Ein Kredit für Weihnachtsbaumkugeln

NASA Astrophysics Data System (ADS)

Tutsch, Sina

Eine Mathematikerin aus dem DFG-Forschungszentrum Matheon arbeitet an Methoden zur dreidimensionalen Visualisierung. Sie hat die Geschäftsidee, Weihnachtsbaumkugeln mit bewegten Hologrammen herzustellen, die sich individuell gestalten lassen, und plant eine Existenzgründung. Aus einem öffentlichen Förderprogramm erhält sie ein günstiges Darlehen in Höhe von 50 000 Euro. Für die Startphase ihres Unternehmens benötigt sie jedoch den vierfachen Betrag.

Etiologies des pleurésies exsudatives: à propos de 424 cas à Madagascar

PubMed Central

Rakotoson, Joëlson Lovaniaina; Andrianasolo, Radonirina Lazasoa; Rakotomizao, Robert Jocelyn; Vololontiana, Marie Danielle Hanta; Ravahatra, Kiady; Rajaoarifetra, Jobeline; Andrianarisoa, Christophe Félix Ange

2011-01-01

Introduction La pleurésie constitue un motif fréquent de consultation en pneumologie. Notre travail a pour objectif de déterminer les étiologies des pleurésies exsudatives afin d'en faciliter les démarches étiologiques. Méthodes Il s'agit d'une étude rétrospective réalisée chez des patients ayant une pleurésie exsudative et bénéficiant une biopsie pleurale à l'aveugle à l'aide de l'aiguille de Castelain, pendant une période de 5 ans (2005 à 2009). Résultats Parmi les 424 patients inclus, 259 hommes (61,08%) et 165 femmes (38,91%) étaient individualisés. Les pleurésies étaient d'origine tuberculeuse dans 298 cas (70, 28%), métastatique dans 63 cas (14,85%), inflammation non spécifique dans 51 cas (12,02%). Des fibres musculaires striées étaient biopsiées dans 12 cas (2,83%). Conclusion La biopsie pleurale occupe une place prépondérante dans la recherche étiologique des pleurésies d'exsudatives à Madagascar où la tuberculose sévit encore en mode endémique. PMID:22145067

Atmospheric influences on the anomalous 2016 Antarctic sea ice decay

NASA Astrophysics Data System (ADS)

Schlosser, Elisabeth; Haumann, F. Alexander; Raphael, Marilyn N.

2018-03-01

In contrast to the Arctic, where total sea ice extent (SIE) has been decreasing for the last three decades, Antarctic SIE has shown a small, but significant, increase during the same time period. However, in 2016, an unusually early onset of the melt season was observed; the maximum Antarctic SIE was already reached as early as August rather than the end of September, and was followed by a rapid decrease. The decay was particularly strong in November, when Antarctic SIE exhibited a negative anomaly (compared to the 1979-2015 average) of approximately 2 million km2. ECMWF Interim reanalysis data showed that the early onset of the melt and the rapid decrease in sea ice area (SIA) and SIE were associated with atmospheric flow patterns related to a positive zonal wave number three (ZW3) index, i.e., synoptic situations leading to strong meridional flow and anomalously strong southward heat advection in the regions of strongest sea ice decline. A persistently positive ZW3 index from May to August suggests that SIE decrease was preconditioned by SIA decrease. In particular, in the first third of November northerly flow conditions in the Weddell Sea and the Western Pacific triggered accelerated sea ice decay, which was continued in the following weeks due to positive feedback effects, leading to the unusually low November SIE. In 2016, the monthly mean Southern Annular Mode (SAM) index reached its second lowest November value since the beginning of the satellite observations. A better spatial and temporal coverage of reliable ice thickness data is needed to assess the change in ice mass rather than ice area.

Biologie statt Philosophie? Evolutionäre Kulturerklärungen und ihre Grenzen

NASA Astrophysics Data System (ADS)

Illies, Christian

Vor über siebzig Jahren fand man in einer Höhle nahe Hohlenstein-Stadel, im heutigen Baden-Württemberg, eine Frau, die keiner bekannten Spezies und nicht einmal eindeutig den Hominiden zugeordnet werden konnte. Wegen ihres Aussehens wurde sie schon bald als "Löwenfrau“ bekannt (unterdessen wird sie als "Löwenmensch“ bezeichnet, da die in solchen Fragen Klarheit schaffenden Geschlechtsteile bei der Figur fehlen und in Zeiten von gender mainstreaming derartige Festlegungen gerne vermieden werden), denn sie hatte eine menschlich-aufrechte, unbehaarte Gestalt mit weiblichen Rundungen, aber zugleich eine Mähne, sowie Augen, Ohren und Schnauze eines Löwen. Eine sehr weitläufige Verwandte des Minotaurus, so schien es, und doch wesentlich älter als alle Bewohner des Olymps, denn vermutlich wurde die knapp 30 cm große Skulptur bereits in der Altsteinzeit vor etwa 32.000 Jahren aus Mammut-Elfenbein geschnitzt. Wir wissen nicht, ob sie kultischen Zwecken diente oder ein Kind mit ihr spielte, ob sie als Glücksbringer für die Jagd oder als Schamanin mit Löwenmaske verehrt und gefürchtet wurde. Aber die Löwenfrau legt nahe, dass der Mensch schon im Morgendämmern seiner Kultur über die eigene Nähe, aber auch Distanz zum Tier nachgedacht haben muss. Die Frage nach der menschlichen Selbstverortung begegnet uns in dieser Figur, und sie bestimmt viele Zeugnisse menschlichen Nachdenkens, welche uns die Altertumswissenschaften vorlegen. Mit dem Begriff "animal rationale“, wie er unter Bezug auf Aristoteles geprägt wurde, findet sie schließlich ihre klassische, für das Abendland lange Zeit maßgebliche Antwort: Der Mensch als Tier, dessen spezifisches Merkmal die Vernunftbegabtheit ist, die ihn zugleich von allen anderen Tieren abgrenzt und über sie stellt. Aber wo genau verläuft die Grenze? Und wie kann der Mensch beides zugleich sein? Die aristotelische Definition beantwortet diese Fragen nach der Doppelnatur nicht, sondern erhebt das offene Rätsel gleichsam zur Wesensbestimmung des Menschen.

Polarizability tensor retrieval for magnetic and plasmonic antenna design

NASA Astrophysics Data System (ADS)

Bernal Arango, Felipe; Femius Koenderink, A.

2013-07-01

A key quantity in the design of plasmonic antennas and metasurfaces, as well as metamaterials, is the electrodynamic polarizability of a single scattering building block. In particular, in the current merging of plasmonics and metamaterials, subwavelength scatterers are judged by their ability to present a large, generally anisotropic electric and magnetic polarizability, as well as a bi-anisotropic magnetoelectric polarizability. This bi-anisotropic response, whereby a magnetic dipole is induced through electric driving, and vice versa, is strongly linked to the optical activity and chiral response of plasmonic metamolecules. We present two distinct methods to retrieve the polarizibility tensor from electrodynamic simulations. As a basis for both, we use the surface integral equation (SIE) method to solve for the scattering response of arbitrary objects exactly. In the first retrieval method, we project scattered fields onto vector spherical harmonics with the aid of an exact discrete spherical harmonic Fourier transform on the unit sphere. In the second, we take the effective current distributions generated by SIE as a basis to calculate dipole moments. We verify that the first approach holds for scatterers of any size, while the second is only approximately correct for small scatterers. We present benchmark calculations, revisiting the zero-forward scattering paradox of Kerker et al (1983 J. Opt. Soc. Am. 73 765-7) and Alù and Engheta (2010 J. Nanophoton. 4 041590), relevant in dielectric scattering cancelation and sensor cloaking designs. Finally, we report the polarizability tensor of split rings, and show that split rings will strongly influence the emission of dipolar single emitters. In the context of plasmon-enhanced emission, split rings can imbue their large magnetic dipole moment on the emission of simple electric dipole emitters. We present a split ring antenna array design that is capable of converting the emission of a single linear dipole emitter in forward and backward beams of directional emission of opposite handedness. This design can, for instance, find application in the spin angular momentum encoding of quantum information.

The role of summer surface wind anomalies in the summer Arctic sea ice extent in 2010 and 2011

NASA Astrophysics Data System (ADS)

Ogi, M.; Wallace, J. M.

2012-12-01

Masayo Ogi 1 and John M. Wallace 2 masayo.ogi@jamstec.go.jp wallace@atmos.washington.edu 1Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan 2 Department of Atmospheric Sciences, University of Washington, Seattle, Washington The seasonal evolutions of Arctic sea ice extent (SIE) during the summers of 2010 and 2011 are contrasted with that in 2007. The June SIE in 2010 was lower than that in 2007 and was the lowest for that calendar month in the 32-year (1979-2010) record. The September SIE in 2010 would have set a new record low had it not been for the fact that the ice retreated more slowly during the summer months in that year than it did in 2007. Hence from early July onward, the SIE in 2010 remained at levels above those observed in 2007. The SIE minimum in September 2010 proved to be the third lowest on record, eclipsed by values in both 2007 and 2008. In spring and summer of 2011, the Arctic SIE was as low as it was in 2007, but the SIE in September 2011 did not reach record low levels. The SIE minimum in 2011 proved to be the second lowest on record for the period of 1979-2011. Summertime atmospheric conditions play an important role in controlling the variations in Arctic SIE. In a previous study based on statistical analysis of data collected prior to 2007, we showed that anticyclonic summertime circulation anomalies over the Arctic Ocean during the summer months favor low September SIE. We also found that the record-low ice summer year 2007 was characterized by a strong anticyclonic circulation anomaly, accompanied by an Ekman drift of ice out of the marginal seas toward the central Arctic and eventually toward the Fram Strait, as evidenced by the tracks of drifting buoys. Here we assess the extent to which year-to-year differences in summer winds over the Arctic might have contributed to the differing rates of retreat of ice during the summers of 2007, 2010, and 2011. Our results show that the May-June (MJ) pattern in 2010 is characterized by strong anticyclonic wind anomalies over the Arctic Ocean. The corresponding pattern for July-August-September (JAS) is dominated by a cyclonic gyre centered over the Kara Sea. The corresponding patterns for 2007 are weak in MJ and strongly anticyclonic in JAS. The JJA pattern in 2011 is characterized by anticyclonic wind anomalies over the Arctic directed toward the Fram Strait, whereas the September pattern exhibits wind anomalies directed away from the Fram Strait across the central Arctic Ocean toward the Chukchi Sea. The corresponding patterns for 2007 are strongly anticyclonic and directed toward the Fram Strait in both JJA and September. In the absence of the late season push by the winds, the ice did not retreat quite as far in 2011 as it did in 2007. We have shown evidence that low level winds over the Arctic play an important role in mediating the rate of retreat of sea ice during summer. Anomalous anticyclonic flow over the interior of the Arctic directed toward the Fram Strait favors rapid retreat and vice versa. We have argued that the relative rankings of the September SIE for the years 2007, 2010 and 2011 are largely attributable to the differing rates of decrease of SIE during these summers, which are a consequence of year-to-year differences in the seasonal evolution of summertime winds over the Arctic.

Incorporating engine health monitoring capability into the SSME Block II controller

NASA Astrophysics Data System (ADS)

Clarke, James W.; Copa, Roderick J.

An account is given of the architecture of the SSME's Block II controller's architecture, its incorporation of smart input electronics (SIE), and the potential benefits of this technology in SSME health-monitoring capabilities. SIE allows the Block II controller to conduct its control functions while simultaneously furnishing the computational capabilities and sensor input interface for any newly defined health-monitoring functions. It is expected that the SIE technology may be directly transferred to any follow-on engine design.

Exhaustive search and solvated interaction energy (SIE) for virtual screening and affinity prediction

NASA Astrophysics Data System (ADS)

Sulea, Traian; Hogues, Hervé; Purisima, Enrico O.

2012-05-01

We carried out a prospective evaluation of the utility of the SIE (solvation interaction energy) scoring function for virtual screening and binding affinity prediction. Since experimental structures of the complexes were not provided, this was an exercise in virtual docking as well. We used our exhaustive docking program, Wilma, to provide high-quality poses that were rescored using SIE to provide binding affinity predictions. We also tested the combination of SIE with our latest solvation model, first shell of hydration (FiSH), which captures some of the discrete properties of water within a continuum model. We achieved good enrichment in virtual screening of fragments against trypsin, with an area under the curve of about 0.7 for the receiver operating characteristic curve. Moreover, the early enrichment performance was quite good with 50% of true actives recovered with a 15% false positive rate in a prospective calculation and with a 3% false positive rate in a retrospective application of SIE with FiSH. Binding affinity predictions for both trypsin and host-guest complexes were generally within 2 kcal/mol of the experimental values. However, the rank ordering of affinities differing by 2 kcal/mol or less was not well predicted. On the other hand, it was encouraging that the incorporation of a more sophisticated solvation model into SIE resulted in better discrimination of true binders from binders. This suggests that the inclusion of proper Physics in our models is a fruitful strategy for improving the reliability of our binding affinity predictions.

Skillful regional prediction of Arctic sea ice on seasonal timescales

NASA Astrophysics Data System (ADS)

Bushuk, Mitchell; Msadek, Rym; Winton, Michael; Vecchi, Gabriel A.; Gudgel, Rich; Rosati, Anthony; Yang, Xiaosong

2017-05-01

Recent Arctic sea ice seasonal prediction efforts and forecast skill assessments have primarily focused on pan-Arctic sea ice extent (SIE). In this work, we move toward stakeholder-relevant spatial scales, investigating the regional forecast skill of Arctic sea ice in a Geophysical Fluid Dynamics Laboratory (GFDL) seasonal prediction system. Using a suite of retrospective initialized forecasts spanning 1981-2015 made with a coupled atmosphere-ocean-sea ice-land model, we show that predictions of detrended regional SIE are skillful at lead times up to 11 months. Regional prediction skill is highly region and target month dependent and generically exceeds the skill of an anomaly persistence forecast. We show for the first time that initializing the ocean subsurface in a seasonal prediction system can yield significant regional skill for winter SIE. Similarly, as suggested by previous work, we find that sea ice thickness initial conditions provide a crucial source of skill for regional summer SIE.

Diagnosing sea ice from the north american multi model ensemble and implications on mid-latitude winter climate

NASA Astrophysics Data System (ADS)

Elders, Akiko; Pegion, Kathy

2017-12-01

Arctic sea ice plays an important role in the climate system, moderating the exchange of energy and moisture between the ocean and the atmosphere. An emerging area of research investigates how changes, particularly declines, in sea ice extent (SIE) impact climate in regions local to and remote from the Arctic. Therefore, both observations and model estimates of sea ice become important. This study investigates the skill of sea ice predictions from models participating in the North American Multi-Model Ensemble (NMME) project. Three of the models in this project provide sea-ice predictions. The ensemble average of these models is used to determine seasonal climate impacts on surface air temperature (SAT) and sea level pressure (SLP) in remote regions such as the mid-latitudes. It is found that declines in fall SIE are associated with cold temperatures in the mid-latitudes and pressure patterns across the Arctic and mid-latitudes similar to the negative phase of the Arctic Oscillation (AO). These findings are consistent with other studies that have investigated the relationship between declines in SIE and mid-latitude weather and climate. In an attempt to include additional NMME models for sea-ice predictions, a proxy for SIE is used to estimate ice extent in the remaining models, using sea surface temperature (SST). It is found that SST is a reasonable proxy for SIE estimation when compared to model SIE forecasts and observations. The proxy sea-ice estimates also show similar relationships to mid-latitude temperature and pressure as the actual sea-ice predictions.

Ruhende Flüssigkeiten und Gase

NASA Astrophysics Data System (ADS)

Heintze, Joachim

Das mechanische Verhalten von Flüssigkeiten und Gasen ist dadurch gekennzeichnet, dass sie keine statische Schubfestigkeit besitzen, andernfalls würden sie nicht beginnen, zu fließen. In ruhenden Flüssigkeiten und Gasen können daher keine Schubspannungen bestehen:

Pleurésie purulente à Nocardia asteroids

PubMed Central

Bopaka, Régis Gothard; Janah, Hind; El Khattabi, Wiam; Aichane, Abdelaziz; Afif, Hicham

2014-01-01

La pleurésie purulente à Nocardia asteroides est rare. Elle survient le plus souvent sur un terrain d'immunodépression. Nous rapportons une observation d'une pleurésie à Nocardia asteroides chez une patiente âgée de 60 ans, chez qui nous avons découvert un diabète. A travers ce travail les auteurs soulignent l'intérêt de la multiplication de prélèvements, de rechercher ce germe sur terrain d'immunodépression et en cas d'isolement, de rechercher la comorbidité. PMID:25574322

Antarctic sea ice increase consistent with intrinsic variability of the Amundsen Sea Low

NASA Astrophysics Data System (ADS)

Turner, John; Hosking, J. Scott; Marshall, Gareth J.; Phillips, Tony; Bracegirdle, Thomas J.

2016-04-01

We investigate the relationship between atmospheric circulation variability and the recent trends in Antarctic sea ice extent (SIE) using Coupled Model Intercomparison Project Phase 5 (CMIP5) atmospheric data, ECMWF Interim reanalysis fields and passive microwave satellite data processed with the Bootstrap version 2 algorithm. Over 1979-2013 the annual mean total Antarctic SIE increased at a rate of 195 × 103 km2 dec-1 (1.6 % dec-1), p < 0.01. The largest regional positive trend of annual mean SIE of 119 × 103 km2 dec-1 (4.0 % dec-1) has been in the Ross Sea sector. Off West Antarctica there is a high correlation between trends in SIE and trends in the near-surface winds. The Ross Sea SIE seasonal trends are positive throughout the year, but largest in spring. The stronger meridional flow over the Ross Sea has been driven by a deepening of the Amundsen Sea Low (ASL). Pre-industrial control and historical simulations from CMIP5 indicate that the observed deepening of the ASL and stronger southerly flow over the Ross Sea are within the bounds of modeled intrinsic variability. The spring trend would need to continue for another 11 years for it to fall outside the 2 standard deviation range seen in 90 % of the simulations.

Oxygen consumption, substrate oxidation, and blood pressure following sprint interval exercise.

PubMed

Chan, Huan Hao; Burns, Stephen Francis

2013-02-01

This study examined the acute effect of sprint interval exercise (SIE) on postexercise oxygen consumption, substrate oxidation, and blood pressure. The participants were 10 healthy males aged 21-27 years. Following overnight fasts, each participant undertook 2 trials in a random balanced order: (i) four 30-s bouts of SIE on a cycle ergometer, separated by 4.5 min of recovery, and (ii) resting (control) in the laboratory for an equivalent period. Time-matched measurements of oxygen consumption, respiratory exchange ratio, and blood pressure were made for 2 h into recovery. Total 2-h oxygen consumption was significantly higher in the SIE than in the control trial (mean ± SD: 31.9 ± 6.7 L vs Exercise: 45.5 ± 6.8 L, p < 0.001). The rate of fat oxidation was 75% higher 2 h after the exercise trial compared with the control trial ( 0.08 ± 0.05 g·min(-1) vs Exercise: 0.14 ± 0.06 g·min(-1), p = 0.035). Systolic blood pressure ( 117 ± 8 mm Hg vs Exercise: 109 ± 8 mm Hg, p < 0.05) and diastolic blood pressure ( 84 ± 6 mm Hg vs Exercise: 77 ± 5 mm Hg, p < 0.05) were significantly lower 2 h after the exercise trial compared with the control trial. These data showed a 42% increase in oxygen consumption (∼13.6 L) over 2 h after a single bout of SIE. Moreover, the rate of fat oxidation increased by 75%, whereas blood pressure was reduced by ∼8 mm Hg 2 h after SIE. Whether these acute benefits of SIE can translate into long-term changes in body composition and an improvement in vascular health needs investigation.

On the discrepancy between observed and CMIP5 multi-model simulated Barents Sea winter sea ice decline

NASA Astrophysics Data System (ADS)

Li, Dawei; Zhang, Rong; Knutson, Thomas R.

2017-04-01

This study aims to understand the relative roles of external forcing versus internal climate variability in causing the observed Barents Sea winter sea ice extent (SIE) decline since 1979. We identify major discrepancies in the spatial patterns of winter Northern Hemisphere sea ice concentration trends over the satellite period between observations and CMIP5 multi-model mean externally forced response. The CMIP5 externally forced decline in Barents Sea winter SIE is much weaker than that observed. Across CMIP5 ensemble members, March Barents Sea SIE trends have little correlation with global mean surface air temperature trends, but are strongly anti-correlated with trends in Atlantic heat transport across the Barents Sea Opening (BSO). Further comparison with control simulations from coupled climate models suggests that enhanced Atlantic heat transport across the BSO associated with regional internal variability may have played a leading role in the observed decline in winter Barents Sea SIE since 1979.

Self-Interaction Error in Density Functional Theory: An Appraisal.

PubMed

Bao, Junwei Lucas; Gagliardi, Laura; Truhlar, Donald G

2018-05-03

Self-interaction error (SIE) is considered to be one of the major sources of error in most approximate exchange-correlation functionals for Kohn-Sham density-functional theory (KS-DFT), and it is large with all local exchange-correlation functionals and with some hybrid functionals. In this work, we consider systems conventionally considered to be dominated by SIE. For these systems, we demonstrate that by using multiconfiguration pair-density functional theory (MC-PDFT), the error of a translated local density-functional approximation is significantly reduced (by a factor of 3) when using an MCSCF density and on-top density, as compared to using KS-DFT with the parent functional; the error in MC-PDFT with local on-top functionals is even lower than the error in some popular KS-DFT hybrid functionals. Density-functional theory, either in MC-PDFT form with local on-top functionals or in KS-DFT form with some functionals having 50% or more nonlocal exchange, has smaller errors for SIE-prone systems than does CASSCF, which has no SIE.

The coat protein and NIa protease of two potyviridae family members independently confer superinfection exclusion

USDA-ARS?s Scientific Manuscript database

Superinfection exclusion (SIE) is an antagonistic virus-virus interaction whereby initial infection by one virus prevents subsequent infection by closely related viruses. Although SIE has been described in diverse viruses infecting plants, humans, and animals, its mechanisms, including involvement o...

Building a sense of virtual community: the role of the features of social networking sites.

PubMed

Chen, Chi-Wen; Lin, Chiun-Sin

2014-07-01

In recent years, social networking sites have received increased attention because of the potential of this medium to transform business by building virtual communities. However, theoretical and empirical studies investigating how specific features of social networking sites contribute to building a sense of virtual community (SOVC)-an important dimension of a successful virtual community-are rare. Furthermore, SOVC scales have been developed, and research on this issue has been called for, but few studies have heeded this call. On the basis of prior literature, this study proposes that perceptions of the three most salient features of social networking sites-system quality (SQ), information quality (IQ), and social information exchange (SIE)-play a key role in fostering SOVC. In particular, SQ is proposed to increase IQ and SIE, and SIE is proposed to enhance IQ, both of which thereafter build SOVC. The research model was examined in the context of Facebook, one of the most popular social networking sites in the world. We adopted Blanchard's scales to measure SOVC. Data gathered using a Web-based questionnaire, and analyzed with partial least squares, were utilized to test the model. The results demonstrate that SIE, SQ, and IQ are the factors that form SOVC. The findings also suggest that SQ plays a fundamental role in supporting SIE and IQ in social networking sites. Implications for theory, practice, and future research directions are discussed.

A Star Image Extractor for the Nano-JASMINE satellite

NASA Astrophysics Data System (ADS)

Yamauchi, M.; Gouda, N.; Kobayashi, Y.; Tsujimoto, T.; Yano, T.; Suganuma, M.; Yamada, Y.; Nakasuka, S.; Sako, N.

2008-07-01

We have developped a software of Star-Image-Extractor (SIE) which works as the on-board real-time image processor. It detects and extracts only the object data from raw image data. SIE has two functions: reducing image data and providing data for the satellite's high accuracy attitude control system.

Design and fabrication of multimode interference couplers based on digital micro-mirror system

NASA Astrophysics Data System (ADS)

Wu, Sumei; He, Xingdao; Shen, Chenbo

2008-03-01

Multimode interference (MMI) couplers, based on the self-imaging effect (SIE), are accepted popularly in integrated optics. According to the importance of MMI devices, in this paper, we present a novel method to design and fabricate MMI couplers. A technology of maskless lithography to make MMI couplers based on a smart digital micro-mirror device (DMD) system is proposed. A 1×4 MMI device is designed as an example, which shows the present method is efficient and cost-effective.

The influence of Y-TZP surface treatment on topography and ceramic/resin cement interfacial fracture toughness.

PubMed

Paes, P N G; Bastian, F L; Jardim, P M

2017-09-01

Consider the efficacy of glass infiltration etching (SIE) treatment as a procedure to modify the zirconia surface resulting in higher interfacial fracture toughness. Y-TZP was subjected to 5 different surface treatments conditions consisting of no treatment (G1), SIE followed by hydrofluoric acid treatment (G2), heat treated at 750°C (G3), hydrofluoric acid treated (G4) and airborne-particle abrasion with alumina particles (G5). The effect of surface treatment on roughness was evaluated by Atomic Force Microscopy providing three different parameters: R a , R sk and surface area variation. The ceramic/resin cement interface was analyzed by Fracture Mechanics K I test with failure mode determined by fractographic analysis. Weibull's analysis was also performed to evaluate the structural integrity of the adhesion zone. G2 and G4 specimens showed very similar, and high R a values but different surface area variation (33% for G2 and 13% for G4) and they presented the highest fracture toughness (K IC ). Weibull's analysis showed G2 (SIE) tendency to exhibit higher K IC values than the other groups but with more data scatter and a higher early failure probability than G4 specimens. Selective glass infiltration etching surface treatment was effective in modifying the zirconia surface roughness, increasing the bonding area and hence the mechanical imbrications at the zirconia/resin cement interface resulting in higher fracture toughness (K IC ) values with higher K IC values obtained when failure probability above 20% was expected (Weibull's distribution) among all the experimental groups. Copyright © 2017 The Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

Reisen im freien Fall - Teil 2: Das Zwillingsparadoxon aus dem Blickwinkel der ART

NASA Astrophysics Data System (ADS)

Sonne, Bernd; Weiß, Reinhard

2013-07-01

Nachdem wir uns mit den Prinzipien der ART und einigen Beispielen vertraut gemacht haben, kommen wir nun zur Berechnung des Zwillingsparadoxons aus Sicht des reisenden Zwillings. Dabei spielt das Äquivalenzprinzip eine große Rolle. Deshalb wird die Bewegungssituation noch einmal erläutert, diesmal aus Sicht von Katrin. Sie befindet sich in ihrem System S'in Ruhe. In ihrem System läuft die Zeit t'ab. Nach dem Start fühlt Katrin jedoch eine Kraft, die sie als Gravitationskraft interpretieren kann. Sie merkt es daran, dass sie in den Sitz gedrückt wird. Nach einiger Zeit werden die Triebwerke abgeschaltet, und das Raumschiff fliegt mit konstanter Geschwindigkeit weiter, Phase 2. Anschließend wird der Schub der Triebwerke solange umgekehrt, bis das Raumschiff irgendwo mit der Geschwindigkeit null am Umkehrpunkt U landet, Phase 3 (Abb. 15.1). Die Erde, auf der sich Michael befindet, bewegt sich mit x'(t') aus Sicht von Katrin im freien Fall von ihr weg, s. das Experiment mit dem steigenden Fahrstuhl in Abschn. 13.2.1.

Psychological Availability between Self-Initiated Expatriates and Host Country Nationals during Their Adjustment: The Moderating Role of Supportive Supervisor Relations.

PubMed

Jannesari, Milad; Wang, Zhongming; McCall, Jacob; Zheng, Boyang

2017-01-01

This research examined the role of psychological availability as a means of psychological engagement between self-initiated expatriates (SIEs) and their host-country nationals (HCNs) colleagues during their work and interaction adjustment. To reveal this process, this study presented the concept of psychological availability, which refers to an individual's belief that they are physically, cognitively, and emotionally ready or confident to engage the self with their colleagues, as a mediator between proactive personality and adjustment. Also, it investigated the relationship between proactive personality and psychological availability and how it was moderated by supportive supervisor relations. We hypothesized, this relationship would be weakened/strengthened when SIEs and HCNs received low/high level of support from their supervisor. This study was conducted as a quantitative study, data was used from 342 SIEs and 342 HCNs working in mainland China. Our finding supported the hypothesis that psychological availability mediated the relationship between proactive personality and their adjustment to an international work environment; in addition, the relationship between proactive personality and psychological availability would be stronger when the level of superiors relations support is high between SIEs and HCNs. This study demonstrated the value of proactive personality as an antecedent effect and supportive supervisor relations as a moderating effect, and investigated how these factors can lead to a sense of psychological availability and boost psychological engagement between SIEs and HCNs in order to improve the adjustment between them.

Psychological Availability between Self-Initiated Expatriates and Host Country Nationals during Their Adjustment: The Moderating Role of Supportive Supervisor Relations

PubMed Central

Jannesari, Milad; Wang, Zhongming; McCall, Jacob; Zheng, Boyang

2017-01-01

This research examined the role of psychological availability as a means of psychological engagement between self-initiated expatriates (SIEs) and their host-country nationals (HCNs) colleagues during their work and interaction adjustment. To reveal this process, this study presented the concept of psychological availability, which refers to an individual’s belief that they are physically, cognitively, and emotionally ready or confident to engage the self with their colleagues, as a mediator between proactive personality and adjustment. Also, it investigated the relationship between proactive personality and psychological availability and how it was moderated by supportive supervisor relations. We hypothesized, this relationship would be weakened/strengthened when SIEs and HCNs received low/high level of support from their supervisor. This study was conducted as a quantitative study, data was used from 342 SIEs and 342 HCNs working in mainland China. Our finding supported the hypothesis that psychological availability mediated the relationship between proactive personality and their adjustment to an international work environment; in addition, the relationship between proactive personality and psychological availability would be stronger when the level of superiors relations support is high between SIEs and HCNs. This study demonstrated the value of proactive personality as an antecedent effect and supportive supervisor relations as a moderating effect, and investigated how these factors can lead to a sense of psychological availability and boost psychological engagement between SIEs and HCNs in order to improve the adjustment between them. PMID:29225587

Using species abundance distribution models and diversity indices for biogeographical analyses

NASA Astrophysics Data System (ADS)

Fattorini, Simone; Rigal, François; Cardoso, Pedro; Borges, Paulo A. V.

2016-01-01

We examine whether Species Abundance Distribution models (SADs) and diversity indices can describe how species colonization status influences species community assembly on oceanic islands. Our hypothesis is that, because of the lack of source-sink dynamics at the archipelago scale, Single Island Endemics (SIEs), i.e. endemic species restricted to only one island, should be represented by few rare species and consequently have abundance patterns that differ from those of more widespread species. To test our hypothesis, we used arthropod data from the Azorean archipelago (North Atlantic). We divided the species into three colonization categories: SIEs, archipelagic endemics (AZEs, present in at least two islands) and native non-endemics (NATs). For each category, we modelled rank-abundance plots using both the geometric series and the Gambin model, a measure of distributional amplitude. We also calculated Shannon entropy and Buzas and Gibson's evenness. We show that the slopes of the regression lines modelling SADs were significantly higher for SIEs, which indicates a relative predominance of a few highly abundant species and a lack of rare species, which also depresses diversity indices. This may be a consequence of two factors: (i) some forest specialist SIEs may be at advantage over other, less adapted species; (ii) the entire populations of SIEs are by definition concentrated on a single island, without possibility for inter-island source-sink dynamics; hence all populations must have a minimum number of individuals to survive natural, often unpredictable, fluctuations. These findings are supported by higher values of the α parameter of the Gambin mode for SIEs. In contrast, AZEs and NATs had lower regression slopes, lower α but higher diversity indices, resulting from their widespread distribution over several islands. We conclude that these differences in the SAD models and diversity indices demonstrate that the study of these metrics is useful for biogeographical purposes.

Comparative study of three methods of estimation of creatinine clearance in critically ill patients.

PubMed

Blasco, V; Antonini, F; Zieleskiewicz, L; Hammad, E; Albanèse, J; Martin, C; Leone, M

2014-05-01

At the bedside, the reference method for creatinine clearance determination is based on the measurement of creatinine concentrations in urine and serum (mCrCl). Several models are available to calculate the creatinine clearance from the serum creatinine concentration. This observational survey aimed at testing the hypothesis that the proposed equations are unreliable to determine accurate creatinine clearance in patients admitted to intensive care unit (ICU). Creatinine clearance was determined by the use of mCrCl. Then, we compared three equations: Cockcroft-Gault (CG), Simplified Modification of Diet in Renal Disease (MDRDs), and Chronic Kidney Disease Epidemiology (CKD-EPI) in 156 consecutive patients within the first 24hours after ICU admission. We tested the hypothesis that the three equations were equivalent. The agreement between the three equations was evaluated by linear regression and Bland and Altman analysis. Bland and Altman analysis showed similar agreement between the three equations. The biases and precisions were -4.8±51, -1.3±50, and 8.2±44 for CG, MDRDs, and CKD-EPI equations, respectively (P>0.05). The precisions were similar for the three equations (P>0.05). The percentages of outliers at ±30% were 44%, 45%, and 49% for CG, MDRDs, and CKD-EPI, respectively (P>0.05). Regarding the high percentage of outliers, the use of these equations cannot be recommended in ICU patients. Copyright © 2014 Société française d’anesthésie et de réanimation (Sfar). Published by Elsevier SAS. All rights reserved.

Evaluation of Additives to Eliminate Free Water from Aviation Fuel Light Obscuration Particle Counts

DTIC Science & Technology

2015-11-01

NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) US Army TARDEC RDTA SIE-ES-FPT- PSD 6501 E. 11 Mile Road...Army TARDEC RDTA SIE-ES-FPT- PSD 6501 E. 11 Mile Road Mail Stop 110 Warren, MI 48397-5000 10. SPONSOR/MONITOR’S ACRONYM(S) 11. SPONSORING

Designing lateral spintronic devices with giant tunnel magnetoresistance and perfect spin injection efficiency based on transition metal dichalcogenides.

PubMed

Zhao, Pei; Li, Jianwei; Jin, Hao; Yu, Lin; Huang, Baibiao; Ying, Dai

2018-04-18

Giant tunnel magnetoresistance (TMR) and perfect spin-injection efficiency (SIE) are extremely significant for modern spintronic devices. Quantum transport properties in a two-dimensional (2D) VS2/MoS2/VS2 magnetic tunneling junction (MTJ) are investigated theoretically within the framework of density functional theory combining with the non-equilibrium Green's functions (DFT-NEGF) method. Our results indicate that the designed MTJ exhibits a TMR with a value up to 4 × 103, which can be used as a switch of spin-electron devices. And due to the huge barrier for spin-down transport, the spin-down electrons could hardly cross the central scattering region, thus achieving a perfect SIE. Furthermore, we also explore for the effect of bias voltage on the TMR and SIE. We find that the TMR increases with the increasing bias voltage, and the SIE is robust against either bias or gate voltage in MTJs, which can serve as effective spin filter devices. Our results can not only give fresh impetus to the research community to build MTJs but also provide potential materials for spintronic devices.

Rigorous Combination of GNSS and VLBI: How it Improves Earth Orientation and Reference Frames

NASA Astrophysics Data System (ADS)

Lambert, S. B.; Richard, J. Y.; Bizouard, C.; Becker, O.

2017-12-01

Current reference series (C04) of the International Earth Rotation and Reference Systems Service (IERS) are produced by a weighted combination of Earth orientation parameters (EOP) time series built up by combination centers of each technique (VLBI, GNSS, Laser ranging, DORIS). In the future, we plan to derive EOP from a rigorous combination of the normal equation systems of the four techniques.We present here the results of a rigorous combination of VLBI and GNSS pre-reduced, constraint-free, normal equations with the DYNAMO geodetic analysis software package developed and maintained by the French GRGS (Groupe de Recherche en GeÌodeÌsie Spatiale). The used normal equations are those produced separately by the IVS and IGS combination centers to which we apply our own minimal constraints.We address the usefulness of such a method with respect to the classical, a posteriori, combination method, and we show whether EOP determinations are improved.Especially, we implement external validations of the EOP series based on comparison with geophysical excitation and examination of the covariance matrices. Finally, we address the potential of the technique for the next generation celestial reference frames, which are currently determined by VLBI only.

Zufällige Signale

NASA Astrophysics Data System (ADS)

Plaßmann, Wilfried

Die hier betrachteten Signale werden auch als stochastische Signale bezeichnet. Sie sind zufällig, d. h. ihr Augenblickswert ist nicht vorhersagbar. Abb. 118.1 zeigt eine Unterteilung nach den Signaleigenschaften. Über die nichtstationären Signale lässt sich keinerlei Aussage machen, und sie werden hier deshalb auch nicht weiter betrachtet. Für die stationären Signale gilt, dass ihr Momentanwert zwar auch nicht vorhergesagt werden kann, dass sie aber trotzdem gewisse auswertbare Eigenschaften besitzen, die allerdings statistischer Art sind und deshalb nur mit den Gesetzen der Wahrscheinlichkeitstheorie erfasst werden können. Zwar sind - theoretisch - für die Anwendung der Wahrscheinlichkeitstheorie unendlich viele Probenwerte zu nehmen, in der Praxis hat sich aber gezeigt, dass man auch mit einer endlichen Anzahl dem gesuchten Wert schon ausreichend nahe kommen kann.

Double and multiple contacts of similar elastic materials

NASA Astrophysics Data System (ADS)

Sundaram, Narayan K.

Ongoing fretting fatigue research has focussed on developing robust contact mechanics solutions for complicated load histories involving normal, shear, moment and bulk loads. For certain indenter profiles and applied loads, the contact patch separates into two disconnected regions. Existing Singular Integral Equation (SIE) techniques do not address these situations. A fast numerical tool is developed to solve such problems for similar elastic materials for a wide range of profiles and load paths including applied moments and remote bulk-stress effects. This tool is then used to investigate two problems in double contacts. The first, to determine the shear configuration space for a biquadratic punch for the generalized Cattaneo-Mindlin problem. The second, to obtain quantitative estimates of the interaction between neighboring cylindrical contacts for both the applied normal load and partial slip problems up to the limits of validity of the halfspace assumption. In double contact problems without symmetry, obtaining a unique solution requires the satisfaction of a condition relating the contact ends, rigid-body rotation and profile function. This condition has the interpretation that a rigid-rod connecting the inner contact ends of an equivalent frictionless double contact of a rigid indenter and halfspace may only undergo rigid body motions. It is also found that the ends of stick-zones, local slips and remote-applied strains in double contact problems are related by an equation expressing tangential surface-displacement continuity. This equation is essential to solve partial-slip problems without contact equivalents. Even when neighboring cylindrical contacts may be treated as non-interacting for the purpose of determining the pressure tractions, this is not generally true if a shear load is applied. The mutual influence of neighboring contacts in partial slip problems is largest at small shear load fractions. For both the pressure and partial slip problems, the interactions are stronger with increasing strength of loading and contact proximity. A new contact algorithm is developed and the SIE method extended to tackle contact problems with an arbitrary number of contact patches with no approximations made about contact interactions. In the case of multiple contact problems determining the correct contact configuration is significantly more complicated than in double contacts, necessitating a new approach. Both the normal contact and partial slip problems are solved. The tool is then used to study contacts of regular rough cylinders, a flat with rounded punch with superimposed sinusoidal roughness and is also applied to analyze the contact of an experimental rough surface with a halfspace. The partial slip results for multiple-contacts are generally consistent with Cattaneo-Mindlin continuum scale results, in that the outermost contacts tend to be in full sliding. Lastly, the influence of plasticity on frictionless multiple contact problems is studied using FEM for two common steel and aluminum alloys. The key findings are that the plasticity decreases the peak pressure and increases both real and apparent contact areas, thus 'blunting' the sharp pressures caused by the contact asperities in pure elasticity. Further, it is found that contact plasticity effects and load for onset of first yield are strongly dependent on roughness amplitude, with higher plasticity effects and lower yield-onset load at higher roughness amplitudes.

Electron correlation and the self-interaction error of density functional theory

NASA Astrophysics Data System (ADS)

Polo, Victor; Kraka, Elfi; Cremer, Dieter

The self-interaction error (SIE) of commonly used DFT functionals has been systematically investigated by comparing the electron density distribution ρ( r ) generated by self-interaction corrected DFT (SIC-DFT) with a series of reference densities obtained by DFT or wavefunction theory (WFT) methods that cover typical electron correlation effects. Although the SIE of GGA functionals is considerably smaller than that of LDA functionals, it has significant consequences for the coverage of electron correlation effects at the DFT level of theory. The exchange SIE mimics long range (non-dynamic) pair correlation effects, and is responsible for the fact that the electron density of DFT exchange-only calculations resembles often that of MP4, MP2 or even CCSD(T) calculations. Changes in the electron density caused by SICDFT exchange are comparable with those that are associated with HF exchange. Correlation functionals contract the density towards the bond and the valence region, thus taking negative charge out of the van der Waals region where these effects are exaggerated by the influence of the SIE of the correlation functional. Hence, SIC-DFT leads in total to a relatively strong redistribution of negative charge from van der Waals, non-bonding, and valence regions of heavy atoms to the bond regions. These changes, although much stronger, resemble those obtained when comparing the densities of hybrid functionals such as B3LYP with the corresponding GGA functional BLYP. Hence, the balanced mixing of local and non-local exchange and correlation effects as it is achieved by hybrid functionals mimics SIC-DFT and can be considered as an economic way to include some SIC into standard DFT. However, the investigation shows also that the SIC-DFT description of molecules is unreliable because the standard functionals used were optimized for DFT including the SIE.

Quelle place pour l’anesthésie locorégionale chez les brûlés?

PubMed Central

Chaibdraa, A.; Medjelekh, M.S.; Saouli, A.; Bentakouk, M.C.

2015-01-01

Summary La pratique de l’anesthésie locorégionale chez les brûlés est limitée par de nombreux facteurs. Elle est considérée comme marginale dans l’approche multimodale du traitement de la douleur par excès de nociception. Ce travail rétrospectif, sur une période de 3 années, porte sur les anesthésies locorégionales (ALR) réalisées. Les résultats obtenus vont permettre, en regard de la rareté des données de la littérature, de formuler quelques suggestions sur la place de cette technique. Il a été recensé 634 ALR, dont 96% chez des adultes. Les membres inférieurs sont les plus concernés (76%). Des anesthésies rachidiennes ont été pratiquées chez 32 patients dont 4 enfants. Les incidents sont peu fréquents (3%) et sans gravité. L’ALR peut représenter une option utile dans la stratégie multimodale de prise en charge de la douleur, la réhabilitation passive précoce et la chirurgie de recouvrement par la greffe de peau. Elle mérite d’être explorée en ambulatoire, dans la mesure où 95% des brûlés ne sont pas hospitalisés. La place de l’anesthésie-locorégionale chez les brûlés devrait susciter plus d’intérêts, pour permettre d’établir des protocoles fondés sur une réflexion pluridisciplinaire. PMID:27279806

Redox Pioneer: Professor Helmut Sies

PubMed Central

Radi, Rafael

2014-01-01

Abstract Professor Helmut Sies Dr. Helmut Sies (MD, 1967) is recognized as a Redox Pioneer, because he authored five articles on oxidative stress, lycopene, and glutathione, each of which has been cited more than 1000 times, and coauthored an article on hydroperoxide metabolism in mammalian systems cited more than 5000 times (Google Scholar). He obtained preclinical education at the University of Tübingen and the University of Munich, clinical training at Munich (MD, 1967) and Paris, and completed Habilitation at Munich (Physiological Chemistry and Physical Biochemistry, 1972). In early research, he first identified hydrogen peroxide (H2O2) as a normal aerobic metabolite and devised a method to quantify H2O2 concentration and turnover in cells. He quantified central redox systems for energy metabolism (NAD, NADP systems) and antioxidant GSH in subcellular compartments. He first described ebselen, a selenoorganic compound, as a glutathione peroxidase mimic. He contributed a fundamental discovery to the physiology of GSH, selenium nutrition, singlet oxygen biochemistry, and health benefits of dietary lycopene and cocoa flavonoids. He has published more than 600 articles, 134 of which are cited at least 100 times, and edited 28 books. His h-index is 115. During the last quarter of the 20th century and well into the 21st, he has served as a scout, trailblazer, and pioneer in redox biology. His formulation of the concept of oxidative stress stimulated and guided research in oxidants and antioxidants; his pioneering research on carotenoids and flavonoids informed nutritional strategies against cancer, cardiovascular disease, and aging; and his quantitative approach to redox biochemistry provides a foundation for modern redox systems biology. Helmut Sies is a true Redox Pioneer. Antioxid. Redox Signal. 21, 2459–2468. The joy of exploring the unknown and finding something novel and noteworthy: what a privilege! —Prof. Helmut Sies PMID:25178739

Stein-Schere-Papier

NASA Astrophysics Data System (ADS)

Springborn, Boris

Wie gewinnt man im Spiel? Die Analyse von Strategien bei Gesellschaftsspielen ist ein Thema der mathematischen Spieltheorie. Mit ihren Methoden kann man aber nicht nur Spiele wie Schach oder Skat untersuchen, sondern auch verschiedenste Konfliktsituationen, bei denen das Schicksal jedes einzelnen Akteurs nicht nur vom eigenen Verhalten abhängt, sondern auch vom Verhalten der anderen, die ebenso wie er versuchen, ein für sie selbst möglichst positives Ergebnis herauszuschlagen. Die Spieltheorie hat großen Einfluss in den Wirtschaftswissenschaften. Auch in der Psychologie, Soziologie, Biologie und der Militärwissenschaft findet sie Anwendung. In der folgenden Aufgabe geht es aber tatsächlich um ein Spiel, und zwar um ein sehr einfaches, das jeder kennt. Trotzdem ist die Lösung nicht ganz einfach, und wer sie findet, hat schon die eine oder andere grundlegende Idee der Spieltheorie verstanden.

Teilchenphysik Pentaquarks - existieren sie wirklich?

NASA Astrophysics Data System (ADS)

Ziegler, Thomas

2005-07-01

Für viel Wirbel sorgte vor zwei Jahren die Entdeckung eines Pentaquarks, eines bis dahin unbekannten Teilchens, das aus vier Quarks und einem Antiquark besteht. Seitdem hat es jedoch Experimente gegeben, welche die Messung nicht bestätigen konnten. Physiker vom Jefferson-Laboratorium in den USA haben nun kürzlich die Ergebnisse eines Experimentes mit sehr hoher Statistik vorgestellt. Auch sie fanden das Pentaquark nicht. Gibt es das Teilchen also gar nicht?

On the relation between orbital-localization and self-interaction errors in the density functional theory treatment of organic semiconductors.

PubMed

Körzdörfer, T

2011-03-07

It is commonly argued that the self-interaction error (SIE) inherent in semilocal density functionals is related to the degree of the electronic localization. Yet at the same time there exists a latent ambiguity in the definitions of the terms "localization" and "self-interaction," which ultimately prevents a clear and readily accessible quantification of this relationship. This problem is particularly pressing for organic semiconductor molecules, in which delocalized molecular orbitals typically alternate with localized ones, thus leading to major distortions in the eigenvalue spectra. This paper discusses the relation between localization and SIEs in organic semiconductors in detail. Its findings provide further insights into the SIE in the orbital energies and yield a new perspective on the failure of self-interaction corrections that identify delocalized orbital densities with electrons. © 2011 American Institute of Physics.

Spatial and Temporal Means and Variability of Arctic Sea Ice Climate Indicators from Satellite Data

NASA Astrophysics Data System (ADS)

Peng, G.; Meier, W.; Bliss, A. C.; Steele, M.; Dickinson, S.

2017-12-01

Arctic sea ice has been undergoing rapid and accelerated loss since satellite-based measurements became available in late 1970s, especially the summer ice coverage. For the Arctic as a whole, the long-term trend for the annual sea ice extent (SIE) minimum is about -13.5±2.93 % per decade change relative to the 1979-2015 climate average, while the trends of the annual SIE minimum for the local regions can range from 0 to up to -42 % per decade. This presentation aims to examine and baseline spatial and temporal means and variability of Arctic sea ice climate indicators, such as the annual SIE minimum and maximum, snow/ice melt onset, etc., from a consistent, inter-calibrated, long-term time series of remote sensing sea ice data for understanding regional vulnerability and monitoring ice state for climate adaptation and risk mitigation.

Flight Screening Program Effects on Attrition in Undergraduate Pilot Training

DTIC Science & Technology

1987-08-01

the final fiveý lesson grades (8-12), suggesting that a UPT screening decision could be made at an earl~er stage of FSP than is the current practice...Does FSP Provide An Opportunity For SIE? ....... .... 6 Training/EAperience Effects of FS?: Does the FSP Give a Training/ Experience Benefit in UPT...effect. FSP Screening: Does FSP Provide an Opportunity for SIE? Some individuals who have had no previous flying experience (other than as passengers) may

Bellingshausen Sea Ice Extent Recorded in an Antarctic Peninsula Ice Core

NASA Technical Reports Server (NTRS)

Porter, Stacy E.; Parkinson, Claire L.; Mosley-Thompson, Ellen

2016-01-01

Annual net accumulation (A(sub n)) from the Bruce Plateau (BP) ice core retrieved from the Antarctic Peninsula exhibits a notable relationship with sea ice extent (SIE) in the Bellingshausen Sea. Over the satellite era, both BP A(sub n) and Bellingshausen SIE are influenced by large-scale climatic factors such as the Amundsen Sea Low, Southern Annular Mode, and Southern Oscillation. In addition to the direct response of BP A(sub n) to Bellingshausen SIE (e.g., more open water as a moisture source), these large-scale climate phenomena also link the BP and the Bellingshausen Sea indirectly such that they exhibit similar responses (e.g., northerly wind anomalies advect warm, moist air to the Antarctic Peninsula and neighboring Bellingshausen Sea, which reduces SIE and increases A(sub n)). Comparison with a time series of fast ice at South Orkney Islands reveals a relationship between BP A(sub n) and sea ice in the northern Weddell Sea that is relatively consistent over the twentieth century, except when it is modulated by atmospheric wave patterns described by the Trans-Polar Index. The trend of increasing accumulation on the Bruce Plateau since approximately 1970 agrees with other climate records and reconstructions in the region and suggests that the current rate of sea ice loss in the Bellingshausen Sea is unrivaled in the twentieth century.

Astronomie, écologie et poésie par Hubert Reeves

DOE Office of Scientific and Technical Information (OSTI.GOV)

None

2010-09-21

Hubert ReevesL'astrophysicien donne une conférence puis s'entretient avec l'écrivain François Bon autour de :"Astronomie, écologie et poésie"Pour plus d'informations : http://outreach.web.cern.ch/outreach/FR/evenements/conferences.htmlNombre de places limité. Réservation obligatoire à la Réception du CERN : +41 22 767 76 76  Soirée diffusée en direct sur le Web : http://webcast.cern.ch/      

Une fistule recto-vaginale rentrant dans le cadre d'un syndrome de Currarino

PubMed Central

Idrissi, Mounia Lakhdar; Babakhoya, Abdeladim; Bouabdellah, Youssef; Hida, Mostapha

2011-01-01

Le syndrome de Currarino (SC) est défini par une triade rassemblant une malformation ano-rectale, une agénésie sacrée et une tumeur pré-sacrée. Nous rapportons le cas d'une fille de 4 ans et demi ayant été admise en consultation de gastro-entérologie pédiatrique pour constipation avec issue de selle à travers un orifice vulvaire. La radiographie du rachis avait montré une agénésie sacrée. Le fistulo-scanner a mis en évidence une fistule recto-vaginale et l'IRM pelvienne a confirmé l'agénésie sacrée et a retrouvé une méningocèle antérieure. La découverte d'une malformation ano-rectale doit faire chercher une autre anomalie de la triade de Currarino. Cette affection, rare, nécessite une prise en charge médico-chirurgicale assez complexe. PMID:22384297

Characteristic hydrolyzing of megalosaccharide by human salivary α-amylase and small intestinal enzymes, and its bioavailability in healthy subjects.

PubMed

Nakamura, Sadako; Takami, Masayuki; Tanabe, Kenichi; Oku, Tsuneyuki

2014-09-01

The digestibility of Megalosaccharide® (newly developed carbohydrate comprising α-1,4-glucosaccharide) was investigated in vitro and in vivo. Isomaltosyl-megalosaccharide® (IMS) and nigerosyl-megalosaccharide® (NMS) contain 20% and 50% of the megalosaccharide fraction (degree of polymerization (DP) 10-35), respectively. IMS was hydrolyzed readily by α-amylase to oligosaccharides (DP ≤ 7), and a small amount of glucose was produced from oligosaccharides by small intestinal enzymes (SIEs). NMS was partially hydrolyzed by α-amylase to oligosaccharides, and a small amount of glucose produced by SIEs. When IMS and NMS were treated by SIEs after treatment with human saliva α-amylase for a few minutes, IMS and NMS were hydrolyzed readily to glucose. Plasma levels of glucose and insulin upon ingestion of 50 g of IMS or NMS were elevated the same as those for 50 g of glucose, and breath hydrogen was not excreted. These results suggest that IMS and NMS are digestible carbohydrates.

Theoretische Konzepte der Physik

NASA Astrophysics Data System (ADS)

Longair, Malcolm S.; Simon, B.; Simon, H.

"Dies ist kein Lehrbuch der theoretischen Physik, auch kein Kompendium der Physikgeschichte ... , vielmehr eine recht anspruchsvolle Sammlung historischer Miniaturen zur Vergangenheit der theoretischen Physik - ihrer "Sternstunden", wenn man so will. Frei vom Zwang, etwas Erschöpfendes vorlegen zu müssen, gelingt dem Autor etwas Seltenes: einen "lebendigen" Zugang zum Ideengebäude der modernen Physik freizulegen, ... zu zeigen, wie Physik in praxi entsteht... Als Vehikel seiner Absichten dienen dem Autor geschichtliche Fallstudien, insgesamt sieben an der Zahl. Aus ihnen extrahiert er das seiner Meinung nach Lehrhafte, dabei bestrebt, mathematische Anachronismen womöglich zu vermeiden... Als Student hätte ich mir diese gescheiten Essays zum Werden unserer heutigen physikalischen Weltsicht gewünscht. Sie sind originell, didaktisch klug und genieren sich auch nicht, von der Faszination zu sprechen, die ... von der Physik ausgeht. Unnötig darauf hinzuweisen, das sie ein gründliches "konventionelles" Studium weder ersetzen wollen noch können, sie vermögen aber, dazu zu ermuntern." #Astronomische Nachrichten (zur englischen Ausgabe)#1

Data-adaptive Harmonic Decomposition and Real-time Prediction of Arctic Sea Ice Extent

NASA Astrophysics Data System (ADS)

Kondrashov, Dmitri; Chekroun, Mickael; Ghil, Michael

2017-04-01

Decline in the Arctic sea ice extent (SIE) has profound socio-economic implications and is a focus of active scientific research. Of particular interest is prediction of SIE on subseasonal time scales, i.e. from early summer into fall, when sea ice coverage in Arctic reaches its minimum. However, subseasonal forecasting of SIE is very challenging due to the high variability of ocean and atmosphere over Arctic in summer, as well as shortness of observational data and inadequacies of the physics-based models to simulate sea-ice dynamics. The Sea Ice Outlook (SIO) by Sea Ice Prediction Network (SIPN, http://www.arcus.org/sipn) is a collaborative effort to facilitate and improve subseasonal prediction of September SIE by physics-based and data-driven statistical models. Data-adaptive Harmonic Decomposition (DAH) and Multilayer Stuart-Landau Models (MSLM) techniques [Chekroun and Kondrashov, 2017], have been successfully applied to the nonlinear stochastic modeling, as well as retrospective and real-time forecasting of Multisensor Analyzed Sea Ice Extent (MASIE) dataset in key four Arctic regions. In particular, DAH-MSLM predictions outperformed most statistical models and physics-based models in real-time 2016 SIO submissions. The key success factors are associated with DAH ability to disentangle complex regional dynamics of MASIE by data-adaptive harmonic spatio-temporal patterns that reduce the data-driven modeling effort to elemental MSLMs stacked per frequency with fixed and small number of model coefficients to estimate.

