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Sample records for avrami equation inadequacy

  1. A test of the Johnson-Mehl-Avrami equation. [for phase transformations

    NASA Technical Reports Server (NTRS)

    Weinberg, Michael C.

    1987-01-01

    The accuracy of the Johnson-Mehl-Avrami (JMA) equation is evaluated for the special case of two-dimensional crystallization. The volume fraction transformed is determined directly by computer modeling, and the evaluation of the secondary phase obtained is compared with predictions of the JMA equation. The JMA equation if found to be highly acccurate over virtually the entire range of the transformation process.

  2. Evaluation of the recrystallization kinetics of hot-melt extruded polymeric solid dispersions using an improved Avrami equation.

    PubMed

    Feng, Xin; Ye, Xingyou; Park, Jun-Bom; Lu, Wenli; Morott, Joe; Beissner, Brad; Lian, Zhuoyang John; Pinto, Elanor; Bi, Vivian; Porter, Stu; Durig, Tom; Majumdar, Soumyajit; Repka, Michael A

    2015-01-01

    The recrystallization of an amorphous drug in a solid dispersion system could lead to a loss in the drug solubility and bioavailability. The primary objective of the current research was to use an improved kinetic model to evaluate the recrystallization kinetics of amorphous structures and to further understand the factors influencing the physical stability of amorphous solid dispersions. Amorphous solid dispersions of fenofibrate with different molecular weights of hydroxypropylcellulose, HPC (Klucel™ LF, EF, ELF) were prepared utilizing hot-melt extrusion technology. Differential scanning calorimetry was utilized to quantitatively analyze the extent of recrystallization in the samples stored at different temperatures and relative humidity (RH) conditions. The experimental data were fitted into the improved kinetics model of a modified Avrami equation to calculate the recrystallization rate constants. Klucel LF, the largest molecular weight among the HPCs used, demonstrated the greatest inhibition of fenofibrate recrystallization. Additionally, the recrystallization rate (k) decreased with increasing polymer content, however exponentially increased with higher temperature. Also k increased linearly rather than exponentially over the range of RH studied. PMID:25224341

  3. Hypnotherapy and Female Sexual Inadequacy

    PubMed Central

    Glick, Daniel

    1972-01-01

    Dr. Glick describes the use of hypnosis in the treatment of primary and secondary frigidity, dyspareunia and psychosomatic symptoms in female sexual inadequacy. He uses case histories to show the various techniques used and the results that can be expected. PMID:20468741

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

    ERIC Educational Resources Information Center

    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…

  5. Crystallization kinetics of lithium niobate glass: determination of the Johnson-Mehl-Avrami-Kolmogorov parameters.

    PubMed

    Choi, H W; Kim, Y H; Rim, Y H; Yang, Y S

    2013-06-28

    The formation of crystalline LiNbO3 (LN) from LN glass has been studied by means of differential scanning calorimetry and in situ synchrotron X-ray diffraction. The LN glass with no glass former was prepared by the polymerized complex method. The isothermal kinetics of the crystallization process is described using the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation and the Avrami exponent n is found to be ~2.0, indicating that the crystallization mechanism is diffusion-controlled growth with a decreasing nucleation rate. The effective activation energy of crystallization calculated from isothermal measurements is 6.51 eV. It is found that the LN glass directly transforms into a rhombohedral LN crystal without any intermediate crystalline phase and most crystal grains are confined within the size of ~40 nm irrespective of different isothermal temperatures. Application of JMAK theory to the non-isothermal thermoanalytical study of crystallization of LN glass is discussed. PMID:23677338

  6. Modeling the cure kinetics of crosslinking free radical polymerizations using the Avrami theory of phase transformation

    SciTech Connect

    Finnegan, G.R.; Shine, A.D.

    1995-12-01

    A model, based on Avrami`s theory of phase transformation, has been developed to describe the cure kinetics of crosslinking free radical polymerizations. The model assumes the growing polymer can be treated as a distinct phase and the nucleation rate is proportional to the initiation rate of the polymerization. The Avrami time exponent was verified to be 4.0. This physically-based, two-parameter model fits vinyl ester resin heat flow data as well as the empirical, four-parameter autocatalytic model, and is capable of describing both neat and fiber-containing resin.

  7. Vitamin D inadequacy in pregnancy: biology, outcomes, and interventions

    Technology Transfer Automated Retrieval System (TEKTRAN)

    A high prevalence of maternal vitamin D inadequacy during pregnancy and at delivery has been demonstrated in various ethnic populations living at different latitudes. Because placental transfer of 25(OH)D is the major source of vitamin D to the developing human fetus, there is growing concern about ...

  8. Model inadequacy and mistaken inferences of trait-dependent speciation.

    PubMed

    Rabosky, Daniel L; Goldberg, Emma E

    2015-03-01

    Species richness varies widely across the tree of life, and there is great interest in identifying ecological, geographic, and other factors that affect rates of species proliferation. Recent methods for explicitly modeling the relationships among character states, speciation rates, and extinction rates on phylogenetic trees- BiSSE, QuaSSE, GeoSSE, and related models-have been widely used to test hypotheses about character state-dependent diversification rates. Here, we document the disconcerting ease with which neutral traits are inferred to have statistically significant associations with speciation rate. We first demonstrate this unfortunate effect for a known model assumption violation: shifts in speciation rate associated with a character not included in the model. We further show that for many empirical phylogenies, characters simulated in the absence of state-dependent diversification exhibit an even higher Type I error rate, indicating that the method is susceptible to additional, unknown model inadequacies. For traits that evolve slowly, the root cause appears to be a statistical framework that does not require replicated shifts in character state and diversification. However, spurious associations between character state and speciation rate arise even for traits that lack phylogenetic signal, suggesting that phylogenetic pseudoreplication alone cannot fully explain the problem. The surprising severity of this phenomenon suggests that many trait-diversification relationships reported in the literature may not be real. More generally, we highlight the need for diagnosing and understanding the consequences of model inadequacy in phylogenetic comparative methods. PMID:25601943

  9. 40 CFR 52.32 - Sanctions following findings of SIP inadequacy.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 40 Protection of Environment 3 2010-07-01 2010-07-01 false Sanctions following findings of SIP inadequacy. 52.32 Section 52.32 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) AIR... following findings of SIP inadequacy. For purposes of the SIP revisions required by § 51.120, EPA may make...

  10. Vitamin E Inadequacy in Humans: Causes and Consequences12

    PubMed Central

    Traber, Maret G.

    2014-01-01

    It is estimated that >90% of Americans do not consume sufficient dietary vitamin E, as α-tocopherol, to meet estimated average requirements. What are the adverse consequences of inadequate dietary α-tocopherol intakes? This review discusses health aspects where inadequate vitamin E status is detrimental and additional vitamin E has reversed the symptoms. In general, plasma α-tocopherol concentrations <12 μmol/L are associated with increased infection, anemia, stunting of growth, and poor outcomes during pregnancy for both the infant and the mother. When low dietary amounts of α-tocopherol are consumed, tissue α-tocopherol needs exceed amounts available, leading to increased damage to target tissues. Seemingly, adequacy of human vitamin E status cannot be assessed from circulating α-tocopherol concentrations, but inadequacy can be determined from “low” values. Circulating α-tocopherol concentrations are very difficult to interpret because, as a person ages, plasma lipid concentrations also increase and these elevations in lipids increase the plasma carriers for α-tocopherol, leading to higher circulating α-tocopherol concentrations. However, abnormal lipoprotein metabolism does not necessarily increase α-tocopherol delivery to tissues. Additional biomarkers of inadequate vitamin E status are needed. Urinary excretion of the vitamin E metabolite α-carboxy-ethyl-hydroxychromanol may fulfill this biomarker role, but it has not been widely studied with regard to vitamin E status in humans or with regard to health benefits. This review evaluated the information available on the adverse consequences of inadequate α-tocopherol status and provides suggestions for avenues for research. PMID:25469382

  11. Crystallisation kinetics of some archetypal ionic liquids: isothermal and non-isothermal determination of the Avrami exponent.

    PubMed

    Pas, Steven J; Dargusch, Matthew S; MacFarlane, Douglas R

    2011-07-01

    The properties of ionic liquids give rise to applications in diverse technology areas including mechanical engineering, mining, aerospace and defence. The arbitrary physical property that defines an ionic liquid is a melting point below 100 °C, and as such, an understanding of crystallisation phenomena is extremely important. This is the first report dealing with the mechanism of crystallisation in ionic liquids. Assuming crystallisation of the ionic liquids is a thermal or mass diffusion-controlled process, the values of the isothermal Avrami exponent obtained from three different ionic liquids with three different anions and cations all indicate that growth occurs with a decreasing nucleation rate (n=1.8-2.2). For one of the ionic liquids it was possible to avoid crystallisation by fast cooling and then observe a devitrification upon heating through the glass transition. The isothermal Avrami exponent of devitrification suggested growth with an increasing nucleating rate (n=4.1), compared to a decreasing nucleation rate when crystallisation occurs on cooling from the melt (n=2.0). Two non-isothermal methods were employed to determine the Avrami exponent of devitrification. Both non-isothermal Avrami exponents were in agreement with the isothermal case (n=4.0-4.15). The applicability of JMAK theory suggests that the nucleation event in the ionic liquids selected is a random stochastic process in the volume of the material. Agreement between the isothermal and non-isothermal techniques for determining the Avrami exponent of devitrification suggests that the pre-exponential factor and the activation energy are independent of thermal history. The heating rate dependence of the glass transition enabled the calculation of the fragility index, which suggests that the ionic liquid is a "strong" glass former. This suggests that the temperature dependence of the rate constant could be close to Arrhenius, as assumed by JMAK theory. More generally, therefore, it can be

  12. High Educational Aspirations Among Pregnant Adolescents Are Related to Pregnancy Unwantedness and Subsequent Parenting Stress and Inadequacy

    PubMed Central

    East, Patricia L.; Barber, Jennifer S.

    2015-01-01

    On the basis of theories of maternal identity development, role conflict, and childbearing motivation, the authors tested whether high educational aspirations among pregnant adolescents are related to the unwantedness of the pregnancy and whether pregnancy unwantedness leads to subsequent parenting stress and inadequacy. Longitudinal data from 100 first-time-pregnant, unmarried Latina adolescents (M age = 17.3 years) were analyzed. Results from structural equation path modeling confirmed these associations, with strong educational ambitions related to greater unwantedness of the pregnancy, which led to feeling trapped by parenting at 6 months postpartum, which in turn was related to unaffectionate parenting and feeling inadequate in mothering at 1 year postpartum. The potential long-term negative consequences of high educational aspirations for pregnant adolescents’ adjustment to parenting are discussed. PMID:25641985

  13. Crystal Growth Simulations To Establish Physically Relevant Kinetic Parameters from the Empirical Kolmogorov-Johnson-Mehl-Avrami Model

    SciTech Connect

    Dill, Eric D.; Folmer, Jacob C.W.; Martin, James D.

    2013-12-05

    A series of simulations was performed to enable interpretation of the material and physical significance of the parameters defined in the Kolmogorov, Johnson and Mehl, and Avrami (KJMA) rate expression commonly used to describe phase boundary controlled reactions of condensed matter. The parameters k, n, and t0 are shown to be highly correlated, which if unaccounted for seriously challenge mechanistic interpretation. It is demonstrated that rate measurements exhibit an intrinsic uncertainty without precise knowledge of the location and orientation of nucleation with respect to the free volume into which it grows. More significantly, it is demonstrated that the KJMA rate constant k is highly dependent on sample size. However, under the simulated conditions of slow nucleation relative to crystal growth, sample volume and sample anisotropy correction affords a means to eliminate the experimental condition dependence of the KJMA rate constant, k, producing the material-specific parameter, the velocity of the phase boundary, vpb.

  14. Crystallization analysis and determination of Avrami exponents of CuAlNi alloy by molecular dynamics simulation

    NASA Astrophysics Data System (ADS)

    Celik, Fatih Ahmet; Kazanc, Sefa

    2013-01-01

    In this study, local atomic rearrangements of Cu-%26.8Al-%2.5Ni ternary alloys (3 A) are investigated during their crystallization processes from amorphous phase using molecular dynamics (MD) simulations. These simulations are based on the Sutton-Chen type of embedded atom method (SCEAM) that employs many-body interactions. In order to analyse the structural development obtained from MD simulation, the simulation techniques are used as bond order parameter, radial distribution function (RDF). Local atomic bonded pairs and short range order properties in the model alloy have been analysed using the Honeycutt-Andersen (HA) method. The kinetics of the crystallization is described by Johnson, Mehl and Avrami (JMA) model, which has been analysed with MD method by using the crystalline bonded pairs. The simulation results show that the structural variation of local atomic bonded pairs is of great importance to understand the crystallization kinetics from amorphous phase to crystal phase during the crystallization.

  15. The Inadequacy of Academic Environment Contributes to Inadequate Teaching and Learning Phenomena

    ERIC Educational Resources Information Center

    Quasim, Shahla; Arif, Muhammad Shahbaz

    2014-01-01

    This study aims at the inadequacy of academic environment as an indicator contributing to the inadequate teaching and learning situation in Pakistan. The main focus is to look into the low proficiency of students in the subject of English at secondary school level. A comprehensive questionnaire was designed from the literature concerned and The…

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

    Technology Transfer Automated Retrieval System (TEKTRAN)

    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...

  17. Interplay between Kolmogorov-Johnson-Mehl-Avrami kinetics and Poisson-Voronoi tessellation

    NASA Astrophysics Data System (ADS)

    Tomellini, M.; Fanfoni, M.

    2016-05-01

    In this paper we investigate the connection between Voronoi tessellation and the KJMA approach of space filling. In particular, we study how nuclei, in their growth, cover a given Voronoi cell. This approach leads to an integral equation for the cell-size distribution function. Starting from the 1D case, that is solved exactly, we extend the results to the dD case. The analysis allows to find a rationale to the phenomenological parameter entering the Gamma distribution function and to improve the description of the transformation through the knowledge of the kinetics of grain formation. Moreover, the nucleus size distribution function has been calculated as a function of the transformed fraction.

  18. Are Dieting and Dietary Inadequacy a Second Hit in the Association with Polycystic Ovary Syndrome Severity?

    PubMed Central

    Huijgen, Nicole A.; Laven, Joop S. E.; Labee, Chantal T.; Louwers, Yvonne V.; Willemsen, Sten P.; Steegers-Theunissen, Régine P. M.

    2015-01-01

    Background The composition of the diet is of increasing importance for the development and maturation of the ovarian follicles. In Polycystic Ovary Syndrome (PCOS) healthy dietary interventions improve the clinical spectrum. We hypothesized that dieting and diet inadequacy in the reproductive life course is associated with impaired programming of ovarian follicles and contributes to the severity of the PCOS phenotype. Methods and Findings To determine associations between the use of a self-initiated diet and diet inadequacy and the severity of the PCOS phenotype, we performed an explorative nested case control study embedded in a periconception cohort of 1,251 patients visiting the preconception outpatient clinic. 218 patients with PCOS and 799 subfertile controls were selected from the cohort and self-administered questionnaires, anthropometric measurements and blood samples were obtained. The Preconception Dietary Risk Score (PDR score), based on the Dutch dietary guidelines, was used to determine diet inadequacy in all women. The PDR score was negatively associated to cobalamin, serum and red blood cell folate and positively to tHcy. PCOS patients (19.9%), in particular the hyperandrogenic (HA) phenotype (22.5%) reported more often the use of a self-initiated diet than controls (13.1%; p = 0.023). The use of an inadequate diet was also significantly higher in PCOS than in controls (PDR score 3.7 vs 3.5; p = 0.017) and every point increase was associated with a more than 1.3 fold higher risk of the HA phenotype (adjusted OR 1.351, 95% CI 1.09–1.68). Diet inadequacy was independently associated with the anti-Müllerian Hormone (AMH) concentration (β 0.084; p = 0.044; 95% CI 0.002 to 0.165) and free androgen index (β 0.128; p = 0.013; 95% CI 0.028 to 0.229) in PCOS patients. Conclusions The use of a self-initiated diet and diet inadequacy is associated with PCOS, in particular with the severe HA phenotype. This novel finding substantiated by the association

  19. Food insecurity is associated with nutrient inadequacies among Canadian adults and adolescents.

    PubMed

    Kirkpatrick, Sharon I; Tarasuk, Valerie

    2008-03-01

    Household food insecurity constrains food selection, but whether the dietary compromises associated with this problem heighten the risk of nutrient inadequacies is unclear. The objectives of this study were to examine the relationship between household food security status and adults' and children's dietary intakes and to estimate the prevalence of nutrient inadequacies among adults and children, differentiating by household food security status. We analyzed 24-h recall and household food security data for persons aged 1-70 y from the 2004 Canadian Community Health Survey (cycle 2.2). The relationship between adults' and children's nutrient and food intakes and household food security status was assessed using regression analysis. Estimates of the prevalence of inadequate nutrient intakes by food security status and age/sex group were calculated using probability assessment methods. Poorer dietary intakes were observed among adolescents and adults in food-insecure households and many of the differences by food security status persisted after accounting for potential confounders in multivariate analyses. Higher estimated prevalences of nutrient inadequacy were apparent among adolescents and adults in food-insecure households, with the differences most marked for protein, vitamin A, thiamin, riboflavin, vitamin B-6, folate, vitamin B-12, magnesium, phosphorus, and zinc. Among children, few differences in dietary intakes by household food security status were apparent and there was little indication of nutrient inadequacy. This study indicates that for adults and, to some degree, adolescents, food insecurity is associated with inadequate nutrient intakes. These findings highlight the need for concerted public policy responses to ameliorate household food insecurity. PMID:18287374

  20. Prevalence of vitamin D inadequacy in European women aged over 80 years.

    PubMed

    Bruyère, Olivier; Slomian, Justine; Beaudart, Charlotte; Buckinx, Fanny; Cavalier, Etienne; Gillain, Sophie; Petermans, Jean; Reginster, Jean-Yves

    2014-01-01

    Inadequate vitamin D status is associated with secondary hyperparathyroidism and increased bone turnover and bone loss, which in turn increases fracture risk. The objective of this study is to assess the prevalence of inadequate vitamin D status in European women aged over 80 years. Assessments of serum 25-hydroxyvitamin D levels (25(OH)D) were performed on 8532 European women with osteoporosis or osteopenia of which 1984 were aged over 80 years. European countries included in the study were: France, Belgium, Denmark, Italy, Poland, Hungary, United Kingdom, Spain and Germany. Two cut-offs of 25(OH)D inadequacy were fixed: <75 nmol/L (30 ng/ml) and <50 nmol/L (20 ng/ml). Mean (SD) age of the patients was 83.4 (2.9) years, body mass index was 25.0 (4.0) kg/m(2) and level of 25(OH)D was 53.3 (26.7) nmol/L (21.4 [10.7] ng/ml). There was a highly significant difference of 25(OH)D level across European countries (p<0.0001). In these women aged over 80 years, the prevalence of 25(OH)D inadequacy was 80.9% and 44.5% when considering cut-offs of 75 and 50 nmol/L, respectively. In the 397 (20.0%) patients taking supplemental vitamin D with or without supplemental calcium, the mean serum 25(OH)D level was significantly higher than in the other patients (65.2 (29.2) nmol/L vs. 50.3 (25.2) nmol/L; P<0.001). This study indicates a high prevalence of vitamin D (25(OH)D) inadequacy in old European women. The prevalence could be even higher in some particular countries. PMID:24784761

  1. Appropriateness of the probability approach with a nutrient status biomarker to assess population inadequacy: a study using vitamin D123

    PubMed Central

    Carriquiry, Alicia L; Bailey, Regan L; Sempos, Christopher T; Yetley, Elizabeth A

    2013-01-01

    Background: There are questions about the appropriate method for the accurate estimation of the population prevalence of nutrient inadequacy on the basis of a biomarker of nutrient status (BNS). Objective: We determined the applicability of a statistical probability method to a BNS, specifically serum 25-hydroxyvitamin D [25(OH)D]. The ability to meet required statistical assumptions was the central focus. Design: Data on serum 25(OH)D concentrations in adults aged 19–70 y from the 2005–2006 NHANES were used (n = 3871). An Institute of Medicine report provided reference values. We analyzed key assumptions of symmetry, differences in variance, and the independence of distributions. We also corrected observed distributions for within-person variability (WPV). Estimates of vitamin D inadequacy were determined. Results: We showed that the BNS [serum 25(OH)D] met the criteria to use the method for the estimation of the prevalence of inadequacy. The difference between observations corrected compared with uncorrected for WPV was small for serum 25(OH)D but, nonetheless, showed enhanced accuracy because of correction. The method estimated a 19% prevalence of inadequacy in this sample, whereas misclassification inherent in the use of the more traditional 97.5th percentile high-end cutoff inflated the prevalence of inadequacy (36%). Conclusions: When the prevalence of nutrient inadequacy for a population is estimated by using serum 25(OH)D as an example of a BNS, a statistical probability method is appropriate and more accurate in comparison with a high-end cutoff. Contrary to a common misunderstanding, the method does not overlook segments of the population. The accuracy of population estimates of inadequacy is enhanced by the correction of observed measures for WPV. PMID:23097269

  2. Some inadequacies of the current human factors certification process of advanced aircraft technologies

    NASA Technical Reports Server (NTRS)

    Paries, Jean

    1994-01-01

    Automation related accidents or serious incidents are not limited to advanced technology aircraft. There is a full history of such accidents with conventional technology aircraft. However, this type of occurrence is far from sparing the newest 'glass cockpit' generation, and it even seems to be a growing contributor to its accident rate. Nevertheless, all these aircraft have been properly certificated according to the relevant airworthiness regulations. Therefore, there is a growing concern that with the technological advancement of air transport aircraft cockpits, the current airworthiness regulations addressing cockpit design and human factors may have reached some level of inadequacy. This paper reviews some aspects of the current airworthiness regulations and certification process related to human factors of cockpit design and focuses on questioning their ability to guarantee the intended safety objectives.

  3. Inadequacies of conventional traffic forecasting in determining the demand for new aircraft

    NASA Technical Reports Server (NTRS)

    Gorham, J. E.

    1978-01-01

    Decisions concerning the selection of new aircraft must take into account the expected volume and character of air traffic in particular future markets. An investigation is, therefore, conducted regarding the currently available approaches for obtaining estimates of air traffic growth. Essentially, air traffic forecasting consists in studying past air traffic growth patterns, attempting to determine what may cause them to change, relating them where possible to such determinants or to other series whose changes they follow in some predictable fashion. Attention is given to the short-shelf life of conventional air traffic forecasts, the observation that most forecasts reflect recent experience, factors which may partially offset the inadequacies of air traffic forecasting technology, the limitations of conventional forecasting, and research useful in identifying a range of future scenarios.

  4. The (in)adequacy of applicative use of quantum cryptography in wireless sensor networks

    NASA Astrophysics Data System (ADS)

    Turkanović, Muhamed; Hölbl, Marko

    2014-10-01

    Recently quantum computation and cryptography principles are exploited in the design of security systems for wireless sensor networks (WSNs), which are consequently named as quantum WSN. Quantum cryptography is presumably secure against any eavesdropper and thus labeled as providing unconditional security. This paper tries to analyze the aspect of the applicative use of quantum principles in WSN. The outcome of the analysis elaborates a summary about the inadequacy of applicative use of quantum cryptography in WSN and presents an overview of all possible applicative challenges and problems while designing quantum-based security systems for WSN. Since WSNs are highly complex frameworks, with many restrictions and constraints, every security system has to be fully compatible and worthwhile. The aim of the paper was to contribute a verdict about this topic, backed up by equitable facts.

  5. Facing inadequacy and being good enough: psychiatric care providers' narratives about experiencing and coping with troubled conscience.

    PubMed

    Dahlqvist, V; Söderberg, A; Norberg, A

    2009-04-01

    The aim of this study is to illuminate the meaning of encounters with a troubled conscience among psychiatric therapists. Psychiatric care involves ethical dilemmas which may affect conscience. Conscience relates to keeping or losing a sense of personal integrity when making judgments about one's actions. Ten psychiatric therapists were interviewed in June 2006. The interviews were tape-recorded, transcribed verbatim and interpreted using a phenomenological-hermeneutic method. Two themes 'Facing inadequacy' and 'Struggling to view oneself as being 'good enough'' are presented. In the therapists interviewed, awareness of their use of power, a sense of powerlessness and a sense of blame gave rise to feelings of betrayals and shameful inadequacy. By sharing their inadequacy with co-workers, they managed to endure the sense of their inadequacy which otherwise would have threatened to paralyse them. Finding consolation in sharing wearing feelings, becoming realistic and attesting their worthiness, they reached reconciliation and found confirmation of being good enough. The findings are interpreted in light of Lögstrup's ethics of trust, according to which conscience alerts us to silent but radical ethical demand and the risk of self-deception. PMID:19291152

  6. Maternal child-feeding practices and dietary inadequacy of 4-year-old children.

    PubMed

    Durão, Catarina; Andreozzi, Valeska; Oliveira, Andreia; Moreira, Pedro; Guerra, António; Barros, Henrique; Lopes, Carla

    2015-09-01

    This study aimed to evaluate the association between maternal perceived responsibility and child-feeding practices and dietary inadequacy of 4-year-old children. We studied 4122 mothers and children enrolled in the population-based birth cohort - Generation XXI (Porto, Portugal). Mothers self-completed the Child Feeding Questionnaire and a scale on covert and overt control, and answered to a food frequency questionnaire in face-to-face interviews. Using dietary guidelines for preschool children, adequacy intervals were defined: fruit and vegetables (F&V) 4-7 times/day; dairy 3-5 times/day; meat and eggs 5-10 times/week; fish 2-4 times/week. Inadequacy was considered as below or above these cut-points. For energy-dense micronutrient-poor foods and beverages (EDF), a tolerable limit was defined (<6 times/week). Associations between maternal perceived responsibility and child-feeding practices (restriction, monitoring, pressure to eat, overt and covert control) and children's diet were examined by logistic regression models. After adjustment for maternal BMI, education, and diet, and children's characteristics (sex, BMI z-scores), restriction, monitoring, overt and covert control were associated with 11-18% lower odds of F&V consumption below the interval defined as adequate. Overt control was also associated with 24% higher odds of their consumption above it. Higher perceived responsibility was associated with higher odds of children consuming F&V and dairy above recommendations. Pressure to eat was positively associated with consumption of dairy above the adequate interval. Except for pressure to eat, maternal practices were associated with 14-27% lower odds of inadequate consumption of EDF. In conclusion, children whose mothers had higher levels of covert control, monitoring, and restriction were less likely to consume F&V below recommendations and EDF above tolerable limits. Higher overt control and pressure to eat were associated, respectively, with higher

  7. Evaluation of Glucose Dehydrogenase and Pyrroloquinoline Quinine (pqq) Mutagenesis that Renders Functional Inadequacies in Host Plants.

    PubMed

    Naveed, Muhammad; Sohail, Younas; Khalid, Nauman; Ahmed, Iftikhar; Mumtaz, Abdul Samad

    2015-08-01

    The rhizospheric zone abutting plant roots usually clutches a wealth of microbes. In the recent past, enormous genetic resources have been excavated with potential applications in host plant interaction and ancillary aspects. Two Pseudomonas strains were isolated and identified through 16S rRNA and rpoD sequence analyses as P. fluorescens QAU67 and P. putida QAU90. Initial biochemical characterization and their root-colonizing traits indicated their potential role in plant growth promotion. Such aerobic systems, involved in gluconic acid production and phosphate solubilization, essentially require the pyrroloquinoline quinine (PQQ)- dependent glucose dehydrogenase (GDH) in the genome. The PCR screening and amplification of GDH and PQQ and subsequent induction of mutagenesis characterized their possible role as antioxidants as well as in growth promotion, as probed in vitro in lettuce and in vivo in rice, bean, and tomato plants. The results showed significant differences (p < or = 0.05) in parameters of plant height, fresh weight, and dry weight, etc., deciphering a clear and in fact complementary role of GDH and PQQ in plant growth promotion. Our study not only provides direct evidence of the in vivo role of GDH and PQQ in host plants but also reveals their functional inadequacy in the event of mutation at either of these loci. PMID:25839331

  8. Cognitive phylogenies, the Darwinian logic of descent, and the inadequacy of cladistic thinking

    PubMed Central

    Theofanopoulou, Constantina; Boeckx, Cedric

    2015-01-01

    There has been a reappraisal of phylogenetic issues in cognitive science, as reconstructing cognitive phylogenies has been considered a key for unveiling the cognitive novelties that set the stage for what makes humans special. In our opinion, the studies made until now have approached cognitive phylogenies in a non-optimal way, and we wish to both highlight their problems, drawing on recent considerations in philosophy of biology. The inadequacy of current visions on cognitive phylogenies stems from the influence of the traditional “linear cladograms,” according to which every seemingly new or more sophisticated feature of a cognitive mechanism, viewed as a novelty, is represented as a node on top of the old and shared elements. We claim that this kind of cladograms does not succeed in depicting the complexity with which traits are distributed across species and, furthermore, that the labels of the nodes of these traditional representational systems fail to capture the “tinkering” nature of evolution. We argue that if we are to conceive of cognitive mechanisms in a multi-dimensional, bottom-up perspective, in accordance with the Darwinian logic of descent, we should rather focus on decomposing these mechanisms into lower-level, generic functions, which have the additional advantage of being implementable in neural matter, which ultimately produces cognition. Doing so renders current constructions of cognitive phylogenies otiose. PMID:26528479

  9. Quality Protein Maize for Africa: Closing the Protein Inadequacy Gap in Vulnerable Populations12

    PubMed Central

    Nuss, Emily T.; Tanumihardjo, Sherry A.

    2011-01-01

    Africa shares a unique relationship with maize (Zea mays). After its introduction from New World explorers, maize was quickly adopted as the cornerstone of local cuisine, especially in sub-Saharan countries. Although maize provides macro- and micronutrients required for humans, it lacks adequate amounts of the essential amino acids lysine and tryptophan. For those consuming >50% of their daily energy from maize, pandemic protein malnutrition may exist. Severe protein and energy malnutrition increases susceptibility to life-threatening diseases such as tuberculosis and gastroenteritis. A nutritionally superior maize cultivar named quality protein maize (QPM) represents nearly one-half century of research dedicated to malnutrition eradication. Compared with traditional maize types, QPM has twice the amount of lysine and tryptophan, as well as protein bioavailability that rivals milk casein. Animal and human studies suggest that substituting QPM for common maize results in improved health. However, QPM’s practical contribution to maize-subsisting populations remains unresolved. Herein, total protein and essential amino acid requirements recommended by the WHO and the Institute of Medicine were applied to estimate QPM target intake levels for young children and adults, and these were compared with mean daily maize intakes by African country. The comparisons revealed that ∼100 g QPM is required for children to maintain adequacy of lysine, the most limiting amino acid, and nearly 500 g is required for adults. This represents a 40% reduction in maize intake relative to common maize to meet protein requirements. The importance of maize in Africa underlines the potential for QPM to assist in closing the protein inadequacy gap. PMID:22332054

  10. [Inadequacy of the content of prenatal care and associated factors in a cohort in the northeast of Brazil].

    PubMed

    Goudard, Marivanda Julia Furtado; Simões, Vanda Maria Ferreira; Batista, Rosângela Fernandes Lucena; Queiroz, Rejane Christine de Souza; Alves, Maria Tereza Seabra Soares de Brito E; Coimbra, Liberata Campos; Martins, Marília da Glória; Barbieri, Marco Antônio; Nathasje, Ian Favero

    2016-04-01

    The scope of this study was to analyze the content of prenatal care in São Luís, Maranhão, Brazil, and the factors associated with its inadequacy. A cross-sectional study was conducted based on data from the birth cohort of São Luís in 2010. The content of prenatal care was defined as inadequate when it did not meet the criteria of the Program for Humanization of Prenatal and Delivery Care, which establishes early initiation of prenatal care, minimum number of medical consultations, basic laboratory tests, tetanus vaccination and obstetric procedures. Poisson regression was used to observe associations of the variables with the outcome. The inadequacy rate was high (60.2%). The variables associated with inadequacy were: class C socioeconomic status (PR = 1.39; CI = 1.26-1.55); class D/E socioeconomic status (PR = 1.60; CI = 1.43-1.79); unqualified/unemployed mother (PR = 1.24; CI = 1.11-1.37); 5-8 years of schooling (PR = 1.12; CI = 1.06-1.19); 0-4 years of schooling (PR = 1.13; CI = 1.01-1.26); not being religious (PR = 1.10; CI = 1.04-1.17); alcohol use during pregnancy (PR = 1.13; CI = 1.06-1.20), and being attended by the public service (PR = 1.75; CI = 1.54-2.00). The results showed inadequacy and inequality of prenatal care, revealing that women of lower socioeconomic status received lower quality care. PMID:27076021

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

    PubMed Central

    Lumen, N.; Monstrey, S.; Ceulemans, P.; van Laecke, E.; Hoebeke, P.

    2008-01-01

    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. PMID:19009034

  12. Properties of plane discrete Poisson-Voronoi tessellations on triangular tiling formed by the Kolmogorov-Johnson-Mehl-Avrami growth of triangular islands

    NASA Astrophysics Data System (ADS)

    Korobov, A.

    2011-08-01

    Discrete uniform Poisson-Voronoi tessellations of two-dimensional triangular tilings resulting from the Kolmogorov-Johnson-Mehl-Avrami (KJMA) growth of triangular islands have been studied. This shape of tiles and islands, rarely considered in the field of random tessellations, is prompted by the birth-growth process of Ir(210) faceting. The growth mode determines a triangular metric different from the Euclidean metric. Kinetic characteristics of tessellations appear to be metric sensitive, in contrast to area distributions. The latter have been studied for the variant of nuclei growth to the first impingement in addition to the conventional case of complete growth. Kiang conjecture works in both cases. The averaged number of neighbors is six for all studied densities of random tessellations, but neighbors appear to be mainly different in triangular and Euclidean metrics. Also, the applicability of the obtained results for simulating birth-growth processes when the 2D nucleation and impingements are combined with the 3D growth in the particular case of similar shape and the same orientation of growing nuclei is briefly discussed.

  13. Development of Continuous Cooling Transformation Diagrams of Zirconium-Niobium Alloy Phase Transformations within the Kolmogorov-Johnson-Mehl-Avrami Framework

    NASA Astrophysics Data System (ADS)

    Kautz, Elizabeth J.

    Microstructure and chemistry of zirconium alloys have a major influence on material performance, including mechanical properties and corrosion resistance. Therefore, it is essential to thoroughly understand processing required to obtain desired microstructures for application in commercial nuclear reactors. Zirconium-niobium alloys are of particular interest for commercial nuclear applications (e.g., in boiling water reactors, pressurized water reactors, Canadian deuterium uranium reactors) due to increased corrosion resistance in aqueous environments over other zirconium alloys. Heat treatments of zirconium-niobium alloys affect overall microstructure, precipitate distributions and size, and ultimately determine material performance. Phase transformations in zirconium-niobium alloys were modeled for a range of niobium concentrations and heat treatment conditions, by conducting controlled experiments. Heat-flux differential scanning calorimetry was performed and data was collected and analyzed for zirconium-niobium alloys with niobium content ranging from 0.6-3.0 weight percent. Continuous cooling transformation diagrams were constructed for slow cooling rate conditions (9-34°C/minute) based on calorimetry test results. A standard operating procedure for performing these calorimetry tests and corresponding data analysis technique was developed specifically to study the zirconium-niobium material system. A mathematical model was developed utilizing the Kolmogorov-Johnson-Mehl-Avrami theory that accurately describes phase transformations upon continuous cooling in zirconium-niobium binary alloys. This model relates fraction of phase transformed to kinetic parameters that were calculated from experimental test results in order to model the phase transformation for various cooling rates from 10-40°C/minute.

  14. Multiple B-vitamin inadequacy amplifies alterations induced by folate depletion in p53 expression and its downstream effector MDM2

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Folate is required for biological methylation and nucleotide synthesis, and it is aberrations in these processes that are thought to be the mechanisms that enhance colorectal carcinogenesis produced by folate inadequacy. These functions of folate also depend on availability of other B-vitamins that ...

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

    PubMed Central

    Bezrati, Ikram; Ben Fradj, Mohamed Kacem; Ouerghi, Nejmeddine; Feki, Moncef; Chaouachi, Anis; Kaabachi, Naziha

    2016-01-01

    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. PMID:27113441

  16. Teaching Equations.

    ERIC Educational Resources Information Center

    Nibbelink, William H.

    1990-01-01

    Proposed is a gradual transition from arithmetic to the idea of an equation with variables in the elementary grades. Vertical and horizontal formats of open sentences, the instructional sequence, vocabulary, and levels of understanding are discussed in this article. (KR)

  17. Beautiful equations

    NASA Astrophysics Data System (ADS)

    Viljamaa, Panu; Jacobs, J. Richard; Chris; JamesHyman; Halma, Matthew; EricNolan; Coxon, Paul

    2014-07-01

    In reply to a Physics World infographic (part of which is given above) about a study showing that Euler's equation was deemed most beautiful by a group of mathematicians who had been hooked up to a functional magnetic-resonance image (fMRI) machine while viewing mathematical expressions (14 May, http://ow.ly/xHUFi).

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

    USGS Publications Warehouse

    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.

  19. Marcus equation

    DOE R&D Accomplishments Database

    1998-09-21

    In the late 1950s to early 1960s Rudolph A. Marcus developed a theory for treating the rates of outer-sphere electron-transfer reactions. Outer-sphere reactions are reactions in which an electron is transferred from a donor to an acceptor without any chemical bonds being made or broken. (Electron-transfer reactions in which bonds are made or broken are referred to as inner-sphere reactions.) Marcus derived several very useful expressions, one of which has come to be known as the Marcus cross-relation or, more simply, as the Marcus equation. It is widely used for correlating and predicting electron-transfer rates. For his contributions to the understanding of electron-transfer reactions, Marcus received the 1992 Nobel Prize in Chemistry. This paper discusses the development and use of the Marcus equation. Topics include self-exchange reactions; net electron-transfer reactions; Marcus cross-relation; and proton, hydride, atom and group transfers.

  20. Marcus equation

    SciTech Connect

    1998-11-01

    In the late 1950s to early 1960s Rudolph A. Marcus developed a theory for treating the rates of outer-sphere electron-transfer reactions. Outer-sphere reactions are reactions in which an electron is transferred from a donor to an acceptor without any chemical bonds being made or broken. (Electron-transfer reactions in which bonds are made or broken are referred to as inner-sphere reactions.) Marcus derived several very useful expressions, one of which has come to be known as the Marcus cross-relation or, more simply, as the Marcus equation. It is widely used for correlating and predicting electron-transfer rates. For his contributions to the understanding of electron-transfer reactions, Marcus received the 1992 Nobel Prize in Chemistry. This paper discusses the development and use of the Marcus equation. Topics include self-exchange reactions; net electron-transfer reactions; Marcus cross-relation; and proton, hydride, atom and group transfers.

  1. Psychometric Inadequacies of the TAAS.

    ERIC Educational Resources Information Center

    Bernal, Ernesto M.

    2000-01-01

    Examines some problems of the Texas Assessment of Academic Skills (TAAS): multiple cutoff scores for passing the test and receiving a high school diploma, and artificially "tricky" items that disproportionately confuse language-minority students. Uses factor analysis and simulations to show ways to improve item selection for the TAAS. (Contains 62…

  2. A systematic review of ultrasound-guided FNA of lesions in the head and neck—focusing on operator, sample inadequacy and presence of on-spot cytology service

    PubMed Central

    Ganguly, A; Burnside, G

    2014-01-01

    The objective of this review is to perform a systematic review of ultrasound-guided fine-needle aspiration (FNA) services for head and neck lesions with assessment of inadequacy rates and related variables such as the presence of immediate cytological assessment. A computer-based systematic search of articles in English language was performed using MEDLINE (1950 to date) from National Health Service evidence healthcare database and PubMed. Full texts of all relevant articles were obtained and scrutinized independently by two authors according to the stated inclusion and exclusion criteria. The primary search identified 932 articles, but only 78 met all the study criteria. The overall inadequacy rate was 9.3%, 16 studies had on-site evaluation by a cytopathologist/specialist clinician with a rate of 6.0%. In seven studies, a cytotechnician was available to either assess the sample or prepare the slides with an average inadequacy rate of 11.4%. In 1 study, the assessment was unclear, but the inadequacy rate for the remaining 54 studies, without immediate assessment, was 10.3%. The rate for the cytopathologist/specialist clinicians was significantly different to no on-site assessment but this was not found for assessment by cytotechnicians. The review suggests that the best results are obtained with a cytopathologist-led FNA service, where the pathologist reviews the specimen immediately, in relation to the clinical context, thereby deciding on adequacy and need for further biopsies. A systematic review looking at ultrasound-guided FNA of head and neck lesions has not been published previously. PMID:25247346

  3. Extended rate equations

    SciTech Connect

    Shore, B.W.

    1981-01-30

    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.

  4. Spin field equations and Heun's equations

    NASA Astrophysics Data System (ADS)

    Jiang, Min; Wang, Xuejing; Li, Zhongheng

    2015-06-01

    The Kerr-Newman-(anti) de Sitter metric is the most general stationary black hole solution to the Einstein-Maxwell equation with a cosmological constant. We study the separability of the equations of the massless scalar (spin s=0), neutrino ( s=1/2), electromagnetic ( s=1), Rarita-Schwinger ( s=3/2), and gravitational ( s=2) fields propagating on this background. We obtain the angular and radial master equations, and show that the master equations are transformed to Heun's equation. Meanwhile, we give the condition of existence of event horizons for Kerr-Newman-(anti) de Sitter spacetime by using Sturm theorem.

  5. Basic lubrication equations

    NASA Technical Reports Server (NTRS)

    Hamrock, B. J.; Dowson, D.

    1981-01-01

    Lubricants, usually Newtonian fluids, are assumed to experience laminar flow. The basic equations used to describe the flow are the Navier-Stokes equation of motion. The study of hydrodynamic lubrication is, from a mathematical standpoint, the application of a reduced form of these Navier-Stokes equations in association with the continuity equation. The Reynolds equation can also be derived from first principles, provided of course that the same basic assumptions are adopted in each case. Both methods are used in deriving the Reynolds equation, and the assumptions inherent in reducing the Navier-Stokes equations are specified. Because the Reynolds equation contains viscosity and density terms and these properties depend on temperature and pressure, it is often necessary to couple the Reynolds with energy equation. The lubricant properties and the energy equation are presented. Film thickness, a parameter of the Reynolds equation, is a function of the elastic behavior of the bearing surface. The governing elasticity equation is therefore presented.

  6. Turbulent flow past a backward-facing step - A critical evaluation of two-equation models

    NASA Technical Reports Server (NTRS)

    Thangam, S.; Speziale, C. G.

    1992-01-01

    The ability of two-equation models to accurately predict separated flows is analyzed from a combined theoretical and computational standpoint. Turbulent flow past a backward facing step is chosen as a test case in an effort to resolve the variety of conflicting results that were published during the past decade concerning the performance of two-equation models. It is found that the errors in the reported predictions of the k-epsilon model have two major origins: (1) numerical problems arising from inadequate resolution, and (2) inaccurate predictions for normal Reynolds stress differences arising from the use of an isotropic eddy viscosity. Inadequacies in near wall modelling play a substantially smaller role. Detailed calculations are presented which strongly indicate the standard k-epsilon model - when modified with an independently calibrated anisotropic eddy viscosity - can yield surprisingly good predictions for the backstep problem.

  7. Chemical Equation Balancing.

    ERIC Educational Resources Information Center

    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)

  8. Equations and closure methods

    NASA Technical Reports Server (NTRS)

    1977-01-01

    Basic differential equations governing compressible turbulent boundary layer flow are reviewed, including conservation of mass and energy, momentum equations derived from Navier-Stokes equations, and equations of state. Closure procedures were broken down into: (1) simple or zeroth-order methods, (2) first-order or mean field closure methods, and (3) second-order or mean turbulence field methods.

