Changes in intensity of precipitation extremes in Romania on very hight temporal scale and implications on the validity of the Clausius-Clapeyron relation

Science.gov (United States)

Busuioc, Aristita; Baciu, Madalina; Breza, Traian; Dumitrescu, Alexandru; Stoica, Cerasela; Baghina, Nina

2016-04-01

Many observational, theoretical and based on climate model simulation studies suggested that warmer climates lead to more intense precipitation events, even when the total annual precipitation is slightly reduced. In this way, it was suggested that extreme precipitation events may increase at Clausius-Clapeyron (CC) rate under global warming and constraint of constant relative humidity. However, recent studies show that the relationship between extreme rainfall intensity and atmospheric temperature is much more complex than would be suggested by the CC relationship and is mainly dependent on precipitation temporal resolution, region, storm type and whether the analysis is conducted on storm events rather than fixed data. The present study presents the dependence between the very hight temporal scale extreme rainfall intensity and daily temperatures, with respect to the verification of the CC relation. To solve this objective, the analysis is conducted on rainfall event rather than fixed interval using the rainfall data based on graphic records including intensities (mm/min.) calculated over each interval with permanent intensity per minute. The annual interval with available a such data (April to October) is considered at 5 stations over the interval 1950-2007. For Bucuresti-Filaret station the analysis is extended over the longer interval (1898-2007). For each rainfall event, the maximum intensity (mm/min.) is retained and these time series are considered for the further analysis (abbreviated in the following as IMAX). The IMAX data were divided based on the daily mean temperature into bins 2oC - wide. The bins with less than 100 values were excluded. The 90th, 99th and 99.9th percentiles were computed from the binned data using the empirical distribution and their variability has been compared to the CC scaling (e.g. exponential relation given by a 7% increase per temperature degree rise). The results show a dependence close to double the CC relation for

Determinação da entalpia de vaporização de líquidos pelo método do isoteniscópio de Smith e Menzies Determination of the enthalpy of vaporization of liquid compounds by the Smith Menzies (isoteniscope method

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Adriana Passarella Gerola

2010-01-01

Full Text Available This article proposes an experimental procedure to determine the enthalpy (and entropy of vaporization of organic liquid compounds, by the Smith-Menzies (isoteniscope method. The values of vapor pressure at different temperatures were obtained and ΔvH (and ΔvS were graphically determined, using the Clausius-Clapeyron equation. The results for diethyl-ether, propanone, ethanol and n-hexane are in very good agreement with those from literature. A historical and thermodynamic discussion on equations that correlates vapor pressures and temperature precedes the experimental proposition.

Dissolution rates and solubility of some metals in liquid gallium and aluminum

International Nuclear Information System (INIS)

Yatsenko, S P; Sabirzyanov, N A; Yatsenko, A S

2008-01-01

The effect of liquid gallium and aluminum on some hard metals leading to dissolution and formation of intermetallic compounds (IMC) under static conditions and rotation of a specimen is studied. The solubility parameters from the Clapeyron-Clausius equation were considered to estimate the stability of still not studied metals. The presented experimental data on solubility and corrosion in a wide temperature range allow to calculate a number of parameters useful in manufacturing and application of master-alloys

Thermochemical study of the monobromonitrobenzene isomers

International Nuclear Information System (INIS)

Ribeiro da Silva, Manuel A.V.; Lobo Ferreira, Ana I.M.C.; Santos, Ana Filipa L.O.M.; Rocha, Ines M.

2010-01-01

The standard (p o = 0.1 MPa) molar enthalpies of formation, of the 2-, 3-, and 4-monobromonitrobenzene isomers, in the crystalline phase, at T = 298.15 K, were derived from the standard massic energies of combustion, in oxygen, at T = 298.15 K, measured by rotating bomb combustion calorimetry. From the temperature dependence of the vapour pressures of these compounds, measured by the Knudsen effusion technique, their standard molar enthalpies of sublimation, at T = 298.15 K, were derived using the Clausius-Clapeyron equation.

Evolution of the Second Law of Thermodynamics

Science.gov (United States)

Raman, V. V.

1970-01-01

Presents the history surrounding the evolution of the second law of thermodynamics. Discusses Sadi Carnot's contributions, but also refers to those by Clapeyron, Thomson, Joule, Clausius, and Boltzman among others. (RR)

Effect of temperature and water activity on heat transfer in parsley leaves in the  range of temperatures 10–30 °C

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Jiří Štencl

2007-01-01

Full Text Available The equilibrium moisture contents of parsley leaves were measured by the gravimetric dynamic method with continuous recording of changes in sample weight. Consequently water activity values were determined. Henderson equation was found to be a good model both for moisture adsorption and desorption. Isosteric heat of sorption was defined and determined in the temperature range of 10–30 °C. Clausius-Clapeyron equation was used to calculate the isosteric heat of sorption since no dependence on temperature in the analysed range was observed. The isosteric heats of sorption (qnst were indicated graphic in the form qnst versus moisture content. Values for isosteric heat of sorption ranged from 54.41 to 46.85 kJ/mol.

Inhomogeneous Monte Carlo simulation of the vapor-liquid equilibrium of benzene between 300 K and 530 K

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J.Janeček

2007-09-01

Full Text Available The inhomogeneous Monte Carlo technique is used in studying the vapor-liquid interface of benzene in a broad range of temperatures using the TraPPE potential field. The obtained values of the VLE parameters are in good agreement with the experimental values as well as with the results from GEMC simulations. In contrast to the GEMC, within one simulation box the inhomogeneous MC technique also yields information on the structural properties of the interphase between the two phases. The values of the vaporization enthalpy and the vapor pressure very well satisfy the Clausius-Clapeyron equation.

A Revision of Clausius Work on the Second Law. 1. On the Lack of Inner Consistency of Clausius Analysis Leading to the Law of Increasing Entropy

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José C. Iñiguez

1999-10-01

Full Text Available Abstract: This paper, the first in a series of four, will expose the lack of inner consistency of the analysis through which Clausius re-expressed the second law of thermodynamics: "Heat cannot, of itself, pass from a colder to a hotter body", as the law of increasing entropy: "The entropy of the universe tends to a maximum". In the two following papers the flaw in Clausius analysis producing the said lack of consistency will be located, corrected and some of its consequences, discussed. Among them the one stating that the identification of the two above written statements of the second law is valid only under certain circumstances. In the fourth and final

The spatial extent of rainfall events and its relation to precipitation scaling

NARCIS (Netherlands)

Lochbihler, K.U.; Lenderink, Geert; Siebesma, A.P.

2017-01-01

Observations show that subdaily precipitation extremes increase with dew point temperature at a rate exceeding the Clausius-Clapeyron (CC) relation. The understanding of this so-called super CC scaling is still incomplete, and observations of convective cell properties could provide important

Thermal expansion and volumetric changes during indium phosphide melting

International Nuclear Information System (INIS)

Glazov, V.M.; Davletov, K.; Nashel'skij, A.Ya.; Mamedov, M.M.

1977-01-01

The results of the measurements of a thermal expansion were summed up at various temperatures as a diagram in coordinates (Δ 1/1) approximately F(t). It was shown that an appreciable deviation of the relationship (Δ1/1) approximately f(t) from the linear law corresponded to a temperature of 500-550 deg C. It was noted that the said deviation was related to an appreciable thermal decomposition of indium phosphide as temperature increased. The strength of the inter-atomic bond of indium phosphide was calculated. Investigated were the volumetric changes of indium phosphide on melting. The resultant data were analyzed with the aid of the Clausius-Clapeyron equation

Gas sorption properties of microporous metal organic frameworks

International Nuclear Information System (INIS)

Lee, JeongYong; Li Jing; Jagiello, Jacek

2005-01-01

A low-temperature gas sorption study has been carried out on four three-dimensional microporous metal organic framework (MMOF) structures and two two-dimensional layered structures. The pore characteristics are analyzed based on the argon adsorption-desorption isotherms at 87 K. The results from hydrogen sorption experiments conducted at 77 and 87 K show that all MMOFs have a relatively high hydrogen uptake, with adsorbed hydrogen densities falling in the range of liquid hydrogen. Isosteric heats of hydrogen adsorption data calculated based on the Clausius-Clapeyron equation are consistent with these observations, indicating strong sorbent-sorbate interactions. - Graphical abstract: Hydrogen adsorption isotherms measured at 77 and 87 K

Methane Hydrate Formation and Dissociation in the Presence of Silica Sand and Bentonite Clay

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Kumar Saw V.

2015-11-01

Full Text Available The formation and dissociation of methane hydrates in a porous media containing silica sand of different sizes and bentonite clay were studied in the presence of synthetic seawater with 3.55 wt% salinity. The phase equilibrium of methane hydrate under different experimental conditions was investigated. The effects of the particle size of silica sand as well as a mixture of bentonite clay and silica sand on methane hydrate formation and its dissociation were studied. The kinetics of hydrate formation was studied under different subcooling conditions to observe its effects on the induction time of hydrate formation. The amount of methane gas encapsulated in hydrate was computed using a real gas equation. The Clausius-Clapeyron equation is used to estimate the enthalpy of hydrate dissociation with measured phase equilibrium data.

Low temperature measurement of the vapor pressures of planetary molecules

Science.gov (United States)

Kraus, George F.

1989-01-01

Interpretation of planetary observations and proper modeling of planetary atmospheres are critically upon accurate laboratory data for the chemical and physical properties of the constitutes of the atmospheres. It is important that these data are taken over the appropriate range of parameters such as temperature, pressure, and composition. Availability of accurate, laboratory data for vapor pressures and equilibrium constants of condensed species at low temperatures is essential for photochemical and cloud models of the atmospheres of the outer planets. In the absence of such data, modelers have no choice but to assume values based on an educated guess. In those cases where higher temperature data are available, a standard procedure is to extrapolate these points to the lower temperatures using the Clausius-Clapeyron equation. Last summer the vapor pressures of acetylene (C2H2) hydrogen cyanide (HCN), and cyanoacetylene (HC3N) was measured using two different methods. At the higher temperatures 1 torr and 10 torr capacitance manometers were used. To measure very low pressures, a technique was used which is based on the infrared absorption of thin film (TFIR). This summer the vapor pressure of acetylene was measured the TFIR method. The vapor pressure of hydrogen sulfide (H2S) was measured using capacitance manometers. Results for H2O agree with literature data over the common range of temperature. At the lower temperatures the data lie slightly below the values predicted by extrapolation of the Clausius-Clapeyron equation. Thin film infrared (TFIR) data for acetylene lie significantly below the values predicted by extrapolation. It is hoped to bridge the gap between the low end of the CM data and the upper end of the TFIR data in the future using a new spinning rotor gauge.

Scaling Potential Evapotranspiration with Greenhouse Warming (Invited)

Science.gov (United States)

Scheff, J.; Frierson, D. M.

2013-12-01

Potential evapotranspiration (PET) is a supply-independent measure of the evaporative demand of a terrestrial climate, of basic importance in climatology, hydrology, and agriculture. Future increases in PET from greenhouse warming are often cited as key drivers of global trends toward drought and aridity. The present work computes recent and business-as-usual-future Penman-Monteith (i.e. physically-based) PET fields at 3-hourly resolution in 14 modern global climate models. The %-change in local annual-mean PET over the upcoming century is almost always positive, modally low double-digit in magnitude, usually increasing with latitude, yet quite divergent between models. These patterns are understood as follows. In every model, the global field of PET %-change is found to be dominated by the direct, positive effects of constant-relative-humidity warming (via increasing vapor pressure deficit and increasing Clausius-Clapeyron slope.) This direct-warming term very accurately scales as the PET-weighted (warm-season daytime) local warming, times 5-6% per degree (related to the Clausius-Clapeyron equation), times an analytic factor ranging from about 0.25 in warm climates to 0.75 in cold climates, plus a small correction. With warming of several degrees, this product is of low double-digit magnitude, and the strong temperature dependence gives the latitude dependence. Similarly, the inter-model spread in the amount of warming gives most of the spread in this term. Additional spread in the total change comes from strong disagreement on radiation, relative-humidity, and windspeed changes, which make smaller yet substantial contributions to the full PET %-change fields.

Anomalous temperature dependence of the superelastic behavior of Ti-Nb-Mo alloys

International Nuclear Information System (INIS)

Al-Zain, Y.; Kim, H.Y.; Koyano, T.; Hosoda, H.; Nam, T.H.; Miyazaki, S.

2011-01-01

The effect of test temperature on the superelasticity of Ti-27Nb and various Ti-Nb-Mo alloys is investigated. A deviation in the stress at which martensitic transformation starts (σ β-α'' ) from the behavior expected from the Clausius-Clapeyron relationship is confirmed in all alloys. The degree of deviation is found to be in inverse proportion to the electron-to-atom ratio. However, no deviation is observed in the stress at which the reverse transformation finishes (σ α''-β ). All alloys exhibit anomalous electrical resistivity during cooling. X-ray diffraction (XRD) and transmission electron microscopy investigations show that the volume fraction of the athermal ω (ω ath ) phase increases with a decrease in temperature. An in situ XRD experiment obtained during a loading-unloading cycle shows that the β and ω ath phases transform into the α'' phase during loading. The annihilation of the ω ath phase within the α'' phase allows σ α''-β to obey the Clausius-Clapeyron relationship. As a result, a large hysteresis loop is produced.

A simple experimental arrangement for measuring the vapour pressures and sublimation enthalpies by the Knudsen effusion method: Application to DNA and RNA bases

International Nuclear Information System (INIS)

Barros, A.L.F. de; Medina, A.; Zappa, F.; Pereira, J.M.; Bessa, E.; Martins, M.H.P.; Coelho, L.F.S.; Wolff, W.; Castro Faria, N.V. de

2006-01-01

We measured the vapour pressure of several DNA and RNA bases-uracil, adenine, guanine, thymine and cytosine-in the 300-450 K range. In each case the sample mass loss rate was measured as function of temperature with a simple setup consisting of a commercial film deposition system and a homemade oven. Afterwards vapour pressure values were extracted from these data using the Knudsen effusion method. Sublimation enthalpy values, obtained from vapour pressure data by applying the Clausius-Clapeyron equation, are in very good agreement with literature values. The results suggest that crystal-based film thickness monitors may be useful in on-line cross-section measurements, monitoring the gas target thickness. They also show the viability of using this oven for producing a biomolecular gas target

Some Consequences of an Analysis of the Kelvin-Clausius Entropy Formulation Based on Traditional Axiomatics

Science.gov (United States)

Jesudason, Christopher G.

2003-09-01

Recently, there have appeared interesting correctives or challenges [Entropy 1999, 1, 111-147] to the Second law formulations, especially in the interpretation of the Clausius equivalent transformations, closely related in area to extensions of the Clausius principle to irreversible processes [Chem. Phys. Lett. 1988, 143(1), 65-70]. Since the traditional formulations are central to science, a brief analysis of some of these newer theories along traditional lines is attempted, based on well-attested axioms which have formed the basis of equilibrium thermodynamics. It is deduced that the Clausius analysis leading to the law of increasing entropy does not follow from the given axioms but it can be proved that for irreversible transitions, the total entropy change of the system and thermal reservoirs (the "Universe") is not negative, even for the case when the reservoirs are not at the same temperature as the system during heat transfer. On the basis of two new simple theorems and three corollaries derived for the correlation between irreversible and reversible pathways and the traditional axiomatics, it is shown that a sequence of reversible states can never be used to describe a corresponding sequence of irreversible states for at least closed systems, thereby restricting the principle of local equilibrium. It is further shown that some of the newer irreversible entropy forms given exhibit some paradoxical properties relative to the standard axiomatics. It is deduced that any reconciliation between the traditional approach and novel theories lie in creating a well defined set of axioms to which all theoretical developments should attempt to be based on unless proven not be useful, in which case there should be consensus in removing such axioms from theory. Clausius' theory of equivalent transformations do not contradict the traditional understanding of heat- work efficiency. It is concluded that the intuitively derived assumptions over the last two centuries seem to

Communication: Glass transition and melting lines of an ionic liquid

Science.gov (United States)

Lima, Thamires A.; Faria, Luiz F. O.; Paschoal, Vitor H.; Ribeiro, Mauro C. C.

2018-05-01

The phase diagram of the ionic liquid 1-butyl-1-methylpyrrolidinium bis(trifluoromethanesufonyl)imide, [Pyrr1,4][NTf2], was explored by synchroton X-ray diffraction and Raman scattering measurements as a function of temperature and pressure. Glass transition Tg(p) and melting Tm(p) temperatures were obtained from atmospheric pressure up to ca. 2.0 GPa. We found that both the Tg(p) and Tm(p) curves follow essentially the same pressure dependence. The similarity of pressure coefficients, dTg/dp ≈ dTm/dp, is explained within the non-equilibrium thermodynamics approach for the glass transition by assuming that one of the Ehrenfest equations is appropriated for Tg(p), whereas Tm(p) follows the Clausius-Clapeyron equation valid for the first-order transitions. The results highlight that ionic liquids are excellent model systems to address fundamental questions related to the glass transition.

Two-phase regime in the magnetic field-temperature phase diagram of a type-II superconductor

International Nuclear Information System (INIS)

Adams, L.L.A.; Halterman, Klaus; Valls, Oriol T.; Goldman, A.M.

2004-01-01

The magnetic field and temperature dependencies of the magnetic moments of superconducting crystals of V 3 Si have been studied. In a constant magnetic field and at temperatures somewhat below the superconducting transition temperature, the moments are hysteretic in temperature. However, the magnetic moment-magnetic field isotherms are reversible and exhibit features that formally resemble the pressure-volume isotherms of the liquid-gas transition. This suggests the existence of a first-order phase transition, a two-phase regime, and a critical point in the superconducting phase diagram. The two phases are disordered vortex configurations with the same magnetization, but with different vortex densities. The entropy change, determined from the data using the Clausius-Clapeyron equation, is consistent with estimates based on the difference in the vortex densities of the two phases

Two-phase regime in the magnetic field-temperature phase diagram of a type-II superconductor

Energy Technology Data Exchange (ETDEWEB)

Adams, L.L.A.; Halterman, Klaus; Valls, Oriol T.; Goldman, A.M

2004-01-01

The magnetic field and temperature dependencies of the magnetic moments of superconducting crystals of V{sub 3}Si have been studied. In a constant magnetic field and at temperatures somewhat below the superconducting transition temperature, the moments are hysteretic in temperature. However, the magnetic moment-magnetic field isotherms are reversible and exhibit features that formally resemble the pressure-volume isotherms of the liquid-gas transition. This suggests the existence of a first-order phase transition, a two-phase regime, and a critical point in the superconducting phase diagram. The two phases are disordered vortex configurations with the same magnetization, but with different vortex densities. The entropy change, determined from the data using the Clausius-Clapeyron equation, is consistent with estimates based on the difference in the vortex densities of the two phases.

Evaluation of melting point of UO2 by molecular dynamics simulation

International Nuclear Information System (INIS)

Arima, Tatsumi; Idemitsu, Kazuya; Inagaki, Yaohiro; Tsujita, Yuichi; Kinoshita, Motoyasu; Yakub, Eugene

2009-01-01

The melting point of UO 2 has been evaluated by molecular dynamics simulation (MD) in terms of interatomic potential, pressure and Schottky defect concentration. The Born-Mayer-Huggins potentials with or without a Morse potential were explored in the present study. Two-phase simulation whose supercell at the initial state consisted of solid and liquid phases gave the melting point comparable to the experimental data using the potential proposed by Yakub. The heat of fusion was determined by the difference in enthalpy at the melting point. In addition, MD calculations showed that the melting point increased with pressure applied to the system. Thus, the Clausius-Clapeyron equation was verified. Furthermore, MD calculations clarified that an addition of Schottky defects, which generated the local disorder in the UO 2 crystal, lowered the melting point.

Melting behavior of SnI4 reexamined

Science.gov (United States)

Fuchizaki, Kazuhiro

2013-12-01

The low-pressure crystalline phase of a molecular crystal, SnI4, has a rising melting curve that breaks abruptly at around 1.5 GPa, beyond which it becomes almost flat, with a slight maximum at about 3 GPa. Although the overall aspect of this melting curve can be captured by the Kumari-Dass-Kechin equation, the values for the parameters involved in the equation were definitely different from those predicted on the basis of the Clapeyron-Clausius relationship. On the other hand, the accuracy of our experimental data prevented us from judging whether the parameters are derivable from the Lindemann melting law, as shown independently by Kumari and Dass, and by Kechin. The Kraut-Kennedy and Magalinskii-Zubov relationships seem to be valid in the low-pressure region where the melting curve is rising. The breakdown of these relationships suggests a qualitative change in the intermolecular interaction upon compression, thereby making the melting behavior unusual.

Martensitic phase transformation in shape-memory alloys

International Nuclear Information System (INIS)

Golestaneh, A.A.

1979-01-01

Isothermal studies are described of the shape-recovery phenomenon, stress-strain behavior, electrical resistivity and thermo-electric power associated with the martensite-parent phase reaction in the Ni-Ti shape-memory alloys. The energy-balance equation that links the reaction kinetics with the strain energy change during the cooling-deforming and heating cycle is analyzed. The strain range in which the Clausius-Clapeyron equation satisfactorily describes this reaction is determined. A large change in the Young's modulus of the specimen is found to be associated with the M → P reaction. A hysteresis loop in the resistivity-temperature plot is found and related to the anomaly in the athermal resistivity changes during cyclic M → P → M transformation. An explanation for the resistivity anomaly is offered. The M structure is found to be electrically negative relative to the P structure. A thermal emf of greater than or equal to 0.12 mV is found at the M-P interface

Thermodynamic consistency of viscoplastic material models involving external variable rates in the evolution equations for the internal variables

International Nuclear Information System (INIS)

Malmberg, T.

1993-09-01

The objective of this study is to derive and investigate thermodynamic restrictions for a particular class of internal variable models. Their evolution equations consist of two contributions: the usual irreversible part, depending only on the present state, and a reversible but path dependent part, linear in the rates of the external variables (evolution equations of ''mixed type''). In the first instance the thermodynamic analysis is based on the classical Clausius-Duhem entropy inequality and the Coleman-Noll argument. The analysis is restricted to infinitesimal strains and rotations. The results are specialized and transferred to a general class of elastic-viscoplastic material models. Subsequently, they are applied to several viscoplastic models of ''mixed type'', proposed or discussed in the literature (Robinson et al., Krempl et al., Freed et al.), and it is shown that some of these models are thermodynamically inconsistent. The study is closed with the evaluation of the extended Clausius-Duhem entropy inequality (concept of Mueller) where the entropy flux is governed by an assumed constitutive equation in its own right; also the constraining balance equations are explicitly accounted for by the method of Lagrange multipliers (Liu's approach). This analysis is done for a viscoplastic material model with evolution equations of the ''mixed type''. It is shown that this approach is much more involved than the evaluation of the classical Clausius-Duhem entropy inequality with the Coleman-Noll argument. (orig.) [de

A comparison of large scale changes in surface humidity over land in observations and CMIP3 general circulation models

International Nuclear Information System (INIS)

Willett, Katharine M; Thorne, Peter W; Jones, Philip D; Gillett, Nathan P

2010-01-01

Observed changes in the HadCRUH global land surface specific humidity and CRUTEM3 surface temperature from 1973 to 1999 are compared to CMIP3 archive climate model simulations with 20th Century forcings. Observed humidity increases are proportionately largest in the Northern Hemisphere, especially in winter. At the largest spatio-temporal scales moistening is close to the Clausius-Clapeyron scaling of the saturated specific humidity (∼7% K -1 ). At smaller scales in water-limited regions, changes in specific humidity are strongly inversely correlated with total changes in temperature. Conversely, in some regions increases are faster than implied by the Clausius-Clapeyron relation. The range of climate model specific humidity seasonal climatology and variance encompasses the observations. The models also reproduce the magnitude of observed interannual variance over all large regions. Observed and modelled trends and temperature-humidity relationships are comparable except for the extratropical Southern Hemisphere where observations exhibit no trend but models exhibit moistening. This may arise from: long-term biases remaining in the observations; the relative paucity of observational coverage; or common model errors. The overall degree of consistency of anthropogenically forced models with the observations is further evidence for anthropogenic influence on the climate of the late 20th century.

Standard molar enthalpies of formation and of sublimation of the terphenyl isomers

International Nuclear Information System (INIS)

Ribeiro da Silva, Manuel A.V.; Santos, Luis M.N.B.F.; Lima, Luis M. Spencer S.

2008-01-01

The standard (p 0 = 0.1 MPa) molar enthalpies of formation in the crystalline phases of ortho, meta and para-terphenyl isomers, at T = 298.15 K, were derived from the standard molar energies of combustion, measured by mini-bomb combustion calorimetry. The Knudsen mass-loss effusion technique was used to measure the dependence of the vapour pressure of the crystals with the temperature, thus deriving their standard molar enthalpies of sublimation by means of the Clausius-Clapeyron equation. Combining the standard molar enthalpies of formation and sublimation of the crystalline terphenyls, the standard molar enthalpies of formation in the gaseous state, at T = 298.15 K, were derived for the three isomers. Results are provided in a table. The results show small but detectable isomerization enthalpies between the terphenyls, indicating the following relative enthalpic stabilities: m- > p- ∼ o-terphenyl

Mathematical Modeling of Moisture Sorption Isotherms and Determination of Isosteric Heats of Sorption of Ziziphus Leaves

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Amel Saad

2014-01-01

Full Text Available Desorption and adsorption equilibrium moisture isotherms of Ziziphus spina-christi leaves were determined using the gravimetric-static method at 30, 40, and 50°C for water activity (aw ranging from 0.057 to 0.898. At a given aw, the results show that the moisture content decreases with increasing temperature. A hysteresis effect was observed. The experimental data of sorption were fitted by eight models (GAB, BET, Henderson-Thompson, modified-Chung Pfost, Halsey, Oswin, Peleg, and Adam and Shove. After evaluating the models according to several criteria, the Peleg and Oswin models were found to be the most suitable for describing the sorption curves. The net isosteric heats of desorption and adsorption of Ziziphus spina-christi leaves were calculated by applying the Clausius-Clapeyron equation to the sorption isotherms and an expression for predicting these thermodynamic properties was given.

Calculational model for condensation of water vapor during an underground nuclear detonation

International Nuclear Information System (INIS)

Knox, R.J.

1975-01-01

An empirally derived mathematical model was developed to calculate the pressure and temperature history during condensation of water vapor in an underground-nuclear-explosion cavity. The condensation process is non-isothermal. Use has been made of the Clapeyron-Clausius equation as a basis for development of the model. Analytic fits to the vapor pressure and the latent heat of vaporization for saturated-water vapor, together with an estimated value for the heat-transfer coefficient, have been used to describe the phenomena. The calculated pressure-history during condensation has been determined to be exponential, with a time constant somewhat less than that observed during the cooling of the superheated steam from the explosion. The behavior of the calculated condensation-pressure compares well with the observed-pressure record (until just prior to cavity collapse) for a particular nuclear-detonation event for which data is available

Generalized Einstein’s Equations from Wald Entropy

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Maulik Parikh

2016-03-01

Full Text Available We derive the gravitational equations of motion of general theories of gravity from thermodynamics applied to a local Rindler horizon through any point in spacetime. Specifically, for a given theory of gravity, we substitute the corresponding Wald entropy into the Clausius relation. Our approach works for all diffeomorphism-invariant theories of gravity in which the Lagrangian is a polynomial in the Riemann tensor.

Measurement of the Clausius-Mossotti second virial coefficients of noable gases

International Nuclear Information System (INIS)

Woo, J.C.; Kromhout, R.A.