Nichtperiodische zeitkontinuierliche Signale

NASA Astrophysics Data System (ADS)

Plaßmann, Wilfried

Nichtperiodische Signale haben eine große Bedeutung für die Nachrichten- und Datenübertragung, weil Information nur in nichtdeterministischen Signalen enthalten ist (Teil "Nachrichtentechnik", Abschn. 92.4.1). Aber auch für die Energie- und Regelungstechnik sind sie von Interesse, weil sie entweder Ein- und Ausschaltvorgänge erfassen oder den Übergang von einem momentan stationären Zustand in einen neuen darstellen (Kurzschluss im Energieversorgungsnetz, Auftreten einer Störgröße im Regelsystem). Die Fourier- und die Laplacetransformation können bei nichtperiodischen zeitkontinuierlichen Signalen eingesetzt werden.

Astronomie, écologie et poésie par Hubert Reeves

ScienceCinema

None

2017-12-09

Hubert ReevesL'astrophysicien donne une conférence puis s'entretient avec l'écrivain François Bon autour de :"Astronomie, écologie et poésie"Pour plus d'informations : http://outreach.web.cern.ch/outreach/FR/evenements/conferences.htmlNombre de places limité. Réservation obligatoire à la Réception du CERN : +41 22 767 76 76  Soirée diffusée en direct sur le Web : http://webcast.cern.ch/      

Exercise-intensity dependent alterations in plasma redox status do not reflect skeletal muscle redox-sensitive protein signaling.

PubMed

Parker, Lewan; Trewin, Adam; Levinger, Itamar; Shaw, Christopher S; Stepto, Nigel K

2018-04-01

Redox homeostasis and redox-sensitive protein signaling play a role in exercise-induced adaptation. The effects of sprint-interval exercise (SIE), high-intensity interval exercise (HIIE) and continuous moderate-intensity exercise (CMIE), on post-exercise plasma redox status are unclear. Furthermore, whether post-exercise plasma redox status reflects skeletal muscle redox-sensitive protein signaling is unknown. In a randomized crossover design, eight healthy adults performed a cycling session of HIIE (5×4min at 75% W max ), SIE (4×30s Wingate's), and CMIE work-matched to HIIE (30min at 50% of W max ). Plasma hydrogen peroxide (H 2 O 2 ), thiobarbituric acid reactive substances (TBARS), superoxide dismutase (SOD) activity, and catalase activity were measured immediately post, 1h, 2h and 3h post-exercise. Plasma redox status biomarkers were correlated with phosphorylation of skeletal muscle p38-MAPK, JNK, NF-κB, and IκBα protein content immediately and 3h post-exercise. Plasma catalase activity was greater with SIE (56.6±3.8Uml -1 ) compared to CMIE (42.7±3.2, p<0.01) and HIIE (49.0±5.5, p=0.07). Peak plasma H 2 O 2 was significantly (p<0.05) greater after SIE (4.6±0.6nmol/ml) and HIIE (4.1±0.4) compared to CMIE (3.3±0.5). Post-exercise plasma TBARS and SOD activity significantly (p<0.05) decreased irrespective of exercise protocol. A significant positive correlation was detected between plasma catalase activity and skeletal muscle p38-MAPK phosphorylation 3h post-exercise (r=0.40, p=0.04). No other correlations were detected (all p>0.05). Low-volume SIE elicited greater post-exercise plasma catalase activity compared to HIIE and CMIE, and greater H 2 O 2 compared to CMIE. Plasma redox status did not, however, adequately reflect skeletal muscle redox-sensitive protein signaling. Copyright © 2017 Sports Medicine Australia. Published by Elsevier Ltd. All rights reserved.

Influence of Ar addition on ozone generation in a non-thermal plasma—a numerical investigation

NASA Astrophysics Data System (ADS)

Chen, Hsin Liang; Lee, How Ming; Chen, Shiaw Huei; Wei, Ta Chin; Been Chang, Moo

2010-10-01

A numerical model based on a dielectric barrier discharge is developed in this study to investigate the influence of Ar addition on ozone generation. The simulation results show good agreement with the experimental data, confirming the validity of the numerical model. The mechanisms regarding how the Ar addition affects ozone generation are investigated with the assistance of a numerical simulation by probing into the following two questions, (1) why the ozone concentration just slightly decreases in the low specific input energy (SIE, the ratio of discharge power to gas flow rate) region even if the inlet O2 concentration is substantially decreased and (2) why the variation of the increased rate of ozone concentration with SIE (i.e. the variation in the slope of ozone concentration versus SIE) is more significant for an O2/Ar mixture plasma. As SIE is relatively low, ozone decomposition through electron-impact and radical attack reactions is less significant because of low ozone concentration and gas temperature. Therefore, the ozone concentration depends mainly on the amount of oxygen atoms generated. The simulation results indicate that the amount of oxygen atoms generated per electronvolt for Ar concentrations of 0%, 10%, 30%, 50% and 80% are 0.178, 0.174, 0.169, 0.165 and 0.166, respectively, explaining why the ozone concentration does not decrease linearly with the inlet O2 concentration in the low SIE region. On the other hand, the simulation results show that increasing Ar concentration would lead to a lower reduced field and a higher gas temperature. The former would lead to an increase in the rate constant of e + O3 → e + O + O2 while the latter would result in a decrease in the rate constant of O + O2 + M → O3 + M and an increase in that of O3 + O → 2O2. The changes in the rate constants of these reactions would have a negative effect on ozone generation, which is the rationale for the second question.

Seasonal regional forecast of the minimum sea ice extent in the LapteV Sea

NASA Astrophysics Data System (ADS)

Tremblay, B.; Brunette, C.; Newton, R.

2017-12-01

Late winter anomaly of sea ice export from the peripheral seas of the Atctic Ocean was found to be a useful predictor for the minimum sea ice extent (SIE) in the Arctic Ocean (Williams et al., 2017). In the following, we present a proof of concept for a regional seasonal forecast of the min SIE for the Laptev Sea based on late winter coastal divergence quantified using a Lagrangian Ice Tracking System (LITS) forced with satellite derived sea-ice drifts from the Polar Pathfinder. Following Nikolaeva and Sesterikov (1970), we track an imaginary line just offshore of coastal polynyas in the Laptev Sea from December of the previous year to May 1 of the following year using LITS. Results show that coastal divergence in the Laptev Sea between February 1st and May 1st is best correlated (r = -0.61) with the following September minimum SIE in accord with previous results from Krumpen et al. (2013, for the Laptev Sea) and Williams et a. (2017, for the pan-Arctic). This gives a maximum seasonal predictability of Laptev Sea min SIE anomalies from observations of approximately 40%. Coastal ice divergence leads to formation of thinner ice that melts earlier in early summer, hence creating areas of open water that have a lower albedo and trigger an ice-albedo feedback. In the Laptev Sea, we find that anomalies of coastal divergence in late winter are amplified threefold to result in the September SIE. We also find a correlation coefficient r = 0.49 between February-March-April (FMA) anomalies of coastal divergence with the FMA averaged AO index. Interestingly, the correlation is stronger, r = 0.61, when comparing the FMA coastal divergence anomalies to the DJFMA averaged AO index. It is hypothesized that the AO index at the beginning of the winter (and the associated anomalous sea ice export) also contains information that impact the magnitude of coastal divergence opening later in the winter. Our approach differs from previous approaches (e.g. Krumpen et al and Williams et al) in that the coastal divergence is quantified directly by following the edge of the mobile pack ice in a Lagrangian manner.

Qualitätsmanagement in molekularbiologischen Laboratorien

NASA Astrophysics Data System (ADS)

Schulze, Manuela

Jedes Laboratorium führt Untersuchungen nach bestem Wissen und Gewissen durch, und jeder Analytiker weiß von sich, dass er/sie gute Arbeit macht. Trotzdem können Analysen des gleichen Probenmaterials in verschiedenen Laboren zu unterschiedlichen Ergebnissen führen. Sofern es sich dabei nicht um Untersuchungen im Bereich der Nachweisgrenze und damit letztlich um statistisch bedingte Unterschiede oder Inhomogenitäten im Probenmaterial handelt, trägt dies nicht zur Vertrauenswürdigkeit von analytischen Untersuchungsergebnissen bei. Mit der zunehmenden Globalisierung der Märkte rückt die gegenseitige Anerkennung von analytischen Resultaten immer stärker in den Vordergrund. Die Vergleichbarkeit von Laborresultaten wird erleichtert, wenn sich die Laboratorien auf die gleichen Richtlinien zur Vorgehensweise und Handhabung ihrer Arbeiten verständigen. Im Bereich der Laboruntersuchungen von Lebensmitteln, Futtermitteln und Saatgut ist als derartige Rischt-Schnur die EN ISO/IEC 17025 [1] anerkannt. Diese Norm enthält alle Anforderungen, die Prüflaboratorien erfüllen müssen, wenn sie nachweisen wollen, dass sie ein Qualitätsmanagementsystem betreiben, technisch (meint: fachlich) kompetent und fähig sind, fachlich fundierte Ergebnisse zu erzielen.

Meilensteine in der Erforschung der kompakten Objekte

NASA Astrophysics Data System (ADS)

Camenzind, Max

Kompakte Objekte besitzen zum einen eine sehr hohe Dichte, und zum anderen sind sie durch die Tatsache charakterisiert, dass keine nuklearen Reaktionen mehr in ihrem Inneren stattfinden können. Aus diesem Grund können sie im Unterschied zu gewöhnlichen Sternen der Gravitation nicht mehr mit dem Druck des thermischen Gases widerstehen. In den Weißen Zwergen bzw. Neutronensternen wird der Gravitation der Quantendruck eines Elektronengases bzw. einer Neutronenflüssigkeit entgegengesetzt. Ein solches Gas besteht aus Elektronen bzw. Neutronen, die auf ihr niedrigstes Energieniveau zusammengepresst wurden. Durch die daraus resultierende hohe Bewegungsenergie der Fermionen wird der sogenannte Quantendruck erzeugt.

Terror mit Atomwaffen: reale Gefahr? Nukleare und Radiologische Waffen

NASA Astrophysics Data System (ADS)

Harigel, Gert G.

2006-01-01

Können Terroristen sich nukleare Massenvernichtungswaffen beschaffen? Dazu müssten sie ausreichende Mengen an waffenfähigem, spaltbarem Material stehlen. Selbst der Bau einer primitiven Atombombe erfordert einen hohen technischen Aufwand und Spezialisten. Wahrscheinlicher ist deshalb der Diebstahl einer kleinen taktischen Kernwaffe. Alternativ könnten Terroristen sich radioaktives Material aus zivilen Quellen beschaffen und daraus eine Schmutzige Bombe bauen. Eine solche radiologische Waffe wäre keine echte Massenvernichtungswaffe, doch ihre psychologische Wirkung könnte stark sein. Das macht sie für Terroristen attraktiv, weswegen diese Gefahr ernst genommen werden muss.

Chips aus Plastik: Organische Elektronik

NASA Astrophysics Data System (ADS)

Kiy, Michael

2003-01-01

Künstliche organische Materialien werden in Zukunft vermehrt in der Elektronik eingesetzt werden. Obwohl sie gute Isolatoren sind, kann ein ausreichend großes elektrisches Feld in ihnen einen elektrischen Strom fließen lassen. Dazu injizieren Metallelektroden freie Ladungsträger wie Elektronen oder Löcher in das organische Material. Diese Ladungsträgerinjektion kann die elektrischen Eigenschaften geeigneter organischer Materialien vom Isolator bis zum Leiter steuern. Eine zukünftige Domäne solcher Kunststoffe werden einfache, billige Chips sein. Bei den Displays könnten sie bald die konventionellen Flüssigkristallanzeigen technisch überflügeln.

Does father-child conflict mediate the association between fathers' postnatal depressive symptoms and children's adjustment problems at 7 years old?

PubMed

Nath, S; Russell, G; Kuyken, W; Psychogiou, L; Ford, T

2016-06-01

Paternal depressive symptoms are associated with children's emotional and behavioural problems, which may be mediated by negative parenting. But there is no research on the influence of paternal depressive symptoms on children's emotion regulation and limited literature investigating fathers' parenting as a mediator in the pathway between paternal depressive symptoms and children's externalizing and internalizing problems. We aimed to investigate the mediating role of father-child conflict (at 3 years) in the association between postnatal paternal depressive symptoms (at 9 months) and children's emotional and behavioural problems (at 7 years) (aim 1). We also examined whether mediation pathways were more pronounced for boys or for girls (aim 2). Secondary data analysis was conducted on the Millennium Cohort Study, when children were 9 months, 3 years and 7 years old (n = 3520). Main study variables were measured by self-report questionnaires. Fathers completed the Rutter Scale (depressive symptoms) and the Parent-Child Relationship Questionnaire (father-child conflict), while mothers completed the Strengths and Difficulties Questionnaire and the Social Behaviour Questionnaire (child emotional and behavioural problems, emotion regulation). We used structural equation modelling to estimate direct, indirect and total effects of paternal depressive symptoms on child outcomes, mediated by father-child conflict whilst adjusting for relevant covariates (maternal depressive symptoms, child temperament, marital conflict, and socio-economic factors such as poverty indicator and fathers' education level). Multi-group and interaction analysis was then conducted to determine the differential effect by gender of the association between paternal depressive symptoms on child outcomes via father-child conflict. Father-child conflict mediated the association between paternal depressive symptoms and emotion regulation problems [standardized indirect effect (SIE) 95% confidence interval (CI) -0.03 to -0.01, p < 0.001; standardized total effect (STE) 95% CI -0.05 to -0.01, p < 0.05] (aim 1). Father-child conflict mediated a larger proportion of the effect in boys (SIE 95% CI -0.03 to -0.01, p < 0.001; STE 95% CI -0.05 to 0.00, p = 0.063) than it did in girls (SIE 95% CI -0.02 to -0.01, p < 0.001; STE 95% CI -0.04 to 0.01, p = 0.216) (aim 2). Father-child conflict may mediate the association between postnatal paternal depressive symptoms and children's emotion regulation problems. Paternal depressive symptoms and father-child conflict resolution may be potential targets in preventative interventions.

On the Impurity Parameters for Impurities Detected in the Eutectics Co-C and Pt-C and Their Role in the Estimate of the Uncertainty in the Eutectic Temperatures

NASA Astrophysics Data System (ADS)

Bloembergen, Pieter; Dong, Wei; Bai, Cheng-Yu; Wang, Tie-Jun

2011-12-01

In this paper, impurity parameters m i and k i have been calculated for a range of impurities I as detected in the eutectics Co-C and Pt-C, by means of the software package Thermo-Calc within the ternary phase spaces Co-C- I and Pt-C- I. The choice of the impurities is based upon a selection out of the results of impurity analyses performed for a representative set of samples for each of the eutectics in study. The analyses in question are glow discharge mass spectrometry (GDMS) or inductively coupled plasma mass spectrometry (ICP-mass). Tables and plots of the impurity parameters against the atomic number Z i of the impurities will be presented, as well as plots demonstrating the validity of van't Hoff's law, the cornerstone to this study, for both eutectics. For the eutectics in question, the uncertainty u( T E - T liq ) in the correction T E - T liq will be derived, where T E and T liq refer to the transition temperature of the pure system and to the liquidus temperature in the limit of zero growth rate of the solid phase during solidification of the actual system, respectively. Uncertainty estimates based upon the current scheme SIE-OME, combining the sum of individual estimates (SIE) and the overall maximum estimate (OME) are compared with two alternative schemes proposed in this paper, designated as IE-IRE, combining individual estimates (IE) and individual random estimates (IRE), and the hybrid scheme SIE-IE-IRE, combining SIE, IE, and IRE.

The Impact of Stratospheric Circulation Extremes on Minimum Arctic Sea Ice Extent

NASA Astrophysics Data System (ADS)

Smith, K. L.; Polvani, L. M.; Tremblay, B.

2017-12-01

The interannual variability of summertime Arctic sea ice extent (SIE) is anti-correlated with the leading mode of extratropical atmospheric variability in preceding winter, the Arctic Oscillation (AO). Given this relationship and the need for better seasonal predictions of Arctic SIE, we here examine the role of stratospheric circulation extremes and stratosphere-troposphere coupling in linking the AO and Arctic SIE variability. We show that extremes in the stratospheric circulation during the winter season, namely stratospheric sudden warming (SSW) and strong polar vortex (SPV) events, are associated with significant anomalies in sea ice concentration in the Bering Straight and the Sea of Okhotsk in winter, the Barents Sea in spring and along the Eurasian coastline in summer in both observations and a fully-coupled, stratosphere-resolving general circulation model. The accompanying figure shows the composite mean sea ice concentration anomalies from the Whole Atmosphere Community Climate Model (WACCM) for SSWs (N = 126, top row) and SPVs (N = 99, bottom row) for winter (a,d), spring (b,e) and summer (c,f). Consistent with previous work on the AO, we find that SSWs, which are followed by the negative phase of the AO at the surface, result in sea ice growth, whereas SPVs, which are followed by the positive phase of the AO at the surface, result in sea ice loss, although the dynamic and thermodynamic processes driving these sea ice anomalies in the three Arctic regions, noted above, are different. Our analysis suggests that the presence or absence of stratospheric circulation extremes in winter may play a non-trivial role in determining total September Arctic SIE when combined with other factors.

Binding pose and affinity prediction in the 2016 D3R Grand Challenge 2 using the Wilma-SIE method

NASA Astrophysics Data System (ADS)

Hogues, Hervé; Sulea, Traian; Gaudreault, Francis; Corbeil, Christopher R.; Purisima, Enrico O.

2018-01-01

The Farnesoid X receptor (FXR) exhibits significant backbone movement in response to the binding of various ligands and can be a challenge for pose prediction algorithms. As part of the D3R Grand Challenge 2, we tested Wilma-SIE, a rigid-protein docking method, on a set of 36 FXR ligands for which the crystal structures had originally been blinded. These ligands covered several classes of compounds. To overcome the rigid protein limitations of the method, we used an ensemble of publicly available structures for FXR from the PDB. The use of the ensemble allowed Wilma-SIE to predict poses with average and median RMSDs of 2.3 and 1.4 Å, respectively. It was quite clear, however, that had we used a single structure for the receptor the success rate would have been much lower. The most successful predictions were obtained on chemical classes for which one or more crystal structures of the receptor bound to a molecule of the same class was available. In the absence of a crystal structure for the class, observing a consensus binding mode for the ligands of the class using one or more receptor structures of other classes seemed to be indicative of a reasonable pose prediction. Affinity prediction proved to be more challenging with generally poor correlation with experimental IC50s (Kendall tau 0.3). Even when the 36 crystal structures were used the accuracy of the predicted affinities was not appreciably improved. A possible cause of difficulty is the internal energy strain arising from conformational differences in the receptor across complexes, which may need to be properly estimated and incorporated into the SIE scoring function.

Ozone synthesis improves by increasing number density of plasma channels and lower voltage in a nonthermal plasma

NASA Astrophysics Data System (ADS)

Arif Malik, Muhammad; Hughes, David

2016-04-01

Improvements in ozone synthesis from air and oxygen by increasing the number density of plasma channels and lower voltage for the same specific input energy (SIE) were explored in a nonthermal plasma based on a sliding discharge. The number of plasma channels and energy per pulse increased in direct proportion to the increase in the effective length of the anode (the high voltage electrode). Decreasing the discharge gap increased the energy per pulse for the same length and allowed the installation of more electrode pairs in the same space. It allowed the increase of the number of plasma channels in the same space to achieve the same SIE at a lower peak voltage with less energy per plasma channel. The ozone concentration gradually increased to ~1500 ppmv (140 to 50 g kWh-1) from air and to ~6000 ppmv (400 to 200 g kWh-1) from oxygen with a gradual increase in the SIE to ~200 J L-1, irrespective of the variations in electrode geometry, applied voltage or flow rate of the feed gas. A gradual increase in SIE beyond 200 J L-1 gradually increased the ozone concentration to a certain maximum value followed by a decline, but the rate of increase and the maximum value was higher for the greater number of plasma channels and lower peak voltage combination. The maximum ozone concentration was ~5000 ppmv (~30 g kWh-1) from air and ~22 000 ppmv (~80 g kWh-1) from oxygen. The results are explained on the basis of characteristics of the plasma and ozone synthesis mechanism.

Method of mechanical quadratures for solving singular integral equations of various types

NASA Astrophysics Data System (ADS)

Sahakyan, A. V.; Amirjanyan, H. A.

2018-04-01

The method of mechanical quadratures is proposed as a common approach intended for solving the integral equations defined on finite intervals and containing Cauchy-type singular integrals. This method can be used to solve singular integral equations of the first and second kind, equations with generalized kernel, weakly singular equations, and integro-differential equations. The quadrature rules for several different integrals represented through the same coefficients are presented. This allows one to reduce the integral equations containing integrals of different types to a system of linear algebraic equations.

The physics of aerobreakup. IV. Strain-thickening liquids

NASA Astrophysics Data System (ADS)

Mitkin, V. V.; Theofanous, T. G.

2017-12-01

We extend our previous work on aerobreakup of Newtonian and viscoelastic-liquid drops to liquids of dense nanoparticle suspensions with strain-thickening rheology. As in the previous work, the scope includes the full range of aerodynamics, from near-incompressible to supersonic flows, covering all regimes of aerobreakup and employing laser-induced-fluorescence visualizations with μs/μm resolutions. The key physics of Rayleigh-Taylor piercing (1st criticality), Shear-Induced Entrainment (SIE, 2nd criticality), and Kelvin-Helmholtz SIE (3rd criticality) are verified and quantified on the same scaling/theoretical approach as in our previous work but with modifications that account for the rheology of these liquids.

The STAT3 HIES mutation is a gain-of-function mutation that activates genes via AGG-element carrying promoters.

PubMed

Xu, Li; Ji, Jin-Jun; Le, Wangping; Xu, Yan S; Dou, Dandan; Pan, Jieli; Jiao, Yifeng; Zhong, Tianfei; Wu, Dehong; Wang, Yumei; Wen, Chengping; Xie, Guan-Qun; Yao, Feng; Zhao, Heng; Fan, Yong-Sheng; Chin, Y Eugene

2015-10-15

Cytokine or growth factor activated STAT3 undergoes multiple post-translational modifications, dimerization and translocation into nuclei, where it binds to serum-inducible element (SIE, 'TTC(N3)GAA')-bearing promoters to activate transcription. The STAT3 DNA binding domain (DBD, 320-494) mutation in hyper immunoglobulin E syndrome (HIES), called the HIES mutation (R382Q, R382W or V463Δ), which elevates IgE synthesis, inhibits SIE binding activity and sensitizes genes such as TNF-α for expression. However, the mechanism by which the HIES mutation sensitizes STAT3 in gene induction remains elusive. Here, we report that STAT3 binds directly to the AGG-element with the consensus sequence 'AGG(N3)AGG'. Surprisingly, the helical N-terminal region (1-355), rather than the canonical STAT3 DBD, is responsible for AGG-element binding. The HIES mutation markedly enhances STAT3 AGG-element binding and AGG-promoter activation activity. Thus, STAT3 is a dual specificity transcription factor that promotes gene expression not only via SIE- but also AGG-promoter activity. © The Author(s) 2015. Published by Oxford University Press on behalf of Nucleic Acids Research.

Syndrome coronarien aigue suite à une injection accidentelle intraveineuse de Bupivacaine

PubMed Central

Koita, Siriman Abdoulaye; Bouhabba, Najib; Salaheddine, Fjouji; Bensghir, Mustapha; Charki, Haimeur

2015-01-01

Les erreurs médicamenteuses constituent une complication très redoutable en anesthésie. La fréquence des erreurs médicamenteuses par administration serait de l'ordre 1/10 000 à 1/1000. Nous rapportons un cas d'injection accidentelle de bupivacaine en intraveineuse directe. Il s'agissait d'un jeune patient classé ASA I qui était prévu pour cure chirurgicale d'une hydrocèle unilatérale sous rachianesthésie. Une injection de 12,5 mg de bupivacaine et 25 µg de fentanyl étaient injectés après un reflux net du liquide céphalorachidien sans incident. Après installation de la rachianesthésie, le début de l'intervention était autorisé sans incidents. Une sédation de confort était décidée. Juste après apparaissait des troubles de rythme à type tachycardie ventriculaire avec une élévation de taux de troponines en post opératoire. L’évolution était marquée par une normalisation de la troponine au troisième jour post opératoire et sorti de l'hôpital au cinquième jour. PMID:26889325

Wissenschaft, die unsere Kultur verändert. Tiefenschichten des Streits um die Evolutionstheorie

NASA Astrophysics Data System (ADS)

Patzelt, Werner J.

Die Evolutionstheorie ist eine der erfolgreichsten wissenschaftlichen Theorien. Sie erlaubt es, unsere Herkunft zu verstehen und riskante Merkmale gerade der menschlichen Spezies zu begreifen. Zugleich ist die Evolutionstheorie eine der umstrittensten Theorien. Das liegt nicht an ihrer empirischen Tragfähigkeit, sondern an ihrem Gegenstand. Sie handelt nämlich nicht nur - wie Hunderte andere wissenschaftliche Theorien - von der "Welt da draußen“, sondern vor allem auch von uns selbst und von unserem Platz in dieser Welt. Den einen gilt sie obendrein als Überwinderin religiösen Aberglaubens, den anderen als neuer Zugang zu Gott und seinem Wirken in der Welt. Ferner sehen die einen in der Evolution eine unbezweifelbare Tatsache gleich der Schwerkraft oder dem Holocaust, die anderen aber eine - noch oder dauerhaft - unbewiesene Hypothese oder gar eine falsche Schöpfungslehre. Und während die meisten Streitfragen solcher Art nach wechselseitig akzeptierten Regeln ‚normaler Wissenschaft‘ geklärt werden, wird bei der Frage nach dem Woher unserer Spezies und Kultur die intellektuelle Zuständigkeit von Wissenschaft mitunter überhaupt bezweifelt. Anscheinend geht es schon um recht tiefe Schichten unserer Kultur und nicht nur der wissenschaftlichen, wenn - wie seit 150 Jahren - um die Evolutionstheorie gestritten wird. Wie sehen diese Schichten aus?

Performance and economic evaluation of the molecular detection of pathogens for patients with severe infections: the EVAMICA open-label, cluster-randomised, interventional crossover trial.

PubMed

Cambau, Emmanuelle; Durand-Zaleski, Isabelle; Bretagne, Stéphane; Brun-Buisson, Christian; Cordonnier, Catherine; Duval, Xavier; Herwegh, Stéphanie; Pottecher, Julien; Courcol, René; Bastuji-Garin, Sylvie

2017-11-01

Microbiological diagnosis (MD) of infections remains insufficient. The resulting empirical antimicrobial therapy leads to multidrug resistance and inappropriate treatments. We therefore evaluated the cost-effectiveness of direct molecular detection of pathogens in blood for patients with severe sepsis (SES), febrile neutropenia (FN) and suspected infective endocarditis (SIE). Patients were enrolled in a multicentre, open-label, cluster-randomised crossover trial conducted during two consecutive periods, randomly assigned as control period (CP; standard diagnostic workup) or intervention period (IP; additional testing with LightCycler ® SeptiFast). Multilevel models used to account for clustering were stratified by clinical setting (SES, FN, SIE). A total of 1416 patients (907 SES, 440 FN, 69 SIE) were evaluated for the primary endpoint (rate of blood MD). For SES patients, the MD rate was higher during IP than during CP [42.6% (198/465) vs. 28.1% (125/442), odds ratio (OR) 1.89, 95% confidence interval (CI) 1.43-2.50; P < 0.001], with an absolute increase of 14.5% (95% CI 8.4-20.7). A trend towards an association was observed for SIE [35.4% (17/48) vs. 9.5% (2/21); OR 6.22 (0.98-39.6)], but not for FN [32.1% (70/218) vs. 30.2% (67/222), P = 0.66]. Overall, turn-around time was shorter during IP than during CP (22.9 vs. 49.5 h, P < 0.001) and hospital costs were similar (median, mean ± SD: IP €14,826, €18,118 ± 17,775; CP €17,828, €18,653 ± 15,966). Bootstrap analysis of the incremental cost-effectiveness ratio showed weak dominance of intervention in SES patients. Addition of molecular detection to standard care improves MD and thus efficiency of healthcare resource usage in patients with SES. ClinicalTrials.gov registration number: NCT00709358.

Anesthésie pour prothése totale de la hanche: à propos de 50 cas

PubMed Central

Serghini, Issam; Qamouss, Youssef; Zoubir, Mohamed; Lalaoui, Jaafar Salim; Koulali, Idrissi Khalid; Boughalem, Mohamed

2015-01-01

La chirurgie de la prothèse totale de la hanche (PTH) est une chirurgie fonctionnelle qui consiste en un remplacement d'une articulation endommagée afin d'améliorer la qualité de vie du patient. L'anesthésie pour PTH exige une préparation rigoureuse à l'intervention, la consultation d'anesthésie sera donc la clef de cette réussite. Nous avons réalisé une étude rétrospective concernant 60 arthroplasties totales de la hanche implantées chez 50 patients adultes, colligée au sevice de Traumatologie et de chirurgie orthopédique à l'Hôpital Militaire Avicenne de Marrakech sur une période étalée de Janvier 2010 au Décembre 2012. Nous avons évalué la prise en charge anesthésique: pré, per et postopératoire des patients opérés pour une PTH. La moyenne d’âge était de 56,5 ans, le sex-ratio était de 1,63 en faveur des hommes. L'indication prédominante était la coxarthrose primitive. L'anesthésie générale était la technique anesthésique la plus utilisée (66% des cas), l'intubation difficile était rencontrée chez 6% de nos patients. La durée moyenne de l'acte chirurgical était de 114 +/- 25,33 mn. 12% de nos patients ont présenté une hypotension artérielle peropératoire. L'incidence de la transfusion homologue perop était de 14%. Nous avons noté 08 cas de complications postop: 03 cas d'infection de la PTH 15 jours après l'intervention, 03 cas de descellement aseptique, 01 cas de luxation de PTH et 01 cas de descellement septique avec un recul moyen de 54 mois. PMID:27047619

Contribution of Increasing Glacial Freshwater Fluxes to Observed Trends in Antarctic Sea Ice

NASA Astrophysics Data System (ADS)

Le Sommer, J.; Merino, N.; Durand, G.; Jourdain, N.; Goosse, H.; Mathiot, P.; Gurvan, M.

2016-02-01

Southern Ocean sea-ice extent has experienced an overall positive trend over recent decades. While the amplitude of this trend is open to debate, the geographical pattern of regional changes has been clearly identified by observations. Mechanisms driving changes in the Antarctic Sea Ice Extent (SIE) are not fully understood and climate models fail to simulate these trends. Changes in different atmospheric features such as SAM or ENSO seem to explain the observed trend of Antartic sea ice, but only partly, since they can not account for the actual amplitude of the observed signal. The increasing injection of freshwater due to the accelerating ice discharge from Antarctica Ice Sheet (AIS) during the last two decades has been proposed as another candidate to contribute to SIE trend. However, the quantity and the distribution of the extra freshwater injection were not properly constrained. Recent glaciological estimations may improve the way the glacial freshwater is injected in the model. Here, we study the role of the glacial freshwater into the observed SIE trend, using the state-of-the-art Antarctic mass loss estimations. Ocean/sea-ice model simulations have been carried out with two different Antarctic freshwater scenarios corresponding to 20-years of Antarctic Ice Sheet evolution. The combination of an improved iceberg model with the most recent glaciological estimations has been applied to account for the most realistic possible Antarctic freshwater evolution scenarios. Results suggest that Antarctica has contributed to almost a 30% of the observed trend in regions of the South Pacific and South East Indian sectors, but has little impact in the South Atlantic sector. We conclude that the observed SIE trend over the last decades is due to a combination of both an atmospheric forcing and the extra freshwater injection. Our results advocates that the evolution of glacial freshwater needs to be correctly represented in climate models.

Revisiting Studies of the Statistical Property of a Strong Gravitational Lens System and Model-Independent Constraint on the Curvature of the Universe

NASA Astrophysics Data System (ADS)

Xia, Jun-Qing; Yu, Hai; Wang, Guo-Jian; Tian, Shu-Xun; Li, Zheng-Xiang; Cao, Shuo; Zhu, Zong-Hong

2017-01-01

In this paper, we use a recently compiled data set, which comprises 118 galactic-scale strong gravitational lensing (SGL) systems to constrain the statistical property of the SGL system as well as the curvature of the universe without assuming any fiducial cosmological model. Based on the singular isothermal ellipsoid (SIE) model of the SGL system, we obtain that the constrained curvature parameter {{{Ω }}}{{k}} is close to zero from the SGL data, which is consistent with the latest result of Planck measurement. More interestingly, we find that the parameter f in the SIE model is strongly correlated with the curvature {{{Ω }}}{{k}}. Neglecting this correlation in the analysis will significantly overestimate the constraining power of SGL data on the curvature. Furthermore, the obtained constraint on f is different from previous results: f=1.105+/- 0.030 (68% confidence level [C.L.]), which means that the standard singular isothermal sphere (SIS) model (f = 1) is disfavored by the current SGL data at more than a 3σ C.L. We also divide all of the SGL data into two parts according to the centric stellar velocity dispersion {σ }{{c}} and find that the larger the value of {σ }{{c}} for the subsample, the more favored the standard SIS model is. Finally, we extend the SIE model by assuming the power-law density profiles for the total mass density, ρ ={ρ }0{(r/{r}0)}-α , and luminosity density, ν ={ν }0{(r/{r}0)}-δ , and obtain the constraints on the power-law indices: α =1.95+/- 0.04 and δ =2.40+/- 0.13 at a 68% C.L. When assuming the power-law index α =δ =γ , this scenario is totally disfavored by the current SGL data, {χ }\\min ,γ 2-{χ }\\min ,{SIE}2≃ 53.

Morbidity in relation to feeding mode in African HIV-exposed, uninfected infants during the first 6 mo of life: the Kesho Bora study123456

PubMed Central

Cournil, Amandine; Read, Jennifer S; Newell, Marie-Louise; Cames, Cécile; Meda, Nicolas; Luchters, Stanley; Mbatia, Grace; Naidu, Kevindra; Gaillard, Philippe; de Vincenzi, Isabelle

2014-01-01

Background: Refraining from breastfeeding to prevent HIV transmission has been associated with increased morbidity and mortality in HIV-exposed African infants. Objective: The objective was to assess risks of common and serious infectious morbidity by feeding mode in HIV-exposed, uninfected infants ≤6 mo of age with special attention to the issue of reverse causality. Design: HIV-infected pregnant women from 5 sites in Burkina Faso, Kenya, and South Africa were enrolled in the prevention of mother-to-child transmission Kesho Bora trial and counseled to either breastfeed exclusively and cease by 6 mo postpartum or formula feed exclusively. Maternal-reported morbidity (fever, diarrhea, and vomiting) and serious infectious events (SIEs) (gastroenteritis and lower respiratory tract infections) were investigated for 751 infants for 2 age periods (0–2.9 and 3–6 mo) by using generalized linear mixed models with breastfeeding as a time-dependent variable and adjustment for study site, maternal education, economic level, and cotrimoxazole prophylaxis. Results: Reported morbidity was not significantly higher in nonbreastfed compared with breastfed infants [OR: 1.31 (95% CI: 0.97, 1.75) and 1.21 (0.90, 1.62) at 0–2.9 and 3–6 mo of age, respectively]. Between 0 and 2.9 mo of age, never-breastfed infants had increased risks of morbidity compared with those of infants who were exclusively breastfed (OR: 1.49; 95% CI: 1.01, 2.2; P = 0.042). The adjusted excess risk of SIEs in nonbreastfed infants was large between 0 and 2.9 mo (OR: 6.0; 95% CI: 2.2, 16.4; P = 0.001). Between 3 and 6 mo, the OR for SIEs was sensitive to the timing of breastfeeding status, i.e., 4.3 (95% CI: 1.2, 15.3; P = 0.02) when defined at end of monthly intervals and 2.0 (95% CI: 0.8, 5.0; P = 0.13) when defined at the beginning of intervals. Of 52 SIEs, 3 mothers reported changes in feeding mode during the SIE although none of the mothers ceased breastfeeding completely. Conclusions: Not breastfeeding was associated with increased risk of serious infections especially between 0 and 2.9 mo of age. The randomized controlled trial component of the Kesho Bora study was registered at Current Controlled Trials (www.controlled-trials.com) as ISRCTN71468401. PMID:25411291

Auf Proteinjagd in der T-Zelle: Einzelmolekül-Mikroskopie

NASA Astrophysics Data System (ADS)

Brameshuber, Mario; Mörtelmaier, Manuel

2004-07-01

Einzelne Moleküle in lebenden Zellen mit Fluoreszenzmikroskopen zu beobachten, ist derzeit noch eine technische Herausforderung. Sie lohnt sich aber: So können erstmals die molekularen Bausteine des Lebens, etwa Proteine, bei ihren Aktivitäten direkt verfolgt werden. Das erlaubt völlig neue Einblicke in die Funktionsmechanismen biologischer Zellen. Ein interessantes Forschungsobjekt sind die T-Zellen, die das Immunsystem steuern. Die Beobachtung einzelner Proteine kann das Rätsel lösen helfen, wie T-Zellen gefährliche von ungefährlichen Erregern unterscheiden können. Damit Einzelmolekül-Mikroskope routinemäßig in Biolabors eingesetzt werden können, müssen sie noch robuster, billiger und einfacher handhabbar werden.

Zeitspiel ist keine Alternative - Warum der Wandel zur Pflicht wird

NASA Astrophysics Data System (ADS)

Dieper, Stephan

"Wege entstehen dadurch, dass man sie geht." (Franz Kafka) Die Welt der Digitalisierung ist voll von Wegen, die jemand gegangen ist, bevor dort ein Weg war. Manche dieser Wege stellten sich als Sackgasse heraus, manche als Abkürzung und aus anderen wurden ganze Wegenetze und Städte. Die Energiewelt wird durch den digitalen Wandel nicht verschont bleiben. Durch die intelligenten Messsysteme und die zugehörigen, neuen Strukturen werden energiefremden Wettbewerbern Chancen zum Markteintritt eröffnet. EVUs müssen sich darauf einstellen, dass der permanente Wandel nicht mehr enden wird. Doch auch den EVUs eröffnen sich Optionen. Um erfolgreich zu sein, müssen sie lernen loszugehen, ohne das genaue Ziel zu kennen.

A new integrable equation combining the modified KdV equation with the negative-order modified KdV equation: multiple soliton solutions and a variety of solitonic solutions

NASA Astrophysics Data System (ADS)

Wazwaz, Abdul-Majid

2018-07-01

A new third-order integrable equation is constructed via combining the recursion operator of the modified KdV equation (MKdV) and its inverse recursion operator. The developed equation will be termed the modified KdV-negative order modified KdV equation (MKdV-nMKdV). The complete integrability of this equation is confirmed by showing that it nicely possesses the Painlevé property. We obtain multiple soliton solutions for the newly developed integrable equation. Moreover, this equation enjoys a variety of solutions which include solitons, peakons, cuspons, negaton, positon, complexiton and other solutions.

On integrability of the Killing equation

NASA Astrophysics Data System (ADS)

Houri, Tsuyoshi; Tomoda, Kentaro; Yasui, Yukinori

2018-04-01

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

Virtuelle Kraftwerke für Smart Markets

NASA Astrophysics Data System (ADS)

Dürr, Thomas; Heyne, Jean-Christoph

In den zurückliegenden Jahren haben insbesondere zwei Trends die Stromversorgung bestimmt: der starke Anstieg der dezentralen und der Ausbau der regenerativen Stromerzeugung, die vor allem in den Verteilnetzen stattfinden. Angesichts dieser Entwicklung gewinnen virtuelle Kraftwerke (VK) immer mehr an Bedeutung. In der frühen Phase waren VK insbesondere eine Möglichkeit, kleine dezentrale Erzeuger zu einer größeren Einheit zu bündeln und sie so marktfähig zu machen. Heute werden sie - überwacht und gesteuert über ein Dezentrales Energie-Management-System (DEMS) - gemeinsam mit Demand Response betrieben, also dem Reagieren eines Energieabnehmers auf Marktpreise. Das Demand Side Management soll zur Flexibilisierung der Industrie beitragen. Da der Ausbau der Übertragungsnetze nur schleppend vorankommt, kann die Nutzung von lastseitiger Flexibilität einen wichtigen Beitrag zur Versorgungssicherheit leisten. Im zweiten Teil des Beitrags geht es um die Entwicklung der Märkte. Großes Interesse besteht immer noch an der Regelenergie, zumal der Bedarf bis 2050 deutlich steigen wird. Die Spotmärkte Intraday und Day-Ahead wachsen kontinuierlich, deshalb werden sie für VK immer wichtiger. Am Ende gibt der Beitrag einen Ausblick auf die künftige Entwicklung, in der Regelenergie- und Spotmärkte noch eine Rolle spielen, aber andere Geschäftsmodelle wichtiger werden. Darüber hinaus geht es um langfristige Entwicklungen, die z. B. zusätzliche Serviceleistungen durch VK betreffen.

Is It Possible to Increase Flap Viability by Hydrostatic Dilation?: An Experimental Study in the Rat Abdominal Fasciocutaneous Flap Model.

PubMed

Sahin, Cihan; Aysal, Bilge Kagan; Ergun, Ozge

2016-08-01

Ergun et al previously demonstrated the efficacy of hydrostatic dilation in a TRAM flap model in an experimental study. We investigated the effect of hydrostatic dilation on a fasciocutaneous flap model. Eighteen female Wistar rats were equally divided into 3 groups, of which 1 served as a control. In the second, the abdominal fasciocutaneous flap surgical delay procedure was performed by division of the left superficial inferior epigastric (SIE) vessels. In the third, hydrostatic dilation was performed on the left SIE artery and vein, with a mean pressure of 300 mm Hg, while elevating the flap on the right-sided SIE pedicle. The groups were compared by microangiography and by the survival ratio of abdominal flaps 7 days after elevation. The mean (SD) flap necrosis rates were as follows: control group, 44.75% (4.31%); delay group, 33.32% (7.11%); and hydrostatic dilation group, 32.51% (5.03%). There was a significant difference between the control group and the other 2 groups (P < 0.05). There was no difference between the delay and hydrostatic dilation groups with respect to surface area necrosis. The microangiographies showed remarkable increased vascularity in the delay and hydrostatic dilation groups. Hydrostatic dilation is a new method of enhancing flap viability that could be used in clinical cases in place of surgical delay once further studies and clinical trials are completed.

Quantum integrability and functional equations

NASA Astrophysics Data System (ADS)

Volin, Dmytro

2010-03-01

In this thesis a general procedure to represent the integral Bethe Ansatz equations in the form of the Reimann-Hilbert problem is given. This allows us to study in simple way integrable spin chains in the thermodynamic limit. Based on the functional equations we give the procedure that allows finding the subleading orders in the solution of various integral equations solved to the leading order by the Wiener-Hopf technics. The integral equations are studied in the context of the AdS/CFT correspondence, where their solution allows verification of the integrability conjecture up to two loops of the strong coupling expansion. In the context of the two-dimensional sigma models we analyze the large-order behavior of the asymptotic perturbative expansion. Obtained experience with the functional representation of the integral equations allowed us also to solve explicitly the crossing equations that appear in the AdS/CFT spectral problem.

Explicit solution of integrated 1 - exp equation for predicting accumulation and decline of concentrations for drugs obeying nonlinear saturation kinetics.

PubMed

Keller, Frieder; Hartmann, Bertram; Czock, David

2009-12-01

To describe nonlinear, saturable pharmacokinetics, the Michaelis-Menten equation is frequently used. However, the Michaelis-Menten equation has no integrated solution for concentrations but only for the time factor. Application of the Lambert W function was proposed recently to obtain an integrated solution of the Michaelis-Menten equation. As an alternative to the Michaelis-Menten equation, a 1 - exp equation has been used to describe saturable kinetics, with the advantage that the integrated 1 - exp equation has an explicit solution for concentrations. We used the integrated 1 - exp equation to predict the accumulation kinetics and the nonlinear concentration decline for a proposed fictive drug. In agreement with the recently proposed method, we found that for the integrated 1 - exp equation no steady state is obtained if the maximum rate of change in concentrations (Vmax) within interval (Tau) is less than the difference between peak and trough concentrations (Vmax x Tau < C peak - C trough).

On the integration of a class of nonlinear systems of ordinary differential equations

NASA Astrophysics Data System (ADS)

Talyshev, Aleksandr A.

2017-11-01

For each associative, commutative, and unitary algebra over the field of real or complex numbers and an integrable nonlinear ordinary differential equation we can to construct integrable systems of ordinary differential equations and integrable systems of partial differential equations. In this paper we consider in some sense the inverse problem. Determine the conditions under which a given system of ordinary differential equations can be represented as a differential equation in some associative, commutative and unitary algebra. It is also shown that associativity is not a necessary condition.

Pratique anesthésique à Lubumbashi: indications, types de chirurgie et types de patient

PubMed Central

Kabey, Alain Kabey a; Lubanga, Muyumba; Tshamba, Mundongo; Kaut, Mukeng; Kakambal, Kaij; Muteya, Manika; Manzanza, Kilembe; Kalal, Kapend

2015-01-01

Introduction Cette étude a pour objectif de décrire la pratique anesthésique dans un pays à faible revenu et où le plateau technique anesthésique est moins équipé. Méthodes Une étude descriptive transversale a été menée durant l'année 2013. L'enquête a concerné les pratiques anesthésiques, les indications chirurgicales et les caractéristiques des malades. L'encodage et l'analyse des données ont été réalisées grâce aux logiciels Epi Info 3.5.3 et Excel 2010. Résultats Nous avons enregistré 2358 patients dont l’âge médian était de 29 + 15 ans, avec 81,5% âgés de 11 à 50 ans. Parmi eux, 67,3% des malades étaient du sexe féminin. Dans ensemble, 62,5% de ces patients étaient pris en charge pour les interventions programmées. L’évaluation du risque anesthésique a montré que 91,9% des patients étaient de la classe ASA I et II. La chirurgie la plus pratiquée était viscérale (46,7%) suivie de la chirurgie gynéco-obstétricale (29,2%). Les différents types d'anesthésie étaient les suivants: anesthésie générale (87,6%), locorégionale (11,8%) et combinée (0,6%). Conclusion La pratique anesthésique dans la population d’étude était dominée par l'anesthésie générale. Les malades étaient au trois quart de sexe féminin et de la classe ASA I et II. Les résultats de cette étude indiquent la nécessité d’évaluer l'issue de cette pratique. La pratique anesthésique à Lubumbashi est tributaire du plateau technique, des compétences du personnel et de l'acceptabilité du type d'anesthésie par les patients. PMID:26523180

Franz Xaver Eder (1914 - 2009) Wanderer zwischen den Welten

NASA Astrophysics Data System (ADS)

Lindner, Sigrid; Hoffmann, Dieter

In seinem Essay "Die Struktur des historischen Universums" vergleicht Siegfried Kracauer die Mikrogeschichte mit den Großaufnahmen etwa von der Hand einer Figur, wie sie in Spielfilmen zwischengeschnitten werden.

Dynamics of a differential-difference integrable (2+1)-dimensional system.

PubMed

Yu, Guo-Fu; Xu, Zong-Wei

2015-06-01

A Kadomtsev-Petviashvili- (KP-) type equation appears in fluid mechanics, plasma physics, and gas dynamics. In this paper, we propose an integrable semidiscrete analog of a coupled (2+1)-dimensional system which is related to the KP equation and the Zakharov equation. N-soliton solutions of the discrete equation are presented. Some interesting examples of soliton resonance related to the two-soliton and three-soliton solutions are investigated. Numerical computations using the integrable semidiscrete equation are performed. It is shown that the integrable semidiscrete equation gives very accurate numerical results in the cases of one-soliton evolution and soliton interactions.

Determination of elementary first integrals of a generalized Raychaudhuri equation by the Darboux integrability method

NASA Astrophysics Data System (ADS)

Choudhury, A. Ghose; Guha, Partha; Khanra, Barun

2009-10-01

The Darboux integrability method is particularly useful to determine first integrals of nonplanar autonomous systems of ordinary differential equations, whose associated vector fields are polynomials. In particular, we obtain first integrals for a variant of the generalized Raychaudhuri equation, which has appeared in string inspired modern cosmology.

Two-dimensional integrating matrices on rectangular grids. [solving differential equations associated with rotating structures

NASA Technical Reports Server (NTRS)

Lakin, W. D.

1981-01-01

The use of integrating matrices in solving differential equations associated with rotating beam configurations is examined. In vibration problems, by expressing the equations of motion of the beam in matrix notation, utilizing the integrating matrix as an operator, and applying the boundary conditions, the spatial dependence is removed from the governing partial differential equations and the resulting ordinary differential equations can be cast into standard eigenvalue form. Integrating matrices are derived based on two dimensional rectangular grids with arbitrary grid spacings allowed in one direction. The derivation of higher dimensional integrating matrices is the initial step in the generalization of the integrating matrix methodology to vibration and stability problems involving plates and shells.

Self-Interest and the Design of Rules.

PubMed

Singh, Manvir; Wrangham, Richard; Glowacki, Luke

2017-12-01

Rules regulating social behavior raise challenging questions about cultural evolution in part because they frequently confer group-level benefits. Current multilevel selection theories contend that between-group processes interact with within-group processes to produce norms and institutions, but within-group processes have remained underspecified, leading to a recent emphasis on cultural group selection as the primary driver of cultural design. Here we present the self-interested enforcement (SIE) hypothesis, which proposes that the design of rules importantly reflects the relative enforcement capacities of competing parties. We show that, in addition to explaining patterns in cultural change and stability, SIE can account for the emergence of much group-functional culture. We outline how this process can stifle or accelerate cultural group selection, depending on various social conditions. Self-interested enforcement has important bearings on the emergence, stability, and change of rules.

Demographic models and IPCC climate projections predict the decline of an emperor penguin population.

PubMed

Jenouvrier, Stéphanie; Caswell, Hal; Barbraud, Christophe; Holland, Marika; Stroeve, Julienne; Weimerskirch, Henri

2009-02-10

Studies have reported important effects of recent climate change on Antarctic species, but there has been to our knowledge no attempt to explicitly link those results to forecasted population responses to climate change. Antarctic sea ice extent (SIE) is projected to shrink as concentrations of atmospheric greenhouse gases (GHGs) increase, and emperor penguins (Aptenodytes forsteri) are extremely sensitive to these changes because they use sea ice as a breeding, foraging and molting habitat. We project emperor penguin population responses to future sea ice changes, using a stochastic population model that combines a unique long-term demographic dataset (1962-2005) from a colony in Terre Adélie, Antarctica and projections of SIE from General Circulation Models (GCM) of Earth's climate included in the most recent Intergovernmental Panel on Climate Change (IPCC) assessment report. We show that the increased frequency of warm events associated with projected decreases in SIE will reduce the population viability. The probability of quasi-extinction (a decline of 95% or more) is at least 36% by 2100. The median population size is projected to decline from approximately 6,000 to approximately 400 breeding pairs over this period. To avoid extinction, emperor penguins will have to adapt, migrate or change the timing of their growth stages. However, given the future projected increases in GHGs and its effect on Antarctic climate, evolution or migration seem unlikely for such long lived species at the remote southern end of the Earth.

Demographic models and IPCC climate projections predict the decline of an emperor penguin population

PubMed Central

Jenouvrier, Stéphanie; Caswell, Hal; Barbraud, Christophe; Holland, Marika; Strœve, Julienne; Weimerskirch, Henri

2009-01-01

Studies have reported important effects of recent climate change on Antarctic species, but there has been to our knowledge no attempt to explicitly link those results to forecasted population responses to climate change. Antarctic sea ice extent (SIE) is projected to shrink as concentrations of atmospheric greenhouse gases (GHGs) increase, and emperor penguins (Aptenodytes forsteri) are extremely sensitive to these changes because they use sea ice as a breeding, foraging and molting habitat. We project emperor penguin population responses to future sea ice changes, using a stochastic population model that combines a unique long-term demographic dataset (1962–2005) from a colony in Terre Adélie, Antarctica and projections of SIE from General Circulation Models (GCM) of Earth's climate included in the most recent Intergovernmental Panel on Climate Change (IPCC) assessment report. We show that the increased frequency of warm events associated with projected decreases in SIE will reduce the population viability. The probability of quasi-extinction (a decline of 95% or more) is at least 36% by 2100. The median population size is projected to decline from ≈6,000 to ≈400 breeding pairs over this period. To avoid extinction, emperor penguins will have to adapt, migrate or change the timing of their growth stages. However, given the future projected increases in GHGs and its effect on Antarctic climate, evolution or migration seem unlikely for such long lived species at the remote southern end of the Earth. PMID:19171908

Population dynamics of spotted owls in the Sierra Nevada, California

USGS Publications Warehouse

Blakesley, J.A.; Seamans, M.E.; Conner, M.M.; Franklin, A.B.; White, Gary C.; Gutierrez, R.J.; Hines, J.E.; Nichols, J.D.; Munton, T.E.; Shaw, D.W.H.; Keane, J.J.; Steger, G.N.; McDonald, T.L.