  9. Biofortified β-carotene rice improves vitamin A intake and reduces the prevalence of inadequacy among women and young children in a simulated analysis in Bangladesh, Indonesia, and the Philippines1

    PubMed Central

    Angeles-Agdeppa, Imelda; Atmarita, Atmarita; Gironella, Glen M; Muslimatun, Siti; Carriquiry, Alicia

    2016-01-01

    Background: Vitamin A deficiency continues to be a major public health problem affecting developing countries where people eat mostly rice as a staple food. In Asia, rice provides up to 80% of the total daily energy intake. Objective: We used existing data sets from Bangladesh, Indonesia, and the Philippines, where dietary intakes have been quantified at the individual level to 1) determine the rice and vitamin A intake in nonpregnant, nonlactating women of reproductive age and in nonbreastfed children 1–3 y old and 2) simulate the amount of change that could be achieved in the prevalence of inadequate intake of vitamin A if rice biofortified with β-carotene were consumed instead of the rice consumed at present. Design: We considered a range of 4–20 parts per million (ppm) of β-carotene content and 10–70% substitution levels for the biofortified rice. Software was used to estimate usual rice and vitamin A intake for the simulation analyses. Results: In an analysis by country, the substitution of biofortified rice for white rice in the optimistic scenario (20 ppm and 70% substitution) decreased the prevalence of vitamin A inadequacy from baseline 78% in women and 71% in children in Bangladesh. In Indonesia and the Philippines, the prevalence of inadequacy fell by 55–60% in women and dropped by nearly 30% in children from baseline. Conclusions: The results of the simulation analysis were striking in that even low substitution levels and modest increases in the β-carotene of rice produced a meaningful decrease in the prevalence of inadequate intake of vitamin A. Increasing the substitution levels had a greater impact than increasing the β-carotene content by >12 ppm. PMID:27510534

  10. Single wall penetration equations

    NASA Technical Reports Server (NTRS)

    Hayashida, K. B.; Robinson, J. H.

    1991-01-01

    Five single plate penetration equations are compared for accuracy and effectiveness. These five equations are two well-known equations (Fish-Summers and Schmidt-Holsapple), two equations developed by the Apollo project (Rockwell and Johnson Space Center (JSC), and one recently revised from JSC (Cour-Palais). They were derived from test results, with velocities ranging up to 8 km/s. Microsoft Excel software was used to construct a spreadsheet to calculate the diameters and masses of projectiles for various velocities, varying the material properties of both projectile and target for the five single plate penetration equations. The results were plotted on diameter versus velocity graphs for ballistic and spallation limits using Cricket Graph software, for velocities ranging from 2 to 15 km/s defined for the orbital debris. First, these equations were compared to each other, then each equation was compared with various aluminum projectile densities. Finally, these equations were compared with test results performed at JSC for the Marshall Space Flight Center. These equations predict a wide variety of projectile diameters at a given velocity. Thus, it is very difficult to choose the 'right' prediction equation. The thickness of a single plate could have a large variation by choosing a different penetration equation. Even though all five equations are empirically developed with various materials, especially for aluminum alloys, one cannot be confident in the shield design with the predictions obtained by the penetration equations without verifying by tests.

  11. Nucleation and growth transformation kinetics

    NASA Astrophysics Data System (ADS)

    Erukhimovitch, V.; Baram, J.

    1995-03-01

    As a result of the reassessment of the Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory for the kinetics of nucleation and growth transformations, an integral-equation formulation has been developed instead of the well-known and widely used Avrami equation. The presented formulation considers interfacial and diffusional growths, in one, two, and three dimensions, with both time-dependent and time-invariant nucleation and growth rates. The integral-equation model corrects reported inadequacies of the KJMA theory when applied in numerous experiments and various solid-state transformations. It is shown that in the example cases examined in this paper, crystallization from the amorphous state in melt-spun ribbons, isothermal aging of CuAlZn, pearlitic transition in an eutectoid steel, and crystallization in a PEKK polymer, the thermodynamic and kinetic interpretation and parameters extracted from best fits of the Avrami equations to the experimental data are erroneous. The KJMA formulation is a simplification of the real physical conditions. The main limitation of the new model is that almost all the integral equations representing the kinetics of solid-state transformations have no analytical solutions.

  12. Interpretation of Bernoulli's Equation.

    ERIC Educational Resources Information Center

    Bauman, Robert P.; Schwaneberg, Rolf

    1994-01-01

    Discusses Bernoulli's equation with regards to: horizontal flow of incompressible fluids, change of height of incompressible fluids, gases, liquids and gases, and viscous fluids. Provides an interpretation, properties, terminology, and applications of Bernoulli's equation. (MVL)

  13. Reflections on Chemical Equations.

    ERIC Educational Resources Information Center

    Gorman, Mel

    1981-01-01

    The issue of how much emphasis balancing chemical equations should have in an introductory chemistry course is discussed. The current heavy emphasis on finishing such equations is viewed as misplaced. (MP)

  14. The Pendulum Equation

    ERIC Educational Resources Information Center

    Fay, Temple H.

    2002-01-01

    We investigate the pendulum equation [theta] + [lambda][squared] sin [theta] = 0 and two approximations for it. On the one hand, we suggest that the third and fifth-order Taylor series approximations for sin [theta] do not yield very good differential equations to approximate the solution of the pendulum equation unless the initial conditions are…

  15. Solving Ordinary Differential Equations

    NASA Technical Reports Server (NTRS)

    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.

  16. Einstein equation at singularities

    NASA Astrophysics Data System (ADS)

    Stoica, Ovidiu-Cristinel

    2014-02-01

    Einstein's equation is rewritten in an equivalent form, which remains valid at the singularities in some major cases. These cases include the Schwarzschild singularity, the Friedmann-Lemaître-Robertson-Walker Big Bang singularity, isotropic singularities, and a class of warped product singularities. This equation is constructed in terms of the Ricci part of the Riemann curvature (as the Kulkarni-Nomizu product between Einstein's equation and the metric tensor).

  17. What Makes a Chemical Equation an Equation?

    ERIC Educational Resources Information Center

    Fensham, Peter J.; Lui, Julia

    2001-01-01

    Explores how well chemistry graduates preparing for teaching can recognize the similarities and differences between the uses of the word "equation" in mathematics and in chemistry. Reports that the conservation similarities were much less frequently recognized than those involved in the creation of new entities. (Author/MM)

  18. Octonic Gravitational Field Equations

    NASA Astrophysics Data System (ADS)

    Demir, Süleyman; Tanişli, Murat; Tolan, Tülay

    2013-08-01

    Generalized field equations of linear gravity are formulated on the basis of octons. When compared to the other eight-component noncommutative hypercomplex number systems, it is demonstrated that associative octons with scalar, pseudoscalar, pseudovector and vector values present a convenient and capable tool to describe the Maxwell-Proca-like field equations of gravitoelectromagnetism in a compact and simple way. Introducing massive graviton and gravitomagnetic monopole terms, the generalized gravitational wave equation and Klein-Gordon equation for linear gravity are also developed.

  19. Octonic massless field equations

    NASA Astrophysics Data System (ADS)

    Demir, Süleyman; Tanişli, Murat; Kansu, Mustafa Emre

    2015-05-01

    In this paper, it is proven that the associative octons including scalar, pseudoscalar, pseudovector and vector values are convenient and capable tools to generalize the Maxwell-Dirac like field equations of electromagnetism and linear gravity in a compact and simple way. Although an attempt to describe the massless field equations of electromagnetism and linear gravity needs the sixteen real component mathematical structures, it is proved that these equations can be formulated in terms of eight components of octons. Furthermore, the generalized wave equation in terms of potentials is derived in the presence of electromagnetic and gravitational charges (masses). Finally, conservation of energy concept has also been investigated for massless fields.

  20. Turbulent separated flow past a backward-facing step: A critical evaluation of two-equation turbulence models

    NASA Technical Reports Server (NTRS)

    Thangam, S.; Speziale, C. G.

    1991-01-01

    The ability of two-equation models to accurately predict separated flows is analyzed from a combined theoretical and computational standpoint. Turbulent flow past a backward facing step is chosen as a test case in an effort to resolve the variety of conflicting results that were published during the past decade concerning the performance of two-equation models. It is found that the errors in the reported predictions of the k-epsilon model have two major origins: (1) numerical problems arising from inadequate resolution, and (2) inaccurate predictions for normal Reynolds stress differences arising from the use of an isotropic eddy viscosity. Inadequacies in near wall modelling play a substantially smaller role. Detailed calculations are presented which strongly indicate the standard k-epsilon model - when modified with an independently calibrated anisotropic eddy viscosity - can yield surprisingly good predictions for the backstep problem.

  1. Octonic Massive Field Equations

    NASA Astrophysics Data System (ADS)

    Demir, Süleyman; Kekeç, Seray

    2016-03-01

    In the present paper we propose the octonic form of massive field equations based on the analogy with electromagnetism and linear gravity. Using the advantages of octon algebra the Maxwell-Dirac-Proca equations have been reformulated in compact and elegant way. The energy-momentum relations for massive field are discussed.

  2. On the Diophantine equation

    NASA Astrophysics Data System (ADS)

    Zahari, N. M.; Sapar, S. H.; Mohd Atan, K. A.

    2013-04-01

    This paper discusses an integral solution (a, b, c) of the Diophantine equations x3n+y3n = 2z2n for n ≥ 2 and it is found that the integral solution of these equation are of the form a = b = t2, c = t3 for any integers t.

  3. The lens equation revisited

    NASA Astrophysics Data System (ADS)

    Molesini, Giuseppe

    2005-02-01

    Problems in the general validity of the lens equations are reported, requiring an assessment of the conditions for correct use. A discussion is given on critical behaviour of the lens equation, and a sign and meaning scheme is provided so that apparent inconsistencies are avoided.

  4. Octonic Massive Field Equations

    NASA Astrophysics Data System (ADS)

    Demir, Süleyman; Kekeç, Seray

    2016-07-01

    In the present paper we propose the octonic form of massive field equations based on the analogy with electromagnetism and linear gravity. Using the advantages of octon algebra the Maxwell-Dirac-Proca equations have been reformulated in compact and elegant way. The energy-momentum relations for massive field are discussed.

  5. Reduced Braginskii equations

    SciTech Connect

    Yagi, M.; Horton, W. )

    1994-07-01

    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 the perpendicular component of Ohm's law be solved to ensure [del][center dot][bold j]=0 for energy conservation.

  6. Linear Equations: Equivalence = Success

    ERIC Educational Resources Information Center

    Baratta, Wendy

    2011-01-01

    The ability to solve linear equations sets students up for success in many areas of mathematics and other disciplines requiring formula manipulations. There are many reasons why solving linear equations is a challenging skill for students to master. One major barrier for students is the inability to interpret the equals sign as anything other than…

  7. The Effective Equation Method

    NASA Astrophysics Data System (ADS)

    Kuksin, Sergei; Maiocchi, Alberto

    In this chapter we present a general method of constructing the effective equation which describes the behavior of small-amplitude solutions for a nonlinear PDE in finite volume, provided that the linear part of the equation is a hamiltonian system with a pure imaginary discrete spectrum. The effective equation is obtained by retaining only the resonant terms of the nonlinearity (which may be hamiltonian, or may be not); the assertion that it describes the limiting behavior of small-amplitude solutions is a rigorous mathematical theorem. In particular, the method applies to the three- and four-wave systems. We demonstrate that different possible types of energy transport are covered by this method, depending on whether the set of resonances splits into finite clusters (this happens, e.g. in case of the Charney-Hasegawa-Mima equation), or is connected (this happens, e.g. in the case of the NLS equation if the space-dimension is at least two). For equations of the first type the energy transition to high frequencies does not hold, while for equations of the second type it may take place. Our method applies to various weakly nonlinear wave systems, appearing in plasma, meteorology and oceanography.

  8. Nonlinear gyrokinetic equations

    SciTech Connect

    Dubin, D.H.E.; Krommes, J.A.; Oberman, C.; Lee, W.W.

    1983-03-01

    Nonlinear gyrokinetic equations are derived from a systematic Hamiltonian theory. The derivation employs Lie transforms and a noncanonical perturbation theory first used by Littlejohn for the simpler problem of asymptotically small gyroradius. For definiteness, we emphasize the limit of electrostatic fluctuations in slab geometry; however, there is a straight-forward generalization to arbitrary field geometry and electromagnetic perturbations. An energy invariant for the nonlinear system is derived, and various of its limits are considered. The weak turbulence theory of the equations is examined. In particular, the wave kinetic equation of Galeev and Sagdeev is derived from an asystematic truncation of the equations, implying that this equation fails to consider all gyrokinetic effects. The equations are simplified for the case of small but finite gyroradius and put in a form suitable for efficient computer simulation. Although it is possible to derive the Terry-Horton and Hasegawa-Mima equations as limiting cases of our theory, several new nonlinear terms absent from conventional theories appear and are discussed.

  9. Volterra difference equations

    NASA Astrophysics Data System (ADS)

    Sultana, Nasrin

    This dissertation consists of five papers in which discrete Volterra equations of different types and orders are studied and results regarding the behavior of their solutions are established. The first paper presents some fundamental results about subexponential sequences. It also illustrates the subexponential solutions of scalar linear Volterra sum-difference equations are asymptotically stable. The exact value of the rate of convergence of asymptotically stable solutions is found by determining the asymptotic behavior of the transient renewal equations. The study of subexponential solutions is also continued in the second and third articles. The second paper investigates the same equation using the same process as considered in the first paper. The discussion focuses on a positive lower bound of the rate of convergence of the asymptotically stable solutions. The third paper addresses the rate of convergence of the solutions of scalar linear Volterra sum-difference equations with delay. The result is proved by developing the rate of convergence of transient renewal delay difference equations. The fourth paper discusses the existence of bounded solutions on an unbounded domain of more general nonlinear Volterra sum-difference equations using the Schaefer fixed point theorem and the Lyapunov direct method. The fifth paper examines the asymptotic behavior of nonoscillatory solutions of higher-order integro-dynamic equations and establishes some new criteria based on so-called time scales, which unifies and extends both discrete and continuous mathematical analysis. Beside these five research papers that focus on discrete Volterra equations, this dissertation also contains an introduction, a section on difference calculus, a section on time scales calculus, and a conclusion.

  10. Stochastic Gauss equations

    NASA Astrophysics Data System (ADS)

    Pierret, Frédéric

    2016-02-01

    We derived the equations of Celestial Mechanics governing the variation of the orbital elements under a stochastic perturbation, thereby generalizing the classical Gauss equations. Explicit formulas are given for the semimajor axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle, and the mean anomaly, which are expressed in term of the angular momentum vector H per unit of mass and the energy E per unit of mass. Together, these formulas are called the stochastic Gauss equations, and they are illustrated numerically on an example from satellite dynamics.

  11. Nonlinear ordinary difference equations

    NASA Technical Reports Server (NTRS)

    Caughey, T. K.

    1979-01-01

    Future space vehicles will be relatively large and flexible, and active control will be necessary to maintain geometrical configuration. While the stresses and strains in these space vehicles are not expected to be excessively large, their cumulative effects will cause significant geometrical nonlinearities to appear in the equations of motion, in addition to the nonlinearities caused by material properties. Since the only effective tool for the analysis of such large complex structures is the digital computer, it will be necessary to gain a better understanding of the nonlinear ordinary difference equations which result from the time discretization of the semidiscrete equations of motion for such structures.

  12. Inadequacy of dipstick proteinuria in hypertensive pregnancy.

    PubMed

    Brown, M A; Buddle, M L

    1995-11-01

    The objective of this study was to determine the accuracy of ward urinalysis and the sensitivity of dipstick testing in the assessment of proteinuria in hypertensive pregnant women. Subjects were 230 consecutive hypertensive pregnant women who were admitted to hospital over a 2-year period. Routine ward urinalyses for protein, obtained on a mid-stream sample before and after a 24-hour urine collection for quantitating proteinuria, were compared with the 24-hour urine protein excretion. As a control for dipstick accuracy, urinalysis was also performed on a mixed aliquot of each of the 24-hour samples by a single observer experienced in urinalysis. True proteinuria was considered as > 300 mg/day. The positive predictive value for urinalysis ranged from 38% (for the precollection test) to 60% (for tests on the aliquot). Negative predictive values were 86-88%. The false negative rates at 'nil' or 'trace' proteinuria ranged from 8-18%. The false positive rates at '3+' (3 g/L) or '4+' (> or = 20 g/L) ranged from 0-17%, at '2+' (1 g/L) from 18-50% and at '1+' (0.3 g/L) from 67-83%. Best results for urinalysis were obtained on the aliquot testing but even under these ideal circumstances there was a high false positive rate (67%) at '1+' (0.3 g/L) urinalysis level. These studies show that in routine clinical practice 'nil' or 'trace' proteinuria will miss significant proteinuria in approximately 1 out of 8 hypertensive pregnant women while '3+' (3 g/L) or '4+' ( > or = 20 g/L) will rarely be a false positive. At urinalysis of '1+' or '2+' a 24-hour urine collection is required to be certain about the presence or absence of proteinuria. Research studies should demand 24-hour urine protein quantitation and not rely solely upon urinalysis results. PMID:8717555

  13. A Comparison of IRT Equating and Beta 4 Equating.

    ERIC Educational Resources Information Center

    Kim, Dong-In; Brennan, Robert; Kolen, Michael

    Four equating methods were compared using four equating criteria: first-order equity (FOE), second-order equity (SOE), conditional mean squared error (CMSE) difference, and the equipercentile equating property. The four methods were: (1) three parameter logistic (3PL) model true score equating; (2) 3PL observed score equating; (3) beta 4 true…

  14. Diophantine Equations and Computation

    NASA Astrophysics Data System (ADS)

    Davis, Martin

    Unless otherwise stated, we’ll work with the natural numbers: N = \\{0,1,2,3, dots\\}. Consider a Diophantine equation F(a1,a2,...,an,x1,x2,...,xm) = 0 with parameters a1,a2,...,an and unknowns x1,x2,...,xm For such a given equation, it is usual to ask: For which values of the parameters does the equation have a solution in the unknowns? In other words, find the set: \\{ mid exists x_1,ldots,x_m [F(a_1,ldots,x_1,ldots)=0] \\} Inverting this, we think of the equation F = 0 furnishing a definition of this set, and we distinguish three classes: a set is called Diophantine if it has such a definition in which F is a polynomial with integer coefficients. We write \\cal D for the class of Diophantine sets.

  15. Regularized Structural Equation Modeling

    PubMed Central

    Jacobucci, Ross; Grimm, Kevin J.; McArdle, John J.

    2016-01-01

    A new method is proposed that extends the use of regularization in both lasso and ridge regression to structural equation models. The method is termed regularized structural equation modeling (RegSEM). RegSEM penalizes specific parameters in structural equation models, with the goal of creating easier to understand and simpler models. Although regularization has gained wide adoption in regression, very little has transferred to models with latent variables. By adding penalties to specific parameters in a structural equation model, researchers have a high level of flexibility in reducing model complexity, overcoming poor fitting models, and the creation of models that are more likely to generalize to new samples. The proposed method was evaluated through a simulation study, two illustrative examples involving a measurement model, and one empirical example involving the structural part of the model to demonstrate RegSEM’s utility. PMID:27398019

  16. Nonlinear differential equations

    SciTech Connect

    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.

  17. Equations For Rotary Transformers

    NASA Technical Reports Server (NTRS)

    Salomon, Phil M.; Wiktor, Peter J.; Marchetto, Carl A.

    1988-01-01

    Equations derived for input impedance, input power, and ratio of secondary current to primary current of rotary transformer. Used for quick analysis of transformer designs. Circuit model commonly used in textbooks on theory of ac circuits.

  18. Equating Training to Education.

    ERIC Educational Resources Information Center

    Davis, Lansing J.

    1993-01-01

    Distinguishes between education and employer-sponsored training in terms of process, purpose, and providers. Concludes that work-related training and postsecondary education are cognates within the classification education, and equating their learning outcomes is appropriate. (SK)

  19. Relativistic Guiding Center Equations

    SciTech Connect

    White, R. B.; Gobbin, M.

    2014-10-01

    In toroidal fusion devices it is relatively easy that electrons achieve relativistic velocities, so to simulate runaway electrons and other high energy phenomena a nonrelativistic guiding center formalism is not sufficient. Relativistic guiding center equations including flute mode time dependent field perturbations are derived. The same variables as used in a previous nonrelativistic guiding center code are adopted, so that a straightforward modifications of those equations can produce a relativistic version.

  20. SIMULTANEOUS DIFFERENTIAL EQUATION COMPUTER

    DOEpatents

    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.

  1. Set Equation Transformation System.

    Energy Science and Technology Software Center (ESTSC)

    2002-03-22

    Version 00 SETS is used for symbolic manipulation of Boolean equations, particularly the reduction of equations by the application of Boolean identities. It is a flexible and efficient tool for performing probabilistic risk analysis (PRA), vital area analysis, and common cause analysis. The equation manipulation capabilities of SETS can also be used to analyze noncoherent fault trees and determine prime implicants of Boolean functions, to verify circuit design implementation, to determine minimum cost fire protectionmore » requirements for nuclear reactor plants, to obtain solutions to combinatorial optimization problems with Boolean constraints, and to determine the susceptibility of a facility to unauthorized access through nullification of sensors in its protection system. Two auxiliary programs, SEP and FTD, are included. SEP performs the quantitative analysis of reduced Boolean equations (minimal cut sets) produced by SETS. The user can manipulate and evaluate the equations to find the probability of occurrence of any desired event and to produce an importance ranking of the terms and events in an equation. FTD is a fault tree drawing program which uses the proprietary ISSCO DISSPLA graphics software to produce an annotated drawing of a fault tree processed by SETS. The DISSPLA routines are not included.« less

  2. O the Derivation of the Schroedinger Equation from Stochastic Mechanics.

    NASA Astrophysics Data System (ADS)

    Wallstrom, Timothy Clarke

    The thesis is divided into four largely independent chapters. The first three chapters treat mathematical problems in the theory of stochastic mechanics. The fourth chapter deals with stochastic mechanisms as a physical theory and shows that the Schrodinger equation cannot be derived from existing formulations of stochastic mechanics, as had previously been believed. Since the drift coefficients of stochastic mechanical diffusions are undefined on the nodes, or zeros of the density, an important problem has been to show that the sample paths stay away from the nodes. In Chapter 1, it is shown that for a smooth wavefunction, the closest approach to the nodes can be bounded solely in terms of the time -integrated energy. The ergodic properties of stochastic mechanical diffusions are greatly complicated by the tendency of the particles to avoid the nodes. In Chapter 2, it is shown that a sufficient condition for a stationary process to be ergodic is that there exist positive t and c such that for all x and y, p^{t} (x,y) > cp(y), and this result is applied to show that the set of spin-1over2 diffusions is uniformly ergodic. In stochastic mechanics, the Bopp-Haag-Dankel diffusions on IR^3times SO(3) are used to represent particles with spin. Nelson has conjectured that in the limit as the particle's moment of inertia I goes to zero, the projections of the Bopp -Haag-Dankel diffusions onto IR^3 converge to a Markovian limit process. This conjecture is proved for the spin-1over2 case in Chapter 3, and the limit process identified as the diffusion naturally associated with the solution to the regular Pauli equation. In Chapter 4 it is shown that the general solution of the stochastic Newton equation does not correspond to a solution of the Schrodinger equation, and that there are solutions to the Schrodinger equation which do not satisfy the Guerra-Morato Lagrangian variational principle. These observations are shown to apply equally to other existing formulations of

  3. The Bernoulli-Poiseuille Equation.

    ERIC Educational Resources Information Center

    Badeer, Henry S.; Synolakis, Costas E.

    1989-01-01

    Describes Bernoulli's equation and Poiseuille's equation for fluid dynamics. Discusses the application of the combined Bernoulli-Poiseuille equation in real flows, such as viscous flows under gravity and acceleration. (YP)

  4. Introducing Chemical Formulae and Equations.

    ERIC Educational Resources Information Center

    Dawson, Chris; Rowell, Jack

    1979-01-01

    Discusses when the writing of chemical formula and equations can be introduced in the school science curriculum. Also presents ways in which formulae and equations learning can be aided and some examples for balancing and interpreting equations. (HM)

  5. Nonlocal electrical diffusion equation

    NASA Astrophysics Data System (ADS)

    Gómez-Aguilar, J. F.; Escobar-Jiménez, R. F.; Olivares-Peregrino, V. H.; Benavides-Cruz, M.; Calderón-Ramón, C.

    2016-07-01

    In this paper, we present an analysis and modeling of the electrical diffusion equation using the fractional calculus approach. This alternative representation for the current density is expressed in terms of the Caputo derivatives, the order for the space domain is 0<β≤1 and for the time domain is 0<γ≤2. We present solutions for the full fractional equation involving space and time fractional derivatives using numerical methods based on Fourier variable separation. The case with spatial fractional derivatives leads to Levy flight type phenomena, while the time fractional equation is related to sub- or super diffusion. We show that the mathematical concept of fractional derivatives can be useful to understand the behavior of semiconductors, the design of solar panels, electrochemical phenomena and the description of anomalous complex processes.

  6. Parallel tridiagonal equation solvers

    NASA Technical Reports Server (NTRS)

    Stone, H. S.

    1974-01-01

    Three parallel algorithms were compared for the direct solution of tridiagonal linear systems of equations. The algorithms are suitable for computers such as ILLIAC 4 and CDC STAR. For array computers similar to ILLIAC 4, cyclic odd-even reduction has the least operation count for highly structured sets of equations, and recursive doubling has the least count for relatively unstructured sets of equations. Since the difference in operation counts for these two algorithms is not substantial, their relative running times may be more related to overhead operations, which are not measured in this paper. The third algorithm, based on Buneman's Poisson solver, has more arithmetic operations than the others, and appears to be the least favorable. For pipeline computers similar to CDC STAR, cyclic odd-even reduction appears to be the most preferable algorithm for all cases.

  7. Body Fat Equations and Electrical Bioimpedance Values in Prediction of Cardiovascular Risk Factors in Eutrophic and Overweight Adolescents

    PubMed Central

    Faria, Franciane Rocha; Faria, Eliane Rodrigues; Cecon, Roberta Stofeles; Barbosa Júnior, Djalma Adão; Franceschini, Sylvia do Carmo Castro; Peluzio, Maria do Carmo Gouveia; Ribeiro, Andréia Queiroz; Lira, Pedro Israel Cabral; Cecon, Paulo Roberto; Priore, Silvia Eloiza

    2013-01-01

    The aim of this study was to analyze body fat anthropometric equations and electrical bioimpedance analysis (BIA) in the prediction of cardiovascular risk factors in eutrophic and overweight adolescents. 210 adolescents were divided into eutrophic group (G1) and overweight group (G2). The percentage of body fat (% BF) was estimated using 10 body fat anthropometric equations and 2 BIA. We measured lipid profiles, uric acid, insulin, fasting glucose, homeostasis model assessment-insulin resistance (HOMA-IR), and blood pressure. We found that 76.7% of the adolescents exhibited inadequacy of at least one biochemical parameter or clinical cardiovascular risk. Higher values of triglycerides (TG) (P = 0.001), insulin, and HOMA-IR (P < 0.001) were observed in the G2 adolescents. In multivariate linear regression analysis, the % BF from equation (5) was associated with TG, diastolic blood pressure, and insulin in G1. Among the G2 adolescents, the % BF estimated by (5) and (9) was associated with LDL, TG, insulin, and the HOMA-IR. Body fat anthropometric equations were associated with cardiovascular risk factors and should be used to assess the nutritional status of adolescents. In this study, equation (5) was associated with a higher number of cardiovascular risk factors independent of the nutritional status of adolescents. PMID:23762051

  8. Kepler Equation solver

    NASA Technical Reports Server (NTRS)

    Markley, F. Landis

    1995-01-01

    Kepler's Equation is solved over the entire range of elliptic motion by a fifth-order refinement of the solution of a cubic equation. This method is not iterative, and requires only four transcendental function evaluations: a square root, a cube root, and two trigonometric functions. The maximum relative error of the algorithm is less than one part in 10(exp 18), exceeding the capability of double-precision computer arithmetic. Roundoff errors in double-precision implementation of the algorithm are addressed, and procedures to avoid them are developed.

  9. Difference equation for superradiance

    NASA Technical Reports Server (NTRS)

    Lee, C. T.

    1974-01-01

    The evolution of a completely excited system of N two-level atoms, distributed over a large region and interacting with all modes of radiation field, is studied. The distinction between r-conserving (RC) and r-nonconserving (RNC) processes is emphasized. Considering the number of photons emitted as the discrete independent variable, the evolution is described by a partial difference equation. Numerical solution of this equation shows the transition from RNC dominance at the beginning to RC dominance later. This is also a transition from incoherent to coherent emission of radiation.

  10. Obtaining Maxwell's equations heuristically

    NASA Astrophysics Data System (ADS)

    Diener, Gerhard; Weissbarth, Jürgen; Grossmann, Frank; Schmidt, Rüdiger

    2013-02-01

    Starting from the experimental fact that a moving charge experiences the Lorentz force and applying the fundamental principles of simplicity (first order derivatives only) and linearity (superposition principle), we show that the structure of the microscopic Maxwell equations for the electromagnetic fields can be deduced heuristically by using the transformation properties of the fields under space inversion and time reversal. Using the experimental facts of charge conservation and that electromagnetic waves propagate with the speed of light, together with Galilean invariance of the Lorentz force, allows us to finalize Maxwell's equations and to introduce arbitrary electrodynamics units naturally.

  11. The halo Boltzmann equation

    NASA Astrophysics Data System (ADS)

    Biagetti, Matteo; Desjacques, Vincent; Kehagias, Alex; Racco, Davide; Riotto, Antonio

    2016-04-01

    Dark matter halos are the building blocks of the universe as they host galaxies and clusters. The knowledge of the clustering properties of halos is therefore essential for the understanding of the galaxy statistical properties. We derive an effective halo Boltzmann equation which can be used to describe the halo clustering statistics. In particular, we show how the halo Boltzmann equation encodes a statistically biased gravitational force which generates a bias in the peculiar velocities of virialized halos with respect to the underlying dark matter, as recently observed in N-body simulations.

  12. The Statistical Drake Equation

    NASA Astrophysics Data System (ADS)

    Maccone, Claudio

    2010-12-01

    We provide the statistical generalization of the Drake equation. From a simple product of seven positive numbers, the Drake equation is now turned into the product of seven positive random variables. We call this "the Statistical Drake Equation". The mathematical consequences of this transformation are then derived. The proof of our results is based on the Central Limit Theorem (CLT) of Statistics. In loose terms, the CLT states that the sum of any number of independent random variables, each of which may be ARBITRARILY distributed, approaches a Gaussian (i.e. normal) random variable. This is called the Lyapunov Form of the CLT, or the Lindeberg Form of the CLT, depending on the mathematical constraints assumed on the third moments of the various probability distributions. In conclusion, we show that: The new random variable N, yielding the number of communicating civilizations in the Galaxy, follows the LOGNORMAL distribution. Then, as a consequence, the mean value of this lognormal distribution is the ordinary N in the Drake equation. The standard deviation, mode, and all the moments of this lognormal N are also found. The seven factors in the ordinary Drake equation now become seven positive random variables. The probability distribution of each random variable may be ARBITRARY. The CLT in the so-called Lyapunov or Lindeberg forms (that both do not assume the factors to be identically distributed) allows for that. In other words, the CLT "translates" into our statistical Drake equation by allowing an arbitrary probability distribution for each factor. This is both physically realistic and practically very useful, of course. An application of our statistical Drake equation then follows. The (average) DISTANCE between any two neighboring and communicating civilizations in the Galaxy may be shown to be inversely proportional to the cubic root of N. Then, in our approach, this distance becomes a new random variable. We derive the relevant probability density

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

    ERIC Educational Resources Information Center

    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…

  14. Balancing Chemical Equations.

    ERIC Educational Resources Information Center

    Savoy, L. G.

    1988-01-01

    Describes a study of students' ability to balance equations. Answers to a test on this topic were analyzed to determine the level of understanding and processes used by the students. Presented is a method to teach this skill to high school chemistry students. (CW)

  15. Structural Equation Model Trees

    ERIC Educational Resources Information Center

    Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman

    2013-01-01

    In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree…

  16. Parallel Multigrid Equation Solver

    Energy Science and Technology Software Center (ESTSC)

    2001-09-07

    Prometheus is a fully parallel multigrid equation solver for matrices that arise in unstructured grid finite element applications. It includes a geometric and an algebraic multigrid method and has solved problems of up to 76 mullion degrees of feedom, problems in linear elasticity on the ASCI blue pacific and ASCI red machines.

  17. A Quadratic Spring Equation

    ERIC Educational Resources Information Center

    Fay, Temple H.

    2010-01-01

    Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…

  18. Generalized reduced magnetohydrodynamic equations

    SciTech Connect

    Kruger, S.E.

    1999-02-01

    A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson. The equations have been programmed into a spectral initial value code and run with shear flow that is consistent with the equilibrium input into the code. Linear results of tearing modes with shear flow are presented which differentiate the effects of shear flow gradients in the layer with the effects of the shear flow decoupling multiple harmonics.

  19. Modelling by Differential Equations

    ERIC Educational Resources Information Center

    Chaachoua, Hamid; Saglam, Ayse

    2006-01-01

    This paper aims to show the close relation between physics and mathematics taking into account especially the theory of differential equations. By analysing the problems posed by scientists in the seventeenth century, we note that physics is very important for the emergence of this theory. Taking into account this analysis, we show the…

  20. Do Differential Equations Swing?

    ERIC Educational Resources Information Center

    Maruszewski, Richard F., Jr.

    2006-01-01

    One of the units of in a standard differential equations course is a discussion of the oscillatory motion of a spring and the associated material on forcing functions and resonance. During the presentation on practical resonance, the instructor may tell students that it is similar to when they take their siblings to the playground and help them on…

  1. Supersymmetric fifth order evolution equations

    SciTech Connect

    Tian, K.; Liu, Q. P.

    2010-03-08

    This paper considers supersymmetric fifth order evolution equations. Within the framework of symmetry approach, we give a list containing six equations, which are (potentially) integrable systems. Among these equations, the most interesting ones include a supersymmetric Sawada-Kotera equation and a novel supersymmetric fifth order KdV equation. For the latter, we supply some properties such as a Hamiltonian structures and a possible recursion operator.

  2. Brownian motion from Boltzmann's equation.

    NASA Technical Reports Server (NTRS)

    Montgomery, D.

    1971-01-01

    Two apparently disparate lines of inquiry in kinetic theory are shown to be equivalent: (1) Brownian motion as treated by the (stochastic) Langevin equation and Fokker-Planck equation; and (2) Boltzmann's equation. The method is to derive the kinetic equation for Brownian motion from the Boltzmann equation for a two-component neutral gas by a simultaneous expansion in the density and mass ratios.

  3. Causal electromagnetic interaction equations

    SciTech Connect

    Zinoviev, Yury M.

    2011-02-15

    For the electromagnetic interaction of two particles the relativistic causal quantum mechanics equations are proposed. These equations are solved for the case when the second particle moves freely. The initial wave functions are supposed to be smooth and rapidly decreasing at the infinity. This condition is important for the convergence of the integrals similar to the integrals of quantum electrodynamics. We also consider the singular initial wave functions in the particular case when the second particle mass is equal to zero. The discrete energy spectrum of the first particle wave function is defined by the initial wave function of the free-moving second particle. Choosing the initial wave functions of the free-moving second particle it is possible to obtain a practically arbitrary discrete energy spectrum.

  4. Biaxial constitutive equation development

    NASA Technical Reports Server (NTRS)

    Jordan, E. H.; Walker, K. P.

    1984-01-01

    In developing the constitutive equations an interdisciplinary approach is being pursued. Specifically, both metallurgical and continuum mechanics considerations are recognized in the formulation. Experiments will be utilized to both explore general qualitative features of the material behavior that needs to be modeled and to provide a means of assessing the validity of the equations being developed. The model under development explicitly recognizes crystallographic slip on the individual slip systems. This makes possible direct representation of specific slip system phenomena. The present constitutive formulation takes the anisotropic creep theory and incorporates two state variables into the model to account for the effect of prior inelastic deformation history on the current rate-dependent response of the material.

  5. Nikolaevskiy equation with dispersion.

    PubMed

    Simbawa, Eman; Matthews, Paul C; Cox, Stephen M

    2010-03-01

    The Nikolaevskiy equation was originally proposed as a model for seismic waves and is also a model for a wide variety of systems incorporating a neutral "Goldstone" mode, including electroconvection and reaction-diffusion systems. It is known to exhibit chaotic dynamics at the onset of pattern formation, at least when the dispersive terms in the equation are suppressed, as is commonly the practice in previous analyses. In this paper, the effects of reinstating the dispersive terms are examined. It is shown that such terms can stabilize some of the spatially periodic traveling waves; this allows us to study the loss of stability and transition to chaos of the waves. The secondary stability diagram ("Busse balloon") for the traveling waves can be remarkably complicated. PMID:20365845

  6. Singularities for PRANDTL'S Equations

    NASA Astrophysics Data System (ADS)

    Lo Bosco, G.; Sammartino, M.; Sciacca, V.

    2006-03-01

    We use a mixed spectral/finite-difference numerical method to investigate the possibility of a finite time blow-up of the solutions of Prandtl's equations for the case of the impulsively started cylinder. Our tool is the complex singularity tracking method. We show that a cubic root singularity seems to develop, in a time that can be made arbitrarily short, from a class of data uniformly bounded in H1.

  7. Multinomial diffusion equation

    NASA Astrophysics Data System (ADS)

    Balter, Ariel; Tartakovsky, Alexandre M.

    2011-06-01

    We describe a new, microscopic model for diffusion that captures diffusion induced fluctuations at scales where the concept of concentration gives way to discrete particles. We show that in the limit as the number of particles N→∞, our model is equivalent to the classical stochastic diffusion equation (SDE). We test our new model and the SDE against Langevin dynamics in numerical simulations, and show that our model successfully reproduces the correct ensemble statistics, while the classical model fails.

  8. Multinomial diffusion equation

    SciTech Connect

    Balter, Ariel I.; Tartakovsky, Alexandre M.

    2011-06-24

    We describe a new, microscopic model for diffusion that captures diffusion induced uctuations at scales where the concept of concentration gives way to discrete par- ticles. We show that in the limit as the number of particles N ! 1, our model is equivalent to the classical stochastic diffusion equation (SDE). We test our new model and the SDE against Langevin dynamics in numerical simulations, and show that our model successfully reproduces the correct ensemble statistics, while the classical model fails.

  9. Student-Generated Equations

    ERIC Educational Resources Information Center

    Vasile, Daniela

    2012-01-01

    We are frequently told that Hong Kong has a model system for learning mathematics. In this article Daniela Vasile notes one short-coming in that the pupils are not taught to problem-solve. She begins with a new class by asking them to write down the craziest equation they can come up with and bases her whole lesson, and the following homework,…

  10. Generalized reduced MHD equations

    SciTech Connect

    Kruger, S.E.; Hegna, C.C.; Callen, J.D.

    1998-07-01

    A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson.

  11. The Drake Equation revisited

    NASA Astrophysics Data System (ADS)

    Konesky, Gregory

    2009-08-01

    In the almost half century since the Drake Equation was first conceived, a number of profound discoveries have been made that require each of the seven variables of this equation to be reconsidered. The discovery of hydrothermal vents on the ocean floor, for example, as well as the ever-increasing extreme conditions in which life is found on Earth, suggest a much wider range of possible extraterrestrial habitats. The growing consensus that life originated very early in Earth's history also supports this suggestion. The discovery of exoplanets with a wide range of host star types, and attendant habitable zones, suggests that life may be possible in planetary systems with stars quite unlike our Sun. Stellar evolution also plays an important part in that habitable zones are mobile. The increasing brightness of our Sun over the next few billion years, will place the Earth well outside the present habitable zone, but will then encompass Mars, giving rise to the notion that some Drake Equation variables, such as the fraction of planets on which life emerges, may have multiple values.

  12. Shock wave structure using nonlinear model Boltzmann equations

    NASA Technical Reports Server (NTRS)

    Segal, Ben Maurice

    1971-01-01

    The structure of a strong plane shock wave in a monatomic rarefied perfect gas is one of the simplest problems able to be posed in kinetic theory, and one of the hardest to solve. Its simplicity lies in the absence of solid boundaries, geometrical complications, or internal molecular energy. Its difficulty arises from the great departure of the gas from equilibrium within the shock, which invalidates many of the techniques used successfully elsewhere in kinetic theory. In addition to this theoretical challenge, the modern development of ballistics and hypersonic flight has helped to stimulate extensive theoretical and experimental interest in the shock problem. The experimenters in turn have encountered great difficulties on account of the very small physical dimensions of shocks. In fact, until very recently indeed, any close comparisons of theoretical and experimental shock structure results have been rather unprofitable due to the inadequacies of both theory and experiment. During the last few years this situation has been appreciably improved by development of the Monte Carlo method. This allows idealized 'experiments' to be performed on large computers instead of in wind tunnels, using a known intermolecular force law. The most developed of these methods has been shown to be equivalent theoretically to the Boltzmann equation and to give results which agree extremely closely with measurements of high accuracy. Thus Monte Carlo results not only form the soundest basis for our present theoretical knowledge of shock wave structure, but, for purposes of developing other theories, can also be considered a very valuable experimental resource. However, such results remain very expensive to obtain. In this thesis we develop more economical kinetic theory methods for the approximate prediction of shock structure, and compare our results with those of the Monte Carlo method.

  13. Differential Equations Compatible with Boundary Rational qKZ Equation

    NASA Astrophysics Data System (ADS)

    Takeyama, Yoshihiro

    2011-10-01

    We give diffierential equations compatible with the rational qKZ equation with boundary reflection. The total system contains the trigonometric degeneration of the bispectral qKZ equation of type (Cěen, Cn) which in the case of type GLn was studied by van Meer and Stokman. We construct an integral formula for solutions to our compatible system in a special case.

  14. The compressible adjoint equations in geodynamics: equations and numerical assessment

    NASA Astrophysics Data System (ADS)

    Ghelichkhan, Siavash; Bunge, Hans-Peter

    2016-04-01

    The adjoint method is a powerful means to obtain gradient information in a mantle convection model relative to past flow structure. While the adjoint equations in geodynamics have been derived for the conservation equations of mantle flow in their incompressible form, the applicability of this approximation to Earth is limited, because density increases by almost a factor of two from the surface to the Core Mantle Boundary. Here we introduce the compressible adjoint equations for the conservation equations in the anelastic-liquid approximation. Our derivation applies an operator formulation in Hilbert spaces, to connect to recent work in seismology (Fichtner et al (2006)) and geodynamics (Horbach et al (2014)), where the approach was used to derive the adjoint equations for the wave equation and incompressible mantle flow. We present numerical tests of the newly derived equations based on twin experiments, focusing on three simulations. A first, termed Compressible, assumes the compressible forward and adjoint equations, and represents the consistent means of including compressibility effects. A second, termed Mixed, applies the compressible forward equation, but ignores compressibility effects in the adjoint equations, where the incompressible equations are used instead. A third simulation, termed Incompressible, neglects compressibility effects entirely in the forward and adjoint equations relative to the reference twin. The compressible and mixed formulations successfully restore earlier mantle flow structure, while the incompressible formulation yields noticeable artifacts. Our results suggest the use of a compressible formulation, when applying the adjoint method to seismically derived mantle heterogeneity structure.

  15. Estimating Equating Error in Observed-Score Equating. Research Report.

    ERIC Educational Resources Information Center

    van der Linden, Wim J.

    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 in the population of examinees. This definition underlies, for example, the well-known approximation to the standard error of equating by Lord (1982).…

  16. Young's equation revisited.

    PubMed

    Makkonen, Lasse

    2016-04-01

    Young's construction for a contact angle at a three-phase intersection forms the basis of all fields of science that involve wetting and capillary action. We find compelling evidence from recent experimental results on the deformation of a soft solid at the contact line, and displacement of an elastic wire immersed in a liquid, that Young's equation can only be interpreted by surface energies, and not as a balance of surface tensions. It follows that the a priori variable in finding equilibrium is not the position of the contact line, but the contact angle. This finding provides the explanation for the pinning of a contact line. PMID:26940644

  17. Noncommutativity and the Friedmann Equations

    NASA Astrophysics Data System (ADS)

    Sabido, M.; Guzmán, W.; Socorro, J.