1980-01-01

The second virial coefficient of the Clausius-Mossotti function has been measured by means of consecutive expansions with a high resolution Fabry-Perot interferometer and a highly stable, single frequency He-Ne laser. The second virial coefficients are obtained for three gases, helium, neon and argon with values of -0.15, 2.5 and 0.2, respectively. The results obtained in this work agree closely with the dc measurements made by Cole and coworker. Both of these experimental results, however, show large inconsistencies with theoretical values. For helium in particular, a negative value is observed both in this work and Cole's, while the careful theoretical approaches call for a larger positive value. (author)

ISOTERMAS DE DESORCION DE HUMEDAD EN PITAHAYA AMARILLA (Selenicereus megalanthus ISOTERMAS DE DESSORÇÃO DE UMIDADE EM PITAIAIÁS AMARELO (Selenicereus megalanthus MOISTURE DESORPTION ISOTHERMS IN YELLOW PITAHAYA (Selenicereus megalanthus

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ALFREDO A. AYALA-APONTE

2012-12-01

, Smith, Oswin y Chung y Fost models. The isosteric heat of adsorption (Qst was determined using the Clausius-Clapeyron equation. The results showed that yellow pitahaya fruits exhibit type III adsorption isotherms and that the equilibrium moisture content (EMC is temperature-dependent. For the same water activity value, the EMC decreased when temperature increased. The GAB model presented the best fit to the experimental values. The Qst dropped from 61.43 a 45.11 kJ/mol when the EMC increased from 0.08 to 0.56 g water/g dry matter, respectively.

Influence of the materials magnetic state on the accurate determination of the magnetocaloric effect

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Forchelet J.

2012-06-01

Full Text Available In this paper, we report a detailed study of the magnetocaloric effect (MCE in different first order magnetic transition (FOMT materials with different situation of the magnetic state (magnetic order. For this purpose, R-Co2, MnAs based compounds were considered in this study. The MCE is discussed in terms of Maxwell relation (MR and Clausius-Clapeyron (C-C equation. The deviation observed between both methods is discussed and analyzed. On the other hand, practically all the reported data of the MCE in the literature are associated to the applied external magnetic field and have not been corrected taking into account the demagnetization effect related to the materials shape. The obtained results demonstrate that this phenomenon can alter drastically the MCE values by cancelling out a large part of the external field, resulting in spurious values of the measured MCE. The effect of the demagnetization field on the magnetocaloric performances is also the subject of this paper.

Thermochemical study of 2,5-dimethyl-3-furancarboxylic acid, 4,5-dimethyl-2-furaldehyde, and 3-acetyl-2,5-dimethylfuran

International Nuclear Information System (INIS)

Ribeiro da Silva, Manuel A.V.; Amaral, Luisa M.P.F.

2011-01-01

The standard (p o = 0.1 MPa) molar enthalpies of formation, in the gaseous state, at T = 298.15 K, for 2,5-dimethyl-3-furancarboxylic acid, 3-acetyl-2,5-dimethylfuran, and 4,5-dimethyl-2-furaldehyde were derived from the values of the standard molar enthalpies of formation, in the condensed phase, and the standard molar enthalpies of phase transition from the condensed to the gaseous state. The values of the standard molar enthalpies of formation of the compounds in the condensed phases were calculated from the measurements of the standard massic energies of combustion obtained by static bomb combustion calorimetry. The enthalpies of vaporization/sublimation were measured by Calvet high temperature microcalorimetry. For 2,5-dimethyl-3-furancarboxylic acid the standard enthalpy of sublimation was also calculated, by the application of the Clausius-Clapeyron equation, to the temperature dependence of the vapor pressures measured by the Knudsen effusion technique. (table)

Study of the enthalpy-entropy mechanism from water sorption of orange seeds (C. sinensis cv. Brazilian for the use of agro-industrial residues as a possible source of vegetable oil production

Directory of Open Access Journals (Sweden)

Daniele Penteado Rosa

2013-02-01

Full Text Available Orange seeds are a promising agroindustry-waste which can be implemented in the extraction and production of vegetable oil. The relationship between moisture content and water activity provides useful information for the processing and storage of this waste item. The aim of this study was to determine the mechanism of water sorption enthalpy-entropy of orange seeds (C. sinensis cv. Brazilians according to the moisture content. Therefore, desorption isotherms were determined at five different temperature (30, 40, 50, 60, and 70 ºC under a wide range of moisture content (0.005-0.057 kg kg-1 d.b. and water activity (0.02-0.756. Theoretical and empirical models were used for modeling the desorption isotherms. An analytical solution of the Clausius-Clapeyron equation was proposed to compute the isosteric heat of sorption, the differential entropy, and Gibbs free energy using the Oswin model when the effect of temperature on the hygroscopic equilibrium was considered.

Vapor pressures and sublimation enthalpies of seven heteroatomic aromatic hydrocarbons measured using the Knudsen effusion technique

International Nuclear Information System (INIS)

Goldfarb, Jillian L.; Suuberg, Eric M.

2010-01-01

The vapor pressures of seven heteroatom-containing cyclic aromatic hydrocarbons, ranging in molecular weight from (168.19 to 208.21) g . mol -1 were measured over the temperature range of (301 to 486) K using the isothermal Knudsen effusion technique. The compounds measured include: anthraquinone, 9-fluorenone, 9-fluorenone oxime, phenoxazine, phenoxathiin, and 9H-pyrido[3,4-b]indole. These solid-state sublimation measurements provided values that are compared to vapor pressures of parent aromatic compounds (anthracene and fluorene) and to others with substituent groups in order to examine the effects of alcohol, ketone, pyridine, and pyrrole functionality on this property. The enthalpies and entropies of sublimation for each compound were determined from the Clausius-Clapeyron equation. Though there is no consistent trend in terms of the effects of substitutions on changes in the enthalpy or entropy of sublimation, we note that the prevalence of enthalpic or entropic driving forces on vapor pressure depend on molecule-specific factors and not merely molecular weight of the substituents.

Numerical simulation of superheated vapor bubble rising in stagnant liquid

Science.gov (United States)

Samkhaniani, N.; Ansari, M. R.

2017-09-01

In present study, the rising of superheated vapor bubble in saturated liquid is simulated using volume of fluid method in OpenFOAM cfd package. The surface tension between vapor-liquid phases is considered using continuous surface force method. In order to reduce spurious current near interface, Lafaurie smoothing filter is applied to improve curvature calculation. Phase change is considered using Tanasawa mass transfer model. The variation of saturation temperature in vapor bubble with local pressure is considered with simplified Clausius-Clapeyron relation. The couple velocity-pressure equation is solved using PISO algorithm. The numerical model is validated with: (1) isothermal bubble rising and (2) one-dimensional horizontal film condensation. Then, the shape and life time history of single superheated vapor bubble are investigated. The present numerical study shows vapor bubble in saturated liquid undergoes boiling and condensation. It indicates bubble life time is nearly linear proportional with bubble size and superheat temperature.

Isotherms and isosteric heat of sorption of two varieties of Peruvian quinoa

Directory of Open Access Journals (Sweden)

Augusto Pumacahua-Ramos

2016-01-01

Full Text Available The isosteric heats of sorption of two varieties of quinoa (Chenopodium quinoaWilld. grain were determined by the static gravimetric method at four temperatures (40, 50, 60 and 70 °C andin relative humidity environments provided by six saturated salt solutions. Six mathematical equations were used to model the experimental data: GAB, Oswin, Henderson, Peleg, Smith and Halsey. The isosteric heat of sorption was determined using the parameters of the GAB model. All the equations were shown to be appropriate by the coefficients of determination (R2 and the mean absolute error (MA%E. The influence of temperature was observed because the adsorption of water by the grains was lower at highertemperatures. The equilibrium moisture contents for security of storage, for long periods of time at water activity lower than 0.65, were 12 -13%. The effect of temperature on the parameters of the GAB model was analysed using the exponential Arrhenius equation. The isosteric heats of sorption were determined by applying the Clausius-Clapeyron equation as a function of humidity. The isosteric heat at 5% moisture for grains of the Blanca de Juli variety was 3663 kJ/kg and for the Pasankalla variety it was 3393 kJ/kg. The experimental data for isosteric heat as a function of humidity were satisfactorily modelled using three mathematical equations.

Aerosols, clouds and radiation

Energy Technology Data Exchange (ETDEWEB)

Twomey, S [University of Arizona, Tucson, AZ (USA). Inst. of Atmospheric Physics

1991-01-01

Most of the so-called 'CO{sub 2} effect' is, in fact, an 'H{sub 2}O effect' brought into play by the climate modeler's assumption that planetary average temperature dictates water-vapor concentration (following Clapeyron-Clausius). That assumption ignores the removal process, which cloud physicists know to be influenced by the aerosol, since the latter primarily controls cloud droplet number and size. Droplet number and size are also influential for shortwave (solar) energy. The reflectance of many thin to moderately thick clouds changes when nuclei concentrations change and make shortwave albedo susceptible to aerosol influence.

Fluid–fluid–solid triple point on melting curves at high temperatures

International Nuclear Information System (INIS)

Norman, G E; Saitov, I M

2016-01-01

An analysis is presented of experimental data where fluid-fluid phase transitions are observed for different substances at high temperatures with triple points on melting curves. Viscosity drops point to the structural character of the transition, whereas conductivity jumps remind of both semiconductor-to-metal and plasma nature. The slope of the phase equilibrium dependencies of pressure on temperature and the consequent change of the specific volume, which follows from the Clapeyron-Clausius equation, are discussed. P(V, T) surfaces are presented and discussed for the phase transitions considered in the vicinity of the triple points. The cases of abnormal P(T) dependencies on curves of phase equilibrium are in the focus of discussion. In particular, a P(V, T) surface is presented when both fluid-fluid and melting P(T) curves are abnormal. Particular attention is paid to warm dense hydrogen and deuterium, where remarkable contradictions exist between data of different authors. The possible connection of the P(V, T) surface peculiarities with the experimental data uncertainties is outlined. (paper)

Experimental thermochemical study of two chlorodinitroaniline isomers

International Nuclear Information System (INIS)

Ribeiro da Silva, Manuel A.V.; Ribeiro da Silva, Maria D.M.C.; Santos, Ana Filipa L.O.M.; Ferreira, Ana I.M.C. Lobo; Galvao, Tiago L.P.

2010-01-01

The standard (p 0 =0.1MPa) molar enthalpies of formation of 2-chloro-4,6-dinitroaniline and 4-chloro-2,6-dinitroaniline, in the gaseous phase, at T = 298.15 K, were derived from the combination of the values of the standard molar enthalpies of formation, in the crystalline phase, and of the standard molar enthalpies of sublimation, at the same temperature. The standard molar enthalpies of formation, in the crystalline phase, were derived from the standard massic energies of combustion, in oxygen, measured by rotating-bomb combustion calorimetry. The standard molar enthalpies of sublimation were calculated, by the application of the Clausius-Clapeyron equation, to the vapour pressures at several temperatures, measured by Knudsen effusion technique. The values of the standard molar enthalpies of formation of 2-chloro-4,6-dinitroaniline and 4-chloro-2,6-dinitroaniline, in the gaseous phase, at T = 298.15 K, are discussed in terms of enthalpic increments, and the enthalpy of isomerization between the two compounds is compared with the same parameter for two isomers of chloronitroaniline, studied in previous works.

Experimental thermochemical study of 2,5- and 2,6-dichloro-4-nitroanilines

International Nuclear Information System (INIS)

Ribeiro da Silva, Manuel A.V.; Ribeiro da Silva, Maria D.M.C.; Lobo Ferreira, Ana I.M.C.; Santos, Ana Filipa L.O.M.; Galvao, Tiago L.P.

2009-01-01

The standard (p o = 0.1 MPa) molar enthalpies of formation of 2,5- and 2,6-dichloro-4-nitroanilines, in the gaseous phase, at T = 298.15 K, were derived from the combination of the values of the standard molar enthalpies of formation in the crystalline phase, at T = 298.15 K, and the standard molar enthalpies of sublimation, of each compound, at the same temperature. The standard molar enthalpies of formation, in the crystalline phase, at T = 298.15 K, were derived from the standard massic energies of combustion of the two isomers, in oxygen, at T = 298.15 K, measured by rotating-bomb combustion calorimetry. The standard molar enthalpies of sublimation were calculated, by application of the Clausius-Clapeyron equation, to the vapour pressures at several temperatures measured by Knudsen effusion technique. The values of the standard (p = 0.1 MPa) molar enthalpies of formation of 2,5- and 2,6-dichloro-4-nitroanilines, in the gaseous phase, at T = 298.15 K, were compared with those estimated by the Cox scheme.

Dissociation heat of mixed-gas hydrate composed of methane and ethane

Energy Technology Data Exchange (ETDEWEB)

Hachikubo, A.; Nakagawa, R.; Kubota, D.; Sakagami, H.; Takahashi, N.; Shoji, H. [Kitami Inst. of Technology, Kitami (Japan)

2008-07-01

Formation and dissociation processes of natural gas hydrates in permafrost, marine and lake sediments are highly controlled by their thermal properties. Dissociation heat of gas hydrates can be estimated from phase equilibrium data using the Clausius-Clapeyron equation. However, this method is applicable for pure gas hydrate and at a temperature of 0 degrees Celsius. Direct calorimetric measurements on gas hydrates using a calorimeter have been developed to obtain thermal properties of gas hydrates, including dissociation heat and heat capacity. Studies have shown that a structure 2 gas hydrate appears in appropriate gas composition of methane and ethane. This paper investigated the effect of ethane concentration on dissociation heat of mixed-gas (methane and ethane) hydrate. Raman spectroscopy was used to confirm the appearance of a structure 2 gas hydrate. The paper identified the experimental procedure and discussed sample preparation, Raman spectroscopy, and calorimetric measurements. A schematic diagram of the calorimeter was also presented. It was concluded that in most cases, two stages of dissociation were found at the dissociation process. 15 refs., 6 figs.

The effect of halogen hetero-atoms on the vapor pressures and thermodynamics of polycyclic aromatic compounds measured via the Knudsen effusion technique

International Nuclear Information System (INIS)

Goldfarb, Jillian L.; Suuberg, Eric M.

2008-01-01

Knowledge of vapor pressures of high molar mass organics is essential to predicting their behavior in combustion systems as well as their fate and transport within the environment. This study involved polycyclic aromatic compounds (PACs) containing halogen hetero-atoms, including bromine and chlorine. The vapor pressures of eight PACs, ranging in molar mass from (212 to 336) g . mol -1 , were measured using the isothermal Knudsen effusion technique over the temperature range of (296 to 408) K. These compounds included those with few or no data available in the literature, namely: 1,4-dibromonaphthalene, 5-bromoacenaphthene, 9-bromoanthracene, 1,5-dibromoanthracene, 9,10-dibromoanthracene, 2-chloroanthracene, 9,10-dichloroanthracene, and 1-bromopyrene. Enthalpies of sublimation of these compounds were determined via application of the Clausius-Clapeyron equation. An analysis is presented on the effects of the addition of halogen hetero-atoms to pure polycyclic aromatic hydrocarbons using these data as well as available literature data. As expected, the addition of halogens onto these PACs increases their enthalpies of sublimation and decreases their vapor pressures as compared to the parent compounds

Vapor pressures and sublimation enthalpies of seven heteroatomic aromatic hydrocarbons measured using the Knudsen effusion technique

Energy Technology Data Exchange (ETDEWEB)

Goldfarb, Jillian L., E-mail: JillianLGoldfarb@gmail.co [Division of Engineering, Brown University, Providence, RI 02912 (United States); Suuberg, Eric M., E-mail: Eric_Suuberg@brown.ed [Division of Engineering, Brown University, Providence, RI 02912 (United States)

2010-06-15

The vapor pressures of seven heteroatom-containing cyclic aromatic hydrocarbons, ranging in molecular weight from (168.19 to 208.21) g . mol{sup -1} were measured over the temperature range of (301 to 486) K using the isothermal Knudsen effusion technique. The compounds measured include: anthraquinone, 9-fluorenone, 9-fluorenone oxime, phenoxazine, phenoxathiin, and 9H-pyrido[3,4-b]indole. These solid-state sublimation measurements provided values that are compared to vapor pressures of parent aromatic compounds (anthracene and fluorene) and to others with substituent groups in order to examine the effects of alcohol, ketone, pyridine, and pyrrole functionality on this property. The enthalpies and entropies of sublimation for each compound were determined from the Clausius-Clapeyron equation. Though there is no consistent trend in terms of the effects of substitutions on changes in the enthalpy or entropy of sublimation, we note that the prevalence of enthalpic or entropic driving forces on vapor pressure depend on molecule-specific factors and not merely molecular weight of the substituents.

Thermodynamic Properties, Sorption Isotherms and Glass Transition Temperature of Cape Gooseberry (Physalis peruviana L.

Directory of Open Access Journals (Sweden)

Jessica López

2014-01-01

Full Text Available Adsorption and desorption isotherms of fresh and dried Cape gooseberry (Physalis peruviana L. were determined at three temperatures (20, 40 and 60 °C using a gravimetric technique. The data obtained were fitted to several models including Guggenheim-Anderson- De Boer (GAB, Brunauer-Emmett-Teller (BET, Henderson, Caurie, Smith, Oswin, Halsey and Iglesias-Chirife. A non-linear least square regression analysis was used to evaluate the models. The Iglesias-Chirife model fitted best the experimental data. Isosteric heat of sorption was also determined from the equilibrium sorption data using the Clausius-Clapeyron equation and was found to decrease exponentially with increasing moisture content. The enthalpy-entropy compensation theory was applied to the sorption isotherms and indicated an enthalpy-controlled sorption process. Glass transition temperature (Tg of Cape gooseberry was also determined by differential scanning calorimetry and modelled as a function of moisture content with the Gordon-Taylor, the Roos and the Khalloufi models, which proved to be excellent tools for predicting glass transition of Cape gooseberry.

Moisture sorption isotherms and thermodynamic properties of bovine leather

Science.gov (United States)

Fakhfakh, Rihab; Mihoubi, Daoued; Kechaou, Nabil

2018-04-01

This study was aimed at the determination of bovine leather moisture sorption characteristics using a static gravimetric method at 30, 40, 50, 60 and 70 °C. The curves exhibit type II behaviour according to the BET classification. The sorption isotherms fitting by seven equations shows that GAB model is able to reproduce the equilibrium moisture content evolution with water activity for moisture range varying from 0.02 to 0.83 kg/kg d.b (0.9898 thermodynamic properties such as isosteric heat of sorption, sorption entropy, spreading pressure, net integral enthalpy and entropy. Net isosteric heat of sorption and differential entropy were evaluated through direct use of moisture isotherms by applying the Clausius-Clapeyron equation and used to investigate the enthalpy-entropy compensation theory. Both sorption enthalpy and entropy for desorption increase to a maximum with increasing moisture content, and then decrease sharply with rising moisture content. Adsorption enthalpy decreases with increasing moisture content. Whereas, adsorption entropy increases smoothly with increasing moisture content to a maximum of 6.29 J/K.mol. Spreading pressure increases with rising water activity. The net integral enthalpy seemed to decrease and then increase to become asymptotic. The net integral entropy decreased with moisture content increase.

Estimating the human influence on Hurricanes Harvey, Irma and Maria

Science.gov (United States)

Wehner, M. F.; Patricola, C. M.; Risser, M. D.

2017-12-01

Attribution of the human-induced climate change influence on the physical characteristics of individual extreme weather events has become an advanced science over the past decade. However, it is only recently that such quantification of anthropogenic influences on event magnitudes and probability of occurrence could be applied to very extreme storms such as hurricanes. We present results from two different classes of attribution studies for the impactful Atlantic hurricanes of 2017. The first is an analysis of the record rainfall amounts during Hurricane Harvey in the Houston, Texas area. We analyzed observed precipitation from the Global Historical Climatology Network with a covariate-based extreme value statistical analysis, accounting for both the external influence of global warming and the internal influence of ENSO. We found that human-induced climate change likely increased Hurricane Harvey's total rainfall by at least 19%, and likely increased the chances of the observed rainfall by a factor of at least 3.5. This suggests that changes exceeded Clausius-Clapeyron scaling, motivating attribution studies using dynamical climate models. The second analysis consists of two sets of hindcast simulations of Hurricanes Harvey, Irma, and Maria using the Weather Research and Forecasting model (WRF) at 4.5 km resolution. The first uses realistic boundary and initial conditions and present-day greenhouse gas forcings while the second uses perturbed conditions and pre-industrial greenhouse has forcings to simulate counterfactual storms without anthropogenic influences. These simulations quantify the fraction of Harvey's precipitation attributable to human activities and test the super Clausius-Clapeyron scaling suggested by the observational analysis. We will further quantify the human influence on intensity for Harvey, Irma, and Maria.

Study of the enthalpy-entropy mechanism from water sorption of orange seeds (C. sinensis cv. Brazilian for the use of agro-industrial residues as a possible source of vegetable oil production Estudo do mecanismo entálpico-entrópico de sorção da água de sementes de laranja (C. sinensis cv. Brasileira, para a utilização de resíduos agroindustriais como uma possível fonte de produção de óleo vegetal

Directory of Open Access Journals (Sweden)

Daniele Penteado Rosa

2013-02-01

Full Text Available Orange seeds are a promising agroindustry-waste which can be implemented in the extraction and production of vegetable oil. The relationship between moisture content and water activity provides useful information for the processing and storage of this waste item. The aim of this study was to determine the mechanism of water sorption enthalpy-entropy of orange seeds (C. sinensis cv. Brazilians according to the moisture content. Therefore, desorption isotherms were determined at five different temperature (30, 40, 50, 60, and 70 ºC under a wide range of moisture content (0.005-0.057 kg kg-1 d.b. and water activity (0.02-0.756. Theoretical and empirical models were used for modeling the desorption isotherms. An analytical solution of the Clausius-Clapeyron equation was proposed to compute the isosteric heat of sorption, the differential entropy, and Gibbs free energy using the Oswin model when the effect of temperature on the hygroscopic equilibrium was considered.As sementes de laranja são resíduos promissores da agroindústria com um alto potencial de aplicação na produção de óleo vegetal. A relação entre o conteúdo de umidade de equilíbrio e a atividade de água fornece informações úteis para seu processamento e armazenamento. O objetivo deste trabalho foi determinar o mecanismo entalpia-entropia de sorção da água de sementes de laranja (C. sinensis cv. Brasileiros em função do teor de umidade. Para isso, isotermas de dessorção das sementes de laranja foram determinados em cinco níveis de temperaturas (30, 40, 50, 60 e 70 ºC em um intervalo de umidade de equilíbrio (0.005-0.057 kg kg-1 d.b. e atividade de água de 0,02-0,756. Modelos teóricos e empíricos foram usados para a modelagem das isotermas de dessorção. A solução analítica da equação de Clausius-Clapeyron foi proposta para calcular o calor isostérico de sorção, a entropia diferencial e a energia livre de Gibbs através do modelo de Oswin quando o

Thermochemical and thermophysical study of 2-thiophenecarboxylic acid hydrazide and 2-furancarboxylic acid hydrazide

International Nuclear Information System (INIS)

Ribeiro da Silva, Manuel A.V.; Amaral, Luisa M.P.F.; Santos, Ana Filipa L.O.M.

2008-01-01

The standard (p 0 = 0.1 MPa) molar energies of combustion, Δ c U m 0 , for the crystalline 2-thiophenecarboxylic acid hydrazide and 2-furancarboxylic acid hydrazide were determined, at the temperature of 298.15 K, by rotating bomb and static bomb combustion calorimetry, respectively. For these compounds, the standard molar enthalpies of sublimation, Δ cr g H m 0 , at T = 298.15 K, were derived by the Clausius-Clapeyron equation, from the temperature dependence of the vapour pressures of these compounds, measured by the Knudsen effusion mass-loss technique. The results are presented in a table. The values were used to derive the standard molar enthalpies of formation of the title compounds in their gaseous phases and the results are discussed in terms of energetic effects of the introduction of the -CONHNH 2 group in the thiophene and furan rings. Using estimated values for the heat capacity differences between the gas and the crystal phases of the studied compounds, the standard (p 0 = 0.1 MPa) molar enthalpies, entropies, and Gibbs energies of sublimation, at T = 298.15 K, were derived

Thermodynamic properties of 5(nitrophenyl) furan-2-carbaldehyde isomers.

Science.gov (United States)

Dibrivnyi, Volodymyr; Sobechko, Iryna; Puniak, Marian; Horak, Yuriy; Obushak, Mykola; Van-Chin-Syan, Yuriy; Andriy, Marshalek; Velychkivska, Nadiia

2015-01-01

The aim of the current work was to determine thermo dynamical properties of 5(2-nitro phenyl)-furan-2-carbaldehyde, 5(3-nitro phenyl)-furan-2-carbaldehyde and 5(4-nitro phenyl)-furan-2-carbaldehyde. The temperature dependence of saturated vapor pressure of 5(2-nitro phenyl)-furan-2-carbaldehyde, 5(3-nitro phenyl)-furan-2-carbaldehyde and 5(4-nitro phenyl)-furan-2-carbaldehyde was determined by Knudsen's effusion method. The results are presented by the Clapeyron-Clausius equation in linear form, and via this form, the standard enthalpies, entropies and Gibbs energies of sublimation and evaporation of compounds were calculated at 298.15 K. The standard molar formation enthalpies of compounds in crystalline state at 298.15 K were determined indirectly by the corresponding standard molar combustion enthalpy, obtained using bomb calorimetry combustion. Determination of the thermodynamic properties for these compounds may contribute to solving practical problems pertaining optimization processes of their synthesis, purification and application and it will also provide a more thorough insight regarding the theoretical knowledge of their nature.Graphical abstract:Generalized structural formula of investigated compounds and their formation enthalpy determination scheme in the gaseous state.

Research on heat and mass transfer model for passive containment cooling system

International Nuclear Information System (INIS)

Jiang Xiaowei; Yu Hongxing; Sun Yufa; Huang Daishun

2013-01-01

Different with the traditional dry style containment design without external cooling, the PCCS design increased the temperature difference between the wall and the containment atmosphere significantly, and also the absolute temperature of the containment surfaces will be lower, affecting properties relevant in the condensation process. A research on the heat and mass transfer model has been done in this paper, especially the improvement on the condensation and evaporation model in the presence of noncondensable gases. Firstly, the Peterson's diffusion layer model was proved to equivalent to the stagnant film model adopted by CONTAIN code using the Clausius-Clapeyron equation, then a factor which can be used to stagnant film model was derived from the comparison between the Y.Liao's generalized diffusion layer model and the Peterson's diffusion layer model. Finally, the model in CONTAIN code used to compute the condensation and evaporation mass flux was modified using the factor, and the Wisconsin condensation tests and Westinghouse film evaporation on heated plate tests were simulated which had proved the improved model can predict more closer value of the heat and mass transfer coefficient to experimental value than original model. (authors)

Numerical modelling of methanol liquid pool fires

Science.gov (United States)

Prasad, Kuldeep; Li, Chiping; Kailasanath, K.; Ndubizu, Chuka; Ananth, Ramagopal; Tatem, P. A.

1999-12-01

The focus of this paper is on numerical modelling of methanol liquid pool fires. A mathematical model is first developed to describe the evaporation and burning of a two-dimensional or axisymmetric pool containing pure liquid methanol. Then, the complete set of unsteady, compressible Navier-Stokes equations for reactive flows are solved in the gas phase to describe the convection of the fuel gases away from the pool surface, diffusion of the gases into the surrounding air and the oxidation of the fuel into product species. Heat transfer into the liquid pool and the metal container through conduction, convection and radiation are modelled by solving a modified form of the energy equation. Clausius-Clapeyron relationships are invoked to model the evaporation rate of a two-dimensional pool of pure liquid methanol. The governing equations along with appropriate boundary and interface conditions are solved using the flux-corrected transport algorithm. Numerical results exhibit a flame structure that compares well with experimental observations. Temperature profiles and burning rates were found to compare favourably with experimental data from single- and three-compartment laboratory burners. The model predicts a puffing frequency of approximately 12 Hz for a 1 cm diameter methanol pool in the absence of any air co-flow. It is also observed that increasing the air co-flow velocity helps in stabilizing the diffusion flame, by pushing the vortical structures away from the flame region.