2010-01-01

The California spotted owl (Strix occidentalis occidentalis) is the only spotted owl subspecies not listed as threatened or endangered under the United States Endangered Species Act despite petitions to list it as threatened. We conducted a meta-analysis of population data for 4 populations in the southern Cascades and Sierra Nevada, California, USA, from 1990 to 2005 to assist a listing evaluation by the United States Fish and Wildlife Service. Our study areas (from N to S) were on the Lassen National Forest (LAS), Eldorado National Forest (ELD), Sierra National Forest (SIE), and Sequoia and Kings Canyon National Parks (SKC). These study areas represented a broad spectrum of habitat and management conditions in these mountain ranges. We estimated apparent survival probability, reproductive output, and rate of population change for spotted owls on individual study areas and for all study areas combined (meta-analysis) using model selection or model-averaging based on maximum-likelihood estimation. We followed a formal protocol to conduct this analysis that was similar to other spotted owl meta-analyses. Consistency of field and analytical methods among our studies reduced confounding methodological effects when evaluating results. We used 991 marked spotted owls in the analysis of apparent survival. Apparent survival probability was higher for adult than for subadult owls. There was little difference in apparent survival between male and female owls. Model-averaged mean estimates of apparent survival probability of adult owls varied from 0.811 ?? 0.021 for females at LAS to 0.890 ?? 0.016 for males at SKC. Apparent survival increased over time for owls of all age classes at LAS and SIE, for adults at ELD, and for second-year subadults and adults at SKC. The meta-analysis of apparent survival, which included only adult owls, confirmed an increasing trend in survival over time. Survival rates were higher for owls on SKC than on the other study areas. We analyzed data from 1,865 observations of reproductive outcomes for female spotted owls. The proportion of subadult females among all territorial females of known age ranged from 0.00 to 0.25 among study areas and years. The proportion of subadults among female spotted owls was negatively related to reproductive output (no. of young fledged/territorial F owl) for ELD and SIE. Eldorado study area and LAS showed an alternate-year trend in reproductive output, with higher output in even-numbered years. Mean annual reproductive output was 0.988 ?? 0.154 for ELD, 0.624 ?? 0.140 for LAS, 0.478 ?? 0.106 for SIE, and 0.555 ?? 0.110 for SKC. Eldorado Study Area exhibited a declining trend and the greatest variation in reproductive output over time, whereas SIE and SKC, which had the lowest reproductive output, had the lowest temporal variation. Meta-analysis confirmed that reproductive output varied among study areas. Reproductive output was highest for adults, followed by second-year subadults, and then by first-year subadults. We used 842 marked subadult and adult owls to estimate population rate of change. Modeling indicated that ??t (??t is the finite rate of population change estimated using the reparameterized JollySeber estimator Pradel 1996) was either stationary (LAS and SIE) or increasing after an initial decrease (ELD and SKC). Mean estimated ??t for the 4 study areas was 1.007 (95 CI 0.9521.066) for ELD; 0.973 (95 CI 0.9461.001) for LAS; 0.992 (95 CI 0.9661.018) for SIE; and 1.006 (95 CI 0.9471.068) for SKC. The best meta-analysis model of population trend indicated that ?? varied across time but was similar in trend among the study areas. Our estimates of realized population change (??t; Franklin et al. 2004), which we estimated as the product 1 ?? ??3 ?? ??4 ?? .?? ??k -1, were based on estimates of ??t from individual study areas and did not require estimating annual population size for each study area. Trends represented the proportion of the population size in the first ye

Guide for SDEC Set up

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bibby, R; Guthrie, E

2009-01-30

The instrument has four collection vials that must be filled with ethylene glycol before operation. Each of the four vials should be labeled 1 through 4 and the empty weights recorded. Fill each vial with 80 mL of ethylene glycol and record the weight again. In order for the instrument to operate properly, the collection vials should always have less than 160 mL of total liquid in them. After completing a sample run, remove the collection vials, use a transfer pipette to remove any liquid that might still be on the air paddler, wipe off any condensation from the exteriormore » of the collection vial and record weight. From the instrument, record the ending volume and the time of operation. The solution mixed in the scintillation vial will be 2 ml of a 95% to 50% ethylene glycol to water mixture. To determine the efficiency of counting at all of these concentrations, a series of vials should be set up that consist of 18 ml of Ultima Gold LLT cocktail mixed with standard, regular deionized water and ethylene glycol. The efficiency curve should be counted in the 'Low Level' count mode with the Luminescence Correction ON and the Color Quench Correction ON. Once the tSIE values are determined, chart the cpm against the tSIE numbers and find the best fit for the data. The resulting equation is to be used to converting tSIE values from the collection vials to efficiency. To determine the background cpm value of the ethylene glycol, count a 2 ml sample of ethylene glycol with 18 ml of Ultima Gold for 100 minutes. To determine the total activity of the sample, take two 2 ml aliquots of sample from the first vial and place in separate scintillation vials. Record the weight of each aliquot. Determine the percentage of total sample each aliquot represents by dividing the aliquot weight by the total solution weight from the vial. Also, determine the percentage of ethylene glycol in the sample by dividing the initial solution weight by the final solution weight and multiplying by 100. Add 18 ml of Ultima Gold to each vial and proceed to count for 100 minutes in a 'Low Level' count mode. Before performing a calculation on the dpm value of each aliquot, a subtraction should be made for the background count rate of the ethylene glycol. Based on the background cpm, multiply the background cpm value by the percentage of ethylene glycol in the collection vial. Once the background value is subtracted, calculate the dpm value of the sample based on the tSIE conversion to efficiency. This will produce a dpm value. To convert this to a total activity of the sample, divide the aliquot dpm value by the decimal percentage of total sample the aliquot represents. This gives the total activity of the sample solution. Take the average of both aliquots as a final result. To convert the total activity from the solution in vial one to activity in air, an empirical formula is used to convert activity/gram from vial one to total activity introduced into the system. After calculation the final result for the vial, divide the total by the mass of the sample in vial one. This gives dpm/g (labeled C{sub m}). To convert this to total dpm measured, C = (128.59 * Cm + 10.837)/V Where: C = Tritium concentration in air (dpm/m{sup 3}) C{sub m} = measured tritium concentration from vial 1 (dpm/g) V = Volume of air sampled through instrument (m{sup 3}). C is the final value of tritium concentration in air.« less

Accurate D-bar Reconstructions of Conductivity Images Based on a Method of Moment with Sinc Basis.

PubMed

Abbasi, Mahdi

2014-01-01

Planar D-bar integral equation is one of the inverse scattering solution methods for complex problems including inverse conductivity considered in applications such as Electrical impedance tomography (EIT). Recently two different methodologies are considered for the numerical solution of D-bar integrals equation, namely product integrals and multigrid. The first one involves high computational burden and the other one suffers from low convergence rate (CR). In this paper, a novel high speed moment method based using the sinc basis is introduced to solve the two-dimensional D-bar integral equation. In this method, all functions within D-bar integral equation are first expanded using the sinc basis functions. Then, the orthogonal properties of their products dissolve the integral operator of the D-bar equation and results a discrete convolution equation. That is, the new moment method leads to the equation solution without direct computation of the D-bar integral. The resulted discrete convolution equation maybe adapted to a suitable structure to be solved using fast Fourier transform. This allows us to reduce the order of computational complexity to as low as O (N (2)log N). Simulation results on solving D-bar equations arising in EIT problem show that the proposed method is accurate with an ultra-linear CR.

Geometry, Heat Equation and Path Integrals on the Poincaré Upper Half-Plane

NASA Astrophysics Data System (ADS)

Kubo, R.

1988-01-01

Geometry, heat equation and Feynman's path integrals are studied on the Poincaré upper half-plane. The fundamental solution to the heat equation partial f/partial t = Delta_{H} f is expressed in terms of a path integral defined on the upper half-plane. It is shown that Kac's statement that Feynman's path integral satisfies the Schrödinger equation is also valid for our case.

Squared eigenfunctions for the Sasa-Satsuma equation

NASA Astrophysics Data System (ADS)

Yang, Jianke; Kaup, D. J.

2009-02-01

Squared eigenfunctions are quadratic combinations of Jost functions and adjoint Jost functions which satisfy the linearized equation of an integrable equation. They are needed for various studies related to integrable equations, such as the development of its soliton perturbation theory. In this article, squared eigenfunctions are derived for the Sasa-Satsuma equation whose spectral operator is a 3×3 system, while its linearized operator is a 2×2 system. It is shown that these squared eigenfunctions are sums of two terms, where each term is a product of a Jost function and an adjoint Jost function. The procedure of this derivation consists of two steps: First is to calculate the variations of the potentials via variations of the scattering data by the Riemann-Hilbert method. The second one is to calculate the variations of the scattering data via the variations of the potentials through elementary calculations. While this procedure has been used before on other integrable equations, it is shown here, for the first time, that for a general integrable equation, the functions appearing in these variation relations are precisely the squared eigenfunctions and adjoint squared eigenfunctions satisfying, respectively, the linearized equation and the adjoint linearized equation of the integrable system. This proof clarifies this procedure and provides a unified explanation for previous results of squared eigenfunctions on individual integrable equations. This procedure uses primarily the spectral operator of the Lax pair. Thus two equations in the same integrable hierarchy will share the same squared eigenfunctions (except for a time-dependent factor). In the Appendix, the squared eigenfunctions are presented for the Manakov equations whose spectral operator is closely related to that of the Sasa-Satsuma equation.

Mathematical Methods for Physics and Engineering Third Edition Paperback Set

NASA Astrophysics Data System (ADS)

Riley, Ken F.; Hobson, Mike P.; Bence, Stephen J.

2006-06-01

Prefaces; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics; Index.

Integrability: mathematical methods for studying solitary waves theory

NASA Astrophysics Data System (ADS)

Wazwaz, Abdul-Majid

2014-03-01

In recent decades, substantial experimental research efforts have been devoted to linear and nonlinear physical phenomena. In particular, studies of integrable nonlinear equations in solitary waves theory have attracted intensive interest from mathematicians, with the principal goal of fostering the development of new methods, and physicists, who are seeking solutions that represent physical phenomena and to form a bridge between mathematical results and scientific structures. The aim for both groups is to build up our current understanding and facilitate future developments, develop more creative results and create new trends in the rapidly developing field of solitary waves. The notion of the integrability of certain partial differential equations occupies an important role in current and future trends, but a unified rigorous definition of the integrability of differential equations still does not exist. For example, an integrable model in the Painlevé sense may not be integrable in the Lax sense. The Painlevé sense indicates that the solution can be represented as a Laurent series in powers of some function that vanishes on an arbitrary surface with the possibility of truncating the Laurent series at finite powers of this function. The concept of Lax pairs introduces another meaning of the notion of integrability. The Lax pair formulates the integrability of nonlinear equation as the compatibility condition of two linear equations. However, it was shown by many researchers that the necessary integrability conditions are the existence of an infinite series of generalized symmetries or conservation laws for the given equation. The existence of multiple soliton solutions often indicates the integrability of the equation but other tests, such as the Painlevé test or the Lax pair, are necessary to confirm the integrability for any equation. In the context of completely integrable equations, studies are flourishing because these equations are able to describe the real features in a variety of vital areas in science, technology and engineering. In recognition of the importance of solitary waves theory and the underlying concept of integrable equations, a variety of powerful methods have been developed to carry out the required analysis. Examples of such methods which have been advanced are the inverse scattering method, the Hirota bilinear method, the simplified Hirota method, the Bäcklund transformation method, the Darboux transformation, the Pfaffian technique, the Painlevé analysis, the generalized symmetry method, the subsidiary ordinary differential equation method, the coupled amplitude-phase formulation, the sine-cosine method, the sech-tanh method, the mapping and deformation approach and many new other methods. The inverse scattering method, viewed as a nonlinear analogue of the Fourier transform method, is a powerful approach that demonstrates the existence of soliton solutions through intensive computations. At the center of the theory of integrable equations lies the bilinear forms and Hirota's direct method, which can be used to obtain soliton solutions by using exponentials. The Bäcklund transformation method is a useful invariant transformation that transforms one solution into another of a differential equation. The Darboux transformation method is a well known tool in the theory of integrable systems. It is believed that there is a connection between the Bäcklund transformation and the Darboux transformation, but it is as yet not known. Archetypes of integrable equations are the Korteweg-de Vries (KdV) equation, the modified KdV equation, the sine-Gordon equation, the Schrödinger equation, the Vakhnenko equation, the KdV6 equation, the Burgers equation, the fifth-order Lax equation and many others. These equations yield soliton solutions, multiple soliton solutions, breather solutions, quasi-periodic solutions, kink solutions, homo-clinic solutions and other solutions as well. The couplings of linear and nonlinear equations were recently discovered and subsequently received considerable attention. The concept of couplings forms a new direction for developing innovative construction methods. The recently obtained results in solitary waves theory highlight new approaches for additional creative ideas, promising further achievements and increased progress in this field. We are grateful to all of the authors who accepted our invitation to contribute to this comment section.

Coprimeness-preserving non-integrable extension to the two-dimensional discrete Toda lattice equation

NASA Astrophysics Data System (ADS)

Kamiya, Ryo; Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji

2017-01-01

We introduce a so-called coprimeness-preserving non-integrable extension to the two-dimensional Toda lattice equation. We believe that this equation is the first example of such discrete equations defined over a three-dimensional lattice. We prove that all the iterates of the equation are irreducible Laurent polynomials of the initial data and that every pair of two iterates is co-prime, which indicate confined singularities of the equation. By reducing the equation to two- or one-dimensional lattices, we obtain coprimeness-preserving non-integrable extensions to the one-dimensional Toda lattice equation and the Somos-4 recurrence.

Calculation of transonic flows using an extended integral equation method

NASA Technical Reports Server (NTRS)

Nixon, D.

1976-01-01

An extended integral equation method for transonic flows is developed. In the extended integral equation method velocities in the flow field are calculated in addition to values on the aerofoil surface, in contrast with the less accurate 'standard' integral equation method in which only surface velocities are calculated. The results obtained for aerofoils in subcritical flow and in supercritical flow when shock waves are present compare satisfactorily with the results of recent finite difference methods.

Fredholm-Volterra Integral Equation with a Generalized Singular Kernel and its Numerical Solutions

NASA Astrophysics Data System (ADS)

El-Kalla, I. L.; Al-Bugami, A. M.

2010-11-01

In this paper, the existence and uniqueness of solution of the Fredholm-Volterra integral equation (F-VIE), with a generalized singular kernel, are discussed and proved in the spaceL2(Ω)×C(0,T). The Fredholm integral term (FIT) is considered in position while the Volterra integral term (VIT) is considered in time. Using a numerical technique we have a system of Fredholm integral equations (SFIEs). This system of integral equations can be reduced to a linear algebraic system (LAS) of equations by using two different methods. These methods are: Toeplitz matrix method and Product Nyström method. A numerical examples are considered when the generalized kernel takes the following forms: Carleman function, logarithmic form, Cauchy kernel, and Hilbert kernel.

Student Solution Manual for Mathematical Methods for Physics and Engineering Third Edition

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2006-03-01

Preface; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics.

Modern Geodetic Measurement Techniques in Gravimetric Studies on the Example of Gypsum Karst in the Siesławice Region

NASA Astrophysics Data System (ADS)

Porzucek, Sławomir; Łój, Monika; Matwij, Karolina; Matwij, Wojciech

2018-03-01

In the region of Siesławice (near Busko-Zdrój, Poland) there are unique phenomena of gypsum karst. Atmospheric factors caused numerous gypsum outcrops, canals and underground voids. The article presents the possibility of using non-invasive gravimetric surveys supplemented with geodetic measurements to illustrate karst changes occurring around the void. The use of modern geodetic measurement techniques including terrestrial and airborne laser scanning enables to generate a digital terrain model and a three-dimensional model of voids. Gravimetric field studies allowed to map the anomalies of the gravitational field of the near-surface zone. Geodetic measurement results have made it possible to accurately determine the terrain correction that supplemented the gravimetric anomaly information. Geophysical interpretation indicate the presence of weathered rocks in the near surface zone and fractures and loosened zones located surround the karst cave.

Anesthésie d’un greffé cardiaque en chirurgie non cardiaque: à propos d’un cas clinique et revue de la littérature

PubMed Central

Nassirou, Oumarou Mahamane Mamane; Jaafari, Abdelhamid; Chlouchi, Abdellatif; Bensghir, Mustapha; Haimeur, Charki

2016-01-01

Le nombre et la durée de survie des patients transplantés cardiaque sont en augmentation. Une partie de ces patients se présentent régulièrement pour une chirurgie générale en dehors de la transplantation cardiaque. L’anesthésie chez ces patients peut être difficile en raison des particularités physiologiques du cœur dénervé et de la gestion du traitement immunosuppresseur avec le risque de rejet et d’infection. Nous discutons la prise en charge anesthésique à travers un cas d’un patient âgé de 60 ans transplanté cardiaque devant subir une chirurgie de cure d’éventration abdominale et une revue de la littérature. PMID:28154639

Specifying the role of the left prefrontal cortex in word selection

PubMed Central

Ries, S. K; Karzmark, C. R.; Navarrete, E.; Knight, R. T.; Dronkers, N. F.

2015-01-01

Word selection allows us to choose words during language production. This is often viewed as a competitive process wherein a lexical representation is retrieved among semantically-related alternatives. The left prefrontal cortex (LPFC) is thought to help overcome competition for word selection through top-down control. However, whether the LPFC is always necessary for word selection remains unclear. We tested 6 LPFC-injured patients and controls in two picture naming paradigms varying in terms of item repetition. Both paradigms elicited the expected semantic interference effects (SIE), reflecting interference caused by semantically-related representations in word selection. However, LPFC patients as a group showed a larger SIE than controls only in the paradigm involving item repetition. We argue that item repetition increases interference caused by semantically-related alternatives, resulting in increased LPFC-dependent cognitive control demands. The remaining network of brain regions associated with word selection appears to be sufficient when items are not repeated. PMID:26291289

Saraca indica Bark Extract Shows In Vitro Antioxidant, Antibreast Cancer Activity and Does Not Exhibit Toxicological Effects

PubMed Central

Yadav, Navneet Kumar; Saini, Karan Singh; Hossain, Zakir; Omer, Ankur; Sharma, Chetan; Gayen, Jiaur R.; Singh, Poonam; Arya, K. R.; Singh, R. K.

2015-01-01

Medicinal plants are used as a complementary and alternative medicine in treatment of various diseases including cancer worldwide, because of their ease of accessibility and cost effectiveness. Multicomposed mixture of compounds present in a plant extract has synergistic activity, increases the therapeutic potential many folds, compensates toxicity, and increases bioavailability. Saraca indica (family Caesalpiniaceae) is one of the most ancient sacred plants with medicinal properties, exhibiting a number of pharmacological effects. Antioxidant, antibreast cancer activity and toxicological evaluation of Saraca indica bark extract (SIE) were carried out in the present study. The results of the study indicated that this herbal preparation has antioxidant and antibreast cancer activity. Toxicological studies suggest that SIE is safer to use and may have a potential to be used as complementary and alternative medicine for breast cancer therapy. PMID:25861411

Von Start-ups lernen - Methoden und Entwicklungsprozesse, die Jungunternehmen erfolgreich machen

NASA Astrophysics Data System (ADS)

Böhme, Eckhart

Die Start-up-Bewegung bringt beständig sog. Disruptoren hervor, die jede Branche betreffen und so gut wie keinen Lebensbereich auslassen. Diese Jungunternehmen, insbesondere aus der Softwarebranche, verfügen zwar nicht über Ressourcen wie etablierte Unternehmen, sie sind jedoch agil, "hungrig", können frei von "Ballast" agieren und treiben die Digitalisierung aller Branchen voran. Aber auch Start-ups können nicht einfach ungetestete Ideen in erfolgreiche Produkte oder Dienstleistungen umwandeln und ihren Erfolg dem Zufall überlassen. Erfolgreiche Jungunternehmen folgen vielmehr einem strukturierten Prozess, um marktgetestete Nutzenversprechen und Geschäftsmodelle zu entwickeln. Zunehmend adaptieren etablierte Unternehmen innovative Entwicklungsprozesse und Methoden. Die Fragestellung für Energieversorgungsunternehmen (EVUs) lautet, welche Methoden, Werkzeuge und Entwicklungsprozesse, die heute bei vielen Start-ups eingesetzt werden, sie aufgreifen können, um das Unternehmen gegenüber Disruptoren robust zu machen?

A new solution procedure for a nonlinear infinite beam equation of motion

NASA Astrophysics Data System (ADS)

Jang, T. S.

2016-10-01

Our goal of this paper is of a purely theoretical question, however which would be fundamental in computational partial differential equations: Can a linear solution-structure for the equation of motion for an infinite nonlinear beam be directly manipulated for constructing its nonlinear solution? Here, the equation of motion is modeled as mathematically a fourth-order nonlinear partial differential equation. To answer the question, a pseudo-parameter is firstly introduced to modify the equation of motion. And then, an integral formalism for the modified equation is found here, being taken as a linear solution-structure. It enables us to formulate a nonlinear integral equation of second kind, equivalent to the original equation of motion. The fixed point approach, applied to the integral equation, results in proposing a new iterative solution procedure for constructing the nonlinear solution of the original beam equation of motion, which consists luckily of just the simple regular numerical integration for its iterative process; i.e., it appears to be fairly simple as well as straightforward to apply. A mathematical analysis is carried out on both natures of convergence and uniqueness of the iterative procedure by proving a contractive character of a nonlinear operator. It follows conclusively,therefore, that it would be one of the useful nonlinear strategies for integrating the equation of motion for a nonlinear infinite beam, whereby the preceding question may be answered. In addition, it may be worth noticing that the pseudo-parameter introduced here has double roles; firstly, it connects the original beam equation of motion with the integral equation, second, it is related with the convergence of the iterative method proposed here.

A new (2+1) dimensional integrable evolution equation for an ion acoustic wave in a magnetized plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mukherjee, Abhik, E-mail: abhik.mukherjee@saha.ac.in; Janaki, M. S., E-mail: ms.janaki@saha.ac.in; Kundu, Anjan, E-mail: anjan.kundu@saha.ac.in

2015-07-15

A new, completely integrable, two dimensional evolution equation is derived for an ion acoustic wave propagating in a magnetized, collisionless plasma. The equation is a multidimensional generalization of a modulated wavepacket with weak transverse propagation, which has resemblance to nonlinear Schrödinger (NLS) equation and has a connection to Kadomtsev-Petviashvili equation through a constraint relation. Higher soliton solutions of the equation are derived through Hirota bilinearization procedure, and an exact lump solution is calculated exhibiting 2D structure. Some mathematical properties demonstrating the completely integrable nature of this equation are described. Modulational instability using nonlinear frequency correction is derived, and the correspondingmore » growth rate is calculated, which shows the directional asymmetry of the system. The discovery of this novel (2+1) dimensional integrable NLS type equation for a magnetized plasma should pave a new direction of research in the field.« less

Algorithms for the computation of solutions of the Ornstein-Zernike equation.

PubMed

Peplow, A T; Beardmore, R E; Bresme, F

2006-10-01

We introduce a robust and efficient methodology to solve the Ornstein-Zernike integral equation using the pseudoarc length (PAL) continuation method that reformulates the integral equation in an equivalent but nonstandard form. This enables the computation of solutions in regions where the compressibility experiences large changes or where the existence of multiple solutions and so-called branch points prevents Newton's method from converging. We illustrate the use of the algorithm with a difficult problem that arises in the numerical solution of integral equations, namely the evaluation of the so-called no-solution line of the Ornstein-Zernike hypernetted chain (HNC) integral equation for the Lennard-Jones potential. We are able to use the PAL algorithm to solve the integral equation along this line and to connect physical and nonphysical solution branches (both isotherms and isochores) where appropriate. We also show that PAL continuation can compute solutions within the no-solution region that cannot be computed when Newton and Picard methods are applied directly to the integral equation. While many solutions that we find are new, some correspond to states with negative compressibility and consequently are not physical.

Integral equations in the study of polar and ionic interaction site fluids

PubMed Central

Howard, Jesse J.

2011-01-01

In this review article we consider some of the current integral equation approaches and application to model polar liquid mixtures. We consider the use of multidimensional integral equations and in particular progress on the theory and applications of three dimensional integral equations. The IEs we consider may be derived from equilibrium statistical mechanical expressions incorporating a classical Hamiltonian description of the system. We give example including salt solutions, inhomogeneous solutions and systems including proteins and nucleic acids. PMID:22383857

Monitoring of water storage in karstic area (Larzac, France) with a iGrav continuous superconducting gravimeter

NASA Astrophysics Data System (ADS)

Le Moigne, N.; Champollion, C.; chery, J.; Deville, S.; Doerflinger, E.; Collard, P.; Flores, B.

2013-12-01

Quantitative knowledge of groundwater storage and transfer in karstic area is crucial for water resources management and protection. As the karst hydro-geological properties are highly heterogeneous and scale dependent, geophysical observations such as gravity are necessary to fill the gap between local (based on boreholes, moisture sensors, ...) and global (based on chemistry, river flow, ...) studies. Since almost 2 years, the iGrav #002 superconducting gravimeter is continuously operating in the French GEK (Géodésie des Eaux Karstiques) observatory in the Larzac karstic plateau (south of France). First the evaluation of the iGrav data (calibration, steps and drift) will be presented. Then a careful analyze of the topographic and building effects will be done. Finally the first interpretation of the hydrogeological signal and the integration an extensive observation dataset (borehole water level, evapotranspiration and electrical resistivity) are studied.

Parasite prevalence, infection intensity and richness in an endangered population, the Atlantic-Gaspésie caribou.

PubMed

Turgeon, Geneviève; Kutz, Susan J; Lejeune, Manigandan; St-Laurent, Martin-Hugues; Pelletier, Fanie

2018-04-01

The Atlantic-Gaspésie caribou ( Rangifer tarandus caribou ) population is a small isolated relict herd considered endangered according to the Canadian Species at Risk Act (SARA). This population has low recruitment and survival rates but the potential role of parasites on individual fitness is unknown. In this context, we explored the parasite status of this population with the aim of 1) assessing the occurrence and intensity of parasite infections and the spatial, temporal and individual variations, 2) quantifying parasite richness and investigating factors such as sex and host body condition that may be associated with this variable and 3) evaluating the effects of parasite infections on survival in the Atlantic-Gaspésie caribou population. We examined fecal samples from 32 animals captured in 2013-2014 for eggs, oocysts and larvae of parasites and detected 7 parasite species: dorsal-spined larvae protostrongylids, presumably Parelaphostrongylus andersoni based on PCR identification of a subset, Nematodirus odocoilei and other unidentified Strongyles, Trichuris sp., Capillaria sp., Moniezia sp. and Eimeria sp. For each caribou, mean parasite species richness was 1.8 ± 1.1 (SD). Sex, body condition, year and capture location did not explain parasite prevalence, intensity of infection or richness except for intensity of infection of Capillaria sp. that was positively influenced by body condition. Parasites did not influence survival although mortality was higher for males than for females. We suggest that the relatively low and common gastrointestinal and protostrongylid parasite infections will not be a short-term threat leading to extinction.

A spectral boundary integral equation method for the 2-D Helmholtz equation

NASA Technical Reports Server (NTRS)

Hu, Fang Q.

1994-01-01

In this paper, we present a new numerical formulation of solving the boundary integral equations reformulated from the Helmholtz equation. The boundaries of the problems are assumed to be smooth closed contours. The solution on the boundary is treated as a periodic function, which is in turn approximated by a truncated Fourier series. A Fourier collocation method is followed in which the boundary integral equation is transformed into a system of algebraic equations. It is shown that in order to achieve spectral accuracy for the numerical formulation, the nonsmoothness of the integral kernels, associated with the Helmholtz equation, must be carefully removed. The emphasis of the paper is on investigating the essential elements of removing the nonsmoothness of the integral kernels in the spectral implementation. The present method is robust for a general boundary contour. Aspects of efficient implementation of the method using FFT are also discussed. A numerical example of wave scattering is given in which the exponential accuracy of the present numerical method is demonstrated.

The application of the least squares finite element method to Abel's integral equation. [with application to glow discharge problem

NASA Technical Reports Server (NTRS)

Balasubramanian, R.; Norrie, D. H.; De Vries, G.

1979-01-01

Abel's integral equation is the governing equation for certain problems in physics and engineering, such as radiation from distributed sources. The finite element method for the solution of this non-linear equation is presented for problems with cylindrical symmetry and the extension to more general integral equations is indicated. The technique was applied to an axisymmetric glow discharge problem and the results show excellent agreement with previously obtained solutions

On one solution of Volterra integral equations of second kind

NASA Astrophysics Data System (ADS)

Myrhorod, V.; Hvozdeva, I.

2016-10-01

A solution of Volterra integral equations of the second kind with separable and difference kernels based on solutions of corresponding equations linking the kernel and resolvent is suggested. On the basis of a discrete functions class, the equations linking the kernel and resolvent are obtained and the methods of their analytical solutions are proposed. A mathematical model of the gas-turbine engine state modification processes in the form of Volterra integral equation of the second kind with separable kernel is offered.

A parameter study of the two-fluid solar wind

NASA Technical Reports Server (NTRS)

Sandbaek, Ornulf; Leer, Egil; Holzer, Thomas E.

1992-01-01

A two-fluid model of the solar wind was introduced by Sturrock and Hartle (1966) and Hartle and Sturrock (1968). In these studies the proton energy equation was integrated neglecting the heat conductive term. Later several authors solved the equations for the two-fluid solar wind model keeping the proton heat conductive term. Methods where the equations are integrated simultaneously outward and inward from the critical point were used. The equations were also integrated inward from a large heliocentric distance. These methods have been applied to cases with low coronal base electron densities and high base temperatures. In this paper we present a method of integrating the two-fluid solar wind equations using an iteration procedure where the equations are integrated separately and the proton flux is kept constant during the integrations. The technique is applicable for a wide range of coronal base densities and temperatures. The method is used to carry out a parameter study of the two-fluid solar wind.

The staircase method: integrals for periodic reductions of integrable lattice equations

NASA Astrophysics Data System (ADS)

van der Kamp, Peter H.; Quispel, G. R. W.

2010-11-01

We show, in full generality, that the staircase method (Papageorgiou et al 1990 Phys. Lett. A 147 106-14, Quispel et al 1991 Physica A 173 243-66) provides integrals for mappings, and correspondences, obtained as traveling wave reductions of (systems of) integrable partial difference equations. We apply the staircase method to a variety of equations, including the Korteweg-De Vries equation, the five-point Bruschi-Calogero-Droghei equation, the quotient-difference (QD)-algorithm and the Boussinesq system. We show that, in all these cases, if the staircase method provides r integrals for an n-dimensional mapping, with 2r, then one can introduce q <= 2r variables, which reduce the dimension of the mapping from n to q. These dimension-reducing variables are obtained as joint invariants of k-symmetries of the mappings. Our results support the idea that often the staircase method provides sufficiently many integrals for the periodic reductions of integrable lattice equations to be completely integrable. We also study reductions on other quad-graphs than the regular {\\ Z}^2 lattice, and we prove linear growth of the multi-valuedness of iterates of high-dimensional correspondences obtained as reductions of the QD-algorithm.

An integrable semi-discrete Degasperis-Procesi equation

NASA Astrophysics Data System (ADS)

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

2017-06-01

Based on our previous work on the Degasperis-Procesi equation (Feng et al J. Phys. A: Math. Theor. 46 045205) and the integrable semi-discrete analogue of its short wave limit (Feng et al J. Phys. A: Math. Theor. 48 135203), we derive an integrable semi-discrete Degasperis-Procesi equation by Hirota’s bilinear method. Furthermore, N-soliton solution to the semi-discrete Degasperis-Procesi equation is constructed. It is shown that both the proposed semi-discrete Degasperis-Procesi equation, and its N-soliton solution converge to ones of the original Degasperis-Procesi equation in the continuum limit.

The Kadomtsev{endash}Petviashvili equation as a source of integrable model equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maccari, A.

1996-12-01

A new integrable and nonlinear partial differential equation (PDE) in 2+1 dimensions is obtained, by an asymptotically exact reduction method based on Fourier expansion and spatiotemporal rescaling, from the Kadomtsev{endash}Petviashvili equation. The integrability property is explicitly demonstrated, by exhibiting the corresponding Lax pair, that is obtained by applying the reduction technique to the Lax pair of the Kadomtsev{endash}Petviashvili equation. This model equation is likely to be of applicative relevance, because it may be considered a consistent approximation of a large class of nonlinear evolution PDEs. {copyright} {ital 1996 American Institute of Physics.}

Simplifying Differential Equations for Multiscale Feynman Integrals beyond Multiple Polylogarithms.

PubMed

Adams, Luise; Chaubey, Ekta; Weinzierl, Stefan

2017-04-07

In this Letter we exploit factorization properties of Picard-Fuchs operators to decouple differential equations for multiscale Feynman integrals. The algorithm reduces the differential equations to blocks of the size of the order of the irreducible factors of the Picard-Fuchs operator. As a side product, our method can be used to easily convert the differential equations for Feynman integrals which evaluate to multiple polylogarithms to an ϵ form.

Solution of the nonlinear mixed Volterra-Fredholm integral equations by hybrid of block-pulse functions and Bernoulli polynomials.

PubMed

Mashayekhi, S; Razzaghi, M; Tripak, O

2014-01-01

A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear mixed Volterra-Fredholm integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

Solution of the Nonlinear Mixed Volterra-Fredholm Integral Equations by Hybrid of Block-Pulse Functions and Bernoulli Polynomials

PubMed Central

Mashayekhi, S.; Razzaghi, M.; Tripak, O.

2014-01-01

A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear mixed Volterra-Fredholm integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. PMID:24523638

Two volume integral equations for the inhomogeneous and anisotropic forward problem in electroencephalography

NASA Astrophysics Data System (ADS)

Rahmouni, Lyes; Mitharwal, Rajendra; Andriulli, Francesco P.

2017-11-01

This work presents two new volume integral equations for the Electroencephalography (EEG) forward problem which, differently from the standard integral approaches in the domain, can handle heterogeneities and anisotropies of the head/brain conductivity profiles. The new formulations translate to the quasi-static regime some volume integral equation strategies that have been successfully applied to high frequency electromagnetic scattering problems. This has been obtained by extending, to the volume case, the two classical surface integral formulations used in EEG imaging and by introducing an extra surface equation, in addition to the volume ones, to properly handle boundary conditions. Numerical results corroborate theoretical treatments, showing the competitiveness of our new schemes over existing techniques and qualifying them as a valid alternative to differential equation based methods.

Algebraic Construction of Exact Difference Equations from Symmetry of Equations

NASA Astrophysics Data System (ADS)

Itoh, Toshiaki

2009-09-01

Difference equations or exact numerical integrations, which have general solutions, are treated algebraically. Eliminating the symmetries of the equation, we can construct difference equations (DCE) or numerical integrations equivalent to some ODEs or PDEs that means both have the same solution functions. When arbitrary functions are given, whether we can construct numerical integrations that have solution functions equal to given function or not are treated in this work. Nowadays, Lie's symmetries solver for ODE and PDE has been implemented in many symbolic software. Using this solver we can construct algebraic DCEs or numerical integrations which are correspond to some ODEs or PDEs. In this work, we treated exact correspondence between ODE or PDE and DCE or numerical integration with Gröbner base and Janet base from the view of Lie's symmetries.

Integral Equations in Computational Electromagnetics: Formulations, Properties and Isogeometric Analysis

NASA Astrophysics Data System (ADS)

Lovell, Amy Elizabeth

Computational electromagnetics (CEM) provides numerical methods to simulate electromagnetic waves interacting with its environment. Boundary integral equation (BIE) based methods, that solve the Maxwell's equations in the homogeneous or piecewise homogeneous medium, are both efficient and accurate, especially for scattering and radiation problems. Development and analysis electromagnetic BIEs has been a very active topic in CEM research. Indeed, there are still many open problems that need to be addressed or further studied. A short and important list includes (1) closed-form or quasi-analytical solutions to time-domain integral equations, (2) catastrophic cancellations at low frequencies, (3) ill-conditioning due to high mesh density, multi-scale discretization, and growing electrical size, and (4) lack of flexibility due to re-meshing when increasing number of forward numerical simulations are involved in the electromagnetic design process. This dissertation will address those several aspects of boundary integral equations in computational electromagnetics. The first contribution of the dissertation is to construct quasi-analytical solutions to time-dependent boundary integral equations using a direct approach. Direct inverse Fourier transform of the time-harmonic solutions is not stable due to the non-existence of the inverse Fourier transform of spherical Hankel functions. Using new addition theorems for the time-domain Green's function and dyadic Green's functions, time-domain integral equations governing transient scattering problems of spherical objects are solved directly and stably for the first time. Additional, the direct time-dependent solutions, together with the newly proposed time-domain dyadic Green's functions, can enrich the time-domain spherical multipole theory. The second contribution is to create a novel method of moments (MoM) framework to solve electromagnetic boundary integral equation on subdivision surfaces. The aim is to avoid the meshing and re-meshing stages to accelerate the design process when the geometry needs to be updated. Two schemes to construct basis functions on the subdivision surface have been explored. One is to use the div-conforming basis function, and the other one is to create a rigorous iso-geometric approach based on the subdivision basis function with better smoothness properties. This new framework provides us better accuracy, more stability and high flexibility. The third contribution is a new stable integral equation formulation to avoid catastrophic cancellations due to low-frequency breakdown or dense-mesh breakdown. Many of the conventional integral equations and their associated post-processing operations suffer from numerical catastrophic cancellations, which can lead to ill-conditioning of the linear systems or serious accuracy problems. Examples includes low-frequency breakdown and dense mesh breakdown. Another instability may come from nontrivial null spaces of involving integral operators that might be related with spurious resonance or topology breakdown. This dissertation presents several sets of new boundary integral equations and studies their analytical properties. The first proposed formulation leads to the scalar boundary integral equations where only scalar unknowns are involved. Besides the requirements of gaining more stability and better conditioning in the resulting linear systems, multi-physics simulation is another driving force for new formulations. Scalar and vector potentials (rather than electromagnetic field) based formulation have been studied for this purpose. Those new contributions focus on different stages of boundary integral equations in an almost independent manner, e.g. isogeometric analysis framework can be used to solve different boundary integral equations, and the time-dependent solutions to integral equations from different formulations can be achieved through the same methodology proposed.

Liouvillian propagators, Riccati equation and differential Galois theory

NASA Astrophysics Data System (ADS)

Acosta-Humánez, Primitivo; Suazo, Erwin

2013-11-01

In this paper a Galoisian approach to building propagators through Riccati equations is presented. The main result corresponds to the relationship between the Galois integrability of the linear Schrödinger equation and the virtual solvability of the differential Galois group of its associated characteristic equation. As the main application of this approach we solve Ince’s differential equation through the Hamiltonian algebrization procedure and the Kovacic algorithm to find the propagator for a generalized harmonic oscillator. This propagator has applications which describe the process of degenerate parametric amplification in quantum optics and light propagation in a nonlinear anisotropic waveguide. Toy models of propagators inspired by integrable Riccati equations and integrable characteristic equations are also presented.

Master equations and the theory of stochastic path integrals

NASA Astrophysics Data System (ADS)

Weber, Markus F.; Frey, Erwin

2017-04-01

This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a ‘generating functional’, which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a ‘forward’ and a ‘backward’ path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon expanding the forward and the backward path integrals around stationary paths, we then discuss and extend a recent method for the computation of rare event probabilities. Besides, we also derive path integral representations for processes with continuous state spaces whose forward and backward master equations admit Kramers-Moyal expansions. A truncation of the backward expansion at the level of a diffusion approximation recovers a classic path integral representation of the (backward) Fokker-Planck equation. One can rewrite this path integral in terms of an Onsager-Machlup function and, for purely diffusive Brownian motion, it simplifies to the path integral of Wiener. To make this review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory and do not assume any knowledge of the latter. The probabilistic structures underpinning various technical concepts, such as coherent states, the Doi-shift, and normal-ordered observables, are thereby made explicit.

Master equations and the theory of stochastic path integrals.

PubMed

Weber, Markus F; Frey, Erwin

2017-04-01

This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master equations have served as a fundamental tool to understand the role of fluctuations in complex biological, chemical, and physical systems. Despite their simple appearance, analyses of master equations most often rely on low-noise approximations such as the Kramers-Moyal or the system size expansion, or require ad-hoc closure schemes for the derivation of low-order moment equations. We focus on numerical and analytical methods going beyond the low-noise limit and provide a unified framework for the study of master equations. After deriving the forward and backward master equations from the Chapman-Kolmogorov equation, we show how the two master equations can be cast into either of four linear partial differential equations (PDEs). Three of these PDEs are discussed in detail. The first PDE governs the time evolution of a generalized probability generating function whose basis depends on the stochastic process under consideration. Spectral methods, WKB approximations, and a variational approach have been proposed for the analysis of the PDE. The second PDE is novel and is obeyed by a distribution that is marginalized over an initial state. It proves useful for the computation of mean extinction times. The third PDE describes the time evolution of a 'generating functional', which generalizes the so-called Poisson representation. Subsequently, the solutions of the PDEs are expressed in terms of two path integrals: a 'forward' and a 'backward' path integral. Combined with inverse transformations, one obtains two distinct path integral representations of the conditional probability distribution solving the master equations. We exemplify both path integrals in analysing elementary chemical reactions. Moreover, we show how a well-known path integral representation of averaged observables can be recovered from them. Upon expanding the forward and the backward path integrals around stationary paths, we then discuss and extend a recent method for the computation of rare event probabilities. Besides, we also derive path integral representations for processes with continuous state spaces whose forward and backward master equations admit Kramers-Moyal expansions. A truncation of the backward expansion at the level of a diffusion approximation recovers a classic path integral representation of the (backward) Fokker-Planck equation. One can rewrite this path integral in terms of an Onsager-Machlup function and, for purely diffusive Brownian motion, it simplifies to the path integral of Wiener. To make this review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory and do not assume any knowledge of the latter. The probabilistic structures underpinning various technical concepts, such as coherent states, the Doi-shift, and normal-ordered observables, are thereby made explicit.

Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations

NASA Astrophysics Data System (ADS)

Eden, Burkhard; Smirnov, Vladimir A.

2016-10-01

We evaluate a four-loop conformal integral, i.e. an integral over four four-dimensional coordinates, by turning to its dimensionally regularized version and applying differential equations for the set of the corresponding 213 master integrals. To solve these linear differential equations we follow the strategy suggested by Henn and switch to a uniformly transcendental basis of master integrals. We find a solution to these equations up to weight eight in terms of multiple polylogarithms. Further, we present an analytical result for the given four-loop conformal integral considered in four-dimensional space-time in terms of single-valued harmonic polylogarithms. As a by-product, we obtain analytical results for all the other 212 master integrals within dimensional regularization, i.e. considered in D dimensions.

Genetic diversity of dihydrochalcone content in Malus germplasm

USDA-ARS?s Scientific Manuscript database

Dihydrochalcones, beneficial phenolic compounds, are abundant in Malus Mill. species, particularly in vegetative tissues and seeds. Phloridzin (phloretin 2'-O-glucoside) is the primary dihydrochalcone in most Malus species including cultivated apple, Malus ×domestica Borkh. A few species contain sie...

Application of the Sumudu Transform to Discrete Dynamic Systems

ERIC Educational Resources Information Center

Asiru, Muniru Aderemi

2003-01-01

The Sumudu transform is an integral transform introduced to solve differential equations and control engineering problems. The transform possesses many interesting properties that make visualization easier and application has been demonstrated in the solution of partial differential equations, integral equations, integro-differential equations and…

Computational Algorithms or Identification of Distributed Parameter Systems

DTIC Science & Technology

1993-04-24

delay-differential equations, Volterra integral equations, and partial differential equations with memory terms . In particular we investigated a...tested for estimating parameters in a Volterra integral equation arising from a viscoelastic model of a flexible structure with Boltzmann damping. In...particular, one of the parameters identified was the order of the derivative in Volterra integro-differential equations containing fractional

Application of integral equation theory to analyze stability of electric field in multimode microwave heating cavity

NASA Astrophysics Data System (ADS)

Tang, Zhengming; Hong, Tao; Chen, Fangyuan; Zhu, Huacheng; Huang, Kama

2017-10-01

Microwave heating uniformity is mainly dependent on and affected by electric field. However, little study has paid attention to its stability characteristics in multimode cavity. In this paper, this problem is studied by the theory of Freedholm integral equation. Firstly, Helmholtz equation and the electric dyadic Green's function are used to derive the electric field integral equation. Then, the stability of electric field is demonstrated as the characteristics of solutions to Freedholm integral equation. Finally, the stability characteristics are obtained and verified by finite element calculation. This study not only can provide a comprehensive interpretation of electric field in multimode cavity but also help us make better use of microwave energy.

A semi-discrete Kadomtsev-Petviashvili equation and its coupled integrable system

NASA Astrophysics Data System (ADS)

Li, Chun-Xia; Lafortune, Stéphane; Shen, Shou-Feng

2016-05-01

We establish connections between two cascades of integrable systems generated from the continuum limits of the Hirota-Miwa equation and its remarkable nonlinear counterpart under the Miwa transformation, respectively. Among these equations, we are mainly concerned with the semi-discrete bilinear Kadomtsev-Petviashvili (KP) equation which is seldomly studied in literature. We present both of its Casorati and Grammian determinant solutions. Through the Pfaffianization procedure proposed by Hirota and Ohta, we are able to derive the coupled integrable system for the semi-discrete KP equation.

Whitham modulation theory for (2  +  1)-dimensional equations of Kadomtsev–Petviashvili type

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Biondini, Gino; Rumanov, Igor

2018-05-01

Whitham modulation theory for certain two-dimensional evolution equations of Kadomtsev–Petviashvili (KP) type is presented. Three specific examples are considered in detail: the KP equation, the two-dimensional Benjamin–Ono (2DBO) equation and a modified KP (m2KP) equation. A unified derivation is also provided. In the case of the m2KP equation, the corresponding Whitham modulation system exhibits features different from the other two. The approach presented here does not require integrability of the original evolution equation. Indeed, while the KP equation is known to be a completely integrable equation, the 2DBO equation and the m2KP equation are not known to be integrable. In each of the cases considered, the Whitham modulation system obtained consists of five first-order quasilinear partial differential equations. The Riemann problem (i.e. the analogue of the Gurevich–Pitaevskii problem) for the one-dimensional reduction of the m2KP equation is studied. For the m2KP equation, the system of modulation equations is used to analyze the linear stability of traveling wave solutions.

Applied Mathematical Methods in Theoretical Physics

NASA Astrophysics Data System (ADS)

Masujima, Michio

2005-04-01

All there is to know about functional analysis, integral equations and calculus of variations in a single volume. This advanced textbook is divided into two parts: The first on integral equations and the second on the calculus of variations. It begins with a short introduction to functional analysis, including a short review of complex analysis, before continuing a systematic discussion of different types of equations, such as Volterra integral equations, singular integral equations of Cauchy type, integral equations of the Fredholm type, with a special emphasis on Wiener-Hopf integral equations and Wiener-Hopf sum equations. After a few remarks on the historical development, the second part starts with an introduction to the calculus of variations and the relationship between integral equations and applications of the calculus of variations. It further covers applications of the calculus of variations developed in the second half of the 20th century in the fields of quantum mechanics, quantum statistical mechanics and quantum field theory. Throughout the book, the author presents over 150 problems and exercises -- many from such branches of physics as quantum mechanics, quantum statistical mechanics, and quantum field theory -- together with outlines of the solutions in each case. Detailed solutions are given, supplementing the materials discussed in the main text, allowing problems to be solved making direct use of the method illustrated. The original references are given for difficult problems. The result is complete coverage of the mathematical tools and techniques used by physicists and applied mathematicians Intended for senior undergraduates and first-year graduates in science and engineering, this is equally useful as a reference and self-study guide.

Green's function solution to heat transfer of a transparent gas through a tube

NASA Technical Reports Server (NTRS)

Frankel, J. I.

1989-01-01

A heat transfer analysis of a transparent gas flowing through a circular tube of finite thickness is presented. This study includes the effects of wall conduction, internal radiative exchange, and convective heat transfer. The natural mathematical formulation produces a nonlinear, integrodifferential equation governing the wall temperature and an ordinary differential equation describing the gas temperature. This investigation proposes to convert the original system of equations into an equivalent system of integral equations. The Green's function method permits the conversion of an integrodifferential equation into a pure integral equation. The proposed integral formulation and subsequent computational procedure are shown to be stable and accurate.

First integrals of the axisymmetric shape equation of lipid membranes

NASA Astrophysics Data System (ADS)

Zhang, Yi-Heng; McDargh, Zachary; Tu, Zhan-Chun

2018-03-01

The shape equation of lipid membranes is a fourth-order partial differential equation. Under the axisymmetric condition, this equation was transformed into a second-order ordinary differential equation (ODE) by Zheng and Liu (Phys. Rev. E 48 2856 (1993)). Here we try to further reduce this second-order ODE to a first-order ODE. First, we invert the usual process of variational calculus, that is, we construct a Lagrangian for which the ODE is the corresponding Euler–Lagrange equation. Then, we seek symmetries of this Lagrangian according to the Noether theorem. Under a certain restriction on Lie groups of the shape equation, we find that the first integral only exists when the shape equation is identical to the Willmore equation, in which case the symmetry leading to the first integral is scale invariance. We also obtain the mechanical interpretation of the first integral by using the membrane stress tensor. Project supported by the National Natural Science Foundation of China (Grant No. 11274046) and the National Science Foundation of the United States (Grant No. 1515007).

Quantifying the influence of safe road systems and legal licensing age on road mortality among young adolescents: steps towards system thinking.

PubMed

Twisk, Divera; Commandeur, Jacques J F; Bos, Niels; Shope, Jean T; Kok, Gerjo

2015-01-01

Based on existing literature, a system thinking approach was used to set up a conceptual model on the interrelationships among the components influencing adolescent road mortality, distinguishing between components at the individual level and at the system level. At the individual level the role of risk behaviour (sometimes deliberate and sometimes from inexperience or other non-deliberate causes) in adolescent road mortality is well documented. However, little is known about the extent to which the 'road system' itself may also have an impact on younger adolescents' road mortality. This, by providing a safe or unsafe road environment for all road users (System-induced exposure) and by allowing access to high-risk vehicles at a young or older age through the legal licensing age. This study seeks to explore these relationships by analysing the extent to which the road mortality of 10 to 17 year olds in various jurisdictions can be predicted from the System-induced Exposure (SiE) in a jurisdiction and from its legal licensing age to drive motor vehicles. SiE was operationalized as the number of road fatalities per 10(5) inhabitants/all ages together, but excluding the 10 to 17 year olds. Data on road fatalities during the years 2001 through 2008 were obtained from the OECD International Road Traffic Accident Database (IRTAD) and from the USA NHTSA's Fatality Analysis Reporting System (FARS) database for 29 early and 10 late licensing jurisdictions. Linear mixed models were fitted with annual 'Adolescent road mortality per capita' for 2001 through 2008 as the dependent variable, and time-dependent 'SiE' and time-independent 'Licensing system' as predictor variables. To control for different levels of motorisation, the time-dependent variable 'Annual per capita vehicle distance travelled' was used as a covariate. Licensing system of a jurisdiction was entered as a categorical predictor variable with late licensing countries as a baseline group. The study found support for the protective effects of SiE on adolescent safety. If SiE increased by one unit, the mortality rate of 10 to 17 year olds increased by 0.487 units. No support was found for a protective effect of late licensing for this age group. Thus, compared to young adolescents who are allowed to drive motor vehicles in early licensing jurisdictions, late licensing does not provide extra protection for pre-license adolescents. This finding is probably the result of the high risks associated with alternative transport modes, such as moped riding and bicycling. Also, the fact that the study only included risks to young adolescents themselves and did not include the risks they might pose to other road users and passengers may have contributed to this finding, because such risks are greater when driving a motor vehicle than riding a moped or a bicycle. Therefore, to advance our understanding of the impact of licensing systems, more study is needed into the benefits of early or late licensing, thereby considering these wider effects as well. Copyright © 2014 Elsevier Ltd. All rights reserved.

Derivation of the Schrodinger Equation from the Hamilton-Jacobi Equation in Feynman's Path Integral Formulation of Quantum Mechanics

ERIC Educational Resources Information Center

Field, J. H.

2011-01-01

It is shown how the time-dependent Schrodinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schrodinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi…

Exponential Methods for the Time Integration of Schroedinger Equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cano, B.; Gonzalez-Pachon, A.

2010-09-30

We consider exponential methods of second order in time in order to integrate the cubic nonlinear Schroedinger equation. We are interested in taking profit of the special structure of this equation. Therefore, we look at symmetry, symplecticity and approximation of invariants of the proposed methods. That will allow to integrate till long times with reasonable accuracy. Computational efficiency is also our aim. Therefore, we make numerical computations in order to compare the methods considered and so as to conclude that explicit Lawson schemes projected on the norm of the solution are an efficient tool to integrate this equation.

Kunststoffe (Polymere)

NASA Astrophysics Data System (ADS)

Weißbach, Wolfgang

Polymere bestehen aus Riesen- oder Makromolekülen, die durch chemische Reaktionen aus einfachen, niedermolekularen Verbindungen entstehen, den Monomeren. Ausgangsstoffe sind überwiegend Kohlenwasserstoffe (KW), die größte Gruppe der C-Verbindungen. Sie müssen reaktionsfähige Stellen besitzen, das sind OH-Gruppen oder Dopppelbindungen.

Extracting laboratory test information from biomedical text

PubMed Central

Kang, Yanna Shen; Kayaalp, Mehmet

2013-01-01

Background: No previous study reported the efficacy of current natural language processing (NLP) methods for extracting laboratory test information from narrative documents. This study investigates the pathology informatics question of how accurately such information can be extracted from text with the current tools and techniques, especially machine learning and symbolic NLP methods. The study data came from a text corpus maintained by the U.S. Food and Drug Administration, containing a rich set of information on laboratory tests and test devices. Methods: The authors developed a symbolic information extraction (SIE) system to extract device and test specific information about four types of laboratory test entities: Specimens, analytes, units of measures and detection limits. They compared the performance of SIE and three prominent machine learning based NLP systems, LingPipe, GATE and BANNER, each implementing a distinct supervised machine learning method, hidden Markov models, support vector machines and conditional random fields, respectively. Results: Machine learning systems recognized laboratory test entities with moderately high recall, but low precision rates. Their recall rates were relatively higher when the number of distinct entity values (e.g., the spectrum of specimens) was very limited or when lexical morphology of the entity was distinctive (as in units of measures), yet SIE outperformed them with statistically significant margins on extracting specimen, analyte and detection limit information in both precision and F-measure. Its high recall performance was statistically significant on analyte information extraction. Conclusions: Despite its shortcomings against machine learning methods, a well-tailored symbolic system may better discern relevancy among a pile of information of the same type and may outperform a machine learning system by tapping into lexically non-local contextual information such as the document structure. PMID:24083058

Pratique de l’analgésie péridurale auprès de 20 parturientes au Centre Hospitalier Universitaire Sylvanus Olympio de Lomé (Togo)

PubMed Central

Egbohou, Pilakimwé; Mouzou, Tabana; Sama, Hamza Doles; Tchétike, Pikabalo; Assénouwé, Sarakawabalo; Akala-Yoba, Gnimdou; Tomta, Kadjika

2017-01-01

Etude prospective et descriptive sur la pratique de l’analgésie péridurale (APD) obstétricale au CHU Sylvanus Olympio (CHU SO) de Lomé. Etude menée de février à juin 2014. Après accord des gestantes choisies au hasard et en l’absence de contre-indication à l’issue de la consultation d’anesthésie, faite au 8ème mois de la grossesse, des femmes ont été retenues pour l’étude. Sur 29 gestantes retenues, 20 (69%) ont bénéficiées de l’APD. Age moyen 30,6±6,6 ans, primigestes : 35%, multipares 50%, Obèses (BMI>30): 25%. Nombre moyen de ponctions: 1,2±0,5; reflux de sang dans le cathéter: 5%, brèche dure-mérienne : 0. Délai moyen d’installation: 8,5 ±2,2mn. Quantité moyenne de bupivacaine isobare à 0,125%: 28,8±8ml; Echelle Numérique à T10min < 3 pour toutes les parturientes. Bloc moteur: 0. Hypotension: 1cas (5%). Mode d’accouchement: voie basse: 19 (95%), césarienne: 1 (5%). Détresse respiratoire à la naissance du nouveau né: 0. Note de satisfaction: 9,8±0,5 /10. L’APD obstétricale est possible au CHU Sylvanus Olympio de Lomé. En attendant sa vulgarisation à toutes les parturientes par la disponibilité des moyens humains et matériels, la réaliser pour ses indications médicales serait un premier pas. PMID:28451033

Discrete integration of continuous Kalman filtering equations for time invariant second-order structural systems

NASA Technical Reports Server (NTRS)

Park, K. C.; Belvin, W. Keith

1990-01-01

A general form for the first-order representation of the continuous second-order linear structural-dynamics equations is introduced to derive a corresponding form of first-order continuous Kalman filtering equations. Time integration of the resulting equations is carried out via a set of linear multistep integration formulas. It is shown that a judicious combined selection of computational paths and the undetermined matrices introduced in the general form of the first-order linear structural systems leads to a class of second-order discrete Kalman filtering equations involving only symmetric sparse N x N solution matrices.