    2010-07-01

    In this paper we study noncommutative scalar field cosmology, we find the noncommutative Friedmann equations as well as the noncommutative Klein-Gordon equation, interestingly the noncommutative contributions are only present up to second order in the noncommutitive parameter.

  18. Solitons and nonlinear wave equations

    SciTech Connect

    Dodd, Roger K.; Eilbeck, J. Chris; Gibbon, John D.; Morris, Hedley C.

    1982-01-01

    A discussion of the theory and applications of classical solitons is presented with a brief treatment of quantum mechanical effects which occur in particle physics and quantum field theory. The subjects addressed include: solitary waves and solitons, scattering transforms, the Schroedinger equation and the Korteweg-de Vries equation, and the inverse method for the isospectral Schroedinger equation and the general solution of the solvable nonlinear equations. Also considered are: isolation of the Korteweg-de Vries equation in some physical examples, the Zakharov-Shabat/AKNS inverse method, kinks and the sine-Gordon equation, the nonlinear Schroedinger equation and wave resonance interactions, amplitude equations in unstable systems, and numerical studies of solitons. 45 references.

  19. Conservational PDF Equations of Turbulence

    NASA Technical Reports Server (NTRS)

    Shih, Tsan-Hsing; Liu, Nan-Suey

    2010-01-01

    Recently we have revisited the traditional probability density function (PDF) equations for the velocity and species in turbulent incompressible flows. They are all unclosed due to the appearance of various conditional means which are modeled empirically. However, we have observed that it is possible to establish a closed velocity PDF equation and a closed joint velocity and species PDF equation through conditions derived from the integral form of the Navier-Stokes equations. Although, in theory, the resulted PDF equations are neither general nor unique, they nevertheless lead to the exact transport equations for the first moment as well as all higher order moments. We refer these PDF equations as the conservational PDF equations. This observation is worth further exploration for its validity and CFD application

  20. The Dirac equation

    SciTech Connect

    Thaller, B.

    1992-01-01

    This monograph treats most of the usual material to be found in texts on the Dirac equation such as the basic formalism of quantum mechanics, representations of Dirac matrices, covariant realization of the Dirac equation, interpretation of negative energies, Foldy-Wouthuysen transformation, Klein's paradox, spherically symmetric interactions and a treatment of the relativistic hydrogen atom, etc., and also provides excellent additional treatments of a variety of other relevant topics. The monograph contains an extensive treatment of the Lorentz and Poincare groups and their representations. The author discusses in depth Lie algebaic and projective representations, covering groups, and Mackey's theory and Wigner's realization of induced representations. A careful classification of external fields with respect to their behavior under Poincare transformations is supplemented by a basic account of self-adjointness and spectral properties of Dirac operators. A state-of-the-art treatment of relativistic scattering theory based on a time-dependent approach originally due to Enss is presented. An excellent introduction to quantum electrodynamics in external fields is provided. Various appendices containing further details, notes on each chapter commenting on the history involved and referring to original research papers and further developments in the literature, and a bibliography covering all relevant monographs and over 500 articles on the subject, complete this text. This book should satisfy the needs of a wide audience, ranging from graduate students in theoretical physics and mathematics to researchers interested in mathematical physics.

  1. Inequivalence between the Schroedinger equation and the Madelung hydrodynamic equations

    SciTech Connect

    Wallstrom, T.C.

    1994-03-01

    By differentiating the Schroedinger equation and separating the real amd imaginary parts, one obtains the Madelung hydrodynamic equations, which have inspired numerous classical interpretations of quantum mechanics. Such interpretations frequently assume that these equations are equivalent to the Schroedinger equation, and thus provide an alternative basis for quantum mechanics. This paper proves that this is incorrect: to recover the Schroedinger equation, one must add by hand a quantization condition, as in the old quantum theory. The implications for various alternative interpretations of quantum mechanics are discussed.

  2. ``Riemann equations'' in bidifferential calculus

    NASA Astrophysics Data System (ADS)

    Chvartatskyi, O.; Müller-Hoissen, F.; Stoilov, N.

    2015-10-01

    We consider equations that formally resemble a matrix Riemann (or Hopf) equation in the framework of bidifferential calculus. With different choices of a first-order bidifferential calculus, we obtain a variety of equations, including a semi-discrete and a fully discrete version of the matrix Riemann equation. A corresponding universal solution-generating method then either yields a (continuous or discrete) Cole-Hopf transformation, or leaves us with the problem of solving Riemann equations (hence an application of the hodograph method). If the bidifferential calculus extends to second order, solutions of a system of "Riemann equations" are also solutions of an equation that arises, on the universal level of bidifferential calculus, as an integrability condition. Depending on the choice of bidifferential calculus, the latter can represent a number of prominent integrable equations, like self-dual Yang-Mills, as well as matrix versions of the two-dimensional Toda lattice, Hirota's bilinear difference equation, (2+1)-dimensional Nonlinear Schrödinger (NLS), Kadomtsev-Petviashvili (KP) equation, and Davey-Stewartson equations. For all of them, a recent (non-isospectral) binary Darboux transformation result in bidifferential calculus applies, which can be specialized to generate solutions of the associated "Riemann equations." For the latter, we clarify the relation between these specialized binary Darboux transformations and the aforementioned solution-generating method. From (arbitrary size) matrix versions of the "Riemann equations" associated with an integrable equation, possessing a bidifferential calculus formulation, multi-soliton-type solutions of the latter can be generated. This includes "breaking" multi-soliton-type solutions of the self-dual Yang-Mills and the (2+1)-dimensional NLS equation, which are parametrized by solutions of Riemann equations.

  3. The Forced Hard Spring Equation

    ERIC Educational Resources Information Center

    Fay, Temple H.

    2006-01-01

    Through numerical investigations, various examples of the Duffing type forced spring equation with epsilon positive, are studied. Since [epsilon] is positive, all solutions to the associated homogeneous equation are periodic and the same is true with the forcing applied. The damped equation exhibits steady state trajectories with the interesting…

  4. Equating with Miditests Using IRT

    ERIC Educational Resources Information Center

    Fitzpatrick, Joseph; Skorupski, William P.

    2016-01-01

    The equating performance of two internal anchor test structures--miditests and minitests--is studied for four IRT equating methods using simulated data. Originally proposed by Sinharay and Holland, miditests are anchors that have the same mean difficulty as the overall test but less variance in item difficulties. Four popular IRT equating methods…

  5. Successfully Transitioning to Linear Equations

    ERIC Educational Resources Information Center

    Colton, Connie; Smith, Wendy M.

    2014-01-01

    The Common Core State Standards for Mathematics (CCSSI 2010) asks students in as early as fourth grade to solve word problems using equations with variables. Equations studied at this level generate a single solution, such as the equation x + 10 = 25. For students in fifth grade, the Common Core standard for algebraic thinking expects them to…

  6. Evaluating Cross-Lingual Equating.

    ERIC Educational Resources Information Center

    Rapp, Joel; Allalouf, Avi

    This study examined the cross-lingual equating process adopted by a large scale testing system in which target language (TL) forms are equated to the source language (SL) forms using a set of translated items. The focus was on evaluating the degree of error inherent in the routine cross-lingual equating of the Verbal Reasoning subtest of the…

  7. Solving Nonlinear Coupled Differential Equations

    NASA Technical Reports Server (NTRS)

    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.

  8. Generalized Klein-Kramers equations

    NASA Astrophysics Data System (ADS)

    Fa, Kwok Sau

    2012-12-01

    A generalized Klein-Kramers equation for a particle interacting with an external field is proposed. The equation generalizes the fractional Klein-Kramers equation introduced by Barkai and Silbey [J. Phys. Chem. B 104, 3866 (2000), 10.1021/jp993491m]. Besides, the generalized Klein-Kramers equation can also recover the integro-differential Klein-Kramers equation for continuous-time random walk; this means that it can describe the subdiffusive and superdiffusive regimes in the long-time limit. Moreover, analytic solutions for first two moments both in velocity and displacement (for force-free case) are obtained, and their dynamic behaviors are investigated.

  9. Multinomial Diffusion Equation

    SciTech Connect

    Balter, Ariel I.; Tartakovsky, Alexandre M.

    2011-06-01

    We have developed a novel stochastic, space/time discrete representation of particle diffusion (e.g. Brownian motion) based on discrete probability distributions. We show that in the limit of both very small time step and large concentration, our description is equivalent to the space/time continuous stochastic diffusion equation. Being discrete in both time and space, our model can be used as an extremely accurate, efficient, and stable stochastic finite-difference diffusion algorithm when concentrations are so small that computationally expensive particle-based methods are usually needed. Through numerical simulations, we show that our method can generate realizations that capture the statistical properties of particle simulations. While our method converges converges to both the correct ensemble mean and ensemble variance very quickly with decreasing time step, but for small concentration, the stochastic diffusion PDE does not, even for very small time steps.

  10. Structural Equation Model Trees

    PubMed Central

    Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman

    2015-01-01

    In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree structures that separate a data set recursively into subsets with significantly different parameter estimates in a SEM. SEM Trees provide means for finding covariates and covariate interactions that predict differences in structural parameters in observed as well as in latent space and facilitate theory-guided exploration of empirical data. We describe the methodology, discuss theoretical and practical implications, and demonstrate applications to a factor model and a linear growth curve model. PMID:22984789

  11. Elliptic scattering equations

    NASA Astrophysics Data System (ADS)

    Cardona, Carlos; Gomez, Humberto

    2016-06-01

    Recently the CHY approach has been extended to one loop level using elliptic functions and modular forms over a Jacobian variety. Due to the difficulty in manipulating these kind of functions, we propose an alternative prescription that is totally algebraic. This new proposal is based on an elliptic algebraic curve embedded in a mathbb{C}{P}^2 space. We show that for the simplest integrand, namely the n - gon, our proposal indeed reproduces the expected result. By using the recently formulated Λ-algorithm, we found a novel recurrence relation expansion in terms of tree level off-shell amplitudes. Our results connect nicely with recent results on the one-loop formulation of the scattering equations. In addition, this new proposal can be easily stretched out to hyperelliptic curves in order to compute higher genus.

  12. Λ scattering equations

    NASA Astrophysics Data System (ADS)

    Gomez, Humberto

    2016-06-01

    The CHY representation of scattering amplitudes is based on integrals over the moduli space of a punctured sphere. We replace the punctured sphere by a double-cover version. The resulting scattering equations depend on a parameter Λ controlling the opening of a branch cut. The new representation of scattering amplitudes possesses an enhanced redundancy which can be used to fix, modulo branches, the location of four punctures while promoting Λ to a variable. Via residue theorems we show how CHY formulas break up into sums of products of smaller (off-shell) ones times a propagator. This leads to a powerful way of evaluating CHY integrals of generic rational functions, which we call the Λ algorithm.

  13. On nonautonomous Dirac equation

    SciTech Connect

    Hovhannisyan, Gro; Liu Wen

    2009-12-15

    We construct the fundamental solution of time dependent linear ordinary Dirac system in terms of unknown phase functions. This construction gives approximate representation of solutions which is useful for the study of asymptotic behavior. Introducing analog of Rayleigh quotient for differential equations we generalize Hartman-Wintner asymptotic integration theorems with the error estimates for applications to the Dirac system. We also introduce the adiabatic invariants for the Dirac system, which are similar to the adiabatic invariant of Lorentz's pendulum. Using a small parameter method it is shown that the change in the adiabatic invariants approaches zero with the power speed as a small parameter approaches zero. As another application we calculate the transition probabilities for the Dirac system. We show that for the special choice of electromagnetic field, the only transition of an electron to the positron with the opposite spin orientation is possible.

  14. Parabolized stability equations

    NASA Astrophysics Data System (ADS)

    Herbert, Thorwald

    1994-04-01

    The parabolized stability equations (PSE) are a new approach to analyze the streamwise evolution of single or interacting Fourier modes in weakly nonparallel flows such as boundary layers. The concept rests on the decomposition of every mode into a slowly varying amplitude function and a wave function with slowly varying wave number. The neglect of the small second derivatives of the slowly varying functions with respect to the streamwise variable leads to an initial boundary-value problem that can be solved by numerical marching procedures. The PSE approach is valid in convectively unstable flows. The equations for a single mode are closely related to those of the traditional eigenvalue problems for linear stability analysis. However, the PSE approach does not exploit the homogeneity of the problem and, therefore, can be utilized to analyze forced modes and the nonlinear growth and interaction of an initial disturbance field. In contrast to the traditional patching of local solutions, the PSE provide the spatial evolution of modes with proper account for their history. The PSE approach allows studies of secondary instabilities without the constraints of the Floquet analysis and reproduces the established experimental, theoretical, and computational benchmark results on transition up to the breakdown stage. The method matches or exceeds the demonstrated capabilities of current spatial Navier-Stokes solvers at a small fraction of their computational cost. Recent applications include studies on localized or distributed receptivity and prediction of transition in model environments for realistic engineering problems. This report describes the basis, intricacies, and some applications of the PSE methodology.

  15. Mode decomposition evolution equations

    PubMed Central

    Wang, Yang; Wei, Guo-Wei; Yang, Siyang

    2011-01-01

    Partial differential equation (PDE) based methods have become some of the most powerful tools for exploring the fundamental problems in signal processing, image processing, computer vision, machine vision and artificial intelligence in the past two decades. The advantages of PDE based approaches are that they can be made fully automatic, robust for the analysis of images, videos and high dimensional data. A fundamental question is whether one can use PDEs to perform all the basic tasks in the image processing. If one can devise PDEs to perform full-scale mode decomposition for signals and images, the modes thus generated would be very useful for secondary processing to meet the needs in various types of signal and image processing. Despite of great progress in PDE based image analysis in the past two decades, the basic roles of PDEs in image/signal analysis are only limited to PDE based low-pass filters, and their applications to noise removal, edge detection, segmentation, etc. At present, it is not clear how to construct PDE based methods for full-scale mode decomposition. The above-mentioned limitation of most current PDE based image/signal processing methods is addressed in the proposed work, in which we introduce a family of mode decomposition evolution equations (MoDEEs) for a vast variety of applications. The MoDEEs are constructed as an extension of a PDE based high-pass filter (Europhys. Lett., 59(6): 814, 2002) by using arbitrarily high order PDE based low-pass filters introduced by Wei (IEEE Signal Process. Lett., 6(7): 165, 1999). The use of arbitrarily high order PDEs is essential to the frequency localization in the mode decomposition. Similar to the wavelet transform, the present MoDEEs have a controllable time-frequency localization and allow a perfect reconstruction of the original function. Therefore, the MoDEE operation is also called a PDE transform. However, modes generated from the present approach are in the spatial or time domain and can be

  16. Langevin equation approach to reactor noise analysis: stochastic transport equation

    SciTech Connect

    Akcasu, A.Z. ); Stolle, A.M. )

    1993-01-01

    The application of the Langevin equation method to the study of fluctuations in the space- and velocity-dependent neutron density as well as in the detector outputs in nuclear reactors is presented. In this case, the Langevin equation is the stochastic linear neutron transport equation with a space- and velocity-dependent random neutron source, often referred to as the noise equivalent source (NES). The power spectral densities (PSDs) of the NESs in the transport equation, as well as in the accompanying detection rate equations, are obtained, and the cross- and auto-power spectral densities of the outputs of pairs of detectors are explicitly calculated. The transport-level expression for the R([omega]) ratio measured in the [sup 252]Cf source-driven noise analysis method is also derived. Finally, the implementation of the Langevin equation approach at different levels of approximation is discussed, and the stochastic one-speed transport and one-group P[sub 1] equations are derived by first integrating the stochastic transport equation over speed and then eliminating the angular dependence by a spherical harmonics expansion. By taking the large transport rate limit in the P[sub 1] description, the stochastic diffusion equation is obtained as well as the PSD of the NES in it. This procedure also leads directly to the stochastic Fick's law.

  17. A spinor representation of Maxwell equations and Dirac equation

    SciTech Connect

    Vaz, J. Jr.; Rodrigues, W.A. Jr.

    1993-02-01

    Using the Clifford bundle formalism and starting from the free Maxwell equations dF = {delta}F = 0 we show by writing F = b{psi}{gamma}{sup 1}{gamma}{sup 2}{psi}{sup *}, where {psi} is a Dirac-Hestenes spinor field, that the Dirac-Hestenes equation (which is the representative of the standard Dirac equation in the Clifford bundle over Minkowski spacetime) is equivalent under general assumptions to those free Maxwell equations. We briefly discuss the implications of our findings for the interpretation of quantum mechanics. 15 refs.

  18. JWL Equation of State

    SciTech Connect

    Menikoff, Ralph

    2015-12-15

    The JWL equation of state (EOS) is frequently used for the products (and sometimes reactants) of a high explosive (HE). Here we review and systematically derive important properties. The JWL EOS is of the Mie-Grueneisen form with a constant Grueneisen coefficient and a constants specific heat. It is thermodynamically consistent to specify the temperature at a reference state. However, increasing the reference state temperature restricts the EOS domain in the (V, e)-plane of phase space. The restrictions are due to the conditions that P ≥ 0, T ≥ 0, and the isothermal bulk modulus is positive. Typically, this limits the low temperature regime in expansion. The domain restrictions can result in the P-T equilibrium EOS of a partly burned HE failing to have a solution in some cases. For application to HE, the heat of detonation is discussed. Example JWL parameters for an HE, both products and reactions, are used to illustrate the restrictions on the domain of the EOS.

  19. A note on "Kepler's equation".

    NASA Astrophysics Data System (ADS)

    Dutka, J.

    1997-07-01

    This note briefly points out the formal similarity between Kepler's equation and equations developed in Hindu and Islamic astronomy for describing the lunar parallax. Specifically, an iterative method for calculating the lunar parallax has been developed by the astronomer Habash al-Hasib al-Marwazi (about 850 A.D., Turkestan), which is surprisingly similar to the iterative method for solving Kepler's equation invented by Leonhard Euler (1707 - 1783).

  20. Electronic representation of wave equation

    NASA Astrophysics Data System (ADS)

    Veigend, Petr; Kunovský, Jiří; Kocina, Filip; Nečasová, Gabriela; Šátek, Václav; Valenta, Václav

    2016-06-01

    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.

  1. Uncertainty of empirical correlation equations

    NASA Astrophysics Data System (ADS)

    Feistel, R.; Lovell-Smith, J. W.; Saunders, P.; Seitz, S.

    2016-08-01

    The International Association for the Properties of Water and Steam (IAPWS) has published a set of empirical reference equations of state, forming the basis of the 2010 Thermodynamic Equation of Seawater (TEOS-10), from which all thermodynamic properties of seawater, ice, and humid air can be derived in a thermodynamically consistent manner. For each of the equations of state, the parameters have been found by simultaneously fitting equations for a range of different derived quantities using large sets of measurements of these quantities. In some cases, uncertainties in these fitted equations have been assigned based on the uncertainties of the measurement results. However, because uncertainties in the parameter values have not been determined, it is not possible to estimate the uncertainty in many of the useful quantities that can be calculated using the parameters. In this paper we demonstrate how the method of generalised least squares (GLS), in which the covariance of the input data is propagated into the values calculated by the fitted equation, and in particular into the covariance matrix of the fitted parameters, can be applied to one of the TEOS-10 equations of state, namely IAPWS-95 for fluid pure water. Using the calculated parameter covariance matrix, we provide some preliminary estimates of the uncertainties in derived quantities, namely the second and third virial coefficients for water. We recommend further investigation of the GLS method for use as a standard method for calculating and propagating the uncertainties of values computed from empirical equations.

  2. Graphical Solution of Polynomial Equations

    ERIC Educational Resources Information Center

    Grishin, Anatole

    2009-01-01

    Graphing utilities, such as the ubiquitous graphing calculator, are often used in finding the approximate real roots of polynomial equations. In this paper the author offers a simple graphing technique that allows one to find all solutions of a polynomial equation (1) of arbitrary degree; (2) with real or complex coefficients; and (3) possessing…

  3. Drug Levels and Difference Equations

    ERIC Educational Resources Information Center

    Acker, Kathleen A.

    2004-01-01

    American university offers a course in finite mathematics whose focus is difference equation with emphasis on real world applications. The conclusion states that students learned to look for growth and decay patterns in raw data, to recognize both arithmetic and geometric growth, and to model both scenarios with graphs and difference equations.

  4. Generalized Multilevel Structural Equation Modeling

    ERIC Educational Resources Information Center

    Rabe-Hesketh, Sophia; Skrondal, Anders; Pickles, Andrew

    2004-01-01

    A unifying framework for generalized multilevel structural equation modeling is introduced. The models in the framework, called generalized linear latent and mixed models (GLLAMM), combine features of generalized linear mixed models (GLMM) and structural equation models (SEM) and consist of a response model and a structural model for the latent…

  5. Complete solution of Boolean equations

    NASA Technical Reports Server (NTRS)

    Tapia, M. A.; Tucker, J. H.

    1980-01-01

    A method is presented for generating a single formula involving arbitary Boolean parameters, which includes in it each and every possible solution of a system of Boolean equations. An alternate condition equivalent to a known necessary and sufficient condition for solving a system of Boolean equations is given.

  6. Students' Understanding of Quadratic Equations

    ERIC Educational Resources Information Center

    López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

    2016-01-01

    Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…

  7. The Equations of Oceanic Motions

    NASA Astrophysics Data System (ADS)

    Müller, Peter

    2006-10-01

    Modeling and prediction of oceanographic phenomena and climate is based on the integration of dynamic equations. The Equations of Oceanic Motions derives and systematically classifies the most common dynamic equations used in physical oceanography, from large scale thermohaline circulations to those governing small scale motions and turbulence. After establishing the basic dynamical equations that describe all oceanic motions, M|ller then derives approximate equations, emphasizing the assumptions made and physical processes eliminated. He distinguishes between geometric, thermodynamic and dynamic approximations and between the acoustic, gravity, vortical and temperature-salinity modes of motion. Basic concepts and formulae of equilibrium thermodynamics, vector and tensor calculus, curvilinear coordinate systems, and the kinematics of fluid motion and wave propagation are covered in appendices. Providing the basic theoretical background for graduate students and researchers of physical oceanography and climate science, this book will serve as both a comprehensive text and an essential reference.

  8. Extended Trial Equation Method for Nonlinear Partial Differential Equations

    NASA Astrophysics Data System (ADS)

    Gepreel, Khaled A.; Nofal, Taher A.

    2015-04-01

    The main objective of this paper is to use the extended trial equation method to construct a series of some new solutions for some nonlinear partial differential equations (PDEs) in mathematical physics. We will construct the solutions in many different functions such as hyperbolic function solutions, trigonometric function solutions, Jacobi elliptic function solutions, and rational functional solutions for the nonlinear PDEs when the balance number is a real number via the Zhiber-Shabat nonlinear differential equation. The balance number of this method is not constant as we shown in other methods, but it is changed by changing the trial equation derivative definition. This method allowed us to construct many new types of solutions. It is shown by using the Maple software package that all obtained solutions satisfy the original PDEs.

  9. Higher derivative gravity: Field equation as the equation of state

    NASA Astrophysics Data System (ADS)

    Dey, Ramit; Liberati, Stefano; Mohd, Arif

    2016-08-01

    One of the striking features of general relativity is that the Einstein equation is implied by the Clausius relation imposed on a small patch of locally constructed causal horizon. The extension of this thermodynamic derivation of the field equation to more general theories of gravity has been attempted many times in the last two decades. In particular, equations of motion for minimally coupled higher-curvature theories of gravity, but without the derivatives of curvature, have previously been derived using a thermodynamic reasoning. In that derivation the horizon slices were endowed with an entropy density whose form resembles that of the Noether charge for diffeomorphisms, and was dubbed the Noetheresque entropy. In this paper, we propose a new entropy density, closely related to the Noetheresque form, such that the field equation of any diffeomorphism-invariant metric theory of gravity can be derived by imposing the Clausius relation on a small patch of local causal horizon.

  10. Sedeonic Equations of Massive Fields

    NASA Astrophysics Data System (ADS)

    Mironov, Sergey V.; Mironov, Victor L.

    2015-01-01

    Prior work on space-time sedeon algebra models relativistic quantum mechanical equation of motion with corresponding field equations, mediated by massive or massless spin-1 or spin-1/2 particles. In the massless spin-1 case, such exchange particles mediate fields in analogy to Maxwell's equations in Lorentz gauge. This paper demonstrates fundamental aspects of massive field's theory, such as gauge invariance, charge conservation, Poynting's theorem, potential of a stationary scalar point source, plane wave solution, and interaction between point sources. We briefly discuss some aspects of sedeonic algebra and their potential physical applications.

  11. Primordial equation of state transitions

    NASA Astrophysics Data System (ADS)

    Aravind, Aditya; Lorshbough, Dustin; Paban, Sonia

    2016-06-01

    We revisit the physics of transitions from a general equation of state parameter to the final stage of slow-roll inflation. We show that it is unlikely for the modes comprising the cosmic microwave background to contain imprints from a preinflationary equation of state transition and still be consistent with observations. We accomplish this by considering observational consistency bounds on the amplitude of excitations resulting from such a transition. As a result, the physics which initially led to inflation likely cannot be probed with observations of the cosmic microwave background. Furthermore, we show that it is unlikely that equation of state transitions may explain the observed low multipole power suppression anomaly.

  12. SETS. Set Equation Transformation System

    SciTech Connect

    Worrel, R.B.

    1992-01-13

    SETS is used for symbolic manipulation of Boolean equations, particularly the reduction of equations by the application of Boolean identities. It is a flexible and efficient tool for performing probabilistic risk analysis (PRA), vital area analysis, and common cause analysis. The equation manipulation capabilities of SETS can also be used to analyze noncoherent fault trees and determine prime implicants of Boolean functions, to verify circuit design implementation, to determine minimum cost fire protection requirements for nuclear reactor plants, to obtain solutions to combinatorial optimization problems with Boolean constraints, and to determine the susceptibility of a facility to unauthorized access through nullification of sensors in its protection system.

  13. Friedmann equation with quantum potential

    SciTech Connect

    Siong, Ch'ng Han; Radiman, Shahidan; Nikouravan, Bijan

    2013-11-27

    Friedmann equations are used to describe the evolution of the universe. Solving Friedmann equations for the scale factor indicates that the universe starts from an initial singularity where all the physical laws break down. However, the Friedmann equations are well describing the late-time or large scale universe. Hence now, many physicists try to find an alternative theory to avoid this initial singularity. In this paper, we generate a version of first Friedmann equation which is added with an additional term. This additional term contains the quantum potential energy which is believed to play an important role at small scale. However, it will gradually become negligible when the universe evolves to large scale.

  14. Evolutions equations in computational anatomy.

    PubMed

    Younes, Laurent; Arrate, Felipe; Miller, Michael I

    2009-03-01

    One of the main purposes in computational anatomy is the measurement and statistical study of anatomical variations in organs, notably in the brain or the heart. Over the last decade, our group has progressively developed several approaches for this problem, all related to the Riemannian geometry of groups of diffeomorphisms and the shape spaces on which these groups act. Several important shape evolution equations that are now used routinely in applications have emerged over time. Our goal in this paper is to provide an overview of these equations, placing them in their theoretical context, and giving examples of applications in which they can be used. We introduce the required theoretical background before discussing several classes of equations of increasingly complexity. These equations include energy minimizing evolutions deriving from Riemannian gradient descent, geodesics, parallel transport and Jacobi fields. PMID:19059343

  15. Overdetermined Systems of Linear Equations.

    ERIC Educational Resources Information Center

    Williams, Gareth

    1990-01-01

    Explored is an overdetermined system of linear equations to find an appropriate least squares solution. A geometrical interpretation of this solution is given. Included is a least squares point discussion. (KR)

  16. Parametric Equations, Maple, and Tubeplots.

    ERIC Educational Resources Information Center

    Feicht, Louis

    1997-01-01

    Presents an activity that establishes a graphical foundation for parametric equations by using a graphing output form called tubeplots from the computer program Maple. Provides a comprehensive review and exploration of many previously learned topics. (ASK)

  17. The thermal-vortex equations

    NASA Technical Reports Server (NTRS)

    Shebalin, John V.

    1987-01-01

    The Boussinesq approximation is extended so as to explicitly account for the transfer of fluid energy through viscous action into thermal energy. Ideal and dissipative integral invariants are discussed, in addition to the general equations for thermal-fluid motion.

  18. Bogoliubov equations and functional mechanics

    NASA Astrophysics Data System (ADS)

    Volovich, I. V.

    2010-09-01

    The functional classical mechanics based on the probability approach, where a particle is described not by a trajectory in the phase space but by a probability distribution, was recently proposed for solving the irreversibility problem, i.e., the problem of matching the time reversibility of microscopic dynamics equations and the irreversibility of macrosystem dynamics. In the framework of functional mechanics, we derive Bogoliubov-Boltzmann-type equations for finitely many particles. We show that a closed equation for a one-particle distribution function can be rigorously derived in functional mechanics without any additional assumptions required in the Bogoliubov method. We consider the possibility of using diffusion processes and the Fokker-Planck-Kolmogorov equation to describe isolated particles.

  19. Improved beam propagation method equations.

    PubMed

    Nichelatti, E; Pozzi, G

    1998-01-01

    Improved beam propagation method (BPM) equations are derived for the general case of arbitrary refractive-index spatial distributions. It is shown that in the paraxial approximation the discrete equations admit an analytical solution for the propagation of a paraxial spherical wave, which converges to the analytical solution of the paraxial Helmholtz equation. The generalized Kirchhoff-Fresnel diffraction integral between the object and the image planes can be derived, with its coefficients expressed in terms of the standard ABCD matrix. This result allows the substitution, in the case of an unaberrated system, of the many numerical steps with a single analytical step. We compared the predictions of the standard and improved BPM equations by considering the cases of a Maxwell fish-eye and of a Luneburg lens. PMID:18268554

  20. Solving Differential Equations in R

    EPA Science Inventory

    Although R is still predominantly applied for statistical analysis and graphical representation, it is rapidly becoming more suitable for mathematical computing. One of the fields where considerable progress has been made recently is the solution of differential equations. Here w...

  1. New determination equation for visibility

    SciTech Connect

    Fang Qiwan; Rao Jionghui; Ying Zhixiang; Tang Haijun; Jiang Chuanfu

    1996-12-31

    Range is an important tactical hard index in designing and manufacturing military laser rangefinders. But in practice it is also a soft index which is influenced by target characteristic and atmospheric visibility. In this article the problems in the range index are analyzed. The way to determine visibility is put forward. Extinction determination equation for visibility is derived. And it is applied in practice, which verifies the determination equation is functional and effective.

  2. Boltzmann equation and hydrodynamic fluctuations.

    PubMed

    Colangeli, Matteo; Kröger, Martin; Ottinger, Hans Christian

    2009-11-01

    We apply the method of invariant manifolds to derive equations of generalized hydrodynamics from the linearized Boltzmann equation and determine exact transport coefficients, obeying Green-Kubo formulas. Numerical calculations are performed in the special case of Maxwell molecules. We investigate, through the comparison with experimental data and former approaches, the spectrum of density fluctuations and address the regime of finite Knudsen numbers and finite frequencies hydrodynamics. PMID:20364972

  3. Hidden Statistics of Schroedinger Equation

    NASA Technical Reports Server (NTRS)

    Zak, Michail

    2011-01-01

    Work was carried out in determination of the mathematical origin of randomness in quantum mechanics and creating a hidden statistics of Schr dinger equation; i.e., to expose the transitional stochastic process as a "bridge" to the quantum world. The governing equations of hidden statistics would preserve such properties of quantum physics as superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods.

  4. Revisiting the Simplified Bernoulli Equation

    PubMed Central

    Heys, Jeffrey J; Holyoak, Nicole; Calleja, Anna M; Belohlavek, Marek; Chaliki, Hari P

    2010-01-01

    Background: The assessment of the severity of aortic valve stenosis is done by either invasive catheterization or non-invasive Doppler Echocardiography in conjunction with the simplified Bernoulli equation. The catheter measurement is generally considered more accurate, but the procedure is also more likely to have dangerous complications. Objective: The focus here is on examining computational fluid dynamics as an alternative method for analyzing the echo data and determining whether it can provide results similar to the catheter measurement. Methods: An in vitro heart model with a rigid orifice is used as a first step in comparing echocardiographic data, which uses the simplified Bernoulli equation, catheterization, and echocardiographic data, which uses computational fluid dynamics (i.e., the Navier-Stokes equations). Results: For a 0.93cm2 orifice, the maximum pressure gradient predicted by either the simplified Bernoulli equation or computational fluid dynamics was not significantly different from the experimental catheter measurement (p > 0.01). For a smaller 0.52cm2 orifice, there was a small but significant difference (p < 0.01) between the simplified Bernoulli equation and the computational fluid dynamics simulation, with the computational fluid dynamics simulation giving better agreement with experimental data for some turbulence models. Conclusion: For this simplified, in vitro system, the use of computational fluid dynamics provides an improvement over the simplified Bernoulli equation with the biggest improvement being seen at higher valvular stenosis levels. PMID:21625471

  5. An Exact Mapping from Navier-Stokes Equation to Schr"odinger Equation via Riccati Equation

    NASA Astrophysics Data System (ADS)

    Christianto, Vic; Smarandache, Florentin

    2010-03-01

    In the present article we argue that it is possible to write down Schr"odinger representation of Navier-Stokes equation via Riccati equation. The proposed approach, while differs appreciably from other method such as what is proposed by R. M. Kiehn, has an advantage, i.e. it enables us extend further to quaternionic and biquaternionic version of Navier-Stokes equation, for instance via Kravchenko's and Gibbon's route. Further observation is of course recommended in order to refute or verify this proposition.

  6. Note on parallel processing techniques for algebraic equations, ordinary differential equations and partial differential equations

    SciTech Connect

    Allidina, A.Y.; Malinowski, K.; Singh, M.G.

    1982-12-01

    The possibilities were explored for enhancing parallelism in the simulation of systems described by algebraic equations, ordinary differential equations and partial differential equations. These techniques, using multiprocessors, were developed to speed up simulations, e.g. for nuclear accidents. Issues involved in their design included suitable approximations to bring the problem into a numerically manageable form and a numerical procedure to perform the computations necessary to solve the problem accurately. Parallel processing techniques used as simulation procedures, and a design of a simulation scheme and simulation procedure employing parallel computer facilities, were both considered.

  7. Solving Parker's transport equation with stochastic differential equations on GPUs

    NASA Astrophysics Data System (ADS)

    Dunzlaff, P.; Strauss, R. D.; Potgieter, M. S.

    2015-07-01

    The numerical solution of transport equations for energetic charged particles in space is generally very costly in terms of time. Besides the use of multi-core CPUs and computer clusters in order to decrease the computation times, high performance calculations on graphics processing units (GPUs) have become available during the last years. In this work we introduce and describe a GPU-accelerated implementation of Parker's equation using Stochastic Differential Equations (SDEs) for the simulation of the transport of energetic charged particles with the CUDA toolkit, which is the focus of this work. We briefly discuss the set of SDEs arising from Parker's transport equation and their application to boundary value problems such as that of the Jovian magnetosphere. We compare the runtimes of the GPU code with a CPU version of the same algorithm. Compared to the CPU implementation (using OpenMP and eight threads) we find a performance increase of about a factor of 10-60, depending on the assumed set of parameters. Furthermore, we benchmark our simulation using the results of an existing SDE implementation of Parker's transport equation.

  8. Turbulent fluid motion 3: Basic continuum equations

    NASA Technical Reports Server (NTRS)

    Deissler, Robert G.

    1991-01-01

    A derivation of the continuum equations used for the analysis of turbulence is given. These equations include the continuity equation, the Navier-Stokes equations, and the heat transfer or energy equation. An experimental justification for using a continuum approach for the study of turbulence is given.

  9. Optimization of one-way wave equations.

    USGS Publications Warehouse

    Lee, M.W.; Suh, S.Y.

    1985-01-01

    The theory of wave extrapolation is based on the square-root equation or one-way equation. The full wave equation represents waves which propagate in both directions. On the contrary, the square-root equation represents waves propagating in one direction only. A new optimization method presented here improves the dispersion relation of the one-way wave equation. -from Authors

  10. How to Obtain the Covariant Form of Maxwell's Equations from the Continuity Equation

    ERIC Educational Resources Information Center

    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.

  11. Fractional-calculus diffusion equation

    PubMed Central

    2010-01-01

    Background Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems. Results The canonical quantization of a system represented classically by one-dimensional Fick's law, and the diffusion equation is carried out according to the Dirac method. A suitable Lagrangian, and Hamiltonian, describing the diffusive system, are constructed and the Hamiltonian is transformed to Schrodinger's equation which is solved. An application regarding implementation of the developed mathematical method to the analysis of diffusion, osmosis, which is a biological application of the diffusion process, is carried out. Schrödinger's equation is solved. Conclusions The plot of the probability function represents clearly the dissipative and drift forces and hence the osmosis, which agrees totally with the macro-scale view, or the classical-version osmosis. PMID:20492677

  12. Students' understanding of quadratic equations

    NASA Astrophysics Data System (ADS)

    López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

    2016-05-01

    Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help students achieve an understanding of quadratic equations with improved interrelation of ideas and more flexible application of solution methods. Semi-structured interviews with eight beginning undergraduate students explored which of the mental constructions conjectured in the genetic decomposition students could do, and which they had difficulty doing. Two of the mental constructions that form part of the genetic decomposition are highlighted and corresponding further data were obtained from the written work of 121 undergraduate science and engineering students taking a multivariable calculus course. The results suggest the importance of explicitly considering these two highlighted mental constructions.

  13. Explicit integration of Friedmann's equation with nonlinear equations of state

    NASA Astrophysics Data System (ADS)

    Chen, Shouxin; Gibbons, Gary W.; Yang, Yisong

    2015-05-01

    In this paper we study the integrability of the Friedmann equations, when the equation of state for the perfect-fluid universe is nonlinear, in the light of the Chebyshev theorem. A series of important, yet not previously touched, problems will be worked out which include the generalized Chaplygin gas, two-term energy density, trinomial Friedmann, Born-Infeld, two-fluid models, and Chern-Simons modified gravity theory models. With the explicit integration, we are able to understand exactly the roles of the physical parameters in various models play in the cosmological evolution which may also offer clues to a profound understanding of the problems in general settings. For example, in the Chaplygin gas universe, a few integrable cases lead us to derive a universal formula for the asymptotic exponential growth rate of the scale factor, of an explicit form, whether the Friedmann equation is integrable or not, which reveals the coupled roles played by various physical sectors and it is seen that, as far as there is a tiny presence of nonlinear matter, conventional linear matter makes contribution to the dark matter, which becomes significant near the phantom divide line. The Friedmann equations also arise in areas of physics not directly related to cosmology. We provide some examples ranging from geometric optics and central orbits to soap films and the shape of glaciated valleys to which our results may be applied.

  14. Maxwell's mixing equation revisited: characteristic impedance equations for ellipsoidal cells.

    PubMed

    Stubbe, Marco; Gimsa, Jan

    2015-07-21

    We derived a series of, to our knowledge, new analytic expressions for the characteristic features of the impedance spectra of suspensions of homogeneous and single-shell spherical, spheroidal, and ellipsoidal objects, e.g., biological cells of the general ellipsoidal shape. In the derivation, we combined the Maxwell-Wagner mixing equation with our expression for the Clausius-Mossotti factor that had been originally derived to describe AC-electrokinetic effects such as dielectrophoresis, electrorotation, and electroorientation. The influential radius model was employed because it allows for a separation of the geometric and electric problems. For shelled objects, a special axial longitudinal element approach leads to a resistor-capacitor model, which can be used to simplify the mixing equation. Characteristic equations were derived for the plateau levels, peak heights, and characteristic frequencies of the impedance as well as the complex specific conductivities and permittivities of suspensions of axially and randomly oriented homogeneous and single-shell ellipsoidal objects. For membrane-covered spherical objects, most of the limiting cases are identical to-or improved with respect to-the known solutions given by researchers in the field. The characteristic equations were found to be quite precise (largest deviations typically <5% with respect to the full model) when tested with parameters relevant to biological cells. They can be used for the differentiation of orientation and the electric properties of cell suspensions or in the analysis of single cells in microfluidic systems. PMID:26200856

  15. Transport equations in tokamak plasmas

    SciTech Connect

    Callen, J. D.; Hegna, C. C.; Cole, A. J.

    2010-05-15

    Tokamak plasma transport equations are usually obtained by flux surface averaging the collisional Braginskii equations. However, tokamak plasmas are not in collisional regimes. Also, ad hoc terms are added for neoclassical effects on the parallel Ohm's law, fluctuation-induced transport, heating, current-drive and flow sources and sinks, small magnetic field nonaxisymmetries, magnetic field transients, etc. A set of self-consistent second order in gyroradius fluid-moment-based transport equations for nearly axisymmetric tokamak plasmas has been developed using a kinetic-based approach. The derivation uses neoclassical-based parallel viscous force closures, and includes all the effects noted above. Plasma processes on successive time scales and constraints they impose are considered sequentially: compressional Alfven waves (Grad-Shafranov equilibrium, ion radial force balance), sound waves (pressure constant along field lines, incompressible flows within a flux surface), and collisions (electrons, parallel Ohm's law; ions, damping of poloidal flow). Radial particle fluxes are driven by the many second order in gyroradius toroidal angular torques on a plasma species: seven ambipolar collision-based ones (classical, neoclassical, etc.) and eight nonambipolar ones (fluctuation-induced, polarization flows from toroidal rotation transients, etc.). The plasma toroidal rotation equation results from setting to zero the net radial current induced by the nonambipolar fluxes. The radial particle flux consists of the collision-based intrinsically ambipolar fluxes plus the nonambipolar fluxes evaluated at the ambipolarity-enforcing toroidal plasma rotation (radial electric field). The energy transport equations do not involve an ambipolar constraint and hence are more directly obtained. The 'mean field' effects of microturbulence on the parallel Ohm's law, poloidal ion flow, particle fluxes, and toroidal momentum and energy transport are all included self-consistently. The

  16. Young's Equation at the Nanoscale

    NASA Astrophysics Data System (ADS)

    Seveno, David; Blake, Terence D.; De Coninck, Joël

    2013-08-01

    In 1805, Thomas Young was the first to propose an equation to predict the value of the equilibrium contact angle of a liquid on a solid. Today, the force exerted by a liquid on a solid, such as a flat plate or fiber, is routinely used to assess this angle. Moreover, it has recently become possible to study wetting at the nanoscale using an atomic force microscope. Here, we report the use of molecular-dynamics simulations to investigate the force distribution along a 15 nm fiber dipped into a liquid meniscus. We find very good agreement between the measured force and that predicted by Young’s equation.

  17. Accurate response surface approximations for weight equations based on structural optimization

    NASA Astrophysics Data System (ADS)

    Papila, Melih

    Accurate weight prediction methods are vitally important for aircraft design optimization. Therefore, designers seek weight prediction techniques with low computational cost and high accuracy, and usually require a compromise between the two. The compromise can be achieved by combining stress analysis and response surface (RS) methodology. While stress analysis provides accurate weight information, RS techniques help to transmit effectively this information to the optimization procedure. The focus of this dissertation is structural weight equations in the form of RS approximations and their accuracy when fitted to results of structural optimizations that are based on finite element analyses. Use of RS methodology filters out the numerical noise in structural optimization results and provides a smooth weight function that can easily be used in gradient-based configuration optimization. In engineering applications RS approximations of low order polynomials are widely used, but the weight may not be modeled well by low-order polynomials, leading to bias errors. In addition, some structural optimization results may have high-amplitude errors (outliers) that may severely affect the accuracy of the weight equation. Statistical techniques associated with RS methodology are sought in order to deal with these two difficulties: (1) high-amplitude numerical noise (outliers) and (2) approximation model inadequacy. The investigation starts with reducing approximation error by identifying and repairing outliers. A potential reason for outliers in optimization results is premature convergence, and outliers of such nature may be corrected by employing different convergence settings. It is demonstrated that outlier repair can lead to accuracy improvements over the more standard approach of removing outliers. The adequacy of approximation is then studied by a modified lack-of-fit approach, and RS errors due to the approximation model are reduced by using higher order polynomials. In

  18. The Forced Soft Spring Equation

    ERIC Educational Resources Information Center

    Fay, T. H.