Sign reversal of transformation entropy change in Co2Cr(Ga,Si) shape memory alloys

International Nuclear Information System (INIS)

Xu, Xiao; Omori, Toshihiro; Kainuma, Ryosuke; Nagasako, Makoto; Kanomata, Takeshi

2015-01-01

In situ X-ray diffraction (XRD) measurements and compression tests were performed on Co 2 Cr(Ga,Si) shape memory alloys. The reentrant martensitic transformation behavior was directly observed during the in situ XRD measurements. The high-temperature parent phase and low-temperature reentrant parent phase were found to have a continuous temperature dependence of lattice parameter, therefore suggesting that they are the same phase in nature. Moreover, compression tests were performed on a parent-phase single crystal sample; an evolution from normal to inverse temperature dependence of critical stress for martensitic transformation was directly observed. Based on the Clausius-Clapeyron analysis, a sign reversal of entropy change can be expected on the same alloy

Relationship between carbon microstructure, adsorption energy and hydrogen adsorption capacity at different temperatures

International Nuclear Information System (INIS)

Jacek Jagiello; Matthias Thommes

2005-01-01

Various microporous materials such as activated carbons, nano-tubes, synthetic microporous carbons as well as metal organic framework materials are being considered for hydrogen storage applications by means of physical adsorption. To develop materials of practical significance for hydrogen storage it is important to understand the relationships between pore sizes, adsorption energies and adsorption capacities. The pore size distribution (PSD) characterization is traditionally obtained from the analysis of nitrogen adsorption isotherms measured at 77 K. However, a portion of the pores accessible to H 2 may not be accessible to N 2 at this temperature. Therefore, it was recently proposed to use the DFT analysis of H 2 adsorption isotherms to characterize pore structure of materials considered for hydrogen storage applications. In present work, adsorption isotherms of H 2 and N 2 at cryogenic temperatures are used for the characterization of carbon materials. Adsorption measurements were performed with Autosorb 1 MP (Quantachrome Instruments, Boynton Beach, Florida, USA). As an example, Fig 1 compares PSDs calculated for the activated carbon sample (F400, Calgon Carbon) using combined H 2 and N 2 data, and using N 2 isotherm only. The nitrogen derived PSD does not include certain amount of micropores which are accessible to H 2 but not to N 2 molecules. Obviously, the difference in the calculated PSDs by the two methods will depend on the actual content of small micropores in a given sample. Carbon adsorption properties can also be characterized by the isosteric heat of adsorption, Qst, related to the adsorption energy and dependent on the carbon pore/surface structure. Fig 2 shows Qst data calculated using the Clausius-Clapeyron equation from H 2 isotherms measured at 77 K and 87 K for the carbon molecular sieve CMS 5A (Takeda), oxidized single wall nano-tubes (SWNT), and graphitized carbon black (Supelco). The Qst values decrease with increasing pore sizes. The

Strong increase in convective precipitation in response to higher temperatures

DEFF Research Database (Denmark)

Berg, P.; Moseley, C.; Härter, Jan Olaf Mirko

2013-01-01

Precipitation changes can affect society more directly than variations in most other meteorological observables, but precipitation is difficult to characterize because of fluctuations on nearly all temporal and spatial scales. In addition, the intensity of extreme precipitation rises markedly...... at higher temperature, faster than the rate of increase in the atmosphere's water-holding capacity, termed the Clausius-Clapeyron rate. Invigoration of convective precipitation (such as thunderstorms) has been favoured over a rise in stratiform precipitation (such as large-scale frontal precipitation......) as a cause for this increase , but the relative contributions of these two types of precipitation have been difficult to disentangle. Here we combine large data sets from radar measurements and rain gauges over Germany with corresponding synoptic observations and temperature records, and separate convective...

Influence of the Ringwoodite-Perovskite transition on mantle convection in spherical geometry as a function of Clapeyron slope and Rayleigh number

Directory of Open Access Journals (Sweden)

M. Wolstencroft

2011-12-01

Full Text Available We investigate the influence on mantle convection of the negative Clapeyron slope ringwoodite to perovskite and ferro-periclase mantle phase transition, which is correlated with the seismic discontinuity at 660 km depth. In particular, we focus on understanding the influence of the magnitude of the Clapeyron slope (as measured by the Phase Buoyancy parameter, P and the vigour of convection (as measured by the Rayleigh number, Ra on mantle convection. We have undertaken 76 simulations of isoviscous mantle convection in spherical geometry, varying Ra and P. Three domains of behaviour were found: layered convection for high Ra and more negative P, whole mantle convection for low Ra and less negative P, and transitional behaviour in an intervening domain. The boundary between the layered and transitional domain was fit by a curve P = α Ra^β where α = −1.05, and β = −0.1, and the fit for the boundary between the transitional and whole mantle convection domain was α = −4.8, and β = −0.25. These two curves converge at Ra ≈ 2.5 × 10⁴ (well below Earth mantle vigour and P ≈ −0.38. Extrapolating to high Ra, which is likely earlier in Earth history, this work suggests a large transitional domain. It is therefore likely that convection in the Archean would have been influenced by this phase change, with Earth being at least in the transitional domain, if not the layered domain.

Experimental thermochemical study of 4,5-dichloro-2-nitroaniline

International Nuclear Information System (INIS)

Ribeiro da Silva, Manuel A.V.; Ribeiro da Silva, Maria D.M.C.; Lobo Ferreira, Ana I.M.C.; Santos, Ana Filipa L.O.M.; Galvao, Tiago L.P.

2009-01-01

The standard (p 0 =0.1MPa) molar enthalpy of formation of 4,5-dichloro-2-nitroaniline, in the gaseous phase, at T = 298.15 K, was derived from the combination of the values of the standard molar enthalpy of formation, in the crystalline phase, at T = 298.15 K, and the standard molar enthalpy of sublimation, at the same temperature. The standard molar enthalpy of formation, in the crystalline phase, at T = 298.15 K, was derived as -(99.7 ± 1.6) kJ . mol -1 from the standard massic energy of combustion, in oxygen, measured by rotating-bomb combustion calorimetry. The standard molar enthalpy of sublimation was calculated, (109.4 ± 0.9) kJ . mol -1 by the application of the Clausius-Clapeyron equation, to the vapour pressures measured at several temperatures by Knudsen effusion technique. The standard molar enthalpies of formation, in the gaseous phase, of the six dichloro-2-nitroaniline isomers and of the four dichloro-4-nitroaniline isomers were estimated by the Cox Scheme and by the Domalski and Hearing group additivity method and compared with the available experimental values. For the Domalski and Hearing group additivity method four new correction terms were derived.

Experimental thermochemical study of 3-acetyl-2-methyl-5-phenylthiophene

International Nuclear Information System (INIS)

Ribeiro da Silva, Manuel A.V.; Santos, Ana Filipa L.O.M.

2010-01-01

The standard (p 0 =0.1MPa) massic energy of combustion, in oxygen, of the crystalline 3-acetyl-2-methyl-5-phenylthiophene was measured, at T = 298.15 K, by rotating-bomb combustion calorimetry, from which the standard molar enthalpy of formation, in the condensed phase, was calculated as Δ f H m 0 (cr)=-(104.3±3.1)kJ.mol -1 . The corresponding standard molar enthalpy of sublimation, at T = 298.15 K, Δ cr g H m 0 =(108.9±0.4)kJ.mol -1 , was derived by the Clausius-Clapeyron equation, from the temperature dependence of the vapour pressures of this compound, measured by the Knudsen effusion mass-loss technique. From the results presented above, the standard molar enthalpy of formation, in the gaseous phase, at T = 298.15 K, was derived, Δ f H m 0 (g)=(4.6±3.1)kJ.mol -1 . This value, in conjunction with the literature values of the experimental enthalpies of formation of thiophene, 2-methylthiophene, and 3-acetylthiophene, was used to predict the enthalpic increment due to the introduction of a phenyl group in the position 2- of the thiophene ring. The calculated increment was compared with the corresponding ones in benzene and pyridine derivatives.

Thermodynamic properties of water sorption of jackfruit (Artocarpus heterophyllus Lam. as a function of moisture content

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Ana Paula Prette

2013-03-01

Full Text Available The Jackfruit tree is one of the most significant trees in tropical home gardens and perhaps the most widespread and useful tree in the important genus Artocarpus. The fruit is susceptible to mechanical and biological damage in the mature state, and some people find the aroma of the fruit objectionable, particularly in confined spaces. The dehydration process could be an alternative for the exploitation of this product, and the relationship between moisture content and water activity provides useful information for its processing and storage. The aim of this study was to determine the thermodynamic properties of the water sorption of jackfruit (Artocarpus heterophyllus Lam. as a function of moisture content. Desorption isotherms of the different parts of the jackfruit (pulp, peduncle, mesocarp, peel, and seed were determined at four different temperatures (313.15, 323.15, 333.15, and 343.15 K in a water activity range of 0.02-0.753 using the static gravimetric method. Theoretical and empirical models were used to model the desorption isotherms. An analytical solution of the Clausius-Clapeyron equation was proposed to calculate the isosteric heat of sorption, the differential entropy, and Gibbs' free energy using the Guggenhein-Anderson-de Boer and Oswin models considering the effect of temperature on the hygroscopic equilibrium.

Correlation vs. Causation: The Effects of Ultrasonic Melt Treatment on Cast Metal Grain Size

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J. B. Ferguson

2014-10-01

Full Text Available Interest in ultrasonic treatment of liquid metal has waxed and waned for nearly 80 years. A review of several experiments representative of ultrasonic cavitation treatment of Al and Mg alloys shows that the theoretical mechanisms thought to be responsible for grain refinement are (1 cavitation-induced increase in melting temperature predicted by the Clausius-Clapeyron equation and (2 cavitation-induced wetting of otherwise unwetted insoluble particles. Neither of these theoretical mechanisms can be directly confirmed by experiment, and though they remain speculative, the available literature generally assumes that one or the other or both mechanisms are active. However, grain size is known to depend on temperature of the liquid, temperature of the mold, and cooling rate of the entire system. From the reviewed experiments, it is difficult to isolate temperature and cooling rate effects on grain size from the theoretical effects. Ultrasonic treatments of Al-A356 were carried out to isolate such effects, and though it was found that ultrasound produced significant grain refinement, the treatments also significantly chilled the liquid and thereby reduced the pouring temperature. The grain sizes attained closely correlated with pouring temperature suggesting that ultrasonic grain refinement is predominantly a result of heat removal by the horn and ultrasonic stirring.

Laser-solid interaction and dynamics of the laser-ablated materials

International Nuclear Information System (INIS)

Chen, K.R.; Leboeuf, J.N.; Geohegan, D.B.; Wood, R.F.; Donato, J.M.; Liu, C.L.; Puretzky, A.A.

1995-01-01

Rapid transformations through the liquid and vapor phases induced by laser-solid interactions are described by the authors' thermal model with the Clausius-Clapeyron equation to determine the vaporization temperature under different surface pressure condition. Hydrodynamic behavior of the vapor during and after ablation is described by gas dynamic equations. These two models are coupled. Modeling results show that lower background pressure results lower laser energy density threshold for vaporization. The ablation rate and the amount of materials removed are proportional to the laser energy density above its threshold. The authors also demonstrate a dynamic source effect that accelerates the unsteady expansion of laser-ablated material in the direction perpendicular to the solid. A dynamic partial ionization effect is studied as well. A self-similar theory shows that the maximum expansion velocity is proportional to c s α, where 1 - α is the slope of the velocity profile. Numerical hydrodynamic modeling is in good agreement with the theory. With these effects, α is reduced. Therefore, the expansion front velocity is significantly higher than that from conventional models. The results are consistent with experiments. They further study how the plume propagates in high background gas condition. Under appropriate conditions, the plume is slowed down, separates with the background, is backward moving, and hits the solid surface. Then, it splits into two parts when it rebounds from the surface. The results from the modeling will be compared with experimental observations where possible

Climate-change driven increase in high intensity rainfall events: Analysis of development in the last decades and towards an extrapolation of future progression

Science.gov (United States)

Müller, Eva; Pfister, Angela; Gerd, Büger; Maik, Heistermann; Bronstert, Axel

2015-04-01

Hydrological extreme events can be triggered by rainfall on different spatiotemporal scales: river floods are typically caused by event durations of between hours and days, while urban flash floods as well as soil erosion or contaminant transport rather result from storms events of very short duration (minutes). Still, the analysis of climate change impacts on rainfall-induced extreme events is usually carried out using daily precipitation data at best. Trend analyses of extreme rainfall at sub-daily or even sub-hourly time scales are rare. In this contribution two lines of research are combined: first, we analyse sub-hourly rainfall data for several decades in three European regions.Second, we investigate the scaling behaviour of heavy short-term precipitation with temperature, i.e. the dependence of high intensity rainfall on the atmospheric temperature at that particular time and location. The trend analysis of high-resolution rainfall data shows for the first time that the frequency of short and intensive storm events in the temperate lowland regions in Germany has increased by up to 0.5 events per year over the last decades. I.e. this trend suggests that the occurrence of these types of storms have multiplied over only a few decades. Parallel to the changes in the rainfall regime, increases in the annual and seasonal average temperature and changes in the occurrence of circulation patterns responsible for the generation of high-intensity storms have been found. The analysis of temporally highly resolved rainfall records from three European regions further indicates that extreme precipitation events are more intense with warmer temperatures during the rainfall event. These observations follow partly the Clausius-Clapeyron relation. Based on this relation one may derive a general rule of maximum rainfall intensity associated to the event temperature, roughly following the Clausius-Clapeyron (CC) relation. This rule might be used for scenarios of future maximum

The Measurement and Interpretation of Transformation Temperatures in Nitinol

Science.gov (United States)

Duerig, T. W.; Pelton, A. R.; Bhattacharya, K.

2017-12-01

A previous paper (Duerig and Bhattacharya in Shap Mem Superelasticity 1:153-161, 2015) introduced several engineering considerations surrounding the R-phase in Nitinol and highlighted a common, if not pervasive, misconception regarding the use of the term Af by the medical device industry. This paper brings additional data to bear on the issue and proposes more accurate terminology. Moreover, a variety of tools are used to establish the forward and reverse stress-temperature phase diagrams for a superelastic wire typical of that used in medical devices. Once established, the two most common methods of measuring transformation temperatures, Differential Scanning Calorimetry and Bend Free Recovery, are tested against the observed behavior. Light is also shed upon the origin of the Clausius-Clapeyron ratio (d σ/d T), the triple point, and why such large variations are reported in superelastic alloys.

A macrothermodynamic approach to the limit of reversible capillary condensation.

Science.gov (United States)

Trens, Philippe; Tanchoux, Nathalie; Galarneau, Anne; Brunel, Daniel; Fubini, Bice; Garrone, Edoardo; Fajula, François; Di Renzo, Francesco

2005-08-30

The threshold of reversible capillary condensation is a well-defined thermodynamic property, as evidenced by corresponding states treatment of literature and experimental data on the lowest closure point of the hysteresis loop in capillary condensation-evaporation cycles for several adsorbates. The nonhysteretical filling of small mesopores presents the properties of a first-order phase transition, confirming that the limit of condensation reversibility does not coincide with the pore critical point. The enthalpy of reversible capillary condensation can be calculated by a Clausius-Clapeyron approach and is consistently larger than the condensation heat in unconfined conditions. Calorimetric data on the capillary condensation of tert-butyl alcohol in MCM-41 silica confirm a 20% increase of condensation heat in small mesopores. This enthalpic advantage makes easier the overcoming of the adhesion forces by the capillary forces and justifies the disappearing of the hysteresis loop.

Entropy: From Thermodynamics to Hydrology

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Demetris Koutsoyiannis

2014-02-01

Full Text Available Some known results from statistical thermophysics as well as from hydrology are revisited from a different perspective trying: (a to unify the notion of entropy in thermodynamic and statistical/stochastic approaches of complex hydrological systems and (b to show the power of entropy and the principle of maximum entropy in inference, both deductive and inductive. The capability for deductive reasoning is illustrated by deriving the law of phase change transition of water (Clausius-Clapeyron from scratch by maximizing entropy in a formal probabilistic frame. However, such deductive reasoning cannot work in more complex hydrological systems with diverse elements, yet the entropy maximization framework can help in inductive inference, necessarily based on data. Several examples of this type are provided in an attempt to link statistical thermophysics with hydrology with a unifying view of entropy.

Experimental study of water desorption isotherms and thin-layer convective drying kinetics of bay laurel leaves

Science.gov (United States)

Ghnimi, Thouraya; Hassini, Lamine; Bagane, Mohamed

2016-12-01

The aim of this work is to determine the desorption isotherms and the drying kinetics of bay laurel leaves ( Laurus Nobilis L.). The desorption isotherms were performed at three temperature levels: 50, 60 and 70 °C and at water activity ranging from 0.057 to 0.88 using the statistic gravimetric method. Five sorption models were used to fit desorption experimental isotherm data. It was found that Kuhn model offers the best fitting of experimental moisture isotherms in the mentioned investigated ranges of temperature and water activity. The Net isosteric heat of water desorption was evaluated using The Clausius-Clapeyron equation and was then best correlated to equilibrium moisture content by the empirical Tsami's equation. Thin layer convective drying curves of bay laurel leaves were obtained for temperatures of 45, 50, 60 and 70 °C, relative humidity of 5, 15, 30 and 45 % and air velocities of 1, 1.5 and 2 m/s. A non linear regression procedure of Levenberg-Marquardt was used to fit drying curves with five semi empirical mathematical models available in the literature, The R2 and χ2 were used to evaluate the goodness of fit of models to data. Based on the experimental drying curves the drying characteristic curve (DCC) has been established and fitted with a third degree polynomial function. It was found that the Midilli Kucuk model was the best semi-empirical model describing thin layer drying kinetics of bay laurel leaves. The bay laurel leaves effective moisture diffusivity and activation energy were also identified.

A SPME-based method for rapidly and accurately measuring the characteristic parameter for DEHP emitted from PVC floorings.

Science.gov (United States)

Cao, J; Zhang, X; Little, J C; Zhang, Y

2017-03-01

Semivolatile organic compounds (SVOCs) are present in many indoor materials. SVOC emissions can be characterized with a critical parameter, y 0 , the gas-phase SVOC concentration in equilibrium with the source material. To reduce the required time and improve the accuracy of existing methods for measuring y 0 , we developed a new method which uses solid-phase microextraction (SPME) to measure the concentration of an SVOC emitted by source material placed in a sealed chamber. Taking one typical indoor SVOC, di-(2-ethylhexyl) phthalate (DEHP), as the example, the experimental time was shortened from several days (even several months) to about 1 day, with relative errors of less than 5%. The measured y 0 values agree well with the results obtained by independent methods. The saturated gas-phase concentration (y sat ) of DEHP was also measured. Based on the Clausius-Clapeyron equation, a correlation that reveals the effects of temperature, the mass fraction of DEHP in the source material, and y sat on y 0 was established. The proposed method together with the correlation should be useful in estimating and controlling human exposure to indoor DEHP. The applicability of the present approach for other SVOCs and other SVOC source materials requires further study. © 2016 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

Estimating enthalpy of vaporization from vapor pressure using Trouton's rule.

Science.gov (United States)

MacLeod, Matthew; Scheringer, Martin; Hungerbühler, Konrad

2007-04-15

The enthalpy of vaporization of liquids and subcooled liquids at 298 K (delta H(VAP)) is an important parameter in environmental fate assessments that consider spatial and temporal variability in environmental conditions. It has been shown that delta H(VAP)P for non-hydrogen-bonding substances can be estimated from vapor pressure at 298 K (P(L)) using an empirically derived linear relationship. Here, we demonstrate that the relationship between delta H(VAP)and PL is consistent with Trouton's rule and the ClausiusClapeyron equation under the assumption that delta H(VAP) is linearly dependent on temperature between 298 K and the boiling point temperature. Our interpretation based on Trouton's rule substantiates the empirical relationship between delta H(VAP) degree and P(L) degrees for non-hydrogen-bonding chemicals with subcooled liquid vapor pressures ranging over 15 orders of magnitude. We apply the relationship between delta H(VAP) degrees and P(L) degrees to evaluate data reported in literature reviews for several important classes of semivolatile environmental contaminants, including polycyclic aromatic hydrocarbons, chlorobenzenes, polychlorinated biphenyls and polychlorinated dibenzo-dioxins and -furans and illustrate the temperature dependence of results from a multimedia model presented as a partitioning map. The uncertainty associated with estimating delta H(VAP)degrees from P(L) degrees using this relationship is acceptable for most environmental fate modeling of non-hydrogen-bonding semivolatile organic chemicals.

Thermochemical study of some dichloroacetophenone isomers

Energy Technology Data Exchange (ETDEWEB)

Ribeiro da Silva, Manuel A.V., E-mail: risilva@fc.up.p [Centro de Investigacao em Quimica, Department of Chemistry and Biochemistry, Faculty of Science, University of Porto, Rua do Campo Alegre, 687, P-4169-007 Porto (Portugal); Amaral, Luisa M.P.F. [Centro de Investigacao em Quimica, Department of Chemistry and Biochemistry, Faculty of Science, University of Porto, Rua do Campo Alegre, 687, P-4169-007 Porto (Portugal)

2011-03-15

The standard (p{sup 0}=0.1MPa) molar enthalpies of formation in the condensed phase, {Delta}{sub f}H{sub m}{sup 0}(cr,l), for 2',4'-, 2',5'-, and 3',4'-dichloroacetophenones were derived from the standard molar energies of combustion, {Delta}{sub c}U{sub m}{sup 0} in oxygen, to yield CO{sub 2}(g) and HCl . 600H{sub 2}O(l), at T = 298.15 K, measured by rotating bomb combustion calorimetry. The standard molar enthalpies of vapourization or sublimation, {Delta}{sub cr,l}{sup g}H{sub m}{sup 0}, of these compounds, at T = 298.15 K were determined by Calvet microcalorimetry. For the 3',4'-dichoroacetophenone, the standard molar enthalpy of sublimation, at T = 298.15 K, was derived by the Clausius-Clapeyron equation, from the temperature dependence of the vapour pressures of this compound, measured by the Knudsen effusion technique. From the values of {Delta}{sub f}H{sub m}{sup 0}(cr,l) and {Delta}{sub cr,l}{sup g}H{sub m}{sup 0} the standard molar enthalpies of formation of the three isomers, in the gaseous phase, {Delta}{sub f}H{sub m}{sup 0}(g), at T = 298.15 K were derived and compared with the same parameters estimated by the Cox Scheme. (table)

Thermodynamic and kinetic verification of tetra-n-butyl ammonium nitrate (TBANO3) as a promoter for the clathrate process applicable to precombustion carbon dioxide capture.

Science.gov (United States)

Babu, Ponnivalavan; Yao, Minghuang; Datta, Stuti; Kumar, Rajnish; Linga, Praveen

2014-03-18

In this study, tetra-n-butyl ammonium nitrate (TBANO3) is evaluated as a promoter for precombustion capture of CO2 via hydrate formation. New hydrate phase equilibrium data for fuel gas (CO2/H2) mixture in presence of TBANO3 of various concentrations of 0.5, 1.0, 2.0, 3.0, and 3.7 mol % was determined and presented. Heat of hydrate dissociation was calculated using Clausius-Clapeyron equation and as the concentration of TBANO3 increases, the heat of hydrate dissociation also increases. Kinetic performance of TBANO3 as a promoter at different concentrations was evaluated at 6.0 MPa and 274.2 K. Based on induction time, gas uptake, separation factor, hydrate phase CO2 composition, and rate of hydrate growth, 1.0 mol % TBANO3 solution was found to be the optimum concentration at the experimental conditions of 6.0 MPa and 274.2 K for gas hydrate formation. A 93.0 mol % CO2 rich stream can be produced with a gas uptake of 0.0132 mol of gas/mol of water after one stage of hydrate formation in the presence of 1.0 mol % TBANO3 solution. Solubility measurements and microscopic images of kinetic measurements provide further insights to understand the reason for 1.0 mol % TBANO3 to be the optimum concentration.

Enthalpy-entropy compensation based on isotherms of mango Compensação entalpia-entropia baseada nas isotermas de mango

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Javier Telis-Romero

2005-06-01

Full Text Available Moisture equilibrium data of mango pulp were determined using the static gravimetric method. Adsorption and desorption isotherms were obtained in the range of 30-70 ºC, to water activities (a w from 0.02 to 0.97. The application of the GAB model to the experimental results, using direct nonlinear regression analysis, provided agreement between experimental and calculated values. The net isosteric heat of sorption was estimated from equilibrium sorption data, using the Clausius-Clapeyron equation. Isosteric heats of sorption were found to increase with increasing temperature and could be well adjusted by an exponential relationship. The enthalpy-entropy compensation theory was applied to sorption isotherms and plots of deltaH versus deltaS provided the isokinetic temperatures, indicating an enthalpy controlled sorption process.Dados de equilíbrio da umidade da polpa de manga foram determinados utilizando-se o método estático gravimétrico. As isotermas de adsorção e dessorção foram obtidas na faixa de 30-70 ºC e as atividades de água (a w de 0,02 a 0,97. A utilização do modelo de GAB nos resultados experimentais, através da análise de regressão não linear, proporcionou um bom ajuste entre os dados experimentais e os valores calculados. O calor isostérico de sorção foi estimado a partir dos dados de equilíbrio de sorção, utilizando-se a equação de Clausius-Clayperon. Notou-se que os calores isostéricos de sorção crescem com o aumento da temperatura e pode ser bem ajustado através de uma relação exponencial. A teoria da compensação entalpia-entropia foi aplicada às isotermas de sorção e gráficos deltaH versus deltaS forneceram as temperaturas isocinéticas, indicando um processo de sorção entalpicamente controlado.

Relationship between carbon microstructure, adsorption energy and hydrogen adsorption capacity at different temperatures

International Nuclear Information System (INIS)

Jagiello, J.; Thommes, M.

2005-01-01

Various microporous materials such as activated carbons, nano-tubes, synthetic micro-porous carbons as well as metal organic framework materials are being considered for hydrogen storage applications by means of physical adsorption. To develop materials of practical significance for hydrogen storage it is important to understand the relationships between pore sizes, adsorption energies and adsorption capacities. The pore size distribution (PSD) characterization is traditionally obtained from the analysis of nitrogen adsorption isotherms measured at 77 K. However, a portion of the pores accessible to H 2 may not be accessible to N 2 at this temperature. Therefore, it was recently proposed to use the DFT analysis of H 2 adsorption isotherms to characterize pore structure of materials considered for hydrogen storage applications [1]. In present work, adsorption isotherms of H 2 and N 2 at cryogenic temperatures are used for the characterization of carbon materials. Adsorption measurements were performed with Autosorb 1 MP [Quantachrome Instruments, Boynton Beach, Florida, USA]. As an example, Fig 1 compares PSDs calculated for the activated carbon sample (F400, Calgon Carbon) using combined H 2 and N 2 data, and using N 2 isotherm only. The nitrogen derived PSD does not include certain amount of micro-pores which are accessible to H 2 but not to N 2 molecules. Obviously, the difference in the calculated PSDs by the two methods will depend on the actual content of small micro-pores in a given sample. Carbon adsorption properties can also be characterized by the isosteric heat of adsorption, Qst, related to the adsorption energy and dependent on the carbon pore/surface structure. Fig 2 shows Qst data calculated using the Clausius-Clapeyron equation from H 2 isotherms measured at 77 K and 87 K for the carbon molecular sieve CMS 5A (Takeda), oxidized single wall nano-tubes (SWNT) [2], and graphitized carbon black (Supelco). The Qst values decrease with increasing pore

Application of physical adsorption thermodynamics to heterogeneous chemistry on polar stratospheric clouds

Science.gov (United States)

Elliott, Scott; Turco, Richard P.; Toon, Owen B.; Hamill, Patrick

1991-01-01

Laboratory isotherms for the binding of several nonheterogeneously active atmospheric gases and for HCl to water ice are translated into adsorptive equilibrium constants and surface enthalpies. Extrapolation to polar conditions through the Clausius Clapeyron relation yields coverage estimates below the percent level for N2, Ar, CO2, and CO, suggesting that the crystal faces of type II stratospheric cloud particles may be regarded as clean with respect to these species. For HCl, and perhaps HF and HNO3, estimates rise to several percent, and the adsorbed layer may offer acid or proton sources alternate to the bulk solid for heterogeneous reactions with stratospheric nitrates. Measurements are lacking for many key atmospheric molecules on water ice, and almost entirely for nitric acid trihydrate as substrate. Adsorptive equilibria enter into gas to particle mass flux descriptions, and the binding energy determines rates for desorption of, and encounter between, potential surface reactants.