Integrability and structural stability of solutions to the Ginzburg-Landau equation

NASA Technical Reports Server (NTRS)

Keefe, Laurence R.

1986-01-01

The integrability of the Ginzburg-Landau equation is studied to investigate if the existence of chaotic solutions found numerically could have been predicted a priori. The equation is shown not to possess the Painleveproperty, except for a special case of the coefficients that corresponds to the integrable, nonlinear Schroedinger (NLS) equation. Regarding the Ginzburg-Landau equation as a dissipative perturbation of the NLS, numerical experiments show all but one of a family of two-tori solutions, possessed by the NLS under particular conditions, to disappear under real perturbations to the NLS coefficients of O(10 to the -6th).

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.

Effective quadrature formula in solving linear integro-differential equations of order two

NASA Astrophysics Data System (ADS)

Eshkuvatov, Z. K.; Kammuji, M.; Long, N. M. A. Nik; Yunus, Arif A. M.

2017-08-01

In this note, we solve general form of Fredholm-Volterra integro-differential equations (IDEs) of order 2 with boundary condition approximately and show that proposed method is effective and reliable. Initially, IDEs is reduced into integral equation of the third kind by using standard integration techniques and identity between multiple and single integrals then truncated Legendre series are used to estimate the unknown function. For the kernel integrals, we have applied Gauss-Legendre quadrature formula and collocation points are chosen as the roots of the Legendre polynomials. Finally, reduce the integral equations of the third kind into the system of algebraic equations and Gaussian elimination method is applied to get approximate solutions. Numerical examples and comparisons with other methods reveal that the proposed method is very effective and dominated others in many cases. General theory of existence of the solution is also discussed.

An integrable family of Monge-Ampère equations and their multi-Hamiltonian structure

NASA Astrophysics Data System (ADS)

Nutku, Y.; Sarioǧlu, Ö.

1993-02-01

We have identified a completely integrable family of Monge-Ampère equations through an examination of their Hamiltonian structure. Starting with a variational formulation of the Monge-Ampère equations we have constructed the first Hamiltonian operator through an application of Dirac's theory of constraints. The completely integrable class of Monge-Ampère equations are then obtained by solving the Jacobi identities for a sufficiently general form of the second Hamiltonian operator that is compatible with the first.

Extremely Fast Numerical Integration of Ocean Surface Wave Dynamics

DTIC Science & Technology

2007-09-30

sub-processor must be added as shown in the blue box of Fig. 1. We first consider the Kadomtsev - Petviashvili (KP) equation ηt + coηx +αηηx + βη ...analytic integration of the so-called “soliton equations ,” I have discovered how the GFT can be used to solved higher order equations for which study...analytical study and extremely fast numerical integration of the extended nonlinear Schroedinger equation for fully three dimensional wave motion

Alternate Solution to Generalized Bernoulli Equations via an Integrating Factor: An Exact Differential Equation Approach

ERIC Educational Resources Information Center

Tisdell, C. C.

2017-01-01

Solution methods to exact differential equations via integrating factors have a rich history dating back to Euler (1740) and the ideas enjoy applications to thermodynamics and electromagnetism. Recently, Azevedo and Valentino presented an analysis of the generalized Bernoulli equation, constructing a general solution by linearizing the problem…

Continuous properties of the data-to-solution map for a generalized μ-Camassa-Holm integrable equation

NASA Astrophysics Data System (ADS)

Yu, Shengqi

2018-05-01

This work studies a generalized μ-type integrable equation with both quadratic and cubic nonlinearities; the μ-Camassa-Holm and modified μ-Camassa-Holm equations are members of this family of equations. It has been shown that the Cauchy problem for this generalized μ-Camassa-Holm integrable equation is locally well-posed for initial data u0 ∈ Hs, s > 5/2. In this work, we further investigate the continuity properties to this equation. It is proved in this work that the data-to-solution map of the proposed equation is not uniformly continuous. It is also found that the solution map is Hölder continuous in the Hr-topology when 0 ≤ r < s with Hölder exponent α depending on both s and r.

More Supernova Surprises

DTIC Science & Technology

2010-09-24

originated in South America. E veryone appreciates the beauty of dai- sies, chrysanthemums, and sunfl ow- ers, and many of us enjoy eating lettuce ...few fossils. On page 1621 of this issue, Barreda et al. ( 1) describe an unusually well-preserved new fossil that sheds light on the history of

Sticktechnologie für medizinische Textilien und Tissue Engineering

NASA Astrophysics Data System (ADS)

Karamuk, Erdal; Mayer, Jörg; Wintermantel, Erich

Textile Strukturen werden in grossem Ausmass als medizinische Implantate eingesetzt, um Weich- und Hartgewebe zu unterstützen oder zu ersetzen. Im Tissue Engineering gewinnen sie an Bedeutung als scaffolds, um biologische Gewebe in vitro zu züchten für anschliessende Implantation oder extrakorporale Anwendungen. Textilien sind gewöhnlich anisotrope zweidimensionale Strukturen mit hoher Steifigkeit in der Ebene und geringer Biegesteifigkeit. Durch eine Vielzahl textiler Prozesse und durch entsprechende Wahl des Fasermaterials ist es möglich, Oberfläche, Porosität und mechanische Anisotropie in hohem Masse zu variieren. Wegen ihrer einzigartigen strukturellen und mechanischen Eigenschaften können faserbasierte Materialien in weitem Masse biologischem Gewebe nachgeahmt werden [1]. Gesticke erweitern das Feld von technischen und besonders medizinischen Textilien, denn sie vereinen sehr hohe strukturelle Variabilität mit der Möglichkeit, mechanische Eigenschaften in einem grossen Bereich einzustellen, um so die mechanischen Anforderungen des Empfängergewebes zu erfüllen (Abb. 42.1).

Zahlen und Rechenvorgänge auf unterschiedlichen Abstraktionsniveaus

NASA Astrophysics Data System (ADS)

Rödler, Klaus

"Das Verständnis geht langsam vor sich!" Diesen wichtigen Satz hörte ich bei einem Vortrag von Martin Lowsky. Auf die hier behandelte Fragestellung übertragen heißt das: Was eine Zahl ist und wie ich sie im Rechenvorgang einsetzen und interpretieren kann, das erschließt sich erst allmählich. Die Zahl des Rechenanfängers ist nicht dieselbe wie die des kompetenten Rechners und es ist nicht die Zahl des Lehrers oder der Lehrerin. Die Zahlen sind nur auf der Oberfläche der Worte und Zeichen gleich. Im Innern, im Verständnis, sind sie völlig verschieden! Ich glaube, dass die Missachtung dieser Divergenz dazu führt, dass manche Kinder in für den Lehrer und Lehrerin nicht nachvollziehbaren Routinen stecken bleiben, einfachste Informationen nicht wirklich integrieren. Die auf beiden Seiten wachsende Verunsicherung durch die nicht erkannte und daher nicht kommunizierbare Diskrepanz im inneren Zahlkonzept stört den allmählichen Aufbau strukturierter Zahlvorstellungen.

Specifying the role of the left prefrontal cortex in word selection.

PubMed

Riès, S K; Karzmark, C R; Navarrete, E; Knight, R T; Dronkers, N F

2015-10-01

Word selection allows us to choose words during language production. This is often viewed as a competitive process wherein a lexical representation is retrieved among semantically-related alternatives. The left prefrontal cortex (LPFC) is thought to help overcome competition for word selection through top-down control. However, whether the LPFC is always necessary for word selection remains unclear. We tested 6 LPFC-injured patients and controls in two picture naming paradigms varying in terms of item repetition. Both paradigms elicited the expected semantic interference effects (SIE), reflecting interference caused by semantically-related representations in word selection. However, LPFC patients as a group showed a larger SIE than controls only in the paradigm involving item repetition. We argue that item repetition increases interference caused by semantically-related alternatives, resulting in increased LPFC-dependent cognitive control demands. The remaining network of brain regions associated with word selection appears to be sufficient when items are not repeated. Copyright © 2015 Elsevier Inc. All rights reserved.

A family of wave equations with some remarkable properties.

PubMed

da Silva, Priscila Leal; Freire, Igor Leite; Sampaio, Júlio Cesar Santos

2018-02-01

We consider a family of homogeneous nonlinear dispersive equations with two arbitrary parameters. Conservation laws are established from the point symmetries and imply that the whole family admits square integrable solutions. Recursion operators are found for two members of the family investigated. For one of them, a Lax pair is also obtained, proving its complete integrability. From the Lax pair, we construct a Miura-type transformation relating the original equation to the Korteweg-de Vries (KdV) equation. This transformation, on the other hand, enables us to obtain solutions of the equation from the kernel of a Schrödinger operator with potential parametrized by the solutions of the KdV equation. In particular, this allows us to exhibit a kink solution to the completely integrable equation from the 1-soliton solution of the KdV equation. Finally, peakon-type solutions are also found for a certain choice of the parameters, although for this particular case the equation is reduced to a homogeneous second-order nonlinear evolution equation.

A New Formulation of Time Domain Boundary Integral Equation for Acoustic Wave Scattering in the Presence of a Uniform Mean Flow

NASA Technical Reports Server (NTRS)

Hu, Fang; Pizzo, Michelle E.; Nark, Douglas M.

2017-01-01

It has been well-known that under the assumption of a constant uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation, in both the time domain and the frequency domain. Compared with solving partial differential equations, numerical methods based on the boundary integral equation have the advantage of a reduced spatial dimension and, hence, requiring only a surface mesh. However, the constant uniform mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the uniform mean flow. In this paper, we argue that the proper boundary condition for the acoustic wave should not have its normal velocity be zero everywhere on the solid surfaces, as has been applied in the literature. A careful study of the acoustic energy conservation equation is presented that shows such a boundary condition in fact leads to erroneous source or sink points on solid surfaces not aligned with the mean flow. A new solid wall boundary condition is proposed that conserves the acoustic energy and a new time domain boundary integral equation is derived. In addition to conserving the acoustic energy, another significant advantage of the new equation is that it is considerably simpler than previous formulations. In particular, tangential derivatives of the solution on the solid surfaces are no longer needed in the new formulation, which greatly simplifies numerical implementation. Furthermore, stabilization of the new integral equation by Burton-Miller type reformulation is presented. The stability of the new formulation is studied theoretically as well as numerically by an eigenvalue analysis. Numerical solutions are also presented that demonstrate the stability of the new formulation.

On a new semi-discrete integrable combination of Burgers and Sharma-Tasso-Olver equation

NASA Astrophysics Data System (ADS)

Zhao, Hai-qiong

2017-02-01

In this paper, a new semi-discrete integrable combination of Burgers and Sharma-Tasso-Olver equation is investigated. The underlying integrable structures like the Lax pair, the infinite number of conservation laws, the Darboux-Bäcklund transformation, and the solutions are presented in the explicit form. The theory of the semi-discrete equation including integrable properties yields the corresponding theory of the continuous counterpart in the continuous limit. Finally, numerical experiments are provided to demonstrate the effectiveness of the developed integrable semi-discretization algorithms.

Calculation of Moment Matrix Elements for Bilinear Quadrilaterals and Higher-Order Basis Functions

DTIC Science & Technology

2016-01-06

methods are known as boundary integral equation (BIE) methods and the present study falls into this category. The numerical solution of the BIE is...iterated integrals. The inner integral involves the product of the free-space Green’s function for the Helmholtz equation multiplied by an appropriate...Website: http://www.wipl-d.com/ 5. Y. Zhang and T. K. Sarkar, Parallel Solution of Integral Equation -Based EM Problems in the Frequency Domain. New

A numerical solution for two-dimensional Fredholm integral equations of the second kind with kernels of the logarithmic potential form

NASA Technical Reports Server (NTRS)

Gabrielsen, R. E.; Uenal, A.

1981-01-01

Two dimensional Fredholm integral equations with logarithmic potential kernels are numerically solved. The explicit consequence of these solutions to their true solutions is demonstrated. The results are based on a previous work in which numerical solutions were obtained for Fredholm integral equations of the second kind with continuous kernels.

Properties of the two-dimensional heterogeneous Lennard-Jones dimers: An integral equation study

PubMed Central

Urbic, Tomaz

2016-01-01

Structural and thermodynamic properties of a planar heterogeneous soft dumbbell fluid are examined using Monte Carlo simulations and integral equation theory. Lennard-Jones particles of different sizes are the building blocks of the dimers. The site-site integral equation theory in two dimensions is used to calculate the site-site radial distribution functions and the thermodynamic properties. Obtained results are compared to Monte Carlo simulation data. The critical parameters for selected types of dimers were also estimated and the influence of the Lennard-Jones parameters was studied. We have also tested the correctness of the site-site integral equation theory using different closures. PMID:27875894

Universal and integrable nonlinear evolution systems of equations in 2+1 dimensions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maccari, A.

1997-08-01

Integrable systems of nonlinear partial differential equations (PDEs) are obtained from integrable equations in 2+1 dimensions, by means of a reduction method of broad applicability based on Fourier expansion and spatio{endash}temporal rescalings, which is asymptotically exact in the limit of weak nonlinearity. The integrability by the spectral transform is explicitly demonstrated, because the corresponding Lax pairs have been derived, applying the same reduction method to the Lax pair of the initial equation. These systems of nonlinear PDEs are likely to be of applicative relevance and have a {open_quotes}universal{close_quotes} character, inasmuch as they may be derived from a very large classmore » of nonlinear evolution equations with a linear dispersive part. {copyright} {ital 1997 American Institute of Physics.}« less

Comparison of various methods for mathematical analysis of the Foucault knife edge test pattern to determine optical imperfections

NASA Technical Reports Server (NTRS)

Gatewood, B. E.

1971-01-01

The linearized integral equation for the Foucault test of a solid mirror was solved by various methods: power series, Fourier series, collocation, iteration, and inversion integral. The case of the Cassegrain mirror was solved by a particular power series method, collocation, and inversion integral. The inversion integral method appears to be the best overall method for both the solid and Cassegrain mirrors. Certain particular types of power series and Fourier series are satisfactory for the Cassegrain mirror. Numerical integration of the nonlinear equation for selected surface imperfections showed that results start to deviate from those given by the linearized equation at a surface deviation of about 3 percent of the wavelength of light. Several possible procedures for calibrating and scaling the input data for the integral equation are described.

Green function of the double-fractional Fokker-Planck equation: path integral and stochastic differential equations.

PubMed

Kleinert, H; Zatloukal, V

2013-11-01

The statistics of rare events, the so-called black-swan events, is governed by non-Gaussian distributions with heavy power-like tails. We calculate the Green functions of the associated Fokker-Planck equations and solve the related stochastic differential equations. We also discuss the subject in the framework of path integration.

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.

Finite-volume spectra of the Lee-Yang model

NASA Astrophysics Data System (ADS)

Bajnok, Zoltan; el Deeb, Omar; Pearce, Paul A.

2015-04-01

We consider the non-unitary Lee-Yang minimal model in three different finite geometries: (i) on the interval with integrable boundary conditions labelled by the Kac labels ( r, s) = (1 , 1) , (1 , 2), (ii) on the circle with periodic boundary conditions and (iii) on the periodic circle including an integrable purely transmitting defect. We apply φ 1,3 integrable perturbations on the boundary and on the defect and describe the flow of the spectrum. Adding a Φ1,3 integrable perturbation to move off-criticality in the bulk, we determine the finite size spectrum of the massive scattering theory in the three geometries via Thermodynamic Bethe Ansatz (TBA) equations. We derive these integral equations for all excitations by solving, in the continuum scaling limit, the TBA functional equations satisfied by the transfer matrices of the associated A 4 RSOS lattice model of Forrester and Baxter in Regime III. The excitations are classified in terms of ( m, n) systems. The excited state TBA equations agree with the previously conjectured equations in the boundary and periodic cases. In the defect case, new TBA equations confirm previously conjectured transmission factors.

The Green's matrix and the boundary integral equations for analysis of time-harmonic dynamics of elastic helical springs.

PubMed

Sorokin, Sergey V

2011-03-01

Helical springs serve as vibration isolators in virtually any suspension system. Various exact and approximate methods may be employed to determine the eigenfrequencies of vibrations of these structural elements and their dynamic transfer functions. The method of boundary integral equations is a meaningful alternative to obtain exact solutions of problems of the time-harmonic dynamics of elastic springs in the framework of Bernoulli-Euler beam theory. In this paper, the derivations of the Green's matrix, of the Somigliana's identities, and of the boundary integral equations are presented. The vibrational power transmission in an infinitely long spring is analyzed by means of the Green's matrix. The eigenfrequencies and the dynamic transfer functions are found by solving the boundary integral equations. In the course of analysis, the essential features and advantages of the method of boundary integral equations are highlighted. The reported analytical results may be used to study the time-harmonic motion in any wave guide governed by a system of linear differential equations in a single spatial coordinate along its axis. © 2011 Acoustical Society of America

Nonzero solutions of nonlinear integral equations modeling infectious disease

DOE Office of Scientific and Technical Information (OSTI.GOV)

Williams, L.R.; Leggett, R.W.

1982-01-01

Sufficient conditions to insure the existence of periodic solutions to the nonlinear integral equation, x(t) = ..integral../sup t//sub t-tau/f(s,x(s))ds, are given in terms of simple product and product integral inequalities. The equation can be interpreted as a model for the spread of infectious diseases (e.g., gonorrhea or any of the rhinovirus viruses) if x(t) is the proportion of infectives at time t and f(t,x(t)) is the proportion of new infectives per unit time.

Numerical integration of asymptotic solutions of ordinary differential equations

NASA Technical Reports Server (NTRS)

Thurston, Gaylen A.

1989-01-01

Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration.

Multistep integration formulas for the numerical integration of the satellite problem

NASA Technical Reports Server (NTRS)

Lundberg, J. B.; Tapley, B. D.

1981-01-01

The use of two Class 2/fixed mesh/fixed order/multistep integration packages of the PECE type for the numerical integration of the second order, nonlinear, ordinary differential equation of the satellite orbit problem. These two methods are referred to as the general and the second sum formulations. The derivation of the basic equations which characterize each formulation and the role of the basic equations in the PECE algorithm are discussed. Possible starting procedures are examined which may be used to supply the initial set of values required by the fixed mesh/multistep integrators. The results of the general and second sum integrators are compared to the results of various fixed step and variable step integrators.

Direct linearizing transform for three-dimensional discrete integrable systems: the lattice AKP, BKP and CKP equations.

PubMed

Fu, Wei; Nijhoff, Frank W

2017-07-01

A unified framework is presented for the solution structure of three-dimensional discrete integrable systems, including the lattice AKP, BKP and CKP equations. This is done through the so-called direct linearizing transform, which establishes a general class of integral transforms between solutions. As a particular application, novel soliton-type solutions for the lattice CKP equation are obtained.

Integrability of the Kruskal--Zabusky Discrete Equation by Multiscale Expansion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Levi, Decio; Scimiterna, Christian

2010-03-08

In 1965 Kruskal and Zabusky in a very famous article in Physical Review Letters introduced the notion of 'soliton' to describe the interaction of solitary waves solutions of the Korteweg de Vries equation (KdV). To do so they introduced a discrete approximation to the KdV, the Kruskal-Zabusky equation (KZ). Here we analyze the KZ equation using the multiscale expansion and show that the equation is only A{sub 2} integrable.

Integrability and Poisson Structures of Three Dimensional Dynamical Systems and Equations of Hydrodynamic Type

NASA Astrophysics Data System (ADS)

Gumral, Hasan

Poisson structure of completely integrable 3 dimensional dynamical systems can be defined in terms of an integrable 1-form. We take advantage of this fact and use the theory of foliations in discussing the geometrical structure underlying complete and partial integrability. We show that the Halphen system can be formulated in terms of a flat SL(2,R)-valued connection and belongs to a non-trivial Godbillon-Vey class. On the other hand, for the Euler top and a special case of 3-species Lotka-Volterra equations which are contained in the Halphen system as limiting cases, this structure degenerates into the form of globally integrable bi-Hamiltonian structures. The globally integrable bi-Hamiltonian case is a linear and the sl_2 structure is a quadratic unfolding of an integrable 1-form in 3 + 1 dimensions. We complete the discussion of the Hamiltonian structure of 2-component equations of hydrodynamic type by presenting the Hamiltonian operators for Euler's equation and a continuum limit of Toda lattice. We present further infinite sequences of conserved quantities for shallow water equations and show that their generalizations by Kodama admit bi-Hamiltonian structure. We present a simple way of constructing the second Hamiltonian operators for N-component equations admitting some scaling properties. The Kodama reduction of the dispersionless-Boussinesq equations and the Lax reduction of the Benney moment equations are shown to be equivalent by a symmetry transformation. They can be cast into the form of a triplet of conservation laws which enable us to recognize a non-trivial scaling symmetry. The resulting bi-Hamiltonian structure generates three infinite sequences of conserved densities.

Time-dependent integral equations of neutron transport for calculating the kinetics of nuclear reactors by the Monte Carlo method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Davidenko, V. D., E-mail: Davidenko-VD@nrcki.ru; Zinchenko, A. S., E-mail: zin-sn@mail.ru; Harchenko, I. K.

2016-12-15

Integral equations for the shape functions in the adiabatic, quasi-static, and improved quasi-static approximations are presented. The approach to solving these equations by the Monte Carlo method is described.

On the solution of integral equations with a generalized cauchy kernal

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1986-01-01

A certain class of singular integral equations that may arise from the mixed boundary value problems in nonhonogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted, the density function is a potential or a displacement and consequently the kernal has strong singularities of the form (t-x)(-2), x(n-2) (t+x)(n), (n is = or 2, 0 x, t b). The complex function theory is used to determine the fundamental function of the problem for the general case and a simple numerical technique is described to solve the integral equation. Two examples from the theory of elasticity are then considered to show the application of the technique.

On the solution of integral equations with strongly singular kernels

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1986-01-01

Some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m ,m greater than or equal 1. Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term (t-x) sup -m , terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results.

On the solution of integral equations with strong ly singular kernels

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1985-01-01

In this paper some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m, m or = 1. Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term (t,x) sup-m, terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results.

On the solution of integral equations with strongly singular kernels

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1987-01-01

Some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m, m greater than or equal 1. Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations. A mixed boundary value problem from the theory of elasticity is considered as an example. Particularly for integral equations where the kernel contains, in addition to the dominant term (t-x) sup-m, terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Urbic, Tomaz, E-mail: tomaz.urbic@fkkt.uni-lj.si; Dias, Cristiano L.

The thermodynamic and structural properties of the planar soft-sites dumbbell fluid are examined by Monte Carlo simulations and integral equation theory. The dimers are built of two Lennard-Jones segments. Site-site integral equation theory in two dimensions is used to calculate the site-site radial distribution functions for a range of elongations and densities and the results are compared with Monte Carlo simulations. The critical parameters for selected types of dimers were also estimated. We analyze the influence of the bond length on critical point as well as tested correctness of site-site integral equation theory with different closures. The integral equations canmore » be used to predict the phase diagram of dimers whose molecular parameters are known.« less

Numerical techniques in radiative heat transfer for general, scattering, plane-parallel media

NASA Technical Reports Server (NTRS)

Sharma, A.; Cogley, A. C.

1982-01-01

The study of radiative heat transfer with scattering usually leads to the solution of singular Fredholm integral equations. The present paper presents an accurate and efficient numerical method to solve certain integral equations that govern radiative equilibrium problems in plane-parallel geometry for both grey and nongrey, anisotropically scattering media. In particular, the nongrey problem is represented by a spectral integral of a system of nonlinear integral equations in space, which has not been solved previously. The numerical technique is constructed to handle this unique nongrey governing equation as well as the difficulties caused by singular kernels. Example problems are solved and the method's accuracy and computational speed are analyzed.

Generalization of Boundary-Layer Momentum-Integral Equations to Three-Dimensional Flows Including Those of Rotating System

NASA Technical Reports Server (NTRS)

Mager, Arthur

1952-01-01

The Navier-Stokes equations of motion and the equation of continuity are transformed so as to apply to an orthogonal curvilinear coordinate system rotating with a uniform angular velocity about an arbitrary axis in space. A usual simplification of these equations as consistent with the accepted boundary-layer theory and an integration of these equations through the boundary layer result in boundary-layer momentum-integral equations for three-dimensional flows that are applicable to either rotating or nonrotating fluid boundaries. These equations are simplified and an approximate solution in closed integral form is obtained for a generalized boundary-layer momentum-loss thickness and flow deflection at the wall in the turbulent case. A numerical evaluation of this solution carried out for data obtained in a curving nonrotating duct shows a fair quantitative agreement with the measures values. The form in which the equations are presented is readily adaptable to cases of steady, three-dimensional, incompressible boundary-layer flow like that over curved ducts or yawed wings; and it also may be used to describe the boundary-layer flow over various rotating surfaces, thus applying to turbomachinery, propellers, and helicopter blades.

Generalized Thomas-Fermi equations as the Lampariello class of Emden-Fowler equations

NASA Astrophysics Data System (ADS)

Rosu, Haret C.; Mancas, Stefan C.

2017-04-01

A one-parameter family of Emden-Fowler equations defined by Lampariello's parameter p which, upon using Thomas-Fermi boundary conditions, turns into a set of generalized Thomas-Fermi equations comprising the standard Thomas-Fermi equation for p = 1 is studied in this paper. The entire family is shown to be non integrable by reduction to the corresponding Abel equations whose invariants do not satisfy a known integrability condition. We also discuss the equivalent dynamical system of equations for the standard Thomas-Fermi equation and perform its phase-plane analysis. The results of the latter analysis are similar for the whole class.

Evaluation of atomic pressure in the multiple time-step integration algorithm.

PubMed

Andoh, Yoshimichi; Yoshii, Noriyuki; Yamada, Atsushi; Okazaki, Susumu

2017-04-15

In molecular dynamics (MD) calculations, reduction in calculation time per MD loop is essential. A multiple time-step (MTS) integration algorithm, the RESPA (Tuckerman and Berne, J. Chem. Phys. 1992, 97, 1990-2001), enables reductions in calculation time by decreasing the frequency of time-consuming long-range interaction calculations. However, the RESPA MTS algorithm involves uncertainties in evaluating the atomic interaction-based pressure (i.e., atomic pressure) of systems with and without holonomic constraints. It is not clear which intermediate forces and constraint forces in the MTS integration procedure should be used to calculate the atomic pressure. In this article, we propose a series of equations to evaluate the atomic pressure in the RESPA MTS integration procedure on the basis of its equivalence to the Velocity-Verlet integration procedure with a single time step (STS). The equations guarantee time-reversibility even for the system with holonomic constrants. Furthermore, we generalize the equations to both (i) arbitrary number of inner time steps and (ii) arbitrary number of force components (RESPA levels). The atomic pressure calculated by our equations with the MTS integration shows excellent agreement with the reference value with the STS, whereas pressures calculated using the conventional ad hoc equations deviated from it. Our equations can be extended straightforwardly to the MTS integration algorithm for the isothermal NVT and isothermal-isobaric NPT ensembles. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Some Exact Solutions of a Nonintegrable Toda-type Equation

NASA Astrophysics Data System (ADS)

Kim, Chanju

2018-05-01

We study a Toda-type equation with two scalar fields which is not integrable and construct two families of exact solutions which are expressed in terms of rational functions. The equation appears in U(1) Chern-Simons theories coupled to two nonrelativistic matter fields with opposite charges. One family of solutions is a trivial embedding of Liouville-type solutions. The other family is obtained by transforming the equation into the Taubes vortex equation on the hyperbolic space. Though the Taubes equation is not integrable, a trivial vacuum solution provides nontrivial solutions to the original Toda-type equation.

Painlevé equations, elliptic integrals and elementary functions

NASA Astrophysics Data System (ADS)

Żołądek, Henryk; Filipuk, Galina

2015-02-01

The six Painlevé equations can be written in the Hamiltonian form, with time dependent Hamilton functions. We present a rather new approach to this result, leading to rational Hamilton functions. By a natural extension of the phase space one gets corresponding autonomous Hamiltonian systems with two degrees of freedom. We realize the Bäcklund transformations of the Painlevé equations as symplectic birational transformations in C4 and we interpret the cases with classical solutions as the cases of partial integrability of the extended Hamiltonian systems. We prove that the extended Hamiltonian systems do not have any additional algebraic first integral besides the known special cases of the third and fifth Painlevé equations. We also show that the original Painlevé equations admit the first integrals expressed in terms of the elementary functions only in the special cases mentioned above. In the proofs we use equations in variations with respect to a parameter and Liouville's theory of elementary functions.

Numerical solution of boundary-integral equations for molecular electrostatics.

PubMed

Bardhan, Jaydeep P

2009-03-07

Numerous molecular processes, such as ion permeation through channel proteins, are governed by relatively small changes in energetics. As a result, theoretical investigations of these processes require accurate numerical methods. In the present paper, we evaluate the accuracy of two approaches to simulating boundary-integral equations for continuum models of the electrostatics of solvation. The analysis emphasizes boundary-element method simulations of the integral-equation formulation known as the apparent-surface-charge (ASC) method or polarizable-continuum model (PCM). In many numerical implementations of the ASC/PCM model, one forces the integral equation to be satisfied exactly at a set of discrete points on the boundary. We demonstrate in this paper that this approach to discretization, known as point collocation, is significantly less accurate than an alternative approach known as qualocation. Furthermore, the qualocation method offers this improvement in accuracy without increasing simulation time. Numerical examples demonstrate that electrostatic part of the solvation free energy, when calculated using the collocation and qualocation methods, can differ significantly; for a polypeptide, the answers can differ by as much as 10 kcal/mol (approximately 4% of the total electrostatic contribution to solvation). The applicability of the qualocation discretization to other integral-equation formulations is also discussed, and two equivalences between integral-equation methods are derived.

A nodal domain theorem for integrable billiards in two dimensions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Samajdar, Rhine; Jain, Sudhir R., E-mail: srjain@barc.gov.in

Eigenfunctions of integrable planar billiards are studied — in particular, the number of nodal domains, ν of the eigenfunctions with Dirichlet boundary conditions are considered. The billiards for which the time-independent Schrödinger equation (Helmholtz equation) is separable admit trivial expressions for the number of domains. Here, we discover that for all separable and non-separable integrable billiards, ν satisfies certain difference equations. This has been possible because the eigenfunctions can be classified in families labelled by the same value of mmodkn, given a particular k, for a set of quantum numbers, m,n. Further, we observe that the patterns in a familymore » are similar and the algebraic representation of the geometrical nodal patterns is found. Instances of this representation are explained in detail to understand the beauty of the patterns. This paper therefore presents a mathematical connection between integrable systems and difference equations. - Highlights: • We find that the number of nodal domains of eigenfunctions of integrable, planar billiards satisfy a class of difference equations. • The eigenfunctions labelled by quantum numbers (m,n) can be classified in terms of mmodkn. • A theorem is presented, realising algebraic representations of geometrical patterns exhibited by the domains. • This work presents a connection between integrable systems and difference equations.« less

Mind your elders: wild soybean’s contribution to soybean aphid resistance

USDA-ARS?s Scientific Manuscript database

Currently, biotype 4 soybean aphid (Aphis glycines Matsamura, SBA) is the most virulent SBA biotype. Overcoming the most aphid resistant genes, SBA biotype 4 has become the greatest challenge in utilizing plant resistance in soybean [Glycine max (L.) Merr.]. Soybean’s wild ancestor Glycine soja (Sie...

Sind Sie fit (Are You in Shape)?: Calisthenics in German.

ERIC Educational Resources Information Center

Wolter, Don

This packet of instructional materials, intended for intermediate and advanced German students, contains a student's section and a teacher's guide focusing on calisthenics. The student section contains three illustrated transcriptions of radio programs on calisthenics for early morning listeners of "Der bayrische Rundfunk" in West Germany.…

Oblique scattering from radially inhomogeneous dielectric cylinders: An exact Volterra integral equation formulation

NASA Astrophysics Data System (ADS)

Tsalamengas, John L.

2018-07-01

We study plane-wave electromagnetic scattering by radially and strongly inhomogeneous dielectric cylinders at oblique incidence. The method of analysis relies on an exact reformulation of the underlying field equations as a first-order 4 × 4 system of differential equations and on the ability to restate the associated initial-value problem in the form of a system of coupled linear Volterra integral equations of the second kind. The integral equations so derived are discretized via a sophisticated variant of the Nyström method. The proposed method yields results accurate up to machine precision without relying on approximations. Numerical results and case studies ably demonstrate the efficiency and high accuracy of the algorithms.

"Das Konkrete ist das Abstrakte, an das man sich schließlich gewöhnt hat." (Laurent Schwartz) Über den Ablauf des mathematischen Verstehens

NASA Astrophysics Data System (ADS)

Lowsky, Martin

Die im Titel genannte Aussage findet sich in den Lebenserinnerungen von Laurent Schwartz (1915-2002), einem der fruchtbarsten Mathematiker, Mitglied der Gruppe Bourbaki. Im Original lautet die Aussage: "un objet concret est un objet abstrait auquel on a fini par s'habituer." Schwartz erläutert sie am Beispiel des Integrals über {e^{-1/2{x^2}}} , das den Wert Wurzel aus 2π hat und in dem sich also die Zahlen e und π verknüpfen. Was Schwartz aber vor allem ausdrücken will, ist dies: Das mathematische Verständnisd geht langsam vor sich und es bedarf der Anstrengung. "Es ist eine Frage der Zeit und der Energie", sagt Schwartz, und gerade dies mache es so schwer, die höhere Mathematik unter das Volk zu bringen. Das Lernen und Lehren von Mathematik laufe eben mühevoll und langsam ab.

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.

FAST TRACK COMMUNICATION: On the Liouvillian solution of second-order linear differential equations and algebraic invariant curves

NASA Astrophysics Data System (ADS)

Man, Yiu-Kwong

2010-10-01

In this communication, we present a method for computing the Liouvillian solution of second-order linear differential equations via algebraic invariant curves. The main idea is to integrate Kovacic's results on second-order linear differential equations with the Prelle-Singer method for computing first integrals of differential equations. Some examples on using this approach are provided.

On randomized algorithms for numerical solution of applied Fredholm integral equations of the second kind

NASA Astrophysics Data System (ADS)

Voytishek, Anton V.; Shipilov, Nikolay M.

2017-11-01

In this paper, the systematization of numerical (implemented on a computer) randomized functional algorithms for approximation of a solution of Fredholm integral equation of the second kind is carried out. Wherein, three types of such algorithms are distinguished: the projection, the mesh and the projection-mesh methods. The possibilities for usage of these algorithms for solution of practically important problems is investigated in detail. The disadvantages of the mesh algorithms, related to the necessity of calculation values of the kernels of integral equations in fixed points, are identified. On practice, these kernels have integrated singularities, and calculation of their values is impossible. Thus, for applied problems, related to solving Fredholm integral equation of the second kind, it is expedient to use not mesh, but the projection and the projection-mesh randomized algorithms.

Initial-boundary value problems associated with the Ablowitz-Ladik system

NASA Astrophysics Data System (ADS)

Xia, Baoqiang; Fokas, A. S.

2018-02-01

We employ the Ablowitz-Ladik system as an illustrative example in order to demonstrate how to analyze initial-boundary value problems for integrable nonlinear differential-difference equations via the unified transform (Fokas method). In particular, we express the solutions of the integrable discrete nonlinear Schrödinger and integrable discrete modified Korteweg-de Vries equations in terms of the solutions of appropriate matrix Riemann-Hilbert problems. We also discuss in detail, for both the above discrete integrable equations, the associated global relations and the process of eliminating of the unknown boundary values.

Simulation electromagnetic scattering on bodies through integral equation and neural networks methods

NASA Astrophysics Data System (ADS)

Lvovich, I. Ya; Preobrazhenskiy, A. P.; Choporov, O. N.

2018-05-01

The paper deals with the issue of electromagnetic scattering on a perfectly conducting diffractive body of a complex shape. Performance calculation of the body scattering is carried out through the integral equation method. Fredholm equation of the second time was used for calculating electric current density. While solving the integral equation through the moments method, the authors have properly described the core singularity. The authors determined piecewise constant functions as basic functions. The chosen equation was solved through the moments method. Within the Kirchhoff integral approach it is possible to define the scattered electromagnetic field, in some way related to obtained electrical currents. The observation angles sector belongs to the area of the front hemisphere of the diffractive body. To improve characteristics of the diffractive body, the authors used a neural network. All the neurons contained a logsigmoid activation function and weighted sums as discriminant functions. The paper presents the matrix of weighting factors of the connectionist model, as well as the results of the optimized dimensions of the diffractive body. The paper also presents some basic steps in calculation technique of the diffractive bodies, based on the combination of integral equation and neural networks methods.

On the solution of integral equations with a generalized cauchy kernel

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1986-01-01

In this paper a certain class of singular integral equations that may arise from the mixed boundary value problems in nonhomogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted, the density function is a potential or a displacement and consequently the kernel has strong singularities of the form (t-x) sup-2, x sup n-2 (t+x) sup n, (n or = 2, 0x,tb). The complex function theory is used to determine the fundamental function of the problem for the general case and a simple numerical technique is described to solve the integral equation. Two examples from the theory of elasticity are then considered to show the application of the technique.

An exterior Poisson solver using fast direct methods and boundary integral equations with applications to nonlinear potential flow

NASA Technical Reports Server (NTRS)

Young, D. P.; Woo, A. C.; Bussoletti, J. E.; Johnson, F. T.

1986-01-01

A general method is developed combining fast direct methods and boundary integral equation methods to solve Poisson's equation on irregular exterior regions. The method requires O(N log N) operations where N is the number of grid points. Error estimates are given that hold for regions with corners and other boundary irregularities. Computational results are given in the context of computational aerodynamics for a two-dimensional lifting airfoil. Solutions of boundary integral equations for lifting and nonlifting aerodynamic configurations using preconditioned conjugate gradient are examined for varying degrees of thinness.

Davidenko’s Method for the Solution of Nonlinear Operator Equations.

DTIC Science & Technology

NONLINEAR DIFFERENTIAL EQUATIONS, NUMERICAL INTEGRATION), OPERATORS(MATHEMATICS), BANACH SPACE , MAPPING (TRANSFORMATIONS), NUMERICAL METHODS AND PROCEDURES, INTEGRALS, SET THEORY, CONVERGENCE, MATRICES(MATHEMATICS)

Integrable Equations in Multi-Dimensions (2+1) are Bi-Hamiltonian Systems,

DTIC Science & Technology

1987-02-01

equation [18]. It should be noted that the 80 equation has more similarities [19] with the Kadomtsev - Petviashvili (KP...Cimento, 39B, 1 (1977). [31] P. Caudrey, Discrete and Periodic Spectral Transforms Related to the Kadomtsev - Petviashvili Equation , preprint U.M.I.S.T. (1985). II ’AI D p-I 4, - -- - -- - - -w 4 ...TOM NONLINEAR STUDIES IDTIC I IELEC )// MAR 2 51988 I / \\ / Integrable Equations in Multi- dimensions (2+1) are Bi-Hamiltonian Systems by A.S.

The non-autonomous YdKN equation and generalized symmetries of Boll equations

NASA Astrophysics Data System (ADS)

Gubbiotti, G.; Scimiterna, C.; Levi, D.

2017-05-01

In this paper, we study the integrability of a class of nonlinear non-autonomous quad graph equations compatible around the cube introduced by Boll in the framework of the generalized Adler, Bobenko, and Suris (ABS) classification. We show that all these equations possess three-point generalized symmetries which are subcases of either the Yamilov discretization of the Krichever-Novikov equation or of its non-autonomous extension. We also prove that all those symmetries are integrable as they pass the algebraic entropy test.

Development and application of a local linearization algorithm for the integration of quaternion rate equations in real-time flight simulation problems

NASA Technical Reports Server (NTRS)

Barker, L. E., Jr.; Bowles, R. L.; Williams, L. H.

1973-01-01

High angular rates encountered in real-time flight simulation problems may require a more stable and accurate integration method than the classical methods normally used. A study was made to develop a general local linearization procedure of integrating dynamic system equations when using a digital computer in real-time. The procedure is specifically applied to the integration of the quaternion rate equations. For this application, results are compared to a classical second-order method. The local linearization approach is shown to have desirable stability characteristics and gives significant improvement in accuracy over the classical second-order integration methods.

Solving Simple Kinetics without Integrals

ERIC Educational Resources Information Center

de la Pen~a, Lisandro Herna´ndez

2016-01-01

The solution of simple kinetic equations is analyzed without referencing any topic from differential equations or integral calculus. Guided by the physical meaning of the rate equation, a systematic procedure is used to generate an approximate solution that converges uniformly to the exact solution in the case of zero, first, and second order…

Extended nonlinear Schrödinger equation with higher-order odd and even terms and its rogue wave solutions.

PubMed

Ankiewicz, Adrian; Wang, Yan; Wabnitz, Stefan; Akhmediev, Nail

2014-01-01

We consider an extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms with variable coefficients. The resulting equation has soliton solutions and approximate rogue wave solutions. We present these solutions up to second order. Moreover, specific constraints on the parameters of higher-order terms provide integrability of the resulting equation, providing a corresponding Lax pair. Particular cases of this equation are the Hirota and the Lakshmanan-Porsezian-Daniel equations. The resulting integrable equation admits exact rogue wave solutions. In particular cases, mentioned above, these solutions are reduced to the rogue wave solutions of the corresponding equations.

Compacton solutions in a class of generalized fifth-order Korteweg-de Vries equations.

PubMed

Cooper, F; Hyman, J M; Khare, A

2001-08-01

Solitons play a fundamental role in the evolution of general initial data for quasilinear dispersive partial differential equations, such as the Korteweg-de Vries (KdV), nonlinear Schrödinger, and the Kadomtsev-Petviashvili equations. These integrable equations have linear dispersion and the solitons have infinite support. We have derived and investigate a new KdV-like Hamiltonian partial differential equation from a four-parameter Lagrangian where the nonlinear dispersion gives rise to solitons with compact support (compactons). The new equation does not seem to be integrable and only mass, momentum, and energy seem to be conserved; yet, the solitons display almost the same modal decompositions and structural stability observed in integrable partial differential equations. The compactons formed from arbitrary initial data, are nonlinearly self-stabilizing, and maintain their coherence after multiple collisions. The robustness of these compactons and the inapplicability of the inverse scattering tools, that worked so well for the KdV equation, make it clear that there is a fundamental mechanism underlying the processes beyond integrability. We have found explicit formulas for multiple classes of compact traveling wave solutions. When there are more than one compacton solution for a particular set of parameters, the wider compacton is the minimum of a reduced Hamiltonian and is the only one that is stable.

Integral equation approach to time-dependent kinematic dynamos in finite domains

NASA Astrophysics Data System (ADS)

Xu, Mingtian; Stefani, Frank; Gerbeth, Gunter

2004-11-01

The homogeneous dynamo effect is at the root of cosmic magnetic field generation. With only a very few exceptions, the numerical treatment of homogeneous dynamos is carried out in the framework of the differential equation approach. The present paper tries to facilitate the use of integral equations in dynamo research. Apart from the pedagogical value to illustrate dynamo action within the well-known picture of the Biot-Savart law, the integral equation approach has a number of practical advantages. The first advantage is its proven numerical robustness and stability. The second and perhaps most important advantage is its applicability to dynamos in arbitrary geometries. The third advantage is its intimate connection to inverse problems relevant not only for dynamos but also for technical applications of magnetohydrodynamics. The paper provides the first general formulation and application of the integral equation approach to time-dependent kinematic dynamos, with stationary dynamo sources, in finite domains. The time dependence is restricted to the magnetic field, whereas the velocity or corresponding mean-field sources of dynamo action are supposed to be stationary. For the spherically symmetric α2 dynamo model it is shown how the general formulation is reduced to a coupled system of two radial integral equations for the defining scalars of the poloidal and toroidal field components. The integral equation formulation for spherical dynamos with general stationary velocity fields is also derived. Two numerical examples—the α2 dynamo model with radially varying α and the Bullard-Gellman model—illustrate the equivalence of the approach with the usual differential equation method. The main advantage of the method is exemplified by the treatment of an α2 dynamo in rectangular domains.

[Need for integration and working conditions of locum anaesthesiologists in community hospitals of a French administrative area].

PubMed

Lieutaud, T

2013-06-01

To evaluate the need for locum anaesthetic coverage and the practical consequences (integration, working conditions, quality and safety) arising during the first 5 days of work, when a temporary position is accepted. MEASURED PARAMETERS: 1) Telephone enquiry of administrative services of community hospitals (CH) in one French administrative area (Rhône-Alpes) about their need for locum anaesthetists; 2) if a position was offered, it was accepted when the participation to on-call duties was delayed after the first 5 days of work; 3) during the working period, the following characteristics were assessed: integration of the locum anesthesiologist among team members, comparison of practice patterns to national guidelines; 4) data from the Platines-website of the French Ministry of Health were used to quantify indicators of activity and size of the hospitals and search for correlations between these parameters and working conditions of the locum anaesthetist. Of the 32 CH questioned, 28 were looking for temporary anaesthetic work force but only 11 (35%) accepted a 5-day period before participation to on-call duties and 17 refused this integration period. Four CH declared not to be looking for temporary work force. Characteristics of integration of the locum anaesthetist and standards of work were very different among centers. No hospital administration had a strategy for evaluation of recruited locums. Temporary work force in anaesthesia is widely required in CH of the Rhône-Alpes area but this practice had not been formalised. No recruitment strategy was observable. This questions about the institutions' requirements for anaesthetic services in French public hospitals. Copyright © 2013 Société française d’anesthésie et de réanimation (Sfar). Published by Elsevier SAS. All rights reserved.

A boundary integral approach to the scattering of nonplanar acoustic waves by rigid bodies

NASA Technical Reports Server (NTRS)

Gallman, Judith M.; Myers, M. K.; Farassat, F.

1990-01-01

The acoustic scattering of an incident wave by a rigid body can be described by a singular Fredholm integral equation of the second kind. This equation is derived by solving the wave equation using generalized function theory, Green's function for the wave equation in unbounded space, and the acoustic boundary condition for a perfectly rigid body. This paper will discuss the derivation of the wave equation, its reformulation as a boundary integral equation, and the solution of the integral equation by the Galerkin method. The accuracy of the Galerkin method can be assessed by applying the technique outlined in the paper to reproduce the known pressure fields that are due to various point sources. From the analysis of these simpler cases, the accuracy of the Galerkin solution can be inferred for the scattered pressure field caused by the incidence of a dipole field on a rigid sphere. The solution by the Galerkin technique can then be applied to such problems as a dipole model of a propeller whose pressure field is incident on a rigid cylinder. This is the groundwork for modeling the scattering of rotating blade noise by airplane fuselages.

Almost analytical Karhunen-Loeve representation of irregular waves based on the prolate spheroidal wave functions

NASA Astrophysics Data System (ADS)

Lee, Gibbeum; Cho, Yeunwoo

2017-11-01

We present an almost analytical new approach to solving the matrix eigenvalue problem or the integral equation in Karhunen-Loeve (K-L) representation of random data such as irregular ocean waves. Instead of solving this matrix eigenvalue problem purely numerically, which may suffer from the computational inaccuracy for big data, first, we consider a pair of integral and differential equations, which are related to the so-called prolate spheroidal wave functions (PSWF). For the PSWF differential equation, the pair of the eigenvectors (PSWF) and eigenvalues can be obtained from a relatively small number of analytical Legendre functions. Then, the eigenvalues in the PSWF integral equation are expressed in terms of functional values of the PSWF and the eigenvalues of the PSWF differential equation. Finally, the analytically expressed PSWFs and the eigenvalues in the PWSF integral equation are used to form the kernel matrix in the K-L integral equation for the representation of exemplary wave data; ordinary irregular waves and rogue waves. We found that the present almost analytical method is better than the conventional data-independent Fourier representation and, also, the conventional direct numerical K-L representation in terms of both accuracy and computational cost. This work was supported by the National Research Foundation of Korea (NRF). (NRF-2017R1D1A1B03028299).

On an example of a system of differential equations that are integrated in Abelian functions

NASA Astrophysics Data System (ADS)

Malykh, M. D.; Sevastianov, L. A.

2017-12-01

The short review of the theory of Abelian functions and its applications in mechanics and analytical theory of differential equations is given. We think that Abelian functions are the natural generalization of commonly used functions because if the general solution of the 2nd order differential equation depends algebraically on the constants of integration, then integrating this equation does not lead out of the realm of commonly used functions complemented by the Abelian functions (Painlevé theorem). We present a relatively simple example of a dynamical system that is integrated in Abelian integrals by “pairing” two copies of a hyperelliptic curve. Unfortunately, initially simple formulas unfold into very long ones. Apparently the theory of Abelian functions hasn’t been finished in the last century because without computer algebra systems it was impossible to complete the calculations to the end. All calculations presented in our report are performed in Sage.

GENERIC Integrators: Structure Preserving Time Integration for Thermodynamic Systems

NASA Astrophysics Data System (ADS)

Öttinger, Hans Christian

2018-04-01

Thermodynamically admissible evolution equations for non-equilibrium systems are known to possess a distinct mathematical structure. Within the GENERIC (general equation for the non-equilibrium reversible-irreversible coupling) framework of non-equilibrium thermodynamics, which is based on continuous time evolution, we investigate the possibility of preserving all the structural elements in time-discretized equations. Our approach, which follows Moser's [1] construction of symplectic integrators for Hamiltonian systems, is illustrated for the damped harmonic oscillator. Alternative approaches are sketched.

The application of the integral equation theory to study the hydrophobic interaction

PubMed Central

Mohorič, Tomaž; Urbic, Tomaz; Hribar-Lee, Barbara

2014-01-01

The Wertheim's integral equation theory was tested against newly obtained Monte Carlo computer simulations to describe the potential of mean force between two hydrophobic particles. An excellent agreement was obtained between the theoretical and simulation results. Further, the Wertheim's integral equation theory with polymer Percus-Yevick closure qualitatively correctly (with respect to the experimental data) describes the solvation structure under conditions where the simulation results are difficult to obtain with good enough accuracy. PMID:24437891

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.

Solving differential equations for Feynman integrals by expansions near singular points

NASA Astrophysics Data System (ADS)

Lee, Roman N.; Smirnov, Alexander V.; Smirnov, Vladimir A.

2018-03-01

We describe a strategy to solve differential equations for Feynman integrals by powers series expansions near singular points and to obtain high precision results for the corresponding master integrals. We consider Feynman integrals with two scales, i.e. non-trivially depending on one variable. The corresponding algorithm is oriented at situations where canonical form of the differential equations is impossible. We provide a computer code constructed with the help of our algorithm for a simple example of four-loop generalized sunset integrals with three equal non-zero masses and two zero masses. Our code gives values of the master integrals at any given point on the real axis with a required accuracy and a given order of expansion in the regularization parameter ɛ.

Comparison of numerical techniques for integration of stiff ordinary differential equations arising in combustion chemistry

NASA Technical Reports Server (NTRS)

Radhakrishnan, K.

1984-01-01

The efficiency and accuracy of several algorithms recently developed for the efficient numerical integration of stiff ordinary differential equations are compared. The methods examined include two general-purpose codes, EPISODE and LSODE, and three codes (CHEMEQ, CREK1D, and GCKP84) developed specifically to integrate chemical kinetic rate equations. The codes are applied to two test problems drawn from combustion kinetics. The comparisons show that LSODE is the fastest code currently available for the integration of combustion kinetic rate equations. An important finding is that an interactive solution of the algebraic energy conservation equation to compute the temperature does not result in significant errors. In addition, this method is more efficient than evaluating the temperature by integrating its time derivative. Significant reductions in computational work are realized by updating the rate constants (k = at(supra N) N exp(-E/RT) only when the temperature change exceeds an amount delta T that is problem dependent. An approximate expression for the automatic evaluation of delta T is derived and is shown to result in increased efficiency.

Differential equations for loop integrals in Baikov representation

NASA Astrophysics Data System (ADS)

Bosma, Jorrit; Larsen, Kasper J.; Zhang, Yang

2018-05-01

We present a proof that differential equations for Feynman loop integrals can always be derived in Baikov representation without involving dimension-shift identities. We moreover show that in a large class of two- and three-loop diagrams it is possible to avoid squared propagators in the intermediate steps of setting up the differential equations.

Monograph - The Numerical Integration of Ordinary Differential Equations.

ERIC Educational Resources Information Center

Hull, T. E.

The materials presented in this monograph are intended to be included in a course on ordinary differential equations at the upper division level in a college mathematics program. These materials provide an introduction to the numerical integration of ordinary differential equations, and they can be used to supplement a regular text on this…

An Analytical Comparison of the Acoustic Analogy and Kirchhoff Formulation for Moving Surfaces

NASA Technical Reports Server (NTRS)

Brentner, Kenneth S.; Farassat, F.

1997-01-01

The Lighthill acoustic analogy, as embodied in the Ffowcs Williams-Hawkings (FW-H) equation, is compared with the Kirchhoff formulation for moving surfaces. A comparison of the two governing equations reveals that the main Kirchhoff advantage (namely nonlinear flow effects are included in the surface integration) is also available to the FW-H method if the integration surface used in the FW-H equation is not assumed impenetrable. The FW-H equation is analytically superior for aeroacoustics because it is based upon the conservation laws of fluid mechanics rather than the wave equation. This means that the FW-H equation is valid even if the integration surface is in the nonlinear region. This is demonstrated numerically in the paper. The Kirchhoff approach can lead to substantial errors if the integration surface is not positioned in the linear region. These errors may be hard to identify. Finally, new metrics based on the Sobolev norm are introduced which may be used to compare input data for both quadrupole noise calculations and Kirchhoff noise predictions.

