (stricture and/or fistula. Six patients underwent erectile implant surgery. In 2 patients the erectile implant had to be removed due to infection or erosion. Conclusion. In case of severe penile inadequacy due to whatever condition, a phalloplasty is the preferred treatment nowadays. The free radial forearm flap is still the method of choice. The anterolateral thigh flap can be a good alternative, especially when free flaps are contraindicated, but sensitivity is markedly inferior in these flaps.

  12. Critical comparison between equation of motion-Green's function methods and configuration interaction methods: analysis of methods and applications

    International Nuclear Information System (INIS)

    Freed, K.F.; Herman, M.F.; Yeager, D.L.

    1980-01-01

    A description is provided of the common conceptual origins of many-body equations of motion and Green's function methods in Liouville operator formulations of the quantum mechanics of atomic and molecular electronic structure. Numerical evidence is provided to show the inadequacies of the traditional strictly perturbative approaches to these methods. Nonperturbative methods are introduced by analogy with techniques developed for handling large configuration interaction calculations and by evaluating individual matrix elements to higher accuracy. The important role of higher excitations is exhibited by the numerical calculations, and explicit comparisons are made between converged equations of motion and configuration interaction calculations for systems where a fundamental theorem requires the equality of the energy differences produced by these different approaches. (Auth.)

  13. Bulletin of Materials Science | Indian Academy of Sciences

    Indian Academy of Sciences (India)

    MDPE) and MDPE–clay nanocomposites have been investigated by differential scanning calorimeter. The modified Avrami, Ozawa, Liu and Ziabicki equations have been applied to describe non-isothermal crystallization process. The results of ...

  14. Influence of TiO{sub 2} Surface Properties on Water Pollution Treatment and Photocatalytic Activity

    Energy Technology Data Exchange (ETDEWEB)

    Zeng, Min [Southwest Univ. of Science and Technology, Mianyang (China)

    2013-03-15

    The titania surface showed different characteristics depending on the charge of the dye molecules. Compared with the MB molecules, the negatively charged MO molecules strongly adsorbed on the titania surface. Furthermore, the decomposition kinetics of the dye molecules by the photocatalytic activity also deepened with the charge of the dye molecules. The relation between the UV irradiation time and the molar ratio of the decomposed dye molecules followed the Avrami equation. According to the results of the analysis by using the Avrami equation, the MO molecules were decomposed on the titania particle surface. In contrast, the MB molecules were decomposed in the aqueous solution. The difference in kinetics was related to the interaction of the dye molecules and the titania surface. These preferential adsorption and decomposition characteristics will improve its applications in water pollution treatment.

  15. Usual Intake Distribution of Vitamins and Prevalence of Inadequacy in a Large Sample of Iranian At-Risk Population: Application of NCI Method.

    Science.gov (United States)

    Heidari, Zahra; Feizi, Awat; Azadbakht, Leila; Sarrafzadegan, Nizal

    2016-01-01

    This study provides an assessment of usual intake distribution of vitamins and estimating prevalence of inadequacy and excess among a large representative sample of middle-aged and elderly people in central regions of Iran. A cross-sectional study that is a second follow-up to the Isfahan Cohort Study (ICS). The study setting included urban and rural areas from 3 cities (Isfahan, Najafabad, and Arak) in central regions of Iran. Subjects included 1922 people aged 40 years and older, with a mean age of 55.9 ± 10.6; 50.4% were male and the majority (79.3%) were urban. Dietary intakes were collected using a 24-hour recall and 2 food records. Distribution of vitamins intake was estimated using traditional and national cancer institute (NCI) methods. The proportion of subjects at risk of vitamin intake inadequacy or excess was estimated using the estimated average requirement (EAR) cut-point method and the tolerable upper intake levels (UL) index. There were differences between values obtained from traditional and NCI methods, particularly in the lower and upper percentiles of the intake distribution. High prevalence of inadequacies for vitamins A, D, E, B2, B3 (especially among females), and B9 was observed. Significant gender differences were found in terms of inadequate intakes for vitamins A, B1, B2, B3, B6, B9, B12, and C (p vitamin intake was observed in the middle-aged and elderly Iranian population. Nutritional interventions particularly through population-based educational programs in order to improve diet variety and consume nutrient supplements may be necessary.

  16. Kinetic Study of Crystallization Process in Fe32Ni36Cr14P12B6 Metallic Glass

    International Nuclear Information System (INIS)

    Lad, Kirit; Pratap, Arun; Rao, T. L. Shanker

    2010-01-01

    Kinetics of crystallization process in a Fe-based metallic glass 2826A (Fe 32 Ni 36 Cr 14 P 12 B 6 ) has been studied with the help of differential scanning calorimetry(DSC). It is found that the 2826A metallic glass exhibits two overlapping crystallization peaks. The activation energy for crystallization (E) and the Avrami exponent (n) for the two crystallization peaks have been obtained using the Kolmogorov-Jhonson-Mehl-Avrami (KJMA) equation. The so-obtained values of E and n have been utilized to derive normalized heat flow curves. It has been observed that the theoretical heat flow curves obtained using KJMA equation show large deviations from the experimental curves for the first peak whereas the curves are in very close agreement for the second peak. This suggests that kinetics of crystallization process during the first peak cannot be described correctly in KJMA formalism.

  17. Kinetic Study of Crystallization Process in Fe32Ni36Cr14P12B6 Metallic Glass

    Science.gov (United States)

    Lad, Kirit; Rao, T. L. Shanker; Pratap, Arun

    2010-06-01

    Kinetics of crystallization process in a Fe-based metallic glass 2826A (Fe32Ni36Cr14P12B6) has been studied with the help of differential scanning calorimetry(DSC). It is found that the 2826A metallic glass exhibits two overlapping crystallization peaks. The activation energy for crystallization (E) and the Avrami exponent (n) for the two crystallization peaks have been obtained using the Kolmogorov-Jhonson-Mehl-Avrami (KJMA) equation. The so-obtained values of E and n have been utilized to derive normalized heat flow curves. It has been observed that the theoretical heat flow curves obtained using KJMA equation show large deviations from the experimental curves for the first peak whereas the curves are in very close agreement for the second peak. This suggests that kinetics of crystallization process during the first peak cannot be described correctly in KJMA formalism.

  18. Non-isothermal crystallization kinetics and characterization of biodegradable poly(butylene succinate-co-neopentyl glycol succinate) copolyesters.

    Science.gov (United States)

    Xie, Wen-Jie; Zhou, Xiao-Ming

    2015-01-01

    Both biodegradable aliphatic neat poly(butylene succinate) (PBS) and poly(butylene succinate-co-neopentyl glycol succinate) (P(BS-co-NPGS)) copolyesters with different 1,4-butanediol/neopentyl glycol ratios were synthesized through a two-step process of transesterification and polycondensation using stannous chloride and 4-Methylbenzenesulfonic acid as the co-catalysts. The structure, non-isothermal crystallization behavior, crystalline morphology and crystal structure of neat PBS and P(BS-co-NPGS) copolyesters were characterized by (1)H NMR, differential scanning calorimetry (DSC), polarized optical microscope (POM) and wide angle X-ray diffraction (WAXD), respectively. The Avrami equation modified by Jeziorny and Mo's method was employed to describe the non-isothermal crystallization kinetics of the neat PBS and its copolyesters. The modified Avrami equation could adequately describe the primary stage of non-isothermal crystallization kinetics of the neat PBS and its copolyesters. Mo's method provided a fairly satisfactory description of the non-isothermal crystallization of neat PBS and its copolyesters. Interestingly, the values of 1/t1/2, Zc and F(T) obtained by the modified Avrami equation and Mo's method analysis indicated that the crystallization rate increased first and then decreased with an increase of NPGS content compared that of neat PBS, whereas the crystallization mechanism almost kept unchanged. The results of tensile testing showed that the ductility of PBS was largely improved by incorporating NPGS units. The elongation at break increased remarkably with increasing NPGS content. In particular, the sample with 20% NPGS content showed around 548% elongation at break. Copyright © 2014 Elsevier B.V. All rights reserved.

  19. Overlapping phase transformations on tempering of a low-alloy steel

    International Nuclear Information System (INIS)

    Valencia Morales, E; Galeano Alvarez, N.J; Vega Leiva, J; Castellanos L M; Villar C E; Antiquera Munoz J; Hernandez R J

    2006-01-01

    The kinetics of precipitation of the primary and independent carbides during tempering of a low-alloy steel are characterized by the application of the Kinetic Theory of the Overlapping Phase Transformations(KTOPT). It is based on the Avrami model and considers two simultaneous precipitation processes. The present set-up allows us to calculate the exponent of the Avrami equation for simultaneous reactions at different rates. Only the dilatometry curves on tempering are required. According to this new formulation, the treatment of the dilatometry records showed different mechanisms of nucleation and growth of the primary and independent carbides. These results are in agreement with the thin foil electron micrographs and hardness tests of the thermally treated samples (au)

  20. Frequency of vitamin D inadequacy among Saudi males visiting a Rheumatology Outpatient Clinic of a tertiary hospital in Al-Qassim region: Effect of vitamin D supplementation

    Directory of Open Access Journals (Sweden)

    Hala Lotfy Fayed

    2017-10-01

    Full Text Available Background: Vitamin D inadequacy (deficiency and insufficiency has become an epidemic with the assumption that women in Arab countries are at a higher risk due to their clothing style of wearing dark colored suits or a veil. Aim of the work: To determine the frequency of vitamin D inadequacy among young adult and early middle-aged males in Al-Qassim region and to study the effect of vitamin D supplementation. Patients and methods: Sixty Saudi males visiting Rheumatology Outpatient Clinic of a tertiary hospital in Al-Qassim region were enrolled and evaluated for musculoskeletal state including assessment of chronic diffuse musculoskeletal pains using Numeric Rating Pain Scale (NRPS and functional evaluation of lower limb proximal muscle power using chair–rise performance test. Serum 25(OHD was evaluated. Vitamin D supplementation was provided for symptomatic subjects. Follow-up clinical evaluation as well as serum 25(OHD measurement after 12 weeks vitamin D3 supplementation was performed. Results: The mean age of the patients was 43.2 ± 6.4 years. 54 (90% had vitamin D inadequacy; 42 (70% deficiency and 12 (20% had insufficiency. Significant increase in baseline serum 25(OHD (13.92 ± 5.67 ng/ml after 12 weeks of supplementation (35.94 ± 4.11 ng/ml with significant decrease in NPRS (7.42 ± 2.12 vs 2.06 ± 2.04 (p < 0.001, as well as significant improvement of functional status scores of chair–rise performance test (93.95 ± 23.56 vs 203.1 ± 58.6 (p < 0.001. Conclusion: Vitamin D inadequacy is a major health problem not only in elderly people or women with in-door residency and dark-colored clothes, but also in Saudi male young adults in Al-Qassim region.

  1. Hot deformation behavior of austenite in HSLA-100 microalloyed steel

    International Nuclear Information System (INIS)

    Momeni, A.; Arabi, H.; Rezaei, A.; Badri, H.; Abbasi, S.M.

    2011-01-01

    Research highlights: → The flow stress is well fitted by the exponential constitutive equation. → The average value of apparent activation energy for hot deformation is 377 kJ mol -1 . → A yield point phenomenon is observed on flow curves at high temperatures. → The Avrami exponent is determined around unity for dynamic recrystallization. - Abstract: Dynamic recrystallization of austenite in the Cu-bearing HSLA-100 steel was investigated by hot compression testing at a temperature range of 850-1150 deg. C and a strain rate of 0.001-1 s -1 . The obtained flow curves at temperatures higher than 950 deg. C were typical of DRX while at lower temperatures the flow curves were associated with work hardening without any indication of DRX. At high temperatures, flow stress exhibited a linear relation with temperature while at temperatures below 950 deg. C the behavior changed to non-linear. Hence, the temperature of 950 deg. C was introduced as the T nr of the alloy. All the flow curves showed a yield point elongation like phenomenon which was attributed to the interaction of solute atoms, notably carbon, and moving dislocations. The maximum elongation associated with the yield point phenomenon was observed at about 950 deg. C. Since the maximum yield point elongation was observed about the calculated T nr , it was concluded that carbon atoms were responsible for it. It was also concluded that the temperature at which the yield point elongation reaches the maximum value increases as strain rate rises. The stress and strain of the characteristic points of DRX flow curves were successfully correlated to the Zener-Hollomon parameter, Z, by power-law equations. The constitutive exponential equation was found more precise than the hyperbolic sine equation for modeling the dependence of flow stress on Z. The apparent activation energy for DRX was determined as 377 kJ mol -1 . The kinetics of DRX was modeled by an Avrami-type equation and the Avrami's exponent was

  2. Effects of Covalent Functionalization of MWCNTs on the Thermal Properties and Non-Isothermal Crystallization Behaviors of PPS Composites

    Directory of Open Access Journals (Sweden)

    Myounguk Kim

    2017-09-01

    Full Text Available In this study, a PPS/MWCNTs composite was prepared with poly(phenylene sulfide (PPS, as well as pristine and covalent functionalized multi-walled carbon nanotubes (MWCNTs via melt-blending techniques. Moreover, the dispersion of the MWCNTs on the PPS matrix was improved by covalent functionalization as can be seen from a Field-Emission Scanning Electron Microscope (FE-SEM images. The thermal properties of the PPS/MWCNTs composites were characterized using a thermal conductivity analyzer, and a differential scanning calorimeter (DSC. To analyze the crystallization behavior of polymers under conditions similar with those in industry, the non-isothermal crystallization behaviors of the PPS/MWCNTs composites were confirmed using various kinetic equations, such as the modified Avrami equation and Avrami-Ozawa combined equation. The crystallization rate of PPS/1 wt % pristine MWCNTs composite (PPSP1 was faster because of the intrinsic nucleation effect of the MWCNTs. However, the crystallization rates of the composites containing covalently-functionalized MWCNTs were slower than PPSP1 because of the destruction of the MWCNTs graphitic structure via covalent functionalization. Furthermore, the activation energies calculated by Kissinger’s method were consistently decreased by covalent functionalization.

  3. On World Religion Adherence Distribution Evolution

    Science.gov (United States)

    Ausloos, Marcel; Petroni, Filippo

    Religious adherence can be considered as a degree of freedom, in a statistical physics sense, for a human agent belonging to a population. The distribution, performance and life time of religions can thus be studied having in mind heterogeneous interacting agent modeling. We present a comprehensive analysis of 58 so-called religions (to be better defined in the main text) as measured through their number of adherents evolutions, between 1900 and 2000, - data taken from the World Christian Trends (Barrett and Johnson, "World Christian Trends AD 30 - AD 2200: Interpreting the Annual Christian Megacensus", William Carey Library, 2001): 40 are considered to be "presently growing" cases, including 11 turn overs in the twentieth century; 18 are "presently decaying", among which 12 are found to have had a recent maximum, in the nineteenth or the twentieth century. The Avrami-Kolmogorov differential equation which usually describes solid state transformations, like crystal growth, is used in each case in order to obtain the preferential attachment parameter introduced previously (Europhys Lett 77:38002, 2007). It is not often found close to unity, though often corresponding to a smooth evolution. However large values suggest the occurrence of extreme cases which we conjecture are controlled by so-called external fields. A few cases indicate the likeliness of a detachment process. We discuss a few growing and decaying religions, and illustrate various fits. Some cases seem to indicate the lack of reliability of the data, but others some marked departure from Avrami law. Whence the Avrami evolution equation might be surely improved, in particular, and somewhat obviously, for the decaying religion cases. We point out two major difficulties in such an analysis: (1) the "precise" original time of apparition of a religion, (2) the time at which there is a maximum number of adherents, both information being necessary for integrating reliably any evolution equation.

  4. Inadequacies of Physical Examination as a Cause of Medical Errors and Adverse Events: A Collection of Vignettes.

    Science.gov (United States)

    Verghese, Abraham; Charlton, Blake; Kassirer, Jerome P; Ramsey, Meghan; Ioannidis, John P A

    2015-12-01

    Oversights in the physical examination are a type of medical error not easily studied by chart review. They may be a major contributor to missed or delayed diagnosis, unnecessary exposure to contrast and radiation, incorrect treatment, and other adverse consequences. Our purpose was to collect vignettes of physical examination oversights and to capture the diversity of their characteristics and consequences. A cross-sectional study using an 11-question qualitative survey for physicians was distributed electronically, with data collected from February to June of 2011. The participants were all physicians responding to e-mail or social media invitations to complete the survey. There were no limitations on geography, specialty, or practice setting. Of the 208 reported vignettes that met inclusion criteria, the oversight was caused by a failure to perform the physical examination in 63%; 14% reported that the correct physical examination sign was elicited but misinterpreted, whereas 11% reported that the relevant sign was missed or not sought. Consequence of the physical examination inadequacy included missed or delayed diagnosis in 76% of cases, incorrect diagnosis in 27%, unnecessary treatment in 18%, no or delayed treatment in 42%, unnecessary diagnostic cost in 25%, unnecessary exposure to radiation or contrast in 17%, and complications caused by treatments in 4%. The mode of the number of physicians missing the finding was 2, but many oversights were missed by many physicians. Most oversights took up to 5 days to identify, but 66 took longer. Special attention and skill in examining the skin and its appendages, as well as the abdomen, groin, and genitourinary area could reduce the reported oversights by half. Physical examination inadequacies are a preventable source of medical error, and adverse events are caused mostly by failure to perform the relevant examination. Copyright © 2015 Elsevier Inc. All rights reserved.

  5. Change of electrical resistivity and Young's modulus during crystallization of amorphous Fe40Ni40B20

    International Nuclear Information System (INIS)

    Stel, J. van der; Veldhuizen, H.B. van; Koebrugge, G.W.; Sietsma, J.; Beukel, A. van den

    1989-01-01

    The kinetics of crystallization of amorphous Fe 40 Ni 40 B 20 is studied by measuring isothermal changes of the electrical resistivity and Young's modulus in the temperature range 600 to 700 K. The results satisfy very well the Johnson-Mehl-Avrami equation for phase transformations with a constant activation energy of 317 kJ/mol and a constant Avrami exponent n ∼ 2. This result is interpreted as two-dimensional growth of pre-existing nuclei which become as thick as the specimen in an early stage of crystallization. The relative change in electrical resistivity upon crystallization strongly depends on the measuring temperature T m , varying from 47% at T m = 77 K to 5% at T m = 600 K. It extrapolates to zero at T m ∼ 700 K. (author)

  6. Phase formation kinetics, hardness and magnetocaloric effect of sub-rapidly solidified LaFe11.6Si1.4 plates during isothermal annealing

    Science.gov (United States)

    Dai, Yuting; Xu, Zhishuai; Luo, Zhiping; Han, Ke; Zhai, Qijie; Zheng, Hongxing

    2018-05-01

    High-temperature phase transition behavior and intrinsic brittleness of NaZn13-type τ1 phase in La-Fe-Si magnetocaloric materials are two key problems from the viewpoint of materials production and practical applications. In the present work, the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation was introduced to quantitatively characterize the formation kinetics of τ1 phase in sub-rapidly solidified LaFe11.6Si1.4 plates during the isothermal annealing process. Avrami index was estimated to be 0.43 (∼0.5), which suggests that the formation of τ1 phase is in a diffusion-controlled one-dimensional growth mode. Meanwhile, it is found that the Vickers hardness as a function of annealing time for sub-rapidly solidified plates also agrees well with the JMAK equation. The Vickers hardness of τ1 phase was estimated to be about 754. Under a magnetic field change of 30 kOe, the maximum magnetic entropy change was about 22.31 J/(kg·K) for plates annealed at 1323 K for 48 h, and the effective magnetic refrigeration capacity reached 191 J/kg.

  7. Universal Rate Model Selector: A Method to Quickly Find the Best-Fit Kinetic Rate Model for an Experimental Rate Profile

    Science.gov (United States)

    2017-08-01

    k2 – k1) 3.3 Universal Kinetic Rate Platform Development Kinetic rate models range from pure chemical reactions to mass transfer...14 8. The rate model that best fits the experimental data is a first-order or homogeneous catalytic reaction ...Avrami (7), and intraparticle diffusion (6) rate equations to name a few. A single fitting algorithm (kinetic rate model ) for a reaction does not

  8. Thermal decomposition of γ-irradiated lead nitrate

    International Nuclear Information System (INIS)

    Nair, S.M.K.; Kumar, T.S.S.

    1990-01-01

    The thermal decomposition of unirradiated and γ-irradiated lead nitrate was studied by the gas evolution method. The decomposition proceeds through initial gas evolution, a short induction period, an acceleratory stage and a decay stage. The acceleratory and decay stages follow the Avrami-Erofeev equation. Irradiation enhances the decomposition but does not affect the shape of the decomposition curve. (author) 10 refs.; 7 figs.; 2 tabs

  9. Non-isothermal crystallization kinetics and characterization of biodegradable poly(butylene succinate-co-neopentyl glycol succinate) copolyesters

    International Nuclear Information System (INIS)

    Xie, Wen-Jie; Zhou, Xiao-Ming

    2015-01-01

    Both biodegradable aliphatic neat poly(butylene succinate) (PBS) and poly(butylene succinate-co-neopentyl glycol succinate) (P(BS-co-NPGS)) copolyesters with different 1,4-butanediol/neopentyl glycol ratios were synthesized through a two-step process of transesterification and polycondensation using stannous chloride and 4-Methylbenzenesulfonic acid as the co-catalysts. The structure, non-isothermal crystallization behavior, crystalline morphology and crystal structure of neat PBS and P(BS-co-NPGS) copolyesters were characterized by 1 H NMR, differential scanning calorimetry (DSC), polarized optical microscope (POM) and wide angle X-ray diffraction (WAXD), respectively. The Avrami equation modified by Jeziorny and Mo's method was employed to describe the non-isothermal crystallization kinetics of the neat PBS and its copolyesters. The modified Avrami equation could adequately describe the primary stage of non-isothermal crystallization kinetics of the neat PBS and its copolyesters. Mo's method provided a fairly satisfactory description of the non-isothermal crystallization of neat PBS and its copolyesters. Interestingly, the values of 1/t 1/2 , Z c and F(T) obtained by the modified Avrami equation and Mo's method analysis indicated that the crystallization rate increased first and then decreased with an increase of NPGS content compared that of neat PBS, whereas the crystallization mechanism almost kept unchanged. The results of tensile testing showed that the ductility of PBS was largely improved by incorporating NPGS units. The elongation at break increased remarkably with increasing NPGS content. In particular, the sample with 20% NPGS content showed around 548% elongation at break. - Highlights: • The incorporation of NPGS units reduced the spherulite size of BS unit. • The existence of NPGS units did not change the crystal structure of BS unit. • The NPGS units incorporated in PBS could significantly improve the ductility of PBS. • The

  10. Controversies of Sex Re-assignment in Genetic Males with Congenital Inadequacy of the Penis.

    Science.gov (United States)

    Raveenthiran, Venkatachalam

    2017-09-01

    Sex assignment in 46XY genetic male children with congenital inadequacy of the penis (CIP) is controversial. Traditionally, children with penile length less than 2 cm at birth are considered unsuitable to be raised as males. They are typically re-assigned to female-sex and feminizing genitoplasty is usually done in infancy. However, the concept of cerebral androgen imprinting has caused paradigm shift in the philosophy of sex re-assignment. Masculinization of the brain, rather than length of the penis, is the modern criterion of sex re-assignment in CIP. This review summarizes the current understanding of the complex issue. In 46XY children with CIP, male-sex assignment appears appropriate in non-hormonal conditions such as idiopathic micropenis, aphallia and exstrophy. Female-sex re-assignment appears acceptable in complete androgen insensitivity (CAIS), while partial androgen insensitivity syndrome (PAIS) patients are highly dissatisfied with the assignment of either sex. Children with 5-alpha reductase deficiency are likely to have spontaneous penile lengthening at puberty. Hence, they are better raised as males. Although female assignment is common in pure gonadal dysgenesis, long-term results are not known to justify the decision.

  11. Conceptual Inadequacy of the Shore and Johnson Axioms for Wide Classes of Complex Systems

    Directory of Open Access Journals (Sweden)

    Constantino Tsallis

    2015-05-01

    Full Text Available It is by now well known that the Boltzmann-Gibbs-von Neumann-Shannon logarithmic entropic functional (\\(S_{BG}\\ is inadequate for wide classes of strongly correlated systems: see for instance the 2001 Brukner and Zeilinger's {\\it Conceptual inadequacy of the Shannon information in quantum measurements}, among many other systems exhibiting various forms of complexity. On the other hand, the Shannon and Khinchin axioms uniquely mandate the BG form \\(S_{BG}=-k\\sum_i p_i \\ln p_i\\; the Shore and Johnson axioms follow the same path. Many natural, artificial and social systems have been satisfactorily approached with nonadditive entropies such as the \\(S_q=k \\frac{1-\\sum_i p_i^q}{q-1}\\ one (\\(q \\in {\\cal R}; \\,S_1=S_{BG}\\, basis of nonextensive statistical mechanics. Consistently, the Shannon 1948 and Khinchine 1953 uniqueness theorems have already been generalized in the literature, by Santos 1997 and Abe 2000 respectively, in order to uniquely mandate \\(S_q\\. We argue here that the same remains to be done with the Shore and Johnson 1980 axioms. We arrive to this conclusion by analyzing specific classes of strongly correlated complex systems that await such generalization.

  12. Inadequacies of Belgium nuclear emergency plans: lessons from the Fukushima catastrophe have not been learned

    International Nuclear Information System (INIS)

    Boilley, David; Josset, Mylene

    2015-01-01

    After having outlined that some Belgium regional authorities made some statements showing that they did not learn lessons neither from the Chernobyl catastrophe, nor from the Fukushima accident, this report aims at examining whether Belgium is well prepared to face a severe nuclear accident occurring within its borders or in neighbouring countries, whether all hypotheses have actually been taken into account, and whether existing emergency plans are realistic. After a presentation of Belgium's situation regarding nuclear plants (Belgium plants and neighbouring French plants), the report presents the content and organisation of the nuclear emergency plan for the Belgium territory at the national, provincial and municipal levels. While outlining inadequacies and weaknesses of the Belgium plan regarding the addressed issues, it discusses the main lessons learned from the Fukushima accident in terms of emergency planning areas, of population sheltering, of iodine-based prophylaxis, of population evacuation, of food supply, of tools (measurement instruments) and human resources, and of public information. In the next parts, the report addresses and discusses trans-border issues, and the commitment of stakeholders

  13. X-Ray Diffraction Profile Analysis for Characterizing Isothermal Aging Behavior of M250 Grade Maraging Steel

    Science.gov (United States)

    Mahadevan, S.; Jayakumar, T.; Rao, B. P. C.; Kumar, Anish; Rajkumar, K. V.; Raj, Baldev

    2008-08-01

    X-ray diffraction (XRD) studies were carried out to characterize aging behavior of M250 grade maraging steel samples subjected to isothermal aging at 755 K for varying durations of 0.25, 1, 3, 10, 40, 70, and 100 hours. Earlier studies had shown typical features of precipitation hardening, wherein the hardness increased to a peak value due to precipitation of intermetallics and decreased upon further aging (overaging) due to reversion of martensite to austenite. Intermetallic precipitates, while coherent, are expected to increase the microstrain in the matrix. Hence, an attempt has been made in the present study to understand the microstructural changes in these samples using XRD line profile analysis. The anisotropic broadening with diffraction angle observed in the simple Williamson Hall (WH) plot has been addressed using the modified WH (mWH) approach, which takes into account the contrast caused by dislocations on line profiles, leading to new scaling factors in the WH plot. The normalized mean square strain and crystallite size estimated from mWH have been used to infer early precipitation and to characterize aging behavior. The normalized mean square strain has been used to determine the Avrami exponent in the Johnson Mehl Avrami (JMA) equation, which deals with the kinetics of precipitation. The Avrami exponent thus determined has matched well with values found by other methods, as reported in literature.

  14. Effect of γ-radiation on crystallization of polycaprolactone

    International Nuclear Information System (INIS)

    Zhu Guangming; Xu, Qianyong; Qin Ruifeng; Yan Hongxia; Liang Guozheng

    2005-01-01

    The crystallization behavior of radiation cross-linked poly(ε-caprolactone) (PCL) was studied by DSC at different cooling rates. The crystallization process was analyzed by the Ozawa equation and the Mo-Zhishen method that is developed from combining the Avrami equation and the Ozawa equation. It was concluded that the crystallization of radiation crosslinked PCL is governed by heterogeneous nucleation and single-dimension growth; the crystal fraction and rates of crystallization are related to the radiation dose and degree of cross-linking; the relationship between relative crystallinity and time follows the Ozawa equation: The higher the degree of crosslinking, the less the crystal velocity constant. The activation energy of crystallization for irradiated PCL is between 65 and 54kJ/mol

  15. Crystallization kinetics of the Cu50Zr50 metallic glass under isothermal conditions

    International Nuclear Information System (INIS)

    Gao, Qian; Jian, Zengyun; Xu, Junfeng; Zhu, Man; Chang, Fange; Han, Amin

    2016-01-01

    Amorphous structure of the melt-spun Cu 50 Zr 50 amorphous alloy ribbons were confirmed by X-ray diffraction (XRD) and high-resolution transmission electron microscopy (HR-TEM). Isothermal crystallization kinetics of these alloy ribbons were investigated using differential scanning calorimetry (DSC). Besides, Arrhenius and Johnson-Mehl-Avrami (JMA) equations were utilized to obtain the isothermal crystallization kinetic parameters. As shown in the results, the local activation energy E α decreases by a large margin at the crystallized volume fraction α<0.1, which proves that crystallization process is increasingly easy. In addition, the local activation energy E α is basically constant at 0.1<α<0.9. Therefore, it turns out that the unchanged barrier is overcome in the crystallization process. Finally, E α rapidly decreases at 0.9<α<1, implying that crystallization becomes easier and easier to proceed. Nucleation activation energy E nucleation is greater than growth activation energy E growth , so nucleation is harder than growth in isothermal process. In terms of the local Avrami exponent n(α), it ranges 1.1–7.4, revealing that isothermal crystallization mechanism is interface-controlled one- two- or three-dimensional growth with different nucleation rates. - Graphical abstract: The local Avrami exponent n(α), it ranges 1.1–7.4, revealing that isothermal crystallization mechanism is interface-controlled one- two- or three-dimensional growth with different nucleation rates. - Highlights: • Isothermal crystallization kinetics of Cu 50 Zr 50 metallic glass was investigated. • The relationship between the local activation energy E α and the crystallized volume fraction α were determined. • The nucleation activation energy E nucleation and grain growth activation energy E growth were obtained. • The local Avrami exponent n(α) was calculated in isothermal model.

  16. Numerical modelling of tools steel hardening. A thermal phenomena and phase transformations

    Directory of Open Access Journals (Sweden)

    T. Domański

    2010-01-01

    Full Text Available This paper the model hardening of tool steel takes into considerations of thermal phenomena and phase transformations in the solid state are presented. In the modelling of thermal phenomena the heat equations transfer has been solved by Finite Elements Method. The graph of continuous heating (CHT and continuous cooling (CCT considered steel are used in the model of phase transformations. Phase altered fractions during the continuous heating austenite and continuous cooling pearlite or bainite are marked in the model by formula Johnson-Mehl and Avrami. For rate of heating >100 K/s the modified equation Koistinen and Marburger is used. Modified equation Koistinen and Marburger identify the forming fraction of martensite.

  17. Study of crystallization kinetics of peek thermoplastics using Nakamura equation

    Science.gov (United States)

    Chalid, Mochamad; Muhammad Joshua Y., B.; Fikri, Arbi Irsyad; Gregory, Noel; Priadi, Dedi; Fatriansyah, Jaka Fajar

    2018-04-01

    We have simulated the time evolution of relative crystallization of PEEK at various cooling rates (10, 15, 20 °C/min) and made comparison with the experiments. The simulation was conducted using Nakamura model which is a modified Avrami model. The model is a 1 cm radius of circle with the cooling plate which was placed in the upper part of the circle. The cooling plate temperature was varied in order to obtain particular cooling rates. The measurement point is located near upper boundary in order to minimize the heat transfer effect. The general trend of time evolution of crystallization was well captured although some discrepancies occured. These discrepancies may be attributed to the heat transfer effect and secondary crystallization.

  18. The Prevalence of Micronutrient Deficiencies and  Inadequacies in the Middle East and Approaches to  Interventions

    Directory of Open Access Journals (Sweden)

    Nahla Hwalla

    2017-03-01

    Full Text Available Micronutrient deficiencies and inadequacies constitute a global health issue, particularly among countries in the Middle East. The objective of this review is to identify micronutrient deficits in the Middle East and to consider current and new approaches to address this problem. Based on the availability of more recent data, this review is primarily focused on countries that are in advanced nutrition transition. Prominent deficits in folate, iron, and vitamin D are noted among children/adolescents, women of childbearing age, pregnant women, and the elderly. Reports indicate that food fortification in the region is sporadic and ineffective, and the use of dietary supplements is low. Nutrition monitoring in the region is limited, and gaps in relevant information present challenges for implementing new policies and approaches to address the problem. Government‐sponsored initiatives are necessary to assess current dietary intakes/patterns, support nutrition education, and to reduce food insecurity, especially among vulnerable population groups. Public–private partnerships should be considered in targeting micronutrient fortification programs and supplementation recommendations as approaches to help alleviate the burden of micronutrient deficiencies and inadequacies in the Middle East.

  19. The bioavailability of iron, zinc, protein and vitamin A is highly variable in French individual diets: Impact on nutrient inadequacy assessment and relation with the animal-to-plant ratio of diets.

    Science.gov (United States)

    Perignon, Marlène; Barré, Tangui; Gazan, Rozenn; Amiot, Marie-Josèphe; Darmon, Nicole

    2018-01-01

    Nutritional adequacy depends on nutrient intakes and bioavailability which strongly varies with the plant- or animal-origin of foods. The aim was to estimate iron, zinc, protein and vitamin A bioavailability from individual diets, and investigate its relation with the animal-to-plant ratio (A/P) of diets. Bioavailability was estimated in 1899 French diets using diet-based algorithms or food-group specific conversion factors. Nutrient inadequacy was estimated based on i) bioavailability calculated in each individual diet and ii) average bioavailability assumed for Western-diets. Mean iron absorption, zinc absorption, protein quality and β-carotene conversion factor were 13%, 30%, 92%, and 17:1, respectively. Bioavailability displayed a high variability between individual diets, poorly explained by their A/P. Using individual bioavailability led to different inadequacy prevalence than with average factors assumed for Western-diets. In this population, the A/P does not seem sufficient to predict nutrient bioavailability and the corresponding recommended intakes. Nutritional adequacy should be assessed using bioavailability accounting for individual diets composition. Copyright © 2016 Elsevier Ltd. All rights reserved.

  20. Inadequacies in the civil nuclear liability regime evident after the Chernobyl accident: the response in the joint protocol of 1988

    International Nuclear Information System (INIS)

    Pelzer, N.

    1993-01-01

    The Joint Protocol of 21 September 1988 Relating to the Application of the Vienna Convention and the Paris Convention, by bridging both Conventions and by broadening thus the area where internationally harmonized nuclear liability law is applicable to nuclear incidents, contributes to doing away with inadequacies in the system of compensation for nuclear damage. On the other hand the Protocol has negative repercussions on the existing liability Conventions. Due to the enlargement of the territorial scope of application the compensation amounts available will be exhausted earlier. In order to avoid an aggravation of the legal position of the victims in the territories of the original Contracting Parties to the Vienna and the Paris Conventions the joint Protocol has to be responded to by a considerable increase of the compensation amounts

  1. Crystallization kinetics and magnetic properties of FeSiCr amorphous alloy powder cores

    Energy Technology Data Exchange (ETDEWEB)

    Xu, Hu-ping [School of Logistics Engineering, Wuhan University of Technology, Wuhan 430063 (China); Wang, Ru-wu, E-mail: ruwuwang@hotmail.com [National Engineering Research Center For Silicon Steel, Wuhan 430080 (China); College of Materials Science and Metallurgical Engineering, Wuhan University of Science and Technology, Wuhan 430081 (China); Wei, Ding [School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan 430074 (China); Zeng, Chun [National Engineering Research Center For Silicon Steel, Wuhan 430080 (China)

    2015-07-01

    The crystallization kinetics of FeSiCr amorphous alloy, characterized by the crystallization activation energy, Avrami exponent and frequency factor, was studied by non-isothermal differential scanning calorimetric (DSC) measurements. The crystallization activation energy and frequency factor of amorphous alloy calculated from Augis–Bennett model were 476 kJ/mol and 5.5×10{sup 18} s{sup −1}, respectively. The Avrami exponent n was calculated to be 2.2 from the Johnson–Mehl–Avrami (JMA) equation. Toroid-shaped Fe-base amorphous powder cores were prepared from the commercial FeSiCr amorphous alloy powder and subsequent cold pressing using binder and insulation. The characteristics of FeSiCr amorphous alloy powder and the effects of compaction pressure and insulation content on the magnetic properties, i.e., effective permeability μ{sub e}, quality factor Q and DC-bias properties of FeSiCr amorphous alloy powder cores, were investigated. The FeSiCr amorphous alloy powder cores exhibit a high value of quality factor and a stable permeability in the frequency range up to 1 MHz, showing superior DC-bias properties with a “percent permeability” of more than 82% at H=100 Oe. - Highlights: • The crystallization kinetics of FeSiCr amorphous alloy was investigated. • The FeSiCr powder cores exhibit a high value of Q and a stable permeability. • The FeSiCr powder cores exhibit superior DC-bias properties.

  2. A balance principle approach for modeling phase transformation kinetics

    International Nuclear Information System (INIS)

    Lusk, M.; Krauss, G.; Jou, H.J.

    1995-01-01

    A balance principle is offered to model volume fraction kinetics of phase transformation kinetics at a continuum level. This microbalance provides a differential equation for transformation kinetics which is coupled to the differential equations governing the mechanical and thermal aspects of the process. Application here is restricted to diffusive transformations for the sake of clarity, although the principle is discussed for martensitic phase transitions as well. Avrami-type kinetics are shown to result from a special class of energy functions. An illustrative example using a 0.5% C Chromium steel demonstrates how TTT and CCT curves can be generated using a particularly simple effective energy function. (orig.)

  3. Differential Equations Compatible with KZ Equations

    International Nuclear Information System (INIS)

    Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.

    2000-01-01

    We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions

  4. Kinetics, isothermal and thermodynamics studies of electrocoagulation removal of basic dye rhodamine B from aqueous solution using steel electrodes

    Science.gov (United States)

    Adeogun, Abideen Idowu; Balakrishnan, Ramesh Babu

    2017-07-01

    Electrocoagulation was used for the removal of basic dye rhodamine B from aqueous solution, and the process was carried out in a batch electrochemical cell with steel electrodes in monopolar connection. The effects of some important parameters such as current density, pH, temperature and initial dye concentration, on the process, were investigated. Equilibrium was attained after 10 min at 30 °C. Pseudo-first-order, pseudo-second-order, Elovich and Avrami kinetic models were used to test the experimental data in order to elucidate the kinetic adsorption process; pseudo-first-order and Avrami models best fitted the data. Experimental data were analysed using six model equations: Langmuir, Freudlinch, Redlich-Peterson, Temkin, Dubinin-Radushkevich and Sips isotherms and it was found that the data fitted well with Sips isotherm model. The study showed that the process depends on current density, temperature, pH and initial dye concentration. The calculated thermodynamics parameters (Δ G°, Δ H° and Δ S°) indicated that the process is spontaneous and endothermic in nature.

  5. The Effect of Prestrain Temperature on Kinetics of Static Recrystallization, Microstructure Evolution, and Mechanical Properties of Low Carbon Steel

    Science.gov (United States)

    Akbari, Edris; Karimi Taheri, Kourosh; Karimi Taheri, Ali

    2018-05-01

    In this research, the samples of a low carbon steel sheet were rolled up to a thickness prestrain of 67% at three different temperatures consisted of room, blue brittleness, and subzero temperature. Microhardness, SEM, and tensile tests were carried out to evaluate the static recrystallization kinetics defined by the Avrami equation, microstructural evolution, and mechanical properties. It was found that the Avrami exponent is altered with change in prestrain temperature and it achieves the value of 1 to 1. 5. Moreover, it was indicated that prestraining at subzero temperature followed by annealing at 600 °C leads to considerable enhancement in tensile properties and kinetics of static recrystallization compared to room and blue brittleness temperatures. The prestraining at blue brittleness temperature followed by annealing treatment caused, however, a higher strength and faster kinetics compared with that at room temperature. It was concluded that although from the steel ductility point of view, the blue brittleness temperature is called an unsuitable temperature, but it can be used as prestraining temperature to develop noticeable combination of strength and ductility in low carbon steel.

  6. Superlattice-like SnSb{sub 4}/Ga{sub 3}Sb{sub 7} thin films for ultrafast switching phase-change memory application

    Energy Technology Data Exchange (ETDEWEB)

    Hu, Yifeng [Tongji University, Key Laboratory of Advanced Civil Engineering Materials of Ministry of Education, Functional Materials Research Laboratory, School of Materials Science and Engineering, Shanghai (China); Jiangsu University of Technology, School of Mathematics and Physics, Changzhou (China); He, Zifang; Zhai, Jiwei [Tongji University, Key Laboratory of Advanced Civil Engineering Materials of Ministry of Education, Functional Materials Research Laboratory, School of Materials Science and Engineering, Shanghai (China); Wu, Pengzhi; Lai, Tianshu [Sun Yat-Sen University, State Key Laboratory of Optoelectronic Materials and Technology, Department of Physics, Guangzhou (China); Song, Sannian; Song, Zhitang [Chinese Academy of Sciences, State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Micro-system and Information Technology, Shanghai (China)

    2015-11-15

    The carrier concentration of Sb-rich phase SnSb{sub 4}, Ga{sub 3}Sb{sub 7} and superlattice-like [SnSb{sub 4}(3.5 nm)/Ga{sub 3}Sb{sub 7}(4 nm)]{sub 7} (SLL-7) thin films as a function of annealing temperature was investigated to explain the reason of resistance change. The activation energy for crystallization was calculated with a Kissinger equation to estimate the thermal stability. In order to illuminate the transition mechanisms, the crystallization kinetics of SLL-7 were explored by using Johnson-Mehl-Avrami theory. The obtained values of Avrami indexes indicate that a one-dimensional growth-dominated mechanism is responsible for the set transition of SLL-7 thin film. X-ray diffractometer and Raman scattering spectra were recorded to investigate the change of crystalline structure. The measurement of atomic force microscopy indicated that SLL-7 thin film has a good smooth surface. A picosecond laser pump-probe system was used to test and verify phase-change speed of the SLL-7 thin film. (orig.)

