Saha Aparna

Indian Academy of Sciences (India)

Home; Journals; Pramana – Journal of Physics. Saha Aparna. Articles written in Pramana – Journal of Physics. Volume 86 Issue 4 April 2016 pp 861-871 Regular. Ionization of Rydberg atoms by the kicks of half-cycle pulses · Chatterjee Supriya Saha Aparna Talukdar B · More Details Abstract Fulltext PDF. We present a ...

S SAHA

Indian Academy of Sciences (India)

Home; Journals; Sadhana. S SAHA. Articles written in Sadhana. Volume 42 Issue 9 September 2017 pp 1459-1471. Influence of yielding base and rigid base on propagation of Rayleigh-type wave in a viscoelastic layer of Voigt type · S SAHA A CHATTOPADHYAY K C MISTRI A K SINGH · More Details Abstract Fulltext PDF.

S Saha

Indian Academy of Sciences (India)

Home; Journals; Sadhana. S Saha. Articles written in Sadhana. Volume 27 Issue 6 December 2002 pp 613-630. Reflection of quasi-P and quasi-SV waves at the free and rigid boundaries of a fibre-reinforced medium · A Chattopadhyay R L K Venkateswarlu S Saha · More Details Abstract Fulltext PDF. The propagation of ...

M N Saha

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education. M N Saha. Articles written in Resonance – Journal of Science Education. Volume 3 Issue 5 May 1998 pp 84-96 Classics. The Origin of Mass in Neutrons and Protons · M N Saha · More Details Fulltext PDF ...

Tanusri Saha-Dasgupta

Indian Academy of Sciences (India)

Email: tanusri@bose.res.in. Tanusri Saha-Dasgupta, SN Bose National Centre for Basic Sciences, Kolkata, elected to Fellowship in 2010. Saha-Dasgupta works in the area of computational condensed matter physics. She is a recipient of Swarnajayanti Fellowship, and the MRSI-ICSC Superconductivity & Materials Science ...

M Saha Sarkar

Indian Academy of Sciences (India)

Home; Journals; Pramana – Journal of Physics. M Saha Sarkar. Articles written in Pramana – Journal of Physics. Volume 57 Issue 1 July 2001 pp 165-169 Contributed Papers : Nuclear spectroscopy. Level structures ofMo – A comparative study · J M Chatterjee M Saha Sarkar S Bhattacharya P Banerjee S Sarkar R P Singh ...

Examination of the Validity of the Saha Equation in a Gas Discharge

Energy Technology Data Exchange (ETDEWEB)

Shaw, J. F.; Kruger, C. H.; Mitchner, M.; Viegas, J. R. [Stanford University, CA (United States)

1966-11-15

-Maxwellian distribution function with depleted tail, are considered. Under some conditions, either mechanism may produce a degree of ionization considerably different from that predicted by the Saha equation at the electron temperature. (author)

Validity of Saha's equation of thermal ionization for negatively charged spherical particles in complex plasmas in thermal equilibrium

International Nuclear Information System (INIS)

Sodha, M. S.; Mishra, S. K.

2011-01-01

The authors have discussed the validity of Saha's equation for the charging of negatively charged spherical particles in a complex plasma in thermal equilibrium, even when the tunneling of the electrons, through the potential energy barrier surrounding the particle is considered. It is seen that the validity requires the probability of tunneling of an electron through the potential energy barrier surrounding the particle to be independent of the direction (inside to outside and vice versa) or in other words the Born's approximation should be valid.

Extended use of a computation method for electrical conductivity-case of non-Saha-equilibrium plasmas

International Nuclear Information System (INIS)

Chen, R.L.W.

1981-01-01

The use of an equation obtained earlier for computing electrical conductivity may be extended to partially ionized gases which depart from the Saha equation, provided the electron velocity distributions do not deviate from the Maxwellian distribution. (author)

Meghnad Saha his life in science and politics

CERN Document Server

Naik, Pramod V

2017-01-01

This biography is a short yet comprehensive overview of the life of Meghnad Saha, the mastermind behind the frequently used Saha equations and a strong contributor to the foundation of science in India. The author explores the lesser known details behind the man who played a major role in building scientific institutions in India, developed the breakthrough theory of thermal ionization, and whose fervor about India’s rapid progress in science and technology, along with concern for uplifting his countrymen and optimizing resources, led him to eventually enter politics and identify the mismanagement of many programs of national importance to Parliament. This book is free of most academic technicalities, so that the reader with general scientific knowledge can read and understand it easily. One interested only in Saha’s contribution to physics can pick up just that part and read it. Conversely, the average reader may skip the technical chapters, and read the book without loss of continuity or generality to s...

Mr Bikash Sinha, Director of SAHA & VECC and Prof. Rolf Heuer, Director general of CERN, sign a collaboration agreements between SAHA (Saha Institute of Nuclear Physics), VECC (Variable Energy Cyclotron Centre), India and CERN ISOLDE.

CERN Multimedia

Maximilien Brice

2009-01-01

Mr Bikash Sinha, Director of SAHA & VECC and Prof. Rolf Heuer, Director general of CERN, sign a collaboration agreements between SAHA (Saha Institute of Nuclear Physics), VECC (Variable Energy Cyclotron Centre), India and CERN ISOLDE.

supradip saha

Indian Academy of Sciences (India)

Marker-assisted introgression of opaque2 allele for rapid conversion of elite hybrids into quality protein maize · FIROZ HOSSAIN VIGNESH MUTHUSAMY NEHA PANDEY ASHISH K. VISHWAKARMA AANCHAL BAVEJA RAJKUMAR U. ZUNJARE NEPOLEAN THIRUNAVUKKARASU SUPRADIP SAHA KANCHIKERI M.

nabanita saha

Indian Academy of Sciences (India)

Home; Journals; Bulletin of Materials Science. NABANITA SAHA. Articles written in Bulletin of Materials Science. Volume 41 Issue 2 April 2018 pp 55. Green synthesis of silver nanoparticles and biopolymer nanocomposites: a comparative study on physico-chemical, antimicrobial and anticancer activity · RAMASUBBA ...

ritabrata saha

Indian Academy of Sciences (India)

RITABRATA SAHA. Articles written in Indian Academy of Sciences Conference Series. Volume 1 Issue 1 December 2017 pp 67-75 Proceedings of the Conference on Perspectives in Nonlinear Dynamics - 2016. Flow dynamic study of a single-phase square NCL using recurrence plot and recurrence quantification.

sanjoy saha

Indian Academy of Sciences (India)

SANJOY SAHA. Articles written in Journal of Chemical Sciences. Volume 130 Issue 1 January 2018 pp 9. Physico-chemical characterization and biological studies of newly synthesized metal complexes of an Ionic liquid-supported Schiff base: 1-{2-[(2-hydroxy-5-bromobenzylidene)amino]ethyl}-3- ethylimidazolium ...

Dipankar Saha

Indian Academy of Sciences (India)

Home; Journals; Journal of Earth System Science. Dipankar Saha. Articles written in Journal of Earth System Science. Volume 123 Issue 6 August 2014 pp 1335-1347. Geomorphologic, stratigraphic and sedimentologic evidences of tectonic activity in Sone–Ganga alluvial tract in Middle Ganga Plain, India · Sudarsan Sahu ...

uttiyoarnab saha

Indian Academy of Sciences (India)

Home; Journals; Pramana – Journal of Physics. UTTIYOARNAB SAHA. Articles written in Pramana – Journal of Physics. Volume 90 Issue 4 April 2018 pp 46 Research Article. Neutron radiation damage studies in the structural materials of a 500 MWe fast breeder reactor using DPA cross-sections from ENDF/B-VII.1.

Quantitative evaluation of SIMS spectra including spectrum interpretation and Saha-Eggert correction

International Nuclear Information System (INIS)

Steiger, W.; Ruedenauer, F.G.

1978-01-01

A spectrum identification program is described, using a computer algorithm which solely relies on the natural isotopic abundances for identification of elemental, molecular and cluster ions. The thermodynamic approach to the quantitative interpretation of SIMS spectra, through the use of the Saha-Eggert equation, is discussed, and a computer program is outlined. (U.K.)

Sayanti Saha

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education. Sayanti Saha. Articles written in Resonance – Journal of Science Education. Volume 10 Issue 3 March 2005 pp 28-34 General Article. “That which we call a rose by any other name would smell as sweet”: How the Nose knows! - Nobel Prize in Physiology or ...

koushik saha

Indian Academy of Sciences (India)

Home; Journals; Journal of Chemical Sciences. KOUSHIK SAHA. Articles written in Journal of Chemical Sciences. Volume 128 Issue 7 July 2016 pp 1025-1032 Regular Article. Reactivity of [Cp*Mo(CO)₃Me] with chalcogenated borohydrides Li[BH₂E₃] and Li[BH₃EFc] (Cp* = (ŋ⁵-C₅Me₅); E = S, Se or Te; ...

Inhibition of multiple pathogenic pathways by histone deacetylase inhibitor SAHA in a corneal alkali-burn injury model

Science.gov (United States)

Li, Xinyu; Zhou, Qinbo; Hanus, Jakub; Anderson, Chastain; Zhang, Hongmei; Dellinger, Michael; Brekken, Rolf; Wang, Shusheng

2013-01-01

Neovascularization (NV) in the cornea is a major cause of vision impairment and corneal blindness. Hemangiogenesis and lymphangiogenesis induced by inflammation underlie the pathogenesis of corneal NV. The current mainstay treatment, corticosteroid, treats the inflammation associated with corneal NV, but is not satisfactory due to such side effects as cataract and the increase in intraocular pressure. It is imperative to develop a novel therapy that specifically targets the hemangiogenesis, lymphangiogenesis and inflammation pathways underlying corneal NV. Histone deacetylase inhibitors (HDACi) have been in clinical trials for cancer and other diseases. In particular, HDACi suberoylanilide hydroxamic acid (SAHA, vorinostat, Zolinza) has been approved by the FDA for the treatment of cutaneous T-cell lymphoma. The functional mechanism of SAHA in cancer and especially in corneal NV remains unclear. Here, we show that topical application of SAHA inhibits neovascularization in an alkali-burn corneal injury model. Mechanistically, SAHA inhibits corneal NV by repressing hemangiogenesis, inflammation pathways and previously overlooked lymphangiogenesis. Topical SAHA is well tolerated on the ocular surface. In addition, the potency of SAHA in corneal NV appears to be comparable to the current steroid therapy. SAHA may possess promising therapeutic potential in alkali-burn corneal injury and other inflammatory neovascularization disorders. PMID:23186311

subhas chandra saha

Indian Academy of Sciences (India)

Home; Journals; Sadhana. SUBHAS CHANDRA SAHA. Articles written in Sadhana. Volume 41 Issue 5 May 2016 pp 549-559. A comparative study of multiple regression analysis and back propagation neural network approaches on plain carbon steel in submerged-arc welding · ABHIJIT SARKAR PRASENJIT DEY R N ...

The ionisation equation in a relativistic gas

International Nuclear Information System (INIS)

Kichenassamy, S.; Krikorian, R.A.

1983-01-01

By deriving the relativistic form of the ionisation equation for a perfect gas it is shown that the usual Saha equation is valid to 3% for temperatures below one hundred million Kelvin. Beyond 10 9 K, the regular Saha equation is seriously incorrect and a relativistic distribution function for electrons must be taken into account. Approximate forms are derived when only the electrons are relativistic (appropriate up to 10 12 K) and also for the ultrarelativistic case (temperatures greater than 10 15 K). (author)

Ionization equilibrium and equation of state in the solar interior

International Nuclear Information System (INIS)

Rogers, F.J.

1984-01-01

Many-body formulations of the equations of state are restated as a set of Saha-like equations. It is shown that the resulting equations are unique and convergent. These equations are similar to the usual Saha equations to the order of the Debye-Huckel theory. Higher order corrections, however, require a more general formulation. It is demonstrated that the positive free energy resulting from the interaction of unscreened particles in high orbits depletes the occupation of these states, without the introduction of shifted energy levels

EFFECTS OF HISTONE DEACETYLASE INHIBITOR, SAHA, ON EFFECTOR AND FOXP3+ REGULATORY T CELLS IN RHESUS MACAQUES

Science.gov (United States)

Johnson, Jennifer; Pahuja, Anil; Graham, Melanie; Hering, Bernhard; Hancock, Wayne W.; Pratima, Bansal-Pakala

2008-01-01

SAHA, a histone deacetylase inhibitor (HDACi), is clinically approved for treatment of cutaneous T-cell lymphoma. Although the exact underlying mechanisms are unknown, HDACi arrest the cell cycle in rapidly proliferating tumor cells and promote their apoptosis. HDACi were also recently shown to enhance the production and suppressive functions of Foxp3+ regulatory T (Treg) cells in rodents, leading us to begin to investigate the actions of HDACi on rhesus monkey T cells for the sake of potential preclinical applications. In this study, we show that SAHA inhibits polyclonal activation and proliferation of rhesus T cells and that the anti-proliferative effects are due to inhibition of T effector (Teff) cells and enhancement of Treg cells. Cryopreserved rhesus macaque splenocytes were CFSE labeled, stimulated with anti-CD3/anti-CD28 and cultured for 5 days in the presence of varying concentrations of SAHA. Samples were then co-stained to evaluate CD4 and CD8 expression. 10 and 5μM concentrations of SAHA were toxic to splenocytes. Proliferation was inhibited by 57% in CD4 cells and 47% in CD8 cells when unseparated splenocytes were cultured with 3 μM SAHA. Effector cells alone showed a decreased inhibition to proliferation when cultured with 3 μM and 1 μM SAHA when compared to Teff plus Treg cells. Our data suggest that SAHA can be used as part of an immunosuppressive protocol to enhance graft survival by limiting Teff cell proliferation as well as increasing Treg cells, thereby promoting tolerance. PMID:18374101

On the Saha Ionization Equation

Indian Academy of Sciences (India)

the equation in terms of rate theory. ... that the said theory is said to be the harbinger of modern astro- ... Parichay (An Introduction to the Universe). Tagore ..... where |e| is the magnitude of the electron's charge and E is the electric field intensity ...

The equation of state and ionization equilibrium of dense aluminum plasma with conductivity verification

International Nuclear Information System (INIS)

Wang, Kun; Shi, Zongqian; Shi, Yuanjie; Bai, Jun; Wu, Jian; Jia, Shenli

2015-01-01

The equation of state, ionization equilibrium, and conductivity are the most important parameters for investigation of dense plasma. The equation of state is calculated with the non-ideal effects taken into consideration. The electron chemical potential and pressure, which are commonly used thermodynamic quantities, are calculated by the non-ideal free energy and compared with results of a semi-empirical equation of state based on Thomas-Fermi-Kirzhnits model. The lowering of ionization potential, which is a crucial factor in the calculation of non-ideal Saha equation, is settled according to the non-ideal free energy. The full coupled non-ideal Saha equation is applied to describe the ionization equilibrium of dense plasma. The conductivity calculated by the Lee-More-Desjarlais model combined with non-ideal Saha equation is compared with experimental data. It provides a possible approach to verify the accuracy of the equation of state and ionization equilibrium

The HDAC inhibitor SAHA does not rescue CFTR membrane expression in Cystic Fibrosis.

Science.gov (United States)

Bergougnoux, Anne; Petit, Aurélie; Knabe, Lucie; Bribes, Estelle; Chiron, Raphaël; De Sario, Albertina; Claustres, Mireille; Molinari, Nicolas; Vachier, Isabelle; Taulan-Cadars, Magali; Bourdin, Arnaud

2017-07-01

The development of suitable Cystic Fibrosis (CF) models for preclinical bench tests of therapeutic candidates is challenging. Indeed, the validation of molecules to rescue the p.Phe508del-CFTR channel (encoded by the Cystic Fibrosis Transmembrane conductance Regulator gene carrying the p.Phe508del mutation) requires taking into account their overall effects on the epithelium. Suberoylanilide Hydroxamic Acid (SAHA), a histone deacetylase inhibitor (HDACi), was previously shown to be a CFTR corrector via proteostasis modulation in CFTR-deficient immortalized cells. Here, we tested SAHA effects on goblet cell metaplasia using an ex vivo model based on the air-liquid interface (ALI) culture of differentiated airway epithelial cells obtained by nasal scraping from CF patients and healthy controls. Ex vivo epithelium grew successfully in ALI cultures with significant rise in the expression of CFTR and of markers of airway epithelial differentiation compared to monolayer cell culture. SAHA decreased CFTR transcript and protein levels in CF and non-CF epithelia. Whereas SAHA induced lysine hyperacetylation, it did not change histone modifications at the CFTR promoter. SAHA reduced MUC5AC and MUC5B expression and inhibited goblet epithelial cell differentiation. Similar effects were obtained in CF and non-CF epithelia. All the effects were fully reversible within five days from SAHA withdrawal. We conclude that, ex vivo, SAHA modulate the structure of airway epithelia without specific effect on CFTR gene and protein suggesting that HDACi cannot be useful for CF treatment. Copyright © 2017. Published by Elsevier Ltd.

SAHA-induced TRAIL-sensitisation of Multiple Myeloma cells is enhanced in 3D cell culture.

Science.gov (United States)

Arhoma, A; Chantry, A D; Haywood-Small, S L; Cross, N A

2017-11-15

Multiple Myeloma (MM) is currently incurable despite many novel therapies. Tumour Necrosis Factor-Related Apoptosis-Inducing Ligand (TRAIL) is a potential anti-tumour agent although effects as a single agent are limited. In this study, we investigated whether the Histone Deacetylase (HDAC) inhibitor SAHA can enhance TRAIL-induced apoptosis and target TRAIL resistance in both suspension culture, and 3D cell culture as a model of disseminated MM lesions that form in bone. The effects of SAHA and/or TRAIL in 6 Multiple Myeloma cell lines were assessed in both suspension cultures and in an Alginate-based 3D cell culture model. The effect of SAHA and/or TRAIL was assessed on apoptosis by assessment of nuclear morphology using Hoechst 33342/Propidium Iodide staining. Viable cell number was assessed by CellTiter-Glo luminescence assay, Caspase-8 and -9 activities were measured by Caspase-Glo™ assay kit. TRAIL-resistant cells were generated by culture of RPMI 8226 and NCI-H929 by acute exposure to TRAIL followed by selection of TRAIL-resistant cells. TRAIL significantly induced apoptosis in a dose-dependent manner in OPM-2, RPMI 8226, NCI-H929, U266, JJN-3 MM cell lines and ADC-1 plasma cell leukaemia cells. SAHA amplified TRAIL responses in all lines except OPM-2, and enhanced TRAIL responses were both via Caspase-8 and -9. SAHA treatment induced growth inhibition that further increased in the combination treatment with TRAIL in MM cells. The co-treatment of TRAIL and SAHA reduced viable cell numbers all cell lines. TRAIL responses were further potentiated by SAHA in 3D cell culture in NCI-H929, RPMI 8226 and U266 at lower TRAIL + SAHA doses than in suspension culture. However TRAIL responses in cells that had been selected for TRAIL resistance were not further enhanced by SAHA treatment. SAHA is a potent sensitizer of TRAIL responses in both TRAIL sensitive and resistant cell lines, in both suspension and 3D culture, however SAHA did not sensitise TRAIL-sensitive cell

Suberoylanilide hydroxamic acid (SAHA) inhibits EGF-induced cell transformation via reduction of cyclin D1 mRNA stability

International Nuclear Information System (INIS)

Zhang, Jingjie; Ouyang, Weiming; Li, Jingxia; Zhang, Dongyun; Yu, Yonghui; Wang, York; Li, Xuejun; Huang, Chuanshu

2012-01-01

Suberoylanilide hydroxamic acid (SAHA) inhibiting cancer cell growth has been associated with its downregulation of cyclin D1 protein expression at transcription level or translation level. Here, we have demonstrated that SAHA inhibited EGF-induced Cl41 cell transformation via the decrease of cyclin D1 mRNA stability and induction of G0/G1 growth arrest. We found that SAHA treatment resulted in the dramatic inhibition of EGF-induced cell transformation, cyclin D1 protein expression and induction of G0/G1 growth arrest. Further studies showed that SAHA downregulation of cyclin D1 was only observed with endogenous cyclin D1, but not with reconstitutionally expressed cyclin D1 in the same cells, excluding the possibility of SAHA regulating cyclin D1 at level of protein degradation. Moreover, SAHA inhibited EGF-induced cyclin d1 mRNA level, whereas it did not show any inhibitory effect on cyclin D1 promoter-driven luciferase reporter activity under the same experimental conditions, suggesting that SAHA may decrease cyclin D1 mRNA stability. This notion was supported by the results that treatment of cells with SAHA decreased the half-life of cyclin D1 mRNA from 6.95 h to 2.57 h. Consistent with downregulation of cyclin D1 mRNA stability, SAHA treatment also attenuated HuR expression, which has been well-characterized as a positive regulator of cyclin D1 mRNA stability. Thus, our study identifies a novel mechanism responsible for SAHA inhibiting cell transformation via decreasing cyclin D1 mRNA stability and induction of G0/G1 growth arrest in Cl41 cells. -- Highlights: ► SAHA inhibits cell transformation in Cl41 cells. ► SAHA suppresses Cyclin D1 protein expression. ► SAHA decreases cyclin D1 mRNA stability.

Comparative accuracy of thermodynamic description of properties of a gas plasma in the Thomas--Fermi and Saha approximations

International Nuclear Information System (INIS)

Iosilevskii, I.L.; Gryaznov, V.K.

1982-01-01

The relation between two methods of thermodynamical calculation of matter in the gas-plasma region is analyzed. These methods are the traditional one, which uses the Saha ionization equilibrium equation, and extrapolation of the Thomas--Fermi approximation with quantum and exchange corrections. These approximations are compared with one another, and also with the results of exact theory at the total ionization limit and with experimental data for a cesium plasma in the partial-ionization region

Emerging Trends in Applied Mathematics: Dedicated to the Memory of Sir Asutosh Mookerjee and Contributions of S.N. Bose, M.N. Saha and N.R. Sen

CERN Document Server

Basu, Uma; De, Soumen

2015-01-01

The book is based on research presentations at the international conference, “Emerging Trends in Applied Mathematics: In the Memory of Sir Asutosh Mookerjee, S.N. Bose, M.N. Saha, and N.R. Sen”, held at the Department of Applied Mathematics, University of Calcutta, during 12–14 February 2014. It focuses on various emerging and challenging topics in the field of applied mathematics and theoretical physics. The book will be a valuable resource for postgraduate students at higher levels and researchers in applied mathematics and theoretical physics. Researchers presented a wide variety of themes in applied mathematics and theoretical physics—such as emergent periodicity in a field of chaos; Ricci flow equation and Poincare conjecture; Bose–Einstein condensation; geometry of local scale invariance and turbulence; statistical mechanics of human resource allocation: mathematical modelling of job-matching in labour markets; contact problem in elasticity; the Saha equation; computational fluid dynamics with...

Up-Regulation of P21 Inhibits TRAIL-Mediated Extrinsic Apoptosis, Contributing Resistance to SAHA in Acute Myeloid Leukemia Cells

Directory of Open Access Journals (Sweden)

Xing Wu

2014-08-01

Full Text Available Background/Aim: P21, a multifunctional cell cycle-regulatory molecule, regulates apoptotic cell death. In this study we examined the effect of altered p21 expression on the sensitivity of acute myeloid leukemia cells in response to HDAC inhibitor SAHA treatment and investigated the underlying mechanism. Methods: Stably transfected HL60 cell lines were established in RPMI-1640 with supplementation of G-418. Cell viability was measured by MTT assay. Western blot was applied to assess the protein expression levels of target genes. Cell apoptosis was monitored by AnnexinV-PE/7AAD assay. Results: We showed HL60 cells that that didn't up-regulate p21 expression were more sensitive to SAHA-mediated apoptosis than NB4 and U937 cells that had increased p21 level. Enforced expression of p21 in HL60 cells reduced sensitivity to SAHA and blocked TRAIL-mediated apoptosis. Conversely, p21 silencing in NB4 cells enhanced SAHA-mediated apoptosis and lethality. Finally, we found that combined treatment with SAHA and rapamycin down-regulated p21 and enhanced apoptosis in AML cells. Conclusion: We conclude that up-regulated p21 expression mediates resistance to SAHA via inhibition of TRAIL apoptotic pathway. P21 may serve as a candidate biomarker to predict responsiveness or resistance to SAHA-based therapy in AML patients. In addition, rapamycin may be an effective agent to override p21-mediated resistance to SAHA in AML patients.

SCADA Sistemi ile Bir İşletmenin Dış Saha Otomasyonu

OpenAIRE

Kılıç, Murat; Özdemir, Şule

2010-01-01

Bu çalışmada, PLC (Programmable Logic Controller: Programlanabilir Mantık Denetleyici) ve SCADA (Supervising Control and Data Acquisition: Veri Tabanlı Kontrol ve Gözetleme) sistemleriyle bir MDF (Medium Density Fiberboard) presi dış saha besleme hattının otomasyonu gerçekleştirilmiştir. Tüm sistem SCADA sayesinde bilgisayar ekranından izlenebilmekte ve kontrol edilebilmektedir. MDF presi dış saha besleme hattı tam otomasyon ile çalışmaktadır. Otomasyon sisteminde PLC yazılımı olarak Siemens ...

Radiosensitization by SAHA in Experimental Colorectal Carcinoma Models-In Vivo Effects and Relevance of Histone Acetylation Status

International Nuclear Information System (INIS)

Folkvord, Sigurd; Ree, Anne Hansen; Furre, Torbjorn; Halvorsen, Thomas; Flatmark, Kjersti

2009-01-01

Purpose: Histone deacetylase inhibitors are being evaluated as antitumor agents in ongoing clinical trials, and promising preclinical results, combined with favorable toxicity profiles, have rendered the drugs as interesting candidates for combination with other treatment modalities, such as radiotherapy. The aim of the present study was to evaluate the radiosensitizing properties of suberoylanilide hydroxamic acid (SAHA) and the possible requirement of histone hyperacetylation at radiation exposure. Methods and materials: Radiosensitization by SAHA was assessed in a colorectal carcinoma cell line and in two colorectal xenograft models by analysis of clonogenic survival and tumor growth delay, respectively. Histone acetylation status at radiation exposure was evaluated by Western blot. Results: In vitro, radiosensitization was demonstrated when cells were preincubated with SAHA, and, in the xenografts, tumor growth was delayed when the mice were treated with fractionated radiation combined with daily SAHA injections compared with radiation alone. Surprisingly, the SAHA-dependent growth delay was still present when radiation was delivered at restored baseline acetylation levels compared with maximal histone hyperacetylation. Conclusion: SAHA was an effective radiosensitizer in experimental colorectal carcinoma models, suggesting that histone deacetylase inhibition might constitute a valuable supplement to current multimodal treatment strategies in rectal cancer. The presence of histone hyperacetylation at radiation was not required to obtain an increased radiation response, questioning the validity of using histone hyperacetylation as a molecular marker for radiosensitivity.

The anti-tumor histone deacetylase inhibitor SAHA and the natural flavonoid curcumin exhibit synergistic neuroprotection against amyloid-beta toxicity.

Directory of Open Access Journals (Sweden)

Jia Meng

Full Text Available With the trend of an increasing aged population worldwide, Alzheimer's disease (AD, an age-related neurodegenerative disorder, as one of the major causes of dementia in elderly people is of growing concern. Despite the many hard efforts attempted during the past several decades in trying to elucidate the pathological mechanisms underlying AD and putting forward potential therapeutic strategies, there is still a lack of effective treatments for AD. The efficacy of many potential therapeutic drugs for AD is of main concern in clinical practice. For example, large bodies of evidence show that the anti-tumor histone deacetylase (HDAC inhibitor, suberoylanilidehydroxamic acid (SAHA, may be of benefit for the treatment of AD; however, its extensive inhibition of HDACs makes it a poor therapeutic. Moreover, the natural flavonoid, curcumin, may also have a potential therapeutic benefit against AD; however, it is plagued by low bioavailability. Therefore, the integrative effects of SAHA and curcumin were investigated as a protection against amyloid-beta neurotoxicity in vitro. We hypothesized that at low doses their synergistic effect would improve therapeutic selectivity, based on experiments that showed that at low concentrations SAHA and curcumin could provide comprehensive protection against Aβ25-35-induced neuronal damage in PC12 cells, strongly implying potent synergism. Furthermore, network analysis suggested that the possible mechanism underlying their synergistic action might be derived from restoration of the damaged functional link between Akt and the CBP/p300 pathway, which plays a crucial role in the pathological development of AD. Thus, our findings provided a feasible avenue for the application of a synergistic drug combination, SAHA and curcumin, in the treatment of AD.

SAHA decreases HDAC 2 and 4 levels in vivo and improves molecular phenotypes in the R6/2 mouse model of Huntington's disease.

Directory of Open Access Journals (Sweden)

Michal Mielcarek

Full Text Available Huntington's disease (HD is a progressive neurological disorder for which there are no disease-modifying treatments. Transcriptional dysregulation is a major molecular feature of HD, which significantly contributes to disease progression. Therefore, the development of histone deacetylase (HDAC inhibitors as therapeutics for HD has been energetically pursued. Suberoylanilide hydroxamic acid (SAHA - a class I HDAC as well an HDAC6 inhibitor, improved motor impairment in the R6/2 mouse model of HD. Recently it has been found that SAHA can also promote the degradation of HDAC4 and possibly other class IIa HDACs at the protein level in various cancer cell lines. To elucidate whether SAHA is a potent modifier of HDAC protein levels in vivo, we performed two independent mouse trials. Both WT and R6/2 mice were chronically treated with SAHA and vehicle. We found that prolonged SAHA treatment causes the degradation of HDAC4 in cortex and brain stem, but not hippocampus, without affecting its transcript levels in vivo. Similarly, SAHA also decreased HDAC2 levels without modifying the expression of its mRNA. Consistent with our previous data, SAHA treatment diminishes Hdac7 transcript levels in both wild type and R6/2 brains and unexpectedly was found to decrease Hdac11 in R6/2 but not wild type. We investigated the effects of SAHA administration on well-characterised molecular readouts of disease progression. We found that SAHA reduces SDS-insoluble aggregate load in the cortex and brain stem but not in the hippocampus of the R6/2 brains, and that this was accompanied by restoration of Bdnf cortical transcript levels.

Design, Synthesis and Biological Evaluation of Histone Deacetylase (HDAC) Inhibitors: Saha (Vorinostat) Analogs and Biaryl Indolyl Benzamide Inhibitors Display Isoform Selectivity

Science.gov (United States)

Negmeldin, Ahmed Thabet

HDAC proteins have emerged as interesting targets for anti-cancer drugs due to their involvement in cancers, as well as several other diseases. Several HDAC inhibitors have been approved by the FDA as anti-cancer drugs, including SAHA (suberoylanilide hydroxamic acid, Vorinostat). Unfortunately, SAHA inhibits most HDAC isoforms, which limit its use as a pharmacological tool and may lead to side effects in the clinic. In this work we were interested in developing isoform selective HDAC inhibitors, which may decrease or eliminate the side effects associated with non-selective inhibitors treatment. In addition, isoform selective HDAC inhibitors can be used as biological tools to help understand the HDAC-related cancer biology. Our strategy was based on synthesis and screening of several derivatives of the non-selective FDA approved drug SAHA substituted at different positions of the linker region. Several SAHA analogs modified at the C4 and C5 positions of the linker were synthesized. The new C4- and C5-modified SAHA libraries, along with the previously synthesized C2-modified SAHA analogs were screened in vitro and in cellulo for HDAC isoform selectivity. Interestingly, several analogs exhibited dual HDAC6/HDAC8 selectivity. Enantioselective syntheses of the pure enantiomers of some of the interesting analogs were performed and the enantiomers were screened in vitro. Among the most interesting analogs, ( R)-C4-benzyl SAHA displayed 520- to 1300-fold selectivity for HDAC6 and HDAC8 over HDAC1, 2, and 3, with IC50 values of 48 and 27 nM with HDAC6 and 8, respectively. Docking studies were performed to provide structural rationale for the observed selectivity of the new analogs. In addition, rational design, synthesis, and screening of several other biaryl indolyl benzamide HDAC inhibitors is discussed, and some showed modest HDAC1 selectivity. The new biaryl indolyl benzamides can be useful to further develop HDAC1 selective inhibitors. The dual HDAC6/8 selective

Evolution of nuclear spectroscopy at Saha Institute of Nuclear Physics

Indian Academy of Sciences (India)

1990 to date a variety of medium energy heavy ions were made available from the BARC-TIFR Pel- letron and the Nuclear Science Centre Pelletron. The state of the art gamma detector arrays in these centres enabled the Saha Institute groups to undertake more sophisticated experiments. Front line nuclear spectroscopy ...

Evolution of nuclear spectroscopy at Saha Institute of Nuclear Physics

Indian Academy of Sciences (India)

Currently Saha Institute is building a multi-element gamma heavy ion neutron array detector (MEGHNAD), which will have six high efficiency clover Ge detector together with charged particle ball and other accessories. The system is expected to be usable in 2002 and will be used in experiments using high energy heavy ...

Nuclear structure studies at Saha Institute of Nuclear Physics using ...

Indian Academy of Sciences (India)

In-beam gamma-ray spectroscopy, carried out at the Saha Institute of Nuclear Physics in the recent past, using heavy-ion projectiles from the pelletron accelerator centres in the country and multi-detector arrays have yielded significant data on the structure of a large number of nuclei spanning different mass regions.

Study of equation-of-state of dense helium

International Nuclear Information System (INIS)

Cai Lingcang; Zhang Lin; Xiang Shikai; Jing Fuqian

2001-01-01

Hugoniot EOS, shock temperature of gas helium plasma (the initial pressure is 1.2 MPa and the initial temperature is 293 K) are measured with the help of shock compression technique and transient radiation pyrometer. The experimental Hugoniot data are good agreement with the theoretical prediction by Saha equation pus Debye-Huckel correction

Synergistic anticancer effects of cisplatin and histone deacetylase inhibitors (SAHA and TSA) on cholangiocarcinoma cell lines.

Science.gov (United States)

Asgar, Md Ali; Senawong, Gulsiri; Sripa, Banchob; Senawong, Thanaset

2016-01-01

Clinical application of cisplatin against cholangiocarcinoma is often associated with resistance and toxicity posing urgent demand for combination therapy. In this study, we evaluated the combined anticancer effect of cisplatin and histone deacetylase inhibitors (HDACIs), suberoylanilide hydroxamic acid (SAHA) and trichostatin A (TSA), on the cholangiocarcinoma KKU-100 and KKU-M214 cell lines. Antiproliferative activity was evaluated using MTT assay. Apoptosis induction and cell cycle arrest were analyzed by flow cytometry. Cell cycle and apoptosis regulating proteins were evaluated by western blot analysis. MTT assay showed that cisplatin, SAHA and TSA dose-dependently reduced the viability of KKU-100 and KKU-M214 cells. The combination of cisplatin and HDACIs exerted significantly more cytotoxicity than the single drugs. Combination indices below 1.0 reflect synergism between cisplatin and HDACIs, leading to positive dose reductions of cisplatin and HDACIs. Cisplatin and HDACIs alone induced G0/G1 phase arrest in KKU-100 cells, but the drug combinations increased sub-G1 percent more than either drug. However, cisplatin and HDACIs alone or in combination increased only the sub-G1 percent in KKU-M214 cells. Annexin V-FITC staining revealed that cisplatin and HDACIs combinations induced more apoptotic cell death of both KKU-100 and KKU-M214 cells than the single drug. In KKU-100 cells, growth inhibition was accompanied by upregulation of p53 and p21 and downregulation of CDK4 and Bcl-2 due to exposure to cisplatin, SAHA and TSA alone or in combination. Moreover, combination of agents exerted higher impacts on protein expression. Single agents or combination did not affect p53 expression, however, combination of cisplatin and HDACIs increased the expression of p21 in KKU-M214 cells. Taken together, cisplatin and HDACIs combination may improve the therapeutic outcome in cholangiocarcinoma patients.

Saha and temperature relaxation approximations for the study of ionization instability in partially ionized plasma

International Nuclear Information System (INIS)

Numano, M.

1976-01-01

The growth rates for the ionization instability obtained using the Saha and temperature relaxation approximations are compared with those obtained from an exact treatment, and the requirements for validity of these two approximations are obtained analytically. For the range of plasma parameters pertinent to MHD power generation it is found that the Saha approximation is valid for relatively high electron temperature, which it becomes inapplicable as the electron temperature is decreased. On the other hand, the temperature relaxation approximation is accurate over a wide range of electron temperature. It is found also that the marginal condition for the ionization instability is correctly obtained from both approximations. (author)

Epigenetic silencing of apoptosis-inducing gene expression can be efficiently overcome by combined SAHA and TRAIL treatment in uterine sarcoma cells.