    2006-01-01

    Through numerical investigations, this paper studies examples of the forced Duffing type spring equation with [epsilon] negative. By performing trial-and-error numerical experiments, the existence is demonstrated of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions. Subharmonic boundaries are…

  19. The Symbolism Of Chemical Equations

    ERIC Educational Resources Information Center

    Jensen, William B.

    2005-01-01

    A question about the historical origin of equal sign and double arrow symbolism in balanced chemical equation is raised. The study shows that Marshall proposed the symbolism in 1902, which includes the use of currently favored double barb for equilibrium reactions.

  20. Mathematics and Reading Test Equating.

    ERIC Educational Resources Information Center

    Lee, Ong Kim; Wright, Benjamin D.

    As part of a larger project to assess changes in student learning resulting from school reform, this study equates levels 6 through 14 of the mathematics and reading comprehension components of Form 7 of the Iowa Tests of Basic Skills (ITBS) with levels 7 through 14 of the mathematics and reading comprehension components of the CPS90 (another…

  1. Optimized solution of Kepler's equation

    NASA Technical Reports Server (NTRS)

    Kohout, J. M.; Layton, L.

    1972-01-01

    A detailed description is presented of KEPLER, an IBM 360 computer program used for the solution of Kepler's equation for eccentric anomaly. The program KEPLER employs a second-order Newton-Raphson differential correction process, and it is faster than previously developed programs by an order of magnitude.

  2. The solution of transcendental equations

    NASA Technical Reports Server (NTRS)

    Agrawal, K. M.; Outlaw, R.

    1973-01-01

    Some of the existing methods to globally approximate the roots of transcendental equations namely, Graeffe's method, are studied. Summation of the reciprocated roots, Whittaker-Bernoulli method, and the extension of Bernoulli's method via Koenig's theorem are presented. The Aitken's delta squared process is used to accelerate the convergence. Finally, the suitability of these methods is discussed in various cases.

  3. Duffing's Equation and Nonlinear Resonance

    ERIC Educational Resources Information Center

    Fay, Temple H.

    2003-01-01

    The phenomenon of nonlinear resonance (sometimes called the "jump phenomenon") is examined and second-order van der Pol plane analysis is employed to indicate that this phenomenon is not a feature of the equation, but rather the result of accumulated round-off error, truncation error and algorithm error that distorts the true bounded solution onto…

  4. Scale Shrinkage in Vertical Equating.

    ERIC Educational Resources Information Center

    Camilli, Gregory; And Others

    1993-01-01

    Three potential causes of scale shrinkage (measurement error, restriction of range, and multidimensionality) in item response theory vertical equating are discussed, and a more comprehensive model-based approach to establishing vertical scales is described. Test data from the National Assessment of Educational Progress are used to illustrate the…

  5. Sonar equations for planetary exploration.

    PubMed

    Ainslie, Michael A; Leighton, Timothy G

    2016-08-01

    The set of formulations commonly known as "the sonar equations" have for many decades been used to quantify the performance of sonar systems in terms of their ability to detect and localize objects submerged in seawater. The efficacy of the sonar equations, with individual terms evaluated in decibels, is well established in Earth's oceans. The sonar equations have been used in the past for missions to other planets and moons in the solar system, for which they are shown to be less suitable. While it would be preferable to undertake high-fidelity acoustical calculations to support planning, execution, and interpretation of acoustic data from planetary probes, to avoid possible errors for planned missions to such extraterrestrial bodies in future, doing so requires awareness of the pitfalls pointed out in this paper. There is a need to reexamine the assumptions, practices, and calibrations that work well for Earth to ensure that the sonar equations can be accurately applied in combination with the decibel to extraterrestrial scenarios. Examples are given for icy oceans such as exist on Europa and Ganymede, Titan's hydrocarbon lakes, and for the gaseous atmospheres of (for example) Jupiter and Venus. PMID:27586766

  6. Perceptions of the Schrodinger equation

    NASA Astrophysics Data System (ADS)

    Efthimiades, Spyros

    2014-03-01

    The Schrodinger equation has been considered to be a postulate of quantum physics, but it is also perceived as the quantum equivalent of the non-relativistic classical energy relation. We argue that the Schrodinger equation cannot be a physical postulate, and we show explicitly that its second space derivative term is wrongly associated with the kinetic energy of the particle. The kinetic energy of a particle at a point is proportional to the square of the momentum, that is, to the square of the first space derivative of the wavefunction. Analyzing particle interactions, we realize that particles have multiple virtual motions and that each motion is accompanied by a wave that has constant amplitude. Accordingly, we define the wavefunction as the superposition of the virtual waves of the particle. In simple interaction settings we can tell what particle motions arise and can explain the outcomes in direct and tangible terms. Most importantly, the mathematical foundation of quantum mechanics becomes clear and justified, and we derive the Schrodinger, Dirac, etc. equations as the conditions the wavefunction must satisfy at each space-time point in order to fulfill the respective total energy equation.

  7. Renaissance Learning Equating Study. Report

    ERIC Educational Resources Information Center

    Sewell, Julie; Sainsbury, Marian; Pyle, Katie; Keogh, Nikki; Styles, Ben

    2007-01-01

    An equating study was carried out in autumn 2006 by the National Foundation for Educational Research (NFER) on behalf of Renaissance Learning, to provide validation evidence for the use of the Renaissance Star Reading and Star Mathematics tests in English schools. The study investigated the correlation between the Star tests and established tests.…

  8. Pendulum Motion and Differential Equations

    ERIC Educational Resources Information Center

    Reid, Thomas F.; King, Stephen C.

    2009-01-01

    A common example of real-world motion that can be modeled by a differential equation, and one easily understood by the student, is the simple pendulum. Simplifying assumptions are necessary for closed-form solutions to exist, and frequently there is little discussion of the impact if those assumptions are not met. This article presents a…

  9. Ordinary Differential Equation System Solver

    Energy Science and Technology Software Center (ESTSC)

    1992-03-05

    LSODE is a package of subroutines for the numerical solution of the initial value problem for systems of first order ordinary differential equations. The package is suitable for either stiff or nonstiff systems. For stiff systems the Jacobian matrix may be treated in either full or banded form. LSODE can also be used when the Jacobian can be approximated by a band matrix.

  10. Empirical equation estimates geothermal gradients

    SciTech Connect

    Kutasov, I.M. )

    1995-01-02

    An empirical equation can estimate geothermal (natural) temperature profiles in new exploration areas. These gradients are useful for cement slurry and mud design and for improving electrical and temperature log interpretation. Downhole circulating temperature logs and surface outlet temperatures are used for predicting the geothermal gradients.

  11. Simulated Equating Using Several Item Response Curves.

    ERIC Educational Resources Information Center

    Boldt, R. F.

    The comparison of item response theory models for the Test of English as a Foreign Language (TOEFL) was extended to an equating context as simulation trials were used to "equate the test to itself." Equating sample data were generated from administration of identical item sets. Equatings that used procedures based on each model (simple item…

  12. Relativistic equations with fractional and pseudodifferential operators

    SciTech Connect

    Babusci, D.; Dattoli, G.; Quattromini, M.

    2011-06-15

    In this paper we use different techniques from the fractional and pseudo-operators calculus to solve partial differential equations involving operators with noninteger exponents. We apply the method to equations resembling generalizations of the heat equations and discuss the possibility of extending the procedure to the relativistic Schroedinger and Dirac equations.

  13. Simple Derivation of the Lindblad Equation

    ERIC Educational Resources Information Center

    Pearle, Philip

    2012-01-01

    The Lindblad equation is an evolution equation for the density matrix in quantum theory. It is the general linear, Markovian, form which ensures that the density matrix is Hermitian, trace 1, positive and completely positive. Some elementary examples of the Lindblad equation are given. The derivation of the Lindblad equation presented here is…

  14. A Versatile Technique for Solving Quintic Equations

    ERIC Educational Resources Information Center

    Kulkarni, Raghavendra G.

    2006-01-01

    In this paper we present a versatile technique to solve several types of solvable quintic equations. In the technique described here, the given quintic is first converted to a sextic equation by adding a root, and the resulting sextic equation is decomposed into two cubic polynomials as factors in a novel fashion. The resultant cubic equations are…

  15. Isothermal Equation Of State For Compressed Solids

    NASA Technical Reports Server (NTRS)

    Vinet, Pascal; Ferrante, John

    1989-01-01

    Same equation with three adjustable parameters applies to different materials. Improved equation of state describes pressure on solid as function of relative volume at constant temperature. Even though types of interatomic interactions differ from one substance to another, form of equation determined primarily by overlap of electron wave functions during compression. Consequently, equation universal in sense it applies to variety of substances, including ionic, metallic, covalent, and rare-gas solids. Only three parameters needed to describe equation for given material.

  16. Integrable (2 k)-Dimensional Hitchin Equations

    NASA Astrophysics Data System (ADS)

    Ward, R. S.

    2016-07-01

    This letter describes a completely integrable system of Yang-Mills-Higgs equations which generalizes the Hitchin equations on a Riemann surface to arbitrary k-dimensional complex manifolds. The system arises as a dimensional reduction of a set of integrable Yang-Mills equations in 4 k real dimensions. Our integrable system implies other generalizations such as the Simpson equations and the non-abelian Seiberg-Witten equations. Some simple solutions in the k = 2 case are described.

  17. Graviton corrections to Maxwell's equations

    NASA Astrophysics Data System (ADS)

    Leonard, Katie E.; Woodard, R. P.

    2012-05-01

    We use dimensional regularization to compute the one loop quantum gravitational contribution to the vacuum polarization on flat space background. Adding the appropriate Bogoliubov-Parsiuk-Hepp-Zimmermann counterterm gives a fully renormalized result which we employ to quantum correct Maxwell’s equations. These equations are solved to show that dynamical photons are unchanged, provided the free state wave functional is appropriately corrected. The response to the instantaneous appearance of a point dipole reveals a perturbative version of the long-conjectured, “smearing of the light cone”. There is no change in the far radiation field produced by an alternating dipole. However, the correction to the static electric field of a point charge shows strengthening at short distances, in contrast to expectations based on the renormalization group. We check for gauge dependence by working out the vacuum polarization in a general 3-parameter family of covariant gauges.

  18. Renewal equations for option pricing

    NASA Astrophysics Data System (ADS)

    Montero, M.

    2008-09-01

    In this paper we will develop a methodology for obtaining pricing expressions for financial instruments whose underlying asset can be described through a simple continuous-time random walk (CTRW) market model. Our approach is very natural to the issue because it is based in the use of renewal equations, and therefore it enhances the potential use of CTRW techniques in finance. We solve these equations for typical contract specifications, in a particular but exemplifying case. We also show how a formal general solution can be found for more exotic derivatives, and we compare prices for alternative models of the underlying. Finally, we recover the celebrated results for the Wiener process under certain limits.

  19. Applications of film thickness equations

    NASA Technical Reports Server (NTRS)

    Hamrock, B. J.; Dowson, D.

    1983-01-01

    A number of applications of elastohydrodynamic film thickness expressions were considered. The motion of a steel ball over steel surfaces presenting varying degrees of conformity was examined. The equation for minimum film thickness in elliptical conjunctions under elastohydrodynamic conditions was applied to roller and ball bearings. An involute gear was also introduced, it was again found that the elliptical conjunction expression yielded a conservative estimate of the minimum film thickness. Continuously variable-speed drives like the Perbury gear, which present truly elliptical elastohydrodynamic conjunctions, are favored increasingly in mobile and static machinery. A representative elastohydrodynamic condition for this class of machinery is considered for power transmission equipment. The possibility of elastohydrodynamic films of water or oil forming between locomotive wheels and rails is examined. The important subject of traction on the railways is attracting considerable attention in various countries at the present time. The final example of a synovial joint introduced the equation developed for isoviscous-elastic regimes of lubrication.

  20. Fresnel Integral Equations: Numerical Properties

    SciTech Connect

    Adams, R J; Champagne, N J II; Davis, B A

    2003-07-22

    A spatial-domain solution to the problem of electromagnetic scattering from a dielectric half-space is outlined. The resulting half-space operators are referred to as Fresnel surface integral operators. When used as preconditioners for nonplanar geometries, the Fresnel operators yield surface Fresnel integral equations (FIEs) which are stable with respect to dielectric constant, discretization, and frequency. Numerical properties of the formulations are discussed.

  1. Linear superposition in nonlinear equations.

    PubMed

    Khare, Avinash; Sukhatme, Uday

    2002-06-17

    Several nonlinear systems such as the Korteweg-de Vries (KdV) and modified KdV equations and lambda phi(4) theory possess periodic traveling wave solutions involving Jacobi elliptic functions. We show that suitable linear combinations of these known periodic solutions yield many additional solutions with different periods and velocities. This linear superposition procedure works by virtue of some remarkable new identities involving elliptic functions. PMID:12059300

  2. Equation of State Project Overview

    SciTech Connect

    Crockett, Scott

    2015-09-11

    A general overview of the Equation of State (EOS) Project will be presented. The goal is to provide the audience with an introduction of what our more advanced methods entail (DFT, QMD, etc.. ) and how these models are being utilized to better constrain the thermodynamic models. These models substantially reduce our regions of interpolation between the various thermodynamic limits. I will also present a variety example of recent EOS work.

  3. ON THE GENERALISED FANT EQUATION.

    PubMed

    Howe, M S; McGowan, R S

    2011-06-20

    An analysis is made of the fluid-structure interactions involved in the production of voiced speech. It is usual to avoid time consuming numerical simulations of the aeroacoustics of the vocal tract and glottis by the introduction of Fant's 'reduced complexity' equation for the glottis volume velocity Q (G. Fant, Acoustic Theory of Speech Production, Mouton, The Hague 1960). A systematic derivation is given of Fant's equation based on the nominally exact equations of aerodynamic sound. This can be done with a degree of approximation that depends only on the accuracy with which the time-varying flow geometry and surface-acoustic boundary conditions can be specified, and replaces Fant's original 'lumped element' heuristic approach. The method determines all of the effective 'source terms' governing Q. It is illustrated by consideration of a simplified model of the vocal system involving a self-sustaining single-mass model of the vocal folds, that uses free streamline theory to account for surface friction and flow separation within the glottis. Identification is made of a new source term associated with the unsteady vocal fold drag produced by their oscillatory motion transverse to the mean flow. PMID:21603054

  4. ON THE GENERALISED FANT EQUATION

    PubMed Central

    Howe, M. S.; McGowan, R. S.

    2011-01-01

    An analysis is made of the fluid-structure interactions involved in the production of voiced speech. It is usual to avoid time consuming numerical simulations of the aeroacoustics of the vocal tract and glottis by the introduction of Fant’s ‘reduced complexity’ equation for the glottis volume velocity Q (G. Fant, Acoustic Theory of Speech Production, Mouton, The Hague 1960). A systematic derivation is given of Fant’s equation based on the nominally exact equations of aerodynamic sound. This can be done with a degree of approximation that depends only on the accuracy with which the time-varying flow geometry and surface-acoustic boundary conditions can be specified, and replaces Fant’s original ‘lumped element’ heuristic approach. The method determines all of the effective ‘source terms’ governing Q. It is illustrated by consideration of a simplified model of the vocal system involving a self-sustaining single-mass model of the vocal folds, that uses free streamline theory to account for surface friction and flow separation within the glottis. Identification is made of a new source term associated with the unsteady vocal fold drag produced by their oscillatory motion transverse to the mean flow. PMID:21603054

  5. The Thin Oil Film Equation

    NASA Technical Reports Server (NTRS)

    Brown, James L.; Naughton, Jonathan W.

    1999-01-01

    A thin film of oil on a surface responds primarily to the wall shear stress generated on that surface by a three-dimensional flow. The oil film is also subject to wall pressure gradients, surface tension effects and gravity. The partial differential equation governing the oil film flow is shown to be related to Burgers' equation. Analytical and numerical methods for solving the thin oil film equation are presented. A direct numerical solver is developed where the wall shear stress variation on the surface is known and which solves for the oil film thickness spatial and time variation on the surface. An inverse numerical solver is also developed where the oil film thickness spatial variation over the surface at two discrete times is known and which solves for the wall shear stress variation over the test surface. A One-Time-Level inverse solver is also demonstrated. The inverse numerical solver provides a mathematically rigorous basis for an improved form of a wall shear stress instrument suitable for application to complex three-dimensional flows. To demonstrate the complexity of flows for which these oil film methods are now suitable, extensive examination is accomplished for these analytical and numerical methods as applied to a thin oil film in the vicinity of a three-dimensional saddle of separation.

  6. The complex chemical Langevin equation

    SciTech Connect

    Schnoerr, David; Sanguinetti, Guido; Grima, Ramon

    2014-07-14

    The chemical Langevin equation (CLE) is a popular simulation method to probe the stochastic dynamics of chemical systems. The CLE’s main disadvantage is its break down in finite time due to the problem of evaluating square roots of negative quantities whenever the molecule numbers become sufficiently small. We show that this issue is not a numerical integration problem, rather in many systems it is intrinsic to all representations of the CLE. Various methods of correcting the CLE have been proposed which avoid its break down. We show that these methods introduce undesirable artefacts in the CLE’s predictions. In particular, for unimolecular systems, these correction methods lead to CLE predictions for the mean concentrations and variance of fluctuations which disagree with those of the chemical master equation. We show that, by extending the domain of the CLE to complex space, break down is eliminated, and the CLE’s accuracy for unimolecular systems is restored. Although the molecule numbers are generally complex, we show that the “complex CLE” predicts real-valued quantities for the mean concentrations, the moments of intrinsic noise, power spectra, and first passage times, hence admitting a physical interpretation. It is also shown to provide a more accurate approximation of the chemical master equation of simple biochemical circuits involving bimolecular reactions than the various corrected forms of the real-valued CLE, the linear-noise approximation and a commonly used two moment-closure approximation.

  7. Nonlocal Equations with Measure Data

    NASA Astrophysics Data System (ADS)

    Kuusi, Tuomo; Mingione, Giuseppe; Sire, Yannick

    2015-08-01

    We develop an existence, regularity and potential theory for nonlinear integrodifferential equations involving measure data. The nonlocal elliptic operators considered are possibly degenerate and cover the case of the fractional p-Laplacean operator with measurable coefficients. We introduce a natural function class where we solve the Dirichlet problem, and prove basic and optimal nonlinear Wolff potential estimates for solutions. These are the exact analogs of the results valid in the case of local quasilinear degenerate equations established by Boccardo and Gallouët (J Funct Anal 87:149-169, 1989, Partial Differ Equ 17:641-655, 1992) and Kilpeläinen and Malý (Ann Scuola Norm Sup Pisa Cl Sci (IV) 19:591-613, 1992, Acta Math 172:137-161, 1994). As a consequence, we establish a number of results that can be considered as basic building blocks for a nonlocal, nonlinear potential theory: fine properties of solutions, Calderón-Zygmund estimates, continuity and boundedness criteria are established via Wolff potentials. A main tool is the introduction of a global excess functional that allows us to prove a nonlocal analog of the classical theory due to Campanato (Ann Mat Pura Appl (IV) 69:321-381, 1965). Our results cover the case of linear nonlocal equations with measurable coefficients, and the one of the fractional Laplacean, and are new already in such cases.

  8. On the generalised Fant equation

    NASA Astrophysics Data System (ADS)

    Howe, M. S.; McGowan, R. S.

    2011-06-01

    An analysis is made of the fluid-structure interactions involved in the production of voiced speech. It is usual to avoid time consuming numerical simulations of the aeroacoustics of the vocal tract and glottis by the introduction of Fant's 'reduced complexity' equation for the glottis volume velocity Q [G. Fant, Acoustic Theory of Speech Production, Mouton, The Hague 1960]. A systematic derivation is given of Fant's equation based on the nominally exact equations of aerodynamic sound. This can be done with a degree of approximation that depends only on the accuracy with which the time-varying flow geometry and surface-acoustic boundary conditions can be specified, and replaces Fant's original 'lumped element' heuristic approach. The method determines all of the effective 'source terms' governing Q. It is illustrated by consideration of a simplified model of the vocal system involving a self-sustaining single-mass model of the vocal folds, that uses free streamline theory to account for surface friction and flow separation within the glottis. Identification is made of a new source term associated with the unsteady vocal fold drag produced by their oscillatory motion transverse to the mean flow.

  9. ADVANCED WAVE-EQUATION MIGRATION

    SciTech Connect

    L. HUANG; M. C. FEHLER

    2000-12-01

    Wave-equation migration methods can more accurately account for complex wave phenomena than ray-tracing-based Kirchhoff methods that are based on the high-frequency asymptotic approximation of waves. With steadily increasing speed of massively parallel computers, wave-equation migration methods are becoming more and more feasible and attractive for imaging complex 3D structures. We present an overview of several efficient and accurate wave-equation-based migration methods that we have recently developed. The methods are implemented in the frequency-space and frequency-wavenumber domains and hence they are called dual-domain methods. In the methods, we make use of different approximate solutions of the scalar-wave equation in heterogeneous media to recursively downward continue wavefields. The approximations used within each extrapolation interval include the Born, quasi-Born, and Rytov approximations. In one of our dual-domain methods, we use an optimized expansion of the square-root operator in the one-way wave equation to minimize the phase error for a given model. This leads to a globally optimized Fourier finite-difference method that is a hybrid split-step Fourier and finite-difference scheme. Migration examples demonstrate that our dual-domain migration methods provide more accurate images than those obtained using the split-step Fourier scheme. The Born-based, quasi-Born-based, and Rytov-based methods are suitable for imaging complex structures whose lateral variations are moderate, such as the Marmousi model. For this model, the computational cost of the Born-based method is almost the same as the split-step Fourier scheme, while other methods takes approximately 15-50% more computational time. The globally optimized Fourier finite-difference method significantly improves the accuracy of the split-step Fourier method for imaging structures having strong lateral velocity variations, such as the SEG/EAGE salt model, at an approximately 30% greater

  10. Exact solutions to the Benney-Luke equation and the Phi-4 equations by using modified simple equation method

    NASA Astrophysics Data System (ADS)

    Akter, Jesmin; Ali Akbar, M.

    The modified simple equation (MSE) method is a competent and highly effective mathematical tool for extracting exact traveling wave solutions to nonlinear evolution equations (NLEEs) arising in science, engineering and mathematical physics. In this article, we implement the MSE method to find the exact solutions involving parameters to NLEEs via the Benney-Luke equation and the Phi-4 equations. The solitary wave solutions are derived from the exact traveling wave solutions when the parameters receive their special values.

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

    ERIC Educational Resources Information Center

    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.

  12. Logistic equation of arbitrary order

    NASA Astrophysics Data System (ADS)

    Grabowski, Franciszek

    2010-08-01

    The paper is concerned with the new logistic equation of arbitrary order which describes the performance of complex executive systems X vs. number of tasks N, operating at limited resources K, at non-extensive, heterogeneous self-organization processes characterized by parameter f. In contrast to the classical logistic equation which exclusively relates to the special case of sub-extensive homogeneous self-organization processes at f=1, the proposed model concerns both homogeneous and heterogeneous processes in sub-extensive and super-extensive areas. The parameter of arbitrary order f, where -∞equation includes all possible cases of a complex executive system’s operation. Furthermore, it allows us to define the optimal matching point between X and N with f as the parameter. It also helps to balance the load in complex systems and to equip artificial systems with self-optimization mechanisms similar to those observed in natural systems.

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

    ERIC Educational Resources Information Center

    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…

  14. Germanium multiphase equation of state

    SciTech Connect

    Crockett, Scott D.; Lorenzi-Venneri, Giulia De; Kress, Joel D.; Rudin, Sven P.

    2014-05-07

    A new SESAME multiphase germanium equation of state (EOS) has been developed using the best available experimental data and density functional theory (DFT) calculations. The equilibrium EOS includes the Ge I (diamond), the Ge II (β-Sn) and the liquid phases. The foundation of the EOS is based on density functional theory calculations which are used to determine the cold curve and the Debye temperature. Results are compared to Hugoniot data through the solid-solid and solid-liquid transitions. We propose some experiments to better understand the dynamics of this element

  15. Advanced lab on Fresnel equations

    NASA Astrophysics Data System (ADS)

    Petrova-Mayor, Anna; Gimbal, Scott

    2015-11-01

    This experimental and theoretical exercise is designed to promote students' understanding of polarization and thin-film coatings for the practical case of a scanning protected-metal coated mirror. We present results obtained with a laboratory scanner and a polarimeter and propose an affordable and student-friendly experimental arrangement for the undergraduate laboratory. This experiment will allow students to apply basic knowledge of the polarization of light and thin-film coatings, develop hands-on skills with the use of phase retarders, apply the Fresnel equations for metallic coating with complex index of refraction, and compute the polarization state of the reflected light.

  16. Research on two equation models

    NASA Technical Reports Server (NTRS)

    Yang, Z.

    1993-01-01

    The k-epsilon model is the most widely used turbulence model in engineering calculations. However, the model has several deficiencies that need to be fixed. This document presents improvements to the capabilities of the k-epsilon model in the following areas: a Galilean and tensorial invariant k-epsilon model for near wall turbulence; a new set of wall functions for attached flows; a new model equation for the dissipation rate, which has a better theoretical basis, contains the contribution of flow inhomogeneity, and captures the effect of the pressure gradient accurately; and a better model for bypass transition due to freestream turbulence.

  17. On the connection of the quadratic Lienard equation with an equation for the elliptic functions

    NASA Astrophysics Data System (ADS)

    Kudryashov, Nikolay A.; Sinelshchikov, Dmitry I.

    2015-07-01

    The quadratic Lienard equation is widely used in many applications. A connection between this equation and a linear second-order differential equation has been discussed. Here we show that the whole family of quadratic Lienard equations can be transformed into an equation for the elliptic functions. We demonstrate that this connection can be useful for finding explicit forms of general solutions of the quadratic Lienard equation. We provide several examples of application of our approach.

  18. The inadequacies of absolute prohibition of reproductive cloning.

    PubMed

    Lee, Martin Lishexian

    2004-02-01

    This study reviews debates on human cloning and its benefits, considers international and domestic laws, and argues that the choice of reproductive means is a human right. In exercise of this right, a balanced approach should be adopted, in order to benefit human society while protecting human dignity adequately. The immaturity of cloning techniques indicates that at the present time human reproductive cloning is too risky. Thus a temporary ban on such cloning is appropriate, but the ban on relevant scientific research and animal experimentation is inappropriate as it denies the spirit of freedom of scientific inquiry, and hinders making the benefits of scientific advancement available to human society as a whole. PMID:15018212

  19. Correctional Recreation Today, A Pitiful Reflection of Our Past Inadequacy.

    ERIC Educational Resources Information Center

    Calloway, Jim

    1981-01-01

    A brief history of correctional recreation from the late 1800s through the time of the Attica riots is presented. Since the prison population is 60 to 70 percent Black, there is an obvious need for greater minority participation in the development of correctional recreation. (JN)

  20. Textbook Sexual Inadequacy? A Review of Sexuality Texts.

    ERIC Educational Resources Information Center

    Goettsch, Stephen L.

    1987-01-01

    Reviews eight current human sexuality textbooks for both their general organization and substantive content. Addresses specifically the content areas of sexual response cycle; sexual disfunction; acquaintance rape; AIDS and sexually transmitted diseases; extramarital sex; abortion; homosexuality; and pornography. Identifies as a recurring fault…

  1. Inadequacy the Health System in Serbia and Corrupt Institutions

    PubMed Central

    Dickov, Veselin

    2012-01-01

    Rapid changes in the health system require a new trained professionals who fully understand the processes of health and organizational problems and have the knowledge and skills that enable them to manage health care services. Health services to their largely rests on a system of solidarity and “socialism”, and only partly on market principle, and more than in other sectors of the economy requires individuals who are able to bridge that gap. Realize savings in the system that one side is not profitable, on the other hand is able to swallow a huge media arts is that simply needs to learn–just relying on common sense and intuition that no longer helps. The increase in costs. Advances in medicine and technology, and discovery of new drugs, namely, the almost daily increase the costs of diagnosis and treatment. Advances in medicine prolongs life expectancy by increasing the number of patients, especially those with chronic diseases, the biggest consumer of drugs and frequent guests hospital. PMID:23678330

  2. Institutional Biosafety Committees and the Inadequacies of Risk Regulation.

    ERIC Educational Resources Information Center

    Bereano, Philip L.

    1984-01-01

    Discusses institutional biosafety committees (IBC) which provide quasi-independent reviews of recombinant DNA work done at an institution. Considers the nature of IBC operation, the National Institutes of Health "Guidelines for Recombinant DNA Research," the composition of IBCs, the intellectual content of IBC deliberations, and issues related to…

  3. Inadequacy of Palliative Training in the Medical School Curriculum.

    PubMed

    Chiu, Nicholas; Cheon, Paul; Lutz, Stephen; Lao, Nicholas; Pulenzas, Natalie; Chiu, Leonard; McDonald, Rachel; Rowbottom, Leigha; Chow, Edward

    2015-12-01

    This report examines the literature on palliative training in the current medical school curriculum. A literature search was conducted to identify relevant articles. Physicians and medical students both report feeling that their training in end-of-life care and in palliative issues is lacking. The literature expresses concerns about the varied and non-uniform approach to palliative care training across medical schools. The authors recommend the development of more palliative training assessment tools in order to aid in the standardization of curriculum involving end-of-life care. In addition, increased exposure to dying patients will aid students in building comfort with palliative care issues. Such a goal may be accomplished through required clerkships or other similar programs. PMID:25487030

  4. Hospital bathrooms and showers: a continuing saga of inadequacy

    PubMed Central

    Monro, Andy; Mulley, Graham P

    2004-01-01

    Previous surveys of UK hospitals have highlighted many deficiencies in the standards of hospital inpatient washing and bathing facilities—especially inadequate access for wheelchair users, insufficient bathing equipment, and unsatisfactory cleanliness and privacy. We conducted a qualitative survey in three hospitals in the North of England to see whether these facilities have improved. There have been some improvements, particularly in the provision of bath hoists, adapted taps, alarm call systems, shower seats and wheelchair access to bathrooms. But many basic problems remain—absent locks and signs, inadequate heating, poor standards of privacy, insufficient bath aids, wet floors, and the inappropriate use of bathrooms as store rooms. The overall condition of hospital bathrooms and showers remains unsatisfactory. Too many hospital bathrooms are austere, cold, smelly and poorly maintained. PMID:15121814

  5. The Educational Inadequacy of Conceptions of Self in Educational Psychology

    ERIC Educational Resources Information Center

    Martin, Jack

    2004-01-01

    Disciplinary and professional psychology have exercised considerable influence over the ways in which Western individuals and societies understand what it is to be a person. During the last half of the 20th century, educational psychologists advanced scientific and humanistic conceptions of the self that removed personhood from the historical,…

  6. Constructing Academic Inadequacy: African American Athletes' Stories of Schooling.

    ERIC Educational Resources Information Center

    Benson, Kirsten F.

    2000-01-01

    This qualitative study interviewed eight academically "at risk" African American athletes at a southeastern university with a major revenue-producing football program. Analysis suggested that the athletes' marginal academic performance was constructed in a system of interrelated practices engaged in by all the significant members of the academic…

  7. Inadequacies of death certification in Beirut: who is responsible?

    PubMed Central

    Sibai, Abla M.; Nuwayhid, Iman; Beydoun, May; Chaaya, Monique

    2002-01-01

    OBJECTIVE: To assess the completeness of data on death certificates over the past 25 years in Beirut, Lebanon, and to examine factors associated with the absence of certifiers' signatures and the non-reporting of the underlying cause of death. METHODS: A systematic 20% sample comprising 2607 death certificates covering the 1974, 1984, 1994, 1997 and 1998 registration periods was retrospectively reviewed for certification practices and missing data. FINDINGS: The information on the death certificates was almost complete in respect of all demographic characteristics of the deceased persons except for occupation and month of birth. Data relating to these variables were missing on approximately 95% and 78% of the certificates, respectively. Around half of the certificates did not carry a certifier's signature. Of those bearing such a signature, 21.6% lacked documentation of the underlying cause of death. The certifier's signature was more likely to be absent on: certificates corresponding to the younger and older age groups than on those of persons aged 15-44 years; those of females than on those of males; those of persons who had been living remotely from the registration governorate than on those of other deceased persons; and those for which there had been delays in registration exceeding six months than on certificates for which registration had been quicker. For certificates that carried the certifier's signature there was no evidence that any of the demographic characteristics of the deceased person was associated with decreased likelihood of reporting an underlying cause of death. CONCLUSION: The responsibility for failure to report causes of death in Beirut lies with families who lack an incentive to call for a physician and with certifying physicians who do not carry out this duty. The deficiencies in death certification are rectifiable. However, any changes should be sensitive to the constraints of the organizational and legal infrastructure governing death registration practices and the medical educational systems in the country. PMID:12163919

  8. Collaboration and the Inadequacy of Current Models of Composition.

    ERIC Educational Resources Information Center

    Clines, Raymond H.

    While models of expressive writing are supposed to encourage individuals to look within and release what is good and true, growing up with such a model may be counterproductive in that writers may never learn to take advantage of social interaction that might be of help in the invention and prewriting stage, and thus fail to realize the benefits…

  9. Solving Equations of Multibody Dynamics

    NASA Technical Reports Server (NTRS)

    Jain, Abhinandan; Lim, Christopher

    2007-01-01

    Darts++ is a computer program for solving the equations of motion of a multibody system or of a multibody model of a dynamic system. It is intended especially for use in dynamical simulations performed in designing and analyzing, and developing software for the control of, complex mechanical systems. Darts++ is based on the Spatial-Operator- Algebra formulation for multibody dynamics. This software reads a description of a multibody system from a model data file, then constructs and implements an efficient algorithm that solves the dynamical equations of the system. The efficiency and, hence, the computational speed is sufficient to make Darts++ suitable for use in realtime closed-loop simulations. Darts++ features an object-oriented software architecture that enables reconfiguration of system topology at run time; in contrast, in related prior software, system topology is fixed during initialization. Darts++ provides an interface to scripting languages, including Tcl and Python, that enable the user to configure and interact with simulation objects at run time.

  10. Langevin Equation for DNA Dynamics

    NASA Astrophysics Data System (ADS)

    Grych, David; Copperman, Jeremy; Guenza, Marina

    Under physiological conditions, DNA oligomers can contain well-ordered helical regions and also flexible single-stranded regions. We describe the site-specific motion of DNA with a modified Rouse-Zimm Langevin equation formalism that describes DNA as a coarse-grained polymeric chain with global structure and local flexibility. The approach has successfully described the protein dynamics in solution and has been extended to nucleic acids. Our approach provides diffusive mode analytical solutions for the dynamics of global rotational diffusion and internal motion. The internal DNA dynamics present a rich energy landscape that accounts for an interior where hydrogen bonds and base-stacking determine structure and experience limited solvent exposure. We have implemented several models incorporating different coarse-grained sites with anisotropic rotation, energy barrier crossing, and local friction coefficients that include a unique internal viscosity and our models reproduce dynamics predicted by atomistic simulations. The models reproduce bond autocorrelation along the sequence as compared to that directly calculated from atomistic molecular dynamics simulations. The Langevin equation approach captures the essence of DNA dynamics without a cumbersome atomistic representation.

  11. Higher spin versus renormalization group equations

    NASA Astrophysics Data System (ADS)

    Sachs, Ivo

    2014-10-01

    We present a variation of earlier attempts to relate renormalization group equations to higher spin equations. We work with a scalar field theory in 3 dimensions. In this case we show that the classical renormalization group equation is a variant of the Vasiliev higher spin equations with Kleinians on AdS4 for a certain subset of couplings. In the large N limit this equivalence extends to the quantum theory away from the conformal fixed points.

  12. Nonlinear SCHRÖDINGER-PAULI Equations

    NASA Astrophysics Data System (ADS)

    Ng, Wei Khim; Parwani, Rajesh R.

    2011-11-01

    We obtain novel nonlinear Schrüdinger-Pauli equations through a formal non-relativistic limit of appropriately constructed nonlinear Dirac equations. This procedure automatically provides a physical regularisation of potential singularities brought forward by the nonlinear terms and suggests how to regularise previous equations studied in the literature. The enhancement of contributions coming from the regularised singularities suggests that the obtained equations might be useful for future precision tests of quantum nonlinearity.

  13. Coupled rotor and fuselage equations of motion

    NASA Technical Reports Server (NTRS)

    Warmbrodt, W.

    1979-01-01

    The governing equations of motion of a helicopter rotor coupled to a rigid body fuselage are derived. A consistent formulation is used to derive nonlinear periodic coefficient equations of motion which are used to study coupled rotor/fuselage dynamics in forward flight. Rotor/fuselage coupling is documented and the importance of an ordering scheme in deriving nonlinear equations of motion is reviewed. The nature of the final equations and the use of multiblade coordinates are discussed.

  14. Wave equation on spherically symmetric Lorentzian metrics

    SciTech Connect

    Bokhari, Ashfaque H.; Al-Dweik, Ahmad Y.; Zaman, F. D.; Kara, A. H.; Karim, M.

    2011-06-15

    Wave equation on a general spherically symmetric spacetime metric is constructed. Noether symmetries of the equation in terms of explicit functions of {theta} and {phi} are derived subject to certain differential constraints. By restricting the metric to flat Friedman case the Noether symmetries of the wave equation are presented. Invertible transformations are constructed from a specific subalgebra of these Noether symmetries to convert the wave equation with variable coefficients to the one with constant coefficients.

  15. One-Equation Algebraic Model Of Turbulence

    NASA Technical Reports Server (NTRS)

    Baldwin, B. S.; Barth, T. J.

    1993-01-01

    One-equation model of turbulence based on standard equations of k-epsilon model of turbulence, where k is turbulent energy and e is rate of dissipation of k. Derivation of one-equation model motivated partly by inaccuracies of flows computed by some Navier-Stokes-equations-solving algorithms incorporating algebraic models of turbulence. Satisfies need to avoid having to determine algebraic length scales.

  16. On a Equation in Finite Algebraically Structures

    ERIC Educational Resources Information Center

    Valcan, Dumitru

    2013-01-01

    Solving equations in finite algebraically structures (semigroups with identity, groups, rings or fields) many times is not easy. Even the professionals can have trouble in such cases. Therefore, in this paper we proposed to solve in the various finite groups or fields, a binomial equation of the form (1). We specify that this equation has been…

  17. Some new modular equations and their applications

    NASA Astrophysics Data System (ADS)

    Yi, Jinhee; Sim, Hyo Seob

    2006-07-01

    Ramanujan derived 23 beautiful eta-function identities, which are certain types of modular equations. We found more than 70 of certain types of modular equations by using Garvan's Maple q-series package. In this paper, we prove some new modular equations which we found by employing the theory of modular form and we give some applications for them.

  18. The Effects of Repeaters on Test Equating.

    ERIC Educational Resources Information Center

    Andrulis, Richard S.; And Others

    The purpose of this investigation was to establish the effects of repeaters on test equating. Since consideration was not given to repeaters in test equating, such as in the derivation of equations by Angoff (1971), the hypothetical effect needed to be established. A case study was examined which showed results on a test as expected; overall mean…

  19. The Effect of Repeaters on Equating

    ERIC Educational Resources Information Center

    Kim, HeeKyoung; Kolen, Michael J.

    2010-01-01

    Test equating might be affected by including in the equating analyses examinees who have taken the test previously. This study evaluated the effect of including such repeaters on Medical College Admission Test (MCAT) equating using a population invariance approach. Three-parameter logistic (3-PL) item response theory (IRT) true score and…

  20. Solving Absolute Value Equations Algebraically and Geometrically

    ERIC Educational Resources Information Center

    Shiyuan, Wei

    2005-01-01

    The way in which students can improve their comprehension by understanding the geometrical meaning of algebraic equations or solving algebraic equation geometrically is described. Students can experiment with the conditions of the absolute value equation presented, for an interesting way to form an overall understanding of the concept.

  1. Local Observed-Score Kernel Equating

    ERIC Educational Resources Information Center

    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. More Issues in Observed-Score Equating

    ERIC Educational Resources Information Center

    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…

  3. Symmetry Breaking for Black-Scholes Equations

    NASA Astrophysics Data System (ADS)

    Yang, Xuan-Liu; Zhang, Shun-Li; Qu, Chang-Zheng

    2007-06-01

    Black-Scholes equation is used to model stock option pricing. In this paper, optimal systems with one to four parameters of Lie point symmetries for Black-Scholes equation and its extension are obtained. Their symmetry breaking interaction associated with the optimal systems is also studied. As a result, symmetry reductions and corresponding solutions for the resulting equations are obtained.

  4. Boundary conditions for the subdiffusion equation

    SciTech Connect

    Shkilev, V. P.

    2013-04-15

    The boundary conditions for the subdiffusion equations are formulated using the continuous-time random walk model, as well as several versions of the random walk model on an irregular lattice. It is shown that the boundary conditions for the same equation in different models have different forms, and this difference considerably affects the solutions of this equation.

  5. Equating Scores from Adaptive to Linear Tests

    ERIC Educational Resources Information Center

    van der Linden, Wim J.

    2006-01-01

    Two local methods for observed-score equating are applied to the problem of equating an adaptive test to a linear test. In an empirical study, the methods were evaluated against a method based on the test characteristic function (TCF) of the linear test and traditional equipercentile equating applied to the ability estimates on the adaptive test…

  6. Shaped cassegrain reflector antenna. [design equations

    NASA Technical Reports Server (NTRS)

    Rao, B. L. J.

    1973-01-01

    Design equations are developed to compute the reflector surfaces required to produce uniform illumination on the main reflector of a cassegrain system when the feed pattern is specified. The final equations are somewhat simple and straightforward to solve (using a computer) compared to the ones which exist already in the literature. Step by step procedure for solving the design equations is discussed in detail.

  7. Effectiveness of Analytic Smoothing in Equipercentile Equating.

    ERIC Educational Resources Information Center

    Kolen, Michael J.

    1984-01-01

    An analytic procedure for smoothing in equipercentile equating using cubic smoothing splines is described and illustrated. The effectiveness of the procedure is judged by comparing the results from smoothed equipercentile equating with those from other equating methods using multiple cross-validations for a variety of sample sizes. (Author/JKS)

  8. Multidimensional soliton equations in inhomogeneous media

    NASA Astrophysics Data System (ADS)

    Degasperis, A.; Manakov, S. V.; Zenchuk, A. I.

    1998-12-01

    We use the general formalism of the overline∂-problem to derive nonlinear PDEs that are soliton equations with coordinate-dependent coefficients. Examples of these novel equations are a reduction of the Darboux equations, and a NWRI-type system.

  9. Stability for a class of difference equations

    NASA Astrophysics Data System (ADS)

    Muroya, Yoshiaki; Ishiwata, Emiko

    2009-06-01

    We consider the following non-autonomous and nonlinear difference equations with unbounded delays: where 0equation to be globally asymptotically stable. These conditions improve the well known stability conditions for linear and nonlinear difference equations.

  10. COST EQUATIONS FOR SMALL DRINKING WATER SYSTEMS

    EPA Science Inventory

    This report presents capital and operation/maintenance cost equations for 33 drinking water treatment processes as applied to small flows (2,500 gpd to 1 mgd). The equations are based on previous cost data development work performed under contract to EPA. These equations provide ...