CANCER MORTALITY AMONG UNITED STATES COUNTIES WITH HAZARDOUS WASTE SITES AND SOLE SOURCE DRINKING WATER CONTAMINATION

EPA Science Inventory

Since the late 1950's more than 750 million tons of toxic wastes have been discarded in an estimated 30,000 to 50,000 hazardous waste sies (HWS). he uncontrolled discarding of chemical wastes creates the potential for risks to human health. tilizing the National Priorities Listin...

Kostenüberwachung und Wirtschaftlichkeitsrechnung

NASA Astrophysics Data System (ADS)

Bauer, Jürgen

Die ERP-Produktkalkulation erfolgt auf der Basis des Mengen- und Wertgerüsts der Produktionsprozesse. Sie greift dabei auf die Stammdaten (Materialstamm, Arbeitsplätze, Arbeitspläne, Stücklisten) zu. Basis ist die übliche Industriekalkulation in der Form einer Zuschlagskalkulation, ergänzt durch Platzkostensätze der Maschinen und Arbeitsplätze (siehe Teil ).

Numerical quadrature methods for integrals of singular periodic functions and their application to singular and weakly singular integral equations

NASA Technical Reports Server (NTRS)

Sidi, A.; Israeli, M.

1986-01-01

High accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations. They are used to obtain accurate quadrature methods for the solution of singular and weakly singular Fredholm integral equations. Such periodic equations are used in the solution of planar elliptic boundary value problems, elasticity, potential theory, conformal mapping, boundary element methods, free surface flows, etc. The use of the quadrature methods is demonstrated with numerical examples.

A Corresponding Lie Algebra of a Reductive homogeneous Group and Its Applications

NASA Astrophysics Data System (ADS)

Zhang, Yu-Feng; Wu, Li-Xin; Rui, Wen-Juan

2015-05-01

With the help of a Lie algebra of a reductive homogeneous space G/K, where G is a Lie group and K is a resulting isotropy group, we introduce a Lax pair for which an expanding (2+1)-dimensional integrable hierarchy is obtained by applying the binormial-residue representation (BRR) method, whose Hamiltonian structure is derived from the trace identity for deducing (2+1)-dimensional integrable hierarchies, which was proposed by Tu, et al. We further consider some reductions of the expanding integrable hierarchy obtained in the paper. The first reduction is just right the (2+1)-dimensional AKNS hierarchy, the second-type reduction reveals an integrable coupling of the (2+1)-dimensional AKNS equation (also called the Davey-Stewartson hierarchy), a kind of (2+1)-dimensional Schrödinger equation, which was once reobtained by Tu, Feng and Zhang. It is interesting that a new (2+1)-dimensional integrable nonlinear coupled equation is generated from the reduction of the part of the (2+1)-dimensional integrable coupling, which is further reduced to the standard (2+1)-dimensional diffusion equation along with a parameter. In addition, the well-known (1+1)-dimensional AKNS hierarchy, the (1+1)-dimensional nonlinear Schrödinger equation are all special cases of the (2+1)-dimensional expanding integrable hierarchy. Finally, we discuss a few discrete difference equations of the diffusion equation whose stabilities are analyzed by making use of the von Neumann condition and the Fourier method. Some numerical solutions of a special stationary initial value problem of the (2+1)-dimensional diffusion equation are obtained and the resulting convergence and estimation formula are investigated. Supported by the Innovation Team of Jiangsu Province hosted by China University of Mining and Technology (2014), the National Natural Science Foundation of China under Grant No. 11371361, the Fundamental Research Funds for the Central Universities (2013XK03), and the Natural Science Foundation of Shandong Province under Grant No. ZR2013AL016

Darwinische Kulturtheorie - Evolutionistische und "evolutionistische`` Theorien sozialen Wandels

NASA Astrophysics Data System (ADS)

Antweiler, Christoph

Evolutionistische Argumentationen außerhalb der Biologie sind weit verbreitet. Wenn sie vertreten werden, heißt das mitnichten, dass sie notwendigerweise von darwinischen Argumenten geprägt sind. Wenn man Evolution und Kultur aus explizit darwinischer Perspektive zusammen bringt, bedeutet das noch lange nicht unbedingt Soziobiologie. Und es bedeutet sicherlich nicht Sozialdarwinismus. Dieser Beitrag soll einen Überblick der so genannten evolutionären Ansätze bzw. evolutionistischen Ansätze zu menschlichen Gesellschaften bzw. Kulturen geben. Es soll gezeigt werden, was in den Ansätzen analytisch zu trennen ist und was synthetisch zusammen gehört. Mein Beitrag ist nicht wissenschaftsgeschichtlich angelegt, sondern systematisch ausgerichtet und hat zwei Schwerpunkte (Antweiler 2008; Antweiler 2009b). Zum einen geht es um kausale Zusammenhänge von organischer Evolution und gesellschaftlichem Wandel. Auf der anderen Seite werden Analogien zwischen biotischer und kultureller Evolution erläutert, die als spezifische Ähnlichkeiten dieser beiden als grundsätzlich verschieden gesehenen Prozesse aufgefasst werden. Dadurch wird die Frage aufgeworfen, ob die Evolution von Organismen einerseits und die Transformation von Gesellschaften bzw. Kulturen andererseits, spezielle Fälle eines allgemeinen Modells von Evolution darstellen.

Solving the hypersingular boundary integral equation in three-dimensional acoustics using a regularization relationship.

PubMed

Yan, Zai You; Hung, Kin Chew; Zheng, Hui

2003-05-01

Regularization of the hypersingular integral in the normal derivative of the conventional Helmholtz integral equation through a double surface integral method or regularization relationship has been studied. By introducing the new concept of discretized operator matrix, evaluation of the double surface integrals is reduced to calculate the product of two discretized operator matrices. Such a treatment greatly improves the computational efficiency. As the number of frequencies to be computed increases, the computational cost of solving the composite Helmholtz integral equation is comparable to that of solving the conventional Helmholtz integral equation. In this paper, the detailed formulation of the proposed regularization method is presented. The computational efficiency and accuracy of the regularization method are demonstrated for a general class of acoustic radiation and scattering problems. The radiation of a pulsating sphere, an oscillating sphere, and a rigid sphere insonified by a plane acoustic wave are solved using the new method with curvilinear quadrilateral isoparametric elements. It is found that the numerical results rapidly converge to the corresponding analytical solutions as finer meshes are applied.

On solvability of boundary value problems for hyperbolic fourth-order equations with nonlocal boundary conditions of integral type

NASA Astrophysics Data System (ADS)

Popov, Nikolay S.

2017-11-01

Solvability of some initial-boundary value problems for linear hyperbolic equations of the fourth order is studied. A condition on the lateral boundary in these problems relates the values of a solution or the conormal derivative of a solution to the values of some integral operator applied to a solution. Nonlocal boundary-value problems for one-dimensional hyperbolic second-order equations with integral conditions on the lateral boundary were considered in the articles by A.I. Kozhanov. Higher-dimensional hyperbolic equations of higher order with integral conditions on the lateral boundary were not studied earlier. The existence and uniqueness theorems of regular solutions are proven. The method of regularization and the method of continuation in a parameter are employed to establish solvability.

Reply to "Comment on 'Defocusing complex short-pulse equation and its multi-dark-soliton solution' ".

PubMed

Feng, Bao-Feng; Ling, Liming; Zhu, Zuonong

2017-08-01

Our paper [Phys. Rev. E 93, 052227 (2016)PREHBM2470-004510.1103/PhysRevE.93.052227], proposing an integrable model for the propagation of ultrashort pulses, has recently received a Comment by Youssoufa et al. [Phys. Rev. E 96, 026201 (2017)10.1103/PhysRevE.96.026201] about a possible flaw in its derivation. We point out that their claim is incorrect since we have stated explicitly that a term is neglected to derive our model equation in our paper. Furthermore, the integrable model is validated by comparing with the normalized Maxwell equation and other known integrable models. Moreover, we show that a similar approximation has to be performed in deriving the same integrable equation as explained in the Comment.

A new aerodynamic integral equation based on an acoustic formula in the time domain

NASA Technical Reports Server (NTRS)

Farassat, F.

1984-01-01

An aerodynamic integral equation for bodies moving at transonic and supersonic speeds is presented. Based on a time-dependent acoustic formula for calculating the noise emanating from the outer portion of a propeller blade travelling at high speed (the Ffowcs Williams-Hawking formulation), the loading terms and a conventional thickness source terms are retained. Two surface and three line integrals are employed to solve an equation for the loading noise. The near-field term is regularized using the collapsing sphere approach to obtain semiconvergence on the blade surface. A singular integral equation is thereby derived for the unknown surface pressure, and is amenable to numerical solutions using Galerkin or collocation methods. The technique is useful for studying the nonuniform inflow to the propeller.

Integrable equations of the infinite nonlinear Schrödinger equation hierarchy with time variable coefficients.

PubMed

Kedziora, D J; Ankiewicz, A; Chowdury, A; Akhmediev, N

2015-10-01

We present an infinite nonlinear Schrödinger equation hierarchy of integrable equations, together with the recurrence relations defining it. To demonstrate integrability, we present the Lax pairs for the whole hierarchy, specify its Darboux transformations and provide several examples of solutions. These resulting wavefunctions are given in exact analytical form. We then show that the Lax pair and Darboux transformation formalisms still apply in this scheme when the coefficients in the hierarchy depend on the propagation variable (e.g., time). This extension thus allows for the construction of complicated solutions within a greatly diversified domain of generalised nonlinear systems.

Classical integrable defects as quasi Bäcklund transformations

NASA Astrophysics Data System (ADS)

Doikou, Anastasia

2016-10-01

We consider the algebraic setting of classical defects in discrete and continuous integrable theories. We derive the ;equations of motion; on the defect point via the space-like and time-like description. We then exploit the structural similarity of these equations with the discrete and continuous Bäcklund transformations. And although these equations are similar they are not exactly the same to the Bäcklund transformations. We also consider specific examples of integrable models to demonstrate our construction, i.e. the Toda chain and the sine-Gordon model. The equations of the time (space) evolution of the defect (discontinuity) degrees of freedom for these models are explicitly derived.

Analytical expressions for the correlation function of a hard sphere dimer fluid

NASA Astrophysics Data System (ADS)

Kim, Soonho; Chang, Jaeeon; Kim, Hwayong

A closed form expression is given for the correlation function of a hard sphere dimer fluid. A set of integral equations is obtained from Wertheim's multidensity Ornstein-Zernike integral equation theory with Percus-Yevick approximation. Applying the Laplace transformation method to the integral equations and then solving the resulting equations algebraically, the Laplace transforms of the individual correlation functions are obtained. By the inverse Laplace transformation, the radial distribution function (RDF) is obtained in closed form out to 3D (D is the segment diameter). The analytical expression for the RDF of the hard dimer should be useful in developing the perturbation theory of dimer fluids.

Analytical expression for the correlation function of a hard sphere chain fluid

NASA Astrophysics Data System (ADS)

Chang, Jaeeon; Kim, Hwayong

A closed form expression is given for the correlation function of flexible hard sphere chain fluid. A set of integral equations obtained from Wertheim's multidensity Ornstein-Zernike integral equation theory with the polymer Percus-Yevick ideal chain approximation is considered. Applying the Laplace transformation method to the integral equations and then solving the resulting equations algebraically, the Laplace transforms of individual correlation functions are obtained. By inverse Laplace transformation the inter- and intramolecular radial distribution functions (RDFs) are obtained in closed forms up to 3D(D is segment diameter). These analytical expressions for the RDFs would be useful in developing the perturbation theory of chain fluids.

Simulation of RF-fields in a fusion device

DOE Office of Scientific and Technical Information (OSTI.GOV)

De Witte, Dieter; Bogaert, Ignace; De Zutter, Daniel

2009-11-26

In this paper the problem of scattering off a fusion plasma is approached from the point of view of integral equations. Using the volume equivalence principle an integral equation is derived which describes the electromagnetic fields in a plasma. The equation is discretized with MoM using conforming basis functions. This reduces the problem to solving a dense matrix equation. This can be done iteratively. Each iteration can be sped up using FFTs.

On the conservation laws and solutions of a (2+1) dimensional KdV-mKdV equation of mathematical physics

NASA Astrophysics Data System (ADS)

Motsepa, Tanki; Masood Khalique, Chaudry

2018-05-01

In this paper, we study a (2+1) dimensional KdV-mKdV equation, which models many physical phenomena of mathematical physics. This equation has two integral terms in it. By an appropriate substitution, we convert this equation into two partial differential equations, which do not have integral terms and are equivalent to the original equation. We then work with the system of two equations and obtain its exact travelling wave solutions in form of Jacobi elliptic functions. Furthermore, we employ the multiplier method to construct conservation laws for the system. Finally, we revert the results obtained into the original variables of the (2+1) dimensional KdV-mKdV equation.

New integrable model of propagation of the few-cycle pulses in an anisotropic microdispersed medium

NASA Astrophysics Data System (ADS)

Sazonov, S. V.; Ustinov, N. V.

2018-03-01

We investigate the propagation of the few-cycle electromagnetic pulses in the anisotropic microdispersed medium. The effects of the anisotropy and spatial dispersion of the medium are created by the two sorts of the two-level atoms. The system of the material equations describing an evolution of the states of the atoms and the wave equations for the ordinary and extraordinary components of the pulses is derived. By applying the approximation of the sudden excitation to exclude the material variables, we reduce this system to the single nonlinear wave equation that generalizes the modified sine-Gordon equation and the Rabelo-Fokas equation. It is shown that this equation is integrable by means of the inverse scattering transformation method if an additional restriction on the parameters is imposed. The multisoliton solutions of this integrable generalization are constructed and investigated.

First integrals and parametric solutions of third-order ODEs admitting {\\mathfrak{sl}(2, {R})}

NASA Astrophysics Data System (ADS)

Ruiz, A.; Muriel, C.

2017-05-01

A complete set of first integrals for any third-order ordinary differential equation admitting a Lie symmetry algebra isomorphic to sl(2, {R}) is explicitly computed. These first integrals are derived from two linearly independent solutions of a linear second-order ODE, without additional integration. The general solution in parametric form can be obtained by using the computed first integrals. The study includes a parallel analysis of the four inequivalent realizations of sl(2, {R}) , and it is applied to several particular examples. These include the generalized Chazy equation, as well as an example of an equation which admits the most complicated of the four inequivalent realizations.

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 Kent in Canterbury, UK (1996), in Sabaudia near Rome, Italy (1998), at the University of Tokyo, Japan (2000), in Giens, France (2002), and in Helsinki, Finland (2004). The SIDE VII meeting was held at the University of Melbourne from 10-14 July 2006. The scientific committee consisted of Nalini Joshi (The University of Sydney), Frank W Nijhoff (University of Leeds), Reinout Quispel (La Trobe University) and Colin Rogers (University of New South Wales). The local organization was in the hands of John A G Roberts and Wolfgang K Schief. Proceedings of all the previous SIDE meetings have been published; the 1994 and 1988 meetings (edited respectively by D Levi, L Vinet and P Winternitz, and by D Levi and O Ragnisco) as volumes of the CRM Proceedings and Lecture Notes (AMS Publications), the 1996 meeting (edited by P Clarkson and F W Nijhoff) as Volume 255 in the LMS Lecture Note Series. Starting from the 1996 meeting the formula of publication has been changed to include rather selected refereed contributions submitted in response to a call for papers issued after the meetings and not restricted to their participants. Thus publications reflecting the scope of the 1996 meeting (edited by J Hietarinta, F W Nijhoff and J Satsuma) appeared in Journal of Physics A: Mathematical and General 34 48 (special issue), and of the 1998 and 2000 meetings (edited respectively by F W Nijhoff, Yu B Suris and C-M Viallet, and by J F van Diejen and R Halburd) in Journal of Nonlinear Mathematical Physics 10 (Suppl. 2) and 12 (Suppl. 2). The aim of this special issue is to benefit from the occasion offered by the SIDE VII meeting, producing an issue containing papers which represent the state-of-the-art knowledge for studying integrability and symmetry properties of difference equations. This special issue features high quality research papers and invited reviews which deal with themes that were covered by the SIDE VII conference. These are in alphabetical order: Algebraic-geometric approaches to integrability. The first section contains a paper by T Hamamoto and K Kajiwara on hypergeometric solutions to the q-Painlevé equation of type A4(1). Discrete geometry. In this category there are three papers. J Cielinski offers a geometric definition and a spectral approach on pseudospherical surfaces on time scales, while A Doliwa considers generalized isothermic lattices. The paper by U Pinkall, B Springborn and S Weiss mann is concerned with a new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow. Integrable systems in statistical physics. Under this heading there is a paper by R J Baxter on corner transfer matrices in statistical mechanics, and a paper by S Boukraa, S Hassani, J-M Maillard, B M McCoy, J-A Weil and N Zenine where the authors consider Fuchs-Painlevé elliptic representation of the Painlevé VI equation. KP lattices and differential-difference hierarchies. In this section we have seven articles. C R Gilson, J J C Nimmo and Y Ohta consider quasideterminant solutions of a non-Abelian Hirota-Miwa equation, while B Grammaticos, A Ramani, V Papageorgiou, J Satsuma and R Willox discuss the construction of lump-like solutions of the Hirota-Miwa equation. J Hietarinta and C Viallet analyze the factorization process for lattice maps searching for integrable cases, the paper by X-B Hu and G-F Yu is concerned with integrable discretizations of the (2+1)-dimensional sinh-Gordon equation, and K Kajiwara, M Mazzocco and Y Ohta consider the Hankel determinant formula of the tau-functions of the Toda equation. Finally, V G Papageorgiou and A G Tongas study Yang-Baxter maps and multi-field integrable lattice equations, and H-Y Wang, X-B Hu and H-W Tam consider the two-dimensional Leznov lattice equation with self-consistent sources. Quantum integrable systems. This category contains a paper on q-extended eigenvectors of the integral and finite Fourier transforms by N M Atakishiyev, J P Rueda and K B Wolf, and an article by S M Sergeev on quantization of three-wave equations. Random matrix theory. This section contains a paper by A V Kitaev on the boundary conditions for scaled random matrix ensembles in the bulk of the spectrum. Symmetries and conservation laws. In this section we have five articles. H Gegen, X-B Hu, D Levi and S Tsujimoto consider a difference-analogue of Davey-Stewartson system giving its discrete Gram-type determinant solution and Lax pair. The paper by D Levi, M Petrera, and C Scimiterna is about the lattice Schwarzian KDV equation and its symmetries, while O G Rasin and P E Hydon study the conservation laws for integrable difference equations. S Saito and N Saitoh discuss recurrence equations associated with invariant varieties of periodic points, and P H van der Kamp presents closed-form expressions for integrals of MKDV and sine-Gordon maps. Ultra-discrete systems. This final category contains an article by C Ormerod on connection matrices for ultradiscrete linear problems. We would like to express our sincerest thanks to all contributors, and to everyone involved in compiling this special issue.

The ε-form of the differential equations for Feynman integrals in the elliptic case

NASA Astrophysics Data System (ADS)

Adams, Luise; Weinzierl, Stefan

2018-06-01

Feynman integrals are easily solved if their system of differential equations is in ε-form. In this letter we show by the explicit example of the kite integral family that an ε-form can even be achieved, if the Feynman integrals do not evaluate to multiple polylogarithms. The ε-form is obtained by a (non-algebraic) change of basis for the master integrals.

Distribution theory for Schrödinger’s integral equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lange, Rutger-Jan, E-mail: rutger-jan.lange@cantab.net

2015-12-15

Much of the literature on point interactions in quantum mechanics has focused on the differential form of Schrödinger’s equation. This paper, in contrast, investigates the integral form of Schrödinger’s equation. While both forms are known to be equivalent for smooth potentials, this is not true for distributional potentials. Here, we assume that the potential is given by a distribution defined on the space of discontinuous test functions. First, by using Schrödinger’s integral equation, we confirm a seminal result by Kurasov, which was originally obtained in the context of Schrödinger’s differential equation. This hints at a possible deeper connection between bothmore » forms of the equation. We also sketch a generalisation of Kurasov’s [J. Math. Anal. Appl. 201(1), 297–323 (1996)] result to hypersurfaces. Second, we derive a new closed-form solution to Schrödinger’s integral equation with a delta prime potential. This potential has attracted considerable attention, including some controversy. Interestingly, the derived propagator satisfies boundary conditions that were previously derived using Schrödinger’s differential equation. Third, we derive boundary conditions for “super-singular” potentials given by higher-order derivatives of the delta potential. These boundary conditions cannot be incorporated into the normal framework of self-adjoint extensions. We show that the boundary conditions depend on the energy of the solution and that probability is conserved. This paper thereby confirms several seminal results and derives some new ones. In sum, it shows that Schrödinger’s integral equation is a viable tool for studying singular interactions in quantum mechanics.« less

A boundary integral approach in primitive variables for free surface flows

NASA Astrophysics Data System (ADS)

Casciola, C.; Piva, R.

The boundary integral formulation, very efficient for free surface potential flows, was considered for its possible extension to rotational flows either inviscid or viscous. We first analyze a general formulation for unsteady Navier-Stokes equations in primitive variables, which reduces to a representation for the Euler equations in the limiting case of Reynolds infinity. A first simplified model for rotational flows, obtained by decoupling kinematics and dynamics, reduces the integral equations to a known kinematical form whose mathematical and numerical properties have been studied. The dynamics equations to complete the model are obtained for the free surface and the wake. A simple and efficient scheme for the study of the non linear evolution of the wave system and its interaction with the body wake is presented. A steady state version for the calculation of the wave resistance is also reported. A second model was proposed for the simulation of rotational separated regions, by coupling the integral equations in velocity with an integral equation for the vorticity at the body boundary. The same procedure may be extended to include the diffusion of the vorticity in the flowfield. The vortex shedding from a cylindrical body in unsteady motion is discussed, as a first application of the model.

Chordwise and compressibility corrections to slender-wing theory

NASA Technical Reports Server (NTRS)

Lomax, Harvard; Sluder, Loma

1952-01-01

Corrections to slender-wing theory are obtained by assuming a spanwise distribution of loading and determining the chordwise variation which satisfies the appropriate integral equation. Such integral equations are set up in terms of the given vertical induced velocity on the center line or, depending on the type of wing plan form, its average value across the span at a given chord station. The chordwise distribution is then obtained by solving these integral equations. Results are shown for flat-plate rectangular, and triangular wings.

The ATOMFT integrator - Using Taylor series to solve ordinary differential equations

NASA Technical Reports Server (NTRS)

Berryman, Kenneth W.; Stanford, Richard H.; Breckheimer, Peter J.

1988-01-01

This paper discusses the application of ATOMFT, an integration package based on Taylor series solution with a sophisticated user interface. ATOMFT has the capabilities to allow the implementation of user defined functions and the solution of stiff and algebraic equations. Detailed examples, including the solutions to several astrodynamics problems, are presented. Comparisons with its predecessor ATOMCC and other modern integrators indicate that ATOMFT is a fast, accurate, and easy method to use to solve many differential equation problems.

Matrix algorithms for solving (in)homogeneous bound state equations

PubMed Central

Blank, M.; Krassnigg, A.

2011-01-01

In the functional approach to quantum chromodynamics, the properties of hadronic bound states are accessible via covariant integral equations, e.g. the Bethe–Salpeter equation for mesons. In particular, one has to deal with linear, homogeneous integral equations which, in sophisticated model setups, use numerical representations of the solutions of other integral equations as part of their input. Analogously, inhomogeneous equations can be constructed to obtain off-shell information in addition to bound-state masses and other properties obtained from the covariant analogue to a wave function of the bound state. These can be solved very efficiently using well-known matrix algorithms for eigenvalues (in the homogeneous case) and the solution of linear systems (in the inhomogeneous case). We demonstrate this by solving the homogeneous and inhomogeneous Bethe–Salpeter equations and find, e.g. that for the calculation of the mass spectrum it is as efficient or even advantageous to use the inhomogeneous equation as compared to the homogeneous. This is valuable insight, in particular for the study of baryons in a three-quark setup and more involved systems. PMID:21760640

Analytical Theory of the Destruction Terms in Dissipation Rate Transport Equations

NASA Technical Reports Server (NTRS)

Rubinstein, Robert; Zhou, Ye

1996-01-01

Modeled dissipation rate transport equations are often derived by invoking various hypotheses to close correlations in the corresponding exact equations. D. C. Leslie suggested that these models might be derived instead from Kraichnan's wavenumber space integrals for inertial range transport power. This suggestion is applied to the destruction terms in the dissipation rate equations for incompressible turbulence, buoyant turbulence, rotating incompressible turbulence, and rotating buoyant turbulence. Model constants like C(epsilon 2) are expressed as integrals; convergence of these integrals implies the absence of Reynolds number dependence in the corresponding destruction term. The dependence of C(epsilon 2) on rotation rate emerges naturally; sensitization of the modeled dissipation rate equation to rotation is not required. A buoyancy related effect which is absent in the exact transport equation for temperature variance dissipation, but which sometimes improves computational predictions, also arises naturally. Both the presence of this effect and the appropriate time scale in the modeled transport equation depend on whether Bolgiano or Kolmogorov inertial range scaling applies. A simple application of these methods leads to a preliminary, dissipation rate equation for rotating buoyant turbulence.

Efficiently and easily integrating differential equations with JiTCODE, JiTCDDE, and JiTCSDE

NASA Astrophysics Data System (ADS)

Ansmann, Gerrit

2018-04-01

We present a family of Python modules for the numerical integration of ordinary, delay, or stochastic differential equations. The key features are that the user enters the derivative symbolically and it is just-in-time-compiled, allowing the user to efficiently integrate differential equations from a higher-level interpreted language. The presented modules are particularly suited for large systems of differential equations such as those used to describe dynamics on complex networks. Through the selected method of input, the presented modules also allow almost complete automatization of the process of estimating regular as well as transversal Lyapunov exponents for ordinary and delay differential equations. We conceptually discuss the modules' design, analyze their performance, and demonstrate their capabilities by application to timely problems.

Asymptotic integration algorithms for first-order ODEs with application to viscoplasticity

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Yao, Minwu; Walker, Kevin P.

1992-01-01

When constructing an algorithm for the numerical integration of a differential equation, one must first convert the known ordinary differential equation (ODE), which is defined at a point, into an ordinary difference equation (O(delta)E), which is defined over an interval. Asymptotic, generalized, midpoint, and trapezoidal, O(delta)E algorithms are derived for a nonlinear first order ODE written in the form of a linear ODE. The asymptotic forward (typically underdamped) and backward (typically overdamped) integrators bound these midpoint and trapezoidal integrators, which tend to cancel out unwanted numerical damping by averaging, in some sense, the forward and backward integrations. Viscoplasticity presents itself as a system of nonlinear, coupled first-ordered ODE's that are mathematically stiff, and therefore, difficult to numerically integrate. They are an excellent application for the asymptotic integrators. Considering a general viscoplastic structure, it is demonstrated that one can either integrate the viscoplastic stresses or their associated eigenstrains.

Invited Paper - Density functional theory: coverage of dynamic and non-dynamic electron correlation effects

NASA Astrophysics Data System (ADS)

Cremer, Dieter

The electron correlation effects covered by density functional theory (DFT) can be assessed qualitatively by comparing DFT densities ρ(r) with suitable reference densities obtained with wavefunction theory (WFT) methods that cover typical electron correlation effects. The analysis of difference densities ρ(DFT)-ρ(WFT) reveals that LDA and GGA exchange (X) functionals mimic non-dynamic correlation effects in an unspecified way. It is shown that these long range correlation effects are caused by the self-interaction error (SIE) of standard X functionals. Self-interaction corrected (SIC) DFT exchange gives, similar to exact exchange, for the bonding region a delocalized exchange hole, and does not cover any correlation effects. Hence, the exchange SIE is responsible for the fact that DFT densities often resemble MP4 or MP2 densities. The correlation functional changes X-only DFT densities in a manner observed when higher order coupling effects between lower order N-electron correlation effects are included. Hybrid functionals lead to changes in the density similar to those caused by SICDFT, which simply reflects the fact that hybrid functionals have been developed to cover part of the SIE and its long range correlation effects in a balanced manner. In the case of spin-unrestricted DFT (UDFT), non-dynamic electron correlation effects enter the calculation both via the X functional and via the wavefunction, which may cause a double-counting of correlation effects. The use of UDFT in the form of permuted orbital and broken-symmetry DFT (PO-UDFT, BS-UDFT) can lead to reasonable descriptions of multireference systems provided certain conditions are fulfilled. More reliable, however, is a combination of DFT and WFT methods, which makes the routine description of multireference systems possible. The development of such methods implies a separation of dynamic and non-dynamic correlation effects. Strategies for accomplishing this goal are discussed in general and tested in practice for CAS (complete active space)-DFT.

Are low altitude alpine tundra ecosystems under threat? A case study from the Parc National de la Gaspésie, Québec

NASA Astrophysics Data System (ADS)

Dumais, Catherine; Ropars, Pascale; Denis, Marie-Pier; Dufour-Tremblay, Geneviève; Boudreau, Stéphane

2014-09-01

According to the 2007 IPCC report, the alpine tundra ecosystems found on low mountains of the northern hemisphere are amongst the most threatened by climate change. A treeline advance or a significant erect shrub expansion could result in increased competition for the arctic-alpine species usually found on mountaintops and eventually lead to their local extinction. The objectives of our study were to identify recent changes in the cover and growth of erect woody vegetation in the alpine tundra of Mont de la Passe, in the Parc National de la Gaspésie (Québec, Canada). The comparison of two orthorectified aerial photos revealed no significant shift of the treeline between 1975 and 2004. During the same period however, shrub species cover increased from 20.2% to 30.4% in the lower alpine zone. Dendrochronological analyses conducted on Betula glandulosa Michx. sampled at three different positions along an altitudinal gradient (low, intermediate and high alpine zone) revealed that the climatic determinants of B. glandulosa radial growth become more complex with increasing altitude. In the lower alpine zone, B. glandulosa radial growth is only significantly associated positively to July temperature. In the intermediate alpine zone, radial growth is associated positively to July temperature but negatively to March temperature. In the high alpine zone, radial growth is positively associated to January, July and August temperature but negatively to March temperature. The positive association between summer temperatures and radial growth suggests that B. glandulosa could potentially benefit from warmer temperatures, a phenomenon that could lead to an increase in its cover over the next few decades. Although alpine tundra vegetation is not threatened in the short-term in the Parc National de la Gaspésie, erect shrub cover, especially B. glandulosa, could likely increase in the near future, threatening the local arctic-alpine flora.

Semi-analytical Karhunen-Loeve representation of irregular waves based on the prolate spheroidal wave functions

NASA Astrophysics Data System (ADS)

Lee, Gibbeum; Cho, Yeunwoo

2018-01-01

A new semi-analytical approach is presented to solving the matrix eigenvalue problem or the integral equation in Karhunen-Loeve (K-L) representation of random data such as irregular ocean waves. Instead of direct numerical approach to this matrix eigenvalue problem, which may suffer from the computational inaccuracy for big data, a pair of integral and differential equations are considered, which are related to the so-called prolate spheroidal wave functions (PSWF). First, the PSWF is expressed as a summation of a small number of the analytical Legendre functions. After substituting them into the PSWF differential equation, a much smaller size matrix eigenvalue problem is obtained than the direct numerical K-L matrix eigenvalue problem. By solving this with a minimal numerical effort, the PSWF and the associated eigenvalue of the PSWF differential equation are obtained. Then, the eigenvalue of the PSWF integral equation is analytically expressed by the functional values of the PSWF and the eigenvalues obtained in the PSWF differential equation. Finally, the analytically expressed PSWFs and the eigenvalues in the PWSF integral equation are used to form the kernel matrix in the K-L integral equation for the representation of exemplary wave data such as ordinary irregular waves. It is found that, with the same accuracy, the required memory size of the present method is smaller than that of the direct numerical K-L representation and the computation time of the present method is shorter than that of the semi-analytical method based on the sinusoidal functions.

The integrated Michaelis-Menten rate equation: déjà vu or vu jàdé?

PubMed

Goličnik, Marko

2013-08-01

A recent article of Johnson and Goody (Biochemistry, 2011;50:8264-8269) described the almost-100-years-old paper of Michaelis and Menten. Johnson and Goody translated this classic article and presented the historical perspective to one of incipient enzyme-reaction data analysis, including a pioneering global fit of the integrated rate equation in its implicit form to the experimental time-course data. They reanalyzed these data, although only numerical techniques were used to solve the model equations. However, there is also the still little known algebraic rate-integration equation in a closed form that enables direct fitting of the data. Therefore, in this commentary, I briefly present the integral solution of the Michaelis-Menten rate equation, which has been largely overlooked for three decades. This solution is expressed in terms of the Lambert W function, and I demonstrate here its use for global nonlinear regression curve fitting, as carried out with the original time-course dataset of Michaelis and Menten.

The Boundary Integral Equation Method for Porous Media Flow

NASA Astrophysics Data System (ADS)

Anderson, Mary P.

Just as groundwater hydrologists are breathing sighs of relief after the exertions of learning the finite element method, a new technique has reared its nodes—the boundary integral equation method (BIEM) or the boundary equation method (BEM), as it is sometimes called. As Liggett and Liu put it in the preface to The Boundary Integral Equation Method for Porous Media Flow, “Lately, the Boundary Integral Equation Method (BIEM) has emerged as a contender in the computation Derby.” In fact, in July 1984, the 6th International Conference on Boundary Element Methods in Engineering will be held aboard the Queen Elizabeth II, en route from Southampton to New York. These conferences are sponsored by the Department of Civil Engineering at Southampton College (UK), whose members are proponents of BIEM. The conferences have featured papers on applications of BIEM to all aspects of engineering, including flow through porous media. Published proceedings are available, as are textbooks on application of BIEM to engineering problems. There is even a 10-minute film on the subject.

Numerical integration of ordinary differential equations of various orders

NASA Technical Reports Server (NTRS)

Gear, C. W.

1969-01-01

Report describes techniques for the numerical integration of differential equations of various orders. Modified multistep predictor-corrector methods for general initial-value problems are discussed and new methods are introduced.

Neglected transport equations: extended Rankine-Hugoniot conditions and J -integrals for fracture

NASA Astrophysics Data System (ADS)

Davey, K.; Darvizeh, R.

2016-09-01

Transport equations in integral form are well established for analysis in continuum fluid dynamics but less so for solid mechanics. Four classical continuum mechanics transport equations exist, which describe the transport of mass, momentum, energy and entropy and thus describe the behaviour of density, velocity, temperature and disorder, respectively. However, one transport equation absent from the list is particularly pertinent to solid mechanics and that is a transport equation for movement, from which displacement is described. This paper introduces the fifth transport equation along with a transport equation for mechanical energy and explores some of the corollaries resulting from the existence of these equations. The general applicability of transport equations to discontinuous physics is discussed with particular focus on fracture mechanics. It is well established that bulk properties can be determined from transport equations by application of a control volume methodology. A control volume can be selected to be moving, stationary, mass tracking, part of, or enclosing the whole system domain. The flexibility of transport equations arises from their ability to tolerate discontinuities. It is insightful thus to explore the benefits derived from the displacement and mechanical energy transport equations, which are shown to be beneficial for capturing the physics of fracture arising from a displacement discontinuity. Extended forms of the Rankine-Hugoniot conditions for fracture are established along with extended forms of J -integrals.

A Tensor-Train accelerated solver for integral equations in complex geometries

NASA Astrophysics Data System (ADS)

Corona, Eduardo; Rahimian, Abtin; Zorin, Denis

2017-04-01

We present a framework using the Quantized Tensor Train (QTT) decomposition to accurately and efficiently solve volume and boundary integral equations in three dimensions. We describe how the QTT decomposition can be used as a hierarchical compression and inversion scheme for matrices arising from the discretization of integral equations. For a broad range of problems, computational and storage costs of the inversion scheme are extremely modest O (log ⁡ N) and once the inverse is computed, it can be applied in O (Nlog ⁡ N) . We analyze the QTT ranks for hierarchically low rank matrices and discuss its relationship to commonly used hierarchical compression techniques such as FMM and HSS. We prove that the QTT ranks are bounded for translation-invariant systems and argue that this behavior extends to non-translation invariant volume and boundary integrals. For volume integrals, the QTT decomposition provides an efficient direct solver requiring significantly less memory compared to other fast direct solvers. We present results demonstrating the remarkable performance of the QTT-based solver when applied to both translation and non-translation invariant volume integrals in 3D. For boundary integral equations, we demonstrate that using a QTT decomposition to construct preconditioners for a Krylov subspace method leads to an efficient and robust solver with a small memory footprint. We test the QTT preconditioners in the iterative solution of an exterior elliptic boundary value problem (Laplace) formulated as a boundary integral equation in complex, multiply connected geometries.

Feynman path integral application on deriving black-scholes diffusion equation for european option pricing

NASA Astrophysics Data System (ADS)

Utama, Briandhika; Purqon, Acep

2016-08-01

Path Integral is a method to transform a function from its initial condition to final condition through multiplying its initial condition with the transition probability function, known as propagator. At the early development, several studies focused to apply this method for solving problems only in Quantum Mechanics. Nevertheless, Path Integral could also apply to other subjects with some modifications in the propagator function. In this study, we investigate the application of Path Integral method in financial derivatives, stock options. Black-Scholes Model (Nobel 1997) was a beginning anchor in Option Pricing study. Though this model did not successfully predict option price perfectly, especially because its sensitivity for the major changing on market, Black-Scholes Model still is a legitimate equation in pricing an option. The derivation of Black-Scholes has a high difficulty level because it is a stochastic partial differential equation. Black-Scholes equation has a similar principle with Path Integral, where in Black-Scholes the share's initial price is transformed to its final price. The Black-Scholes propagator function then derived by introducing a modified Lagrange based on Black-Scholes equation. Furthermore, we study the correlation between path integral analytical solution and Monte-Carlo numeric solution to find the similarity between this two methods.

An integral equation-based numerical solver for Taylor states in toroidal geometries

NASA Astrophysics Data System (ADS)

O'Neil, Michael; Cerfon, Antoine J.

2018-04-01

We present an algorithm for the numerical calculation of Taylor states in toroidal and toroidal-shell geometries using an analytical framework developed for the solution to the time-harmonic Maxwell equations. Taylor states are a special case of what are known as Beltrami fields, or linear force-free fields. The scheme of this work relies on the generalized Debye source representation of Maxwell fields and an integral representation of Beltrami fields which immediately yields a well-conditioned second-kind integral equation. This integral equation has a unique solution whenever the Beltrami parameter λ is not a member of a discrete, countable set of resonances which physically correspond to spontaneous symmetry breaking. Several numerical examples relevant to magnetohydrodynamic equilibria calculations are provided. Lastly, our approach easily generalizes to arbitrary geometries, both bounded and unbounded, and of varying genus.

CALL FOR PAPERS: Special issue on Symmetries and Integrability of Difference Equations

NASA Astrophysics Data System (ADS)

Doliwa, Adam; Korhonen, Risto; Lafortune, Stephane

2006-10-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and General entitled `Special issue on Symmetries and Integrability of Difference Equations' as featured at the SIDE VII meeting held during July 2006 in Melbourne (http://web.maths.unsw.edu.au/%7Eschief/side/side.html). Participants at that meeting, as well as other researchers working in the field of difference equations and discrete systems, are invited to submit a research paper to this issue. This meeting was the seventh of a series of biennial meetings devoted to the study of integrable difference equations and related topics. 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, just as 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, quantum field theory, etc. It is thus crucial to develop tools to study and solve difference equations. While the theory of symmetry and integrability for differential equations is now well-established, this is not yet the case for discrete equations. The situation has undergone impressive development in recent years and has affected a broad range of fields, including the theory of special functions, quantum integrable systems, numerical analysis, cellular automata, representations of quantum groups, symmetries of difference equations, discrete (difference) geometry, etc. Consequently, the aim of the special issue is to benefit from the occasion offered by the SIDE VII meeting to provide a collection of papers which represent the state-of-the-art knowledge for studying integrability and symmetry properties of difference equations. Scope of the special issue The special issue will feature papers which deal with themes that were covered by the SIDE VII Conference. These are •Integrability testing •Discrete geometry and visualization •Laurent phenomena and cluster algebras •Ultra-discrete systems •Random matrix theory •Algebraic-geometric approaches to integrability •Yang-Baxter equations •Quantum and classical integrable systems •Difference Galois theory Editorial policy •The subject of the paper should relate to the subject of the meeting. The Guest Editors will reserve the right to judge whether a contribution fits the scope of the topic of the special issue. •Contributions will be refereed and processed according to the usual procedure of the journal. •Conference papers may be based on already published work but should either •contain significant additional new results and/or insights or •give a survey of the present state of the art, a critical assessment of the present understanding of a topic, and a discussion of open problems. •Papers submitted by non-participants should be original and contain substantial new results. Guidelines for preparation of contributions • The deadline for contributed papers will be 15 January 2007. •There is a page limit of 16 printed pages (approximately 9600 words) per contribution. For submitted papers exceeding this length the Guest Editors reserve the right to request a reduction in length. Further advice on document preparation can be found at www.iop.org/Journals/jphysa •Contributions to the special issue should if possible be submitted electronically by web upload at www.iop.org/Journals/jphysa, or by email to jphysa@iop.org, quoting 'J. Phys. A Special Issue: SIDE VII'. Submissions should ideally be in standard LaTeX form; we are, however, able to accept most formats including Microsoft Word. Please see the website for further information on electronic submissions. •Authors unable to submit electronically may send hard-copy contributions to: Publishing Administrators, Journal of Physics A, Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK, enclosing electronic code on floppy disk if available and quoting 'J. Phys. A Special Issue: SIDE VII'. • All contributions should be accompanied by a read-me file or covering letter giving the postal and email address for correspondence. The Publishing Office should be notified of any subsequent change of address. •The special issue will be published in the paper and online version of the journal. The corresponding author of each contribution will receive a complimentary copy of the issue.

On Reductions of the Hirota-Miwa Equation

NASA Astrophysics Data System (ADS)

Hone, Andrew N. W.; Kouloukas, Theodoros E.; Ward, Chloe

2017-07-01

The Hirota-Miwa equation (also known as the discrete KP equation, or the octahedron recurrence) is a bilinear partial difference equation in three independent variables. It is integrable in the sense that it arises as the compatibility condition of a linear system (Lax pair). The Hirota-Miwa equation has infinitely many reductions of plane wave type (including a quadratic exponential gauge transformation), defined by a triple of integers or half-integers, which produce bilinear ordinary difference equations of Somos/Gale-Robinson type. Here it is explained how to obtain Lax pairs and presymplectic structures for these reductions, in order to demonstrate Liouville integrability of some associated maps, certain of which are related to reductions of discrete Toda and discrete KdV equations.

Infinitesimal Bäcklund Transformation and Conservation Laws for Non-autonomous Systems

NASA Astrophysics Data System (ADS)

Mahato, G.; Chowdhury, A. Roy

We have observed that it is possible to extend the concept of the infinitesimal Bäcklund transformation of Steudel to the case of non-autonomous systems. We have discussed the situation with the cylindrical KdV as example. The interesting point to note is that though the B.T. for Ckdv does not possess the usual property of generating one soliton in a single operation, yet it generates an infinite number of symmetries, which corroborates with those obtained through the expansion of the resolvant of the linear operator associated with the equation.Translated AbstractInfinitesimale Bäcklund-Transformation und Erhaltungsgesetze nichtautonomer SystemeWir finden, daß es möglich ist, das Steudelsche Konzept der infinitesimalen Bäcklund-Transformation auf den Fall nichtautonomer Systeme zu übertragen. Als ein Beispiel wird die Situation bei einer zylindrischen KdV-Gleichung pehandelt. Der interessante Punkt ist dabei, daß die Bäcklund-Transformation - obwohl sie für die zylindrische KdV-Gleichung die übliche Eigenschaft, ein Soliton durch eine einzige Operation zu erzeugen, nicht besitzt - doch eine unendliche Zahl von Symmetrien erzeugt. Das bestätigt die Ergebnisse, die man durch Entwicklung der Resolvente des mit der Gleichung verknüpften linearen Operators erhält.

Symmetric and arbitrarily high-order Birkhoff-Hermite time integrators and their long-time behaviour for solving nonlinear Klein-Gordon equations

NASA Astrophysics Data System (ADS)

Liu, Changying; Iserles, Arieh; Wu, Xinyuan

2018-03-01

The Klein-Gordon equation with nonlinear potential occurs in a wide range of application areas in science and engineering. Its computation represents a major challenge. The main theme of this paper is the construction of symmetric and arbitrarily high-order time integrators for the nonlinear Klein-Gordon equation by integrating Birkhoff-Hermite interpolation polynomials. To this end, under the assumption of periodic boundary conditions, we begin with the formulation of the nonlinear Klein-Gordon equation as an abstract second-order ordinary differential equation (ODE) and its operator-variation-of-constants formula. We then derive a symmetric and arbitrarily high-order Birkhoff-Hermite time integration formula for the nonlinear abstract ODE. Accordingly, the stability, convergence and long-time behaviour are rigorously analysed once the spatial differential operator is approximated by an appropriate positive semi-definite matrix, subject to suitable temporal and spatial smoothness. A remarkable characteristic of this new approach is that the requirement of temporal smoothness is reduced compared with the traditional numerical methods for PDEs in the literature. Numerical results demonstrate the advantage and efficiency of our time integrators in comparison with the existing numerical approaches.

Soliton solution and gauge equivalence for an integrable nonlocal complex modified Korteweg-de Vries equation

NASA Astrophysics Data System (ADS)

Ma, Li-Yuan; Shen, Shou-Feng; Zhu, Zuo-Nong

2017-10-01

In this paper, we prove that an integrable nonlocal complex modified Korteweg-de Vries (mKdV) equation introduced by Ablowitz and Musslimani [Nonlinearity 29, 915-946 (2016)] is gauge equivalent to a spin-like model. From the gauge equivalence, one can see that there exists significant difference between the nonlocal complex mKdV equation and the classical complex mKdV equation. Through constructing the Darboux transformation for nonlocal complex mKdV equation, a variety of exact solutions including dark soliton, W-type soliton, M-type soliton, and periodic solutions are derived.

Grundlagen der zeichnerischen Darstellung

NASA Astrophysics Data System (ADS)

Döring, Peter

Eine Technische Zeichnung muss nach DIN 6774 Teil 1 in der Weise angefertigt werden, dass sie übersichtlich, unmissverständlich, auch in verkleinertem Maßstab lesbar bleibt, kostengünstig reproduzierbar und dauerhaft archivierbar ist. Zu dem Zweck benötigt man entsprechendes Papier und angepasstes Zeichengerät. Heute ist die Anfertigung mit entsprechenden Rechnerprogrammen möglich.

Richtfunktechnik

NASA Astrophysics Data System (ADS)

Plaßmann, Wilfried

Die Nachrichtenübertragung über Richtfunkstrecken wird neben der Übertragung über Kabel eingesetzt. Gegenüber der Rundfunk- und Fernsehübertragung weist sie den Unterschied auf, dass Sender und Empfänger ortsfest sind. Da es nur einen Empfänger gibt, kann die Übertragung mit einem gerichteten elektromagnetischen Feld erfolgen. Die Besonderheit dieser Technik wird hier dargestellt.

Impact of climate change on projected runoff from mountain snowpack of the King’s Rivershed in California

USDA-ARS?s Scientific Manuscript database

The Central Valley of California, like most dryland agricultural areas in the Southwest United States, relies heavily on winter snowpack for water resources. Projections of future climate in the Sierra Mountains of California calls for a warmer climate regime that will impact the snowpack in the Sie...

Kants Theorie der Sonne: Physikgeschichte

NASA Astrophysics Data System (ADS)

Jacobi, Manfred

2005-01-01

Im Rahmen seiner Kosmogonie entwickelte der junge Immanuel Kant eine Theorie der Sonne. Sie ist ein einzigartiges Zeugnis seiner intuitiven Vorstellungskraft und beweist auch die Leistungsfähigkeit der damaligen, vorwiegend von Newton geprägten Weltsicht. Entstehung, Aufbau und Dynamik der Sonne werden in Kants Theorie ebenso erklärt wie etwa das Phänomen der Sonnenflecken.

SPRECHEN SIE GOETHE, A SYNOPTIC ESSAY.

ERIC Educational Resources Information Center

BUSACCA, BASIL

THE WAY IN WHICH WE CONCEIVE OF REALITY IS DEPENDENT UPON THE LANGUAGE SYSTEM WE USE. EACH LANGUAGE SYSTEM, WHETHER THAT OF A WHOLE CULTURE, A SUBCULTURE, OR AN INDIVIDUAL, EMBODIES IN ITS VOCABULARY AND SYNTAX AND RULES OF "GRAMMAR" A SET OF ASSUMPTIONS ABOUT THE NATURE OF REALITY AND THE CORRECT WAYS TO MAKE SENSE OF THINGS. THUS, UNDERSTANDING…

Solvability of a Nonlinear Integral Equation in Dynamical String Theory

NASA Astrophysics Data System (ADS)

Khachatryan, A. Kh.; Khachatryan, Kh. A.

2018-04-01

We investigate an integral equation of the convolution type with a cubic nonlinearity on the entire real line. This equation has a direct application in open-string field theory and in p-adic string theory and describes nonlocal interactions. We prove that there exists a one-parameter family of bounded monotonic solutions and calculate the limits of solutions constructed at infinity.

Modelling gas dynamics in 1D ducts with abrupt area change

NASA Astrophysics Data System (ADS)

Menina, R.; Saurel, R.; Zereg, M.; Houas, L.

2011-09-01

Most gas dynamic computations in industrial ducts are done in one dimension with cross-section-averaged Euler equations. This poses a fundamental difficulty as soon as geometrical discontinuities are present. The momentum equation contains a non-conservative term involving a surface pressure integral, responsible for momentum loss. Definition of this integral is very difficult from a mathematical standpoint as the flow may contain other discontinuities (shocks, contact discontinuities). From a physical standpoint, geometrical discontinuities induce multidimensional vortices that modify the surface pressure integral. In the present paper, an improved 1D flow model is proposed. An extra energy (or entropy) equation is added to the Euler equations expressing the energy and turbulent pressure stored in the vortices generated by the abrupt area variation. The turbulent energy created by the flow-area change interaction is determined by a specific estimate of the surface pressure integral. Model's predictions are compared with 2D-averaged results from numerical solution of the Euler equations. Comparison with shock tube experiments is also presented. The new 1D-averaged model improves the conventional cross-section-averaged Euler equations and is able to reproduce the main flow features.

Some integrable maps and their Hirota bilinear forms

NASA Astrophysics Data System (ADS)

Hone, A. N. W.; Kouloukas, T. E.; Quispel, G. R. W.

2018-01-01

We introduce a two-parameter family of birational maps, which reduces to a family previously found by Demskoi, Tran, van der Kamp and Quispel (DTKQ) when one of the parameters is set to zero. The study of the singularity confinement pattern for these maps leads to the introduction of a tau function satisfying a homogeneous recurrence which has the Laurent property, and the tropical (or ultradiscrete) analogue of this homogeneous recurrence confirms the quadratic degree growth found empirically by Demskoi et al. We prove that the tau function also satisfies two different bilinear equations, each of which is a reduction of the Hirota-Miwa equation (also known as the discrete KP equation, or the octahedron recurrence). Furthermore, these bilinear equations are related to reductions of particular two-dimensional integrable lattice equations, of discrete KdV or discrete Toda type. These connections, as well as the cluster algebra structure of the bilinear equations, allow a direct construction of Poisson brackets, Lax pairs and first integrals for the birational maps. As a consequence of the latter results, we show how each member of the family can be lifted to a system that is integrable in the Liouville sense, clarifying observations made previously in the original DTKQ case.

Applying integrals of motion to the numerical solution of differential equations

NASA Technical Reports Server (NTRS)

Vezewski, D. J.

1980-01-01

A method is developed for using the integrals of systems of nonlinear, ordinary, differential equations in a numerical integration process to control the local errors in these integrals and reduce the global errors of the solution. The method is general and can be applied to either scalar or vector integrals. A number of example problems, with accompanying numerical results, are used to verify the analysis and support the conjecture of global error reduction.

Sixth-Order Lie Group Integrators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Forest, E.

1990-03-01

In this paper we present the coefficients of several 6th order symplectic integrator of the type developed by R. Ruth. To get these results we fully exploit the connection with Lie groups. This integrator, as well as all the explicit integrators of Ruth, may be used in any equation where some sort of Lie bracket is preserved. In fact, if the Lie operator governing the equation of motion is separable into two solvable parts, the Ruth integrators can be used.

Applying integrals of motion to the numerical solution of differential equations

NASA Technical Reports Server (NTRS)

Jezewski, D. J.

1979-01-01

A method is developed for using the integrals of systems of nonlinear, ordinary differential equations in a numerical integration process to control the local errors in these integrals and reduce the global errors of the solution. The method is general and can be applied to either scaler or vector integrals. A number of example problems, with accompanying numerical results, are used to verify the analysis and support the conjecture of global error reduction.

Extension of the KLI approximation toward the exact optimized effective potential.

PubMed

Iafrate, G J; Krieger, J B

2013-03-07

The integral equation for the optimized effective potential (OEP) is utilized in a compact form from which an accurate OEP solution for the spin-unrestricted exchange-correlation potential, Vxcσ, is obtained for any assumed orbital-dependent exchange-correlation energy functional. The method extends beyond the Krieger-Li-Iafrate (KLI) approximation toward the exact OEP result. The compact nature of the OEP equation arises by replacing the integrals involving the Green's function terms in the traditional OEP equation by an equivalent first-order perturbation theory wavefunction often referred to as the "orbital shift" function. Significant progress is then obtained by solving the equation for the first order perturbation theory wavefunction by use of Dalgarno functions which are determined from well known methods of partial differential equations. The use of Dalgarno functions circumvents the need to explicitly address the Green's functions and the associated problems with "sum over states" numerics; as well, the Dalgarno functions provide ease in dealing with inherent singularities arising from the origin and the zeros of the occupied orbital wavefunctions. The Dalgarno approach for finding a solution to the OEP equation is described herein, and a detailed illustrative example is presented for the special case of a spherically symmetric exchange-correlation potential. For the case of spherical symmetry, the relevant Dalgarno function is derived by direct integration of the appropriate radial equation while utilizing a user friendly method which explicitly treats the singular behavior at the origin and at the nodal singularities arising from the zeros of the occupied states. The derived Dalgarno function is shown to be an explicit integral functional of the exact OEP Vxcσ, thus allowing for the reduction of the OEP equation to a self-consistent integral equation for the exact exchange-correlation potential; the exact solution to this integral equation can be determined by iteration with the natural zeroth order correction given by the KLI exchange-correlation potential. Explicit analytic results are provided to illustrate the first order iterative correction beyond the KLI approximation. The derived correction term to the KLI potential explicitly involves spatially weighted products of occupied orbital densities in any assumed orbital-dependent exchange-correlation energy functional; as well, the correction term is obtained with no adjustable parameters. Moreover, if the equation for the exact optimized effective potential is further iterated, one can obtain the OEP as accurately as desired.