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Leopold F Fröhlich

Full Text Available The lack of knowledge about molecular pathology of uterine sarcomas with a representation of 3-7% of all malignant uterine tumors prevents the establishment of effective therapy protocols. Here, we explored advanced therapeutic options to the previously discovered antitumorigenic effects of the histone deacetylase (HDAC inhibitor suberoylanilide hydroxamic acid (SAHA by combined treatment with the tumor necrosis factor-related apoptosis-inducing ligand (TRAIL/Apo-2L. In addition, we investigated the uterine sarcoma cell lines, MES-SA and ESS-1, regarding the underlying molecular mechanisms of SAHA and TRAIL-induced apoptosis and their resistance towards TRAIL. Compared to single SAHA or TRAIL treatment, the combination of SAHA with TRAIL led to complete cell death of both tumor cell lines after 24 to 48 hours. In contrast to single SAHA treatment, apoptosis occured faster and was more pronounced in ESS-1 cells than in MES-SA cells. Induction of SAHA- and TRAIL-induced apoptosis was accompanied by upregulation of the intrinsic apoptotic pathway via reduction of mitochondrial membrane potential, caspase-3, -6, and -7 activation, and PARP cleavage, but was also found to be partially caspase-independent. Apoptosis resistance was caused by reduced expression of caspase-8 and DR 4/TRAIL-R1 in ESS-1 and MES-SA cells, respectively, due to epigenetic silencing by DNA hypermethylation of gene promoter sequences. Treatment with the demethylating agent 5-Aza-2'-deoxycytidine or gene transfer therefore restored gene expression and increased the sensitivity of both cell lines against TRAIL-induced apoptosis. Our data provide evidence that deregulation of epigenetic silencing by histone acetylation and DNA hypermethylation might play a fundamental role in the origin of uterine sarcomas. Therefore, tumor growth might be efficiently overcome by a cytotoxic combinatorial treatment of HDAC inhibitors with TRAIL.

SAHA (Vorinostat Corrects Inhibitory Synaptic Deficits Caused by Missense Epilepsy Mutations to the GABAA Receptor γ2 Subunit

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Nela Durisic

2018-03-01

Full Text Available The GABAA receptor (GABAAR α1 subunit A295D epilepsy mutation reduces the surface expression of α1A295Dβ2γ2 GABAARs via ER-associated protein degradation. Suberanilohydroxamic acid (SAHA, also known as Vorinostat was recently shown to correct the misfolding of α1A295D subunits and thereby enhance the functional surface expression of α1A295Dβ2γ2 GABAARs. Here we investigated whether SAHA can also restore the surface expression of γ2 GABAAR subunits that incorporate epilepsy mutations (N40S, R43Q, P44S, R138G known to reduce surface expression via ER-associated protein degradation. As a control, we also investigated the γ2K289M epilepsy mutation that impairs gating without reducing surface expression. Effects of mutations were evaluated on inhibitory postsynaptic currents (IPSCs mediated by the major synaptic α1β2γ2 GABAAR isoform. Recordings were performed in neuron-HEK293 cell artificial synapses to minimise contamination by GABAARs of undefined subunit composition. Transfection with α1β2γ2N40S, α1β2γ2R43Q, α1β2γ2P44S and α1β2γ2R138G subunits produced IPSCs with decay times slower than those of unmutated α1β2γ2 GABAARs due to the low expression of mutant γ2 subunits and the correspondingly high expression of slow-decaying α1β2 GABAARs. SAHA pre-treatment significantly accelerated the decay time constants of IPSCs consistent with the upregulation of mutant γ2 subunit expression. This increase in surface expression was confirmed by immunohistochemistry. SAHA had no effect on either the IPSC kinetics or surface expression levels of α1β2γ2K289M GABAARs, confirming its specificity for ER-retained mutant γ2 subunits. We also found that α1β2γ2K289M GABAARs and SAHA-treated α1β2γ2R43Q, α1β2γ2P44S and α1β2γ2R138G GABAARs all mediated IPSCs that decayed at significantly faster rates than wild type receptors as temperature was increased from 22 to 40°C. This may help explain why these mutations cause febrile

Ovarian SAHA syndrome is associated with a more insulin-resistant profile and represents an independent risk factor for glucose abnormalities in women with polycystic ovary syndrome: a prospective controlled study.

Science.gov (United States)

Dalamaga, Maria; Papadavid, Evangelia; Basios, Georgios; Vaggopoulos, Vassilios; Rigopoulos, Dimitrios; Kassanos, Dimitrios; Trakakis, Eftihios

2013-12-01

SAHA syndrome is characterized by the tetrad: seborrhea, acne, hirsutism, and androgenetic alopecia. No previous study has examined the prevalence of glucose abnormalities in ovarian SAHA and explored whether it may be an independent risk factor for glucose abnormalities. In a prospective controlled study, we investigated the spectrum of glucose abnormalities in ovarian SAHA and explored whether it is associated with a more insulin-resistant profile. In all, 316 patients with a diagnosis of polycystic ovary syndrome (PCOS) (56 with SAHA) and 102 age-matched healthy women were examined and underwent a 2-hour oral glucose tolerance test. Serum glucose homeostasis parameters, hormones, and adipokines were determined. SAHA prevalence was 17.7% in patients with PCOS and predominance of the severe PCOS phenotype. Ovarian SAHA was independently associated with a more insulin-resistant profile (higher homeostatic model assessment of insulin resistance score, lower quantitative insulin sensitivity check index [QUICKI] and MATSUDA indices, and relative hypoadiponectinemia), and represented an independent risk factor for glucose abnormalities regardless of anthropometric features, age, and PCOS phenotype. There was no performance of skin biopsies. The prompt recognition of SAHA syndrome in women with PCOS permits an earlier diagnosis and surveillance of metabolic abnormalities, especially in Mediterranean PCOS population exhibiting a lower prevalence of glucose abnormalities. Copyright © 2013 American Academy of Dermatology, Inc. Published by Mosby, Inc. All rights reserved.

Kinetic and Thermodynamic Rationale for SAHA Being a Preferential Human HDAC8 Inhibitor as Compared to the Structurally Similar Ligand, TSA

Science.gov (United States)

Singh, Raushan K.; Lall, Naveena; Leedahl, Travis S.; McGillivray, Abigail; Mandal, Tanmay; Haldar, Manas; Mallik, Sanku; Cook, Gregory; Srivastava, D.K.

2013-01-01

Of the different hydroxamate-based histone deacetylase (HDAC) inhibitors, Suberoylanilide hydroxamic acid (SAHA) has been approved by the FDA for treatment of T-cell lymphoma. Interestingly, a structurally similar inhibitor, Trichostatin A (TSA), which has a higher in vitro inhibitory-potency against HDAC8, reportedly shows a poor efficacy in clinical settings. In order to gain the molecular insight into the above discriminatory feature, we performed transient kinetic and isothermal titration calorimetric studies for the interaction of SAHA and TSA to the recombinant form of human HDAC8. The transient kinetic data revealed that the binding of both the inhibitors to the enzyme showed the biphasic profiles, which represented an initial encounter of enzyme with the inhibitor followed by the isomerization of the transient enzyme-inhibitor complexes. The temperature-dependent transient kinetic studies with the above inhibitors revealed that the bimolecular process is primarily dominated by favorable enthalpic changes, as opposed to the isomerization step; which is solely contributed by entropic changes. The standard binding-enthalpy (ΔH0) of SAHA, deduced from the transient kinetic as well as the isothermal titration calorimetric experiments, was 2–3 kcal/mol higher as compared to TSA. The experimental data presented herein suggests that SAHA serves as a preferential (target-specific/selective) HDAC8 inhibitor as compared to TSA. Arguments are presented that the detailed kinetic and thermodynamic studies may guide in the rational design of HDAC inhibitors as therapeutic agents. PMID:24079912

Iron complexation to histone deacetylase inhibitors SAHA and LAQ824 in PEGylated liposomes can considerably improve pharmacokinetics in rats.

Science.gov (United States)

Wang, Yan; Tu, Sheng; Steffen, Dana; Xiong, May

2014-01-01

The formulation of histone deacetylase inhibitors (HDACi) is challenging due to poor water solubility and rapid elimination of drugs in vivo. This study investigated the effects of complexing iron (Fe3+) to the HDACi suberoylanilide hydroxamic acid (SAHA) and LAQ824 (LAQ) prior to their encapsulation into PEGylated liposomes, and investigated whether this technique could improve drug solubility, in vitro release and in vivo pharmacokinetic (PK) properties. METHODS. The reaction stoichiometry, binding constants and solubility were measured for Fe complexes of SAHA and LAQ. The complexes were passively encapsulated into PEGylated liposomes and characterized by size distribution, zeta-potential, encapsulation efficiency (EE), and in vitro drug release studies. PC-3 cells were used to verify the in vitro anticancer activity of the formulations. In vivo pharmacokinetic properties of liposomal LAQ-Fe (L-LAQ-Fe) was evaluated in rats. RESULTS. SAHA and LAQ form complexes with Fe at 1:1 stoichiometric ratio, with a binding constant on the order of 104 M-1. Fe complexation improved the aqueous solubility and the liposomal encapsulation efficiency of SAHA and LAQ (29-35% EE, final drug concentration > 1 mM). Liposomal encapsulated complexes (L-HDACi-Fe) exhibited sustained in vitro release properties compared to L-HDACi but cytotoxicity on PC-3 cells was comparable to free drugs. The PK of L-LAQ-Fe revealed 15-fold improvement in the plasma t1/2 (12.11 h)and 211-fold improvement in the AUC∞ (105.7 µg·h/ml) compared to free LAQ (0.79 h, 0.5 µg·h/ml). Similarly, the plasma t1/2 of Fe was determined to be 11.83 h in a separate experiment using radioactive Fe-59. The majority of Fe-59 activity was found in liver and spleen of rats and correlates with liposomal uptake by the mononuclear phagocyte system. CONCLUSIONS. We have demonstrated that encapsulation of Fe complexes of HDACi into PEGylated liposomes can improve overall drug aqueous solubility, in vitro release and in

Improved Durand-equation for multiple application

International Nuclear Information System (INIS)

Weber, M.

1986-01-01

The applicability of Durand's equation could be improved for general use by applying suitable parameters representing the grain-size distribution. Thus, the Durand equation cannot only describe polydisperse (pseudo)-homogeneous or heterogeneous transportation, but also solid-fluid mixtures containing a certain amount of fine particles. Even non-Newtonian influences can be taken into account. The applicability of the extended Durand equation for polydisperse mixtures will be demonstrated by measurement data. With respect to this, the transition between pseudohomogeneous and heterogeneous transport has been considered on the basis of measured concentration profiles

Difference and differential equations with applications in queueing theory

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Haghighi, Aliakbar Montazer

2013-01-01

  A Useful Guide to the Interrelated Areas of Differential Equations, Difference Equations, and Queueing Models Difference and Differential Equations with Applications in Queueing Theory presents the unique connections between the methods and applications of differential equations, difference equations, and Markovian queues. Featuring a comprehensive collection of

Draft genome sequence of the extremely halophilic Halorubrum sp. SAH-A6 isolated from rock salts of the Danakil depression, Ethiopia

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Ashagrie Gibtan

2016-12-01

Full Text Available The draft genome sequence of Halorubrum sp. SAH-A6, isolated from commercial rock salts of the Danakil depression, Ethiopia. The genome comprised 3,325,770 bp, with the G + C content of 68.0%. The strain has many genes which are responsible for secondary metabolites biosynthesis, transport and catabolism as compared to other Halorubrum archaea members. Abundant genes responsible for numerous transport systems, solute accumulation, and aromatic/sulfur decomposition were detected. The first genomic analysis encourages further research on comparative genomics, and biotechnological applications. The NCBI accession number for this genome is SAMN04278861 and ID: 4278861 and strain deposited with accession number KCTC 43215.

International Conference on Differential and Difference Equations with Applications

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Došlá, Zuzana; Došlý, Ondrej; Kloeden, Peter

2016-01-01

Aimed at the community of mathematicians working on ordinary and partial differential equations, difference equations, and functional equations, this book contains selected papers based on the presentations at the International Conference on Differential and Difference Equations and Applications (ICDDEA) 2015, dedicated to the memory of Professor Georg Sell. Contributions include new trends in the field of differential and difference equations, applications of differential and difference equations, as well as high-level survey results. The main aim of this recurring conference series is to promote, encourage, cooperate, and bring together researchers in the fields of differential and difference equations. All areas of differential and difference equations are represented, with special emphasis on applications.

The Histone Deacetylase Inhibitors MS-275 and SAHA Suppress the p38 Mitogen-Activated Protein Kinase Signaling Pathway and Chemotaxis in Rheumatoid Arthritic Synovial Fibroblastic E11 Cells

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Hai-Shu Lin

2013-11-01

Full Text Available MS-275 (entinostat and SAHA (vorinostat, two histone deacetylase (HDAC inhibitors currently in oncological trials, have displayed potent anti-rheumatic activities in rodent models of rheumatoid arthritis (RA. To further elucidate their anti-inflammatory mechanisms, the impact of MS-275 and SAHA on the p38 mitogen-activated protein kinase (MAPK signaling pathway and chemotaxis was assessed in human rheumatoid arthritic synovial fibroblastic E11 cells. MS-275 and SAHA significantly suppressed the expression of p38α  MAPK, but induced the expression of MAPK phosphatase-1 (MKP-1, an endogenous suppressor of p38α  in E11 cells. At the same time, the association between p38α and MKP-1 was up-regulated and consequently, the activation (phosphorylation of p38α  was inhibited. Moreover, MS-275 and SAHA suppressed granulocyte chemotactic protein-2 (GCP-2, monocyte chemotactic protein-2 (MCP-2 and macrophage migration inhibitory factor (MIF in E11 cells in a concentration-dependent manner. Subsequently, E11-driven migration of THP-1 and U937 monocytes was inhibited. In summary, suppression of the p38 MAPK signaling pathway and chemotaxis appear to be important anti-rheumatic mechanisms of action of these HDAC inhibitors.

Trends in differential equations and applications

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Neble, María; Galván, José

2016-01-01

This work collects the most important results presented at the Congress on Differential Equations and Applications/Congress on Applied Mathematics (CEDYA/CMA) in Cádiz (Spain) in 2015. It supports further research in differential equations, numerical analysis, mechanics, control and optimization. In particular, it helps readers gain an overview of specific problems of interest in the current mathematical research related to different branches of applied mathematics. This includes the analysis of nonlinear partial differential equations, exact solutions techniques for ordinary differential equations, numerical analysis and numerical simulation of some models arising in experimental sciences and engineering, control and optimization, and also trending topics on numerical linear Algebra, dynamical systems, and applied mathematics for Industry. This volume is mainly addressed to any researcher interested in the applications of mathematics, especially in any subject mentioned above. It may be also useful to PhD s...

22nd International Conference on Difference Equations and Applications

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Hamaya, Yoshihiro; Matsunaga, Hideaki; Pötzsche, Christian

2017-01-01

This volume contains the proceedings of the 22nd International Conference on Difference Equations and Applications, held at Osaka Prefecture University, Osaka, Japan, in July 2016. The conference brought together both experts and novices in the theory and applications of difference equations and discrete dynamical systems. The volume features papers in difference equations and discrete dynamical systems with applications to mathematical sciences and, in particular, mathematical biology and economics. This book will appeal to researchers, scientists, and educators who work in the fields of difference equations, discrete dynamical systems, and their applications.

Navier-Stokes equations an introduction with applications

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Łukaszewicz, Grzegorz

2016-01-01

This volume is devoted to the study of the Navier–Stokes equations, providing a comprehensive reference for a range of applications: from students to engineers and mathematicians involved in research on fluid mechanics, dynamical systems, and mathematical modeling. Equipped with only a basic knowledge of calculus, functional analysis, and partial differential equations, the reader is introduced to the concept and applications of the Navier–Stokes equations through a series of fully self-contained chapters. Including lively illustrations that complement and elucidate the text, and a collection of exercises at the end of each chapter, this book is an indispensable, accessible, classroom-tested tool for teaching and understanding the Navier–Stokes equations. Incompressible Navier–Stokes equations describe the dynamic motion (flow) of incompressible fluid, the unknowns being the velocity and pressure as functions of location (space) and time variables. A solution to these equations predicts the behavior o...

20th International Conference on Difference Equations and Applications

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Ding, Yiming; Došlý, Ondřej

2015-01-01

These proceedings of the 20th International Conference on Difference Equations and Applications cover the areas of difference equations, discrete dynamical systems, fractal geometry, difference equations and biomedical models, and discrete models in the natural sciences, social sciences and engineering. The conference was held at the Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences (Hubei, China), under the auspices of the International Society of Difference Equations (ISDE) in July 2014. Its purpose was to bring together renowned researchers working actively in the respective fields, to discuss the latest developments, and to promote international cooperation on the theory and applications of difference equations. This book will appeal to researchers and scientists working in the fields of difference equations, discrete dynamical systems and their applications.

19th International Conference on Difference Equations and Applications

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Cushing, Jim; Elaydi, Saber

2014-01-01

This volume contains the proceedings of the 19th International Conference on Difference Equations and Applications, held at Sultan Qaboos University, Muscat, Oman in May 2013. The conference brought together experts and novices in the theory and applications of difference equations and discrete dynamical systems. The volume features papers in difference equations and discrete time dynamical systems with applications to mathematical sciences and, in particular, mathematical biology, ecology, and epidemiology. It includes four invited papers and eight contributed papers. Topics covered include: competitive exclusion through discrete time models, Benford solutions of linear difference equations, chaos and wild chaos in Lorenz-type systems, advances in periodic difference equations, the periodic decomposition problem, dynamic selection systems and replicator equations, and asymptotic equivalence of difference equations in Banach Space. This book will appeal to researchers, scientists, and educators who work in th...

18th International Conference on Difference Equations and Applications

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Cushing, Jim; Elaydi, Saber; Pinto, Alberto

2016-01-01

These proceedings of the 18th International Conference on Difference Equations and Applications cover a number of different aspects of difference equations and discrete dynamical systems, as well as the interplay between difference equations and dynamical systems. The conference was organized by the Department of Mathematics at the Universitat Autònoma de Barcelona (UAB) under the auspices of the International Society of Difference Equations (ISDE) and held in Barcelona (Catalonia, Spain) in July 2012. Its purpose was to bring together experts and novices in these fields to discuss the latest developments. The book gathers contributions in the field of combinatorial and topological dynamics, complex dynamics, applications of difference equations to biology, chaotic linear dynamics, economic dynamics and control and asymptotic behavior, and periodicity of difference equations. As such it is of interest to researchers and scientists engaged in the theory and applications of difference equations and discrete dy...

Structural equation modeling methods and applications

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Wang, Jichuan

2012-01-01

A reference guide for applications of SEM using Mplus Structural Equation Modeling: Applications Using Mplus is intended as both a teaching resource and a reference guide. Written in non-mathematical terms, this book focuses on the conceptual and practical aspects of Structural Equation Modeling (SEM). Basic concepts and examples of various SEM models are demonstrated along with recently developed advanced methods, such as mixture modeling and model-based power analysis and sample size estimate for SEM. The statistical modeling program, Mplus, is also featured and provides researchers with a

Ordinary differential equations principles and applications

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Nandakumaran, A K; George, Raju K

2017-01-01

Written in a clear, logical and concise manner, this comprehensive resource allows students to quickly understand the key principles, techniques and applications of ordinary differential equations. Important topics including first and second order linear equations, initial value problems and qualitative theory are presented in separate chapters. The concepts of two point boundary value problems, physical models and first order partial differential equations are discussed in detail. The text uses tools of calculus and real analysis to get solutions in explicit form. While discussing first order linear systems, linear algebra techniques are used. The real-life applications are interspersed throughout the book to invoke reader's interest. The methods and tricks to solve numerous mathematical problems with sufficient derivations and explanation are provided. The proofs of theorems are explained for the benefit of the readers.

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

KAUST Repository

Zygalakis, K. C.

2011-01-01

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

Effects of treatment with suppressive combination antiretroviral drug therapy and the histone deacetylase inhibitor suberoylanilide hydroxamic acid; (SAHA on SIV-infected Chinese rhesus macaques.

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Binhua Ling

Full Text Available Viral reservoirs-persistent residual virus despite combination antiretroviral therapy (cART-remain an obstacle to cure of HIV-1 infection. Difficulty studying reservoirs in patients underscores the need for animal models that mimics HIV infected humans on cART. We studied SIV-infected Chinese-origin rhesus macaques (Ch-RM treated with intensive combination antiretroviral therapy (cART and 3 weeks of treatment with the histone deacetyalse inhibitor, suberoylanilide hydroxamic acid (SAHA.SIVmac251 infected Ch-RM received reverse transcriptase inhibitors PMPA and FTC and integrase inhibitor L-870812 beginning 7 weeks post infection. Integrase inhibitor L-900564 and boosted protease inhibitor treatment with Darunavir and Ritonavir were added later. cART was continued for 45 weeks, with daily SAHA administered for the last 3 weeks, followed by euthanasia/necropsy. Plasma viral RNA and cell/tissue-associated SIV gag RNA and DNA were quantified by qRT-PCR/qPCR, with flow cytometry monitoring changes in immune cell populations.Upon cART initiation, plasma viremia declined, remaining <30 SIV RNA copy Eq/ml during cART, with occasional blips. Decreased viral replication was associated with decreased immune activation and partial restoration of intestinal CD4+ T cells. SAHA was well tolerated but did not result in demonstrable treatment-associated changes in plasma or cell associated viral parameters.The ability to achieve and sustain virological suppression makes cART-suppressed, SIV-infected Ch-RM a potentially useful model to evaluate interventions targeting residual virus. However, despite intensive cART over one year, persistent viral DNA and RNA remained in tissues of all three animals. While well tolerated, three weeks of SAHA treatment did not demonstrably impact viral RNA levels in plasma or tissues; perhaps reflecting dosing, sampling and assay limitations.

Abel integral equations analysis and applications

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Gorenflo, Rudolf

1991-01-01

In many fields of application of mathematics, progress is crucially dependent on the good flow of information between (i) theoretical mathematicians looking for applications, (ii) mathematicians working in applications in need of theory, and (iii) scientists and engineers applying mathematical models and methods. The intention of this book is to stimulate this flow of information. In the first three chapters (accessible to third year students of mathematics and physics and to mathematically interested engineers) applications of Abel integral equations are surveyed broadly including determination of potentials, stereology, seismic travel times, spectroscopy, optical fibres. In subsequent chapters (requiring some background in functional analysis) mapping properties of Abel integral operators and their relation to other integral transforms in various function spaces are investi- gated, questions of existence and uniqueness of solutions of linear and nonlinear Abel integral equations are treated, and for equatio...

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

Science.gov (United States)

Sudao, Bilige; Wang, Xiaomin

2015-01-01

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

International conference on differential and difference equations with applications

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Caraballo, Tomás; Kloeden, Peter; Graef, John

2018-01-01

This book gathers papers from the International Conference on Differential & Difference Equations and Applications 2017 (ICDDEA 2017), held in Lisbon, Portugal on June 5-9, 2017. The editors have compiled the strongest research presented at the conference, providing readers with valuable insights into new trends in the field, as well as applications and high-level survey results. The goal of the ICDDEA was to promote fruitful collaborations between researchers in the fields of differential and difference equations. All areas of differential and difference equations are represented, with a special emphasis on applications.

Critical spaces for quasilinear parabolic evolution equations and applications

Science.gov (United States)

Prüss, Jan; Simonett, Gieri; Wilke, Mathias

2018-02-01

We present a comprehensive theory of critical spaces for the broad class of quasilinear parabolic evolution equations. The approach is based on maximal Lp-regularity in time-weighted function spaces. It is shown that our notion of critical spaces coincides with the concept of scaling invariant spaces in case that the underlying partial differential equation enjoys a scaling invariance. Applications to the vorticity equations for the Navier-Stokes problem, convection-diffusion equations, the Nernst-Planck-Poisson equations in electro-chemistry, chemotaxis equations, the MHD equations, and some other well-known parabolic equations are given.

Hamiltonian partial differential equations and applications

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Nicholls, David; Sulem, Catherine

2015-01-01

This book is a unique selection of work by world-class experts exploring the latest developments in Hamiltonian partial differential equations and their applications. Topics covered within are representative of the field’s wide scope, including KAM and normal form theories, perturbation and variational methods, integrable systems, stability of nonlinear solutions as well as applications to cosmology, fluid mechanics and water waves. The volume contains both surveys and original research papers and gives a concise overview of the above topics, with results ranging from mathematical modeling to rigorous analysis and numerical simulation. It will be of particular interest to graduate students as well as researchers in mathematics and physics, who wish to learn more about the powerful and elegant analytical techniques for Hamiltonian partial differential equations.

EFFECTS OF HISTONE DEACETYLASE INHIBITOR, SAHA, ON EFFECTOR AND FOXP3+ REGULATORY T CELLS IN RHESUS MACAQUES

OpenAIRE

Johnson, Jennifer; Pahuja, Anil; Graham, Melanie; Hering, Bernhard; Hancock, Wayne W.; Pratima, Bansal-Pakala

2008-01-01

SAHA, a histone deacetylase inhibitor (HDACi), is clinically approved for treatment of cutaneous T-cell lymphoma. Although the exact underlying mechanisms are unknown, HDACi arrest the cell cycle in rapidly proliferating tumor cells and promote their apoptosis. HDACi were also recently shown to enhance the production and suppressive functions of Foxp3+ regulatory T (Treg) cells in rodents, leading us to begin to investigate the actions of HDACi on rhesus monkey T cells for the sake of potenti...

Semilinear Kolmogorov Equations and Applications to Stochastic Optimal Control

International Nuclear Information System (INIS)

Masiero, Federica

2005-01-01

Semilinear parabolic differential equations are solved in a mild sense in an infinite-dimensional Hilbert space. Applications to stochastic optimal control problems are studied by solving the associated Hamilton-Jacobi-Bellman equation. These results are applied to some controlled stochastic partial differential equations

Partial differential equations methods, applications and theories

CERN Document Server

Hattori, Harumi

2013-01-01

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

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

CERN Document Server

Schiesser, William E

2014-01-01

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

Combined Treatment with Low Concentrations of Decitabine and SAHA Causes Cell Death in Leukemic Cell Lines but Not in Normal Peripheral Blood Lymphocytes

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Barbora Brodská

2013-01-01

Full Text Available Epigenetic therapy reverting aberrant acetylation or methylation offers the possibility to target preferentially tumor cells and to preserve normal cells. Combination epigenetic therapy may further improve the effect of individual drugs. We investigated combined action of demethylating agent decitabine and histone deacetylase inhibitor SAHA (Vorinostat on different leukemic cell lines in comparison with peripheral blood lymphocytes. Large decrease of viability, as well as huge p21WAF1 induction, reactive oxygen species formation, and apoptotic features due to combined decitabine and SAHA action were detected in leukemic cell lines irrespective of their p53 status, while essentially no effect was observed in response to the combined drug action in normal peripheral blood lymphocytes of healthy donors. p53-dependent apoptotic pathway was demonstrated to participate in the wtp53 CML-T1 leukemic cell line response, while significant influence of reactive oxygen species on viability decrease has been detected in p53-null HL-60 cell line.

Picone-type inequalities for nonlinear elliptic equations and their applications

Directory of Open Access Journals (Sweden)

Takaŝi Kusano

2001-01-01

Full Text Available Picone-type inequalities are derived for nonlinear elliptic equations, and Sturmian comparison theorems are established as applications. Oscillation theorems for forced super-linear elliptic equations and superlinear-sublinear elliptic equations are also obtained.

Exact solutions to the Lienard equation and its applications

International Nuclear Information System (INIS)

Feng Zhaosheng

2004-01-01

In this paper, a kind of explicit exact solutions to the Lienard equation is obtained, and the applications of the result in seeking traveling solitary wave solution of the nonlinear Schroedinger equation are presented

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

CERN Document Server

Schiesser, William E

2014-01-01

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

Nonlinear Fokker-Planck Equations Fundamentals and Applications

CERN Document Server

Frank, Till Daniel

2005-01-01

Providing an introduction to the theory of nonlinear Fokker-Planck equations, this book discusses fundamental properties of transient and stationary solutions, emphasizing the stability analysis of stationary solutions by means of self-consistency equations, linear stability analysis, and Lyapunov's direct method. Also treated are Langevin equations and correlation functions. Nonlinear Fokker-Planck Equations addresses various phenomena such as phase transitions, multistability of systems, synchronization, anomalous diffusion, cut-off solutions, travelling-wave solutions and the emergence of power law solutions. A nonlinear Fokker-Planck perspective to quantum statistics, generalized thermodynamics, and linear nonequilibrium thermodynamics is given. Theoretical concepts are illustrated where possible by simple examples. The book also reviews several applications in the fields of condensed matter physics, the physics of porous media and liquid crystals, accelerator physics, neurophysics, social sciences, popul...

Partial differential equations and their applications

International Nuclear Information System (INIS)

Gauthier-Villars

1998-01-01

This book is dedicated to the French mathematician J.L.Lions. It represents a compilation of articles from about 80 authors. The topics treated are diverse but the more or less commune matter is the study of the characteristics of some partial differential equations. Stability, optimal approximation, numerical resolution, particular applications are among the subjects reviewed. An article deals with the MHD stability of fusion plasmas in tokamaks, another presents the scientific and technical challenges of nuclear energy in France. The latter that contains no equations can be considered as an enjoyable break in a sea of about 40 mathematical articles. (A.C.)

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

International Nuclear Information System (INIS)

Wang Baodong; Song Lina; Zhang Hongqing

2007-01-01

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

Neutral Backward Stochastic Functional Differential Equations and Their Application

OpenAIRE

Wei, Wenning

2013-01-01

In this paper we are concerned with a new type of backward equations with anticipation which we call neutral backward stochastic functional differential equations. We obtain the existence and uniqueness and prove a comparison theorem. As an application, we discuss the optimal control of neutral stochastic functional differential equations, establish a Pontryagin maximum principle, and give an explicit optimal value for the linear optimal control.

Application of Exp-function method for (2 + 1)-dimensional nonlinear evolution equations

International Nuclear Information System (INIS)

Bekir, Ahmet; Boz, Ahmet

2009-01-01

In this paper, the Exp-function method is used to construct solitary and soliton solutions of (2 + 1)-dimensional nonlinear evolution equations. (2 + 1)-dimensional breaking soliton (Calogero) equation, modified Zakharov-Kuznetsov and Konopelchenko-Dubrovsky equations are chosen to illustrate the effectiveness of the method. The method is straightforward and concise, and its applications are promising. The Exp-function method presents a wider applicability for handling nonlinear wave equations.

New variable separation approach: application to nonlinear diffusion equations

International Nuclear Information System (INIS)

Zhang Shunli; Lou, S Y; Qu Changzheng

2003-01-01

The concept of the derivative-dependent functional separable solution (DDFSS), as a generalization to the functional separable solution, is proposed. As an application, it is used to discuss the generalized nonlinear diffusion equations based on the generalized conditional symmetry approach. As a consequence, a complete list of canonical forms for such equations which admit the DDFSS is obtained and some exact solutions to the resulting equations are described

New application of Exp-function method for improved Boussinesq equation

Energy Technology Data Exchange (ETDEWEB)

Abdou, M.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt); Department of Physics, Faculty of Education for Girls, Science Departments, King Khalid University, Bisha (Saudi Arabia)], E-mail: m_abdou_eg@yahoo.com; Soliman, A.A. [Department of Mathematics, Faculty of Education (AL-Arish) Suez Canal University, AL-Arish 45111 (Egypt); Department of Mathematics, Teacher' s College (Bisha), King Khalid University, Bisha, PO Box 551 (Saudi Arabia)], E-mail: asoliman_99@yahoo.com; El-Basyony, S.T. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt)

2007-10-01

The Exp-function method is used to obtain generalized solitary solutions and periodic solutions for nonlinear evolution equations arising in mathematical physics with the aid of symbolic computation method, namely, the improved Boussinesq equation. The method is straightforward and concise, and its applications is promising for other nonlinear evolution equations in mathematical physics.

Hyperbolic partial differential equations populations, reactors, tides and waves theory and applications

CERN Document Server

Witten, Matthew

1983-01-01

Hyperbolic Partial Differential Equations, Volume 1: Population, Reactors, Tides and Waves: Theory and Applications covers three general areas of hyperbolic partial differential equation applications. These areas include problems related to the McKendrick/Von Foerster population equations, other hyperbolic form equations, and the numerical solution.This text is composed of 15 chapters and begins with surveys of age specific population interactions, populations models of diffusion, nonlinear age dependent population growth with harvesting, local and global stability for the nonlinear renewal eq

Equation of state of fluid helium at high temperatures and densities

Science.gov (United States)

Cai, Lingcang; Chen, Qifeng; Gu, Yunjun; Zhang, Ying; Zhou, Xianming; Jing, Fuqian

2005-03-01

Hugoniot curves and shock temperatures of gas helium with initial temperature 293 K and three initial pressures 0.6, 1.2, and 5.0 MPa were measured up to 15000 K using a two-stage light-gas gun and transient radiation pyrometer. It was found that the calculated Hugoniot EOS of gas helium at the same initial pressure using Saha equation with Debye-Hückel correction was in good agreement with the experimental data. The curve of the calculated shock wave velocity with the particle velocity of gas helium which is shocked from the initial pressure 5 MPa and temperature 293 K, i.e., the D ≈ u relation, D= C 0+λ u ( uionization degree of the shocked gas helium reaches 10-3.

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

International Nuclear Information System (INIS)

Yomba, Emmanuel

2005-01-01

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

Saha equation, single and two particle states

International Nuclear Information System (INIS)

Kraeft, W.D.; Girardeau, M.D.; Strege, B.

1990-01-01

Single and two particle porperties in dense plasma are discussed in connection with their role in the mass action law for a partially ionized plasma. The two particle bound states are nearly density independent, while the continuum is essentially shifted. The single particle states are damped, and their energy has a negative shift and a parabolic behaviour for small momenta. (orig.)

Application of an analytical method for solution of thermal hydraulic conservation equations

Energy Technology Data Exchange (ETDEWEB)

Fakory, M.R. [Simulation, Systems & Services Technologies Company (S3 Technologies), Columbia, MD (United States)

1995-09-01

An analytical method has been developed and applied for solution of two-phase flow conservation equations. The test results for application of the model for simulation of BWR transients are presented and compared with the results obtained from application of the explicit method for integration of conservation equations. The test results show that with application of the analytical method for integration of conservation equations, the Courant limitation associated with explicit Euler method of integration was eliminated. The results obtained from application of the analytical method (with large time steps) agreed well with the results obtained from application of explicit method of integration (with time steps smaller than the size imposed by Courant limitation). The results demonstrate that application of the analytical approach significantly improves the numerical stability and computational efficiency.

In silico modification of Zn2+ binding group of suberoylanilide hydroxamic acid (SAHA) by organoselenium compounds as Homo sapiens class II HDAC inhibitor of cervical cancer

Science.gov (United States)

Sumo Friend Tambunan, Usman; Bakri, Ridla; Aditya Parikesit, Arli; Ariyani, Titin; Dyah Puspitasari, Ratih; Kerami, Djati

2016-02-01

Cervical cancer is the most common cancer in women, and ranks seventh of all cancers worldwide, with 529000 cases in 2008 and more than 85% cases occur in developing countries. One way to treat this cancer is through the inhibition of HDAC enzymes which play a strategic role in the regulation of gene expression. Suberoyl Anilide Hydroxamic Acid (SAHA) or Vorinostat is a drug which commercially available to treat the cancer, but still has some side effects. This research present in silico SAHA modification in Zinc Binding Group (ZBG) by organoselenium compound to get ligands which less side effect. From molecular docking simulation, and interaction analysis, there are five best ligands, namely CC27, HA27, HB28, IB25, and KA7. These five ligands have better binding affinity than the standards, and also have interaction with Zn2+ cofactor of inhibited HDAC enzymes. This research is expected to produce more potent HDAC inhibitor as novel drug for cervical cancer treatment.

Differential equations and applications recent advances

CERN Document Server

2014-01-01

Differential Equations and Applications : Recent Advances focus on the latest developments in Nonlinear Dynamical Systems, Neural Networks, Fluid Dynamics, Fractional Differential Systems, Mathematical Modelling and Qualitative Theory. Different aspects such as Existence, Stability, Controllability, Viscosity and Numerical Analysis for different systems have been discussed in this book. This book will be of great interest and use to researchers in Applied Mathematics, Engineering and Mathematical Physics.

Alternative approach to the surface-excitation model

International Nuclear Information System (INIS)

Krohn, V.E.

1981-01-01

Although the development of the surface-excitation model of sputtered-ion emission involved a detailed description of the ionization process, one can arrive at the same result by assuming an equilibrium treatment, e.g. the Saha-Langmuir equation, with the temperature falling as the collision casade develops. This suggests that, even if situations are found where the surface-excitation model is successful, it does not follow that the original detailed description of the ionization process is correct. Nevertheless, the surface-excitation model does contain an interesting new idea which should not be overlooked, i.e. that atoms sputtered during the early stages of a collision cascade will be relatively energetic, and to the extent that the Saha-Langmuir equation has some applicability, will have a probability of positive ionization which will be low for atoms of low ionization potential (I phi), relative to lower-energy atoms emitted during the later stages of the collision cascade. The extended abstract will discuss recent experimental results

International Conference on Delay Differential and Difference Equations and Applications

CERN Document Server

Pituk, Mihály; Recent Advances in Delay Differential and Difference Equations

2014-01-01

Delay differential and difference equations serve as models for a range of processes in biology, physics, engineering, and control theory. In this volume, the participants of the International Conference on Delay Differential and Difference Equations and Applications, Balatonfüred, Hungary, July 15-19, 2013 present recent research in this quickly-evolving field. The papers relate to the existence, asymptotic, and oscillatory properties of the solutions; stability theory; numerical approximations; and applications to real world phenomena using deterministic and stochastic discrete and continuous dynamical systems.