The atmospheric wet pool: definition and comparison with the oceanic warm pool

Institute of Scientific and Technical Information of China (English)

ZHANG Caiyun; CHEN Ge

2008-01-01

The oceanic warm pool (OWP) defined by sea surface temperature (SST) is known as the "heat reservoir" in the ocean. The warmest portion in the ocean mirrors the fact that the wettest region with the largest accumulation of water vapor (WV) in the atmosphere, termed atmospheric wet pool (AWP), should be identified because of the well-known Clausius-Clapeyron relationship between SST and WV. In this study, we used 14-year simultaneous observations of WV and SST from January 1988 to December 2001 to define the AWP and investigate its coupling and co-variations with the OWP. The joint examination of the area variations, centroid locations, and zonal migrations of the AWP and OWP lead to a number of interesting findings. The results hopefully can contribute to our understanding of the air-sea interaction in general and characterization of El Nifio/La Nina events in particular.

Comportamento higroscópico de partes aéreas de pimenta-de-macaco (Piper aduncum L.

Directory of Open Access Journals (Sweden)

Carolina de L. O. C. e Silva

2015-04-01

Full Text Available Isotermas de dessorção de pimenta-de-macaco foram determinadas pelo método gravimétrico estático nas temperaturas de 35, 45 e 55 ºC, com umidade relativa variando de 5,5-81%. Três modelos matemáticos foram aplicados para analisar os dados experimentais. O modelo de GAB modificado apresentou o melhor ajuste aos dados experimentais. O calor isostérico e a entropia diferencial foram determinados pela aplicação das equações de Clausius-Clapeyron e Gibbs-Helmholtz, respectivamente. O calor isostérico e a entropia da isoterma de dessorção apresentaram comportamento similar. A teoria da compensação entalpia-entropia foi aplicada às isotermas indicando que o mecanismo de dessorção de umidade das partes aéreas de pimenta-de-macaco é controlado pela entalpia.

ISOTERMAS DE ADSORCIÓN DE BIOPLÁSTICOS DE HARINA DE YUCA MOLDEADOS POR COMPRESIÓN ISOTERMAS DE ADSORÇÃO DE FARINHA DE MANDIOCA BIOPLÁSTICOS MOLDADAS POR COMPRESSÃO ADSORPTION ISOTHERMS OF CASSAVA FLOUR BIOPLASTICS COMPRESSION MOLDED

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DIANA P NAVIA

2011-06-01

�C para a variedade MBRA 383, enquanto o modelo de GAB foi a 35°C por MBRA 383. Calor isostérico de sorção diminuiu com o aumento do teor de umidade de equilíbrio foi encontrado um valor máximo de 87 kJ/mol e 78 kJ/mol, e mínima de 44,6 kJ/mol e 44,5 kJ/mol em amostras preparadas com o CM 7951-5 e MBRA 383, respectivamente.Water adsorption and isosteric heat were evaluated in biopolymers made from flour of two varieties of cassava (CM 7951-5 and MBRA 383, fique dust and glycerol by compression molding technique. The adsorption isotherms of polymeric samples were performed at 15,25, and 35°C in a water activity range of 0.12 to 0.98, using a gravimetric method. The adsorption experimental data were adjusted using the GAB, Caurie, Oswin, Smith, Henderson and Peleg models. The sorption isosteric heat (Qst was determined with Clausius-Clapeyron equation. The results showed that the Peleg model was adjusted appropriately to experimental values of adsorption at 15, 25 and 35°C in the samples prepared with the variety CM 7951-5 and 15 and 25°C for the variety MBRA 383, while the GAB model was at 35°C for MBRA 383. Isosteric heat of sorption decreased with increase in equilibrium moisture content finding the maximum in 87Kj/mol and 78 Kj/mol, and minimum in 44.6 Kj/mol and 44.5 Kj/mol in samples made with CM 7951-5y MBRA 383 respectively.

Density, viscosity, and saturated vapor pressure of ethyl trifluoroacetate

International Nuclear Information System (INIS)

Huang, Zhixian; Jiang, Haiming; Li, Ling; Wang, Hongxing; Qiu, Ting

2015-01-01

Highlights: • Density of ethyl trifluoroacetate was measured and its thermal expansion coefficient was determined. • Viscosity of ethyl trifluoroacetate was measured and fitted to the Andrade equation. • Saturated vapor pressure of ethyl trifluoroacetate was reported. • The Clausius–Clapeyron equation was used to calculate the molar evaporation enthalpy of ethyl trifluoroacetate. - Abstract: The properties of ethyl trifluoroacetate (CF 3 COOCH 2 CH 3 ) were measured as a function of temperature: density (278.08 to 322.50) K, viscosity (293.45 to 334.32) K, saturated vapor pressure (293.35 to 335.65) K. The density data were fitted to a quadratic polynomial equation, and the viscosity data were regressed to the Andrade equation. The correlation coefficient (R 2 ) of equations for density and viscosity are 0.9997 and 0.9999, respectively. The correlation between saturated vapor pressures and temperatures was achieved with a maximum absolute relative deviation of 0.142%. In addition, the molar evaporation enthalpy in the range of T = (293.35 to 335.65) K was estimated by the Clausius–Clapeyron equation

Adsorption of Volatile Organic Compounds from Aqueous Solution by Granular Activated Carbon in Batch System

International Nuclear Information System (INIS)

Zeinali, F.; Ghoreyshi, A. A.; Najafpour, G.

2011-01-01

Chlorinated hydrocarbons and aromatics are the major volatile organic compounds that contaminate the ground water and industrial waste waters. The best way to overcome this problem is to recover the dissolved compounds in water. In order to evaluate the potential ability of granular activated carbon for recovery of volatile organic compounds from water, the equilibrium adsorption was investigated. This study deals with the adsorption of dichloromethane as a typical chlorinated volatile organic compound and toluene as the representative of aromatic volatile organic compounds on a commercial granular activated carbon. The adsorption isotherms of these two volatile organic compounds on granular activated carbon were measured at three different temperatures, toluene at 293, 303 and 313 K and dichloromethane at 298, 303 and 313 K within their solubility concentration range in water. The maximum adsorption capacity of dichloromethane and toluene adsorption by granular activated carbon was 4 and 0.2 mol/Kg-1, respectively. The experimental data obtained were correlated with different adsorption isotherm models. The Langmuir model was well adapted to the description of dichloromethane adsorption on granular activated carbon at all three temperatures, while the adsorption of toluene on granular activated carbon was found to be well described by the Langmuir-BET hybrid model at all three temperatures. The heat of adsorption was also calculated based on the thermodynamic equation of Clausius Clapeyron, which indicates the adsorption process is endothermic for both compounds.

Development and characterization of a new encapsulating agent from orange juice by-products.

Science.gov (United States)

Kaderides, Kyriakos; Goula, Athanasia M

2017-10-01

The replacement of maltodextrins as carriers for the spray drying of sticky and sugar based bioactives is an important development for the food industry. In this work, orange juice industry by-product was used to obtain a high dietary fiber powder to be used as carrier material. This powder was characterized with respect to its physical and chemical properties related to the process of encapsulation by spray drying. Adsorption isotherms of orange waste powder were determined at 30, 45, and 60°C. The data were fitted to several models including two-parameter (BET, Halsey, Smith, and Oswin), three-parameter (GAB), and four-parameter (Peleg) relationships. The GAB model best fitted the experimental data. The isosteric heat of sorption was determined from the equilibrium sorption data using the Clausius-Clapeyron equation. Isosteric heats of sorption were found to decrease exponentially with increasing moisture content. The enthalpy-entropy compensation theory was applied to the sorption isotherms and indicated an enthalpy controlled sorption process. Glass transition temperatures (T g ) of orange waste powder conditioned at various water activities were determined and a strong plasticizing effect of water on T g was found. These data were satisfactory correlated by the Gordon and Taylor model. The critical water activity and moisture content for the orange waste powder were 0.82 and 0.18g water/g solids, respectively, at a storage temperature of 25°C. Copyright © 2017 Elsevier Ltd. All rights reserved.

Quasi-continuous transition from a Fermi liquid to a spin liquid in κ-(ET)2Cu2(CN)3.

Science.gov (United States)

Furukawa, Tetsuya; Kobashi, Kazuhiko; Kurosaki, Yosuke; Miyagawa, Kazuya; Kanoda, Kazushi

2018-01-22

The Mott metal-insulator transition-a manifestation of Coulomb interactions among electrons-is known as a discontinuous transition. Recent theoretical studies, however, suggest that the transition is continuous if the Mott insulator carries a spin liquid with a spinon Fermi surface. Here, we demonstrate the case of a quasi-continuous Mott transition from a Fermi liquid to a spin liquid in an organic triangular-lattice system κ-(ET) 2 Cu 2 (CN) 3 . Transport experiments performed under fine pressure tuning have found that as the Mott transition is approached, the Fermi liquid coherence temperature continuously falls to the scale of kelvins, with a divergent quasi-particle decay rate on the metal side, and the charge gap continuously closes on the insulator side. A Clausius-Clapeyron analysis provides thermodynamic evidence for the extremely weak first-order nature of the transition. These results provide additional support for the existence of a spinon Fermi surface, which becomes an electron Fermi surface when charges are delocalized.

Atmospheric concentration characteristics and gas-particle partitioning of PCBs in a rural area of eastern Germany

International Nuclear Information System (INIS)

Mandalakis, Manolis; Stephanou, Euripides G.

2007-01-01

Atmospheric concentrations of polychlorinated biphenyls (PCBs) were measured in 14 successive daytime and nighttime air samples collected from Melpitz, a rural site in eastern Germany. The average total concentration of PCBs was 110+/-80pgm -3 and they were predominately present in the gas phase (∼95%). Composition of individual congeners closely resembled those of Clophen A30 and Aroclor 1232. Partial vapor pressures of PCBs were well correlated with temperature and the steep slopes obtained from Clausius-Clapeyron plots (-4500 to -8000) indicated that evaporation from adjacent land surfaces still controls the atmospheric levels of these pollutants. Particle-gas partitioning coefficients (K P ) of PCBs were well correlated with the respective sub-cooled vapor pressures (P L o ), but the slopes obtained from logK P versus logP L o plots (-0.16 to -0.59) deviated significantly from the expected value of -1. Overall, gas-particle partitioning of PCBs was better simulated by Junge-Pankow than octanol/air partition coefficient-based model

Why does tropical convective available potential energy (CAPE) increase with warming?

Science.gov (United States)

Seeley, Jacob T.; Romps, David M.

2015-12-01

Recent work has produced a theory for tropical convective available potential energy (CAPE) that highlights the Clausius-Clapeyron (CC) scaling of the atmosphere's saturation deficit as a driver of increases in CAPE with warming. Here we test this so-called "zero-buoyancy" theory for CAPE by modulating the saturation deficit of cloud-resolving simulations of radiative-convective equilibrium in two ways: changing the sea surface temperature (SST) and changing the environmental relative humidity (RH). For earthlike and warmer SSTs, undilute parcel buoyancy in the lower troposphere is insensitive to increasing SST because of a countervailing CC scaling that balances the increase in the saturation deficit; however, buoyancy increases dramatically with SST in the upper troposphere. Conversely, in the RH experiment, undilute buoyancy throughout the troposphere increases monotonically with decreasing RH. We show that the zero-buoyancy theory successfully predicts these contrasting behaviors, building confidence that it describes the fundamental physics of CAPE and its response to warming.

Corresponding Relation between Warm Season Precipitation Extremes and Surface Air Temperature in South China

Institute of Scientific and Technical Information of China (English)

SUN; Wei; LI; Jian; YU; Ru-Cong

2013-01-01

Hourly data of 42 rain gauges over South China during 1966–2005 were used to analyze the corresponding relation between precipitation extremes and surface air temperature in the warm season(May to October).The results show that below 25℃,both daily and hourly precipitation extremes in South China increase with rising temperature.More extreme events transit to the two-time Clausius-Clapeyron(CC)relationship at lower temperatures.Daily as well as hourly precipitation extremes have a decreasing tendency nearly above 25℃,among which the decrease of hourly extremes is much more significant.In order to investigate the efects of rainfall durations,hourly precipitation extremes are presented by short duration and long duration precipitation,respectively.Results show that the dramatic decrease of hourly rainfall intensities above 25℃ is mainly caused by short duration precipitation,and long duration precipitation extremes rarely occur in South China when surface air temperature surpasses 28℃.

Attributable Human-Induced Changes in the Likelihood and Magnitude of the Observed Extreme Precipitation during Hurricane Harvey

Science.gov (United States)

Risser, Mark D.; Wehner, Michael F.

2017-12-01

Record rainfall amounts were recorded during Hurricane Harvey in the Houston, Texas, area, leading to widespread flooding. We analyze observed precipitation from the Global Historical Climatology Network with a covariate-based extreme value statistical analysis, accounting for both the external influence of global warming and the internal influence of El Niño-Southern Oscillation. We find that human-induced climate change likely increased the chances of the observed precipitation accumulations during Hurricane Harvey in the most affected areas of Houston by a factor of at least 3.5. Further, precipitation accumulations in these areas were likely increased by at least 18.8% (best estimate of 37.7%), which is larger than the 6-7% associated with an attributable warming of 1°C in the Gulf of Mexico and Clausius-Clapeyron scaling. In a Granger causality sense, these statements provide lower bounds on the impact of climate change and motivate further attribution studies using dynamical climate models.

Stress- and Magnetic Field-Induced Martensitic Transformation at Cryogenic Temperatures in Fe-Mn-Al-Ni Shape Memory Alloys

Science.gov (United States)

Xia, Ji; Xu, Xiao; Miyake, Atsushi; Kimura, Yuta; Omori, Toshihiro; Tokunaga, Masashi; Kainuma, Ryosuke

2017-12-01

Stress-induced and magnetic-field-induced martensitic transformation behaviors at low temperatures were investigated for Fe-Mn-Al-Ni alloys. The magnetic-field-induced reverse martensitic transformation was directly observed by in situ optical microscopy. Magnetization measurements under pulsed magnetic fields up to 50 T were carried out at temperatures between 4.2 and 125 K on a single-crystal sample; full magnetic-field-induced reverse martensitic transformation was confirmed at all tested temperatures. Compression tests from 10 to 100 K were conducted on a single-crystal sample; full shape recovery was obtained at all tested temperatures. It was found that the temperature dependence of both the critical stress and critical magnetic field is small and that the transformation hysteresis is less sensitive to temperature even at cryogenic temperatures. The temperature dependence of entropy change during martensitic transformation up to 100 K was then derived using the Clausius-Clapeyron relation with critical stresses and magnetic fields.

Analysis on flow characteristic of nuclear heating reactor

International Nuclear Information System (INIS)

Jiang Shengyao; Wu Xinxin

1997-06-01

The experiment was carried out on the test loop HRTL-5, which simulates the geometry and system design of a 5 MW Nuclear heating reactor. The analysis was based on a one-dimensional two-phase flow drift model with conservation equations for mass, steam mass, energy and momentum. Clausius-Clapeyron equation was used for the calculation of flashing front in the riser. A set of ordinary equation, which describes the behavior of two-phase flow in the natural circulation system, was derived through integration of the above conservation equations in subcooled boiling region, bulk boiling region in the heated section and in the riser. The method of time-domain was used for the calculation. Both static and dynamic results are presented. System pressure, inlet subcooling and heat flux are varied as input parameters. The results show that, firstly, subcooled boiling in the heated section and void flashing in the riser have significant influence on the distribution of the void fraction, mass flow rate and stability of the system, especially at lower pressure, secondly, in a wide range of two-phase flow conditions, only subcooled boiling occurs in the heated section. For the designed two-phase regime operation of the 5 MW nuclear heating reactor, the temperature at the core exit has not reaches its saturation value. Thirdly, the mechanism of two-phase flow oscillation, namely, 'zero-pressure-drop', is described. In the wide range of inlet subcooling (0 K<ΔT<28 K) there exists three regions for system flow condition, namely, (1) stable two-phase flow, (2) bulk and subcooled boiling unstable flow, (3) subcooled boiling and single phase stable flow. The response of mass flow rate, after a small disturbance in the heat flux, is showed in the above inlet subcooling range, and based on it the instability map of the system is given through experiment and calculation. (3 refs., 9 figs.)

Thermodynamic properties of water sorption of jackfruit (Artocarpus heterophyllus Lam. as a function of moisture content Propriedades termodinâmicas de sorção de água da jaca (Artocarpus heterophyllus Lam. em função do teor de umidade

Directory of Open Access Journals (Sweden)

Ana Paula Prette

2013-03-01

Full Text Available The Jackfruit tree is one of the most significant trees in tropical home gardens and perhaps the most widespread and useful tree in the important genus Artocarpus. The fruit is susceptible to mechanical and biological damage in the mature state, and some people find the aroma of the fruit objectionable, particularly in confined spaces. The dehydration process could be an alternative for the exploitation of this product, and the relationship between moisture content and water activity provides useful information for its processing and storage. The aim of this study was to determine the thermodynamic properties of the water sorption of jackfruit (Artocarpus heterophyllus Lam. as a function of moisture content. Desorption isotherms of the different parts of the jackfruit (pulp, peduncle, mesocarp, peel, and seed were determined at four different temperatures (313.15, 323.15, 333.15, and 343.15 K in a water activity range of 0.02-0.753 using the static gravimetric method. Theoretical and empirical models were used to model the desorption isotherms. An analytical solution of the Clausius-Clapeyron equation was proposed to calculate the isosteric heat of sorption, the differential entropy, and Gibbs' free energy using the Guggenhein-Anderson-de Boer and Oswin models considering the effect of temperature on the hygroscopic equilibrium.A jaqueira é uma das árvores mais significativas nos quintais tropicais e, talvez, a árvore mais importante e útil do gênero Artocarpus. O fruto é suscetível a danos mecânicos e biológicos no estado maduro, e seu aroma é desagradável para algumas pessoas, quando em espaços fechados. O processo de desidratação pode ser uma alternativa para a exploração deste produto, e a relação entre a umidade e a atividade de água fornece informações úteis para seu processamento e armazenamento. O objetivo do trabalho foi determinar as propriedades termodinâmicas de sorção da água em frutos de jaca (Artocarpus

Vapor Pressure Data and Analysis for Selected Organophosphorus Compounds, CMMP, DPMP, DMEP, and DEEP: Extrapolation of High-Temperature Data

Science.gov (United States)

2018-04-01

comparison. The correlation equations are presented using two common units systems , one with temperature given in kelvin (T) and pressure in pascal...This report documents vapor pressure data and correlations for four phosphonate ester compounds that have molecular structures similar to those of...Antoine equation Clausius–Clapeyron equation Enthalpy of vaporization Volatility Differential scanning calorimetry (DSC) Vapor saturation Normal boiling

Isotermas de adsorción en harina de maíz (Zea mays L. Isotermas de adsorção em farinha de milho (Zea mays L.

Directory of Open Access Journals (Sweden)

Antonio Vega Gálvez

2006-12-01

Full Text Available El objetivo de este trabajo fue determinar las isotermas de adsorción de humedad de harina de maíz a tres temperaturas (7, 22 y 45 °C para el rango de a w entre 0,10 y 0,95. Las isotermas se modelaron utilizando siete ecuaciones comúnmente aplicadas en alimentos. La calidad de ajuste se evaluó con el coeficiente de regresión (r² y el porcentaje de error medio relativo (% E, en función de los cuales se observó que los modelos propuestos por GAB, Oswin y Halsey ajustaron de mejor manera los datos experimentales. La humedad de la monocapa (Xm y la humedad de seguridad (X S presentaron dependencia con la temperatura con valores de Ea de 13,6 y 3,3 kJ/mol, respectivamente. Se cálculo el calor isostérico de adsorción (Q S usando la ecuación de Clausius-Clapeyron, obteniéndose un máximo de 21 kJ/mol, para una humedad de 0,075 g agua/g m.s., este parámetro se modeló utilizando la ecuación propuesta por Tsami.O objectivo deste trabalho foi determinar as isotermas de adsorção de umidade da farinha de milho a três temperaturas (7, 22 e 45 °C para um rango de a w entre 0,10 e 0,95. As isotermas foram modelizadas por meio de sete equações normalmente utilizadas em alimentos. A qualidade do ajuste foi avaliada mediante o coeficiente de regressão (r² e a porcentagem de erro médio relativo (% E, em função dos quais se observou que os modelos propostos por GAB, Oswin e Halsey apresentaram um melhor ajuste dos dados experimentais. A umidade da monocapa (Xm e a umidade de segurança (X S mostraram dependência da temperatura com valores de Ea de 13,6 e 3,3 kJ/mol, respectivamente. Calculou-se o calor isostérico de adsorção (Q S utilizando-se a equação de Clausius-Clapeyron, obtendo-se um máximo de 21 kJ/mol. Para uma umidade de 0,075 g água/g m.s., este parâmetro modelizou-se utilizando a equação proposta por Tsami.

Moisture sorption–desorption characteristics and the corresponding thermodynamic properties of carvedilol phosphate

Directory of Open Access Journals (Sweden)

Ravikiran Allada

2017-01-01

Full Text Available Aims: Carvedilol phosphate (CDP is a nonselective beta-blocker used for the treatment of heart failures and hypertension. In this work, moisture sorption–desorption characteristics and thermodynamic properties of CDP have been investigated. Materials and Methods: The isotherms were determined using dynamic vapor sorption analyzer at different humidity conditions (0%–90% relative humidity and three pharmaceutically relevant temperatures (20°C, 30°C, and 40°C. The experimental sorption data determined were fitted to various models, namely, Brunauer–Emmett–Teller; Guggenheim-Anderson-De Boer (GAB; Peleg; and modified GAB. Isosteric heats of sorption were evaluated through the direct use of sorption isotherms by means of the Clausius-Clapeyron equation. Statistical Analysis Used: The sorption model parameters were determined from the experimental sorption data using nonlinear regression analysis, and mean relative percentage deviation (P, correlation (Correl, root mean square error, and model efficiency were considered as the criteria to select the best fit model. Results: The sorption–desorption isotherms have sigmoidal shape – confirming to Type II isotherms. Based on the statistical data analysis, modified GAB model was found to be more adequate to explain sorption characteristics of CDP. It is noted that the rate of adsorption and desorption is specific to the temperature at which it was being studied. It is observed that isosteric heat of sorption decreased with increasing equilibrium moisture content. Conclusions: The calculation of the thermodynamic properties was further used to draw an understanding of the properties of water and energy requirements associated with the sorption behavior. The sorption–desorption data and the set of equations are useful in the simulation of processing, handling, and storage of CDP and further behavior during manufacture and storage of CDP formulations.

A new method to determine the water activity and the net isosteric heats of sorption for low moisture foods at elevated temperatures.

Science.gov (United States)

Tadapaneni, Ravi Kiran; Yang, Ren; Carter, Brady; Tang, Juming

2017-12-01

In recent years, research studies have shown that the thermal resistance of foodborne pathogens in the low moisture foods is greatly influenced by the water activity (a w ) at temperatures relevant to thermal treatments for pathogen control. Yet, there has been a lack of an effective method for accurate measurement of a w at those temperatures. Thus, the main aim of this study was to evaluate a new method for measuring a w of food samples at elevated temperatures. An improved thermal cell with a relative humidity and temperature sensor was used to measure the a w of the three different food samples, namely, organic wheat flour, almond flour, and non-fat milk powder, over the temperature range between 20 and 80°C. For a constant moisture content, the a w data was used to estimate the net isosteric heat of sorption (q st ). The q st values were then used in the Clausius Clapeyron equation (CCE) equation to estimate the moisture sorption isotherm for all test food samples at different temperatures. For all the tested samples of any fixed moisture content, a w value generally increased with the temperature. The energy for sorption decreased with increasing moisture content. With the experimentally determined q st value, CCE describes well about the changes in a w of the food samples between 20 and 80°C. This study presents a method to obtain a w of a food sample for a specific moisture content at different temperatures which could be extended to obtain q st values for different moisture contents and hence, the moisture sorption isotherm of a food sample at different temperatures. Copyright © 2017 Elsevier Ltd. All rights reserved.

MODELADO DE LAS ISOTERMAS DE SORCIÓN Y DEL CALOR ISOSTÉRICO DE SORCIÓN EN PULPA DE MANGO cv. TOMMY ATKINS MODELAGEM DE ISOTERMAS DE SORÇÃO E CALOR ISOSTÉRICO DE SORÇÃO DE POLPA DE MANGA cv. TOMMY ATKINS MODELING SORPTION ISOTHERMS AND ISOSTERIC HEAT OF SORPTION OF MANGO PULP cv. TOMMY ATKINS

Directory of Open Access Journals (Sweden)

JOSÉ BON

2012-12-01

polpa de manga (Mangifera indica L. cv. Tommy Atkins foi analisada para determinar as isotermas de sorção. A atividade de água foi medida empregando um higrômetro elétrico a cinco diferentes temperaturas (10, 20, 30, 40 e 50 °C e amplas faixas de conteúdo de umidade (2.829 - 0.031 kg kg-1 b.s. e atividade de água (0.977 - 0.215. O modelo de teórico de GAB e os modelos empíricos de (Oswin, Henderson, Halsey e Ratti foram empregados para modelar as isotermas de sorção. Depois de considerar diferentes critérios, o modelo de GAB apresentou a melhor opção para representar o equilíbrio higroscópico da polpa de manga (RMSE = 0.057, VAR = 0.996.As isotermas mostraram um comportamento acorde aos materiais agroalimentícios e similar ao reportado para polpa de manga de outras variedades. O calor isostérico de sorção foi calculado utilizando a equação de Clausius-Clapeyron a partir do modelo de GAB. Observou-se uma diminuição no calor isostérico de sorção quando aumentou o conteúdo de umidade de equilíbrio, com um grande efeito da umidade em valores abaixo de 0.8 kg kg-1 (b.s..Mango is an agricultural product of great economic importance for various developing countries, which has increased demand for its nutritional properties and exotic characteristics. The relationship between moisture content and water activity provides useful information for mango processing, especially for drying and storage operations. Water activity and moisture content of mango pulp (Mangiferaindica L. cv. Tommy Atkins were analyzed to determine the sorption isotherms. The water activity was measured using an electric hygrometer at five different temperatures (10, 20, 30, 40 and 50 °C and wide ranges of moisture content (2.829-0.031 kg kg-1 d.b. and water activity (0.977-0.215. One theoretical (GAB and four empirical equations (Oswin, Henderson, Halsey and Ratti were used for modeling the sorption isotherms. After following several criteria to evaluate the models, the GAB

Unified first law and some general prescription. A redefinition of surface gravity

Energy Technology Data Exchange (ETDEWEB)

Haldar, Sourav; Bhattacharjee, Sudipto; Chakraborty, Subenoy [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India)

2017-09-15

The paper contains an extensive study of the unified first law (UFL) in the Friedmann-Robertson-Walker spacetime model. By projecting the UFL along the Kodama vector the second Friedmann equation can be obtained. Also studying the UFL on the event horizon it is found that the Clausius relation cannot be obtained from the UFL by projecting it along the tangent to the event horizon as it can be for the trapping horizon. However, it is shown in the present work that Clausius relation can be obtained by projecting the UFL along the Kodama vector on the horizon and the result is found to be true for any horizon. Finally motivated by the Unruh temperature for the Rindler observer, surface gravity is redefined and a Clausius relation is obtained from the UFL by projecting it along a vector analogous to the Kodama vector. (orig.)