Extension of the KLI approximation toward the exact optimized effective potential

NASA Astrophysics Data System (ADS)

Iafrate, G. J.; Krieger, J. B.

2013-03-01

The integral equation for the optimized effective potential (OEP) is utilized in a compact form from which an accurate OEP solution for the spin-unrestricted exchange-correlation potential, Vxcσ, is obtained for any assumed orbital-dependent exchange-correlation energy functional. The method extends beyond the Krieger-Li-Iafrate (KLI) approximation toward the exact OEP result. The compact nature of the OEP equation arises by replacing the integrals involving the Green's function terms in the traditional OEP equation by an equivalent first-order perturbation theory wavefunction often referred to as the "orbital shift" function. Significant progress is then obtained by solving the equation for the first order perturbation theory wavefunction by use of Dalgarno functions which are determined from well known methods of partial differential equations. The use of Dalgarno functions circumvents the need to explicitly address the Green's functions and the associated problems with "sum over states" numerics; as well, the Dalgarno functions provide ease in dealing with inherent singularities arising from the origin and the zeros of the occupied orbital wavefunctions. The Dalgarno approach for finding a solution to the OEP equation is described herein, and a detailed illustrative example is presented for the special case of a spherically symmetric exchange-correlation potential. For the case of spherical symmetry, the relevant Dalgarno function is derived by direct integration of the appropriate radial equation while utilizing a user friendly method which explicitly treats the singular behavior at the origin and at the nodal singularities arising from the zeros of the occupied states. The derived Dalgarno function is shown to be an explicit integral functional of the exact OEP Vxcσ, thus allowing for the reduction of the OEP equation to a self-consistent integral equation for the exact exchange-correlation potential; the exact solution to this integral equation can be determined by iteration with the natural zeroth order correction given by the KLI exchange-correlation potential. Explicit analytic results are provided to illustrate the first order iterative correction beyond the KLI approximation. The derived correction term to the KLI potential explicitly involves spatially weighted products of occupied orbital densities in any assumed orbital-dependent exchange-correlation energy functional; as well, the correction term is obtained with no adjustable parameters. Moreover, if the equation for the exact optimized effective potential is further iterated, one can obtain the OEP as accurately as desired.

Efficient Solution of Three-Dimensional Problems of Acoustic and Electromagnetic Scattering by Open Surfaces

NASA Technical Reports Server (NTRS)

Turc, Catalin; Anand, Akash; Bruno, Oscar; Chaubell, Julian

2011-01-01

We present a computational methodology (a novel Nystrom approach based on use of a non-overlapping patch technique and Chebyshev discretizations) for efficient solution of problems of acoustic and electromagnetic scattering by open surfaces. Our integral equation formulations (1) Incorporate, as ansatz, the singular nature of open-surface integral-equation solutions, and (2) For the Electric Field Integral Equation (EFIE), use analytical regularizes that effectively reduce the number of iterations required by iterative linear-algebra solution based on Krylov-subspace iterative solvers.

On the complete and partial integrability of non-Hamiltonian systems

NASA Astrophysics Data System (ADS)

Bountis, T. C.; Ramani, A.; Grammaticos, B.; Dorizzi, B.

1984-11-01

The methods of singularity analysis are applied to several third order non-Hamiltonian systems of physical significance including the Lotka-Volterra equations, the three-wave interaction and the Rikitake dynamo model. Complete integrability is defined and new completely integrable systems are discovered by means of the Painlevé property. In all these cases we obtain integrals, which reduce the equations either to a final quadrature or to an irreducible second order ordinary differential equation (ODE) solved by Painlevé transcendents. Relaxing the Painlevé property we find many partially integrable cases whose movable singularities are poles at leading order, with In( t- t0) terms entering at higher orders. In an Nth order, generalized Rössler model a precise relation is established between the partial fulfillment of the Painlevé conditions and the existence of N - 2 integrals of the motion.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Shouxin; Gibbons, Gary W.; Yang, Yisong, E-mail: chensx@henu.edu.cn, E-mail: gwg1@damtp.cam.ac.uk, E-mail: yisongyang@nyu.edu

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 generalmore » 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.« less

Integrability of systems of two second-order ordinary differential equations admitting four-dimensional Lie algebras

PubMed Central

Gazizov, R. K.

2017-01-01

We suggest an algorithm for integrating systems of two second-order ordinary differential equations with four symmetries. In particular, if the admitted transformation group has two second-order differential invariants, the corresponding system can be integrated by quadratures using invariant representation and the operator of invariant differentiation. Otherwise, the systems reduce to partially uncoupled forms and can also be integrated by quadratures. PMID:28265184

Integrability of systems of two second-order ordinary differential equations admitting four-dimensional Lie algebras.

PubMed

Gainetdinova, A A; Gazizov, R K

2017-01-01

We suggest an algorithm for integrating systems of two second-order ordinary differential equations with four symmetries. In particular, if the admitted transformation group has two second-order differential invariants, the corresponding system can be integrated by quadratures using invariant representation and the operator of invariant differentiation. Otherwise, the systems reduce to partially uncoupled forms and can also be integrated by quadratures.

A multi-domain spectral method for time-fractional differential equations

NASA Astrophysics Data System (ADS)

Chen, Feng; Xu, Qinwu; Hesthaven, Jan S.

2015-07-01

This paper proposes an approach for high-order time integration within a multi-domain setting for time-fractional differential equations. Since the kernel is singular or nearly singular, two main difficulties arise after the domain decomposition: how to properly account for the history/memory part and how to perform the integration accurately. To address these issues, we propose a novel hybrid approach for the numerical integration based on the combination of three-term-recurrence relations of Jacobi polynomials and high-order Gauss quadrature. The different approximations used in the hybrid approach are justified theoretically and through numerical examples. Based on this, we propose a new multi-domain spectral method for high-order accurate time integrations and study its stability properties by identifying the method as a generalized linear method. Numerical experiments confirm hp-convergence for both time-fractional differential equations and time-fractional partial differential equations.

Differential Galois theory and non-integrability of planar polynomial vector fields

NASA Astrophysics Data System (ADS)

Acosta-Humánez, Primitivo B.; Lázaro, J. Tomás; Morales-Ruiz, Juan J.; Pantazi, Chara

2018-06-01

We study a necessary condition for the integrability of the polynomials vector fields in the plane by means of the differential Galois Theory. More concretely, by means of the variational equations around a particular solution it is obtained a necessary condition for the existence of a rational first integral. The method is systematic starting with the first order variational equation. We illustrate this result with several families of examples. A key point is to check whether a suitable primitive is elementary or not. Using a theorem by Liouville, the problem is equivalent to the existence of a rational solution of a certain first order linear equation, the Risch equation. This is a classical problem studied by Risch in 1969, and the solution is given by the "Risch algorithm". In this way we point out the connection of the non integrability with some higher transcendent functions, like the error function.

Complex quantum Hamilton-Jacobi equation with Bohmian trajectories: Application to the photodissociation dynamics of NOCl

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

2014-03-14

The complex quantum Hamilton-Jacobi equation-Bohmian trajectories (CQHJE-BT) method is introduced as a synthetic trajectory method for integrating the complex quantum Hamilton-Jacobi equation for the complex action function by propagating an ensemble of real-valued correlated Bohmian trajectories. Substituting the wave function expressed in exponential form in terms of the complex action into the time-dependent Schrödinger equation yields the complex quantum Hamilton-Jacobi equation. We transform this equation into the arbitrary Lagrangian-Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation describing the rate of change in the complex action transported along Bohmian trajectories is simultaneouslymore » integrated with the guidance equation for Bohmian trajectories, and the time-dependent wave function is readily synthesized. The spatial derivatives of the complex action required for the integration scheme are obtained by solving one moving least squares matrix equation. In addition, the method is applied to the photodissociation of NOCl. The photodissociation dynamics of NOCl can be accurately described by propagating a small ensemble of trajectories. This study demonstrates that the CQHJE-BT method combines the considerable advantages of both the real and the complex quantum trajectory methods previously developed for wave packet dynamics.« less

A novel approach to solve nonlinear Fredholm integral equations of the second kind.

PubMed

Li, Hu; Huang, Jin

2016-01-01

In this paper, we present a novel approach to solve nonlinear Fredholm integral equations of the second kind. This algorithm is constructed by the integral mean value theorem and Newton iteration. Convergence and error analysis of the numerical solutions are given. Moreover, Numerical examples show the algorithm is very effective and simple.

A Note on ;New Hierarchies of Integrable Lattice Equations and Associated Properties: Darboux Transformation Conservation Laws and Integrable Coupling; [Rep. Math. Phys. 67 (2011), 259

NASA Astrophysics Data System (ADS)

Xu, Xi-Xiang

2016-12-01

We prove that two new hierarchies of integrable lattice equations in [Rep. Math. Phys.67 (2011), 259] can be respectively changed into the famous relativistic Toda lattice hierarchies in the polynomial and the rational forms by means of a simple transformation.

Proceedings of the 1993 Scientific Conference on Obscuration and Aerosol Research Held in Aberdeen Proving Ground on 22-24 Jun 1993

DTIC Science & Technology

1994-03-01

equation (4.1.27) is not a finite rank integral equation, it suggests that an approxi- mate finite rank integral equation Pf" = Pg + APL(K~p) Pfa 4 \\PNPfa...Harry Salem Richard Farrell Mark Seaver Dennis F Flanigan George Sehmel David Freund Jungshik Shin Robert H Frickel Orazio I Sindoni Edward Fry Michael

Variational iteration method — a promising technique for constructing equivalent integral equations of fractional order

NASA Astrophysics Data System (ADS)

Wang, Yi-Hong; Wu, Guo-Cheng; Baleanu, Dumitru

2013-10-01

The variational iteration method is newly used to construct various integral equations of fractional order. Some iterative schemes are proposed which fully use the method and the predictor-corrector approach. The fractional Bagley-Torvik equation is then illustrated as an example of multi-order and the results show the efficiency of the variational iteration method's new role.

Boundary regularized integral equation formulation of the Helmholtz equation in acoustics.

PubMed

Sun, Qiang; Klaseboer, Evert; Khoo, Boo-Cheong; Chan, Derek Y C

2015-01-01

A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field owing to radiating bodies in acoustic wave problems. This method facilitates the use of higher order surface elements to represent boundaries, resulting in a significant reduction in the problem size with improved precision. Problems with extreme geometric aspect ratios can also be handled without diminished precision. When combined with the CHIEF method, uniqueness of the solution of the exterior acoustic problem is assured without the need to solve hypersingular integrals.

Boundary regularized integral equation formulation of the Helmholtz equation in acoustics

PubMed Central

Sun, Qiang; Klaseboer, Evert; Khoo, Boo-Cheong; Chan, Derek Y. C.

2015-01-01

A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field owing to radiating bodies in acoustic wave problems. This method facilitates the use of higher order surface elements to represent boundaries, resulting in a significant reduction in the problem size with improved precision. Problems with extreme geometric aspect ratios can also be handled without diminished precision. When combined with the CHIEF method, uniqueness of the solution of the exterior acoustic problem is assured without the need to solve hypersingular integrals. PMID:26064591

Integrability of the one dimensional Schrödinger equation

NASA Astrophysics Data System (ADS)

Combot, Thierry

2018-02-01

We present a definition of integrability for the one-dimensional Schrödinger equation, which encompasses all known integrable systems, i.e., systems for which the spectrum can be explicitly computed. For this, we introduce the class of rigid functions, built as Liouvillian functions, but containing all solutions of rigid differential operators in the sense of Katz, and a notion of natural of boundary conditions. We then make a complete classification of rational integrable potentials. Many new integrable cases are found, some of them physically interesting.

Fractional calculus in hydrologic modeling: A numerical perspective

PubMed Central

Benson, David A.; Meerschaert, Mark M.; Revielle, Jordan

2013-01-01

Fractional derivatives can be viewed either as handy extensions of classical calculus or, more deeply, as mathematical operators defined by natural phenomena. This follows the view that the diffusion equation is defined as the governing equation of a Brownian motion. In this paper, we emphasize that fractional derivatives come from the governing equations of stable Lévy motion, and that fractional integration is the corresponding inverse operator. Fractional integration, and its multi-dimensional extensions derived in this way, are intimately tied to fractional Brownian (and Lévy) motions and noises. By following these general principles, we discuss the Eulerian and Lagrangian numerical solutions to fractional partial differential equations, and Eulerian methods for stochastic integrals. These numerical approximations illuminate the essential nature of the fractional calculus. PMID:23524449

Traveling wave solutions to a reaction-diffusion equation

NASA Astrophysics Data System (ADS)

Feng, Zhaosheng; Zheng, Shenzhou; Gao, David Y.

2009-07-01

In this paper, we restrict our attention to traveling wave solutions of a reaction-diffusion equation. Firstly we apply the Divisor Theorem for two variables in the complex domain, which is based on the ring theory of commutative algebra, to find a quasi-polynomial first integral of an explicit form to an equivalent autonomous system. Then through this first integral, we reduce the reaction-diffusion equation to a first-order integrable ordinary differential equation, and a class of traveling wave solutions is obtained accordingly. Comparisons with the existing results in the literature are also provided, which indicates that some analytical results in the literature contain errors. We clarify the errors and instead give a refined result in a simple and straightforward manner.

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. PMID:27547075

Soliton solutions for ABS lattice equations: I. Cauchy matrix approach

NASA Astrophysics Data System (ADS)

Nijhoff, Frank; Atkinson, James; Hietarinta, Jarmo

2009-10-01

In recent years there have been new insights into the integrability of quadrilateral lattice equations, i.e. partial difference equations which are the natural discrete analogues of integrable partial differential equations in 1+1 dimensions. In the scalar (i.e. single-field) case, there now exist classification results by Adler, Bobenko and Suris (ABS) leading to some new examples in addition to the lattice equations 'of KdV type' that were known since the late 1970s and early 1980s. In this paper, we review the construction of soliton solutions for the KdV-type lattice equations and use those results to construct N-soliton solutions for all lattice equations in the ABS list except for the elliptic case of Q4, which is left to a separate treatment.

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

PubMed

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

2015-04-08

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

Reaction formulation for radiation and scattering from plates, corner reflectors and dielectric-coated cylinders

NASA Technical Reports Server (NTRS)

Wang, N. N.

1974-01-01

The reaction concept is employed to formulate an integral equation for radiation and scattering from plates, corner reflectors, and dielectric-coated conducting cylinders. The surface-current density on the conducting surface is expanded with subsectional bases. The dielectric layer is modeled with polarization currents radiating in free space. Maxwell's equation and the boundary conditions are employed to express the polarization-current distribution in terms of the surface-current density on the conducting surface. By enforcing reaction tests with an array of electric test sources, the moment method is employed to reduce the integral equation to a matrix equation. Inversion of the matrix equation yields the current distribution, and the scattered field is then obtained by integrating the current distribution. The theory, computer program and numerical results are presented for radiation and scattering from plates, corner reflectors, and dielectric-coated conducting cylinders.

Plane elasto-plastic analysis of v-notched plate under bending by boundary integral equation method. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Rzasnicki, W.

1973-01-01

A method of solution is presented, which, when applied to the elasto-plastic analysis of plates having a v-notch on one edge and subjected to pure bending, will produce stress and strain fields in much greater detail than presently available. Application of the boundary integral equation method results in two coupled Fredholm-type integral equations, subject to prescribed boundary conditions. These equations are replaced by a system of simultaneous algebraic equations and solved by a successive approximation method employing Prandtl-Reuss incremental plasticity relations. The method is first applied to number of elasto-static problems and the results compared with available solutions. Good agreement is obtained in all cases. The elasto-plastic analysis provides detailed stress and strain distributions for several cases of plates with various notch angles and notch depths. A strain hardening material is assumed and both plane strain and plane stress conditions are considered.

Bending of Euler-Bernoulli nanobeams based on the strain-driven and stress-driven nonlocal integral models: a numerical approach

NASA Astrophysics Data System (ADS)

Oskouie, M. Faraji; Ansari, R.; Rouhi, H.

2018-04-01

Eringen's nonlocal elasticity theory is extensively employed for the analysis of nanostructures because it is able to capture nanoscale effects. Previous studies have revealed that using the differential form of the strain-driven version of this theory leads to paradoxical results in some cases, such as bending analysis of cantilevers, and recourse must be made to the integral version. In this article, a novel numerical approach is developed for the bending analysis of Euler-Bernoulli nanobeams in the context of strain- and stress-driven integral nonlocal models. This numerical approach is proposed for the direct solution to bypass the difficulties related to converting the integral governing equation into a differential equation. First, the governing equation is derived based on both strain-driven and stress-driven nonlocal models by means of the minimum total potential energy. Also, in each case, the governing equation is obtained in both strong and weak forms. To solve numerically the derived equations, matrix differential and integral operators are constructed based upon the finite difference technique and trapezoidal integration rule. It is shown that the proposed numerical approach can be efficiently applied to the strain-driven nonlocal model with the aim of resolving the mentioned paradoxes. Also, it is able to solve the problem based on the strain-driven model without inconsistencies of the application of this model that are reported in the literature.

Elliptic Euler-Poisson-Darboux equation, critical points and integrable systems

NASA Astrophysics Data System (ADS)

Konopelchenko, B. G.; Ortenzi, G.

2013-12-01

The structure and properties of families of critical points for classes of functions W(z,{\\overline{z}}) obeying the elliptic Euler-Poisson-Darboux equation E(1/2, 1/2) are studied. General variational and differential equations governing the dependence of critical points in variational (deformation) parameters are found. Explicit examples of the corresponding integrable quasi-linear differential systems and hierarchies are presented. There are the extended dispersionless Toda/nonlinear Schrödinger hierarchies, the ‘inverse’ hierarchy and equations associated with the real-analytic Eisenstein series E(\\beta ,{\\overline{\\beta }};1/2) among them. The specific bi-Hamiltonian structure of these equations is also discussed.

Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (4).

PubMed

Murase, Kenya

2016-01-01

Partial differential equations are often used in the field of medical physics. In this (final) issue, the methods for solving the partial differential equations were introduced, which include separation of variables, integral transform (Fourier and Fourier-sine transforms), Green's function, and series expansion methods. Some examples were also introduced, in which the integral transform and Green's function methods were applied to solving Pennes' bioheat transfer equation and the Fourier series expansion method was applied to Navier-Stokes equation for analyzing the wall shear stress in blood vessels.Finally, the author hopes that this series will be helpful for people who engage in medical physics.

A Bifurcation Problem for a Nonlinear Partial Differential Equation of Parabolic Type,

DTIC Science & Technology

NONLINEAR DIFFERENTIAL EQUATIONS, INTEGRATION), (*PARTIAL DIFFERENTIAL EQUATIONS, BOUNDARY VALUE PROBLEMS), BANACH SPACE , MAPPING (TRANSFORMATIONS), SET THEORY, TOPOLOGY, ITERATIONS, STABILITY, THEOREMS

Integrability of the coupled cubic-quintic complex Ginzburg-Landau equations and multiple-soliton solutions via mathematical methods

NASA Astrophysics Data System (ADS)

Selima, Ehab S.; Seadawy, Aly R.; Yao, Xiaohua; Essa, F. A.

2018-02-01

This paper is devoted to study the (1+1)-dimensional coupled cubic-quintic complex Ginzburg-Landau equations (cc-qcGLEs) with complex coefficients. This equation can be used to describe the nonlinear evolution of slowly varying envelopes of periodic spatial-temporal patterns in a convective binary fluid. Dispersion relation and properties of cc-qcGLEs are constructed. Painlevé analysis is used to check the integrability of cc-qcGLEs and to establish the Bäcklund transformation form. New traveling wave solutions and a general form of multiple-soliton solutions of cc-qcGLEs are obtained via the Bäcklund transformation and simplest equation method with Bernoulli, Riccati and Burgers’ equations as simplest equations.

Integral Equations and Scattering Solutions for a Square-Well Potential.

ERIC Educational Resources Information Center

Bagchi, B.; Seyler, R. G.

1979-01-01

Derives Green's functions and integral equations for scattering solutions subject to a variety of boundary conditions. Exact solutions are obtained for the case of a finite spherical square-well potential, and properties of these solutions are discussed. (Author/HM)

The statistical theory of the fracture of fragile bodies. Part 2: The integral equation method

NASA Technical Reports Server (NTRS)

Kittl, P.

1984-01-01

It is demonstrated how with the aid of a bending test, the Weibull fracture risk function can be determined - without postulating its analytical form - by resolving an integral equation. The respective solutions for rectangular and circular section beams are given. In the first case the function is expressed as an algorithm and in the second, in the form of series. Taking into account that the cumulative fracture probability appearing in the solution to the integral equation must be continuous and monotonically increasing, any case of fabrication or selection of samples can be treated.

"Lösen Sie Schachtelsätze Möglichst Auf"': The Impact of Editorial Guidelines on Sentence Splitting in German Business Article Translations

ERIC Educational Resources Information Center

Bisiada, Mario

2016-01-01

Sentence splitting is assumed to occur mainly in translations from languages that prefer a hierarchical discourse structure, such as German, to languages that prefer an incremental structure. This article challenges that assumption by presenting findings from a diachronic corpus study of English-German business article translations, which shows…

Charting the Course of the Voyenno-Morskoy Flot: Soviet Naval Strategy towards the Year 2000

DTIC Science & Technology

1991-05-13

December 1987, in Steven P. Adragna , "Doctrine and Strategy," Orbis, 33.2 (1989): 168. 37 requirements are a reduction in the si-e of the armed forces...Patriotic War 1941-45. Trans. U.S. Naval Institute. Moscow: Voyenizdat, 1973. Adragna , Stephen P. "A New Soviet Military? Doctrine and Strategy." Orbis 33.2

Investigating the Effects of Low Temperature Annealing of Amorphous Corrosion Resistant Alloys.

DTIC Science & Technology

1980-11-01

Ray Diffraction.................................................... 6 Differential Scanning Calorimetry....................................... 9...17 LIST OF FIGURES Figure 1. X- Ray Diffraction Results From Fe32Ni 36Cr 4P 2 B Annealed for One Hour at...Various Temperatures (Cr Ka Radiation) ................................. 7 Figure 2. X- Ray Diffraction Results From FeU2NiaeCr14SieB Annealed for One

Pronominal Address in German: Rules, Anarchy and Embarrassment Potential

ERIC Educational Resources Information Center

Kretzenbacher, Heinz L.; Clyne, Michael; Schupbach, Doris

2006-01-01

Choice of address forms, a socially crucial feature in German communication, is context-dependent on situations (a) where the unmarked form of address is "du" (T), (b) where it is "Sie" (V), and (c) where the two systems (a and b) coexist. The first two situations are, apart from their fuzzy edges, rather clearcut. The third situation, however,…

Implementing Project SIED: Special Education Teachers' Perceptions of a Simplified Technology Decision-Making Process for App Identification and Evaluation

ERIC Educational Resources Information Center

Schmidt, Matthew M.; Lin, Meng-Fen Grace; Paek, Seungoh; MacSuga-Gage, Ashley; Gage, Nicholas A.

2017-01-01

The worldwide explosion in popularity of mobile devices has created a dramatic increase in mobile software (apps) that are quick and easy to find and install, cheap, disposable, and usually single purpose. Hence, teachers need an equally streamlined and simplified decision-making process to help them identify educational apps--an approach that…

Intrahospital transport of critically ill patients (excluding newborns) recommendations of the Société de Réanimation de Langue Française (SRLF), the Société Française d'Anesthésie et de Réanimation (SFAR), and the Société Française de Médecine d'Urgence (SFMU).

PubMed

Quenot, Jean-Pierre; Milési, Christophe; Cravoisy, Aurély; Capellier, Gilles; Mimoz, Olivier; Fourcade, Olivier; Gueugniaud, Pierre-Yves

2012-02-03

Critically ill adult patients often require multiple examinations in the hospital and need transport from one department to another, or even between hospitals. However, to date, no guidelines exist regarding optimum practices for transport of these fragile patients. We present recommendations for intrahospital transport of critically ill patients, excluding newborns, developed by an expert group of the French-Language Society of Intensive Care (Société de Réanimation de Langue Française (SRLF), the Société Française d'Anesthésie et de Réanimation (SFAR), and the Société Française de Médecine d'Urgence (SFMU). The recommendations cover five fields of application: epidemiology of adverse events; equipment, monitoring, and maintenance; preparation of patient before transport; human resources and training for caregivers involved in transport processes; and guidelines for planning, structure, and traceability of transport processes.

Sea salt sodium record from Talos Dome (East Antarctica) as a potential proxy of the Antarctic past sea ice extent.

PubMed

Severi, M; Becagli, S; Caiazzo, L; Ciardini, V; Colizza, E; Giardi, F; Mezgec, K; Scarchilli, C; Stenni, B; Thomas, E R; Traversi, R; Udisti, R

2017-06-01

Antarctic sea ice has shown an increasing trend in recent decades, but with strong regional differences from one sector to another of the Southern Ocean. The Ross Sea and the Indian sectors have seen an increase in sea ice during the satellite era (1979 onwards). Here we present a record of ssNa + flux in the Talos Dome region during a 25-year period spanning from 1979 to 2003, showing that this marker could be used as a potential proxy for reconstructing the sea ice extent in the Ross Sea and Western Pacific Ocean at least for recent decades. After finding a positive relationship between the maxima in sea ice extent for a 25-year period, we used this relationship in the TALDICE record in order to reconstruct the sea ice conditions over the 20th century. Our tentative reconstruction highlighted a decline in the sea ice extent (SIE) starting in the 1950s and pointed out a higher variability of SIE starting from the 1960s and that the largest sea ice extents of the last century occurred during the 1990s. Copyright © 2017 Elsevier Ltd. All rights reserved.

Comparison of Two Different Ultrasound Devices Using Strain Elastography Technology in the Diagnosis of Breast Lesions Related to the Histologic Results.

PubMed

Farrokh, André; Schaefer, Fritz; Degenhardt, Friedrich; Maass, Nicolai

2018-05-01

This study was conducted to provide evidence that elastograms of two different devices and different manufacturers using the same technical approach provide the same diagnoses. A total of 110 breast lesions were prospectively analysed by two experts in ultrasound, using the strain elastography function from two different manufacturers (Hitachi HI-RTE, Hitachi Medical Systems, Wiesbaden, Germany; and Siemens eSie Touch, Siemens Medical Systems, Erlangen, Germany). Results were compared with the histopathologic results. Applying the Bowker test of symmetry, no statistically significant difference between the two elastography functions of these two devices was found (p = 0.120). The Cohen's kappa of k = 0.591 showed moderate strength of agreement between the two elastograms. The two examiners yielded moderate strength of agreement analysing the elastograms (Hitachi HI-RTE, k = 0.478; Siemens eSie Touch, k = 0.441). In conclusion, evidence is provided that elastograms of the same lesion generated by two different ultrasound devices equipped with a strain elastography function do not significantly differ. Copyright © 2018 World Federation for Ultrasound in Medicine and Biology. Published by Elsevier Inc. All rights reserved.

Evaluation of Arctic Clouds And Their Response to External Forcing in Climate Models

NASA Astrophysics Data System (ADS)

Wang, Y.; Jiang, J. H.; Ming, Y.; Su, H.; Yung, Y. L.

2017-12-01

A warming Arctic is undergoing significant environmental changes, mostly evidenced by the reduction in Arctic sea-ice extent (SIE). However, the role of Arctic clouds in determining the sea ice melting remains elusive, as different phases of clouds can induce either positive or negative radiative forcing in different seasons. The possible cloud feedbacks following the opened ocean surface are also debatable due to variations of polar boundary structure. Therefore, Arctic cloud simulation has long been considered as the largest source of uncertainty in the climate sensitivity assessment. Other local or remote atmospheric factors, such as poleward moisture and heat transport as well as atmospheric aerosols seeding liquid and ice clouds, further complicate our understanding of the Arctic cloud change. Our recent efforts focus on the post-CMIP5 and CMIP6 models, which improve atmospheric compositions, cloud macro- and microphysics, convection parameterizations, etc. In this study, we utilize long-term satellite measurements with high-resolution coverage and broad wavelength spectrum to evaluate the mean states and variations of mixed-phase clouds in the Arctic, along with the concurrent moisture and SIE measurements. The model sensitivity experiments to understand external perturbations on the atmosphere-cryosphere coupling in the Arctic will be presented.

Asian International Students at an Australian University: Mapping the Paths between Integrative Motivation, Competence in L2 Communication, Cross-Cultural Adaptation and Persistence with Structural Equation Modelling

ERIC Educational Resources Information Center

Yu, Baohua

2013-01-01

This study examined the interrelationships of integrative motivation, competence in second language (L2) communication, sociocultural adaptation, academic adaptation and persistence of international students at an Australian university. Structural equation modelling demonstrated that the integrative motivation of international students has a…

Development of volume equations using data obtained by upper stem dendrometry with Monte Carlo integration: preliminary results for eastern redcedar

Treesearch

Thomas B. Lynch; Rodney E. Will; Rider Reynolds

2013-01-01

Preliminary results are given for development of an eastern redcedar (Juniperus virginiana) cubic-volume equation based on measurements of redcedar sample tree stem volume using dendrometry with Monte Carlo integration. Monte Carlo integration techniques can be used to provide unbiased estimates of stem cubic-foot volume based on upper stem diameter...

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

NASA Astrophysics Data System (ADS)

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

2009-11-01

The concept of integrability was introduced in classical mechanics in the 19th century for finite dimensional continuous Hamiltonian systems. It was extended to certain classes of nonlinear differential equations in the second half of the 20th century with the discovery of the inverse scattering transform and the birth of soliton theory. Also at the end of the 19th century Lie group theory was invented as a powerful tool for obtaining exact analytical solutions of large classes of differential equations. Together, Lie group theory and integrability theory in its most general sense provide the main tools for solving nonlinear differential equations. Like differential equations, difference equations play an important role in physics and other sciences. They occur very naturally in the description of phenomena that are genuinely discrete. Indeed, they may actually be more fundamental than differential equations if space-time is actually discrete at very short distances. On the other hand, even when treating continuous phenomena described by differential equations it is very often necessary to resort to numerical methods. This involves a discretization of the differential equation, i.e. a replacement of the differential equation by a difference one. Given the well developed and understood techniques of symmetry and integrability for differential equations a natural question to ask is whether it is possible to develop similar techniques for difference equations. The aim is, on one hand, to obtain powerful methods for solving `integrable' difference equations and to establish practical integrability criteria, telling us when the methods are applicable. On the other hand, Lie group methods can be adapted to solve difference equations analytically. Finally, integrability and symmetry methods can be combined with numerical methods to obtain improved numerical solutions of differential equations. The origin of the SIDE meetings goes back to the early 1990s and the first meeting with the name `Symmetries and Integrability of Discrete Equations (SIDE)' was held in Estérel, Québec, Canada. This was organized by D Levi, P Winternitz and L Vinet. After the success of the first meeting the scientific community decided to hold bi-annual SIDE meetings. They were held in 1996 at the University of Kent (UK), 1998 in Sabaudia (Italy), 2000 at the University of Tokyo (Japan), 2002 in Giens (France), 2004 in Helsinki (Finland) and in 2006 at the University of Melbourne (Australia). In 2008 the SIDE 8 meeting was again organized near Montreal, in Ste-Adèle, Québec, Canada. The SIDE 8 International Advisory Committee (also the SIDE steering committee) consisted of Frank Nijhoff, Alexander Bobenko, Basil Grammaticos, Jarmo Hietarinta, Nalini Joshi, Decio Levi, Vassilis Papageorgiou, Junkichi Satsuma, Yuri Suris, Claude Vialet and Pavel Winternitz. The local organizing committee consisted of Pavel Winternitz, John Harnad, Véronique Hussin, Decio Levi, Peter Olver and Luc Vinet. Financial support came from the Centre de Recherches Mathématiques in Montreal and the National Science Foundation (through the University of Minnesota). Proceedings of the first three SIDE meetings were published in the LMS Lecture Note series. Since 2000 the emphasis has been on publishing selected refereed articles in response to a general call for papers issued after the conference. This allows for a wider author base, since the call for papers is not restricted to conference participants. The SIDE topics thus are represented in special issues of Journal of Physics A: Mathematical and General 34 (48) and Journal of Physics A: Mathematical and Theoretical, 40 (42) (SIDE 4 and SIDE 7, respectively), Journal of Nonlinear Mathematical Physics 10 (Suppl. 2) and 12 (Suppl. 2) (SIDE 5 and SIDE 6 respectively). The SIDE 8 meeting was organized around several topics and the contributions to this special issue reflect the diversity presented during the meeting. The papers presented at the SIDE 8 meeting were organized into the following special sessions: geometry of discrete and continuous Painlevé equations; continuous symmetries of discrete equations—theory and computational applications; algebraic aspects of discrete equations; singularity confinement, algebraic entropy and Nevanlinna theory; discrete differential geometry; discrete integrable systems and isomonodromy transformations; special functions as solutions of difference and q-difference equations. This special issue of the journal is organized along similar lines. The first three articles are topical review articles appearing in alphabetical order (by first author). The article by Doliwa and Nieszporski describes the Darboux transformations in a discrete setting, namely for the discrete second order linear problem. The article by Grammaticos, Halburd, Ramani and Viallet concentrates on the integrability of the discrete systems, in particular they describe integrability tests for difference equations such as singularity confinement, algebraic entropy (growth and complexity), and analytic and arithmetic approaches. The topical review by Konopelchenko explores the relationship between the discrete integrable systems and deformations of associative algebras. All other articles are presented in alphabetical order (by first author). The contributions were solicited from all participants as well as from the general scientific community. The contributions published in this special issue can be loosely grouped into several overlapping topics, namely: •Geometry of discrete and continuous Painlevé equations (articles by Spicer and Nijhoff and by Lobb and Nijhoff). •Continuous symmetries of discrete equations—theory and applications (articles by Dorodnitsyn and Kozlov; Levi, Petrera and Scimiterna; Scimiterna; Ste-Marie and Tremblay; Levi and Yamilov; Rebelo and Winternitz). •Yang--Baxter maps (article by Xenitidis and Papageorgiou). •Algebraic aspects of discrete equations (articles by Doliwa and Nieszporski; Konopelchenko; Tsarev and Wolf). •Singularity confinement, algebraic entropy and Nevanlinna theory (articles by Grammaticos, Halburd, Ramani and Viallet; Grammaticos, Ramani and Tamizhmani). •Discrete integrable systems and isomonodromy transformations (article by Dzhamay). •Special functions as solutions of difference and q-difference equations (articles by Atakishiyeva, Atakishiyev and Koornwinder; Bertola, Gekhtman and Szmigielski; Vinet and Zhedanov). •Other topics (articles by Atkinson; Grünbaum Nagai, Kametaka and Watanabe; Nagiyev, Guliyeva and Jafarov; Sahadevan and Uma Maheswari; Svinin; Tian and Hu; Yao, Liu and Zeng). This issue is the result of the collaboration of many individuals. We would like to thank the authors who contributed and everyone else involved in the preparation of this special issue.

Solving modal equations of motion with initial conditions using MSC/NASTRAN DMAP. Part 1: Implementing exact mode superposition

NASA Technical Reports Server (NTRS)

Abdallah, Ayman A.; Barnett, Alan R.; Ibrahim, Omar M.; Manella, Richard T.

1993-01-01

Within the MSC/NASTRAN DMAP (Direct Matrix Abstraction Program) module TRD1, solving physical (coupled) or modal (uncoupled) transient equations of motion is performed using the Newmark-Beta or mode superposition algorithms, respectively. For equations of motion with initial conditions, only the Newmark-Beta integration routine has been available in MSC/NASTRAN solution sequences for solving physical systems and in custom DMAP sequences or alters for solving modal systems. In some cases, one difficulty with using the Newmark-Beta method is that the process of selecting suitable integration time steps for obtaining acceptable results is lengthy. In addition, when very small step sizes are required, a large amount of time can be spent integrating the equations of motion. For certain aerospace applications, a significant time savings can be realized when the equations of motion are solved using an exact integration routine instead of the Newmark-Beta numerical algorithm. In order to solve modal equations of motion with initial conditions and take advantage of efficiencies gained when using uncoupled solution algorithms (like that within TRD1), an exact mode superposition method using MSC/NASTRAN DMAP has been developed and successfully implemented as an enhancement to an existing coupled loads methodology at the NASA Lewis Research Center.

Matrix Methods for Solving Hartree-Fock Equations in Atomic Structure Calculations and Line Broadening

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gomez, Thomas; Nagayama, Taisuke; Fontes, Chris

Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods). Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numericalmore » complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange) part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. Here, this technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.« less

Matrix Methods for Solving Hartree-Fock Equations in Atomic Structure Calculations and Line Broadening

DOE PAGES

Gomez, Thomas; Nagayama, Taisuke; Fontes, Chris; ...

2018-04-23

Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods). Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numericalmore » complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange) part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. Here, this technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.« less

Evaluating Feynman integrals by the hypergeometry

NASA Astrophysics Data System (ADS)

Feng, Tai-Fu; Chang, Chao-Hsi; Chen, Jian-Bin; Gu, Zhi-Hua; Zhang, Hai-Bin

2018-02-01

The hypergeometric function method naturally provides the analytic expressions of scalar integrals from concerned Feynman diagrams in some connected regions of independent kinematic variables, also presents the systems of homogeneous linear partial differential equations satisfied by the corresponding scalar integrals. Taking examples of the one-loop B0 and massless C0 functions, as well as the scalar integrals of two-loop vacuum and sunset diagrams, we verify our expressions coinciding with the well-known results of literatures. Based on the multiple hypergeometric functions of independent kinematic variables, the systems of homogeneous linear partial differential equations satisfied by the mentioned scalar integrals are established. Using the calculus of variations, one recognizes the system of linear partial differential equations as stationary conditions of a functional under some given restrictions, which is the cornerstone to perform the continuation of the scalar integrals to whole kinematic domains numerically with the finite element methods. In principle this method can be used to evaluate the scalar integrals of any Feynman diagrams.

On the Formulation of Weakly Singular Displacement/Traction Integral Equations; and Their Solution by the MLPG Method

NASA Technical Reports Server (NTRS)

Atluri, Satya N.; Shen, Shengping

2002-01-01

In this paper, a very simple method is used to derive the weakly singular traction boundary integral equation based on the integral relationships for displacement gradients. The concept of the MLPG method is employed to solve the integral equations, especially those arising in solid mechanics. A moving Least Squares (MLS) interpolation is selected to approximate the trial functions in this paper. Five boundary integral Solution methods are introduced: direct solution method; displacement boundary-value problem; traction boundary-value problem; mixed boundary-value problem; and boundary variational principle. Based on the local weak form of the BIE, four different nodal-based local test functions are selected, leading to four different MLPG methods for each BIE solution method. These methods combine the advantages of the MLPG method and the boundary element method.

The geometric approach to sets of ordinary differential equations and Hamiltonian dynamics

NASA Technical Reports Server (NTRS)

Estabrook, F. B.; Wahlquist, H. D.

1975-01-01

The calculus of differential forms is used to discuss the local integration theory of a general set of autonomous first order ordinary differential equations. Geometrically, such a set is a vector field V in the space of dependent variables. Integration consists of seeking associated geometric structures invariant along V: scalar fields, forms, vectors, and integrals over subspaces. It is shown that to any field V can be associated a Hamiltonian structure of forms if, when dealing with an odd number of dependent variables, an arbitrary equation of constraint is also added. Families of integral invariants are an immediate consequence. Poisson brackets are isomorphic to Lie products of associated CT-generating vector fields. Hamilton's variational principle follows from the fact that the maximal regular integral manifolds of a closed set of forms must include the characteristics of the set.

High-order solution methods for grey discrete ordinates thermal radiative transfer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maginot, Peter G., E-mail: maginot1@llnl.gov; Ragusa, Jean C., E-mail: jean.ragusa@tamu.edu; Morel, Jim E., E-mail: morel@tamu.edu

This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

High-order solution methods for grey discrete ordinates thermal radiative transfer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

This paper presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

High-order solution methods for grey discrete ordinates thermal radiative transfer

DOE PAGES

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

2016-09-29

This paper presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

AKNS hierarchy, Darboux transformation and conservation laws of the 1D nonautonomous nonlinear Schroedinger equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao Dun; Center for Interdisciplinary Studies, Lanzhou University, Lanzhou 730000; Zhang Yujuan

2011-04-15

By constructing nonisospectral Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy, we investigate the nonautonomous nonlinear Schroedinger (NLS) equations which have been used to describe the Feshbach resonance management in matter-wave solitons in Bose-Einstein condensate and the dispersion and nonlinearity managements for optical solitons. It is found that these equations are some special cases of a new integrable model of nonlocal nonautonomous NLS equations. Based on the Lax pairs, the Darboux transformation and conservation laws are explored. It is shown that the local external potentials would break down the classical infinite number of conservation laws. The result indicates that the integrability of the nonautonomous NLSmore » systems may be nontrivial in comparison to the conventional concept of integrability in the canonical case.« less

Particle connectedness and cluster formation in sequential depositions of particles: integral-equation theory.

PubMed

Danwanichakul, Panu; Glandt, Eduardo D

2004-11-15

We applied the integral-equation theory to the connectedness problem. The method originally applied to the study of continuum percolation in various equilibrium systems was modified for our sequential quenching model, a particular limit of an irreversible adsorption. The development of the theory based on the (quenched-annealed) binary-mixture approximation includes the Ornstein-Zernike equation, the Percus-Yevick closure, and an additional term involving the three-body connectedness function. This function is simplified by introducing a Kirkwood-like superposition approximation. We studied the three-dimensional (3D) system of randomly placed spheres and 2D systems of square-well particles, both with a narrow and with a wide well. The results from our integral-equation theory are in good accordance with simulation results within a certain range of densities.

Particle connectedness and cluster formation in sequential depositions of particles: Integral-equation theory

NASA Astrophysics Data System (ADS)

Danwanichakul, Panu; Glandt, Eduardo D.

2004-11-01

We applied the integral-equation theory to the connectedness problem. The method originally applied to the study of continuum percolation in various equilibrium systems was modified for our sequential quenching model, a particular limit of an irreversible adsorption. The development of the theory based on the (quenched-annealed) binary-mixture approximation includes the Ornstein-Zernike equation, the Percus-Yevick closure, and an additional term involving the three-body connectedness function. This function is simplified by introducing a Kirkwood-like superposition approximation. We studied the three-dimensional (3D) system of randomly placed spheres and 2D systems of square-well particles, both with a narrow and with a wide well. The results from our integral-equation theory are in good accordance with simulation results within a certain range of densities.

Integrable particle systems vs solutions to the KP and 2D Toda equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ruijsenaars, S.N.

Starting from the relation between integrable relativistic N-particle systems with hyperbolic interactions and elementary N-soliton solutions to the KP and 2D Toda equations, we show how fusion properties of the soliton solutions are mirrored by fusion properties of the Poisson commuting particle dynamics. We also obtain previously known relations between elliptic solutions and integrable N-particle systems with elliptic interactions, without invoking finite-gap integration theory. {copyright} 1997 Academic Press, Inc.

Theoretical Investigation of Thermo-Mechanical Behavior of Carbon Nanotube-Based Composites Using the Integral Transform Method

NASA Technical Reports Server (NTRS)

Pawloski, Janice S.

2001-01-01

This project uses the integral transform technique to model the problem of nanotube behavior as an axially symmetric system of shells. Assuming that the nanotube behavior can be described by the equations of elasticity, we seek a stress function x which satisfies the biharmonic equation: del(exp 4) chi = [partial deriv(r(exp 2)) + partial deriv(r) + partial deriv(z(exp 2))] chi = 0. The method of integral transformations is used to transform the differential equation. The symmetry with respect to the z-axis indicates that we only need to consider the sine transform of the stress function: X(bar)(r,zeta) = integral(from 0 to infinity) chi(r,z)sin(zeta,z) dz.

Dusty Pair Plasma—Wave Propagation and Diffusive Transition of Oscillations

NASA Astrophysics Data System (ADS)

Atamaniuk, Barbara; Turski, Andrzej J.

2011-11-01

The crucial point of the paper is the relation between equilibrium distributions of plasma species and the type of propagation or diffusive transition of plasma response to a disturbance. The paper contains a unified treatment of disturbance propagation (transport) in the linearized Vlasov electron-positron and fullerene pair plasmas containing charged dust impurities, based on the space-time convolution integral equations. Electron-positron-dust/ion (e-p-d/i) plasmas are rather widespread in nature. Space-time responses of multi-component linearized Vlasov plasmas on the basis of multiple integral equations are invoked. An initial-value problem for Vlasov-Poisson/Ampère equations is reduced to the one multiple integral equation and the solution is expressed in terms of forcing function and its space-time convolution with the resolvent kernel. The forcing function is responsible for the initial disturbance and the resolvent is responsible for the equilibrium velocity distributions of plasma species. By use of resolvent equations, time-reversibility, space-reflexivity and the other symmetries are revealed. The symmetries carry on physical properties of Vlasov pair plasmas, e.g., conservation laws. Properly choosing equilibrium distributions for dusty pair plasmas, we can reduce the resolvent equation to: (i) the undamped dispersive wave equations, (ii) and diffusive transport equations of oscillations.

All Source Sensor Integration Using an Extended Kalman Filter

DTIC Science & Technology

2012-03-22

Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 All...Positioning System . . . . . . . . . . . . . . . . . . 1 ASPN All Source Positioning Navigation . . . . . . . . . . . . . . 2 DARPA Defense Advanced...equations are developed for sensor preprocessed mea- 1 surements, and these navigation equations are not dependent upon the integrating filter. That is

Multi-Hamiltonian structure of Plebanski's second heavenly equation

NASA Astrophysics Data System (ADS)

Neyzi, F.; Nutku, Y.; Sheftel, M. B.

2005-09-01

We show that Plebanski's second heavenly equation, when written as a first-order nonlinear evolutionary system, admits multi-Hamiltonian structure. Therefore by Magri's theorem it is a completely integrable system. Thus it is an example of a completely integrable system in four dimensions.

Time-dependent spectral renormalization method

NASA Astrophysics Data System (ADS)

Cole, Justin T.; Musslimani, Ziad H.

2017-11-01

The spectral renormalization method was introduced by Ablowitz and Musslimani (2005) as an effective way to numerically compute (time-independent) bound states for certain nonlinear boundary value problems. In this paper, we extend those ideas to the time domain and introduce a time-dependent spectral renormalization method as a numerical means to simulate linear and nonlinear evolution equations. The essence of the method is to convert the underlying evolution equation from its partial or ordinary differential form (using Duhamel's principle) into an integral equation. The solution sought is then viewed as a fixed point in both space and time. The resulting integral equation is then numerically solved using a simple renormalized fixed-point iteration method. Convergence is achieved by introducing a time-dependent renormalization factor which is numerically computed from the physical properties of the governing evolution equation. The proposed method has the ability to incorporate physics into the simulations in the form of conservation laws or dissipation rates. This novel scheme is implemented on benchmark evolution equations: the classical nonlinear Schrödinger (NLS), integrable PT symmetric nonlocal NLS and the viscous Burgers' equations, each of which being a prototypical example of a conservative and dissipative dynamical system. Numerical implementation and algorithm performance are also discussed.

Numerical integration of KPZ equation with restrictions

NASA Astrophysics Data System (ADS)

Torres, M. F.; Buceta, R. C.

2018-03-01

In this paper, we introduce a novel integration method of Kardar–Parisi–Zhang (KPZ) equation. It is known that if during the discrete integration of the KPZ equation the nearest-neighbor height-difference exceeds a critical value, instabilities appear and the integration diverges. One way to avoid these instabilities is to replace the KPZ nonlinear-term by a function of the same term that depends on a single adjustable parameter which is able to control pillars or grooves growing on the interface. Here, we propose a different integration method which consists of directly limiting the value taken by the KPZ nonlinearity, thereby imposing a restriction rule that is applied in each integration time-step, as if it were the growth rule of a restricted discrete model, e.g. restricted-solid-on-solid (RSOS). Taking the discrete KPZ equation with restrictions to its dimensionless version, the integration depends on three parameters: the coupling constant g, the inverse of the time-step k, and the restriction constant ε which is chosen to eliminate divergences while keeping all the properties of the continuous KPZ equation. We study in detail the conditions in the parameters’ space that avoid divergences in the 1-dimensional integration and reproduce the scaling properties of the continuous KPZ with a particular parameter set. We apply the tested methodology to the d-dimensional case (d = 3, 4 ) with the purpose of obtaining the growth exponent β, by establishing the conditions of the coupling constant g under which we recover known values reached by other authors, particularly for the RSOS model. This method allows us to infer that d  =  4 is not the critical dimension of the KPZ universality class, where the strong-coupling phase disappears.

Integrability in AdS/CFT correspondence: quasi-classical analysis

NASA Astrophysics Data System (ADS)

Gromov, Nikolay

2009-06-01

In this review, we consider a quasi-classical method applicable to integrable field theories which is based on a classical integrable structure—the algebraic curve. We apply it to the Green-Schwarz superstring on the AdS5 × S5 space. We show that the proposed method reproduces perfectly the earlier results obtained by expanding the string action for some simple classical solutions. The construction is explicitly covariant and is not based on a particular parameterization of the fields and as a result is free from ambiguities. On the other hand, the finite size corrections in some particularly important scaling limit are studied in this paper for a system of Bethe equations. For the general superalgebra \\su(N|K) , the result for the 1/L corrections is obtained. We find an integral equation which describes these corrections in a closed form. As an application, we consider the conjectured Beisert-Staudacher (BS) equations with the Hernandez-Lopez dressing factor where the finite size corrections should reproduce quasi-classical results around a general classical solution. Indeed, we show that our integral equation can be interpreted as a sum of all physical fluctuations and thus prove the complete one-loop consistency of the BS equations. We demonstrate that any local conserved charge (including the AdS energy) computed from the BS equations is indeed given at one loop by the sum of the charges of fluctuations with an exponential precision for large S5 angular momentum of the string. As an independent result, the BS equations in an \\su(2) sub-sector were derived from Zamolodchikovs's S-matrix. The paper is based on the author's PhD thesis.

Elimination of secular terms from the differential equations for the elements of perturbed two-body motion

NASA Technical Reports Server (NTRS)

Bond, Victor R.; Fraietta, Michael F.

1991-01-01

In 1961, Sperling linearized and regularized the differential equations of motion of the two-body problem by changing the independent variable from time to fictitious time by Sundman's transformation (r = dt/ds) and by embedding the two-body energy integral and the Laplace vector. In 1968, Burdet developed a perturbation theory which was uniformly valid for all types of orbits using a variation of parameters approach on the elements which appeared in Sperling's equations for the two-body solution. In 1973, Bond and Hanssen improved Burdet's set of differential equations by embedding the total energy (which is a constant when the potential function is explicitly dependent upon time.) The Jacobian constant was used as an element to replace the total energy in a reformulation of the differential equations of motion. In the process, another element which is proportional to a component of the angular momentum was introduced. Recently trajectories computed during numerical studies of atmospheric entry from circular orbits and low thrust beginning in near-circular orbits exhibited numerical instability when solved by the method of Bond and Gottlieb (1989) for long time intervals. It was found that this instability was due to secular terms which appear on the righthand sides of the differential equations of some of the elements. In this paper, this instability is removed by the introduction of another vector integral called the delta integral (which replaces the Laplace Vector) and another scalar integral which removes the secular terms. The introduction of these integrals requires a new derivation of the differential equations for most of the elements. For this rederivation, the Lagrange method of variation of parameters is used, making the development more concise. Numerical examples of this improvement are presented.

Does the supersymmetric integrability imply the integrability of Bosonic sector

DOE Office of Scientific and Technical Information (OSTI.GOV)

Popowicz, Ziemowit

2010-03-08

The answer is no. This is demonstrated for two equations that belong to the supersymmetric Manin-Radul N = 1 Kadomtsev-Petviashvili (MRSKP) hierarchy. The first one is the N = 1 supersymmetric Sawada-Kotera equation recently considered by Tian and Liu. We define the bi-Hamiltonian structure for this equation which however does not reduce in the bosonic limit to the known bi-Hamiltonian structure. The second equation is obtained from the Lax operator of the fifth order in the supersymmetric derivatives which in the bosonic sector reduces to the system of interacted two KdV equations discovered by Drinfeld and Sokolov in 1981 andmore » later rediscovered by Sakovich and Foursov.« less

Solution of steady and unsteady transonic-vortex flows using Euler and full-potential equations

NASA Technical Reports Server (NTRS)

Kandil, Osama A.; Chuang, Andrew H.; Hu, Hong

1989-01-01

Two methods are presented for inviscid transonic flows: unsteady Euler equations in a rotating frame of reference for transonic-vortex flows and integral solution of full-potential equation with and without embedded Euler domains for transonic airfoil flows. The computational results covered: steady and unsteady conical vortex flows; 3-D steady transonic vortex flow; and transonic airfoil flows. The results are in good agreement with other computational results and experimental data. The rotating frame of reference solution is potentially efficient as compared with the space fixed reference formulation with dynamic gridding. The integral equation solution with embedded Euler domain is computationally efficient and as accurate as the Euler equations.

Connectivity as an alternative to boundary integral equations: Construction of bases

PubMed Central

Herrera, Ismael; Sabina, Federico J.

1978-01-01

In previous papers Herrera developed a theory of connectivity that is applicable to the problem of connecting solutions defined in different regions, which occurs when solving partial differential equations and many problems of mechanics. In this paper we explain how complete connectivity conditions can be used to replace boundary integral equations in many situations. We show that completeness is satisfied not only in steady-state problems such as potential, reduced wave equation and static and quasi-static elasticity, but also in time-dependent problems such as heat and wave equations and dynamical elasticity. A method to obtain bases of connectivity conditions, which are independent of the regions considered, is also presented. PMID:16592522

Subprograms for integrating the equations of motion of satellites. FORTRAN 4

NASA Technical Reports Server (NTRS)

Prokhorenko, V. I.

1980-01-01

The subprograms for the formation of the right members of the equations of motion of artificial Earth satellites (AES), integration of systems of differential equations by Adams' method, and the calculation of the values of various functions from the AES parameters of motion are described. These subprograms are written in the FORTRAN 4 language and constitute an essential part of the package of applied programs for the calculation of navigational parameters AES.

Student Solution Manual for Essential Mathematical Methods for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-02-01

1. Matrices and vector spaces; 2. Vector calculus; 3. Line, surface and volume integrals; 4. Fourier series; 5. Integral transforms; 6. Higher-order ODEs; 7. Series solutions of ODEs; 8. Eigenfunction methods; 9. Special functions; 10. Partial differential equations; 11. Solution methods for PDEs; 12. Calculus of variations; 13. Integral equations; 14. Complex variables; 15. Applications of complex variables; 16. Probability; 17. Statistics.

Essential Mathematical Methods for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-02-01

1. Matrices and vector spaces; 2. Vector calculus; 3. Line, surface and volume integrals; 4. Fourier series; 5. Integral transforms; 6. Higher-order ODEs; 7. Series solutions of ODEs; 8. Eigenfunction methods; 9. Special functions; 10. Partial differential equations; 11. Solution methods for PDEs; 12. Calculus of variations; 13. Integral equations; 14. Complex variables; 15. Applications of complex variables; 16. Probability; 17. Statistics; Appendices; Index.