Advances in differential equations and applications

CERN Document Server

Martínez, Vicente

2014-01-01

The book contains a selection of contributions given at the 23rd Congress on Differential Equations and Applications (CEDYA) / 13th Congress of Applied Mathematics (CMA) that took place at Castellon, Spain, in 2013. CEDYA is renowned as the congress of the Spanish Society of Applied Mathematics (SEMA) and constitutes the main forum and meeting point for applied mathematicians in Spain. The papers included in this book have been selected after a thorough refereeing process and provide a good summary of the recent activity developed by different groups working mainly in Spain on applications of mathematics to several fields of science and technology. The purpose is to provide a useful reference of academic and industrial researchers working in the area of numerical analysis and its applications.

The NO-pair equation---Fundamental problems, numerical solutions and applications

International Nuclear Information System (INIS)

Martensson-Pendrill, A.

1989-01-01

The solution of inhomogeneous two-particle differential equations is a powerful method for treating correlation effects in the non-relativistic case and is reviewed briefly. The relativistic generalization, the so-called Dirac-Coulomb equation, is complicated by the need to distinguish between positive and negative energy states. The construction and use of projection operators onto positive energy states are presented and the application of the pair equation to other properties such as parity non-conservation is discussed

Applications of Multilevel Structural Equation Modeling to Cross-Cultural Research

Science.gov (United States)

Cheung, Mike W.-L.; Au, Kevin

2005-01-01

Multilevel structural equation modeling (MSEM) has been proposed as an extension to structural equation modeling for analyzing data with nested structure. We have begun to see a few applications in cross-cultural research in which MSEM fits well as the statistical model. However, given that cross-cultural studies can only afford collecting data…

Histone deacetylase inhibitors SAHA and sodium butyrate block G1-to-S cell cycle progression in neurosphere formation by adult subventricular cells

Directory of Open Access Journals (Sweden)

Doughty Martin L

2011-05-01

Full Text Available Abstract Background Histone deacetylases (HDACs are enzymes that modulate gene expression and cellular processes by deacetylating histones and non-histone proteins. While small molecule inhibitors of HDAC activity (HDACi are used clinically in the treatment of cancer, pre-clinical treatment models suggest they also exert neuroprotective effects and stimulate neurogenesis in neuropathological conditions. However, the direct effects of HDACi on cell cycle progression and proliferation, two properties required for continued neurogenesis, have not been fully characterized in adult neural stem cells (NSCs. In this study, we examined the effects of two broad class I and class II HDACi on adult mouse NSCs, the hydroxamate-based HDACi suberoylanilide hydroxamic acid (vorinostat, SAHA and the short chain fatty acid HDACi sodium butyrate. Results We show that both HDACi suppress the formation of neurospheres by adult mouse NSCs grown in proliferation culture conditions in vitro. DNA synthesis is significantly inhibited in adult mouse NSCs exposed to either SAHA or sodium butyrate and inhibition is associated with an arrest in the G1 phase of the cell cycle. HDACi exposure also resulted in transcriptional changes in adult mouse NSCs. Cdk inhibitor genes p21 and p27 transcript levels are increased and associated with elevated H3K9 acetylation levels at proximal promoter regions of p21 and p27. mRNA levels for notch effector Hes genes and Spry-box stem cell transcription factors are downregulated, whereas pro-neural transcription factors Neurog1 and Neurod1 are upregulated. Lastly, we show HDAC inhibition under proliferation culture conditions leads to long-term changes in cell fate in adult mouse NSCs induced to differentiate in vitro. Conclusion SAHA and sodium butyrate directly regulate cdk inhibitor transcription to control cell cycle progression in adult mouse NSCs. HDAC inhibition results in G1 arrest in adult mouse NSCs and transcriptional changes

Application of the finite element method to the neutron transport equation

International Nuclear Information System (INIS)

Martin, W.R.

1976-01-01

This paper examines the theoretical and practical application of the finite element method to the neutron transport equation. It is shown that in principle the system of equations obtained by application of the finite element method can be solved with certain physical restrictions concerning the criticality of the medium. The convergence of this approximate solution to the exact solution with mesh refinement is examined, and a non-optical estimate of the convergence rate is obtained analytically. It is noted that the numerical results indicate a faster convergence rate and several approaches to obtain this result analytically are outlined. The practical application of the finite element method involved the development of a computer code capable of solving the neutron transport equation in 1-D plane geometry. Vacuum, reflecting, or specified incoming boundary conditions may be analyzed, and all are treated as natural boundary conditions. The time-dependent transport equation is also examined and it is shown that the application of the finite element method in conjunction with the Crank-Nicholson time discretization method results in a system of algebraic equations which is readily solved. Numerical results are given for several critical slab eigenvalue problems, including anisotropic scattering, and the results compare extremely well with benchmark results. It is seen that the finite element code is more efficient than a standard discrete ordinates code for certain problems. A problem with severe heterogeneities is considered and it is shown that the use of discontinuous spatial and angular elements results in a marked improvement in the results. Finally, time-dependent problems are examined and it is seen that the phenomenon of angular mode separation makes the numerical treatment of the transport equation in slab geometry a considerable challenge, with the result that the angular mesh has a dominant effect on obtaining acceptable solutions

Ordinary differential equations with applications in molecular biology.

Science.gov (United States)

Ilea, M; Turnea, M; Rotariu, M

2012-01-01

Differential equations are of basic importance in molecular biology mathematics because many biological laws and relations appear mathematically in the form of a differential equation. In this article we presented some applications of mathematical models represented by ordinary differential equations in molecular biology. The vast majority of quantitative models in cell and molecular biology are formulated in terms of ordinary differential equations for the time evolution of concentrations of molecular species. Assuming that the diffusion in the cell is high enough to make the spatial distribution of molecules homogenous, these equations describe systems with many participating molecules of each kind. We propose an original mathematical model with small parameter for biological phospholipid pathway. All the equations system includes small parameter epsilon. The smallness of epsilon is relative to the size of the solution domain. If we reduce the size of the solution region the same small epsilon will result in a different condition number. It is clear that the solution for a smaller region is less difficult. We introduce the mathematical technique known as boundary function method for singular perturbation system. In this system, the small parameter is an asymptotic variable, different from the independent variable. In general, the solutions of such equations exhibit multiscale phenomena. Singularly perturbed problems form a special class of problems containing a small parameter which may tend to zero. Many molecular biology processes can be quantitatively characterized by ordinary differential equations. Mathematical cell biology is a very active and fast growing interdisciplinary area in which mathematical concepts, techniques, and models are applied to a variety of problems in developmental medicine and bioengineering. Among the different modeling approaches, ordinary differential equations (ODE) are particularly important and have led to significant advances

Inverse operator method for solutions of nonlinear dynamical equations and some typical applications

International Nuclear Information System (INIS)

Fang Jinqing; Yao Weiguang

1993-01-01

The inverse operator method (IOM) is described briefly. We have realized the IOM for the solutions of nonlinear dynamical equations by the mathematics-mechanization (MM) with computers. They can then offer a new and powerful method applicable to many areas of physics. We have applied them successfully to study the chaotic behaviors of some nonlinear dynamical equations. As typical examples, the well-known Lorentz equation, generalized Duffing equation and two coupled generalized Duffing equations are investigated by using the IOM and the MM. The results are in good agreement with those given by Runge-Kutta method. So the IOM realized by the MM is of potential application valuable in nonlinear physics and many other fields

Linear matrix differential equations of higher-order and applications

Directory of Open Access Journals (Sweden)

Mustapha Rachidi

2008-07-01

Full Text Available In this article, we study linear differential equations of higher-order whose coefficients are square matrices. The combinatorial method for computing the matrix powers and exponential is adopted. New formulas representing auxiliary results are obtained. This allows us to prove properties of a large class of linear matrix differential equations of higher-order, in particular results of Apostol and Kolodner are recovered. Also illustrative examples and applications are presented.

Fractional gradient and its application to the fractional advection equation

OpenAIRE

D'Ovidio, M.; Garra, R.

2013-01-01

In this paper we provide a definition of fractional gradient operators, related to directional derivatives. We develop a fractional vector calculus, providing a probabilistic interpretation and mathematical tools to treat multidimensional fractional differential equations. A first application is discussed in relation to the d-dimensional fractional advection-dispersion equation. We also study the connection with multidimensional L\\'evy processes.

Antisociální chování dospívajících: výsledky české části mezinárodního projektu SAHA

Czech Academy of Sciences Publication Activity Database

Sobotková, Veronika

2011-01-01

Roč. 8, č. 5 (2011), s. 6-7 ISSN 1214-8717 R&D Project s: GA AV ČR IBS7025354 Institutional research plan: CEZ:AV0Z70250504 Keywords : antisocial behavior * adolescence * SAHA project Subject RIV: AN - Psychology

Determination of particle concentrations in multitemperature plasmas

International Nuclear Information System (INIS)

Richley, E.; Tuma, D.T.

1982-01-01

The use of the multitemperature Saha equation (MSE) of Prigogine 1 and Patapov 2 for calculating particle concentrations in plasmas is shown to be an invalid procedure. Errors greater than one order of magnitude in the electron density in high-pressure argon and nitrogen electric arc plasmas can be easily incurred by using the multitemperature Saha equation. The alternative kinetic method for calculating concentrations is shown to be based on firm concepts. Simpliying procedures and computational techniques for calculating concentrations with the kinetic method are illustrated with examples

Multiscale functions, scale dynamics, and applications to partial differential equations

Science.gov (United States)

Cresson, Jacky; Pierret, Frédéric

2016-05-01

Modeling phenomena from experimental data always begins with a choice of hypothesis on the observed dynamics such as determinism, randomness, and differentiability. Depending on these choices, different behaviors can be observed. The natural question associated to the modeling problem is the following: "With a finite set of data concerning a phenomenon, can we recover its underlying nature? From this problem, we introduce in this paper the definition of multi-scale functions, scale calculus, and scale dynamics based on the time scale calculus [see Bohner, M. and Peterson, A., Dynamic Equations on Time Scales: An Introduction with Applications (Springer Science & Business Media, 2001)] which is used to introduce the notion of scale equations. These definitions will be illustrated on the multi-scale Okamoto's functions. Scale equations are analysed using scale regimes and the notion of asymptotic model for a scale equation under a particular scale regime. The introduced formalism explains why a single scale equation can produce distinct continuous models even if the equation is scale invariant. Typical examples of such equations are given by the scale Euler-Lagrange equation. We illustrate our results using the scale Newton's equation which gives rise to a non-linear diffusion equation or a non-linear Schrödinger equation as asymptotic continuous models depending on the particular fractional scale regime which is considered.

Evolutionary equations with applications in natural sciences

CERN Document Server

Mokhtar-Kharroubi, Mustapha

2015-01-01

With the unifying theme of abstract evolutionary equations, both linear and nonlinear, in a complex environment, the book presents a multidisciplinary blend of topics, spanning the fields of theoretical and applied functional analysis, partial differential equations, probability theory and numerical analysis applied to various models coming from theoretical physics, biology, engineering and complexity theory. The unique features of the book are: the first simultaneous presentation of two complementary approaches to fragmentation and coagulation problems, by weak compactness methods and by using semigroup techniques, comprehensive exposition of probabilistic methods of analysis of long term dynamics of dynamical systems, semigroup analysis of biological problems and cutting edge pattern formation theory. The book will appeal to postgraduate students and researchers specializing in applications of mathematics to problems arising in natural sciences and engineering.

Applications of the Peng-Robinson Equation of State Using MATLAB[R

Science.gov (United States)

Nasri, Zakia; Binous, Housam

2009-01-01

A single equation of state (EOS) such as the Peng-Robinson (PR) EOS can accurately describe both the liquid and vapor phase. We present several applications of this equation of state, including estimation of pure component properties and computation of the vapor-liquid equilibrium (VLE) diagram for binary mixtures. We perform high-pressure…

Numerical Solution of Differential Algebraic Equations and Applications

DEFF Research Database (Denmark)

Thomsen, Per Grove

2005-01-01

These lecture notes have been written as part of a special course on the numerical solution of Differential Algebraic Equations and applications . The course was held at IMM in the spring of 2005. The authors of the different chapters have all taken part in the course and the chapters are written...

Simple equation method for nonlinear partial differential equations and its applications

Directory of Open Access Journals (Sweden)

Taher A. Nofal

2016-04-01

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

Parametrically Excited Oscillations of Second-Order Functional Differential Equations and Application to Duffing Equations with Time Delay Feedback

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Mervan Pašić

2014-01-01

Full Text Available We study oscillatory behaviour of a large class of second-order functional differential equations with three freedom real nonnegative parameters. According to a new oscillation criterion, we show that if at least one of these three parameters is large enough, then the main equation must be oscillatory. As an application, we study a class of Duffing type quasilinear equations with nonlinear time delayed feedback and their oscillations excited by the control gain parameter or amplitude of forcing term. Finally, some open questions and comments are given for the purpose of further study on this topic.

Computing generalized Langevin equations and generalized Fokker-Planck equations.

Science.gov (United States)

Darve, Eric; Solomon, Jose; Kia, Amirali

2009-07-07

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

Equations involving Malliavin calculus operators applications and numerical approximation

CERN Document Server

Levajković, Tijana

2017-01-01

This book provides a comprehensive and unified introduction to stochastic differential equations and related optimal control problems. The material is new and the presentation is reader-friendly. A major contribution of the book is the development of generalized Malliavin calculus in the framework of white noise analysis, based on chaos expansion representation of stochastic processes and its application for solving several classes of stochastic differential equations with singular data involving the main operators of Malliavin calculus. In addition, applications in optimal control and numerical approximations are discussed.  The book is divided into four chapters. The first, entitled White Noise Analysis and Chaos Expansions, includes notation and provides the reader with the theoretical background needed to understand the subsequent chapters.  In Chapter 2, Generalized Operators of Malliavin Calculus, the Malliavin derivative operator, the Skorokhod integral and the Ornstein-Uhlenbeck operator are introdu...

Application of the N/D-method to the Roy equations

International Nuclear Information System (INIS)

Heemskerk, A.C.

1978-01-01

The subject of this thesis is the study and numerical application of the Roy equations for elastic pion-pion scattering. These equations were introduced by S.M. Roy in 1971 and express the minimal requirements any ππ partial wave amplitude should satisfy, such as analyticity and crossing symmetry. When combined with the unitarity relations for the partial waves a complete system of equations (the Roy system) results valid in the low-energy region. The author has studied the existance and uniqueness question for the Roy system and developed successful strategies to solve the system by means of iteration. Several solutions are presented and discussed. The main ingredients in the present approach are a) the use of the N/D-method to regularize the singular Roy equations and implement unitarity and b) the introduction of various iteration methods which do not need any derivatives to solve the resulting nonlinear system of equations numerically. (Auth.)

Optimal control penalty finite elements - Applications to integrodifferential equations

Science.gov (United States)

Chung, T. J.

The application of the optimal-control/penalty finite-element method to the solution of integrodifferential equations in radiative-heat-transfer problems (Chung et al.; Chung and Kim, 1982) is discussed and illustrated. The nonself-adjointness of the convective terms in the governing equations is treated by utilizing optimal-control cost functions and employing penalty functions to constrain auxiliary equations which permit the reduction of second-order derivatives to first order. The OCPFE method is applied to combined-mode heat transfer by conduction, convection, and radiation, both without and with scattering and viscous dissipation; the results are presented graphically and compared to those obtained by other methods. The OCPFE method is shown to give good results in cases where standard Galerkin FE fail, and to facilitate the investigation of scattering and dissipation effects.

Modelling with the master equation solution methods and applications in social and natural sciences

CERN Document Server

Haag, Günter

2017-01-01

This book presents the theory and practical applications of the Master equation approach, which provides a powerful general framework for model building in a variety of disciplines. The aim of the book is to not only highlight different mathematical solution methods, but also reveal their potential by means of practical examples. Part I of the book, which can be used as a toolbox, introduces selected statistical fundamentals and solution methods for the Master equation. In Part II and Part III, the Master equation approach is applied to important applications in the natural and social sciences. The case studies presented mainly hail from the social sciences, including urban and regional dynamics, population dynamics, dynamic decision theory, opinion formation and traffic dynamics; however, some applications from physics and chemistry are treated as well, underlining the interdisciplinary modelling potential of the Master equation approach. Drawing upon the author’s extensive teaching and research experience...

Differential equations methods and applications

CERN Document Server

Said-Houari, Belkacem

2015-01-01

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

Integral equations and their applications

CERN Document Server

Rahman, M

2007-01-01

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

Studies on EOS of shock-generated argon plasmas

International Nuclear Information System (INIS)

Wang Fanhou; Jing Fuqian

2001-01-01

The equation of state for argon plasma, covering the thermodynamic states of 10000-30000 K in temperature and 0.0133-0.166 GPa in pressure, is computed using the Saha model and Debye-Huckel correction. Comparisons of the measured EOS with the calculated ones demonstrate the Saha model and Debye-Huckel correction can be used to well describe the essential behavior of argon plasma under the thermodynamic condition above-mentioned

General existence principles for Stieltjes differential equations with applications to mathematical biology

Science.gov (United States)

López Pouso, Rodrigo; Márquez Albés, Ignacio

2018-04-01

Stieltjes differential equations, which contain equations with impulses and equations on time scales as particular cases, simply consist on replacing usual derivatives by derivatives with respect to a nondecreasing function. In this paper we prove new existence results for functional and discontinuous Stieltjes differential equations and we show that such general results have real world applications. Specifically, we show that Stieltjes differential equations are specially suitable to study populations which exhibit dormant states and/or very short (impulsive) periods of reproduction. In particular, we construct two mathematical models for the evolution of a silkworm population. Our first model can be explicitly solved, as it consists on a linear Stieltjes equation. Our second model, more realistic, is nonlinear, discontinuous and functional, and we deduce the existence of solutions by means of a result proven in this paper.

Application of the Exp-function method to the equal-width wave equation

International Nuclear Information System (INIS)

Biazar, J; Ayati, Z

2008-01-01

In this paper, the Exp-function method is used to find an exact solution of the equal-width wave (EW) equation. The method is straightforward and concise, and its applications are promising. It is shown that the Exp-function method, with the help of symbolic computation, provides a very effective and powerful mathematical tool for solving the EW equation.

Application of finite Fourier transformation for the solution of the diffusion equation

International Nuclear Information System (INIS)

Kobayashi, Keisuke

1991-01-01

The application of the finite Fourier transformation to the solution of the neutron diffusion equation in one dimension, two dimensional x-y and triangular geometries is discussed. It can be shown that the equation obtained by the Nodal Green's function method in Cartesian coordinates can be derived as a special case of the finite Fourier transformation method. (author)

Nonlinear Delay Discrete Inequalities and Their Applications to Volterra Type Difference Equations

Directory of Open Access Journals (Sweden)

Yu Wu

2010-01-01

Full Text Available Delay discrete inequalities with more than one nonlinear term are discussed, which generalize some known results and can be used in the analysis of various problems in the theory of certain classes of discrete equations. Application examples to show boundedness and uniqueness of solutions of a Volterra type difference equation are also given.

Differential Equations Compatible with KZ Equations

International Nuclear Information System (INIS)

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

2000-01-01

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

Difference equations theory, applications and advanced topics

CERN Document Server

Mickens, Ronald E

2015-01-01

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

Fluid phases of hydrogen-bound states and thermodynamical properties

International Nuclear Information System (INIS)

Ebeling, W.; Kraeft, W.D.

1985-08-01

The fluid phases of hydrogen and especially the existence of two critical points, the density dependence of the two - particle states and the effective interactions are discussed. An effective Schroedinger equation and a Saha equation are given. (author)

Exact polynomial solutions of second order differential equations and their applications

International Nuclear Information System (INIS)

Zhang Yaozhong

2012-01-01

We find all polynomials Z(z) such that the differential equation where X(z), Y(z), Z(z) are polynomials of degree at most 4, 3, 2, respectively, has polynomial solutions S(z) = ∏ n i=1 (z − z i ) of degree n with distinct roots z i . We derive a set of n algebraic equations which determine these roots. We also find all polynomials Z(z) which give polynomial solutions to the differential equation when the coefficients of X(z) and Y(z) are algebraically dependent. As applications to our general results, we obtain the exact (closed-form) solutions of the Schrödinger-type differential equations describing: (1) two Coulombically repelling electrons on a sphere; (2) Schrödinger equation from the kink stability analysis of φ 6 -type field theory; (3) static perturbations for the non-extremal Reissner–Nordström solution; (4) planar Dirac electron in Coulomb and magnetic fields; and (5) O(N) invariant decatic anharmonic oscillator. (paper)

Tokamak fluidlike equations, with applications to turbulence and transport in H mode discharges

International Nuclear Information System (INIS)

Kim, Y.B.; Biglari, H.; Carreras, B.A.; Diamond, P.H.; Groebner, R.J.; Kwon, O.J.; Spong, D.A.; Callen, J.D.; Chang, Z.; Hollenberg, J.B.; Sundaram, A.K.; Terry, P.W.; Wang, J.F.

1990-01-01

Significant progress has been made in developing tokamak fluidlike equations which are valid in all collisionality regimes in toroidal devices, and their applications to turbulence and transport in tokamaks. The areas highlighted in this paper include: the rigorous derivation of tokamak fluidlike equations via a generalized Chapman-Enskog procedure in various collisionality regimes and on various time scales; their application to collisionless and collisional drift wave models in a sheared slab geometry; applications to neoclassical drift wave turbulence; i.e. neoclassical ion-temperature-gradient-driven turbulence and neoclassical electron-drift-wave turbulence; applications to neoclassical bootstrap-current-driven turbulence; numerical simulation of nonlinear bootstrap-current-driven turbulence and tearing mode turbulence; transport in Hot-Ion H mode discharges. 20 refs., 3 figs

The H-N method for solving linear transport equation: theory and application

International Nuclear Information System (INIS)

Kaskas, A.; Gulecyuz, M.C.; Tezcan, C.

2002-01-01

The system of singular integral equation which is obtained from the integro-differential form of the linear transport equation as a result of Placzec lemma is solved. Application are given using the exit distributions and the infinite medium Green's function. The same theoretical results are also obtained with the use of the singular eigenfunction of the method of elementary solutions

Structural Equation Modeling with Mplus Basic Concepts, Applications, and Programming

CERN Document Server

Byrne, Barbara M

2011-01-01

Modeled after Barbara Byrne's other best-selling structural equation modeling (SEM) books, this practical guide reviews the basic concepts and applications of SEM using Mplus Versions 5 & 6. The author reviews SEM applications based on actual data taken from her own research. Using non-mathematical language, it is written for the novice SEM user. With each application chapter, the author "walks" the reader through all steps involved in testing the SEM model including: an explanation of the issues addressed illustrated and annotated testing of the hypothesized and post hoc models expl

Direct application of Padé approximant for solving nonlinear differential equations.

Science.gov (United States)

Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Garcia-Gervacio, Jose Luis; Huerta-Chua, Jesus; Morales-Mendoza, Luis Javier; Gonzalez-Lee, Mario

2014-01-01

This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant. 34L30.

Scale-invariance underlying the logistic equation and its social applications

Energy Technology Data Exchange (ETDEWEB)

Hernando, A., E-mail: alberto.hernando@irsamc.ups-tlse.fr [Laboratoire Collisions, Agrégats, Réactivité, IRSAMC, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse Cedex 09 (France); Plastino, A., E-mail: plastino@fisica.unlp.edu.ar [National University La Plata, IFLP-CCT-CONICET, C.C. 727, 1900 La Plata (Argentina); Universitat de les Illes Balears and IFISC-CSIC, 07122 Palma de Mallorca (Spain)

2013-01-03

On the basis of dynamical principles we i) advance a derivation of the Logistic Equation (LE), widely employed (among multiple applications) in the simulation of population growth, and ii) demonstrate that scale-invariance and a mean-value constraint are sufficient and necessary conditions for obtaining it. We also generalize the LE to multi-component systems and show that the above dynamical mechanisms underlie a large number of scale-free processes. Examples are presented regarding city-populations, diffusion in complex networks, and popularity of technological products, all of them obeying the multi-component logistic equation in an either stochastic or deterministic way.

2013 CIME Course Vector-valued Partial Differential Equations and Applications

CERN Document Server

Marcellini, Paolo

2017-01-01

Collating different aspects of Vector-valued Partial Differential Equations and Applications, this volume is based on the 2013 CIME Course with the same name which took place at Cetraro, Italy, under the scientific direction of John Ball and Paolo Marcellini. It contains the following contributions: The pullback equation (Bernard Dacorogna), The stability of the isoperimetric inequality (Nicola Fusco), Mathematical problems in thin elastic sheets: scaling limits, packing, crumpling and singularities (Stefan Müller), and Aspects of PDEs related to fluid flows (Vladimir Sverák). These lectures are addressed to graduate students and researchers in the field.

Scale-invariance underlying the logistic equation and its social applications

International Nuclear Information System (INIS)

Hernando, A.; Plastino, A.

2013-01-01

On the basis of dynamical principles we i) advance a derivation of the Logistic Equation (LE), widely employed (among multiple applications) in the simulation of population growth, and ii) demonstrate that scale-invariance and a mean-value constraint are sufficient and necessary conditions for obtaining it. We also generalize the LE to multi-component systems and show that the above dynamical mechanisms underlie a large number of scale-free processes. Examples are presented regarding city-populations, diffusion in complex networks, and popularity of technological products, all of them obeying the multi-component logistic equation in an either stochastic or deterministic way.

Solving the radiation diffusion and energy balance equations using pseudo-transient continuation

International Nuclear Information System (INIS)

Shestakov, A.I.; Greenough, J.A.; Howell, L.H.

2005-01-01

We develop a scheme for the system coupling the radiation diffusion and matter energy balance equations. The method is based on fully implicit, first-order, backward Euler differencing; Picard-Newton iterations solve the nonlinear system. We show that iterating on the radiation energy density and the emission source is more robust. Since the Picard-Newton scheme may not converge for all initial conditions and time steps, pseudo-transient continuation (Ψtc) is introduced. The combined Ψtc-Picard-Newton scheme is analyzed. We derive conditions on the Ψtc parameter that guarantee physically meaningful iterates, e.g., positive energies. Successive Ψtc iterates are bounded and the radiation energy density and emission source tend to equilibrate. The scheme is incorporated into a multiply dimensioned, massively parallel, Eulerian, radiation-hydrodynamic computer program with automatic mesh refinement (AMR). Three examples are presented that exemplify the scheme's performance. (1) The Pomraning test problem that models radiation flow into cold matter. (2) A similar, but more realistic problem simulating the propagation of an ionization front into tenuous hydrogen gas with a Saha model for the equation-of-state. (3) A 2D axisymmetric (R,Z) simulation with real materials featuring jetting, radiatively driven, interacting shocks

Application of the Radiative Transfer Equation (RTE) to Scattering by ...

African Journals Online (AJOL)

Application of the Radiative Transfer Equation (RTE) to Scattering by a Dust Aerosol Layer. ... Incident radiation in its journey through the atmosphere before reaching the earth surface encounters particles of different sizes and composition such as dust aerosols resulting in interactions that lead to absorption and scattering.

Fourier method for three-dimensional partial differential equations in periodic geometry. Application: HELIAC

International Nuclear Information System (INIS)

Shestakov, A.I.; Mirin, A.A.

1984-01-01

A numerical method based on Fourier expansions and finite differences is presented. The method is demonstrated by solving a scalar, three-dimensional elliptic equation arising in MFE research, but has applicability to a wider class of problems. The scheme solves equations whose solutions are expected to be periodic in one or more of the independent variables

A boundary integral equation for boundary element applications in multigroup neutron diffusion theory

International Nuclear Information System (INIS)

Ozgener, B.

1998-01-01

A boundary integral equation (BIE) is developed for the application of the boundary element method to the multigroup neutron diffusion equations. The developed BIE contains no explicit scattering term; the scattering effects are taken into account by redefining the unknowns. Boundary elements of the linear and constant variety are utilised for validation of the developed boundary integral formulation

Solutions for confluent and double-confluent Heun equations and some applications

Energy Technology Data Exchange (ETDEWEB)

El-Jaick, Lea Jaccoud; Figueiredo, Bartolomeu D.B. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)

2008-07-01

This paper examines some solutions for confluent and double-confluent Heun equations and their applications to the Schroedinger equation with quasi-exactly solvable potentials. In the first place, we review two Leaver's solutions in series of regular and irregular confluent hypergeometric functions for the confluent equation [E. W. Leaver, J. Math. Phys. 27, 1238 (1986)] and introduce an additional expansion in series of irregular confluent hypergeometric functions. Then, we find the conditions under which one of these solutions can be written as a linear combination of the others. In the second place, by means of limiting procedures we generate solutions for the double-confluent equation as well as for special limits of both the confluent and double-confluent equations. In the third place, solutions of the Heun equations are used to solve the one-dimensional Schroedinger equation for quasi-exactly solvable potentials. We consider a symmetric and an asymmetric double-Morse potentials which appear in the theory of quantum spin systems [O. B. Zaslavskii and V. V. Ulyanov, Sov. Phys. JETP 60, 991 (1984)], a bottomless volcano-type potential which gives degenerate eigenstates [S. Kar and R. R. Parwani, Europhys. Lett., 80, 30004 (2007)], and a potential which leads to quasi normal modes, that is, to solutions presenting complex energies [H. T. Cho and C. L. Ho, J. Phys. A: Math. Theor. 40, 1325 (2007)]. (author)

Solutions for confluent and double-confluent Heun equations and some applications

International Nuclear Information System (INIS)

El-Jaick, Lea Jaccoud; Figueiredo, Bartolomeu D.B.

2008-01-01

This paper examines some solutions for confluent and double-confluent Heun equations and their applications to the Schroedinger equation with quasi-exactly solvable potentials. In the first place, we review two Leaver's solutions in series of regular and irregular confluent hypergeometric functions for the confluent equation [E. W. Leaver, J. Math. Phys. 27, 1238 (1986)] and introduce an additional expansion in series of irregular confluent hypergeometric functions. Then, we find the conditions under which one of these solutions can be written as a linear combination of the others. In the second place, by means of limiting procedures we generate solutions for the double-confluent equation as well as for special limits of both the confluent and double-confluent equations. In the third place, solutions of the Heun equations are used to solve the one-dimensional Schroedinger equation for quasi-exactly solvable potentials. We consider a symmetric and an asymmetric double-Morse potentials which appear in the theory of quantum spin systems [O. B. Zaslavskii and V. V. Ulyanov, Sov. Phys. JETP 60, 991 (1984)], a bottomless volcano-type potential which gives degenerate eigenstates [S. Kar and R. R. Parwani, Europhys. Lett., 80, 30004 (2007)], and a potential which leads to quasi normal modes, that is, to solutions presenting complex energies [H. T. Cho and C. L. Ho, J. Phys. A: Math. Theor. 40, 1325 (2007)]. (author)

Application of Monte Carlo method to solving boundary value problem of differential equations

International Nuclear Information System (INIS)

Zuo Yinghong; Wang Jianguo

2012-01-01

This paper introduces the foundation of the Monte Carlo method and the way how to generate the random numbers. Based on the basic thought of the Monte Carlo method and finite differential method, the stochastic model for solving the boundary value problem of differential equations is built. To investigate the application of the Monte Carlo method to solving the boundary value problem of differential equations, the model is used to solve Laplace's equations with the first boundary condition and the unsteady heat transfer equation with initial values and boundary conditions. The results show that the boundary value problem of differential equations can be effectively solved with the Monte Carlo method, and the differential equations with initial condition can also be calculated by using a stochastic probability model which is based on the time-domain finite differential equations. Both the simulation results and theoretical analyses show that the errors of numerical results are lowered as the number of simulation particles is increased. (authors)

Analysis and application of diffusion equations involving a new fractional derivative without singular kernel

Directory of Open Access Journals (Sweden)

Lihong Zhang

2017-11-01

Full Text Available In this article, a family of nonlinear diffusion equations involving multi-term Caputo-Fabrizio time fractional derivative is investigated. Some maximum principles are obtained. We also demonstrate the application of the obtained results by deriving some estimation for solution to reaction-diffusion equations.

Ordinary differential equations

CERN Document Server

Greenberg, Michael D

2014-01-01

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

Solving the transport equation with quadratic finite elements: Theory and applications

International Nuclear Information System (INIS)

Ferguson, J.M.

1997-01-01

At the 4th Joint Conference on Computational Mathematics, the author presented a paper introducing a new quadratic finite element scheme (QFEM) for solving the transport equation. In the ensuing year the author has obtained considerable experience in the application of this method, including solution of eigenvalue problems, transmission problems, and solution of the adjoint form of the equation as well as the usual forward solution. He will present detailed results, and will also discuss other refinements of his transport codes, particularly for 3-dimensional problems on rectilinear and non-rectilinear grids

Improvements to the RADIOM non-LTE model

Science.gov (United States)

Busquet, M.; Colombant, D.; Klapisch, M.; Fyfe, D.; Gardner, J.

2009-12-01

In 1993, we proposed the RADIOM model [M. Busquet, Phys. Fluids 85 (1993) 4191] where an ionization temperature T z is used to derive non-LTE properties from LTE data. T z is obtained from an "extended Saha equation" where unbalanced transitions, like radiative decay, give the non-LTE behavior. Since then, major improvements have been made. T z has been shown to be more than a heuristic value, but describes the actual distribution of excited and ionized states and can be understood as an "effective temperature". Therefore we complement the extended Saha equation by introducing explicitly the auto-ionization/dielectronic capture. Also we use the SCROLL model to benchmark the computed values of T z.

A spatial application of a vegetation productivity equation for neo-soil reconstruction

International Nuclear Information System (INIS)

Burley, J.B.

1999-01-01

Reclamation specialists are interested in the application of recently developed soil productivity equations for post-mining reclamation planning and design. This paper presents the application of one recently developed soil productivity equation to a surface coal mine site in Mercer County, North Dakota. Geographic information systems (GIS) technology (Map*Factory 1.1) was combined with a soil productivity equation developed by the author to generate a GIS script to calculate a site's pre-mining productivity per 10 meter grid cell and then summed to calculate the grand and the expected average soil productivity for the site, resulting in a pre-mining baseline numerical spatial scores. Several post-mining alternatives were evaluated to study various soil management strategies to restore post-mining soil productivity, including: an abandoned mine landscape treatment, a reconstructed topsoil treatment with graded gentile slopes, and a reconstructed topsoil treatment with soil improvements. The results indicated that the abandoned mine scenario was significantly different than the other three treatments (ple0.05), with the reconstructed topsoil treatment with soil amendments generating the greatest estimated productivity

Ionization equilibrium in dense plasmas

International Nuclear Information System (INIS)

Ying, R.

1987-01-01

The average degree of ionization for a strongly coupled plasma is investigated and calculated. Two widely used approaches: the Saha equation method and the Thomas-Fermi (TF) statistical atomic model are adopted to determine the degree of ionization. Both methods are modified in a number of ways to include the strong-coupling effect in the plasma. In the Saha equation approach, the strong-coupling effects are introduced through: (i) a replacement of the Coulomb potential by a screened Debye potential; (ii) adoption of the Planck-Larkin partition function; (iii) description of the electron component by Fermi-Dirac statistics. The calculated degree of ionization exceeds that obtained from the original Saha equation, exhibits a minimum as a function of the density and shows an abrupt phase transition from weakly ionized to a fully ionized state. The zero-temperature TF model for compressed ions and the finite-temperature TF model for ions are investigated for the first time. In order to take into account the strong-coupling effect in a systematic way, a strong-coupling TF model is set up. Favorable results with the relatively simple approximations indicate that the newly established strong-coupling TF model is a more systematic and physically consistent approach

Derivation of gyrotron's reduced equations and its application on the analysis of resonant cavities

International Nuclear Information System (INIS)

Correa, R.A.; Barroso, J.J.; Montes, A.

1988-05-01

In this paper, it is presented a derivation of a reduced set of equations for the electron motion, based upon Lorentz equation, where the applicability conditions and approximations employed are clearly indicated. As an example of practical interest, scaling relations are discussed in the analysis of cavities appropriate for high efficiency operation. (author)

Advantages and Disadvantages of Using MATLAB/ode45 for Solving Differential Equations in Engineering Applications

OpenAIRE

Waleed K. Ahmed

2013-01-01

The present paper demonstrates the route used for solving differential equations for the engineering applications at UAEU. Usually students at the Engineering Requirements Unit (ERU) stage of the Faculty of Engineering at the UAEU must enroll in a course of Differential Equations and Engineering Applications (MATH 2210) as a prerequisite for the subsequent stages of their study. Mainly, one of the objectives of this course is that the students practice MATLAB software package during the cours...

Existence Results for Some Nonlinear Functional-Integral Equations in Banach Algebra with Applications

Directory of Open Access Journals (Sweden)

Lakshmi Narayan Mishra

2016-04-01

Full Text Available In the present manuscript, we prove some results concerning the existence of solutions for some nonlinear functional-integral equations which contains various integral and functional equations that considered in nonlinear analysis and its applications. By utilizing the techniques of noncompactness measures, we operate the fixed point theorems such as Darbo's theorem in Banach algebra concerning the estimate on the solutions. The results obtained in this paper extend and improve essentially some known results in the recent literature. We also provide an example of nonlinear functional-integral equation to show the ability of our main result.