  7. Nursing students experienced personal inadequacy, vulnerability and transformation during their patient care encounter: A qualitative meta-synthesis.

    Science.gov (United States)

    Kaldal, Maiken Holm; Kristiansen, Jette; Uhrenfeldt, Lisbeth

    2018-05-01

    To identify, appraise and synthesize the best available evidence exploring nursing students' experiences of professional patient care encounters in a hospital unit. The Joanna Briggs Institute (JBI) guidelines were followed and a meta-synthesis was conducted. Qualitative research articles were considered for inclusion in the review, and JBI's meta-aggregative approach to synthesizing qualitative evidence was followed. An extensive search for relevant literature was undertaken in scientific databases. Data were extracted from the included research articles, and qualitative research findings were pooled using the Qualitative Assessment and Review Instrument. This involved categorization of findings on the basis of similarity of meaning and aggregation of these categories to produce a comprehensive set of synthesized findings. A total of five research articles met the inclusion criteria and were included in the review. The review process resulted in 46 subcategories that were aggregated into 13 categories. The categories generated four synthesized findings: personal existence; personal learning and development; being a professional fellow human; and clinical learning environment. We meta-synthesized that: Nursing students experienced personal inadequacy, vulnerability and a transformation during their patient care encounter. Copyright © 2018 Elsevier Ltd. All rights reserved.

  8. Kinetics modeling of precipitation with characteristic shape during post-implantation annealing

    Directory of Open Access Journals (Sweden)

    Kun-Dar Li

    2015-11-01

    Full Text Available In this study, we investigated the precipitation with characteristic shape in the microstructure during post-implantation annealing via a theoretical modeling approach. The processes of precipitates formation and evolution during phase separation were based on a nucleation and growth mechanism of atomic diffusion. Different stages of the precipitation, including the nucleation, growth and coalescence, were distinctly revealed in the numerical simulations. In addition, the influences of ion dose, temperature and crystallographic symmetry on the processes of faceted precipitation were also demonstrated. To comprehend the kinetic mechanism, the simulation results were further analyzed quantitatively by the Kolmogorov-Johnson-Mehl-Avrami (KJMA equation. The Avrami exponents obtained from the regression curves varied from 1.47 to 0.52 for different conditions. With the increase of ion dose and temperature, the nucleation and growth of precipitations were expedited in accordance with the shortened incubation time and the raised coefficient of growth rate. A miscellaneous shape of precipitates in various crystallographic symmetry systems could be simulated through this anisotropic model. From the analyses of the kinetics, more fundamental information about the nucleation and growth mechanism of faceted precipitation during post-implantation annealing was acquired for future application.

  9. p-Euler equations and p-Navier-Stokes equations

    Science.gov (United States)

    Li, Lei; Liu, Jian-Guo

    2018-04-01

    We propose in this work new systems of equations which we call p-Euler equations and p-Navier-Stokes equations. p-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the 'momentum' is the signed (p - 1)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier-Stokes equations. If γ = p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier-Stokes equations in Rd for γ = p and p ≥ d ≥ 2 through a compactness criterion.

  10. Equating error in observed-score equating

    NARCIS (Netherlands)

    van der Linden, Willem J.

    2006-01-01

    Traditionally, error in equating observed scores on two versions of a test is defined as the difference between the transformations that equate the quantiles of their distributions in the sample and population of test takers. But it is argued that if the goal of equating is to adjust the scores of

  11. equateIRT: An R Package for IRT Test Equating

    Directory of Open Access Journals (Sweden)

    Michela Battauz

    2015-12-01

    Full Text Available The R package equateIRT implements item response theory (IRT methods for equating different forms composed of dichotomous items. In particular, the IRT models included are the three-parameter logistic model, the two-parameter logistic model, the one-parameter logistic model and the Rasch model. Forms can be equated when they present common items (direct equating or when they can be linked through a chain of forms that present common items in pairs (indirect or chain equating. When two forms can be equated through different paths, a single conversion can be obtained by averaging the equating coefficients. The package calculates direct and chain equating coefficients. The averaging of direct and chain coefficients that link the same two forms is performed through the bisector method. Furthermore, the package provides analytic standard errors of direct, chain and average equating coefficients.

  12. Computing generalized Langevin equations and generalized Fokker-Planck equations.

    Science.gov (United States)

    Darve, Eric; Solomon, Jose; Kia, Amirali

    2009-07-07

    The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.

  13. Development of kinetics equations from the Boltzmann equation; Etablissement des equations de la cinetique a partir de l'equation de Boltzmann

    Energy Technology Data Exchange (ETDEWEB)

    Plas, R.

    1962-07-01

    The author reports a study on kinetics equations for a reactor. He uses the conventional form of these equations but by using a dynamic multiplication factor. Thus, constants related to delayed neutrons are not modified by efficiency factors. The author first describes the theoretic kinetic operation of a reactor and develops the associated equations. He reports the development of equations for multiplication factors.

  14. Simulation of the hot flow behaviour of a medium carbon microalloyed steel. Part 2. Dynamic recrystallization: onset and kinetics

    International Nuclear Information System (INIS)

    Cabrera, J.M.; Al Omar, A.; Prado, J.M.

    1997-01-01

    According to the part 1 of this work, in this second part the dynamic recrystallization of a commercial medium carbon microalloyed steel is characterized from the point of view of its onset and kinetics. For this purpose uniaxial hot compression tests were carried out over a range of five orders of magnitude in strain rate and 300 degree centigree of temperature. Experimental results are compared with those reported in the literature and the possible effect of dynamic precipitation is also analyzed. It is verified that the kinetics of dynamics recrystallization can balefully be described by the classical Avrami equation. (Author) 42 refs

  15. Layer-by-layer films from tartrazine dye with bovine serum albumin

    Science.gov (United States)

    de Souza, Nara C.; Flores, Júlio C. Johner; Silva, Josmary R.

    2009-12-01

    We report on the preparation and study of the adsorption process of layer-by-layer films of tartrazine alternated with bovine serum albumin. UV-Vis spectroscopy indicated that the films form J-aggregates of tartrazine. Adsorption kinetics was fitted by the Johnson-Mehl-Avrami equation and surface morphological analyses by atomic force microscopy suggested that the J-aggregates were column-shaped, which was attributed to the column-like symmetry of the tartrazine molecules. The columnar structures that formed probably arose from the juxtaposition of smaller aggregates that were already present at the beginning of film growth.

  16. Simple equation method for nonlinear partial differential equations and its applications

    Directory of Open Access Journals (Sweden)

    Taher A. Nofal

    2016-04-01

    Full Text Available In this article, we focus on the exact solution of the some nonlinear partial differential equations (NLPDEs such as, Kodomtsev–Petviashvili (KP equation, the (2 + 1-dimensional breaking soliton equation and the modified generalized Vakhnenko equation by using the simple equation method. In the simple equation method the trial condition is the Bernoulli equation or the Riccati equation. It has been shown that the method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering problems.

  17. Extended rate equations

    International Nuclear Information System (INIS)

    Shore, B.W.

    1981-01-01

    The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence

  18. Research on the hot deformation behavior of a Fe-Ni-Cr alloy (800H) at temperatures above 1000 °C

    Science.gov (United States)

    Cao, Yu; Di, Hongshuang

    2015-10-01

    Considering the pinning effect of fine carbides on grain boundaries, hot compression tests were performed above the dissolution temperature of Cr23C6 to investigate the hot deformation behavior of a Fe-Ni-Cr alloy (800H). The results show that the single peak stress associated with dynamic recrystalization (DRX) became more distinct at higher temperature and lower strain rate. The process of DRX was thoroughly stimulated when deformed above 1000 °C. Constitutive equations for hot deformation were established by regression analysis of conventional hyperbolic sine equation. The relationships between Zener-Hollomon parameter (Z) and the characteristic points of flow curves were established using the power law relation. Furthermore, kernel average misorientation (KAM) and grain orientation spread (GOS) were used to map the distribution of local misorientation and estimate the fraction of DRX, respectively. The critical strain and peak strain were used to predict the kinetics of DRX with the Avrami-type equation.

  19. Isothermal crystallization and melting behavior of polypropylene/layered double hydroxide nanocomposites

    International Nuclear Information System (INIS)

    Lonkar, Sunil P.; Singh, R.P.

    2009-01-01

    The effect of layered double hydroxide (LDH) nanolayers on the crystallization behavior of polypropylene (PP) was studied based on the preparation of nanocomposites by a melt intercalation method. The isothermal crystallization kinetics and subsequent melting behavior of PP/LDH hybrids were studied with differential scanning calorimetry (DSC), polarized optical microscopy (POM), and wide-angle X-ray diffraction (WAXD). Studies revealed that the LDH promoted heterogeneous nucleation, accelerating the crystallization of PP. The Avrami equation successfully describes the isothermal crystallization kinetics of PP/LDH hybrids and signifies heterogeneous nucleation in crystal growth of PP. The varying values of Avrami exponent (n) and half crystallization time (t 1/2 ) of PP and PP/LDH hybrids describes overall crystallization behavior. The crystallite size (D hkl ) and distribution of different crystallites in PP varied in presence of LDH. A significant increase in melting temperature is observed for PP/LDH hybrids. The POM showed that smaller and less perfect crystals were formed in nanocomposites because of molecular interaction between PP chains and LDH. The value of fold surface free energy (σ e ) of PP chains decreased with increasing LDH content. Finally, the overall results signify that LDH at nanometer level acted as nucleating agent and accelerate the overall crystallization process of PP.

  20. Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

    Directory of Open Access Journals (Sweden)

    Hamidreza Rezazadeh

    2014-05-01

    Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.

  1. Performance estimates for personnel access control systems

    International Nuclear Information System (INIS)

    Bradley, R.G.

    1980-10-01

    Current performance estimates for personnel access control systems use estimates of Type I and Type II verification errors. A system performance equation which addresses normal operation, the insider, and outside adversary attack is developed. Examination of this equation reveals the inadequacy of classical Type I and II error evaluations which require detailed knowledge of the adversary threat scenario for each specific installation. Consequently, new performance measures which are consistent with the performance equation and independent of the threat are developed as an aid in selecting personnel access control systems

  2. Movement and effects of spilled oil over the outer continental shelf; inadequacy of existent data for the Baltimore Canyon Trough area

    Science.gov (United States)

    Knebel, Harley J.

    1974-01-01

    A deductive approach to the problem of determining the movement and effects of spilled oil over the Outer Continental Shelf requires that the potential paths of oil be determined first, in order that critical subareas may be defined for later studies. The paths of spilled oil, in turn, depend primarily on the temporal and spatial variability of four factors: the thermohaline structure of the waters, the circulation of the water, the winds, and the distribution of suspended matter. A review of the existent data concerning these factors for the Baltimore Canyon Trough area (a relatively well studied segment of the Continental Shelf) reveals that the movement and dispersal of potential oil spills cannot be reliably predicted. Variations in the thermohaline structure of waters and in the distribution of suspended matter are adequately known; the uncertainty is due to insufficient wind and storm statistics and to the lack of quantitative understanding of the relationship between the nontidal drift and its basic driving mechanisms. Similar inadequacies should be anticipated for other potentially leasable areas of the shelf because an understanding of the movement of spilled oil has not been the underlying aim of most previous studies.

  3. A generalization of the simplest equation method and its application to (3+1)-dimensional KP equation and generalized Fisher equation

    International Nuclear Information System (INIS)

    Zhao, Zhonglong; Zhang, Yufeng; Han, Zhong; Rui, Wenjuan

    2014-01-01

    In this paper, the simplest equation method is used to construct exact traveling solutions of the (3+1)-dimensional KP equation and generalized Fisher equation. We summarize the main steps of the simplest equation method. The Bernoulli and Riccati equation are used as simplest equations. This method is straightforward and concise, and it can be applied to other nonlinear partial differential equations

  4. Analytic moment method calculations of the drift wave spectrum

    International Nuclear Information System (INIS)

    Thayer, D.R.; Molvig, K.

    1985-11-01

    A derivation and approximate solution of renormalized mode coupling equations describing the turbulent drift wave spectrum is presented. Arguments are given which indicate that a weak turbulence formulation of the spectrum equations fails for a system with negative dissipation. The inadequacy of the weak turbulence theory is circumvented by utilizing a renormalized formation. An analytic moment method is developed to approximate the solution of the nonlinear spectrum integral equations. The solution method employs trial functions to reduce the integral equations to algebraic equations in basic parameters describing the spectrum. An approximate solution of the spectrum equations is first obtained for a mode dissipation with known solution, and second for an electron dissipation in the NSA

  5. Influence of coolant motion on structure of hardened steel element

    Directory of Open Access Journals (Sweden)

    A. Kulawik

    2008-08-01

    Full Text Available Presented paper is focused on volumetric hardening process using liquid low melting point metal as a coolant. Effect of convective motion of the coolant on material structure after hardening is investigated. Comparison with results obtained for model neglecting motion of liquid is executed. Mathematical and numerical model based on Finite Element Metod is described. Characteristic Based Split (CBS method is used to uncouple velocities and pressure and finally to solve Navier-Stokes equation. Petrov-Galerkin formulation is employed to stabilize convective term in heat transport equation. Phase transformations model is created on the basis of Johnson-Mehl and Avrami laws. Continuous cooling diagram (CTPc for C45 steel is exploited in presented model of phase transformations. Temporary temperatures, phases participation, thermal and structural strains in hardening element and coolant velocities are shown and discussed.

  6. Analysis of wave equation in electromagnetic field by Proca equation

    International Nuclear Information System (INIS)

    Pamungkas, Oky Rio; Soeparmi; Cari

    2017-01-01

    This research is aimed to analyze wave equation for the electric and magnetic field, vector and scalar potential, and continuity equation using Proca equation. Then, also analyze comparison of the solution on Maxwell and Proca equation for scalar potential and electric field, both as a function of distance and constant wave number. (paper)

  7. Comparison of Kernel Equating and Item Response Theory Equating Methods

    Science.gov (United States)

    Meng, Yu

    2012-01-01

    The kernel method of test equating is a unified approach to test equating with some advantages over traditional equating methods. Therefore, it is important to evaluate in a comprehensive way the usefulness and appropriateness of the Kernel equating (KE) method, as well as its advantages and disadvantages compared with several popular item…

  8. Integral equations

    CERN Document Server

    Moiseiwitsch, B L

    2005-01-01

    Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco

  9. Partial Differential Equations

    CERN Document Server

    1988-01-01

    The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.

  10. Nonlinear evolution equations

    CERN Document Server

    Uraltseva, N N

    1995-01-01

    This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p

  11. FMTLxLyLz DIMENSIONAL EQUAT DIMENSIONAL EQUATION ...

    African Journals Online (AJOL)

    eobe

    plant made of 12mm thick steel plate was used in de steel plate ... water treatment plant. ... ameters affecting filtration processes were used to derive an equation usin ..... system. However, in deriving the equation onl terms are incorporated.

  12. Kinetic equations for an unstable plasma; Equations cinetiques d'un plasma instable

    Energy Technology Data Exchange (ETDEWEB)

    Laval, G; Pellat, R [Commissariat a l' Energie Atomique, Fontenay-aux-Roses (France). Centre d' Etudes Nucleaires

    1968-07-01

    In this work, we establish the plasma kinetic equations starting from the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy of equations. We demonstrate that relations existing between correlation functions may help to justify the truncation of the hierarchy. Then we obtain the kinetic equations of a stable or unstable plasma. They do not reduce to an equation for the one-body distribution function, but generally involve two coupled equations for the one-body distribution function and the spectral density of the fluctuating electric field. We study limiting cases where the Balescu-Lenard equation, the quasi-linear theory, the Pines-Schrieffer equations and the equations of weak turbulence in the random phase approximation are recovered. At last we generalise the H-theorem for the system of equations and we define conditions for irreversible behaviour. (authors) [French] Dans ce travail nous etablissons les equations cinetiques d'un plasma a partir des equations de la recurrence de Bogoliubov, Born, Green, Kirkwood et Yvon. Nous demontrons qu'entre les fonctions de correlation d'un plasma existent des relations qui permettent de justifier la troncature de la recurrence. Nous obtenons alors les equations cinetiques d'un plasma stable ou instable. En general elles ne se reduisent pas a une equation d'evolution pour la densite simple, mais se composent de deux equations couplees portant sur la densite simple et la densite spectrale du champ electrique fluctuant. Nous etudions le cas limites ou l'on retrouve l'equation de Balescu-Lenard, les equations de la theorie quasi-lineaire, les equations de Pines et Schrieffer et les equations de la turbulence faible dans l'approximation des phases aleatoires. Enfin, nous generalisons le theoreme H pour ce systeme d'equations et nous precisons les conditions d'evolution irreversible. (auteurs)

  13. equate: An R Package for Observed-Score Linking and Equating

    Directory of Open Access Journals (Sweden)

    Anthony D. Albano

    2016-10-01

    Full Text Available The R package equate contains functions for observed-score linking and equating under single-group, equivalent-groups, and nonequivalent-groups with anchor test(s designs. This paper introduces these designs and provides an overview of observed-score equating with details about each of the supported methods. Examples demonstrate the basic functionality of the equate package.

  14. Kinetic study of the annealing reactions in Cu-Ni-Fe alloys

    International Nuclear Information System (INIS)

    Donoso, E.

    2014-01-01

    The thermal aging of a Cu-45Ni-4Fe, Cu-34Ni-11Fe and Cu-33Ni-22Fe alloys tempered from 1173 K have been studied from Differential Scanning Calorimetry (DSC) and microhardness measurements. The analysis of DSC curves, from room temperature to 950 K, shows the presence of one exothermic reaction associated to the formation of FeNi 3 phase nucleating from a modulate structure, and one endothermic peak attributed to dissolution of this phase. Kinetic parameters were obtained using the usual Avrami-Erofeev equation, modified Kissinger method and integrated kinetic functions. Microhardness measurements confirmed the formation and dissolution of the FeNi 3 phase. (Author)

  15. Chemical Equation Balancing.

    Science.gov (United States)

    Blakley, G. R.

    1982-01-01

    Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)

  16. A new auxiliary equation and exact travelling wave solutions of nonlinear equations

    International Nuclear Information System (INIS)

    Sirendaoreji

    2006-01-01

    A new auxiliary ordinary differential equation and its solutions are used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the auxiliary equation which has more new exact solutions. More new exact travelling wave solutions are obtained for the quadratic nonlinear Klein-Gordon equation, the combined KdV and mKdV equation, the sine-Gordon equation and the Whitham-Broer-Kaup equations

  17. On a functional equation related to the intermediate long wave equation

    International Nuclear Information System (INIS)

    Hone, A N W; Novikov, V S

    2004-01-01

    We resolve an open problem stated by Ablowitz et al (1982 J. Phys. A: Math. Gen. 15 781) concerning the integral operator appearing in the intermediate long wave equation. We explain how this is resolved using the perturbative symmetry approach introduced by one of us with Mikhailov. By solving a certain functional equation, we prove that the intermediate long wave equation and the Benjamin-Ono equation are the unique integrable cases within a particular class of integro-differential equations. Furthermore, we explain how the perturbative symmetry approach is naturally extended to treat equations on a periodic domain. (letter to the editor)

  18. Some New Integrable Equations from the Self-Dual Yang-Mills Equations

    International Nuclear Information System (INIS)

    Ivanova, T.A.; Popov, A.D.

    1994-01-01

    Using the symmetry reductions of the self-dual Yang-Mills (SDYM) equations in (2+2) dimensions, we introduce new integrable equations which are 'deformations' of the chiral model in (2+1) dimensions, generalized nonlinear Schroedinger, Korteweg-de Vries, Toda lattice, Garnier, Euler-Arnold, generalized Calogero-Moser and Euler-Calogero-Moser equations. The Lax pairs for all of these equations are derived by the symmetry reductions of the Lax pair for the SDYM equations. 34 refs

  19. Auxiliary equation method for solving nonlinear partial differential equations

    International Nuclear Information System (INIS)

    Sirendaoreji,; Jiong, Sun

    2003-01-01

    By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation

  20. The equationally-defined commutator a study in equational logic and algebra

    CERN Document Server

    Czelakowski, Janusz

    2015-01-01

    This monograph introduces and explores the notions of a commutator equation and the equationally-defined commutator from the perspective of abstract algebraic logic.  An account of the commutator operation associated with equational deductive systems is presented, with an emphasis placed on logical aspects of the commutator for equational systems determined by quasivarieties of algebras.  The author discusses the general properties of the equationally-defined commutator, various centralization relations for relative congruences, the additivity and correspondence properties of the equationally-defined commutator, and its behavior in finitely generated quasivarieties. Presenting new and original research not yet considered in the mathematical literature, The Equationally-Defined Commutator will be of interest to professional algebraists and logicians, as well as graduate students and other researchers interested in problems of modern algebraic logic.

  1. A Comparison between Linear IRT Observed-Score Equating and Levine Observed-Score Equating under the Generalized Kernel Equating Framework

    Science.gov (United States)

    Chen, Haiwen

    2012-01-01

    In this article, linear item response theory (IRT) observed-score equating is compared under a generalized kernel equating framework with Levine observed-score equating for nonequivalent groups with anchor test design. Interestingly, these two equating methods are closely related despite being based on different methodologies. Specifically, when…

  2. Characterization of 3-D particle distribution and effects on recrystallization studied by computer simulation

    International Nuclear Information System (INIS)

    Fridy, J.M.; Marthinsen, K.; Rouns, T.N.; Lippert, K.B.; Nes, E.; Richmond, O.

    1992-12-01

    Artificial particle distribution in three dimensions with different degree of clustering have been generated and used as nucleation sites for the simulation of particle stimulated recrystallization with site saturation nucleation kinetics. The clustering has a strong effect on both the Avrami exponent and the resulting sectioned grain size distributions. The Avrami exponent decreases rapidly from the expected value of 3 with the degree of clustering. A value of less than 1.5 is obtained for the Avrami exponent with a strongly clustered distribution of nucleation sites. The size distributions of sectioned grain areas are considerably broadened with clustering, but are still far from the log-normal distributions observed experimentally. A computer program has been developed to generate particle distributions whose pair correlation functions match experimentally measured functions. 15 refs., 6 figs

  3. Five-dimensional Monopole Equation with Hedge-Hog Ansatz and Abel's Differential Equation

    OpenAIRE

    Kihara, Hironobu

    2008-01-01

    We review the generalized monopole in the five-dimensional Euclidean space. A numerical solution with the Hedge-Hog ansatz is studied. The Bogomol'nyi equation becomes a second order autonomous non-linear differential equation. The equation can be translated into the Abel's differential equation of the second kind and is an algebraic differential equation.

  4. Differential equations a dynamical systems approach ordinary differential equations

    CERN Document Server

    Hubbard, John H

    1991-01-01

    This is a corrected third printing of the first part of the text Differential Equations: A Dynamical Systems Approach written by John Hubbard and Beverly West. The authors' main emphasis in this book is on ordinary differential equations. The book is most appropriate for upper level undergraduate and graduate students in the fields of mathematics, engineering, and applied mathematics, as well as the life sciences, physics and economics. Traditional courses on differential equations focus on techniques leading to solutions. Yet most differential equations do not admit solutions which can be written in elementary terms. The authors have taken the view that a differential equations defines functions; the object of the theory is to understand the behavior of these functions. The tools the authors use include qualitative and numerical methods besides the traditional analytic methods. The companion software, MacMath, is designed to bring these notions to life.

  5. Differential equations

    CERN Document Server

    Barbu, Viorel

    2016-01-01

    This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.

  6. New Equating Methods and Their Relationships with Levine Observed Score Linear Equating under the Kernel Equating Framework

    Science.gov (United States)

    Chen, Haiwen; Holland, Paul

    2010-01-01

    In this paper, we develop a new curvilinear equating for the nonequivalent groups with anchor test (NEAT) design under the assumption of the classical test theory model, that we name curvilinear Levine observed score equating. In fact, by applying both the kernel equating framework and the mean preserving linear transformation of…

  7. Relations between nonlinear Riccati equations and other equations in fundamental physics

    International Nuclear Information System (INIS)

    Schuch, Dieter

    2014-01-01

    Many phenomena in the observable macroscopic world obey nonlinear evolution equations while the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. Linearizing nonlinear dynamics would destroy the fundamental property of this theory, however, it can be shown that quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown that the information about the dynamics of quantum systems with analytical solutions can not only be obtainable from the time-dependent Schrödinger equation but equally-well from a complex Riccati equation. Comparison with supersymmetric quantum mechanics shows that even additional information can be obtained from the nonlinear formulation. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation for any potential. Extension of the Riccati formulation to include irreversible dissipative effects is straightforward. Via (real and complex) Riccati equations, other fields of physics can also be treated within the same formalism, e.g., statistical thermodynamics, nonlinear dynamical systems like those obeying a logistic equation as well as wave equations in classical optics, Bose- Einstein condensates and cosmological models. Finally, the link to abstract ''quantizations'' such as the Pythagorean triples and Riccati equations connected with trigonometric and hyperbolic functions will be shown

  8. Bridging the Knowledge Gaps between Richards' Equation and Budyko Equation

    Science.gov (United States)

    Wang, D.

    2017-12-01

    The empirical Budyko equation represents the partitioning of mean annual precipitation into evaporation and runoff. Richards' equation, based on Darcy's law, represents the movement of water in unsaturated soils. The linkage between Richards' equation and Budyko equation is presented by invoking the empirical Soil Conservation Service curve number (SCS-CN) model for computing surface runoff at the event-scale. The basis of the SCS-CN method is the proportionality relationship, i.e., the ratio of continuing abstraction to its potential is equal to the ratio of surface runoff to its potential value. The proportionality relationship can be derived from the Richards' equation for computing infiltration excess and saturation excess models at the catchment scale. Meanwhile, the generalized proportionality relationship is demonstrated as the common basis of SCS-CN method, monthly "abcd" model, and Budyko equation. Therefore, the linkage between Darcy's law and the emergent pattern of mean annual water balance at the catchment scale is presented through the proportionality relationship.

  9. Partial differential equations

    CERN Document Server

    Evans, Lawrence C

    2010-01-01

    This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...

  10. Nonlinear Dirac Equations

    Directory of Open Access Journals (Sweden)

    Wei Khim Ng

    2009-02-01

    Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.

  11. Functional equations with causal operators

    CERN Document Server

    Corduneanu, C

    2003-01-01

    Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with causal operators. Functional Equations with Causal Operators explains the connection between equations with causal operators and the classical types of functional equations encountered by mathematicians and engineers. It details the fundamentals of linear equations and stability theory and provides several applications and examples.

  12. Isochronal and isothermal crystallization kinetics of amorphous Fe-based alloys

    International Nuclear Information System (INIS)

    Zhang, J.T.; Wang, W.M.; Ma, H.J.; Li, G.H.; Li, R.; Zhang, Z.H.

    2010-01-01

    Using the differential scanning calorimetry (DSC), the isochronal and isothermal crystallization kinetics of amorphous Fe 61 Co 9-x Zr 8 Mo 5 W x B 17 (x = 0 and 2) ribbons was investigated by the Kissinger equation and by the Kolmogorov-Johnson-Mehl-Avrami and Ranganathan-Heimendahl equations, respectively. The results show that tungsten can improve the activation energy E 1 K for the first crystallization in the isochronal annealing process and activation energy E n for the nucleation in the isothermal annealing process, which can be ascribed to the dissolution of tungsten in the amorphous phase. Meanwhile, tungsten can decrease the activation energy E 2 K for the second crystallization in the isochronal annealing process and growth activation energy E g in the isothermal annealing process, which is possibly associated with the formation of W-rich compound after the early nucleation process.

  13. High-temperature dehydration of talc: a kinetics study using in situ X-ray powder diffraction

    Science.gov (United States)

    Wang, Duojun; Yi, Li; Huang, Bojin; Liu, Chuanjiang

    2015-06-01

    High-temperature in situ X-ray powder diffraction patterns were used to study the dehydration kinetics of natural talc with a size of 10-15 µm. The talc was annealed from 1073 to 1223 K, and the variations in the characteristic peaks corresponding to talc with the time were recorded to determine the reaction progress. The decomposition of talc occurred, and peaks corresponding to talc and peaks corresponding to enstatite and quartz were observed. The enstatite and talc exhibited a topotactic relationship. The dehydration kinetics of talc was studied as a function of temperature between 1073 and 1223 K. The kinetics data could be modeled using an Avrami equation that considers nucleation and growth processes ? where n varies from 0.4 to 0.8. The rate constant (k) equation for the natural talc is ? The reaction mechanism for the dehydration of talc is a heterogeneous nucleation and growth mechanism.

  14. MODELING OF STRAIN-INDUCED PRECIPITATION KINETICS IN Nb MICROALLOYED STEELS

    Institute of Scientific and Technical Information of China (English)

    X.G. Zhou; Z.Y. Liu; D. Wu; Z.Li; C.M. Li

    2006-01-01

    On the basis of the thermodynamic calculation of precipitation and considering the effect of strain on the precipitation behavior and chemical composition (Si and Mn), the kinetics of precipitation from austenite has been investigated for different temperatures and strains. Nucleation theory and the solubility product of niobium, carbon, and nitrogen in austenite have been used to derive equations for the start time of precipitation as a function of temperature and composition. The value of n in Avrami equation was determined using the available experimental data from the published reports, which indicated that n is a constant independent of temperature and the end time of precipitation is a function of n and the start time of precipitation. The values of the start time and end time of precipitation predicted by the new model are compared with the experimental values and a good agreement was obtained between both.

  15. Evaluating Equating Results: Percent Relative Error for Chained Kernel Equating

    Science.gov (United States)

    Jiang, Yanlin; von Davier, Alina A.; Chen, Haiwen

    2012-01-01

    This article presents a method for evaluating equating results. Within the kernel equating framework, the percent relative error (PRE) for chained equipercentile equating was computed under the nonequivalent groups with anchor test (NEAT) design. The method was applied to two data sets to obtain the PRE, which can be used to measure equating…

  16. Handbook of integral equations

    CERN Document Server

    Polyanin, Andrei D

    2008-01-01

    This handbook contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equations that arise in mathematics, physics, engineering, the sciences, and economics. This second edition includes new chapters on mixed multidimensional equations and methods of integral equations for ODEs and PDEs, along with over 400 new equations with exact solutions. With many examples added for illustrative purposes, it presents new material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions.

  17. Ordinary differential equations

    CERN Document Server

    Greenberg, Michael D

    2014-01-01

    Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps

  18. Fractional Schroedinger equation

    International Nuclear Information System (INIS)

    Laskin, Nick

    2002-01-01

    Some properties of the fractional Schroedinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schroedinger equation we find the energy spectra of a hydrogenlike atom (fractional 'Bohr atom') and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schroedinger equations

  19. Introduction to differential equations

    CERN Document Server

    Taylor, Michael E

    2011-01-01

    The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponen

  20. Stochastic optimal control, forward-backward stochastic differential equations and the Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Paul, Wolfgang; Koeppe, Jeanette [Institut fuer Physik, Martin Luther Universitaet, 06099 Halle (Germany); Grecksch, Wilfried [Institut fuer Mathematik, Martin Luther Universitaet, 06099 Halle (Germany)

    2016-07-01

    The standard approach to solve a non-relativistic quantum problem is through analytical or numerical solution of the Schroedinger equation. We show a way to go around it. This way is based on the derivation of the Schroedinger equation from conservative diffusion processes and the establishment of (several) stochastic variational principles leading to the Schroedinger equation under the assumption of a kinematics described by Nelson's diffusion processes. Mathematically, the variational principle can be considered as a stochastic optimal control problem linked to the forward-backward stochastic differential equations of Nelson's stochastic mechanics. The Hamilton-Jacobi-Bellmann equation of this control problem is the Schroedinger equation. We present the mathematical background and how to turn it into a numerical scheme for analyzing a quantum system without using the Schroedinger equation and exemplify the approach for a simple 1d problem.

  1. Averaged RMHD equations

    International Nuclear Information System (INIS)

    Ichiguchi, Katsuji

    1998-01-01

    A new reduced set of resistive MHD equations is derived by averaging the full MHD equations on specified flux coordinates, which is consistent with 3D equilibria. It is confirmed that the total energy is conserved and the linearized equations for ideal modes are self-adjoint. (author)

  2. Differential equations

    CERN Document Server

    Tricomi, FG

    2013-01-01

    Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff

  3. Review of aerosol problems and the theory of aerosol physics with particular reference to sodium cooled fast reactors

    International Nuclear Information System (INIS)

    Williams, R.J.

    1978-01-01

    Processes that would govern the development, transport, and removal of aerosols, which are of interest in the study of hypothetical core disruptive situations in pool type sodium cooled fast reactors, are discussed. Theoretical descriptions of these processes are presented and known inadequacies indicated. The interpretation of experimental data and numeric solution of the governing equations is briefly considered. (author)

  4. How to obtain the covariant form of Maxwell's equations from the continuity equation

    International Nuclear Information System (INIS)

    Heras, Jose A

    2009-01-01

    The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell's equations in which charge conservation is emphasized as the fundamental axiom underlying these equations

  5. Kinetic study of the annealing reactions in Cu-Ni-Fe alloys; Estudio cinetico de las reacciones de recocido en aleaciones de Cu-Ni-Fe

    Energy Technology Data Exchange (ETDEWEB)

    Donoso, E.

    2014-07-01

    The thermal aging of a Cu-45Ni-4Fe, Cu-34Ni-11Fe and Cu-33Ni-22Fe alloys tempered from 1173 K have been studied from Differential Scanning Calorimetry (DSC) and microhardness measurements. The analysis of DSC curves, from room temperature to 950 K, shows the presence of one exothermic reaction associated to the formation of FeNi{sub 3} phase nucleating from a modulate structure, and one endothermic peak attributed to dissolution of this phase. Kinetic parameters were obtained using the usual Avrami-Erofeev equation, modified Kissinger method and integrated kinetic functions. Microhardness measurements confirmed the formation and dissolution of the FeNi{sub 3} phase. (Author)

  6. A generalized simplest equation method and its application to the Boussinesq-Burgers equation.

    Science.gov (United States)

    Sudao, Bilige; Wang, Xiaomin

    2015-01-01

    In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method.

  7. On separable Pauli equations

    International Nuclear Information System (INIS)

    Zhalij, Alexander

    2002-01-01

    We classify (1+3)-dimensional Pauli equations for a spin-(1/2) particle interacting with the electro-magnetic field, that are solvable by the method of separation of variables. As a result, we obtain the 11 classes of vector-potentials of the electro-magnetic field A(t,x(vector sign))=(A 0 (t,x(vector sign)), A(vector sign)(t,x(vector sign))) providing separability of the corresponding Pauli equations. It is established, in particular, that the necessary condition for the Pauli equation to be separable into second-order matrix ordinary differential equations is its equivalence to the system of two uncoupled Schroedinger equations. In addition, the magnetic field has to be independent of spatial variables. We prove that coordinate systems and the vector-potentials of the electro-magnetic field providing the separability of the corresponding Pauli equations coincide with those for the Schroedinger equations. Furthermore, an efficient algorithm for constructing all coordinate systems providing the separability of Pauli equation with a fixed vector-potential of the electro-magnetic field is developed. Finally, we describe all vector-potentials A(t,x(vector sign)) that (a) provide the separability of Pauli equation, (b) satisfy vacuum Maxwell equations without currents, and (c) describe non-zero magnetic field

  8. Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation

    Science.gov (United States)

    Vitanov, Nikolay K.; Dimitrova, Zlatinka I.

    2018-03-01

    We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schrödinger equation. It is shown that the methodology works also for other equations of the nonlinear Schrödinger kind.

  9. Elliptic and solitary wave solutions for Bogoyavlenskii equations system, couple Boiti-Leon-Pempinelli equations system and Time-fractional Cahn-Allen equation

    Directory of Open Access Journals (Sweden)

    Mostafa M.A. Khater

    Full Text Available In this article and for the first time, we introduce and describe Khater method which is a new technique for solving nonlinear partial differential equations (PDEs.. We apply this method for each of the following models Bogoyavlenskii equation, couple Boiti-Leon-Pempinelli system and Time-fractional Cahn-Allen equation. Khater method is very powerful, Effective, felicitous and fabulous method to get exact and solitary wave solution of (PDEs.. Not only just like that but it considers too one of the general methods for solving that kind of equations since it involves some methods as we will see in our discuss of the results. We make a comparison between the results of this new method and another method. Keywords: Bogoyavlenskii equations system, Couple Boiti-Leon-Pempinelli equations system, Time-fractional Cahn-Allen equation, Khater method, Traveling wave solutions, Solitary wave solutions

  10. Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation

    Directory of Open Access Journals (Sweden)

    Vitanov Nikolay K.

    2018-03-01

    Full Text Available We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schrödinger equation. It is shown that the methodology works also for other equations of the nonlinear Schrödinger kind.

  11. Integrable dissipative nonlinear second order differential equations via factorizations and Abel equations

    Energy Technology Data Exchange (ETDEWEB)

    Mancas, Stefan C. [Department of Mathematics, Embry–Riddle Aeronautical University, Daytona Beach, FL 32114-3900 (United States); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis Potosí, SLP (Mexico)

    2013-09-02

    We emphasize two connections, one well known and another less known, between the dissipative nonlinear second order differential equations and the Abel equations which in their first-kind form have only cubic and quadratic terms. Then, employing an old integrability criterion due to Chiellini, we introduce the corresponding integrable dissipative equations. For illustration, we present the cases of some integrable dissipative Fisher, nonlinear pendulum, and Burgers–Huxley type equations which are obtained in this way and can be of interest in applications. We also show how to obtain Abel solutions directly from the factorization of second order nonlinear equations.

  12. On the Existence and the Applications of Modified Equations for Stochastic Differential Equations

    KAUST Repository

    Zygalakis, K. C.

    2011-01-01

    In this paper we describe a general framework for deriving modified equations for stochastic differential equations (SDEs) with respect to weak convergence. Modified equations are derived for a variety of numerical methods, such as the Euler or the Milstein method. Existence of higher order modified equations is also discussed. In the case of linear SDEs, using the Gaussianity of the underlying solutions, we derive an SDE which the numerical method solves exactly in the weak sense. Applications of modified equations in the numerical study of Langevin equations is also discussed. © 2011 Society for Industrial and Applied Mathematics.

  13. An Auxiliary Equation for the Bellman Equation in a One-Dimensional Ergodic Control

    International Nuclear Information System (INIS)

    Fujita, Y.

    2001-01-01

    In this paper we consider the Bellman equation in a one-dimensional ergodic control. Our aim is to show the existence and the uniqueness of its solution under general assumptions. For this purpose we introduce an auxiliary equation whose solution gives the invariant measure of the diffusion corresponding to an optimal control. Using this solution, we construct a solution to the Bellman equation. Our method of using this auxiliary equation has two advantages in the one-dimensional case. First, we can solve the Bellman equation under general assumptions. Second, this auxiliary equation gives an optimal Markov control explicitly in many examples

  14. Covariant field equations in supergravity

    Energy Technology Data Exchange (ETDEWEB)

    Vanhecke, Bram [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium); Ghent University, Faculty of Physics, Gent (Belgium); Proeyen, Antoine van [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium)

    2017-12-15

    Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  15. Covariant field equations in supergravity

    International Nuclear Information System (INIS)

    Vanhecke, Bram; Proeyen, Antoine van

    2017-01-01

    Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  16. Reduction of lattice equations to the Painlevé equations: PIV and PV

    Science.gov (United States)

    Nakazono, Nobutaka

    2018-02-01

    In this paper, we construct a new relation between Adler-Bobenko-Suris equations and Painlevé equations. Moreover, using this connection we construct the difference-differential Lax representations of the fourth and fifth Painlevé equations.

  17. Test equating methods and practices

    CERN Document Server

    Kolen, Michael J

    1995-01-01

    In recent years, many researchers in the psychology and statistical communities have paid increasing attention to test equating as issues of using multiple test forms have arisen and in response to criticisms of traditional testing techniques This book provides a practically oriented introduction to test equating which both discusses the most frequently used equating methodologies and covers many of the practical issues involved The main themes are - the purpose of equating - distinguishing between equating and related methodologies - the importance of test equating to test development and quality control - the differences between equating properties, equating designs, and equating methods - equating error, and the underlying statistical assumptions for equating The authors are acknowledged experts in the field, and the book is based on numerous courses and seminars they have presented As a result, educators, psychometricians, professionals in measurement, statisticians, and students coming to the subject for...

  18. On generalized fractional vibration equation

    International Nuclear Information System (INIS)

    Dai, Hongzhe; Zheng, Zhibao; Wang, Wei

    2017-01-01

    Highlights: • The paper presents a generalized fractional vibration equation for arbitrary viscoelastically damped system. • Some classical vibration equations can be derived from the developed equation. • The analytic solution of developed equation is derived under some special cases. • The generalized equation is particularly useful for developing new fractional equivalent linearization method. - Abstract: In this paper, a generalized fractional vibration equation with multi-terms of fractional dissipation is developed to describe the dynamical response of an arbitrary viscoelastically damped system. It is shown that many classical equations of motion, e.g., the Bagley–Torvik equation, can be derived from the developed equation. The Laplace transform is utilized to solve the generalized equation and the analytic solution under some special cases is derived. Example demonstrates the generalized transfer function of an arbitrary viscoelastic system.

  19. Differential equations for dummies

    CERN Document Server

    Holzner, Steven

    2008-01-01

    The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.