An experimental study on pseudoelasticity of a NiTi-based damper for civil applications

Science.gov (United States)

Nespoli, Adelaide; Bassani, Enrico; Della Torre, Davide; Donnini, Riccardo; Villa, Elena; Passaretti, Francesca

2017-10-01

In this work, a pseudoelastic damper composed by NiTi wires is tested at 0.5, 1 and 2 Hz for 1000 mechanical cycles. The damping performances were evaluated by three key parameters: the damping capacity, the dissipated energy per cycle and the maximum force. During testing, the temperature of the pseudoelastic elements was registered as well. Results show that the damper assures a bi-directional motion throughout the 1000 cycles together with the maintenance of the recentering. It was observed a stabilization process in the first 50 mechanical cycles, where the key parameters reach stable values; in particular it was found that the damping capacity and the dissipated energy both decrease with frequency. Besides, the mean temperature of the pseudoleastic elements reaches a stable value during tests and confirms the different response of the pseudoelastic wires accordingly with the specific length and stain. Finally, interesting thermal effects were observed at 1 and 2 Hz: at these frequencies and at high strains, the maximum force increases but the temperature of the NiTi wire decreases being in contraddiction with the Clausius-Clapeyron law.

Effects of sample size on estimation of rainfall extremes at high temperatures

Science.gov (United States)

Boessenkool, Berry; Bürger, Gerd; Heistermann, Maik

2017-09-01

High precipitation quantiles tend to rise with temperature, following the so-called Clausius-Clapeyron (CC) scaling. It is often reported that the CC-scaling relation breaks down and even reverts for very high temperatures. In our study, we investigate this reversal using observational climate data from 142 stations across Germany. One of the suggested meteorological explanations for the breakdown is limited moisture supply. Here we argue that, instead, it could simply originate from undersampling. As rainfall frequency generally decreases with higher temperatures, rainfall intensities as dictated by CC scaling are less likely to be recorded than for moderate temperatures. Empirical quantiles are conventionally estimated from order statistics via various forms of plotting position formulas. They have in common that their largest representable return period is given by the sample size. In small samples, high quantiles are underestimated accordingly. The small-sample effect is weaker, or disappears completely, when using parametric quantile estimates from a generalized Pareto distribution (GPD) fitted with L moments. For those, we obtain quantiles of rainfall intensities that continue to rise with temperature.

Statistical thermodynamics of nonequilibrium processes

CERN Document Server

Keizer, Joel

1987-01-01

The structure of the theory ofthermodynamics has changed enormously since its inception in the middle of the nineteenth century. Shortly after Thomson and Clausius enunciated their versions of the Second Law, Clausius, Maxwell, and Boltzmann began actively pursuing the molecular basis of thermo­ dynamics, work that culminated in the Boltzmann equation and the theory of transport processes in dilute gases. Much later, Onsager undertook the elucidation of the symmetry oftransport coefficients and, thereby, established himself as the father of the theory of nonequilibrium thermodynamics. Com­ bining the statistical ideas of Gibbs and Langevin with the phenomenological transport equations, Onsager and others went on to develop a consistent statistical theory of irreversible processes. The power of that theory is in its ability to relate measurable quantities, such as transport coefficients and thermodynamic derivatives, to the results of experimental measurements. As powerful as that theory is, it is linear and...

Thermodynamic study of 1,2,3-triphenylbenzene and 1,3,5-triphenylbenzene

International Nuclear Information System (INIS)

Ribeiro da Silva, Manuel A.V.; Santos, Luis M.N.B.F.; Lima, Luis M. Spencer S.

2010-01-01

The energetic study of 1,2,3-triphenylbenzene (1,2,3-TPhB) and 1,3,5-triphenylbenzene (1,3,5-TPhB) isomers was carried out by making use of the mini-bomb combustion calorimetry and Knudsen mass-loss effusion techniques. The mini-bomb combustion calorimetry technique was used to derive the standard (p o = 0.1 MPa) molar enthalpies of formation in the crystalline state from the measured standard molar energies of combustion for both isomers. The Knudsen mass-loss effusion technique was used to measure the dependence with the temperature of the vapour pressure of crystalline 1,2,3-TPhB, which allowed the derivation of the standard molar enthalpy of sublimation, by application of the Clausius-Clapeyron equation. The sublimation study of 1,3,5-TPhB had been performed previously. From the combination of data obtained by both techniques, the standard molar enthalpies of formation in the gaseous state, for both isomers, at T = 298.15 K, were calculated. The results indicate a higher stability of the 1,3,5-TPhB isomer relative to 1,2,3-TPhB, similarly to the terphenyls. Nevertheless, the 1,2,3-TPhB isomer is not as energetically destabilized as one might expect, supporting the existence of a π-π displacive stacking interaction between both pairs of outer phenyl rings. The volatility difference between the two isomers is ruled by the enthalpy of sublimation. The volatility of the 1,2,3-TPhB is two orders of magnitude higher than the 1,3,5-TPhB isomer, at T = 298.15 K.

Exploring the Clapeyron Equation and the Phase Rule Using a Mechanical Drawing Toy

Science.gov (United States)

Darvesh, Katherine V.

2013-01-01

The equilibrium between phases is a key concept from the introductory physical chemistry curriculum. Phase diagrams display which phase is the most stable at a given temperature and pressure. If more than one phase has the lowest Gibbs energy, then those phases are in equilibrium under those conditions. An activity designed to demonstrate the…

Optimization of the drying of Moringa oleifera leaves by ...

African Journals Online (AJOL)

Moringa oleifera leaves are increasingly used as a dietary supplement. The present study deals with the estimation of its thermophysical properties. It is based on the Clausius-Clayperon and Gibbs-Helmholtz equations. This study required knowledge of the sorption isotherms obtained by the static gravimetric method in the ...

Seasonal trends in vegetation and atmospheric concentrations of PAHs and PBDEs near a sanitary landfill

Science.gov (United States)

St-Amand, Annick D.; Mayer, Paul M.; Blais, Jules M.

Spruce needle and atmospheric (gaseous and particulate-bound) concentrations were surveyed near a sanitary landfill from February 2004 to June 2005. The influence of several parameters such as temperature, relative humidity, wind speed and direction, as well as increased domestic heating during the winter was assessed. In general, polybrominated diphenyl ethers (PBDE) and polycyclic aromatic hydrocarbons (PAH) concentrations in spruce needles increased over time and decreased following snowmelt with a minimum coinciding with bud burst of deciduous trees. Atmospheric concentrations of PBDE and PAH, both particulate-bound and gaseous phase, were linked to daily weather events and thus showed more variability than those in spruce needles. Highest PAH concentrations were encountered during the winter, likely reflecting increased emission from heating homes. Pseudo Clausius-Clapeyron plots revealed higher PBDE gaseous concentrations with increasing temperature, but showed no correlation between PAH gaseous concentrations and temperature as this effect was obscured by seasonal emission patterns. Finally, air mass back trajectories and local wind directions revealed that particulate-bound PBDEs, along with both gaseous and particulate-bound PAHs were from local sources, whereas gaseous PBDEs were likely from distant sources.

Thermodynamic properties of Heusler Fe2VSi

Science.gov (United States)

Ito, Masakazu; Kai, Keita; Furuta, Tatsuya; Manaka, Hirotaka; Terada, Norio; Hiroi, Masahiko; Kondo, Akihiro; Kindo, Koichi

2018-05-01

We investigated temperature, T, dependence of magnetization, M(T), electrical resistivity, ρ(T), and specific heat, Cp(T), for the Heusler compound Fe2VSi. M(T) shows anomalies at TN1 ˜ 115 K and at TN2 ˜ 35 K. The anomaly at TN1 is caused by the magnetic transition with a crystal structural change. On the other hand, ρ(T) and Cp(T) show only anomaly at TN1, and no trace of anomaly at TN2 is observed. Because of the irreversibility of M(T), which is the characteristic of spin-glass freezing, appears below TN2, a spin-glass freezing may occur at TN2. From the analogy of the Heusler compound (Fe1-xVx ) 3Si with the cubic D03 crystal structure, (0 ≤ x ≤ 0.2), we suggested that the atomic disorder of V site by the Fe atoms gives rise to the magnetic frustration. This could be cause for the spin-glass freezing. By the Clausius-Clapeyron relation, pressure, P, derivative of TN1, (d/TN 1 d P ), is estimated to be ˜-10 K/Gpa.

Growing importance of atmospheric water demands on the hydrologcial condition of East Asia

Science.gov (United States)

Park, C. E.; Ho, C. H.; Jeong, S. J.; Park, H.

2015-12-01

As global temperature increases, enhanced exchange of fresh water between the surface and atmosphere expected to make dry regions drier and wet regions wetter. This concept is well fitted for the ocean, but oversimplified for the land. How the climate change causes the complex patterns of the continental dryness change is one of challenging questions. Here we investigate the observed dryness changes of the land surface by examining the quantitative influence of several climate parameters on the background aridity changes over East Asia, containing various climate regimes from cold-arid to warm-humid regions, using observations of 189 stations covering the period from 1961 to 2010. Overall mean aridity trend is changed from negative to positive around early 1990s. The turning of dryness trend is largely influenced by sharp increase in atmospheric water demands, regardless of the background climate. The warming induced increase in water demands is larger in warm-humid regions than in cold-arid region due to the Clausius-Clapeyron relation between air temperature and saturation vapor pressure. The results show the drying of anthropogenic warming already begins and influences on the patterns of dryness change over the land surface.

Enhanced hydrological extremes in the western United States under global warming through the lens of water vapor wave activity

Energy Technology Data Exchange (ETDEWEB)

Lu, Jian; Xue, Daokai; Gao, Yang; Chen, Gang; Leung, Lai-Yung; Staten, Paul W.

2018-04-23

Understanding how regional hydrological extremes would respond to warming is a grand challenge to the community of climate change research. To address this challenge, we construct an analysis framework based on column integrated water vapor (CWV) wave activity to diagnose the wave component of the hydrological cycle that contributes to hydrological extremes. By applying the analysis to the historical and future climate projections from the CMIP5 models, we found that the wet-versus-dry disparity of daily net precipitation along a zonal band can increase at a super Clausius-Clapeyron rate due to the enhanced stirring length of wave activity at the poleward flank of the mean storm track. The local variant of CWV wave activity reveals the unique characteristics of atmospheric rivers (ARs) in terms of their transport function, enhanced mixing and hydrological cycling rate (HC). Under RCP8.5, the local moist wave activity increases by ~40% over the northeastern Pacific by the end of the 21st century, indicating more ARs hitting the west coast, giving rise to a ~20% increase in the related hydrological extremes − $ despite a weakening of the local HC.

Spacetime thermodynamics in the presence of torsion

Science.gov (United States)

Dey, Ramit; Liberati, Stefano; Pranzetti, Daniele

2017-12-01

It was shown by Jacobson in 1995 that the Einstein equation can be derived as a local constitutive equation for an equilibrium spacetime thermodynamics. With the aim to understand if such thermodynamical description is an intrinsic property of gravitation, many attempts have been made so far to generalize this treatment to a broader class of gravitational theories. Here we consider the case of the Einstein-Cartan theory as a prototype of theories with nonpropagating torsion. In doing so, we study the properties of Killing horizons in the presence of torsion, establish the notion of local causal horizon in Riemann-Cartan spacetimes, and derive the generalized Raychaudhuri equation for these kinds of geometries. Then, starting with the entropy that can be associated to these local causal horizons, we derive the Einstein-Cartan equation by implementing the Clausius equation. We outline two ways of proceeding with the derivation depending on whether we take torsion as a geometric field or as a matter field. In both cases we need to add internal entropy production terms to the Clausius equation as the shear and twist cannot be taken to be 0 a priori for our setup. This fact implies the necessity of a nonequilibrium thermodynamics treatment for the local causal horizon. Furthermore, it implies that a nonzero twist at the horizon in general contributes to the Hartle-Hawking tidal heating for black holes with possible implications for future observations.

Solid vapor pressure for five heavy PAHs via the Knudsen effusion method

International Nuclear Information System (INIS)

Fu Jinxia; Suuberg, Eric M.

2011-01-01

Highlights: → We report on vapor pressures and enthalpies of fusion and sublimation of five heavy PAHs. → Solid vapor pressures were measured using Knudsen effusion method. → Solid vapor pressures for benzo[b]fluoranthene, and indeno[1,2,3-cd]pyrene have not been published in the open literature. → Reported subcooled liquid state vapor pressures may or may not lend themselves to correction to sublimation vapor pressure. → Subcooled liquid state vapor pressures might sometimes actually be closer to actual solid state sublimation vapor pressures. - Abstract: Polycyclic aromatic hydrocarbons (PAHs) are compounds resulting from incomplete combustion and many fuel processing operations, and they are commonly found as subsurface environmental contaminants at sites of former manufactured gas plants. Knowledge of their vapor pressures is the key to predict their fate and transport in the environment. The present study involves five heavy PAHs, i.e. benzo[b]fluoranthene, benzo[k]fluoranthene, benzo[ghi]perylene, indeno[1,2,3-cd]pyrene, and dibenz[a,h]anthracene, which are all as priority pollutants classified by the US EPA. The vapor pressures of these heavy PAHs were measured by using Knudsen effusion method over the temperature range of (364 to 454) K. The corresponding values of the enthalpy of sublimation were calculated from the Clausius-Clapeyron equation. The enthalpy of fusion for the five PAHs was also measured by using differential scanning calorimetry and used to convert earlier published sub-cooled liquid vapor pressure data to solid vapor pressure in order to compare with the present results. These adjusted values do not agree with the present measured actual solid vapor pressure values for these PAHs, but there is good agreement between present results and other earlier published sublimation data.

Thermophysical properties of fluids: dynamic viscosity and thermal conductivity

Science.gov (United States)

Latini, G.

2017-11-01

Thermophysical properties of fluids strongly depend upon atomic and molecular structure, complex systems governed by physics laws providing the time evolution. Theoretically the knowledge of the initial position and velocity of each atom, of the interaction forces and of the boundary conditions, leads to the solution; actually this approach contains too many variables and it is generally impossible to obtain an acceptable solution. In many cases it is only possible to calculate or to measure some macroscopic properties of fluids (pressure, temperature, molar volume, heat capacities...). The ideal gas “law,” PV = nRT, was one of the first important correlations of properties and the deviations from this law for real gases were usefully proposed. Moreover the statistical mechanics leads for example to the “hard-sphere” model providing the link between the transport properties and the molecular size and speed of the molecules. Further approximations take into account the intermolecular interactions (the potential functions) which can be used to describe attractions and repulsions. In any case thermodynamics reduces experimental or theoretical efforts by relating one physical property to another: the Clausius-Clapeyron equation provides a classical example of this method and the PVT function must be known accurately. However, in spite of the useful developments in molecular theory and computers technology, often it is usual to search for physical properties when the existing theories are not reliable and experimental data are not available: the required value of the physical or thermophysical property must be estimated or predicted (very often estimation and prediction are improperly used as synonymous). In some cases empirical correlations are useful, if it is clearly defined the range of conditions on which they are based. This work is concerned with dynamic viscosity µ and thermal conductivity λ and is based on clear and important rules to be respected

Relation between the conditions of helium ion implantation and helium void equilibrium parameters

International Nuclear Information System (INIS)

Neklyudov, I.M.; Rybalko, V.F.; Ruzhitskij, V.V.; Tolstolutskaya, G.D.

1981-01-01

The conditions of helium thermodynamic equilibrium in a system of voids produced by helium ion bombardment of a metal sample are studied. As an initial equation for description of the equilibrium the Clapeyron equation was used. The equation is obtained relating basic parameters of helium voids (average diameter and density) to irradiation parameters (dose, ion energy (straggling)) and properties of the metal (surface tension coefficient, yield strength). Comparison of the calculations with experimental data on helium in nickel found in literature shows that the equation yields satisfactory resutls for the dose range 1.10 16 -1x10 17 cm -2 and temperatures T [ru

Nitrous oxide: Saturation properties and the phase diagram

International Nuclear Information System (INIS)

Ferreira, A.G.M.; Lobo, L.Q.

2009-01-01

The experimental values of the coordinates of the triple point and of the critical point of nitrous oxide registered in the literature were assessed and those judged as most reliable have been selected. Empirical equations have been found for the vapour pressure, sublimation and fusion curves. The virial coefficients and saturation properties as functions of temperature along the equilibrium curves are described by reduced equations. They were used in arriving at the molar enthalpies at the triple point and the normal boiling temperature. Equations for the sublimation and fusion curves resulting from the exactly integrated Clapeyron equation compare favourably with the results from the empirical treatment and the experimental data.

Suitability criterion for a refrigerant for use in solar operated sorption refrigerator

International Nuclear Information System (INIS)

Tabassum, S.A.; Mir, M.S.

1996-01-01

The thermodynamics of a sorption refrigeration cycle has been discussed representing the cycle on a clapeyron digram. The minimum generation temperature required has been determined using the 'd-a' equation which represents the sorption equilibrium of the pair, and Gibbs free energy relation. The mathematical relation developed provides a totally new basis for determination of suitability of a particular refrigerant. (author)

Suitability criterion for a refrigerant for use in solar operated sorption refrigerator

Energy Technology Data Exchange (ETDEWEB)

Tabassum, S A; Mir, M S [University of Engineering and Technology, Lahore (Pakistan). Dept. of Mechanical Engineering

1996-06-01

The thermodynamics of a sorption refrigeration cycle has been discussed representing the cycle on a clapeyron digram. The minimum generation temperature required has been determined using the `d-a` equation which represents the sorption equilibrium of the pair, and Gibbs free energy relation. The mathematical relation developed provides a totally new basis for determination of suitability of a particular refrigerant. (author).

How much might additional half a degree from a global warming of 1.5°C affects the extreme precipitation change in China?

Science.gov (United States)

Li, W.; Jiang, Z.

2017-12-01

In order to strengthen the global respond to the dangerous of global warming, Paris Agreement sets out two long-term warming goals: limiting global warming to well below 2˚C and purse effort to below 1.5˚C above pre-industrial levels. However, future climate change risks in those two warming targets show significant regional differences. This article aims to study the intensity and frequency of extreme precipitation change over China under those two global warming targets by using CMIP5 models under RCP4.5 and RCP8.5 scenario. Focus is put on the effects of the additional half degree in changing the extreme precipitation. Results show that the changes of extreme precipitation are independent of the RCP scenarios when global warming reaches the same threshold. Intensity of extreme precipitation averaged over China increase by around 6% and 11% when global warming reaches 1.5˚C and 2˚C, respectively. The additional half a degree increase makes the intensity of extreme precipitation averaged over China to increase by 4.5%, which translates to an increase close to the Clausius-Clapeyron scaling. Return period decreases by 5 years for the extra half degree warming when the 20-year return values are considered at the reference level.

Thermal study of monovalent-divalent phase transition in npBifc-F1TCNQ System

International Nuclear Information System (INIS)

Sato, Michiko; Nishio, Yutaka; Kajita, Koji; Mochida, Tomoyuki

2009-01-01

In a new molecular solid composed of di-neopentyl-biferrocene (npBifc) and fluorotetracyanoquinodimethane (F 1 TCNQ) 3 , Mochida reported the discovery of a reversible valence transfer that can be regarded as an 'ionic(I)-ionic(II)' phase transfer between the monovalent state (D + A - ) and the divalent state (D 2+ A 2- ). We have studied thermo-dynamical properties of this transformation for this complex using the differential thermal analyses (DTA). We observed a broad excess specific heat with multi-peaks attributed to micro-domain structure over the corresponding temperature range (100-150K) accompanied by temperature hysteresis of 7K. The transition entropy (ΔS) was determined to be 22 ± 2 J/mol-K and almost satisfied a Clausius-Clapeyron relation. These experimental results provide an experimental confirmation of the first order phase transition for the monovalent-divalent transfer. At the transition, we observe that the electronic degrees of freedom remained constant values, while large entropy absorbed crossing from low temperature phase to high temperature one is contributed by the lattice one. We finally estimated the internal energy and concluded that delicate energy valance between Madelung, ionization and affinity energies enable this system to exhibit a temperature induce monovalent-divalent phase transition.

Thermal study of monovalent-divalent phase transition in npBifc-F{sub 1}TCNQ System

Energy Technology Data Exchange (ETDEWEB)

Sato, Michiko; Nishio, Yutaka; Kajita, Koji [Department of Physics, Faculty of Science, Toho University, Miyama 2-2-1, Funabashi, Chiba, 274-8510 (Japan); Mochida, Tomoyuki, E-mail: nishio@ph.sci.toho-u.ac.j [Department of Chemistry, Faculty of Science, Kobe University, Rokkodai, Nada, Kobe 657-8501 (Japan)

2009-03-01

In a new molecular solid composed of di-neopentyl-biferrocene (npBifc) and fluorotetracyanoquinodimethane (F{sub 1}TCNQ){sub 3}, Mochida reported the discovery of a reversible valence transfer that can be regarded as an 'ionic(I)-ionic(II)' phase transfer between the monovalent state (D{sup +}A{sup -}) and the divalent state (D{sup 2+}A{sup 2-}). We have studied thermo-dynamical properties of this transformation for this complex using the differential thermal analyses (DTA). We observed a broad excess specific heat with multi-peaks attributed to micro-domain structure over the corresponding temperature range (100-150K) accompanied by temperature hysteresis of 7K. The transition entropy (DELTAS) was determined to be 22 +- 2 J/mol-K and almost satisfied a Clausius-Clapeyron relation. These experimental results provide an experimental confirmation of the first order phase transition for the monovalent-divalent transfer. At the transition, we observe that the electronic degrees of freedom remained constant values, while large entropy absorbed crossing from low temperature phase to high temperature one is contributed by the lattice one. We finally estimated the internal energy and concluded that delicate energy valance between Madelung, ionization and affinity energies enable this system to exhibit a temperature induce monovalent-divalent phase transition.

EFFECT OF DRYING METHODS ON THE THERMODYNAMIC PROPERTIES OF BLACKBERRY PULP POWDER

Directory of Open Access Journals (Sweden)

GLORIA I. GIRALDO GÓMEZ

2011-01-01

Full Text Available Se obtuvieron cuatros clases de polvos deshidratados de mora encapsulados con maltodextrina utilizando secado por vibro-fluidizacion (VF, por aspersion (SD vacio (VD y liofilizacion (FD. Se determinaron los datos de de humedad de equilibrio de los polvos de pulpa de mora con 18% de maltodextrina a temperaturas de 20, 30, 40 y 50°C usando el metodo estatico gravimetrico para el intervalo de actividad de agua entre 0.06.0.90. Los valores experimentales del contenido de humedad de equilibrio en funcion de la actividad de agua fueron ajustados con el modelo de Guggenheim.Anderson.de Boer (GAB hallandose una buena concordancia entre los valores experimentales y los calculados. El calor isosterico de sorcion, calculado utilizando la ecuacion de Clausius.Clapeyron a partir de los datos de equilibrio, se incremento con el aumento de la temperatura y fue ajustado con una relacion exponencial. Para muestras de polvos liofilizadas, vibrofluidizadas y a vacio, el calor de sorcion fue menor (mas negativo que los calculados para muestras secas en el secador por aspersion. La teoria de la compensacion entalpia-entropia fue aplicada a las isotermas de sorcion y de las graficas de AH contra AS se obtuvieron las temperaturas isocineticas, indicando un proceso de sorcion controlado por la entalpia.

Linkage Between Hourly Precipitation Events and Atmospheric Temperature Changes over China during the Warm Season

Science.gov (United States)

Miao, Chiyuan; Sun, Qiaohong; Borthwick, Alistair G. L.; Duan, Qingyun

2016-01-01

We investigated changes in the temporospatial features of hourly precipitation during the warm season over mainland China. The frequency and amount of hourly precipitation displayed latitudinal zonation, especially for light and moderate precipitation, which showed successive downward change over time in northeastern and southern China. Changes in the precipitation amount resulted mainly from changes in frequency rather than changes in intensity. We also evaluated the linkage between hourly precipitation and temperature variations and found that hourly precipitation extreme was more sensitive to temperature than other categories of precipitation. A strong dependency of hourly precipitation on temperature occurred at temperatures colder than the median daily temperature; in such cases, regression slopes were greater than the Clausius-Clapeyron (C-C) relation of 7% per degree Celsius. Regression slopes for 31.6%, 59.8%, 96.9%, and 99.1% of all stations were greater than 7% per degree Celsius for the 75th, 90th, 99th, and 99.9th percentiles for precipitation, respectively. The mean regression slopes within the 99.9th percentile of precipitation were three times the C-C rate. Hourly precipitation showed a strong negative relationship with daily maximum temperature and the diurnal temperature range at most stations, whereas the equivalent correlation for daily minimum temperature was weak. PMID:26931350

Linking increases in hourly precipitation extremes to atmospheric temperature and moisture changes

International Nuclear Information System (INIS)

Lenderink, Geert; Van Meijgaard, Erik

2010-01-01

Relations between hourly precipitation extremes and atmospheric temperature and moisture derived for the present-day climate are studied with the aim of understanding the behavior (and the uncertainty in predictions) of hourly precipitation extremes in a changing climate. A dependency of hourly precipitation extremes on the daily mean 2 m temperature of approximately two times the Clausius-Clapeyron (CC) relation is found for temperatures above 10 deg. C. This is a robust relation obtained in four observational records across western Europe. A dependency following the CC relation can be explained by the observed increase in atmospheric (absolute) humidity with temperature, whereas the enhanced dependency (compared to the CC relation) appears to be caused by dynamical feedbacks owing to excess latent heat release in extreme showers. Integrations with the KNMI regional climate model RACMO2 at 25 km grid spacing show that changes in hourly precipitation extremes may indeed considerably exceed the prediction from the CC relation. The results suggests that increases of + 70% or even more are possible by the end of this century. However, a different regional model (CLM operated at ETHZ) predicts much smaller increases; this is probably caused by a too strong sensitivity of this model to a decrease in relative humidity.

MOISTURE ADSORPTION ISOTHERMS IN YELLOW PITAHAYA (Selenicereusmegalanthus

Directory of Open Access Journals (Sweden)

ALFREDO AYALA APONTE

2011-01-01

Full Text Available Se determinaron las isotermas de adsorción de humedad en pitahaya amarrilla a 15, 25, y 35ºC mediante el método gravímetro en el intervalo de actividad de agua (aw entre 0.111 y 0.901. Los valores experimentales de adsorción se ajustaron mediante los modelos de GAB, BET, Henderson, Smith, Caurie, y Peleg. El calor isostérico de adsorción (Qst se determinó mediante la ecuación de Clausius- Clapeyron. Los resultados mostraron que las isotermas fueron de tipo III. El contenido de humedad de equilibrio (CHE presentó dependencia con la temperatura, disminuyendo con el aumento de esta para un valor constante de aw. El modelo GAB fue el que presentó mejor ajuste de los valores experimentales. El Qst disminuyó con el aumento del CHE, variando de 57.154 a 45.79 kJ/mol para humedades de 0.05 y 0.4 (g agua/g ms, respectivamente. Estos resultados son de interés para establecer las mejores condiciones de almacenamiento de la pitahaya deshidratada, así como la predicción de la vida útil, y el diseño de empaque.