Modelling of a multi-temperature plasma composition

International Nuclear Information System (INIS)

Liani, B.; Benallal, R.; Bentalha, Z.

2005-01-01

Knowledge of plasma composition is very important for various plasma applications and prediction of plasma properties. The authors use the Saha equation and Debye length equation to calculate the non-local thermodynamic-equilibrium plasma composition. It has been shown that the model to 2T with T representing the temperature (electron temperature and heavy-particle temperature) described by Chen and Han [J. Phys. D 32(1999)1711] can be applied for a mixture of gases, where each atomic species has its own temperature, but the model to 4T is more general because it can be applicable to temperatures distant enough of the heavy particles. This can occur in a plasma composed of big- or macro-molecules. The electron temperature T e varies in the range 8000∼20000 K at atmospheric pressure. (authors)

Calculation of thermodynamic functions of aluminum plasma for high-energy-density systems

International Nuclear Information System (INIS)

Shumaev, V. V.

2016-01-01

The results of calculating the degree of ionization, the pressure, and the specific internal energy of aluminum plasma in a wide temperature range are presented. The TERMAG computational code based on the Thomas–Fermi model was used at temperatures T > 105 K, and the ionization equilibrium model (Saha model) was applied at lower temperatures. Quantitatively similar results were obtained in the temperature range where both models are applicable. This suggests that the obtained data may be joined to produce a wide-range equation of state.

Nonlinear Dirac Equations

Directory of Open Access Journals (Sweden)

Wei Khim Ng

2009-02-01

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

Application of Stochastic Partial Differential Equations to Reservoir Property Modelling

KAUST Repository

Potsepaev, R.

2010-09-06

Existing algorithms of geostatistics for stochastic modelling of reservoir parameters require a mapping (the \\'uvt-transform\\') into the parametric space and reconstruction of a stratigraphic co-ordinate system. The parametric space can be considered to represent a pre-deformed and pre-faulted depositional environment. Existing approximations of this mapping in many cases cause significant distortions to the correlation distances. In this work we propose a coordinate free approach for modelling stochastic textures through the application of stochastic partial differential equations. By avoiding the construction of a uvt-transform and stratigraphic coordinates, one can generate realizations directly in the physical space in the presence of deformations and faults. In particular the solution of the modified Helmholtz equation driven by Gaussian white noise is a zero mean Gaussian stationary random field with exponential correlation function (in 3-D). This equation can be used to generate realizations in parametric space. In order to sample in physical space we introduce a stochastic elliptic PDE with tensor coefficients, where the tensor is related to correlation anisotropy and its variation is physical space.

Hybrid Approximation of Solutions of Nonlinear Operator Equations and Application to Equation of Hammerstein-Type

International Nuclear Information System (INIS)

Ofoedu, Eric U.; Malonza, David M.

2010-07-01

In this paper we study the hybrid iterative scheme to find a common element of a set of solutions of generalized mixed equilibrium problem, a set of common fixed points of finite family of weak relatively nonexpansive mapping, and null spaces of finite family of γ-inverse strongly monotone mappings in a 2-uniformly convex and uniformly smooth real Banach space. Our results extend, improve and generalize the results of several authors which were announced recently. An application of our theorem to the solution of equations of Hammerstein-type is of independent interest. (author)

Analysis, Verification, and Application of Equations and Procedures for Design of Exhaust-pipe Shrouds

Science.gov (United States)

Ellerbrock, Herman H.; Wcislo, Chester R.; Dexter, Howard E.

1947-01-01

Investigations were made to develop a simplified method for designing exhaust-pipe shrouds to provide desired or maximum cooling of exhaust installations. Analysis of heat exchange and pressure drop of an adequate exhaust-pipe shroud system requires equations for predicting design temperatures and pressure drop on cooling air side of system. Present experiments derive such equations for usual straight annular exhaust-pipe shroud systems for both parallel flow and counter flow. Equations and methods presented are believed to be applicable under certain conditions to the design of shrouds for tail pipes of jet engines.

Thermodynamic properties and transport coefficients of a two-temperature polytetrafluoroethylene vapor plasma for ablation-controlled discharge applications

International Nuclear Information System (INIS)

Wang, Haiyan; Qi, Haiyang; Wang, Weizong; Yan, Joseph D; Geng, Jinyue; Wu, Yaowu

2017-01-01

Ablation-controlled plasmas have been used in a range of technical applications where local thermodynamic equilibrium (LTE) is often violated near the wall due to the strong cooling effect caused by the ablation of wall materials. The thermodynamic and transport properties of ablated polytetrafluoroethylene (PTFE) vapor, which determine the flowing plasma behavior in such applications, are calculated based on a two-temperature model at atmospheric pressure. To our knowledge, no data for PTFE have been reported in the literature. The species composition and thermodynamic properties are numerically determined using the two-temperature Saha equation and the Guldberg–Waage equation according to van de Sanden et al ’s derivation. The transport coefficients, including viscosity, thermal conductivity and electrical conductivity, are calculated with the most recent collision interaction potentials using Devoto’s electron and heavy-particle decoupling approach but expanded to the third-order approximation (second-order for viscosity) in the frame of the Chapman–Enskog method. Results are computed for different degrees of thermal non-equilibrium, i.e. the ratio of electron to heavy-particle temperatures, from 1 to 10, with electron temperature ranging from 300 to 40 000 K. Plasma transport properties in the LTE state obtained from the present work are compared with existing published results and the causes for the discrepancy analyzed. The two-temperature plasma properties calculated in the present work enable the modeling of wall ablation-controlled plasma processes. (paper)

Thermodynamic properties and transport coefficients of a two-temperature polytetrafluoroethylene vapor plasma for ablation-controlled discharge applications

Science.gov (United States)

Wang, Haiyan; Wang, Weizong; Yan, Joseph D.; Qi, Haiyang; Geng, Jinyue; Wu, Yaowu

2017-10-01

Ablation-controlled plasmas have been used in a range of technical applications where local thermodynamic equilibrium (LTE) is often violated near the wall due to the strong cooling effect caused by the ablation of wall materials. The thermodynamic and transport properties of ablated polytetrafluoroethylene (PTFE) vapor, which determine the flowing plasma behavior in such applications, are calculated based on a two-temperature model at atmospheric pressure. To our knowledge, no data for PTFE have been reported in the literature. The species composition and thermodynamic properties are numerically determined using the two-temperature Saha equation and the Guldberg-Waage equation according to van de Sanden et al’s derivation. The transport coefficients, including viscosity, thermal conductivity and electrical conductivity, are calculated with the most recent collision interaction potentials using Devoto’s electron and heavy-particle decoupling approach but expanded to the third-order approximation (second-order for viscosity) in the frame of the Chapman-Enskog method. Results are computed for different degrees of thermal non-equilibrium, i.e. the ratio of electron to heavy-particle temperatures, from 1 to 10, with electron temperature ranging from 300 to 40 000 K. Plasma transport properties in the LTE state obtained from the present work are compared with existing published results and the causes for the discrepancy analyzed. The two-temperature plasma properties calculated in the present work enable the modeling of wall ablation-controlled plasma processes.

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

International Nuclear Information System (INIS)

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

2014-01-01

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

Beginning partial differential equations

CERN Document Server

O'Neil, Peter V

2014-01-01

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

Behavioral momentum theory: equations and applications.

Science.gov (United States)

Nevin, John A; Shahan, Timothy A

2011-01-01

Behavioral momentum theory provides a quantitative account of how reinforcers experienced within a discriminative stimulus context govern the persistence of behavior that occurs in that context. The theory suggests that all reinforcers obtained in the presence of a discriminative stimulus increase resistance to change, regardless of whether those reinforcers are contingent on the target behavior, are noncontingent, or are even contingent on an alternative behavior. In this paper, we describe the equations that constitute the theory and address their application to issues of particular importance in applied settings. The theory provides a framework within which to consider the effects of interventions such as extinction, noncontingent reinforcement, differential reinforcement of alternative behavior, and other phenomena (e.g., resurgence). Finally, the theory predicts some counterintuitive and potentially counterproductive effects of alternative reinforcement, and can serve as an integrative guide for intervention when its terms are identified with the relevant conditions of applied settings.

Numerical methods for differential equations and applications

International Nuclear Information System (INIS)

Ixaru, L.G.

1984-01-01

This book is addressed to persons who, without being professionals in applied mathematics, are often faced with the problem of numerically solving differential equations. In each of the first three chapters a definite class of methods is discussed for the solution of the initial value problem for ordinary differential equations: multistep methods; one-step methods; and piecewise perturbation methods. The fourth chapter is mainly focussed on the boundary value problems for linear second-order equations, with a section devoted to the Schroedinger equation. In the fifth chapter the eigenvalue problem for the radial Schroedinger equation is solved in several ways, with computer programs included. (Auth.)

Normal Forms for Retarded Functional Differential Equations and Applications to Bogdanov-Takens Singularity

Science.gov (United States)

Faria, T.; Magalhaes, L. T.

The paper addresses, for retarded functional differential equations (FDEs), the computation of normal forms associated with the flow on a finite-dimensional invariant manifold tangent to invariant spaces for the infinitesimal generator of the linearized equation at a singularity. A phase space appropriate to the computation of these normal forms is introduced, and adequate nonresonance conditions for the computation of the normal forms are derived. As an application, the general situation of Bogdanov-Takens singularity and its versal unfolding for scalar retarded FDEs with nondegeneracy at second order is considered, both in the general case and in the case of differential-delay equations of the form ẋ( t) = ƒ( x( t), x( t-1)).

Dichotomies for generalized ordinary differential equations and applications

Science.gov (United States)

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

2018-03-01

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

Some applications of linear difference equations in finance with wolfram|alpha and maple

Directory of Open Access Journals (Sweden)

Dana Rıhová

2014-12-01

Full Text Available The principle objective of this paper is to show how linear difference equations can be applied to solve some issues of financial mathematics. We focus on the area of compound interest and annuities. In both cases we determine appropriate recursive rules, which constitute the first order linear difference equations with constant coefficients, and derive formulas required for calculating examples. Finally, we present possibilities of application of two selected computer algebra systems Wolfram|Alpha and Maple in this mathematical area.

Application of finite element method in the solution of transport equation

International Nuclear Information System (INIS)

Maiorino, J.R.; Vieira, W.J.

1985-01-01

It is presented the application of finite element method in the solution of second order transport equation (self-adjoint) for the even parity flux. The angular component is treated by expansion in Legendre polinomials uncoupled of the spatial component, which is approached by an expansion in base functions, interpolated in each spatial element. (M.C.K.) [pt

Application of Local Fractional Series Expansion Method to Solve Klein-Gordon Equations on Cantor Sets

Directory of Open Access Journals (Sweden)

Ai-Min Yang

2014-01-01

Full Text Available We use the local fractional series expansion method to solve the Klein-Gordon equations on Cantor sets within the local fractional derivatives. The analytical solutions within the nondifferential terms are discussed. The obtained results show the simplicity and efficiency of the present technique with application to the problems of the liner differential equations on Cantor sets.

Some properties of matter at very HTGH temperatures and high pressures (equations of state, opacity); Quelques proprietes de la matiere aux tres hautes temperatures et fortes pressions (equation d'etat, opacite)

Energy Technology Data Exchange (ETDEWEB)

Gervat, A [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

1964-06-15

The Thomas-Fermi equations which' are zero-order approximations of the Hartree-Fock equations, make it possible to study some aspects of the behaviour of matter at high pressures. In the first chapter is considered the calculation of 1 values which do not require the Schroedinger equation to be solved. The values of the quantum and exchange corrections give the zone of validity of the theory. For each R and T pair it is possible to calculate the energy and the pressure. For the calculation of the energy 'it has been necessary, in the region close to the nucleus where the corrections diverge, to replace the density given by the Thomas-Fermi theory by that deduced from the wave-functions which, in the small region, are very similar to that of a hydrogen atom of charge z. The calculation of the degree of ionization is particularly simple and does not require the Saha equations to be solved. Besides the distribution of electrons in the r space it is simple to determine the distribution according to the quantum number I, and this for each value of the R, T pair. In the second chapter, the introduction of the, Thomas and Fermi potential into the Schroedinger equation makes it possible to obtain the energy spectrum of a perfect isolated atom supposed to represent an average atom of the hot, compressed matter. The changes in the levels with increasing temperature and pressure can be deduced from this. It is particular easy with this model to interpret the phenomenon of ionization caused by pressure. A knowledge of the wave functions makes it possible to calculate the transition probabilities which, coupled with the occupation probabilities, lead to the opacity coefficients. Only the bound-free and free-free transitions have been considered but these latter include, because of the properties of the model used, a large part of bound-bound or band-band transitions. Finally, the use of the Thomas-Fermi potential for the calculation of bands is particularly suitable for

Functional analytic methods in complex analysis and applications to partial differential equations

International Nuclear Information System (INIS)

Mshimba, A.S.A.; Tutschke, W.

1990-01-01

The volume contains 24 lectures given at the Workshop on Functional Analytic Methods in Complex Analysis and Applications to Partial Differential Equations held in Trieste, Italy, between 8-19 February 1988, at the ICTP. A separate abstract was prepared for each of these lectures. Refs and figs

Atomic Emission Spectra Diagnosis and Electron Density Measurement of Semiconductor Bridge (SCB) Plasma

International Nuclear Information System (INIS)

Feng Hongyan; Zhu Shunguan; Zhang Lin; Wan Xiaoxia; Li Yan; Shen Ruiqi

2010-01-01

Emission spectra of a semiconductor bridge (SCB) plasma in a visible range was studied in air. The electron density was measured in a conventional way from the broadening of the A1 I 394.4 nm Stark width. Based on the Saha equation, a system for recording the intensity of Si I 390.5 nm and Si II 413.1 nm was designed. With this technique, the SCB plasma electron density was measured well and accurately. Moreover, the electron density distribution Vs time was acquired from one SCB discharge. The individual result from the broadening of the Al I 394.4 nm Stark width and Saha equation was all in the range of 10 15 cm -3 to 10 16 cm -3 . Finally the presumption of the local thermodynamic equilibrium (LTE) condition was validated.

Introductory Applications of Partial Differential Equations With Emphasis on Wave Propagation and Diffusion

CERN Document Server

Lamb, George L

1995-01-01

INTRODUCTORY APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATIONS. With Emphasis on Wave Propagation and Diffusion. This is the ideal text for students and professionals who have some familiarity with partial differential equations, and who now wish to consolidate and expand their knowledge. Unlike most other texts on this topic, it interweaves prior knowledge of mathematics and physics, especially heat conduction and wave motion, into a presentation that demonstrates their interdependence. The result is a superb teaching text that reinforces the reader's understanding of both mathematics and physic

Malliavin Calculus With Applications to Stochastic Partial Differential Equations

CERN Document Server

Sanz-Solé, Marta

2005-01-01

Developed in the 1970s to study the existence and smoothness of density for the probability laws of random vectors, Malliavin calculus--a stochastic calculus of variation on the Wiener space--has proven fruitful in many problems in probability theory, particularly in probabilistic numerical methods in financial mathematics.This book presents applications of Malliavin calculus to the analysis of probability laws of solutions to stochastic partial differential equations driven by Gaussian noises that are white in time and coloured in space. The first five chapters introduce the calculus itself

Application of cellular neural network (CNN) method to the nuclear reactor dynamics equations

International Nuclear Information System (INIS)

Hadad, K.; Piroozmand, A.

2007-01-01

This paper describes the application of a multilayer cellular neural network (CNN) to model and solve the nuclear reactor dynamic equations. An equivalent electrical circuit is analyzed and the governing equations of a bare, homogeneous reactor core are modeled via CNN. The validity of the CNN result is compared with numerical solution of the system of nonlinear governing partial differential equations (PDE) using MATLAB. Steady state as well as transient simulations, show very good comparison between the two methods. We used our CNN model to simulate space-time response of different reactivity excursions in a typical nuclear reactor. On line solution of reactor dynamic equations is used as an aid to reactor operation decision making. The complete algorithm could also be implemented using very large scale integrated circuit (VLSI) circuitry. The efficiency of the calculation method makes it useful for small size nuclear reactors such as the ones used in space missions

Optimal Assignment Problem Applications of Finite Mathematics to Business and Economics. [and] Difference Equations with Applications. Applications of Difference Equations to Economics and Social Sciences. [and] Selected Applications of Mathematics to Finance and Investment. Applications of Elementary Algebra to Finance. [and] Force of Interest. Applications of Calculus to Finance. UMAP Units 317, 322, 381, 382.

Science.gov (United States)

Gale, David; And Others

Four units make up the contents of this document. The first examines applications of finite mathematics to business and economies. The user is expected to learn the method of optimization in optimal assignment problems. The second module presents applications of difference equations to economics and social sciences, and shows how to: 1) interpret…

Analytic solution of vector model kinetic equations with constant kernel and their applications

International Nuclear Information System (INIS)

Latyshev, A.V.

1993-01-01

For the first time exact solutions the heif-space boundary value problems for model kinetic equations is obtained. Here x > 0, μ is an element of (-∞, 0) union (0, +∞), Σ = diag {σ 1 , σ 2 }, C = [c ij ] - 2 x 2-matrix, Ψ (x, μ) is vector-column with elements ψ 1 and ψ 2 . Exact solution of the diffusion slip flow of the binary gas mixture as a application for the model Boltzmann equation with collision operator in the McCormack's form is found. 18 refs

Application of Bridge Pier Scour Equations for Large Woody Vegetation

Science.gov (United States)

2016-07-01

velocities and, thus, reduces boundary shear stress , the primary driver of sediment erosion. Even if this vegetation should become uprooted, the smaller...ER D C TR -1 6- 10 Application of Bridge Pier Scour Equations for Large Woody Vegetation En gi ne er R es ea rc h an d D ev el op m...K. Corcoran, and Kevin S. Holden July 2016 Approved for public release ; distribution is unlimited. The U.S. Army Engineer Research and

General form of the Euler-Poisson-Darboux equation and application of the transmutation method

Directory of Open Access Journals (Sweden)

Elina L. Shishkina

2017-07-01

Full Text Available In this article, we find solution representations in the compact integral form to the Cauchy problem for a general form of the Euler-Poisson-Darboux equation with Bessel operators via generalized translation and spherical mean operators for all values of the parameter k, including also not studying before exceptional odd negative values. We use a Hankel transform method to prove results in a unified way. Under additional conditions we prove that a distributional solution is a classical one too. A transmutation property for connected generalized spherical mean is proved and importance of applying transmutation methods for differential equations with Bessel operators is emphasized. The paper also contains a short historical introduction on differential equations with Bessel operators and a rather detailed reference list of monographs and papers on mathematical theory and applications of this class of differential equations.

Application of wavelets to singular integral scattering equations

International Nuclear Information System (INIS)

Kessler, B.M.; Payne, G.L.; Polyzou, W.N.

2004-01-01

The use of orthonormal wavelet basis functions for solving singular integral scattering equations is investigated. It is shown that these basis functions lead to sparse matrix equations which can be solved by iterative techniques. The scaling properties of wavelets are used to derive an efficient method for evaluating the singular integrals. The accuracy and efficiency of the wavelet transforms are demonstrated by solving the two-body T-matrix equation without partial wave projection. The resulting matrix equation which is characteristic of multiparticle integral scattering equations is found to provide an efficient method for obtaining accurate approximate solutions to the integral equation. These results indicate that wavelet transforms may provide a useful tool for studying few-body systems

An irrational trial equation method and its applications

Indian Academy of Sciences (India)

equation method which is different from those direct methods. Liu's key idea is that exact solution to a differential equation can be given by solving an integration. For example, consider a differential equation of u. We always assume that its exact solution satisfies a solvable equation u = F(u). Therefore, our task is just to find.

Hardy inequality on time scales and its application to half-linear dynamic equations

Directory of Open Access Journals (Sweden)

Řehák Pavel

2005-01-01

Full Text Available A time-scale version of the Hardy inequality is presented, which unifies and extends well-known Hardy inequalities in the continuous and in the discrete setting. An application in the oscillation theory of half-linear dynamic equations is given.

Efficacy and Safety Comparison Between Suberoylanilide Hydroxamic Acid and Mitomycin C in Reducing the Risk of Corneal Haze After PRK Treatment In Vivo.

Science.gov (United States)

Anumanthan, Govindaraj; Sharma, Ajay; Waggoner, Michael; Hamm, Chuck W; Gupta, Suneel; Hesemann, Nathan P; Mohan, Rajiv R

2017-12-01

This study compared the efficacy and safety of suberoylanilide hydroxamic acid (SAHA) and mitomycin C (MMC) up to 4 months in the prevention of corneal haze induced by photorefractive keratectomy (PRK) in rabbits in vivo. Corneal haze in rabbits was produced with -9.00 diopter PRK. A single application of SAHA (25 μM) or MMC (0.02%) was applied topically immediately after PRK. Effects of the two drugs were analyzed by slit-lamp microscope, specular microscope, TUNEL assay, and immunofluorescence. Single topical adjunct use of SAHA (25 μM) or MMC (0.02%) after PRK attenuated more than 95% corneal haze and myofibroblast formation (P PRK in rabbits in vivo. SAHA exhibited significantly reduced short- and long-term damage to the corneal endothelium compared to MMC in rabbits. SAHA is an effective and potentially safer alternative to MMC for the prevention of corneal haze after PRK. Clinical trials are warranted. [J Refract Surg. 2017;33(12):834-839.]. Copyright 2017, SLACK Incorporated.

A new generalized algebra method and its application in the (2 + 1) dimensional Boiti-Leon-Pempinelli equation

International Nuclear Information System (INIS)

Ren Yujie; Liu Shutian; Zhang Hongqing

2007-01-01

In the present paper, some types of general solutions of a first-order nonlinear ordinary differential equation with six degree are given and a new generalized algebra method is presented to find more exact solutions of nonlinear differential equations. As an application of the method and the solutions of this equation, we choose the (2 + 1) dimensional Boiti Leon Pempinelli equation to illustrate the validity and advantages of the method. As a consequence, more new types and general solutions are found which include rational solutions and irrational solutions and so on. The new method can also be applied to other nonlinear differential equations in mathematical physics

Application of the equations of radioactive growth and decay to geochronological models and explicit solution of the equations by Laplace transformation

International Nuclear Information System (INIS)

Catchen, G.L.

1984-01-01

A recently developed method of pore-fluid age determination assumes secular equilibrium in the 238 U decay chain. The efficacy of this approximation is investigated using computer evaluations of the equations that give the time evolution of the 238 U decay chain, i.e. the solution of the equations of radioactive growth and decay. This analysis is performed considering two alternative geochemical scenarios to that of secular equilibrium - only 238 U present initially and 238 U and 234 U present initially. In addition, the effects of the 235 U decay chain are also determined in a similar fashion. These particular examples were chosen to show that more sophisticated geochronological models for many dating applications can be developed using such computer calculations. To facilitate such analyses, a solution of the equations of radioactive growth and decay for an arbitrary initial condition is derived using the Laplace transformation method and matrix algebra. Other solutions - both general and special - that are found in some well-known textbooks are reviewed. (orig.)

Proposal of limit moment equation applicable to planar/non-planar flaw in wall thinned pipes under bending

International Nuclear Information System (INIS)

Tsuji, Masataka; Meshii, Toshiyuki

2011-01-01

Highlights: → A limit moment equation applicable to planar/non-planar flaw of 0 ≤ θ ≤ π found in wall thinned straight pipes was proposed. → An idea to rationally classify planar/non-planar flaw in wall thinned pipes was proposed. → The equation based on the experimental observation focused on the fracture mode. - Abstract: In this paper, a limit bending moment equation applicable to all types of planar and non-planar flaws in wall-thinned straight pipes under bending was proposed. A system to rationally classify the planar/non-planar flaws in wall-thinned pipes was suggested based on experimental observations focused on the fracture mode. The results demonstrate the importance of distinguishing between axial and circumferential long flaws in wall-thinned pipes.

Laplace transform overcoming principle drawbacks in application of the variational iteration method to fractional heat equations

Directory of Open Access Journals (Sweden)

Wu Guo-Cheng

2012-01-01

Full Text Available This note presents a Laplace transform approach in the determination of the Lagrange multiplier when the variational iteration method is applied to time fractional heat diffusion equation. The presented approach is more straightforward and allows some simplification in application of the variational iteration method to fractional differential equations, thus improving the convergence of the successive iterations.

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

Science.gov (United States)

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

2015-04-08

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

Some applications of the Faddeev-Yakubovsky equations to the cold-atom physics

International Nuclear Information System (INIS)

Carbonell, J.; Deltuva, A.; Lazauskas, R.

2011-01-01

We present some recent applications of the Faddeev-Yakubovsky equations in describing atomic bound and scattering problems. We consider the scattering of a charged particle X by atomic hydrogen with special interest in X = p,e ± , systems of cold bosonic molecules and the bound and scattering properties of N=3 and N=4 atomic 4 He multimers. (authors)

Introduction to partial differential equations with applications

CERN Document Server

Zachmanoglou, E C

1988-01-01

This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.

Functional equations with causal operators

CERN Document Server

Corduneanu, C

2003-01-01

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

Fractional Schroedinger equation

International Nuclear Information System (INIS)

Laskin, Nick

2002-01-01

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

Workload Characterization of CFD Applications Using Partial Differential Equation Solvers

Science.gov (United States)

Waheed, Abdul; Yan, Jerry; Saini, Subhash (Technical Monitor)

1998-01-01

Workload characterization is used for modeling and evaluating of computing systems at different levels of detail. We present workload characterization for a class of Computational Fluid Dynamics (CFD) applications that solve Partial Differential Equations (PDEs). This workload characterization focuses on three high performance computing platforms: SGI Origin2000, EBM SP-2, a cluster of Intel Pentium Pro bases PCs. We execute extensive measurement-based experiments on these platforms to gather statistics of system resource usage, which results in workload characterization. Our workload characterization approach yields a coarse-grain resource utilization behavior that is being applied for performance modeling and evaluation of distributed high performance metacomputing systems. In addition, this study enhances our understanding of interactions between PDE solver workloads and high performance computing platforms and is useful for tuning these applications.

Some physical applications of fractional Schroedinger equation

International Nuclear Information System (INIS)

Guo Xiaoyi; Xu Mingyu

2006-01-01

The fractional Schroedinger equation is solved for a free particle and for an infinite square potential well. The fundamental solution of the Cauchy problem for a free particle, the energy levels and the normalized wave functions of a particle in a potential well are obtained. In the barrier penetration problem, the reflection coefficient and transmission coefficient of a particle from a rectangular potential wall is determined. In the quantum scattering problem, according to the fractional Schroedinger equation, the Green's function of the Lippmann-Schwinger integral equation is given

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

International Nuclear Information System (INIS)

Lu, Bin

2012-01-01

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

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

CERN Document Server

Shubin, M

1994-01-01

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

Sine-Gordon equation and its application to tectonic stress transfer

Science.gov (United States)

Bykov, Victor G.

2014-07-01

An overview is given on remarkable progress that has been made in theoretical studies of solitons and other nonlinear wave patterns, excited during the deformation of fault block (fragmented) geological media. The models that are compliant with the classical and perturbed sine-Gordon equations have only been chosen. In these mathematical models, the rotation angle of blocks (fragments) and their translatory displacement of the medium are used as dynamic variables. A brief description of the known models and their geophysical and geodynamic applications is given. These models reproduce the kinematic and dynamic features of the traveling deformation front (kink, soliton) generated in the fragmented media. It is demonstrated that the sine-Gordon equation is applicable to the description of series of the observed seismic data, modeling of strain waves, as well as the features related to fault dynamics and the subduction slab, including slow earthquakes, periodicity of episodic tremor and slow slip (ETS) events, and migration pattern of tremors. The study shows that simple heuristic models and analytical and numerical computations can explain triggering of seismicity by transient processes, such as stress changes associated with solitary strain waves in crustal faults. The need to develop the above-mentioned new (nonlinear) mathematical models of the deformed fault and fragmented media was caused by the reason that it is impossible to explain a lot of the observed effects, particularly, slow redistribution and migration of stresses in the lithosphere, within the framework of the linear elasticity theory.

On some three-dimensional problems of piezoelectricity | Saha ...

African Journals Online (AJOL)

The problem of an elliptical crack embedded in an unbounded transversely isotropic piezoelectric medium and subjected to remote normal loading is considered first. The integral equation method developed by Roy and his coworkers has been applied suitably with proper modifications to solve the problem. The method ...

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

International Nuclear Information System (INIS)

Kotel'nikov, G.A.

1994-01-01

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

Learning Qualitative Differential Equation models: a survey of algorithms and applications.

Science.gov (United States)

Pang, Wei; Coghill, George M

2010-03-01

Over the last two decades, qualitative reasoning (QR) has become an important domain in Artificial Intelligence. QDE (Qualitative Differential Equation) model learning (QML), as a branch of QR, has also received an increasing amount of attention; many systems have been proposed to solve various significant problems in this field. QML has been applied to a wide range of fields, including physics, biology and medical science. In this paper, we first identify the scope of this review by distinguishing QML from other QML systems, and then review all the noteworthy QML systems within this scope. The applications of QML in several application domains are also introduced briefly. Finally, the future directions of QML are explored from different perspectives.

About peculiarities of application of the method of fast expansions in the solution of the Navier-Stokes equations

Directory of Open Access Journals (Sweden)

A. D. Chernyshov

2017-01-01

Full Text Available The brief presentation of the method of fast expansions is given to solve nonlinear differential equations. Application  rules of the operator of fast expansions are specified for solving differential equations. According to the method of fast expansions, an unknown function can be represented as the sum of the boundary function and Fourier series sines and cosines for one variable. The special construction of the boundary functions leads to reasonably fast convergence of the Fourier series, so that for engineering calculations, it is sufficient to consider only the first three members. The method is applicable both to linear and nonlinear integro-differential systems. By means of applying the method of fast expansions to nonlinear Navier-Stokes equations the problem is reduced to a closed system of ordinary differential equations, which solution doesn't represent special difficulties. We can reapply the method of fast expansions to the resulting system of differential equations and reduce the original problem to a system of algebraic equations. If the problem is n-dimensional, then after n-fold application of the method of fast expansions the problem will be reduced to a closed algebraic system. Finally, we obtain an analytic-form solution of complicated boundary value problem in partial derivatives. The flow of an incompressible viscous fluid of Navier–Stokes is considered in a curvilinear pipe. The problem is reduced to solving a closed system of ordinary differential equations with boundary conditions by the method of fast expansions. The article considers peculiarities of finding the coefficients of boundary functions and Fourier coefficients for the zero-order and first-order operators of fast expansions. Obtaining the analytic-form solution is of great interest, because it allows to analyze and to investigate the influence of various factors on the properties of the viscous fluid in specific cases.

Differential equations

CERN Document Server

Barbu, Viorel

2016-01-01

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

The analysis of fractional differential equations an application-oriented exposition using differential operators of Caputo type

CERN Document Server

Diethelm, Kai

2010-01-01

Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.

Solvability of a class of systems of infinite-dimensional integral equations and their application in statistical mechanics

International Nuclear Information System (INIS)

Gonchar, N.S.

1986-01-01

This paper presents a mathematical method developed for investigating a class of systems of infinite-dimensional integral equations which have application in statistical mechanics. Necessary and sufficient conditions are obtained for the uniqueness and bifurcation of the solution of this class of systems of equations. Problems of equilibrium statistical mechanics are considered on the basis of this method

Nonlinear Variation of Parameters Formula for Impulsive Differential Equations with Initial Time Difference and Application

Directory of Open Access Journals (Sweden)

Peiguang Wang

2014-01-01

Full Text Available This paper establishes variation of parameters formula for impulsive differential equations with initial time difference. As an application, one of the results is used to investigate stability properties of solutions.

The parabolic equation method for outdoor sound propagation

DEFF Research Database (Denmark)

Arranz, Marta Galindo

The parabolic equation method is a versatile tool for outdoor sound propagation. The present study has focused on the Cranck-Nicolson type Parabolic Equation method (CNPE). Three different applications of the CNPE method have been investigated. The first two applications study variations of the g......The parabolic equation method is a versatile tool for outdoor sound propagation. The present study has focused on the Cranck-Nicolson type Parabolic Equation method (CNPE). Three different applications of the CNPE method have been investigated. The first two applications study variations...

The calculation of electron chemical potential and ion charge state and their influence on plasma conductivity in electrical explosion of metal wire

International Nuclear Information System (INIS)

Shi, Zongqian; Wang, Kun; Li, Yao; Shi, Yuanjie; Wu, Jian; Jia, Shenli

2014-01-01

The electron chemical potential and ion charge state (average ion charge and ion distribution) are important parameters in calculating plasma conductivity in electrical explosion of metal wire. In this paper, the calculating method of electron chemical potential and ion charge state is discussed at first. For the calculation of electron chemical potential, the ideal free electron gas model and Thomas-Fermi model are compared and analyzed in terms of the coupling constant of plasma. The Thomas-Fermi ionization model, which is used to calculate ion charge state, is compared with the method based on Saha equation. Furthermore, the influence of electron degenerated energy levels and ion excited states in Saha equation on the ion charge state is also analyzed. Then the influence of different calculating methods of electron chemical potential and ion charge state on plasma conductivity is discussed by applying them in the Lee-More conductivity model

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

Energy Technology Data Exchange (ETDEWEB)

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

1968-12-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

1968-12-01

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

High-density equation of state for helium and its application to bubbles in solids

International Nuclear Information System (INIS)

Wolfer, W.G.

1980-06-01

Helium, produced by transmutations or injected, causes bubble formation in solids at elevated temperatures. For small bubbles, the gas pressure required to balance the surface tension reaches values which far exceed those obtainable in experiments to measure the equation of state for helium gas. Therefore, empirical gas laws cannot be considered applicable to the fluid-like densities existing in small bubbles. In order to remedy this situation, an equation of state for helium was developed from the theory of the liquid state. At very low densities, this theoretically derived equation of state agrees with experimental results. For high densities, however, gas pressures are predicted which are significantly higher than those derived from the ideal gas law, but also significantly lower than pressures obtained with the van der Waals law. When applied to equilibrium bubbles in solids, it is found that the high-density equation of state leads to less bubble swelling than the van der Waals law, but more than the ideal gas law. Furthermore, the number of helium atoms in equilibrium bubbles is nearly independent of temperature

Partial differential equations and boundary-value problems with applications

CERN Document Server

Pinsky, Mark A

2011-01-01

Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems-rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate th

Applicability of angular flux discontinuity factor preserving region-wise leakage for integro-differential transport equation

International Nuclear Information System (INIS)

Sakamoto, Tatsuya; Endo, Tomohiro; Yamamoto, Akio

2014-01-01

In the current core analysis, spatial homogenization is utilized to reduce the computational time. The discontinuity factor (DF) is one of the effective correction factors to reduce spatial homogenization error. The DF in diffusion equation is widely used; on the other hand the DF in transport equation has not been put to practical use although several efforts have been carried out. In this paper, the angular flux discontinuity factor (AFDF) as the DF for the integro-differential transport equation (e.g., the discrete-ordinate method, the method of characteristics) is theoretically described and its applicability is discussed. The AFDF is used to preserve the region-wise neutron leakage at each spatial mesh and defined as a ratio of heterogeneous and homogeneous angular fluxes at the homogenized region surface. In a homogeneous calculation with the AFDF, the angular flux is discontinuous at the region surface. In this paper the applicability of the AFDF to fuel pin cell homogenization is verified for one-dimensional slab geometry. As a result of this verification, it is confirmed that the AFDF has the capability to reduce the spatial homogenization error of fuel pin cell homogenization. (author)

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

Energy Technology Data Exchange (ETDEWEB)

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

2013-09-02

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

Magnetic Positioning Equations Theory and Applications

CERN Document Server

Esh, Mordechay

2012-01-01

In the study of Magnetic Positioning Equations, it is possible to calculate and create analytical expressions for the intensity of magnetic fields when the coordinates x, y and z are known; identifying the inverse expressions is more difficult. This book is designed to explore the discovery of how to get the coordinates of analytical expressions x, y and z when the intensity of the magnetic fields are known. The discovery also deals with the problem of how to analyze, define and design any type of transmitter along with its positioning equation(s).Presents new simple mathematical solution expr

Thermodynamics of atomic and ionized hydrogen: analytical results versus equation-of-state tables and Monte Carlo data.