  20. Every Equation Tells a Story: Using Equation Dictionaries in Introductory Geophysics

    Science.gov (United States)

    Caplan-Auerbach, Jacqueline

    2009-01-01

    Many students view equations as a series of variables and operators into which numbers should be plugged rather than as representative of a physical process. To solve a problem they may simply look for an equation with the correct variables and assume it meets their needs, rather than selecting an equation that represents the appropriate physical…

  1. Fundamental equations for two-phase flow. Part 1: general conservation equations. Part 2: complement and remarks; Equations fondamentales des ecoulements diphasiques. Premiere partie: equations generales de conservation. Deuxieme partie: complements et remarques

    Energy Technology Data Exchange (ETDEWEB)

    Delhaye, J M [Commissariat a l' Energie Atomique, 38 - Grenoble (France). Centre d' Etudes Nucleaires

    1968-12-01

    This report deals with the general equations of mass conservation, of momentum conservation, and energy conservation in the case of a two-phase flow. These equations are presented in several forms starting from integral equations which are assumed initially a priori. 1. Equations with local instantaneous variables, and interfacial conditions; 2. Equations with mean instantaneous variables in a cross-section, and practical applications: these equations include an important experimental value which is the ratio of the cross-section of passage of one phase to the total cross-section of a flow-tube. 3. Equations with a local statistical mean, and equations averaged over a period of time: A more advanced attempt to relate theory and experiment consists in taking the statistical averages of local equations. Equations are then obtained involving variables which are averaged over a period of time with the help of an ergodic assumption. 4. Combination of statistical averages and averages over a cross-section: in this study are considered the local variables averaged statistically, then averaged over the cross-section, and also the variables averaged over the section and then averaged statistically. 5. General equations concerning emulsions: In this case a phase exists in a locally very finely divided form. This peculiarity makes it possible to define a volume concentration, and to draw up equations which have numerous applications. - Certain points arising in the first part of this report concerning general mass conservation equations for two-phase flow have been completed and clarified. The terms corresponding to the interfacial tension have been introduced into the general equations. The interfacial conditions have thus been generalized. A supplementary step has still to be carried out: it has, in effect, been impossible to take the interfacial tension into account in the case of emulsions. It was then appeared interesting to compare this large group of fundamental

  2. Fundamental equations for two-phase flow. Part 1: general conservation equations. Part 2: complement and remarks; Equations fondamentales des ecoulements diphasiques. Premiere partie: equations generales de conservation. Deuxieme partie: complements et remarques

    Energy Technology Data Exchange (ETDEWEB)

    Delhaye, J.M. [Commissariat a l' Energie Atomique, 38 - Grenoble (France). Centre d' Etudes Nucleaires

    1968-12-01

    This report deals with the general equations of mass conservation, of momentum conservation, and energy conservation in the case of a two-phase flow. These equations are presented in several forms starting from integral equations which are assumed initially a priori. 1. Equations with local instantaneous variables, and interfacial conditions; 2. Equations with mean instantaneous variables in a cross-section, and practical applications: these equations include an important experimental value which is the ratio of the cross-section of passage of one phase to the total cross-section of a flow-tube. 3. Equations with a local statistical mean, and equations averaged over a period of time: A more advanced attempt to relate theory and experiment consists in taking the statistical averages of local equations. Equations are then obtained involving variables which are averaged over a period of time with the help of an ergodic assumption. 4. Combination of statistical averages and averages over a cross-section: in this study are considered the local variables averaged statistically, then averaged over the cross-section, and also the variables averaged over the section and then averaged statistically. 5. General equations concerning emulsions: In this case a phase exists in a locally very finely divided form. This peculiarity makes it possible to define a volume concentration, and to draw up equations which have numerous applications. - Certain points arising in the first part of this report concerning general mass conservation equations for two-phase flow have been completed and clarified. The terms corresponding to the interfacial tension have been introduced into the general equations. The interfacial conditions have thus been generalized. A supplementary step has still to be carried out: it has, in effect, been impossible to take the interfacial tension into account in the case of emulsions. It was then appeared interesting to compare this large group of fundamental

  3. Isothermal Crystallization Kinetics of HDPE/HA Compounds Irradiated with Sterilization Doses of Gamma Rays

    International Nuclear Information System (INIS)

    Albano, C.

    2006-01-01

    The objective of this work was to study the isothermal crystallization of High Density Polyethylene/Hydroxyapatite nanocomposites, with 2 and 5 ppc of HA, irradiated with 25 kGy (sterilization dose) of γ-Ray from a 60 C o source, at a rate of 4.8 kGy/h in air and at room temperature. The selected crystallization temperatures were 118, 117, 116 and 115 degree. The crystallization kinetics was analyzed using the Avrami's model whose parameters were optimized using a non-linear regression technique. Regression results show that the Avrami exponent varies between 1.8 and 1.5, meaning that the spherulitic growth is mainly two dimensional. Values for specific crystallization constant 'k' were found to be higher for HDPE/HA compounds than for pure HDPE, clearly indicating the presence of an HA nucleation effect. It was also observed that values for the specific crystallization constant 'k' decreases with increasing temperatures, being this effect more noticeable for HDPE/HA compounds than for pure HDPE. Regarding to irradiated samples, their 'k' values were found to be lower than those for non irradiated samples, the difference getting more significant with decreasing crystallization temperature. Simulation of experimental data with the Avrami's model show a clear influence of the crystallization temperature, the HA content in the sample and the amount of applied radiation. It was also observed that the Avrami model correlates satisfactorily experimental data for not irradiated samples of pure HDPE and HDPE/HA compounds at the highest crystallization (T c ). However, as the crystallization temperature decreases, the values simulated with the Avrami model increasingly deviate from experimental data, specifically at the highest values of the relative crystallinity. This effect is even stronger on irradiated samples of HDPE and HDPE/HA compounds

  4. Equating TIMSS Mathematics Subtests with Nonlinear Equating Methods Using NEAT Design: Circle-Arc Equating Approaches

    Science.gov (United States)

    Ozdemir, Burhanettin

    2017-01-01

    The purpose of this study is to equate Trends in International Mathematics and Science Study (TIMSS) mathematics subtest scores obtained from TIMSS 2011 to scores obtained from TIMSS 2007 form with different nonlinear observed score equating methods under Non-Equivalent Anchor Test (NEAT) design where common items are used to link two or more test…

  5. Isochronal and isothermal crystallization kinetics of amorphous Fe-based alloys

    Energy Technology Data Exchange (ETDEWEB)

    Zhang, J.T. [Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials, Ministry of Education, Shandong University, Jinan 250061 (China); Wang, W.M., E-mail: weiminw@sdu.edu.cn [Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials, Ministry of Education, Shandong University, Jinan 250061 (China); Key Lab of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004 (China); Ma, H.J.; Li, G.H.; Li, R.; Zhang, Z.H. [Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials, Ministry of Education, Shandong University, Jinan 250061 (China)

    2010-06-10

    Using the differential scanning calorimetry (DSC), the isochronal and isothermal crystallization kinetics of amorphous Fe{sub 61}Co{sub 9-x}Zr{sub 8}Mo{sub 5}W{sub x}B{sub 17} (x = 0 and 2) ribbons was investigated by the Kissinger equation and by the Kolmogorov-Johnson-Mehl-Avrami and Ranganathan-Heimendahl equations, respectively. The results show that tungsten can improve the activation energy E{sub 1}{sup K} for the first crystallization in the isochronal annealing process and activation energy E{sub n} for the nucleation in the isothermal annealing process, which can be ascribed to the dissolution of tungsten in the amorphous phase. Meanwhile, tungsten can decrease the activation energy E{sub 2}{sup K} for the second crystallization in the isochronal annealing process and growth activation energy E{sub g} in the isothermal annealing process, which is possibly associated with the formation of W-rich compound after the early nucleation process.

  6. Dynamic Diffraction Studies on the Crystallization, Phase Transformation, and Activation Energies in Anodized Titania Nanotubes

    Directory of Open Access Journals (Sweden)

    Hani Albetran

    2018-02-01

    Full Text Available The influence of calcination time on the phase transformation and crystallization kinetics of anodized titania nanotube arrays was studied using in-situ isothermal and non-isothermal synchrotron radiation diffraction from room temperature to 900 °C. Anatase first crystallized at 400 °C, while rutile crystallized at 550 °C. Isothermal heating of the anodized titania nanotubes by an increase in the calcination time at 400, 450, 500, 550, 600, and 650 °C resulted in a slight reduction in anatase abundance, but an increase in the abundance of rutile because of an anatase-to-rutile transformation. The Avrami equation was used to model the titania crystallization mechanism and the Arrhenius equation was used to estimate the activation energies of the titania phase transformation. Activation energies of 22 (10 kJ/mol for the titanium-to-anatase transformation, and 207 (17 kJ/mol for the anatase-to-rutile transformation were estimated.

  7. Dynamic Diffraction Studies on the Crystallization, Phase Transformation, and Activation Energies in Anodized Titania Nanotubes.

    Science.gov (United States)

    Albetran, Hani; Vega, Victor; Prida, Victor M; Low, It-Meng

    2018-02-23

    The influence of calcination time on the phase transformation and crystallization kinetics of anodized titania nanotube arrays was studied using in-situ isothermal and non-isothermal synchrotron radiation diffraction from room temperature to 900 °C. Anatase first crystallized at 400 °C, while rutile crystallized at 550 °C. Isothermal heating of the anodized titania nanotubes by an increase in the calcination time at 400, 450, 500, 550, 600, and 650 °C resulted in a slight reduction in anatase abundance, but an increase in the abundance of rutile because of an anatase-to-rutile transformation. The Avrami equation was used to model the titania crystallization mechanism and the Arrhenius equation was used to estimate the activation energies of the titania phase transformation. Activation energies of 22 (10) kJ/mol for the titanium-to-anatase transformation, and 207 (17) kJ/mol for the anatase-to-rutile transformation were estimated.

  8. Solving polynomial differential equations by transforming them to linear functional-differential equations

    OpenAIRE

    Nahay, John Michael

    2008-01-01

    We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order Abel differential equation with two nonlinear terms in order to demonstrate in as much detail as possible the computations necessary for a complete solution. We mention in our section on further developments that the basic transformation idea can be generali...

  9. Lorentz-force equations as Heisenberg equations for a quantum system in the euclidean space

    International Nuclear Information System (INIS)

    Rodriguez D, R.

    2007-01-01

    In an earlier work, the dynamic equations for a relativistic charged particle under the action of electromagnetic fields were formulated by R. Yamaleev in terms of external, as well as internal momenta. Evolution equations for external momenta, the Lorentz-force equations, were derived from the evolution equations for internal momenta. The mapping between the observables of external and internal momenta are related by Viete formulae for a quadratic polynomial, the characteristic polynomial of the relativistic dynamics. In this paper we show that the system of dynamic equations, can be cast into the Heisenberg scheme for a four-dimensional quantum system. Within this scheme the equations in terms of internal momenta play the role of evolution equations for a state vector, whereas the external momenta obey the Heisenberg equation for an operator evolution. The solutions of the Lorentz-force equation for the motion inside constant electromagnetic fields are presented via pentagonometric functions. (Author)

  10. Differential Equation over Banach Algebra

    OpenAIRE

    Kleyn, Aleks

    2018-01-01

    In the book, I considered differential equations of order $1$ over Banach $D$-algebra: differential equation solved with respect to the derivative; exact differential equation; linear homogeneous equation. In noncommutative Banach algebra, initial value problem for linear homogeneous equation has infinitely many solutions.

  11. Elements of partial differential equations

    CERN Document Server

    Sneddon, Ian Naismith

    1957-01-01

    Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory.Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing independent st

  12. New exact solutions to MKDV-Burgers equation and (2 + 1)-dimensional dispersive long wave equation via extended Riccati equation method

    International Nuclear Information System (INIS)

    Kong Cuicui; Wang Dan; Song Lina; Zhang Hongqing

    2009-01-01

    In this paper, with the aid of symbolic computation and a general ansaetz, we presented a new extended rational expansion method to construct new rational formal exact solutions to nonlinear partial differential equations. In order to illustrate the effectiveness of this method, we apply it to the MKDV-Burgers equation and the (2 + 1)-dimensional dispersive long wave equation, then several new kinds of exact solutions are successfully obtained by using the new ansaetz. The method can also be applied to other nonlinear partial differential equations.

  13. Introduction to partial differential equations

    CERN Document Server

    Greenspan, Donald

    2000-01-01

    Designed for use in a one-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, second-order partial differential equations, wave equation, potential equation, heat equation, approximate solution of partial differential equations, and more. Exercises appear at the ends of most chapters. 1961 edition.

  14. A New Fractional Projective Riccati Equation Method for Solving Fractional Partial Differential Equations

    International Nuclear Information System (INIS)

    Feng Qing-Hua

    2014-01-01

    In this paper, a new fractional projective Riccati equation method is proposed to establish exact solutions for fractional partial differential equations in the sense of modified Riemann—Liouville derivative. This method can be seen as the fractional version of the known projective Riccati equation method. For illustrating the validity of this method, we apply this method to solve the space-time fractional Whitham—Broer—Kaup (WBK) equations and the nonlinear fractional Sharma—Tasso—Olever (STO) equation, and as a result, some new exact solutions for them are obtained. (general)

  15. A new sine-Gordon equation expansion algorithm to investigate some special nonlinear differential equations

    International Nuclear Information System (INIS)

    Yan Zhenya

    2005-01-01

    A new transformation method is developed using the general sine-Gordon travelling wave reduction equation and a generalized transformation. With the aid of symbolic computation, this method can be used to seek more types of solutions of nonlinear differential equations, which include not only the known solutions derived by some known methods but new solutions. Here we choose the double sine-Gordon equation, the Magma equation and the generalized Pochhammer-Chree (PC) equation to illustrate the method. As a result, many types of new doubly periodic solutions are obtained. Moreover when using the method to these special nonlinear differential equations, some transformations are firstly needed. The method can be also extended to other nonlinear differential equations

  16. Singular stochastic differential equations

    CERN Document Server

    Cherny, Alexander S

    2005-01-01

    The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.

  17. Reactimeter dispersion equation

    OpenAIRE

    A.G. Yuferov

    2016-01-01

    The aim of this work is to derive and analyze a reactimeter metrological model in the form of the dispersion equation which connects reactimeter input/output signal dispersions with superimposed random noise at the inlet. It is proposed to standardize the reactimeter equation form, presenting the main reactimeter computing unit by a convolution equation. Hence, the reactimeter metrological characteristics are completely determined by this unit hardware function which represents a transient re...

  18. Symmetries and Invariants of the Time-dependent Oscillator Equation and the Envelope Equation

    CERN Document Server

    Qin, Hong

    2005-01-01

    Single-particle dynamics in a time-dependent focusing field is examined. The existence of the Courant-Snyder invariant* is fundamentally the result of the corresponding symmetry admitted by the oscillator equation with time-dependent frequency.** A careful analysis of the admitted symmetries reveals a deeper connection between the nonlinear envelope equation and the oscillator equation. A general theorem regarding the symmetries and invariants of the envelope equation, which includes the existence of the Courant-Snyder invariant as a special case, is demonstrated. The symmetries of the envelope equation enable a fast algorithm for finding matched solutions without using the conventional iterative shooting method.

  19. A generalized fractional sub-equation method for fractional differential equations with variable coefficients

    International Nuclear Information System (INIS)

    Tang, Bo; He, Yinnian; Wei, Leilei; Zhang, Xindong

    2012-01-01

    In this Letter, a generalized fractional sub-equation method is proposed for solving fractional differential equations with variable coefficients. Being concise and straightforward, this method is applied to the space–time fractional Gardner equation with variable coefficients. As a result, many exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. It is shown that the considered method provides a very effective, convenient and powerful mathematical tool for solving many other fractional differential equations in mathematical physics. -- Highlights: ► Study of fractional differential equations with variable coefficients plays a role in applied physical sciences. ► It is shown that the proposed algorithm is effective for solving fractional differential equations with variable coefficients. ► The obtained solutions may give insight into many considerable physical processes.

  20. True amplitude wave equation migration arising from true amplitude one-way wave equations

    Science.gov (United States)

    Zhang, Yu; Zhang, Guanquan; Bleistein, Norman

    2003-10-01

    One-way wave operators are powerful tools for use in forward modelling and inversion. Their implementation, however, involves introduction of the square root of an operator as a pseudo-differential operator. Furthermore, a simple factoring of the wave operator produces one-way wave equations that yield the same travel times as the full wave equation, but do not yield accurate amplitudes except for homogeneous media and for almost all points in heterogeneous media. Here, we present augmented one-way wave equations. We show that these equations yield solutions for which the leading order asymptotic amplitude as well as the travel time satisfy the same differential equations as the corresponding functions for the full wave equation. Exact representations of the square-root operator appearing in these differential equations are elusive, except in cases in which the heterogeneity of the medium is independent of the transverse spatial variables. Here, we address the fully heterogeneous case. Singling out depth as the preferred direction of propagation, we introduce a representation of the square-root operator as an integral in which a rational function of the transverse Laplacian appears in the integrand. This allows us to carry out explicit asymptotic analysis of the resulting one-way wave equations. To do this, we introduce an auxiliary function that satisfies a lower dimensional wave equation in transverse spatial variables only. We prove that ray theory for these one-way wave equations leads to one-way eikonal equations and the correct leading order transport equation for the full wave equation. We then introduce appropriate boundary conditions at z = 0 to generate waves at depth whose quotient leads to a reflector map and an estimate of the ray theoretical reflection coefficient on the reflector. Thus, these true amplitude one-way wave equations lead to a 'true amplitude wave equation migration' (WEM) method. In fact, we prove that applying the WEM imaging condition

  1. First-order partial differential equations

    CERN Document Server

    Rhee, Hyun-Ku; Amundson, Neal R

    2001-01-01

    This first volume of a highly regarded two-volume text is fully usable on its own. After going over some of the preliminaries, the authors discuss mathematical models that yield first-order partial differential equations; motivations, classifications, and some methods of solution; linear and semilinear equations; chromatographic equations with finite rate expressions; homogeneous and nonhomogeneous quasilinear equations; formation and propagation of shocks; conservation equations, weak solutions, and shock layers; nonlinear equations; and variational problems. Exercises appear at the end of mo

  2. Equating Multidimensional Tests under a Random Groups Design: A Comparison of Various Equating Procedures

    Science.gov (United States)

    Lee, Eunjung

    2013-01-01

    The purpose of this research was to compare the equating performance of various equating procedures for the multidimensional tests. To examine the various equating procedures, simulated data sets were used that were generated based on a multidimensional item response theory (MIRT) framework. Various equating procedures were examined, including…

  3. Comparing the IRT Pre-equating and Section Pre-equating: A Simulation Study.

    Science.gov (United States)

    Hwang, Chi-en; Cleary, T. Anne

    The results obtained from two basic types of pre-equatings of tests were compared: the item response theory (IRT) pre-equating and section pre-equating (SPE). The simulated data were generated from a modified three-parameter logistic model with a constant guessing parameter. Responses of two replication samples of 3000 examinees on two 72-item…

  4. Beginning partial differential equations

    CERN Document Server

    O'Neil, Peter V

    2014-01-01

    A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or

  5. A new formulation of equations of compressible fluids by analogy with Maxwell's equations

    International Nuclear Information System (INIS)

    Kambe, Tsutomu

    2010-01-01

    A compressible ideal fluid is governed by Euler's equation of motion and equations of continuity, entropy and vorticity. This system can be reformulated in a form analogous to that of electromagnetism governed by Maxwell's equations with source terms. The vorticity plays the role of magnetic field, while the velocity field plays the part of a vector potential and the enthalpy (of isentropic flows) plays the part of a scalar potential in electromagnetism. The evolution of source terms of fluid Maxwell equations is determined by solving the equations of motion and continuity. The equation of sound waves can be derived from this formulation, where time evolution of the sound source is determined by the equation of motion. The theory of vortex sound of aeroacoustics is included in this formulation. It is remarkable that the forces acting on a point mass moving in a velocity field of an inviscid fluid are analogous in their form to the electric force and Lorentz force in electromagnetism. The significance of the reformulation is interpreted by examples taken from fluid mechanics. This formulation can be extended to viscous fluids without difficulty. The Maxwell-type equations are unchanged by the viscosity effect, although the source terms have additional terms due to viscosities.

  6. Investigation of crystallization kinetics and deformation behavior in supercooled liquid region of CuZr-based bulk metallic glass

    Energy Technology Data Exchange (ETDEWEB)

    Yang, Ke; Fan, Xinhui; Li, Bing; Li, Yanhong; Wang, Xin; Xu, Xuanxuan [Xi' an Technological Univ. (China). School of Material and Chemical Engineering

    2017-08-15

    In this paper, a systematic study of crystallization kinetics and deformation behavior is presented for (Cu{sub 50}Zr{sub 50}){sub 94}Al{sub 6} bulk metallic glass in the supercooled liquid region. Crystallization results showed that the activation energy for (Cu{sub 50}Zr{sub 50}){sub 94}Al{sub 6} was calculated using the Arrhenius equation in isothermal mode and the Kissinger-Akahira-Sunose method in non-isothermal mode. The activation energy was quite high compared with other bulk metallic glasses. Based on isothermal transformation kinetics described by the Johson-Mehl-Avrami model, the average Avrami exponent of about 3.05 implies a mainly diffusion controlled three-dimensional growth with an increasing nucleation rate during the crystallization. For warm deformation, the results showed that deformation behavior, composed of homogeneous and inhomogeneous deformation, is strongly dependent on strain rate and temperature. The homogeneous deformation transformed from non-Newtonian flow to Newtonian flow with a decrease in strain rate and an increase in temperature. It was found that the crystallization during high temperature deformation is induced by heating. The appropriate working temperature/strain rate combination for the alloy forming, without in-situ crystallization, was deduced by constructing an empirical deformation map. The optimum process condition for (Cu{sub 50}Zr{sub 50}){sub 94}Al{sub 6} can be expressed as T∝733 K and ∝ ε 10{sup -3} s{sup -1}.

  7. Simulación de la fluencia en caliente de un acero microaleado con un contenido medio de carbono. II parte. Recristalización dinámica: inicio y cinética

    Directory of Open Access Journals (Sweden)

    Cabrera, J. M.

    1997-06-01

    Full Text Available According to the part 1 of this work, in this second part the dynamic recrystallization of a commercial medium carbon microalloyed steel is characterized from the point of view of its onset and kinetics. For this purpose uniaxial hot compression tests were carried out over a range of five orders of magnitude in strain rate and 300 °C of temperature. Experimental results are compared with those reported in the literature and the possible effect of dynamic precipitation is also analyzed. It is verified that the kinetics of dynamic recrystallization can faithfully be described by the classical Avrami equation.

    Siguiendo el planteamiento efectuado en la I parte de este trabajo, en esta II parte se caracteriza la recristalización dinámica de un acero comercial microaleado con un contenido medio de carbono desde el punto de vista de su inicio y de su cinética. Con este objeto se efectuaron ensayos de compresión uniaxial en caliente en un intervalo de cinco órdenes de magnitud en velocidad de deformación y 300 °C de temperatura. Los resultados experimentales se comparan con los resultados reportados por diversos autores y se analizan los posibles efectos de precipitación dinámica. Se verifica que la cinética de la recristalización dinámica puede representarse fielmente por la ecuación de Avrami.

  8. Degenerate nonlinear diffusion equations

    CERN Document Server

    Favini, Angelo

    2012-01-01

    The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...

  9. Computational partial differential equations using Matlab

    CERN Document Server

    Li, Jichun

    2008-01-01

    Brief Overview of Partial Differential Equations The parabolic equations The wave equations The elliptic equations Differential equations in broader areasA quick review of numerical methods for PDEsFinite Difference Methods for Parabolic Equations Introduction Theoretical issues: stability, consistence, and convergence 1-D parabolic equations2-D and 3-D parabolic equationsNumerical examples with MATLAB codesFinite Difference Methods for Hyperbolic Equations IntroductionSome basic difference schemes Dissipation and dispersion errors Extensions to conservation lawsThe second-order hyperbolic PDE

  10. Integrable systems of partial differential equations determined by structure equations and Lax pair

    International Nuclear Information System (INIS)

    Bracken, Paul

    2010-01-01

    It is shown how a system of evolution equations can be developed both from the structure equations of a submanifold embedded in three-space as well as from a matrix SO(6) Lax pair. The two systems obtained this way correspond exactly when a constraint equation is selected and imposed on the system of equations. This allows for the possibility of selecting the coefficients in the second fundamental form in a general way.

  11. Drift-Diffusion Equation

    Directory of Open Access Journals (Sweden)

    K. Banoo

    1998-01-01

    equation in the discrete momentum space. This is shown to be similar to the conventional drift-diffusion equation except that it is a more rigorous solution to the Boltzmann equation because the current and carrier densities are resolved into M×1 vectors, where M is the number of modes in the discrete momentum space. The mobility and diffusion coefficient become M×M matrices which connect the M momentum space modes. This approach is demonstrated by simulating electron transport in bulk silicon.

  12. Symmetries of the Euler compressible flow equations for general equation of state

    Energy Technology Data Exchange (ETDEWEB)

    Boyd, Zachary M. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Ramsey, Scott D. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Baty, Roy S. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2015-10-15

    The Euler compressible flow equations exhibit different Lie symmetries depending on the equation of state (EOS) of the medium in which the flow occurs. This means that, in general, different types of similarity solution will be available in different flow media. We present a comprehensive classification of all EOS’s to which the Euler equations apply, based on the Lie symmetries admitted by the corresponding flow equations, restricting to the case of 1-D planar, cylindrical, or spherical geometry. The results are conveniently summarized in tables. This analysis also clarifies past work by Axford and Ovsiannikov on symmetry classification.

  13. Alternatives to the Dirac equation

    International Nuclear Information System (INIS)

    Girvin, S.M.; Brownstein, K.R.

    1975-01-01

    Recent work by Biedenharn, Han, and van Dam (BHvD) has questioned the uniqueness of the Dirac equation. BHvD have obtained a two-component equation as an alternate to the Dirac equation. Although they later show their alternative to be unitarily equivalent to the Dirac equation, certain physical differences were claimed. BHvD attribute the existence of this alternate equation to the fact that their factorizing matrices were position-dependent. To investigate this, we factor the Klein-Gordon equation in spherical coordinates allowing the factorizing matrices to depend arbitrarily upon theta and phi. It is shown that despite this additional freedom, and without involving any relativistic covariance, the conventional four-component Dirac equation is the only possibility

  14. Nonlinear differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Dresner, L.

    1988-01-01

    This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.

  15. Nonlinear differential equations

    International Nuclear Information System (INIS)

    Dresner, L.

    1988-01-01

    This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics

  16. Semilinear Schrödinger equations

    CERN Document Server

    Cazenave, Thierry

    2003-01-01

    The nonlinear Schrödinger equation has received a great deal of attention from mathematicians, in particular because of its applications to nonlinear optics. It is also a good model dispersive equation, since it is often technically simpler than other dispersive equations, such as the wave or Korteweg-de Vries equation. Particularly useful tools in studying the nonlinear Schrödinger equation are energy and Strichartz's estimates. This book presents various mathematical aspects of the nonlinear Schrödinger equation. It examines both problems of local nature (local existence of solutions, unique

  17. Quantum linear Boltzmann equation

    International Nuclear Information System (INIS)

    Vacchini, Bassano; Hornberger, Klaus

    2009-01-01

    We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal background gas. A heuristic derivation of this Lindblad master equation is presented, based on the requirement of translation-covariance and on the relation to the classical linear Boltzmann equation. After analyzing its general symmetry properties and the associated relaxation dynamics, we discuss a quantum Monte Carlo method for its numerical solution. We then review important limiting forms of the quantum linear Boltzmann equation, such as the case of quantum Brownian motion and pure collisional decoherence, as well as the application to matter wave optics. Finally, we point to the incorporation of quantum degeneracies and self-interactions in the gas by relating the equation to the dynamic structure factor of the ambient medium, and we provide an extension of the equation to include internal degrees of freedom.

  18. Exact Solutions to Nonlinear Schroedinger Equation and Higher-Order Nonlinear Schroedinger Equation

    International Nuclear Information System (INIS)

    Ren Ji; Ruan Hangyu

    2008-01-01

    We study solutions of the nonlinear Schroedinger equation (NLSE) and higher-order nonlinear Schroedinger equation (HONLSE) with variable coefficients. By considering all the higher-order effect of HONLSE as a new dependent variable, the NLSE and HONLSE can be changed into one equation. Using the generalized Lie group reduction method (GLGRM), the abundant solutions of NLSE and HONLSE are obtained

  19. Nonlinear diffusion equations

    CERN Document Server

    Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning

    2001-01-01

    Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which

  20. On the F-equation

    International Nuclear Information System (INIS)

    Kalinowski, M.W.; Szymanowski, L.

    1982-03-01

    A generalization of the Truesdell F-equations is proposed and some solutions to them - generalized Fox F-functions - are found. It is also shown that a non-linear difference-differential equation, which does not belong to the Truesdell class, nevertheless may be transformed into the standard F-equation. (author)

  1. How to obtain the covariant form of Maxwell's equations from the continuity equation

    Energy Technology Data Exchange (ETDEWEB)

    Heras, Jose A [Departamento de Ciencias Basicas, Universidad Autonoma Metropolitana, Unidad Azcapotzalco, Av. San Pablo No. 180, Col. Reynosa, 02200, Mexico D. F. (Mexico); Departamento de Fisica y Matematicas, Universidad Iberoamericana, Prolongacion Paseo de la Reforma 880, Mexico D. F. 01210 (Mexico)

    2009-07-15

    The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell's equations in which charge conservation is emphasized as the fundamental axiom underlying these equations.

  2. Linear integral equations and soliton systems

    International Nuclear Information System (INIS)

    Quispel, G.R.W.

    1983-01-01

    A study is presented of classical integrable dynamical systems in one temporal and one spatial dimension. The direct linearizations are given of several nonlinear partial differential equations, for example the Korteweg-de Vries equation, the modified Korteweg-de Vries equation, the sine-Gordon equation, the nonlinear Schroedinger equation, and the equation of motion for the isotropic Heisenberg spin chain; the author also discusses several relations between these equations. The Baecklund transformations of these partial differential equations are treated on the basis of a singular transformation of the measure (or equivalently of the plane-wave factor) occurring in the corresponding linear integral equations, and the Baecklund transformations are used to derive the direct linearization of a chain of so-called modified partial differential equations. Finally it is shown that the singular linear integral equations lead in a natural way to the direct linearizations of various nonlinear difference-difference equations. (Auth.)

  3. Lectures on partial differential equations

    CERN Document Server

    Petrovsky, I G

    1992-01-01

    Graduate-level exposition by noted Russian mathematician offers rigorous, transparent, highly readable coverage of classification of equations, hyperbolic equations, elliptic equations and parabolic equations. Wealth of commentary and insight invaluable for deepening understanding of problems considered in text. Translated from the Russian by A. Shenitzer.

  4. Reduction operators of Burgers equation.

    Science.gov (United States)

    Pocheketa, Oleksandr A; Popovych, Roman O

    2013-02-01

    The solution of the problem on reduction operators and nonclassical reductions of the Burgers equation is systematically treated and completed. A new proof of the theorem on the special "no-go" case of regular reduction operators is presented, and the representation of the coefficients of operators in terms of solutions of the initial equation is constructed for this case. All possible nonclassical reductions of the Burgers equation to single ordinary differential equations are exhaustively described. Any Lie reduction of the Burgers equation proves to be equivalent via the Hopf-Cole transformation to a parameterized family of Lie reductions of the linear heat equation.

  5. Study of the precipitation-recrystallization interaction in a vanadium micro alloyed steel with 0.35 % C

    International Nuclear Information System (INIS)

    Quispe, A.B.; Medina, S.F.; Cabrera, J.M.; Prado, J.M.

    1998-01-01

    A method is described which allows to study the interaction recrystallization-induced precipitation by the deformation of vanadium micro alloyed steel and 0.35% C. By means of torsion tests and applying the Back Extrapolation method, the recrystallized fraction at different temperatures has been determined. When the precipitation begins, the recrystallized fraction does not follow the Avrami's equation. This allows to know the instant when precipitation starts (P s ) and the instant when precipitation finishes (P f ). Therefore, Recrystallization-Precipitation-Time-Temperature (RPTT) diagrams can be obtained, which graphically show the interaction Recrystallization-Precipitation and simultaneously allows the determination of the static recrystallization critical temperature (SRCT). This temperature represents the limit between the two phases, before and after precipitation. (Author) 10 refs

  6. Numerical model to predict microstructure of the heat treated of steel elements

    Directory of Open Access Journals (Sweden)

    T. Domański

    2011-04-01

    Full Text Available In work the presented numerical models of tool steel hardening processes take into account thermal phenomena and phase transformations. Numerical algorithm of thermal phenomena was based on the Finite Elements Methods of the heat transfer equations. In the model of phase transformations, in simulations heating process continuous heating (CHT was applied, whereas in cooling process continuous cooling (CCT of the steel at issue. The phase fraction transformed (austenite during heating and fractions during cooling of ferrite, pearlite or bainite are determined by Johnson-Mehl-Avrami formulas. The nescent fraction of martensite is determined by Koistinen and Marburger formula or modified Koistinen and Marburger formula. In the simulations of hardening was subject the fang lathe of cone (axisymmetrical object made of tool steel.

  7. The magnetic field experiment onboard Equator-S and its scientific possibilities

    Directory of Open Access Journals (Sweden)

    K.-H. Fornacon

    1999-12-01

    Full Text Available The special feature of the ringcore fluxgate magnetometer on Equator-S is the high time and field resolution. The scientific aim of the experiment is the investigation of waves in the 10–100 picotesla range with a time resolution up to 64 Hz. The instrument characteristics and the influence of the spacecraft on the magnetic field measurement will be discussed. The work shows that the applied pre- and inflight calibration techniques are sufficient to suppress spacecraft interferences. The offset in spin axis direction was determined for the first time with an independent field measurement by the Equator-S Electron Drift Instrument. The data presented gives an impression of the accuracy of the measurement.Key words. Magnetospheric physics (instruments and techniques · Space plasma physics (instruments and techniques

  8. The magnetic field experiment onboard Equator-S and its scientific possibilities

    Directory of Open Access Journals (Sweden)

    K.-H. Fornacon

    Full Text Available The special feature of the ringcore fluxgate magnetometer on Equator-S is the high time and field resolution. The scientific aim of the experiment is the investigation of waves in the 10–100 picotesla range with a time resolution up to 64 Hz. The instrument characteristics and the influence of the spacecraft on the magnetic field measurement will be discussed. The work shows that the applied pre- and inflight calibration techniques are sufficient to suppress spacecraft interferences. The offset in spin axis direction was determined for the first time with an independent field measurement by the Equator-S Electron Drift Instrument. The data presented gives an impression of the accuracy of the measurement.

    Key words. Magnetospheric physics (instruments and techniques · Space plasma physics (instruments and techniques

  9. Methods for Equating Mental Tests.

    Science.gov (United States)

    1984-11-01

    1983) compared conventional and IRT methods for equating the Test of English as a Foreign Language ( TOEFL ) after chaining. Three conventional and...three IRT equating methods were examined in this study; two sections of TOEFL were each (separately) equated. The IRT methods included the following: (a...group. A separate base form was established for each of the six equating methods. Instead of equating the base-form TOEFL to itself, the last (eighth

  10. Supersymmetric quasipotential equations

    International Nuclear Information System (INIS)

    Zaikov, R.P.

    1981-01-01

    A supersymmetric extension of the Logunov-Tavkhelidze quasipotential approach is suggested. The supersymmetric Bethe- Salpeter equation is an initial equation. The transition from the four-time to the two-time Green function is made in the super- center-of-mass system. The two-time Green function has no inverse function in the whole spinor space. The resolvent operator if found using the Majorana character of the spinor wave function. The supersymmetric quasipotential equation is written. The consideration is carried out in the framework of the theory of chiral scalar superfields [ru

  11. Ordinary differential equations

    CERN Document Server

    Miller, Richard K

    1982-01-01

    Ordinary Differential Equations is an outgrowth of courses taught for a number of years at Iowa State University in the mathematics and the electrical engineering departments. It is intended as a text for a first graduate course in differential equations for students in mathematics, engineering, and the sciences. Although differential equations is an old, traditional, and well-established subject, the diverse backgrounds and interests of the students in a typical modern-day course cause problems in the selection and method of presentation of material. In order to compensate for this diversity,

  12. Uncertain differential equations

    CERN Document Server

    Yao, Kai

    2016-01-01

    This book introduces readers to the basic concepts of and latest findings in the area of differential equations with uncertain factors. It covers the analytic method and numerical method for solving uncertain differential equations, as well as their applications in the field of finance. Furthermore, the book provides a number of new potential research directions for uncertain differential equation. It will be of interest to researchers, engineers and students in the fields of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, automation, economics, and management science.

  13. Introduction to nonlinear dispersive equations

    CERN Document Server

    Linares, Felipe

    2015-01-01

    This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg–de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research. The second edition of Introdu...

  14. Generalized Lorentz-Force equations

    International Nuclear Information System (INIS)

    Yamaleev, R.M.

    2001-01-01

    Guided by Nambu (n+1)-dimensional phase space formalism we build a new system of dynamic equations. These equations describe a dynamic state of the corporeal system composed of n subsystems. The dynamic equations are formulated in terms of dynamic variables of the subsystems as well as in terms of dynamic variables of the corporeal system. These two sets of variables are related respectively as roots and coefficients of the n-degree polynomial equation. In the special n=2 case, this formalism reproduces relativistic dynamics for the charged spinning particles

  15. A new evolution equation

    International Nuclear Information System (INIS)

    Laenen, E.

    1995-01-01

    We propose a new evolution equation for the gluon density relevant for the region of small x B . It generalizes the GLR equation and allows deeper penetration in dense parton systems than the GLR equation does. This generalization consists of taking shadowing effects more comprehensively into account by including multigluon correlations, and allowing for an arbitrary initial gluon distribution in a hadron. We solve the new equation for fixed α s . We find that the effects of multigluon correlations on the deep-inelastic structure function are small. (orig.)

  16. Thermoviscous Model Equations in Nonlinear Acoustics

    DEFF Research Database (Denmark)

    Rasmussen, Anders Rønne

    Four nonlinear acoustical wave equations that apply to both perfect gasses and arbitrary fluids with a quadratic equation of state are studied. Shock and rarefaction wave solutions to the equations are studied. In order to assess the accuracy of the wave equations, their solutions are compared...... to solutions of the basic equations from which the wave equations are derived. A straightforward weakly nonlinear equation is the most accurate for shock modeling. A higher order wave equation is the most accurate for modeling of smooth disturbances. Investigations of the linear stability properties...... of solutions to the wave equations, reveal that the solutions may become unstable. Such instabilities are not found in the basic equations. Interacting shocks and standing shocks are investigated....

  17. Invalidity of the spectral Fokker-Planck equation forCauchy noise driven Langevin equation

    DEFF Research Database (Denmark)

    Ditlevsen, Ove Dalager

    2004-01-01

    -called alpha-stable noise (or Levy noise) the Fokker-Planck equation no longer exists as a partial differential equation for the probability density because the property of finite variance is lost. In stead it has been attempted to formulate an equation for the characteristic function (the Fourier transform...

  18. Difference equations theory, applications and advanced topics

    CERN Document Server

    Mickens, Ronald E

    2015-01-01

    THE DIFFERENCE CALCULUS GENESIS OF DIFFERENCE EQUATIONS DEFINITIONS DERIVATION OF DIFFERENCE EQUATIONS EXISTENCE AND UNIQUENESS THEOREM OPERATORS ∆ AND E ELEMENTARY DIFFERENCE OPERATORS FACTORIAL POLYNOMIALS OPERATOR ∆−1 AND THE SUM CALCULUS FIRST-ORDER DIFFERENCE EQUATIONS INTRODUCTION GENERAL LINEAR EQUATION CONTINUED FRACTIONS A GENERAL FIRST-ORDER EQUATION: GEOMETRICAL METHODS A GENERAL FIRST-ORDER EQUATION: EXPANSION TECHNIQUES LINEAR DIFFERENCE EQUATIONSINTRODUCTION LINEARLY INDEPENDENT FUNCTIONS FUNDAMENTAL THEOREMS FOR HOMOGENEOUS EQUATIONSINHOMOGENEOUS EQUATIONS SECOND-ORDER EQUATIONS STURM-LIOUVILLE DIFFERENCE EQUATIONS LINEAR DIFFERENCE EQUATIONS INTRODUCTION HOMOGENEOUS EQUATIONS CONSTRUCTION OF A DIFFERENCE EQUATION HAVING SPECIFIED SOLUTIONS RELATIONSHIP BETWEEN LINEAR DIFFERENCE AND DIFFERENTIAL EQUATIONS INHOMOGENEOUS EQUATIONS: METHOD OF UNDETERMINED COEFFICIENTS INHOMOGENEOUS EQUATIONS: OPERATOR METHODS z-TRANSFORM METHOD SYSTEMS OF DIFFERENCE EQUATIONS LINEAR PARTIAL DIFFERENCE EQUATI...

  19. Weak self-adjoint differential equations

    International Nuclear Information System (INIS)

    Gandarias, M L

    2011-01-01

    The concepts of self-adjoint and quasi self-adjoint equations were introduced by Ibragimov (2006 J. Math. Anal. Appl. 318 742-57; 2007 Arch. ALGA 4 55-60). In Ibragimov (2007 J. Math. Anal. Appl. 333 311-28), a general theorem on conservation laws was proved. In this paper, we generalize the concept of self-adjoint and quasi self-adjoint equations by introducing the definition of weak self-adjoint equations. We find a class of weak self-adjoint quasi-linear parabolic equations. The property of a differential equation to be weak self-adjoint is important for constructing conservation laws associated with symmetries of the differential equation. (fast track communication)

  20. Solutions of system of P1 equations without use of auxiliary differential equations coupled

    International Nuclear Information System (INIS)

    Martinez, Aquilino Senra; Silva, Fernando Carvalho da; Cardoso, Carlos Eduardo Santos

    2000-01-01

    The system of P1 equations is composed by two equations coupled itself one for the neutron flux and other for the current. Usually this system is solved by definitions of two integrals parameters, which are named slowing down densities of the flux and the current. Hence, the system P1 can be change from integral to only two differential equations. However, there are two new differentials equations that may be solved with the initial system. The present work analyzes this procedure and studies a method, which solve the P1 equations directly, without definitions of slowing down densities. (author)

  1. Equations of radiation hydrodynamics

    International Nuclear Information System (INIS)

    Mihalas, D.