  11. Spectrum Analysis of Some Kinetic Equations

    NASA Astrophysics Data System (ADS)

    Yang, Tong; Yu, Hongjun

    2016-05-01

    We analyze the spectrum structure of some kinetic equations qualitatively by using semigroup theory and linear operator perturbation theory. The models include the classical Boltzmann equation for hard potentials with or without angular cutoff and the Landau equation with {γ≥q-2} . As an application, we show that the solutions to these two fundamental equations are asymptotically equivalent (mod time decay rate {t^{-5/4}} ) as {tto∞} to that of the compressible Navier-Stokes equations for initial data around an equilibrium state.

  12. The Riesz-Bessel Fractional Diffusion Equation

    SciTech Connect

    Anh, V.V. McVinish, R.

    2004-05-15

    This paper examines the properties of a fractional diffusion equation defined by the composition of the inverses of the Riesz potential and the Bessel potential. The first part determines the conditions under which the Green function of this equation is the transition probability density function of a Levy motion. This Levy motion is obtained by the subordination of Brownian motion, and the Levy representation of the subordinator is determined. The second part studies the semigroup formed by the Green function of the fractional diffusion equation. Applications of these results to certain evolution equations is considered. Some results on the numerical solution of the fractional diffusion equation are also provided.

  13. Bogomol'nyi equations of classical solutions

    NASA Astrophysics Data System (ADS)

    Atmaja, Ardian N.; Ramadhan, Handhika S.

    2014-11-01

    We review the Bogomol'nyi equations and investigate an alternative route in obtaining it. It can be shown that the known Bogomol'nyi-Prasad-Sommerfield equations can be derived directly from the corresponding Euler-Lagrange equations via the separation of variables, without having to appeal to the Hamiltonian. We apply this technique to the Dirac-Born-Infeld solitons and obtain the corresponding equations and the potentials. This method is suitable for obtaining the first-order equations and determining the allowed potentials for noncanonical defects.

  14. Sparse dynamics for partial differential equations

    PubMed Central

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

    2013-01-01

    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. PMID:23533273

  15. Binomial moment equations for stochastic reaction systems.

    PubMed

    Barzel, Baruch; Biham, Ofer

    2011-04-15

    A highly efficient formulation of moment equations for stochastic reaction networks is introduced. It is based on a set of binomial moments that capture the combinatorics of the reaction processes. The resulting set of equations can be easily truncated to include moments up to any desired order. The number of equations is dramatically reduced compared to the master equation. This formulation enables the simulation of complex reaction networks, involving a large number of reactive species much beyond the feasibility limit of any existing method. It provides an equation-based paradigm to the analysis of stochastic networks, complementing the commonly used Monte Carlo simulations. PMID:21568538

  16. Model Equations: "Black Box" Reconstruction

    NASA Astrophysics Data System (ADS)

    Bezruchko, Boris P.; Smirnov, Dmitry A.

    Black box reconstruction is both the most difficult and the most tempting modelling problem when any prior information about an appropriate model structure is lacking. An intriguing thing is that a model capable of reproducing an observed behaviour or predicting further evolution should be obtained only from an observed time series, i.e. "from nothing" at first sight. Chances for a success are not large. Even more so, a "good" model would become a valuable tool to characterise an object and understand its dynamics. Lack of prior information causes one to utilise universal model structures, e.g. artificial neural networks, radial basis functions and algebraic polynomials are included in the right-hand sides of dynamical model equations. Such models are often multi-dimensional and involve quite many free parameters.

  17. Evolution equation for quantum coherence

    NASA Astrophysics Data System (ADS)

    Hu, Ming-Liang; Fan, Heng

    2016-07-01

    The estimation of the decoherence process of an open quantum system is of both theoretical significance and experimental appealing. Practically, the decoherence can be easily estimated if the coherence evolution satisfies some simple relations. We introduce a framework for studying evolution equation of coherence. Based on this framework, we prove a simple factorization relation (FR) for the l1 norm of coherence, and identified the sets of quantum channels for which this FR holds. By using this FR, we further determine condition on the transformation matrix of the quantum channel which can support permanently freezing of the l1 norm of coherence. We finally reveal the universality of this FR by showing that it holds for many other related coherence and quantum correlation measures.

  18. The equations of medieval cosmology

    NASA Astrophysics Data System (ADS)

    Buonanno, Roberto; Quercellini, Claudia

    2009-04-01

    In Dantean cosmography the Universe is described as a series of concentric spheres with all the known planets embedded in their rotation motion, the Earth located at the centre and Lucifer at the centre of the Earth. Beyond these "celestial spheres", Dante represents the "angelic choirs" as other nine spheres surrounding God. The rotation velocity increases with decreasing distance from God, that is with increasing Power (Virtù). We show that, adding Power as an additional fourth dimension to space, the modern equations governing the expansion of a closed Universe (i.e. with the density parameter Ω0 > 1) in the space-time, can be applied to the medieval Universe as imaged by Dante in his Divine Comedy. In this representation, the Cosmos acquires a unique description and Lucifer is not located at the centre of the hyperspheres.

  19. Evolution equation for quantum coherence

    PubMed Central

    Hu, Ming-Liang; Fan, Heng

    2016-01-01

    The estimation of the decoherence process of an open quantum system is of both theoretical significance and experimental appealing. Practically, the decoherence can be easily estimated if the coherence evolution satisfies some simple relations. We introduce a framework for studying evolution equation of coherence. Based on this framework, we prove a simple factorization relation (FR) for the l1 norm of coherence, and identified the sets of quantum channels for which this FR holds. By using this FR, we further determine condition on the transformation matrix of the quantum channel which can support permanently freezing of the l1 norm of coherence. We finally reveal the universality of this FR by showing that it holds for many other related coherence and quantum correlation measures. PMID:27382933

  20. Entropic corrections to Friedmann equations

    NASA Astrophysics Data System (ADS)

    Sheykhi, Ahmad

    2010-05-01

    Recently, Verlinde discussed that gravity can be understood as an entropic force caused by changes in the information associated with the positions of material bodies. In Verlinde’s argument, the area law of the black hole entropy plays a crucial role. However, the entropy-area relation can be modified from the inclusion of quantum effects, motivated from the loop quantum gravity. In this note, by employing this modified entropy-area relation, we derive corrections to Newton’s law of gravitation as well as modified Friedmann equations by adopting the viewpoint that gravity can be emerged as an entropic force. Our study further supports the universality of the log correction and provides a strong consistency check on Verlinde’s model.

  1. Evolution equation for quantum coherence.

    PubMed

    Hu, Ming-Liang; Fan, Heng

    2016-01-01

    The estimation of the decoherence process of an open quantum system is of both theoretical significance and experimental appealing. Practically, the decoherence can be easily estimated if the coherence evolution satisfies some simple relations. We introduce a framework for studying evolution equation of coherence. Based on this framework, we prove a simple factorization relation (FR) for the l1 norm of coherence, and identified the sets of quantum channels for which this FR holds. By using this FR, we further determine condition on the transformation matrix of the quantum channel which can support permanently freezing of the l1 norm of coherence. We finally reveal the universality of this FR by showing that it holds for many other related coherence and quantum correlation measures. PMID:27382933

  2. Inferring Mathematical Equations Using Crowdsourcing

    PubMed Central

    Wasik, Szymon

    2015-01-01

    Crowdsourcing, understood as outsourcing work to a large network of people in the form of an open call, has been utilized successfully many times, including a very interesting concept involving the implementation of computer games with the objective of solving a scientific problem by employing users to play a game—so-called crowdsourced serious games. Our main objective was to verify whether such an approach could be successfully applied to the discovery of mathematical equations that explain experimental data gathered during the observation of a given dynamic system. Moreover, we wanted to compare it with an approach based on artificial intelligence that uses symbolic regression to find such formulae automatically. To achieve this, we designed and implemented an Internet game in which players attempt to design a spaceship representing an equation that models the observed system. The game was designed while considering that it should be easy to use for people without strong mathematical backgrounds. Moreover, we tried to make use of the collective intelligence observed in crowdsourced systems by enabling many players to collaborate on a single solution. The idea was tested on several hundred players playing almost 10,000 games and conducting a user opinion survey. The results prove that the proposed solution has very high potential. The function generated during weeklong tests was almost as precise as the analytical solution of the model of the system and, up to a certain complexity level of the formulae, it explained data better than the solution generated automatically by Eureqa, the leading software application for the implementation of symbolic regression. Moreover, we observed benefits of using crowdsourcing; the chain of consecutive solutions that led to the best solution was obtained by the continuous collaboration of several players. PMID:26713846

  3. Inferring Mathematical Equations Using Crowdsourcing.

    PubMed

    Wasik, Szymon; Fratczak, Filip; Krzyskow, Jakub; Wulnikowski, Jaroslaw

    2015-01-01

    Crowdsourcing, understood as outsourcing work to a large network of people in the form of an open call, has been utilized successfully many times, including a very interesting concept involving the implementation of computer games with the objective of solving a scientific problem by employing users to play a game-so-called crowdsourced serious games. Our main objective was to verify whether such an approach could be successfully applied to the discovery of mathematical equations that explain experimental data gathered during the observation of a given dynamic system. Moreover, we wanted to compare it with an approach based on artificial intelligence that uses symbolic regression to find such formulae automatically. To achieve this, we designed and implemented an Internet game in which players attempt to design a spaceship representing an equation that models the observed system. The game was designed while considering that it should be easy to use for people without strong mathematical backgrounds. Moreover, we tried to make use of the collective intelligence observed in crowdsourced systems by enabling many players to collaborate on a single solution. The idea was tested on several hundred players playing almost 10,000 games and conducting a user opinion survey. The results prove that the proposed solution has very high potential. The function generated during weeklong tests was almost as precise as the analytical solution of the model of the system and, up to a certain complexity level of the formulae, it explained data better than the solution generated automatically by Eureqa, the leading software application for the implementation of symbolic regression. Moreover, we observed benefits of using crowdsourcing; the chain of consecutive solutions that led to the best solution was obtained by the continuous collaboration of several players. PMID:26713846

  4. Exact solution to fractional logistic equation

    NASA Astrophysics Data System (ADS)

    West, Bruce J.

    2015-07-01

    The logistic equation is one of the most familiar nonlinear differential equations in the biological and social sciences. Herein we provide an exact solution to an extension of this equation to incorporate memory through the use of fractional derivatives in time. The solution to the fractional logistic equation (FLE) is obtained using the Carleman embedding technique that allows the nonlinear equation to be replaced by an infinite-order set of linear equations, which we then solve exactly. The formal series expansion for the initial value solution of the FLE is shown to be expressed in terms of a series of weighted Mittag-Leffler functions that reduces to the well known analytic solution in the limit where the fractional index for the derivative approaches unity. The numerical integration to the FLE provides an excellent fit to the analytic solution. We propose this approach as a general technique for solving a class of nonlinear fractional differential equations.

  5. 10. Exploring the Conformal Constraint Equations

    NASA Astrophysics Data System (ADS)

    Butscher, Adrian

    One method of studying the asymptotic structure of spacetime is to apply Penrose's conformal rescaling technique. In this setting, the rescaled Einstein equations for the metric and the conformal factor in the unphysical spacetime degenerate where the conformal factor vanishes, namely at the boundary representing null infinity. This problem can be avoided by means of a technique of H. Friedrich, which replaces the Einstein equations in the unphysical spacetime by an equivalent system of equations which is regular at the boundary. The initial value problem for these equations produces a system of constraint equations known as the conformal constraint equations. This work describes some of the properties of the conformal constraint equations and develops a perturbative method of generating solutions near Euclidean space under certain simplifying assumptions.

  6. Solving Space-Time Fractional Differential Equations by Using Modified Simple Equation Method

    NASA Astrophysics Data System (ADS)

    Kaplan, Melike; Akbulut, Arzu; Bekir, Ahmet

    2016-05-01

    In this article, we establish new and more general traveling wave solutions of space-time fractional Klein–Gordon equation with quadratic nonlinearity and the space-time fractional breaking soliton equations using the modified simple equation method. The proposed method is so powerful and effective to solve nonlinear space-time fractional differential equations by with modified Riemann–Liouville derivative.

  7. Exact solutions of the time-fractional Fisher equation by using modified trial equation method

    NASA Astrophysics Data System (ADS)

    Tandogan, Yusuf Ali; Bildik, Necdet

    2016-06-01

    In this study, modified trial equation method has been proposed to obtain precise solutions of nonlinear fractional differential equation. Using the modified test equation method, we obtained some new exact solutions of the time fractional nonlinear Fisher equation. The obtained results are classified as a soliton solution, singular solutions, rational function solutions and periodic solutions.

  8. The properties of the first equation of the Vlasov chain of equations

    NASA Astrophysics Data System (ADS)

    Perepelkin, E. E.; Sadovnikov, B. I.; Inozemtseva, N. G.

    2015-05-01

    A derivation of the first Vlasov equation as a well-known Schrödinger equation for the probabilistic description of a system and families of the classic diffusion equations and heat conduction for the deterministic description of physical systems was inferred. A physical meaning of the phase of the wave function which is a scalar potential of the probabilistic flow velocity is demonstrated. Occurrence of the velocity potential vortex component leads to the Pauli equation for one of the spinar components. A scheme for the construction of the Schrödinger equation solution from the Vlasov equation solution and vice-versa is shown. A process of introduction of the potential to the Schrödinger equation and its interpretation are given. The analysis of the potential properties gives us the Maxwell equation, the equation of the kinematic point movement, and the equation for movement of the medium within electromagnetic fields.

  9. Complex PT-symmetric nonlinear Schrödinger equation and Burgers equation.

    PubMed

    Yan, Zhenya

    2013-04-28

    The complex -symmetric nonlinear wave models have drawn much attention in recent years since the complex -symmetric extensions of the Korteweg-de Vries (KdV) equation were presented in 2007. In this review, we focus on the study of the complex -symmetric nonlinear Schrödinger equation and Burgers equation. First of all, we briefly introduce the basic property of complex symmetry. We then report on exact solutions of one- and two-dimensional nonlinear Schrödinger equations (known as the Gross-Pitaevskii equation in Bose-Einstein condensates) with several complex -symmetric potentials. Finally, some complex -symmetric extension principles are used to generate some complex -symmetric nonlinear wave equations starting from both -symmetric (e.g. the KdV equation) and non- -symmetric (e.g. the Burgers equation) nonlinear wave equations. In particular, we discuss exact solutions of some representative ones of the complex -symmetric Burgers equation in detail. PMID:23509385

  10. Dust levitation about Itokawa's equator

    NASA Astrophysics Data System (ADS)

    Hartzell, C.; Zimmerman, M.; Takahashi, Y.

    2014-07-01

    levitation about Itokawa, we must include accurate plasma and gravity models. We use a 2D PIC code (described in [8]) to model the plasma environment about Itokawa's equator. The plasma model includes photoemission and shadowing. Thus, we model the plasma environment for various solar incidence angles. The plasma model gives us the 2D electric field components and the plasma potential. We model the gravity field around the equatorial cross-section using an Interior Gravity model [9]. The gravity model is based on the shape model acquired by the Hayabusa mission team and, unlike other models, is quick and accurate close to the surface of the body. Due to the nonspherical shape of Itokawa, the electrostatic force and the gravity may not be collinear. Given our accurate plasma and gravity environments, we are able to simulate the trajectories of dust grains about the equator of Itokawa. When modeling the trajectories of the grains, the current to the grains is calculated using Nitter et al.'s formulation [10] with the plasma sheath parameters provided by our PIC model (i.e., the potential minimum, the potential at the surface, and the sheath type). Additionally, we are able to numerically locate the equilibria about which dust grains may levitate. Interestingly, we observe that equilibria exist for grains up to 20 microns in radius about Itokawa's equator when the Sun is illuminating Itokawa's 'otter tail'. This grain size is significantly larger than the stably levitating grains we observed using our 1D plasma and gravity models. Conclusions and Future Work: The possibility of dust levitation above asteroids has implications both for our understanding of their evolution and for the design of future missions to these bodies. Using detailed gravity and plasma models, we are above to propagate the trajectories of dust particles about Itokawa's equator and identify the equilibria about which these grains will levitate. Using these simulations, we see that grains up to 20 microns

  11. The telegraph equation in charged particle transport

    NASA Technical Reports Server (NTRS)

    Gombosi, T. I.; Jokipii, J. R.; Kota, J.; Lorencz, K.; Williams, L. L.

    1993-01-01

    We present a new derivation of the telegraph equation which modifies its coefficients. First, an infinite order partial differential equation is obtained for the velocity space solid angle-averaged phase-space distribution of particles which underwent at least a few collisions. It is shown that, in the lowest order asymptotic expansion, this equation simplifies to the well-known diffusion equation. The second-order asymptotic expansion for isotropic small-angle scattering results in a modified telegraph equation with a signal propagation speed of v(5/11) exp 1/2 instead of the usual v/3 exp 1/2. Our derivation of a modified telegraph equation follows from an expansion of the Boltzmann equation in the relevant smallness parameters and not from a truncation of an eigenfunction expansion. This equation is consistent with causality. It is shown that, under steady state conditions in a convecting plasma, the telegraph equation may be regarded as a diffusion equation with a modified transport coefficient, which describes a combination of diffusion and cosmic-ray inertia.

  12. On some differential transformations of hypergeometric equations

    NASA Astrophysics Data System (ADS)

    Hounkonnou, M. N.; Ronveaux, A.

    2015-04-01

    Many algebraic transformations of the hypergeometric equation σ(x)z"(x) + τ(x)z'(x) + lz(x) = 0, where σ, τ, l are polynomial functions of degrees 2 (at most), 1, 0, respectively, are well known. Some of them involve x = x(t), a polynomial of degree r, in order to recover the Heun equation, extension of the hypergeometric equation by one more singularity. The case r = 2 was investigated by K. Kuiken (see 1979 SIAM J. Math. Anal. 10 (3) 655-657) and extended to r = 3,4, 5 by R. S. Maier (see 2005 J. Differ. Equat. 213 171 - 203). The transformations engendered by the function y(x) = A(x)z(x), also very popular in mathematics and physics, are used to get from the hypergeometric equation, for instance, the Schroedinger equation with appropriate potentials, as well as Heun and confluent Heun equations. This work addresses a generalization of Kimura's approach proposed in 1971, based on differential transformations of the hypergeometric equations involving y(x) = A(x)z(x) + B(x)z'(x). Appropriate choices of A(x) and B(x) permit to retrieve the Heun equations as well as equations for some exceptional polynomials. New relations are obtained for Laguerre and Hermite polynomials.

  13. Exact and explicit solitary wave solutions to some nonlinear equations

    SciTech Connect

    Jiefang Zhang

    1996-08-01

    Exact and explicit solitary wave solutions are obtained for some physically interesting nonlinear evolutions and wave equations in physics and other fields by using a special transformation. These equations include the KdV-Burgers equation, the MKdV-Burgers equation, the combined KdV-MKdV equation, the Newell-Whitehead equation, the dissipative {Phi}{sup 4}-model equation, the generalized Fisher equation, and the elastic-medium wave equation.

  14. Three-body equations for nuclear reactions

    SciTech Connect

    Chao, S.H.

    1980-01-01

    The problem of calculating three-body differential cross sections for two-body interactions which are local in configuration space is considered. The integral equations of Faddeev and recent modifications are reviewed. The difficulties both in solving and interpreting the various equations are discussed. An alternative set of exact operator equations is proposed. This new set of operator equations involve the two-body potentials directly rather than the two-body t-matrices. The solutions represent quantities different from those of previous equations. The formal structure of the operator equations is similar to but different from the Faddeev equations. It is demonstrated that the equations contain no terms which correspond to disconnected diagrams. The transformation of the equations to the Faddeev equations is given. Integral equations are obtained using the momentum representation. Only Cauchy-type singularities occur in the Green's function, and the equations have unique solutions. No off-energy shell t-matrices are required. Transition amplitudes are obtained from the solutions by quadrature, so that effects which result from the nature of the final state can be separated from the three-body effects. The angular momentum reduction of Omnes is used to obtain two-dimensional coupled integral equations. A method of numerical solution is developed using a generalization of the approximate product integration method due to Young. Examples corresponding to the reactions /sup 16/O(d,p)/sup 17/O g.s and /sup 16/O(d,d)/sup 16/O in two dimensions and /sup 16/O(d,p)/sup 17/O* (0.87 MeV) in three dimensions for a deuteron enegy of 5 MeV are considered using Gaussian potentials. The convergence of the summation over angular momentum is examined and a comparison is made with experiment to obtain the spectroscopic factor for the 0.87 MeV state of /sup 17/O.

  15. Cosmic-Ray Modulation Equations

    NASA Astrophysics Data System (ADS)

    Moraal, H.

    2013-06-01

    The temporal variation of the cosmic-ray intensity in the heliosphere is called cosmic-ray modulation. The main periodicity is the response to the 11-year solar activity cycle. Other variations include a 27-day solar rotation variation, a diurnal variation, and irregular variations such as Forbush decreases. General awareness of the importance of this cosmic-ray modulation has greatly increased in the last two decades, mainly in communities studying cosmogenic nuclides, upper atmospheric physics and climate, helio-climatology, and space weather, where corrections need to be made for these modulation effects. Parameterized descriptions of the modulation are even used in archeology and in planning the flight paths of commercial passenger jets. The qualitative, physical part of the modulation is generally well-understood in these communities. The mathematical formalism that is most often used to quantify it is the so-called Force-Field approach, but the origins of this approach are somewhat obscure and it is not always used correct. This is mainly because the theory was developed over more than 40 years, and all its aspects are not collated in a single document. This paper contains a formal mathematical description intended for these wider communities. It consists of four parts: (1) a description of the relations between four indicators of "energy", namely energy, speed, momentum and rigidity, (2) the various ways of how to count particles, (3) the description of particle motion with transport equations, and (4) the solution of such equations, and what these solutions mean. Part (4) was previously described in Caballero-Lopez and Moraal (J. Geophys. Res, 109: A05105, doi: 10.1029/2003JA010358, 2004). Therefore, the details are not all repeated here. The style of this paper is not to be rigorous. It rather tries to capture the relevant tools to do modulation studies, to show how seemingly unrelated results are, in fact, related to one another, and to point out the

  16. Stability analysis of ecomorphodynamic equations

    NASA Astrophysics Data System (ADS)

    Bärenbold, F.; Crouzy, B.; Perona, P.

    2016-02-01

    In order to shed light on the influence of riverbed vegetation on river morphodynamics, we perform a linear stability analysis on a minimal model of vegetation dynamics coupled with classical one- and two-dimensional Saint-Venant-Exner equations of morphodynamics. Vegetation is modeled as a density field of rigid, nonsubmerged cylinders and affects flow via a roughness change. Furthermore, vegetation is assumed to develop following a logistic dependence and may be uprooted by flow. First, we perform the stability analysis of the reduced one-dimensional framework. As a result of the competitive interaction between vegetation growth and removal through uprooting, we find a domain in the parameter space where originally straight rivers are unstable toward periodic longitudinal patterns. For realistic values of the sediment transport parameter, the dominant longitudinal wavelength is determined by the parameters of the vegetation model. Bed topography is found to adjust to the spatial pattern fixed by vegetation. Subsequently, the stability analysis is repeated for the two-dimensional framework, where the system may evolve toward alternate or multiple bars. On a fixed bed, we find instability toward alternate bars due to flow-vegetation interaction, but no multiple bars. Both alternate and multiple bars are present on a movable, vegetated bed. Finally, we find that the addition of vegetation to a previously unvegetated riverbed favors instability toward alternate bars and thus the development of a single course rather than braiding.

  17. Silicon Nitride Equation of State

    NASA Astrophysics Data System (ADS)

    Swaminathan, Pazhayannur; Brown, Robert

    2015-06-01

    This report presents the development a global, multi-phase equation of state (EOS) for the ceramic silicon nitride (Si3N4) . Structural forms include amorphous silicon nitride normally used as a thin film and three crystalline polymorphs. Crystalline phases include hexagonal α-Si3N4, hexagonalβ-Si3N4, and the cubic spinel c-Si3N4. Decomposition at about 1900 °C results in a liquid silicon phase and gas phase products such as molecular nitrogen, atomic nitrogen, and atomic silicon. The silicon nitride EOS was developed using EOSPro which is a new and extended version of the PANDA II code. Both codes are valuable tools and have been used successfully for a variety of material classes. Both PANDA II and EOSPro can generate a tabular EOS that can be used in conjunction with hydrocodes. The paper describes the development efforts for the component solid phases and presents results obtained using the EOSPro phase transition model to investigate the solid-solid phase transitions in relation to the available shock data. Furthermore, the EOSPro mixture model is used to develop a model for the decomposition products and then combined with the single component solid models to study the global phase diagram. Sponsored by the NASA Goddard Space Flight Center Living With a Star program office.

  18. Equation of state of polytetrafluoroethylene

    NASA Astrophysics Data System (ADS)

    Bourne, N. K.; Gray, G. T.

    2003-06-01

    The present drive to make munitions as safe as is feasible and to develop predictive models describing their constitutive response, has led to the development and production of plastic bonded explosives and propellants. There is a range of elastomers used as binder materials with the energetic components. One of these is known as Kel-F-800™ (poly-chloro-trifluroethylene) whose structure is in some ways analogous to that of poly-tetrafluoroethylene (PTFE or Teflon). Thus, it is of interest to assess the mechanical behavior of Teflon and to compare the response of five different production Teflon materials, two of which were produced in pedigree form, one as-received product, and two from previous in-depth literature studies. The equations of state of these variants were quantified by conducting a series of shock impact experiments in which both pressure-particle velocity and shock velocity-particle velocity dependencies were measured. The compressive behavior of Teflon, based upon the results of this study, appears to be independent of the production route and additives introduced.

  19. Dirac equations with confining potentials

    NASA Astrophysics Data System (ADS)

    Noble, J. H.; Jentschura, U. D.

    2015-01-01

    This paper is devoted to a study of relativistic eigenstates of Dirac particles which are simultaneously bound by a static Coulomb potential and added linear confining potentials. Under certain conditions, despite the addition of radially symmetric, linear confining potentials, specific bound-state energies surprisingly preserve their exact Dirac-Coulomb values. The generality of the "preservation mechanism" is investigated. To this end, a Foldy-Wouthuysen transformation is used to calculate the corrections to the spin-orbit coupling induced by the linear confining potentials. We find that the matrix elements of the effective operators obtained from the scalar, and time-like confining potentials mutually cancel for specific ratios of the prefactors of the effective operators, which must be tailored to the preservation mechanism. The result of the Foldy-Wouthuysen transformation is used to verify that the preservation is restricted (for a given Hamiltonian) to only one reference state, rather than traceable to a more general relationship among the obtained effective low-energy operators. The results derived from the nonrelativistic effective operators are compared to the fully relativistic radial Dirac equations. Furthermore, we show that the preservation mechanism does not affect antiparticle (negative-energy) states.

  20. Scalable Equation of State Capability

    SciTech Connect

    Epperly, T W; Fritsch, F N; Norquist, P D; Sanford, L A

    2007-12-03

    The purpose of this techbase project was to investigate the use of parallel array data types to reduce the memory footprint of the Livermore Equation Of State (LEOS) library. Addressing the memory scalability of LEOS is necessary to run large scientific simulations on IBM BG/L and future architectures with low memory per processing core. We considered using normal MPI, one-sided MPI, and Global Arrays to manage the distributed array and ended up choosing Global Arrays because it was the only communication library that provided the level of asynchronous access required. To reduce the runtime overhead using a parallel array data structure, a least recently used (LRU) caching algorithm was used to provide a local cache of commonly used parts of the parallel array. The approach was initially implemented in a isolated copy of LEOS and was later integrated into the main trunk of the LEOS Subversion repository. The approach was tested using a simple test. Testing indicated that the approach was feasible, and the simple LRU caching had a 86% hit rate.

  1. Double distributions and evolution equations

    SciTech Connect

    A.V. Radyushkin

    1998-05-01

    Applications of perturbative QCD to deeply virtual Compton scattering and hard exclusive meson electroproduction processes require a generalization of usual parton distributions for the case when long-distance information is accumulated in nonforward matrix elements < p{prime} {vert_bar}O(0,z){vert_bar}p > of quark and gluon light-cone operators. In their previous papers the authors used two types of nonperturbative functions parameterizing such matrix elements: double distributions F(x,y;t) and nonforward distribution functions F{sub {zeta}}(X;t). Here they discuss in more detail the double distributions (DD's) and evolution equations which they satisfy. They propose simple models for F(x,y;t=0) DD's with correct spectral and symmetry properties which also satisfy the reduction relations connecting them to the usual parton densities f(x). In this way, they obtain self-consistent models for the {zeta}-dependence of nonforward distributions. They show that, for small {zeta}, one can easily obtain nonforward distributions (in the X > {zeta} region) from the parton densities: F{sub {zeta}} (X;t=0) {approx} f(X{minus}{zeta}/2).

  2. Stochastic differential equation model to Prendiville processes

    SciTech Connect

    Granita; Bahar, Arifah

    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. Remarks on the Kuramoto-Sivashinsky equation

    SciTech Connect

    Nicolaenko, B.; Scheurer, B.

    1983-01-01

    We report here a joint work in progress on the Kuramoto-Sivashinsky equation. The question we address is the analytical study of a fourth order nonlinear evolution equation. This equation has been obtained by Sivashinsky in the context of combustion and independently by Kuramoto in the context of reaction diffusion-systems. Both were motivated by (nonlinear) stability of travelling waves. Numerical calculations have been done on this equation. All the results seem to indicate a chaotic behavior of the solution. Therefore, the analytical study is of interest in analogy with the Burger's and Navier-Stokes equations. Here we give some existence and uniqueness results for the equation in space dimension one, and we also study a fractional step method of numerical resolution. In a forthcoming joint paper with R. Temam, we will study the asymptotic behavior, as t approaches infinity, of the solution of (0.1) and give an estimate on the number of determining modes.

  4. A state estimation of Liu equations

    NASA Astrophysics Data System (ADS)

    Ananyev, B. I.

    2015-11-01

    This paper is concerned with state estimation problems for so-called Liu equations. These equations are counterparts of well-known Ito ones and they were introduced by B. Liu under elaboration of his uncertain theory. The Liu equations may be solved backward and they represent a more convenient object for the state estimation problem solution especially for the case when distributions of disturbances are unknown. Using the dynamic programming principle, we derive an equation for the informational set consisting of all states that are compatible with measuring data. Special cases of Liu equations and constraints for disturbances are examined. Among them the linear equations with quadratic constraints are considered in most details. Some examples are also given.

  5. Comparison of logistic equations for population growth.

    PubMed

    Jensen, A L

    1975-12-01

    Two different forms of the logistic equation for population growth appear in the ecological literature. In the form of the logistic equation that appears in recent ecology textbooks the parameters are the instantaneous rate of natural increase per individual and the carrying capacity of the environment. In the form of the logistic equation that appears in some older literature the parameters are the instantaneous birth rate per individual and the carrying capacity. The decision whether to use one form or the other depends on which form of the equation is biologically more realistic. In this study the form of the logistic equation in which the instantaneous birth rate per individual is a parameter is shown to be more realistic in terms of the birth and death processes of population growth. Application of the logistic equation to calculate yield from an exploited fish population also shows that the parameters must be the instantaneous birth rate per individual and the carrying capacity. PMID:1203427

  6. Darboux transformation for the NLS equation

    SciTech Connect

    Aktosun, Tuncay; Mee, Cornelis van der

    2010-03-08

    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.

  7. Exact solutions of population balance equation

    NASA Astrophysics Data System (ADS)

    Lin, Fubiao; Flood, Adrian E.; Meleshko, Sergey V.

    2016-07-01

    Population balance equations have been used to model a wide range of processes including polymerization, crystallization, cloud formation, and cell dynamics, but the lack of analytical solutions necessitates the use of numerical techniques. The one-dimensional homogeneous population balance equation with time dependent but size independent growth rate and time dependent nucleation rate is investigated. The corresponding system of equations is solved analytically in this paper.

  8. Dielectric polarization evolution equations and relaxation times

    SciTech Connect

    Baker-Jarvis, James; Riddle, Bill; Janezic, Michael D.

    2007-05-15

    In this paper we develop dielectric polarization evolution equations, and the resulting frequency-domain expressions, and relationships for the resulting frequency dependent relaxation times. The model is based on a previously developed equation that was derived using statistical-mechanical theory. We extract relaxation times from dielectric data and give illustrative examples for the harmonic oscillator and derive expressions for the frequency-dependent relaxation times and a time-domain integrodifferential equation for the Cole-Davidson model.

  9. The Boltzmann equation in the difference formulation

    SciTech Connect

    Szoke, Abraham; Brooks III, Eugene D.

    2015-05-06

    First we recall the assumptions that are needed for the validity of the Boltzmann equation and for the validity of the compressible Euler equations. We then present the difference formulation of these equations and make a connection with the time-honored Chapman - Enskog expansion. We discuss the hydrodynamic limit and calculate the thermal conductivity of a monatomic gas, using a simplified approximation for the collision term. Our formulation is more consistent and simpler than the traditional derivation.

  10. Switched electrical networks and bilinear equations

    NASA Technical Reports Server (NTRS)

    Wood, J. R.

    1974-01-01

    An investigation is conducted concerning the state equations which arise in the description of power processing systems. Attention is given to the role played by Lie groups and Lie algebras in the characterization of the dynamical features of the systems. The bilinear equations used for the representation of the network characteristics are discussed along with the nature of the solutions for the equations. The application of the described approaches is illustrated with the aid of a number of network examples.

  11. Chandrasekhar equations for infinite dimensional systems

    NASA Technical Reports Server (NTRS)

    Ito, K.; Powers, R. K.

    1985-01-01

    Chandrasekhar equations are derived for linear time invariant systems defined on Hilbert spaces using a functional analytic technique. An important consequence of this is that the solution to the evolutional Riccati equation is strongly differentiable in time and one can define a strong solution of the Riccati differential equation. A detailed discussion on the linear quadratic optimal control problem for hereditary differential systems is also included.

  12. Partitioning And Packing Equations For Parallel Processing

    NASA Technical Reports Server (NTRS)

    Arpasi, Dale J.; Milner, Edward J.

    1989-01-01

    Algorithm developed to identify parallelism in set of coupled ordinary differential equations that describe physical system and to divide set into parallel computational paths, along with parts of solution proceeds independently of others during at least part of time. Path-identifying algorithm creates number of paths consisting of equations that must be computed serially and table that gives dependent and independent arguments and "can start," "can end," and "must end" times of each equation. "Must end" time used subsequently by packing algorithm.

  13. Geometrical and Graphical Solutions of Quadratic Equations.

    ERIC Educational Resources Information Center

    Hornsby, E. John, Jr.

    1990-01-01

    Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)

  14. Some remarks on unilateral matrix equations

    SciTech Connect

    Cerchiai, Bianca L.; Zumino, Bruno

    2001-02-01

    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.

  15. Analytic solutions of the relativistic Boltzmann equation

    NASA Astrophysics Data System (ADS)

    Hatta, Yoshitaka; Martinez, Mauricio; Xiao, Bo-Wen

    2015-04-01

    We present new analytic solutions to the relativistic Boltzmann equation within the relaxation time approximation. We first obtain spherically expanding solutions which are the kinetic counterparts of the exact solutions of the Israel-Stewart equation in the literature. This allows us to compare the solutions of the kinetic and hydrodynamic equations at an analytical level. We then derive a novel boost-invariant solution of the Boltzmann equation which has an unconventional dependence on the proper time. The existence of such a solution is also suggested in second-order hydrodynamics and fluid-gravity correspondence.

  16. Non-Markovian stochastic evolution equations

    NASA Astrophysics Data System (ADS)

    Costanza, G.

    2014-05-01

    Non-Markovian continuum stochastic and deterministic equations are derived from a set of discrete stochastic and deterministic evolution equations. Examples are given of discrete evolution equations whose updating rules depend on two or more previous time steps. Among them, the continuum stochastic evolution equation of the Newton second law, the stochastic evolution equation of a wave equation, the stochastic evolution equation for the scalar meson field, etc. are obtained as special cases. Extension to systems of evolution equations and other extensions are considered and examples are given. The concept of isomorphism and almost isomorphism are introduced in order to compare the coefficients of the continuum evolution equations of two different smoothing procedures that arise from two different approaches. Usually these discrepancies arising from two sources: On the one hand, the use of different representations of the generalized functions appearing in the models and, on the other hand, the different approaches used to describe the models. These new concept allows to overcome controversies that were appearing during decades in the literature.

  17. Integral equations for flows in wind tunnels

    NASA Technical Reports Server (NTRS)

    Fromme, J. A.; Golberg, M. A.

    1979-01-01

    This paper surveys recent work on the use of integral equations for the calculation of wind tunnel interference. Due to the large number of possible physical situations, the discussion is limited to two-dimensional subsonic and transonic flows. In the subsonic case, the governing boundary value problems are shown to reduce to a class of Cauchy singular equations generalizing the classical airfoil equation. The theory and numerical solution are developed in some detail. For transonic flows nonlinear singular equations result, and a brief discussion of the work of Kraft and Kraft and Lo on their numerical solution is given. Some typical numerical results are presented and directions for future research are indicated.

  18. Integral equations for resonance and virtual states

    SciTech Connect

    Orlov, Y.V.; Turovtsev, V.V.

    1984-05-01

    Integral equations are derived for the resonance and virtual (antibound) states consisting of two or three bodies. The derivation is based on the analytic continuation of the integral equations of scattering theory to nonphysical energy sheets. The resulting equations can be used to exhibit the analytic properties of amplitudes that are necessary for practical calculations using the equations for the quasistationary levels and Gamov wave functions derived in this paper. The Fourier transformation and the normalization rule for the wave function are generalized to the case of nonstationary states. The energy of the antibound state of the tritium nucleus is calculated for a ''realistic'' local potential.

  19. Exact Travelling Wave Solutions of the Nonlinear Evolution Equations by Auxiliary Equation Method

    NASA Astrophysics Data System (ADS)

    Kaplan, Melike; Akbulut, Arzu; Bekir, Ahmet

    2015-10-01

    The auxiliary equation method presents wide applicability to handling nonlinear wave equations. In this article, we establish new exact travelling wave solutions of the nonlinear Zoomeron equation, coupled Higgs equation, and equal width wave equation. The travelling wave solutions are expressed by the hyperbolic functions, trigonometric functions, and rational functions. It is shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering. Throughout the article, all calculations are made with the aid of the Maple packet program.

  20. Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation

    SciTech Connect

    He, Xiaoyi; Lou, Li-Shi Lou, Li-Shi

    1997-12-01

    In this paper, the lattice Boltzmann equation is directly derived from the Boltzmann equation. It is shown that the lattice Boltzmann equation is a special discretized form of the Boltzmann equation. Various approximations for the discretization of the Boltzmann equation in both time and phase space are discussed in detail. A general procedure to derive the lattice Boltzmann model from the continuous Boltzmann equation is demonstrated explicitly. The lattice Boltzmann models derived include the two-dimensional 6-bit, 7-bit, and 9-bit, and three-dimensional 27-bit models. {copyright} {ital 1997} {ital The American Physical Society}

  1. Cylindrical nonlinear Schroedinger equation versus cylindrical Korteweg-de Vries equation

    SciTech Connect

    Fedele, Renato; De Nicola, Sergio; Grecu, Dan; Visinescu, Anca; Shukla, Padma K.

    2008-10-15

    A correspondence between the family of cylindrical nonlinear Schroedinger (cNLS) equations and the one of cylindrical Korteweg-de Vries (cKdV) equations is constructed. It associates non stationary solutions of the first family with the ones of the second family. This is done by using a correspondence, recently found, between the families of generalized NLS equation and generalized KdV equation, and their solutions in the form of travelling waves, respectively. In particular, non-stationary soliton-like solutions of the cNLS equation can be associated with non-stationary soliton-like solutions of cKdV equation.

  2. Multidimensional quasilinear first-order equations and multivalued solutions of the elliptic and hyperbolic equations

    NASA Astrophysics Data System (ADS)

    Zhuravlev, V. M.

    2016-03-01

    We discuss an extension of the theory of multidimensional second-order equations of the elliptic and hyperbolic types related to multidimensional quasilinear autonomous first-order partial differential equations. Calculating the general integrals of these equations allows constructing exact solutions in the form of implicit functions. We establish a connection with hydrodynamic equations. We calculate the number of free functional parameters of the constructed solutions. We especially construct and analyze implicit solutions of the Laplace and d'Alembert equations in a coordinate space of arbitrary finite dimension. In particular, we construct generalized Penrose-Rindler solutions of the d'Alembert equation in 3+1 dimensions.

  3. Relation between the Rayleigh equation in diffraction theory and the equation based on Green's formula

    NASA Astrophysics Data System (ADS)

    Tatarskii, V. I.

    1995-06-01

    The steps necessary to produce the Rayleigh equation that is based on the Rayleigh hypothesis from the equation that is based on the Green's formula are shown. First a definition is given for the scattering amplitude that is true not only in the far zone of diffraction but also near the scattering surface. With this definition the Rayleigh equation coincides with the rigorous equation for the surface secondary sources that is based on Green's formula. The Rayleigh hypothesis is equivalent to substituting the far-zone expression of the scattering amplitude into this rigorous equation. In this case it turns out to be the equation not for the sources but directly for the scattering amplitude, which is the main advantage of this method. For comparing the Rayleigh equation with the initial rigorous equation, the Rayleigh equation is represented in terms of secondary sources. The kernel of this equation contains an integral that converges for positive and diverges for negative values of some parameter. It is shown that if we regularize this integral, defining it for the negative values of this parameter as an analytical continuation from the domain of positive values, this kernel becomes equal to the kernel of the initial rigorous equation. It follows that the formal perturbation series for the scattering amplitude obtained from the Rayleigh equation and from Green's equation always coincide. This means that convergence of the perturbation series is a sufficient condition

  4. A primitive pseudo wave equation formulation for solving the harmonic shallow water equations

    NASA Astrophysics Data System (ADS)

    Westerink, J. J.; Connor, J. J.; Stolzenbach, K. D.

    A finite element method formulation for solving the harmonic shallow water equations in their primitive or unmodified form is developed and analysed. The scheme, referred to as the Primitive Pseudo Wave Equation Formulation (PPWE), involves developing a weak weighted residual form of the continuity equation and furthermore forming a pseudo wave equation by substituting the discretized form of the momentum equation into the discretized form of the continuity equation. The final set of equations to be solved, the pseudo wave equation and the primitive momentum equations, deceptively resemble the discretized equations of the wave equation formulation of Lynch and Gray. Despite this resemblance, Fourier analysis indicates that the PPWE scheme is still fundamentally primitive. However, application of the PPWE scheme to a set of stringent test problems results in very good solutions with well controlled nodal oscillations. It is shown that this low degree of spurious oscillations is due to the treatment of the boundary conditions such that elevation is taken as an essential condition and normal flux is taken as a natural condition. This particular boundary condition treatment is suggested by the formation of the pseudo wave equation. Furthermore, even though the equation re-arrangement does not in itself effect the solutions, it does make the scheme much more efficient.

  5. The Forced van der Pol Equation

    ERIC Educational Resources Information Center

    Fay, Temple H.

    2009-01-01

    We report on a study of the forced van der Pol equation x + [epsilon](x[superscript 2] - 1)x + x = F cos[omega]t, by solving numerically the differential equation for a variety of values of the parameters [epsilon], F and [omega]. In doing so, many striking and interesting trajectories can be discovered and phenomena such as frequency entrainment,…

  6. Equations of state for detonation problems

    SciTech Connect

    Davis, W.C.

    1997-08-01

    The words `Equation of State` have usually been used in the detonation physics community to mean whatever information about the materials involved that would make it possible to solve the problem at hand. As the problems have become more complicated and the computer simulation more detailed, better and better equations of state have been developed and used. Still, most equations of state have been limited to use in solving the hydrodynamic equations for an inviscid, non-heat-conducting, non-radiating, non-reacting fluid. All the information in these equations of state is about the mechanical properties. There is no information about the temperature, entropy, or specific heat. The focus of this paper is not on providing a new equation of state that will allow the solution of all problems, but to discuss the restrictions on equations of state, and the effect of those restrictions on their properties. Later, when there are more data, it will be time to search for the best equations of state for all the various problems.