Notes on Well-Posed, Ensemble Averaged Conservation Equations for Multiphase, Multi-Component, and Multi-Material Flows

International Nuclear Information System (INIS)

Ray A. Berry

2005-01-01

At the INL researchers and engineers routinely encounter multiphase, multi-component, and/or multi-material flows. Some examples include: Reactor coolant flows Molten corium flows Dynamic compaction of metal powders Spray forming and thermal plasma spraying Plasma quench reactor Subsurface flows, particularly in the vadose zone Internal flows within fuel cells Black liquor atomization and combustion Wheat-chaff classification in combine harvesters Generation IV pebble bed, high temperature gas reactor The complexity of these flows dictates that they be examined in an averaged sense. Typically one would begin with known (or at least postulated) microscopic flow relations that hold on the ''small'' scale. These include continuum level conservation of mass, balance of species mass and momentum, conservation of energy, and a statement of the second law of thermodynamics often in the form of an entropy inequality (such as the Clausius-Duhem inequality). The averaged or macroscopic conservation equations and entropy inequalities are then obtained from the microscopic equations through suitable averaging procedures. At this stage a stronger form of the second law may also be postulated for the mixture of phases or materials. To render the evolutionary material flow balance system unique, constitutive equations and phase or material interaction relations are introduced from experimental observation, or by postulation, through strict enforcement of the constraints or restrictions resulting from the averaged entropy inequalities. These averaged equations form the governing equation system for the dynamic evolution of these mixture flows. Most commonly, the averaging technique utilized is either volume or time averaging or a combination of the two. The flow restrictions required for volume and time averaging to be valid can be severe, and violations of these restrictions are often found. A more general, less restrictive (and far less commonly used) type of averaging known as

A study of fluid alkali metals in the critical region

International Nuclear Information System (INIS)

Balasubramanian, R.

2006-01-01

On the basis of the generalised van der Waals equation of state, Riedel's thermodynamic similarity parameter, a measure of the temperature dependence of vapour pressure in the critical region is determined for caesium, rubidium and potassium. This generalised equation differs from the known van der Waals equation of state by the modified expression for molecular pressure. The results of determination of Riedel's thermodynamic similarity parameter of caesium, rubidium and potassium are in good agreement with experimental data. Moreover, the given generalised van der Waals equation of state yields a better fit with experimental data on Riedel's thermodynamic similarity parameter for fluid alkali metals when compared with other correlations such as Van Ness and Abbott equation, Pitzer expansion, Pitzer acentric factor correlation, modified Rackett technique, Lee-Kesler vapour pressure relation and Clausius-Clayperon equation

Microstructural evolution and mechanical properties of hypereutectic ...

Indian Academy of Sciences (India)

Administrator

2013-07-06

Jul 6, 2013 ... dered (Hekmat-Ardakan et al 2010; Choi and Li 2012). Usually, the .... According to Clapeyron equation (Yu et al 1999) m. 2. 1 m. (. ) d d ,. T V. V. T. P. H. -. = ∆. (1) .... Jung H K, Seo P K and Kang C G 2001 J. Mater. Process. Technol ... Res. 14 141. Zhang H H, Duan H L, Shao G J, Xu L P, Yin J L and Yan B.

Thermomechanical theory of materials undergoing large elastic and viscoplastic deformation (AWBA development program)

International Nuclear Information System (INIS)

Martin, S.E.; Newman, J.B.

1980-11-01

A thermomechanical theory of large deformation elastic-inelastic material behavior is developed which is based on a multiplicative decomposition of the strain. Very general assumptions are made for the elastic and inelastic constitutive relations and effects such as thermally-activated creep, fast-neutron-flux-induced creep and growth, annealing, and strain recovery are compatible with the theory. Reduced forms of the constitutive equations are derived by use of the second law of thermodynamics in the form of the Clausius-Duhem inequality. Observer invariant equations are derived by use of an invariance principle which is a generalization of the principle of material frame indifference

A study of fluid alkali metals in the critical region

Energy Technology Data Exchange (ETDEWEB)

Balasubramanian, R. [Department of Physics, Kongu Engineering College, Perundurai, Erode 638 052, Tamil Nadu (India)]. E-mail: drrbala@yahoo.com

2006-05-31

On the basis of the generalised van der Waals equation of state, Riedel's thermodynamic similarity parameter, a measure of the temperature dependence of vapour pressure in the critical region is determined for caesium, rubidium and potassium. This generalised equation differs from the known van der Waals equation of state by the modified expression for molecular pressure. The results of determination of Riedel's thermodynamic similarity parameter of caesium, rubidium and potassium are in good agreement with experimental data. Moreover, the given generalised van der Waals equation of state yields a better fit with experimental data on Riedel's thermodynamic similarity parameter for fluid alkali metals when compared with other correlations such as Van Ness and Abbott equation, Pitzer expansion, Pitzer acentric factor correlation, modified Rackett technique, Lee-Kesler vapour pressure relation and Clausius-Clayperon equation.

Volatility of atmospherically relevant alkylaminium carboxylate salts.

Science.gov (United States)

Lavi, Avi; Segre, Enrico; Gomez-Hernandez, Mario; Zhang, Renyi; Rudich, Yinon

2015-05-14

Heterogeneous neutralization reactions of ammonia and alkylamines with sulfuric acid play an important role in aerosol formation and particle growth. However, little is known about the physical and chemical properties of alkylaminium salts of organic acids. In this work we studied the thermal stability and volatility of alkylaminium carboxylate salts of short aliphatic alkylamines with monocarboxylic and dicarboxylic acids. The enthalpy of vaporization and saturation vapor pressure at 298 K were derived using the kinetic model of evaporation and the Clausius-Clapeyron relation. The vapor pressure of alkylaminium dicarboxylate salts is ∼10(-6) Pa, and the vaporization enthalpy ranges from 73 to 134 kJ mol(-1). Alkylaminium monocarboxylate salts show high thermal stability, and their thermograms do not follow our evaporation model. Hence, we inferred their vapor pressure from their thermograms as comparable to that of ammonium sulfate (∼10(-9) Pa). Further characterization showed that alkylaminium monocarboxylates are room temperature protic ionic liquids (RTPILs) that are more hygroscopic than ammonium sulfate (AS). We suggest that the irregular thermograms result from an incomplete neutralization reaction leading to a mixture of ionic and nonionic compounds. We conclude that these salts are expected to contribute to new particle formation and particle growth under ambient conditions and can significantly enhance the CCN activity of mixed particles in areas where SO2 emissions are regulated.

Phase relationships of the system Fe-Ni-S and structure of the high-pressure phase of (Fe1-xNix)3S2

Science.gov (United States)

Urakawa, Satoru; Kamuro, Ryota; Suzuki, Akio; Kikegawa, Takumi

2018-04-01

The phase relationships of the Fe-Ni-S system at 15 GPa were studied by high pressure quench experiments. The stability fields of (Fe,Ni)3S and (Fe,Ni)3S2 and the melting relationships of the Fe-Ni-S system were determined as a function of Ni content. The (Fe,Ni)3S solid solution is stable in the composition of Ni/(Fe + Ni) > 0.7 and melts incongruently into an Fe-Ni alloy + liquid. The (Fe,Ni)3S2 makes a complete solid solution and melts incongruently into (Fe,Ni)S + liquid, whose structure was determined to show Cmcm-orthorhombic symmetry by in situ synchrotron X-ray diffraction experiments. The eutectic contains about 30 at.% of S, and its temperature decreases with increasing Ni content with a rate of ∼5 K/at.% from 1175 K. The density of the Fe-FeS eutectic composition (Fe70S30) liquid is evaluated to be 6.93 ± 0.08 g/cm3 at 15 GPa and 1200 K based on the Clausius-Clapeyron relations and densities of subsolidus phases. The Fe-Ni-S liquids are a primary sulfur-bearing phase in the deep mantle with a reducing condition (250-660 km depth), and they would play a significant role in the carbon cycle as a carbon host as well as in the generation of diamond.

In-situ studies of stress- and magnetic-field-induced phase transformation in a polymer-bonded Ni-Co-Mn-In composite

International Nuclear Information System (INIS)

Liu, D.M.; Nie, Z.H.; Wang, G.; Wang, Y.D.; Brown, D.E.; Pearson, J.; Liaw, P.K.; Ren, Y.

2010-01-01

A polymer-bonded Ni 45 Co 5 Mn 36.6 In 13.4 ferromagnetic shape-memory composite was fabricated, having magnetic-field-driven shape recovery properties. The thermo-magnetization curves of the composite suggested that the magnetic-field-induced reverse martensitic transformation occurs in the composite. The effects of temperature, stress, and magnetic-field on the phase transformation properties were systematically investigated using an in-situ high-energy X-ray diffraction technique. A temperature-induced reversible martensitic phase transformation was confirmed within the composite, showing a broad phase transformation interval. Stress-induced highly textured martensite was observed in the composite during uniaxial compressive loading, with a residual strain after unloading. The origin of the textured martensite can be explained by the grain-orientation-dependent Bain distortion energy. A recovery strain of ∼1.76% along the compression direction was evidenced in the pre-strained composite with an applied magnetic-field of 5 T. This recovery was caused by the magnetic-field-induced reverse martensitic phase transformation. The phase transformation properties of the ferromagnetic shape-memory composite, different from its bulk alloys, can be well explained by the Clausius-Clapeyron relation. The large magnetic-field-induced strain, together with good ductility and low cost, make the polymer-bonded Ni-Co-Mn-In composites potential candidates for magnetic-field-driven actuators.

Impacts of half a degree additional warming on the Asian summer monsoon rainfall characteristics

Science.gov (United States)

Lee, Donghyun; Min, Seung-Ki; Fischer, Erich; Shiogama, Hideo; Bethke, Ingo; Lierhammer, Ludwig; Scinocca, John F.

2018-04-01

This study investigates the impacts of global warming of 1.5 °C and 2.0 °C above pre-industrial conditions (Paris Agreement target temperatures) on the South Asian and East Asian monsoon rainfall using five atmospheric global climate models participating in the ‘Half a degree Additional warming, Prognosis and Projected Impacts’ (HAPPI) project. Mean and extreme precipitation is projected to increase under warming over the two monsoon regions, more strongly in the 2.0 °C warmer world. Moisture budget analysis shows that increases in evaporation and atmospheric moisture lead to the additional increases in mean precipitation with good inter-model agreement. Analysis of daily precipitation characteristics reveals that more-extreme precipitation will have larger increase in intensity and frequency responding to the half a degree additional warming, which is more clearly seen over the South Asian monsoon region, indicating non-linear scaling of precipitation extremes with temperature. Strong inter-model relationship between temperature and precipitation intensity further demonstrates that the increased moisture with warming (Clausius-Clapeyron relation) plays a critical role in the stronger intensification of more-extreme rainfall with warming. Results from CMIP5 coupled global climate models under a transient warming scenario confirm that half a degree additional warming would bring more frequent and stronger heavy precipitation events, exerting devastating impacts on the human and natural system over the Asian monsoon region.

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

Some empirical rules concerning the vapor pressure curve revisited

International Nuclear Information System (INIS)

Velasco, S.; White, J.A.

2014-01-01

Highlights: • A Claussius–Claperyron equation is obtained in the Pitzer corresponding states scheme. • Some well-known empirical rules for the vapor pressure are rewritten in terms of the Pitzer acentric factor. • The Guggenheim point follows the corresponding state scheme better than the normal boiling point. • The Ambrose–Walton vapor pressure equation yields excellent agreement with NIST data in all considered cases. -- Abstract: A form for the Clausius–Clapeyron vapor-pressure equation is obtained in the Pitzer corresponding states scheme. This equation allows one to rewrite the well-known Trouton, Guldberg, van Laar and Guggenheim rules in terms of the acentric factor ω. The original forms of these empirical rules are recovered for some particular values of ω. The proposed rules are checked by analyzing National Institute of Standards and Technology (NIST) data on the liquid-vapor coexistence curve for 105 fluids. These rules have been also analyzed by using the well-known Ambrose–Walton (AW) vapor pressure equation

Sensitivity of Rainfall Extremes Under Warming Climate in Urban India

Science.gov (United States)

Ali, H.; Mishra, V.

2017-12-01

Extreme rainfall events in urban India halted transportation, damaged infrastructure, and affected human lives. Rainfall extremes are projected to increase under the future climate. We evaluated the relationship (scaling) between rainfall extremes at different temporal resolutions (daily, 3-hourly, and 30 minutes), daily dewpoint temperature (DPT) and daily air temperature at 850 hPa (T850) for 23 urban areas in India. Daily rainfall extremes obtained from Global Surface Summary of Day Data (GSOD) showed positive regression slopes for most of the cities with median of 14%/K for the period of 1979-2013 for DPT and T850, which is higher than Clausius-Clapeyron (C-C) rate ( 7%). Moreover, sub-daily rainfall extremes are more sensitive to both DPT and T850. For instance, 3-hourly rainfall extremes obtained from Tropical Rainfall Measurement Mission (TRMM 3B42 V7) showed regression slopes more than 16%/K aginst DPT and T850 for the period of 1998-2015. Half-hourly rainfall extremes from the Integrated Multi-satellitE Retrievals (IMERGE) of Global precipitation mission (GPM) also showed higher sensitivity against changes in DPT and T850. The super scaling of rainfall extremes against changes in DPT and T850 can be attributed to convective nature of precipitation in India. Our results show that urban India may witness non-stationary rainfall extremes, which, in turn will affect stromwater designs and frequency and magniture of urban flooding.

Dynamic and thermodynamic processes driving the January 2014 precipitation record in southern UK

Science.gov (United States)

Oueslati, B.; Yiou, P.; Jezequel, A.

2017-12-01

Regional extreme precipitation are projected to intensify as a response to planetary climate change, with important impacts on societies. Understanding and anticipating those events remain a major challenge. In this study, we revisit the mechanisms of winter precipitation record that occurred in southern United Kingdom in January 2014. The physical drivers of this event are analyzed using the water vapor budget. Precipitation changes are decomposed into dynamic contributions, related to changes in atmospheric circulation, and thermodynamic contributions, related to changes in water vapor. We attempt to quantify the relative importance of the two contributions during this event and examine the applicability of Clausius-Clapeyron scaling. This work provides a physical interpretation of the mechanisms associated with Southern UK's wettest event, which is complementary to other studies based on statistical approaches (Schaller et al., 2016, Yiou et al., 2017). The analysis is carried out using the ERA-Interim reanalysis. This is motivated by the horizontal resolution of this dataset. It is then applied to present-day simulations and future projections of CMIP5 models on selected extreme precipitation events in southern UK that are comparable to January 2014 in terms of atmospheric circulation.References:Schaller, N. et al. Human influence on climate in the 2014 southern England winter floods and their impacts, Nature Clim. Change, 2016, 6, 627-634 Yiou, P., et al. A statistical framework for conditional extreme event attribution Advances in Statistical Climatology, Meteorology and Oceanography, 2017, 3, 17-31

Measuring the greenhouse effect and radiative forcing through the atmosphere

Science.gov (United States)

Philipona, Rolf; Kräuchi, Andreas; Brocard, Emmanuel

2013-04-01

In spite of a large body of existing measurements of incoming shortwave solar radiation and outgoing longwave terrestrial radiation at the Earth's surface and at the top of the atmosphere, there are few observations documenting how radiation profiles change through the atmosphere - information that is necessary to fully quantify the greenhouse effect of the Earth's atmosphere. Using weather balloons and specific radiometer equipped radiosondes, we continuously measured shortwave and longwave radiation fluxes from the surface of the Earth up to altitudes of 35 kilometers in the upper stratosphere. Comparing radiation profiles from night measurements with different amounts of water vapor, we show evidence of large greenhouse forcing. We show, that under cloud free conditions, water vapor increases with Clausius-Clapeyron ( 7% / K), and longwave downward radiation at the surface increases by 8 Watts per square meter per Kelvin. The longwave net radiation however, shows a positive increase (downward) of 2.4 Watts per square meter and Kelvin at the surface, which decreases with height and shows a similar but negative increase (upward) at the tropopause. Hence, increased tropospheric water vapor increases longwave net radiation towards the ground and towards space, and produces a heating of 0.42 Kelvin per Watt per square meter at the surface. References: Philipona et al., 2012: Solar and thermal radiation profiles and radiative forcing measured through the atmosphere. Geophys. Res. Lett., 39, L13806, doi: 10.1029/2012GL052087.

Observed increase in extreme daily rainfall in the French Mediterranean

Science.gov (United States)

Ribes, Aurélien; Thao, Soulivanh; Vautard, Robert; Dubuisson, Brigitte; Somot, Samuel; Colin, Jeanne; Planton, Serge; Soubeyroux, Jean-Michel

2018-04-01

We examine long-term trends in the historical record of extreme precipitation events occurring over the French Mediterranean area. Extreme events are considered in terms of their intensity, frequency, extent and precipitated volume. Changes in intensity are analysed via an original statistical approach where the annual maximum rainfall amounts observed at each measurement station are aggregated into a univariate time-series according to their dependence. The mean intensity increase is significant and estimated at + 22% (+ 7 to + 39% at the 90% confidence level) over the 1961-2015 period. Given the observed warming over the considered area, this increase is consistent with a rate of about one to three times that implied by the Clausius-Clapeyron relationship. Changes in frequency and other spatial features are investigated through a Generalised Linear Model. Changes in frequency for events exceeding high thresholds (about 200 mm in 1 day) are found to be significant, typically near a doubling of the frequency, but with large uncertainties in this change ratio. The area affected by severe events and the water volume precipitated during those events also exhibit significant trends, with an increase by a factor of about 4 for a 200 mm threshold, again with large uncertainties. All diagnoses consistently point toward an intensification of the most extreme events over the last decades. We argue that it is difficult to explain the diagnosed trends without invoking the human influence on climate.

DETERMINACIÓN DE ISOTERMAS DE ADSORCIÓN DE AGUA ENBIOCOMPUESTOS DE HARINA TERMOPLÁSTICA Y FIQUE

Directory of Open Access Journals (Sweden)

DIANA PAOLA NAVIA P.

Full Text Available Materiales compuestos de harina termoplástica de yuca reforzados con fibra de fique fueron elaborados por la técnica de termo-compresión empleando harina de dos variedades de yuca (MPER 183 y CM 4574-7, plastificada con glicerol. Los materiales fueron sometidos a ensayos de adsorción de vapor de agua mediante el método gravimétrico a 15, 25y 35°C en el intervalo de actividad de agua entre 0,12 y 0,98. Los valores experimentales de adsorción fueron modelados matemáticamente usando las ecuaciones de GAB, Caurie, Oswin, Smith, Henderson y Peleg. El calor isostérico de adsorción (Qst se determinó mediante la ecuación de Clausius-Clapeyron. Los resultados mostraron que todas las isotermas fueron de tipo III. El factor variedad de yuca no influenció significativamente(p>0,05 sobre el contenido de humedad de equilibrio, mientras que la temperatura si mostródiferencias significativas (p<0,05 en valores de actividad de agua superiores a 0,85. A temperatura de almacenamiento de 15 y 25 °C el modelo que mejor ajustó los resultados experimentales fue Peleg, mientras a 35 °C se obtuvo un mejor ajuste con el modelo de GAB. El Qst disminuyó con el incremento en el contenido de humedad de equilibrio, variando entre 66 y 44 kJ/mol.

Some thermodynamic properties of hydrogen chloride and deuterium chloride

Energy Technology Data Exchange (ETDEWEB)

Henderson, C; Lewis, D G; Prichard, P C; Staveley, L A.K.; Fonseca, I M.A.; Lobo, L Q

1986-01-01

The molar volume of HCl has been measured from 162 to 236 K, and of DCl from 160 to 218 K. Direct measurements of the vapour pressure of HCl have been made from 159 to 220 K, and of DCl from 158 to 188 K. In addition, the difference in the vapour pressure of the two isotopic forms has been measured from 159 to 226 K. At lower temperatures, the vapour pressure of HCl exceeds that of DCl but above 223.35 K that position is reversed. The vapour pressure of each substance has been fitted to a Wagner equation. These equations have been used in conjunction with the Clapeyron equation to calculate the molar enthalpies of vaporization. If r is the ratio of the vapour pressure of HCl to that of DCl, the values of r conform very closely to the equation T ln r = - A + C/T, where A and C are constants.

Theoretical Studies on Expressions of Condensed-Phase Photoionization Cross Section

International Nuclear Information System (INIS)

Ma Xiaoguang; Wang Meishan; Wang Dehua; Qu Zhaojun

2006-01-01

A set of general expressions for photoionization cross sections of atoms or molecules embedded in a medium and a dielectric influence function are derived based on Maxwell's equations and the Beer-Lambert's law in this work. The applications are performed for the photoionization process of solid gold both in the Clausius-Mossotti (virtual cavity) model and the Glauber-Lewenstein (real cavity) model firstly. The results show that the present theoretical expressions of photoionization cross section can be used to describe the photoionization process of atoms in condensed matter properly.

Sum rules for the quarkonium systems

International Nuclear Information System (INIS)

Burnel, A.; Caprasse, H.

1980-01-01

In the framework of the radial Schroedinger equation we derive in a very simple way sum rules relating the potential to physical quantities such as the energy eigenvalues and the square of the lth derivative of the eigenfunctions at the origin. These sum rules contain as particular cases well-known results such as the quantum version of the Clausius theorem in classical mechanics as well as Kramers's relations for the Coulomb potential. Several illustrations are given and the possibilities of applying them to the quarkonium systems are considered

Unified first law and the thermodynamics of the apparent horizon in the FRW universe

International Nuclear Information System (INIS)

Cai Ronggen; Cao Liming

2007-01-01

In this paper we revisit the relation between the Friedmann equations and the first law of thermodynamics. We find that the unified first law first proposed by Hayward to treat the outertrapping horizon of a dynamical black hole can be used to the apparent horizon (a kind of inner trapping horizon in the context of the FRW cosmology) of the FRW universe. We discuss three kinds of gravity theorties: Einstein theory, Lovelock thoery, and scalar-tensor theory. In Einstein theory, the first law of thermodynamics is always satisfied on the apparent horizon. In Lovelock theory, treating the higher derivative terms as an effective energy-momentum tensor, we find that this method can give the same entropy formula for the apparent horizon as that of black hole horizon. This implies that the Clausius relation holds for the Lovelock theory. In scalar-tensor gravity, we find, by using the same procedure, the Clausius relation no longer holds. This indicates that the apparent horizon of the FRW universe in the scalar-tensor gravity corresponds to a system of nonequilibrium thermodynamics. We show this point by using the method developed recently by Eling et al. for dealing with the f(R) gravity

p-Euler equations and p-Navier-Stokes equations

Science.gov (United States)

Li, Lei; Liu, Jian-Guo

2018-04-01

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

Equating error in observed-score equating

NARCIS (Netherlands)

van der Linden, Willem J.

2006-01-01

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

The role of transients in the Mid Summer Drought over the Tropical Americas

Science.gov (United States)

Herrera, E.; Magaña Rueda, V.; Caetano, E.

2013-05-01

The Mid Summer Drought (MSD) has raised the interested of those interested in regional climate dynamics since it appears to be a unique characteristic of the tropical Americas climate. The MSD corresponds to a relative minimum in summer precipitation between July and August in the Mesoamerican region. Several theories have been posed to explain its origin including the annual cycle march of the ITCZ, a teleconnection from the Asian monsoon region, or an air sea interaction process that relates the warm pools over the eastern Pacific and the Caribbean Sea. However, none of them has addressed the various characteristics of the MSD described by Magaña et al (1999) and Magaña and Caetano (2005). In the present paper, the role of the transient mean flow interaction over the Caribbean Sea is explored. The Caribbean Low Level Jet (CLLJ) and the transients interact in such a way that the CLLJ reaches maximum intensity when the MSD occurs. This is a period of minimum Perturbation Kinetic Energy in the region, suggesting that a CLLJ stronger than approximately 15 m/s tends to inhibit the amplification of eddies. Transients are crucial dynamic elements to produce precipitation over the Mexico and Central American region. Over the eastern Pacific warm pool, tropical convection and sea surface temperature are related by a sort of Clausius Clapeyron exponential equation. However, there are two branches for the relationship, one for the first maximum in tropical convection during June, and a second one during September, with a relative minimum corresponding to the MSD in July - August. The most interesting aspect of such patterns is that while the June exponential curves occurs at SST larger than 28°C, the curve corresponding to September takes place at lower SSTs, suggesting that transient activity in this period is necessary to enhance tropical convective activity during the latter part of the summer rains in the region. This is exactly the period when PKE increases over the

Energy Storage Analysis of a Mixed R161/MOF-5 Nanoparticle Nanofluid Based on Molecular Simulations.

Science.gov (United States)

Wang, Qiang; Tang, Shengli; Li, Leilei

2018-05-20

The thermal properties of refrigerants can be modified by adding porous nanoparticles into them. Here, molecular simulations, including molecular dynamics and grand canonical Monte Carlo, were employed to study the thermal energy storage properties of an R161/MOF-5 nanofluid. The results show that the thermodynamic energy change of MOF-5 nanoparticles is linear to the temperature. The adsorption heat calculated by grand canonical Monte Carlo is close to that calculated by the Clausius⁻Clapeyron equation. Additionally, a negative enhancement of the thermal energy storage capacity of the R161/MOF-5 nanofluid is found near the phase transition area.

Calculation on the heat of gasification for the saturated liquid of D2

International Nuclear Information System (INIS)

Ge Fangfang; China Academy of Engineering Physics, Mianyang; Zhu Zhenghe; Wang Hongbin; Zhou Weimin; Chen Hao; Liu Hongjie

2005-01-01

In general, the saturated stream is regarded as the ideal gas for calculating the heat of gasification for the saturated liquid. However, the result of calculation was not consistent with the general law if D 2 was treated as the ideal gas under T c =38.34 K, the critical temperature. Considering the change of the volume from the liquid state to the gas state, this paper implored the Clapeyron differential equation and the equation of vapor-liquid equilibrium, and then obtained the heat of gasification and the entropy from 20 K to 38 K and the saturation curve. The method avoided regarding the saturate gas D 2 as the ideal gas and ignoring the volume change from the liquid state to the gas state, improving the calculation exactitude. (authors)

Sensitivity of extreme precipitation to temperature: the variability of scaling factors from a regional to local perspective

Science.gov (United States)

Schroeer, K.; Kirchengast, G.

2018-06-01

Potential increases in extreme rainfall induced hazards in a warming climate have motivated studies to link precipitation intensities to temperature. Increases exceeding the Clausius-Clapeyron (CC) rate of 6-7%/°C-1 are seen in short-duration, convective, high-percentile rainfall at mid latitudes, but the rates of change cease or revert at regionally variable threshold temperatures due to moisture limitations. It is unclear, however, what these findings mean in term of the actual risk of extreme precipitation on a regional to local scale. When conditioning precipitation intensities on local temperatures, key influences on the scaling relationship such as from the annual cycle and regional weather patterns need better understanding. Here we analyze these influences, using sub-hourly to daily precipitation data from a dense network of 189 stations in south-eastern Austria. We find that the temperature sensitivities in the mountainous western region are lower than in the eastern lowlands. This is due to the different weather patterns that cause extreme precipitation in these regions. Sub-hourly and hourly intensities intensify at super-CC and CC-rates, respectively, up to temperatures of about 17 °C. However, we also find that, because of the regional and seasonal variability of the precipitation intensities, a smaller scaling factor can imply a larger absolute change in intensity. Our insights underline that temperature precipitation scaling requires careful interpretation of the intent and setting of the study. When this is considered, conditional scaling factors can help to better understand which influences control the intensification of rainfall with temperature on a regional scale.