    1982-01-01

    The purpose of this paper is to give an overview of the role of radiation in the transport of energy and momentum in a combined matter-radiation fluid. The transport equation for a moving radiating fluid is presented in both a fully Eulerian and a fully Lagrangian formulation, along with conservation equations describing the dynamics of the fluid. Special attention is paid to the problem of deriving equations that are mutually consistent in each frame, and between frames, to 0(v/c). A detailed analysis is made to show that in situations of broad interest, terms that are formally of 0(v/c) actually dominate the solution, demonstrating that it is esential (1) to pay scrupulous attention to the question of the frame dependence in formulating the equations; and (2) to solve the equations to 0(v/c) in quite general circumstances. These points are illustrated in the context of the nonequilibrium radiation diffusion limit, and a sketch of how the Lagrangian equations are to be solved will be presented

  2. Bayesian quantification of thermodynamic uncertainties in dense gas flows

    International Nuclear Information System (INIS)

    Merle, X.; Cinnella, P.

    2015-01-01

    A Bayesian inference methodology is developed for calibrating complex equations of state used in numerical fluid flow solvers. Precisely, the input parameters of three equations of state commonly used for modeling the thermodynamic behavior of the so-called dense gas flows, – i.e. flows of gases characterized by high molecular weights and complex molecules, working in thermodynamic conditions close to the liquid–vapor saturation curve – are calibrated by means of Bayesian inference from reference aerodynamic data for a dense gas flow over a wing section. Flow thermodynamic conditions are such that the gas thermodynamic behavior strongly deviates from that of a perfect gas. In the aim of assessing the proposed methodology, synthetic calibration data – specifically, wall pressure data – are generated by running the numerical solver with a more complex and accurate thermodynamic model. The statistical model used to build the likelihood function includes a model-form inadequacy term, accounting for the gap between the model output associated to the best-fit parameters and the true phenomenon. Results show that, for all of the relatively simple models under investigation, calibrations lead to informative posterior probability density distributions of the input parameters and improve the predictive distribution significantly. Nevertheless, calibrated parameters strongly differ from their expected physical values. The relationship between this behavior and model-form inadequacy is discussed. - Highlights: • Development of a Bayesian inference procedure for calibrating dense-gas flow solvers. • Complex thermodynamic models calibrated by using aerodynamic data for the flow. • Preliminary Sobol analysis used to reduce parameter space. • Piecewise polynomial surrogate model constructed to reduce computational cost. • Calibration results show the crucial role played by model-form inadequacies

  3. The numerical solution of linear multi-term fractional differential equations: systems of equations

    Science.gov (United States)

    Edwards, John T.; Ford, Neville J.; Simpson, A. Charles

    2002-11-01

    In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.

  4. A Comparison of Kernel Equating and Traditional Equipercentile Equating Methods and the Parametric Bootstrap Methods for Estimating Standard Errors in Equipercentile Equating

    Science.gov (United States)

    Choi, Sae Il

    2009-01-01

    This study used simulation (a) to compare the kernel equating method to traditional equipercentile equating methods under the equivalent-groups (EG) design and the nonequivalent-groups with anchor test (NEAT) design and (b) to apply the parametric bootstrap method for estimating standard errors of equating. A two-parameter logistic item response…

  5. Monge-Ampere equations and tensorial functors

    International Nuclear Information System (INIS)

    Tunitsky, Dmitry V

    2009-01-01

    We consider differential-geometric structures associated with Monge-Ampere equations on manifolds and use them to study the contact linearization of such equations. We also consider the category of Monge-Ampere equations (the morphisms are contact diffeomorphisms) and a number of subcategories. We are chiefly interested in subcategories of Monge-Ampere equations whose objects are locally contact equivalent to equations linear in the second derivatives (semilinear equations), linear in derivatives, almost linear, linear in the second derivatives and independent of the first derivatives, linear, linear and independent of the first derivatives, equations with constant coefficients or evolution equations. We construct a number of functors from the category of Monge-Ampere equations and from some of its subcategories to the category of tensorial objects (that is, multi-valued sections of tensor bundles). In particular, we construct a pseudo-Riemannian metric for every generic Monge-Ampere equation. These functors enable us to establish effectively verifiable criteria for a Monge-Ampere equation to belong to the subcategories listed above.

  6. 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.

  7. Nutrient intakes, major food sources and dietary inadequacies of Inuit adults living in three remote communities in Nunavut, Canada.

    Science.gov (United States)

    Sharma, S; Hopping, B N; Roache, C; Sheehy, T

    2013-12-01

    Inuit in Nunavut, Canada, are currently undergoing a nutritional transition that may contribute to an increased prevalence of chronic disease. Information is lacking about the extent to which contemporary Inuit diets are meeting current dietary recommendations. A culturally appropriate quantitative food frequency questionnaire (QFFQ) developed and validated for Inuit in Nunavut, Canada, was used to assess food and nutrient intake in a cross-sectional sample of adults. Participants included 175 women and 36 men with mean (SD) ages of 42.4 (13.2) and 42.1 (15.0) years, respectively. The response rate for those who completed the study was 79% with 208 QFFQs included for analysis. Reported mean daily energy intakes were: men 15,171 kJ (3626 kcal); women 11,593 kJ (2771 kcal). Dietary inadequacy was expressed as the percentage of participants reporting intakes below the sex- and age-specific estimated average requirements (EARs). For nutrients without EARs, adequate intakes were used. Energy and sodium intakes exceeded the recommendations. Less than 10% of participants met recommendations for dietary fibre intake. Vitamin E intakes were below EARs for ≥97% of participants, whereas >20% reported inadequate vitamin A, folate and magnesium intakes. Among women, >50% reported inadequate calcium and vitamin D intakes. Non-nutrient-dense foods contributed 30% of energy, 73% of sugars and 22% of fat. Traditional foods contributed 56% of protein and 49% of iron. The present study demonstrates a relatively high prevalence of inadequate nutrient intakes among Inuit. The results may be used to monitor the nutrition transition among Inuit, evaluate nutritional interventions, and inform public health policy decision-making. © 2013 The Authors Journal of Human Nutrition and Dietetics © 2013 The British Dietetic Association Ltd.

  8. Analytic solutions of hydrodynamics equations

    International Nuclear Information System (INIS)

    Coggeshall, S.V.

    1991-01-01

    Many similarity solutions have been found for the equations of one-dimensional (1-D) hydrodynamics. These special combinations of variables allow the partial differential equations to be reduced to ordinary differential equations, which must then be solved to determine the physical solutions. Usually, these reduced ordinary differential equations are solved numerically. In some cases it is possible to solve these reduced equations analytically to obtain explicit solutions. In this work a collection of analytic solutions of the 1-D hydrodynamics equations is presented. These can be used for a variety of purposes, including (i) numerical benchmark problems, (ii) as a basis for analytic models, and (iii) to provide insight into more complicated solutions

  9. The modified simplest equation method to look for exact solutions of nonlinear partial differential equations

    OpenAIRE

    Efimova, Olga Yu.

    2010-01-01

    The modification of simplest equation method to look for exact solutions of nonlinear partial differential equations is presented. Using this method we obtain exact solutions of generalized Korteweg-de Vries equation with cubic source and exact solutions of third-order Kudryashov-Sinelshchikov equation describing nonlinear waves in liquids with gas bubbles.

  10. Equationally Noetherian property of Ershov algebras

    OpenAIRE

    Dvorzhetskiy, Yuriy

    2014-01-01

    This article is about equationally Noetherian and weak equationally Noetherian property of Ershov algebras. Here we show two canonical forms of the system of equations over Ershov algebras and two criteria of equationally Noetherian and weak equationally Noetherian properties.

  11. Differential equations extended to superspace

    International Nuclear Information System (INIS)

    Torres, J.; Rosu, H.C.

    2003-01-01

    We present a simple SUSY Ns = 2 superspace extension of the differential equations in which the sought solutions are considered to be real superfields but maintaining the common derivative operators and the coefficients of the differential equations unaltered. In this way, we get self consistent systems of coupled differential equations for the components of the superfield. This procedure is applied to the Riccati equation, for which we obtain in addition the system of coupled equations corresponding to the components of the general superfield solution. (Author)

  12. Differential equations extended to superspace

    Energy Technology Data Exchange (ETDEWEB)

    Torres, J. [Instituto de Fisica, Universidad de Guanajuato, A.P. E-143, Leon, Guanajuato (Mexico); Rosu, H.C. [Instituto Potosino de Investigacion Cientifica y Tecnologica, A.P. 3-74, Tangamanga, San Luis Potosi (Mexico)

    2003-07-01

    We present a simple SUSY Ns = 2 superspace extension of the differential equations in which the sought solutions are considered to be real superfields but maintaining the common derivative operators and the coefficients of the differential equations unaltered. In this way, we get self consistent systems of coupled differential equations for the components of the superfield. This procedure is applied to the Riccati equation, for which we obtain in addition the system of coupled equations corresponding to the components of the general superfield solution. (Author)

  13. Integral equation for inhomogeneous condensed bosons generalizing the Gross-Pitaevskii differential equation

    International Nuclear Information System (INIS)

    Angilella, G.G.N.; Pucci, R.; March, N.H.

    2004-01-01

    We give here the derivation of a Gross-Pitaevskii-type equation for inhomogeneous condensed bosons. Instead of the original Gross-Pitaevskii differential equation, we obtain an integral equation that implies less restrictive assumptions than are made in the very recent study of Pieri and Strinati [Phys. Rev. Lett. 91, 030401 (2003)]. In particular, the Thomas-Fermi approximation and the restriction to small spatial variations of the order parameter invoked in their study are avoided

  14. Iterative Splitting Methods for Differential Equations

    CERN Document Server

    Geiser, Juergen

    2011-01-01

    Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources. It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave equations. In the theoretical part of the book, the author discusses the main theorems and results of the stability and consistency analysis for ordinary differential equations. He then presents extensions of the iterative splitting methods to partial differential

  15. Algorithm for research of mathematical physics equations symmetries. Symmetries of the free Schroedinger equation

    International Nuclear Information System (INIS)

    Kotel'nikov, G.A.

    1994-01-01

    An algorithm id proposed for research the symmetries of mathematical physics equation. The application of this algorithm to the Schroedinger equation permitted to establish, that in addition to the known symmetry the Schroedinger equation possesses also the relativistic symmetry

  16. Generalized quantal equation of motion

    International Nuclear Information System (INIS)

    Morsy, M.W.; Embaby, M.

    1986-07-01

    In the present paper, an attempt is made for establishing a generalized equation of motion for quantal objects, in which intrinsic self adjointness is naturally built in, independently of any prescribed representation. This is accomplished by adopting Hamilton's principle of least action, after incorporating, properly, the quantal features and employing the generalized calculus of variations, without being restricted to fixed end points representation. It turns out that our proposed equation of motion is an intrinsically self-adjoint Euler-Lagrange's differential equation that ensures extremization of the quantal action as required by Hamilton's principle. Time dependence is introduced and the corresponding equation of motion is derived, in which intrinsic self adjointness is also achieved. Reducibility of the proposed equation of motion to the conventional Schroedinger equation is examined. The corresponding continuity equation is established, and both of the probability density and the probability current density are identified. (author)

  17. Higher order field equations. II

    International Nuclear Information System (INIS)

    Tolhoek, H.A.

    1977-01-01

    In a previous paper wave propagation was studied according to a sixth-order partial differential equation involving a complex mass M. The corresponding Yang-Feldman integral equations (indicated as SM-YF-equations), were formulated using modified Green's functions Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x), which then incorporate the partial differential equation together with certain boundary conditions. In this paper certain limit properties of these modified Green's functions are derived: (a) It is shown that for mod(M)→infinity the Green's functions Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x) approach the Green's functions Δsub(R)(x) and Δsub(A)(x) of the corresponding KG-equation (Klein-Gordon equation). (b) It is further shown that the asymptotic behaviour of Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x) is the same as of Δsub(R)(x) and Δsub(A)(x)-and also the same as for Dsub(R)(x) and Dsub(A)(x) for t→+-infinity;, where Dsub(R) and Dsub(A) are the Green's functions for the KG-equation with mass zero. It is essential to take limits in the sense of distribution theory in both cases (a) and (b). The property (b) indicates that the wave propagation properties of the SM-YF-equations, the KG-equation with finite mass and the KG-equation with mass zero are closely related in an asymptotic sense. (Auth.)

  18. Bäcklund transformation of fractional Riccati equation and its applications to nonlinear fractional partial differential equations

    International Nuclear Information System (INIS)

    Lu, Bin

    2012-01-01

    In this Letter, the fractional derivatives in the sense of modified Riemann–Liouville derivative and the Bäcklund transformation of fractional Riccati equation are employed for constructing the exact solutions of nonlinear fractional partial differential equations. The power of this manageable method is presented by applying it to several examples. This approach can also be applied to other nonlinear fractional differential equations. -- Highlights: ► Backlund transformation of fractional Riccati equation is presented. ► A new method for solving nonlinear fractional differential equations is proposed. ► Three important fractional differential equations are solved successfully. ► Some new exact solutions of the fractional differential equations are obtained.

  19. Equational type logic

    NARCIS (Netherlands)

    Manca, V.; Salibra, A.; Scollo, Giuseppe

    1990-01-01

    Equational type logic is an extension of (conditional) equational logic, that enables one to deal in a single, unified framework with diverse phenomena such as partiality, type polymorphism and dependent types. In this logic, terms may denote types as well as elements, and atomic formulae are either

  20. Reduced Braginskii equations

    International Nuclear Information System (INIS)

    Yagi, M.; Horton, W.

    1994-01-01

    A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite β that the perpendicular component of Ohm's law be solved to ensure ∇·j=0 for energy conservation

  1. Model Compaction Equation

    African Journals Online (AJOL)

    The currently proposed model compaction equation was derived from data sourced from the. Niger Delta and it relates porosity to depth for sandstones under hydrostatic pressure condition. The equation is useful in predicting porosity and compaction trend in hydrostatic sands of the. Niger Delta. GEOLOGICAL SETTING OF ...

  2. Reduction of infinite dimensional equations

    Directory of Open Access Journals (Sweden)

    Zhongding Li

    2006-02-01

    Full Text Available In this paper, we use the general Legendre transformation to show the infinite dimensional integrable equations can be reduced to a finite dimensional integrable Hamiltonian system on an invariant set under the flow of the integrable equations. Then we obtain the periodic or quasi-periodic solution of the equation. This generalizes the results of Lax and Novikov regarding the periodic or quasi-periodic solution of the KdV equation to the general case of isospectral Hamiltonian integrable equation. And finally, we discuss the AKNS hierarchy as a special example.

  3. Construction of Chained True Score Equipercentile Equatings under the Kernel Equating (KE) Framework and Their Relationship to Levine True Score Equating. Research Report. ETS RR-09-24

    Science.gov (United States)

    Chen, Haiwen; Holland, Paul

    2009-01-01

    In this paper, we develop a new chained equipercentile equating procedure for the nonequivalent groups with anchor test (NEAT) design under the assumptions of the classical test theory model. This new equating is named chained true score equipercentile equating. We also apply the kernel equating framework to this equating design, resulting in a…

  4. Applied partial differential equations

    CERN Document Server

    Logan, J David

    2004-01-01

    This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory. This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of t...

  5. Equations of motion derived from a generalization of Einstein's equation for the gravitational field

    International Nuclear Information System (INIS)

    Mociutchi, C.

    1980-01-01

    The extended Einstein's equation, combined with a vectorial theory of maxwellian type of the gravitational field, leads to: a) the equation of motion; b) the equation of the trajectory for the static case of spherical symmetry, the test particle having a rest mass other than zero, and c) the propagation of light on null geodesics. All the basic tests of the theory given by Einstein's extended equation. Thus, the new theory of gravitation suggested by us is competitive. (author)

  6. The Wouthuysen equation

    NARCIS (Netherlands)

    M. Hazewinkel (Michiel)

    1995-01-01

    textabstractDedication: I dedicate this paper to Prof. P.C. Baayen, at the occasion of his retirement on 20 December 1994. The beautiful equation which forms the subject matter of this paper was invented by Wouthuysen after he retired. The four complex variable Wouthuysen equation arises from an

  7. Approach in Theory of Nonlinear Evolution Equations: The Vakhnenko-Parkes Equation

    Directory of Open Access Journals (Sweden)

    V. O. Vakhnenko

    2016-01-01

    Full Text Available A variety of methods for examining the properties and solutions of nonlinear evolution equations are explored by using the Vakhnenko equation (VE as an example. The VE, which arises in modelling the propagation of high-frequency waves in a relaxing medium, has periodic and solitary traveling wave solutions some of which are loop-like in nature. The VE can be written in an alternative form, known as the Vakhnenko-Parkes equation (VPE, by a change of independent variables. The VPE has an N-soliton solution which is discussed in detail. Individual solitons are hump-like in nature whereas the corresponding solution to the VE comprises N-loop-like solitons. Aspects of the inverse scattering transform (IST method, as applied originally to the KdV equation, are used to find one- and two-soliton solutions to the VPE even though the VPE’s spectral equation is third-order and not second-order. A Bäcklund transformation for the VPE is used to construct conservation laws. The standard IST method for third-order spectral problems is used to investigate solutions corresponding to bound states of the spectrum and to a continuous spectrum. This leads to N-soliton solutions and M-mode periodic solutions, respectively. Interactions between these types of solutions are investigated.

  8. Parallels between control PDE's (Partial Differential Equations) and systems of ODE's (Ordinary Differential Equations)

    Science.gov (United States)

    Hunt, L. R.; Villarreal, Ramiro

    1987-01-01

    System theorists understand that the same mathematical objects which determine controllability for nonlinear control systems of ordinary differential equations (ODEs) also determine hypoellipticity for linear partial differentail equations (PDEs). Moreover, almost any study of ODE systems begins with linear systems. It is remarkable that Hormander's paper on hypoellipticity of second order linear p.d.e.'s starts with equations due to Kolmogorov, which are shown to be analogous to the linear PDEs. Eigenvalue placement by state feedback for a controllable linear system can be paralleled for a Kolmogorov equation if an appropriate type of feedback is introduced. Results concerning transformations of nonlinear systems to linear systems are similar to results for transforming a linear PDE to a Kolmogorov equation.

  9. Exact results for the Boltzmann equation and Smoluchowski's coagulation equation

    International Nuclear Information System (INIS)

    Hendriks, E.M.

    1983-01-01

    Almost no analytical solutions have been found for realistic intermolecular forces, largely due to the complicated structure of the collision term which calls for the construction of simplified models, in which as many physical properties are maintained as possible. In the first three chapters of this thesis such model Boltzmann equations are studied. Only spatially homogeneous gases with isotropic distribution functions are considered. Chapter I considers transition kernels, chapter II persistent scattering models and chapter III very hard particles. The second part of this dissertation deals with Smoluchowski's coagulation equation for the size distribution function in a coagulating system, with chapters devoted to the following topics: kinetics of gelation and universality, coagulation equations with gelation and exactly soluble models of nucleation. (Auth./C.F.)

  10. Generalización de la ecuación de transformación de fases al análisis de la cinética de cristalización no-isoterma. Aplicación a la aleación vítrea Cu0.10As0.40Se0.50

    Directory of Open Access Journals (Sweden)

    Jiménez-Garay, R.

    2000-08-01

    Full Text Available The techniques of differential thermal analysis are frequently employed to study the kinetics of the transformation reactions and, in particular, the crystallization of the glassy alloys. The corresponding thermal data can be analyzed by the Kissinger method, which was originally derived for the study of homogeneous reactions. The consensus in the literature, in several decades, was that such applications (i.e. to heterogeneous solid state transformations of the Kissinger method are not valid. In the present work the principal objections to the mentioned applications are addressed and alternative derivations of theoretical results are provided. These results demonstrate that the Kissinger method is valid for heterogeneous reactions of the type described by Johnson-Mehl-Avrami equation in the isothermal case. Also the isothermal and non-isothermal data on crystallization of the Cu0.10As0.40Se0.50 glassy alloy are given. The experimental results and the discussion carried out here, help to clarify the effects of incubation time in non-isothermal transformation kinetics and provide a further demonstration of validity of the generalized Johnson-Mehl-Avrami theory for the description of heterogeneous solid state transformations.Las técnicas de análisis térmico diferencial se emplean con frecuencia para estudiar la cinética de las reacciones de transformación y, en particular la de la cristalización de aleaciones vítreas. Los datos térmicos correspondientes pueden analizarse por el método de Kissinger, que se desarrolló originalmente para el estudio de reacciones homogéneas. Durante varias décadas, el consenso en la literatura fue que tales aplicaciones (es decir, a transformaciones heterogéneas de estado sólido del método de Kissinger no eran válidas. En el presente trabajo se señalan las principales objeciones a las aplicaciones mencionadas y se da una deducción alternativa de los resultados teóricos. Estos resultados demuestran

  11. Hybrid quantum-classical master equations

    International Nuclear Information System (INIS)

    Diósi, Lajos

    2014-01-01

    We discuss hybrid master equations of composite systems, which are hybrids of classical and quantum subsystems. A fairly general form of hybrid master equations is suggested. Its consistency is derived from the consistency of Lindblad quantum master equations. We emphasize that quantum measurement is a natural example of exact hybrid systems. We derive a heuristic hybrid master equation of time-continuous position measurement (monitoring). (paper)

  12. Quantum equations from Brownian motions

    International Nuclear Information System (INIS)

    Rajput, B.S.

    2011-01-01

    Classical Schrodinger and Dirac equations have been derived from Brownian motions of a particle, it has been shown that the classical Schrodinger equation can be transformed to usual Schrodinger Quantum equation on applying Heisenberg uncertainty principle between position and momentum while Dirac Quantum equation follows it's classical counter part on applying Heisenberg uncertainly principle between energy and time without applying any analytical continuation. (author)

  13. B-splines and Faddeev equations

    International Nuclear Information System (INIS)

    Huizing, A.J.

    1990-01-01

    Two numerical methods for solving the three-body equations describing relativistic pion deuteron scattering have been investigated. For separable two body interactions these equations form a set of coupled one-dimensional integral equations. They are plagued by singularities which occur in the kernel of the integral equations as well as in the solution. The methods to solve these equations differ in the way they treat the singularities. First the Fuda-Stuivenberg method is discussed. The basic idea of this method is an one time iteration of the set of integral equations to treat the logarithmic singularities. In the second method, the spline method, the unknown solution is approximated by splines. Cubic splines have been used with cubic B-splines as basis. If the solution is approximated by a linear combination of basis functions, an integral equation can be transformed into a set of linear equations for the expansion coefficients. This set of linear equations is solved by standard means. Splines are determined by points called knots. A proper choice of splines to approach the solution stands for a proper choice of the knots. The solution of the three-body scattering equations has a square root behaviour at a certain point. Hence it was investigated how the knots should be chosen to approximate the square root function by cubic B-splines in an optimal way. Before applying this method to solve numerically the three-body equations describing pion-deuteron scattering, an analytically solvable example has been constructed with a singularity structure of both kernel and solution comparable to those of the three-body equations. The accuracy of the numerical solution was determined to a large extent by the accuracy of the approximation of the square root part. The results for a pion laboratory energy of 47.4 MeV agree very well with those from literature. In a complete calculation for 47.7 MeV the spline method turned out to be a factor thousand faster than the Fuda

  14. Reduced Braginskii equations

    International Nuclear Information System (INIS)

    Yagi, M.; Horton, W.

    1993-11-01

    A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite β that we solve the perpendicular component of Ohm's law to conserve the physical energy while ensuring the relation ∇ · j = 0

  15. New multiple soliton solutions to the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation

    International Nuclear Information System (INIS)

    Chen Huaitang; Zhang Hongqing

    2004-01-01

    A generalized tanh function method is used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the Riccati equation which has more new solutions. More new multiple soliton solutions are obtained for the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation

  16. An interpolation between the wave and diffusion equations through the fractional evolution equations Dirac like

    International Nuclear Information System (INIS)

    Pierantozzi, T.; Vazquez, L.

    2005-01-01

    Through fractional calculus and following the method used by Dirac to obtain his well-known equation from the Klein-Gordon equation, we analyze a possible interpolation between the Dirac and the diffusion equations in one space dimension. We study the transition between the hyperbolic and parabolic behaviors by means of the generalization of the D'Alembert formula for the classical wave equation and the invariance under space and time inversions of the interpolating fractional evolution equations Dirac like. Such invariance depends on the values of the fractional index and is related to the nonlocal property of the time fractional differential operator. For this system of fractional evolution equations, we also find an associated conserved quantity analogous to the Hamiltonian for the classical Dirac case

  17. Equationally Compact Acts : Coproducts / Peeter Normak

    Index Scriptorium Estoniae

    Normak, Peeter

    1998-01-01

    In this article equational compactness of acts and its generalizations are discussed. As equational compactness does not carry over to coproducts a slight generalization of c-equational campactness is introduced. It is proved that a coproduct of acts is c-equationally compact if and only if all components are c-equationally campact

  18. Supersymmetric two-particle equations

    International Nuclear Information System (INIS)

    Sissakyan, A.N.; Skachkov, N.B.; Shevchenko, O.Yu.

    1986-01-01

    In the framework of the scalar superfield model, a particular case of which is the well-known Wess-Zumino model, the supersymmetric Schwinger equations are found. On their basis with the use of the second Legendre transformation the two-particle supersymmetric Edwards and Bethe-Salpeter equations are derived. A connection of the kernels and inhomogeneous terms of these equations with generating functional of the second Legendre transformation is found

  19. Solving Ordinary Differential Equations

    Science.gov (United States)

    Krogh, F. T.

    1987-01-01

    Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

  20. Numerical resolution of Navier-Stokes equations coupled to the heat equation

    International Nuclear Information System (INIS)

    Zenouda, Jean-Claude

    1970-08-01

    The author proves a uniqueness theorem for the time dependent Navier-Stokes equations coupled with heat flow in the two-dimensional case. He studies stability and convergence of several finite - difference schemes to solve these equations. Numerical experiments are done in the case of a square domain. (author) [fr

  1. Reduced Braginskii equations

    Energy Technology Data Exchange (ETDEWEB)

    Yagi, M. [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Horton, W. [Texas Univ., Austin, TX (United States). Inst. for Fusion Studies

    1993-11-01

    A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite {beta} that we solve the perpendicular component of Ohm`s law to conserve the physical energy while ensuring the relation {del} {center_dot} j = 0.

  2. Improving multilevel Monte Carlo for stochastic differential equations with application to the Langevin equation.

    Science.gov (United States)

    Müller, Eike H; Scheichl, Rob; Shardlow, Tony

    2015-04-08

    This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the multilevel Monte Carlo (MLMC) method for stochastic differential equations (SDEs) and especially the Langevin equation. We use modified equations analysis as an alternative to strong-approximation theory for the integrator, and we apply this to introduce MLMC for Langevin-type equations with integrators based on operator splitting. We combine this with extrapolation and investigate the use of discrete random variables in place of the Gaussian increments, which is a well-known technique for the weak approximation of SDEs. We show that, for small-noise problems, discrete random variables can lead to an increase in efficiency of almost two orders of magnitude for practical levels of accuracy.

  3. A new sub-equation method applied to obtain exact travelling wave solutions of some complex nonlinear equations

    International Nuclear Information System (INIS)

    Zhang Huiqun

    2009-01-01

    By using a new coupled Riccati equations, a direct algebraic method, which was applied to obtain exact travelling wave solutions of some complex nonlinear equations, is improved. And the exact travelling wave solutions of the complex KdV equation, Boussinesq equation and Klein-Gordon equation are investigated using the improved method. The method presented in this paper can also be applied to construct exact travelling wave solutions for other nonlinear complex equations.

  4. Construction and accuracy of partial differential equation approximations to the chemical master equation.

    Science.gov (United States)

    Grima, Ramon

    2011-11-01

    The mesoscopic description of chemical kinetics, the chemical master equation, can be exactly solved in only a few simple cases. The analytical intractability stems from the discrete character of the equation, and hence considerable effort has been invested in the development of Fokker-Planck equations, second-order partial differential equation approximations to the master equation. We here consider two different types of higher-order partial differential approximations, one derived from the system-size expansion and the other from the Kramers-Moyal expansion, and derive the accuracy of their predictions for chemical reactive networks composed of arbitrary numbers of unimolecular and bimolecular reactions. In particular, we show that the partial differential equation approximation of order Q from the Kramers-Moyal expansion leads to estimates of the mean number of molecules accurate to order Ω(-(2Q-3)/2), of the variance of the fluctuations in the number of molecules accurate to order Ω(-(2Q-5)/2), and of skewness accurate to order Ω(-(Q-2)). We also show that for large Q, the accuracy in the estimates can be matched only by a partial differential equation approximation from the system-size expansion of approximate order 2Q. Hence, we conclude that partial differential approximations based on the Kramers-Moyal expansion generally lead to considerably more accurate estimates in the mean, variance, and skewness than approximations of the same order derived from the system-size expansion.

  5. Linear determining equations for differential constraints

    International Nuclear Information System (INIS)

    Kaptsov, O V

    1998-01-01

    A construction of differential constraints compatible with partial differential equations is considered. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the classical determining equations used in the search for admissible Lie operators. As applications of this approach equations of an ideal incompressible fluid and non-linear heat equations are discussed

  6. Transmission problem for the Laplace equation and the integral equation method

    Czech Academy of Sciences Publication Activity Database

    Medková, Dagmar

    2012-01-01

    Roč. 387, č. 2 (2012), s. 837-843 ISSN 0022-247X Institutional research plan: CEZ:AV0Z10190503 Keywords : transmission problem * Laplace equation * boundary integral equation Subject RIV: BA - General Mathematics Impact factor: 1.050, year: 2012 http://www.sciencedirect.com/science/article/pii/S0022247X11008985

  7. Introduction to partial differential equations

    CERN Document Server

    Borthwick, David

    2016-01-01

    This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise.Within each section the author creates a narrative that answers the five questions: (1) What is the scientific problem we are trying to understand? (2) How do we model that with PDE? (3) What techniques can we use to analyze the PDE? (4) How do those techniques apply to this equation? (5) What information or insight did we obtain by developing and analyzing the PDE? The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspiration for the development of methods.

  8. Differential equations methods and applications

    CERN Document Server

    Said-Houari, Belkacem

    2015-01-01

    This book presents a variety of techniques for solving ordinary differential equations analytically and features a wealth of examples. Focusing on the modeling of real-world phenomena, it begins with a basic introduction to differential equations, followed by linear and nonlinear first order equations and a detailed treatment of the second order linear equations. After presenting solution methods for the Laplace transform and power series, it lastly presents systems of equations and offers an introduction to the stability theory. To help readers practice the theory covered, two types of exercises are provided: those that illustrate the general theory, and others designed to expand on the text material. Detailed solutions to all the exercises are included. The book is excellently suited for use as a textbook for an undergraduate class (of all disciplines) in ordinary differential equations. .

  9. Gauge-invariant flow equation

    Science.gov (United States)

    Wetterich, C.

    2018-06-01

    We propose a closed gauge-invariant functional flow equation for Yang-Mills theories and quantum gravity that only involves one macroscopic gauge field or metric. It is based on a projection on physical and gauge fluctuations. Deriving this equation from a functional integral we employ the freedom in the precise choice of the macroscopic field and the effective average action in order to realize a closed and simple form of the flow equation.

  10. Fundamental equations for two-phase flow. Part 1: general conservation equations. Part 2: complement and remarks

    International Nuclear Information System (INIS)

    Delhaye, J.M.

    1968-12-01

    This report deals with the general equations of mass conservation, of momentum conservation, and energy conservation in the case of a two-phase flow. These equations are presented in several forms starting from integral equations which are assumed initially a priori. 1. Equations with local instantaneous variables, and interfacial conditions; 2. Equations with mean instantaneous variables in a cross-section, and practical applications: these equations include an important experimental value which is the ratio of the cross-section of passage of one phase to the total cross-section of a flow-tube. 3. Equations with a local statistical mean, and equations averaged over a period of time: A more advanced attempt to relate theory and experiment consists in taking the statistical averages of local equations. Equations are then obtained involving variables which are averaged over a period of time with the help of an ergodic assumption. 4. Combination of statistical averages and averages over a cross-section: in this study are considered the local variables averaged statistically, then averaged over the cross-section, and also the variables averaged over the section and then averaged statistically. 5. General equations concerning emulsions: In this case a phase exists in a locally very finely divided form. This peculiarity makes it possible to define a volume concentration, and to draw up equations which have numerous applications. - Certain points arising in the first part of this report concerning general mass conservation equations for two-phase flow have been completed and clarified. The terms corresponding to the interfacial tension have been introduced into the general equations. The interfacial conditions have thus been generalized. A supplementary step has still to be carried out: it has, in effect, been impossible to take the interfacial tension into account in the case of emulsions. It was then appeared interesting to compare this large group of fundamental

  11. Partial differential equations II elements of the modern theory equations with constant coefficients

    CERN Document Server

    Shubin, M

    1994-01-01

    This book, the first printing of which was published as Volume 31 of the Encyclopaedia of Mathematical Sciences, contains a survey of the modern theory of general linear partial differential equations and a detailed review of equations with constant coefficients. Readers will be interested in an introduction to microlocal analysis and its applications including singular integral operators, pseudodifferential operators, Fourier integral operators and wavefronts, a survey of the most important results about the mixed problem for hyperbolic equations, a review of asymptotic methods including short wave asymptotics, the Maslov canonical operator and spectral asymptotics, a detailed description of the applications of distribution theory to partial differential equations with constant coefficients including numerous interesting special topics.

  12. Comparison between results of solution of Burgers' equation and Laplace's equation by Galerkin and least-square finite element methods

    Science.gov (United States)

    Adib, Arash; Poorveis, Davood; Mehraban, Farid

    2018-03-01

    In this research, two equations are considered as examples of hyperbolic and elliptic equations. In addition, two finite element methods are applied for solving of these equations. The purpose of this research is the selection of suitable method for solving each of two equations. Burgers' equation is a hyperbolic equation. This equation is a pure advection (without diffusion) equation. This equation is one-dimensional and unsteady. A sudden shock wave is introduced to the model. This wave moves without deformation. In addition, Laplace's equation is an elliptical equation. This equation is steady and two-dimensional. The solution of Laplace's equation in an earth dam is considered. By solution of Laplace's equation, head pressure and the value of seepage in the directions X and Y are calculated in different points of earth dam. At the end, water table is shown in the earth dam. For Burgers' equation, least-square method can show movement of wave with oscillation but Galerkin method can not show it correctly (the best method for solving of the Burgers' equation is discrete space by least-square finite element method and discrete time by forward difference.). For Laplace's equation, Galerkin and least square methods can show water table correctly in earth dam.

  13. INVARIANTS OF GENERALIZED RAPOPORT-LEAS EQUATIONS

    Directory of Open Access Journals (Sweden)

    Elena N. Kushner

    2018-01-01

    Full Text Available For the generalized Rapoport-Leas equations, algebra of differential invariants is constructed with respect to point transformations, that is, transformations of independent and dependent variables. The finding of a general transformation of this type reduces to solving an extremely complicated functional equation. Therefore, following the approach of Sophus Lie, we restrict ourselves to the search for infinitesimal transformations which are generated by translations along the trajectories of vector fields. The problem of finding these vector fields reduces to the redefined system decision of linear differential equations with respect to their coefficients. The Rapoport-Leas equations arise in the study of nonlinear filtration processes in porous media, as well as in other areas of natural science: for example, these equations describe various physical phenomena: two-phase filtration in a porous medium, filtration of a polytropic gas, and propagation of heat at nuclear explosion. They are vital topic for research: in recent works of Bibikov, Lychagin, and others, the analysis of the symmetries of the generalized Rapoport-Leas equations has been carried out; finite-dimensional dynamics and conditions of attractors existence have been found. Since the generalized RapoportLeas equations are nonlinear partial differential equations of the second order with two independent variables; the methods of the geometric theory of differential equations are used to study them in this paper. According to this theory differential equations generate subvarieties in the space of jets. This makes it possible to use the apparatus of modern differential geometry to study differential equations. We introduce the concept of admissible transformations, that is, replacements of variables that do not derive equations outside the class of the Rapoport-Leas equations. Such transformations form a Lie group. For this Lie group there are differential invariants that separate

  14. On matrix fractional differential equations

    Directory of Open Access Journals (Sweden)

    Adem Kılıçman

    2017-01-01

    Full Text Available The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices. Also, we show the theorem of non-homogeneous matrix fractional partial differential equation with some illustrative examples to demonstrate the effectiveness of the new methodology. The main objective of this article is to discuss the Laplace transform method based on operational matrices of fractional derivatives for solving several kinds of linear fractional differential equations. Moreover, we present the operational matrices of fractional derivatives with Laplace transform in many applications of various engineering systems as control system. We present the analytical technique for solving fractional-order, multi-term fractional differential equation. In other words, we propose an efficient algorithm for solving fractional matrix equation.

  15. Integral equations and their applications

    CERN Document Server

    Rahman, M

    2007-01-01

    For many years, the subject of functional equations has held a prominent place in the attention of mathematicians. In more recent years this attention has been directed to a particular kind of functional equation, an integral equation, wherein the unknown function occurs under the integral sign. The study of this kind of equation is sometimes referred to as the inversion of a definite integral. While scientists and engineers can already choose from a number of books on integral equations, this new book encompasses recent developments including some preliminary backgrounds of formulations of integral equations governing the physical situation of the problems. It also contains elegant analytical and numerical methods, and an important topic of the variational principles. Primarily intended for senior undergraduate students and first year postgraduate students of engineering and science courses, students of mathematical and physical sciences will also find many sections of direct relevance. The book contains eig...

  16. Equations of motion for a (non-linear) scalar field model as derived from the field equations

    International Nuclear Information System (INIS)

    Kaniel, S.; Itin, Y.

    2006-01-01

    The problem of derivation of the equations of motion from the field equations is considered. Einstein's field equations have a specific analytical form: They are linear in the second order derivatives and quadratic in the first order derivatives of the field variables. We utilize this particular form and propose a novel algorithm for the derivation of the equations of motion from the field equations. It is based on the condition of the balance between the singular terms of the field equation. We apply the algorithm to a non-linear Lorentz invariant scalar field model. We show that it results in the Newton law of attraction between the singularities of the field moved on approximately geodesic curves. The algorithm is applicable to the N-body problem of the Lorentz invariant field equations. (Abstract Copyright [2006], Wiley Periodicals, Inc.)

  17. The relativistic electron wave equation

    International Nuclear Information System (INIS)

    Dirac, P.A.M.

    1977-08-01

    The paper was presented at the European Conference on Particle Physics held in Budapest between the 4th and 9th July of 1977. A short review is given on the birth of the relativistic electron wave equation. After Schroedinger has shown the equivalence of his wave mechanics and the matrix mechanics of Heisenberg, a general transformation theory was developed by the author. This theory required a relativistic wave equation linear in delta/delta t. As the Klein--Gordon equation available at this time did not satisfy this condition the development of a new equation became necessary. The equation which was found gave the value of the electron spin and magnetic moment automatically. (D.P.)

  18. Equation with the many fathers

    DEFF Research Database (Denmark)

    Kragh, Helge

    1984-01-01

    In this essay I discuss the origin and early development of the first relativistic wave equation, known as the Klein-Gordon equation. In 1926 several physicists, among them Klein, Fock, Schrödinger, and de Broglie, announced this equation as a candidate for a relativistic generalization of the us...... as electrodynamics. Although this ambitious attempt attracted some interest in 1926, its impact on the mainstream of development in quantum mechanics was virtually nil....... of the usual Schrödinger equation. In most of the early versions the Klein-Gordon equation was connected with the general theory of relativity. Klein and some other physicists attempted to express quantum mechanics within a five-dimensional unified theory, embracing general relativity as well...

  19. Solving (2 + 1)-dimensional sine-Poisson equation by a modified variable separated ordinary differential equation method

    International Nuclear Information System (INIS)

    Ka-Lin, Su; Yuan-Xi, Xie

    2010-01-01

    By introducing a more general auxiliary ordinary differential equation (ODE), a modified variable separated ordinary differential equation method is presented for solving the (2 + 1)-dimensional sine-Poisson equation. As a result, many explicit and exact solutions of the (2 + 1)-dimensional sine-Poisson equation are derived in a simple manner by this technique. (general)

  20. On the Saha Ionization Equation

    Indian Academy of Sciences (India)

    Abstract. We revisit the Saha Ionization Equation in order to highlightthe rich interdisciplinary content of the equation thatstraddles distinct areas of spectroscopy, thermodynamics andchemical reactions. In a self-contained discussion, relegatedto an appendix, we delve further into the hidden message ofthe equation in terms ...

  1. Application of a Lie group admitted by a homogeneous equation for group classification of a corresponding inhomogeneous equation

    Science.gov (United States)

    Long, Feng-Shan; Karnbanjong, Adisak; Suriyawichitseranee, Amornrat; Grigoriev, Yurii N.; Meleshko, Sergey V.

    2017-07-01

    This paper proposes an algorithm for group classification of a nonhomogeneous equation using the group analysis provided for the corresponding homogeneous equation. The approach is illustrated by a partial differential equation, an integro-differential equation, and a delay partial differential equation.

  2. Neoclassical MHD equations for tokamaks

    International Nuclear Information System (INIS)

    Callen, J.D.; Shaing, K.C.

    1986-03-01

    The moment equation approach to neoclassical-type processes is used to derive the flows, currents and resistive MHD-like equations for studying equilibria and instabilities in axisymmetric tokamak plasmas operating in the banana-plateau collisionality regime (ν* approx. 1). The resultant ''neoclassical MHD'' equations differ from the usual reduced equations of resistive MHD primarily by the addition of the important viscous relaxation effects within a magnetic flux surface. The primary effects of the parallel (poloidal) viscous relaxation are: (1) Rapid (approx. ν/sub i/) damping of the poloidal ion flow so the residual flow is only toroidal; (2) addition of the bootstrap current contribution to Ohm's laws; and (3) an enhanced (by B 2 /B/sub theta/ 2 ) polarization drift type term and consequent enhancement of the perpendicular dielectric constant due to parallel flow inertia, which causes the equations to depend only on the poloidal magnetic field B/sub theta/. Gyroviscosity (or diamagnetic vfiscosity) effects are included to properly treat the diamagnetic flow effects. The nonlinear form of the neoclassical MHD equations is derived and shown to satisfy an energy conservation equation with dissipation arising from Joule and poloidal viscous heating, and transport due to classical and neoclassical diffusion

  3. The extended Fan's sub-equation method and its application to KdV-MKdV, BKK and variant Boussinesq equations

    International Nuclear Information System (INIS)

    Yomba, Emmanuel

    2005-01-01

    An extended Fan's sub-equation method is used for constructing exact travelling wave solutions of nonlinear partial differential equations (NLPDEs). The key idea of this method is to take full advantage of the general elliptic equation involving five parameters which has more new solutions and whose degeneracies can lead to special sub-equations involving three parameters. More new solutions are obtained for KdV-MKdV, Broer-Kaup-Kupershmidt (BKK) and variant Boussinesq equations. Then we present a technique which not only gives us a clear relation among this general elliptic equation and other sub-equations involving three parameters (Riccati equation, first kind elliptic equation, auxiliary ordinary equation, generalized Riccati equation and so on), but also provides an approach to construct new exact solutions to NLPDEs

  4. On the relation between elementary partial difference equations and partial differential equations

    NARCIS (Netherlands)

    van den Berg, I.P.