General pulsed-field gradient signal attenuation expression based on a fractional integral modified-Bloch equation

NASA Astrophysics Data System (ADS)

Lin, Guoxing

2018-10-01

Anomalous diffusion has been investigated in many polymer and biological systems. The analysis of PFG anomalous diffusion relies on the ability to obtain the signal attenuation expression. However, the general analytical PFG signal attenuation expression based on the fractional derivative has not been previously reported. Additionally, the reported modified-Bloch equations for PFG anomalous diffusion in the literature yielded different results due to their different forms. Here, a new integral type modified-Bloch equation based on the fractional derivative for PFG anomalous diffusion is proposed, which is significantly different from the conventional differential type modified-Bloch equation. The merit of the integral type modified-Bloch equation is that the original properties of the contributions from linear or nonlinear processes remain unchanged at the instant of the combination. From the modified-Bloch equation, the general solutions are derived, which includes the finite gradient pulse width (FGPW) effect. The numerical evaluation of these PFG signal attenuation expressions can be obtained either by the Adomian decomposition, or a direct integration method that is fast and practicable. The theoretical results agree with the continuous-time random walk (CTRW) simulations performed in this paper. Additionally, the relaxation effect in PFG anomalous diffusion is found to be different from that in PFG normal diffusion. The new modified-Bloch equations and their solutions provide a fundamental tool to analyze PFG anomalous diffusion in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI).

Solution of differential equations by application of transformation groups

NASA Technical Reports Server (NTRS)

Driskell, C. N., Jr.; Gallaher, L. J.; Martin, R. H., Jr.

1968-01-01

Report applies transformation groups to the solution of systems of ordinary differential equations and partial differential equations. Lies theorem finds an integrating factor for appropriate invariance group or groups can be found and can be extended to partial differential equations.

On the solubility of certain classes of non-linear integral equations in p-adic string theory

NASA Astrophysics Data System (ADS)

Khachatryan, Kh. A.

2018-04-01

We study classes of non-linear integral equations that have immediate application to p-adic mathematical physics and to cosmology. We prove existence and uniqueness theorems for non-trivial solutions in the space of bounded functions.

Addendum to "Free energies from integral equation theories: enforcing path independence".

PubMed

Kast, Stefan M

2006-01-01

The variational formalism developed for the analysis of the path dependence of free energies from integral equation theories [S. M. Kast, Phys. Rev. E 67, 041203 (2003)] is extended in order to allow for the three-dimensional treatment of arbitrarily shaped solutes.

Numerical analysis of composite STEEL-CONCRETE SECTIONS using integral equation of Volterra

NASA Astrophysics Data System (ADS)

Partov, Doncho; Kantchev, Vesselin

2011-09-01

The paper presents analysis of the stress and deflections changes due to creep in statically determinate composite steel-concrete beam. The mathematical model involves the equation of equilibrium, compatibility and constitutive relationship, i.e. an elastic law for the steel part and an integral-type creep law of Boltzmann — Volterra for the concrete part. On the basis of the theory of the viscoelastic body of Arutyunian-Trost-Bažant for determining the redistribution of stresses in beam section between concrete plate and steel beam with respect to time "t", two independent Volterra integral equations of the second kind have been derived. Numerical method based on linear approximation of the singular kernal function in the integral equation is presented. Example with the model proposed is investigated. The creep functions is suggested by the model CEB MC90-99 and the "ACI 209R-92 model. The elastic modulus of concrete E c (t) is assumed to be constant in time `t'. The obtained results from the both models are compared.

The Application of a Boundary Integral Equation Method to the Prediction of Ducted Fan Engine Noise

NASA Technical Reports Server (NTRS)

Dunn, M. H.; Tweed, J.; Farassat, F.

1999-01-01

The prediction of ducted fan engine noise using a boundary integral equation method (BIEM) is considered. Governing equations for the BIEM are based on linearized acoustics and describe the scattering of incident sound by a thin, finite-length cylindrical duct in the presence of a uniform axial inflow. A classical boundary value problem (BVP) is derived that includes an axisymmetric, locally reacting liner on the duct interior. Using potential theory, the BVP is recast as a system of hypersingular boundary integral equations with subsidiary conditions. We describe the integral equation derivation and solution procedure in detail. The development of the computationally efficient ducted fan noise prediction program TBIEM3D, which implements the BIEM, and its utility in conducting parametric noise reduction studies are discussed. Unlike prediction methods based on spinning mode eigenfunction expansions, the BIEM does not require the decomposition of the interior acoustic field into its radial and axial components which, for the liner case, avoids the solution of a difficult complex eigenvalue problem. Numerical spectral studies are presented to illustrate the nexus between the eigenfunction expansion representation and BIEM results. We demonstrate BIEM liner capability by examining radiation patterns for several cases of practical interest.

Yang-Baxter maps, discrete integrable equations and quantum groups

NASA Astrophysics Data System (ADS)

Bazhanov, Vladimir V.; Sergeev, Sergey M.

2018-01-01

For every quantized Lie algebra there exists a map from the tensor square of the algebra to itself, which by construction satisfies the set-theoretic Yang-Baxter equation. This map allows one to define an integrable discrete quantum evolution system on quadrilateral lattices, where local degrees of freedom (dynamical variables) take values in a tensor power of the quantized Lie algebra. The corresponding equations of motion admit the zero curvature representation. The commuting Integrals of Motion are defined in the standard way via the Quantum Inverse Problem Method, utilizing Baxter's famous commuting transfer matrix approach. All elements of the above construction have a meaningful quasi-classical limit. As a result one obtains an integrable discrete Hamiltonian evolution system, where the local equation of motion are determined by a classical Yang-Baxter map and the action functional is determined by the quasi-classical asymptotics of the universal R-matrix of the underlying quantum algebra. In this paper we present detailed considerations of the above scheme on the example of the algebra Uq (sl (2)) leading to discrete Liouville equations, however the approach is rather general and can be applied to any quantized Lie algebra.

A new method for true and spurious eigensolutions of arbitrary cavities using the combined Helmholtz exterior integral equation formulation method.

PubMed

Chen, I L; Chen, J T; Kuo, S R; Liang, M T

2001-03-01

Integral equation methods have been widely used to solve interior eigenproblems and exterior acoustic problems (radiation and scattering). It was recently found that the real-part boundary element method (BEM) for the interior problem results in spurious eigensolutions if the singular (UT) or the hypersingular (LM) equation is used alone. The real-part BEM results in spurious solutions for interior problems in a similar way that the singular integral equation (UT method) results in fictitious solutions for the exterior problem. To solve this problem, a Combined Helmholtz Exterior integral Equation Formulation method (CHEEF) is proposed. Based on the CHEEF method, the spurious solutions can be filtered out if additional constraints from the exterior points are chosen carefully. Finally, two examples for the eigensolutions of circular and rectangular cavities are considered. The optimum numbers and proper positions for selecting the points in the exterior domain are analytically studied. Also, numerical experiments were designed to verify the analytical results. It is worth pointing out that the nodal line of radiation mode of a circle can be rotated due to symmetry, while the nodal line of the rectangular is on a fixed position.

On the integrable elliptic cylindrical Kadomtsev-Petviashvili equation.

PubMed

Khusnutdinova, K R; Klein, C; Matveev, V B; Smirnov, A O

2013-03-01

There exist two versions of the Kadomtsev-Petviashvili (KP) equation, related to the Cartesian and cylindrical geometries of the waves. In this paper, we derive and study a new version, related to the elliptic cylindrical geometry. The derivation is given in the context of surface waves, but the derived equation is a universal integrable model applicable to generic weakly nonlinear weakly dispersive waves. We also show that there exist nontrivial transformations between all three versions of the KP equation associated with the physical problem formulation, and use them to obtain new classes of approximate solutions for water waves.

A complete and partial integrability technique of the Lorenz system

NASA Astrophysics Data System (ADS)

Bougoffa, Lazhar; Al-Awfi, Saud; Bougouffa, Smail

2018-06-01

In this paper we deal with the well-known nonlinear Lorenz system that describes the deterministic chaos phenomenon. We consider an interesting problem with time-varying phenomena in quantum optics. Then we establish from the motion equations the passage to the Lorenz system. Furthermore, we show that the reduction to the third order non linear equation can be performed. Therefore, the obtained differential equation can be analytically solved in some special cases and transformed to Abel, Dufing, Painlevé and generalized Emden-Fowler equations. So, a motivating technique that permitted a complete and partial integrability of the Lorenz system is presented.

Open groups of constraints. Integrating arbitrary involutions

NASA Astrophysics Data System (ADS)

Batalin, Igor; Marnelius, Robert

1998-11-01

A new type of quantum master equation is presented which is expressed in terms of a recently introduced quantum antibracket. The equation involves only two operators: an extended nilpotent BFV-BRST charge and an extended ghost charge. It is proposed to determine the generalized quantum Maurer-Cartan equations for arbitrary open groups. These groups are the integration of constraints in arbitrary involutions. The only condition for this is that the constraint operators may be embedded in an odd nilpotent operator, the BFV-BRST charge. The proposal is verified at the quasigroup level. The integration formulas are also used to construct a generating operator for quantum antibrackets of operators in arbitrary involutions.

Pseudodynamic systems approach based on a quadratic approximation of update equations for diffuse optical tomography.

PubMed

Biswas, Samir Kumar; Kanhirodan, Rajan; Vasu, Ram Mohan; Roy, Debasish

2011-08-01

We explore a pseudodynamic form of the quadratic parameter update equation for diffuse optical tomographic reconstruction from noisy data. A few explicit and implicit strategies for obtaining the parameter updates via a semianalytical integration of the pseudodynamic equations are proposed. Despite the ill-posedness of the inverse problem associated with diffuse optical tomography, adoption of the quadratic update scheme combined with the pseudotime integration appears not only to yield higher convergence, but also a muted sensitivity to the regularization parameters, which include the pseudotime step size for integration. These observations are validated through reconstructions with both numerically generated and experimentally acquired data.

A study of numerical methods of solution of the equations of motion of a controlled satellite under the influence of gravity gradient torque

NASA Technical Reports Server (NTRS)

Thompson, J. F.; Mcwhorter, J. C.; Siddiqi, S. A.; Shanks, S. P.

1973-01-01

Numerical methods of integration of the equations of motion of a controlled satellite under the influence of gravity-gradient torque are considered. The results of computer experimentation using a number of Runge-Kutta, multi-step, and extrapolation methods for the numerical integration of this differential system are presented, and particularly efficient methods are noted. A large bibliography of numerical methods for initial value problems for ordinary differential equations is presented, and a compilation of Runge-Kutta and multistep formulas is given. Less common numerical integration techniques from the literature are noted for further consideration.

A numerical scheme to solve unstable boundary value problems

NASA Technical Reports Server (NTRS)

Kalnay Derivas, E.

1975-01-01

A new iterative scheme for solving boundary value problems is presented. It consists of the introduction of an artificial time dependence into a modified version of the system of equations. Then explicit forward integrations in time are followed by explicit integrations backwards in time. The method converges under much more general conditions than schemes based in forward time integrations (false transient schemes). In particular it can attain a steady state solution of an elliptical system of equations even if the solution is unstable, in which case other iterative schemes fail to converge. The simplicity of its use makes it attractive for solving large systems of nonlinear equations.

Integrable discretisations for a class of nonlinear Schrödinger equations on Grassmann algebras

NASA Astrophysics Data System (ADS)

Grahovski, Georgi G.; Mikhailov, Alexander V.

2013-12-01

Integrable discretisations for a class of coupled (super) nonlinear Schrödinger (NLS) type of equations are presented. The class corresponds to a Lax operator with entries in a Grassmann algebra. Elementary Darboux transformations are constructed. As a result, Grassmann generalisations of the Toda lattice and the NLS dressing chain are obtained. The compatibility (Bianchi commutativity) of these Darboux transformations leads to integrable Grassmann generalisations of the difference Toda and NLS equations. The resulting systems will have discrete Lax representations provided by the set of two consistent elementary Darboux transformations. For the two discrete systems obtained, initial value and initial-boundary problems are formulated.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thompson, S.

This report describes the use of several subroutines from the CORLIB core mathematical subroutine library for the solution of a model fluid flow problem. The model consists of the Euler partial differential equations. The equations are spatially discretized using the method of pseudo-characteristics. The resulting system of ordinary differential equations is then integrated using the method of lines. The stiff ordinary differential equation solver LSODE (2) from CORLIB is used to perform the time integration. The non-stiff solver ODE (4) is used to perform a related integration. The linear equation solver subroutines DECOMP and SOLVE are used to solve linearmore » systems whose solutions are required in the calculation of the time derivatives. The monotone cubic spline interpolation subroutines PCHIM and PCHFE are used to approximate water properties. The report describes the use of each of these subroutines in detail. It illustrates the manner in which modules from a standard mathematical software library such as CORLIB can be used as building blocks in the solution of complex problems of practical interest. 9 refs., 2 figs., 4 tabs.« less

The aerodynamics of propellers and rotors using an acoustic formulation in the time domain

NASA Technical Reports Server (NTRS)

Long, L. N.

1983-01-01

The aerodynamics of propellers and rotors is especially complicated because of the highly three-dimensional and compressible nature of the flow field. However, in linearized theory the problem is governed by the wave equation, and a numerically-efficient integral formulation can be derived. This reduces the problem from one in space to one over a surface. Many such formulations exist in the aeroacoustics literature, but these become singular integral equations if one naively tries to use them to predict surface pressures, i.e., for aerodynamics. The present paper illustrates how one must interpret these equations in order to obtain nonambiguous results. After the regularized form of the integral equation is derived, a method for solving it numerically is described. This preliminary computer code uses Legendre-Gaussian quadrature to solve the equation. Numerical results are compared to experimental results for ellipsoids, wings, and rotors, including effects due to lift. Compressibility and the farfield boundary conditions are satisfied automatically using this method.

Numerical solution of the quantum Lenard-Balescu equation for a non-degenerate one-component plasma

DOE PAGES

Scullard, Christian R.; Belt, Andrew P.; Fennell, Susan C.; ...

2016-09-01

We present a numerical solution of the quantum Lenard-Balescu equation using a spectral method, namely an expansion in Laguerre polynomials. This method exactly conserves both particles and kinetic energy and facilitates the integration over the dielectric function. To demonstrate the method, we solve the equilibration problem for a spatially homogeneous one-component plasma with various initial conditions. Unlike the more usual Landau/Fokker-Planck system, this method requires no input Coulomb logarithm; the logarithmic terms in the collision integral arise naturally from the equation along with the non-logarithmic order-unity terms. The spectral method can also be used to solve the Landau equation andmore » a quantum version of the Landau equation in which the integration over the wavenumber requires only a lower cutoff. We solve these problems as well and compare them with the full Lenard-Balescu solution in the weak-coupling limit. Finally, we discuss the possible generalization of this method to include spatial inhomogeneity and velocity anisotropy.« less

K(m, n) equations with fifth order symmetries and their integrability

NASA Astrophysics Data System (ADS)

Tian, Kai

2018-03-01

For K(m, n) equation ut =Dx3(un) + αDx(um) , all non-degenerate (n ≠ 0) cases admitting fifth order symmetries are identified, including K(m1, 1), K(m2 , - 1 / 2) and K(m3 , - 2) , where m1 = 0 , 1 , 2 , 3 , m2 = - 1 / 2 , 0 , 1 , 3 / 2 and m3 = - 2 , - 1 , 0 , 1 . For five less studied cases, namely K(0 , - 2) , K(- 1 , - 2) , K(- 2 , - 2) , K(- 1 / 2 , - 1 / 2) and K(3 / 2 , - 1 / 2) , bi-Hamiltonian structures are established through their invertible links with some famous integrable equations. Hence, all cases, having fifth order symmetries, of K(m, n) equation are integrable in the bi-Hamiltonian sense. As an interesting observation, their Hamiltonian operators are linearly combinations of Dx, Dx3 , uDx +Dx u and Dx u Dx-1uDx, basic ingredients in the bi-Hamiltonian theory of Korteweg-de Vries and modified Korteweg-de Vries equations.

Vertically Integrated Models for Carbon Storage Modeling in Heterogeneous Domains

NASA Astrophysics Data System (ADS)

Bandilla, K.; Celia, M. A.

2017-12-01

Numerical modeling is an essential tool for studying the impacts of geologic carbon storage (GCS). Injection of carbon dioxide (CO2) into deep saline aquifers leads to multi-phase flow (injected CO2 and resident brine), which can be described by a set of three-dimensional governing equations, including mass-balance equation, volumetric flux equations (modified Darcy), and constitutive equations. This is the modeling approach on which commonly used reservoir simulators such as TOUGH2 are based. Due to the large density difference between CO2 and brine, GCS models can often be simplified by assuming buoyant segregation and integrating the three-dimensional governing equations in the vertical direction. The integration leads to a set of two-dimensional equations coupled with reconstruction operators for vertical profiles of saturation and pressure. Vertically-integrated approaches have been shown to give results of comparable quality as three-dimensional reservoir simulators when applied to realistic CO2 injection sites such as the upper sand wedge at the Sleipner site. However, vertically-integrated approaches usually rely on homogeneous properties over the thickness of a geologic layer. Here, we investigate the impact of general (vertical and horizontal) heterogeneity in intrinsic permeability, relative permeability functions, and capillary pressure functions. We consider formations involving complex fluvial deposition environments and compare the performance of vertically-integrated models to full three-dimensional models for a set of hypothetical test cases consisting of high permeability channels (streams) embedded in a low permeability background (floodplains). The domains are randomly generated assuming that stream channels can be represented by sinusoidal waves in the plan-view and by parabolas for the streams' cross-sections. Stream parameters such as width, thickness and wavelength are based on values found at the Ketzin site in Germany. Results from the vertically-integrated approach are compared to results using TOUGH2, both in terms of depth-averaged saturation and vertical saturation profiles.

Integral equation methods for computing likelihoods and their derivatives in the stochastic integrate-and-fire model.

PubMed

Paninski, Liam; Haith, Adrian; Szirtes, Gabor

2008-02-01

We recently introduced likelihood-based methods for fitting stochastic integrate-and-fire models to spike train data. The key component of this method involves the likelihood that the model will emit a spike at a given time t. Computing this likelihood is equivalent to computing a Markov first passage time density (the probability that the model voltage crosses threshold for the first time at time t). Here we detail an improved method for computing this likelihood, based on solving a certain integral equation. This integral equation method has several advantages over the techniques discussed in our previous work: in particular, the new method has fewer free parameters and is easily differentiable (for gradient computations). The new method is also easily adaptable for the case in which the model conductance, not just the input current, is time-varying. Finally, we describe how to incorporate large deviations approximations to very small likelihoods.

Hamiltonian structure of real Monge - Ampère equations

NASA Astrophysics Data System (ADS)

Nutku, Y.

1996-06-01

The variational principle for the real homogeneous Monge - Ampère equation in two dimensions is shown to contain three arbitrary functions of four variables. There exist two different specializations of this variational principle where the Lagrangian is degenerate and furthermore contains an arbitrary function of two variables. The Hamiltonian formulation of these degenerate Lagrangian systems requires the use of Dirac's theory of constraints. As in the case of most completely integrable systems the constraints are second class and Dirac brackets directly yield the Hamiltonian operators. Thus the real homogeneous Monge - Ampère equation in two dimensions admits two classes of infinitely many Hamiltonian operators, namely a family of local, as well as another family non-local Hamiltonian operators and symplectic 2-forms which depend on arbitrary functions of two variables. The simplest non-local Hamiltonian operator corresponds to the Kac - Moody algebra of vector fields and functions on the unit circle. Hamiltonian operators that belong to either class are compatible with each other but between classes there is only one compatible pair. In the case of real Monge - Ampère equations with constant right-hand side this compatible pair is the only pair of Hamiltonian operators that survives. Then the complete integrability of all these real Monge - Ampère equations follows by Magri's theorem. Some of the remarkable properties we have obtained for the Hamiltonian structure of the real homogeneous Monge - Ampère equation in two dimensions turn out to be generic to the real homogeneous Monge - Ampère equation and the geodesic flow for the complex homogeneous Monge - Ampère equation in arbitrary number of dimensions. Hence among all integrable nonlinear evolution equations in one space and one time dimension, the real homogeneous Monge - Ampère equation is distinguished as one that retains its character as an integrable system in multiple dimensions.

AN INTEGRAL EQUATION REPRESENTATION OF WIDE-BAND ELECTROMAGNETIC SCATTERING BY THIN SHEETS

EPA Science Inventory

An efficient, accurate numerical modeling scheme has been developed, based on the integral equation solution to compute electromagnetic (EM) responses of thin sheets over a wide frequency band. The thin-sheet approach is useful for simulating the EM response of a fracture system ...

Separation of variables in the special diagonal Hamilton-Jacobi equation: Application to the dynamical problem of a particle constrained on a moving surface

NASA Technical Reports Server (NTRS)

Blanchard, D. L.; Chan, F. K.

1973-01-01

For a time-dependent, n-dimensional, special diagonal Hamilton-Jacobi equation a necessary and sufficient condition for the separation of variables to yield a complete integral of the form was established by specifying the admissible forms in terms of arbitrary functions. A complete integral was then expressed in terms of these arbitrary functions and also the n irreducible constants. As an application of the results obtained for the two-dimensional Hamilton-Jacobi equation, analysis was made for a comparatively wide class of dynamical problems involving a particle moving in Euclidean three-dimensional space under the action of external forces but constrained on a moving surface. All the possible cases in which this equation had a complete integral of the form were obtained and these are tubulated for reference.

[Anthrax meningoencephalitis: a case following a cutaneous lesion in Morocco].

PubMed

Ziadi, A; Hachimi, A; Soraa, N; Tassi, N; Nejmi, H; Elkhayari, M; Samkaoui, M A

2014-05-01

Anthrax meningoencephalitis is very rare especially following skin location. We report a case of meningoencephalitis secondary to skin lesion. The diagnosis is based on clinical presentation and confirmed by microbiological tests. Its evolution remains fatal despite aggressive resuscitation. Copyright © 2014 Société française d’anesthésie et de réanimation (Sfar). Published by Elsevier SAS. All rights reserved.

Adaptive Modeling and Real-Time Simulation

DTIC Science & Technology

1984-01-01

34 Artificial Inteligence , Vol. 13, pp. 27-39 (1980). Describes circumscription which is just the assumption that everything that is known to have a particular... Artificial Intelligence Truth Maintenance Planning Resolution Modeling Wcrld Models ~ .. ~2.. ASSTR AT (Coninue n evrse sieIf necesaran Identfy by...represents a marriage of (1) the procedural-network st, planning technology developed in artificial intelligence with (2) the PERT/CPM technology developed in

Demographic, Social, and Economic Profile of States: Spring 1976. Current Population Reports, Series P-20, No. 334.

ERIC Educational Resources Information Center

Norton, Arthur J., Ed.

This report presents statistics for the total United States, regions, divisions, and each of the 50 states and the District of Columbia based upon the 1976 Survey of Income and Education (SIE). The data provide a profile of the social and economic characteristics of the individual states. There are two sections of text: Demographic and Social…

Coalitions: Organizational, Political, Command & Control Challenges

DTIC Science & Technology

2009-05-01

coalitions, leur histoire récente, les caractéristiques et les défis des coalitions militaires et, enfin, les obstacles rencontrés par les...caractéristiques générales. Une brève histoire des coalitions militaires du 20ième siècle est présentée, suivie d’une évaluation de leur évolution

Comparison of Wood Preservatives in Stake Tests (1983 Progress Report).

DTIC Science & Technology

1983-12-01

to "X-disease" (hyperkeratosis) in cattle . These oils are therefore not recommended for preservative treatment of wood with which cattle 4 may come in...welam Molmol(W sies saidal) liss. 6.1 of- - - - a. - 0 a . .F a e o a mWi is . 0 .1 a s - - - - - m - - * - l e t a 1 4i .8 blawaeted castrate asis

Epidural anaesthesia for caesarean section in pituitary dwarfism.

PubMed

Li, Hongbo; Li, Ruihua; Lang, Bao

2017-04-01

We describe the anaesthetic management for caesarean section in a 32-year-old patient with pituitary dwarfism. In addition to supportive treatment, we offered a postoperative epidural analgesia pump. The patient recovered well without any complications. Copyright © 2016 Société française d'anesthésie et de réanimation (Sfar). Published by Elsevier Masson SAS. All rights reserved.

Liouvillian integrability of gravitating static isothermal fluid spheres

NASA Astrophysics Data System (ADS)

Iacono, Roberto; Llibre, Jaume

2014-10-01

We examine the integrability properties of the Einstein field equations for static, spherically symmetric fluid spheres, complemented with an isothermal equation of state, ρ = np. In this case, Einstein's equations can be reduced to a nonlinear, autonomous second order ordinary differential equation (ODE) for m/R (m is the mass inside the radius R) that has been solved analytically only for n = -1 and n = -3, yielding the cosmological solutions by De Sitter and Einstein, respectively, and for n = -5, case for which the solution can be derived from the De Sitter's one using a symmetry of Einstein's equations. The solutions for these three cases are of Liouvillian type, since they can be expressed in terms of elementary functions. Here, we address the question of whether Liouvillian solutions can be obtained for other values of n. To do so, we transform the second order equation into an equivalent autonomous Lotka-Volterra quadratic polynomial differential system in {R}^2, and characterize the Liouvillian integrability of this system using Darboux theory. We find that the Lotka-Volterra system possesses Liouvillian first integrals for n = -1, -3, -5, which descend from the existence of invariant algebraic curves of degree one, and for n = -6, a new solvable case, associated to an invariant algebraic curve of higher degree (second). For any other value of n, eventual first integrals of the Lotka-Volterra system, and consequently of the second order ODE for the mass function must be non-Liouvillian. This makes the existence of other solutions of the isothermal fluid sphere problem with a Liouvillian metric quite unlikely.

The geovisualisation window of the temporal and spatial variability for Volunteered Geographic Information activities

NASA Astrophysics Data System (ADS)

Medynska-Gulij, Beata; Myszczuk, Miłosz

2012-11-01

This study presents an attempt to design geographical visualisation tools that allow to tackle the immensity of spatial data provided by Volunteered Geographic Information (VGI), both in terms of temporal and spatial aspects. In accordance with the assumptions made at the conceptual stage, the final action was the implementation of the window entitled ‘Geovisualisation of the Panoramio.com Activities in District of Poznan 2011’ into the web browser. The concept has been based on a division of the geovisualisation window into three panels, of which the most important - in order to capture spatial variability - have statistical maps at the general level (dot map and choropleth map), while at the detailed level - a dot map on a topographic reference map or tourist map. For two ranges, temporal variability is presented by graphs, while a review of attributes of individual activities of the social website in question is set forward in the table panel. The element that visually interlinks all of the panels is the emphasised individual activity. Problemem podjetym w tych badaniach stało sie wykorzystanie metod z nurtu geograficznej wizualizacji do wskazania cech fenomenu VGI w zakresie zmiennosci czasowo-przestrzennej. Zgodnie z załozeniami poczynionymi w etapie koncepcyjnym finalnym działaniem stało sie zaimplementowanie do przegladarki internetowej okna pod tytułem: ”Geowizualizacja aktywnosci społecznosci Panoramio.com w powiecie poznanskim w 2011 roku”. Koncepcja została oparta na podziale okna geowizualizacji na trzy panele, z których najwazniejsze znaczenie dla uchwycenia zmiennosci przestrzennej na poziomie ogólnym ma kartogram, natomiast na poziomie szczegółowym mapa kropkowa wyswietlana na podkładzie mapy topograficznej lub turystycznej. Zmiennosc czasowa w dwóch zakresach prezentuja wykresy, a przeglad atrybutów poszczególnych aktywnosci prezentowanego portalu społecznosciowego zapewnia tabela. Elementem spajajacym wizualnie wszystkie panele jest wyeksponowana graficznie pojedyncza aktywnosc. Przetwarzanie danych odbyło sie w srodowisku open source, a technologia funkcjonowania aplikacji okna geowizualizacji bazowała na zastosowaniu asynchronicznych zapytan do serwera WWW oraz serwera baz danych co zapewnia sprawne "odswiezanie” poszczególnych paneli.

How do the radiative effects of springtime clouds and water vapor modulate the melt onset of Arctic sea ice?

NASA Astrophysics Data System (ADS)

Huang, Y.; Dong, X.; Xi, B.; Deng, Y.

2017-12-01

Earlier studies show that there is a strong positive correlation between the mean onset date of snow melt north of 70°N and the minimum Arctic sea ice extent (SIE) in September. Based on satellite records from 1980 to 2016, the September Arctic SIE minimum is most sensitive to the early melt onset over the Siberian Sea (73°-84°N, 90°-155°), which is defined as the area of focus (AOF) in this analysis. The day with melt onset exceeding 10% area of the AOF is marked as the initial melt date for a given year. With this definition, a strong positive correlation (r=0.59 at 99% confidence level) is found between the initial melt date over the AOF and the September SIE minimum over the Arctic. Daily anomalies of cloud and radiation properties are compared between six years with earliest initial melt dates (1990, 2012, 2007, 2003, 1991, 2016) and six years with latest initial melt dates (1996, 1984, 1983, 1982, 1987, 1992) using the NASA MERRA-2 reanalysis. Our results suggest that higher cloud water path (CWP) and precipitable water vapor (PWV) are clearly associated with early melt onset years through the period of mid-March to August. Major contrasts in CWP are found between the early and late onset years in a period of approximately 30 days prior to the onset to 30 days after the onset. As a result, the early melt onset years exhibit positive anomalies for downward longwave flux at the surface and negative anomalies for downward shortwave flux, shortwave cloud radiative effect (CRE) as well as net CRE. The negative net CRE is over-compensated by the positive longwave flux anomaly associated with elevated PWV, contributing to early melt onsets. The temporal evolution of CRE and PWV radiative effect during the entire melting season will be documented together with an analysis tracing the dynamical, mid-latitude origins of increased CWP and PWV prior to initial melt onsets.

Development of computational methods for unsteady aerodynamics at the NASA Langley Research Center

NASA Technical Reports Server (NTRS)

Yates, E. Carson, Jr.; Whitlow, Woodrow, Jr.

1987-01-01

The current scope, recent progress, and plans for research and development of computational methods for unsteady aerodynamics at the NASA Langley Research Center are reviewed. Both integral equations and finite difference methods for inviscid and viscous flows are discussed. Although the great bulk of the effort has focused on finite difference solution of the transonic small perturbation equation, the integral equation program is given primary emphasis here because it is less well known.

Development of computational methods for unsteady aerodynamics at the NASA Langley Research Center

NASA Technical Reports Server (NTRS)

Yates, E. Carson, Jr.; Whitlow, Woodrow, Jr.

1987-01-01

The current scope, recent progress, and plans for research and development of computational methods for unsteady aerodynamics at the NASA Langley Research Center are reviewed. Both integral-equations and finite-difference method for inviscid and viscous flows are discussed. Although the great bulk of the effort has focused on finite-difference solution of the transonic small-perturbation equation, the integral-equation program is given primary emphasis here because it is less well known.

Equation for the Nakanishi Weight Function Using the Inverse Stieltjes Transform

NASA Astrophysics Data System (ADS)

Karmanov, V. A.; Carbonell, J.; Frederico, T.

2018-05-01

The bound state Bethe-Salpeter amplitude was expressed by Nakanishi in terms of a smooth weight function g. By using the generalized Stieltjes transform, we derive an integral equation for the Nakanishi function g for a bound state case. It has the standard form g= \\hat{V} g, where \\hat{V} is a two-dimensional integral operator. The prescription for obtaining the kernel V starting with the kernel K of the Bethe-Salpeter equation is given.

The Riemann-Lanczos equations in general relativity and their integrability

NASA Astrophysics Data System (ADS)

Dolan, P.; Gerber, A.

2008-06-01

The aim of this paper is to examine the Riemann-Lanczos equations and how they can be made integrable. They consist of a system of linear first-order partial differential equations that arise in general relativity, whereby the Riemann curvature tensor is generated by an unknown third-order tensor potential field called the Lanczos tensor. Our approach is based on the theory of jet bundles, where all field variables and all their partial derivatives of all relevant orders are treated as independent variables alongside the local manifold coordinates (xa) on the given space-time manifold M. This approach is adopted in (a) Cartan's method of exterior differential systems, (b) Vessiot's dual method using vector field systems, and (c) the Janet-Riquier theory of systems of partial differential equations. All three methods allow for the most general situations under which integrability conditions can be found. They give equivalent results, namely, that involutivity is always achieved at all generic points of the jet manifold M after a finite number of prolongations. Two alternative methods that appear in the general relativity literature to find integrability conditions for the Riemann-Lanczos equations generate new partial differential equations for the Lanczos potential that introduce a source term, which is nonlinear in the components of the Riemann tensor. We show that such sources do not occur when either of method (a), (b), or (c) are used.

Solving the hypersingular boundary integral equation for the Burton and Miller formulation.

PubMed

Langrenne, Christophe; Garcia, Alexandre; Bonnet, Marc

2015-11-01

This paper presents an easy numerical implementation of the Burton and Miller (BM) formulation, where the hypersingular Helmholtz integral is regularized by identities from the associated Laplace equation and thus needing only the evaluation of weakly singular integrals. The Helmholtz equation and its normal derivative are combined directly with combinations at edge or corner collocation nodes not used when the surface is not smooth. The hypersingular operators arising in this process are regularized and then evaluated by an indirect procedure based on discretized versions of the Calderón identities linking the integral operators for associated Laplace problems. The method is valid for acoustic radiation and scattering problems involving arbitrarily shaped three-dimensional bodies. Unlike other approaches using direct evaluation of hypersingular integrals, collocation points still coincide with mesh nodes, as is usual when using conforming elements. Using higher-order shape functions (with the boundary element method model size kept fixed) reduces the overall numerical integration effort while increasing the solution accuracy. To reduce the condition number of the resulting BM formulation at low frequencies, a regularized version α = ik/(k(2 )+ λ) of the classical BM coupling factor α = i/k is proposed. Comparisons with the combined Helmholtz integral equation Formulation method of Schenck are made for four example configurations, two of them featuring non-smooth surfaces.

Metrisability of Painlevé equations

NASA Astrophysics Data System (ADS)

Contatto, Felipe; Dunajski, Maciej

2018-02-01

We solve the metrisability problem for the six Painlevé equations, and more generally for all 2nd order ordinary differential equations with the Painlevé property, and determine for which of these equations their integral curves are geodesics of a (pseudo) Riemannian metric on a surface.

Degenerate variational integrators for magnetic field line flow and guiding center trajectories

NASA Astrophysics Data System (ADS)

Ellison, C. L.; Finn, J. M.; Burby, J. W.; Kraus, M.; Qin, H.; Tang, W. M.

2018-05-01

Symplectic integrators offer many benefits for numerically approximating solutions to Hamiltonian differential equations, including bounded energy error and the preservation of invariant sets. Two important Hamiltonian systems encountered in plasma physics—the flow of magnetic field lines and the guiding center motion of magnetized charged particles—resist symplectic integration by conventional means because the dynamics are most naturally formulated in non-canonical coordinates. New algorithms were recently developed using the variational integration formalism; however, those integrators were found to admit parasitic mode instabilities due to their multistep character. This work eliminates the multistep character, and therefore the parasitic mode instabilities via an adaptation of the variational integration formalism that we deem "degenerate variational integration." Both the magnetic field line and guiding center Lagrangians are degenerate in the sense that the resultant Euler-Lagrange equations are systems of first-order ordinary differential equations. We show that retaining the same degree of degeneracy when constructing discrete Lagrangians yields one-step variational integrators preserving a non-canonical symplectic structure. Numerical examples demonstrate the benefits of the new algorithms, including superior stability relative to the existing variational integrators for these systems and superior qualitative behavior relative to non-conservative algorithms.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Manjunath, Naren; Samajdar, Rhine; Jain, Sudhir R., E-mail: srjain@barc.gov.in

Recently, the nodal domain counts of planar, integrable billiards with Dirichlet boundary conditions were shown to satisfy certain difference equations in Samajdar and Jain (2014). The exact solutions of these equations give the number of domains explicitly. For complete generality, we demonstrate this novel formulation for three additional separable systems and thus extend the statement to all integrable billiards.

UXO Discrimination in Cases with Overlapping Signatures

DTIC Science & Technology

2007-03-07

13. APPENDIX B: HFE -BIEM ..........................................................................................................290 - 7...First principals numerical solutions developed were a Hybrid Finite Element – Boundary Integral Equation Method ( HFE -BIEM) body of revolution (BOR...attacks, namely the Method of Auxiliary Sources (MAS) and the Hybrid Finite Element – Boundary Integral Equation Method ( HFE -BIEM). These work

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

The Schrödinger–Langevin equation with linear dissipation is integrated by propagating an ensemble of Bohmian trajectories for the ground state of quantum systems. Substituting the wave function expressed in terms of the complex action into the Schrödinger–Langevin equation yields the complex quantum Hamilton–Jacobi equation with linear dissipation. We transform this equation into the arbitrary Lagrangian–Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation is simultaneously integrated with the trajectory guidance equation. Then, the computational method is applied to the harmonic oscillator, the double well potential, and the ground vibrational state of methyl iodide.more » The excellent agreement between the computational and the exact results for the ground state energies and wave functions shows that this study provides a synthetic trajectory approach to the ground state of quantum systems.« less

Schrödinger–Langevin equation with quantum trajectories for photodissociation dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

The Schrödinger–Langevin equation is integrated to study the wave packet dynamics of quantum systems subject to frictional effects by propagating an ensemble of quantum trajectories. The equations of motion for the complex action and quantum trajectories are derived from the Schrödinger–Langevin equation. The moving least squares approach is used to evaluate the spatial derivatives of the complex action required for the integration of the equations of motion. Computational results are presented and analyzed for the evolution of a free Gaussian wave packet, a two-dimensional barrier model, and the photodissociation dynamics of NOCl. The absorption spectrum of NOCl obtained from themore » Schrödinger–Langevin equation displays a redshift when frictional effects increase. This computational result agrees qualitatively with the experimental results in the solution-phase photochemistry of NOCl.« less

Derivation of exact master equation with stochastic description: dissipative harmonic oscillator.

PubMed

Li, Haifeng; Shao, Jiushu; Wang, Shikuan

2011-11-01

A systematic procedure for deriving the master equation of a dissipative system is reported in the framework of stochastic description. For the Caldeira-Leggett model of the harmonic-oscillator bath, a detailed and elementary derivation of the bath-induced stochastic field is presented. The dynamics of the system is thereby fully described by a stochastic differential equation, and the desired master equation would be acquired with statistical averaging. It is shown that the existence of a closed-form master equation depends on the specificity of the system as well as the feature of the dissipation characterized by the spectral density function. For a dissipative harmonic oscillator it is observed that the correlation between the stochastic field due to the bath and the system can be decoupled, and the master equation naturally results. Such an equation possesses the Lindblad form in which time-dependent coefficients are determined by a set of integral equations. It is proved that the obtained master equation is equivalent to the well-known Hu-Paz-Zhang equation based on the path-integral technique. The procedure is also used to obtain the master equation of a dissipative harmonic oscillator in time-dependent fields.

General relaxation schemes in multigrid algorithms for higher order singularity methods

NASA Technical Reports Server (NTRS)

Oskam, B.; Fray, J. M. J.

1981-01-01

Relaxation schemes based on approximate and incomplete factorization technique (AF) are described. The AF schemes allow construction of a fast multigrid method for solving integral equations of the second and first kind. The smoothing factors for integral equations of the first kind, and comparison with similar results from the second kind of equations are a novel item. Application of the MD algorithm shows convergence to the level of truncation error of a second order accurate panel method.

Mathematics for Physics

NASA Astrophysics Data System (ADS)

Stone, Michael; Goldbart, Paul

2009-07-01

Preface; 1. Calculus of variations; 2. Function spaces; 3. Linear ordinary differential equations; 4. Linear differential operators; 5. Green functions; 6. Partial differential equations; 7. The mathematics of real waves; 8. Special functions; 9. Integral equations; 10. Vectors and tensors; 11. Differential calculus on manifolds; 12. Integration on manifolds; 13. An introduction to differential topology; 14. Group and group representations; 15. Lie groups; 16. The geometry of fibre bundles; 17. Complex analysis I; 18. Applications of complex variables; 19. Special functions and complex variables; Appendixes; Reference; Index.

Theory of Soliton Waves.

DTIC Science & Technology

1984-11-01

equation of Kadomtsev and Petviashvili (1970): (ut + 6uu x + U )x = 3 a Uyy, 0 - ± 1. (12) This equation turns out to be integrable for a = ± 1. For...1982b: "Comments on Inverse Scattering for the Kadomtsev - Petviashvili equation ", in Math methods in Hydro. & Integrability in Dyn. Systems, A. I. P. Conf...358. . Joseph, R. I., 1977: J. Phys. A., vol 10, p L225-L227. Kadomtsev , B. B. and Petviashvili , V. I., 1970: Soy. Phys. Doklady, vol 15, pp 539-541

Exact time-dependent solutions for a self-regulating gene.

PubMed

Ramos, A F; Innocentini, G C P; Hornos, J E M

2011-06-01

The exact time-dependent solution for the stochastic equations governing the behavior of a binary self-regulating gene is presented. Using the generating function technique to rephrase the master equations in terms of partial differential equations, we show that the model is totally integrable and the analytical solutions are the celebrated confluent Heun functions. Self-regulation plays a major role in the control of gene expression, and it is remarkable that such a microscopic model is completely integrable in terms of well-known complex functions.

Integral Equation for the Equilibrium State of Colliding Electron Beams

DOE Office of Scientific and Technical Information (OSTI.GOV)

Warnock, Robert L.

2002-11-11

We study a nonlinear integral equation for the equilibrium phase distribution of stored colliding electron beams. It is analogous to the Haissinski equation, being derived from Vlasov-Fokker-Planck theory, but is quite different in form. We prove existence of a unique solution, thus the existence of a unique equilibrium state, for sufficiently small current. This is done for the Chao-Ruth model of the beam-beam interaction in one degree of freedom. We expect no difficulty in generalizing the argument to more realistic models.

Conservation properties of numerical integration methods for systems of ordinary differential equations

NASA Technical Reports Server (NTRS)

Rosenbaum, J. S.

1976-01-01

If a system of ordinary differential equations represents a property conserving system that can be expressed linearly (e.g., conservation of mass), it is then desirable that the numerical integration method used conserve the same quantity. It is shown that both linear multistep methods and Runge-Kutta methods are 'conservative' and that Newton-type methods used to solve the implicit equations preserve the inherent conservation of the numerical method. It is further shown that a method used by several authors is not conservative.

Solution of some types of differential equations: operational calculus and inverse differential operators.

PubMed

Zhukovsky, K

2014-01-01

We present a general method of operational nature to analyze and obtain solutions for a variety of equations of mathematical physics and related mathematical problems. We construct inverse differential operators and produce operational identities, involving inverse derivatives and families of generalised orthogonal polynomials, such as Hermite and Laguerre polynomial families. We develop the methodology of inverse and exponential operators, employing them for the study of partial differential equations. Advantages of the operational technique, combined with the use of integral transforms, generating functions with exponentials and their integrals, for solving a wide class of partial derivative equations, related to heat, wave, and transport problems, are demonstrated.

Some Exact Results for the Schroedinger Wave Equation with a Time Dependent Potential

NASA Technical Reports Server (NTRS)

Campbell, Joel

2009-01-01

The time dependent Schroedinger equation with a time dependent delta function potential is solved exactly for many special cases. In all other cases the problem can be reduced to an integral equation of the Volterra type. It is shown that by knowing the wave function at the origin, one may derive the wave function everywhere. Thus, the problem is reduced from a PDE in two variables to an integral equation in one. These results are used to compare adiabatic versus sudden changes in the potential. It is shown that adiabatic changes in the p otential lead to conservation of the normalization of the probability density.

Bukhvostov-Lipatov model and quantum-classical duality

NASA Astrophysics Data System (ADS)

Bazhanov, Vladimir V.; Lukyanov, Sergei L.; Runov, Boris A.

2018-02-01

The Bukhvostov-Lipatov model is an exactly soluble model of two interacting Dirac fermions in 1 + 1 dimensions. The model describes weakly interacting instantons and anti-instantons in the O (3) non-linear sigma model. In our previous work [arxiv:arXiv:1607.04839] we have proposed an exact formula for the vacuum energy of the Bukhvostov-Lipatov model in terms of special solutions of the classical sinh-Gordon equation, which can be viewed as an example of a remarkable duality between integrable quantum field theories and integrable classical field theories in two dimensions. Here we present a complete derivation of this duality based on the classical inverse scattering transform method, traditional Bethe ansatz techniques and analytic theory of ordinary differential equations. In particular, we show that the Bethe ansatz equations defining the vacuum state of the quantum theory also define connection coefficients of an auxiliary linear problem for the classical sinh-Gordon equation. Moreover, we also present details of the derivation of the non-linear integral equations determining the vacuum energy and other spectral characteristics of the model in the case when the vacuum state is filled by 2-string solutions of the Bethe ansatz equations.

Nonlocal equation for the superconducting gap parameter

NASA Astrophysics Data System (ADS)

Simonucci, S.; Strinati, G. Calvanese

2017-08-01

The properties are considered in detail of a nonlocal (integral) equation for the superconducting gap parameter, which is obtained by a coarse-graining procedure applied to the Bogoliubov-de Gennes (BdG) equations over the whole coupling-versus-temperature phase diagram associated with the superfluid phase. It is found that the limiting size of the coarse-graining procedure, which is dictated by the range of the kernel of this integral equation, corresponds to the size of the Cooper pairs over the whole coupling-versus-temperature phase diagram up to the critical temperature, even when Cooper pairs turn into composite bosons on the BEC side of the BCS-BEC crossover. A practical method is further implemented to solve numerically this integral equation in an efficient way, which is based on a novel algorithm for calculating the Fourier transforms. Application of this method to the case of an isolated vortex, throughout the BCS-BEC crossover and for all temperatures in the superfluid phase, helps clarifying the nature of the length scales associated with a single vortex and the kinds of details that are in practice disposed off by the coarse-graining procedure on the BdG equations.

On the Full-Discrete Extended Generalised q-Difference Toda System

NASA Astrophysics Data System (ADS)

Li, Chuanzhong; Meng, Anni

2017-08-01

In this paper, we construct a full-discrete integrable difference equation which is a full-discretisation of the generalised q-Toda equation. Meanwhile its soliton solutions are constructed to show its integrable property. Further the Lax pairs of an extended generalised full-discrete q-Toda hierarchy are also constructed. To show the integrability, the bi-Hamiltonian structure and tau symmetry of the extended full-discrete generalised q-Toda hierarchy are given.

An explicit predictor-corrector solver with applications to Burgers' equation

NASA Technical Reports Server (NTRS)

Dey, S. K.; Dey, C.

1983-01-01

Forward Euler's explicit, finite-difference formula of extrapolation, is used as a predictor and a convex formula as a corrector to integrate differential equations numerically. An application has been made to Burger's equation.

Continual approach at T=0 in the mean field theory of incommensurate magnetic states in the frustrated Heisenberg ferromagnet with an easy axis anisotropy

NASA Astrophysics Data System (ADS)

Martynov, S. N.; Tugarinov, V. I.; Martynov, A. S.

2017-10-01

The algorithm of approximate solution was developed for the differential equation describing the anharmonical change of the spin orientation angle in the model of ferromagnet with the exchange competition between nearest and next nearest magnetic neighbors and the easy axis exchange anisotropy. The equation was obtained from the collinearity constraint on the discrete lattice. In the low anharmonicity approximation the equation is resulted to an autonomous form and is integrated in quadratures. The obvious dependence of the angle velocity and second derivative of angle from angle and initial condition was derived by expanding the first integral of the equation in the Taylor series in vicinity of initial condition. The ground state of the soliton solutions was calculated by a numerical minimization of the energy integral. The evaluation of the used approximation was made for a triple point of the phase diagram.

An integrated algorithm for hypersonic fluid-thermal-structural numerical simulation

NASA Astrophysics Data System (ADS)

Li, Jia-Wei; Wang, Jiang-Feng

2018-05-01

In this paper, a fluid-structural-thermal integrated method is presented based on finite volume method. A unified integral equations system is developed as the control equations for physical process of aero-heating and structural heat transfer. The whole physical field is discretized by using an up-wind finite volume method. To demonstrate its capability, the numerical simulation of Mach 6.47 flow over stainless steel cylinder shows a good agreement with measured values, and this method dynamically simulates the objective physical processes. Thus, the integrated algorithm proves to be efficient and reliable.

Methods of Attenuation Correction for Dual-Wavelength and Dual-Polarization Weather Radar Data

NASA Technical Reports Server (NTRS)

Meneghini, R.; Liao, L.

2007-01-01

In writing the integral equations for the median mass diameter and number concentration, or comparable parameters of the raindrop size distribution, it is apparent that the forms of the equations for dual-polarization and dual-wavelength radar data are identical when attenuation effects are included. The differential backscattering and extinction coefficients appear in both sets of equations: for the dual-polarization equations, the differences are taken with respect to polarization at a fixed frequency while for the dual-wavelength equations, the differences are taken with respect to frequency at a fixed polarization. An alternative to the integral equation formulation is that based on the k-Z (attenuation coefficient-radar reflectivity factor) parameterization. This-technique was originally developed for attenuating single-wavelength radars, a variation of which has been applied to the TRMM Precipitation Radar data (PR). Extensions of this method have also been applied to dual-polarization data. In fact, it is not difficult to show that nearly identical equations are applicable as well to dualwavelength radar data. In this case, the equations for median mass diameter and number concentration take the form of coupled, but non-integral equations. Differences between this and the integral equation formulation are a consequence of the different ways in which attenuation correction is performed under the two formulations. For both techniques, the equations can be solved either forward from the radar outward or backward from the final range gate toward the radar. Although the forward-going solutions tend to be unstable as the attenuation out to the range of interest becomes large in some sense, an independent estimate of path attenuation is not required. This is analogous to the case of an attenuating single-wavelength radar where the forward solution to the Hitschfeld-Bordan equation becomes unstable as the attenuation increases. To circumvent this problem, the equations can be expressed in the form of a final-value problem so that the recursion begins at the far range gate and proceeds inward towards the radar. Solving the problem in this way traditionally requires estimates of path attenuation to the final gate: in the case of orthogonal linear polarizations, the attenuations at horizontal and vertical polarizations (same frequency) are required while in the dual-wavelength case, attenuations at the two frequencies (same polarization) are required.

A new numerical approach for uniquely solvable exterior Riemann-Hilbert problem on region with corners

NASA Astrophysics Data System (ADS)

Zamzamir, Zamzana; Murid, Ali H. M.; Ismail, Munira

2014-06-01

Numerical solution for uniquely solvable exterior Riemann-Hilbert problem on region with corners at offcorner points has been explored by discretizing the related integral equation using Picard iteration method without any modifications to the left-hand side (LHS) and right-hand side (RHS) of the integral equation. Numerical errors for all iterations are converge to the required solution. However, for certain problems, it gives lower accuracy. Hence, this paper presents a new numerical approach for the problem by treating the generalized Neumann kernel at LHS and the function at RHS of the integral equation. Due to the existence of the corner points, Gaussian quadrature is employed which avoids the corner points during numerical integration. Numerical example on a test region is presented to demonstrate the effectiveness of this formulation.

Multi-off-grid methods in multi-step integration of ordinary differential equations

NASA Technical Reports Server (NTRS)

Beaudet, P. R.

1974-01-01

Description of methods of solving first- and second-order systems of differential equations in which all derivatives are evaluated at off-grid locations in order to circumvent the Dahlquist stability limitation on the order of on-grid methods. The proposed multi-off-grid methods require off-grid state predictors for the evaluation of the n derivatives at each step. Progressing forward in time, the off-grid states are predicted using a linear combination of back on-grid state values and off-grid derivative evaluations. A comparison is made between the proposed multi-off-grid methods and the corresponding Adams and Cowell on-grid integration techniques in integrating systems of ordinary differential equations, showing a significant reduction in the error at larger step sizes in the case of the multi-off-grid integrator.

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…

Classical Yang-Baxter equations and quantum integrable systems

NASA Astrophysics Data System (ADS)

Jurčo, Branislav

1989-06-01

Quantum integrable models associated with nondegenerate solutions of classical Yang-Baxter equations related to the simple Lie algebras are investigated. These models are diagonalized for rational and trigonometric solutions in the cases of sl(N)/gl(N)/, o(N) and sp(N) algebras. The analogy with the quantum inverse scattering method is demonstrated.

The Transmission Line as a Simple Example for Introducing Integral Equations to Undergraduates

ERIC Educational Resources Information Center

Rothwell, E. J.

2009-01-01

Integral equations are becoming a common means for describing problems in electromagnetics, and so it is important to expose students to methods for their solution. Typically this is done using examples in antennas, scattering, or electrostatics. Unfortunately, many difficult issues arise in the formulation and solution of the associated…

Space-time domain solutions of the wave equation by a non-singular boundary integral method and Fourier transform.

PubMed

Klaseboer, Evert; Sepehrirahnama, Shahrokh; Chan, Derek Y C

2017-08-01

The general space-time evolution of the scattering of an incident acoustic plane wave pulse by an arbitrary configuration of targets is treated by employing a recently developed non-singular boundary integral method to solve the Helmholtz equation in the frequency domain from which the space-time solution of the wave equation is obtained using the fast Fourier transform. The non-singular boundary integral solution can enforce the radiation boundary condition at infinity exactly and can account for multiple scattering effects at all spacings between scatterers without adverse effects on the numerical precision. More generally, the absence of singular kernels in the non-singular integral equation confers high numerical stability and precision for smaller numbers of degrees of freedom. The use of fast Fourier transform to obtain the time dependence is not constrained to discrete time steps and is particularly efficient for studying the response to different incident pulses by the same configuration of scatterers. The precision that can be attained using a smaller number of Fourier components is also quantified.

European Science Notes Information Bulletin Reports on Current European/ Middle Eastern Science

DTIC Science & Technology

1990-01-01

because they permit a high degree of error then converted into system-specific data by coupling tolerance. Other knowledge- based approaches offer the...Reducing development costs and development time ing an increasingly powerful focus for business activities . " Simplifying the design process In the...systems. Sie- The immediate goal of telecommunications efforts is a mens is actively involved in defining and implementing configuration based on ISDN and

Targeting the cell wall of Mycobacterium tuberculosis: a molecular modeling investigation of the interaction of imipenem and meropenem with L,D-transpeptidase 2.