  7. Euler's Amazing Way to Solve Equations.

    ERIC Educational Resources Information Center

    Flusser, Peter

    1992-01-01

    Presented is a series of examples that illustrate a method of solving equations developed by Leonhard Euler based on an unsubstantiated assumption. The method integrates aspects of recursion relations and sequences of converging ratios and can be extended to polynomial equation with infinite exponents. (MDH)

  8. The Effects of Repeaters on Test Equating.

    ERIC Educational Resources Information Center

    Andrulis, Richard S.; And Others

    1978-01-01

    The effects of repeaters (testees included in both administrations of two forms of a test) on the test equating process are examined. It is shown that repeaters do effect test equating and tend to lower the cutoff point for passing the test. (JKS)

  9. Congeneric Models and Levine's Linear Equating Procedures.

    ERIC Educational Resources Information Center

    Brennan, Robert L.

    In 1955, R. Levine introduced two linear equating procedures for the common-item non-equivalent populations design. His procedures make the same assumptions about true scores; they differ in terms of the nature of the equating function used. In this paper, two parameterizations of a classical congeneric model are introduced to model the variables…

  10. On solvable Dirac equation with polynomial potentials

    SciTech Connect

    Stachowiak, Tomasz

    2011-01-15

    One-dimensional Dirac equation is analyzed with regard to the existence of exact (or closed-form) solutions for polynomial potentials. The notion of Liouvillian functions is used to define solvability, and it is shown that except for the linear potentials the equation in question is not solvable.

  11. Fractional transport equation on random fractals

    NASA Astrophysics Data System (ADS)

    Zeng, Qiuhua; Li, Houqiang; Fang, Yaquan

    1998-12-01

    According to the ways of H.E. Roman and M. Giona with the constitutive equation of diffusive particles in isotropic and homogeneous three dimensions and the Laplace transform we derive the multiscaling fractional transport equation in disordered fractal media, whose solution is consistent with literature results.

  12. Hopf algebras and Dyson-Schwinger equations

    NASA Astrophysics Data System (ADS)

    Weinzierl, Stefan

    2016-06-01

    In this paper I discuss Hopf algebras and Dyson-Schwinger equations. This paper starts with an introduction to Hopf algebras, followed by a review of the contribution and application of Hopf algebras to particle physics. The final part of the paper is devoted to the relation between Hopf algebras and Dyson-Schwinger equations.

  13. Student Understanding of Chemical Equation Balancing.

    ERIC Educational Resources Information Center

    Yarroch, W. L.

    1985-01-01

    Results of interviews with high school chemistry students (N=14) during equation-solving sessions indicate that those who were able to construct diagrams consistent with notation of their balanced equation possessed good concepts of subscript and the balancing rule. Implications for chemistry teaching are discussed. (DH)

  14. Singular perturbation equations for flexible satellites

    NASA Technical Reports Server (NTRS)

    Huang, T. C.; Das, A.

    1980-01-01

    Force equations of motion of the individual flexible elements of a satellite were obtained in a previous paper. Moment equations of motion of the composite bodies of a flexible satellite are to be developed using two sets of equations which form the basic system for any dynamic model of flexible satellites. This basic system consists of a set of N-coupled, nonlinear, ordinary, or partial differential equations, for a flexible satellite with n generalized, structural position coordinates. For single composite body satellites, N is equal to (n + 3); for dual-spin systems, N is equal to (n + 9). These equations involve time derivatives up to the second order. The study shows a method of avoiding this linearization by reducing the N equations to 3 or 9 nonlinear, coupled, first order, ordinary, differential equations involving only the angular velocities of the composite bodies. The solutions for these angular velocities lead to linear equations in the n generalized structural position coordinates, which can be solved by known methods.

  15. The Specific Analysis of Structural Equation Models

    ERIC Educational Resources Information Center

    McDonald, Roderick P.

    2004-01-01

    Conventional structural equation modeling fits a covariance structure implied by the equations of the model. This treatment of the model often gives misleading results because overall goodness of fit tests do not focus on the specific constraints implied by the model. An alternative treatment arising from Pearl's directed acyclic graph theory…

  16. Entropy viscosity method applied to Euler equations

    SciTech Connect

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

    2013-07-01

    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)

  17. Modeling Projects in a Differential Equations Course.

    ERIC Educational Resources Information Center

    Claus-McGahan, Elly

    1998-01-01

    Discusses the value of student-designed, in-depth, modeling projects in a differential equations course and how to prepare students. Provides excerpts from worksheets, a list of computer software for Macintosh that can be used in teaching differential equations, and an annotated bibliography. (Author/ASK)

  18. Rate equations for sodium catalyzed quartz dissolution

    NASA Astrophysics Data System (ADS)

    Rimstidt, J. Donald

    2015-10-01

    Quartz dissolution rate data were fit to an equation that predicts the dissolution flux (J, mol/m2 sec) as a function of temperature (T, K), sodium concentration (mNa+, molal), and hydrogen ion activity (aH+). The same data fit equally well to an equation that expresses the rate as a function of temperature, sodium concentration, and hydroxide ion activity (aOH-) . These equations are more convenient to use than those given by Bickmore et al. (2008) because rates can be predicted without the implementation of a surface speciation model. They predict that at 25 °C quartz dissolves more than 200 times faster in seawater than in pure water. These two equations fit the data just as well as five other equations from Bickmore et al. (2008) that are based on surface species concentrations. All of these rate equations contain information about the reaction mechanism(s) for quartz dissolution but that information is ambiguous because the independent variables used to develop the equations are correlated. This means that rate equations alone cannot be used to infer the dissolution mechanism. Existing surface complexation, surface charge, terrace-ledge-kink, and Lewis acid-base models must be modified and amalgamated in order to develop a reliable model of the reaction mechanism(s).

  19. Equations for Automotive-Transmission Performance

    NASA Technical Reports Server (NTRS)

    Chazanoff, S.; Aston, M. B.; Chapman, C. P.

    1984-01-01

    Curve-fitting procedure ensures high confidence levels. Threedimensional plot represents performance of small automatic transmission coasting in second gear. In equation for plot, PL power loss, S speed and T torque. Equations applicable to manual and automatic transmissions over wide range of speed, torque, and efficiency.

  20. Solving Differential Equations Using Modified Picard Iteration

    ERIC Educational Resources Information Center

    Robin, W. A.

    2010-01-01

    Many classes of differential equations are shown to be open to solution through a method involving a combination of a direct integration approach with suitably modified Picard iterative procedures. The classes of differential equations considered include typical initial value, boundary value and eigenvalue problems arising in physics and…

  1. The non-compact Weyl equation

    NASA Astrophysics Data System (ADS)

    Doikou, Anastasia; Ioannidou, Theodora

    2011-04-01

    A non-compact version of the Weyl equation is proposed, based on the infinite dimensional spin zero representation of the mathfrak{s}{mathfrak{l}_2} algebra. Solutions of the aforementioned equation are obtained in terms of the Kummer functions. In this context, we discuss the ADHMN approach in order to construct the corresponding non-compact BPS monopoles.

  2. Lie algebras and linear differential equations.

    NASA Technical Reports Server (NTRS)

    Brockett, R. W.; Rahimi, A.

    1972-01-01

    Certain symmetry properties possessed by the solutions of linear differential equations are examined. For this purpose, some basic ideas from the theory of finite dimensional linear systems are used together with the work of Wei and Norman on the use of Lie algebraic methods in differential equation theory.

  3. Does the Wave Equation Really Work?

    ERIC Educational Resources Information Center

    Armstead, Donald C.; Karls, Michael A.

    2006-01-01

    The wave equation is a classic partial differential equation that one encounters in an introductory course on boundary value problems or mathematical physics, which can be used to describe the vertical displacement of a vibrating string. Using a video camera and Wave-in-Motion software to record displacement data from a vibrating string or spring,…

  4. MACSYMA's symbolic ordinary differential equation solver

    NASA Technical Reports Server (NTRS)

    Golden, J. P.

    1977-01-01

    The MACSYMA's symbolic ordinary differential equation solver ODE2 is described. The code for this routine is delineated, which is of interest because it is written in top-level MACSYMA language, and may serve as a good example of programming in that language. Other symbolic ordinary differential equation solvers are mentioned.

  5. Symbolic Solution of Linear Differential Equations

    NASA Technical Reports Server (NTRS)

    Feinberg, R. B.; Grooms, R. G.

    1981-01-01

    An algorithm for solving linear constant-coefficient ordinary differential equations is presented. The computational complexity of the algorithm is discussed and its implementation in the FORMAC system is described. A comparison is made between the algorithm and some classical algorithms for solving differential equations.

  6. Solving Cubic Equations by Polynomial Decomposition

    ERIC Educational Resources Information Center

    Kulkarni, Raghavendra G.

    2011-01-01

    Several mathematicians struggled to solve cubic equations, and in 1515 Scipione del Ferro reportedly solved the cubic while participating in a local mathematical contest, but did not bother to publish his method. Then it was Cardano (1539) who first published the solution to the general cubic equation in his book "The Great Art, or, The Rules of…

  7. Lattice Boltzmann equation for relativistic quantum mechanics.

    PubMed

    Succi, Sauro

    2002-03-15

    Relativistic versions of the quantum lattice Boltzmann equation are discussed. It is shown that the inclusion of nonlinear interactions requires the standard collision operator to be replaced by a pair of dynamic fields coupling to the relativistic wave function in a way which can be described by a multicomponent complex lattice Boltzmann equation. PMID:16210189

  8. Energy Equation Approximation in Fluid Mechanics

    NASA Technical Reports Server (NTRS)

    Goldstein, Arthur W.

    1959-01-01

    There is some confusion in the literature of fluid mechanics in regard to the correct form of the energy equation for the study of the flow of nearly incompressible fluids. Several forms of the energy equation and their use are therefore discussed in this note.

  9. Reduction of dispersionless coupled Korteweg-de Vries equations to the Euler-Darboux equation

    NASA Astrophysics Data System (ADS)

    Matsuno, Yoshimasa

    2001-04-01

    A quasilinear hyperbolic system of two first-order equations is introduced. The system is linearized by means of the hodograph transformation combined with Riemann's method of characteristics. In the process of linearization, the main step is to explicitly express the characteristic velocities in terms of the Riemann invariants. The procedure is shown to be performed by quadrature only for specific combinations of the parameters in the system. We then apply the method developed here to the dispersionless versions of the typical coupled Korteweg-de Vries (cKdV) equations including the Broer-Kaup, Ito, Hirota-Satsuma, and Bogoyavlenskii equations and show that these equations are transformed into the classical Euler-Darboux equation. A more general quasilinear system of equations is also considered with application to the dispersionless cKdV equations for the Jaulent-Miodek and Nutku-Ög˜uz equations.

  10. Turbulence kinetic energy equation for dilute suspensions

    NASA Technical Reports Server (NTRS)

    Abou-Arab, T. W.; Roco, M. C.

    1989-01-01

    A multiphase turbulence closure model is presented which employs one transport equation, namely the turbulence kinetic energy equation. The proposed form of this equation is different from the earlier formulations in some aspects. The power spectrum of the carrier fluid is divided into two regions, which interact in different ways and at different rates with the suspended particles as a function of the particle-eddy size ratio and density ratio. The length scale is described algebraically. A mass/time averaging procedure for the momentum and kinetic energy equations is adopted. The resulting turbulence correlations are modeled under less retrictive assumptions comparative to previous work. The closures for the momentum and kinetic energy equations are given. Comparisons of the predictions with experimental results on liquid-solid jet and gas-solid pipe flow show satisfactory agreement.

  11. Covariant Conformal Decomposition of Einstein Equations

    NASA Astrophysics Data System (ADS)

    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.

  12. Hybrid method for the chemical master equation

    SciTech Connect

    Hellander, Andreas Loetstedt, Per

    2007-11-10

    The chemical master equation is solved by a hybrid method coupling a macroscopic, deterministic description with a mesoscopic, stochastic model. The molecular species are divided into one subset where the expected values of the number of molecules are computed and one subset with species with a stochastic variation in the number of molecules. The macroscopic equations resemble the reaction rate equations and the probability distribution for the stochastic variables satisfy a master equation. The probability distribution is obtained by the Stochastic Simulation Algorithm due to Gillespie. The equations are coupled via a summation over the mesoscale variables. This summation is approximated by Quasi-Monte Carlo methods. The error in the approximations is analyzed. The hybrid method is applied to three chemical systems from molecular cell biology.

  13. The focusing energy-critical Hartree equation

    NASA Astrophysics Data System (ADS)

    Li, Dong; Miao, Changxing; Zhang, Xiaoyi

    We consider the focusing energy-critical nonlinear Hartree equation iu+Δu=-(|∗|)u. We proved that if a maximal-lifespan solution u:I×R→C satisfies sup‖∇u(t)‖2<‖∇W‖2, where W is the static solution of the equation, then the maximal-lifespan I=R, moreover, the solution scatters in both time directions. For spherically symmetric initial data, similar result has been obtained in [C. Miao, G. Xu, L. Zhao, Global wellposedness, scattering and blowup for the energy-critical, focusing Hartree equation in the radial case, Colloq. Math., in press]. The argument is an adaptation of the recent work of R. Killip and M. Visan [R. Killip, M. Visan, The focusing energy-critical nonlinear Schrödinger equation in dimensions five and higher, preprint] on energy-critical nonlinear Schrödinger equations.

  14. Completeness of solutions of Bethe's equations.

    PubMed

    Hao, Wenrui; Nepomechie, Rafael I; Sommese, Andrew J

    2013-11-01

    We consider the Bethe equations for the isotropic spin-1/2 Heisenberg quantum spin chain with periodic boundary conditions. We formulate a conjecture for the number of solutions with pairwise distinct roots of these equations, in terms of numbers of so-called singular (or exceptional) solutions. Using homotopy continuation methods, we find all such solutions of the Bethe equations for chains of length up to 14. The numbers of these solutions are in perfect agreement with the conjecture. We also discuss an indirect method of finding solutions of the Bethe equations by solving the Baxter T-Q equation. We briefly comment on implications for thermodynamical computations based on the string hypothesis. PMID:24329220

  15. Singular perturbation equations for flexible satellites

    NASA Technical Reports Server (NTRS)

    Huang, T. C.; Das, A.

    1973-01-01

    The dynamic model of a flexible satellite with n generalized structural position coordinates requires the solution of a set of N coupled nonlinear ordinary or partial differential equations. For single composite body satellites, N is equal to (n + 3). For dual-spin systems, N is equal to (n + 9). These equations usually involve time derivatives up to the second order. For large values of n, linearization of the system has so far been the only practicable way of solution. The present study shows a method of avoiding this linearization by reducing the N equations to three or nine nonlinear, coupled, first-order ordinary differential equations involving only the angular velocities of the composite bodies. The solutions for these angular velocities lead to linear equations in the n generalized structural position coordinates, which can then be solved by known methods.

  16. Classical non-Markovian Boltzmann equation

    SciTech Connect

    Alexanian, Moorad

    2014-08-01

    The modeling of particle transport involves anomalous diffusion, (x²(t) ) ∝ t{sup α} with α ≠ 1, with subdiffusive transport corresponding to 0 < α < 1 and superdiffusive transport to α > 1. These anomalies give rise to fractional advection-dispersion equations with memory in space and time. The usual Boltzmann equation, with only isolated binary collisions, is Markovian and, in particular, the contributions of the three-particle distribution function are neglected. We show that the inclusion of higher-order distribution functions give rise to an exact, non-Markovian Boltzmann equation with resulting transport equations for mass, momentum, and kinetic energy with memory in both time and space. The two- and the three-particle distribution functions are considered under the assumption that the two- and the three-particle correlation functions are translationally invariant that allows us to obtain advection-dispersion equations for modeling transport in terms of spatial and temporal fractional derivatives.

  17. Riemann equation for prime number diffusion

    NASA Astrophysics Data System (ADS)

    Chen, Wen; Liang, Yingjie

    2015-05-01

    This study makes the first attempt to propose the Riemann diffusion equation to describe in a manner of partial differential equation and interpret in physics of diffusion the classical Riemann method for prime number distribution. The analytical solution of this equation is the well-known Riemann representation. The diffusion coefficient is dependent on natural number, a kind of position-dependent diffusivity diffusion. We find that the diffusion coefficient of the Riemann diffusion equation is nearly a straight line having a slope 0.99734 in the double-logarithmic axis. Consequently, an approximate solution of the Riemann diffusion equation is obtained, which agrees well with the Riemann representation in predicting the prime number distribution. Moreover, we interpret the scale-free property of prime number distribution via a power law function with 1.0169 the scale-free exponent in respect to logarithmic transform of the natural number, and then the fractal characteristic of prime number distribution is disclosed.

  18. Almost periodic solutions to difference equations

    NASA Technical Reports Server (NTRS)

    Bayliss, A.

    1975-01-01

    The theory of Massera and Schaeffer relating the existence of unique almost periodic solutions of an inhomogeneous linear equation to an exponential dichotomy for the homogeneous equation was completely extended to discretizations by a strongly stable difference scheme. In addition it is shown that the almost periodic sequence solution will converge to the differential equation solution. The preceding theory was applied to a class of exponentially stable partial differential equations to which one can apply the Hille-Yoshida theorem. It is possible to prove the existence of unique almost periodic solutions of the inhomogeneous equation (which can be approximated by almost periodic sequences) which are the solutions to appropriate discretizations. Two methods of discretizations are discussed: the strongly stable scheme and the Lax-Wendroff scheme.

  19. Planck-scale corrections to Friedmann equation

    NASA Astrophysics Data System (ADS)

    Awad, Adel; Ali, Ahmed

    2014-04-01

    Recently, Verlinde proposed that gravity is an emergent phenomenon which originates from an entropic force. In this work, we extend Verlinde's proposal to accommodate generalized uncertainty principles (GUP), which are suggested by some approaches to quantum gravity such as string theory, black hole physics and doubly special relativity (DSR). Using Verlinde's proposal and two known models of GUPs, we obtain modifications to Newton's law of gravitation as well as the Friedmann equation. Our modification to the Friedmann equation includes higher powers of the Hubble parameter which is used to obtain a corresponding Raychaudhuri equation. Solving this equation, we obtain a leading Planck-scale correction to Friedmann-Robertson-Walker (FRW) solutions for the p = ωp equation of state.

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

    NASA Astrophysics Data System (ADS)

    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.

  1. Derivation of the high field semiconductor equations

    SciTech Connect

    Hagan, P.S. ); Cox, R.W. ); Wagner, B.A. . Dept. of Mathematics)

    1991-01-01

    Electron and hole densities evolve in x-z phase space according to Boltzmann equations. When the mean free path of the particles is short and electric force on the particles is weak, a well-known expansion can be used to solve the Boltzmann equation. This asymptotic solution shows that the spatial density of electrons and holes evolves according to diffusion-drift equations. As devices become smaller, electric fields become stronger, which renders the Basic Semiconductor Equations increasingly inaccurate. To remedy this problem, we use singular perturbation techniques to obtain a new asymptotic expansion for the Boltzmann equation. Like the Hilbert expansion, the new expansion requires the mean free path to be short compared to all macroscopic length scales. However, it does not require the electric forces to be weak. The new expansion shows that spatial densities obey diffusion-drift equations as before, but the diffusivity D and mobility {mu} turn out to be nonlinear functions of the electric field. In particular, our analysis determines the field-dependent mobilities {mu}(E) and diffusivities D(E) directly from the scattering operator. By carrying out this asymptotic expansion to higher order, we obtain the high frequency corrections to the drift velocity and diffusivity, and also the corrections due to gradients in the electric field. Remarkably, we find that Einsteins's relation is still satisfied, even with these corrections. The new diffusion-drift equations, together with Poissons' equation for the electric field, form the high-field semiconductor equations, which can be expected to be accurate regardless of the strength of the electric fields within the semiconductor. In addition, our analysis determines the entire momentum distribution of the particles, so we derive a very accurate first moment model for semi-conductors by substituting the asymptotically-correct distribution back into the Boltzmann equation and taking moments.

  2. Variational particle scheme for the porous medium equation and for the system of isentropic Euler equations

    SciTech Connect

    Westdickenberg, Michael; Wilkening, Jon

    2008-12-10

    We introduce variational particle schemes for the porous medium equation and the system of isentropic Euler equations in one space dimension. The methods are motivated by the interpretation of each of these partial differential equations as a 'steepest descent' on a suitable abstract manifold. We show that our methods capture very well the nonlinear features of the flows.

  3. Test Equating Procedures: A Primer on the Logic and Applications of Test Equating.

    ERIC Educational Resources Information Center

    Buras, Avery

    The logic and uses of test equating are discussed, including three methods of test equating. The focus is on the conceptual underpinnings of each test equating method, rather than on the mathematics of the procedures. Additional consideration is given to the assumptions of each method and its respective strengths and weaknesses. A commonly…

  4. Statistical Models and Inference for the True Equating Transformation in the Context of Local Equating

    ERIC Educational Resources Information Center

    González, B. Jorge; von Davier, Matthias

    2013-01-01

    Based on Lord's criterion of equity of equating, van der Linden (this issue) revisits the so-called local equating method and offers alternative as well as new thoughts on several topics including the types of transformations, symmetry, reliability, and population invariance appropriate for equating. A remarkable aspect is to define equating…

  5. Solution Methods for Certain Evolution Equations

    NASA Astrophysics Data System (ADS)

    Vega-Guzman, Jose Manuel

    Solution methods for certain linear and nonlinear evolution equations are presented in this dissertation. Emphasis is placed mainly on the analytical treatment of nonautonomous differential equations, which are challenging to solve despite the existent numerical and symbolic computational software programs available. Ideas from the transformation theory are adopted allowing one to solve the problems under consideration from a non-traditional perspective. First, the Cauchy initial value problem is considered for a class of nonautonomous and inhomogeneous linear diffusion-type equation on the entire real line. Explicit transformations are used to reduce the equations under study to their corresponding standard forms emphasizing on natural relations with certain Riccati(and/or Ermakov)-type systems. These relations give solvability results for the Cauchy problem of the parabolic equation considered. The superposition principle allows to solve formally this problem from an unconventional point of view. An eigenfunction expansion approach is also considered for this general evolution equation. Examples considered to corroborate the efficacy of the proposed solution methods include the Fokker-Planck equation, the Black-Scholes model and the one-factor Gaussian Hull-White model. The results obtained in the first part are used to solve the Cauchy initial value problem for certain inhomogeneous Burgers-type equation. The connection between linear (the Diffusion-type) and nonlinear (Burgers-type) parabolic equations is stress in order to establish a strong commutative relation. Traveling wave solutions of a nonautonomous Burgers equation are also investigated. Finally, it is constructed explicitly the minimum-uncertainty squeezed states for quantum harmonic oscillators. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. It is shown that the product of the variances attains the required minimum value

  6. Turning Equations Into Stories: Using "Equation Dictionaries" in an Introductory Geophysics Class

    NASA Astrophysics Data System (ADS)

    Caplan-Auerbach, J.

    2008-12-01

    To students with math fear, equations can be intimidating and overwhelming. This discomfort is reflected in some of the frequent questions heard in introductory geophysics: "which equation should I use?" and "does T stand for travel time or period?" Questions such as these indicate that many students view equations as a series of variables and operators rather than as a representation of a physical process. To solve a problem they may simply look for an equation with the correct variables and assume that it meets their needs, rather than selecting an equation that represents the appropriate physical process. These issues can be addressed by encouraging students to think of equations as stories, and to describe them in prose. This is the goal of the Equation Dictionary project, used in Western Washington University's introductory geophysics course. Throughout the course, students create personal equation dictionaries, adding an entry each time an equation is introduced. Entries consist of (a) the equation itself, (b) a brief description of equation variables, (c) a prose description of the physical process described by the equation, and (d) any additional notes that help them understand the equation. Thus, rather than simply writing down the equations for the velocity of body waves, a student might write "The speed of a seismic body wave is controlled by the material properties of the medium through which it passes." In a study of gravity a student might note that the International Gravity Formula describes "the expected value of g at a given latitude, correcting for Earth's shape and rotation." In writing these definitions students learn that equations are simplified descriptions of physical processes, and that understanding the process is more useful than memorizing a sequence of variables. Dictionaries also serve as formula sheets for exams, which encourages students to write definitions that are meaningful to them, and to organize their thoughts clearly. Finally

  7. On the thermo-acoustic Fant equation

    NASA Astrophysics Data System (ADS)

    Murray, P. R.; Howe, M. S.

    2012-07-01

    A 'reduced complexity' equation is derived to investigate combustion instabilities of a Rijke burner. The equation is nonlinear and furnishes limit cycle solutions for finite amplitude burner modes. It is a generalisation to combustion flows of the Fant equation used to investigate the production of voiced speech by unsteady throttling of flow by the vocal folds [G. Fant, Acoustic Theory of Speech Production. Mouton, The Hague, 1960]. In the thermo-acoustic problem the throttling occurs at the flame holder. The Fant equation governs the unsteady volume flow past the flame holder which, in turn, determines the acoustics of the entire system. The equation includes a fully determinate part that depends on the geometry of the flame holder and the thermo-acoustic system, and terms defined by integrals involving thermo-aerodynamic sources, such as a flame and vortex sound sources. These integrals provide a clear indication of what must be known about the flow to obtain a proper understanding of the dynamics of the thermo-acoustic system. Illustrative numerical results are presented for the linearised equation. This governs the growth rates of the natural acoustic modes, determined by system geometry, boundary conditions and mean temperature distribution, which are excited into instability by unsteady heat release from the flame and damped by large scale vorticity production and radiation losses into the environment. In addition, the equation supplies information about the 'combustion modes' excited by the local time-delay feedback dynamics of the flame.

  8. Moment equations for a piecewise deterministic PDE

    NASA Astrophysics Data System (ADS)

    Bressloff, Paul C.; Lawley, Sean D.

    2015-03-01

    We analyze a piecewise deterministic PDE consisting of the diffusion equation on a finite interval Ω with randomly switching boundary conditions and diffusion coefficient. We proceed by spatially discretizing the diffusion equation using finite differences and constructing the Chapman-Kolmogorov (CK) equation for the resulting finite-dimensional stochastic hybrid system. We show how the CK equation can be used to generate a hierarchy of equations for the r-th moments of the stochastic field, which take the form of r-dimensional parabolic PDEs on {{Ω }r} that couple to lower order moments at the boundaries. We explicitly solve the first and second order moment equations (r = 2). We then describe how the r-th moment of the stochastic PDE can be interpreted in terms of the splitting probability that r non-interacting Brownian particles all exit at the same boundary; although the particles are non-interacting, statistical correlations arise due to the fact that they all move in the same randomly switching environment. Hence the stochastic diffusion equation describes two levels of randomness: Brownian motion at the individual particle level and a randomly switching environment. Finally, in the limit of fast switching, we use a quasi-steady state approximation to reduce the piecewise deterministic PDE to an SPDE with multiplicative Gaussian noise in the bulk and a stochastically-driven boundary.

  9. Klein-Gordon Equation in Hydrodynamical Form

    SciTech Connect

    Wong, Cheuk-Yin

    2010-01-01

    We follow and modify the Feshbach-Villars formalism by separating the Klein-Gordon equation into two coupled time-dependent Schroedinger equations for the particle and antiparticle wave functions with positive probability densities. We find that the equation of motion for the probability densities is in the form of relativistic hydrodynamics where various forces have their physical and classical counterparts. An additional element is the presence of the quantum stress tensor that depends on the derivatives of the amplitude of the wave function.

  10. Schrödinger equation revisited

    PubMed Central

    Schleich, Wolfgang P.; Greenberger, Daniel M.; Kobe, Donald H.; Scully, Marlan O.

    2013-01-01

    The time-dependent Schrödinger equation is a cornerstone of quantum physics and governs all phenomena of the microscopic world. However, despite its importance, its origin is still not widely appreciated and properly understood. We obtain the Schrödinger equation from a mathematical identity by a slight generalization of the formulation of classical statistical mechanics based on the Hamilton–Jacobi equation. This approach brings out most clearly the fact that the linearity of quantum mechanics is intimately connected to the strong coupling between the amplitude and phase of a quantum wave. PMID:23509260

  11. Fokker-Planck equation in mirror research

    SciTech Connect

    Post, R.F.

    1983-08-11

    Open confinement systems based on the magnetic mirror principle depend on the maintenance of particle distributions that may deviate substantially from Maxwellian distributions. Mirror research has therefore from the beginning relied on theoretical predictions of non-equilibrium rate processes obtained from solutions to the Fokker-Planck equation. The F-P equation plays three roles: Design of experiments, creation of classical standards against which to compare experiment, and predictions concerning mirror based fusion power systems. Analytical and computational approaches to solving the F-P equation for mirror systems will be reviewed, together with results and examples that apply to specific mirror systems, such as the tandem mirror.

  12. Scattering equations and global duality of residues

    NASA Astrophysics Data System (ADS)

    Søgaard, Mads; Zhang, Yang

    2016-05-01

    We examine the polynomial form of the scattering equations by means of computational algebraic geometry. The scattering equations are the backbone of the Cachazo-He-Yuan (CHY) representation of the S-matrix. We explain how the Bezoutian matrix facilitates the calculation of amplitudes in the CHY formalism, without explicitly solving the scattering equations or summing over the individual residues. Since for n -particle scattering the size of the Bezoutian matrix grows only as (n -3 )×(n -3 ), our algorithm is very efficient for analytic and numeric amplitude computations.

  13. Fractional diffusion equations coupled by reaction terms

    NASA Astrophysics Data System (ADS)

    Lenzi, E. K.; Menechini Neto, R.; Tateishi, A. A.; Lenzi, M. K.; Ribeiro, H. V.

    2016-09-01

    We investigate the behavior for a set of fractional reaction-diffusion equations that extend the usual ones by the presence of spatial fractional derivatives of distributed order in the diffusive term. These equations are coupled via the reaction terms which may represent reversible or irreversible processes. For these equations, we find exact solutions and show that the spreading of the distributions is asymptotically governed by the same the long-tailed distribution. Furthermore, we observe that the coupling introduced by reaction terms creates an interplay between different diffusive regimes leading us to a rich class of behaviors related to anomalous diffusion.

  14. Minimal relativistic three-particle equations

    SciTech Connect

    Lindesay, J.

    1981-07-01

    A minimal self-consistent set of covariant and unitary three-particle equations is presented. Numerical results are obtained for three-particle bound states, elastic scattering and rearrangement of bound pairs with a third particle, and amplitudes for breakup into states of three free particles. The mathematical form of the three-particle bound state equations is explored; constraints are set upon the range of eigenvalues and number of eigenstates of these one parameter equations. The behavior of the number of eigenstates as the two-body binding energy decreases to zero in a covariant context generalizes results previously obtained non-relativistically by V. Efimov.

  15. Time-reversal and the Bessel equation

    NASA Astrophysics Data System (ADS)

    Alfinito, Eleonora; Vitiello, Giuseppe

    2015-07-01

    The system of two damped/amplified oscillator equations is of widespread interest in the study of many physical problems and phenomena, from inflationary models of the Universe to thermal field theories, in condensed matter physics as well in high energy physics, and also in neuroscience. In this report we review the equivalence, in a suitable parametrization, between such a system of equations and the Bessel equations. In this connection, we discuss the breakdown of loop-antiloop symmetry, its relation with time-reversal symmetry and the mechanism of group contraction. Euclidean algebras such as e(2) and e(3) are also discussed in relation with Virasoro-like algebra.

  16. Some problems in fractal differential equations

    NASA Astrophysics Data System (ADS)

    Su, Weiyi

    2016-06-01

    Based upon the fractal calculus on local fields, or p-type calculus, or Gibbs-Butzer calculus ([1],[2]), we suggest a constructive idea for "fractal differential equations", beginning from some special examples to a general theory. However, this is just an original idea, it needs lots of later work to support. In [3], we show example "two dimension wave equations with fractal boundaries", and in this note, other examples, as well as an idea to construct fractal differential equations are shown.

  17. Solutions of the coupled Higgs field equations.

    PubMed

    Talukdar, Benoy; Ghosh, Swapan K; Saha, Aparna; Pal, Debabrata

    2013-07-01

    By an appropriate choice for the phase of the complex nucleonic field and going over to the traveling coordinate, we reduce the coupled Higgs equations to the Hamiltonian form and treat the resulting equation using the dynamical system theory. We present a phase-space analysis of its stable points. The results of our study demonstrate that the equation can support both traveling- and standing-wave solutions. The traveling-wave solution appears in the form of a soliton and resides in the midst of doubly periodic standing-wave solutions. PMID:23944601

  18. Schrödinger equation revisited.

    PubMed

    Schleich, Wolfgang P; Greenberger, Daniel M; Kobe, Donald H; Scully, Marlan O

    2013-04-01

    The time-dependent Schrödinger equation is a cornerstone of quantum physics and governs all phenomena of the microscopic world. However, despite its importance, its origin is still not widely appreciated and properly understood. We obtain the Schrödinger equation from a mathematical identity by a slight generalization of the formulation of classical statistical mechanics based on the Hamilton-Jacobi equation. This approach brings out most clearly the fact that the linearity of quantum mechanics is intimately connected to the strong coupling between the amplitude and phase of a quantum wave. PMID:23509260

  19. The gBL transport equations

    SciTech Connect

    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/GAMMAT 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.

  20. A SYMPLECTIC INTEGRATOR FOR HILL'S EQUATIONS

    SciTech Connect

    Quinn, Thomas; Barnes, Rory; Perrine, Randall P.; Richardson, Derek C.

    2010-02-15

    Hill's equations are an approximation that is useful in a number of areas of astrophysics including planetary rings and planetesimal disks. We derive a symplectic method for integrating Hill's equations based on a generalized leapfrog. This method is implemented in the parallel N-body code, PKDGRAV, and tested on some simple orbits. The method demonstrates a lack of secular changes in orbital elements, making it a very useful technique for integrating Hill's equations over many dynamical times. Furthermore, the method allows for efficient collision searching using linear extrapolation of particle positions.

  1. Entanglement Equilibrium and the Einstein Equation

    NASA Astrophysics Data System (ADS)

    Jacobson, Ted

    2016-05-01

    A link between the semiclassical Einstein equation and a maximal vacuum entanglement hypothesis is established. The hypothesis asserts that entanglement entropy in small geodesic balls is maximized at fixed volume in a locally maximally symmetric vacuum state of geometry and quantum fields. A qualitative argument suggests that the Einstein equation implies the validity of the hypothesis. A more precise argument shows that, for first-order variations of the local vacuum state of conformal quantum fields, the vacuum entanglement is stationary if and only if the Einstein equation holds. For nonconformal fields, the same conclusion follows modulo a conjecture about the variation of entanglement entropy.

  2. Entanglement Equilibrium and the Einstein Equation.

    PubMed

    Jacobson, Ted

    2016-05-20

    A link between the semiclassical Einstein equation and a maximal vacuum entanglement hypothesis is established. The hypothesis asserts that entanglement entropy in small geodesic balls is maximized at fixed volume in a locally maximally symmetric vacuum state of geometry and quantum fields. A qualitative argument suggests that the Einstein equation implies the validity of the hypothesis. A more precise argument shows that, for first-order variations of the local vacuum state of conformal quantum fields, the vacuum entanglement is stationary if and only if the Einstein equation holds. For nonconformal fields, the same conclusion follows modulo a conjecture about the variation of entanglement entropy. PMID:27258860

  3. The Drake Equation in an astrobiological context

    NASA Astrophysics Data System (ADS)

    Konesky, Gregory A.

    2010-09-01

    The Drake Equation was originally composed as an attempt to quantify the potential number of extraterrestrial civilizations in our Galaxy which we might be able to detect using a radio telescope. Since this equation was first formulated, nearly 50 years ago, we have discovered that life on Earth arose very early in its history, and has filled virtually every habitable, potentially extreme, niche available. This suggests that simple forms of life might be plentiful where possible, and can be observed remotely by atmospheric biosignatures in the host planet. We consider modifications to the Drake Equation to reflect this new understanding.

  4. Some More Solutions of Burgers' Equation

    NASA Astrophysics Data System (ADS)

    Kumar, Mukesh; Kumar, Raj

    2015-01-01

    In this work, similarity solutions of viscous one-dimensional Burgers' equation are attained by using Lie group theory. The symmetry generators are used for constructing Lie symmetries with commuting infinitesimal operators which lead the governing partial differential equation (PDE) to ordinary differential equation (ODE). Most of the constructed solutions are found in terms of Bessel functions which are new as far as authors are aware. Effect of various parameters in the evolutional profile of the solutions are shown graphically and discussed them physically.

  5. Using worksheets to solve the Einstein equation

    NASA Astrophysics Data System (ADS)

    Moore, Thomas A.

    2016-05-01

    This article describes how one can use worksheets to guide undergraduate students through the process of finding solutions to specific cases of the Einstein equation of general relativity. The worksheets provide expressions for a metric's Christoffel symbols and Ricci tensor components for fairly general metrics. Students can use a worksheet to adapt these expressions to specific cases where symmetry or other considerations constrain the metric components' dependencies, and then use the worksheet's results to reduce the Einstein equation to a set of simpler differential equations that they can solve. This article illustrates the process for both a diagonal metric and a metric with one off-diagonal element.

  6. Formulas for precession. [motion of mean equator

    NASA Technical Reports Server (NTRS)

    Kinoshita, H.

    1975-01-01

    Literal expressions for the precessional motion of the mean equator referred to an arbitrary epoch are constructed. Their numerical representations, based on numerical values recommended at the working meeting of the International Astronomical Union Commission held in Washington in September 1974, are obtained. In constructing the equations of motion, the second-order secular perturbation and the secular perturbation due to the long-periodic terms in the motions of the moon and the sun are taken into account. These perturbations contribute more to the motion of the mean equator than does the term due to the secular perturbation of the orbital eccentricity of the sun.

  7. The zero dispersion limits of nonlinear wave equations

    SciTech Connect

    Tso, T.

    1992-01-01

    In chapter 2 the author uses functional analytic methods and conservation laws to solve the initial-value problem for the Korteweg-de Vries equation, the Benjamin-Bona-Mahony equation, and the nonlinear Schroedinger equation for initial data that satisfy some suitable conditions. In chapter 3 the energy estimates are used to show that the strong convergence of the family of the solutions of the KdV equation obtained in chapter 2 in H[sup 3](R) as [epsilon] [yields] 0; also, it is shown that the strong L[sup 2](R)-limit of the solutions of the BBM equation as [epsilon] [yields] 0 before a critical time. In chapter 4 the author uses the Whitham modulation theory and averaging method to find the 2[pi]-periodic solutions and the modulation equations of the KdV equation, the BBM equation, the Klein-Gordon equation, the NLS equation, the mKdV equation, and the P-system. It is shown that the modulation equations of the KdV equation, the K-G equation, the NLS equation, and the mKdV equation are hyperbolic but those of the BBM equation and the P-system are not hyperbolic. Also, the relations are studied of the KdV equation and the mKdV equation. Finally, the author studies the complex mKdV equation to compare with the NLS equation, and then study the complex gKdV equation.

  8. A Generalized Simplest Equation Method and Its Application to the Boussinesq-Burgers Equation

    PubMed Central

    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. PMID:25973605

  9. Generalized Directional Gradients, Backward Stochastic Differential Equations and Mild Solutions of Semilinear Parabolic Equations

    SciTech Connect

    Fuhrman, Marco Tessitore, Gianmario

    2005-05-15

    We study a forward-backward system of stochastic differential equations in an infinite-dimensional framework and its relationships with a semilinear parabolic differential equation on a Hilbert space, in the spirit of the approach of Pardoux-Peng. We prove that the stochastic system allows us to construct a unique solution of the parabolic equation in a suitable class of locally Lipschitz real functions. The parabolic equation is understood in a mild sense which requires the notion of a generalized directional gradient, that we introduce by a probabilistic approach and prove to exist for locally Lipschitz functions.The use of the generalized directional gradient allows us to cover various applications to option pricing problems and to optimal stochastic control problems (including control of delay equations and reaction-diffusion equations),where the lack of differentiability of the coefficients precludes differentiability of solutions to the associated parabolic equations of Black-Scholes or Hamilton-Jacobi-Bellman type.

  10. Recursion operators, conservation laws, and integrability conditions for difference equations

    NASA Astrophysics Data System (ADS)

    Mikhailov, A. V.; Wang, Jing Ping; Xenitidis, P.

    2011-04-01

    We attempt to propose an algebraic approach to the theory of integrable difference equations. We define the concept of a recursion operator for difference equations and show that it generates an infinite sequence of symmetries and canonical conservation laws for a difference equation. As in the case of partial differential equations, these canonical densities can serve as integrability conditions for difference equations. We obtain the recursion operators for the Viallet equation and all the Adler-Bobenko-Suris equations.

  11. On Blowup in Supercritical Wave Equations

    NASA Astrophysics Data System (ADS)

    Donninger, Roland; Schörkhuber, Birgit

    2016-03-01

    We study the blowup behavior for the focusing energy-supercritical semilinear wave equation in 3 space dimensions without symmetry assumptions on the data. We prove the stability in {H^2× H^1} of the ODE blowup profile.

  12. THE BERNOULLI EQUATION AND COMPRESSIBLE FLOW THEORIES

    EPA Science Inventory

    The incompressible Bernoulli equation is an analytical relationship between pressure, kinetic energy, and potential energy. As perhaps the simplest and most useful statement for describing laminar flow, it buttresses numerous incompressible flow models that have been developed ...

  13. Systems of fuzzy equations in structural mechanics

    NASA Astrophysics Data System (ADS)

    Skalna, Iwona; Rama Rao, M. V.; Pownuk, Andrzej

    2008-08-01

    Systems of linear and nonlinear equations with fuzzy parameters are relevant to many practical problems arising in structure mechanics, electrical engineering, finance, economics and physics. In this paper three methods for solving such equations are discussed: method for outer interval solution of systems of linear equations depending linearly on interval parameters, fuzzy finite element method proposed by Rama Rao and sensitivity analysis method. The performance and advantages of presented methods are described with illustrative examples. Extended version of the present paper can be downloaded from the web page of the UTEP [I. Skalna, M.V. Rama Rao, A. Pownuk, Systems of fuzzy equations in structural mechanics, The University of Texas at El Paso, Department of Mathematical Sciences Research Reports Series, , Texas Research Report No. 2007-01, 2007].

  14. Writing Chemical Equations: An Introductory Experiment

    ERIC Educational Resources Information Center

    LeMay, H. Eugene, Jr.; Kemp, Kenneth C.

    1975-01-01

    Describes an experiment in which possible products of a series of reactions are tabulated together with properties which may be useful in identifying each substance. The student deduces the products and writes a balanced chemical equation for the reaction. (GS)

  15. Radiative Damping and Functional Differential Equations

    NASA Astrophysics Data System (ADS)

    Raju, Suvrat; Raju, C. K.

    We propose a general technique to solve the classical many-body problem with radiative damping. We modify the short-distance structure of Maxwell electrodynamics. This allows us to avoid runaway solutions as if we had a covariant model of extended particles. The resulting equations of motion are functional differential equations (FDEs) rather than ordinary differential equations (ODEs). Using recently developed numerical techniques for stiff, retarded FDEs, we solve these equations for the one-body central force problem with radiative damping. Our results indicate that locally the magnitude of radiation damping may be well approximated by the standard third-order expression but the global properties of our solutions are dramatically different. We comment on the two-body problem and applications to quantum field theory and quantum mechanics.

  16. Solar Cycle: Magnetized March to Equator

    NASA Video Gallery

    Bands of magnetized solar material – with alternating south and north polarity – march toward the sun's equator. Comparing the evolution of the bands with the sunspot number in each hemisphere over...

  17. Approximate probability distributions of the master equation

    NASA Astrophysics Data System (ADS)

    Thomas, Philipp; Grima, Ramon

    2015-07-01

    Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation using orthogonal polynomials. The solution is given in two alternative formulations: a series with continuous and a series with discrete support, both of which can be systematically truncated. While both approximations satisfy the system size expansion of the master equation, the continuous distribution approximations become increasingly negative and tend to oscillations with increasing truncation order. In contrast, the discrete approximations rapidly converge to the underlying non-Gaussian distributions. The theory is shown to lead to particularly simple analytical expressions for the probability distributions of molecule numbers in metabolic reactions and gene expression systems.