    1998-01-01

    The nonstandard stroboscopy method links discrete-time ordinary difference equations of first-order and continuous-time, ordinary differential equations of first order. We extend this method to the second order, and also to an elementary, yet general class of partial difference/differential

  5. A novel numerical flux for the 3D Euler equations with general equation of state

    KAUST Repository

    Toro, Eleuterio F.; Castro, Cristó bal E.; Bok Jik, Lee

    2015-01-01

    Euler equations for ideal gases and its extension presented in this paper is threefold: (i) we solve the three-dimensional Euler equations on general meshes; (ii) we use a general equation of state; and (iii) we achieve high order of accuracy in both

  6. From ordinary to partial differential equations

    CERN Document Server

    Esposito, Giampiero

    2017-01-01

    This book is addressed to mathematics and physics students who want to develop an interdisciplinary view of mathematics, from the age of Riemann, Poincaré and Darboux to basic tools of modern mathematics. It enables them to acquire the sensibility necessary for the formulation and solution of difficult problems, with an emphasis on concepts, rigour and creativity. It consists of eight self-contained parts: ordinary differential equations; linear elliptic equations; calculus of variations; linear and non-linear hyperbolic equations; parabolic equations; Fuchsian functions and non-linear equations; the functional equations of number theory; pseudo-differential operators and pseudo-differential equations. The author leads readers through the original papers and introduces new concepts, with a selection of topics and examples that are of high pedagogical value.

  7. Completely integrable operator evolutionary equations

    International Nuclear Information System (INIS)

    Chudnovsky, D.V.

    1979-01-01

    The authors present natural generalizations of classical completely integrable equations where the functions are replaced by arbitrary operators. Among these equations are the non-linear Schroedinger, the Korteweg-de Vries, and the modified KdV equations. The Lax representation and the Baecklund transformations are presented. (Auth.)

  8. On the fluid-dynamical approximation to the Boltzmann equation at the level of the Navier-Stokes equation

    International Nuclear Information System (INIS)

    Kawashima, S.; Matsumara, A.; Nishida, T.

    1979-01-01

    The compressible and heat-conductive Navier-Stokes equation obtained as the second approximation of the formal Chapman-Enskog expansion is investigated on its relations to the original nonlinear Boltzmann equation and also to the incompressible Navier-Stokes equation. The solutions of the Boltzmann equation and the incompressible Navier-Stokes equation for small initial data are proved to be asymptotically equivalent (mod decay rate tsup(-5/4)) as t → + infinitely to that of the compressible Navier-Stokes equation for the corresponding initial data. (orig.) 891 HJ/orig. 892 MKO

  9. Solution of radial spin-1 field equation in Robertson-Walker space-time via Heun's equation

    International Nuclear Information System (INIS)

    Zecca, A.

    2010-01-01

    The spin-1 field equation is considered in Robertson-Walker spacetime. The problem of the solution of the separated radial equations, previously discussed in the flat space-time case, is solved also for both the closed and open curvature case. The radial equation is reduced to Heun's differential equation that recently has been widely reconsidered. It is shown that the solution of the present Heun equation does not fall into the class of polynomial-like or hypergeometric functions. Heun's operator results also non-factorisable. The properties follow from application of general theorems and power series expansion. In the positive curvature case of the universe a discrete energy spectrum of the system is found. The result follows by requiring a polynomial-like behaviour of at least one component of the spinor field. Developments and applications of the theory suggest further study of the solution of Heun's equation.

  10. Differential equations I essentials

    CERN Document Server

    REA, Editors of

    2012-01-01

    REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Differential Equations I covers first- and second-order equations, series solutions, higher-order linear equations, and the Laplace transform.

  11. Beginning partial differential equations

    CERN Document Server

    O'Neil, Peter V

    2011-01-01

    A rigorous, yet accessible, introduction to partial differential equations-updated in a valuable new edition Beginning Partial Differential Equations, Second Edition provides a comprehensive introduction to partial differential equations (PDEs) with a special focus on the significance of characteristics, solutions by Fourier series, integrals and transforms, properties and physical interpretations of solutions, and a transition to the modern function space approach to PDEs. With its breadth of coverage, this new edition continues to present a broad introduction to the field, while also addres

  12. Enhanced apatite formation on Ti metal heated in PO2-controlled nitrogen atmosphere.

    Science.gov (United States)

    Hashimoto, Masami; Hayashi, Kazumi; Kitaoka, Satoshi

    2013-10-01

    The oxynitridation of biomedical titanium metal under a precisely regulated oxygen partial pressure (PO2) of 10(-14)Pa in nitrogen atmosphere at 973 K for 1 h strongly enhanced apatite formation compared with that on Ti heated in air. The factors governing the high apatite-forming ability are discussed from the viewpoint of the surface properties of Ti heated under a PO2 of 10(-14)Pa in nitrogen atmosphere determined from X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS) and zeta potential measurements. Nitrogen (N)-doped TiO2 (interstitial N) was formed on pure Ti heated under a PO2 of 10(-14)Pa in nitrogen atmosphere at 973 K. The XPS O1s main peak shifted toward a lower binding energy upon heating under a PO2 of 10(-14)Pa. This shift may be due to the formation of oxygen vacancies. This Ti surface had a positive zeta potential of approximately 20 mV. According to time-of-flight secondary ion mass spectroscopy results, PO4(3-) ions were predominantly adsorbed on Ti soaked in simulated body fluid (SBF) after heat treatment, followed by calcium ions. It was concluded that the apatite formation kinetics can be described using the Avrami-Erofeev equation with an Avrami index of n=2, which implies the instantaneous nucleation of apatite on the surface of Ti soaked in SBF after heat treatment at 973 K under a PO2 of 10(-14)Pa. Copyright © 2013 Elsevier B.V. All rights reserved.

  13. Banking on the equator. Are banks that adopted the equator principles different from non-adopters?

    NARCIS (Netherlands)

    Scholtens, B.; Dam, L.

    We analyze the performance of banks that adopted the Equator Principles. The Equator Principles are designed to assure sustainable development in project finance. The social, ethical, and environmental policies of the adopters differ significantly from those of banks that did not adopt the Equator

  14. Hartree--Fock density matrix equation

    International Nuclear Information System (INIS)

    Cohen, L.; Frishberg, C.

    1976-01-01

    An equation for the Hartree--Fock density matrix is discussed and the possibility of solving this equation directly for the density matrix instead of solving the Hartree--Fock equation for orbitals is considered. Toward that end the density matrix is expanded in a finite basis to obtain the matrix representative equation. The closed shell case is considered. Two numerical schemes are developed and applied to a number of examples. One example is given where the standard orbital method does not converge while the method presented here does

  15. Exact solutions to sine-Gordon-type equations

    International Nuclear Information System (INIS)

    Liu Shikuo; Fu Zuntao; Liu Shida

    2006-01-01

    In this Letter, sine-Gordon-type equations, including single sine-Gordon equation, double sine-Gordon equation and triple sine-Gordon equation, are systematically solved by Jacobi elliptic function expansion method. It is shown that different transformations for these three sine-Gordon-type equations play different roles in obtaining exact solutions, some transformations may not work for a specific sine-Gordon equation, while work for other sine-Gordon equations

  16. dimensional Jaulent–Miodek equations

    Indian Academy of Sciences (India)

    (2+1)-dimensional Jaulent–Miodek equation; the first integral method; kinks; ... and effective method for solving nonlinear partial differential equations which can ... of the method employed and exact kink and soliton solutions are constructed ...

  17. Random walk and the heat equation

    CERN Document Server

    Lawler, Gregory F

    2010-01-01

    The heat equation can be derived by averaging over a very large number of particles. Traditionally, the resulting PDE is studied as a deterministic equation, an approach that has brought many significant results and a deep understanding of the equation and its solutions. By studying the heat equation by considering the individual random particles, however, one gains further intuition into the problem. While this is now standard for many researchers, this approach is generally not presented at the undergraduate level. In this book, Lawler introduces the heat equation and the closely related notion of harmonic functions from a probabilistic perspective. The theme of the first two chapters of the book is the relationship between random walks and the heat equation. The first chapter discusses the discrete case, random walk and the heat equation on the integer lattice; and the second chapter discusses the continuous case, Brownian motion and the usual heat equation. Relationships are shown between the two. For exa...

  18. Stochastic multistep polarization switching in ferroelectrics

    Science.gov (United States)

    Genenko, Y. A.; Khachaturyan, R.; Schultheiß, J.; Ossipov, A.; Daniels, J. E.; Koruza, J.

    2018-04-01

    Consecutive stochastic 90° polarization switching events, clearly resolved in recent experiments, are described by a nucleation and growth multistep model. It extends the classical Kolmogorov-Avrami-Ishibashi approach and includes possible consecutive 90°- and parallel 180° switching events. The model predicts the results of simultaneous time-resolved macroscopic measurements of polarization and strain, performed on a tetragonal Pb (Zr ,Ti ) O3 ceramic in a wide range of electric fields over a time domain of seven orders of magnitude. It allows the determination of the fractions of individual switching processes, their characteristic switching times, activation fields, and respective Avrami indices.

  19. Reactor pressure boundary material; the modeling for the prediction of the welding characteristics of SA508-cl.3 pressure vessel steel welds

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Chang Hee; Uhm, Sang Ho; Seo, Young Dae; Moon, Younk Ju; Kim, Bum Joo; Shim, Min Hyo [Hanyang University, Seoul (Korea)

    2002-03-01

    A metallurgical model for predicting the welding characteristics such as final microstructure and mechanical properties of HAZ was established and various kinetic parameters which was necessary to the model were measured and formulated through isothermal grain growth and isothermal transformation experiments. This model consisted of two sub-models; Grain growth model and Transformation model. Grain growth model was developed to calculate the thermal cycle from heat input and the change of austenite grain size which occurred during heating cycle. Transformation model described the phase transition behavior and predicted the final mechanical properties determined by structure-property relationships. The isothermal kinetics of grain growth and dissolution of precipitates were respectively described by well-known equation, dD/dt = M( {delta}F{sub e}ff ){sup m} and Whelan's analytical model. Isothermal transformation kinetics was expressed by Avrami equation. The reliabilities of each model were evaluated by HAZ microstructural simulation tests. It was found the both models were in good agreement. The applicability of this model was discussed by illustrating the results of the model. 129 refs., 81 figs., 11 tabs. (Author)

  20. On-line monitoring of lithium carbonate dissolution

    Energy Technology Data Exchange (ETDEWEB)

    Sun, Yuzhu; Song, Xingfu; Wang, Jin; Luo, Yan; Yu, Jianguo [National Engineering Research Center for Integrated Utilization Salt Lake Resources, East China University of Science and Technology, Shanghai (China)

    2009-11-15

    Dissolution of lithium carbonate (Li{sub 2}CO{sub 3}) in aqueous solution was investigated using three on-line apparatuses: the concentration of Li{sub 2}CO{sub 3} was measured by electrical conductivity equipment; CLD (Chord Length Distribution) was monitored by FBRM (Focused Beam Reflectance Measurement); crystal image was observed by PVM (Particle Video Microscope). Results show dissolution rate goes up with a decrease of particle size, and with an increase in temperature; stirring speed causes little impact on dissolution; ultrasound facilitates dissolution obviously. The CLD evolution and crystal images of Li{sub 2}CO{sub 3}powders in stirred fluid were observed detailedly by FBRM and PVM during dissolution. Experimental data were fitted to Avrami model, through which the activation energy was found to be 34.35 kJ/mol. PBE (Population Balance Equation) and moment transform were introduced to calculate dissolution kinetics, obtaining correlation equations of particle size decreasing rate as a function of temperature and undersaturation. (copyright 2009 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

  1. Numerical estimation of phase transformations in solid state during Yb:YAG laser heating of steel sheets

    Energy Technology Data Exchange (ETDEWEB)

    Kubiak, Marcin, E-mail: kubiak@imipkm.pcz.pl; Piekarska, Wiesława; Domański, Tomasz; Saternus, Zbigniew [Institute of Mechanics and Machine Design Foundations, Częstochowa University of Technology, Dąbrowskiego 73, 42-200 Częstochowa (Poland); Stano, Sebastian [Welding Technologies Department, Welding Institute, Błogosławionego Czesława 16-18, 44-100 Gliwice (Poland)

    2015-03-10

    This work concerns the numerical modeling of heat transfer and phase transformations in solid state occurring during the Yb:YAG laser beam heating process. The temperature field is obtained by the numerical solution into transient heat transfer equation with convective term. The laser beam heat source model is developed using the Kriging interpolation method with experimental measurements of Yb:YAG laser beam profile taken into account. Phase transformations are calculated on the basis of Johnson - Mehl - Avrami (JMA) and Koistinen - Marburger (KM) kinetics models as well as continuous heating transformation (CHT) and continuous cooling transformation (CCT) diagrams for S355 steel. On the basis of developed numerical algorithms 3D computer simulations are performed in order to predict temperature history and phase transformations in Yb:YAG laser heating process.

  2. On integrability of the Killing equation

    Science.gov (United States)

    Houri, Tsuyoshi; Tomoda, Kentaro; Yasui, Yukinori

    2018-04-01

    Killing tensor fields have been thought of as describing the hidden symmetry of space(-time) since they are in one-to-one correspondence with polynomial first integrals of geodesic equations. Since many problems in classical mechanics can be formulated as geodesic problems in curved space and spacetime, solving the defining equation for Killing tensor fields (the Killing equation) is a powerful way to integrate equations of motion. Thus it has been desirable to formulate the integrability conditions of the Killing equation, which serve to determine the number of linearly independent solutions and also to restrict the possible forms of solutions tightly. In this paper, we show the prolongation for the Killing equation in a manner that uses Young symmetrizers. Using the prolonged equations, we provide the integrability conditions explicitly.

  3. Algebraic entropy for differential-delay equations

    OpenAIRE

    Viallet, Claude M.

    2014-01-01

    We extend the definition of algebraic entropy to a class of differential-delay equations. The vanishing of the entropy, as a structural property of an equation, signals its integrability. We suggest a simple way to produce differential-delay equations with vanishing entropy from known integrable differential-difference equations.

  4. Hyperbolic partial differential equations

    CERN Document Server

    Witten, Matthew

    1986-01-01

    Hyperbolic Partial Differential Equations III is a refereed journal issue that explores the applications, theory, and/or applied methods related to hyperbolic partial differential equations, or problems arising out of hyperbolic partial differential equations, in any area of research. This journal issue is interested in all types of articles in terms of review, mini-monograph, standard study, or short communication. Some studies presented in this journal include discretization of ideal fluid dynamics in the Eulerian representation; a Riemann problem in gas dynamics with bifurcation; periodic M

  5. Dynamical equations for the optical potential

    International Nuclear Information System (INIS)

    Kowalski, K.L.

    1981-01-01

    Dynamical equations for the optical potential are obtained starting from a wide class of N-particle equations. This is done with arbitrary multiparticle interactions to allow adaptation to few-body models of nuclear reactions and including all effects of nucleon identity. Earlier forms of the optical potential equations are obtained as special cases. Particular emphasis is placed upon obtaining dynamical equations for the optical potential from the equations of Kouri, Levin, and Tobocman including all effects of particle identity

  6. Group foliation of finite difference equations

    Science.gov (United States)

    Thompson, Robert; Valiquette, Francis

    2018-06-01

    Using the theory of equivariant moving frames, a group foliation method for invariant finite difference equations is developed. This method is analogous to the group foliation of differential equations and uses the symmetry group of the equation to decompose the solution process into two steps, called resolving and reconstruction. Our constructions are performed algorithmically and symbolically by making use of discrete recurrence relations among joint invariants. Applications to invariant finite difference equations that approximate differential equations are given.

  7. Manhattan equation for the operational amplifier

    OpenAIRE

    Mishonov, Todor M.; Danchev, Victor I.; Petkov, Emil G.; Gourev, Vassil N.; Dimitrova, Iglika M.; Varonov, Albert M.

    2018-01-01

    A differential equation relating the voltage at the output of an operational amplifier $U_0$ and the difference between the input voltages ($U_{+}$ and $U_{-}$) has been derived. The crossover frequency $f_0$ is a parameter in this operational amplifier master equation. The formulas derived as a consequence of this equation find applications in thousands of specifications for electronic devices but as far as we know, the equation has never been published. Actually, the master equation of oper...

  8. Concepts in quantum mechanics

    CERN Document Server

    Mathur, Vishnu S

    2008-01-01

    NEED FOR QUANTUM MECHANICS AND ITS PHYSICAL BASIS Inadequacy of Classical Description for Small Systems Basis of Quantum Mechanics Representation of States Dual Vectors: Bra and Ket Vectors Linear Operators Adjoint of a Linear Operator Eigenvalues and Eigenvectors of a Linear Operator Physical Interpretation Observables and Completeness Criterion Commutativity and Compatibility of Observables Position and Momentum Commutation Relations Commutation Relation and the Uncertainty ProductAppendix: Basic Concepts in Classical MechanicsREPRESENTATION THEORY Meaning of Representation How to Set up a Representation Representatives of a Linear Operator Change of Representation Coordinate Representation Replacement of Momentum Observable p by -ih d/dqIntegral Representation of Dirac Bracket A2|F|A1> The Momentum Representation Dirac Delta FunctionRelation between the Coordinate and Momentum RepresentationsEQUATIONS OF MOTIONSchrödinger Equation of Motion Schrödinger Equation in the Coordinate Representation Equation o...

  9. Benney's long wave equations

    International Nuclear Information System (INIS)

    Lebedev, D.R.

    1979-01-01

    Benney's equations of motion of incompressible nonviscous fluid with free surface in the approximation of long waves are analyzed. The connection between the Lie algebra of Hamilton plane vector fields and the Benney's momentum equations is shown

  10. The forced nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Kaup, D.J.; Hansen, P.J.

    1985-01-01

    The nonlinear Schroedinger equation describes the behaviour of a radio frequency wave in the ionosphere near the reflexion point where nonlinear processes are important. A simple model of this phenomenon leads to the forced nonlinear Schroedinger equation in terms of a nonlinear boundary value problem. A WKB analysis of the time evolution equations for the nonlinear Schroedinger equation in the inverse scattering transform formalism gives a crude order of magnitude estimation of the qualitative behaviour of the solutions. This estimation is compared with the numerical solutions. (D.Gy.)

  11. Solving Nonlinear Coupled Differential Equations

    Science.gov (United States)

    Mitchell, L.; David, J.

    1986-01-01

    Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.

  12. Structural Equation and Mei Conserved Quantity of Mei Symmetry for Appell Equations in Holonomic Systems with Unilateral Constraints

    International Nuclear Information System (INIS)

    Jia Liqun; Cui Jinchao; Zhang Yaoyu; Luo Shaokai

    2009-01-01

    Structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints are investigated. Appell equations and differential equations of motion for holonomic mechanic systems with unilateral constraints are established. The definition and the criterion of Mei symmetry for Appell equations in holonomic systems with unilateral constraints under the infinitesimal transformations of groups are also given. The expressions of the structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints expressed by Appell functions are obtained. An example is given to illustrate the application of the results. (general)

  13. Direct 'delay' reductions of the Toda equation

    International Nuclear Information System (INIS)

    Joshi, Nalini

    2009-01-01

    A new direct method of obtaining reductions of the Toda equation is described. We find a canonical and complete class of all possible reductions under certain assumptions. The resulting equations are ordinary differential-difference equations, sometimes referred to as delay-differential equations. The representative equation of this class is hypothesized to be a new version of one of the classical Painleve equations. The Lax pair associated with this equation is obtained, also by reduction. (fast track communication)

  14. Reduction of the equation for lower hybrid waves in a plasma to a nonlinear Schroedinger equation

    Science.gov (United States)

    Karney, C. F. F.

    1977-01-01

    Equations describing the nonlinear propagation of waves in an anisotropic plasma are rarely exactly soluble. However it is often possible to make approximations that reduce the exact equations into a simpler equation. The use of MACSYMA to make such approximations, and so reduce the equation describing lower hybrid waves into the nonlinear Schrodinger equation which is soluble by the inverse scattering method is demonstrated. MACSYMA is used at several stages in the calculation only because there is a natural division between calculations that are easiest done by hand, and those that are easiest done by machine.

  15. Quadratic Diophantine equations

    CERN Document Server

    Andreescu, Titu

    2015-01-01

    This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems, and applications. Moreover, the exposition aptly demonstrates many applications of results and techniques from the study of Pell-type equations to other problems in number theory. The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis.

  16. Quantum-statistical kinetic equations

    International Nuclear Information System (INIS)

    Loss, D.; Schoeller, H.

    1989-01-01

    Considering a homogeneous normal quantum fluid consisting of identical interacting fermions or bosons, the authors derive an exact quantum-statistical generalized kinetic equation with a collision operator given as explicit cluster series where exchange effects are included through renormalized Liouville operators. This new result is obtained by applying a recently developed superoperator formalism (Liouville operators, cluster expansions, symmetrized projectors, P q -rule, etc.) to nonequilibrium systems described by a density operator ρ(t) which obeys the von Neumann equation. By means of this formalism a factorization theorem is proven (being essential for obtaining closed equations), and partial resummations (leading to renormalized quantities) are performed. As an illustrative application, the quantum-statistical versions (including exchange effects due to Fermi-Dirac or Bose-Einstein statistics) of the homogeneous Boltzmann (binary collisions) and Choh-Uhlenbeck (triple collisions) equations are derived

  17. A linearizing transformation for the Korteweg-de Vries equation; generalizations to higher-dimensional nonlinear partial differential equations

    NARCIS (Netherlands)

    Dorren, H.J.S.

    1998-01-01

    It is shown that the Korteweg–de Vries (KdV) equation can be transformed into an ordinary linear partial differential equation in the wave number domain. Explicit solutions of the KdV equation can be obtained by subsequently solving this linear differential equation and by applying a cascade of

  18. PREFACE: Symmetries and integrability of difference equations Symmetries and integrability of difference equations

    Science.gov (United States)

    Levi, Decio; Olver, Peter; Thomova, Zora; Winternitz, Pavel

    2009-11-01

    The concept of integrability was introduced in classical mechanics in the 19th century for finite dimensional continuous Hamiltonian systems. It was extended to certain classes of nonlinear differential equations in the second half of the 20th century with the discovery of the inverse scattering transform and the birth of soliton theory. Also at the end of the 19th century Lie group theory was invented as a powerful tool for obtaining exact analytical solutions of large classes of differential equations. Together, Lie group theory and integrability theory in its most general sense provide the main tools for solving nonlinear differential equations. Like differential equations, difference equations play an important role in physics and other sciences. They occur very naturally in the description of phenomena that are genuinely discrete. Indeed, they may actually be more fundamental than differential equations if space-time is actually discrete at very short distances. On the other hand, even when treating continuous phenomena described by differential equations it is very often necessary to resort to numerical methods. This involves a discretization of the differential equation, i.e. a replacement of the differential equation by a difference one. Given the well developed and understood techniques of symmetry and integrability for differential equations a natural question to ask is whether it is possible to develop similar techniques for difference equations. The aim is, on one hand, to obtain powerful methods for solving `integrable' difference equations and to establish practical integrability criteria, telling us when the methods are applicable. On the other hand, Lie group methods can be adapted to solve difference equations analytically. Finally, integrability and symmetry methods can be combined with numerical methods to obtain improved numerical solutions of differential equations. The origin of the SIDE meetings goes back to the early 1990s and the first

  19. Local instant conservation equations

    International Nuclear Information System (INIS)

    Delaje, Dzh.

    1984-01-01

    Local instant conservation equations for two-phase flow are derived. Derivation of the equation starts from the recording of integral laws of conservation for a fixed reference volume, containing both phases. Transformation of the laws, using the Leibniz rule and Gauss theory permits to obtain the sum of two integrals as to the volume and integral as to the surface. Integrals as to the volume result in local instant differential equations, in particular derivatives for each phase, and integrals as to the surface reflect local instant conditions of a jump on interface surface

  20. Differential equations problem solver

    CERN Document Server

    Arterburn, David R

    2012-01-01

    REA's Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies.The Differential Equations Problem Solver is the perfect resource for any class, any exam, and

  1. Local Observed-Score Kernel Equating

    Science.gov (United States)

    Wiberg, Marie; van der Linden, Wim J.; von Davier, Alina A.

    2014-01-01

    Three local observed-score kernel equating methods that integrate methods from the local equating and kernel equating frameworks are proposed. The new methods were compared with their earlier counterparts with respect to such measures as bias--as defined by Lord's criterion of equity--and percent relative error. The local kernel item response…

  2. Numerical solution of Boltzmann's equation

    International Nuclear Information System (INIS)

    Sod, G.A.

    1976-04-01

    The numerical solution of Boltzmann's equation is considered for a gas model consisting of rigid spheres by means of Hilbert's expansion. If only the first two terms of the expansion are retained, Boltzmann's equation reduces to the Boltzmann-Hilbert integral equation. Successive terms in the Hilbert expansion are obtained by solving the same integral equation with a different source term. The Boltzmann-Hilbert integral equation is solved by a new very fast numerical method. The success of the method rests upon the simultaneous use of four judiciously chosen expansions; Hilbert's expansion for the distribution function, another expansion of the distribution function in terms of Hermite polynomials, the expansion of the kernel in terms of the eigenvalues and eigenfunctions of the Hilbert operator, and an expansion involved in solving a system of linear equations through a singular value decomposition. The numerical method is applied to the study of the shock structure in one space dimension. Numerical results are presented for Mach numbers of 1.1 and 1.6. 94 refs, 7 tables, 1 fig

  3. The Dirac equation and its solutions

    CERN Document Server

    Bagrov, Vladislav G

    2014-01-01

    Dirac equations are of fundamental importance for relativistic quantum mechanics and quantum electrodynamics. In relativistic quantum mechanics, the Dirac equation is referred to as one-particle wave equation of motion for electron in an external electromagnetic field. In quantum electrodynamics, exact solutions of this equation are needed to treat the interaction between the electron and the external field exactly.In particular, all propagators of a particle, i.e., the various Green's functions, are constructed in a certain way by using exact solutions of the Dirac equation.

  4. The Dirac equation and its solutions

    International Nuclear Information System (INIS)

    Bagrov, Vladislav G.; Gitman, Dmitry; P.N. Lebedev Physical Institute, Moscow; Tomsk State Univ., Tomsk

    2013-01-01

    The Dirac equation is of fundamental importance for relativistic quantum mechanics and quantum electrodynamics. In relativistic quantum mechanics, the Dirac equation is referred to as one-particle wave equation of motion for electron in an external electromagnetic field. In quantum electrodynamics, exact solutions of this equation are needed to treat the interaction between the electron and the external field exactly. In particular, all propagators of a particle, i.e., the various Green's functions, are constructed in a certain way by using exact solutions of the Dirac equation.

  5. Ecological and general systems an introduction to systems ecology

    CERN Document Server

    Odum, Howard T.

    1994-01-01

    Using an energy systems language that combines energetics, kinetics, information, cybernetics, and simulation, Ecological and General Systems compares models of many fields of science, helping to derive general systems principles. First published as Systems Ecology in 1983, Ecological and General Systems proposes principles of self-organization and the designs that prevail by maximizing power and efficiency. Comparisons to fifty other systems languages are provided. Innovative presentations are given on earth homeostasis (Gaia); the inadequacy of presenting equations without network relationships and energy constraints; the alternative interpretation of high entropy complexity as adaptive structure; basic equations of ecological economics; and the energy basis of scientific hierarchy.

  6. The modified extended Fan's sub-equation method and its application to (2 + 1)-dimensional dispersive long wave equation

    International Nuclear Information System (INIS)

    Yomba, Emmanuel

    2005-01-01

    By using a modified extended Fan's sub-equation method, we have obtained new and more general solutions including a series of non-travelling wave and coefficient function solutions namely: soliton-like solutions, triangular-like solutions, single and combined non-degenerative Jacobi elliptic wave function-like solutions for the (2 + 1)-dimensional dispersive long wave equation. The most important achievement of this method lies on the fact that, we have succeeded in one move to give all the solutions which can be previously obtained by application of at least four methods (method using Riccati equation, or first kind elliptic equation, or auxiliary ordinary equation, or generalized Riccati equation as mapping equation)

  7. 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

  8. Chew-Low equations as Cremoma transformations

    International Nuclear Information System (INIS)

    Rerikh, K.V.

    1982-01-01

    The Chew-Low equations for the p-wave pion-nucleon scattering with the crossing-symmetry matrix (3x3) are investigated in their well-known formulation as a system of nonlinear difference equations. These equations interpreted as geometrical transformations are shown to be a special case of the Cremona transformaions. Using the properties of the Cremona transformations we obtain the general 3-parametric functional equation on invariant algebraic and nonalgebraic curves in the space solutions of the Chew- Low equations. It is proved that there exists only one invariant algebraic curve, the parabola corresponding to the well-known solution. Analysis of the general functional equation on invariant nonalgebraic curves makes it possible to select in addition to this parabola 3 invariant forms defining implicitly 3 nonalgebraic curves and to concretize for them the general equation by means of fixing the parameters. From the transformational properties of the invariant forms with respect to the Cremona transformations, there follows an important result that the ration of these forms in proper powers is the general integral of the nonlinear system of the Chew-Low equations, which is an even antiperiodic function. The structure of the second general integral is given and the functional equations which determinne this integral are presented [ru

  9. General particle transport equation. Final report

    International Nuclear Information System (INIS)

    Lafi, A.Y.; Reyes, J.N. Jr.

    1994-12-01

    The general objectives of this research are as follows: (1) To develop fundamental models for fluid particle coalescence and breakage rates for incorporation into statistically based (Population Balance Approach or Monte Carlo Approach) two-phase thermal hydraulics codes. (2) To develop fundamental models for flow structure transitions based on stability theory and fluid particle interaction rates. This report details the derivation of the mass, momentum and energy conservation equations for a distribution of spherical, chemically non-reacting fluid particles of variable size and velocity. To study the effects of fluid particle interactions on interfacial transfer and flow structure requires detailed particulate flow conservation equations. The equations are derived using a particle continuity equation analogous to Boltzmann's transport equation. When coupled with the appropriate closure equations, the conservation equations can be used to model nonequilibrium, two-phase, dispersed, fluid flow behavior. Unlike the Eulerian volume and time averaged conservation equations, the statistically averaged conservation equations contain additional terms that take into account the change due to fluid particle interfacial acceleration and fluid particle dynamics. Two types of particle dynamics are considered; coalescence and breakage. Therefore, the rate of change due to particle dynamics will consider the gain and loss involved in these processes and implement phenomenological models for fluid particle breakage and coalescence

  10. Analytical solutions of time-fractional models for homogeneous Gardner equation and non-homogeneous differential equations

    Directory of Open Access Journals (Sweden)

    Olaniyi Samuel Iyiola

    2014-09-01

    Full Text Available In this paper, we obtain analytical solutions of homogeneous time-fractional Gardner equation and non-homogeneous time-fractional models (including Buck-master equation using q-Homotopy Analysis Method (q-HAM. Our work displays the elegant nature of the application of q-HAM not only to solve homogeneous non-linear fractional differential equations but also to solve the non-homogeneous fractional differential equations. The presence of the auxiliary parameter h helps in an effective way to obtain better approximation comparable to exact solutions. The fraction-factor in this method gives it an edge over other existing analytical methods for non-linear differential equations. Comparisons are made upon the existence of exact solutions to these models. The analysis shows that our analytical solutions converge very rapidly to the exact solutions.

  11. Electronic representation of wave equation

    Energy Technology Data Exchange (ETDEWEB)

    Veigend, Petr; Kunovský, Jiří, E-mail: kunovsky@fit.vutbr.cz; Kocina, Filip; Nečasová, Gabriela; Valenta, Václav [University of Technology, Faculty of Information Technology, Božetěchova 2, 612 66 Brno (Czech Republic); Šátek, Václav [IT4Innovations, VŠB Technical University of Ostrava, 17. listopadu 15/2172, 708 33 Ostrava-Poruba (Czech Republic); University of Technology, Faculty of Information Technology, Božetěchova 2, 612 66 Brno (Czech Republic)

    2016-06-08

    The Taylor series method for solving differential equations represents a non-traditional way of a numerical solution. Even though this method is not much preferred in the literature, experimental calculations done at the Department of Intelligent Systems of the Faculty of Information Technology of TU Brno have verified that the accuracy and stability of the Taylor series method exceeds the currently used algorithms for numerically solving differential equations. This paper deals with solution of Telegraph equation using modelling of a series small pieces of the wire. Corresponding differential equations are solved by the Modern Taylor Series Method.

  12. The Dirac equation for accountants

    International Nuclear Information System (INIS)

    Ord, G.N.

    2006-01-01

    In the context of relativistic quantum mechanics, derivations of the Dirac equation usually take the form of plausibility arguments based on experience with the Schroedinger equation. The primary reason for this is that we do not know what wavefunctions physically represent, so derivations have to rely on formal arguments. There is however a context in which the Dirac equation in one dimension is directly related to a classical generating function. In that context, the derivation of the Dirac equation is an exercise in counting. We provide this derivation here and discuss its relationship to quantum mechanics

  13. Polygons of differential equations for finding exact solutions

    International Nuclear Information System (INIS)

    Kudryashov, Nikolai A.; Demina, Maria V.

    2007-01-01

    A method for finding exact solutions of nonlinear differential equations is presented. Our method is based on the application of polygons corresponding to nonlinear differential equations. It allows one to express exact solutions of the equation studied through solutions of another equation using properties of the basic equation itself. The ideas of power geometry are used and developed. Our approach has a pictorial interpretation, which is illustrative and effective. The method can be also applied for finding transformations between solutions of differential equations. To demonstrate the method application exact solutions of several equations are found. These equations are: the Korteveg-de Vries-Burgers equation, the generalized Kuramoto-Sivashinsky equation, the fourth-order nonlinear evolution equation, the fifth-order Korteveg-de Vries equation, the fifth-order modified Korteveg-de Vries equation and the sixth-order nonlinear evolution equation describing turbulent processes. Some new exact solutions of nonlinear evolution equations are given

  14. Unsplit complex frequency shifted perfectly matched layer for second-order wave equation using auxiliary differential equations.

    Science.gov (United States)

    Gao, Yingjie; Zhang, Jinhai; Yao, Zhenxing

    2015-12-01

    The complex frequency shifted perfectly matched layer (CFS-PML) can improve the absorbing performance of PML for nearly grazing incident waves. However, traditional PML and CFS-PML are based on first-order wave equations; thus, they are not suitable for second-order wave equation. In this paper, an implementation of CFS-PML for second-order wave equation is presented using auxiliary differential equations. This method is free of both convolution calculations and third-order temporal derivatives. As an unsplit CFS-PML, it can reduce the nearly grazing incidence. Numerical experiments show that it has better absorption than typical PML implementations based on second-order wave equation.

  15. The Dirac equation and its solutions

    Energy Technology Data Exchange (ETDEWEB)

    Bagrov, Vladislav G. [Tomsk State Univ., Tomsk (Russian Federation). Dept. of Quantum Field Theroy; Gitman, Dmitry [Sao Paulo Univ. (Brazil). Inst. de Fisica; P.N. Lebedev Physical Institute, Moscow (Russian Federation); Tomsk State Univ., Tomsk (Russian Federation). Faculty of Physics

    2013-07-01

    The Dirac equation is of fundamental importance for relativistic quantum mechanics and quantum electrodynamics. In relativistic quantum mechanics, the Dirac equation is referred to as one-particle wave equation of motion for electron in an external electromagnetic field. In quantum electrodynamics, exact solutions of this equation are needed to treat the interaction between the electron and the external field exactly. In particular, all propagators of a particle, i.e., the various Green's functions, are constructed in a certain way by using exact solutions of the Dirac equation.

  16. On the Inclusion of Difference Equation Problems and Z Transform Methods in Sophomore Differential Equation Classes

    Science.gov (United States)

    Savoye, Philippe

    2009-01-01

    In recent years, I started covering difference equations and z transform methods in my introductory differential equations course. This allowed my students to extend the "classical" methods for (ordinary differential equation) ODE's to discrete time problems arising in many applications.

  17. Boussinesq evolution equations

    DEFF Research Database (Denmark)

    Bredmose, Henrik; Schaffer, H.; Madsen, Per A.

    2004-01-01

    This paper deals with the possibility of using methods and ideas from time domain Boussinesq formulations in the corresponding frequency domain formulations. We term such frequency domain models "evolution equations". First, we demonstrate that the numerical efficiency of the deterministic...... Boussinesq evolution equations of Madsen and Sorensen [Madsen, P.A., Sorensen, O.R., 1993. Bound waves and triad interactions in shallow water. Ocean Eng. 20 359-388] can be improved by using Fast Fourier Transforms to evaluate the nonlinear terms. For a practical example of irregular waves propagating over...... a submerged bar, it is demonstrated that evolution equations utilising FFT can be solved around 100 times faster than the corresponding time domain model. Use of FFT provides an efficient bridge between the frequency domain and the time domain. We utilise this by adapting the surface roller model for wave...

  18. Fractional Diffusion Equations and Anomalous Diffusion

    Science.gov (United States)

    Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin

    2018-01-01

    Preface; 1. Mathematical preliminaries; 2. A survey of the fractional calculus; 3. From normal to anomalous diffusion; 4. Fractional diffusion equations: elementary applications; 5. Fractional diffusion equations: surface effects; 6. Fractional nonlinear diffusion equation; 7. Anomalous diffusion: anisotropic case; 8. Fractional Schrödinger equations; 9. Anomalous diffusion and impedance spectroscopy; 10. The Poisson–Nernst–Planck anomalous (PNPA) models; References; Index.

  19. 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.

  20. 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.

  1. Abstract methods in partial differential equations

    CERN Document Server

    Carroll, Robert W

    2012-01-01

    Detailed, self-contained treatment examines modern abstract methods in partial differential equations, especially abstract evolution equations. Suitable for graduate students with some previous exposure to classical partial differential equations. 1969 edition.

  2. Generalization of Einstein's gravitational field equations

    Science.gov (United States)

    Moulin, Frédéric

    2017-12-01

    The Riemann tensor is the cornerstone of general relativity, but as is well known it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show that this equation, written in n dimensions, contains the energy-momentum tensor for matter and that of the gravitational field itself. This new 4-index equation remains completely within the framework of general relativity and emerges as a natural generalization of the familiar 2-index Einstein equation. Due to the presence of the Weyl tensor, we show that this equation contains much more information, which fully justifies the use of a fourth-order theory.

  3. Extraction of dynamical equations from chaotic data

    International Nuclear Information System (INIS)

    Rowlands, G.; Sprott, J.C.

    1991-02-01

    A method is described for extracting from a chaotic time series a system of equations whose solution reproduces the general features of the original data even when these are contaminated with noise. The equations facilitate calculation of fractal dimension, Lyapunov exponents and short-term predictions. The method is applied to data derived from numerical solutions of the Logistic equation, the Henon equations, the Lorenz equations and the Roessler equations. 10 refs., 5 figs

  4. The AGL equation from the dipole picture

    International Nuclear Information System (INIS)

    Gay Ducati, M.B.; Goncalves, V.P.

    1999-01-01

    The AGL equation includes all multiple pomeron exchanges in the double logarithmic approximation (DLA) limit, leading to a unitarized gluon distribution in the small x regime. This equation was originally obtained using the Glauber-Mueller approach. We demonstrate in this paper that the AGL equation and, consequently, the GLR equation, can also be obtained from the dipole picture in the double logarithmic limit, using an evolution equation, recently proposed, which includes all multiple pomeron exchanges in the leading logarithmic approximation. Our conclusion is that the AGL equation is a good candidate for a unitarized evolution equation at small x in the DLA limit

  5. Singularly perturbed Burger-Huxley equation: Analytical solution ...

    African Journals Online (AJOL)

    user

    solutions of singularly perturbed nonlinear differential equations. ... for solving generalized Burgers-Huxley equation but this equation is not singularly ...... Solitary waves solutions of the generalized Burger Huxley equations, Journal of.

  6. Baecklund transformations for integrable lattice equations

    International Nuclear Information System (INIS)

    Atkinson, James

    2008-01-01

    We give new Baecklund transformations (BTs) for some known integrable (in the sense of being multidimensionally consistent) quadrilateral lattice equations. As opposed to the natural auto-BT inherent in every such equation, these BTs are of two other kinds. Specifically, it is found that some equations admit additional auto-BTs (with Baecklund parameter), whilst some pairs of apparently distinct equations admit a BT which connects them

  7. 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.

  8. What happens to linear properties as we move from the Klein-Gordon equation to the sine-Gordon equation

    International Nuclear Information System (INIS)

    Kovalyov, Mikhail

    2010-01-01

    In this article the sets of solutions of the sine-Gordon equation and its linearization the Klein-Gordon equation are discussed and compared. It is shown that the set of solutions of the sine-Gordon equation possesses a richer structure which partly disappears during linearization. Just like the solutions of the Klein-Gordon equation satisfy the linear superposition principle, the solutions of the sine-Gordon equation satisfy a nonlinear superposition principle.

  9. Sparse dynamics for partial differential equations.

    Science.gov (United States)

    Schaeffer, Hayden; Caflisch, Russel; Hauck, Cory D; Osher, Stanley

    2013-04-23

    We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to the coefficients of the basis approximation. By reducing or compressing the information needed to represent the solution at every step, only the essential dynamics are represented. In many cases, there are natural bases derived from the differential equations, which promote sparsity. We find that our method successfully reduces the dynamics of convection equations, diffusion equations, weak shocks, and vorticity equations with high-frequency source terms.