Science.gov (United States)

Alastuey, A; Ballenegger, V

2012-12-01

We compute thermodynamical properties of a low-density hydrogen gas within the physical picture, in which the system is described as a quantum electron-proton plasma interacting via the Coulomb potential. Our calculations are done using the exact scaled low-temperature (SLT) expansion, which provides a rigorous extension of the well-known virial expansion-valid in the fully ionized phase-into the Saha regime where the system is partially or fully recombined into hydrogen atoms. After recalling the SLT expansion of the pressure [A. Alastuey et al., J. Stat. Phys. 130, 1119 (2008)], we obtain the SLT expansions of the chemical potential and of the internal energy, up to order exp(-|E_{H}|/kT) included (E_{H}≃-13.6 eV). Those truncated expansions describe the first five nonideal corrections to the ideal Saha law. They account exactly, up to the considered order, for all effects of interactions and thermal excitations, including the formation of bound states (atom H, ions H^{-} and H_{2}^{+}, molecule H_{2},⋯) and atom-charge and atom-atom interactions. Among the five leading corrections, three are easy to evaluate, while the remaining ones involve well-defined internal partition functions for the molecule H_{2} and ions H^{-} and H_{2}^{+}, for which no closed-form analytical formula exist currently. We provide accurate low-temperature approximations for those partition functions by using known values of rotational and vibrational energies. We compare then the predictions of the SLT expansion, for the pressure and the internal energy, with, on the one hand, the equation-of-state tables obtained within the opacity program at Livermore (OPAL) and, on the other hand, data of path integral quantum Monte Carlo (PIMC) simulations. In general, a good agreement is found. At low densities, the simple analytical SLT formulas reproduce the values of the OPAL tables up to the last digit in a large range of temperatures, while at higher densities (ρ∼10^{-2} g/cm^{3}), some

Quadratic Diophantine equations

CERN Document Server

Andreescu, Titu

2015-01-01

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

Kramers-Moyal expansion for stochastic differential equations with single and multiple delays: Applications to financial physics and neurophysics

International Nuclear Information System (INIS)

Frank, T.D.

2007-01-01

We present a generalized Kramers-Moyal expansion for stochastic differential equations with single and multiple delays. In particular, we show that the delay Fokker-Planck equation derived earlier in the literature is a special case of the proposed Kramers-Moyal expansion. Applications for bond pricing and a self-inhibitory neuron model are discussed

The histone deacetylase inhibitor SAHA acts in synergism with fenretinide and doxorubicin to control growth of rhabdoid tumor cells

International Nuclear Information System (INIS)

Kerl, Kornelius; Eveslage, Maria; Jung, Manfred; Meisterernst, Michael; Frühwald, Michael; Ries, David; Unland, Rebecca; Borchert, Christiane; Moreno, Natalia; Hasselblatt, Martin; Jürgens, Heribert; Kool, Marcel; Görlich, Dennis

2013-01-01

Rhabdoid tumors are highly aggressive malignancies affecting infants and very young children. In many instances these tumors are resistant to conventional type chemotherapy necessitating alternative approaches. Proliferation assays (MTT), apoptosis (propidium iodide/annexin V) and cell cycle analysis (DAPI), RNA expression microarrays and western blots were used to identify synergism of the HDAC (histone deacetylase) inhibitor SAHA with fenretinide, tamoxifen and doxorubicin in rhabdoidtumor cell lines. HDAC1 and HDAC2 are overexpressed in primary rhabdoid tumors and rhabdoid tumor cell lines. Targeting HDACs in rhabdoid tumors induces cell cycle arrest and apoptosis. On the other hand HDAC inhibition induces deregulated gene programs (MYCC-, RB program and the stem cell program) in rhabdoid tumors. These programs are in general associated with cell cycle progression. Targeting these activated pro-proliferative genes by combined approaches of HDAC-inhibitors plus fenretinide, which inhibits cyclinD1, exhibit strong synergistic effects on induction of apoptosis. Furthermore, HDAC inhibition sensitizes rhabdoid tumor cell lines to cell death induced by chemotherapy. Our data demonstrate that HDAC inhibitor treatment in combination with fenretinide or conventional chemotherapy is a promising tool for the treatment of chemoresistant rhabdoid tumors

Adjustment of pipe flow explicit friction factor equations for application to tube bundles

International Nuclear Information System (INIS)

Wiltz, Christopher L.; Bowen, Mike D.; Von Olnhausen, Wayne A.

2005-01-01

Full text of publication follows: The accurate determination of single phase friction losses or friction pressure drop in tube bundles is essential in the thermal-hydraulic analyses of components such as nuclear fuel assemblies, heat exchangers and steam generators. Such friction losses are normally calculated using a friction factor, f, along with the experimental observation that the friction pressure drop in a pipe is proportional to the dynamic pressure (1/2 ρV 2 ) of the flow: ΔP = 1/2 ρV 2 (fL/D). In this equation L is the pipe or tube bundle length and D is the hydraulic diameter of the pipe or tube bundle. The friction factor is normally calculated using one of a number of explicit friction factor equations. A significant amount of work has been accomplished in developing explicit friction factor equations. These explicit equations range from approximations, which were developed for ease of numerical evaluation, to those which are mathematically complex but yield very good fits to the test data. These explicit friction factor equations are based on a large experimental data base, nearly all of which comes from pipe flow geometry information, and have been historically applied to tube bundles. This paper presents an adjustment method which may be applied to various explicit friction factor equations developed for pipe flow to accurately predict the friction factor for tube bundles. The characteristic of the adjustment is based on experimental friction pressure loss data obtained by Framatome ANP through flow testing of a nuclear fuel assembly (tube bundle) at its Richland Test Facility (RTF). Through adjustment of previously developed explicit friction factor equations for pipe flow, the vast amount of historical development and experimentation in the area of single phase pipe flow friction loss may be incorporated into the evaluation of single phase friction losses within tube bundles. Comparisons of the application of one or more of the previously

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

Energy Technology Data Exchange (ETDEWEB)

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

1990-03-01

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

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

International Nuclear Information System (INIS)

Zhou Xin

1990-01-01

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

Application of the Laplace-Borel transformation to the representation of analytical solutions of Duffing's equation

Science.gov (United States)

Truong, K. V.; Unal, Aynur; Tobak, M.

1989-01-01

Various features of the solutions of Duffing's equation are described using a representation of the solutions in the Laplace-Borel transform domain. An application of this technique is illustrated for the symmetry-breaking bifurcation of a hard spring.

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

International Nuclear Information System (INIS)

Zecca, A.

2010-01-01

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

Approximate solutions to Mathieu's equation

Science.gov (United States)

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

2018-06-01

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

Application of thin-layer Navier-Stokes equations near maximum lift

Science.gov (United States)

Anderson, W. K.; Thomas, J. L.; Rumsey, C. L.

1984-01-01

The flowfield about a NACA 0012 airfoil at a Mach number of 0.3 and Reynolds number of 1 million is computed through an angle of attack range, up to 18 deg, corresponding to conditions up to and beyond the maximum lift coefficient. Results obtained using the compressible thin-layer Navier-Stokes equations are presented as well as results from the compressible Euler equations with and without a viscous coupling procedure. The applicability of each code is assessed and many thin-layer Navier-Stokes benchmark solutions are obtained which can be used for comparison with other codes intended for use at high angles of attack. Reasonable agreement of the Navier-Stokes code with experiment and the viscous-inviscid interaction code is obtained at moderate angles of attack. An unsteady solution is obtained with the thin-layer Navier-Stokes code at the highest angle of attack considered. The maximum lift coefficient is overpredicted, however, in comparison to experimental data, which is attributed to the presence of a laminar separation bubble near the leading edge not modeled in the computations. Two comparisons with experimental data are also presented at a higher Mach number.

Hierarchical Matrices Method and Its Application in Electromagnetic Integral Equations

Directory of Open Access Journals (Sweden)

Han Guo

2012-01-01

Full Text Available Hierarchical (H- matrices method is a general mathematical framework providing a highly compact representation and efficient numerical arithmetic. When applied in integral-equation- (IE- based computational electromagnetics, H-matrices can be regarded as a fast algorithm; therefore, both the CPU time and memory requirement are reduced significantly. Its kernel independent feature also makes it suitable for any kind of integral equation. To solve H-matrices system, Krylov iteration methods can be employed with appropriate preconditioners, and direct solvers based on the hierarchical structure of H-matrices are also available along with high efficiency and accuracy, which is a unique advantage compared to other fast algorithms. In this paper, a novel sparse approximate inverse (SAI preconditioner in multilevel fashion is proposed to accelerate the convergence rate of Krylov iterations for solving H-matrices system in electromagnetic applications, and a group of parallel fast direct solvers are developed for dealing with multiple right-hand-side cases. Finally, numerical experiments are given to demonstrate the advantages of the proposed multilevel preconditioner compared to conventional “single level” preconditioners and the practicability of the fast direct solvers for arbitrary complex structures.

Linear determining equations for differential constraints

International Nuclear Information System (INIS)

Kaptsov, O V

1998-01-01

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

Stationary solutions of linear stochastic delay differential equations: applications to biological systems.

Science.gov (United States)

Frank, T D; Beek, P J

2001-08-01

Recently, Küchler and Mensch [Stochastics Stochastics Rep. 40, 23 (1992)] derived exact stationary probability densities for linear stochastic delay differential equations. This paper presents an alternative derivation of these solutions by means of the Fokker-Planck approach introduced by Guillouzic [Phys. Rev. E 59, 3970 (1999); 61, 4906 (2000)]. Applications of this approach, which is argued to have greater generality, are discussed in the context of stochastic models for population growth and tracking movements.

Singular stochastic differential equations

CERN Document Server

Cherny, Alexander S

2005-01-01

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

Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications

Directory of Open Access Journals (Sweden)

Xiao-Li Ding

2018-01-01

Full Text Available In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. We firstly decompose homogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions into independent differential subequations, and give their analytical solutions. Then, we use the variation of constant parameters to obtain the solutions of nonhomogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. Finally, we give three examples to demonstrate the applicability of our obtained results.

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

Science.gov (United States)

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

2017-07-01

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

Solution of differential equations by application of transformation groups

Science.gov (United States)

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.

Solutions manual to accompany Ordinary differential equations

CERN Document Server

Greenberg, Michael D

2014-01-01

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

An introduction to differential equations and their applications

CERN Document Server

Farlow, Stanley J

2006-01-01

This introductory text explores 1st- and 2nd-order differential equations, series solutions, the Laplace transform, difference equations, much more. Numerous figures, problems with solutions, notes. 1994 edition. Includes 268 figures and 23 tables.

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

Science.gov (United States)

Savoye, Philippe

2009-01-01

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

Application of Reproducing Kernel Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations

Directory of Open Access Journals (Sweden)

Omar Abu Arqub

2012-01-01

Full Text Available This paper investigates the numerical solution of nonlinear Fredholm-Volterra integro-differential equations using reproducing kernel Hilbert space method. The solution ( is represented in the form of series in the reproducing kernel space. In the mean time, the n-term approximate solution ( is obtained and it is proved to converge to the exact solution (. Furthermore, the proposed method has an advantage that it is possible to pick any point in the interval of integration and as well the approximate solution and its derivative will be applicable. Numerical examples are included to demonstrate the accuracy and applicability of the presented technique. The results reveal that the method is very effective and simple.

Polygons of differential equations for finding exact solutions

International Nuclear Information System (INIS)

Kudryashov, Nikolai A.; Demina, Maria V.

2007-01-01

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

Applications of Lie-group methods to the equations of magnetohydrodynamics

International Nuclear Information System (INIS)

Mandrekas, J.

1987-01-01

The invariance properties of various sets of magnetohydrodynamic (MHD) equations are studied using techniques from the theory of differential forms. Equations considered include the ideal MHD equations in different geometries and with different magnetic field configurations, the MHD equations in the presence of gravitational forces due to self-attraction or external fields, and the MHD equations including finite thermal conductivity and magnetic viscosity. The knowledge of the group structure of these equations is then used to introduce similarity variables to these equations. For each choice of similarity variables, the original set of partial differential equations is transformed into a set of ordinary differential equations and the most general form of the initial conditions is determined. Three cases are studied in detail and the corresponding sets of ordinary differential equations are solved numerically: the problem of a blast wave in an inhomogeneous atmosphere, the problem of a piston moving according to a power law in time, and the problem of a piston moving according to an exponential law in time

Semilinear Schrödinger equations

CERN Document Server

Cazenave, Thierry

2003-01-01

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

Differential equations for dummies

CERN Document Server

Holzner, Steven

2008-01-01

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

On implicit abstract neutral nonlinear differential equations

Energy Technology Data Exchange (ETDEWEB)

Hernández, Eduardo, E-mail: lalohm@ffclrp.usp.br [Universidade de São Paulo, Departamento de Computação e Matemática, Faculdade de Filosofia Ciências e Letras de Ribeirão Preto (Brazil); O’Regan, Donal, E-mail: donal.oregan@nuigalway.ie [National University of Ireland, School of Mathematics, Statistics and Applied Mathematics (Ireland)

2016-04-15

In this paper we continue our developments in Hernández and O’Regan (J Funct Anal 261:3457–3481, 2011) on the existence of solutions for abstract neutral differential equations. In particular we extend the results in Hernández and O’Regan (J Funct Anal 261:3457–3481, 2011) for the case of implicit nonlinear neutral equations and we focus on applications to partial “nonlinear” neutral differential equations. Some applications involving partial neutral differential equations are presented.

High pressure generation by laser driven shock waves: application to equation of state measurement; Generation de hautes pressions par choc laser: application a la mesure d'equations d'etat

Energy Technology Data Exchange (ETDEWEB)

Benuzzi, A

1997-12-15

This work is dedicated to shock waves and their applications to the study of the equation of state of compressed matter.This document is divided into 6 chapters: 1) laser-produced plasmas and abrasion processes, 2) shock waves and the equation of state, 3) relative measuring of the equation of state, 4) comparison between direct and indirect drive to compress the target, 5) the measurement of a new parameter: the shock temperature, and 6) control and measurement of the pre-heating phase. In this work we have reached relevant results, we have shown for the first time the possibility of generating shock waves of very high quality in terms of spatial distribution, time dependence and of negligible pre-heating phase with direct laser radiation. We have shown that the shock pressure stays unchanged as time passes for targets whose thickness is over 10 {mu}m. A relative measurement of the equation of state has been performed through the simultaneous measurement of the velocity of shock waves passing through 2 different media. The great efficiency of the direct drive has allowed us to produce pressures up to 40 Mbar. An absolute measurement of the equation of state requires the measurement of 2 parameters, we have then performed the measurement of the colour temperature of an aluminium target submitted to laser shocks. A simple model has been developed to infer the shock temperature from the colour temperature. The last important result is the assessment of the temperature of the pre-heating phase that is necessary to know the media in which the shock wave propagates. The comparison of the measured values of the reflectivity of the back side of the target with the computed values given by an adequate simulation has allowed us to deduce the evolution of the temperature of the pre-heating phase. (A.C.)

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

International Nuclear Information System (INIS)

Yomba, Emmanuel

2005-01-01

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

Uncertain differential equations

CERN Document Server

Yao, Kai

2016-01-01

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

Development of C++ Application Program for Solving Quadratic Equation in Elementary School in Nigeria

Science.gov (United States)

Bandele, Samuel Oye; Adekunle, Adeyemi Suraju

2015-01-01

The study was conducted to design, develop and test a c++ application program CAP-QUAD for solving quadratic equation in elementary school in Nigeria. The package was developed in c++ using object-oriented programming language, other computer program that were also utilized during the development process is DevC++ compiler, it was used for…

Energy-state formulation of lumped volume dynamic equations with application to a simplified free piston Stirling engine

Science.gov (United States)

Daniele, C. J.; Lorenzo, C. F.

1979-01-01

Lumped volume dynamic equations are derived using an energy-state formulation. This technique requires that kinetic and potential energy state functions be written for the physical system being investigated. To account for losses in the system, a Rayleigh dissipation function is also formed. Using these functions, a Lagrangian is formed and using Lagrange's equation, the equations of motion for the system are derived. The results of the application of this technique to a lumped volume are used to derive a model for the free-piston Stirling engine. The model was simplified and programmed on an analog computer. Results are given comparing the model response with experimental data.

Boundary Shape Control of the Navier-Stokes Equations and Applications

Institute of Scientific and Technical Information of China (English)

Kaitai LI; Jian SU; Aixiang HUANG

2010-01-01

In this paper,the geometrical design for the blade's surface(s)in an impeller or for the profile of an aircraft,is modeled from the mathematical point of view by a boundary shape control problem for the Navier-Stokes equations.The objective function is the sum of a global dissipative function and the power of the fluid.The control variables are the geometry of the boundary and the state equations are the Navier-Stokes equations.The Euler-Lagrange equations of the optimal control problem are derived,which are an elliptic boundary value system of fourth order,coupled with the Navier-Stokes equations.The authors also prove the existence of the solution of the optimal control problem,the existence of the solution of the Navier-Stokes equations with mixed boundary conditions,the weak continuity of the solution of the Navier-Stokes equations with respect to the geometry shape of the blade's surface and the existence of solutions of the equations for the G(a)teaux derivative of the solution of the Navier-Stokes equations with respect to the geometry of the boundary.

Numerical approximations of difference functional equations and applications

Directory of Open Access Journals (Sweden)

Zdzisław Kamont

2005-01-01

Full Text Available We give a theorem on the error estimate of approximate solutions for difference functional equations of the Volterra type. We apply this general result in the investigation of the stability of difference schemes generated by nonlinear first order partial differential functional equations and by parabolic problems. We show that all known results on difference methods for initial or initial boundary value problems can be obtained as particular cases of this general and simple result. We assume that the right hand sides of equations satisfy nonlinear estimates of the Perron type with respect to functional variables.

Application of partial differential equation modeling of the control/structural dynamics of flexible spacecraft

Science.gov (United States)

Taylor, Lawrence W., Jr.; Rajiyah, H.

1991-01-01

Partial differential equations for modeling the structural dynamics and control systems of flexible spacecraft are applied here in order to facilitate systems analysis and optimization of these spacecraft. Example applications are given, including the structural dynamics of SCOLE, the Solar Array Flight Experiment, the Mini-MAST truss, and the LACE satellite. The development of related software is briefly addressed.

Dispersive traveling wave solutions of the Equal-Width and Modified Equal-Width equations via mathematical methods and its applications

Science.gov (United States)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

The Equal-Width and Modified Equal-Width equations are used as a model in partial differential equations for the simulation of one-dimensional wave transmission in nonlinear media with dispersion processes. In this article we have employed extend simple equation method and the exp(-varphi(ξ)) expansion method to construct the exact traveling wave solutions of equal width and modified equal width equations. The obtained results are novel and have numerous applications in current areas of research in mathematical physics. It is exposed that our method, with the help of symbolic computation, provides a effective and powerful mathematical tool for solving different kind nonlinear wave problems.

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

International Nuclear Information System (INIS)

Utama, Briandhika; Purqon, Acep

2016-01-01

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. (paper)

Structural equation modeling in pediatric psychology: overview and review of applications.

Science.gov (United States)

Nelson, Timothy D; Aylward, Brandon S; Steele, Ric G

2008-08-01

To describe the use of structural equation modeling (SEM) in the Journal of Pediatric Psychology (JPP) and to discuss the usefulness of SEM applications in pediatric psychology research. The use of SEM in JPP between 1997 and 2006 was examined and compared to leading journals in clinical psychology, clinical child psychology, and child development. SEM techniques were used in psychology research, although investigations employing these methods are becoming more prevalent. Despite its infrequent use to date, SEM is a potentially useful tool for advancing pediatric psychology research with a number of advantages over traditional statistical methods.

Fractional Diffusion Equations and Anomalous Diffusion

Science.gov (United States)

Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin

2018-01-01

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

Application of the Fokker-Plank-Kolmogorov equation for affluence forecast to hydropower reservoirs (Betania Case)

International Nuclear Information System (INIS)

Dominguez Calle, Efrain Antonio

2004-01-01

This paper shows a modeling technique to forecast probability density curves for the flows that represent the monthly affluence to hydropower reservoirs. Briefly, the factors that require affluence forecast in terms of probabilities, the ranges of existing forecast methods as well as the contradiction between those techniques and the real requirements of decision-making procedures are pointed out. The mentioned contradiction is resolved applying the Fokker-Planck-Kolmogorov equation that describes the time evolution of a stochastic process that can be considered as markovian. We show the numerical scheme for this equation, its initial and boundary conditions, and its application results in the case of Betania's reservoir

Yosida approximations of stochastic differential equations in infinite dimensions and applications

CERN Document Server

Govindan, T E

2016-01-01

This research monograph brings together, for the first time, the varied literature on Yosida approximations of stochastic differential equations (SDEs) in infinite dimensions and their applications into a single cohesive work. The author provides a clear and systematic introduction to the Yosida approximation method and justifies its power by presenting its applications in some practical topics such as stochastic stability and stochastic optimal control. The theory assimilated spans more than 35 years of mathematics, but is developed slowly and methodically in digestible pieces. The book begins with a motivational chapter that introduces the reader to several different models that play recurring roles throughout the book as the theory is unfolded, and invites readers from different disciplines to see immediately that the effort required to work through the theory that follows is worthwhile. From there, the author presents the necessary prerequisite material, and then launches the reader into the main discussi...

A particular type of summability of divergent power series, with an application to difference equations

NARCIS (Netherlands)

Immink, G.K.

We define a "weak Borel-sum" for a class of formal power series. This is a generalization of the ordinary Borel-sum with applications in the theory of locally analytic difference equations. We explain its relation to a particular type of accelerosum obtained by the use of a weak acceleration

Structural equation modeling with EQS basic concepts, applications, and programming

CERN Document Server

Byrne, Barbara M

2013-01-01

Readers who want a less mathematical alternative to the EQS manual will find exactly what they're looking for in this practical text. Written specifically for those with little to no knowledge of structural equation modeling (SEM) or EQS, the author's goal is to provide a non-mathematical introduction to the basic concepts of SEM by applying these principles to EQS, Version 6.1. The book clearly demonstrates a wide variety of SEM/EQS applications that include confirmatory factor analytic and full latent variable models. Written in a "user-friendly" style, the author "walks" the reader through the varied steps involved in the process of testing SEM models: model specification and estimation, assessment of model fit, EQS output, and interpretation of findings. Each of the book's applications is accompanied by: a statement of the hypothesis being tested, a schematic representation of the model, explanations of the EQS input and output files, tips on how to use the pull-down menus, and the data file upon which ...

XV and XVI SERC Main Schools in Theoretical High Energy Physics held at the Saha Institute of Nuclear Physics and Harish-Chandra Research Institute

CERN Document Server

2005-01-01

Current research in High Energy Physics focuses on a number of enigmatic issues that go beyond the very successful Standard Model of particle physics. Among these are the problem of neutrino mass, the (as yet) unobserved Higgs particle, the quark-gluon plasma, quantum aspects of gravity, and the so--called hierarchy problem. Satisfactory resolution of these important questions will take much research effort in both theory and experiment. The Science & Engineering Research Council, Department of Science & Technology has sponsored a series of SERC Schools in Theoretical High Energy Physics over the past several years, to provide instruction and training to graduate students working for research degrees. This book is an outcome of the schools held at the Saha Institute of Nuclear Physics, Kolkata in 2000, and at the Harish-Chandra Research Institute, Allahabad in 2001. Based on lectures by active researchers in the field---Rajiv Gavai, Debashis Ghoshal, Dileep Jatkar, Anjan Joshipura, Biswarup Mukhopadhy...

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

Science.gov (United States)

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.

Partial Differential Equations Modeling and Numerical Simulation

CERN Document Server

Glowinski, Roland

2008-01-01

This book is dedicated to Olivier Pironneau. For more than 250 years partial differential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at first and then those originating from human activity and technological development. Mechanics, physics and their engineering applications were the first to benefit from the impact of partial differential equations on modeling and design, but a little less than a century ago the Schrödinger equation was the key opening the door to the application of partial differential equations to quantum chemistry, for small atomic and molecular systems at first, but then for systems of fast growing complexity. Mathematical modeling methods based on partial differential equations form an important part of contemporary science and are widely used in engineering and scientific applications. In this book several experts in this field present their latest results and discuss trends in the numerical analy...

Semi-groups of operators and some of their applications to partial differential equations

International Nuclear Information System (INIS)

Kisynski, J.

1976-01-01

Basic notions and theorems of the theory of one-parameter semi-groups of linear operators are given, illustrated by some examples concerned with linear partial differential operators. For brevity, some important and widely developed parts of the semi-group theory such as the general theory of holomorphic semi-groups or the theory of temporally inhomogeneous evolution equations are omitted. This omission includes also the very important application of semi-groups to investigating stochastic processes. (author)

Application of the Extended Grunwald-Winstein Equation to Solvolyses of n-Propyl Chloroformate

OpenAIRE

Kyong, Jin Burm; Won, Hoshik; Kevill, Dennis N.

2005-01-01

Abstract: Application of the extended Grunwald-Winstein equation to solvolyses of n-propyl chloroformate in a variety of pure and binary solvents indicates an addition-elimination pathway in the majority of the solvents but an ionization pathway in the solvents of highest ionizing power and lowest nucleophilicity. For methanolysis, a solvent deuterium isotope effect of 2.17 is compatible with the incorporation of general-base catalysis into the substitution process. Activation parameters are ...

Lie symmetries in differential equations

International Nuclear Information System (INIS)

Pleitez, V.

1979-01-01

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

Group foliation of finite difference equations

Science.gov (United States)

Thompson, Robert; Valiquette, Francis

2018-06-01

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

Manhattan equation for the operational amplifier

OpenAIRE

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

2018-01-01

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

Coupled Higgs field equation and Hamiltonian amplitude equation ...

Indian Academy of Sciences (India)

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

Strong Maximum Principle for Multi-Term Time-Fractional Diffusion Equations and its Application to an Inverse Source Problem

OpenAIRE

Liu, Yikan

2015-01-01

In this paper, we establish a strong maximum principle for fractional diffusion equations with multiple Caputo derivatives in time, and investigate a related inverse problem of practical importance. Exploiting the solution properties and the involved multinomial Mittag-Leffler functions, we improve the weak maximum principle for the multi-term time-fractional diffusion equation to a stronger one, which is parallel to that for its single-term counterpart as expected. As a direct application, w...

Iterative methods for nonlinear set-valued operators of the monotone type with applications to operator equations

International Nuclear Information System (INIS)

Chidume, C.E.

1989-06-01

The fixed points of set-valued operators satisfying a condition of monotonicity type in real Banach spaces with uniformly convex dual spaces are approximated by recursive averaging processes. Applications to important classes of linear and nonlinear operator equations are also presented. (author). 33 refs

Alternative equations of gravitation

International Nuclear Information System (INIS)

Pinto Neto, N.

1983-01-01

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

Partial differential equations of first order and their applications to physics

CERN Document Server

López, Gustavo

2012-01-01

This book tries to point out the mathematical importance of the Partial Differential Equations of First Order (PDEFO) in Physics and Applied Sciences. The intention is to provide mathematicians with a wide view of the applications of this branch in physics, and to give physicists and applied scientists a powerful tool for solving some problems appearing in Classical Mechanics, Quantum Mechanics, Optics, and General Relativity. This book is intended for senior or first year graduate students in mathematics, physics, or engineering curricula. This book is unique in the sense that it covers the applications of PDEFO in several branches of applied mathematics, and fills the theoretical gap between the formal mathematical presentation of the theory and the pure applied tool to physical problems that are contained in other books. Improvements made in this second edition include corrected typographical errors; rewritten text to improve the flow and enrich the material; added exercises in all chapters; new applicati...

Hyperbolic partial differential equations

CERN Document Server

Witten, Matthew

1986-01-01

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

A separable approach to the Bethe-Salpeter equation and its application to nucleon-nucleon scattering

International Nuclear Information System (INIS)

Schwarz, K.; Froehlich, J.; Zingl, H.F.K.

1980-01-01

The Bethe-Salpeter equation is solved in closed form with the help of a four dimensional separable 'potential'. For possible applications to three-nucleon investigations the authors have fitted all nucleon-nucleon S-wave phase shifts in a sufficient way by this method; in addition they also present an example for a P-wave. (Auth.)

A new Riccati equation rational expansion method and its application to (2 + 1)-dimensional Burgers equation

International Nuclear Information System (INIS)

Wang Qi; Chen Yong; Zhang Hongqing

2005-01-01

In this paper, we present a new Riccati equation rational expansion method to uniformly construct a series of exact solutions for nonlinear evolution equations. Compared with most existing tanh methods and other sophisticated methods, the proposed method not only recover some known solutions, but also find some new and general solutions. The solutions obtained in this paper include rational triangular periodic wave solutions, rational solitary wave solutions and rational wave solutions. The efficiency of the method can be demonstrated on (2 + 1)-dimensional Burgers equation

Some Aspects of Extended Kinetic Equation

Directory of Open Access Journals (Sweden)

Dilip Kumar

2015-09-01

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

Langevin equations with multiplicative noise: application to domain growth

International Nuclear Information System (INIS)

Sancho, J.M.; Hernandez-Machado, A.; Ramirez-Piscina, L.; Lacasta, A.M.

1993-01-01

Langevin equations of Ginzburg-Landau form with multiplicative noise, are proposed to study the effects of fluctuations in domain growth. These equations are derived from a coarse-grained methodology. The Cahn-Hilliard-Cook linear stability analysis predicts some effects in the transitory regime. We also derive numerical algorithms for the computer simulation of these equations. The numerical results corroborate the analytical productions of the linear analysis. We also present simulation results for spinodal decomposition at large times. (author). 28 refs, 2 figs

Applications of the Soave-Redlich-Kwong Equations of State Using Mathematic

Science.gov (United States)

Sun, Lanyi; Zhai, Cheng; Zhang, Hui

The application of the Peng-Robinson equations of state (PR EOS) using Matlab and Mathematic has already been demonstrated. In this paper, using Mathematic to solve Soave-Redlich-Kwong (SRK) EOS, as well as the estimation of pure component properties, plotting of vapor-liquid equilibrium (VLE) diagram and calculation of chemical equilibrium, is presented. First the SRK EOS is used to predict several pure-component properties, such as liquid and gas molar volumes for isobutane. The vapor-liquid isobaric diagram is then plotted for a binary mixture composed of n-pentane and n-hexane under the pressures of 2*10^5 and 8*10^5 Pa respectively.

Recent applications of the Boltzmann master equation to heavy ion precompound decay phenomena

International Nuclear Information System (INIS)

Blann, M.; Remington, B.A.

1988-06-01

The Boltzmann master equation (BME) is described and used as a tool to interpret preequilibrium neutron emission from heavy ion collisions gated on evaporation residue or fission fragments. The same approach is used to interpret neutron spectra gated on deep inelastic and quasi-elastic heavy ion collisions. Less successful applications of BME to proton inclusive data with 40 MeV/u incident 12 C ions are presented, and improvements required in the exciton injection term are discussed

Inverse scattering transform for the time dependent Schrödinger equation with applications to the KPI equation

Science.gov (United States)

Zhou, Xin

1990-03-01

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

Developing prediction equations and a mobile phone application to identify infants at risk of obesity.

Science.gov (United States)

Santorelli, Gillian; Petherick, Emily S; Wright, John; Wilson, Brad; Samiei, Haider; Cameron, Noël; Johnson, William

2013-01-01

Advancements in knowledge of obesity aetiology and mobile phone technology have created the opportunity to develop an electronic tool to predict an infant's risk of childhood obesity. The study aims were to develop and validate equations for the prediction of childhood obesity and integrate them into a mobile phone application (App). Anthropometry and childhood obesity risk data were obtained for 1868 UK-born White or South Asian infants in the Born in Bradford cohort. Logistic regression was used to develop prediction equations (at 6 ± 1.5, 9 ± 1.5 and 12 ± 1.5 months) for risk of childhood obesity (BMI at 2 years >91(st) centile and weight gain from 0-2 years >1 centile band) incorporating sex, birth weight, and weight gain as predictors. The discrimination accuracy of the equations was assessed by the area under the curve (AUC); internal validity by comparing area under the curve to those obtained in bootstrapped samples; and external validity by applying the equations to an external sample. An App was built to incorporate six final equations (two at each age, one of which included maternal BMI). The equations had good discrimination (AUCs 86-91%), with the addition of maternal BMI marginally improving prediction. The AUCs in the bootstrapped and external validation samples were similar to those obtained in the development sample. The App is user-friendly, requires a minimum amount of information, and provides a risk assessment of low, medium, or high accompanied by advice and website links to government recommendations. Prediction equations for risk of childhood obesity have been developed and incorporated into a novel App, thereby providing proof of concept that childhood obesity prediction research can be integrated with advancements in technology.

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

International Nuclear Information System (INIS)

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

2012-01-01

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

Scattering integral equations and four nucleon problem

International Nuclear Information System (INIS)

Narodetskii, I.M.

1980-01-01

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

A short course on functional equations based upon recent applications to the social and behavioral sciences

CERN Document Server

Aczél, J

1987-01-01

Recently I taught short courses on functional equations at several universities (Barcelona, Bern, Graz, Hamburg, Milan, Waterloo). My aim was to introduce the most important equations and methods of solution through actual (not artifi­ cial) applications which were recent and with which I had something to do. Most of them happened to be related to the social or behavioral sciences. All were originally answers to questions posed by specialists in the respective applied fields. Here I give a somewhat extended version of these lectures, with more recent results and applications included. As previous knowledge just the basic facts of calculus and algebra are supposed. Parts where somewhat more (measure theory) is needed and sketches of lengthier calcula­ tions are set in fine print. I am grateful to Drs. J. Baker (Waterloo, Ont.), W. Forg-Rob (Innsbruck, Austria) and C. Wagner (Knoxville, Tenn.) for critical remarks and to Mrs. Brenda Law for care­ ful computer-typing of the manuscript (in several versions). A...

Applications of exact traveling wave solutions of Modified Liouville and the Symmetric Regularized Long Wave equations via two new techniques

Science.gov (United States)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

In this current work, we employ novel methods to find the exact travelling wave solutions of Modified Liouville equation and the Symmetric Regularized Long Wave equation, which are called extended simple equation and exp(-Ψ(ξ))-expansion methods. By assigning the different values to the parameters, different types of the solitary wave solutions are derived from the exact traveling wave solutions, which shows the efficiency and precision of our methods. Some solutions have been represented by graphical. The obtained results have several applications in physical science.

Measurement-based perturbation theory and differential equation parameter estimation with applications to satellite gravimetry

Science.gov (United States)

Xu, Peiliang

2018-06-01

The numerical integration method has been routinely used by major institutions worldwide, for example, NASA Goddard Space Flight Center and German Research Center for Geosciences (GFZ), to produce global gravitational models from satellite tracking measurements of CHAMP and/or GRACE types. Such Earth's gravitational products have found widest possible multidisciplinary applications in Earth Sciences. The method is essentially implemented by solving the differential equations of the partial derivatives of the orbit of a satellite with respect to the unknown harmonic coefficients under the conditions of zero initial values. From the mathematical and statistical point of view, satellite gravimetry from satellite tracking is essentially the problem of estimating unknown parameters in the Newton's nonlinear differential equations from satellite tracking measurements. We prove that zero initial values for the partial derivatives are incorrect mathematically and not permitted physically. The numerical integration method, as currently implemented and used in mathematics and statistics, chemistry and physics, and satellite gravimetry, is groundless, mathematically and physically. Given the Newton's nonlinear governing differential equations of satellite motion with unknown equation parameters and unknown initial conditions, we develop three methods to derive new local solutions around a nominal reference orbit, which are linked to measurements to estimate the unknown corrections to approximate values of the unknown parameters and the unknown initial conditions. Bearing in mind that satellite orbits can now be tracked almost continuously at unprecedented accuracy, we propose the measurement-based perturbation theory and derive global uniformly convergent solutions to the Newton's nonlinear governing differential equations of satellite motion for the next generation of global gravitational models. Since the solutions are global uniformly convergent, theoretically speaking

Application of homotopy perturbation method for systems of Volterra integral equations of the first kind

International Nuclear Information System (INIS)

Biazar, J.; Eslami, M.; Aminikhah, H.

2009-01-01

In this article, an application of He's homotopy perturbation method is applied to solve systems of Volterra integral equations of the first kind. Some non-linear examples are prepared to illustrate the efficiency and simplicity of the method. Applying the method for linear systems is so easily that it does not worth to have any example.

Geophysical interpretation using integral equations

CERN Document Server

Eskola, L

1992-01-01

Along with the general development of numerical methods in pure and applied to apply integral equations to geophysical modelling has sciences, the ability improved considerably within the last thirty years or so. This is due to the successful derivation of integral equations that are applicable to the modelling of complex structures, and efficient numerical algorithms for their solution. A significant stimulus for this development has been the advent of fast digital computers. The purpose of this book is to give an idea of the principles by which boundary-value problems describing geophysical models can be converted into integral equations. The end results are the integral formulas and integral equations that form the theoretical framework for practical applications. The details of mathematical analysis have been kept to a minimum. Numerical algorithms are discussed only in connection with some illustrative examples involving well-documented numerical modelling results. The reader is assu­ med to have a back...

Application of Ruze Equation for Inflatable Aperture Antennas

Science.gov (United States)

Welch, Bryan W.