Multimodel evaluation of cloud phase transition using satellite and reanalysis data

Science.gov (United States)

Cesana, G.; Waliser, D. E.; Jiang, X.; Li, J.-L. F.

2015-08-01

We take advantage of climate simulations from two multimodel experiments to characterize and evaluate the cloud phase partitioning in 16 general circulation models (GCMs), specifically the vertical structure of the transition between liquid and ice in clouds. We base our analysis on the ratio of ice condensates to the total condensates (phase ratio, PR). Its transition at 90% (PR90) and its links with other relevant variables are evaluated using the GCM-Oriented Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation Cloud Product climatology, reanalysis data, and other satellite observations. In 13 of 16 models, the PR90 transition height occurs too low (6 km to 8.4 km) and at temperatures too warm (-13.9°C to -32.5°C) compared to observations (8.6 km, -33.7°C); features consistent with a lack of supercooled liquid with respect to ice above 6.5 km. However, this bias would be slightly reduced by using the lidar simulator. In convective regimes (more humid air and precipitation), the observed cloud phase transition occurs at a warmer temperature than for subsidence regimes (less humid air and precipitation). Only few models manage to roughly replicate the observed correlations with humidity (5/16), vertical velocity (5/16), and precipitation (4/16); 3/16 perform well for all these parameters (MPI-ESM, NCAR-CAM5, and NCHU). Using an observation-based Clausius-Clapeyron phase diagram, we illustrate that the Bergeron-Findeisen process is a necessary condition for models to represent the observed features. Finally, the best models are those that include more complex microphysics.

equateIRT: An R Package for IRT Test Equating

Directory of Open Access Journals (Sweden)

Michela Battauz

2015-12-01

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

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.

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

Energy Technology Data Exchange (ETDEWEB)

Plas, R.

1962-07-01

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

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.

Extended rate equations

International Nuclear Information System (INIS)

Shore, B.W.

1981-01-01

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

Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

Directory of Open Access Journals (Sweden)

Hamidreza Rezazadeh

2014-05-01

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

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

Analysis of wave equation in electromagnetic field by Proca equation

International Nuclear Information System (INIS)

Pamungkas, Oky Rio; Soeparmi; Cari

2017-01-01

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

Comparison of Kernel Equating and Item Response Theory Equating Methods

Science.gov (United States)

Meng, Yu

2012-01-01

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

Integral equations

CERN Document Server

Moiseiwitsch, B L

2005-01-01

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

Partial Differential Equations

CERN Document Server

1988-01-01

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

Nonlinear evolution equations

CERN Document Server

Uraltseva, N N

1995-01-01

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

FMTLxLyLz DIMENSIONAL EQUAT DIMENSIONAL EQUATION ...

African Journals Online (AJOL)

eobe

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

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

Energy Technology Data Exchange (ETDEWEB)

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

1968-07-01

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

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

Directory of Open Access Journals (Sweden)

Anthony D. Albano

2016-10-01

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

Carnot to Clausius: Caloric to Entropy

Science.gov (United States)

Newburgh, Ronald

2009-01-01

This paper discusses how the Carnot engine led to the formulation of the second law of thermodynamics and entropy. The operation of the engine is analysed both in terms of heat as the caloric fluid and heat as a form of energy. A keystone of Carnot's thinking was the absolute conservation of caloric. Although the Carnot analysis was partly…

Thermodynamics of flat FLRW universe in Rastall theory

International Nuclear Information System (INIS)

Moradpour, H.

2016-01-01

In this paper, after referring to the Rastall theory, we address some of its cosmological consequences. Moreover, bearing the Clausius relation in mind, using Friedman equations in Rastall theory and the Cai–Kim temperature, we obtain a relation for the apparent horizon entropy of a flat FLRW universe. In addition, we impose the entropy positivity condition on the obtained relation for the horizon entropy, to find some constraints on the Rastall parameters. Moreover, we investigate the second and generalized second laws of thermodynamics. The results of considering a dominated prefect fluid of constant state parameter are also addressed helping us familiarize with the Rastall theory.

Thermodynamics of flat FLRW universe in Rastall theory

Energy Technology Data Exchange (ETDEWEB)

Moradpour, H., E-mail: h.moradpour@riaam.ac.ir

2016-06-10

In this paper, after referring to the Rastall theory, we address some of its cosmological consequences. Moreover, bearing the Clausius relation in mind, using Friedman equations in Rastall theory and the Cai–Kim temperature, we obtain a relation for the apparent horizon entropy of a flat FLRW universe. In addition, we impose the entropy positivity condition on the obtained relation for the horizon entropy, to find some constraints on the Rastall parameters. Moreover, we investigate the second and generalized second laws of thermodynamics. The results of considering a dominated prefect fluid of constant state parameter are also addressed helping us familiarize with the Rastall theory.

Quantitative approach to relate dielectric constant studies with TSDC studies of 50 MeV Si ion irradiated kapton-H polymide

International Nuclear Information System (INIS)

Quamara, J.K.; Garg, Maneesha; Sridharbabu, Y.; Prabhavathi, T.

2003-01-01

Temperature and frequency dependent dielectric behaviour has been investigated for pristine and swift heavy ion irradiated (Si ion, 50 MeV energy) kapton-H polyimide in the temperature range of 30 to 250 deg C at frequencies 120 Hz, 1 kHz, 10 kHz and 100 kHz respectively. The dielectric relaxation behaviour of the same samples was also studied using thermally stimulated discharge current (TSDC) technique. A quantitative approach is developed using a well-known Clausius Mossotti equation to relate the TSDC findings to the dielectric constant studies. An overall increase in the dielectric constant of the irradiated samples are also in conformity to the TSDC findings. (author)

Multi-model Projection of July-August Climate Extreme Changes over China under CO2 Doubling. Part Ⅰ:Precipitation

Institute of Scientific and Technical Information of China (English)

LI Hongmei; FENG Lei; ZHOU Tianjun

2011-01-01

Potential changes in precipitation extremes in July-August over China in response to CO2 doubling are analyzed based on the output of 24 coupled climate models from the Twentieth-Century Climate in Coupled Models (20C3M) experiment and the 1％ per year CO2 increase experiment (to doubling) (lpctto2x) of phase 3 of the Coupled Model Inter-comparison Project (CMIP3). Evaluation of the models' performance in simulating the mean state shows that the majority of models fairly reproduce the broad spatial pattern of observed precipitation. However, all the models underestimate extreme precipitation by ～50％. The spread among the models over the Tibetan Plateau is ～2-3 times larger than that over the other areas.Models with higher resolution generally perform better than those with lower resolutions in terms of spatial pattern and precipitation amount. Under the lpctto2x scenario, the ratio between the absolute value of MME extreme precipitation change and model spread is larger than that of total precipitation, indicating a relatively robust change of extremes. The change of extreme precipitation is more homogeneous than the total precipitation. Analysis on the output of Geophysical Fluid Dynamics Laboratory coupled climate model version 2.1 (GFDL-CM2.1) indicates that the spatially consistent increase of surface temperature and water vapor content contribute to the large increase of extreme precipitation over contiguous China,which follows the Clausius-Clapeyron relationship. Whereas, the meridionally tri-polar pattern of mean precipitation change over eastern China is dominated by the change of water vapor convergence, which is determined by the response of monsoon circulation to global warming.

Chemical Equation Balancing.

Science.gov (United States)

Blakley, G. R.

1982-01-01

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

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

International Nuclear Information System (INIS)

Sirendaoreji

2006-01-01

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

Historique en grandes enjambées de la thermodynamique de l'équilibre

Science.gov (United States)

Hertz, J.

2004-12-01

La Thermodynamique, une science totalement nouvelle au XIXème siècle, a germé en France en contrepoint des idées du siècle des Lumières, dans le milieu particulier des anciens élèves de l’Ecole Polytechnique, officiers supérieurs formés pour l’armée républicaine ou napoléonienne, mais qui ne trouvaient plus leur place dans l’armée de la Restauration. Ils se convertissaient en ingénieurs civils des métiers industriels en pleine expansion, comme le développement de la machine à vapeur ou des chemins de fer. La plupart d’entre eux, plutôt libre-penseurs, adhéraient aux idées scientistes du « positivisme », véhiculées dans les Loges de la Franc-Maçonnerie du Grand Orient de France et plus particulièrement dans les cercles Saint-Simoniens, premiers adeptes du socialisme industriel. C’est ainsi que naquit en 1824, dans le cerveau subtil mais brouillon de Sadi Carnot toute la vision illuminée de cette science nouvelle, incompréhensible pour ses contemporains. Elle ressuscita en 1834 sous la plume d’un Emile Clapeyron qui avait pris conscience de l’immensité de l’œuvre de Sadi Carnot. Mais le rappel de Clapeyron demeura également sans écho pendant dix années. Le réveil de la Thermodynamique se fera désormais hors de France par des hommes de grande pratique religieuse et généralement protestants. C’est ainsi que William Thomson en Ecosse et Rudolph Clausius, venu de Prusse, achevèrent l’œuvre de leurs deux prédécesseurs et que la Thermodynamique mécano-thermique fut définitivement établie en 1864. La thermodynamique chimique peut être attribuée à un seul génie mathématicien, Josiah Willard Gibbs qui travaillait tout seul au Yale College de New-Haven, dans le Connecticut, et rédigea sa nouvelle théorie entre 1875 et 1878. Enfin l’interprétation statistique du second principe sera l’œuvre en 1877 d’un Autrichien, Ludwig Boltzmann, homme génial mais fragile qui eut le temps d’insuffler ses id

On a functional equation related to the intermediate long wave equation

International Nuclear Information System (INIS)

Hone, A N W; Novikov, V S

2004-01-01

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

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

International Nuclear Information System (INIS)

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

1994-01-01

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

Auxiliary equation method for solving nonlinear partial differential equations

International Nuclear Information System (INIS)

Sirendaoreji,; Jiong, Sun

2003-01-01

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

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

CERN Document Server

Czelakowski, Janusz

2015-01-01

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

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

Science.gov (United States)

Chen, Haiwen

2012-01-01

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

Vapour pressure of trideuterioammonia

Energy Technology Data Exchange (ETDEWEB)

Calado, J.C.G.; Lopes, J.N.C.; Rebelo, L.P.N. (Instituto Superior Tecnico, Lisbon (Portugal). Centro de Quimica Estrutural)

1992-09-01

The H-to-D vapour-pressure isotope effect in liquid ammonia has been measured at 62 temperatures between 228 K and 260 K. The vapour pressures, corrected to 100 per cent nuclidic purity, have been fitted to the equation: T ln r = A+B/T+CT, where r is the vapour-pressure ratio p(NH[sub 3])/p(ND[sub 3]). The fit yielded the parameters: A = -8.22508 K, B = 12338.2 K[sup 2], and C = -0.05544. Comparisons with the results of other authors were made in order to clarify some discrepancies found in the literature. Our values are in accord with the previous results of King et al. and an extrapolation of the fitted equation down to the triple-point temperature gave good agreement with the published results. The fitted equation was used in conjunction with the Clapeyron equation to calculate the difference in the molar enthalpies of vaporization between NH[sub 3] and ND[sub 3]. At T = 230 K that difference is -846 J.mol[sup -1] decreasing to -747 J.mol[sup -1] at 260 K. (author).

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

OpenAIRE

Kihara, Hironobu

2008-01-01

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

Differential equations a dynamical systems approach ordinary differential equations

CERN Document Server

Hubbard, John H

1991-01-01

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

Two-Phase Equilibrium Properties in Charged Topological Dilaton AdS Black Holes

Directory of Open Access Journals (Sweden)

Hui-Hua Zhao

2016-01-01

Full Text Available We discuss phase transition of the charged topological dilaton AdS black holes by Maxwell equal area law. The two phases involved in the phase transition could coexist and we depict the coexistence region in P-v diagrams. The two-phase equilibrium curves in P-T diagrams are plotted, the Clapeyron equation for the black hole is derived, and the latent heat of isothermal phase transition is investigated. We also analyze the parameters of the black hole that could have an effect on the two-phase coexistence. The results show that the black holes may go through a small-large phase transition similar to that of a usual nongravity thermodynamic system.

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.

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

Science.gov (United States)

Chen, Haiwen; Holland, Paul

2010-01-01

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

Relations between nonlinear Riccati equations and other equations in fundamental physics

International Nuclear Information System (INIS)

Schuch, Dieter

2014-01-01

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

Bridging the Knowledge Gaps between Richards' Equation and Budyko Equation

Science.gov (United States)

Wang, D.

2017-12-01

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

Partial differential equations

CERN Document Server

Evans, Lawrence C

2010-01-01

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

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.

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.

Evaluating Equating Results: Percent Relative Error for Chained Kernel Equating

Science.gov (United States)

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

2012-01-01

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

Handbook of integral equations

CERN Document Server

Polyanin, Andrei D

2008-01-01

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

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

Thermodynamics of the Apparent Horizon in FRW Universe with Massive Gravity

International Nuclear Information System (INIS)

Li Hui; Zhang Yi

2013-01-01

Applying Clausius relation with energy-supply defined by the unified first law of thermodynamics formalism to the apparent horizon of a massive gravity model in cosmology proposed lately, the corrected entropic formula of the apparent horizon is obtained with the help of the modified Friedmann equations. This entropy-area relation, together with the identified Misner-Sharp internal energy, verifies the first law of thermodynamics for the apparent horizon with a volume change term for consistency. On the other hand, by means of the corrected entropy-area formula and the Clausius relation δQ = T d S, where the heat Bow δQ is the energy-supply of pure matter projecting on the vector ξ tangent to the apparent horizon and should be looked on as the amount of energy crossing the apparent horizon during the time interval dt and the temperature of the apparent horizon for energy crossing during the same interval is 1/(2πr A ), the modified Friedmann equations governing the dynamical evolution of the universe are reproduced with the known energy density and pressure of massive graviton. The integration constant is found to correspond to a cosmological term which could be absorbed into the energy density of matter. Having established the correspondence of massive cosmology with the unified first law of thermodynamics on the apparent horizon, the validity of the generalized second law of thermodynamics is also discussed by assuming the thermal equilibrium between the apparent horizon and the matter field bounded by the apparent horizon. It is found that, in the limit H c → 0, which recovers the Minkowski reference metric solution in the fiat case, the generalized second law of thermodynamics holds if α 3 + 4α 4 3 = α 4 = 0, the generalized second law of thermodynamics could be violated. (general)

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

Introduction to differential equations

CERN Document Server

Taylor, Michael E

2011-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2016-07-01

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

Averaged RMHD equations

International Nuclear Information System (INIS)

Ichiguchi, Katsuji

1998-01-01

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

Differential equations

CERN Document Server

Tricomi, FG

2013-01-01

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

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

International Nuclear Information System (INIS)

Heras, Jose A

2009-01-01

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

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.

On separable Pauli equations

International Nuclear Information System (INIS)

Zhalij, Alexander

2002-01-01

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

Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation

Science.gov (United States)

Vitanov, Nikolay K.; Dimitrova, Zlatinka I.

2018-03-01

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

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

Directory of Open Access Journals (Sweden)

Mostafa M.A. Khater

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

Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation

Directory of Open Access Journals (Sweden)

Vitanov Nikolay K.

2018-03-01

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

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.

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.

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

International Nuclear Information System (INIS)

Fujita, Y.

2001-01-01

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

Covariant field equations in supergravity

Energy Technology Data Exchange (ETDEWEB)

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

2017-12-15

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

Covariant field equations in supergravity

International Nuclear Information System (INIS)

Vanhecke, Bram; Proeyen, Antoine van

2017-01-01

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

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

Science.gov (United States)

Nakazono, Nobutaka

2018-02-01

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

Test equating methods and practices

CERN Document Server

Kolen, Michael J

1995-01-01

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

On generalized fractional vibration equation

International Nuclear Information System (INIS)

Dai, Hongzhe; Zheng, Zhibao; Wang, Wei

2017-01-01

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

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.

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

Science.gov (United States)

Caplan-Auerbach, Jacqueline

2009-01-01

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

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

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

Science.gov (United States)

Ozdemir, Burhanettin

2017-01-01

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

A Hamiltonian approach to Thermodynamics

Energy Technology Data Exchange (ETDEWEB)

Baldiotti, M.C., E-mail: baldiotti@uel.br [Departamento de Física, Universidade Estadual de Londrina, 86051-990, Londrina-PR (Brazil); Fresneda, R., E-mail: rodrigo.fresneda@ufabc.edu.br [Universidade Federal do ABC, Av. dos Estados 5001, 09210-580, Santo André-SP (Brazil); Molina, C., E-mail: cmolina@usp.br [Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, Av. Arlindo Bettio 1000, CEP 03828-000, São Paulo-SP (Brazil)

2016-10-15

In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac’s theory of constrained systems is extensively used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases. - Highlights: • A strictly Hamiltonian approach to Thermodynamics is proposed. • Dirac’s theory of constrained systems is extensively used. • Thermodynamic equations of state are realized as constraints. • Thermodynamic potentials are related by canonical transformations.

A Hamiltonian approach to Thermodynamics

International Nuclear Information System (INIS)

Baldiotti, M.C.; Fresneda, R.; Molina, C.

2016-01-01

In the present work we develop a strictly Hamiltonian approach to Thermodynamics. A thermodynamic description based on symplectic geometry is introduced, where all thermodynamic processes can be described within the framework of Analytic Mechanics. Our proposal is constructed on top of a usual symplectic manifold, where phase space is even dimensional and one has well-defined Poisson brackets. The main idea is the introduction of an extended phase space where thermodynamic equations of state are realized as constraints. We are then able to apply the canonical transformation toolkit to thermodynamic problems. Throughout this development, Dirac’s theory of constrained systems is extensively used. To illustrate the formalism, we consider paradigmatic examples, namely, the ideal, van der Waals and Clausius gases. - Highlights: • A strictly Hamiltonian approach to Thermodynamics is proposed. • Dirac’s theory of constrained systems is extensively used. • Thermodynamic equations of state are realized as constraints. • Thermodynamic potentials are related by canonical transformations.

The Role of Long-Lived Greenhouse Gases as Principal LW Control Knob that Governs the Global Surface Temperature for Past and Future Climate Change

Science.gov (United States)

Lacis, Andrew A.; Hansen, James E.; Russell, Gary L.; Oinas, Valdar; Jonas, Jeffrey

2013-01-01

The climate system of the Earth is endowed with a moderately strong greenhouse effect that is characterized by non-condensing greenhouse gases (GHGs) that provide the core radiative forcing. Of these, the most important is atmospheric CO2. There is a strong feedback contribution to the greenhouse effect by water vapor and clouds that is unique in the solar system, exceeding the core radiative forcing due to the non-condensing GHGs by a factor of three. The significance of the non-condensing GHGs is that once they have been injected into the atmosphere, they remain there virtually indefinitely because they do not condense and precipitate from the atmosphere, their chemical removal time ranging from decades to millennia. Water vapor and clouds have only a short lifespan, with their distribution determined by the locally prevailing meteorological conditions, subject to Clausius-Clapeyron constraint. Although solar irradiance is the ultimate energy source that powers the terrestrial greenhouse effect, there has been no discernible long-term trend in solar irradiance since precise monitoring began in the late 1970s. This leaves atmospheric CO2 as the effective control knob driving the current global warming trend. Over geological time scales, volcanoes are the principal source of atmospheric CO2, and the weathering of rocks is the principal sink, with the biosphere participating as both a source and a sink. The problem at hand is that human industrial activity is causing atmospheric CO2, to increase by 2 ppm per year, whereas the interglacial rate has been 0.005 ppm per year. This is a geologically unprecedented rate to turn the CO2 climate control knob. This is causing the global warming that threatens the global environment.

Exploring the Links in Monthly to Decadal Variability of the Atmospheric Water Balance Over the Wettest Regions in ERA-20C

Science.gov (United States)

Nogueira, M.

2017-10-01

Monthly-to-decadal variability of the regional precipitation over Intertropical Convergence Zone and north-Atlantic and north-Pacific storm tracks was investigated using ERA-20C reanalysis. Satellite-based precipitation (P) and evaporation (E) climatological patterns were well reproduced by ERA-20C. Regional P and E monthly time series displayed 20% differences, but these decreased rapidly with time scale ( 10% at yearly time scales). Spectral analysis showed good scale-by-scale statistical agreement between ERA-20C and observations. Using ERA-Interim showed no improvement despite the much wider range of information assimilated (including satellites). Remarkably high Detrended Cross-Correlation Analysis coefficients (ρDCCA > 0.7 and often ρDCCA > 0.9) revealed tight links between the nonperiodic variability of P, moisture divergence (DIV), and pressure velocity (ω) at monthly-to-decadal time scales over all the wet regions. In contrast, ρDCCA was essentially nonsignificant between nonperiodic P and E or sea surface temperature (SST). Thus, the nonperiodic monthly-to-decadal variability of precipitation in these regions is almost fully controlled by dynamics and not by local E or SST (suggested by Clausius-Clapeyron relation). Analysis of regional nonperiodic standard deviations and power spectra (and respective spectral exponents, β) provided further robustness to this conclusion. Finally, clear transitions in β for P, DIV, and ω between tropical and storm track regions were found. The latter is dominated by transient storms, with energy accumulation at synoptic scales and β β values (0.2 to 0.4) were found in the tropics, implying longer-range autocorrelations and slower decreasing variability and information creation with time scale, consistent with the important forcing from internal modes of variability (e.g., El Niño-Southern Oscillation).

Observed change in extreme daily rainfalls in the French Mediterranean

Science.gov (United States)

Ribes, Aurélien; Thao, Soulivanh; Vautard, Robert; Dubuisson, Brigitte; Somot, Samuel; Colin, Jeanne; Planton, Serge; Soubeyroux, Jean-Michel

2017-04-01

In spite of a relatively dry mean climate, the Mediterranean regions in Southern France use to experience heavy rainfalls over short durations - typically a few minutes to one day. Here we examine long-term trends in the historical record of extreme precipitation events occurring over the French Mediterranean area, where many long homogeneous time-series are available. Extreme events are considered in terms of their intensity, frequency, extent and precipitated volume. Changes in intensity are analysed via an original statistical approach where the annual maximum rainfall observed at each measurement station are aggregated into a univariate time-series, according to their statistical dependence. This procedure substantially enhances the signal-to-noise ratio. The mean intensity increase is significant and estimated at +22% (+7% to +39% at the 90% confidence level) over the 1961-2015 period. Given the observed warming over the considered area, this increase is consistent with a rate of about one to three times that implied by the Clausius-Clapeyron relationship. Changes in frequency and other spatial features are investigated through a Generalised Linear Model. Changes in frequencies for events exceeding high thresholds (about 200mm in one day) are found to be significant, typically near a doubling of the frequency, but with large uncertainties in this risk ratio. The area affected by severe events and the water volume precipitated during those events also exhibit significant trends, with an increase by a factor of about 4 for a 200mm threshold, again with large uncertainties. All diagnoses consistently point toward an intensification of the most extreme events during the last decades. We argue that the diagnosed trends can hardly be explained without invoking the human influence on climate.

Attribution of Extreme Rainfall Events in the South of France Using EURO-CORDEX Simulations

Science.gov (United States)

Luu, L. N.; Vautard, R.; Yiou, P.

2017-12-01

The Mediterranean region regularly undergoes episodes of intense precipitation in the fall season that exceed 300mm a day. This study focuses on the role of climate change on the dynamics of the events that occur in the South of France. We used an ensemble of 10 EURO-CORDEX model simulations with two horizontal resolutions (EUR-11: 0.11° and EUR-44: 0.44°) for the attribution of extreme rainfall in the fall in the Cevennes mountain range (South of France). The biases of the simulations were corrected with simple scaling adjustment and a quantile correction (CDFt). This produces five datasets including EUR-44 and EUR-11 with and without scaling adjustment and CDFt-EUR-11, on which we test the impact of resolution and bias correction on the extremes. Those datasets, after pooling all of models together, are fitted by a stationary Generalized Extreme Value distribution for several periods to estimate a climate change signal in the tail of distribution of extreme rainfall in the Cévenne region. Those changes are then interpreted by a scaling model that links extreme rainfall with mean and maximum daily temperature. The results show that higher-resolution simulations with bias adjustment provide a robust and confident increase of intensity and likelihood of occurrence of autumn extreme rainfall in the area in current climate in comparison with historical climate. The probability (exceedance probability) of 1-in-1000-year event in historical climate may increase by a factor of 1.8 under current climate with a confident interval of 0.4 to 5.3 following the CDFt bias-adjusted EUR-11. The change of magnitude appears to follow the Clausius-Clapeyron relation that indicates a 7% increase in rainfall per 1oC increase in temperature.

Evaluation of empirical relationships between extreme rainfall and daily maximum temperature in Australia

Science.gov (United States)

Herath, Sujeewa Malwila; Sarukkalige, Ranjan; Nguyen, Van Thanh Van

2018-01-01

Understanding the relationships between extreme daily and sub-daily rainfall events and their governing factors is important in order to analyse the properties of extreme rainfall events in a changing climate. Atmospheric temperature is one of the dominant climate variables which has a strong relationship with extreme rainfall events. In this study, a temperature-rainfall binning technique is used to evaluate the dependency of extreme rainfall on daily maximum temperature. The Clausius-Clapeyron (C-C) relation was found to describe the relationship between daily maximum temperature and a range of rainfall durations from 6 min up to 24 h for seven Australian weather stations, the stations being located in Adelaide, Brisbane, Canberra, Darwin, Melbourne, Perth and Sydney. The analysis shows that the rainfall - temperature scaling varies with location, temperature and rainfall duration. The Darwin Airport station shows a negative scaling relationship, while the other six stations show a positive relationship. To identify the trend in scaling relationship over time the same analysis is conducted using data covering 10 year periods. Results indicate that the dependency of extreme rainfall on temperature also varies with the analysis period. Further, this dependency shows an increasing trend for more extreme short duration rainfall and a decreasing trend for average long duration rainfall events at most stations. Seasonal variations of the scale changing trends were analysed by categorizing the summer and autumn seasons in one group and the winter and spring seasons in another group. Most of 99th percentile of 6 min, 1 h and 24 h rain durations at Perth, Melbourne and Sydney stations show increasing trend for both groups while Adelaide and Darwin show decreasing trend. Furthermore, majority of scaling trend of 50th percentile are decreasing for both groups.

The role of long-lived greenhouse gases as principal LW control knob that governs the global surface temperature for past and future climate change

Energy Technology Data Exchange (ETDEWEB)

Lacis, Andrew A.; Hansen, James E.; Russell, Gary L.; Oinas, Valdar; Jonas, Jeffrey [NASA Goddard Inst. for Space Studies, New York (United States)], e-mail: Andrew.A.Lacis@nasa.gov

2013-11-15

The climate system of the Earth is endowed with a moderately strong greenhouse effect that is characterised by non-condensing greenhouse gases (GHGs) that provide the core radiative forcing. Of these, the most important is atmospheric CO{sub 2}. There is a strong feedback contribution to the greenhouse effect by water vapour and clouds that is unique in the solar system, exceeding the core radiative forcing due to the non-condensing GHGs by a factor of three. The significance of the non-condensing GHGs is that once they have been injected into the atmosphere, they remain there virtually indefinitely because they do not condense and precipitate from the atmosphere, their chemical removal time ranging from decades to millennia. Water vapour and clouds have only a short lifespan, with their distribution determined by the locally prevailing meteorological conditions, subject to Clausius-Clapeyron constraint. Although solar irradiance is the ultimate energy source that powers the terrestrial greenhouse effect, there has been no discern able long-term trend in solar irradiance since precise monitoring began in the late seventies. This leaves atmospheric CO{sub 2} as the effective control knob driving the current global warming trend. Over geological time scales, volcanoes are the principal source of atmospheric CO{sub 2}, and the weathering of rocks is the principal sink, with the biosphere participating as both a source and a sink. The problem at hand is that human industrial activity is causing atmospheric CO{sub 2}, to increase by 2 ppm yr{sup -1}, whereas the interglacial rate has been 0.005 ppm yr{sup -1}. This is a geologically unprecedented rate to turn the CO{sub 2} climate control knob. This is causing the global warming that threatens the global environment.