  10. Complex centers of polynomial differential equations

    Directory of Open Access Journals (Sweden)

    Mohamad Ali M. Alwash

    2007-07-01

    Full Text Available We present some results on the existence and nonexistence of centers for polynomial first order ordinary differential equations with complex coefficients. In particular, we show that binomial differential equations without linear terms do not have complex centers. Classes of polynomial differential equations, with more than two terms, are presented that do not have complex centers. We also study the relation between complex centers and the Pugh problem. An algorithm is described to solve the Pugh problem for equations without complex centers. The method of proof involves phase plane analysis of the polar equations and a local study of periodic solutions.

  11. Numerical solutions of diffusive logistic equation

    International Nuclear Information System (INIS)

    Afrouzi, G.A.; Khademloo, S.

    2007-01-01

    In this paper we investigate numerically positive solutions of a superlinear Elliptic equation on bounded domains. The study of Diffusive logistic equation continues to be an active field of research. The subject has important applications to population migration as well as many other branches of science and engineering. In this paper the 'finite difference scheme' will be developed and compared for solving the one- and three-dimensional Diffusive logistic equation. The basis of the analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach, developed from many authors these years

  12. Applied partial differential equations

    CERN Document Server

    Logan, J David

    2015-01-01

    This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs.  Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory. The concise treatment of the subject is maintained in this third edition covering all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. In this third edition, text remains intimately tied to applications in heat transfer, wave motion, biological systems, and a variety other topics in pure and applied science. The text offers flexibility to instructors who, for example, may wish to insert topics from biology or numerical methods at any time in the course. The exposition is presented in a friendly, easy-to-read, style, with mathematical ideas motivated from physical problems. Many exercises and worked e...

  13. The generalized Airy diffusion equation

    Directory of Open Access Journals (Sweden)

    Frank M. Cholewinski

    2003-08-01

    Full Text Available Solutions of a generalized Airy diffusion equation and an associated nonlinear partial differential equation are obtained. Trigonometric type functions are derived for a third order generalized radial Euler type operator. An associated complex variable theory and generalized Cauchy-Euler equations are obtained. Further, it is shown that the Airy expansions can be mapped onto the Bessel Calculus of Bochner, Cholewinski and Haimo.

  14. Exact Solutions of a Fractional-Type Differential-Difference Equation Related to Discrete MKdV Equation

    International Nuclear Information System (INIS)

    Aslan İsmail

    2014-01-01

    The extended simplest equation method is used to solve exactly a new differential-difference equation of fractional-type, proposed by Narita [J. Math. Anal. Appl. 381 (2011) 963] quite recently, related to the discrete MKdV equation. It is shown that the model supports three types of exact solutions with arbitrary parameters: hyperbolic, trigonometric and rational, which have not been reported before. (general)

  15. Inverse scattering transform for the time dependent Schroedinger equation with applications to the KPI equation

    Energy Technology Data Exchange (ETDEWEB)

    Xin, Zhou [Wisconsin Univ., Madison (USA). Dept. of Mathematics

    1990-03-01

    For the direct-inverse scattering transform of the time dependent Schroedinger equation, rigorous results are obtained based on an operator-triangular-factorization approach. By viewing the equation as a first order operator equation, similar results as for the first order n x n matrix system are obtained. The nonlocal Riemann-Hilbert problem for inverse scattering is shown to have solution. (orig.).

  16. Inverse scattering transform for the time dependent Schroedinger equation with applications to the KPI equation

    International Nuclear Information System (INIS)

    Zhou Xin

    1990-01-01

    For the direct-inverse scattering transform of the time dependent Schroedinger equation, rigorous results are obtained based on an operator-triangular-factorization approach. By viewing the equation as a first order operator equation, similar results as for the first order n x n matrix system are obtained. The nonlocal Riemann-Hilbert problem for inverse scattering is shown to have solution. (orig.)

  17. Darboux transformation for the NLS equation

    International Nuclear Information System (INIS)

    Aktosun, Tuncay; Mee, Cornelis van der

    2010-01-01

    We analyze a certain class of integral equations associated with Marchenko equations and Gel'fand-Levitan equations. Such integral equations arise through a Fourier transformation on various ordinary differential equations involving a spectral parameter. When the integral operator is perturbed by a finite-rank perturbation, we explicitly evaluate the change in the solution in terms of the unperturbed quantities and the finite-rank perturbation. We show that this result provides a fundamental approach to derive Darboux transformations for various systems of ordinary differential operators. We illustrate our theory by providing the explicit Darboux transformation for the Zakharov-Shabat system and show how the potential and wave function change when a simple discrete eigenvalue is added to the spectrum, and thus we also provide a one-parameter family of Darboux transformations for the nonlinear Schroedinger equation.

  18. Equation for the superfluid gap obtained by coarse graining the Bogoliubov-de Gennes equations throughout the BCS-BEC crossover

    Science.gov (United States)

    Simonucci, S.; Strinati, G. C.

    2014-02-01

    We derive a nonlinear differential equation for the gap parameter of a superfluid Fermi system by performing a suitable coarse graining of the Bogoliubov-de Gennes (BdG) equations throughout the BCS-BEC crossover, with the aim of replacing the time-consuming solution of the original BdG equations by the simpler solution of this novel equation. We perform a favorable numerical test on the validity of this new equation over most of the temperature-coupling phase diagram, by an explicit comparison with the full solution of the original BdG equations for an isolated vortex. We also show that the new equation reduces both to the Ginzburg-Landau equation for Cooper pairs in weak coupling close to the critical temperature and to the Gross-Pitaevskii equation for composite bosons in strong coupling at low temperature.

  19. Ultradiscrete sine-Gordon Equation over Symmetrized Max-Plus Algebra, and Noncommutative Discrete and Ultradiscrete sine-Gordon Equations

    Directory of Open Access Journals (Sweden)

    Kenichi Kondo

    2013-11-01

    Full Text Available Ultradiscretization with negative values is a long-standing problem and several attempts have been made to solve it. Among others, we focus on the symmetrized max-plus algebra, with which we ultradiscretize the discrete sine-Gordon equation. Another ultradiscretization of the discrete sine-Gordon equation has already been proposed by previous studies, but the equation and the solutions obtained here are considered to directly correspond to the discrete counterpart. We also propose a noncommutative discrete analogue of the sine-Gordon equation, reveal its relations to other integrable systems including the noncommutative discrete KP equation, and construct multisoliton solutions by a repeated application of Darboux transformations. Moreover, we derive a noncommutative ultradiscrete analogue of the sine-Gordon equation and its 1-soliton and 2-soliton solutions, using the symmetrized max-plus algebra. As a result, we have a complete set of commutative and noncommutative versions of continuous, discrete, and ultradiscrete sine-Gordon equations.

  20. The multi-order envelope periodic solutions to the nonlinear Schrodinger equation and cubic nonlinear Schrodinger equation

    International Nuclear Information System (INIS)

    Xiao Yafeng; Xue Haili; Zhang Hongqing

    2011-01-01

    Based on Jacobi elliptic function and the Lame equation, the perturbation method is applied to get the multi-order envelope periodic solutions of the nonlinear Schrodinger equation and cubic nonlinear Schrodinger equation. These multi-order envelope periodic solutions can degenerate into the different envelope solitary solutions. (authors)

  1. Differential-algebraic solutions of the heat equation

    OpenAIRE

    Buchstaber, Victor M.; Netay, Elena Yu.

    2014-01-01

    In this work we introduce the notion of differential-algebraic ansatz for the heat equation and explicitly construct heat equation and Burgers equation solutions given a solution of a homogeneous non-linear ordinary differential equation of a special form. The ansatz for such solutions is called the $n$-ansatz, where $n+1$ is the order of the differential equation.

  2. The Camassa-Holm equation as an incompressible Euler equation: A geometric point of view

    Science.gov (United States)

    Gallouët, Thomas; Vialard, François-Xavier

    2018-04-01

    The group of diffeomorphisms of a compact manifold endowed with the L2 metric acting on the space of probability densities gives a unifying framework for the incompressible Euler equation and the theory of optimal mass transport. Recently, several authors have extended optimal transport to the space of positive Radon measures where the Wasserstein-Fisher-Rao distance is a natural extension of the classical L2-Wasserstein distance. In this paper, we show a similar relation between this unbalanced optimal transport problem and the Hdiv right-invariant metric on the group of diffeomorphisms, which corresponds to the Camassa-Holm (CH) equation in one dimension. Geometrically, we present an isometric embedding of the group of diffeomorphisms endowed with this right-invariant metric in the automorphisms group of the fiber bundle of half densities endowed with an L2 type of cone metric. This leads to a new formulation of the (generalized) CH equation as a geodesic equation on an isotropy subgroup of this automorphisms group; On S1, solutions to the standard CH thus give radially 1-homogeneous solutions of the incompressible Euler equation on R2 which preserves a radial density that has a singularity at 0. An other application consists in proving that smooth solutions of the Euler-Arnold equation for the Hdiv right-invariant metric are length minimizing geodesics for sufficiently short times.

  3. Five-equation and robust three-equation methods for solution verification of large eddy simulation

    Science.gov (United States)

    Dutta, Rabijit; Xing, Tao

    2018-02-01

    This study evaluates the recently developed general framework for solution verification methods for large eddy simulation (LES) using implicitly filtered LES of periodic channel flows at friction Reynolds number of 395 on eight systematically refined grids. The seven-equation method shows that the coupling error based on Hypothesis I is much smaller as compared with the numerical and modeling errors and therefore can be neglected. The authors recommend five-equation method based on Hypothesis II, which shows a monotonic convergence behavior of the predicted numerical benchmark ( S C ), and provides realistic error estimates without the need of fixing the orders of accuracy for either numerical or modeling errors. Based on the results from seven-equation and five-equation methods, less expensive three and four-equation methods for practical LES applications were derived. It was found that the new three-equation method is robust as it can be applied to any convergence types and reasonably predict the error trends. It was also observed that the numerical and modeling errors usually have opposite signs, which suggests error cancellation play an essential role in LES. When Reynolds averaged Navier-Stokes (RANS) based error estimation method is applied, it shows significant error in the prediction of S C on coarse meshes. However, it predicts reasonable S C when the grids resolve at least 80% of the total turbulent kinetic energy.

  4. Partial differential equations for scientists and engineers

    CERN Document Server

    Farlow, Stanley J

    1993-01-01

    Most physical phenomena, whether in the domain of fluid dynamics, electricity, magnetism, mechanics, optics, or heat flow, can be described in general by partial differential equations. Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations.This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing th

  5. On a complex differential Riccati equation

    International Nuclear Information System (INIS)

    Khmelnytskaya, Kira V; Kravchenko, Vladislav V

    2008-01-01

    We consider a nonlinear partial differential equation for complex-valued functions which is related to the two-dimensional stationary Schroedinger equation and enjoys many properties similar to those of the ordinary differential Riccati equation such as the famous Euler theorems, the Picard theorem and others. Besides these generalizations of the classical 'one-dimensional' results, we discuss new features of the considered equation including an analogue of the Cauchy integral theorem

  6. Some Aspects of Extended Kinetic Equation

    Directory of Open Access Journals (Sweden)

    Dilip Kumar

    2015-09-01

    Full Text Available Motivated by the pathway model of Mathai introduced in 2005 [Linear Algebra and Its Applications, 396, 317–328] we extend the standard kinetic equations. Connection of the extended kinetic equation with fractional calculus operator is established. The solution of the general form of the fractional kinetic equation is obtained through Laplace transform. The results for the standard kinetic equation are obtained as the limiting case.

  7. Analytical model of stress field in submerged arc welding butt joint with thorough penetration

    Directory of Open Access Journals (Sweden)

    Winczek Jerzy

    2018-01-01

    Full Text Available Analytical model of temporary and residual stresses for butt welding with thorough penetration was described assuming planar section hypothesis and using integral equations of stress equilibrium of the bar and simple Hooke’s law. In solution the effect of phase transformations (structure changes and structural strains has been taken into account. Phase transformations during heating are limited by temperature values at the beginning and at the end of austenitic transformation, depending on chemical composition of steel while the progress of phase transformations during cooling is determined on the basis of TTT-welding diagram. Temperature values at the beginning and at the end of transformation are conditioned by the speed of heating. Kinetics of diffusional transformation is described basing on Johnson-Mehl-Avrami-Kolmogorov equation, while martensitic transformation, basing on Koistinen-Marburger equation. Stresses in elasto-plastic state are determined by iteration, using elastic solutions method with changeable longitudinal modulus of elasticity, conditioned by stress-strain curve. Computations of stress field have been conducted for one-side butt welded of two steel flats made from S235 steel. It has enabled a clear interpretation of influence of temperature field and phase transformation on stresses caused by welding using Submerged Arc Welding (SAW method.

  8. Formulation of anisotropic Hill criteria for the description of an aluminium alloy behaviour during the channel die compression test

    International Nuclear Information System (INIS)

    Gavrus, A.; Francillette, H.

    2007-01-01

    During the last years the study of the plastic deformation modes and the anisotropic mechanical behaviour of aluminium alloys have been the subject of many investigations. This paper deals with a phenomenological identification of an anisotropic Hill constitutive equation of aluminium AU4G samples using a channel die compression device at room temperature. By considering the different possible orientations of the samples in the channel die device, three initial textures, named ND (normal direction Z), LD (longitudinal direction X) and TD (transverse direction Y), were defined with the corresponding stresses σND, σLD and σTD. To describe the anisotropy of the material, a quadratic Hill criteria is used. An Avrami type equation based on the mixture of the hardening and softening phenomena is used to describe variation of each stress component with the equivalent plastic strain. The identification of the parameters of the law is made using an identification software (OPTPAR) and a good correlation between the experimental stresses and computed ones is obtained. The variation of the Hill parameters with a proposed equivalent strain, describing the deformation history of the material, is analysed. Finally, using the expressions of F, G, H and N, the constitutive equation of the normal anisotropy in the plane XY is obtained

  9. Lax representations for matrix short pulse equations

    Science.gov (United States)

    Popowicz, Z.

    2017-10-01

    The Lax representation for different matrix generalizations of Short Pulse Equations (SPEs) is considered. The four-dimensional Lax representations of four-component Matsuno, Feng, and Dimakis-Müller-Hoissen-Matsuno equations are obtained. The four-component Feng system is defined by generalization of the two-dimensional Lax representation to the four-component case. This system reduces to the original Feng equation, to the two-component Matsuno equation, or to the Yao-Zang equation. The three-component version of the Feng equation is presented. The four-component version of the Matsuno equation with its Lax representation is given. This equation reduces the new two-component Feng system. The two-component Dimakis-Müller-Hoissen-Matsuno equations are generalized to the four-parameter family of the four-component SPE. The bi-Hamiltonian structure of this generalization, for special values of parameters, is defined. This four-component SPE in special cases reduces to the new two-component SPE.

  10. Optimal Control for Stochastic Delay Evolution Equations

    Energy Technology Data Exchange (ETDEWEB)

    Meng, Qingxin, E-mail: mqx@hutc.zj.cn [Huzhou University, Department of Mathematical Sciences (China); Shen, Yang, E-mail: skyshen87@gmail.com [York University, Department of Mathematics and Statistics (Canada)

    2016-08-15

    In this paper, we investigate a class of infinite-dimensional optimal control problems, where the state equation is given by a stochastic delay evolution equation with random coefficients, and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation. We first prove the continuous dependence theorems for stochastic delay evolution equations and anticipated backward stochastic evolution equations, and show the existence and uniqueness of solutions to anticipated backward stochastic evolution equations. Then we establish necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, we apply stochastic maximum principles to study two examples, an infinite-dimensional linear-quadratic control problem with delay and an optimal control of a Dirichlet problem for a stochastic partial differential equation with delay. Further applications of the two examples to a Cauchy problem for a controlled linear stochastic partial differential equation and an optimal harvesting problem are also considered.

  11. Exact traveling wave solutions of modified KdV-Zakharov-Kuznetsov equation and viscous Burgers equation.

    Science.gov (United States)

    Islam, Md Hamidul; Khan, Kamruzzaman; Akbar, M Ali; Salam, Md Abdus

    2014-01-01

    Mathematical modeling of many physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear partial differential equations (NPDEs) plays a significant role in the study of nonlinear physical phenomena. In this article, we construct the traveling wave solutions of modified KDV-ZK equation and viscous Burgers equation by using an enhanced (G '/G) -expansion method. A number of traveling wave solutions in terms of unknown parameters are obtained. Derived traveling wave solutions exhibit solitary waves when special values are given to its unknown parameters. 35C07; 35C08; 35P99.

  12. Analysis of discrete reaction-diffusion equations for autocatalysis and continuum diffusion equations for transport

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Chi-Jen [Iowa State Univ., Ames, IA (United States)

    2013-01-01

    In this thesis, we analyze both the spatiotemporal behavior of: (A) non-linear “reaction” models utilizing (discrete) reaction-diffusion equations; and (B) spatial transport problems on surfaces and in nanopores utilizing the relevant (continuum) diffusion or Fokker-Planck equations. Thus, there are some common themes in these studies, as they all involve partial differential equations or their discrete analogues which incorporate a description of diffusion-type processes. However, there are also some qualitative differences, as shall be discussed below.

  13. Differential equation analysis in biomedical science and engineering ordinary differential equation applications with R

    CERN Document Server

    Schiesser, William E

    2014-01-01

    Features a solid foundation of mathematical and computational tools to formulate and solve real-world ODE problems across various fields With a step-by-step approach to solving ordinary differential equations (ODEs), Differential Equation Analysis in Biomedical Science and Engineering: Ordinary Differential Equation Applications with R successfully applies computational techniques for solving real-worldODE problems that are found in a variety of fields, including chemistry, physics, biology,and physiology. The book provides readers with the necessary knowledge to reproduce andextend the comp

  14. The physics behind Van der Burgh's empirical equation, providing a new predictive equation for salinity intrusion in estuaries

    Science.gov (United States)

    Zhang, Zhilin; Savenije, Hubert H. G.

    2017-07-01

    The practical value of the surprisingly simple Van der Burgh equation in predicting saline water intrusion in alluvial estuaries is well documented, but the physical foundation of the equation is still weak. In this paper we provide a connection between the empirical equation and the theoretical literature, leading to a theoretical range of Van der Burgh's coefficient of 1/2 residual circulation. This type of mixing is relevant in the wider part of alluvial estuaries where preferential ebb and flood channels appear. Subsequently, this dispersion equation is combined with the salt balance equation to obtain a new predictive analytical equation for the longitudinal salinity distribution. Finally, the new equation was tested and applied to a large database of observations in alluvial estuaries, whereby the calibrated K values appeared to correspond well to the theoretical range.

  15. Wave equations for pulse propagation

    International Nuclear Information System (INIS)

    Shore, B.W.

    1987-01-01

    Theoretical discussions of the propagation of pulses of laser radiation through atomic or molecular vapor rely on a number of traditional approximations for idealizing the radiation and the molecules, and for quantifying their mutual interaction by various equations of propagation (for the radiation) and excitation (for the molecules). In treating short-pulse phenomena it is essential to consider coherent excitation phenomena of the sort that is manifest in Rabi oscillations of atomic or molecular populations. Such processes are not adequately treated by rate equations for excitation nor by rate equations for radiation. As part of a more comprehensive treatment of the coupled equations that describe propagation of short pulses, this memo presents background discussion of the equations that describe the field. This memo discusses the origin, in Maxwell's equations, of the wave equation used in the description of pulse propagation. It notes the separation into lamellar and solenoidal (or longitudinal and transverse) and positive and negative frequency parts. It mentions the possibility of separating the polarization field into linear and nonlinear parts, in order to define a susceptibility or index of refraction and, from these, a phase and group velocity. The memo discusses various ways of characterizing the polarization characteristics of plane waves, that is, of parameterizing a transverse unit vector, such as the Jones vector, the Stokes vector, and the Poincare sphere. It discusses the connection between macroscopically defined quantities, such as the intensity or, more generally, the Stokes parameters, and microscopic field amplitudes. The material presented here is a portion of a more extensive treatment of propagation to be presented separately. The equations presented here have been described in various books and articles. They are collected here as a summary and review of theory needed when treating pulse propagation

  16. Constitutive equations for two-phase flows

    International Nuclear Information System (INIS)

    Boure, J.A.

    1974-12-01

    The mathematical model of a system of fluids consists of several kinds of equations complemented by boundary and initial conditions. The first kind equations result from the application to the system, of the fundamental conservation laws (mass, momentum, energy). The second kind equations characterize the fluid itself, i.e. its intrinsic properties and in particular its mechanical and thermodynamical behavior. They are the mathematical model of the particular fluid under consideration, the laws they expressed are so called the constitutive equations of the fluid. In practice the constitutive equations cannot be fully stated without reference to the conservation laws. Two classes of model have been distinguished: mixture model and two-fluid models. In mixture models, the mixture is considered as a single fluid. Besides the usual friction factor and heat transfer correlations, a single constitutive law is necessary. In diffusion models, the mixture equation of state is replaced by the phasic equations of state and by three consitutive laws, for phase change mass transfer, drift velocity and thermal non-equilibrium respectively. In the two-fluid models, the two phases are considered separately; two phasic equations of state, two friction factor correlations, two heat transfer correlations and four constitutive laws are included [fr

  17. Multi-diffusive nonlinear Fokker–Planck equation

    International Nuclear Information System (INIS)

    Ribeiro, Mauricio S; Casas, Gabriela A; Nobre, Fernando D

    2017-01-01

    Nonlinear Fokker–Planck equations, characterized by more than one diffusion term, have appeared recently in literature. Here, it is shown that these equations may be derived either from approximations in a master equation, or from a Langevin-type approach. An H-theorem is proven, relating these Fokker–Planck equations to an entropy composed by a sum of contributions, each of them associated with a given diffusion term. Moreover, the stationary state of the Fokker–Planck equation is shown to coincide with the equilibrium state, obtained by extremization of the entropy, in the sense that both procedures yield precisely the same equation. Due to the nonlinear character of this equation, the equilibrium probability may be obtained, in most cases, only by means of numerical approaches. Some examples are worked out, where the equilibrium probability distribution is computed for nonlinear Fokker–Planck equations presenting two diffusion terms, corresponding to an entropy characterized by a sum of two contributions. It is shown that the resulting equilibrium distribution, in general, presents a form that differs from a sum of the equilibrium distributions that maximizes each entropic contribution separately, although in some cases one may construct such a linear combination as a good approximation for the equilibrium distribution. (paper)

  18. Correct Linearization of Einstein's Equations

    Directory of Open Access Journals (Sweden)

    Rabounski D.

    2006-06-01

    Full Text Available Regularly Einstein's equations can be reduced to a wave form (linearly dependent from the second derivatives of the space metric in the absence of gravitation, the space rotation and Christoffel's symbols. As shown here, the origin of the problem is that one uses the general covariant theory of measurement. Here the wave form of Einstein's equations is obtained in the terms of Zelmanov's chronometric invariants (physically observable projections on the observer's time line and spatial section. The obtained equations depend on solely the second derivatives even if gravitation, the space rotation and Christoffel's symbols. The correct linearization proves: the Einstein equations are completely compatible with weak waves of the metric.

  19. Integral equation for Coulomb problem

    International Nuclear Information System (INIS)

    Sasakawa, T.

    1986-01-01

    For short range potentials an inhomogeneous (homogeneous) Lippmann-Schwinger integral equation of the Fredholm type yields the wave function of scattering (bound) state. For the Coulomb potential, this statement is no more valid. It has been felt difficult to express the Coulomb wave function in a form of an integral equation with the Coulomb potential as the perturbation. In the present paper, the author shows that an inhomogeneous integral equation of a Volterra type with the Coulomb potential as the perturbation can be constructed both for the scattering and the bound states. The equation yielding the binding energy is given in an integral form. The present treatment is easily extended to the coupled Coulomb problems

  20. Household food insecurity is associated with a higher burden of obesity and risk of dietary inadequacies among mothers in Beirut, Lebanon.

    Science.gov (United States)

    Jomaa, Lamis; Naja, Farah; Cheaib, Ruba; Hwalla, Nahla

    2017-06-12

    Mixed evidence exists with respect to the association between household food insecurity (HFIS) and obesity in low-to-middle income countries (LMICs), particularly among women. This study aimed to measure socioeconomic correlates of HFIS and explores its association with dietary intake and odds of obesity among mothers in Lebanon, a middle-income country undergoing nutrition transition. A cross-sectional study was conducted among a representative sample of households (n = 378) in Beirut, Lebanon. Surveys were completed with mothers of children Food Insecurity Access Scale (HFIAS). Dietary intake was assessed using the multiple pass 24-h recall method. Associations between HFIS (food vs food insecure) and socio-demographic characteristics were reported using crude and adjusted odds ratios. The odds of consuming food secure and food insecure households were explored. In addition, logistic regression analyses were conducted to explore the association of HFIS with obesity (BMI ≥ 30 kg/m2) and at-risk waist circumference (WC ≥ 80 cm) among mothers. HFIS was found among 50% of study sample and was inversely associated with household income and mother's educational level, even after adjusting for other socioeconomic variables (p food insecure households reported consuming significantly less dairy products, fruits, and nuts yet more breads and sweets; and they had higher odds of consuming food insecure mothers had 1.73 odds of obesity (95% CI: 1.02-2.92) compared to food secure mothers. High HFIS prevalence was reported among urban Lebanese households. Mothers from food insecure households had a high risk of dietary inadequacy and obesity. Adequate evidence-based public health strategies are needed to reduce the vulnerability of mothers to food insecurity in LMIC settings and alleviate their risk of a high burden of nutrient insecurity and obesity.

  1. A fractional Dirac equation and its solution

    International Nuclear Information System (INIS)

    Muslih, Sami I; Agrawal, Om P; Baleanu, Dumitru

    2010-01-01

    This paper presents a fractional Dirac equation and its solution. The fractional Dirac equation may be obtained using a fractional variational principle and a fractional Klein-Gordon equation; both methods are considered here. We extend the variational formulations for fractional discrete systems to fractional field systems defined in terms of Caputo derivatives. By applying the variational principle to a fractional action S, we obtain the fractional Euler-Lagrange equations of motion. We present a Lagrangian and a Hamiltonian for the fractional Dirac equation of order α. We also use a fractional Klein-Gordon equation to obtain the fractional Dirac equation which is the same as that obtained using the fractional variational principle. Eigensolutions of this equation are presented which follow the same approach as that for the solution of the standard Dirac equation. We also provide expressions for the path integral quantization for the fractional Dirac field which, in the limit α → 1, approaches to the path integral for the regular Dirac field. It is hoped that the fractional Dirac equation and the path integral quantization of the fractional field will allow further development of fractional relativistic quantum mechanics.

  2. Linear superposition solutions to nonlinear wave equations

    International Nuclear Information System (INIS)

    Liu Yu

    2012-01-01

    The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics. The linear superposition solutions to the generalized KdV equation K(2,2,1), the Oliver water wave equation, and the k(n, n) equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed

  3. Systematic Equation Formulation

    DEFF Research Database (Denmark)

    Lindberg, Erik

    2007-01-01

    A tutorial giving a very simple introduction to the set-up of the equations used as a model for an electrical/electronic circuit. The aim is to find a method which is as simple and general as possible with respect to implementation in a computer program. The “Modified Nodal Approach”, MNA, and th......, and the “Controlled Source Approach”, CSA, for systematic equation formulation are investigated. It is suggested that the kernel of the P Spice program based on MNA is reprogrammed....

  4. International Workshop on Elliptic and Parabolic Equations

    CERN Document Server

    Schrohe, Elmar; Seiler, Jörg; Walker, Christoph

    2015-01-01

    This volume covers the latest research on elliptic and parabolic equations and originates from the international Workshop on Elliptic and Parabolic Equations, held September 10-12, 2013 at the Leibniz Universität Hannover. It represents a collection of refereed research papers and survey articles written by eminent scientist on advances in different fields of elliptic and parabolic partial differential equations, including singular Riemannian manifolds, spectral analysis on manifolds, nonlinear dispersive equations, Brownian motion and kernel estimates, Euler equations, porous medium type equations, pseudodifferential calculus, free boundary problems, and bifurcation analysis.

  5. Differential equation analysis in biomedical science and engineering partial differential equation applications with R

    CERN Document Server

    Schiesser, William E

    2014-01-01

    Features a solid foundation of mathematical and computational tools to formulate and solve real-world PDE problems across various fields With a step-by-step approach to solving partial differential equations (PDEs), Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R successfully applies computational techniques for solving real-world PDE problems that are found in a variety of fields, including chemistry, physics, biology, and physiology. The book provides readers with the necessary knowledge to reproduce and extend the com

  6. The generalized Fermat equation

    NARCIS (Netherlands)

    Beukers, F.

    2006-01-01

    This article will be devoted to generalisations of Fermat’s equation xn + yn = zn. Very soon after the Wiles and Taylor proof of Fermat’s Last Theorem, it was wondered what would happen if the exponents in the three term equation would be chosen differently. Or if coefficients other than 1 would

  7. On matrix fractional differential equations

    OpenAIRE

    Adem Kılıçman; Wasan Ajeel Ahmood

    2017-01-01

    The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices. Also, we show the theorem of non-homogeneous matrix fractional partial differential equation with some illustrative examples to demonstrate the effectiveness of the new methodology. The main objec...

  8. Minimal solution for inconsistent singular fuzzy matrix equations

    Directory of Open Access Journals (Sweden)

    M. Nikuie

    2013-10-01

    Full Text Available The fuzzy matrix equations $Ailde{X}=ilde{Y}$ is called a singular fuzzy matrix equations while the coefficients matrix of its equivalent crisp matrix equations be a singular matrix. The singular fuzzy matrix equations are divided into two parts: consistent singular matrix equations and inconsistent fuzzy matrix equations. In this paper, the inconsistent singular fuzzy matrix equations is studied and the effect of generalized inverses in finding minimal solution of an inconsistent singular fuzzy matrix equations are investigated.

  9. Inadequacies of Dogmatic Realism

    National Research Council Canada - National Science Library

    Exner, Philip J

    1996-01-01

    ... This dichotomy between America's innate political Idealism and its operational pragmatism has plagued U S foreign policy since it emerged as a world power at the turn of the century and has often...

  10. Notes on the infinity Laplace equation

    CERN Document Server

    Lindqvist, Peter

    2016-01-01

    This BCAM SpringerBriefs is a treaty of the Infinity-Laplace Equation, which has inherited many features from the ordinary Laplace Equation, and is based on lectures by the author. The Infinity.Laplace Equation has delightful counterparts to the Dirichlet integral, the mean value property, the Brownian motion, Harnack's inequality, and so on. This "fully non-linear" equation has applications to image processing and to mass transfer problems, and it provides optimal Lipschitz extensions of boundary values.

  11. New solutions of Heun's general equation

    International Nuclear Information System (INIS)

    Ishkhanyan, Artur; Suominen, Kalle-Antti

    2003-01-01

    We show that in four particular cases the derivative of the solution of Heun's general equation can be expressed in terms of a solution to another Heun's equation. Starting from this property, we use the Gauss hypergeometric functions to construct series solutions to Heun's equation for the mentioned cases. Each of the hypergeometric functions involved has correct singular behaviour at only one of the singular points of the equation; the sum, however, has correct behaviour. (letter to the editor)

  12. Pseudodifferential equations over non-Archimedean spaces

    CERN Document Server

    Zúñiga-Galindo, W A

    2016-01-01

    Focusing on p-adic and adelic analogues of pseudodifferential equations, this monograph presents a very general theory of parabolic-type equations and their Markov processes motivated by their connection with models of complex hierarchic systems. The Gelfand-Shilov method for constructing fundamental solutions using local zeta functions is developed in a p-adic setting and several particular equations are studied, such as the p-adic analogues of the Klein-Gordon equation. Pseudodifferential equations for complex-valued functions on non-Archimedean local fields are central to contemporary harmonic analysis and mathematical physics and their theory reveals a deep connection with probability and number theory. The results of this book extend and complement the material presented by Vladimirov, Volovich and Zelenov (1994) and Kochubei (2001), which emphasize spectral theory and evolution equations in a single variable, and Albeverio, Khrennikov and Shelkovich (2010), which deals mainly with the theory and applica...

  13. New exact solutions of (2 + 1)-dimensional Gardner equation via the new sine-Gordon equation expansion method

    International Nuclear Information System (INIS)

    Chen Yong; Yan Zhenya

    2005-01-01

    In this paper (2 + 1)-dimensional Gardner equation is investigated using a sine-Gordon equation expansion method, which was presented via a generalized sine-Gordon reduction equation and a new transformation. As a consequence, it is shown that the method is more powerful to obtain many types of new doubly periodic solutions of (2 + 1)-dimensional Gardner equation. In particular, solitary wave solutions are also given as simple limits of doubly periodic solutions

  14. Relativistic wave equations and compton scattering

    International Nuclear Information System (INIS)

    Sutanto, S.H.; Robson, B.A.

    1998-01-01

    Full text: Recently an eight-component relativistic wave equation for spin-1/2 particles was proposed.This equation was obtained from a four-component spin-1/2 wave equation (the KG1/2 equation), which contains second-order derivatives in both space and time, by a procedure involving a linearisation of the time derivative analogous to that introduced by Feshbach and Villars for the Klein-Gordon equation. This new eight-component equation gives the same bound-state energy eigenvalue spectra for hydrogenic atoms as the Dirac equation but has been shown to predict different radiative transition probabilities for the fine structure of both the Balmer and Lyman a-lines. Since it has been shown that the new theory does not always give the same results as the Dirac theory, it is important to consider the validity of the new equation in the case of other physical problems. One of the early crucial tests of the Dirac theory was its application to the scattering of a photon by a free electron: the so-called Compton scattering problem. In this paper we apply the new theory to the calculation of Compton scattering to order e 2 . It will be shown that in spite of the considerable difference in the structure of the new theory and that of Dirac the cross section is given by the Klein-Nishina formula

  15. Generalized estimating equations

    CERN Document Server

    Hardin, James W

    2002-01-01

    Although powerful and flexible, the method of generalized linear models (GLM) is limited in its ability to accurately deal with longitudinal and clustered data. Developed specifically to accommodate these data types, the method of Generalized Estimating Equations (GEE) extends the GLM algorithm to accommodate the correlated data encountered in health research, social science, biology, and other related fields.Generalized Estimating Equations provides the first complete treatment of GEE methodology in all of its variations. After introducing the subject and reviewing GLM, the authors examine th

  16. Partial differential equations

    CERN Document Server

    Agranovich, M S

    2002-01-01

    Mark Vishik's Partial Differential Equations seminar held at Moscow State University was one of the world's leading seminars in PDEs for over 40 years. This book celebrates Vishik's eightieth birthday. It comprises new results and survey papers written by many renowned specialists who actively participated over the years in Vishik's seminars. Contributions include original developments and methods in PDEs and related fields, such as mathematical physics, tomography, and symplectic geometry. Papers discuss linear and nonlinear equations, particularly linear elliptic problems in angles and gener

  17. Quantum Gross-Pitaevskii Equation

    Directory of Open Access Journals (Sweden)

    Jutho Haegeman, Damian Draxler, Vid Stojevic, J. Ignacio Cirac, Tobias J. Osborne, Frank Verstraete

    2017-07-01

    Full Text Available We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational manifold of continuous matrix product states. This allows for a full quantum description of many body system ---including entanglement and correlations--- and thus extends significantly beyond the usual mean-field description of the Gross-Pitaevskii equation, which is known to fail for (quasi one-dimensional systems. By linearizing around a stationary solution, we furthermore derive an associated generalization of the Bogoliubov -- de Gennes equations. This framework is applied to compute the steady state response amplitude to a periodic perturbation of the potential.

  18. Example Solar Electric Propulsion System asteroid tours using variational calculus

    Science.gov (United States)

    Burrows, R. R.

    1985-01-01

    Exploration of the asteroid belt with a vehicle utilizing a Solar Electric Propulsion System has been proposed in past studies. Some of those studies illustrated multiple asteroid rendezvous with trajectories obtained using approximate methods. Most of the inadequacies of those approximations are overcome in this paper, which uses the calculus of variations to calculate the trajectories and associated payloads of four asteroid tours. The modeling, equations, and solution techniques are discussed, followed by a presentation of the results.

  19. Partial differential equations of mathematical physics

    CERN Document Server

    Sobolev, S L

    1964-01-01

    Partial Differential Equations of Mathematical Physics emphasizes the study of second-order partial differential equations of mathematical physics, which is deemed as the foundation of investigations into waves, heat conduction, hydrodynamics, and other physical problems. The book discusses in detail a wide spectrum of topics related to partial differential equations, such as the theories of sets and of Lebesgue integration, integral equations, Green's function, and the proof of the Fourier method. Theoretical physicists, experimental physicists, mathematicians engaged in pure and applied math

  20. Reduced kinetic equations: An influence functional approach

    International Nuclear Information System (INIS)

    Wio, H.S.

    1985-01-01

    The author discusses a scheme for obtaining reduced descriptions of multivariate kinetic equations based on the 'influence functional' method of Feynmann. It is applied to the case of Fokker-Planck equations showing the form that results for the reduced equation. The possibility of Markovian or non-Markovian reduced description is discussed. As a particular example, the reduction of the Kramers equation to the Smoluchwski equation in the limit of high friction is also discussed

  1. An inverse problem in a parabolic equation

    Directory of Open Access Journals (Sweden)

    Zhilin Li

    1998-11-01

    Full Text Available In this paper, an inverse problem in a parabolic equation is studied. An unknown function in the equation is related to two integral equations in terms of heat kernel. One of the integral equations is well-posed while another is ill-posed. A regularization approach for constructing an approximate solution to the ill-posed integral equation is proposed. Theoretical analysis and numerical experiment are provided to support the method.

  2. On the fundamental equation of nonequilibrium statistical physics—Nonequilibrium entropy evolution equation and the formula for entropy production rate

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    In this paper the author presents an overview on his own research works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type’s Langevin equation in 6N dimensional phase space or its equivalent Liouville diffusion equation. This equation is time-reversed asymmetrical. It shows that the form of motion of particles in statistical thermodynamic systems has the drift-diffusion duality, and the law of motion of statistical thermodynamics is expressed by a superposition of both the law of dynamics and the stochastic velocity and possesses both determinism and probability. Hence it is different from the law of motion of particles in dynamical systems. The stochastic diffusion motion of the particles is the microscopic origin of macroscopic irreversibility. Starting from this fundamental equation the BBGKY diffusion equation hierarchy, the Boltzmann collision diffusion equation, the hydrodynamic equations such as the mass drift-diffusion equation, the Navier-Stokes equation and the thermal conductivity equation have been derived and presented here. What is more important, we first constructed a nonlinear evolution equation of nonequilibrium entropy density in 6N, 6 and 3 dimensional phase space, predicted the existence of entropy diffusion. This entropy evolution equation plays a leading role in nonequilibrium entropy theory, it reveals that the time rate of change of nonequilibrium entropy density originates together from its drift, diffusion and production in space. From this evolution equation, we presented a formula for entropy production rate (i.e. the law of entropy increase) in 6N and 6 dimensional phase space, proved that internal attractive force in nonequilibrium system can result in entropy decrease while internal repulsive force leads to another entropy increase, and derived a common expression for this entropy decrease rate or

  3. Completely integrable operator evolution equations. II

    International Nuclear Information System (INIS)

    Chudnovsky, D.V.

    1979-01-01

    The author continues the investigation of operator classical completely integrable systems. The main attention is devoted to the stationary operator non-linear Schroedinger equation. It is shown that this equation can be used for separation of variables for a large class of completely integrable equations. (Auth.)

  4. Alternative equations of gravitation

    International Nuclear Information System (INIS)

    Pinto Neto, N.

    1983-01-01

    It is shown, trough a new formalism, that the quantum fluctuation effects of the gravitational field in Einstein's equations are analogs to the effects of a continuum medium in Maxwell's Electrodynamics. Following, a real example of the applications of these equations is studied. Qunatum fluctuations effects as perturbation sources in Minkowski and Friedmann Universes are examined. (L.C.) [pt

  5. Semigroup methods for evolution equations on networks

    CERN Document Server

    Mugnolo, Delio

    2014-01-01

    This concise text is based on a series of lectures held only a few years ago and originally intended as an introduction to known results on linear hyperbolic and parabolic equations.  Yet the topic of differential equations on graphs, ramified spaces, and more general network-like objects has recently gained significant momentum and, well beyond the confines of mathematics, there is a lively interdisciplinary discourse on all aspects of so-called complex networks. Such network-like structures can be found in virtually all branches of science, engineering and the humanities, and future research thus calls for solid theoretical foundations.      This book is specifically devoted to the study of evolution equations – i.e., of time-dependent differential equations such as the heat equation, the wave equation, or the Schrödinger equation (quantum graphs) – bearing in mind that the majority of the literature in the last ten years on the subject of differential equations of graphs has been devoted to ellip...

  6. Extreme compression behaviour of equations of state

    International Nuclear Information System (INIS)

    Shanker, J.; Dulari, P.; Singh, P.K.

    2009-01-01

    The extreme compression (P→∞) behaviour of various equations of state with K' ∞ >0 yields (P/K) ∞ =1/K' ∞ , an algebraic identity found by Stacey. Here P is the pressure, K the bulk modulus, K ' =dK/dP, and K' ∞ , the value of K ' at P→∞. We use this result to demonstrate further that there exists an algebraic identity also between the higher pressure derivatives of bulk modulus which is satisfied at extreme compression by different types of equations of state such as the Birch-Murnaghan equation, Poirier-Tarantola logarithmic equation, generalized Rydberg equation, Keane's equation and the Stacey reciprocal K-primed equation. The identity has been used to find a relationship between λ ∞ , the third-order Grueneisen parameter at P→∞, and pressure derivatives of bulk modulus with the help of the free-volume formulation without assuming any specific form of equation of state.

  7. Perturbation theory for continuous stochastic equations

    International Nuclear Information System (INIS)

    Chechetkin, V.R.; Lutovinov, V.S.