2008-01-01

Inflatable aperture reflector antennas are an emerging technology that NASA is investigating for potential uses in science and exploration missions. As inflatable aperture antennas have not been proven fully qualified for space missions, they must be characterized properly so that the behavior of the antennas can be known in advance. To properly characterize the inflatable aperture antenna, testing must be performed in a relevant environment, such as a vacuum chamber. Since the capability of having a radiofrequency (RF) test facility inside a vacuum chamber did not exist at NASA Glenn Research Center, a different methodology had to be utilized. The proposal to test an inflatable aperture antenna in a vacuum chamber entailed performing a photogrammetry study of the antenna surface by using laser ranging measurements. A root-mean-square (rms) error term was derived from the photogrammetry study to calculate the antenna surface loss as described by the Ruze equation. However, initial testing showed that problems existed in using the Ruze equation to calculate the loss due to errors on the antenna surface. This study utilized RF measurements obtained in a near-field antenna range and photogrammetry data taken from a laser range scanner to compare the expected performance of the test antenna (via the Ruze equation) with the actual RF patterns and directivity measurements. Results showed that the Ruze equation overstated the degradation in the directivity calculation. Therefore, when the photogrammetry study is performed on the test antennas in the vacuum chamber, a more complex equation must be used in light of the fact that the Ruze theory overstates the loss in directivity for inflatable aperture reflector antennas.

Applicability of the Galerkin method to the approximate solution of the multigroup diffusion equation

International Nuclear Information System (INIS)

Obradovic, D.

1970-04-01

In the study of the nuclear reactors space-time behaviour the modal analysis is very often used though some basic mathematical problems connected with application of this methods are still unsolved. In this paper the modal analysis is identified as a set of the methods in the mathematical literature known as the Galerkin methods (or projection methods, or sometimes direct methods). Using the results of the mathematical investigations of these methods the applicability of the Galerkin type methods to the calculations of the eigenvalue and eigenvectors of the stationary and non-stationary diffusion operator, as well as for the solutions of the corresponding functional equations, is established (author)

Application of He’s Variational Iteration Method to Nonlinear Helmholtz Equation and Fifth-Order KDV Equation

DEFF Research Database (Denmark)

Miansari, Mo; Miansari, Me; Barari, Amin

2009-01-01

In this article, He’s variational iteration method (VIM), is implemented to solve the linear Helmholtz partial differential equation and some nonlinear fifth-order Korteweg-de Vries (FKdV) partial differential equations with specified initial conditions. The initial approximations can be freely c...

COMPARISON THEOREMS AND APPLICATIONS OF OSCILLATION OF NEUTRAL DIFFERENTIAL EQUATIONS

Institute of Scientific and Technical Information of China (English)

燕居让

1991-01-01

We first establish comparison theorems of the oscillation for a higher-order neutral delaydifferential equation. By these comparison theorems, the criterion of oscillation propertiesof neutral delay differential equation is reduced to that of nonneutral delay differential equa-tion, from which we give a series of oscillation theorems for neutral delay differentialequation.

Differential equations with applications in cancer diseases.

Science.gov (United States)

Ilea, M; Turnea, M; Rotariu, M

2013-01-01

Mathematical modeling is a process by which a real world problem is described by a mathematical formulation. The cancer modeling is a highly challenging problem at the frontier of applied mathematics. A variety of modeling strategies have been developed, each focusing on one or more aspects of cancer. The vast majority of mathematical models in cancer diseases biology are formulated in terms of differential equations. We propose an original mathematical model with small parameter for the interactions between these two cancer cell sub-populations and the mathematical model of a vascular tumor. We work on the assumption that, the quiescent cells' nutrient consumption is long. One the equations system includes small parameter epsilon. The smallness of epsilon is relative to the size of the solution domain. MATLAB simulations obtained for transition rate from the quiescent cells' nutrient consumption is long, we show a similar asymptotic behavior for two solutions of the perturbed problem. In this system, the small parameter is an asymptotic variable, different from the independent variable. The graphical output for a mathematical model of a vascular tumor shows the differences in the evolution of the tumor populations of proliferating, quiescent and necrotic cells. The nutrient concentration decreases sharply through the viable rim and tends to a constant level in the core due to the nearly complete necrosis in this region. Many mathematical models can be quantitatively characterized by ordinary differential equations or partial differential equations. The use of MATLAB in this article illustrates the important role of informatics in research in mathematical modeling. The study of avascular tumor growth cells is an exciting and important topic in cancer research and will profit considerably from theoretical input. Interpret these results to be a permanent collaboration between math's and medical oncologists.

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

Science.gov (United States)

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…

Computer Applications in Balancing Chemical Equations.

Science.gov (United States)

Kumar, David D.

2001-01-01

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

Resonance – Journal of Science Education | News

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education; Volume 3; Issue 5. Issue front cover thumbnail Issue back cover thumbnail. Volume 3, Issue 5. May 1998, pages 1-98. pp 1-1 Editorial. Editorial · N Mukunda · More Details Fulltext PDF. pp 2-2 Article-in-a-Box. Thermal Ionisation and the Saha Equation!

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

International Nuclear Information System (INIS)

Jia Liqun; Cui Jinchao; Zhang Yaoyu; Luo Shaokai

2009-01-01

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

Notes on the infinity Laplace equation

CERN Document Server

Lindqvist, Peter

2016-01-01

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

Quantum linear Boltzmann equation

International Nuclear Information System (INIS)

Vacchini, Bassano; Hornberger, Klaus

2009-01-01

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

Inverse problems in ordinary differential equations and applications

CERN Document Server

Llibre, Jaume

2016-01-01

This book is dedicated to study the inverse problem of ordinary differential equations, that is it focuses in finding all ordinary differential equations that satisfy a given set of properties. The Nambu bracket is the central tool in developing this approach. The authors start characterizing the ordinary differential equations in R^N which have a given set of partial integrals or first integrals. The results obtained are applied first to planar polynomial differential systems with a given set of such integrals, second to solve the 16th Hilbert problem restricted to generic algebraic limit cycles, third for solving the inverse problem for constrained Lagrangian and Hamiltonian mechanical systems, fourth for studying the integrability of a constrained rigid body. Finally the authors conclude with an analysis on nonholonomic mechanics, a generalization of the Hamiltonian principle, and the statement an solution of the inverse problem in vakonomic mechanics.

Covariant solutions of the Bethe-Salpeter equation and an application to the nucleon structure function

International Nuclear Information System (INIS)

Williams, A.G.

1998-01-01

There is a need for covariant solutions of bound state equations in order to construct realistic QCD based models of mesons and baryons. Furthermore, we ideally need to know the structure of these bound states in all kinematical regimes, which makes a direct solution in Minkowski space (without any 3-dimensional reductions) desirable. The Bethe-Salpeter equation (BSE) for bound states in scalar theories is reformulated and solved for arbitrary scattering kernels in terms of a generalized spectral representation directly in Minkowski space. This differs from the conventional Euclidean approach, where the BSE can only be solved in ladder approximation after a Wick rotation. An application of covariant Bethe-Salpeter solutions to a quark-diquark model of the nucleon is also briefly discussed. (orig.)

Iterative solutions of finite difference diffusion equations

International Nuclear Information System (INIS)

Menon, S.V.G.; Khandekar, D.C.; Trasi, M.S.

1981-01-01

The heterogeneous arrangement of materials and the three-dimensional character of the reactor physics problems encountered in the design and operation of nuclear reactors makes it necessary to use numerical methods for solution of the neutron diffusion equations which are based on the linear Boltzmann equation. The commonly used numerical method for this purpose is the finite difference method. It converts the diffusion equations to a system of algebraic equations. In practice, the size of this resulting algebraic system is so large that the iterative methods have to be used. Most frequently used iterative methods are discussed. They include : (1) basic iterative methods for one-group problems, (2) iterative methods for eigenvalue problems, and (3) iterative methods which use variable acceleration parameters. Application of Chebyshev theorem to iterative methods is discussed. The extension of the above iterative methods to multigroup neutron diffusion equations is also considered. These methods are applicable to elliptic boundary value problems in reactor design studies in particular, and to elliptic partial differential equations in general. Solution of sample problems is included to illustrate their applications. The subject matter is presented in as simple a manner as possible. However, a working knowledge of matrix theory is presupposed. (M.G.B.)

Nonlinear equation of the modes in circular slab waveguides and its application.

Science.gov (United States)

Zhu, Jianxin; Zheng, Jia

2013-11-20

In this paper, circularly curved inhomogeneous waveguides are transformed into straight inhomogeneous waveguides first by a conformal mapping. Then, the differential transfer matrix method is introduced and adopted to deduce the exact dispersion relation for modes. This relation itself is complex and difficult to solve, but it can be approximated by a simpler nonlinear equation in practical applications, which is close to the exact relation and quite easy to analyze. Afterward, optimized asymptotic solutions are obtained and act as initial guesses for the following Newton's iteration. Finally, very accurate solutions are achieved in the numerical experiment.

Structural Equation Modeling: Theory and Applications in Forest Management

Directory of Open Access Journals (Sweden)

Tzeng Yih Lam

2012-01-01

Full Text Available Forest ecosystem dynamics are driven by a complex array of simultaneous cause-and-effect relationships. Understanding this complex web requires specialized analytical techniques such as Structural Equation Modeling (SEM. The SEM framework and implementation steps are outlined in this study, and we then demonstrate the technique by application to overstory-understory relationships in mature Douglas-fir forests in the northwestern USA. A SEM model was formulated with (1 a path model representing the effects of successively higher layers of vegetation on late-seral herbs through processes such as light attenuation and (2 a measurement model accounting for measurement errors. The fitted SEM model suggested a direct negative effect of light attenuation on late-seral herbs cover but a direct positive effect of northern aspect. Moreover, many processes have indirect effects mediated through midstory vegetation. SEM is recommended as a forest management tool for designing silvicultural treatments and systems for attaining complex arrays of management objectives.

Application of high-power lasers to equation-of-state research at ultrahigh pressures

International Nuclear Information System (INIS)

Trainor, R.J.; Graboske, H.C.; Long, K.S.; Shaner, J.W.

1978-01-01

The application of high-power pulsed lasers to ultrahigh pressure equation-of-state (EOS) experiments is discussed. It is shown that pressures along the principal Hugoniot between 1 and 10 TPa can be produced with existing lasers used for inertial-confinement fusion research. The relevance of measurements in this pressure regime to improving our understanding of condensed matter physics is also discussed. New experimental techniques as well as potential experimental problems are described, and EOS experiments on the Janus and Argus laser systems are proposed

A Laplace transform certified reduced basis method; application to the heat equation and wave equation

OpenAIRE

Knezevic, David; Patera, Anthony T.; Huynh, Dinh Bao Phuong

2010-01-01

We present a certified reduced basis (RB) method for the heat equation and wave equation. The critical ingredients are certified RB approximation of the Laplace transform; the inverse Laplace transform to develop the time-domain RB output approximation and rigorous error bound; a (Butterworth) filter in time to effect the necessary “modal” truncation; RB eigenfunction decomposition and contour integration for Offline–Online decomposition. We present numerical results to demonstrate the accura...

Fokker-Planck equation resolution for N variables-Application examples

International Nuclear Information System (INIS)

Munoz Roldan, A.; Garcia-Olivares, A.

1994-01-01

A set of problems which are reducible to Fokker-Planck equations are presented. Those problems have been solved by using the CHAPKOL library. This library of programs solves stochastic ''Fokker-Planck'' equations in one or several dimensions by using the Chapman-Kolmogorov integral. This method calculates the probability distribution at a time t+dt from a distribution given at time t through a convolution integral in which the integrant is the product of the distribution function at time t and the Green function of the Fokker-Planck equation. The method have some numerical advantages when compared with finite differences algorithms. The accuracy of the method is analysed in several specific cases

On the use of the Lie group technique for differential equations with a small parameter: Approximate solutions and integrable equations

International Nuclear Information System (INIS)

Burde, G.I.

2002-01-01

A new approach to the use of the Lie group technique for partial and ordinary differential equations dependent on a small parameter is developed. In addition to determining approximate solutions to the perturbed equation, the approach allows constructing integrable equations that have solutions with (partially) prescribed features. Examples of application of the approach to partial differential equations are given

A generalized auxiliary equation method and its application to nonlinear Klein-Gordon and generalized nonlinear Camassa-Holm equations

International Nuclear Information System (INIS)

Yomba, Emmanuel

2008-01-01

With the aid of symbolic computation, a generalized auxiliary equation method is proposed to construct more general exact solutions to two types of NLPDEs. First, we present new family of solutions to a nonlinear Klein-Gordon equation, by using this auxiliary equation method including a new first-order nonlinear ODE with six-degree nonlinear term proposed by Sirendaoreji. Then, we apply an indirect F-function method very close to the F-expansion method to solve the generalized Camassa-Holm equation with fully nonlinear dispersion and fully nonlinear convection C(l,n,p). Taking advantage of the new first-order nonlinear ODE with six degree nonlinear term, this indirect F-function method is used to map the solutions of C(l,n,p) equations to those of that nonlinear ODE. As a result, we can successfully obtain in a unified way, many exact solutions

Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations.

Science.gov (United States)

Tornøe, Christoffer W; Overgaard, Rune V; Agersø, Henrik; Nielsen, Henrik A; Madsen, Henrik; Jonsson, E Niclas

2005-08-01

The objective of the present analysis was to explore the use of stochastic differential equations (SDEs) in population pharmacokinetic/pharmacodynamic (PK/PD) modeling. The intra-individual variability in nonlinear mixed-effects models based on SDEs is decomposed into two types of noise: a measurement and a system noise term. The measurement noise represents uncorrelated error due to, for example, assay error while the system noise accounts for structural misspecifications, approximations of the dynamical model, and true random physiological fluctuations. Since the system noise accounts for model misspecifications, the SDEs provide a diagnostic tool for model appropriateness. The focus of the article is on the implementation of the Extended Kalman Filter (EKF) in NONMEM for parameter estimation in SDE models. Various applications of SDEs in population PK/PD modeling are illustrated through a systematic model development example using clinical PK data of the gonadotropin releasing hormone (GnRH) antagonist degarelix. The dynamic noise estimates were used to track variations in model parameters and systematically build an absorption model for subcutaneously administered degarelix. The EKF-based algorithm was successfully implemented in NONMEM for parameter estimation in population PK/PD models described by systems of SDEs. The example indicated that it was possible to pinpoint structural model deficiencies, and that valuable information may be obtained by tracking unexplained variations in parameters.

Dynamics of interaction of ultrashort laser pulses with solid targets

International Nuclear Information System (INIS)

Cang Yu; Wang Wei; Zhang Jie

2001-01-01

Using Saha equation, a simple model is proposed for the dynamics of interaction between ultrashort laser pulses and solid targets. An adiabatic expansion model is adopted to study the expansion phase after the heating phase. Temporal evolvement of the dynamics of the interaction is obtained, from which the electron temperature, density, ionization balances can be determined

Numerical solutions of diffusive logistic equation

International Nuclear Information System (INIS)

Afrouzi, G.A.; Khademloo, S.

2007-01-01

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

Introduction to ordinary differential equations

CERN Document Server

Rabenstein, Albert L

1966-01-01

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

Applied partial differential equations

CERN Document Server

Logan, J David

2004-01-01

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

Non-autonomous equations with unpredictable solutions

Science.gov (United States)

Akhmet, Marat; Fen, Mehmet Onur

2018-06-01

To make research of chaos more amenable to investigating differential and discrete equations, we introduce the concepts of an unpredictable function and sequence. The topology of uniform convergence on compact sets is applied to define unpredictable functions [1,2]. The unpredictable sequence is defined as a specific unpredictable function on the set of integers. The definitions are convenient to be verified as solutions of differential and discrete equations. The topology is metrizable and easy for applications with integral operators. To demonstrate the effectiveness of the approach, the existence and uniqueness of the unpredictable solution for a delay differential equation are proved as well as for quasilinear discrete systems. As a corollary of the theorem, a similar assertion for a quasilinear ordinary differential equation is formulated. The results are demonstrated numerically, and an application to Hopfield neural networks is provided. In particular, Poincaré chaos near periodic orbits is observed. The completed research contributes to the theory of chaos as well as to the theory of differential and discrete equations, considering unpredictable solutions.

An Improved Recurrent Neural Network for Complex-Valued Systems of Linear Equation and Its Application to Robotic Motion Tracking.

Science.gov (United States)

Ding, Lei; Xiao, Lin; Liao, Bolin; Lu, Rongbo; Peng, Hua

2017-01-01

To obtain the online solution of complex-valued systems of linear equation in complex domain with higher precision and higher convergence rate, a new neural network based on Zhang neural network (ZNN) is investigated in this paper. First, this new neural network for complex-valued systems of linear equation in complex domain is proposed and theoretically proved to be convergent within finite time. Then, the illustrative results show that the new neural network model has the higher precision and the higher convergence rate, as compared with the gradient neural network (GNN) model and the ZNN model. Finally, the application for controlling the robot using the proposed method for the complex-valued systems of linear equation is realized, and the simulation results verify the effectiveness and superiorness of the new neural network for the complex-valued systems of linear equation.

Generalized Meir-Keeler Type ψ-Contractive Mappings and Applications to Common Solution of Integral Equations

Directory of Open Access Journals (Sweden)

Huseyin Isik

2017-03-01

Full Text Available The goal of the present article to introduce the notion of generalized Meir-Keeler type ψ-contractions and prove some coupled common fixed point results for such type of contractions. The theorems proved herein extend, generalize and improve some results of the existing literature. Several examples and an application to integral equations are also given in order to illustrate the genuineness of our results.

Kinetic Boltzmann, Vlasov and Related Equations

CERN Document Server

Sinitsyn, Alexander; Vedenyapin, Victor

2011-01-01

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

New solutions of the confluent Heun equation

Directory of Open Access Journals (Sweden)

Harold Exton

1998-05-01

Full Text Available New compact triple series solutions of the confluent Heun equation (CHE are obtained by the appropriate applications of the Laplace transform and its inverse to a suitably constructed system of soluble differential equations. The computer-algebra package MAPLE V is used to tackle an auxiliary system of non-linear algebraic equations. This study is partly motivated by the relationship between the CHE and certain Schrödininger equations.

Application of viscoplastic constitutive equations in finite element programs

International Nuclear Information System (INIS)

Hornberger, K.; Stamm, H.

1987-04-01

The general mathematical formulation of frequently used viscoplastic constitutive equations is explained and Robinson's model is discussed in more detail. The implementation of viscoplastic constitutive equations into Finite Element programs (such as ABAQUS) is described using Robinson's model as an example. For the numerical integration both an explicit (explicit Euler) and an implicit (generalized midpoint rule) integration scheme is utilized in combination with a time step control strategy. In the implicit integration scheme, convergence in solving a system of nonlinear algebraic equation is improved introducing a projection method. The efficiency of the implemented procedures is demonstrated for different homogeneous load cases as well as for creep loading and strain controlled cyclic loading of a perforated plate. (orig./HP) [de

Fokker-Planck equation resolution for N variables. Application examples

International Nuclear Information System (INIS)

Munoz, A.; Garcia-Olivares, A.

1994-01-01

A set of problems which are reducible to Fokker-Planck equations are presented. Those problems have been solved by using the CHAPKOL library. This library of programs solves stochastic Fokker-Plank equations in one or several dimensions by using the Chapman- Kolmogorov integral. This method calculates the probability distribution at a time t + dt from a distribution given at time t through a convolution integral in which the integration is the product of the distribution function at time t and the Green function of the Fokker-Planck equation. The method have some numerical advantages when compared with finite differences algorithms. The accuracy of the method is analysed in several specific cases. (Author) 9 refs

A Padé approximant approach to two kinds of transcendental equations with applications in physics

International Nuclear Information System (INIS)

Luo, Qiang; Wang, Zhidan; Han, Jiurong

2015-01-01

In this paper, we obtain the analytical solutions of two kinds of transcendental equations with numerous applications in college physics by means of the Lagrange inversion theorem. Afterwards we rewrite them in the form of a ratio of rational polynomials by a second-order Padé approximant from a practical and instructional perspective. Our method is illustrated in a pedagogical manner for the benefit of students at the undergraduate level. The approximate formulas introduced in the paper can be applied to abundant examples in physics textbooks, such as Fraunhofer single-slit diffraction, Wien’s displacement law, and the Schrödinger equation with single- or double-δ potential. These formulas, consequently, can reach considerable accuracies according to the numerical results; therefore, they promise to act as valuable ingredients in the standard teaching curriculum. (paper)

Solution of the reactor point kinetics equations by MATLAB computing

Directory of Open Access Journals (Sweden)

Singh Sudhansu S.

2015-01-01

Full Text Available The numerical solution of the point kinetics equations in the presence of Newtonian temperature feedback has been a challenging issue for analyzing the reactor transients. Reactor point kinetics equations are a system of stiff ordinary differential equations which need special numerical treatments. Although a plethora of numerical intricacies have been introduced to solve the point kinetics equations over the years, some of the simple and straightforward methods still work very efficiently with extraordinary accuracy. As an example, it has been shown recently that the fundamental backward Euler finite difference algorithm with its simplicity has proven to be one of the most effective legacy methods. Complementing the back-ward Euler finite difference scheme, the present work demonstrates the application of ordinary differential equation suite available in the MATLAB software package to solve the stiff reactor point kinetics equations with Newtonian temperature feedback effects very effectively by analyzing various classic benchmark cases. Fair accuracy of the results implies the efficient application of MATLAB ordinary differential equation suite for solving the reactor point kinetics equations as an alternate method for future applications.

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

International Nuclear Information System (INIS)

Esmail, S.F.H.

2006-01-01

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

How Should Equation Balancing Be Taught?

Science.gov (United States)

Porter, Spencer K.

1985-01-01

Matrix methods and oxidation-number methods are currently advocated and used for balancing equations. This article shows how balancing equations can be introduced by a third method which is related to a fundamental principle, is easy to learn, and is powerful in its application. (JN)

Method of moving frames to solve time-dependent Maxwell's equations on anisotropic curved surfaces: Applications to invisible cloak and ELF propagation

Science.gov (United States)

Chun, Sehun

2017-07-01

Applying the method of moving frames to Maxwell's equations yields two important advancements for scientific computing. The first is the use of upwind flux for anisotropic materials in Maxwell's equations, especially in the context of discontinuous Galerkin (DG) methods. Upwind flux has been available only to isotropic material, because of the difficulty of satisfying the Rankine-Hugoniot conditions in anisotropic media. The second is to solve numerically Maxwell's equations on curved surfaces without the metric tensor and composite meshes. For numerical validation, spectral convergences are displayed for both two-dimensional anisotropic media and isotropic spheres. In the first application, invisible two-dimensional metamaterial cloaks are simulated with a relatively coarse mesh by both the lossless Drude model and the piecewisely-parametered layered model. In the second application, extremely low frequency propagation on various surfaces such as spheres, irregular surfaces, and non-convex surfaces is demonstrated.

Stochastic equations theory and applications in acoustics, hydrodynamics, magnetohydrodynamics, and radiophysics

CERN Document Server

Klyatskin, Valery I

2015-01-01

This monograph set presents a consistent and self-contained framework of stochastic dynamic systems with maximal possible completeness. Volume 1 presents the basic concepts, exact results, and asymptotic approximations of the theory of stochastic equations on the basis of the developed functional approach. This approach offers a possibility of both obtaining exact solutions to stochastic problems for a number of models of fluctuating parameters and constructing various asymptotic buildings. Ideas of statistical topography are used to discuss general issues of generating coherent structures from chaos with probability one, i.e., almost in every individual realization of random parameters. The general theory is illustrated with certain problems and applications of stochastic mathematical physics in various fields such as mechanics, hydrodynamics, magnetohydrodynamics, acoustics, optics, and radiophysics.  

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

International Nuclear Information System (INIS)

Kaniel, S.; Itin, Y.

2006-01-01

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

Enhanced suppression of tumor growth by concomitant treatment of human lung cancer cells with suberoylanilide hydroxamic acid and arsenic trioxide

International Nuclear Information System (INIS)

Chien, Chia-Wen; Yao, Ju-Hsien; Chang, Shih-Yu; Lee, Pei-Chih; Lee, Te-Chang

2011-01-01

The efficacy of arsenic trioxide (ATO) against acute promyelocytic leukemia (APL) and relapsed APL has been well documented. ATO may cause DNA damage by generating reactive oxygen intermediates. Suberoylanilide hydroxamic acid (SAHA), a histone deacetylase inhibitor, modulates gene and protein expression via histone-dependent or -independent pathways that may result in chromatin decondensation, cell cycle arrest, differentiation, and apoptosis. We investigated whether ATO and SAHA act synergistically to enhance the death of cancer cells. Our current findings showed that combined treatment with ATO and SAHA resulted in enhanced suppression of non-small-cell lung carcinoma in vitro in H1299 cells and in vivo in a xenograft mouse model. Flow cytometric analysis of annexin V+ cells showed that apoptotic cell death was significantly enhanced after combined treatment with ATO and SAHA. At the doses used, ATO did not interfere with cell cycle progression, but SAHA induced p21 expression and led to G1 arrest. A Comet assay demonstrated that ATO, but not SAHA, induced DNA strand breaks in H1299 cells; however, co-treatment with SAHA significantly increased ATO-induced DNA damage. Moreover, SAHA enhanced acetylation of histone H3 and sensitized genomic DNA to DNase I digestion. Our results suggest that SAHA may cause chromatin relaxation and increase cellular susceptibility to ATO-induced DNA damage. Combined administration of SAHA and ATO may be an effective approach to the treatment of lung cancer. -- Highlights: ► ATO and SAHA are therapeutic agents with different action modes. ► Combination of ATO and SAHA synergistically inhibits tumor cell growth. ► SAHA loosens chromatin structure resulting in increased sensitivity to DNase I. ► ATO-induced DNA damage and apoptosis are enhanced by co-treatment with SAHA.

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

International Nuclear Information System (INIS)

Delhaye, J.M.

1968-12-01

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

Numerical Methods for Partial Differential Equations

CERN Document Server

Guo, Ben-yu

1987-01-01

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

Nonlinear elliptic equations of the second order

CERN Document Server

Han, Qing

2016-01-01

Nonlinear elliptic differential equations are a diverse subject with important applications to the physical and social sciences and engineering. They also arise naturally in geometry. In particular, much of the progress in the area in the twentieth century was driven by geometric applications, from the Bernstein problem to the existence of Kähler-Einstein metrics. This book, designed as a textbook, provides a detailed discussion of the Dirichlet problems for quasilinear and fully nonlinear elliptic differential equations of the second order with an emphasis on mean curvature equations and on Monge-Ampère equations. It gives a user-friendly introduction to the theory of nonlinear elliptic equations with special attention given to basic results and the most important techniques. Rather than presenting the topics in their full generality, the book aims at providing self-contained, clear, and "elementary" proofs for results in important special cases. This book will serve as a valuable resource for graduate stu...

Inverse operator theory method mathematics-mechanization for the solutions of nonlinear equations and some typical applications in nonlinear physics

International Nuclear Information System (INIS)

Fang Jinqing; Yao Weiguang

1992-12-01

Inverse operator theory method (IOTM) has developed rapidly in the last few years. It is an effective and useful procedure for quantitative solution of nonlinear or stochastic continuous dynamical systems. Solutions are obtained in series form for deterministic equations, and in the case of stochastic equation it gives statistic measures of the solution process. A very important advantage of the IOTM is to eliminate a number of restrictive and assumption on the nature of stochastic processes. Therefore, it provides more realistic solutions. The IOTM and its mathematics-mechanization (MM) are briefly introduced. They are used successfully to study the chaotic behaviors of the nonlinear dynamical systems for the first time in the world. As typical examples, the Lorentz equation, generalized Duffing equation, two coupled generalized Duffing equations are investigated by the use of the IOTM and the MM. The results are in good agreement with ones by the Runge-Kutta method (RKM). It has higher accuracy and faster convergence. So the IOTM realized by the MM is of potential application valuable in nonlinear science

The Monge-Ampère equation

CERN Document Server

Gutiérrez, Cristian E

2016-01-01

Now in its second edition, this monograph explores the Monge-Ampère equation and the latest advances in its study and applications. It provides an essentially self-contained systematic exposition of the theory of weak solutions, including regularity results by L. A. Caffarelli. The geometric aspects of this theory are stressed using techniques from harmonic analysis, such as covering lemmas and set decompositions. An effort is made to present complete proofs of all theorems, and examples and exercises are offered to further illustrate important concepts. Some of the topics considered include generalized solutions, non-divergence equations, cross sections, and convex solutions. New to this edition is a chapter on the linearized Monge-Ampère equation and a chapter on interior Hölder estimates for second derivatives. Bibliographic notes, updated and expanded from the first edition, are included at the end of every chapter for further reading on Monge-Ampère-type equations and their diverse applications in th...

A textbook on ordinary differential equations

CERN Document Server

Ahmad, Shair

2015-01-01

This book offers readers a primer on the theory and applications of Ordinary Differential Equations. The style used is simple, yet thorough and rigorous. Each chapter ends with a broad set of exercises that range from the routine to the more challenging and thought-provoking. Solutions to selected exercises can be found at the end of the book. The book contains many interesting examples on topics such as electric circuits, the pendulum equation, the logistic equation, the Lotka-Volterra system, the Laplace Transform, etc., which introduce students to a number of interesting aspects of the theory and applications. The work is mainly intended for students of Mathematics, Physics, Engineering, Computer Science and other areas of the natural and social sciences that use ordinary differential equations, and who have a firm grasp of Calculus and a minimal understanding of the basic concepts used in Linear Algebra. It also studies a few more advanced topics, such as Stability Theory and Boundary Value Problems, whic...

On matrix fractional differential equations

Directory of Open Access Journals (Sweden)

Adem Kılıçman

2017-01-01

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

Application of the Poisson-Nernst-Planck equations to the migration test

DEFF Research Database (Denmark)

Krabbenhøft, Kristian; Krabbenhøft, Jørgen

2008-01-01

The Poisson-Nernst-Planck (PNP) equations are applied to model the migration test. A detailed analysis of the equations is presented and the effects of a number of common, simplifying assumptions are quantified. In addition, closed-form solutions for the effective chloride diffusivity based...... on the full PNP equations are derived, a number of experiments are analyzed in detail, and a new, truly accelerated migration test is proposed. Finally, we present a finite element procedure for numerical solution of the PNP equations....

Isostable reduction with applications to time-dependent partial differential equations.

Science.gov (United States)

Wilson, Dan; Moehlis, Jeff

2016-07-01

Isostables and isostable reduction, analogous to isochrons and phase reduction for oscillatory systems, are useful in the study of nonlinear equations which asymptotically approach a stationary solution. In this work, we present a general method for isostable reduction of partial differential equations, with the potential power to reduce the dimensionality of a nonlinear system from infinity to 1. We illustrate the utility of this reduction by applying it to two different models with biological relevance. In the first example, isostable reduction of the Fokker-Planck equation provides the necessary framework to design a simple control strategy to desynchronize a population of pathologically synchronized oscillatory neurons, as might be relevant to Parkinson's disease. Another example analyzes a nonlinear reaction-diffusion equation with relevance to action potential propagation in a cardiac system.

An imbedding theorem and its applications in degenerate elliptic equations

International Nuclear Information System (INIS)

Duong Minh Duc.

1988-06-01

We improve the Rellich-Kondrachov theorem and apply it to study strongly degenerate and singular elliptic equations. We obtain the maximum principle, Harnacks's inequality and global regularity for solutions of those equations. (author). 11 refs

Linear measure functional differential equations with infinite delay

OpenAIRE

Monteiro, G. (Giselle Antunes); Slavík, A.

2014-01-01

We use the theory of generalized linear ordinary differential equations in Banach spaces to study linear measure functional differential equations with infinite delay. We obtain new results concerning the existence, uniqueness, and continuous dependence of solutions. Even for equations with a finite delay, our results are stronger than the existing ones. Finally, we present an application to functional differential equations with impulses.

Exact solutions for nonlinear evolution equations using Exp-function method

International Nuclear Information System (INIS)

Bekir, Ahmet; Boz, Ahmet

2008-01-01

In this Letter, the Exp-function method is used to construct solitary and soliton solutions of nonlinear evolution equations. The Klein-Gordon, Burger-Fisher and Sharma-Tasso-Olver equations are chosen to illustrate the effectiveness of the method. The method is straightforward and concise, and its applications are promising. The Exp-function method presents a wider applicability for handling nonlinear wave equations

Histone Deacetylase Inhibitor Induced Radiation Sensitization Effects on Human Cancer Cells after Photon and Hadron Radiation Exposure

Directory of Open Access Journals (Sweden)

Ariungerel Gerelchuluun

2018-02-01

Full Text Available Suberoylanilide hydroxamic acid (SAHA is a histone deacetylase inhibitor, which has been widely utilized throughout the cancer research field. SAHA-induced radiosensitization in normal human fibroblasts AG1522 and lung carcinoma cells A549 were evaluated with a combination of γ-rays, proton, and carbon ion exposure. Growth delay was observed in both cell lines during SAHA treatment; 2 μM SAHA treatment decreased clonogenicity and induced cell cycle block in G1 phase but 0.2 μM SAHA treatment did not show either of them. Low LET (Linear Energy Transfer irradiated A549 cells showed radiosensitization effects on cell killing in cycling and G1 phase with 0.2 or 2 μM SAHA pretreatment. In contrast, minimal sensitization was observed in normal human cells after low and high LET radiation exposure. The potentially lethal damage repair was not affected by SAHA treatment. SAHA treatment reduced the rate of γ-H2AX foci disappearance and suppressed RAD51 and RPA (Replication Protein A focus formation. Suppression of DNA double strand break repair by SAHA did not result in the differences of SAHA-induced radiosensitization between human cancer cells and normal cells. In conclusion, our results suggest SAHA treatment will sensitize cancer cells to low and high LET radiation with minimum effects to normal cells.

Exact analytical solution of time-independent neutron transport equation, and its applications to systems with a point source

International Nuclear Information System (INIS)

Mikata, Y.

2014-01-01

Highlights: • An exact solution for the one-speed neutron transport equation is obtained. • This solution as well as its derivation are believed to be new. • Neutron flux for a purely absorbing material with a point neutron source off the origin is obtained. • Spherically as well as cylindrically piecewise constant cross sections are studied. • Neutron flux expressions for a point neutron source off the origin are believed to be new. - Abstract: An exact analytical solution of the time-independent monoenergetic neutron transport equation is obtained in this paper. The solution is applied to systems with a point source. Systematic analysis of the solution of the time-independent neutron transport equation, and its applications represent the primary goal of this paper. To the best of the author’s knowledge, certain key results on the scalar neutron flux as well as their derivations are new. As an application of these results, a scalar neutron flux for a purely absorbing medium with a spherically piecewise constant cross section and an isotropic point neutron source off the origin as well as that for a cylindrically piecewise constant cross section with a point neutron source off the origin are obtained. Both of these results are believed to be new

Global Bifurcation from Intervals for the Monge-Ampère Equations and Its Applications

Directory of Open Access Journals (Sweden)

Wenguo Shen

2018-01-01

Full Text Available We shall establish the global bifurcation results from the trivial solutions axis or from infinity for the Monge-Ampère equations: det(D2u=λm(x-uN+m(xf1(x,-u,-u′,λ+f2(x,-u,-u′,λ, in B, u(x=0, on ∂B, where D2u=(∂2u/∂xi∂xj is the Hessian matrix of u, where B is the unit open ball of RN, m∈C(B¯,[0,+∞ is a radially symmetric weighted function and m(r:=m(x≢0 on any subinterval of [0,1], λ is a positive parameter, and the nonlinear term f1,f2∈C(B¯×R+3,R+, but f1 is not necessarily differentiable at the origin and infinity with respect to u, where R+=[0,+∞. Some applications are given to the Monge-Ampère equations and we use global bifurcation techniques to prove our main results.

Systems of quasilinear equations and their applications to gas dynamics

CERN Document Server

Roždestvenskiĭ, B L; Schulenberger, J R

1983-01-01

This book is essentially a new edition, revised and augmented by results of the last decade, of the work of the same title published in 1968 by "Nauka." It is devoted to mathematical questions of gas dynamics. Topics covered include Foundations of the Theory of Systems of Quasilinear Equations of Hyperbolic Type in Two Independent Variables; Classical and Generalized Solutions of One-Dimensional Gas Dynamics; Difference Methods for Solving the Equations of Gas Dynamics; and Generalized Solutions of Systems of Quasilinear Equations of Hyperbolic Type.

Subordination principle for fractional evolution equations

NARCIS (Netherlands)

Bazhlekova, E.G.

2000-01-01

The abstract Cauchy problem for the fractional evolution equation Daa = Au, a > 0, (1) where A is a closed densely de??ned operator in a Banach space, is investigated. The subordination principle, presented earlier in [J. P r ??u s s, Evolutionary In- tegral Equations and Applications. Birkh??auser,

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

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Olaniyi Samuel Iyiola

2014-09-01

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

Is the Spencer-Attix cavity equation applicable for solid-state detectors irradiated in megavoltage electron beams?

International Nuclear Information System (INIS)

Mobit, P.N.; Sandison, G.A.; Calgary Univ., AB

2001-01-01

The applicability of the Spencer-Attix cavity equation in determining absorbed doses in water using solid state detectors irradiated by megavoltage electron beams have been examined. The calculations were performed using the EGSnrc Monte Carlo code. This work is an extension of a recently published article examining the perturbation of dose by solid state detectors in megavoltage electron beams. (orig.)

Conservation laws derived by the Neutral-Action Method. A simple application to the Schroedinger equation

International Nuclear Information System (INIS)

Nordbrock, U.; Kienzler, R.