  18. How Maxwell's equations came to light

    NASA Astrophysics Data System (ADS)

    Mahon, Basil

    2015-01-01

    The nineteenth-century Scottish physicist James Clerk Maxwell made groundbreaking contributions to many areas of science including thermodynamics and colour vision. However, he is best known for his equations that unified electricity, magnetism and light.

  19. Lyapunov Spectra in Diffusion Replicator Equation

    NASA Astrophysics Data System (ADS)

    Orihashi, Kenji; Aizawa, Yoji

    2008-11-01

    Statistical Properties of the turbulence in the diffusion replicator equation of three species are numerically studied. The maximal Lyapunov exponent and Lyapunov dimension are derived precisely. Further, these characteristics obey some characteristic scaling laws.

  20. Connecting Related Rates and Differential Equations

    ERIC Educational Resources Information Center

    Brandt, Keith

    2012-01-01

    This article points out a simple connection between related rates and differential equations. The connection can be used for in-class examples or homework exercises, and it is accessible to students who are familiar with separation of variables.

  1. Turbulent disruptions from the Strauss equations

    NASA Technical Reports Server (NTRS)

    Dahlburg, J. P.; Montgomery, D.; Matthaeus, W. H.

    1985-01-01

    Preliminary results are reported from application of a three-dimensional spectral method model to the solution of the Strauss (1976) reduced MHD equations. The investigation was focused on describing MHD turbulence in a current-carrying bounded magnetofluid. A cylindrical geometry with a square cross-section was considered, with the walls being rigid perfect conductors with free-slip boundary conditions. A uniform magnetic field and the electric current density both point in the z-direction. Initial conditions are specified which feature small amounts of random noise expressed as Fourier modes. Linearized equations are defined for tracing the movement to equlibrium conditions or other temporal development. The model is further refined with nonlinear equations to examine the effects of the appearance of disruptions. Comparisons are drawn between solutions obtained with linear and nonlinear equations, with an eye to the associated physical realities.

  2. Engineering integrable nonautonomous nonlinear Schroedinger equations

    SciTech Connect

    He Xugang; Zhao Dun; Li Lin; Luo Honggang

    2009-05-15

    We investigate Painleve integrability of a generalized nonautonomous one-dimensional nonlinear Schroedinger (NLS) equation with time- and space-dependent dispersion, nonlinearity, and external potentials. Through the Painleve analysis some explicit requirements on the dispersion, nonlinearity, dissipation/gain, and the external potential as well as the constraint conditions are identified. It provides an explicit way to engineer integrable nonautonomous NLS equations at least in the sense of Painleve integrability. Furthermore analytical solutions of this class of integrable nonautonomous NLS equations can be obtained explicitly from the solutions of the standard NLS equation by a general transformation. The result provides a significant way to control coherently the soliton dynamics in the corresponding nonlinear systems, as that in Bose-Einstein condensate experiments. We analyze explicitly the soliton dynamics under the nonlinearity management and the external potentials and discuss its application in the matter-wave dynamics. Some comparisons with the previous works have also been discussed.

  3. Underwater photogrammetric theoretical equations and technique

    NASA Astrophysics Data System (ADS)

    Fan, Ya-bing; Huang, Guiping; Qin, Gui-qin; Chen, Zheng

    2011-12-01

    In order to have a high level of accuracy of measurement in underwater close-range photogrammetry, this article deals with a study of three varieties of model equations according to the way of imaging upon the water. First, the paper makes a careful analysis for the two varieties of theoretical equations and finds out that there are some serious limitations in practical application and has an in-depth study for the third model equation. Second, one special project for this measurement has designed correspondingly. Finally, one rigid antenna has been tested by underwater photogrammetry. The experimental results show that the precision of 3D coordinates measurement is 0.94mm, which validates the availability and operability in practical application with this third equation. It can satisfy the measurement requirements of refraction correction, improving levels of accuracy of underwater close-range photogrammetry, as well as strong antijamming and stabilization.

  4. Switched electrical networks and bilinear equations

    NASA Technical Reports Server (NTRS)

    Wood, J. R.

    1974-01-01

    State equations arising in the description of power processing systems are described. The role played by Lie groups and Lie algebras in characterizing the inherent dynamical features of these systems is outlined, and network examples are presented for illustration.

  5. Finite scale equations for compressible fluid flow

    SciTech Connect

    Margolin, Len G

    2008-01-01

    Finite-scale equations (FSE) describe the evolution of finite volumes of fluid over time. We discuss the FSE for a one-dimensional compressible fluid, whose every point is governed by the Navier-Stokes equations. The FSE contain new momentum and internal energy transport terms. These are similar to terms added in numerical simulation for high-speed flows (e.g. artificial viscosity) and for turbulent flows (e.g. subgrid scale models). These similarities suggest that the FSE may provide new insight as a basis for computational fluid dynamics. Our analysis of the FS continuity equation leads to a physical interpretation of the new transport terms, and indicates the need to carefully distinguish between volume-averaged and mass-averaged velocities in numerical simulation. We make preliminary connections to the other recent work reformulating Navier-Stokes equations.

  6. Effective density terms in proper integral equations

    NASA Astrophysics Data System (ADS)

    Dyer, Kippi M.; Perkyns, John S.; Pettitt, B. Montgomery

    2005-11-01

    Two complementary routes to a new integral equation theory for site-site molecular fluids are presented. First, a simple approximation to a subset of the atomic site bridge functions in the diagrammatically proper integral equation theory is presented. This in turn leads to a form analogous to the reactive fluid theory, in which the normalization of the intramolecular distribution function and the value of the off-diagonal elements in the density matrix of the proper integral equations are the means of propagating the bridge function approximation. Second, a derivation from a topological expansion of a model for the single-site activity followed by a topological reduction and low-order truncation is given. This leads to an approximate numerical value for the new density coefficient. The resulting equations give a substantial improvement over the standard construction as shown with a series of simple diatomic model calculations.

  7. Viscous Boussinesq equations for internal waves

    NASA Astrophysics Data System (ADS)

    Liu, Chi-Min

    2016-04-01

    In this poster, Boussinesq wave equations for internal wave propagation in a two-fluid system bounded by two impermeable plates are derived and analyzed. Using the perturbation method as well as the Padé approximation, a set of three equations accurate up to the fourth order are derived and displayed by three unknowns: the interfacial elevation, upper and lower velocity potentials at arbitrary vertical positions. No limitation on nonlinearity is made while weakly dispersive effects are originally considered in the derivation. The derived equations are examined by comparing its dispersion relation with those of existing models to verify the accuracy. The results show that present model equations provide an excellent base for simulating internal waves not only in shallower configuration but also medium configuration.

  8. A New Interptrtation of Drake-Equation

    NASA Astrophysics Data System (ADS)

    Hetesi, Z.; Regaly, Z.

    Some aspects of modern astrobiology that play an essential role in the Search for Extraterrestrial Intelligence (SETI) are critically investigated. Specifically the factors in the Drake equation are considered and proposals for modifications made. It is argued there may be a more civilized way of life than a communicative one. The impact on the equation of the probability of the existence of communicative civilizations in our Galaxy is investigated considering likelihood-theory and the possible channel of communication. The issues that arise are new elements in the probability equation (i.e. deviations from the traditional Drake equation factors). It is concluded that while the existence of Extraterrestrial Intelligence may be high the probability of communication maybe less than the results of former estimations.

  9. Numerical Solution for Navier-Stokes Equations

    NASA Technical Reports Server (NTRS)

    Warsi, Z. U. A.; Weed, R. A.; Thompson, J. F.

    1982-01-01

    Carefully selected blend of computational techniques solves complete set of equations for viscous, unsteady, hypersonic flow in general curvilinear coordinates. New algorithm has tested computation of axially directed flow about blunt body having shape similar to that of such practical bodies as wide-body aircraft or artillery shells. Method offers significant computational advantages because of conservation-law form of equations and because it reduces amount of metric data required.

  10. Normal Forms for Nonautonomous Differential Equations

    NASA Astrophysics Data System (ADS)

    Siegmund, Stefan

    2002-01-01

    We extend Henry Poincarés normal form theory for autonomous differential equations x=f(x) to nonautonomous differential equations x=f(t, x). Poincarés nonresonance condition λj-∑ni=1 ℓiλi≠0 for eigenvalues is generalized to the new nonresonance condition λj∩∑ni=1 ℓiλi=∅ for spectral intervals.

  11. Classification of integrable B-equations

    NASA Astrophysics Data System (ADS)

    van der Kamp, Peter H.

    We classify integrable equations which have the form u t=a 1u n+K(v 0,v 1,…), v t=a 2v n, where a 1,a 2∈ C, n∈ N and K a quadratic polynomial in derivatives of v. This is done using the symbolic calculus, biunit coordinates and the Lech-Mahler theorem. Furthermore we present a method, based on resultants, to determine whether an equation is in a hierarchy of lower order.

  12. Legendre transformations and Clairaut-type equations

    NASA Astrophysics Data System (ADS)

    Lavrov, Peter M.; Merzlikin, Boris S.

    2016-05-01

    It is noted that the Legendre transformations in the standard formulation of quantum field theory have the form of functional Clairaut-type equations. It is shown that in presence of composite fields the Clairaut-type form holds after loop corrections are taken into account. A new solution to the functional Clairaut-type equation appearing in field theories with composite fields is found.

  13. Curvature tensors unified field equations on SEXn

    NASA Astrophysics Data System (ADS)

    Chung, Kyung Tae; Lee, Il Young

    1988-09-01

    We study the curvature tensors and field equations in the n-dimensional SE manifold SEXn. We obtain several basic properties of the vectors S λ and U λ and then of the SE curvature tensor and its contractions, such as a generalized Ricci identity, a generalized Bianchi identity, and two variations of the Bianchi identity satisfied by the SE Einstein tensor. Finally, a system of field equations is discussed in SEXn and one of its particular solutions is constructed and displayed.

  14. The Einstein Relation for the KPZ Equation

    NASA Astrophysics Data System (ADS)

    Gonçalves, Patrícia; Jara, Milton

    2015-03-01

    We compute the non-universal constants in the KPZ equation in one dimension, in terms of the thermodynamical quantities associated to the underlying microscopic dynamics. In particular, we derive the second-order Einstein relation for the transport coefficient of the KPZ equation, in terms of the conserved quantity , the diffusion coefficient , the strength of the asymmetry and the static compressibility of the system.

  15. Computation of virial coefficients from integral equations.

    PubMed

    Zhang, Cheng; Lai, Chun-Liang; Pettitt, B Montgomery

    2015-06-01

    A polynomial-time method of computing the virial coefficients from an integral equation framework is presented. The method computes the truncated density expansions of the correlation functions by series transformations, and then extracts the virial coefficients from the density components. As an application, the method was used in a hybrid-closure integral equation with a set of self-consistent conditions, which produced reasonably accurate virial coefficients for the hard-sphere fluid and Gaussian model in high dimensions. PMID:26049482

  16. Computation of virial coefficients from integral equations

    NASA Astrophysics Data System (ADS)

    Zhang, Cheng; Lai, Chun-Liang; Pettitt, B. Montgomery

    2015-06-01

    A polynomial-time method of computing the virial coefficients from an integral equation framework is presented. The method computes the truncated density expansions of the correlation functions by series transformations, and then extracts the virial coefficients from the density components. As an application, the method was used in a hybrid-closure integral equation with a set of self-consistent conditions, which produced reasonably accurate virial coefficients for the hard-sphere fluid and Gaussian model in high dimensions.

  17. Approximate Solutions Of Equations Of Steady Diffusion

    NASA Technical Reports Server (NTRS)

    Edmonds, Larry D.

    1992-01-01

    Rigorous analysis yields reliable criteria for "best-fit" functions. Improved "curve-fitting" method yields approximate solutions to differential equations of steady-state diffusion. Method applies to problems in which rates of diffusion depend linearly or nonlinearly on concentrations of diffusants, approximate solutions analytic or numerical, and boundary conditions of Dirichlet type, of Neumann type, or mixture of both types. Applied to equations for diffusion of charge carriers in semiconductors in which mobilities and lifetimes of charge carriers depend on concentrations.

  18. The degeneracy of the free Dirac equation

    SciTech Connect

    Gupta, V. . School of Physics Tata Inst. of Fundamental Research, Bombay ); McKellar, B.H.J. . School of Physics); Wu, D.D. . School of Physics Institute of High Energy Physics, Beijing, BJ . Electron LINAC Dept. General Atomics, San Diego, CA )

    1991-08-01

    Parity-mixed solutions of the free Dirac equation with the same 4-momentum are considered. The first-order EM energy has an electric dipole moment term whose value depends on the mixing angle. Further implications of this degeneracy to perturbative calculations are discussed. It is argued that the properties of the Dirac equation with the Coulomb potential can be used to decide the mixing angle, which should be zero.

  19. A Gallium multiphase equation of state

    SciTech Connect

    Crockett, Scott D; Greeff, Carl

    2009-01-01

    A new SESAME multiphase Gallium equation of state (EOS) has been developed. The equation of state includes three of the solid phases (Ga I, Ga II, Ga III) and a fluid phase (liquid/gas). The EOS includes consistent latent heat between the phases. We compare the results to the liquid Hugoniol data. We also explore the possibility of re-freezing via dynamic means such as isentropic and shock compression.

  20. Dual Diagonalization of Reactive Transport Equations

    NASA Astrophysics Data System (ADS)

    Yeh, G.; Tsai, C.

    2013-12-01

    One solves a system of species transport equations in the primitive approach to reactive transport modeling. This approach is not able to decouple equilibrium reaction rates from species concentrations. This problem has been overcome with the approach to diagonalizing the reaction matrix since mid 1990's, which yields the same number of transport equations for reaction-extents. In the diagonalization approach, first, a subset of reaction- extent transport equations is solved for concentrations of components and kinetic-variables. Then, the component, kinetic-variable, and mass action equations are solved for all species concentrations. Finally, the equilibrium reaction rates are posterior computed. The difficulty in this approach is that the solution of species concentrations in the second step is a stiff problem when the concentrations of master species are small compared to those of equilibrium species. To overcome the problem of stiffness, we propose a dual diagonalization approach. Here, a second diagonalization is performed on the decomposed unit matrix to yield species concentrations, each as a linear function of reaction extents. In this dual diagonalization approach, four steps are needed to complete the modeling. First, component and kinetic-variable transport equations are solved for the concentrations of components (a subset of reaction-extents) and kinetic-variables (another subset of reaction-extents). Second, the set of mass action equations written in terms of reaction extents are solved for equilibrium-variables (yet another subset of reaction-extents). Third, species concentrations are posterior obtained by solving the set of linear equations defining reaction-extents. Fourth, equilibrium rates are posterior calculated with transport equations for equilibrium-variables. Several example problems will be used to demonstrate the efficiency of this approach. Keywords: Reactive Transport, Reaction-Extent, Component, Kinetic-Variable, Equilibrium

  1. Efficient High-Pressure State Equations

    NASA Technical Reports Server (NTRS)

    Harstad, Kenneth G.; Miller, Richard S.; Bellan, Josette

    1997-01-01

    A method is presented for a relatively accurate, noniterative, computationally efficient calculation of high-pressure fluid-mixture equations of state, especially targeted to gas turbines and rocket engines. Pressures above I bar and temperatures above 100 K are addressed The method is based on curve fitting an effective reference state relative to departure functions formed using the Peng-Robinson cubic state equation Fit parameters for H2, O2, N2, propane, methane, n-heptane, and methanol are given.

  2. Nonlinear quantum equations: Classical field theory

    SciTech Connect

    Rego-Monteiro, M. A.; Nobre, F. D.

    2013-10-15

    An exact classical field theory for nonlinear quantum equations is presented herein. It has been applied recently to a nonlinear Schrödinger equation, and it is shown herein to hold also for a nonlinear generalization of the Klein-Gordon equation. These generalizations were carried by introducing nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard, linear equations, are recovered in the limit q→ 1. The main characteristic of this field theory consists on the fact that besides the usual Ψ(x(vector sign),t), a new field Φ(x(vector sign),t) needs to be introduced in the Lagrangian, as well. The field Φ(x(vector sign),t), which is defined by means of an additional equation, becomes Ψ{sup *}(x(vector sign),t) only when q→ 1. The solutions for the fields Ψ(x(vector sign),t) and Φ(x(vector sign),t) are found herein, being expressed in terms of a q-plane wave; moreover, both field equations lead to the relation E{sup 2}=p{sup 2}c{sup 2}+m{sup 2}c{sup 4}, for all values of q. The fact that such a classical field theory works well for two very distinct nonlinear quantum equations, namely, the Schrödinger and Klein-Gordon ones, suggests that this procedure should be appropriate for a wider class nonlinear equations. It is shown that the standard global gauge invariance is broken as a consequence of the nonlinearity.

  3. Program for solution of ordinary differential equations

    NASA Technical Reports Server (NTRS)

    Sloate, H.

    1973-01-01

    A program for the solution of linear and nonlinear first order ordinary differential equations is described and user instructions are included. The program contains a new integration algorithm for the solution of initial value problems which is particularly efficient for the solution of differential equations with a wide range of eigenvalues. The program in its present form handles up to ten state variables, but expansion to handle up to fifty state variables is being investigated.

  4. Analytical methods for solving the Boltzmann equation

    NASA Astrophysics Data System (ADS)

    Struminskii, V. V.

    The principal analytical methods for solving the Boltzmann equation are reviewed, and a very general solution is proposed. The method makes it possible to obtain a solution to the Cauchy problem for the nonlinear Boltzmann equation and thus determine the applicability regions for the various analytical methods. The method proposed here also makes it possible to demonstrate that Hilbert's theorem of macroscopic causality does not apply and Hilbert's paradox does not exist.

  5. Lump solutions of the BKP equation

    NASA Astrophysics Data System (ADS)

    Gilson, C. R.; Nimmo, J. J. C.

    1990-07-01

    Rational solutions of the BKP equation which decay to zero in all directions in the plane are obtained. These solutions are analogous to the lump solutions of the KPI equation. Properties of the single lump solution are described and the form of the N-lump solution is given. It is shown that single lump solutions are only non-singular for spectral parameters lying in certain regions of the complex plane.

  6. Consistent lattice Boltzmann equations for phase transitions.

    PubMed

    Siebert, D N; Philippi, P C; Mattila, K K

    2014-11-01

    Unlike conventional computational fluid dynamics methods, the lattice Boltzmann method (LBM) describes the dynamic behavior of fluids in a mesoscopic scale based on discrete forms of kinetic equations. In this scale, complex macroscopic phenomena like the formation and collapse of interfaces can be naturally described as related to source terms incorporated into the kinetic equations. In this context, a novel athermal lattice Boltzmann scheme for the simulation of phase transition is proposed. The continuous kinetic model obtained from the Liouville equation using the mean-field interaction force approach is shown to be consistent with diffuse interface model using the Helmholtz free energy. Density profiles, interface thickness, and surface tension are analytically derived for a plane liquid-vapor interface. A discrete form of the kinetic equation is then obtained by applying the quadrature method based on prescribed abscissas together with a third-order scheme for the discretization of the streaming or advection term in the Boltzmann equation. Spatial derivatives in the source terms are approximated with high-order schemes. The numerical validation of the method is performed by measuring the speed of sound as well as by retrieving the coexistence curve and the interface density profiles. The appearance of spurious currents near the interface is investigated. The simulations are performed with the equations of state of Van der Waals, Redlich-Kwong, Redlich-Kwong-Soave, Peng-Robinson, and Carnahan-Starling. PMID:25493907

  7. A closure scheme for chemical master equations

    PubMed Central

    Smadbeck, Patrick; Kaznessis, Yiannis N.

    2013-01-01

    Probability reigns in biology, with random molecular events dictating the fate of individual organisms, and propelling populations of species through evolution. In principle, the master probability equation provides the most complete model of probabilistic behavior in biomolecular networks. In practice, master equations describing complex reaction networks have remained unsolved for over 70 years. This practical challenge is a reason why master equations, for all their potential, have not inspired biological discovery. Herein, we present a closure scheme that solves the master probability equation of networks of chemical or biochemical reactions. We cast the master equation in terms of ordinary differential equations that describe the time evolution of probability distribution moments. We postulate that a finite number of moments capture all of the necessary information, and compute the probability distribution and higher-order moments by maximizing the information entropy of the system. An accurate order closure is selected, and the dynamic evolution of molecular populations is simulated. Comparison with kinetic Monte Carlo simulations, which merely sample the probability distribution, demonstrates this closure scheme is accurate for several small reaction networks. The importance of this result notwithstanding, a most striking finding is that the steady state of stochastic reaction networks can now be readily computed in a single-step calculation, without the need to simulate the evolution of the probability distribution in time. PMID:23940327

  8. The Jeffcott equations in nonlinear rotordynamics

    NASA Technical Reports Server (NTRS)

    Zalik, R. A.

    1987-01-01

    The Jeffcott equations are a system of coupled differential equations representing the behavior of a rotating shaft. This is a simple model which allows investigation of the basic dynamic behavior of rotating machinery. Nolinearities can be introduced by taking into consideration deadband, side force, and rubbing, among others. The properties of the solutions of the Jeffcott equations with deadband are studied. In particular, it is shown how bounds for the solution of these equations can be obtained from bounds for the solutions of the linearized equations. By studying the behavior of the Fourier transforms of the solutions, we are also able to predict the onset of destructive vibrations. These conclusions are verified by means of numerical solutions of the equations, and of power spectrum density (PSD) plots. This study offers insight into a possible detection method to determine pump stability margins during flight and hot fire tests, and was motivated by the need to explain a phenomenon observed in the development phase of the cryogenic pumps of the Space Shuttle, during hot fire ground testing; namely, the appearance of vibrations at frequencies that could not be accounted for by means of linear models.

  9. Oscillations and Rolling for Duffing's Equation

    NASA Astrophysics Data System (ADS)

    Aref'eva, I. Ya.; Piskovskiy, E. V.; Volovich, I. V.

    2013-01-01

    The Duffing equation has been used to model nonlinear dynamics not only in mechanics and electronics but also in biology and in neurology for the brain process modeling. Van der Pol's method is often used in nonlinear dynamics to improve perturbation theory results when describing small oscillations. However, in some other problems of nonlinear dynamics particularly in case of Duffing-Higgs equation in field theory, for the Einsten-Friedmann equations in cosmology and for relaxation processes in neurology not only small oscillations regime is of interest but also the regime of slow rolling. In the present work a method for approximate solution to nonlinear dynamics equations in the rolling regime is developed. It is shown that in order to improve perturbation theory in the rolling regime it turns out to be effective to use an expansion in hyperbolic functions instead of trigonometric functions as it is done in van der Pol's method in case of small oscillations. In particular the Duffing equation in the rolling regime is investigated using solution expressed in terms of elliptic functions. Accuracy of obtained approximation is estimated. The Duffing equation with dissipation is also considered.

  10. Dynamical systems theory for the Gardner equation

    NASA Astrophysics Data System (ADS)

    Saha, Aparna; Talukdar, B.; Chatterjee, Supriya

    2014-02-01

    The Gardner equation ut+auux+bu2ux+μuxxx=0 is a generic mathematical model for weakly nonlinear and weakly dispersive wave propagation when the effects of higher-order nonlinearity become significant. Using the so-called traveling wave ansatz u (x,t)=φ(ξ), ξ =x-vt (where v is the velocity of the wave) we convert the (1+1)-dimensional partial differential equation to a second-order ordinary differential equation in ϕ with an arbitrary constant and treat the latter equation by the methods of the dynamical systems theory. With some special attention on the equilibrium points of the equation, we derive an analytical constraint for admissible values of the parameters a, b, and μ. From the Hamiltonian form of the system we confirm that, in addition to the usual bright soliton solution, the equation can be used to generate three different varieties of internal waves of which one is a dark soliton recently observed in water [A. Chabchoub et al., Phys. Rev. Lett. 110, 124101 (2013), 10.1103/PhysRevLett.110.124101].

  11. Forces Associated with Nonlinear Nonholonomic Constraint Equations

    NASA Technical Reports Server (NTRS)

    Roithmayr, Carlos M.; Hodges, Dewey H.

    2010-01-01

    A concise method has been formulated for identifying a set of forces needed to constrain the behavior of a mechanical system, modeled as a set of particles and rigid bodies, when it is subject to motion constraints described by nonholonomic equations that are inherently nonlinear in velocity. An expression in vector form is obtained for each force; a direction is determined, together with the point of application. This result is a consequence of expressing constraint equations in terms of dot products of vectors rather than in the usual way, which is entirely in terms of scalars and matrices. The constraint forces in vector form are used together with two new analytical approaches for deriving equations governing motion of a system subject to such constraints. If constraint forces are of interest they can be brought into evidence in explicit dynamical equations by employing the well-known nonholonomic partial velocities associated with Kane's method; if they are not of interest, equations can be formed instead with the aid of vectors introduced here as nonholonomic partial accelerations. When the analyst requires only the latter, smaller set of equations, they can be formed directly; it is not necessary to expend the labor to form the former, larger set first and subsequently perform matrix multiplications.

  12. Dynamical systems theory for the Gardner equation.

    PubMed

    Saha, Aparna; Talukdar, B; Chatterjee, Supriya

    2014-02-01

    The Gardner equation u(t) + auu(x) + bu(2)u(x)+μu(xxx) = 0 is a generic mathematical model for weakly nonlinear and weakly dispersive wave propagation when the effects of higher-order nonlinearity become significant. Using the so-called traveling wave ansatz u(x,t) = φ(ξ), ξ = x-vt (where v is the velocity of the wave) we convert the (1+1)-dimensional partial differential equation to a second-order ordinary differential equation in ϕ with an arbitrary constant and treat the latter equation by the methods of the dynamical systems theory. With some special attention on the equilibrium points of the equation, we derive an analytical constraint for admissible values of the parameters a, b, and μ. From the Hamiltonian form of the system we confirm that, in addition to the usual bright soliton solution, the equation can be used to generate three different varieties of internal waves of which one is a dark soliton recently observed in water [A. Chabchoub et al., Phys. Rev. Lett. 110, 124101 (2013)]. PMID:25353592

  13. Iterative solution of the semiconductor device equations

    SciTech Connect

    Bova, S.W.; Carey, G.F.

    1996-12-31

    Most semiconductor device models can be described by a nonlinear Poisson equation for the electrostatic potential coupled to a system of convection-reaction-diffusion equations for the transport of charge and energy. These equations are typically solved in a decoupled fashion and e.g. Newton`s method is used to obtain the resulting sequences of linear systems. The Poisson problem leads to a symmetric, positive definite system which we solve iteratively using conjugate gradient. The transport equations lead to nonsymmetric, indefinite systems, thereby complicating the selection of an appropriate iterative method. Moreover, their solutions exhibit steep layers and are subject to numerical oscillations and instabilities if standard Galerkin-type discretization strategies are used. In the present study, we use an upwind finite element technique for the transport equations. We also evaluate the performance of different iterative methods for the transport equations and investigate various preconditioners for a few generalized gradient methods. Numerical examples are given for a representative two-dimensional depletion MOSFET.

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

    NASA Astrophysics Data System (ADS)

    Schuch, Dieter

    2014-10-01

    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.

  15. Group Invariance Properties of the Inviscid Compressible Flow Equations for a Modified Tait Equation of State

    NASA Astrophysics Data System (ADS)

    Ramsey, Scott; Baty, Roy

    2015-11-01

    This work considers the group invariance properties of the inviscid compressible flow equations (Euler equations) under the assumptions of one-dimensional symmetry and a modified Tait equation of state (EOS) closure model. When written in terms of an adiabatic bulk modulus, a transformed version of these equations is found to be identical to that for an ideal gas EOS. As a result, the Lie group invariance structure of these equations - and their subsequent reduction to a lower-order system - is identical to the published results for the ideal gas case. Following the reduction of the Euler equations to a system of ordinary differential equations, a variety of elementary closed-form solutions are derived. These solutions are then used in conjunction with the Rankine-Hugoniot conditions to construct discontinuous shock wave and free surface solutions that are analogous to the classical Noh, Sedov, Guderley, and Hunter similarity solutions of the Euler equations for an ideal gas EOS. The versions of these problems for the modified Tait EOS are found to be semi-analytic in that a transcendental root extraction (and in some cases numerical integration of ordinary differential equations) enables solution of the relevant equations.

  16. Dark soliton solutions of (N+1)-dimensional nonlinear evolution equations

    NASA Astrophysics Data System (ADS)

    Demiray, Seyma Tuluce; Bulut, Hasan

    2016-06-01

    In this study, we investigate exact solutions of (N+1)-dimensional double sinh-Gordon equation and (N+1)-dimensional generalized Boussinesq equation by using generalized Kudryashov method. (N+1)-dimensional double sinh-Gordon equation and (N+1)-dimensional generalized Boussinesq equation can be returned to nonlinear ordinary differential equation by suitable transformation. Then, generalized Kudryashov method has been used to seek exact solutions of the (N+1)-dimensional double sinh-Gordon equation and (N+1)-dimensional generalized Boussinesq equation. Also, we obtain dark soliton solutions for these (N+1)-dimensional nonlinear evolution equations. Finally, we denote that this method can be applied to solve other nonlinear evolution equations.

  17. Asymptotic-preserving Boltzmann model equations for binary gas mixture

    NASA Astrophysics Data System (ADS)

    Liu, Sha; Liang, Yihua

    2016-02-01

    An improved system of Boltzmann model equations is developed for binary gas mixture. This system of model equations has a complete asymptotic preserving property that can strictly recover the Navier-Stokes equations in the continuum limit with the correct constitutive relations and the correct viscosity, thermal conduction, diffusion, and thermal diffusion coefficients. In this equation system, the self- and cross-collision terms in Boltzmann equations are replaced by single relaxation terms. In monocomponent case, this system of equations can be reduced to the commonly used Shakhov equation. The conservation property and the H theorem which are important for model equations are also satisfied by this system of model equations.

  18. Asymptotic-preserving Boltzmann model equations for binary gas mixture.

    PubMed

    Liu, Sha; Liang, Yihua

    2016-02-01

    An improved system of Boltzmann model equations is developed for binary gas mixture. This system of model equations has a complete asymptotic preserving property that can strictly recover the Navier-Stokes equations in the continuum limit with the correct constitutive relations and the correct viscosity, thermal conduction, diffusion, and thermal diffusion coefficients. In this equation system, the self- and cross-collision terms in Boltzmann equations are replaced by single relaxation terms. In monocomponent case, this system of equations can be reduced to the commonly used Shakhov equation. The conservation property and the H theorem which are important for model equations are also satisfied by this system of model equations. PMID:26986408

  19. A Regression Equation for Determining the Dimensionality of Data.

    ERIC Educational Resources Information Center

    Keeling, Kellie B.

    2000-01-01

    Developed a new regression equation to estimate the mean value of eigenvalues in parallel analysis and studied the performance of the equation in comparison with previously published regression equations through simulation. Performance of the new equation was comparable to that of the LCHF equation of G. Lautenschlager and others (1989). (SLD)

  20. A Graphical Approach to Evaluating Equating Using Test Characteristic Curves

    ERIC Educational Resources Information Center

    Wyse, Adam E.; Reckase, Mark D.

    2011-01-01

    An essential concern in the application of any equating procedure is determining whether tests can be considered equated after the tests have been placed onto a common scale. This article clarifies one equating criterion, the first-order equity property of equating, and develops a new method for evaluating equating that is linked to this…

  1. Regularized 13 moment equations for hard sphere molecules: Linear bulk equations

    NASA Astrophysics Data System (ADS)

    Struchtrup, Henning; Torrilhon, Manuel

    2013-05-01

    The regularized 13 moment equations of rarefied gas dynamics are derived for a monatomic hard sphere gas in the linear regime. The equations are based on an extended Grad-type moment system, which is systematically reduced by means of the Order of Magnitude Method [H. Struchtrup, "Stable transport equations for rarefied gases at high orders in the Knudsen number," Phys. Fluids 16(11), 3921-3934 (2004)], 10.1063/1.1782751. Chapman-Enskog expansion of the final equations yields the linear Burnett and super-Burnett equations. While the Burnett coefficients agree with literature values, this seems to be the first time that super-Burnett coefficients are computed for a hard sphere gas. As a first test of the equations the dispersion and damping of sound waves is considered.

  2. Bäcklund transformation of matrix equations and a discrete matrix first Painlevé equation

    NASA Astrophysics Data System (ADS)

    Gordoa, P. R.; Pickering, A.; Zhu, Z. N.

    2013-08-01

    We show that the known auto-Bäcklund transformation for the matrix second Painlevé equation can be generalized to a much wider class of equations. This auto-Bäcklund transformation is an involution and so cannot be used on its own to generate an infinite sequence of different solutions, although for particular equations a second auto-Bäcklund transformation allows this to be done. We also give a Bäcklund transformation for this general class of matrix equations. For the matrix second Painlevé equation we also give a coalescence limit, and a construction of special integrals and of a discrete matrix first Painlevé equation.

  3. Symbolic computation of recurrence equations for the Chebyshev series solution of linear ODE's. [ordinary differential equations

    NASA Technical Reports Server (NTRS)

    Geddes, K. O.

    1977-01-01

    If a linear ordinary differential equation with polynomial coefficients is converted into integrated form then the formal substitution of a Chebyshev series leads to recurrence equations defining the Chebyshev coefficients of the solution function. An explicit formula is presented for the polynomial coefficients of the integrated form in terms of the polynomial coefficients of the differential form. The symmetries arising from multiplication and integration of Chebyshev polynomials are exploited in deriving a general recurrence equation from which can be derived all of the linear equations defining the Chebyshev coefficients. Procedures for deriving the general recurrence equation are specified in a precise algorithmic notation suitable for translation into any of the languages for symbolic computation. The method is algebraic and it can therefore be applied to differential equations containing indeterminates.

  4. Transition between free-space Helmholtz equation solutions with plane sources and parabolic wave equation solutions.

    PubMed

    Mahillo-Isla, R; Gonźalez-Morales, M J; Dehesa-Martínez, C

    2011-06-01

    The slowly varying envelope approximation is applied to the radiation problems of the Helmholtz equation with a planar single-layer and dipolar sources. The analyses of such problems provide procedures to recover solutions of the Helmholtz equation based on the evaluation of solutions of the parabolic wave equation at a given plane. Furthermore, the conditions that must be fulfilled to apply each procedure are also discussed. The relations to previous work are given as well. PMID:21643384

  5. Global well-posedness for the 2D dispersive SQG equation and inviscid Boussinesq equations

    NASA Astrophysics Data System (ADS)

    Wan, Renhui; Chen, Jiecheng

    2016-08-01

    In this paper, we obtain global well-posedness for the 2D dispersive SQG equation and inviscid Boussinesq equations. Our works are consistent with the corresponding works by Elgindi-Widmayer (SIAM J Math Anal 47:4672-4684, 2015) in the special case {A=κ=1}. In addition, our result concerning the SQG equation can be regarded as the borderline case of the work by Cannone et al. (Proc Lond Math Soc 106:650-674, 2013).

  6. Alternative to the Kohn-Sham equations: The Pauli potential differential equation

    NASA Astrophysics Data System (ADS)

    Levämäki, H.; Nagy, Á.; Kokko, K.; Vitos, L.

    2015-12-01

    A recently developed theoretical framework of performing self-consistent orbital-free (OF) density functional theory (DFT) calculations at Kohn-Sham DFT level accuracy is tested in practice. The framework is valid for spherically symmetric systems. Numerical results for the Beryllium atom are presented and compared to accurate Kohn-Sham data. These calculations make use of a differential equation that we have developed for the so called Pauli potential, a key quantity in OF-DFT. The Pauli potential differential equation and the OF Euler equation form a system of two coupled differential equations, which have to be solved simultaneously within the DFT self-consistent loop.

  7. Solving fuzzy polynomial equation and the dual fuzzy polynomial equation using the ranking method

    NASA Astrophysics Data System (ADS)

    Rahman, Nurhakimah Ab.; Abdullah, Lazim

    2014-06-01

    Fuzzy polynomials with trapezoidal and triangular fuzzy numbers have attracted interest among some researchers. Many studies have been done by researchers to obtain real roots of fuzzy polynomials. As a result, there are many numerical methods involved in obtaining the real roots of fuzzy polynomials. In this study, we will present the solution to the fuzzy polynomial equation and dual fuzzy polynomial equation using the ranking method of fuzzy numbers and subsequently transforming fuzzy polynomials to crisp polynomials. This transformation is performed using the ranking method based on three parameters, namely Value, Ambiguity and Fuzziness. Finally, we illustrate our approach with two numerical examples for fuzzy polynomial equation and dual fuzzy polynomial equation.

  8. Surfaces specified by integrable systems of partial differential equations determined by structure equations and Lax pair

    NASA Astrophysics Data System (ADS)

    Bracken, Paul

    2010-04-01

    A system of evolution equations can be developed from the structure equations for a submanifold embedded in a three-dimensional space. It is seen how these same equations can be obtained from a generalized matrix Lax pair provided a single constraint equation is imposed. This can be done in Euclidean space as well as in Minkowski space. The integrable systems which result from this process can be thought of as generalizing the SO(3) and SO(2,1) Lax pairs which have been studied previously.

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

    SciTech Connect

    Boyd, Zachary M.; Ramsey, Scott D.; Baty, Roy S.

    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.

  10. Gravitationally coupled Dirac equation for antimatter

    NASA Astrophysics Data System (ADS)

    Jentschura, U. D.

    2013-03-01

    The coupling of antimatter to gravity is of general interest because of conceivable cosmological consequences (“surprises”) related to dark energy and the cosmological constant. Here, we revisit the derivation of the gravitationally coupled Dirac equation and find that the prefactor of a result given previously by Brill and Wheeler [Rev. Mod. Phys.RMPHAT0034-686110.1103/RevModPhys.29.465 29, 465 (1957)] for the affine connection matrix is in need of a correction. We also discuss the conversion of the curved-space Dirac equation from the so-called “East-Coast” to the “West-Coast” convention, in order to bring the gravitationally coupled Dirac equation to a form where it can easily be unified with the electromagnetic coupling as it is commonly used in modern particle physics calculations. The Dirac equation describes antiparticles as negative-energy states. We find a symmetry of the gravitationally coupled Dirac equation, which connects particle and antiparticle solutions for a general space-time metric of the Schwarzschild type and implies that particles and antiparticles experience the same coupling to the gravitational field, including all relativistic quantum corrections of motion. Our results demonstrate the consistency of quantum mechanics with general relativity and imply that a conceivable difference of gravitational interaction of hydrogen and antihydrogen should directly be attributed to a a “fifth force” (“quintessence”).

  11. Reanalysis of the equation for simple action

    PubMed Central

    Warren-Boulton, Frederick R.; Silberberg, Alan; Gray, Michael; Ollom, Randolph

    1985-01-01

    De Villiers and Herrnstein (1976) have shown that the equation for simple action, derived from the matching law, predicts change in behavioral output for some 40 experiments in which the value of a single source of reinforcement has been varied. Using only the positive-reinforcement studies they cite that used five or more different reinforcement values, we found the high percentage of variance they report accommodated by this equation (94%) is predicated on instances of averaging rates of behavioral output before making a least-squares fit of the equation. In our reanalysis, which minimizes rate averaging, only 78% of the data variance is accommodated. This diminished data-variance accommodation can be improved by adding parameters that permit the equation's scaling constant to change as a function of reinforcement. Although these parameters permit acceptable levels of accommodation of data variance, they correspond to no obvious psychological processes. These findings support the view that the equation for simple action is an inadequate model for behavioral output. PMID:16812416

  12. Riemann equation for prime number diffusion.

    PubMed

    Chen, Wen; Liang, Yingjie

    2015-05-01

    This study makes the first attempt to propose the Riemann diffusion equation to describe in a manner of partial differential equation and interpret in physics of diffusion the classical Riemann method for prime number distribution. The analytical solution of this equation is the well-known Riemann representation. The diffusion coefficient is dependent on natural number, a kind of position-dependent diffusivity diffusion. We find that the diffusion coefficient of the Riemann diffusion equation is nearly a straight line having a slope 0.99734 in the double-logarithmic axis. Consequently, an approximate solution of the Riemann diffusion equation is obtained, which agrees well with the Riemann representation in predicting the prime number distribution. Moreover, we interpret the scale-free property of prime number distribution via a power law function with 1.0169 the scale-free exponent in respect to logarithmic transform of the natural number, and then the fractal characteristic of prime number distribution is disclosed. PMID:26026319

  13. The Pseudo-Maxwell Equations Revisited

    NASA Astrophysics Data System (ADS)

    Stavroudis, Orestes N.

    1982-02-01

    The so-called pseudo-Maxwell are a set of partial differential eauations that strongly resemble the Maxwell equations, yet are based only on Fermat's principle, the idea of an orthotomic system of rays, and certain theorems from differential gecmetry. From Fermat's principle, applying the Euler equation from the variational calculus, one obtains the ray equation whose solutions describe ray paths in an inhomogeneous medium. We define an aggregate of such rays as an orthotomic system if it is possible to find a sur-face orthogonal to all rays in the aggregate. Making use of the Frenet equations from differential geometry, one may derive relationships between certain geometrical vectors and their derivatives. These are the pseudo-Maxwell equations. Their existence is' paradoxical. Are they merely a mathematical artifact, an accidental quirk of the notation we are accustomed to use? Or do they indicate that there is more geometry lurking in the physics of electricity and magnetism than we ever dreamed of in our philosophies?

  14. FAST TRACK COMMUNICATION Quasi self-adjoint nonlinear wave equations

    NASA Astrophysics Data System (ADS)

    Ibragimov, N. H.; Torrisi, M.; Tracinà, R.

    2010-11-01

    In this paper we generalize the classification of self-adjoint second-order linear partial differential equation to a family of nonlinear wave equations with two independent variables. We find a class of quasi self-adjoint nonlinear equations which includes the self-adjoint linear equations as a particular case. The property of a differential equation to be quasi self-adjoint is important, e.g. for constructing conservation laws associated with symmetries of the differential equation.

  15. Evolution equations for multi-time wavefunctions

    NASA Astrophysics Data System (ADS)

    Petrat, Soren Philipp

    Multi-time wavefunctions are of particular interest in relativistic quantum mechanics. A multi-time wavefunction has separate time-variables for each particle; this makes it a manifestly Lorentz-invariant object. The time-evolution equations are systems of Schrodinger equations; one for each particle's time variable and each with a certain Hamiltonian. We derive conditions under which these systems of equations have a common solution. Also, we derive three main results about concrete multi-time models. First we show that a model proposed by Durr and Tumulka in 2001 is inconsistent. The second result is a consistent model for a constant number of particles with a cutoff pair potential. The third result is a consistent theory for a simple quantum field theoretic model with creation and annihilation of particles. Existence and uniqueness of solutions is proven for both models.

  16. Absorbing layers for the Dirac equation

    SciTech Connect

    Pinaud, Olivier

    2015-05-15

    This work is devoted to the construction of perfectly matched layers (PML) for the Dirac equation, that not only arises in relativistic quantum mechanics but also in the dynamics of electrons in graphene or in topological insulators. While the resulting equations are stable at the continuous level, some care is necessary in order to obtain a stable scheme at the discrete level. This is related to the so-called fermion doubling problem. For this matter, we consider the numerical scheme introduced by Hammer et al. [19], and combine it with the discretized PML equations. We state some arguments for the stability of the resulting scheme, and perform simulations in two dimensions. The perfectly matched layers are shown to exhibit, in various configurations, superior absorption than the absorbing potential method and the so-called transport-like boundary conditions.

  17. Lorentz Abraham Force and Power Equations

    NASA Astrophysics Data System (ADS)

    Yaghjian, Arthur D.