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

OpenAIRE

Nahay, John Michael

2008-01-01

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

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

International Nuclear Information System (INIS)

Rodriguez D, R.

2007-01-01

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

Differential Equation over Banach Algebra

OpenAIRE

Kleyn, Aleks

2018-01-01

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

Elements of partial differential equations

CERN Document Server

Sneddon, Ian Naismith

1957-01-01

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

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

International Nuclear Information System (INIS)

Kong Cuicui; Wang Dan; Song Lina; Zhang Hongqing

2009-01-01

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

Introduction to partial differential equations

CERN Document Server

Greenspan, Donald

2000-01-01

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

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

International Nuclear Information System (INIS)

Feng Qing-Hua

2014-01-01

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

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

International Nuclear Information System (INIS)

Yan Zhenya

2005-01-01

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

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.

Reactimeter dispersion equation

OpenAIRE

A.G. Yuferov

2016-01-01

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

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

CERN Document Server

Qin, Hong

2005-01-01

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

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

International Nuclear Information System (INIS)

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

2012-01-01

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

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

Science.gov (United States)

Zhang, Yu; Zhang, Guanquan; Bleistein, Norman

2003-10-01

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

First-order partial differential equations

CERN Document Server

Rhee, Hyun-Ku; Amundson, Neal R

2001-01-01

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

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

Science.gov (United States)

Lee, Eunjung

2013-01-01

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

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

Science.gov (United States)

Hwang, Chi-en; Cleary, T. Anne

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

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

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

International Nuclear Information System (INIS)

Kambe, Tsutomu

2010-01-01

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

Degenerate nonlinear diffusion equations

CERN Document Server

Favini, Angelo

2012-01-01

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

Computational partial differential equations using Matlab

CERN Document Server

Li, Jichun

2008-01-01

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

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

International Nuclear Information System (INIS)

Bracken, Paul

2010-01-01

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

Drift-Diffusion Equation

Directory of Open Access Journals (Sweden)

K. Banoo

1998-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2015-10-15

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

Alternatives to the Dirac equation

International Nuclear Information System (INIS)

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

1975-01-01

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

Nonlinear differential equations

Energy Technology Data Exchange (ETDEWEB)

Dresner, L.

1988-01-01

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

Nonlinear differential equations

International Nuclear Information System (INIS)

Dresner, L.

1988-01-01

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

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

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.

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

International Nuclear Information System (INIS)

Ren Ji; Ruan Hangyu

2008-01-01

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

Nonlinear diffusion equations

CERN Document Server

Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning

2001-01-01

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

On the F-equation

International Nuclear Information System (INIS)

Kalinowski, M.W.; Szymanowski, L.

1982-03-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2009-07-15

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

Linear integral equations and soliton systems

International Nuclear Information System (INIS)

Quispel, G.R.W.

1983-01-01

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

Non-isothermal theory of thermoelastic shells under large deformations. Pt. 2

International Nuclear Information System (INIS)

Malmberg, T.

1988-09-01

The entropy condition for the virtual agencies and the integral Clausius-Duhem entropy inequality are evaluated for two shell concepts. This is accompanied by a direct ansatz for the two-dimensional constitutive relations which have to be form-invariant under observer transformations. The two-dimensional mechanical constitutive relations are of special interest; they relate weighted averages of the stresses across the shell thickness (e.g. moments of 0., 1. and 2. order) and kinematic quantities as well as quantities characterizing the temperature field. The study is concluded by the derivation of the corresponding kinematic, dynamic and thermal boundary conditions. Also the development is supplemented by a component representation of the shell equations referred to the undeformed reference configuration using Lagrangian coordinates. (orig./DG) [de

Thermodynamics of heterogeneous and anisotropic nonlinear ferroelastic crystals

Directory of Open Access Journals (Sweden)

Restuccia, Liliana

2008-02-01

Full Text Available In a previous paper, in a geometrized framework for the description of simple materials with internal variables, the specific example of ferroelastic crystals with anisotropy grain-tensors à la Maruszewski was considered and the relevant structure of the entropy 1-form was derived. In this contribution the linear morphism defined on the fibre bundle of the process and the transformation induced by the process are obtained as new results within the geometrical model. Furthermore, Clausius-Duhem inequality for these media is exploited, and, using a Maugin technique (see also Colemann-Noll procedure, the laws of state, the extra entropy flux and the residual dissipation inequality are worked out. Finally, following Maugin, the heat equation in the first and the second form are derived.

Mineral dielectric constants and the oxide additivity rule

International Nuclear Information System (INIS)

Shannon, R.D.; Subramanian, M.A.; Mariano, A.N.; Rossman, G.R.

1989-01-01

The 1 MHz dielectric constants of a variety of synthetic aluminate garnets: Y 3 Al 5 O 12 , Ho 3 Al 5 O 12 , Y 2.93 Nd .07 Sc 2 Al 3 O 12 and Gd 2.95 Nd .05 Sc 1.98 Cr .02 Al 3 O 12 and several silicates: CaB 2 Si 2 O 8 (danburite), Ca 3 Al 2 Si 3 O 12 (grossular) and Mg 2 Al 4 Si 5 O 18 (cordierite) were determined using the two-terminal method with edge corrections. These data and polarizabilities derived from the published single crystal dielectric constants of simple oxides were used to compare compound polarizabilities obtained from the Clausius-Mosotti equation and the oxide additivity rule

Lectures on partial differential equations

CERN Document Server

Petrovsky, I G

1992-01-01

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

Reduction operators of Burgers equation.

Science.gov (United States)

Pocheketa, Oleksandr A; Popovych, Roman O

2013-02-01

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

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

Directory of Open Access Journals (Sweden)

K.-H. Fornacon

1999-12-01

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

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

Directory of Open Access Journals (Sweden)

K.-H. Fornacon

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

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

Methods for Equating Mental Tests.

Science.gov (United States)

1984-11-01

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

Supersymmetric quasipotential equations

International Nuclear Information System (INIS)

Zaikov, R.P.

1981-01-01

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

Ordinary differential equations

CERN Document Server

Miller, Richard K

1982-01-01

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

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.

Introduction to nonlinear dispersive equations

CERN Document Server

Linares, Felipe

2015-01-01

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

Generalized Lorentz-Force equations

International Nuclear Information System (INIS)

Yamaleev, R.M.

2001-01-01

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

A new evolution equation

International Nuclear Information System (INIS)

Laenen, E.

1995-01-01

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

Thermoviscous Model Equations in Nonlinear Acoustics

DEFF Research Database (Denmark)

Rasmussen, Anders Rønne

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

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

DEFF Research Database (Denmark)

Ditlevsen, Ove Dalager

2004-01-01

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

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...

Weak self-adjoint differential equations

International Nuclear Information System (INIS)

Gandarias, M L

2011-01-01

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

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

International Nuclear Information System (INIS)

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

2000-01-01

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

Equations of radiation hydrodynamics

International Nuclear Information System (INIS)

Mihalas, D.

1982-01-01

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

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

Science.gov (United States)

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

2002-11-01

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

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

Science.gov (United States)

Choi, Sae Il

2009-01-01

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

Monge-Ampere equations and tensorial functors

International Nuclear Information System (INIS)

Tunitsky, Dmitry V

2009-01-01

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

Nonlinear integrodifferential equations as discrete systems

Science.gov (United States)

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

1999-06-01

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

Analytic solutions of hydrodynamics equations

International Nuclear Information System (INIS)

Coggeshall, S.V.

1991-01-01

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

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

OpenAIRE

Efimova, Olga Yu.

2010-01-01

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

Equationally Noetherian property of Ershov algebras

OpenAIRE

Dvorzhetskiy, Yuriy

2014-01-01

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

Differential equations extended to superspace

International Nuclear Information System (INIS)

Torres, J.; Rosu, H.C.

2003-01-01

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

Differential equations extended to superspace

Energy Technology Data Exchange (ETDEWEB)

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

2003-07-01

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

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

International Nuclear Information System (INIS)

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

2004-01-01

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

Iterative Splitting Methods for Differential Equations

CERN Document Server

Geiser, Juergen

2011-01-01

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

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

Generalized quantal equation of motion

International Nuclear Information System (INIS)

Morsy, M.W.; Embaby, M.

1986-07-01

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

Higher order field equations. II

International Nuclear Information System (INIS)

Tolhoek, H.A.

1977-01-01

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

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.

Equational type logic

NARCIS (Netherlands)

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

1990-01-01

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

Reduced Braginskii equations

International Nuclear Information System (INIS)

Yagi, M.; Horton, W.

1994-01-01

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

Model Compaction Equation

African Journals Online (AJOL)

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

Reduction of infinite dimensional equations

Directory of Open Access Journals (Sweden)

Zhongding Li

2006-02-01

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

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

Science.gov (United States)

Chen, Haiwen; Holland, Paul

2009-01-01

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

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...

Thermogravimetric evaluation of the suitability of precursors for MOCVD

International Nuclear Information System (INIS)

Kunte, G V; Shivashankar, S A; Umarji, A M

2008-01-01

A method based on the Langmuir equation for the estimation of vapour pressure and enthalpy of sublimation of subliming compounds is described. The variable temperature thermogravimetric/differential thermogravimetric (TG/DTG) curve of benzoic acid is used to arrive at the instrument parameters. Employing these parameters, the vapour pressure–temperature curves are derived for salicylic acid and camphor from their TG/DTG curves. The values match well with vapour pressure data in the literature, obtained by effusion methods. By employing the Clausius–Clapeyron equation, the enthalpy of sublimation could be calculated. Extending the method further, two precursors for metal-organic chemical vapour deposition (MOCVD) of titanium oxide bis-isopropyl bis tert-butyl 2-oxobutanoato titanium, Ti(O i Pr) 2 (tbob) 2 , and bis-oxo-bis-tertbutyl 2-oxobutanoato titanium, [TiO(tbob) 2 ] 2 , have been evaluated. The complex Ti(O i Pr) 2 (tbob) 2 is found to be a more suitable precursor. This approach can be helpful in quickly screening for the suitability of a compound as a CVD precursor

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

International Nuclear Information System (INIS)

Mociutchi, C.

1980-01-01

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

The Wouthuysen equation

NARCIS (Netherlands)

M. Hazewinkel (Michiel)

1995-01-01

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

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

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V. O. Vakhnenko

2016-01-01

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

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

Science.gov (United States)

Hunt, L. R.; Villarreal, Ramiro

1987-01-01

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

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

International Nuclear Information System (INIS)

Hendriks, E.M.

1983-01-01

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

Hybrid quantum-classical master equations

International Nuclear Information System (INIS)

Diósi, Lajos

2014-01-01

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

Quantum equations from Brownian motions

International Nuclear Information System (INIS)

Rajput, B.S.

2011-01-01

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

B-splines and Faddeev equations

International Nuclear Information System (INIS)

Huizing, A.J.

1990-01-01

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

Reduced Braginskii equations

International Nuclear Information System (INIS)

Yagi, M.; Horton, W.

1993-11-01

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

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

International Nuclear Information System (INIS)

Chen Huaitang; Zhang Hongqing

2004-01-01

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

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

International Nuclear Information System (INIS)

Pierantozzi, T.; Vazquez, L.

2005-01-01

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

Equationally Compact Acts : Coproducts / Peeter Normak

Index Scriptorium Estoniae

Normak, Peeter

1998-01-01

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

Supersymmetric two-particle equations

International Nuclear Information System (INIS)

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

1986-01-01

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

Solving Ordinary Differential Equations

Science.gov (United States)

Krogh, F. T.

1987-01-01

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

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

International Nuclear Information System (INIS)

Zenouda, Jean-Claude

1970-08-01

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

Reduced Braginskii equations

Energy Technology Data Exchange (ETDEWEB)

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

1993-11-01

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

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.

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

International Nuclear Information System (INIS)

Zhang Huiqun

2009-01-01

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

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

Science.gov (United States)

Grima, Ramon

2011-11-01

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

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

Critical behavior of the dielectric constant in asymmetric fluids.

Science.gov (United States)

Bertrand, C E; Sengers, J V; Anisimov, M A

2011-12-08

By applying a thermodynamic theory that incorporates the concept of complete scaling, we derive the asymptotic temperature dependence of the critical behavior of the dielectric constant above the critical temperature along the critical isochore and below the critical temperature along the coexistence curve. The amplitudes of the singular terms in the temperature expansions are related to the changes of the critical temperature and the critical chemical potential upon the introduction of an electric field. The results of the thermodynamic theory are then compared with the critical behavior implied by the classical Clausius-Mossotti approximation. The Clausius-Mossotti approximation fails to account for any singular temperature dependence of the dielectric constant above the critical temperature. Below the critical temperature it produces an apparent asymmetric critical behavior with singular terms similar to those implied by the thermodynamic theory, but with significantly different coefficients. We conclude that the Clausius-Mossotti approximation only can account for the observed asymptotic critical behavior of the dielectric constant when the dependence of the critical temperature on the electric field is negligibly small. © 2011 American Chemical Society

Transmission problem for the Laplace equation and the integral equation method

Czech Academy of Sciences Publication Activity Database

Medková, Dagmar

2012-01-01

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

Introduction to partial differential equations

CERN Document Server

Borthwick, David

2016-01-01

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

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. .

Gauge-invariant flow equation

Science.gov (United States)

Wetterich, C.

2018-06-01

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

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

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.

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

Science.gov (United States)

Adib, Arash; Poorveis, Davood; Mehraban, Farid

2018-03-01

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

INVARIANTS OF GENERALIZED RAPOPORT-LEAS EQUATIONS

Directory of Open Access Journals (Sweden)

Elena N. Kushner

2018-01-01

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

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.

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...

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.)

The relativistic electron wave equation

International Nuclear Information System (INIS)

Dirac, P.A.M.

1977-08-01

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

Equation with the many fathers

DEFF Research Database (Denmark)

Kragh, Helge

1984-01-01

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

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

International Nuclear Information System (INIS)

Ka-Lin, Su; Yuan-Xi, Xie

2010-01-01

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

On the Saha Ionization Equation

Indian Academy of Sciences (India)

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

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.

Neoclassical MHD equations for tokamaks

International Nuclear Information System (INIS)

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

1986-03-01

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

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

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

NARCIS (Netherlands)

van den Berg, I.P.

1998-01-01

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

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

KAUST Repository

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

2015-01-01

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

From ordinary to partial differential equations

CERN Document Server

Esposito, Giampiero

2017-01-01

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

Completely integrable operator evolutionary equations

International Nuclear Information System (INIS)

Chudnovsky, D.V.

1979-01-01

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

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

International Nuclear Information System (INIS)

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

1979-01-01

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

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.

Differential equations I essentials

CERN Document Server

REA, Editors of

2012-01-01

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

Beginning partial differential equations

CERN Document Server

O'Neil, Peter V

2011-01-01

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

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

NARCIS (Netherlands)

Scholtens, B.; Dam, L.

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

Hartree--Fock density matrix equation

International Nuclear Information System (INIS)

Cohen, L.; Frishberg, C.

1976-01-01

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

Exact solutions to sine-Gordon-type equations

International Nuclear Information System (INIS)

Liu Shikuo; Fu Zuntao; Liu Shida

2006-01-01

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

dimensional Jaulent–Miodek equations

Indian Academy of Sciences (India)

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

Random walk and the heat equation

CERN Document Server

Lawler, Gregory F

2010-01-01

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

On integrability of the Killing equation

Science.gov (United States)

Houri, Tsuyoshi; Tomoda, Kentaro; Yasui, Yukinori

2018-04-01

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

Algebraic entropy for differential-delay equations

OpenAIRE

Viallet, Claude M.

2014-01-01

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

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

Dynamical equations for the optical potential

International Nuclear Information System (INIS)

Kowalski, K.L.

1981-01-01

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

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...

Benney's long wave equations

International Nuclear Information System (INIS)

Lebedev, D.R.

1979-01-01

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

The forced nonlinear Schroedinger equation

International Nuclear Information System (INIS)

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

1985-01-01

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

Solving Nonlinear Coupled Differential Equations

Science.gov (United States)

Mitchell, L.; David, J.

1986-01-01

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

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)

Direct 'delay' reductions of the Toda equation

International Nuclear Information System (INIS)

Joshi, Nalini

2009-01-01

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

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

Science.gov (United States)

Karney, C. F. F.

1977-01-01

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

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.

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

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

NARCIS (Netherlands)

Dorren, H.J.S.

1998-01-01

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

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

Science.gov (United States)

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

2009-11-01

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

Local instant conservation equations

International Nuclear Information System (INIS)

Delaje, Dzh.

1984-01-01

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

Differential equations problem solver

CERN Document Server

Arterburn, David R

2012-01-01

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

Local Observed-Score Kernel Equating

Science.gov (United States)

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

2014-01-01

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

Numerical solution of Boltzmann's equation

International Nuclear Information System (INIS)

Sod, G.A.

1976-04-01

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

The Dirac equation and its solutions

CERN Document Server

Bagrov, Vladislav G

2014-01-01

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

The Dirac equation and its solutions

International Nuclear Information System (INIS)

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

2013-01-01

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

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)

Painleve test and discrete Boltzmann equations

International Nuclear Information System (INIS)

Euler, N.; Steeb, W.H.

1989-01-01

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

Chew-Low equations as Cremoma transformations

International Nuclear Information System (INIS)

Rerikh, K.V.

1982-01-01

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

General particle transport equation. Final report

International Nuclear Information System (INIS)

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

1994-12-01

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

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

Directory of Open Access Journals (Sweden)

Olaniyi Samuel Iyiola

2014-09-01

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

Electronic representation of wave equation

Energy Technology Data Exchange (ETDEWEB)

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

2016-06-08

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

The Dirac equation for accountants

International Nuclear Information System (INIS)

Ord, G.N.

2006-01-01

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

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

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

Science.gov (United States)

Gao, Yingjie; Zhang, Jinhai; Yao, Zhenxing

2015-12-01

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

The Dirac equation and its solutions

Energy Technology Data Exchange (ETDEWEB)

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

2013-07-01

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

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.

Boussinesq evolution equations

DEFF Research Database (Denmark)

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

2004-01-01

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

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.

Exact discretization of Schrödinger equation

Energy Technology Data Exchange (ETDEWEB)

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

2016-01-08

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

Exact discretization of Schrödinger equation

International Nuclear Information System (INIS)

Tarasov, Vasily E.

2016-01-01

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

Abstract methods in partial differential equations

CERN Document Server

Carroll, Robert W

2012-01-01

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

Generalization of Einstein's gravitational field equations

Science.gov (United States)

Moulin, Frédéric

2017-12-01

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

Extraction of dynamical equations from chaotic data

International Nuclear Information System (INIS)

Rowlands, G.; Sprott, J.C.

1991-02-01

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

The AGL equation from the dipole picture

International Nuclear Information System (INIS)

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

1999-01-01

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

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

African Journals Online (AJOL)

user

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

Baecklund transformations for integrable lattice equations

International Nuclear Information System (INIS)

Atkinson, James

2008-01-01

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

Integrable discretizations of the short pulse equation

International Nuclear Information System (INIS)

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

2010-01-01

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

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

International Nuclear Information System (INIS)

Kovalyov, Mikhail

2010-01-01

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

Sparse dynamics for partial differential equations.

Science.gov (United States)

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

2013-04-23

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

Complex centers of polynomial differential equations

Directory of Open Access Journals (Sweden)

Mohamad Ali M. Alwash

2007-07-01

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

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

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...

The generalized Airy diffusion equation

Directory of Open Access Journals (Sweden)

Frank M. Cholewinski

2003-08-01

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

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

International Nuclear Information System (INIS)

Aslan İsmail

2014-01-01

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

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.)

Darboux transformation for the NLS equation

International Nuclear Information System (INIS)

Aktosun, Tuncay; Mee, Cornelis van der

2010-01-01

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

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

Science.gov (United States)

Simonucci, S.; Strinati, G. C.

2014-02-01

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

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

International Nuclear Information System (INIS)

Xiao Yafeng; Xue Haili; Zhang Hongqing

2011-01-01

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

Differential-algebraic solutions of the heat equation

OpenAIRE

Buchstaber, Victor M.; Netay, Elena Yu.

2014-01-01

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

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

Science.gov (United States)

Gallouët, Thomas; Vialard, François-Xavier

2018-04-01

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

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

Science.gov (United States)

Dutta, Rabijit; Xing, Tao

2018-02-01

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

Partial differential equations for scientists and engineers

CERN Document Server

Farlow, Stanley J

1993-01-01

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

On a complex differential Riccati equation

International Nuclear Information System (INIS)

Khmelnytskaya, Kira V; Kravchenko, Vladislav V

2008-01-01

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

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.

Lax representations for matrix short pulse equations

Science.gov (United States)

Popowicz, Z.

2017-10-01

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

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.

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

Science.gov (United States)

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

2014-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2013-01-01

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

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

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

Science.gov (United States)

Zhang, Zhilin; Savenije, Hubert H. G.

2017-07-01

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

Wave equations for pulse propagation

International Nuclear Information System (INIS)

Shore, B.W.

1987-01-01

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

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

Multi-diffusive nonlinear Fokker–Planck equation

International Nuclear Information System (INIS)

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

2017-01-01

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

Correct Linearization of Einstein's Equations

Directory of Open Access Journals (Sweden)

Rabounski D.

2006-06-01

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

Integral equation for Coulomb problem

International Nuclear Information System (INIS)

Sasakawa, T.

1986-01-01

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

Coupled simulation of a system for the utilization of exhaust heat and cooling of the interior of commercial vehicles; Gekoppelte Simulation eines Abgaswaermenutzungs- und Fahrzeugkuehlsystems im Nutzfahrzeug

Energy Technology Data Exchange (ETDEWEB)

Ambros, Peter; Fezer, Axel; Kapitel, Julian [TheSys GmbH, Kirchentellinsfurt (Germany)

2012-11-01

Based on a simulation software called GT-Suite by Gamma Technology, a one-dimensional model of a waste-heat recovery system with utility vehicle boundary conditions was developed. Using this model, it is possible to simulate stationary operating points of this type WHR. A Clausius-Rankine cycle is used in the power-heat cogeneration. The Clausius-Rankine cycle is linked to the exhaust system by two boilers. The first boiler is installed in the main exhaust steam, the second boiler is implemented in the exhaust gas recirculation. Besides the waste-heat recovery system, the integrated cooling system of the vehicle is also modeled. (orig.)

A fractional Dirac equation and its solution

International Nuclear Information System (INIS)

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

2010-01-01

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

Linear superposition solutions to nonlinear wave equations

International Nuclear Information System (INIS)

Liu Yu

2012-01-01

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

Systematic Equation Formulation

DEFF Research Database (Denmark)

Lindberg, Erik

2007-01-01

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

International Workshop on Elliptic and Parabolic Equations

CERN Document Server

Schrohe, Elmar; Seiler, Jörg; Walker, Christoph

2015-01-01

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

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

The generalized Fermat equation

NARCIS (Netherlands)

Beukers, F.

2006-01-01

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

On matrix fractional differential equations

OpenAIRE

Adem Kılıçman; Wasan Ajeel Ahmood

2017-01-01

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

Minimal solution for inconsistent singular fuzzy matrix equations

Directory of Open Access Journals (Sweden)

M. Nikuie

2013-10-01

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

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.

New solutions of Heun's general equation

International Nuclear Information System (INIS)

Ishkhanyan, Artur; Suominen, Kalle-Antti

2003-01-01

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

Pseudodifferential equations over non-Archimedean spaces

CERN Document Server

Zúñiga-Galindo, W A

2016-01-01

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

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

International Nuclear Information System (INIS)

Chen Yong; Yan Zhenya

2005-01-01

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

Relativistic wave equations and compton scattering

International Nuclear Information System (INIS)

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

1998-01-01

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

Generalized estimating equations

CERN Document Server

Hardin, James W

2002-01-01

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

Partial differential equations

CERN Document Server

Agranovich, M S

2002-01-01

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

Quantum Gross-Pitaevskii Equation

Directory of Open Access Journals (Sweden)

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

2017-07-01

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

Partial differential equations of mathematical physics

CERN Document Server

Sobolev, S L

1964-01-01

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

Reduced kinetic equations: An influence functional approach

International Nuclear Information System (INIS)

Wio, H.S.

1985-01-01

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

An inverse problem in a parabolic equation

Directory of Open Access Journals (Sweden)

Zhilin Li

1998-11-01

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

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

Institute of Scientific and Technical Information of China (English)

无

2010-01-01

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

Completely integrable operator evolution equations. II

International Nuclear Information System (INIS)

Chudnovsky, D.V.

1979-01-01

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

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

Semigroup methods for evolution equations on networks

CERN Document Server

Mugnolo, Delio

2014-01-01

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

Extreme compression behaviour of equations of state

International Nuclear Information System (INIS)

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

2009-01-01

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

Perturbation theory for continuous stochastic equations

International Nuclear Information System (INIS)

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

1987-01-01

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

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.

Developments in functional equations and related topics

CERN Document Server

Ciepliński, Krzysztof; Rassias, Themistocles

2017-01-01

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

Transport equation solving methods

International Nuclear Information System (INIS)

Granjean, P.M.

1984-06-01

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

Statistical Methods for Stochastic Differential Equations

CERN Document Server

Kessler, Mathieu; Sorensen, Michael

2012-01-01

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

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

Multidimensional singular integrals and integral equations

CERN Document Server

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

1965-01-01

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

Semiclassical regularization of Vlasov equations and wavepackets for nonlinear Schrödinger equations

Science.gov (United States)

Athanassoulis, Agissilaos

2018-03-01

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

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

Functional Fourier transforms and the loop equation

International Nuclear Information System (INIS)

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

1986-01-01

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

dimensional Nizhnik–Novikov–Veselov equations

Indian Academy of Sciences (India)

2017-03-22

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

Symmetry properties of fractional diffusion equations

Energy Technology Data Exchange (ETDEWEB)

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

2009-10-15

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

The Modified Enskog Equation for Mixtures

NARCIS (Netherlands)

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

1973-01-01

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

Some remarks on unilateral matrix equations

International Nuclear Information System (INIS)

Cerchiai, Bianca L.; Zumino, Bruno

2001-01-01

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

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.

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.

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

International Nuclear Information System (INIS)

Scully, M O

2008-01-01

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

Stochastic Differential Equations and Kondratiev Spaces

Energy Technology Data Exchange (ETDEWEB)

Vaage, G.

1995-05-01

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

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

International Nuclear Information System (INIS)

Ablowitz, Mark J; Curtis, Christopher W

2011-01-01

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

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

Science.gov (United States)

Ablowitz, Mark J.; Curtis, Christopher W.

2011-05-01

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

Equations of motion in phase space

International Nuclear Information System (INIS)

Broucke, R.

1979-01-01

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

Asymptotic problems for stochastic partial differential equations

Science.gov (United States)

Salins, Michael

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

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

Entropy viscosity method applied to Euler equations

International Nuclear Information System (INIS)

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

2013-01-01

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

Computing with linear equations and matrices

International Nuclear Information System (INIS)

Churchhouse, R.F.

1983-01-01

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

Integrable peakon equations with cubic nonlinearity

International Nuclear Information System (INIS)

Hone, Andrew N W; Wang, J P

2008-01-01

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