2007-01-01

Conservation laws are a recognized tool in physical and engineering sciences. The classical procedure to construct conservation laws is to apply Noether's Theorem. It requires the existence of a Lagrange-function for the system under consideration. Two unknown sets of functions have to be found. A broader class of such laws is obtainable, if Noether's Theorem is used together with the Bessel-Hagen extension, raising the number of sets of unknown functions to three. By using the recently developed Neutral-Action Method, the same conservation laws can be obtained by calculating only one unknown set of functions. Moreover the Neutral Action Method can also be applied in the absence of a Lagrangian, since only the governing differential equations are required for this procedure. In the paper, an application of this method to the Schroedinger equation is presented. (authors)

Quantum-statistical kinetic equations

International Nuclear Information System (INIS)

Loss, D.; Schoeller, H.

1989-01-01

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

Problems in differential equations

CERN Document Server

Brenner, J L

2013-01-01

More than 900 problems and answers explore applications of differential equations to vibrations, electrical engineering, mechanics, and physics. Problem types include both routine and nonroutine, and stars indicate advanced problems. 1963 edition.

Nielsen number and differential equations

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Andres Jan

2005-01-01

Full Text Available In reply to a problem of Jean Leray (application of the Nielsen theory to differential equations, two main approaches are presented. The first is via Poincaré's translation operator, while the second one is based on the Hammerstein-type solution operator. The applicability of various Nielsen theories is discussed with respect to several sorts of differential equations and inclusions. Links with the Sharkovskii-like theorems (a finite number of periodic solutions imply infinitely many subharmonics are indicated, jointly with some further consequences like the nontrivial -structure of solutions of initial value problems. Some illustrating examples are supplied and open problems are formulated.

Application of flexible model in neutron dynamics equations

International Nuclear Information System (INIS)

Liu Cheng; Zhao Fuyu; Fu Xiangang

2009-01-01

Big errors will occur in the modeling by multimode methodology when the available core physical parameter sets are insufficient. In this paper, the fuzzy logic membership function is introduced to figure out the values of these parameters on any point of lifetime through limited several sets of values, and thus to obtain the neutron dynamics equations on any point of lifetime. In order to overcome the effect of subjectivity in the membership function selection on the parameter calculation, quadratic optimization is carried out to the membership function by genetic algorithm, to result in a more accurate neutron kinetics equation on any point of lifetime. (authors)

Exact solutions for modified Korteweg-de Vries equation

International Nuclear Information System (INIS)

Sarma, Jnanjyoti

2009-01-01

Using the simple wave or traveling wave solution technique, many different types of solutions are derived for modified Korteweg-de Vries (KdV) equation. The solutions are obtained from the set of nonlinear algebraic equations, which can be derived from the modified Korteweg-de Vries (KdV) equation by using the hyperbolic transformation method. The method can be applicable for similar nonlinear wave equations.

Application of the Extended Grunwald-Winstein Equation to Solvolyses of n-Propyl Chloroformate

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Dennis N. Kevill

2005-01-01

Full Text Available Abstract: Application of the extended Grunwald-Winstein equation to solvolyses of n-propyl chloroformate in a variety of pure and binary solvents indicates an addition-elimination pathway in the majority of the solvents but an ionization pathway in the solvents of highest ionizing power and lowest nucleophilicity. For methanolysis, a solvent deuterium isotope effect of 2.17 is compatible with the incorporation of general-base catalysis into the substitution process. Activation parameters are consistent with the duality of mechanism. Very modest positive salt effects are observed on adding chloride or bromide salts to the ethanolysis.

Soliton solutions to the fifth-order Korteweg-de Vries equation and their applications to surface and internal water waves

Science.gov (United States)

Khusnutdinova, K. R.; Stepanyants, Y. A.; Tranter, M. R.

2018-02-01

We study solitary wave solutions of the fifth-order Korteweg-de Vries equation which contains, besides the traditional quadratic nonlinearity and third-order dispersion, additional terms including cubic nonlinearity and fifth order linear dispersion, as well as two nonlinear dispersive terms. An exact solitary wave solution to this equation is derived, and the dependence of its amplitude, width, and speed on the parameters of the governing equation is studied. It is shown that the derived solution can represent either an embedded or regular soliton depending on the equation parameters. The nonlinear dispersive terms can drastically influence the existence of solitary waves, their nature (regular or embedded), profile, polarity, and stability with respect to small perturbations. We show, in particular, that in some cases embedded solitons can be stable even with respect to interactions with regular solitons. The results obtained are applicable to surface and internal waves in fluids, as well as to waves in other media (plasma, solid waveguides, elastic media with microstructure, etc.).

Novel algorithm of large-scale simultaneous linear equations

International Nuclear Information System (INIS)

Fujiwara, T; Hoshi, T; Yamamoto, S; Sogabe, T; Zhang, S-L

2010-01-01

We review our recently developed methods of solving large-scale simultaneous linear equations and applications to electronic structure calculations both in one-electron theory and many-electron theory. This is the shifted COCG (conjugate orthogonal conjugate gradient) method based on the Krylov subspace, and the most important issue for applications is the shift equation and the seed switching method, which greatly reduce the computational cost. The applications to nano-scale Si crystals and the double orbital extended Hubbard model are presented.

The Bach equations in spin-coefficient form

Science.gov (United States)

Forbes, Hamish

2018-06-01

Conformal gravity theories are defined by field equations that determine only the conformal structure of the spacetime manifold. The Bach equations represent an early example of such a theory, we present them here in component form in terms of spin- and boost-weighted spin-coefficients using the compacted spin-coefficient formalism. These equations can be used as an efficient alternative to the standard tensor form. As a simple application we solve the Bach equations for pp-wave and static spherically symmetric spacetimes.

Extended sine-Gordon Equation Method and Its Application to Maccari's System

International Nuclear Information System (INIS)

Song Lina; Zhang Hongqing

2005-01-01

An extended sine-Gordon equation method is proposed to construct exact travelling wave solutions to Maccari's equation based upon a generalized sine-Gordon equation. It is shown that more new travelling wave solutions can be found by this new method, which include bell-shaped soliton solutions, kink-shaped soliton solutions, periodic wave solution, and new travelling waves.

Influence of partial ionization and scattering states on the solar interior structure

International Nuclear Information System (INIS)

Ulrich, R.K.

1982-01-01

The equation of state for the solar interior is normally assumed to be a fully ionized gas corrected by the Debye-Hueckel Coulomb interaction, partial degeneracy, and radiation pressure. The assumption of full ionization is dropped in this paper, and the influence of scattering states is included. The theory of scattering states appears to be new to astrophysics. This theory has been developed by Larkin and is discussed thoroughly by Ebeling, Kraft, and Kremp. The effect of scattering states eliminates the need to invoke a process of ''pressure ionization'' for which no satisfactory theory exists. Six solar models which include varying forms of the equation of state are discussed. The Saha equation without scattering states gives a neutrino counting rate of 7.41 SNU for the 37 Cl experiment, while assumed ionization for T>3 x 10 5 K gives 8.87 SNU, and the Saha equation with the lowest order effect of scattering states (Planck-Larkin equation) gives 8.83 SNU. Inclusion of the second virial coefficient due to scattering states brings the result to 9.02 SNU. The changes of quantities such as central temperature and the temperature at the base of the convective envelope are small and bear a similar relationship among the models. The initial hydrogen abundance of the model including the second virial coefficient due to scattering states is in good agreement with that found for the Orion nebula and B stars, i.e., log (N/sub He//N/sub H/)+12 = 10.97

Differential equations with Mathematica

CERN Document Server

Abell, Martha L

2004-01-01

The Third Edition of the Differential Equations with Mathematica integrates new applications from a variety of fields,especially biology, physics, and engineering. The new handbook is also completely compatible with recent versions of Mathematica and is a perfect introduction for Mathematica beginners.* Focuses on the most often used features of Mathematica for the beginning Mathematica user* New applications from a variety of fields, including engineering, biology, and physics* All applications were completed using recent versions of Mathematica

Soliton equations and Hamiltonian systems

CERN Document Server

Dickey, L A

2002-01-01

The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics. For a long time, books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this output followed one single work by Gardner, Green, Kruskal, and Mizura on the Korteweg-de Vries equation (KdV), which had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water. Besides its obvious practical use, this theory is attractive also becau

Three equations of state and their application to transition metals

International Nuclear Information System (INIS)

Tian Ronggang; Sun Jiuxun; Yang Wei; Yu Fei

2010-01-01

A modified generalized Morse (mGMSE) equation of state (EOS) is proposed that can incorporate the cohesive energy data correctly. It is compared with a four-parameter modified Rose (MR) EOS, which is proposed by following Rose's approach, and the Murnaghan (MNH) EOS. The MR, mGMSE and MNH EOSs are applied to five transition metals and then compared to the available experimental compression data. The results obtained show that for all pressure ranges, the mGMSE EOS fits experimental data most accurately. From a comparison of the variation in pressure and energy versus the compression ratio between MR and mGMSE EOSs, it is clear that the pressure and energy of the MR EOS oscillate both in the neighborhood of (V/V 0 ) ∼ 0.005 and in the range (V/V 0 )> 1. Generally speaking, the mGMSE EOS has many evident advantages over the other two EOSs, while the practical applications of the MR EOS are seriously limited because of physically incorrect oscillations.

Three equations of state and their application to transition metals

Science.gov (United States)

Ronggang, Tian; Jiuxun, Sun; Wei, Yang; Fei, Yu

2010-10-01

A modified generalized Morse (mGMSE) equation of state (EOS) is proposed that can incorporate the cohesive energy data correctly. It is compared with a four-parameter modified Rose (MR) EOS, which is proposed by following Rose's approach, and the Murnaghan (MNH) EOS. The MR, mGMSE and MNH EOSs are applied to five transition metals and then compared to the available experimental compression data. The results obtained show that for all pressure ranges, the mGMSE EOS fits experimental data most accurately. From a comparison of the variation in pressure and energy versus the compression ratio between MR and mGMSE EOSs, it is clear that the pressure and energy of the MR EOS oscillate both in the neighborhood of (V/V0 ) ≈ 0.005 and in the range (V/V0 )> 1. Generally speaking, the mGMSE EOS has many evident advantages over the other two EOSs, while the practical applications of the MR EOS are seriously limited because of physically incorrect oscillations.

Partial differential equations an accessible route through theory and applications

CERN Document Server

Vasy, András

2015-01-01

This text on partial differential equations is intended for readers who want to understand the theoretical underpinnings of modern PDEs in settings that are important for the applications without using extensive analytic tools required by most advanced texts. The assumed mathematical background is at the level of multivariable calculus and basic metric space material, but the latter is recalled as relevant as the text progresses. The key goal of this book is to be mathematically complete without overwhelming the reader, and to develop PDE theory in a manner that reflects how researchers would think about the material. A concrete example is that distribution theory and the concept of weak solutions are introduced early because while these ideas take some time for the students to get used to, they are fundamentally easy and, on the other hand, play a central role in the field. Then, Hilbert spaces that are quite important in the later development are introduced via completions which give essentially all the fea...

Application of Peleg's equation to describe creep responses of potatoes under constant and variable storage conditions.

Science.gov (United States)

Solomon, W K; Jindal, V K

2017-06-01

The application of Peleg's equation to characterize creep behavior of potatoes during storage was investigated. Potatoes were stored at 25, 15, 5C, and variable (fluctuating) temperature for 16 or 26 weeks. The Peleg equation adequately described the creep response of potatoes during storage at all storage conditions (R 2  = .97to .99). Peleg constant k 1 exhibited a significant (p creep responses during storage or processing will be potentially helpful to better understand the phenomenon. The model parameters from such model could be used to relate rheological properties of raw and cooked potatoes. Moreover, the model parameters could be used to establish relationship between instrumental and sensory attributes which will help in the prediction of sensory attributes from instrumental data. © 2016 Wiley Periodicals, Inc.

Application of the principal fractional meta-trigonometric functions for the solution of linear commensurate-order time-invariant fractional differential equations.

Science.gov (United States)

Lorenzo, C F; Hartley, T T; Malti, R

2013-05-13

A new and simplified method for the solution of linear constant coefficient fractional differential equations of any commensurate order is presented. The solutions are based on the R-function and on specialized Laplace transform pairs derived from the principal fractional meta-trigonometric functions. The new method simplifies the solution of such fractional differential equations and presents the solutions in the form of real functions as opposed to fractional complex exponential functions, and thus is directly applicable to real-world physics.

New Trace Bounds for the Product of Two Matrices and Their Applications in the Algebraic Riccati Equation

Directory of Open Access Journals (Sweden)

Liu Jianzhou

2009-01-01

Full Text Available By using singular value decomposition and majorization inequalities, we propose new inequalities for the trace of the product of two arbitrary real square matrices. These bounds improve and extend the recent results. Further, we give their application in the algebraic Riccati equation. Finally, numerical examples have illustrated that our results are effective and superior.

Graphical analyses of connected-kernel scattering equations

International Nuclear Information System (INIS)

Picklesimer, A.

1983-01-01

Simple graphical techniques are employed to obtain a new (simultaneous) derivation of a large class of connected-kernel scattering equations. This class includes the Rosenberg, Bencze-Redish-Sloan, and connected-kernel multiple scattering equations as well as a host of generalizations of these and other equations. The basic result is the application of graphical methods to the derivation of interaction-set equations. This yields a new, simplified form for some members of the class and elucidates the general structural features of the entire class

Application of a nodal collocation approximation for the multidimensional PL equations to the 3D Takeda benchmark problems

International Nuclear Information System (INIS)

Capilla, M.; Talavera, C.F.; Ginestar, D.; Verdú, G.

2012-01-01

Highlights: ► The multidimensional P L approximation to the nuclear transport equation is reviewed. ► A nodal collocation method is developed for the spatial discretization of P L equations. ► Advantages of the method are lower dimension and good characterists of the associated algebraic eigenvalue problem. ► The P L nodal collocation method is implemented into the computer code SHNC. ► The SHNC code is verified with 2D and 3D benchmark eigenvalue problems from Takeda and Ikeda, giving satisfactory results. - Abstract: P L equations are classical approximations to the neutron transport equations, which are obtained expanding the angular neutron flux in terms of spherical harmonics. These approximations are useful to study the behavior of reactor cores with complex fuel assemblies, for the homogenization of nuclear cross-sections, etc., and most of these applications are in three-dimensional (3D) geometries. In this work, we review the multi-dimensional P L equations and describe a nodal collocation method for the spatial discretization of these equations for arbitrary odd order L, which is based on the expansion of the spatial dependence of the fields in terms of orthonormal Legendre polynomials. The performance of the nodal collocation method is studied by means of obtaining the k eff and the stationary power distribution of several 3D benchmark problems. The solutions are obtained are compared with a finite element method and a Monte Carlo method.

Lyapunov stability and its application to systems of ordinary differential equations

Science.gov (United States)

Kennedy, E. W.

1979-01-01

An outline and a brief introduction to some of the concepts and implications of Lyapunov stability theory are presented. Various aspects of the theory are illustrated by the inclusion of eight examples, including the Cartesian coordinate equations of the two-body problem, linear and nonlinear (Van der Pol's equation) oscillatory systems, and the linearized Kustaanheimo-Stiefel element equations for the unperturbed two-body problem.

Newton's laws of motion in form of Riccati equation

OpenAIRE

Nowakowski, M.; Rosu, H. C.

2001-01-01

We discuss two applications of Riccati equation to Newton's laws of motion. The first one is the motion of a particle under the influence of a power law central potential $V(r)=k r^{\\epsilon}$. For zero total energy we show that the equation of motion can be cast in the Riccati form. We briefly show here an analogy to barotropic Friedmann-Robertson-Lemaitre cosmology where the expansion of the universe can be also shown to obey a Riccati equation. A second application in classical mechanics, ...

Application of Four-Point Newton-EGSOR iteration for the numerical solution of 2D Porous Medium Equations

Science.gov (United States)

Chew, J. V. L.; Sulaiman, J.

2017-09-01

Partial differential equations that are used in describing the nonlinear heat and mass transfer phenomena are difficult to be solved. For the case where the exact solution is difficult to be obtained, it is necessary to use a numerical procedure such as the finite difference method to solve a particular partial differential equation. In term of numerical procedure, a particular method can be considered as an efficient method if the method can give an approximate solution within the specified error with the least computational complexity. Throughout this paper, the two-dimensional Porous Medium Equation (2D PME) is discretized by using the implicit finite difference scheme to construct the corresponding approximation equation. Then this approximation equation yields a large-sized and sparse nonlinear system. By using the Newton method to linearize the nonlinear system, this paper deals with the application of the Four-Point Newton-EGSOR (4NEGSOR) iterative method for solving the 2D PMEs. In addition to that, the efficiency of the 4NEGSOR iterative method is studied by solving three examples of the problems. Based on the comparative analysis, the Newton-Gauss-Seidel (NGS) and the Newton-SOR (NSOR) iterative methods are also considered. The numerical findings show that the 4NEGSOR method is superior to the NGS and the NSOR methods in terms of the number of iterations to get the converged solutions, the time of computation and the maximum absolute errors produced by the methods.

Operational matrices with respect to Hermite polynomials and their applications in solving linear dierential equations with variable coecients

Directory of Open Access Journals (Sweden)

A. Aminataei

2014-05-01

Full Text Available In this paper, a new and ecient approach is applied for numerical approximation of the linear dierential equations with variable coecients based on operational matrices with respect to Hermite polynomials. Explicit formulae which express the Hermite expansioncoecients for the moments of derivatives of any dierentiable function in terms of the original expansion coecients of the function itself are given in the matrix form. The mainimportance of this scheme is that using this approach reduces solving the linear dierentialequations to solve a system of linear algebraic equations, thus greatly simplifying the problem. In addition, two experiments are given to demonstrate the validity and applicability of the method

Stochastic porous media equations

CERN Document Server

Barbu, Viorel; Röckner, Michael

2016-01-01

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

On the Equational Definition of the Least Prefixed Point

DEFF Research Database (Denmark)

Santocanale, Luigi

2001-01-01

We show how to axiomatize by equations the least prefixed point of an order preserving function and discuss the domain of application of the proposed method. Thus, we generalize the well known equational axiomatization of Propositional Dynamic Logic to a complete equational axiomatization of the ...

On a class of nonlocal wave equations from applications

Science.gov (United States)

Beyer, Horst Reinhard; Aksoylu, Burak; Celiker, Fatih

2016-06-01

We study equations from the area of peridynamics, which is a nonlocal extension of elasticity. The governing equations form a system of nonlocal wave equations. We take a novel approach by applying operator theory methods in a systematic way. On the unbounded domain ℝn, we present three main results. As main result 1, we find that the governing operator is a bounded function of the governing operator of classical elasticity. As main result 2, a consequence of main result 1, we prove that the peridynamic solutions strongly converge to the classical solutions by utilizing, for the first time, strong resolvent convergence. In addition, main result 1 allows us to incorporate local boundary conditions, in particular, into peridynamics. This avenue of research is developed in companion papers, providing a remedy for boundary effects. As main result 3, employing spherical Bessel functions, we give a new practical series representation of the solution which allows straightforward numerical treatment with symbolic computation.

From differential to difference equations for first order ODEs

Science.gov (United States)

Freed, Alan D.; Walker, Kevin P.

1991-01-01

When constructing an algorithm for the numerical integration of a differential equation, one should first convert the known ordinary differential equation (ODE) into an ordinary difference equation. Given this difference equation, one can develop an appropriate numerical algorithm. This technical note describes the derivation of two such ordinary difference equations applicable to a first order ODE. The implicit ordinary difference equation has the same asymptotic expansion as the ODE itself, whereas the explicit ordinary difference equation has an asymptotic that is similar in structure but different in value when compared with that of the ODE.

Vorinostat enhances chemosensitivity to arsenic trioxide in K562 cell line

Directory of Open Access Journals (Sweden)

Nainong Li

2015-05-01

Full Text Available Objective. This study aimed to investigate the chemosensitive augmentation effect and mechanism of HDAC inhibitor Vorinostat (SAHA in combination with arsenic trioxide (ATO on proliferation and apoptosis of K562 cells.Methods. The CCK-8 assay was used to compare proliferation of the cells. Annexin-V and PI staining by flow cytometry and acridine orange/ethidium bromide stains were used to detect and quantify apoptosis. Western blot was used to detect expression of p21, Akt, pAkt, p210, Acetyl-Histone H3, and Acetyl-Histone H4 proteins.Results. SAHA and ATO inhibited proliferation of K562 cells in an additive and time- and dose-dependent manner. SAHA in combination with ATO showed significant apoptosis of K562 cells in comparison to the single drugs alone (p < 0.01. Both SAHA and ATO alone and in combination showed lower levels of p210 expression. SAHA and SAHA and ATO combined treatment showed increased levels of Acetyl-Histone H3 and Acetyl-Histone H4 protein expression. SAHA alone showed increased expression of p21, while ATO alone and in combination with SAHA showed no significant change. SAHA and ATO combined therapy showed lower levels of Akt and pAkt protein expression than SAHA or ATO alone.Conclusion. SAHA and ATO combined treatment inhibited proliferation, induced apoptosis, and showed a chemosensitive augmentation effect on K562 cells. The mechanism might be associated with increasing histone acetylation levels as well as regulating the Akt signaling pathway.

Applied partial differential equations

CERN Document Server

Logan, J David

2015-01-01

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

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

Directory of Open Access Journals (Sweden)

Kenichi Kondo

2013-11-01

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

The application of Legendre-tau approximation to parameter identification for delay and partial differential equations

Science.gov (United States)

Ito, K.

1983-01-01

Approximation schemes based on Legendre-tau approximation are developed for application to parameter identification problem for delay and partial differential equations. The tau method is based on representing the approximate solution as a truncated series of orthonormal functions. The characteristic feature of the Legendre-tau approach is that when the solution to a problem is infinitely differentiable, the rate of convergence is faster than any finite power of 1/N; higher accuracy is thus achieved, making the approach suitable for small N.

The Application Strategy of Iterative Solution Methodology to Matrix Equations in Hydraulic Solver Package, SPACE

International Nuclear Information System (INIS)

Na, Y. W.; Park, C. E.; Lee, S. Y.

2009-01-01

As a part of the Ministry of Knowledge Economy (MKE) project, 'Development of safety analysis codes for nuclear power plants', KOPEC has been developing the hydraulic solver code package applicable to the safety analyses of nuclear power plants (NPP's). The matrices of the hydraulic solver are usually sparse and may be asymmetric. In the earlier stage of this project, typical direct matrix solver packages MA48 and MA28 had been tested as matrix solver for the hydraulic solver code, SPACE. The selection was based on the reasonably reliable performance experience from their former version MA18 in RELAP computer code. In the later stage of this project, the iterative methodologies have been being tested in the SPACE code. Among a few candidate iterative solution methodologies tested so far, the biconjugate gradient stabilization methodology (BICGSTAB) has shown the best performance in the applicability test and in the application to the SPACE code. Regardless of all the merits of using the direct solver packages, there are some other aspects of tackling the iterative solution methodologies. The algorithm is much simpler and easier to handle. The potential problems related to the robustness of the iterative solution methodologies have been resolved by applying pre-conditioning methods adjusted and modified as appropriate to the application in the SPACE code. The application strategy of conjugate gradient method was introduced in detail by Schewchuk, Golub and Saad in the middle of 1990's. The application of his methodology to nuclear engineering in Korea started about the same time and is still going on and there are quite a few examples of application to neutronics. Besides, Yang introduced a conjugate gradient method programmed in C++ language. The purpose of this study is to assess the performance and behavior of the iterative solution methodology compared to those of the direct solution methodology still being preferred due to its robustness and reliability. The

Analysis of Caputo Impulsive Fractional Order Differential Equations with Applications

Directory of Open Access Journals (Sweden)

Lakshman Mahto

2013-01-01

Full Text Available We use Sadovskii's fixed point method to investigate the existence and uniqueness of solutions of Caputo impulsive fractional differential equations of order with one example of impulsive logistic model and few other examples as well. We also discuss Caputo impulsive fractional differential equations with finite delay. The results proven are new and compliment the existing one.

Application of the trial equation method for solving some nonlinear ...

Indian Academy of Sciences (India)

Therefore, our aim is just to find the function F. Liu has obtained a number of exact solutions to many nonlinear differential equations when F(u) is a polynomial or a rational function. ... In this study, we apply the trial equation method to seek exact solutions of the ... twice and setting the integration constant to zero, we have.

Optimal Control for Stochastic Delay Evolution Equations

Energy Technology Data Exchange (ETDEWEB)

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

2016-08-15

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

Stochastic Optimal Prediction with Application to Averaged Euler Equations

Energy Technology Data Exchange (ETDEWEB)

Bell, John [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Chorin, Alexandre J. [Univ. of California, Berkeley, CA (United States); Crutchfield, William [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

2017-04-24

Optimal prediction (OP) methods compensate for a lack of resolution in the numerical solution of complex problems through the use of an invariant measure as a prior measure in the Bayesian sense. In first-order OP, unresolved information is approximated by its conditional expectation with respect to the invariant measure. In higher-order OP, unresolved information is approximated by a stochastic estimator, leading to a system of random or stochastic differential equations. We explain the ideas through a simple example, and then apply them to the solution of Averaged Euler equations in two space dimensions.

Lie and Q-Conditional Symmetries of Reaction-Diffusion-Convection Equations with Exponential Nonlinearities and Their Application for Finding Exact Solutions

Directory of Open Access Journals (Sweden)

Roman Cherniha

2018-04-01

Full Text Available This review is devoted to search for Lie and Q-conditional (nonclassical symmetries and exact solutions of a class of reaction-diffusion-convection equations with exponential nonlinearities. A complete Lie symmetry classification of the class is derived via two different algorithms in order to show that the result depends essentially on the type of equivalence transformations used for the classification. Moreover, a complete description of Q-conditional symmetries for PDEs from the class in question is also presented. It is shown that all the well-known results for reaction-diffusion equations with exponential nonlinearities follow as particular cases from the results derived for this class of reaction-diffusion-convection equations. The symmetries obtained for constructing exact solutions of the relevant equations are successfully applied. The exact solutions are compared with those found by means of different techniques. Finally, an application of the exact solutions for solving boundary-value problems arising in population dynamics is presented.

Inequalities for differential and integral equations

CERN Document Server

Ames, William F

1997-01-01

Inequalities for Differential and Integral Equations has long been needed; it contains material which is hard to find in other books. Written by a major contributor to the field, this comprehensive resource contains many inequalities which have only recently appeared in the literature and which can be used as powerful tools in the development of applications in the theory of new classes of differential and integral equations. For researchers working in this area, it will be a valuable source of reference and inspiration. It could also be used as the text for an advanced graduate course.Key Features* Covers a variety of linear and nonlinear inequalities which find widespread applications in the theory of various classes of differential and integral equations* Contains many inequalities which have only recently appeared in literature and cannot yet be found in other books* Provides a valuable reference to engineers and graduate students

Stochastic equations for complex systems theoretical and computational topics

CERN Document Server

Bessaih, Hakima

2015-01-01

Mathematical analyses and computational predictions of the behavior of complex systems are needed to effectively deal with weather and climate predictions, for example, and the optimal design of technical processes. Given the random nature of such systems and the recognized relevance of randomness, the equations used to describe such systems usually need to involve stochastics.  The basic goal of this book is to introduce the mathematics and application of stochastic equations used for the modeling of complex systems. A first focus is on the introduction to different topics in mathematical analysis. A second focus is on the application of mathematical tools to the analysis of stochastic equations. A third focus is on the development and application of stochastic methods to simulate turbulent flows as seen in reality.  This book is primarily oriented towards mathematics and engineering PhD students, young and experienced researchers, and professionals working in the area of stochastic differential equations ...

An introduction to the theory of the Boltzmann equation

CERN Document Server

Harris, Stewart

2011-01-01

Boltzmann's equation (or Boltzmann-like equations) appears extensively in such disparate fields as laser scattering, solid-state physics, nuclear transport, and beyond the conventional boundaries of physics and engineering, in the fields of cellular proliferation and automobile traffic flow. This introductory graduate-level course for students of physics and engineering offers detailed presentations of the basic modern theory of Boltzmann's equation, including representative applications using both Boltzmann's equation and the model Boltzmann equations developed within the text. It emphasizes

Backward stochastic differential equations from linear to fully nonlinear theory

CERN Document Server

Zhang, Jianfeng

2017-01-01

This book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations. Their main applications and numerical algorithms, as well as many exercises, are included. The book focuses on ideas and clarity, with most results having been solved from scratch and most theories being motivated from applications. It can be considered a starting point for junior researchers in the field, and can serve as a textbook for a two-semester graduate course in probability theory and stochastic analysis. It is also accessible for graduate students majoring in financial engineering.

Suberoylanilide hydroxamic acid increases anti-cancer effect of tumor necrosis factor-α through up-regulation of TNF receptor 1 in lung cancer cells.

Science.gov (United States)

You, Bo Ra; Han, Bo Ram; Park, Woo Hyun

2017-03-14

Suberoylanilide hydroxamic acid (SAHA) as a histone deacetylase (HDAC) inhibitor has anti-cancer effect. Here, we evaluated the effect of SAHA on HDAC activity and cell growth in many normal lung and cancer cells. We observed that the HDAC activities of lung cancer cells were higher than that of normal lung cells. SAHA inhibited the growth of lung cancer cells regardless of the inhibitory effect on HDAC. This agent induced a G2/M phase arrest and apoptosis, which was accompanied by mitochondrial membrane potential (MMP: ΔΨm) loss in lung cancer cells. However, SAHA did not induce cell death in normal lung cells. All tested caspase inhibitors prevented apoptotic cell death in SAHA-treated A549 and Calu-6 lung cancer cells. Treatment with tumor necrosis factor-alpha (TNF-α) enhanced apoptosis in SAHA-treated lung cancer cells through caspase-8 and caspase-9 activations. Especially, SAHA increased the expression level of TNF-α receptor 1 (TNFR1), especially acetylation of the region of TNFR1 promoter -223/-29 in lung cancer cells. The down-regulation of TNFR1 suppressed apoptosis in TNF-α and SAHA-treated lung cancer cells. In conclusion, SAHA inhibited the growth of lung cancer cells via a G2/M phase arrest and caspase-dependent apoptosis. SAHA also enhanced apoptotic effect of TNF-α in human lung cancer cells through up-regulation of TNFR1. TNF-α may be a key to improve anti-cancer effect of HDAC inhibitors.

Dynamics with infinitely many derivatives: variable coefficient equations

International Nuclear Information System (INIS)

Barnaby, Neil; Kamran, Niky

2008-01-01

Infinite order differential equations have come to play an increasingly significant role in theoretical physics. Field theories with infinitely many derivatives are ubiquitous in string field theory and have attracted interest recently also from cosmologists. Crucial to any application is a firm understanding of the mathematical structure of infinite order partial differential equations. In our previous work we developed a formalism to study the initial value problem for linear infinite order equations with constant coefficients. Our approach relied on the use of a contour integral representation for the functions under consideration. In many applications, including the study of cosmological perturbations in nonlocal inflation, one must solve linearized partial differential equations about some time-dependent background. This typically leads to variable coefficient equations, in which case the contour integral methods employed previously become inappropriate. In this paper we develop the theory of a particular class of linear infinite order partial differential equations with variable coefficients. Our formalism is particularly well suited to the types of equations that arise in nonlocal cosmological perturbation theory. As an example to illustrate our formalism we compute the leading corrections to the scalar field perturbations in p-adic inflation and show explicitly that these are small on large scales.

Kinetic equations for clean superconductors: Application to the flux flow hall effect

International Nuclear Information System (INIS)

Kopnin, N.B.

1994-01-01

The kinetic equations for clean superconductors (l>>ζ) are derived. expanding the equations for the time dependent Green functions in the quasiclassical parameter, the new contributions are found which contain the derivatives of the distribution functions with respect to the quasiparticle momentum. The transition from the ultra-clean case (no relaxation) to a relaxation-dominated behavior, for which the kinetic equations coincide with the usual quasiclassical approximation, occurs for the relaxation time of the order of ℎE F /Δ 2 . The kinetic equations can be used for various dynamic processes in superconductors including the flux-flow Hall effect. The derived equations, after necessary modifications for the p-wave pairing, are especially suitable for nonstationary problems in the theory of superfluidity of 3 He

Differential equations driven by rough paths with jumps

Science.gov (United States)

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.

Electron transfer dynamics: Zusman equation versus exact theory

International Nuclear Information System (INIS)

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

2009-01-01

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

Derivation of Pal-Bell equations for two-point reactors, and its application to correlation measurements at KUCA

International Nuclear Information System (INIS)

Murata, Naoyuki; Yamane, Yoshihiro; Nishina, Kojiro; Shiroya, Seiji; Kanda, Keiji.

1980-01-01

A probability is defined for an event in which m neutrons exist at time t sub(f) in core I of a coupled-core system, originating from a neutron injected into the core I at an earlier time t; we call it P sub(I,I,m)(t sub(f)/t). Similarly, P sub(I,II,m)(t sub(f)/t) is defined as the probability for m neutrons to exist in core II of the system at time t sub(f), originating from a neutron injected into the core I at time t. Then a system of coupled equations are derived for the generating functions G sub(Ij)(z, t sub(f)/t) = μP sub(Ijm)(t sub(f)/t).z sup(m), where j = I, II. By similar procedures equations are derived for the generating functions associated with joint probability of the following events: a given combination of numbers of neutrons are detected during given series of detection time intervals by a detector inserted in one of the cores. The above two kinds of systems of equations can be regarded as a two-point version of Pal-Bell's equations. As the application of these formulations, analyzing formula for correlation measurements, namely (1) Feynman-alpha experiment and (2) Rossi-alpha experiment of Orndoff-type, are derived, and their feasibility is verified by experiments carried out at KUCA. (author)

A generic validation methodology and its application to a set of multi-axial creep damage constitutive equations

International Nuclear Information System (INIS)

Xu Qiang

2005-01-01

A generic validation methodology for a set of multi-axial creep damage constitutive equations is proposed and its use is illustrated with 0.5Cr0.5Mo0.25V ferritic steel which is featured as brittle or intergranular rupture. The objective of this research is to develop a methodology to guide systematically assess the quality of a set of multi-axial creep damage constitutive equations in order to ensure its general applicability. This work adopted a total quality assurance approach and expanded as a Four Stages procedure (Theories and Fundamentals, Parameter Identification, Proportional Load, and Non-proportional load). Its use is illustrated with 0.5Cr0.5Mo0.25V ferritic steel and this material is chosen due to its industry importance, the popular use of KRH type of constitutive equations, and the available qualitative experimental data including damage distribution from notched bar test. The validation exercise clearly revealed the deficiencies existed in the KRH formulation (in terms of mathematics and physics of damage mechanics) and its incapability to predict creep deformation accurately. Consequently, its use should be warned, which is particularly important due to its wide use as indicated in literature. This work contributes to understand the rational for formulation and the quality assurance of a set of constitutive equations in creep damage mechanics as well as in general damage mechanics. (authors)

Application of the bifurcation method to the modified Boussinesq equation

Directory of Open Access Journals (Sweden)

Shaoyong Li

2014-08-01

Firstly, we give a property of the solutions of the equation, that is, if $1+u(x, t$ is a solution, so is $1-u(x, t$. Secondly, by using the bifurcation method of dynamical systems we obtain some explicit expressions of solutions for the equation, which include kink-shaped solutions, blow-up solutions, periodic blow-up solutions and solitary wave solutions. Some previous results are extended.

Linear q-nonuniform difference equations

International Nuclear Information System (INIS)

Bangerezako, Gaspard

2010-01-01

We introduce basic concepts of q-nonuniform differentiation and integration and study linear q-nonuniform difference equations and systems, as well as their application in q-nonuniform difference linear control systems. (author)

Interpreting experimental data on egg production--applications of dynamic differential equations.

Science.gov (United States)

France, J; Lopez, S; Kebreab, E; Dijkstra, J

2013-09-01

This contribution focuses on applying mathematical models based on systems of ordinary first-order differential equations to synthesize and interpret data from egg production experiments. Models based on linear systems of differential equations are contrasted with those based on nonlinear systems. Regression equations arising from analytical solutions to linear compartmental schemes are considered as candidate functions for describing egg production curves, together with aspects of parameter estimation. Extant candidate functions are reviewed, a role for growth functions such as the Gompertz equation suggested, and a function based on a simple new model outlined. Structurally, the new model comprises a single pool with an inflow and an outflow. Compartmental simulation models based on nonlinear systems of differential equations, and thus requiring numerical solution, are next discussed, and aspects of parameter estimation considered. This type of model is illustrated in relation to development and evaluation of a dynamic model of calcium and phosphorus flows in layers. The model consists of 8 state variables representing calcium and phosphorus pools in the crop, stomachs, plasma, and bone. The flow equations are described by Michaelis-Menten or mass action forms. Experiments that measure Ca and P uptake in layers fed different calcium concentrations during shell-forming days are used to evaluate the model. In addition to providing a useful management tool, such a simulation model also provides a means to evaluate feeding strategies aimed at reducing excretion of potential pollutants in poultry manure to the environment.

Exact integration of the unsteady incompressible Navier-Stokes equations, gauge criteria, and applications

Science.gov (United States)

Scholle, M.; Gaskell, P. H.; Marner, F.