    1987-01-01

    The various general perturbational schemes for continuous stochastic equations are considered. These schemes have many analogous features with the iterational solution of Schwinger equation for S-matrix. The following problems are discussed: continuous stochastic evolution equations for probability distribution functionals, evolution equations for equal time correlators, perturbation theory for Gaussian and Poissonian additive noise, perturbation theory for birth and death processes, stochastic properties of systems with multiplicative noise. The general results are illustrated by diffusion-controlled reactions, fluctuations in closed systems with chemical processes, propagation of waves in random media in parabolic equation approximation, and non-equilibrium phase transitions in systems with Poissonian breeding centers. The rate of irreversible reaction X + X → A (Smoluchowski process) is calculated with the use of general theory based on continuous stochastic equations for birth and death processes. The threshold criterion and range of fluctuational region for synergetic phase transition in system with Poissonian breeding centers are also considered. (author)

  8. The improved fractional sub-equation method and its applications to the space–time fractional differential equations in fluid mechanics

    International Nuclear Information System (INIS)

    Guo, Shimin; Mei, Liquan; Li, Ying; Sun, Youfa

    2012-01-01

    By introducing a new general ansätz, the improved fractional sub-equation method is proposed to construct analytical solutions of nonlinear evolution equations involving Jumarie's modified Riemann–Liouville derivative. By means of this method, the space–time fractional Whitham–Broer–Kaup and generalized Hirota–Satsuma coupled KdV equations are successfully solved. The obtained results show that the proposed method is quite effective, promising and convenient for solving nonlinear fractional differential equations. -- Highlights: ► We propose a novel method for nonlinear fractional differential equations. ► Two important fractional differential equations in fluid mechanics are solved successfully. ► Some new exact solutions of the fractional differential equations are obtained. ► These solutions will advance the understanding of nonlinear physical phenomena.

  9. Developments in functional equations and related topics

    CERN Document Server

    Ciepliński, Krzysztof; Rassias, Themistocles

    2017-01-01

    This book presents current research on Ulam stability for functional equations and inequalities. Contributions from renowned scientists emphasize fundamental and new results, methods and techniques. Detailed examples are given to theories to further understanding at the graduate level for students in mathematics, physics, and engineering. Key topics covered in this book include: Quasi means Approximate isometries Functional equations in hypergroups Stability of functional equations Fischer-Muszély equation Haar meager sets and Haar null sets Dynamical systems Functional equations in probability theory Stochastic convex ordering Dhombres functional equation Nonstandard analysis and Ulam stability This book is dedicated in memory of Staniłsaw Marcin Ulam, who posed the fundamental problem concerning approximate homomorphisms of groups in 1940; which has provided the stimulus for studies in the stability of functional equations and inequalities.

  10. Transport equation solving methods

    International Nuclear Information System (INIS)

    Granjean, P.M.

    1984-06-01

    This work is mainly devoted to Csub(N) and Fsub(N) methods. CN method: starting from a lemma stated by Placzek, an equivalence is established between two problems: the first one is defined in a finite medium bounded by a surface S, the second one is defined in the whole space. In the first problem the angular flux on the surface S is shown to be the solution of an integral equation. This equation is solved by Galerkin's method. The Csub(N) method is applied here to one-velocity problems: in plane geometry, slab albedo and transmission with Rayleigh scattering, calculation of the extrapolation length; in cylindrical geometry, albedo and extrapolation length calculation with linear scattering. Fsub(N) method: the basic integral transport equation of the Csub(N) method is integrated on Case's elementary distributions; another integral transport equation is obtained: this equation is solved by a collocation method. The plane problems solved by the Csub(N) method are also solved by the Fsub(N) method. The Fsub(N) method is extended to any polynomial scattering law. Some simple spherical problems are also studied. Chandrasekhar's method, collision probability method, Case's method are presented for comparison with Csub(N) and Fsub(N) methods. This comparison shows the respective advantages of the two methods: a) fast convergence and possible extension to various geometries for Csub(N) method; b) easy calculations and easy extension to polynomial scattering for Fsub(N) method [fr

  11. Statistical Methods for Stochastic Differential Equations

    CERN Document Server

    Kessler, Mathieu; Sorensen, Michael

    2012-01-01

    The seventh volume in the SemStat series, Statistical Methods for Stochastic Differential Equations presents current research trends and recent developments in statistical methods for stochastic differential equations. Written to be accessible to both new students and seasoned researchers, each self-contained chapter starts with introductions to the topic at hand and builds gradually towards discussing recent research. The book covers Wiener-driven equations as well as stochastic differential equations with jumps, including continuous-time ARMA processes and COGARCH processes. It presents a sp

  12. Kinetic Boltzmann, Vlasov and Related Equations

    CERN Document Server

    Sinitsyn, Alexander; Vedenyapin, Victor

    2011-01-01

    Boltzmann and Vlasov equations played a great role in the past and still play an important role in modern natural sciences, technique and even philosophy of science. Classical Boltzmann equation derived in 1872 became a cornerstone for the molecular-kinetic theory, the second law of thermodynamics (increasing entropy) and derivation of the basic hydrodynamic equations. After modifications, the fields and numbers of its applications have increased to include diluted gas, radiation, neutral particles transportation, atmosphere optics and nuclear reactor modelling. Vlasov equation was obtained in

  13. Multidimensional singular integrals and integral equations

    CERN Document Server

    Mikhlin, Solomon Grigorievich; Stark, M; Ulam, S

    1965-01-01

    Multidimensional Singular Integrals and Integral Equations presents the results of the theory of multidimensional singular integrals and of equations containing such integrals. Emphasis is on singular integrals taken over Euclidean space or in the closed manifold of Liapounov and equations containing such integrals. This volume is comprised of eight chapters and begins with an overview of some theorems on linear equations in Banach spaces, followed by a discussion on the simplest properties of multidimensional singular integrals. Subsequent chapters deal with compounding of singular integrals

  14. Semiclassical regularization of Vlasov equations and wavepackets for nonlinear Schrödinger equations

    Science.gov (United States)

    Athanassoulis, Agissilaos

    2018-03-01

    We consider the semiclassical limit of nonlinear Schrödinger equations with initial data that are well localized in both position and momentum (non-parametric wavepackets). We recover the Wigner measure (WM) of the problem, a macroscopic phase-space density which controls the propagation of the physical observables such as mass, energy and momentum. WMs have been used to create effective models for wave propagation in: random media, quantum molecular dynamics, mean field limits, and the propagation of electrons in graphene. In nonlinear settings, the Vlasov-type equations obtained for the WM are often ill-posed on the physically interesting spaces of initial data. In this paper we are able to select the measure-valued solution of the 1  +  1 dimensional Vlasov-Poisson equation which correctly captures the semiclassical limit, thus finally resolving the non-uniqueness in the seminal result of Zhang et al (2012 Comm. Pure Appl. Math. 55 582-632). The same approach is also applied to the Vlasov-Dirac-Benney equation with small wavepacket initial data, extending several known results.

  15. Introduction to ordinary differential equations

    CERN Document Server

    Rabenstein, Albert L

    1966-01-01

    Introduction to Ordinary Differential Equations is a 12-chapter text that describes useful elementary methods of finding solutions using ordinary differential equations. This book starts with an introduction to the properties and complex variable of linear differential equations. Considerable chapters covered topics that are of particular interest in applications, including Laplace transforms, eigenvalue problems, special functions, Fourier series, and boundary-value problems of mathematical physics. Other chapters are devoted to some topics that are not directly concerned with finding solutio

  16. Functional Fourier transforms and the loop equation

    International Nuclear Information System (INIS)

    Bershadskii, M.A.; Vaisburd, I.D.; Migdal, A.A.

    1986-01-01

    The Migdal-Makeenko momentum-space loop equation is investigated. This equation is derived from the ordinary loop equation by taking the Fourier transform of the Wilson functional. A perturbation theory is constructed for the new equation and it is proved that the action of the loop operator is determined by vertex functions which coincide with those of the previous equation. It is shown how the ghost loop arises in direct iterations of the momentum-space equation with respect to the coupling constant. A simple example is used to illustrate the mechanism of appearance of an integration in the interior loops in transition to observables

  17. dimensional Nizhnik–Novikov–Veselov equations

    Indian Academy of Sciences (India)

    2017-03-22

    Mar 22, 2017 ... order differential equations with modified Riemann–Liouville derivatives into integer-order differential equations, ... tered in a variety of scientific and engineering fields ... devoted to the advanced calculus can be easily applied.

  18. Phase chemistry and microstructure evolution in silver-clad (Bi2-xPbx)Sr2Ca2Cu3Oy filaments

    International Nuclear Information System (INIS)

    Luo, J.S.; Merchant, N.; Maroni, V.A.; Escorcia-Aparicio, E.; Gruen, D.M.; Tani, B.S.; Riley, G.N. Jr.; Carter, W.L.

    1992-08-01

    The reaction kinetics and mechanism that control the conversion of (Bi,Pb) 2 Sr 2 CaCu 2 O z (Bi-2212) + alkaline earth cuporates to (Bi, Pb) 2 Sr 2 Ca 2 Cu 3 O y (Bi-2223) in silver-clad wires were investigated as a function of equilibration temperature and time at a fixed oxygen partial pressure (7.5% O 2 ). Measured values for the fractional conversion of Bi-2223 versus time have been evaluated based on the Avrami equation. SEM and TEM studies of partially and fully converted wires have revealed that (1) the growth of Bi-2223 is two-dimensional and controlled by a diffusion process, (2) liquid phases are present during part of the Bi-2212 -> Bi-2212 conversion, and (3) segregation of the second phases occurs in early time domains of the reaction

  19. Microstructural stability and mechanical properties of a high nitrogen super duplex stainless steel

    Energy Technology Data Exchange (ETDEWEB)

    Nilsson, J.-O. [AB Sandvik Steel, Sandviken (Sweden). Dept. of Phys. Metall.; Kangas, P.; Wilson, A. [AB Sandvik Steel, Sandviken (Sweden). Dept. of Tube Research; Karlsson, T. [Swedish Inst. for Metals Research, Stockholm (Sweden)

    1999-07-01

    A time temperature transformation (TTT)-diagram with respect to the formation of intermetallic phase in the range 700-1000 C has been assessed by point counting for a 29Cr-6Ni-2Mo-0.38N super duplex stainless steel. Using a computer program developed by the authors a continuous cooling transformation (CCT)-diagram was calculated from the TTT-diagram assuming that the transformation can be described by an Avrami type equation. A comparison of impact toughness and hardness showed that toughness was a very sensitive measure of intermetallic phase formation while hardness was insensitive and showed no significant increase until the material was catastrophically brittle. It was found that Thermo-Calc could be used in a qualitative manner for predicting microstructural changes at various temperatures but was unable to predict variables such as dissolution temperature and volume percentage with accuracy. (orig.)

  20. Symmetry properties of fractional diffusion equations

    Energy Technology Data Exchange (ETDEWEB)

    Gazizov, R K; Kasatkin, A A; Lukashchuk, S Yu [Ufa State Aviation Technical University, Karl Marx strausse 12, Ufa (Russian Federation)], E-mail: gazizov@mail.rb.ru, E-mail: alexei_kasatkin@mail.ru, E-mail: lsu@mail.rb.ru

    2009-10-15

    In this paper, nonlinear anomalous diffusion equations with time fractional derivatives (Riemann-Liouville and Caputo) of the order of 0-2 are considered. Lie point symmetries of these equations are investigated and compared. Examples of using the obtained symmetries for constructing exact solutions of the equations under consideration are presented.

  1. The Modified Enskog Equation for Mixtures

    NARCIS (Netherlands)

    Beijeren, H. van; Ernst, M.H.

    1973-01-01

    In a previous paper it was shown that a modified form of the Enskog equation, applied to mixtures of hard spheres, should be considered as the correct extension of the usual Enskog equation to the case of mixtures. The main argument was that the modified Enskog equation leads to linear transport

  2. Some remarks on unilateral matrix equations

    International Nuclear Information System (INIS)

    Cerchiai, Bianca L.; Zumino, Bruno

    2001-01-01

    We briefly review the results of our paper LBNL-46775: We study certain solutions of left-unilateral matrix equations. These are algebraic equations where the coefficients and the unknown are square matrices of the same order, or, more abstractly, elements of an associative, but possibly noncommutative algebra, and all coefficients are on the left. Recently such equations have appeared in a discussion of generalized Born-Infeld theories. In particular, two equations, their perturbative solutions and the relation between them are studied, applying a unified approach based on the generalized Bezout theorem for matrix polynomials

  3. Numerical Methods for Partial Differential Equations

    CERN Document Server

    Guo, Ben-yu

    1987-01-01

    These Proceedings of the first Chinese Conference on Numerical Methods for Partial Differential Equations covers topics such as difference methods, finite element methods, spectral methods, splitting methods, parallel algorithm etc., their theoretical foundation and applications to engineering. Numerical methods both for boundary value problems of elliptic equations and for initial-boundary value problems of evolution equations, such as hyperbolic systems and parabolic equations, are involved. The 16 papers of this volume present recent or new unpublished results and provide a good overview of current research being done in this field in China.

  4. Stochastic porous media equations

    CERN Document Server

    Barbu, Viorel; Röckner, Michael

    2016-01-01

    Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.

  5. The time dependent Schrodinger equation revisited I: quantum field and classical Hamilton-Jacobi routes to Schrodinger's wave equation

    International Nuclear Information System (INIS)

    Scully, M O

    2008-01-01

    The time dependent Schrodinger equation is frequently 'derived' by postulating the energy E → i h-bar (∂/∂t) and momentum p-vector → ( h-bar /i)∇ operator relations. In the present paper we review the quantum field theoretic route to the Schrodinger wave equation which treats time and space as parameters, not operators. Furthermore, we recall that a classical (nonlinear) wave equation can be derived from the classical action via Hamiltonian-Jacobi theory. By requiring the wave equation to be linear we again arrive at the Schrodinger equation, without postulating operator relations. The underlying philosophy is operational: namely 'a particle is what a particle detector detects.' This leads us to a useful physical picture combining the wave (field) and particle paradigms which points the way to the time-dependent Schrodinger equation

  6. Stochastic Differential Equations and Kondratiev Spaces

    Energy Technology Data Exchange (ETDEWEB)

    Vaage, G.

    1995-05-01

    The purpose of this mathematical thesis was to improve the understanding of physical processes such as fluid flow in porous media. An example is oil flowing in a reservoir. In the first of five included papers, Hilbert space methods for elliptic boundary value problems are used to prove the existence and uniqueness of a large family of elliptic differential equations with additive noise without using the Hermite transform. The ideas are then extended to the multidimensional case and used to prove existence and uniqueness of solution of the Stokes equations with additive noise. The second paper uses functional analytic methods for partial differential equations and presents a general framework for proving existence and uniqueness of solutions to stochastic partial differential equations with multiplicative noise, for a large family of noises. The methods are applied to equations of elliptic, parabolic as well as hyperbolic type. The framework presented can be extended to the multidimensional case. The third paper shows how the ideas from the second paper can be extended to study the moving boundary value problem associated with the stochastic pressure equation. The fourth paper discusses a set of stochastic differential equations. The fifth paper studies the relationship between the two families of Kondratiev spaces used in the thesis. 102 refs.

  7. On the evolution of perturbations to solutions of the Kadomtsev-Petviashvilli equation using the Benney-Luke equation

    International Nuclear Information System (INIS)

    Ablowitz, Mark J; Curtis, Christopher W

    2011-01-01

    The Benney-Luke equation, which arises as a long wave asymptotic approximation of water waves, contains the Kadomtsev-Petviashvilli (KP) equation as a leading-order maximal balanced approximation. The question analyzed is how the Benney-Luke equation modifies the so-called web solutions of the KP equation. It is found that the Benney-Luke equation introduces dispersive radiation which breaks each of the symmetric soliton-like humps well away from the interaction region of the KP web solution into a tail of multi-peaked oscillating profiles behind the main solitary hump. Computation indicates that the wave structure is modified near the center of the interaction region. Both analytical and numerical techniques are employed for working with non-periodic, non-decaying solutions on unbounded domains.

  8. On the evolution of perturbations to solutions of the Kadomtsev-Petviashvilli equation using the Benney-Luke equation

    Science.gov (United States)

    Ablowitz, Mark J.; Curtis, Christopher W.

    2011-05-01

    The Benney-Luke equation, which arises as a long wave asymptotic approximation of water waves, contains the Kadomtsev-Petviashvilli (KP) equation as a leading-order maximal balanced approximation. The question analyzed is how the Benney-Luke equation modifies the so-called web solutions of the KP equation. It is found that the Benney-Luke equation introduces dispersive radiation which breaks each of the symmetric soliton-like humps well away from the interaction region of the KP web solution into a tail of multi-peaked oscillating profiles behind the main solitary hump. Computation indicates that the wave structure is modified near the center of the interaction region. Both analytical and numerical techniques are employed for working with non-periodic, non-decaying solutions on unbounded domains.

  9. Equations of motion in phase space

    International Nuclear Information System (INIS)

    Broucke, R.

    1979-01-01

    The article gives a general review of methods of constructing equations of motion of a classical dynamical system. The emphasis is however on the linear Lagrangian in phase space and the corresponding form of Pfaff's equations of motion. A detailed examination of the problem of changes of variables in phase space is first given. It is shown that the Linear Lagrangian theory falls very naturally out of the classical quadratic Lagrangian theory; we do this with the use of the well-known Lagrange multiplier method. Another important result is obtained very naturally as a by-product of this analysis. If the most general set of 2n variables (coordinates in phase space) is used, the coefficients of the equations of motion are the Poisson Brackets of these variables. This is therefore the natural way of introducing not only Poisson Brackets in Dynamics formulations but also the associated Lie Algebras and their important properties and consequences. We give then several examples to illustrate the first-order equations of motion and their simplicity in relation to general changes of variables. The first few examples are elementary (the harmonic Oscillator) while the last one concerns the motion of a rigid body about a fixed point. In the next three sections we treat the first-order equations of motion as derived from a Linear differential form, sometimes called Birkhoff's equations. We insist on the generality of the equations and especially on the unity of the space-time concept: the time t and the coordinates are here completely identical variables, without any privilege to t. We give a brief review of Cartan's 2-form and the corresponding equations of motion. As an illustration the standard equations of aircraft flight in a vertical plane are derived from Cartan's exterior differential 2-form. Finally we mention in the last section the differential forms that were proposed by Gallissot for the derivation of equations of motion

  10. Asymptotic problems for stochastic partial differential equations

    Science.gov (United States)

    Salins, Michael

    Stochastic partial differential equations (SPDEs) can be used to model systems in a wide variety of fields including physics, chemistry, and engineering. The main SPDEs of interest in this dissertation are the semilinear stochastic wave equations which model the movement of a material with constant mass density that is exposed to both determinstic and random forcing. Cerrai and Freidlin have shown that on fixed time intervals, as the mass density of the material approaches zero, the solutions of the stochastic wave equation converge uniformly to the solutions of a stochastic heat equation, in probability. This is called the Smoluchowski-Kramers approximation. In Chapter 2, we investigate some of the multi-scale behaviors that these wave equations exhibit. In particular, we show that the Freidlin-Wentzell exit place and exit time asymptotics for the stochastic wave equation in the small noise regime can be approximated by the exit place and exit time asymptotics for the stochastic heat equation. We prove that the exit time and exit place asymptotics are characterized by quantities called quasipotentials and we prove that the quasipotentials converge. We then investigate the special case where the equation has a gradient structure and show that we can explicitly solve for the quasipotentials, and that the quasipotentials for the heat equation and wave equation are equal. In Chapter 3, we study the Smoluchowski-Kramers approximation in the case where the material is electrically charged and exposed to a magnetic field. Interestingly, if the system is frictionless, then the Smoluchowski-Kramers approximation does not hold. We prove that the Smoluchowski-Kramers approximation is valid for systems exposed to both a magnetic field and friction. Notably, we prove that the solutions to the second-order equations converge to the solutions of the first-order equation in an Lp sense. This strengthens previous results where convergence was proved in probability.

  11. Scattering integral equations and four nucleon problem

    International Nuclear Information System (INIS)

    Narodetskii, I.M.

    1980-01-01

    Existing results from the application of integral equation technique to the four-nucleon bound states and scattering are reviewed. The first numerical calculations of the four-body integral equations have been done ten years ago. Yet, it is still widely believed that these equations are too complicated to solve numerically. The purpose of this review is to provide a clear and elementary introduction in the integral equation method and to demonstrate its usefulness in physical applications. The presentation is based on the quasiparticle approach. This permits a simple interpretation of the equations in terms of quasiparticle scattering. The mathematical basis for the quasiparticle approach is the Hilbert-Schmidt method of the Fredholm integral equation theory. The first part of this review contains a detailed discussion of the Hilbert-Schmidt expansion as applied to the 2-particle amplitudes and to the kernel of the four-body equations. The second part contains the discussion of the four-body quasiparticle equations and of the resed forullts obtain bound states and scattering

  12. Entropy viscosity method applied to Euler equations

    International Nuclear Information System (INIS)

    Delchini, M. O.; Ragusa, J. C.; Berry, R. A.

    2013-01-01

    The entropy viscosity method [4] has been successfully applied to hyperbolic systems of equations such as Burgers equation and Euler equations. The method consists in adding dissipative terms to the governing equations, where a viscosity coefficient modulates the amount of dissipation. The entropy viscosity method has been applied to the 1-D Euler equations with variable area using a continuous finite element discretization in the MOOSE framework and our results show that it has the ability to efficiently smooth out oscillations and accurately resolve shocks. Two equations of state are considered: Ideal Gas and Stiffened Gas Equations Of State. Results are provided for a second-order time implicit schemes (BDF2). Some typical Riemann problems are run with the entropy viscosity method to demonstrate some of its features. Then, a 1-D convergent-divergent nozzle is considered with open boundary conditions. The correct steady-state is reached for the liquid and gas phases with a time implicit scheme. The entropy viscosity method correctly behaves in every problem run. For each test problem, results are shown for both equations of state considered here. (authors)

  13. Computing with linear equations and matrices

    International Nuclear Information System (INIS)

    Churchhouse, R.F.

    1983-01-01

    Systems of linear equations and matrices arise in many disciplines. The equations may accurately represent conditions satisfied by a system or, more likely, provide an approximation to a more complex system of non-linear or differential equations. The system may involve a few or many thousand unknowns and each individual equation may involve few or many of them. Over the past 50 years a vast literature on methods for solving systems of linear equations and the associated problems of finding the inverse or eigenvalues of a matrix has been produced. These lectures cover those methods which have been found to be most useful for dealing with such types of problem. References are given where appropriate and attention is drawn to the possibility of improved methods for use on vector and parallel processors. (orig.)

  14. Integrable peakon equations with cubic nonlinearity

    International Nuclear Information System (INIS)

    Hone, Andrew N W; Wang, J P

    2008-01-01

    We present a new integrable partial differential equation found by Vladimir Novikov. Like the Camassa-Holm and Degasperis-Procesi equations, this new equation admits peaked soliton (peakon) solutions, but it has nonlinear terms that are cubic, rather than quadratic. We give a matrix Lax pair for V Novikov's equation, and show how it is related by a reciprocal transformation to a negative flow in the Sawada-Kotera hierarchy. Infinitely many conserved quantities are found, as well as a bi-Hamiltonian structure. The latter is used to obtain the Hamiltonian form of the finite-dimensional system for the interaction of N peakons, and the two-body dynamics (N = 2) is explicitly integrated. Finally, all of this is compared with some analogous results for another cubic peakon equation derived by Zhijun Qiao. (fast track communication)

  15. Advanced functional evolution equations and inclusions

    CERN Document Server

    Benchohra, Mouffak

    2015-01-01

    This book presents up-to-date results on abstract evolution equations and differential inclusions in infinite dimensional spaces. It covers equations with time delay and with impulses, and complements the existing literature in functional differential equations and inclusions. The exposition is devoted to both local and global mild solutions for some classes of functional differential evolution equations and inclusions, and other densely and non-densely defined functional differential equations and inclusions in separable Banach spaces or in Fréchet spaces. The tools used include classical fixed points theorems and the measure-of non-compactness, and each chapter concludes with a section devoted to notes and bibliographical remarks. This monograph is particularly useful for researchers and graduate students studying pure and applied mathematics, engineering, biology and all other applied sciences.

  16. State-dependent neutral delay equations from population dynamics.

    Science.gov (United States)

    Barbarossa, M V; Hadeler, K P; Kuttler, C

    2014-10-01

    A novel class of state-dependent delay equations is derived from the balance laws of age-structured population dynamics, assuming that birth rates and death rates, as functions of age, are piece-wise constant and that the length of the juvenile phase depends on the total adult population size. The resulting class of equations includes also neutral delay equations. All these equations are very different from the standard delay equations with state-dependent delay since the balance laws require non-linear correction factors. These equations can be written as systems for two variables consisting of an ordinary differential equation (ODE) and a generalized shift, a form suitable for numerical calculations. It is shown that the neutral equation (and the corresponding ODE--shift system) is a limiting case of a system of two standard delay equations.

  17. Derivation of the neutron diffusion equation

    International Nuclear Information System (INIS)

    Mika, J.R.; Banasiak, J.

    1994-01-01

    We discuss the diffusion equation as an asymptotic limit of the neutron transport equation for large scattering cross sections. We show that the classical asymptotic expansion procedure does not lead to the diffusion equation and present two modified approaches to overcome this difficulty. The effect of the initial layer is also discussed. (authors). 9 refs

  18. Wave-equation dispersion inversion

    KAUST Repository

    Li, Jing

    2016-12-08

    We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained from Rayleigh waves recorded by vertical-component geophones. Similar to wave-equation traveltime tomography, the complicated surface wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the phase-velocity and frequency domains. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2-D or 3-D S-wave velocity models. This procedure, denoted as wave-equation dispersion inversion (WD), does not require the assumption of a layered model and is significantly less prone to the cycle-skipping problems of full waveform inversion. The synthetic and field data examples demonstrate that WD can approximately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic data and the inversion of dispersion curves associated with Love waves.

  19. Dichotomies for generalized ordinary differential equations and applications

    Science.gov (United States)

    Bonotto, E. M.; Federson, M.; Santos, F. L.

    2018-03-01

    In this work we establish the theory of dichotomies for generalized ordinary differential equations, introducing the concepts of dichotomies for these equations, investigating their properties and proposing new results. We establish conditions for the existence of exponential dichotomies and bounded solutions. Using the correspondences between generalized ordinary differential equations and other equations, we translate our results to measure differential equations and impulsive differential equations. The fact that we work in the framework of generalized ordinary differential equations allows us to manage functions with many discontinuities and of unbounded variation.

  20. Formal truncations of connected kernel equations

    International Nuclear Information System (INIS)

    Dixon, R.M.

    1977-01-01

    The Connected Kernel Equations (CKE) of Alt, Grassberger and Sandhas (AGS); Kouri, Levin and Tobocman (KLT); and Bencze, Redish and Sloan (BRS) are compared against reaction theory criteria after formal channel space and/or operator truncations have been introduced. The Channel Coupling Class concept is used to study the structure of these CKE's. The related wave function formalism of Sandhas, of L'Huillier, Redish and Tandy and of Kouri, Krueger and Levin are also presented. New N-body connected kernel equations which are generalizations of the Lovelace three-body equations are derived. A method for systematically constructing fewer body models from the N-body BRS and generalized Lovelace (GL) equations is developed. The formally truncated AGS, BRS, KLT and GL equations are analyzed by employing the criteria of reciprocity and two-cluster unitarity. Reciprocity considerations suggest that formal truncations of BRS, KLT and GL equations can lead to reciprocity-violating results. This study suggests that atomic problems should employ three-cluster connected truncations and that the two-cluster connected truncations should be a useful starting point for nuclear systems

  1. Systematic tools for chemical equation balancing

    International Nuclear Information System (INIS)

    Filby, E.E.; Idaho National Engineering Lab., Idaho Falls, ID; Idaho Univ., Idaho Falls, ID

    1989-01-01

    One of the most important skills that chemists and chemical engineers must develop is the ability to balance chemical equations. The normal first method taught is ''balancing by inspection'', which is sometimes explained as simply ''mental algebra.'' Every textbook surveyed for this paper presents equation balancing first as a matter of trial and error; this includes four very recently published books. Very little further guidance is provided until oxidation-reduction reactions must be balanced. The most commonly taught approaches for balancing, redox equations have been the oxidation state change and ion-electron methods. Unfortunately, redox reactions are usually treated as a new topic, and what the student has teamed about ''ordinary'' equations is of little or no help. All too often, these contradictions simply confuse and frustrate students, and equation balancing is relegated to the status of a black art. This is ironic because such,confusion and frustration is not necessary: Chemical equations can, in fact, be balanced by explicitly definable mathematical methods. The purpose of this paper is to outline the algebraic methods involved

  2. Fast sweeping method for the factored eikonal equation

    Science.gov (United States)

    Fomel, Sergey; Luo, Songting; Zhao, Hongkai

    2009-09-01

    We develop a fast sweeping method for the factored eikonal equation. By decomposing the solution of a general eikonal equation as the product of two factors: the first factor is the solution to a simple eikonal equation (such as distance) or a previously computed solution to an approximate eikonal equation. The second factor is a necessary modification/correction. Appropriate discretization and a fast sweeping strategy are designed for the equation of the correction part. The key idea is to enforce the causality of the original eikonal equation during the Gauss-Seidel iterations. Using extensive numerical examples we demonstrate that (1) the convergence behavior of the fast sweeping method for the factored eikonal equation is the same as for the original eikonal equation, i.e., the number of iterations for the Gauss-Seidel iterations is independent of the mesh size, (2) the numerical solution from the factored eikonal equation is more accurate than the numerical solution directly computed from the original eikonal equation, especially for point sources.

  3. Maxwell's equations, quantum physics and the quantum graviton

    International Nuclear Information System (INIS)

    Gersten, Alexander; Moalem, Amnon

    2011-01-01

    Quantum wave equations for massless particles and arbitrary spin are derived by factorizing the d'Alembertian operator. The procedure is extensively applied to the spin one photon equation which is related to Maxwell's equations via the proportionality of the photon wavefunction Ψ to the sum E + iB of the electric and magnetic fields. Thus Maxwell's equations can be considered as the first quantized one-photon equation. The photon wave equation is written in two forms, one with additional explicit subsidiary conditions and second with the subsidiary conditions implicitly included in the main equation. The second equation was obtained by factorizing the d'Alembertian with 4×4 matrix representation of 'relativistic quaternions'. Furthermore, scalar Lagrangian formalism, consistent with quantization requirements is developed using derived conserved current of probability and normalization condition for the wavefunction. Lessons learned from the derivation of the photon equation are used in the derivation of the spin two quantum equation, which we call the quantum graviton. Quantum wave equation with implicit subsidiary conditions, which factorizes the d'Alembertian with 8×8 matrix representation of relativistic quaternions, is derived. Scalar Lagrangian is formulated and conserved probability current and wavefunction normalization are found, both consistent with the definitions of quantum operators and their expectation values. We are showing that the derived equations are the first quantized equations of the photon and the graviton.

  4. On the reduction of the multidimensional stationary Schroedinger equation to a first-order equation and its relation to the pseudoanalytic function theory

    Energy Technology Data Exchange (ETDEWEB)

    Kravchenko, Vladislav V [Departmento de Telecomunicaciones, SEPI, Escuela Superior de IngenierIa Mecanica y Electrica, Instituto Politecnico Nacional, CP 07738 Mexico DF (Mexico)

    2005-01-28

    Given a particular solution of a one-dimensional stationary Schroedinger equation this equation of second order can be reduced to a first-order linear ordinary differential equation. This is done with the aid of an auxiliary Riccati differential equation. In the present work we show that the same fact is true in a multidimensional situation also. For simplicity we consider the case of two or three independent variables. One particular solution of the stationary Schroedinger equation allows us to reduce this second-order equation to a linear first-order quaternionic differential equation. As in the one-dimensional case this is done with the aid of an auxiliary quaternionic Riccati equation. The resulting first-order quaternionic equation is equivalent to the static Maxwell system and is closely related to the Dirac equation. In the case of two independent variables it is the well-known Vekua equation from theory of pseudoanalytic (or generalized analytic) functions. Nevertheless, we show that even in this case it is very useful to consider not only complex valued functions, solutions of the Vekua equation, but complete quaternionic functions. In this way the first-order quaternionic equation represents two separate Vekua equations, one of which gives us solutions of the Schroedinger equation and the other one can be considered as an auxiliary equation of a simpler structure. Moreover for the auxiliary equation we always have the corresponding Bers generating pair (F, G), the base of the Bers theory of pseudoanalytic functions, and what is very important, the Bers derivatives of solutions of the auxiliary equation give us solutions of the main Vekua equation and as a consequence of the Schroedinger equation. Based on this fact we obtain an analogue of the Cauchy integral theorem for solutions of the stationary Schroedinger equation. Other results from theory of pseudoanalytic functions can be written for solutions of the Schroedinger equation. Moreover, for an ample

  5. Drift-free kinetic equations for turbulent dispersion

    Science.gov (United States)

    Bragg, A.; Swailes, D. C.; Skartlien, R.

    2012-11-01

    The dispersion of passive scalars and inertial particles in a turbulent flow can be described in terms of probability density functions (PDFs) defining the statistical distribution of relevant scalar or particle variables. The construction of transport equations governing the evolution of such PDFs has been the subject of numerous studies, and various authors have presented formulations for this type of equation, usually referred to as a kinetic equation. In the literature it is often stated, and widely assumed, that these PDF kinetic equation formulations are equivalent. In this paper it is shown that this is not the case, and the significance of differences among the various forms is considered. In particular, consideration is given to which form of equation is most appropriate for modeling dispersion in inhomogeneous turbulence and most consistent with the underlying particle equation of motion. In this regard the PDF equations for inertial particles are considered in the limit of zero particle Stokes number and assessed against the fully mixed (zero-drift) condition for fluid points. A long-standing question regarding the validity of kinetic equations in the fluid-point limit is answered; it is demonstrated formally that one version of the kinetic equation (derived using the Furutsu-Novikov method) provides a model that satisfies this zero-drift condition exactly in both homogeneous and inhomogeneous systems. In contrast, other forms of the kinetic equation do not satisfy this limit or apply only in a limited regime.

  6. Coupled Higgs field equation and Hamiltonian amplitude equation ...

    Indian Academy of Sciences (India)

    Home; Journals; Pramana – Journal of Physics; Volume 79; Issue 1. Coupled Higgs field equation and ... School of Mathematics and Computer Applications, Thapar University, Patiala 147 004, India; Department of Mathematics, Jaypee University of Information Technology, Waknaghat, Distt. Solan 173 234, India ...

  7. Coupled Higgs field equation and Hamiltonian amplitude equation ...

    Indian Academy of Sciences (India)

    the rational functions are obtained. Keywords. ... differential equations as is evident by the number of research papers, books and a new symbolic software .... Now using (2.11), (2.14) in (2.8) with C1 = 0 and integrating once we get. P. 2 = − β.

  8. Equational theories of tropical sernirings

    DEFF Research Database (Denmark)

    Aceto, Luca; Esik, Zoltan; Ingolfsdottir, Anna

    2003-01-01

    examples of such structures are the (max,+) semiring and the tropical semiring. It is shown that none of the exotic semirings commonly considered in the literature has a finite basis for its equations, and that similar results hold for the commutative idempotent weak semirings that underlie them. For each......This paper studies the equational theories of various exotic semirings presented in the literature. Exotic semirings are semirings whose underlying carrier set is some subset of the set of real numbers equipped with binary operations of minimum or maximum as sum, and addition as product. Two prime...... of these commutative idempotent weak semirings, the paper offers characterizations of the equations that hold in them, decidability results for their equational theories, explicit descriptions of the free algebras in the varieties they generate, and relative axiomatization results. Udgivelsesdato: APR 11...

  9. A generalized Zakharov-Shabat equation with finite-band solutions and a soliton-equation hierarchy with an arbitrary parameter

    International Nuclear Information System (INIS)

    Zhang Yufeng; Tam, Honwah; Feng Binlu

    2011-01-01

    Highlights: → A generalized Zakharov-Shabat equation is obtained. → The generalized AKNS vector fields are established. → The finite-band solution of the g-ZS equation is obtained. → By using a Lie algebra presented in the paper, a new soliton hierarchy with an arbitrary parameter is worked out. - Abstract: In this paper, a generalized Zakharov-Shabat equation (g-ZS equation), which is an isospectral problem, is introduced by using a loop algebra G ∼ . From the stationary zero curvature equation we define the Lenard gradients {g j } and the corresponding generalized AKNS (g-AKNS) vector fields {X j } and X k flows. Employing the nonlinearization method, we obtain the generalized Zhakharov-Shabat Bargmann (g-ZS-B) system and prove that it is Liouville integrable by introducing elliptic coordinates and evolution equations. The explicit relations of the X k flows and the polynomial integrals {H k } are established. Finally, we obtain the finite-band solutions of the g-ZS equation via the Abel-Jacobian coordinates. In addition, a soliton hierarchy and its Hamiltonian structure with an arbitrary parameter k are derived.

  10. A new extended elliptic equation rational expansion method and its application to (2 + 1)-dimensional Burgers equation

    International Nuclear Information System (INIS)

    Wang Baodong; Song Lina; Zhang Hongqing

    2007-01-01

    In this paper, we present a new elliptic equation rational expansion method to uniformly construct a series of exact solutions for nonlinear partial differential equations. As an application of the method, we choose the (2 + 1)-dimensional Burgers equation to illustrate the method and successfully obtain some new and more general solutions

  11. More Issues in Observed-Score Equating

    Science.gov (United States)

    van der Linden, Wim J.

    2013-01-01

    This article is a response to the commentaries on the position paper on observed-score equating by van der Linden (this issue). The response focuses on the more general issues in these commentaries, such as the nature of the observed scores that are equated, the importance of test-theory assumptions in equating, the necessity to use multiple…

  12. Approximate solutions to Mathieu's equation

    Science.gov (United States)

    Wilkinson, Samuel A.; Vogt, Nicolas; Golubev, Dmitry S.; Cole, Jared H.

    2018-06-01

    Mathieu's equation has many applications throughout theoretical physics. It is especially important to the theory of Josephson junctions, where it is equivalent to Schrödinger's equation. Mathieu's equation can be easily solved numerically, however there exists no closed-form analytic solution. Here we collect various approximations which appear throughout the physics and mathematics literature and examine their accuracy and regimes of applicability. Particular attention is paid to quantities relevant to the physics of Josephson junctions, but the arguments and notation are kept general so as to be of use to the broader physics community.

  13. Galois theory of difference equations

    CERN Document Server

    Put, Marius

    1997-01-01

    This book lays the algebraic foundations of a Galois theory of linear difference equations and shows its relationship to the analytic problem of finding meromorphic functions asymptotic to formal solutions of difference equations. Classically, this latter question was attacked by Birkhoff and Tritzinsky and the present work corrects and greatly generalizes their contributions. In addition results are presented concerning the inverse problem in Galois theory, effective computation of Galois groups, algebraic properties of sequences, phenomena in positive characteristics, and q-difference equations. The book is aimed at advanced graduate researchers and researchers.

  14. Integral equation methods for electromagnetics

    CERN Document Server

    Volakis, John

    2012-01-01

    This text/reference is a detailed look at the development and use of integral equation methods for electromagnetic analysis, specifically for antennas and radar scattering. Developers and practitioners will appreciate the broad-based approach to understanding and utilizing integral equation methods and the unique coverage of historical developments that led to the current state-of-the-art. In contrast to existing books, Integral Equation Methods for Electromagnetics lays the groundwork in the initial chapters so students and basic users can solve simple problems and work their way up to the mo

  15. An integral transform of the Salpeter equation

    International Nuclear Information System (INIS)

    Krolikowski, W.

    1980-03-01

    We find a new form of relativistic wave equation for two spin-1/2 particles, which arises by an integral transformation (in the position space) of the wave function in the Salpeter equation. The non-locality involved in this transformation is extended practically over the Compton wavelength of the lighter of two particles. In the case of equal masses the new equation assumes the form of the Breit equation with an effective integral interaction. In the one-body limit it reduces to the Dirac equation also with an effective integral interaction. (author)

  16. Brownian motion of spins; generalized spin Langevin equation

    International Nuclear Information System (INIS)

    Jayannavar, A.M.

    1990-03-01

    We derive the Langevin equations for a spin interacting with a heat bath, starting from a fully dynamical treatment. The obtained equations are non-Markovian with multiplicative fluctuations and concomitant dissipative terms obeying the fluctuation-dissipation theorem. In the Markovian limit our equations reduce to the phenomenological equations proposed by Kubo and Hashitsume. The perturbative treatment on our equations lead to Landau-Lifshitz equations and to other known results in the literature. (author). 16 refs

  17. Attractors for equations of mathematical physics

    CERN Document Server

    Chepyzhov, Vladimir V

    2001-01-01

    One of the major problems in the study of evolution equations of mathematical physics is the investigation of the behavior of the solutions to these equations when time is large or tends to infinity. The related important questions concern the stability of solutions or the character of the instability if a solution is unstable. In the last few decades, considerable progress in this area has been achieved in the study of autonomous evolution partial differential equations. For a number of basic evolution equations of mathematical physics, it was shown that the long time behavior of their soluti

  18. About the solvability of matrix polynomial equations

    OpenAIRE

    Netzer, Tim; Thom, Andreas

    2016-01-01

    We study self-adjoint matrix polynomial equations in a single variable and prove existence of self-adjoint solutions under some assumptions on the leading form. Our main result is that any self-adjoint matrix polynomial equation of odd degree with non-degenerate leading form can be solved in self-adjoint matrices. We also study equations of even degree and equations in many variables.

  19. Invariant imbedding equations for linear scattering problems

    International Nuclear Information System (INIS)

    Apresyan, L.

    1988-01-01

    A general form of the invariant imbedding equations is investigated for the linear problem of scattering by a bounded scattering volume. The conditions for the derivability of such equations are described. It is noted that the possibility of the explicit representation of these equations for a sphere and for a layer involves the separation of variables in the unperturbed wave equation

  20. Monge-Ampere equations and characteristic connection functors

    International Nuclear Information System (INIS)

    Tunitskii, D V

    2001-01-01

    We investigate contact equivalence of Monge-Ampere equations. We define a category of Monge-Ampere equations and introduce the notion of a characteristic connection functor. This functor maps the category of Monge-Ampere equations to the category of affine connections. We give a constructive description of the characteristic connection functors corresponding to three subcategories, which include a large class of Monge-Ampere equations of elliptic and hyperbolic type. This essentially reduces the contact equivalence problem for Monge-Ampere equations in the cases under study to the equivalence problem for affine connections. Using E. Cartan's familiar theory, we are thus able to state and prove several criteria of contact equivalence for a large class of elliptic and hyperbolic Monge-Ampere equations

  1. Lie symmetries in differential equations

    International Nuclear Information System (INIS)

    Pleitez, V.