PubMed

Silva, José Rogério A; Bishai, William R; Govender, Thavendran; Lamichhane, Gyanu; Maguire, Glenn E M; Kruger, Hendrik G; Lameira, Jeronimo; Alves, Cláudio N

2016-01-01

The single crystal X-ray structure of the extracellular portion of the L,D-transpeptidase (ex-LdtMt2 - residues 120-408) enzyme was recently reported. It was observed that imipenem and meropenem inhibit activity of this enzyme, responsible for generating L,D-transpeptide linkages in the peptidoglycan layer of Mycobacterium tuberculosis. Imipenem is more active and isothermal titration calorimetry experiments revealed that meropenem is subjected to an entropy penalty upon binding to the enzyme. Herein, we report a molecular modeling approach to obtain a molecular view of the inhibitor/enzyme interactions. The average binding free energies for nine commercially available inhibitors were calculated using MM/GBSA and Solvation Interaction Energy (SIE) approaches and the calculated energies corresponded well with the available experimentally observed results. The method reproduces the same order of binding energies as experimentally observed for imipenem and meropenem. We have also demonstrated that SIE is a reasonably accurate and cost-effective free energy method, which can be used to predict carbapenem affinities for this enzyme. A theoretical explanation was offered for the experimental entropy penalty observed for meropenem, creating optimism that this computational model can serve as a potential computational model for other researchers in the field.

Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1994-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that are currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

Alternate solution to generalized Bernoulli equations via an integrating factor: an exact differential equation approach

NASA Astrophysics Data System (ADS)

Tisdell, C. C.

2017-08-01

Solution methods to exact differential equations via integrating factors have a rich history dating back to Euler (1740) and the ideas enjoy applications to thermodynamics and electromagnetism. Recently, Azevedo and Valentino presented an analysis of the generalized Bernoulli equation, constructing a general solution by linearizing the problem through a substitution. The purpose of this note is to present an alternative approach using 'exact methods', illustrating that a substitution and linearization of the problem is unnecessary. The ideas may be seen as forming a complimentary and arguably simpler approach to Azevedo and Valentino that have the potential to be assimilated and adapted to pedagogical needs of those learning and teaching exact differential equations in schools, colleges, universities and polytechnics. We illustrate how to apply the ideas through an analysis of the Gompertz equation, which is of interest in biomathematical models of tumour growth.

Two-layer interfacial flows beyond the Boussinesq approximation: a Hamiltonian approach

NASA Astrophysics Data System (ADS)

Camassa, R.; Falqui, G.; Ortenzi, G.

2017-02-01

The theory of integrable systems of Hamiltonian PDEs and their near-integrable deformations is used to study evolution equations resulting from vertical-averages of the Euler system for two-layer stratified flows in an infinite two-dimensional channel. The Hamiltonian structure of the averaged equations is obtained directly from that of the Euler equations through the process of Hamiltonian reduction. Long-wave asymptotics together with the Boussinesq approximation of neglecting the fluids’ inertia is then applied to reduce the leading order vertically averaged equations to the shallow-water Airy system, albeit in a non-trivial way. The full non-Boussinesq system for the dispersionless limit can then be viewed as a deformation of this well known equation. In a perturbative study of this deformation, a family of approximate constants of the motion are explicitly constructed and used to find local solutions of the evolution equations by means of hodograph-like formulae.

Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1995-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that we currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Karr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

Concepts for radically increasing the numerical convergence rate of the Euler equations

NASA Technical Reports Server (NTRS)

Nixon, David; Tzuoo, Keh-Lih; Caruso, Steven C.; Farshchi, Mohammad; Klopfer, Goetz H.; Ayoub, Alfred

1987-01-01

Integral equation and finite difference methods have been developed for solving transonic flow problems using linearized forms of the transonic small disturbance and Euler equations. A key element is the use of a strained coordinate system in which the shock remains fixed. Additional criteria are developed to determine the free parameters in the coordinate straining; these free parameters are functions of the shock location. An integral equation analysis showed that the shock is located by ensuring that no expansion shocks exist in the solution. The expansion shock appears as oscillations in the solution near the sonic line, and the correct shock location is determined by removing these oscillations. A second objective was to study the ability of the Euler equation to model separated flow.

Fractional-order difference equations for physical lattices and some applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

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

2015-10-15

Fractional-order operators for physical lattice models based on the Grünwald-Letnikov fractional differences are suggested. We use an approach based on the models of lattices with long-range particle interactions. The fractional-order operators of differentiation and integration on physical lattices are represented by kernels of lattice long-range interactions. In continuum limit, these discrete operators of non-integer orders give the fractional-order derivatives and integrals with respect to coordinates of the Grünwald-Letnikov types. As examples of the fractional-order difference equations for physical lattices, we give difference analogs of the fractional nonlocal Navier-Stokes equations and the fractional nonlocal Maxwell equations for lattices with long-range interactions.more » Continuum limits of these fractional-order difference equations are also suggested.« less

Asymptotic integration algorithms for nonhomogeneous, nonlinear, first order, ordinary differential equations

NASA Technical Reports Server (NTRS)

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

1991-01-01

New methods for integrating systems of stiff, nonlinear, first order, ordinary differential equations are developed by casting the differential equations into integral form. Nonlinear recursive relations are obtained that allow the solution to a system of equations at time t plus delta t to be obtained in terms of the solution at time t in explicit and implicit forms. Examples of accuracy obtained with the new technique are given by considering systems of nonlinear, first order equations which arise in the study of unified models of viscoplastic behaviors, the spread of the AIDS virus, and predator-prey populations. In general, the new implicit algorithm is unconditionally stable, and has a Jacobian of smaller dimension than that which is acquired by current implicit methods, such as the Euler backward difference algorithm; yet, it gives superior accuracy. The asymptotic explicit and implicit algorithms are suitable for solutions that are of the growing and decaying exponential kinds, respectively, whilst the implicit Euler-Maclaurin algorithm is superior when the solution oscillates, i.e., when there are regions in which both growing and decaying exponential solutions exist.

Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations

NASA Astrophysics Data System (ADS)

Gerdt, Vladimir P.; Blinkov, Yuri A.; Mozzhilkin, Vladimir V.

2006-05-01

In this paper we present an algorithmic approach to the generation of fully conservative difference schemes for linear partial differential equations. The approach is based on enlargement of the equations in their integral conservation law form by extra integral relations between unknown functions and their derivatives, and on discretization of the obtained system. The structure of the discrete system depends on numerical approximation methods for the integrals occurring in the enlarged system. As a result of the discretization, a system of linear polynomial difference equations is derived for the unknown functions and their partial derivatives. A difference scheme is constructed by elimination of all the partial derivatives. The elimination can be achieved by selecting a proper elimination ranking and by computing a Gröbner basis of the linear difference ideal generated by the polynomials in the discrete system. For these purposes we use the difference form of Janet-like Gröbner bases and their implementation in Maple. As illustration of the described methods and algorithms, we construct a number of difference schemes for Burgers and Falkowich-Karman equations and discuss their numerical properties.

A fast and well-conditioned spectral method for singular integral equations

NASA Astrophysics Data System (ADS)

Slevinsky, Richard Mikael; Olver, Sheehan

2017-03-01

We develop a spectral method for solving univariate singular integral equations over unions of intervals by utilizing Chebyshev and ultraspherical polynomials to reformulate the equations as almost-banded infinite-dimensional systems. This is accomplished by utilizing low rank approximations for sparse representations of the bivariate kernels. The resulting system can be solved in O (m2 n) operations using an adaptive QR factorization, where m is the bandwidth and n is the optimal number of unknowns needed to resolve the true solution. The complexity is reduced to O (mn) operations by pre-caching the QR factorization when the same operator is used for multiple right-hand sides. Stability is proved by showing that the resulting linear operator can be diagonally preconditioned to be a compact perturbation of the identity. Applications considered include the Faraday cage, and acoustic scattering for the Helmholtz and gravity Helmholtz equations, including spectrally accurate numerical evaluation of the far- and near-field solution. The JULIA software package SingularIntegralEquations.jl implements our method with a convenient, user-friendly interface.

Integrable structure in discrete shell membrane theory

PubMed Central

Schief, W. K.

2014-01-01

We present natural discrete analogues of two integrable classes of shell membranes. By construction, these discrete shell membranes are in equilibrium with respect to suitably chosen internal stresses and external forces. The integrability of the underlying equilibrium equations is proved by relating the geometry of the discrete shell membranes to discrete O surface theory. We establish connections with generalized barycentric coordinates and nine-point centres and identify a discrete version of the classical Gauss equation of surface theory. PMID:24808755

Integrable structure in discrete shell membrane theory.

PubMed

Schief, W K

2014-05-08

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

On the numeric integration of dynamic attitude equations

NASA Technical Reports Server (NTRS)

Crouch, P. E.; Yan, Y.; Grossman, Robert

1992-01-01

We describe new types of numerical integration algorithms developed by the authors. The main aim of the algorithms is to numerically integrate differential equations which evolve on geometric objects, such as the rotation group. The algorithms provide iterates which lie on the prescribed geometric object, either exactly, or to some prescribed accuracy, independent of the order of the algorithm. This paper describes applications of these algorithms to the evolution of the attitude of a rigid body.

Evaluation of the path integral for flow through random porous media

NASA Astrophysics Data System (ADS)

Westbroek, Marise J. E.; Coche, Gil-Arnaud; King, Peter R.; Vvedensky, Dimitri D.

2018-04-01

We present a path integral formulation of Darcy's equation in one dimension with random permeability described by a correlated multivariate lognormal distribution. This path integral is evaluated with the Markov chain Monte Carlo method to obtain pressure distributions, which are shown to agree with the solutions of the corresponding stochastic differential equation for Dirichlet and Neumann boundary conditions. The extension of our approach to flow through random media in two and three dimensions is discussed.

A solution for two-dimensional Fredholm integral equations of the second kind with periodic, semiperiodic, or nonperiodic kernels. [integral representation of the stationary Navier-Stokes problem

NASA Technical Reports Server (NTRS)

Gabrielsen, R. E.; Uenal, A.

1981-01-01

A numerical scheme for solving two dimensional Fredholm integral equations of the second kind is developed. The proof of the convergence of the numerical scheme is shown for three cases: the case of periodic kernels, the case of semiperiodic kernels, and the case of nonperiodic kernels. Applications to the incompressible, stationary Navier-Stokes problem are of primary interest.

Particle Size Distributions in Atmospheric Clouds

NASA Technical Reports Server (NTRS)

Paoli, Roberto; Shariff, Karim

2003-01-01

In this note, we derive a transport equation for a spatially integrated distribution function of particles size that is suitable for sparse particle systems, such as in atmospheric clouds. This is done by integrating a Boltzmann equation for a (local) distribution function over an arbitrary but finite volume. A methodology for evolving the moments of the integrated distribution is presented. These moments can be either tracked for a finite number of discrete populations ('clusters') or treated as continuum variables.

A method for computing the kernel of the downwash integral equation for arbitrary complex frequencies

NASA Technical Reports Server (NTRS)

Desmarais, R. N.; Rowe, W. S.

1984-01-01

For the design of active controls to stabilize flight vehicles, which requires the use of unsteady aerodynamics that are valid for arbitrary complex frequencies, algorithms are derived for evaluating the nonelementary part of the kernel of the integral equation that relates unsteady pressure to downwash. This part of the kernel is separated into an infinite limit integral that is evaluated using Bessel and Struve functions and into a finite limit integral that is expanded in series and integrated termwise in closed form. The developed series expansions gave reliable answers for all complex reduced frequencies and executed faster than exponential approximations for many pressure stations.

Integrals and integral equations in linearized wing theory

NASA Technical Reports Server (NTRS)

Lomax, Harvard; Heaslet, Max A; Fuller, Franklyn B

1951-01-01

The formulas of subsonic and supersonic wing theory for source, doublet, and vortex distributions are reviewed and a systematic presentation is provided which relates these distributions to the pressure and to the vertical induced velocity in the plane of the wing. It is shown that care must be used in treating the singularities involved in the analysis and that the order of integration is not always reversible. Concepts suggested by the irreversibility of order of integration are shown to be useful in the inversion of singular integral equations when operational techniques are used. A number of examples are given to illustrate the methods presented, attention being directed to supersonic flight speed.

Evaluating Simultaneous Integrals

ERIC Educational Resources Information Center

Kwong, Harris

2012-01-01

Many integrals require two successive applications of integration by parts. During the process, another integral of similar type is often invoked. We propose a method which can integrate these two integrals simultaneously. All we need is to solve a linear system of equations.

Computational attributes of the integral form of the equation of transfer

NASA Technical Reports Server (NTRS)

Frankel, J. I.

1991-01-01

Difficulties can arise in radiative and neutron transport calculations when a highly anisotropic scattering phase function is present. In the presence of anisotropy, currently used numerical solutions are based on the integro-differential form of the linearized Boltzmann transport equation. This paper, departs from classical thought and presents an alternative numerical approach based on application of the integral form of the transport equation. Use of the integral formalism facilitates the following steps: a reduction in dimensionality of the system prior to discretization, the use of symbolic manipulation to augment the computational procedure, and the direct determination of key physical quantities which are derivable through the various Legendre moments of the intensity. The approach is developed in the context of radiative heat transfer in a plane-parallel geometry, and results are presented and compared with existing benchmark solutions. Encouraging results are presented to illustrate the potential of the integral formalism for computation. The integral formalism appears to possess several computational attributes which are well-suited to radiative and neutron transport calculations.

Frobenius manifolds and Frobenius algebra-valued integrable systems

NASA Astrophysics Data System (ADS)

Strachan, Ian A. B.; Zuo, Dafeng

2017-06-01

The notion of integrability will often extend from systems with scalar-valued fields to systems with algebra-valued fields. In such extensions the properties of, and structures on, the algebra play a central role in ensuring integrability is preserved. In this paper, a new theory of Frobenius algebra-valued integrable systems is developed. This is achieved for systems derived from Frobenius manifolds by utilizing the theory of tensor products for such manifolds, as developed by Kaufmann (Int Math Res Not 19:929-952, 1996), Kontsevich and Manin (Inv Math 124: 313-339, 1996). By specializing this construction, using a fixed Frobenius algebra A, one can arrive at such a theory. More generally, one can apply the same idea to construct an A-valued topological quantum field theory. The Hamiltonian properties of two classes of integrable evolution equations are then studied: dispersionless and dispersive evolution equations. Application of these ideas are discussed, and as an example, an A-valued modified Camassa-Holm equation is constructed.

Computation of Sound Propagation by Boundary Element Method

NASA Technical Reports Server (NTRS)

Guo, Yueping

2005-01-01

This report documents the development of a Boundary Element Method (BEM) code for the computation of sound propagation in uniform mean flows. The basic formulation and implementation follow the standard BEM methodology; the convective wave equation and the boundary conditions on the surfaces of the bodies in the flow are formulated into an integral equation and the method of collocation is used to discretize this equation into a matrix equation to be solved numerically. New features discussed here include the formulation of the additional terms due to the effects of the mean flow and the treatment of the numerical singularities in the implementation by the method of collocation. The effects of mean flows introduce terms in the integral equation that contain the gradients of the unknown, which is undesirable if the gradients are treated as additional unknowns, greatly increasing the sizes of the matrix equation, or if numerical differentiation is used to approximate the gradients, introducing numerical error in the computation. It is shown that these terms can be reformulated in terms of the unknown itself, making the integral equation very similar to the case without mean flows and simple for numerical implementation. To avoid asymptotic analysis in the treatment of numerical singularities in the method of collocation, as is conventionally done, we perform the surface integrations in the integral equation by using sub-triangles so that the field point never coincide with the evaluation points on the surfaces. This simplifies the formulation and greatly facilitates the implementation. To validate the method and the code, three canonic problems are studied. They are respectively the sound scattering by a sphere, the sound reflection by a plate in uniform mean flows and the sound propagation over a hump of irregular shape in uniform flows. The first two have analytical solutions and the third is solved by the method of Computational Aeroacoustics (CAA), all of which are used to compare the BEM solutions. The comparisons show very good agreements and validate the accuracy of the BEM approach implemented here.

Time-symmetric integration in astrophysics

NASA Astrophysics Data System (ADS)

Hernandez, David M.; Bertschinger, Edmund

2018-04-01

Calculating the long-term solution of ordinary differential equations, such as those of the N-body problem, is central to understanding a wide range of dynamics in astrophysics, from galaxy formation to planetary chaos. Because generally no analytic solution exists to these equations, researchers rely on numerical methods that are prone to various errors. In an effort to mitigate these errors, powerful symplectic integrators have been employed. But symplectic integrators can be severely limited because they are not compatible with adaptive stepping and thus they have difficulty in accommodating changing time and length scales. A promising alternative is time-reversible integration, which can handle adaptive time-stepping, but the errors due to time-reversible integration in astrophysics are less understood. The goal of this work is to study analytically and numerically the errors caused by time-reversible integration, with and without adaptive stepping. We derive the modified differential equations of these integrators to perform the error analysis. As an example, we consider the trapezoidal rule, a reversible non-symplectic integrator, and show that it gives secular energy error increase for a pendulum problem and for a Hénon-Heiles orbit. We conclude that using reversible integration does not guarantee good energy conservation and that, when possible, use of symplectic integrators is favoured. We also show that time-symmetry and time-reversibility are properties that are distinct for an integrator.

Additive noise-induced Turing transitions in spatial systems with application to neural fields and the Swift Hohenberg equation

NASA Astrophysics Data System (ADS)

Hutt, Axel; Longtin, Andre; Schimansky-Geier, Lutz

2008-05-01

This work studies the spatio-temporal dynamics of a generic integral-differential equation subject to additive random fluctuations. It introduces a combination of the stochastic center manifold approach for stochastic differential equations and the adiabatic elimination for Fokker-Planck equations, and studies analytically the systems’ stability near Turing bifurcations. In addition two types of fluctuation are studied, namely fluctuations uncorrelated in space and time, and global fluctuations, which are constant in space but uncorrelated in time. We show that the global fluctuations shift the Turing bifurcation threshold. This shift is proportional to the fluctuation variance. Applications to a neural field equation and the Swift-Hohenberg equation reveal the shift of the bifurcation to larger control parameters, which represents a stabilization of the system. All analytical results are confirmed by numerical simulations of the occurring mode equations and the full stochastic integral-differential equation. To gain some insight into experimental manifestations, the sum of uncorrelated and global additive fluctuations is studied numerically and the analytical results on global fluctuations are confirmed qualitatively.

A general integral form of the boundary-layer equation for incompressible flow with an application to the calculation of the separation point of turbulent boundary layers

NASA Technical Reports Server (NTRS)

Tetervin, Neal; Lin, Chia Chiao

1951-01-01

A general integral form of the boundary-layer equation, valid for either laminar or turbulent incompressible boundary-layer flow, is derived. By using the experimental finding that all velocity profiles of the turbulent boundary layer form essentially a single-parameter family, the general equation is changed to an equation for the space rate of change of the velocity-profile shape parameter. The lack of precise knowledge concerning the surface shear and the distribution of the shearing stress across turbulent boundary layers prevented the attainment of a reliable method for calculating the behavior of turbulent boundary layers.

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.

Aerodynamics Via Acoustics: Application of Acoustic Formulas for Aerodynamic Calculations

NASA Technical Reports Server (NTRS)

Farassat, F.; Myers, M. K.

1986-01-01

Prediction of aerodynamic loads on bodies in arbitrary motion is considered from an acoustic point of view, i.e., in a frame of reference fixed in the undisturbed medium. An inhomogeneous wave equation which governs the disturbance pressure is constructed and solved formally using generalized function theory. When the observer is located on the moving body surface there results a singular linear integral equation for surface pressure. Two different methods for obtaining such equations are discussed. Both steady and unsteady aerodynamic calculations are considered. Two examples are presented, the more important being an application to propeller aerodynamics. Of particular interest for numerical applications is the analytical behavior of the kernel functions in the various integral equations.

The influence of a wind tunnel on helicopter rotational noise: Formulation of analysis

NASA Technical Reports Server (NTRS)

Mosher, M.

1984-01-01

An analytical model is discussed that can be used to examine the effects of wind tunnel walls on helicopter rotational noise. A complete physical model of an acoustic source in a wind tunnel is described and a simplified version is then developed. This simplified model retains the important physical processes involved, yet it is more amenable to analysis. The simplified physical model is then modeled as a mathematical problem. An inhomogeneous partial differential equation with mixed boundary conditions is set up and then transformed into an integral equation. Details of generating a suitable Green's function and integral equation are included and the equation is discussed and also given for a two-dimensional case.

The Integration of Teacher's Pedagogical Content Knowledge Components in Teaching Linear Equation

ERIC Educational Resources Information Center

Yusof, Yusminah Mohd.; Effandi, Zakaria

2015-01-01

This qualitative research aimed to explore the integration of the components of pedagogical content knowledge (PCK) in teaching Linear Equation with one unknown. For the purpose of the study, a single local case study with multiple participants was used. The selection of the participants was made based on various criteria: having more than 5 years…

Novel Methods for Electromagnetic Simulation and Design

DTIC Science & Technology

2016-08-03

The resulting discretized integral equations are compatible with fast multipoleaccelerated solvers and will form the basis for high fidelity...expansion”) which are high-order, efficient and easy to use on arbitrarily triangulated surfaces. The resulting discretized integral equations are...created a user interface compatible with both low and high order discretizations , and implemented the generalized Debye approach of [4]. The

Stability and square integrability of derivatives of solutions of nonlinear fourth order differential equations with delay.

PubMed

Korkmaz, Erdal

2017-01-01

In this paper, we give sufficient conditions for the boundedness, uniform asymptotic stability and square integrability of the solutions to a certain fourth order non-autonomous differential equations with delay by using Lyapunov's second method. The results obtained essentially improve, include and complement the results in the literature.

Spinning particle and gauge theories as integrability conditions

NASA Astrophysics Data System (ADS)

Eisenberg, Yeshayahu

1992-02-01

Starting from a new four dimensional spinning point particle we obtain new representations of the standard four dimensional gauge field equations in terms of a generalized space (Minkowski + light cone). In terms of this new formulation we define linear systems whose integrability conditions imply the massive Dirac-Maxwell and the Yang-Mills equations. Research supported by the Rothschild Fellowship.

Integrable Semi-discrete Kundu-Eckhaus Equation: Darboux Transformation, Breather, Rogue Wave and Continuous Limit Theory

NASA Astrophysics Data System (ADS)

Zhao, Hai-qiong; Yuan, Jinyun; Zhu, Zuo-nong

2018-02-01

To get more insight into the relation between discrete model and continuous counterpart, a new integrable semi-discrete Kundu-Eckhaus equation is derived from the reduction in an extended Ablowitz-Ladik hierarchy. The integrability of the semi-discrete model is confirmed by showing the existence of Lax pair and infinite number of conservation laws. The dynamic characteristics of the breather and rational solutions have been analyzed in detail for our semi-discrete Kundu-Eckhaus equation to reveal some new interesting phenomena which was not found in continuous one. It is shown that the theory of the discrete system including Lax pair, Darboux transformation and explicit solutions systematically yields their continuous counterparts in the continuous limit.

Simulation of a steady-state integrated human thermal system.

NASA Technical Reports Server (NTRS)

Hsu, F. T.; Fan, L. T.; Hwang, C. L.

1972-01-01

The mathematical model of an integrated human thermal system is formulated. The system consists of an external thermal regulation device on the human body. The purpose of the device (a network of cooling tubes held in contact with the surface of the skin) is to maintain the human body in a state of thermoneutrality. The device is controlled by varying the inlet coolant temperature and coolant mass flow rate. The differential equations of the model are approximated by a set of algebraic equations which result from the application of the explicit forward finite difference method to the differential equations. The integrated human thermal system is simulated for a variety of combinations of the inlet coolant temperature, coolant mass flow rate, and metabolic rates.

PAN AIR: A Computer Program for Predicting Subsonic or Supersonic Linear Potential Flows About Arbitrary Configurations Using a Higher Order Panel Method. Volume 1; Theory Document (Version 1.1)

NASA Technical Reports Server (NTRS)

Magnus, Alfred E.; Epton, Michael A.

1981-01-01

An outline of the derivation of the differential equation governing linear subsonic and supersonic potential flow is given. The use of Green's Theorem to obtain an integral equation over the boundary surface is discussed. The engineering techniques incorporated in the PAN AIR (Panel Aerodynamics) program (a discretization method which solves the integral equation for arbitrary first order boundary conditions) are then discussed in detail. Items discussed include the construction of the compressibility transformations, splining techniques, imposition of the boundary conditions, influence coefficient computation (including the concept of the finite part of an integral), computation of pressure coefficients, and computation of forces and moments.

Solving Modal Equations of Motion with Initial Conditions Using MSC/NASTRAN DMAP. Part 2; Coupled Versus Uncoupled Integration

NASA Technical Reports Server (NTRS)

Barnett, Alan R.; Ibrahim, Omar M.; Abdallah, Ayman A.; Sullivan, Timothy L.

1993-01-01

By utilizing MSC/NASTRAN DMAP (Direct Matrix Abstraction Program) in an existing NASA Lewis Research Center coupled loads methodology, solving modal equations of motion with initial conditions is possible using either coupled (Newmark-Beta) or uncoupled (exact mode superposition) integration available within module TRD1. Both the coupled and newly developed exact mode superposition methods have been used to perform transient analyses of various space systems. However, experience has shown that in most cases, significant time savings are realized when the equations of motion are integrated using the uncoupled solver instead of the coupled solver. Through the results of a real-world engineering analysis, advantages of using the exact mode superposition methodology are illustrated.

Hagedorn Temperature of AdS5/CFT4 via Integrability

NASA Astrophysics Data System (ADS)

Harmark, Troels; Wilhelm, Matthias

2018-02-01

We establish a framework for calculating the Hagedorn temperature of AdS5/CFT4 via integrability. Concretely, we derive the thermodynamic Bethe ansatz equations that yield the Hagedorn temperature of planar N =4 super Yang-Mills theory at any value of the 't Hooft coupling. We solve these equations perturbatively at weak coupling via the associated Y system, confirming the known results at tree level and one-loop order as well as deriving the previously unknown two-loop Hagedorn temperature. Finally, we comment on solving the equations at finite coupling.

Bilinear, trilinear forms, and exact solution of certain fourth order integrable difference equations

NASA Astrophysics Data System (ADS)

Sahadevan, R.; Rajakumar, S.

2008-03-01

A systematic investigation of finding bilinear or trilinear representations of fourth order autonomous ordinary difference equation, x(n +4)=F(x(n),x(n+1),x(n+2),x(n+3)) or xn +4=F(xn,xn +1,xn +2,xn +3), is made. As an illustration, we consider fourth order symplectic integrable difference equations reported by [Capel and Sahadevan, Physica A 289, 86 (2001)] and derived their bilinear or trilinear forms. Also, it is shown that the obtained bilinear representations admit exact solution of rational form.

On the solution of integral equations with a generalized Cauchy kernel

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1987-01-01

A numerical technique is developed analytically to solve a class of singular integral equations occurring in mixed boundary-value problems for nonhomogeneous elastic media with discontinuities. The approach of Kaya and Erdogan (1987) is extended to treat equations with generalized Cauchy kernels, reformulating the boundary-value problems in terms of potentials as the unknown functions. The numerical implementation of the solution is discussed, and results for an epoxy-Al plate with a crack terminating at the interface and loading normal to the crack are presented in tables.

Singularity Preserving Numerical Methods for Boundary Integral Equations

NASA Technical Reports Server (NTRS)

Kaneko, Hideaki (Principal Investigator)

1996-01-01

In the past twelve months (May 8, 1995 - May 8, 1996), under the cooperative agreement with Division of Multidisciplinary Optimization at NASA Langley, we have accomplished the following five projects: a note on the finite element method with singular basis functions; numerical quadrature for weakly singular integrals; superconvergence of degenerate kernel method; superconvergence of the iterated collocation method for Hammersteion equations; and singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel. This final report consists of five papers describing these projects. Each project is preceeded by a brief abstract.

Analytical methods for solving boundary value heat conduction problems with heterogeneous boundary conditions on lines. I - Review

NASA Astrophysics Data System (ADS)

Kartashov, E. M.

1986-10-01

Analytical methods for solving boundary value problems for the heat conduction equation with heterogeneous boundary conditions on lines, on a plane, and in space are briefly reviewed. In particular, the method of dual integral equations and summator series is examined with reference to stationary processes. A table of principal solutions to dual integral equations and pair summator series is proposed which presents the known results in a systematic manner. Newly obtained results are presented in addition to the known ones.

A New Scheme of Integrability for (bi)Hamiltonian PDE

NASA Astrophysics Data System (ADS)

De Sole, Alberto; Kac, Victor G.; Valeri, Daniele

2016-10-01

We develop a new method for constructing integrable Hamiltonian hierarchies of Lax type equations, which combines the fractional powers technique of Gelfand and Dickey, and the classical Hamiltonian reduction technique of Drinfeld and Sokolov. The method is based on the notion of an Adler type matrix pseudodifferential operator and the notion of a generalized quasideterminant. We also introduce the notion of a dispersionless Adler type series, which is applied to the study of dispersionless Hamiltonian equations. Non-commutative Hamiltonian equations are discussed in this framework as well.

On time discretizations for spectral methods. [numerical integration of Fourier and Chebyshev methods for dynamic partial differential equations

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Turkel, E.

1980-01-01

New methods are introduced for the time integration of the Fourier and Chebyshev methods of solution for dynamic differential equations. These methods are unconditionally stable, even though no matrix inversions are required. Time steps are chosen by accuracy requirements alone. For the Fourier method both leapfrog and Runge-Kutta methods are considered. For the Chebyshev method only Runge-Kutta schemes are tested. Numerical calculations are presented to verify the analytic results. Applications to the shallow water equations are presented.

On the existence of mosaic-skeleton approximations for discrete analogues of integral operators

NASA Astrophysics Data System (ADS)

Kashirin, A. A.; Taltykina, M. Yu.

2017-09-01

Exterior three-dimensional Dirichlet problems for the Laplace and Helmholtz equations are considered. By applying methods of potential theory, they are reduced to equivalent Fredholm boundary integral equations of the first kind, for which discrete analogues, i.e., systems of linear algebraic equations (SLAEs) are constructed. The existence of mosaic-skeleton approximations for the matrices of the indicated systems is proved. These approximations make it possible to reduce the computational complexity of an iterative solution of the SLAEs. Numerical experiments estimating the capabilities of the proposed approach are described.

A method for exponential propagation of large systems of stiff nonlinear differential equations

NASA Technical Reports Server (NTRS)

Friesner, Richard A.; Tuckerman, Laurette S.; Dornblaser, Bright C.; Russo, Thomas V.

1989-01-01

A new time integrator for large, stiff systems of linear and nonlinear coupled differential equations is described. For linear systems, the method consists of forming a small (5-15-term) Krylov space using the Jacobian of the system and carrying out exact exponential propagation within this space. Nonlinear corrections are incorporated via a convolution integral formalism; the integral is evaluated via approximate Krylov methods as well. Gains in efficiency ranging from factors of 2 to 30 are demonstrated for several test problems as compared to a forward Euler scheme and to the integration package LSODE.

Differential equations driven by rough paths with jumps

NASA Astrophysics Data System (ADS)

Friz, Peter K.; Zhang, Huilin

2018-05-01

We develop the rough path counterpart of Itô stochastic integration and differential equations driven by general semimartingales. This significantly enlarges the classes of (Itô/forward) stochastic differential equations treatable with pathwise methods. A number of applications are discussed.

The integration of the motion equations of low-orbiting earth satellites using Taylor's method

NASA Astrophysics Data System (ADS)

Krivov, A. V.; Chernysheva, N. A.

1990-04-01

A method for the numerical integration of the equations of motion for a satellite is proposed, taking the earth's oblateness and atmospheric drag into account. The method is based on Taylor's representation of the solution to the corresponding polynomial system. The algorithm for choosing the integration step and error estimation is constructed. The method is realized as a subrouting package. The method is applied to a low-orbiting earth satellite and the results are compared with those obtained using Everhart's method.

Numerical solution of linear and nonlinear Fredholm integral equations by using weighted mean-value theorem.

PubMed

Altürk, Ahmet

2016-01-01

Mean value theorems for both derivatives and integrals are very useful tools in mathematics. They can be used to obtain very important inequalities and to prove basic theorems of mathematical analysis. In this article, a semi-analytical method that is based on weighted mean-value theorem for obtaining solutions for a wide class of Fredholm integral equations of the second kind is introduced. Illustrative examples are provided to show the significant advantage of the proposed method over some existing techniques.

On the boundedness and integration of non-oscillatory solutions of certain linear differential equations of second order.

PubMed

Tunç, Cemil; Tunç, Osman

2016-01-01

In this paper, certain system of linear homogeneous differential equations of second-order is considered. By using integral inequalities, some new criteria for bounded and [Formula: see text]-solutions, upper bounds for values of improper integrals of the solutions and their derivatives are established to the considered system. The obtained results in this paper are considered as extension to the results obtained by Kroopnick (2014) [1]. An example is given to illustrate the obtained results.

On the extraction of pressure fields from PIV velocity measurements in turbines

NASA Astrophysics Data System (ADS)

Villegas, Arturo; Diez, Fancisco J.

2012-11-01

In this study, the pressure field for a water turbine is derived from particle image velocimetry (PIV) measurements. Measurements are performed in a recirculating water channel facility. The PIV measurements include calculating the tangential and axial forces applied to the turbine by solving the integral momentum equation around the airfoil. The results are compared with the forces obtained from the Blade Element Momentum theory (BEMT). Forces are calculated by using three different methods. In the first method, the pressure fields are obtained from PIV velocity fields by solving the Poisson equation. The boundary conditions are obtained from the Navier-Stokes momentum equations. In the second method, the pressure at the boundaries is determined by spatial integration of the pressure gradients along the boundaries. In the third method, applicable only to incompressible, inviscid, irrotational, and steady flow, the pressure is calculated using the Bernoulli equation. This approximated pressure is known to be accurate far from the airfoil and outside of the wake for steady flows. Additionally, the pressure is used to solve for the force from the integral momentum equation on the blade. From the three methods proposed to solve for pressure and forces from PIV measurements, the first one, which is solved by using the Poisson equation, provides the best match to the BEM theory calculations.

Opening of an interface flaw in a layered elastic half-plane under compressive loading

NASA Technical Reports Server (NTRS)

Kennedy, J. M.; Fichter, W. B.; Goree, J. G.

1984-01-01

A static analysis is given of the problem of an elastic layer perfectly bonded, except for a frictionless interface crack, to a dissimilar elastic half-plane. The free surface of the layer is loaded by a finite pressure distribution directly over the crack. The problem is formulated using the two dimensional linear elasticity equations. Using Fourier transforms, the governing equations are converted to a pair of coupled singular integral equations. The integral equations are reduced to a set of simultaneous algebraic equations by expanding the unknown functions in a series of Jacobi polynomials and then evaluating the singular Cauchy-type integrals. The resulting equations are found to be ill-conditioned and, consequently, are solved in the least-squares sense. Results from the analysis show that, under a normal pressure distribution on the free surface of the layer and depending on the combination of geometric and material parameters, the ends of the crack can open. The resulting stresses at the crack-tips are singular, implying that crack growth is possible. The extent of the opening and the crack-top stress intensity factors depend on the width of the pressure distribution zone, the layer thickness, and the relative material properties of the layer and half-plane.

Some operational tools for solving fractional and higher integer order differential equations: A survey on their mutual relations

NASA Astrophysics Data System (ADS)

Kiryakova, Virginia S.

2012-11-01

The Laplace Transform (LT) serves as a basis of the Operational Calculus (OC), widely explored by engineers and applied scientists in solving mathematical models for their practical needs. This transform is closely related to the exponential and trigonometric functions (exp, cos, sin) and to the classical differentiation and integration operators, reducing them to simple algebraic operations. Thus, the classical LT and the OC give useful tool to handle differential equations and systems with constant coefficients. Several generalizations of the LT have been introduced to allow solving, in a similar way, of differential equations with variable coefficients and of higher integer orders, as well as of fractional (arbitrary non-integer) orders. Note that fractional order mathematical models are recently widely used to describe better various systems and phenomena of the real world. This paper surveys briefly some of our results on classes of such integral transforms, that can be obtained from the LT by means of "transmutations" which are operators of the generalized fractional calculus (GFC). On the list of these Laplace-type integral transforms, we consider the Borel-Dzrbashjan, Meijer, Krätzel, Obrechkoff, generalized Obrechkoff (multi-index Borel-Dzrbashjan) transforms, etc. All of them are G- and H-integral transforms of convolutional type, having as kernels Meijer's G- or Fox's H-functions. Besides, some special functions (also being G- and H-functions), among them - the generalized Bessel-type and Mittag-Leffler (M-L) type functions, are generating Gel'fond-Leontiev (G-L) operators of generalized differentiation and integration, which happen to be also operators of GFC. Our integral transforms have operational properties analogous to those of the LT - they do algebrize the G-L generalized integrations and differentiations, and thus can serve for solving wide classes of differential equations with variable coefficients of arbitrary, including non-integer order. Throughout the survey, we illustrate the parallels in the relationships: Laplace type integral transforms - special functions as kernels - operators of generalized integration and differentiation generated by special functions - special functions as solutions of related differential equations. The role of the so-called Special Functions of Fractional Calculus is emphasized.

Square-integrable solutions to a family of nonlinear schrödinger equations from nonlinear quantum theory

NASA Astrophysics Data System (ADS)

Teismann, Holger

2005-10-01

We consider nonlinear Schrödinger equations which have been proposed as fundamental equations of nonlinear quantum theories. The equations are singular in that the wave function ψ appears in the denominator of rational expressions. To avoid the problem of zeros of ψ it is natural to make the ansatz ψ = e ν. This ansatz, however, conflicts with the—physically motivated—requirement that the solutions ψ be square integrable. We show that this conflict can be resolved by considering an unusual function space whose definition involves the derivative ∇ ν of ν. This function space turns out to be dense subset of L2 and the equations can be solved in the L2-sense (as desired) by first solving an evolutionary system for ∇ ν and then transforming back to ψ.

Rational first integrals of geodesic equations and generalised hidden symmetries

NASA Astrophysics Data System (ADS)

Aoki, Arata; Houri, Tsuyoshi; Tomoda, Kentaro

2016-10-01

We discuss novel generalisations of Killing tensors, which are introduced by considering rational first integrals of geodesic equations. We introduce the notion of inconstructible generalised Killing tensors, which cannot be constructed from ordinary Killing tensors. Moreover, we introduce inconstructible rational first integrals, which are constructed from inconstructible generalised Killing tensors, and provide a method for checking the inconstructibility of a rational first integral. Using the method, we show that the rational first integral of the Collinson-O’Donnell solution is not inconstructible. We also provide several examples of metrics admitting an inconstructible rational first integral in two and four-dimensions, by using the Maciejewski-Przybylska system. Furthermore, we attempt to generalise other hidden symmetries such as Killing-Yano tensors.

Variational objective analysis for cyclone studies

NASA Technical Reports Server (NTRS)

Achtemeier, Gary L.

1989-01-01

Significant accomplishments during 1987 to 1988 are summarized with regard to each of the major project components. Model 1 requires satisfaction of two nonlinear horizontal momentum equations, the integrated continuity equation, and the hydrostatic equation. Model 2 requires satisfaction of model 1 plus the thermodynamic equation for a dry atmosphere. Model 3 requires satisfaction of model 2 plus the radiative transfer equation. Model 4 requires satisfaction of model 3 plus a moisture conservation equation and a parameterization for moist processes.

Symbolic programming language in molecular multicenter integral problem

NASA Astrophysics Data System (ADS)

Safouhi, Hassan; Bouferguene, Ahmed

It is well known that in any ab initio molecular orbital (MO) calculation, the major task involves the computation of molecular integrals, among which the computation of three-center nuclear attraction and Coulomb integrals is the most frequently encountered. As the molecular system becomes larger, computation of these integrals becomes one of the most laborious and time-consuming steps in molecular systems calculation. Improvement of the computational methods of molecular integrals would be indispensable to further development in computational studies of large molecular systems. To develop fast and accurate algorithms for the numerical evaluation of these integrals over B functions, we used nonlinear transformations for improving convergence of highly oscillatory integrals. These methods form the basis of new methods for solving various problems that were unsolvable otherwise and have many applications as well. To apply these nonlinear transformations, the integrands should satisfy linear differential equations with coefficients having asymptotic power series in the sense of Poincaré, which in their turn should satisfy some limit conditions. These differential equations are very difficult to obtain explicitly. In the case of molecular integrals, we used a symbolic programming language (MAPLE) to demonstrate that all the conditions required to apply these nonlinear transformation methods are satisfied. Differential equations are obtained explicitly, allowing us to demonstrate that the limit conditions are also satisfied.

Time step rescaling recovers continuous-time dynamical properties for discrete-time Langevin integration of nonequilibrium systems.

PubMed

Sivak, David A; Chodera, John D; Crooks, Gavin E

2014-06-19

When simulating molecular systems using deterministic equations of motion (e.g., Newtonian dynamics), such equations are generally numerically integrated according to a well-developed set of algorithms that share commonly agreed-upon desirable properties. However, for stochastic equations of motion (e.g., Langevin dynamics), there is still broad disagreement over which integration algorithms are most appropriate. While multiple desiderata have been proposed throughout the literature, consensus on which criteria are important is absent, and no published integration scheme satisfies all desiderata simultaneously. Additional nontrivial complications stem from simulating systems driven out of equilibrium using existing stochastic integration schemes in conjunction with recently developed nonequilibrium fluctuation theorems. Here, we examine a family of discrete time integration schemes for Langevin dynamics, assessing how each member satisfies a variety of desiderata that have been enumerated in prior efforts to construct suitable Langevin integrators. We show that the incorporation of a novel time step rescaling in the deterministic updates of position and velocity can correct a number of dynamical defects in these integrators. Finally, we identify a particular splitting (related to the velocity Verlet discretization) that has essentially universally appropriate properties for the simulation of Langevin dynamics for molecular systems in equilibrium, nonequilibrium, and path sampling contexts.

Analysis of R&M Technology Improvement Rationale for Maintainability Index Models.

DTIC Science & Technology

1980-10-01

Pon" I . 2-57404/OR-52553 NONOI CIITSAALGUSE 4. T171;9 rid Sie) S. Type or REPORT & PERIOD COVERED Analysis of R &M Technology...77/02/04 Single Element Structure Systems o.. 58 iv [ I .. . . ., -... ,. - . .. .111l . ... . . ... . ... r . .... ,-.. . .... .. I . TABLE OF CONTENTS...reasonable and whether the Reliability and Maintainability ( R &M) design ’features stated in a contractor’s proposal could result in a 34% reduction i

General Purpose Electronic Test Equipment (GPETE) Acquisition Considerations for Automated Calibration.

DTIC Science & Technology

1983-06-01

of this repat) U7NCLASSIFIED ISo. OECLASSI PICATION/i DOWNGRADING SCHEDULE IS, OIS? UUTION STATEMENT (fo Sie ftepoe) Approved for public release...26 1. GPETS Initial Outfitt ng (GINO) ..... 26 2. GPETE End Item Replacement (GEIR) * . . 27 D. GINO REQUIREMENTS DETERMINYATION .. . . . 28 E...interval of a sample of 305 GPETE items increased from 8.8 tc 13.6 months. The estimated annual savings resui- ng from this increase was 18.000

Quantum spectral curve for ( q, t)-matrix model

NASA Astrophysics Data System (ADS)

Zenkevich, Yegor

2018-02-01

We derive quantum spectral curve equation for ( q, t)-matrix model, which turns out to be a certain difference equation. We show that in Nekrasov-Shatashvili limit this equation reproduces the Baxter TQ equation for the quantum XXZ spin chain. This chain is spectral dual to the Seiberg-Witten integrable system associated with the AGT dual gauge theory.

A New Factorisation of a General Second Order Differential Equation

ERIC Educational Resources Information Center

Clegg, Janet

2006-01-01

A factorisation of a general second order ordinary differential equation is introduced from which the full solution to the equation can be obtained by performing two integrations. The method is compared with traditional methods for solving these type of equations. It is shown how the Green's function can be derived directly from the factorisation…

Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations That Arise from Nonlinear Two-Point Boundary Value Problems

NASA Technical Reports Server (NTRS)

Sidi, Avram; Pennline, James A.

1999-01-01

In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + definite integral of g(x, t)F(t,y(t))dt with limits between 0 and 1,0 less than or equal to x les than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integral equations arise, e.g., when one applied Green's function techniques to nonlinear two-point boundary value problems of the form y "(x) =f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and y(l) = y(sub l), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trepezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal rule, thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.

Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations that Arise from Nonlinear Two-Point Boundary Value Problems

NASA Technical Reports Server (NTRS)

Sidi, Avram; Pennline, James A.

1999-01-01

In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + integral(0 to 1) g(x,t) F(t, y(t)) dt, 0 less than or equal to x less than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integrals equations arise, e.g., when one applies Green's function techniques to nonlinear two-point boundary value problems of the form U''(x) = f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and g(l) = y(sub 1), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trapezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.

Modular Expression Language for Ordinary Differential Equation Editing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blake, Robert C.

MELODEEis a system for describing systems of initial value problem ordinary differential equations, and a compiler for the language that produces optimized code to integrate the differential equations. Features include rational polynomial approximation for expensive functions and automatic differentiation for symbolic jacobians

Volume integrals associated with the inhomogeneous Helmholtz equation. Part 1: Ellipsoidal region

NASA Technical Reports Server (NTRS)

Fu, L. S.; Mura, T.

1983-01-01

Problems of wave phenomena in fields of acoustics, electromagnetics and elasticity are often reduced to an integration of the inhomogeneous Helmholtz equation. Results are presented for volume integrals associated with the Helmholtz operator, nabla(2) to alpha(2), for the case of an ellipsoidal region. By using appropriate Taylor series expansions and multinomial theorem, these volume integrals are obtained in series form for regions r 4' and r r', where r and r' are distances from the origin to the point of observation and source, respectively. Derivatives of these integrals are easily evaluated. When the wave number approaches zero, the results reduce directly to the potentials of variable densities.

A T Matrix Method Based upon Scalar Basis Functions

NASA Technical Reports Server (NTRS)

Mackowski, D.W.; Kahnert, F. M.; Mishchenko, Michael I.

2013-01-01

A surface integral formulation is developed for the T matrix of a homogenous and isotropic particle of arbitrary shape, which employs scalar basis functions represented by the translation matrix elements of the vector spherical wave functions. The formulation begins with the volume integral equation for scattering by the particle, which is transformed so that the vector and dyadic components in the equation are replaced with associated dipole and multipole level scalar harmonic wave functions. The approach leads to a volume integral formulation for the T matrix, which can be extended, by use of Green's identities, to the surface integral formulation. The result is shown to be equivalent to the traditional surface integral formulas based on the VSWF basis.

Cauchy-Jost function and hierarchy of integrable equations

NASA Astrophysics Data System (ADS)

Boiti, M.; Pempinelli, F.; Pogrebkov, A. K.

2015-11-01

We describe the properties of the Cauchy-Jost (also known as Cauchy-Baker-Akhiezer) function of the Kadomtsev-Petviashvili-II equation. Using the bar partial -method, we show that for this function, all equations of the Kadomtsev-Petviashvili-II hierarchy are given in a compact and explicit form, including equations for the Cauchy-Jost function itself, time evolutions of the Jost solutions, and evolutions of the potential of the heat equation.

Kinetic Equation for a Soliton Gas and Its Hydrodynamic Reductions

NASA Astrophysics Data System (ADS)

El, G. A.; Kamchatnov, A. M.; Pavlov, M. V.; Zykov, S. A.

2011-04-01

We introduce and study a new class of kinetic equations, which arise in the description of nonequilibrium macroscopic dynamics of soliton gases with elastic collisions between solitons. These equations represent nonlinear integro-differential systems and have a novel structure, which we investigate by studying in detail the class of N-component `cold-gas' hydrodynamic reductions. We prove that these reductions represent integrable linearly degenerate hydrodynamic type systems for arbitrary N which is a strong evidence in favour of integrability of the full kinetic equation. We derive compact explicit representations for the Riemann invariants and characteristic velocities of the hydrodynamic reductions in terms of the `cold-gas' component densities and construct a number of exact solutions having special properties (quasiperiodic, self-similar). Hydrodynamic symmetries are then derived and investigated. The obtained results shed light on the structure of a continuum limit for a large class of integrable systems of hydrodynamic type and are also relevant to the description of turbulent motion in conservative compressible flows.

Integrated force method versus displacement method for finite element analysis

NASA Technical Reports Server (NTRS)

Patnaik, S. N.; Berke, L.; Gallagher, R. H.

1991-01-01

A novel formulation termed the integrated force method (IFM) has been developed in recent years for analyzing structures. In this method all the internal forces are taken as independent variables, and the system equilibrium equations (EEs) are integrated with the global compatibility conditions (CCs) to form the governing set of equations. In IFM the CCs are obtained from the strain formulation of St. Venant, and no choices of redundant load systems have to be made, in constrast to the standard force method (SFM). This property of IFM allows the generation of the governing equation to be automated straightforwardly, as it is in the popular stiffness method (SM). In this report IFM and SM are compared relative to the structure of their respective equations, their conditioning, required solution methods, overall computational requirements, and convergence properties as these factors influence the accuracy of the results. Overall, this new version of the force method produces more accurate results than the stiffness method for comparable computational cost.

A geometric viewpoint on generalized hydrodynamics

NASA Astrophysics Data System (ADS)

Doyon, Benjamin; Spohn, Herbert; Yoshimura, Takato

2018-01-01

Generalized hydrodynamics (GHD) is a large-scale theory for the dynamics of many-body integrable systems. It consists of an infinite set of conservation laws for quasi-particles traveling with effective ("dressed") velocities that depend on the local state. We show that these equations can be recast into a geometric dynamical problem. They are conservation equations with state-independent quasi-particle velocities, in a space equipped with a family of metrics, parametrized by the quasi-particles' type and speed, that depend on the local state. In the classical hard rod or soliton gas picture, these metrics measure the free length of space as perceived by quasi-particles; in the quantum picture, they weigh space with the density of states available to them. Using this geometric construction, we find a general solution to the initial value problem of GHD, in terms of a set of integral equations where time appears explicitly. These integral equations are solvable by iteration and provide an extremely efficient solution algorithm for GHD.

An efficient computational method for solving nonlinear stochastic Itô integral equations: Application for stochastic problems in physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heydari, M.H., E-mail: heydari@stu.yazd.ac.ir; The Laboratory of Quantum Information Processing, Yazd University, Yazd; Hooshmandasl, M.R., E-mail: hooshmandasl@yazd.ac.ir

Because of the nonlinearity, closed-form solutions of many important stochastic functional equations are virtually impossible to obtain. Thus, numerical solutions are a viable alternative. In this paper, a new computational method based on the generalized hat basis functions together with their stochastic operational matrix of Itô-integration is proposed for solving nonlinear stochastic Itô integral equations in large intervals. In the proposed method, a new technique for computing nonlinear terms in such problems is presented. The main advantage of the proposed method is that it transforms problems under consideration into nonlinear systems of algebraic equations which can be simply solved. Errormore » analysis of the proposed method is investigated and also the efficiency of this method is shown on some concrete examples. The obtained results reveal that the proposed method is very accurate and efficient. As two useful applications, the proposed method is applied to obtain approximate solutions of the stochastic population growth models and stochastic pendulum problem.« less

Integrated force method versus displacement method for finite element analysis

NASA Technical Reports Server (NTRS)

Patnaik, Surya N.; Berke, Laszlo; Gallagher, Richard H.

1990-01-01

A novel formulation termed the integrated force method (IFM) has been developed in recent years for analyzing structures. In this method all the internal forces are taken as independent variables, and the system equilibrium equations (EE's) are integrated with the global compatibility conditions (CC's) to form the governing set of equations. In IFM the CC's are obtained from the strain formulation of St. Venant, and no choices of redundant load systems have to be made, in constrast to the standard force method (SFM). This property of IFM allows the generation of the governing equation to be automated straightforwardly, as it is in the popular stiffness method (SM). In this report IFM and SM are compared relative to the structure of their respective equations, their conditioning, required solution methods, overall computational requirements, and convergence properties as these factors influence the accuracy of the results. Overall, this new version of the force method produces more accurate results than the stiffness method for comparable computational cost.

Equations on knot polynomials and 3d/5d duality

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mironov, A.; Morozov, A.; ITEP, Moscow

2012-09-24

We briefly review the current situation with various relations between knot/braid polynomials (Chern-Simons correlation functions), ordinary and extended, considered as functions of the representation and of the knot topology. These include linear skein relations, quadratic Plucker relations, as well as 'differential' and (quantum) A-polynomial structures. We pay a special attention to identity between the A-polynomial equations for knots and Baxter equations for quantum relativistic integrable systems, related through Seiberg-Witten theory to 5d super-Yang-Mills models and through the AGT relation to the q-Virasoro algebra. This identity is an important ingredient of emerging a 3d- 5d generalization of the AGT relation. Themore » shape of the Baxter equation (including the values of coefficients) depend on the choice of the knot/braid. Thus, like the case of KP integrability, where (some, so far torus) knots parameterize particular points of the Universal Grassmannian, in this relation they parameterize particular points in the moduli space of many-body integrable systems of relativistic type.« less

Orientation-dependent integral equation theory for a two-dimensional model of water

NASA Astrophysics Data System (ADS)

Urbič, T.; Vlachy, V.; Kalyuzhnyi, Yu. V.; Dill, K. A.

2003-03-01

We develop an integral equation theory that applies to strongly associating orientation-dependent liquids, such as water. In an earlier treatment, we developed a Wertheim integral equation theory (IET) that we tested against NPT Monte Carlo simulations of the two-dimensional Mercedes Benz model of water. The main approximation in the earlier calculation was an orientational averaging in the multidensity Ornstein-Zernike equation. Here we improve the theory by explicit introduction of an orientation dependence in the IET, based upon expanding the two-particle angular correlation function in orthogonal basis functions. We find that the new orientation-dependent IET (ODIET) yields a considerable improvement of the predicted structure of water, when compared to the Monte Carlo simulations. In particular, ODIET predicts more long-range order than the original IET, with hexagonal symmetry, as expected for the hydrogen bonded ice in this model. The new theoretical approximation still errs in some subtle properties; for example, it does not predict liquid water's density maximum with temperature or the negative thermal expansion coefficient.

Solution of the classical Yang-Baxter equation with an exotic symmetry, and integrability of a multi-species boson tunnelling model

NASA Astrophysics Data System (ADS)

Links, Jon

2017-03-01

Solutions of the classical Yang-Baxter equation provide a systematic method to construct integrable quantum systems in an algebraic manner. A Lie algebra can be associated with any solution of the classical Yang-Baxter equation, from which commuting transfer matrices may be constructed. This procedure is reviewed, specifically for solutions without skew-symmetry. A particular solution with an exotic symmetry is identified, which is not obtained as a limiting expansion of the usual Yang-Baxter equation. This solution facilitates the construction of commuting transfer matrices which will be used to establish the integrability of a multi-species boson tunnelling model. The model generalises the well-known two-site Bose-Hubbard model, to which it reduces in the one-species limit. Due to the lack of an apparent reference state, application of the algebraic Bethe Ansatz to solve the model is prohibitive. Instead, the Bethe Ansatz solution is obtained by the use of operator identities and tensor product decompositions.