2018-04-01

An exact first integral of the full, unsteady, incompressible Navier-Stokes equations is achieved in its most general form via the introduction of a tensor potential and parallels drawn with Maxwell's theory. Subsequent to this gauge freedoms are explored, showing that when used astutely they lead to a favourable reduction in the complexity of the associated equation set and number of unknowns, following which the inviscid limit case is discussed. Finally, it is shown how a change in gauge criteria enables a variational principle for steady viscous flow to be constructed having a self-adjoint form. Use of the new formulation is demonstrated, for different gauge variants of the first integral as the starting point, through the solution of a hierarchy of classical three-dimensional flow problems, two of which are tractable analytically, the third being solved numerically. In all cases the results obtained are found to be in excellent accord with corresponding solutions available in the open literature. Concurrently, the prescription of appropriate commonly occurring physical and necessary auxiliary boundary conditions, incorporating for completeness the derivation of a first integral of the dynamic boundary condition at a free surface, is established, together with how the general approach can be advantageously reformulated for application in solving unsteady flow problems with periodic boundaries.

Lagrange-Noether method for solving second-order differential equations

Institute of Scientific and Technical Information of China (English)

Wu Hui-Bin; Wu Run-Heng

2009-01-01

The purpose of this paper is to provide a new method called the Lagrange-Noether method for solving second-order differential equations. The method is,firstly,to write the second-order differential equations completely or partially in the form of Lagrange equations,and secondly,to obtain the integrals of the equations by using the Noether theory of the Lagrange system. An example is given to illustrate the application of the result.

Three equations of state and their application to transition metals

Energy Technology Data Exchange (ETDEWEB)

Tian Ronggang; Sun Jiuxun; Yang Wei; Yu Fei, E-mail: sjx@uestc.edu.c [Department of Applied Physics, University of Electronic Science and Technology of China, Chengdu 610054 (China)

2010-10-15

A modified generalized Morse (mGMSE) equation of state (EOS) is proposed that can incorporate the cohesive energy data correctly. It is compared with a four-parameter modified Rose (MR) EOS, which is proposed by following Rose's approach, and the Murnaghan (MNH) EOS. The MR, mGMSE and MNH EOSs are applied to five transition metals and then compared to the available experimental compression data. The results obtained show that for all pressure ranges, the mGMSE EOS fits experimental data most accurately. From a comparison of the variation in pressure and energy versus the compression ratio between MR and mGMSE EOSs, it is clear that the pressure and energy of the MR EOS oscillate both in the neighborhood of (V/V{sub 0}) {approx} 0.005 and in the range (V/V{sub 0})> 1. Generally speaking, the mGMSE EOS has many evident advantages over the other two EOSs, while the practical applications of the MR EOS are seriously limited because of physically incorrect oscillations.

Numerical method for the eigenvalue problem and the singular equation by using the multi-grid method and application to ordinary differential equation

International Nuclear Information System (INIS)

Kanki, Takashi; Uyama, Tadao; Tokuda, Shinji.

1995-07-01

In the numerical method to compute the matching data which are necessary for resistive MHD stability analyses, it is required to solve the eigenvalue problem and the associated singular equation. An iterative method is developed to solve the eigenvalue problem and the singular equation. In this method, the eigenvalue problem is replaced with an equivalent nonlinear equation and a singular equation is derived from Newton's method for the nonlinear equation. The multi-grid method (MGM), a high speed iterative method, can be applied to this method. The convergence of the eigenvalue and the eigenvector, and the CPU time in this method are investigated for a model equation. It is confirmed from the numerical results that this method is effective for solving the eigenvalue problem and the singular equation with numerical stability and high accuracy. It is shown by improving the MGM that the CPU time for this method is 50 times shorter than that of the direct method. (author)

Differential equation of exospheric lateral transport and its application to terrestrial hydrogen

Science.gov (United States)

Hodges, R. R., Jr.

1973-01-01

The differential equation description of exospheric lateral transport of Hodges and Johnson is reformulated to extend its utility to light gases. Accuracy of the revised equation is established by applying it to terrestrial hydrogen. The resulting global distributions for several static exobase models are shown to be essentially the same as those that have been computed by Quessette using an integral equation approach. The present theory is subsequently used to elucidate the effects of nonzero lateral flow, exobase rotation, and diurnal tidal winds on the hydrogen distribution. Finally it is shown that the differential equation of exospheric transport is analogous to a diffusion equation. Hence it is practical to consider exospheric transport as a continuation of thermospheric diffusion, a concept that alleviates the need for an artificial exobase dividing thermosphere and exosphere.

Geometric discretization of the multidimensional Dirac delta distribution - Application to the Poisson equation with singular source terms

Science.gov (United States)

Egan, Raphael; Gibou, Frédéric

2017-10-01

We present a discretization method for the multidimensional Dirac distribution. We show its applicability in the context of integration problems, and for discretizing Dirac-distributed source terms in Poisson equations with constant or variable diffusion coefficients. The discretization is cell-based and can thus be applied in a straightforward fashion to Quadtree/Octree grids. The method produces second-order accurate results for integration. Superlinear convergence is observed when it is used to model Dirac-distributed source terms in Poisson equations: the observed order of convergence is 2 or slightly smaller. The method is consistent with the discretization of Dirac delta distribution for codimension one surfaces presented in [1,2]. We present Quadtree/Octree construction procedures to preserve convergence and present various numerical examples, including multi-scale problems that are intractable with uniform grids.

An extended Jacobi elliptic function rational expansion method and its application to (2+1)-dimensional dispersive long wave equation

International Nuclear Information System (INIS)

Wang Qi; Chen Yong; Zhang Hongqing

2005-01-01

With the aid of computerized symbolic computation, a new elliptic function rational expansion method is presented by means of a new general ansatz, in which periodic solutions of nonlinear partial differential equations that can be expressed as a finite Laurent series of some of 12 Jacobi elliptic functions, is more powerful than exiting Jacobi elliptic function methods and is very powerful to uniformly construct more new exact periodic solutions in terms of rational formal Jacobi elliptic function solution of nonlinear partial differential equations. As an application of the method, we choose a (2+1)-dimensional dispersive long wave equation to illustrate the method. As a result, we can successfully obtain the solutions found by most existing Jacobi elliptic function methods and find other new and more general solutions at the same time. Of course, more shock wave solutions or solitary wave solutions can be gotten at their limit condition

A first course in differential equations

CERN Document Server

Logan, J David

2015-01-01

The third edition of this concise, popular textbook on elementary differential equations gives instructors an alternative to the many voluminous texts on the market. It presents a thorough treatment of the standard topics in an accessible, easy-to-read, format. The overarching perspective of the text conveys that differential equations are about applications. This book illuminates the mathematical theory in the text with a wide variety of applications that will appeal to students in physics, engineering, the biosciences, economics and mathematics. Instructors are likely to find that the first four or five chapters are suitable for a first course in the subject. This edition contains a healthy increase over earlier editions in the number of worked examples and exercises, particularly those routine in nature. Two appendices include a review with practice problems, and a MATLAB® supplement that gives basic codes and commands for solving differential equations. MATLAB® is not required; students are encouraged t...

Real solutions to equations from geometry

CERN Document Server

Sottile, Frank

2011-01-01

Understanding, finding, or even deciding on the existence of real solutions to a system of equations is a difficult problem with many applications outside of mathematics. While it is hopeless to expect much in general, we know a surprising amount about these questions for systems which possess additional structure often coming from geometry. This book focuses on equations from toric varieties and Grassmannians. Not only is much known about these, but such equations are common in applications. There are three main themes: upper bounds on the number of real solutions, lower bounds on the number of real solutions, and geometric problems that can have all solutions be real. The book begins with an overview, giving background on real solutions to univariate polynomials and the geometry of sparse polynomial systems. The first half of the book concludes with fewnomial upper bounds and with lower bounds to sparse polynomial systems. The second half of the book begins by sampling some geometric problems for which all ...

Evolution operator equation: Integration with algebraic and finite difference methods. Applications to physical problems in classical and quantum mechanics and quantum field theory

Energy Technology Data Exchange (ETDEWEB)

Dattoli, Giuseppe; Torre, Amalia [ENEA, Centro Ricerche Frascati, Rome (Italy). Dipt. Innovazione; Ottaviani, Pier Luigi [ENEA, Centro Ricerche Bologna (Italy); Vasquez, Luis [Madris, Univ. Complutense (Spain). Dept. de Matemateca Aplicado

1997-10-01

The finite-difference based integration method for evolution-line equations is discussed in detail and framed within the general context of the evolution operator picture. Exact analytical methods are described to solve evolution-like equations in a quite general physical context. The numerical technique based on the factorization formulae of exponential operator is then illustrated and applied to the evolution-operator in both classical and quantum framework. Finally, the general view to the finite differencing schemes is provided, displaying the wide range of applications from the classical Newton equation of motion to the quantum field theory.

Exact non-linear equations for cosmological perturbations

Energy Technology Data Exchange (ETDEWEB)

Gong, Jinn-Ouk [Asia Pacific Center for Theoretical Physics, Pohang 37673 (Korea, Republic of); Hwang, Jai-chan [Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu 41566 (Korea, Republic of); Noh, Hyerim [Korea Astronomy and Space Science Institute, Daejeon 34055 (Korea, Republic of); Wu, David Chan Lon; Yoo, Jaiyul, E-mail: jinn-ouk.gong@apctp.org, E-mail: jchan@knu.ac.kr, E-mail: hr@kasi.re.kr, E-mail: clwu@physik.uzh.ch, E-mail: jyoo@physik.uzh.ch [Center for Theoretical Astrophysics and Cosmology, Institute for Computational Science, Universität Zürich, CH-8057 Zürich (Switzerland)

2017-10-01

We present a complete set of exact and fully non-linear equations describing all three types of cosmological perturbations—scalar, vector and tensor perturbations. We derive the equations in a thoroughly gauge-ready manner, so that any spatial and temporal gauge conditions can be employed. The equations are completely general without any physical restriction except that we assume a flat homogeneous and isotropic universe as a background. We also comment briefly on the application of our formulation to the non-expanding Minkowski background.

Reparametrization invariance and the Schroedinger equation

International Nuclear Information System (INIS)

Tkach, V.I.; Pashnev, A.I.; Rosales, J.J.

1999-01-01

A time-dependent Schroedinger equation for systems invariant under the reparametrization of time is considered. We develop the two-stage procedure of construction such systems from a given initial ones, which are not invariant under the time reparametrization. One of the first-class constraints of the systems in such description becomes the time-dependent Schroedinger equation. The procedure is applicable in the supersymmetric theories as well. The n = 2 supersymmetric quantum mechanics is coupled to world-line supergravity, and the local supersymmetric action is constructed leading to the square root representation of the time-dependent Schroedinger equation

A Discrete-Time Recurrent Neural Network for Solving Rank-Deficient Matrix Equations With an Application to Output Regulation of Linear Systems.

Science.gov (United States)

Liu, Tao; Huang, Jie

2017-04-17

This paper presents a discrete-time recurrent neural network approach to solving systems of linear equations with two features. First, the system of linear equations may not have a unique solution. Second, the system matrix is not known precisely, but a sequence of matrices that converges to the unknown system matrix exponentially is known. The problem is motivated from solving the output regulation problem for linear systems. Thus, an application of our main result leads to an online solution to the output regulation problem for linear systems.

Development and application of a three-parameter RK-PR equation of state

DEFF Research Database (Denmark)

Cismondi, Martin; Mollerup, Jørgen

2005-01-01

In this work, we confirm the somehow previously expressed but not widespread idea that the limitations of cubic equations of state like Soave-Redlich-Kwong equation (SRK) or Peng-Robinson equation (PR) are a consequence of their two-parameter density dependence rather than of their empiric......-PR) equation offers the best performance among cubic three-parameter density functionalities. A simple temperature dependence was developed and a straightforward parameterization procedure established. This simple - and optimized from pure compound data - three-parameter equation of state (3P-EoS) will allow...... in a later stage, by systematic study and comparison to other types of 3P-EoS, to find out what the actual possibilities and limitations of cubic EoS are in the modelling of phase equilibria for asymmetric systems. (c) 2005 Elsevier B.V. All rights reserved....

Derivation of a new kinetic equation. Application to the determination of viscosity coefficients

International Nuclear Information System (INIS)

Frey, Jean-Jacques

1970-01-01

By introducing a new hypothesis concerning the closure in the B.B.G.K.Y. equation system, an approximate expression for f 12 is obtained. By inserting this expression in the first B.B.G.K.Y. equation, a new kinetic equation results. It is verified that this equation does in fact give the fluid mechanics equations, and new expressions for the shear and expansion viscosity coefficients are obtained. The numerical calculations which have been carried out show that very satisfactory agreement exists with experimental results. (author) [fr

Bright solitons in coupled defocusing NLS equation supported by coupling: Application to Bose-Einstein condensation

International Nuclear Information System (INIS)

Adhikari, Sadhan K.

2005-01-01

We demonstrate the formation of bright solitons in coupled self-defocusing nonlinear Schroedinger (NLS) equation supported by attractive coupling. As an application we use a time-dependent dynamical mean-field model to study the formation of stable bright solitons in two-component repulsive Bose-Einstein condensates (BECs) supported by interspecies attraction in a quasi one-dimensional geometry. When all interactions are repulsive, there cannot be bright solitons. However, bright solitons can be formed in two-component repulsive BECs for a sufficiently attractive interspecies interaction, which induces an attractive effective interaction among bosons of same type

An effective method for finding special solutions of nonlinear differential equations with variable coefficients

International Nuclear Information System (INIS)

Qin Maochang; Fan Guihong

2008-01-01

There are many interesting methods can be utilized to construct special solutions of nonlinear differential equations with constant coefficients. However, most of these methods are not applicable to nonlinear differential equations with variable coefficients. A new method is presented in this Letter, which can be used to find special solutions of nonlinear differential equations with variable coefficients. This method is based on seeking appropriate Bernoulli equation corresponding to the equation studied. Many well-known equations are chosen to illustrate the application of this method

Direct solution of the biharmonic equation on rectangular regions and the Poisson equation on irregular regions

International Nuclear Information System (INIS)

Buzbee, B.L.; Dorr, F.W.

1974-01-01

The discrete biharmonic equation on a rectangular region and the discrete Poisson equation on an irregular region can be treated as modifications to matrix problems with very special structure. It is shown how to use the direct method of matrix decomposition to formulate an effective numerical algorithm for these problems. For typical applications the operation count is O(N 3 ) for an N x N grid. Numerical comparisons with other techniques are included. (U.S.)

Invariant manifolds and applications for functional differential equations of mixed type

NARCIS (Netherlands)

Hupkes, Hermen Jan

2008-01-01

Differential equations posed on discrete lattices have by now become a popular modelling tool used in a wide variety of scientific disciplines. Such equations allow the inclusion of non-local interactions into models and lead to interesting dynamical and pattern-forming behaviour. Although many

New solitary wave solutions of (3 + 1)-dimensional nonlinear extended Zakharov-Kuznetsov and modified KdV-Zakharov-Kuznetsov equations and their applications

Science.gov (United States)

Lu, Dianchen; Seadawy, A. R.; Arshad, M.; Wang, Jun

In this paper, new exact solitary wave, soliton and elliptic function solutions are constructed in various forms of three dimensional nonlinear partial differential equations (PDEs) in mathematical physics by utilizing modified extended direct algebraic method. Soliton solutions in different forms such as bell and anti-bell periodic, dark soliton, bright soliton, bright and dark solitary wave in periodic form etc are obtained, which have large applications in different branches of physics and other areas of applied sciences. The obtained solutions are also presented graphically. Furthermore, many other nonlinear evolution equations arising in mathematical physics and engineering can also be solved by this powerful, reliable and capable method. The nonlinear three dimensional extended Zakharov-Kuznetsov dynamica equation and (3 + 1)-dimensional modified KdV-Zakharov-Kuznetsov equation are selected to show the reliability and effectiveness of the current method.

Decomposition of a hierarchy of nonlinear evolution equations

International Nuclear Information System (INIS)

Geng Xianguo

2003-01-01

The generalized Hamiltonian structures for a hierarchy of nonlinear evolution equations are established with the aid of the trace identity. Using the nonlinearization approach, the hierarchy of nonlinear evolution equations is decomposed into a class of new finite-dimensional Hamiltonian systems. The generating function of integrals and their generator are presented, based on which the finite-dimensional Hamiltonian systems are proved to be completely integrable in the Liouville sense. As an application, solutions for the hierarchy of nonlinear evolution equations are reduced to solving the compatible Hamiltonian systems of ordinary differential equations

Theory of a higher-order Sturm-Liouville equation

CERN Document Server

Kozlov, Vladimir

1997-01-01

This book develops a detailed theory of a generalized Sturm-Liouville Equation, which includes conditions of solvability, classes of uniqueness, positivity properties of solutions and Green's functions, asymptotic properties of solutions at infinity. Of independent interest, the higher-order Sturm-Liouville equation also proved to have important applications to differential equations with operator coefficients and elliptic boundary value problems for domains with non-smooth boundaries. The book addresses graduate students and researchers in ordinary and partial differential equations, and is accessible with a standard undergraduate course in real analysis.

Towards a Unified Quark-Hadron-Matter Equation of State for Applications in Astrophysics and Heavy-Ion Collisions

Directory of Open Access Journals (Sweden)

Niels-Uwe F. Bastian

2018-05-01

Full Text Available We outline an approach to a unified equation of state for quark-hadron matter on the basis of a Φ − derivable approach to the generalized Beth-Uhlenbeck equation of state for a cluster decomposition of thermodynamic quantities like the density. To this end we summarize the cluster virial expansion for nuclear matter and demonstrate the equivalence of the Green’s function approach and the Φ − derivable formulation. As an example, the formation and dissociation of deuterons in nuclear matter is discussed. We formulate the cluster Φ − derivable approach to quark-hadron matter which allows to take into account the specifics of chiral symmetry restoration and deconfinement in triggering the Mott-dissociation of hadrons. This approach unifies the description of a strongly coupled quark-gluon plasma with that of a medium-modified hadron resonance gas description which are contained as limiting cases. The developed formalism shall replace the common two-phase approach to the description of the deconfinement and chiral phase transition that requires a phase transition construction between separately developed equations of state for hadronic and quark matter phases. Applications to the phenomenology of heavy-ion collisions and astrophysics are outlined.

The HDAC inhibitor SAHA improves depressive-like behavior of CRTC1-deficient mice: possible relevance for treatment-resistant depression

KAUST Repository

Meylan, Elsa M.; Halfon, Olivier; Magistretti, Pierre J.; Cardinaux, Jean-René

2016-01-01

Major depression is a highly complex disabling psychiatric disorder affecting millions of people worldwide. Despite the availability of several classes of antidepressants, a substantial percentage of patients are unresponsive to these medications. A better understanding of the neurobiology of depression and the mechanisms underlying antidepressant response is thus critically needed. We previously reported that mice lacking CREB-regulated transcription coactivator 1 (CRTC1) exhibit a depressive-like phenotype and a blunted antidepressant response to the selective serotonin reuptake inhibitor fluoxetine. In this study, we similarly show that Crtc1‒/‒ mice are resistant to the antidepressant effect of chronic desipramine in a behavioral despair paradigm. Supporting the blunted response to this tricyclic antidepressant, we found that desipramine does not significantly increase the expression of Bdnf and Nr4a1-3 in the hippocampus and prefrontal cortex of Crtc1‒/‒ mice. Epigenetic regulation of neuroplasticity gene expression has been associated with depression and antidepressant response, and histone deacetylase (HDAC) inhibitors have been shown to have antidepressant-like properties. Here, we show that unlike conventional antidepressants, chronic systemic administration of the HDAC inhibitor SAHA partially rescues the depressive-like behavior of Crtc1‒/‒ mice. This behavioral effect is accompanied by an increased expression of Bdnf, but not Nr4a1-3, in the prefrontal cortex of these mice, suggesting that this epigenetic intervention restores the expression of a subset of genes by acting downstream of CRTC1. These findings suggest that CRTC1 alterations may be associated with treatment-resistant depression, and support the interesting possibility that targeting HDACs may be a useful therapeutic strategy in antidepressant development.

The HDAC inhibitor SAHA improves depressive-like behavior of CRTC1-deficient mice: possible relevance for treatment-resistant depression

KAUST Repository

Meylan, Elsa M.

2016-03-09

Major depression is a highly complex disabling psychiatric disorder affecting millions of people worldwide. Despite the availability of several classes of antidepressants, a substantial percentage of patients are unresponsive to these medications. A better understanding of the neurobiology of depression and the mechanisms underlying antidepressant response is thus critically needed. We previously reported that mice lacking CREB-regulated transcription coactivator 1 (CRTC1) exhibit a depressive-like phenotype and a blunted antidepressant response to the selective serotonin reuptake inhibitor fluoxetine. In this study, we similarly show that Crtc1‒/‒ mice are resistant to the antidepressant effect of chronic desipramine in a behavioral despair paradigm. Supporting the blunted response to this tricyclic antidepressant, we found that desipramine does not significantly increase the expression of Bdnf and Nr4a1-3 in the hippocampus and prefrontal cortex of Crtc1‒/‒ mice. Epigenetic regulation of neuroplasticity gene expression has been associated with depression and antidepressant response, and histone deacetylase (HDAC) inhibitors have been shown to have antidepressant-like properties. Here, we show that unlike conventional antidepressants, chronic systemic administration of the HDAC inhibitor SAHA partially rescues the depressive-like behavior of Crtc1‒/‒ mice. This behavioral effect is accompanied by an increased expression of Bdnf, but not Nr4a1-3, in the prefrontal cortex of these mice, suggesting that this epigenetic intervention restores the expression of a subset of genes by acting downstream of CRTC1. These findings suggest that CRTC1 alterations may be associated with treatment-resistant depression, and support the interesting possibility that targeting HDACs may be a useful therapeutic strategy in antidepressant development.

Functional stochastic differential equations: mathematical theory of nonlinear parabolic systems with applications in field theory and statistical mechanics

International Nuclear Information System (INIS)

Doering, C.R.

1985-01-01

Applications of nonlinear parabolic stochastic differential equations with additive colored noise in equilibrium and nonequilibrium statistical mechanics and quantum field theory are developed in detail, providing a new unified mathematical approach to many problems. The existence and uniqueness of solutions to these equations is established, and some of the properties of the solutions are investigated. In particular, asymptotic expansions for the correlation functions of the solutions are introduced and compared to rigorous nonperturbative bounds on the moments. It is found that the perturbative analysis is in qualitative disagreement with the exact result in models corresponding to cut-off self-interacting nonperturbatively renormalizable scalar quantum field theories. For these theories the nonlinearities cannot be considered as perturbations of the linearized theory

Elliptic equation for random walks. Application to transport in microporous media

DEFF Research Database (Denmark)

Shapiro, Alexander

2007-01-01

We consider a process of random walks with arbitrary residence time distribution. We show that in many cases this process may not be described by the classical (Fick) parabolic diffusion equation, but an elliptic equation. An additional term proportional to the second time derivative takes into a...

Combined Sinh-Cosh-Gordon equation: Symmetry reductions, exact ...

African Journals Online (AJOL)

Combined Sinh-Cosh-Gordon equation: Symmetry reductions, exact solutions and conservation laws. ... In this paper we study the combined sinh-cosh-Gordon equation, which arises in mathematical physics and has a wide range of scientific applications that range from chemical reactions to water surface gravity waves.

COMPARISON THEOREM OF BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS

Institute of Scientific and Technical Information of China (English)

无

2010-01-01

This paper is devoted to deriving a comparison theorem of solutions to backward doubly stochastic differential equations driven by Brownian motion and backward It-Kunita integral. By the application of this theorem, we give an existence result of the solutions to these equations with continuous coefficients.

General solution of Bateman equations for nuclear transmutations

International Nuclear Information System (INIS)

Cetnar, Jerzy

2006-01-01

The paper concerns the linear chain method of solving Bateman equations for nuclear transmutation in derivation of the general solution for linear chain with repeated transitions and thus elimination of existing numerical problems. In addition, applications of derived equations for transmutation trajectory analysis method is presented

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

KAUST Repository

Toro, Eleuterio F.

2015-09-30

Here we extend the flux vector splitting approach recently proposed in (E F Toro and M E Vázquez-Cendón. Flux splitting schemes for the Euler equations. Computers and Fluids. Vol. 70, Pages 1-12, 2012). The scheme was originally presented for the 1D Euler equations for ideal gases and its extension presented in this paper is threefold: (i) we solve the three-dimensional Euler equations on general meshes; (ii) we use a general equation of state; and (iii) we achieve high order of accuracy in both space and time through application of the semi-discrete ADER methodology on general meshes. The resulting methods are systematically assessed for accuracy, robustness and efficiency on a carefully selected suite of test problems. Formal high accuracy is assessed through convergence rates studies for schemes of up to 4th order of accuracy in both space and time on unstructured meshes.

Stability theory for dynamic equations on time scales

CERN Document Server

Martynyuk, Anatoly A

2016-01-01

This monograph is a first in the world to present three approaches for stability analysis of solutions of dynamic equations. The first approach is based on the application of dynamic integral inequalities and the fundamental matrix of solutions of linear approximation of dynamic equations. The second is based on the generalization of the direct Lyapunovs method for equations on time scales, using scalar, vector and matrix-valued auxiliary functions. The third approach is the application of auxiliary functions (scalar, vector, or matrix-valued ones) in combination with differential dynamic inequalities. This is an alternative comparison method, developed for time continuous and time discrete systems. In recent decades, automatic control theory in the study of air- and spacecraft dynamics and in other areas of modern applied mathematics has encountered problems in the analysis of the behavior of solutions of time continuous-discrete linear and/or nonlinear equations of perturbed motion. In the book “Men of Ma...

An application of transverse momentum dependent evolution equations in QCD

International Nuclear Information System (INIS)

Ceccopieri, Federico A.; Trentadue, Luca

2008-01-01

The properties and behaviour of the solutions of the recently obtained k t -dependent QCD evolution equations are investigated. When used to reproduce transverse momentum spectra of hadrons in Semi-Inclusive DIS, an encouraging agreement with data is found. The present analysis also supports at the phenomenological level the factorization properties of the Semi-Inclusive DIS cross-sections in terms of k t -dependent distributions. Further improvements and possible developments of the proposed evolution equations are envisaged

Numerical solution of the Maxwell-Vlasov equations in the periodic regime. Application to the study of isotope separation by ion cyclotron resonance; Resolution numerique des equations de Maxwell-Vlasov en regime periodique. Application a l'etude de la separation isotopique par resonance cyclotron ionique

Energy Technology Data Exchange (ETDEWEB)

Omnes, P

1999-01-25

This work is dedicated to the study of the behaviour of a magnetic confined plasma that is excited by a purely sinusoidal electric current delivered by an antenna. The response of the electrons to the electromagnetic field is considered as linear,whereas the ions of the plasma are represented by a non-relativistic Vlasov equation. In order to avoid transients, the coupled Maxwell-Vlasov equations are solved in a periodic mode and in a bounded domain. An equivalent electric conductivity tensor has been defined, this tensor is a linear operator that links the electric current generated by the movement of the particles to the electromagnetic field. Theoretical considerations can assure the existence and uniqueness of a periodical solution to Vlasov equations and of a solution to Maxwell equations in harmonic mode. The system of equations is periodical and has been solved by using an iterative method. The application of this method to the simulation of a isotopic separation device based on ionic cyclotron resonance has shown that the convergence is reached in a few iterations and that the solution is valid. Furthermore a method based on a finite-volume formulation of Maxwell equations in the time domain is presented. 2 new variables are defined in order to better take into account the Gauss' law and the conservation of the magnetic flux, the new system is still hyperbolic. The parallelization of the process has been successfully realized. (A.C.)

Partial differential equations an introduction

CERN Document Server

Colton, David

2004-01-01

Intended for a college senior or first-year graduate-level course in partial differential equations, this text offers students in mathematics, engineering, and the applied sciences a solid foundation for advanced studies in mathematics. Classical topics presented in a modern context include coverage of integral equations and basic scattering theory. This complete and accessible treatment includes a variety of examples of inverse problems arising from improperly posed applications. Exercises at the ends of chapters, many with answers, offer a clear progression in developing an understanding of

The Positive Properties of Green’s Function for Fractional Differential Equations and Its Applications

Directory of Open Access Journals (Sweden)

Fuquan Jiang

2013-01-01

Full Text Available We consider the properties of Green’s function for the nonlinear fractional differential equation boundary value problem: D0+αu(t+f(t,u(t+e(t=0,0applications of Green’s function, we give some multiple positive solutions for singular boundary value problems by means of Schauder fixed-point theorem.

Exact harmonic solutions to Guyer-Krumhansl-type equation and application to heat transport in thin films

Science.gov (United States)

Zhukovsky, K.; Oskolkov, D.

2018-03-01

A system of hyperbolic-type inhomogeneous differential equations (DE) is considered for non-Fourier heat transfer in thin films. Exact harmonic solutions to Guyer-Krumhansl-type heat equation and to the system of inhomogeneous DE are obtained in Cauchy- and Dirichlet-type conditions. The contribution of the ballistic-type heat transport, of the Cattaneo heat waves and of the Fourier heat diffusion is discussed and compared with each other in various conditions. The application of the study to the ballistic heat transport in thin films is performed. Rapid evolution of the ballistic quasi-temperature component in low-dimensional systems is elucidated and compared with slow evolution of its diffusive counterpart. The effect of the ballistic quasi-temperature component on the evolution of the complete quasi-temperature is explored. In this context, the influence of the Knudsen number and of Cauchy- and Dirichlet-type conditions on the evolution of the temperature distribution is explored. The comparative analysis of the obtained solutions is performed.

Finite elements for partial differential equations: An introductory survey

International Nuclear Information System (INIS)

Succi, S.

1988-03-01

After presentation of the basic ideas behind the theory of the Finite Element Method, the application of the method to three equations of particular interest in Physics and Engineering is discussed in some detail, namely, a one-dimensional Sturm-Liouville problem, a two-dimensional linear Fokker-Planck equation and a two-dimensional nonlinear Navier-Stokes equation. 6 refs, 8 figs

Duffin-Kemmer-Petiau equation under a scalar Coulomb interaction

International Nuclear Information System (INIS)

Hassanabadi, H.; Yazarloo, B. H.; Zarrinkamar, S.; Rajabi, A. A.

2011-01-01

Approximate analytical solutions of a Duffin-Kemmer-Petiau (DKP) equation are obtained via an elegant ansatz after successive transformations. Apart from the wide application of the DKP equation in both cosmology and theoretical nuclear physics as well as the physical significance of the Coulomb interaction, this is particularly important as we have provided a solution to the corresponding Heun equation.

Development of a magnetohydrodynamic code for axisymmetric, high-β plasmas with complex magnetic fields

International Nuclear Information System (INIS)

Cook, G.O. Jr.

1982-12-01

The Topolotron is an axisymmetric, toroidal magnetic fusion concept in which two-dimensional effects are important, as well as all three magnetic field components. The particular MHD model employed is basically the one-fluid, two-temperature model using classical Braginskii transport with viscous effects ignored. The model is augmented by Saha-Boltzmann dissociation and partial ionization physics, a simple radiation loss mechanism, and an additional resistivity due to electron-neutral collisions. While retaining all velocity and magnetic field components, the assumption of axisymmetry is made, and the resulting equations are expanded in cylindrical coordinates. The major approximation technique is then applied: spline collocation, which reduces these equations to a set of ordinary differential equations

Constitutive equations for two-phase flows

International Nuclear Information System (INIS)

Boure, J.A.

1974-12-01

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

Applications of Boltzmann Langevin equation to nuclear collisions

International Nuclear Information System (INIS)

Suraud, E.; Belkacem, M.; Stryjewski, J.; Ayik, S.

1991-01-01

An approximate method for obtaining numerical solutions of the Boltzmann-Langevin equation is proposed. The method is applied to calculate the time evolution of the mean value and dispersion of the quadrupole and octupole moments of the momentum distribution in nucleus-nucleus collisions, and some consequences are discussed

Newton's laws of motion in the form of a Riccati equation

International Nuclear Information System (INIS)

Nowakowski, Marek; Rosu, Haret C.

2002-01-01

We discuss two applications of a Riccati equation to Newton's laws of motion. The first one is the motion of a particle under the influence of a power law central potential V(r)=kr ε . For zero total energy we show that the equation of motion can be cast in the Riccati form. We briefly show here an analogy to barotropic Friedmann-Robertson-Lemaitre cosmology where the expansion of the universe can be also shown to obey a Riccati equation. A second application in classical mechanics, where again the Riccati equation appears naturally, are problems involving quadratic friction. We use methods reminiscent to nonrelativistic supersymmetry to generalize and solve such problems

Newton's laws of motion in the form of a Riccati equation.

Science.gov (United States)

Nowakowski, Marek; Rosu, Haret C

2002-04-01

We discuss two applications of a Riccati equation to Newton's laws of motion. The first one is the motion of a particle under the influence of a power law central potential V(r)=kr(epsilon). For zero total energy we show that the equation of motion can be cast in the Riccati form. We briefly show here an analogy to barotropic Friedmann-Robertson-Lemaitre cosmology where the expansion of the universe can be also shown to obey a Riccati equation. A second application in classical mechanics, where again the Riccati equation appears naturally, are problems involving quadratic friction. We use methods reminiscent to nonrelativistic supersymmetry to generalize and solve such problems.

Application of Littlewood-Paley decomposition to the regularity of Boltzmann type kinetic equations; Application de la decomposition de Littlewood-Paley a la regularite pour des equations cinetiques de type Boltzmann

Energy Technology Data Exchange (ETDEWEB)

EL Safadi, M

2007-03-15

We study the regularity of kinetic equations of Boltzmann type.We use essentially Littlewood-Paley method from harmonic analysis, consisting mainly in working with dyadics annulus. We shall mainly concern with the homogeneous case, where the solution f(t,x,v) depends only on the time t and on the velocities v, while working with realistic and singular cross-sections (non cutoff). In the first part, we study the particular case of Maxwellian molecules. Under this hypothesis, the structure of the Boltzmann operator and his Fourier transform write in a simple form. We show a global C{sup {infinity}} regularity. Then, we deal with the case of general cross-sections with 'hard potential'. We are interested in the Landau equation which is limit equation to the Boltzmann equation, taking in account grazing collisions. We prove that any weak solution belongs to Schwartz space S. We demonstrate also a similar regularity for the case of Boltzmann equation. Let us note that our method applies directly for all dimensions, and proofs are often simpler compared to other previous ones. Finally, we finish with Boltzmann-Dirac equation. In particular, we adapt the result of regularity obtained in Alexandre, Desvillettes, Wennberg and Villani work, using the dissipation rate connected with Boltzmann-Dirac equation. (author)

NodHex3D: An application for solving the neutron diffusion equations in hexagonal-Z geometry and steady state

International Nuclear Information System (INIS)

Esquivel E, J.; Del Valle G, E.

2014-10-01

The system called NodHex3D is a graphical application that allows the solution of the neutron diffusion equation. The system considers fuel assemblies of hexagonal cross section. This application arose from the idea of expanding the development of neutron own codes, used primarily for academic purposes. The advantage associated with the use of NodHex3D, is that the kernel configuration and fuel batches is dynamically without affecting directly the base source code of the solution of the neutron diffusion equation. In addition to the kernel configuration to use, specify the values for the cross sections for each batch of fuel used, these values are: diffusion coefficient, removal cross section, absorption cross section, fission cross section and dispersion cross section. Important also, considering that the system is able to perform calculations for various energy groups. As evidence of the operation of NodHex3D, was proposed to model three-dimensional core of a nuclear reactor VVER-1000, based on the reference problem AER-FCM-101. The configuration of the reactor core consists of fuel assemblies (25 batches), composed of seven distinct materials, one of which reflector material, vacuum boundary conditions on the surface delimiting the reactor core. The diffusion equation for two energy groups solves, obtaining the value of the effective neutron multiplication factor. The obtained results are compared to those documented in the reference problem and by 3-DNT codes. (Author)

System of adjoint P1 equations for neutron moderation

International Nuclear Information System (INIS)

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

2000-01-01

In some applications of perturbation theory, it is necessary know the adjoint neutron flux, which is obtained by the solution of adjoint neutron diffusion equation. However, the multigroup constants used for this are weighted in only the direct neutron flux, from the solution of direct P1 equations. In this work, this procedure is questioned and the adjoint P1 equations are derived by the neutron transport equation, the reversion operators rules and analogies between direct and adjoint parameters. (author)

Modified Darboux transformations with foreign auxiliary equations

International Nuclear Information System (INIS)

Schulze-Halberg, Axel

2011-01-01

We construct a new type of first-order Darboux transformations for the stationary Schroedinger equation. In contrast to the conventional case, our Darboux transformations support arbitrary (foreign) auxiliary equations. We show that among other applications, our formalism can be used to systematically construct Darboux transformations for Schroedinger equations with energy-dependent potentials, including a recent result (Lin et al., 2007) as a special case. -- Highlights: → We generalize the Darboux transformation for the Schroedinger equation. → By admitting arbitrary auxiliary functions, we provide a new tool for generating solutions. → As a special case we recover a recent result on energy-dependent potentials. → We extend the latter result to very general energy-dependence.

Un solveur HLLT pour les equations de Saint-Venant et traitement ...

African Journals Online (AJOL)