    1979-01-01

    A study of ordinary and Partial Differential equations using the symmetries of Lie groups is made. Following such a study, an application to the Helmholtz, Line-Gordon, Korleweg-de Vries, Burguer, Benjamin-Bona-Mahony and wave equations is carried out [pt

  2. Estimating glomerular filtration rate using the new CKD-EPI equation and other equations in patients with autosomal dominant polycystic kidney disease

    DEFF Research Database (Denmark)

    Orskov, Bjarne; Borresen, Malene L; Feldt-Rasmussen, Bo

    2010-01-01

    (CKD-EPI) equation, the Cockcroft-Gault equation adjusted for body surface area and the MDRD equation with cystatin C. Performance was evaluated by mean bias, precision and accuracy. RESULTS: The MDRD equation with cystatin C had 97% of GFR estimates within 30% of measured GFR (accuracy). Both the CKD-EPI....... The CKD-EPI or the Cockcroft-Gault equations showed better performance compared to the 4-variable MDRD equation....

  3. Nonadiabatic quantum Vlasov equation for Schwinger pair production

    International Nuclear Information System (INIS)

    Kim, Sang Pyo; Schubert, Christian

    2011-01-01

    Using Lewis-Riesenfeld theory, we derive an exact nonadiabatic master equation describing the time evolution of the QED Schwinger pair-production rate for a general time-varying electric field. This equation can be written equivalently as a first-order matrix equation, as a Vlasov-type integral equation, or as a third-order differential equation. In the last version it relates to the Korteweg-de Vries equation, which allows us to construct an exact solution using the well-known one-soliton solution to that equation. The case of timelike delta function pulse fields is also briefly considered.

  4. On the precise connection between the GRW master equation and master equations for the description of decoherence

    Energy Technology Data Exchange (ETDEWEB)

    Vacchini, Bassano [Dipartimento di Fisica dell' Universita di Milano, Via Celoria 16, 20133 Milan (Italy); Istituto Nazionale di Fisica Nucleare, sezione di Milano, Via Celoria 16, 20133 Milan (Italy)

    2007-03-09

    We point out that the celebrated GRW master equation is invariant under translations, reflecting the homogeneity of space, thus providing a particular realization of a general class of translation-covariant Markovian master equations. Such master equations are typically used for the description of decoherence due to momentum transfers between the system and environment. Building on this analogy we show the exact relationship between the GRW master equation and decoherence master equations, further providing a collisional decoherence model formally equivalent to the GRW master equation. This allows for a direct comparison of order of magnitudes of relevant parameters. This formal analogy should not lead to confusion on the utterly different spirit of the two research fields, in particular it has to be stressed that the decoherence approach does not lead to a solution of the measurement problem. Building on this analogy however the feasibility of the extension of spontaneous localization models in order to avoid the infinite energy growth is discussed. Apart from a particular case considered in the paper, it appears that the amplification mechanism is generally spoiled by such modifications.

  5. Partial differential equations methods, applications and theories

    CERN Document Server

    Hattori, Harumi

    2013-01-01

    This volume is an introductory level textbook for partial differential equations (PDE's) and suitable for a one-semester undergraduate level or two-semester graduate level course in PDE's or applied mathematics. Chapters One to Five are organized according to the equations and the basic PDE's are introduced in an easy to understand manner. They include the first-order equations and the three fundamental second-order equations, i.e. the heat, wave and Laplace equations. Through these equations we learn the types of problems, how we pose the problems, and the methods of solutions such as the separation of variables and the method of characteristics. The modeling aspects are explained as well. The methods introduced in earlier chapters are developed further in Chapters Six to Twelve. They include the Fourier series, the Fourier and the Laplace transforms, and the Green's functions. The equations in higher dimensions are also discussed in detail. This volume is application-oriented and rich in examples. Going thr...

  6. on the properties of solutions and some applications on the TOV differential equation with a model of nuclear equation of state

    International Nuclear Information System (INIS)

    Esmail, S.F.H.

    2006-01-01

    the mathematical formulation of numerous physical problems results in differential equations actually non-linear differential equations . in our study we are interested in solutions of differential equations which describe the structure of neutron star in non-relativistic and relativistic cases. the aim of this work is to determine the mass and the radius of a neutron star, by solving the tolmann-oppenheimer-volkoff (TOV) differential equation using different models of the nuclear equation of state (EOS). analytically solutions are obtained for a simple form of the nuclear equation of state of Clayton model and poly trope model. for a more realistic equation of state the TOV differential equation is solved numerically using rung -Kutta method

  7. Consistent three-equation model for thin films

    Science.gov (United States)

    Richard, Gael; Gisclon, Marguerite; Ruyer-Quil, Christian; Vila, Jean-Paul

    2017-11-01

    Numerical simulations of thin films of newtonian fluids down an inclined plane use reduced models for computational cost reasons. These models are usually derived by averaging over the fluid depth the physical equations of fluid mechanics with an asymptotic method in the long-wave limit. Two-equation models are based on the mass conservation equation and either on the momentum balance equation or on the work-energy theorem. We show that there is no two-equation model that is both consistent and theoretically coherent and that a third variable and a three-equation model are required to solve all theoretical contradictions. The linear and nonlinear properties of two and three-equation models are tested on various practical problems. We present a new consistent three-equation model with a simple mathematical structure which allows an easy and reliable numerical resolution. The numerical calculations agree fairly well with experimental measurements or with direct numerical resolutions for neutral stability curves, speed of kinematic waves and of solitary waves and depth profiles of wavy films. The model can also predict the flow reversal at the first capillary trough ahead of the main wave hump.

  8. A Note of Extended Proca Equations and Superconductivity

    Directory of Open Access Journals (Sweden)

    Christianto V.

    2009-01-01

    Full Text Available It has been known for quite long time that the electrodynamics of Maxwell equations can be extended and generalized further into Proca equations. The implications of in- troducing Proca equations include an alternative description of superconductivity, via extending London equations. In the light of another paper suggesting that Maxwell equations can be written using quaternion numbers, then we discuss a plausible exten- sion of Proca equation using biquaternion number. Further implications and experi- ments are recommended.

  9. Relativistic three-particle dynamical equations: I. Theoretical development

    International Nuclear Information System (INIS)

    Adhikari, S.K.; Tomio, L.; Frederico, T.

    1993-11-01

    Starting from the two-particle Bethe-Salpeter equation in the ladder approximation and integrating over the time component of momentum, three dimensional scattering integral equations satisfying constrains of relativistic unitarity and covariance are rederived. These equations were first derived by Weinberg and by Blankenbecler and Sugar. These two-particle equations are shown to be related by a transformation of variables. Hence it is shown to perform and relate dynamical calculation using these two equations. Similarly, starting from the Bethe-Salpeter-Faddeev equation for the three-particle system and integrating over the time component of momentum, several three dimensional three-particle scattering equations satisfying constraints of relativistic unitary and covariance are derived. Two of these three-particle equations are related by a transformation of variables as in the two-particle case. The three-particle equations obtained are very practical and suitable for performing relativistic scattering calculations. (author)

  10. Lectures on nonlinear evolution equations initial value problems

    CERN Document Server

    Racke, Reinhard

    2015-01-01

    This book mainly serves as an elementary, self-contained introduction to several important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The book employs the classical method of continuation of local solutions with the help of a priori estimates obtained for small data. The existence and uniqueness of small, smooth solutions that are defined for all values of the time parameter are investigated. Moreover, the asymptotic behavior of the solutions is described as time tends to infinity. The methods for nonlinear wave equations are discussed in detail. Other examples include the equations of elasticity, heat equations, the equations of thermoelasticity, Schrödinger equations, Klein-Gordon equations, Maxwell equations and plate equations. To emphasize the importance of studying the conditions under which small data problems offer global solutions, some blow-up results are briefly described. Moreover, the prospects for corresponding initial-boundary value p...

  11. Nonlinear von Neumann equations for quantum dissipative systems

    International Nuclear Information System (INIS)

    Messer, J.; Baumgartner, B.

    1978-01-01

    For pure states nonlinear Schroedinger equations, the so-called Schroedinger-Langevin equations are well-known to model quantum dissipative systems of the Langevin type. For mixtures it is shown that these wave equations do not extend to master equations, but to corresponding nonlinear von Neumann equations. Solutions for the damped harmonic oscillator are discussed. (Auth.)

  12. Nonlinear von Neumann equations for quantum dissipative systems

    International Nuclear Information System (INIS)

    Messer, J.; Baumgartner, B.

    For pure states nonlinear Schroedinger equations, the so-called Schroedinger-Langevin equations are well-known to model quantum dissipative systems of the Langevin type. For mixtures it is shown that these wave equations do not extend to master equations, but to corresponding nonlinear von Neumann equations. Solutions for the damped harmonic oscillator are discussed. (Author)

  13. Equations of state for light water

    International Nuclear Information System (INIS)

    Rubin, G.A.; Granziera, M.R.

    1983-01-01

    The equations of state for light water were developed, based on the tables of Keenan and Keyes. Equations are presented, describing the specific volume, internal energy, enthalpy and entropy of saturated steam, superheated vapor and subcooled liquid as a function of pressure and temperature. For each property, several equations are shown, with different precisions and different degress of complexity. (Author) [pt

  14. Quasi-exact solutions of nonlinear differential equations

    OpenAIRE

    Kudryashov, Nikolay A.; Kochanov, Mark B.

    2014-01-01

    The concept of quasi-exact solutions of nonlinear differential equations is introduced. Quasi-exact solution expands the idea of exact solution for additional values of parameters of differential equation. These solutions are approximate solutions of nonlinear differential equations but they are close to exact solutions. Quasi-exact solutions of the the Kuramoto--Sivashinsky, the Korteweg--de Vries--Burgers and the Kawahara equations are founded.

  15. On polynomial solutions of the Heun equation

    International Nuclear Information System (INIS)

    Gurappa, N; Panigrahi, Prasanta K

    2004-01-01

    By making use of a recently developed method to solve linear differential equations of arbitrary order, we find a wide class of polynomial solutions to the Heun equation. We construct the series solution to the Heun equation before identifying the polynomial solutions. The Heun equation extended by the addition of a term, -σ/x, is also amenable for polynomial solutions. (letter to the editor)

  16. Dirac equations for generalised Yang-Mills systems

    International Nuclear Information System (INIS)

    Lechtenfeld, O.; Nahm, W.; Tchrakian, D.H.

    1985-06-01

    We present Dirac equations in 4p dimensions for the generalised Yang-Mills (GYM) theories introduced earlier. These Dirac equations are related to the self-duality equations of the GYM and are checked to be elliptic in a 'BPST' background. In this background these Dirac equations are integrated exactly. The possibility of imposing supersymmetry in the GYM-Dirac system is investigated, with negative results. (orig.)

  17. Generalised master equations for wave equation separation in a Kerr or Kerr-Newman black hole background

    International Nuclear Information System (INIS)

    Carter, B.; McLenaghan, R.G.

    1982-01-01

    It is shown how previous general formulae for the separated radial and angular parts of the massive, charged scalar (Klein, Gordon) wave equation on one hand, and of the zero mass, neutral, but higher spin (neutrino, electromagnetic and gravitational) wave equations on the other hand may be combined in a more general formula which also covers the case of the full massive charged Dirac equation in a Kerr or Kerr-Newman background space. (Auth.)

  18. SIMULTANEOUS DIFFERENTIAL EQUATION COMPUTER

    Science.gov (United States)

    Collier, D.M.; Meeks, L.A.; Palmer, J.P.

    1960-05-10

    A description is given for an electronic simulator for a system of simultaneous differential equations, including nonlinear equations. As a specific example, a homogeneous nuclear reactor system including a reactor fluid, heat exchanger, and a steam boiler may be simulated, with the nonlinearity resulting from a consideration of temperature effects taken into account. The simulator includes three operational amplifiers, a multiplier, appropriate potential sources, and interconnecting R-C networks.

  19. Structural Equations and Causation

    OpenAIRE

    Hall, Ned

    2007-01-01

    Structural equations have become increasingly popular in recent years as tools for understanding causation. But standard structural equations approaches to causation face deep problems. The most philosophically interesting of these consists in their failure to incorporate a distinction between default states of an object or system, and deviations therefrom. Exploring this problem, and how to fix it, helps to illuminate the central role this distinction plays in our causal thinking.

  20. The Integral Equation Method and the Neumann Problem for the Poisson Equation on NTA Domains

    Czech Academy of Sciences Publication Activity Database

    Medková, Dagmar

    2009-01-01

    Roč. 63, č. 21 (2009), s. 227-247 ISSN 0378-620X Institutional research plan: CEZ:AV0Z10190503 Keywords : Poisson equation * Neumann problem * integral equation method Subject RIV: BA - General Mathematics Impact factor: 0.477, year: 2009

  1. Stochastic differential equation model to Prendiville processes

    International Nuclear Information System (INIS)

    Granita; Bahar, Arifah

    2015-01-01

    The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution

  2. Stochastic differential equation model to Prendiville processes

    Energy Technology Data Exchange (ETDEWEB)

    Granita, E-mail: granitafc@gmail.com [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); Bahar, Arifah [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310, Johor Malaysia (Malaysia); UTM Center for Industrial & Applied Mathematics (UTM-CIAM) (Malaysia)

    2015-10-22

    The Prendiville process is another variation of the logistic model which assumes linearly decreasing population growth rate. It is a continuous time Markov chain (CTMC) taking integer values in the finite interval. The continuous time Markov chain can be approximated by stochastic differential equation (SDE). This paper discusses the stochastic differential equation of Prendiville process. The work started with the forward Kolmogorov equation in continuous time Markov chain of Prendiville process. Then it was formulated in the form of a central-difference approximation. The approximation was then used in Fokker-Planck equation in relation to the stochastic differential equation of the Prendiville process. The explicit solution of the Prendiville process was obtained from the stochastic differential equation. Therefore, the mean and variance function of the Prendiville process could be easily found from the explicit solution.

  3. Spectral theories for linear differential equations

    International Nuclear Information System (INIS)

    Sell, G.R.

    1976-01-01

    The use of spectral analysis in the study of linear differential equations with constant coefficients is not only a fundamental technique but also leads to far-reaching consequences in describing the qualitative behaviour of the solutions. The spectral analysis, via the Jordan canonical form, will not only lead to a representation theorem for a basis of solutions, but will also give a rather precise statement of the (exponential) growth rates of various solutions. Various attempts have been made to extend this analysis to linear differential equations with time-varying coefficients. The most complete such extensions is the Floquet theory for equations with periodic coefficients. For time-varying linear differential equations with aperiodic coefficients several authors have attempted to ''extend'' the Foquet theory. The precise meaning of such an extension is itself a problem, and we present here several attempts in this direction that are related to the general problem of extending the spectral analysis of equations with constant coefficients. The main purpose of this paper is to introduce some problems of current research. The primary problem we shall examine occurs in the context of linear differential equations with almost periodic coefficients. We call it ''the Floquet problem''. (author)

  4. Spurious solutions in few-body equations

    International Nuclear Information System (INIS)

    Adhikari, S.K.; Gloeckle, W.

    1979-01-01

    After Faddeev and Yakubovskii showed how to write connected few-body equations which are free from discrete spurious solutions various authors have proposed different connected few-body scattering equations. Federbush first pointed out that Weinberg's formulation admits the existence of discrete spurious solutions. In this paper we investigate the possibility and consequence of the existence of spurious solutions in some of the few-body formulations. Contrary to a proof by Hahn, Kouri, and Levin and by Bencze and Tandy the channel coupling array scheme of Kouri, Levin, and Tobocman which is also the starting point of a formulation by Hahn is shown to admit spurious solutions. We can show that the set of six coupled four-body equations proposed independently by Mitra, Gillespie, Sugar, and Panchapakesan, by Rosenberg, by Alessandrini, and by Takahashi and Mishima and the seven coupled four-body equations proposed by Sloan and related by matrix multipliers to basic sets which correspond uniquely to the Schroedinger equation. These multipliers are likely to give spurious solutions to these equations. In all these cases spuriosities are shown to have no hazardous consequence if one is interested in studying the scattering problem

  5. Multiphase averaging of periodic soliton equations

    International Nuclear Information System (INIS)

    Forest, M.G.

    1979-01-01

    The multiphase averaging of periodic soliton equations is considered. Particular attention is given to the periodic sine-Gordon and Korteweg-deVries (KdV) equations. The periodic sine-Gordon equation and its associated inverse spectral theory are analyzed, including a discussion of the spectral representations of exact, N-phase sine-Gordon solutions. The emphasis is on physical characteristics of the periodic waves, with a motivation from the well-known whole-line solitons. A canonical Hamiltonian approach for the modulational theory of N-phase waves is prescribed. A concrete illustration of this averaging method is provided with the periodic sine-Gordon equation; explicit averaging results are given only for the N = 1 case, laying a foundation for a more thorough treatment of the general N-phase problem. For the KdV equation, very general results are given for multiphase averaging of the N-phase waves. The single-phase results of Whitham are extended to general N phases, and more importantly, an invariant representation in terms of Abelian differentials on a Riemann surface is provided. Several consequences of this invariant representation are deduced, including strong evidence for the Hamiltonian structure of N-phase modulational equations

  6. Electron transfer dynamics: Zusman equation versus exact theory

    International Nuclear Information System (INIS)

    Shi Qiang; Chen Liping; Nan Guangjun; Xu Ruixue; Yan Yijing

    2009-01-01

    The Zusman equation has been widely used to study the effect of solvent dynamics on electron transfer reactions. However, application of this equation is limited by the classical treatment of the nuclear degrees of freedom. In this paper, we revisit the Zusman equation in the framework of the exact hierarchical equations of motion formalism, and show that a high temperature approximation of the hierarchical theory is equivalent to the Zusman equation in describing electron transfer dynamics. Thus the exact hierarchical formalism naturally extends the Zusman equation to include quantum nuclear dynamics at low temperatures. This new finding has also inspired us to rescale the original hierarchical equations and incorporate a filtering algorithm to efficiently propagate the hierarchical equations. Numerical exact results are also presented for the electron transfer reaction dynamics and rate constant calculations.

  7. Mathematical modeling and the two-phase constitutive equations

    International Nuclear Information System (INIS)

    Boure, J.A.

    1975-01-01

    The problems raised by the mathematical modeling of two-phase flows are summarized. The models include several kinds of equations, which cannot be discussed independently, such as the balance equations and the constitutive equations. A review of the various two-phase one-dimensional models proposed to date, and of the constitutive equations they imply, is made. These models are either mixture models or two-fluid models. Due to their potentialities, the two-fluid models are discussed in more detail. To avoid contradictions, the form of the constitutive equations involved in two-fluid models must be sufficiently general. A special form of the two-fluid models, which has particular advantages, is proposed. It involves three mixture balance equations, three balance equations for slip and thermal non-equilibriums, and the necessary constitutive equations [fr

  8. Exact solitary waves of the Fisher equation

    International Nuclear Information System (INIS)

    Kudryashov, Nikolai A.

    2005-01-01

    New method is presented to search exact solutions of nonlinear differential equations. This approach is used to look for exact solutions of the Fisher equation. New exact solitary waves of the Fisher equation are given

  9. Covariant Conformal Decomposition of Einstein Equations

    Science.gov (United States)

    Gourgoulhon, E.; Novak, J.

    It has been shown1,2 that the usual 3+1 form of Einstein's equations may be ill-posed. This result has been previously observed in numerical simulations3,4. We present a 3+1 type formalism inspired by these works to decompose Einstein's equations. This decomposition is motivated by the aim of stable numerical implementation and resolution of the equations. We introduce the conformal 3-``metric'' (scaled by the determinant of the usual 3-metric) which is a tensor density of weight -2/3. The Einstein equations are then derived in terms of this ``metric'', of the conformal extrinsic curvature and in terms of the associated derivative. We also introduce a flat 3-metric (the asymptotic metric for isolated systems) and the associated derivative. Finally, the generalized Dirac gauge (introduced by Smarr and York5) is used in this formalism and some examples of formulation of Einstein's equations are shown.

  10. Controllability and stabilization of parabolic equations

    CERN Document Server

    Barbu, Viorel

    2018-01-01

    This monograph presents controllability and stabilization methods in control theory that solve parabolic boundary value problems. Starting from foundational questions on Carleman inequalities for linear parabolic equations, the author addresses the controllability of parabolic equations on a variety of domains and the spectral decomposition technique for representing them. This method is, in fact, designed for use in a wider class of parabolic systems that include the heat and diffusion equations. Later chapters develop another process that employs stabilizing feedback controllers with a finite number of unstable modes, with special attention given to its use in the boundary stabilization of Navier–Stokes equations for the motion of viscous fluid. In turn, these applied methods are used to explore related topics like the exact controllability of stochastic parabolic equations with linear multiplicative noise. Intended for graduate students and researchers working on control problems involving nonlinear diff...

  11. Differential equations and finite groups

    NARCIS (Netherlands)

    Put, Marius van der; Ulmer, Felix

    2000-01-01

    The classical solution of the Riemann-Hilbert problem attaches to a given representation of the fundamental group a regular singular linear differential equation. We present a method to compute this differential equation in the case of a representation with finite image. The approach uses Galois

  12. Soliton equations and Hamiltonian systems

    CERN Document Server

    Dickey, L A

    2002-01-01

    The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics. For a long time, books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this output followed one single work by Gardner, Green, Kruskal, and Mizura on the Korteweg-de Vries equation (KdV), which had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water. Besides its obvious practical use, this theory is attractive also becau

  13. The gBL transport equations

    International Nuclear Information System (INIS)

    Mynick, H.E.

    1989-05-01

    The transport equations arising from the ''generalized Balescu- Lenard'' (gBL) collision operator are obtained, and some of their properties examined. The equations contain neoclassical and turbulent transport as two special cases, having the same structure. The resultant theory offers potential explanation for a number of results not well understood, including the anomalous pinch, observed ratios of Q/ΓT on TFTR, and numerical reproduction of ASDEX profiles by a model for turbulent transport invoked without derivation, but by analogy to neoclassical theory. The general equations are specialized to consideration of a number of particular transport mechanisms of interest. 10 refs

  14. Singularly perturbed Burger-Huxley equation: Analytical solution ...

    African Journals Online (AJOL)

    user

    numbers, Navier-Stokes flows with large Reynolds numbers, chemical reactor ... It is to observe the layer behavior of the solution for smaller values of ε leading to singular ...... Burger equation, momentum gas equation and heat equation.

  15. ON THE EQUIVALENCE OF THE ABEL EQUATION

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    This article uses the reflecting function of Mironenko to study some complicated differential equations which are equivalent to the Abel equation. The results are applied to discuss the behavior of solutions of these complicated differential equations.

  16. Inverse scattering transform for the time dependent Schrödinger equation with applications to the KPI equation

    Science.gov (United States)

    Zhou, Xin

    1990-03-01

    For the direct-inverse scattering transform of the time dependent Schrödinger equation, rigorous results are obtained based on an opertor-triangular-factorization approach. By viewing the equation as a first order operator equation, similar results as for the first order n x n matrix system are obtained. The nonlocal Riemann-Hilbert problem for inverse scattering is shown to have solution.

  17. New solutions of the confluent Heun equation

    Directory of Open Access Journals (Sweden)

    Harold Exton

    1998-05-01

    Full Text Available New compact triple series solutions of the confluent Heun equation (CHE are obtained by the appropriate applications of the Laplace transform and its inverse to a suitably constructed system of soluble differential equations. The computer-algebra package MAPLE V is used to tackle an auxiliary system of non-linear algebraic equations. This study is partly motivated by the relationship between the CHE and certain Schrödininger equations.

  18. Stationary axisymmetric Einstein--Maxwell field equations

    International Nuclear Information System (INIS)

    Catenacci, R.; Diaz Alonso, J.

    1976-01-01

    We show the existence of a formal identity between Einstein's and Ernst's stationary axisymmetric gravitational field equations and the Einstein--Maxwell and the Ernst equations for the electrostatic and magnetostatic axisymmetric cases. Our equations are invariant under very simple internal symmetry groups, and one of them appears to be new. We also obtain a method for associating two stationary axisymmetric vacuum solutions with every electrostatic known

  19. A novel numerical flux for the 3D Euler equations with general equation of state

    KAUST Repository

    Toro, Eleuterio F.

    2015-09-30

    Here we extend the flux vector splitting approach recently proposed in (E F Toro and M E Vázquez-Cendón. Flux splitting schemes for the Euler equations. Computers and Fluids. Vol. 70, Pages 1-12, 2012). The scheme was originally presented for the 1D Euler equations for ideal gases and its extension presented in this paper is threefold: (i) we solve the three-dimensional Euler equations on general meshes; (ii) we use a general equation of state; and (iii) we achieve high order of accuracy in both space and time through application of the semi-discrete ADER methodology on general meshes. The resulting methods are systematically assessed for accuracy, robustness and efficiency on a carefully selected suite of test problems. Formal high accuracy is assessed through convergence rates studies for schemes of up to 4th order of accuracy in both space and time on unstructured meshes.

  20. Non-isothermal cold crystallization kinetics of poly(3-hydoxybutyrate) filled with zinc oxide

    Energy Technology Data Exchange (ETDEWEB)

    Ries, Andreas, E-mail: ries750@yahoo.com.br [Electrical Engineering Department, Federal University of Paraíba, João Pessoa, PB 58051-900 (Brazil); Canedo, Eduardo L. [Materials Engineering Department, Federal University of Campina Grande, Campina Grande, PB 58429-900 (Brazil); Souto, Cícero R. [Electrical Engineering Department, Federal University of Paraíba, João Pessoa, PB 58051-900 (Brazil); Wellen, Renate M.R. [Materials Engineering Department, Federal University of Paraíba, João Pessoa, PB 58051-900 (Brazil)

    2016-08-10

    Highlights: • Non-isothermal cold crystallization kinetics of PHB filled with ZnO is presented. • Pseudo-Avrami model is best for describing an individual crystallization condition. • Mo model is allows to judge the kinetics of a condition untested in this work. • ZnO affects the kinetics irregularly. - Abstract: The non-isothermal cold crystallization kinetics of poly(3-hydroxybutyrate) (PHB) and PHB-ZnO composites, with ZnO content of 1%, 5% and 10% per weight, was investigated at different heating rates (5, 7.5, 10, 15, 20 and 30 °C/min) using differential scanning calorimetry. Both, Kissinger and Friedman activation energies predict correctly the slowest and fastest crystallizing composition. It was further found, that ZnO can neither be classified as a crystallization accelerator, nor as a crystallization inhibitor; its action is strongly concentration dependent. The empirical Pseudo-Avrami model has the best overall capability for fitting the experimental kinetic data. However, since the Pseudo-Avrami exponent was found to vary irregularly with heating rate and filler content, this model should not be applied for kinetic predictions of an arbitrary composition or an untested heating rate. In such cases, Mo's model should be used.

  1. A Priori Regularity of Parabolic Partial Differential Equations

    KAUST Repository

    Berkemeier, Francisco

    2018-01-01

    In this thesis, we consider parabolic partial differential equations such as the heat equation, the Fokker-Planck equation, and the porous media equation. Our aim is to develop methods that provide a priori estimates for solutions with singular

  2. Trajectory attractors of equations of mathematical physics

    International Nuclear Information System (INIS)

    Vishik, Marko I; Chepyzhov, Vladimir V

    2011-01-01

    In this survey the method of trajectory dynamical systems and trajectory attractors is described, and is applied in the study of the limiting asymptotic behaviour of solutions of non-linear evolution equations. This method is especially useful in the study of dissipative equations of mathematical physics for which the corresponding Cauchy initial-value problem has a global (weak) solution with respect to the time but the uniqueness of this solution either has not been established or does not hold. An important example of such an equation is the 3D Navier-Stokes system in a bounded domain. In such a situation one cannot use directly the classical scheme of construction of a dynamical system in the phase space of initial conditions of the Cauchy problem of a given equation and find a global attractor of this dynamical system. Nevertheless, for such equations it is possible to construct a trajectory dynamical system and investigate a trajectory attractor of the corresponding translation semigroup. This universal method is applied for various types of equations arising in mathematical physics: for general dissipative reaction-diffusion systems, for the 3D Navier-Stokes system, for dissipative wave equations, for non-linear elliptic equations in cylindrical domains, and for other equations and systems. Special attention is given to using the method of trajectory attractors in approximation and perturbation problems arising in complicated models of mathematical physics. Bibliography: 96 titles.

  3. Nonlinear hydrodynamic equations for superfluid helium in aerogel

    International Nuclear Information System (INIS)

    Brusov, Peter N.; Brusov, Paul P.

    2003-01-01

    Aerogel in superfluids is studied very intensively during last decade. The importance of these systems is connected to the fact that this allows to investigate the influence of impurities on superfluidity. We have derived for the first time nonlinear hydrodynamic equations for superfluid helium in aerogel. These equations are generalization of McKenna et al. equations for nonlinear hydrodynamics case and could be used to study sound propagation phenomena in aerogel-superfluid system, in particular--to study sound conversion phenomena. We have obtained two alternative sets of equations, one of which is a generalization of a traditional set of nonlinear hydrodynamics equations for the case of an aerogel-superfluid system and, the other one represents a la Putterman equations (equation for v→ s is replaced by equation for A→=((ρ n )/(ρσ))w→, where w→=v→ n -v→ s )

  4. Local p-Adic Differential Equations

    NARCIS (Netherlands)

    Put, Marius van der; Taelman, Lenny

    2006-01-01

    This paper studies divergence in solutions of p-adic linear local differential equations. Such divergence is related to the notion of p-adic Liouville numbers. Also, the influence of the divergence on the differential Galois groups of such differential equations is explored. A complete result is

  5. Extremal Kähler metrics and Bach-Merkulov equations

    Science.gov (United States)

    Koca, Caner

    2013-08-01

    In this paper, we study a coupled system of equations on oriented compact 4-manifolds which we call the Bach-Merkulov equations. These equations can be thought of as the conformally invariant version of the classical Einstein-Maxwell equations. Inspired by the work of C. LeBrun on Einstein-Maxwell equations on compact Kähler surfaces, we give a variational characterization of solutions to Bach-Merkulov equations as critical points of the Weyl functional. We also show that extremal Kähler metrics are solutions to these equations, although, contrary to the Einstein-Maxwell analogue, they are not necessarily minimizers of the Weyl functional. We illustrate this phenomenon by studying the Calabi action on Hirzebruch surfaces.

  6. Equations of macrotransport in reactor fuel assemblies

    International Nuclear Information System (INIS)

    Sorokin, A.P.; Zhukov, A.V.; Kornienko, Yu.N.; Ushakov, P.A.

    1986-01-01

    The rigorous statement of equations of macrotransport is obtained. These equations are bases for channel-by-channel methods of thermohydraulic calculations of reactor fuel assemblies within the scope of the model of discontinuous multiphase coolant flow (including chemical reactions); they also describe a wide range of problems on thermo-physical reactor fuel assembly justification. It has been carried out by smoothing equations of mass, momentum and enthalpy transfer in cross section of each phase of the elementary fuel assembly subchannel. The equation for cross section flows is obtaind by smoothing the equation of momentum transfer on the interphase. Interaction of phases on the channel boundary is described using the Stanton number. The conclusion is performed using the generalized equation of substance transfer. The statement of channel-by-channel method without the scope of homogeneous flow model is given

  7. Diffusion phenomenon for linear dissipative wave equations

    KAUST Repository

    Said-Houari, Belkacem

    2012-01-01

    In this paper we prove the diffusion phenomenon for the linear wave equation. To derive the diffusion phenomenon, a new method is used. In fact, for initial data in some weighted spaces, we prove that for {equation presented} decays with the rate {equation presented} [0,1] faster than that of either u or v, where u is the solution of the linear wave equation with initial data {equation presented} [0,1], and v is the solution of the related heat equation with initial data v 0 = u 0 + u 1. This result improves the result in H. Yang and A. Milani [Bull. Sci. Math. 124 (2000), 415-433] in the sense that, under the above restriction on the initial data, the decay rate given in that paper can be improved by t -γ/2. © European Mathematical Society.

  8. Multi-component WKI equations and their conservation laws

    Energy Technology Data Exchange (ETDEWEB)

    Qu Changzheng [Department of Mathematics, Northwest University, Xi' an 710069 (China) and Center for Nonlinear Studies, Northwest University, Xi' an 710069 (China)]. E-mail: qu_changzheng@hotmail.com; Yao Ruoxia [Department of Computer Sciences, East China Normal University, Shanghai 200062 (China); Department of Computer Sciences, Weinan Teacher' s College, Weinan 715500 (China); Liu Ruochen [Department of Mathematics, Northwest University, Xi' an 710069 (China)

    2004-10-25

    In this Letter, a two-component WKI equation is obtained by using the fact that when curvature and torsion of a space curve satisfy the vector modified KdV equation, a graph of the curve satisfies the two-component WKI equation, which is a natural generalization to the WKI equation. It is shown that the two-component WKI equation can be solved in terms of the extended WKI scheme, and it admits an infinite number of conservation laws. In the same vein, a n-component generalization to the WKI equation is proposed.

  9. Growth of meromorphic solutions of delay differential equations

    OpenAIRE

    Halburd, Rod; Korhonen, Risto

    2016-01-01

    Necessary conditions are obtained for certain types of rational delay differential equations to admit a non-rational meromorphic solution of hyper-order less than one. The equations obtained include delay Painlev\\'e equations and equations solved by elliptic functions.

  10. Geophysical interpretation using integral equations

    CERN Document Server

    Eskola, L

    1992-01-01

    Along with the general development of numerical methods in pure and applied to apply integral equations to geophysical modelling has sciences, the ability improved considerably within the last thirty years or so. This is due to the successful derivation of integral equations that are applicable to the modelling of complex structures, and efficient numerical algorithms for their solution. A significant stimulus for this development has been the advent of fast digital computers. The purpose of this book is to give an idea of the principles by which boundary-value problems describing geophysical models can be converted into integral equations. The end results are the integral formulas and integral equations that form the theoretical framework for practical applications. The details of mathematical analysis have been kept to a minimum. Numerical algorithms are discussed only in connection with some illustrative examples involving well-documented numerical modelling results. The reader is assu­ med to have a back...

  11. Integrodifferential equation approach. Pt. 1

    International Nuclear Information System (INIS)

    Oehm, W.; Sofianos, S.A.; Fiedeldey, H.; South Africa Univ., Pretoria. Dept. of Physics); Fabre de la Ripelle, M.; South Africa Univ., Pretoria. Dept. of Physics)

    1990-02-01

    A single integrodifferential equation in two variables, valid for A nucleons interacting by pure Wigner forces, which has previously only been solved in the extreme and uncoupled adiabatic approximations is now solved exactly for three- and four-nucleon systems. The results are in good agreement with the values obtained for the binding energies by means of an empirical interpolation formula. This validates all our previous conclusions, in particular that the omission of higher (than two) order correlations in our four-body equation only produces a rather small underbinding. The integrodifferential equation approach (IDEA) is here also extended to spin-dependent forces of the Malfliet-Tjon type, resulting in two coupled integrodifferential equations in two variables. The exact solution and the interpolated adiabatic approximation are again in good agreement. The inclusion of the hypercentral part of the two-body interaction in the definition of the Faddeev-type components again leads to substantial improvement for fully local potentials, acting in all partial waves. (orig.)

  12. Modeling and Finite Element Analysis for the Dynamic Recrystallization Behavior of Ti-5Al-5Mo-5V-3Cr-1Zr Near β Titanium Alloy During Hot Deformation

    Science.gov (United States)

    Lv, Ya-ping; Li, Shao-jun; Zhang, Xiao-yong; Li, Zhi-you; Zhou, Ke-chao

    2018-04-01

    Evolution for the dynamic recrystallization (DRX) volume fraction of Ti-5Al-5Mo-5V-3Cr-1Zr near β titanium alloy during hot deformation was characterized by using the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation. To determine the equation parameters, a series of thermal simulation experiments at the temperature of 1023-1098 K and strain rate of 0.001-1 s‒1 to the true strain of 0.7 were conducted to obtain the essential data about stress σ and strain ɛ. By further transforming the relationship of σ versus ɛ into the relationship of strain hardening rate dσ/dɛ versus σ, two characteristic strains at the beginning of DRX (critical strain ɛc) and at the peak stress (peak strain ɛp) were identified from the dσ/dɛ-σ curves. Sequentially, the parameters in the JMAK equation were determined from the linear fitting of the different relationships among critical strain ɛc, peak strain ɛp and deformation conditions (including temperature T, strain rate \\dot ɛ and strain ɛ). The as-obtained JMAK equation was expressed as XDRX=1-exp[-0.0053((ɛ-ɛc)/ɛc)2.1], where ɛc=0.6053ɛp and ɛp=0.0031 \\dot ɛ .0081exp(28,781/RT). Finally, the JMAK equation was implanted into finite element program to simulate the hot compression of thermal simulation experiments. The simulation predictions and experimental results about the DRX volume fraction distribution showed a good consistency.

  13. Numerical methods for differential equations and applications

    International Nuclear Information System (INIS)

    Ixaru, L.G.

    1984-01-01

    This book is addressed to persons who, without being professionals in applied mathematics, are often faced with the problem of numerically solving differential equations. In each of the first three chapters a definite class of methods is discussed for the solution of the initial value problem for ordinary differential equations: multistep methods; one-step methods; and piecewise perturbation methods. The fourth chapter is mainly focussed on the boundary value problems for linear second-order equations, with a section devoted to the Schroedinger equation. In the fifth chapter the eigenvalue problem for the radial Schroedinger equation is solved in several ways, with computer programs included. (Auth.)

  14. Nonlinear wave equations

    CERN Document Server

    Li, Tatsien

    2017-01-01

    This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.

  15. Ermakov-Pinney equation in scalar field cosmologies

    International Nuclear Information System (INIS)

    Hawkins, Rachael M.; Lidsey, James E.

    2002-01-01

    It is shown that the dynamics of cosmologies sourced by a mixture of perfect fluids and self-interacting scalar fields are described by the nonlinear, Ermakov-Pinney equation. The general solution of this equation can be expressed in terms of particular solutions to a related, linear differential equation. This characteristic is employed to derive exact cosmologies in the inflationary and quintessential scenarios. The relevance of the Ermakov-Pinney equation to the braneworld scenario is discussed

  16. ON DIFFERENTIAL EQUATIONS, INTEGRABLE SYSTEMS, AND GEOMETRY

    OpenAIRE

    Enrique Gonzalo Reyes Garcia

    2004-01-01

    ON DIFFERENTIAL EQUATIONS, INTEGRABLE SYSTEMS, AND GEOMETRY Equations in partial derivatives appeared in the 18th century as essential tools for the analytic study of physical models and, later, they proved to be fundamental for the progress of mathematics. For example, fundamental results of modern differential geometry are based on deep theorems on differential equations. Reciprocally, it is possible to study differential equations through geometrical means just like it was done by o...

  17. Action principles for the Vlasov equation

    International Nuclear Information System (INIS)

    Ye, H.; Morrison, P.J.

    1992-01-01

    Five action principles for the Vlasov--Poisson and Vlasov--Maxwell equations, which differ by the variables incorporated to describe the distribution of particles in phase space, are presented. Three action principles previously known for the Vlasov--Maxwell equations are altered so as to produce the Vlasov--Poisson equation upon variation with respect to only the particle variables, and one action principle previously known for the Vlasov--Poisson equation is altered to produce the Vlasov--Maxwell equations upon variations with respect to particle and field variables independently. Also, a new action principle for both systems, which is called the leaf action, is presented. This new action has the desirable features of using only a single generating function as the dynamical variable for describing the particle distribution, and manifestly preserving invariants of the system known as Casimir invariants. The relationships between the various actions are described, and it is shown that the leaf action is a link between actions written in terms of Lagrangian and Eulerian variables

  18. Canonical reduction of self-dual Yang-Mills equations to Fitzhugh-Nagumo equation and exact solutions

    International Nuclear Information System (INIS)

    Sayed, S.M.; Gharib, G.M.

    2009-01-01

    The (constrained) canonical reduction of four-dimensional self-dual Yang-Mills theory to two-dimensional Fitzhugh-Nagumo and the real Newell-Whitehead equations are considered. On the other hand, other methods and transformations are developed to obtain exact solutions for the original two-dimensional Fitzhugh-Nagumo and Newell-Whitehead equations. The corresponding gauge potential A μ and the gauge field strengths F μν are also obtained. New explicit and exact traveling wave and solitary solutions (for Fitzhugh-Nagumo and Newell-Whitehead equations) are obtained by using an improved sine-cosine method and the Wu's elimination method with the aid of Mathematica.

  19. Elliptic equation rational expansion method and new exact travelling solutions for Whitham-Broer-Kaup equations

    International Nuclear Information System (INIS)

    Chen Yong; Wang Qi; Li Biao

    2005-01-01

    Based on a new general ansatz and a general subepuation, a new general algebraic method named elliptic equation rational expansion method is devised for constructing multiple travelling wave solutions in terms of rational special function for nonlinear evolution equations (NEEs). We apply the proposed method to solve Whitham-Broer-Kaup equation and explicitly construct a series of exact solutions which include rational form solitary wave solution, rational form triangular periodic wave solutions and rational wave solutions as special cases. In addition, the links among our proposed method with the method by Fan [Chaos, Solitons and Fractals 2004;20:609], are also clarified generally

  20. Differential equations inverse and direct problems

    CERN Document Server

    Favini, Angelo

    2006-01-01

    DEGENERATE FIRST ORDER IDENTIFICATION PROBLEMS IN BANACH SPACES A NONISOTHERMAL DYNAMICAL GINZBURG-LANDAU MODEL OF SUPERCONDUCTIVITY. EXISTENCE AND UNIQUENESS THEOREMSSOME GLOBAL IN TIME RESULTS FOR INTEGRODIFFERENTIAL PARABOLIC INVERSE PROBLEMSFOURTH ORDER ORDINARY DIFFERENTIAL OPERATORS WITH GENERAL WENTZELL BOUNDARY CONDITIONSTUDY OF ELLIPTIC DIFFERENTIAL EQUATIONS IN UMD SPACESDEGENERATE INTEGRODIFFERENTIAL EQUATIONS OF PARABOLIC TYPE EXPONENTIAL ATTRACTORS FOR SEMICONDUCTOR EQUATIONSCONVERGENCE TO STATIONARY STATES OF SOLUTIONS TO THE SEMILINEAR EQUATION OF VISCOELASTICITY ASYMPTOTIC BEHA