    Toward the end of the nineteenth century Lorentz modeled the electron (“vibrating charged particle,” as he called it) by a spherical shell of uniform surface charge density and set about the difficult task of deriving the equation of motion of this electron model by determining, from Maxwell's equations and the Lorentz force law, the retarded self electromagnetic force that the fields of the accelerating charge distribution exert upon the charge itself [1]. (This initial work of Lorentz in 1892 on a moving charged sphere appeared five years before J.J. Thomson's “discovery” of the electron. It is summarized in English by J.Z. Buchwald [2, app. 7].) With the help of Abraham,1 a highly successful theory of the moving electron model was completed by the early 1900's [3, 4]. Before Einstein's papers [5, 6] on special relativity appeared in 1905, they had derived the following force equation of motion

  18. Equation of Motion of a Quantum Vortex

    NASA Astrophysics Data System (ADS)

    Cox, Timothy; Stamp, Philip

    Understanding the motion of vortices in quantum fluids is key to understanding the dynamics of such fluids. The motion of quantum vortices has long been understood in terms of the Hall-Vinen-Iordanski (HVI) equations. A fully quantum mechanical treatment of vortex motion in a two-dimensional Bose superfluid leads to a modified version of the HVI equations which include significant history dependent forces and a fluctuating noise force. The dynamics deviates from that described by the HVI equations when the frequency of motion is higher than the temperature. We describe the consequences of the memory and noise for the motion of a single superfluid vortex as well as the circumstances under which their effects should be experimentally observable.

  19. A thermal equation for flame quenching

    NASA Technical Reports Server (NTRS)

    Potter, A E , Jr; Berlad, A I

    1956-01-01

    An approximate thermal equation was derived for quenching distance based on a previously proposed diffusional treatment. The quenching distance was expressed in terms of the thermal conductivity, the fuel mole fraction, the heat capacity, the rate of the rate-controlling chemical reaction, a constant that depends on the geometry of the quenching surface, and one empirical constant. The effect of pressure on quenching distance was shown to be inversely proportional to the pressure dependence of the flame reaction, with small correction necessitated by the effect of pressure on flame temperature. The equation was used with the Semenov equation for burning velocity to show that the quenching distance was inversely proportional to burning velocity and pressure at any given initial temperature and equivalence ratio.

  20. PREFACE: Symmetries and Integrability of Difference Equations

    NASA Astrophysics Data System (ADS)

    Doliwa, Adam; Korhonen, Risto; Lafortune, Stéphane

    2007-10-01

    The notion of integrability was first introduced in the 19th century in the context of classical mechanics with the definition of Liouville integrability for Hamiltonian flows. Since then, several notions of integrability have been introduced for partial and ordinary differential equations. Closely related to integrability theory is the symmetry analysis of nonlinear evolution equations. Symmetry analysis takes advantage of the Lie group structure of a given equation to study its properties. Together, integrability theory and symmetry analysis provide the main method by which nonlinear evolution equations can be solved explicitly. Difference equations (DE), like differential equations, are important in numerous fields of science and have a wide variety of applications in such areas as mathematical physics, computer visualization, numerical analysis, mathematical biology, economics, combinatorics, and quantum field theory. It is thus crucial to develop tools to study and solve DEs. While the theory of symmetry and integrability for differential equations is now largely well-established, this is not yet the case for discrete equations. Although over recent years there has been significant progress in the development of a complete analytic theory of difference equations, further tools are still needed to fully understand, for instance, the symmetries, asymptotics and the singularity structure of difference equations. The series of SIDE meetings on Symmetries and Integrability of Difference Equations started in 1994. Its goal is to provide a platform for an international and interdisciplinary communication for researchers working in areas associated with integrable discrete systems, such as classical and quantum physics, computer science and numerical analysis, mathematical biology and economics, discrete geometry and combinatorics, theory of special functions, etc. The previous SIDE meetings took place in Estérel near Montréal, Canada (1994), at the University of

  1. Embedding methods for the steady Euler equations

    NASA Technical Reports Server (NTRS)

    Chang, S. H.; Johnson, G. M.

    1983-01-01

    An approach to the numerical solution of the steady Euler equations is to embed the first-order Euler system in a second-order system and then to recapture the original solution by imposing additional boundary conditions. Initial development of this approach and computational experimentation with it were previously based on heuristic physical reasoning. This has led to the construction of a relaxation procedure for the solution of two-dimensional steady flow problems. The theoretical justification for the embedding approach is addressed. It is proven that, with the appropriate choice of embedding operator and additional boundary conditions, the solution to the embedded system is exactly the one to the original Euler equations. Hence, solving the embedded version of the Euler equations will not produce extraneous solutions.

  2. Efficient inverse solution of Kepler's equation

    NASA Technical Reports Server (NTRS)

    Boltz, Frederick W.

    1986-01-01

    A bicubic polynomial approximation to Kepler's equation for elliptic orbits is shown to provide accurate starting values for efficient numerical solution of this equation for eccentric anomaly. In the approximate equation, a cubic in mean anomaly is set equal to a cubic in eccentric anomaly. The coefficients in the two cubics are obtained as functions of eccentricity by specifying values of function and slope at the midpoint and the endpoint of the complete interval (0 to pi). The initial estimate of eccentric anomaly to use in an iteration formula is obtained by evaluating the cubic in mean anomaly and finding the single real root of the cubic in eccentric anomaly. Numerical results are presented which indicate that the estimate accuracy of this method is roughly an order of magnitude better than that of other recently-reported formulas.

  3. Differential equation models for sharp threshold dynamics.

    PubMed

    Schramm, Harrison C; Dimitrov, Nedialko B

    2014-01-01

    We develop an extension to differential equation models of dynamical systems to allow us to analyze probabilistic threshold dynamics that fundamentally and globally change system behavior. We apply our novel modeling approach to two cases of interest: a model of infectious disease modified for malware where a detection event drastically changes dynamics by introducing a new class in competition with the original infection; and the Lanchester model of armed conflict, where the loss of a key capability drastically changes the effectiveness of one of the sides. We derive and demonstrate a step-by-step, repeatable method for applying our novel modeling approach to an arbitrary system, and we compare the resulting differential equations to simulations of the system's random progression. Our work leads to a simple and easily implemented method for analyzing probabilistic threshold dynamics using differential equations. PMID:24184349

  4. Stochastic Differential Equation of Earthquakes Series

    NASA Astrophysics Data System (ADS)

    Mariani, Maria C.; Tweneboah, Osei K.; Gonzalez-Huizar, Hector; Serpa, Laura

    2016-07-01

    This work is devoted to modeling earthquake time series. We propose a stochastic differential equation based on the superposition of independent Ornstein-Uhlenbeck processes driven by a Γ (α, β ) process. Superposition of independent Γ (α, β ) Ornstein-Uhlenbeck processes offer analytic flexibility and provides a class of continuous time processes capable of exhibiting long memory behavior. The stochastic differential equation is applied to the study of earthquakes by fitting the superposed Γ (α, β ) Ornstein-Uhlenbeck model to earthquake sequences in South America containing very large events (Mw ≥ 8). We obtained very good fit of the observed magnitudes of the earthquakes with the stochastic differential equations, which supports the use of this methodology for the study of earthquakes sequence.

  5. Stochastic Differential Equation of Earthquakes Series

    NASA Astrophysics Data System (ADS)

    Mariani, Maria C.; Tweneboah, Osei K.; Gonzalez-Huizar, Hector; Serpa, Laura

    2016-05-01

    This work is devoted to modeling earthquake time series. We propose a stochastic differential equation based on the superposition of independent Ornstein-Uhlenbeck processes driven by a Γ (α, β ) process. Superposition of independent Γ (α, β ) Ornstein-Uhlenbeck processes offer analytic flexibility and provides a class of continuous time processes capable of exhibiting long memory behavior. The stochastic differential equation is applied to the study of earthquakes by fitting the superposed Γ (α, β ) Ornstein-Uhlenbeck model to earthquake sequences in South America containing very large events (Mw ≥ 8). We obtained very good fit of the observed magnitudes of the earthquakes with the stochastic differential equations, which supports the use of this methodology for the study of earthquakes sequence.

  6. Stokes equation in a toy CD hovercraft

    NASA Astrophysics Data System (ADS)

    de Izarra, Charles; de Izarra, Grégoire

    2011-01-01

    This paper deals with the study of a toy CD hovercraft used in the fluid mechanics course for undergraduate students to illustrate the lubrication theory described by the Stokes equation. An experimental characterization of the toy hovercraft (measurements of the air flow value, of the pressure in the balloon and of the thickness of the air film under the hovercraft) allows us to evaluate a reduced Reynolds number R*. Since R* < 1, it is possible to simplify the Navier-Stokes equation that is reduced to the Stokes equation, on the basis of the lubrication theory. The pressure gradient in the air flow is calculated, allowing us to establish the lifting force applied on the toy hovercraft. In addition, these results are applied to a larger scale hovercraft.

  7. Nondiffracting accelerating wave packets of Maxwell's equations.

    PubMed

    Kaminer, Ido; Bekenstein, Rivka; Nemirovsky, Jonathan; Segev, Mordechai

    2012-04-20

    We present the nondiffracting spatially accelerating solutions of the Maxwell equations. Such beams accelerate in a circular trajectory, thus generalizing the concept of Airy beams to the full domain of the wave equation. For both TE and TM polarizations, the beams exhibit shape-preserving bending which can have subwavelength features, and the Poynting vector of the main lobe displays a turn of more than 90°. We show that these accelerating beams are self-healing, analyze their properties, and find the new class of accelerating breathers: self-bending beams of periodically oscillating shapes. Finally, we emphasize that in their scalar form, these beams are the exact solutions for nondispersive accelerating wave packets of the most common wave equation describing time-harmonic waves. As such, this work has profound implications to many linear wave systems in nature, ranging from acoustic and elastic waves to surface waves in fluids and membranes. PMID:22680719

  8. Stability of a Quartic Functional Equation

    PubMed Central

    2014-01-01

    We obtain the general solution of the generalized quartic functional equation f(x + my) + f(x − my) = 2(7m − 9)(m − 1)f(x) + 2m2(m2 − 1)f(y)−(m − 1)2f(2x) + m2{f(x + y) + f(x − y)} for a fixed positive integer m. We prove the Hyers-Ulam stability for this quartic functional equation by the directed method and the fixed point method on real Banach spaces. We also investigate the Hyers-Ulam stability for the mentioned quartic functional equation in non-Archimedean spaces. PMID:24587750

  9. Braces and the Yang-Baxter Equation

    NASA Astrophysics Data System (ADS)

    Cedó, Ferran; Jespers, Eric; Okniński, Jan

    2014-04-01

    Several aspects of relations between braces and non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation are discussed and many consequences are derived. In particular, for each positive integer n a finite square-free multipermutation solution of the Yang-Baxter equation with multipermutation level n and an abelian involutive Yang-Baxter group is constructed. This answers a problem of Gateva-Ivanova and Cameron. It is proved that finite non-degenerate involutive set-theoretic solutions of the Yang-Baxter equation whose associated involutive Yang-Baxter group is abelian are multipermutation solutions. Earlier the authors proved this with the additional square-free hypothesis on the solutions. It is also proved that finite square-free non-degenerate involutive set-theoretic solutions associated to a left brace are multipermutation solutions.

  10. On the Position Measurement Equation of XNAV

    NASA Astrophysics Data System (ADS)

    Yao, G. Z.; Fei, B. J.; Xiao, Y.

    2012-03-01

    The position measurement equation of XNAV (X-ray pulsar-based autonomous navigation) reveals the relation between the TOA and receiving position of X-ray signal . For navigation , TOA is often rewritten in the form of difference between TOA and some preset ``time reference''. The ``time reference'' may be the true TOA at SSB, or some ``equivalent TOA'' at SSB. Because the true TOA at SSB is difficult to obtain, the ``equivalent TOA'' is more convenient for navigation. From the expression of ``true TOA'', the expression of the ``equivalent TOA'' is derived, and the physical origin of each item is analyzed. The ``equivalent TOA'' consists of those items irrelevant to the craft, but relevant to the background. Then in the new measurement equation, the time difference concentrates on the items directly relevant to the position of the craft. The new equations has the time accuracy of 0.1 ns.

  11. Symmetry Breaking And The Nilpotent Dirac Equation

    SciTech Connect

    Rowlands, Peter

    2004-08-19

    A multivariate 4-vector representation for space-time and a quaternion representation for mass and the electric, strong and weak charges leads to a nilpotent form of the Dirac equation, which packages the entire physical information available about a fermion state. The nilpotent state vector breaks the symmetry between the strong, electric and weak interactions, by associating their respective charges with vector, scalar and pseudoscalar operators, leading directly to the SU(3) x SU(2)L x U(1) symmetry, and to particle structures and mass-generating states. In addition, the nilpotent Dirac equation has just three solutions for spherically-symmetric distance-dependent potentials, and these correspond once again to those that would be expected for the three interactions: linear for the strong interaction; inverse linear for the electromagnetic; and a harmonic oscillator-type solution, which can be equated with the dipolar annihilation and creation mechanisms of the weak interaction.

  12. Pdf - Transport equations for chemically reacting flows

    NASA Technical Reports Server (NTRS)

    Kollmann, W.

    1989-01-01

    The closure problem for the transport equations for pdf and the characteristic functions of turbulent, chemically reacting flows is addressed. The properties of the linear and closed equations for the characteristic functional for Eulerian and Lagrangian variables are established, and the closure problem for the finite-dimensional case is discussed for pdf and characteristic functions. It is shown that the closure for the scalar dissipation term in the pdf equation developed by Dopazo (1979) and Kollmann et al. (1982) results in a single integral, in contrast to the pdf, where double integration is required. Some recent results using pdf methods obtained for turbulent flows with combustion, including effects of chemical nonequilibrium, are discussed.

  13. Full-deautonomisation of a lattice equation

    NASA Astrophysics Data System (ADS)

    Willox, R.; Mase, T.; Ramani, A.; Grammaticos, B.

    2016-07-01

    In this letter we report on the unexpected possibility of applying the full-deautonomisation approach we recently proposed for predicting the algebraic entropy of second-order birational mappings, to discrete lattice equations. Moreover, we show, on two examples, that the full-deautonomisation technique can in fact also be successfully applied to reductions of these lattice equations to mappings with orders higher than 2. In particular, we apply this technique to a recently discovered lattice equation that has confined singularities while being nonintegrable, and we show that our approach accurately predicts this nonintegrable character. Finally, we demonstrate how our method can even be used to predict the algebraic entropy for some nonconfining higher order mappings.

  14. Compact stars with quadratic equation of state

    NASA Astrophysics Data System (ADS)

    Ngubelanga, Sifiso A.; Maharaj, Sunil D.; Ray, Subharthi

    2015-05-01

    We provide new exact solutions to the Einstein-Maxwell system of equations for matter configurations with anisotropy and charge. The spacetime is static and spherically symmetric. A quadratic equation of state is utilised for the matter distribution. By specifying a particular form for one of the gravitational potentials and the electric field intensity we obtain new exact solutions in isotropic coordinates. In our general class of models, an earlier model with a linear equation of state is regained. For particular choices of parameters we regain the masses of the stars PSR J1614-2230, 4U 1608-52, PSR J1903+0327, EXO 1745-248 and SAX J1808.4-3658. A comprehensive physical analysis for the star PSR J1903+0327 reveals that our model is reasonable.

  15. Absorbing layers for the Dirac equation

    NASA Astrophysics Data System (ADS)

    Pinaud, Olivier

    2015-05-01

    This work is devoted to the construction of perfectly matched layers (PML) for the Dirac equation, that not only arises in relativistic quantum mechanics but also in the dynamics of electrons in graphene or in topological insulators. While the resulting equations are stable at the continuous level, some care is necessary in order to obtain a stable scheme at the discrete level. This is related to the so-called fermion doubling problem. For this matter, we consider the numerical scheme introduced by Hammer et al. [19], and combine it with the discretized PML equations. We state some arguments for the stability of the resulting scheme, and perform simulations in two dimensions. The perfectly matched layers are shown to exhibit, in various configurations, superior absorption than the absorbing potential method and the so-called transport-like boundary conditions.

  16. The generalized diffusion-convection equation

    NASA Technical Reports Server (NTRS)

    Jones, Frank C.

    1990-01-01

    Starting from the Boltzmann equation, a transport equation is derived for energetic particles in a moving magnetized plasma in which the scattering centers that keep the particles quasi-isotropic are moving with a velocity that is not necessarily the same as that of the plasma. The scattering is characterized by three very loose constraints: (1) there is a rest frame for each scatterer in which the particles scatter elastically; (2) in this frame the scattering will not disturb an isotropic distribution; and (3) the momentum transfer in an average collision may be described by a tensor operating on the particles original momentum. Since the strength of the scattering is not specified, the derivation should be as valid for plasma microturbulence as for hard-sphere scattering. The results show clearly which phenomena are responsible for tying the particles to the plasma in the transport equation.

  17. Dynamic discretization method for solving Kepler's equation

    NASA Astrophysics Data System (ADS)

    Feinstein, Scott A.; McLaughlin, Craig A.

    2006-09-01

    Kepler’s equation needs to be solved many times for a variety of problems in Celestial Mechanics. Therefore, computing the solution to Kepler’s equation in an efficient manner is of great importance to that community. There are some historical and many modern methods that address this problem. Of the methods known to the authors, Fukushima’s discretization technique performs the best. By taking more of a system approach and combining the use of discretization with the standard computer science technique known as dynamic programming, we were able to achieve even better performance than Fukushima. We begin by defining Kepler’s equation for the elliptical case and describe existing solution methods. We then present our dynamic discretization method and show the results of a comparative analysis. This analysis will demonstrate that, for the conditions of our tests, dynamic discretization performs the best.

  18. A derivation of the beam equation

    NASA Astrophysics Data System (ADS)

    Duque, Daniel

    2016-01-01

    The Euler-Bernoulli equation describing the deflection of a beam is a vital tool in structural and mechanical engineering. However, its derivation usually entails a number of intermediate steps that may confuse engineering or science students at the beginnig of their undergraduate studies. We explain how this equation may be deduced, beginning with an approximate expression for the energy, from which the forces and finally the equation itself may be obtained. The description is begun at the level of small ‘particles’, and the continuum level is taken later on. However, when a computational solution is sought, the description turns back to the discrete level again. We first consider the easier case of a string under tension, and then focus on the beam. Numerical solutions for several loads are obtained.

  19. Turbulent solutions of equations of fluid motion

    NASA Technical Reports Server (NTRS)

    Deissler, R. G.

    1985-01-01

    Some turbulent solutions of the unaveraged Navier-Stokes equations (equations of fluid motion) are reviewed. Those equations are solved numerically in order to study the nonlinear physics of incompressible turbulent flow. The three components of the mean-square velocity fluctuations are initially equal for the conditions chosen. The resulting solutions show characteristics of turbulence, such as the linear and nonlinear excitation of small-scale fluctuations. For the stronger fluctuations the initially nonrandom flow develops into an apparently random turbulence. The cases considered include turbulence that is statistically homogeneous or inhomogeneous and isotropic or anisotropic. A statistically steady-state turbulence is obtained by using a spatially periodic body force. Various turbulence processes, including the transfer of energy between eddy sizes and between directional components and the production, dissipation, and spatial diffusion of turbulence, are considered. It is concluded that the physical processes occurring in turbulence can be profitably studied numerically.

  20. Propagating Qualitative Values Through Quantitative Equations

    NASA Technical Reports Server (NTRS)

    Kulkarni, Deepak

    1992-01-01

    In most practical problems where traditional numeric simulation is not adequate, one need to reason about a system with both qualitative and quantitative equations. In this paper, we address the problem of propagating qualitative values represented as interval values through quantitative equations. Previous research has produced exponential-time algorithms for approximate solution of the problem. These may not meet the stringent requirements of many real time applications. This paper advances the state of art by producing a linear-time algorithm that can propagate a qualitative value through a class of complex quantitative equations exactly and through arbitrary algebraic expressions approximately. The algorithm was found applicable to Space Shuttle Reaction Control System model.

  1. New scale-relativistic derivations of Pauli and Dirac equations

    NASA Astrophysics Data System (ADS)

    Hammad, F.

    2008-02-01

    In scale relativity, quantum mechanics is recovered by transcribing the classical equations of motion to fractal spaces and demanding, as dictated by the principle of scale relativity, that the form of these equations be preserved. In the framework of this theory, however, the form of the classical energy equations both in the relativistic and nonrelativistic cases are not preserved. Aiming to get full covariance, i.e., to restore to these equations their classical forms, we show that the scale-relativistic form of the Schrödinger equation yields the Pauli equation, whilst the Pissondes's scale-relativistic form of the Klein-Gordon equation gives the Dirac equation.

  2. Fractional Fokker-Planck equation for fractal media.

    PubMed

    Tarasov, Vasily E

    2005-06-01

    We consider the fractional generalizations of equation that defines the medium mass. We prove that the fractional integrals can be used to describe the media with noninteger mass dimensions. Using fractional integrals, we derive the fractional generalization of the Chapman-Kolmogorov equation (Smolukhovski equation). In this paper fractional Fokker-Planck equation for fractal media is derived from the fractional Chapman-Kolmogorov equation. Using the Fourier transform, we get the Fokker-Planck-Zaslavsky equations that have fractional coordinate derivatives. The Fokker-Planck equation for the fractal media is an equation with fractional derivatives in the dual space. PMID:16035878

  3. What physics is encoded in Maxwell's equations?

    NASA Astrophysics Data System (ADS)

    Kosyakov, B. P.

    2005-08-01

    We reconstruct Maxwell's equations showing that a major part of the information encoded in them is taken from topological properties of spacetime, and the residual information, divorced from geometry, which represents the physical contents of electrodynamics, %these equations, translates into four assumptions:(i) locality; (ii) linearity; %of the dynamical law; (iii) identity of the charge-source and the charge-coupling; and (iv) lack of magnetic monopoles. However, a closer inspection of symmetries peculiar to electrodynamics shows that these assumptions may have much to do with geometry. Maxwell's equations tell us that we live in a three-dimensional space with trivial (Euclidean) topology; time is a one-dimensional unidirectional and noncompact continuum; and spacetime is endowed with a light cone structure readable in the conformal invariance of electrodynamics. Our geometric feelings relate to the fact that Maxwell's equations are built in our brain, hence our space and time orientation, our visualization and imagination capabilities are ensured by perpetual instinctive processes of solving Maxwell's equations. People are usually agree in their observations of angle relations, for example, a right angle is never confused with an angle slightly different from right. By contrast, we may disagree in metric issues, say, a colour-blind person finds the light wave lengths quite different from those found by a man with normal vision. This lends support to the view that conformal invariance of Maxwell's equations is responsible for producing our notion of space. Assuming that our geometric intuition is guided by our innate realization of electrodynamical laws, some abnormal mental phenomena, such as clairvoyance, may have a rational explanation.

  4. Lagrangian aspects of the axisymmetric Euler equation

    NASA Astrophysics Data System (ADS)

    Preston, Stephen C.; Sarria, Alejandro

    2016-03-01

    In this paper we are interested in geometric aspects of blowup in the axisymmetric three-dimensional (3D) Euler equations with swirl on a cylinder. Writing the equations in Lagrangian form for the flow derivative along either the axis or the boundary and imposing oddness on the vertical component of the flow, we extend some blowup criteria due to Chae, Constantin and Wu related to assumptions on the sign of the pressure Hessian. In addition. we give a geometric interpretation of the results, both in terms of the local geometry along trajectories and in terms of the Riemannian geometry of the volume-preserving diffeomorphism group.

  5. Solving a specific Thue-Mahler equation

    NASA Astrophysics Data System (ADS)

    Tzanakis, N.; de Weger, B. M. M.

    1991-10-01

    The diophantine equation {x^3} - 3x{y^2} - {y^3} = ± {3^{{n_0}}}{17^{{n_1}}}{19^{{n_2}}} is completely solved as follows. First, a large upper bound for the variables is obtained from the theory of linear forms in p-adic and real logarithms of algebraic numbers. Then this bound is reduced to a manageable size by p-adic and real computational diophantine approximation, based on the {L^3} -algorithm. Finally the complete list of solutions is found in a sieving process. The method is in principle applicable to any Thue-Mahler equation, as the authors will show in a forthcoming paper.

  6. Thermoelastic constitutive equations for chemically hardening materials

    NASA Technical Reports Server (NTRS)

    Shaffer, B. W.; Levitsky, M.

    1974-01-01

    Thermoelastic constitutive equations are derived for a material undergoing solidification or hardening as the result of a chemical reaction. The derivation is based upon a two component model whose composition is determined by the degree of hardening, and makes use of strain-energy considerations. Constitutive equations take the form of stress rate-strain rate relations, in which the coefficients are time-dependent functions of the composition. Specific results are developed for the case of a material of constant bulk modulus which undergoes a transition from an initial liquidlike state into an isotropic elastic solid. Potential applications are discussed.

  7. Elimination and recursions in the scattering equations

    NASA Astrophysics Data System (ADS)

    Cardona, Carlos; Kalousios, Chrysostomos

    2016-05-01

    We use the elimination theory to explicitly construct the (n - 3) ! order polynomial in one of the variables of the scattering equations. The answer can be given either in terms of a determinant of Sylvester type of dimension (n - 3) ! or a determinant of Bézout type of dimension (n - 4) !. We present a recursive formula for the Sylvester determinant. Expansion of the determinants yields expressions in terms of Plücker coordinates. Elimination of the rest of the variables of the scattering equations is also presented.

  8. Constitutive equations of ageing polymeric materials

    NASA Technical Reports Server (NTRS)

    Peng, S. T. J.

    1985-01-01

    The constitutive equation for the relaxation behavior of time-dependent, chemically unstable materials developed by Valanis and Peng (1983), which used the irreversible thermodynamics of internal variables in Eyring's absolute reaction theory and yielded a theoretical expression for the effect of chemical crosslink density on the relaxation rate, is presently applied to the creep behavior of a network polymer which is undergoing a scission process. In particular, two equations are derived which may for the first time show the relations between mechanical models and internal variables in the creep expressions, using a three-element model with a Maxwell element.

  9. A multigrid method for the Euler equations

    NASA Technical Reports Server (NTRS)

    Jespersen, D. C.

    1983-01-01

    A multigrid algorithm has been developed for the numerical solution of the steady two-dimensional Euler equations. Flux vector splitting and one-sided differencing are employed to define the spatial discretization. Newton's method is used to solve the nonlinear equations, and a multigrid solver is used on each linear problem. The relaxation scheme for the linear problems is symmetric Gauss-Seidel. Standard restriction and interpolation operators are employed. Local mode analysis is used to predict the convergence rate of the multigrid process on the linear problems. Computed results for transonic flows over airfoils are presented.

  10. Space station rotational equations of motion

    NASA Technical Reports Server (NTRS)

    Rheinfurth, M. H.; Carroll, S. N.

    1985-01-01

    Dynamic equations of motion are developed which describe the rotational motion for a large space structure having rotating appendages. The presence of the appendages produce torque coupling terms which are dependent on the inertia properties of the appendages and the rotational rates for both the space structure and the appendages. These equations were formulated to incorporate into the Space Station Attitude Control and Stabilization Test Bed to accurately describe the influence rotating solar arrays and thermal radiators have on the dynamic behavior of the Space Station.

  11. Regularized Grad equations for multicomponent plasmas

    NASA Astrophysics Data System (ADS)

    Magin, Thierry E.; Martins, Gérald; Torrilhon, Manuel

    2011-05-01

    The moment method of Grad is used to derive macroscopic conservation equations for multicomponent plasmas for small and moderate Knudsen numbers, accounting for the electromagnetic field influence and thermal nonequilibrium. In the low Knudsen number limit, the equations derived are fully consistent with those obtained by means of the Chapman-Enskog method. In particular, we have retieved the Kolesnikov effect coupling electrons and heavy particles in the case of the Boltzmann moment systems. Finally, a regularization procedure is proposed to achieve continuous shock structures at all Mach numbers.

  12. Wigner-Lindblad Equations for Quantum Friction.

    PubMed

    Bondar, Denys I; Cabrera, Renan; Campos, Andre; Mukamel, Shaul; Rabitz, Herschel A

    2016-05-01

    Dissipative forces are ubiquitous and thus constitute an essential part of realistic physical theories. However, quantization of dissipation has remained an open challenge for nearly a century. We construct a quantum counterpart of classical friction, a velocity-dependent force acting against the direction of motion. In particular, a translationary invariant Lindblad equation is derived satisfying the appropriate dynamical relations for the coordinate and momentum (i.e., the Ehrenfest equations). Numerical simulations establish that the model approximately equilibrates. These findings significantly advance a long search for a universally valid Lindblad model of quantum friction and open opportunities for exploring novel dissipation phenomena. PMID:27078510

  13. Preconditioning the Helmholtz Equation for Rigid Ducts

    NASA Technical Reports Server (NTRS)

    Baumeister, Kenneth J.; Kreider, Kevin L.

    1998-01-01

    An innovative hyperbolic preconditioning technique is developed for the numerical solution of the Helmholtz equation which governs acoustic propagation in ducts. Two pseudo-time parameters are used to produce an explicit iterative finite difference scheme. This scheme eliminates the large matrix storage requirements normally associated with numerical solutions to the Helmholtz equation. The solution procedure is very fast when compared to other transient and steady methods. Optimization and an error analysis of the preconditioning factors are present. For validation, the method is applied to sound propagation in a 2D semi-infinite hard wall duct.

  14. Space Time Defined by Stress Equation

    NASA Astrophysics Data System (ADS)

    Yanagisawa, H.

    2004-07-01

    Time can never be measured directly. Time is calculated from changed lengths and angles by using all clocks. In addition, an atomic absolute clock and an atomic absolute telemeter have a contradictory relation to depend on each other. Of course, there is no absolute time. The time of all clocks are changed by energy states such as gravity or temperature. Here, I report an equation relating time to energy. It was deduced from my stress equation (dE/dt=kE). t=log E(t)/E(0)/k The relation of time to changed energy was shown.

  15. General surface equations for glancing incidence telescopes

    NASA Technical Reports Server (NTRS)

    Saha, Timo T.

    1987-01-01

    A generalized set of equations are derived for two mirror glancing incidence telescopes using Fermat's principle, a differential form of the law of reflection, the generalized sine condition, and a ray propagation equation described in vector form as a theoretical basis. The resulting formulation groups the possible telescope configurations into three distinct classes which are the Wolter, Wolter-Schwarzschild, and higher-order telescopes in which the Hettrick-Bowyer types are a subset. Eight configurations are possible within each class depending on the sign and magnitude of the parameters.

  16. Algorithms For Integrating Nonlinear Differential Equations

    NASA Technical Reports Server (NTRS)

    Freed, A. D.; Walker, K. P.

    1994-01-01

    Improved algorithms developed for use in numerical integration of systems of nonhomogenous, nonlinear, first-order, ordinary differential equations. In comparison with integration algorithms, these algorithms offer greater stability and accuracy. Several asymptotically correct, thereby enabling retention of stability and accuracy when large increments of independent variable used. Accuracies attainable demonstrated by applying them to systems of nonlinear, first-order, differential equations that arise in study of viscoplastic behavior, spread of acquired immune-deficiency syndrome (AIDS) virus and predator/prey populations.

  17. General surface equations for glancing incidence telescopes.

    PubMed

    Saha, T T

    1987-02-15

    A generalized set of equations are derived for two mirror glancing incidence telescopes using Fermat's principle, a differential form of the law of reflection, the generalized sine condition, and a ray propagation equation described in vector form as a theoretical basis. The resulting formulation groups the possible telescope configurations into three distinct classes which are the Wolter, Wolter-Schwarzschild, and higherorder telescopes in which the Hettrick-Bowyer types are a subset. Eight configurations are possible within each class depending on the sign and magnitude of the parameters. PMID:20454195

  18. Geometric superalgebra and the Dirac equation

    NASA Astrophysics Data System (ADS)

    Keller, Jaime; Rodríguez, Adán

    1992-01-01

    A unified mathematical approach to spinors and multivectors or superalgebra is constructed in a form useful to study the mathematical description of matter and its interaction fields. The formalism then encompasses both points of view: multivectors for the description of (space-time) geometry and the description of the integer spin, interaction fields, and spinor representations suitable for the description of half odd integer, matter fields. An application is made to study the change of the Dirac equation under the spinors to multivectors (to scalars) mapping. The physical and geometric content of the multivector solutions of the Dirac-Hestenes equation is clearly shown.

  19. Sensitivity Analysis of Differential-Algebraic Equations and Partial Differential Equations

    SciTech Connect

    Petzold, L; Cao, Y; Li, S; Serban, R

    2005-08-09

    Sensitivity analysis generates essential information for model development, design optimization, parameter estimation, optimal control, model reduction and experimental design. In this paper we describe the forward and adjoint methods for sensitivity analysis, and outline some of our recent work on theory, algorithms and software for sensitivity analysis of differential-algebraic equation (DAE) and time-dependent partial differential equation (PDE) systems.

  20. Localization of the eigenvalues of linear integral equations with applications to linear ordinary differential equations.

    NASA Technical Reports Server (NTRS)

    Sloss, J. M.; Kranzler, S. K.

    1972-01-01

    The equivalence of a considered integral equation form with an infinite system of linear equations is proved, and the localization of the eigenvalues of the infinite system is expressed. Error estimates are derived, and the problems of finding upper bounds and lower bounds for the eigenvalues are solved simultaneously.

  1. Convergence of Galerkin approximations for operator Riccati equations: A nonlinear evolution equation approach

    NASA Technical Reports Server (NTRS)

    Rosen, I. G.

    1988-01-01

    An approximation and convergence theory was developed for Galerkin approximations to infinite dimensional operator Riccati differential equations formulated in the space of Hilbert-Schmidt operators on a separable Hilbert space. The Riccati equation was treated as a nonlinear evolution equation with dynamics described by a nonlinear monotone perturbation of a strongly coercive linear operator. A generic approximation result was proven for quasi-autonomous nonlinear evolution system involving accretive operators which was then used to demonstrate the Hilbert-Schmidt norm convergence of Galerkin approximations to the solution of the Riccati equation. The application of the results was illustrated in the context of a linear quadratic optimal control problem for a one dimensional heat equation.

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

    NASA Technical Reports Server (NTRS)

    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.

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

    PubMed Central

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

    2015-01-01

    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.

  4. Ballistic Limit Equation for Single Wall Titanium

    NASA Technical Reports Server (NTRS)

    Ratliff, J. M.; Christiansen, Eric L.; Bryant, C.

    2009-01-01

    Hypervelocity impact tests and hydrocode simulations were used to determine the ballistic limit equation (BLE) for perforation of a titanium wall, as a function of wall thickness. Two titanium alloys were considered, and separate BLEs were derived for each. Tested wall thicknesses ranged from 0.5mm to 2.0mm. The single-wall damage equation of Cour-Palais [ref. 1] was used to analyze the Ti wall's shielding effectiveness. It was concluded that the Cour-Palais single-wall equation produced a non-conservative prediction of the ballistic limit for the Ti shield. The inaccurate prediction was not a particularly surprising result; the Cour-Palais single-wall BLE contains shield material properties as parameters, but it was formulated only from tests of different aluminum alloys. Single-wall Ti shield tests were run (thicknesses of 2.0 mm, 1.5 mm, 1.0 mm, and 0.5 mm) on Ti 15-3-3-3 material custom cut from rod stock. Hypervelocity impact (HVI) tests were used to establish the failure threshold empirically, using the additional constraint that the damage scales with impact energy, as was indicated by hydrocode simulations. The criterion for shield failure was defined as no detached spall from the shield back surface during HVI. Based on the test results, which confirmed an approximately energy-dependent shield effectiveness, the Cour-Palais equation was modified.

  5. Controlled-aperture wave-equation migration

    SciTech Connect

    Huang, L.; Fehler, Michael C.; Sun, H.; Li, Z.

    2003-01-01

    We present a controlled-aperture wave-equation migration method that no1 only can reduce migration artiracts due to limited recording aperlurcs and determine image weights to balance the efl'ects of limited-aperture illumination, but also can improve thc migration accuracy by reducing the slowness perturbations within thc controlled migration regions. The method consists of two steps: migration aperture scan and controlled-aperture migration. Migration apertures for a sparse distribution of shots arc determined using wave-equation migration, and those for the other shots are obtained by interpolation. During the final controlled-aperture niigration step, we can select a reference slowness in c;ontrollecl regions of the slowness model to reduce slowncss perturbations, and consequently increase the accuracy of wave-equation migration inel hods that makc use of reference slownesses. In addition, the computation in the space domain during wavefield downward continuation is needed to be conducted only within the controlled apertures and therefore, the computational cost of controlled-aperture migration step (without including migration aperture scan) is less than the corresponding uncontrolled-aperture migration. Finally, we can use the efficient split-step Fourier approach for migration-aperture scan, then use other, more accurate though more expensive, wave-equation migration methods to perform thc final controlled-apertio.ee migration to produce the most accurate image.

  6. Renormalization group equations for the CKM matrix

    SciTech Connect

    Kielanowski, P.; Juarez W, S. R.; Montes de Oca Y, J. H.

    2008-12-01

    We derive the one loop renormalization group equations for the Cabibbo-Kobayashi-Maskawa (CKM) matrix for the standard model, its two Higgs extension, and the minimal supersymmetric extension in a novel way. The derived equations depend only on a subset of the model parameters of the renormalization group equations for the quark Yukawa couplings so the CKM matrix evolution cannot fully test the renormalization group evolution of the quark Yukawa couplings. From the derived equations we obtain the invariant of the renormalization group evolution for three models which is the angle {phi}{sub 2} of the unitarity triangle. For the special case of the standard model and its extensions with v{sub 1}{approx_equal}v{sub 2} we demonstrate that also the shape of the unitarity triangle and the Buras-Wolfenstein parameters {rho} and {eta} are conserved. The invariance of the angles of the unitarity triangle means that it is not possible to find a model in which the CKM matrix might have a simple, special form at asymptotic energies.

  7. Observed Score Linear Equating with Covariates

    ERIC Educational Resources Information Center

    Branberg, Kenny; Wiberg, Marie

    2011-01-01

    This paper examined observed score linear equating in two different data collection designs, the equivalent groups design and the nonequivalent groups design, when information from covariates (i.e., background variables correlated with the test scores) was included. The main purpose of the study was to examine the effect (i.e., bias, variance, and…

  8. Recent Progress on Certain Quartic Diophantine Equations

    NASA Astrophysics Data System (ADS)

    Walsh, P. G.

    2008-01-01

    Wilhelm Ljunggren proved many results on quartic Diophantine equations of the form aX4-bY2 = c, with c∈{±1,-2,±4}. Noticeably absent from this set of values of c is c = 2. We describe some recent progress on this problem, and discuss some open problems which require further study.

  9. Dilations and the Equation of a Line

    ERIC Educational Resources Information Center

    Yopp, David A.

    2016-01-01

    Students engage in proportional reasoning when they use covariance and multiple comparisons. Without rich connections to proportional reasoning, students may develop inadequate understandings of linear relationships and the equations that model them. Teachers can improve students' understanding of linear relationships by focusing on realistic…

  10. From Arithmetic Sequences to Linear Equations

    ERIC Educational Resources Information Center

    Matsuura, Ryota; Harless, Patrick

    2012-01-01

    The first part of the article focuses on deriving the essential properties of arithmetic sequences by appealing to students' sense making and reasoning. The second part describes how to guide students to translate their knowledge of arithmetic sequences into an understanding of linear equations. Ryota Matsuura originally wrote these lessons for…

  11. Procedural Embodiment and Magic in Linear Equations

    ERIC Educational Resources Information Center

    de Lima, Rosana Nogueira; Tall, David

    2008-01-01

    How do students think about algebra? Here we consider a theoretical framework which builds from natural human functioning in terms of embodiment--perceiving the world, acting on it and reflecting on the effect of the actions--to shift to the use of symbolism to solve linear equations. In the main, the students involved in this study do not…

  12. Solves the Multigroup Neutron Diffusion Equation

    Energy Science and Technology Software Center (ESTSC)

    1995-06-23

    GNOMER is a program which solves the multigroup neutron diffusion equation in 1D, 2D and 3D cartesian geometry. The program is designed to calculate the global core power distributions (with thermohydraulic feedbacks), as well as power distribution and homogenized cross sections over a fuel assembly.

  13. Nonlinear Resonance and Duffing's Spring Equation

    ERIC Educational Resources Information Center

    Fay, Temple H.

    2006-01-01

    This note discusses the boundary in the frequency--amplitude plane for boundedness of solutions to the forced spring Duffing type equation. For fixed initial conditions and fixed parameter [epsilon] results are reported of a systematic numerical investigation on the global stability of solutions to the initial value problem as the parameters F and…

  14. Relations Among Systems of Electromagnetic Equations

    ERIC Educational Resources Information Center

    page, Chester H.

    1970-01-01

    Contends that the equations of electromagnetism, whether in rationalized or non-rationalized form, express an invariant set of physical relationships. The relationships among corresponding symbols are given and applied to precise statements about the relation between the oersted and the amphere per meter, the abampere and the ampere, etc.…

  15. 'Footballs', conical singularities, and the Liouville equation

    SciTech Connect

    Redi, Michele

    2005-02-15

    We generalize the football shaped extra dimensions scenario to an arbitrary number of branes. The problem is related to the solution of the Liouville equation with singularities, and explicit solutions are presented for the case of three branes. The tensions of the branes do not need to be tuned with each other but only satisfy mild global constraints.

  16. Computer Applications in Balancing Chemical Equations.

    ERIC Educational Resources Information Center

    Kumar, David D.

    2001-01-01

    Discusses computer-based approaches to balancing chemical equations. Surveys 13 methods, 6 based on matrix, 2 interactive programs, 1 stand-alone system, 1 developed in algorithm in Basic, 1 based on design engineering, 1 written in HyperCard, and 1 prepared for the World Wide Web. (Contains 17 references.) (Author/YDS)

  17. Systems of Linear Equations on a Spreadsheet.

    ERIC Educational Resources Information Center

    Bosch, William W.; Strickland, Jeff

    1998-01-01

    The Optimizer in Quattro Pro and the Solver in Excel software programs make solving linear and nonlinear optimization problems feasible for business mathematics students. Proposes ways in which the Optimizer or Solver can be coaxed into solving systems of linear equations. (ASK)

  18. Equations with Technology: Different Tools, Different Views

    ERIC Educational Resources Information Center

    Drijvers, Paul; Barzel, Barbel

    2012-01-01

    Has technology revolutionised the mathematics classroom, or is it still a device waiting to be exploited for the benefit of the learner? There are applets that will enable the user to solve complex equations at the push of a button. So, does this jeopardise other methods, make other methods redundant, or even diminish other methods in the mind of…

  19. On the Burgers-Poisson equation

    NASA Astrophysics Data System (ADS)

    Grunert, K.; Nguyen, Khai T.

    2016-09-01

    In this paper, we prove the existence and uniqueness of weak entropy solutions to the Burgers-Poisson equation for initial data in L1 (R). In addition an Oleinik type estimate is established and some criteria on local smoothness and wave breaking for weak entropy solutions are provided.

  20. Undular bore theory for the Gardner equation.

    PubMed

    Kamchatnov, A M; Kuo, Y-H; Lin, T-C; Horng, T-L; Gou, S-C; Clift, R; El, G A; Grimshaw, R H J

    2012-09-01

    We develop modulation theory for undular bores (dispersive shock waves) in the framework of the Gardner, or extended Korteweg-de Vries (KdV), equation, which is a generic mathematical model for weakly nonlinear and weakly dispersive wave propagation, when effects of higher order nonlinearity become important. Using a reduced version of the finite-gap integration method we derive the Gardner-Whitham modulation system in a Riemann invariant form and show that it can be mapped onto the well-known modulation system for the Korteweg-de Vries equation. The transformation between the two counterpart modulation systems is, however, not invertible. As a result, the study of the resolution of an initial discontinuity for the Gardner equation reveals a rich phenomenology of solutions which, along with the KdV-type simple undular bores, include nonlinear trigonometric bores, solibores, rarefaction waves, and composite solutions representing various combinations of the above structures. We construct full parametric maps of such solutions for both signs of the cubic nonlinear term in the Gardner equation. Our classification is supported by numerical simulations. PMID:23031043